diff --git a/CODEOWNERS b/CODEOWNERS new file mode 100644 index 00000000000..19656ea7bfd --- /dev/null +++ b/CODEOWNERS @@ -0,0 +1,6 @@ +* @armfazh @cjpatton @claucece @Lekensteyn @wbl +src/circl @armfazh +src/crypto/tls @claucece @Lekensteyn +src/crypto/x509 @wbl @cjpatton +src/internal/cpu @armfazh +src/net/http @Lekensteyn diff --git a/VERSION b/VERSION new file mode 100644 index 00000000000..c71ed7040d3 --- /dev/null +++ b/VERSION @@ -0,0 +1 @@ +go1.16-devel-cf diff --git a/cf-copy-from-circle.py b/cf-copy-from-circle.py new file mode 100644 index 00000000000..a4fda471e40 --- /dev/null +++ b/cf-copy-from-circle.py @@ -0,0 +1,83 @@ +# Temporary file: copies Dilithium from Cloudflare's circl library into crypto. + +import os +import sys +import tempfile +import subprocess + +base = os.path.dirname(os.path.abspath(sys.argv[0])) + +REPO = 'https://github.com/cloudflare/circl' +BRANCH = 'master' + +circl = os.path.join(base, 'src/circl') + +if os.path.exists(circl): + print("Removing old circl ...") + subprocess.check_call(['rm', '-r', '-f', circl]) + +with tempfile.TemporaryDirectory() as d: + print(f"Cloning {REPO} branch {BRANCH} ...") + subprocess.check_call(['git', 'clone', REPO, '--branch', BRANCH], + cwd=d) + + print("Copying ...") + subprocess.check_call(['cp', '-r', + os.path.join(d, 'circl'), + circl, + ]) + +print("Removing avo sourcecode (for now) ...") +# XXX figure out a way to prevent ./src/all.sh from trying to build the +# asm folders that require avo. +subprocess.check_call(['rm', '-r', + os.path.join(circl, 'simd/keccakf1600/internal/asm'), + os.path.join(circl, 'sign/dilithium/internal/common/asm'), + os.path.join(circl, 'pke/kyber/internal/common/asm'), +]) + +print("Removing templates (for now) ...") +# XXX figure out a way to prevent build/deps_test.go from trying to pase +# the templates. +subprocess.check_call(['rm', '-r', + os.path.join(circl, 'sign/dilithium/templates'), + os.path.join(circl, 'sign/dilithium/gen.go'), +]) + +#print("Removing unused packages ...") +#subprocess.check_call(['rm', '-r', '-f', +# os.path.join(circl, 'group'), +#]) + +print("Removing misc cruft ...") +subprocess.check_call(['rm', '-r', '-f', + os.path.join(circl, '.git'), + os.path.join(circl, 'go.mod'), + os.path.join(circl, 'go.sum'), + os.path.join(circl, '.etc'), + os.path.join(circl, 'Makefile'), + os.path.join(circl, 'codecov.yml'), +]) + +print("Correcting import paths ...") + +def correct(fn): + with open(fn, 'rb') as f: + s = f.read() + s = s.replace( + b'github.com/cloudflare/circl', + b'circl', + ).replace( + b'golang.org/x/sys/cpu', + b'internal/cpu', + ) + with open(fn, 'wb') as f: + f.write(s) + +for subdir, _, files in os.walk(circl): + for fn in files: + correct(os.path.join(subdir, fn)) + + +print("Formatting ....") +subprocess.check_call(['go', 'fmt', './...'], cwd=circl) diff --git a/src/circl/.github/workflows/ci-actions.yml b/src/circl/.github/workflows/ci-actions.yml new file mode 100644 index 00000000000..d9a2ca47d24 --- /dev/null +++ b/src/circl/.github/workflows/ci-actions.yml @@ -0,0 +1,73 @@ +name: CIRCL +on: + push: + branches: + - master + pull_request: + branches: + - master +jobs: + amd64_job: + name: Go-${{matrix.GOVER}}/amd64 + runs-on: ubuntu-18.04 + strategy: + matrix: + GOVER: ['1.16', '1.15', '1.14', '1.13', '1.12'] + steps: + - name: Checkout + uses: actions/checkout@v2 + - name: Linting + uses: golangci/golangci-lint-action@v2 + with: + version: v1.29 + args: --config=./.etc/golangci.yml ./... + - name: Setup Go-${{ matrix.GOVER }} + uses: actions/setup-go@v2 + with: + go-version: ${{ matrix.GOVER }} + - name: Verifying Code + run: | + go generate -v ./... && test -z "$(git status --porcelain)" + go vet ./... + - name: Building + run: go build -v ./... + - name: Testing + run: go test -v -count=1 ./... + exotic_job: + name: Go-${{matrix.CFG[2]}}/${{matrix.CFG[0]}} + runs-on: ubuntu-18.04 + strategy: + matrix: + CFG: [ [arm64,arm64v8,1.16] ] + steps: + - uses: actions/checkout@v2 + - name: Enabling Docker Experimental + run: | + echo $'{\n "experimental": true\n}' | sudo tee /etc/docker/daemon.json + sudo service docker restart + - name: Pulling Images + run: | + docker pull -q multiarch/qemu-user-static + docker pull -q --platform linux/${{matrix.CFG[0]}} ${{matrix.CFG[1]}}/golang:${{matrix.CFG[2]}} + docker run --rm --privileged multiarch/qemu-user-static --reset -p yes + - name: Testing + run: | + docker run --rm -v `pwd`:`pwd` -w `pwd` ${{matrix.CFG[1]}}/golang:${{matrix.CFG[2]}} go test -v ./... + coverage_amd64_job: + needs: [ amd64_job ] + if: github.event_name == 'push' + runs-on: ubuntu-18.04 + name: amd64/coverage + steps: + - name: Checkout + uses: actions/checkout@v2 + - name: Setup Go + uses: actions/setup-go@v2 + with: + go-version: '1.16' + - name: Produce Coverage + run: go test -race -coverprofile=./coverage.txt -covermode=atomic ./... + - name: Upload Codecov + uses: codecov/codecov-action@v1 + with: + file: ./coverage.txt diff --git a/src/circl/.gitignore b/src/circl/.gitignore new file mode 100644 index 00000000000..61a92a74401 --- /dev/null +++ b/src/circl/.gitignore @@ -0,0 +1,2 @@ +build/ +go.mod diff --git a/src/circl/LICENSE b/src/circl/LICENSE new file mode 100644 index 00000000000..67edaa90a04 --- /dev/null +++ b/src/circl/LICENSE @@ -0,0 +1,57 @@ +Copyright (c) 2019 Cloudflare. All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + + * Redistributions of source code must retain the above copyright +notice, this list of conditions and the following disclaimer. + * Redistributions in binary form must reproduce the above +copyright notice, this list of conditions and the following disclaimer +in the documentation and/or other materials provided with the +distribution. + * Neither the name of Cloudflare nor the names of its +contributors may be used to endorse or promote products derived from +this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +======================================================================== + +Copyright (c) 2009 The Go Authors. All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + + * Redistributions of source code must retain the above copyright +notice, this list of conditions and the following disclaimer. + * Redistributions in binary form must reproduce the above +copyright notice, this list of conditions and the following disclaimer +in the documentation and/or other materials provided with the +distribution. + * Neither the name of Google Inc. nor the names of its +contributors may be used to endorse or promote products derived from +this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/src/circl/README.md b/src/circl/README.md new file mode 100644 index 00000000000..62cdd5e6b80 --- /dev/null +++ b/src/circl/README.md @@ -0,0 +1,105 @@ + + +# CIRCL + +[![CIRCL](https://circl/workflows/CIRCL/badge.svg)](https://circl/actions) +[![GoDoc](https://godoc.org/circl?status.svg)](https://pkg.go.dev/circl?tab=overview) +[![Go Report Card](https://goreportcard.com/badge/circl)](https://goreportcard.com/report/circl) +[![codecov](https://codecov.io/gh/cloudflare/circl/branch/master/graph/badge.svg)](https://codecov.io/gh/cloudflare/circl) + +**CIRCL** (Cloudflare Interoperable, Reusable Cryptographic Library) is a collection +of cryptographic primitives written in Go. The goal of this library is to be used as a tool for +experimental deployment of cryptographic algorithms targeting Post-Quantum (PQ) and Elliptic +Curve Cryptography (ECC). + +## Security Disclaimer + +🚨 This library is offered as-is, and without a guarantee. Therefore, it is expected that changes in the code, repository, and API occur in the future. We recommend to take caution before using this library in a production application since part of its content is experimental. + +## Installation + +You can get it by typing: + +```sh +go get -u circl +``` + +## Versioning + +Version numbers are [Semvers](https://semver.org/). We release a minor version for new functionality, a major version for breaking API changes, and increment the patchlevel for bugfixes. + +## Implemented Primitives + +| Category | Algorithms | Description | Applications | +|-----------|------------|-------------|--------------| +| PQ Key Exchange | SIDH | SIDH provide key exchange mechanisms using ephemeral keys. | Post-quantum key exchange in TLS | +| PQ Key Exchange | cSIDH | Isogeny based drop-in replacement for Diffie–Hellman | Post-Quantum Key exchange. | +| PQ KEM | SIKE | SIKE is a key encapsulation mechanism (KEM). | Post-quantum key exchange in TLS | +| Key Exchange | X25519, X448 | RFC-7748 provides new key exchange mechanisms based on Montgomery elliptic curves. | TLS 1.3. Secure Shell. | +| Key Exchange | FourQ | One of the fastest elliptic curves at 128-bit security level. | Experimental for key agreement and digital signatures. | +| Key Exchange / Digital signatures | P-384 | Our optimizations reduce the burden when moving from P-256 to P-384. | ECDSA and ECDH using Suite B at top secret level. | +| Digital Signatures | Ed25519, Ed448 | RFC-8032 provides new signature schemes based on Edwards curves. | Digital certificates and authentication. | +| Key Encapsulation | P-256, P-384, P-521, X25519 and X448 | Key encapsulation methods based on Diffie-Hellman. | HPKE | +| Hybrid Public-Key Encryption | Base, Auth, PSK, AuthPSK | [HPKE](https://www.ietf.org/archive/id/draft-irtf-cfrg-hpke-07.html) is a combination of KEM and AEAD. | TLS | +| PQ KEM/PKE | Kyber | Lattice (M-LWE) based IND-CCA2 secure key encapsulation mechanism and IND-CPA secure public key encryption | Post-Quantum Key exchange | +| PQ Digital Signatures | Dilithium, Hybrid modes | Lattice (Module LWE) based signature scheme | Post-Quantum PKI | + +### Work in Progress + +| Category | Algorithms | Description | Applications | +|----------|------------|-------------|--------------| +| Hashing to Elliptic Curve Groups | Several algorithms: Elligator2, Ristretto, SWU, Icart. | Protocols based on elliptic curves require hash functions that map bit strings to points on an elliptic curve. | VOPRF. OPAQUE. PAKE. Verifiable random functions. | +| Bilinear Pairings | Plans for moving BN256 to stronger pairing curves. | A bilineal pairing is a mathematical operation that enables the implementation of advanced cryptographic protocols, such as identity-based encryption (IBE), short digital signatures (BLS), and attribute-based encryption (ABE). | Geo Key Manager, Randomness Beacon, Ethereum and other blockchain applications. | +| PQ KEM | HRSS-SXY | Lattice (NTRU) based key encapsulation mechanism. | Key exchange for low-latency environments | +| PQ Digital Signatures | SPHINCS+ | Stateless hash-based signature scheme | Post-Quantum PKI | + +## Testing and Benchmarking + +Library comes with number of make targets which can be used for testing and +benchmarking: + +- ``test`` performs testing of the binary. +- ``bench`` runs benchmarks. +- ``cover`` produces coverage. +- ``lint`` runs set of linters on the code base. + +## Contributing + +To contribute, fork this repository and make your changes, and then make a Pull +Request. A Pull Request requires approval of the admin team and a successful +CI build. + +## How to Cite + +To cite CIRCL, use one of the following formats and update with the date +you accessed this project. + +APA Style + +``` +Faz-Hernández, A. and Kwiatkowski, K. (2019). Introducing CIRCL: +An Advanced Cryptographic Library. Cloudflare. Available at +https://circl. Accessed Feb 2021. +``` + +Bibtex Source + +```bibtex +@manual{circl, + title = {Introducing CIRCL: An Advanced Cryptographic Library}, + author = {Armando Faz-Hern\'{a}ndez and Kris Kwiatkowski}, + organization = {Cloudflare}, + abstract = {{CIRCL (Cloudflare Interoperable, Reusable Cryptographic Library) is + a collection of cryptographic primitives written in Go. The goal + of this library is to be used as a tool for experimental + deployment of cryptographic algorithms targeting Post-Quantum (PQ) + and Elliptic Curve Cryptography (ECC).}}, + note = {Available at \url{https://circl}. Accessed Feb 2021}, + month = jun, + year = {2019} +} +``` + +## License + +The project is licensed under the [BSD-3-Clause License](./LICENSE). diff --git a/src/circl/dh/csidh/consts.go b/src/circl/dh/csidh/consts.go new file mode 100644 index 00000000000..7ef31cce076 --- /dev/null +++ b/src/circl/dh/csidh/consts.go @@ -0,0 +1,104 @@ +package csidh + +const ( + // pbits is a bitsize of prime p + pbits = 511 + // primeCount number of Elkies primes used for constructing p + primeCount = 74 + // (2*5+1)^74 is roughly 2^256 + expMax = int8(5) + // size of the limbs, pretty much hardcoded to 64-bit words + limbBitSize = 64 + // size of the limbs in bytes + limbByteSize = limbBitSize >> 3 + // Number of limbs for a field element + numWords = 8 + // PrivateKeySize is a size of cSIDH/512 private key in bytes. + PrivateKeySize = 37 + // PublicKeySize is a size of cSIDH/512 public key in bytes. + PublicKeySize = 64 + // SharedSecretSize is a size of cSIDH/512 shared secret in bytes. + SharedSecretSize = 64 +) + +var ( + // Elkies primes up to 374 + prime 587 + // p = 4 * product(Elkies primes) - 1 + primes = [primeCount]uint64{ + 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, 0x0017, 0x001D, 0x001F, 0x0025, + 0x0029, 0x002B, 0x002F, 0x0035, 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, + 0x0059, 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, 0x0083, 0x0089, 0x008B, + 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD, 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, + 0x00C7, 0x00D3, 0x00DF, 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107, + 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137, 0x0139, 0x013D, 0x014B, + 0x0151, 0x015B, 0x015D, 0x0161, 0x0167, 0x016F, 0x0175, 0x024B} + + p = fp{ + 0x1B81B90533C6C87B, 0xC2721BF457ACA835, + 0x516730CC1F0B4F25, 0xA7AAC6C567F35507, + 0x5AFBFCC69322C9CD, 0xB42D083AEDC88C42, + 0xFC8AB0D15E3E4C4A, 0x65B48E8F740F89BF, + } + + /* Montgomery R = 2^512 mod p */ + one = fp{ + 0xC8FC8DF598726F0A, 0x7B1BC81750A6AF95, + 0x5D319E67C1E961B4, 0xB0AA7275301955F1, + 0x4A080672D9BA6C64, 0x97A5EF8A246EE77B, + 0x06EA9E5D4383676A, 0x3496E2E117E0EC80, + } + + // 2 in Montgomery domain + two = fp{ + 0x767762E5FD1E1599, 0x33C5743A49A0B6F6, + 0x68FC0C0364C77443, 0xB9AA1E24F83F56DB, + 0x3914101F20520EFB, 0x7B1ED6D95B1542B4, + 0x114A8BE928C8828A, 0x03793732BBB24F40, + } + + // -2 in Montgomery domain + twoNeg = fp{ + 0xA50A561F36A8B2E2, 0x8EACA7BA0E0BF13E, + 0xE86B24C8BA43DAE2, 0xEE00A8A06FB3FE2B, + 0x21E7ECA772D0BAD1, 0x390E316192B3498E, + 0xEB4024E83575C9C0, 0x623B575CB85D3A7F, + } + + // 4 in Montgomery domain + four = fp{ + 0xECEEC5CBFA3C2B32, 0x678AE87493416DEC, + 0xD1F81806C98EE886, 0x73543C49F07EADB6, + 0x7228203E40A41DF7, 0xF63DADB2B62A8568, + 0x229517D251910514, 0x06F26E6577649E80, + } + + // 4 * sqrt(p) + fourSqrtP = fp{ + 0x17895E71E1A20B3F, 0x38D0CD95F8636A56, + 0x142B9541E59682CD, 0x856F1399D91D6592, + 0x0000000000000002, + } + + // -p^-1 mod 2^64 + pNegInv = fp{ + 0x66c1301f632e294d, + } + + // (p-1)/2. Used as exponent, hence not in + // montgomery domain + pMin1By2 = fp{ + 0x8DC0DC8299E3643D, 0xE1390DFA2BD6541A, + 0xA8B398660F85A792, 0xD3D56362B3F9AA83, + 0x2D7DFE63499164E6, 0x5A16841D76E44621, + 0xFE455868AF1F2625, 0x32DA4747BA07C4DF, + } + + // p-1 mod 2^64. Used as exponent, hence not + // in montgomery domain + pMin1 = fp{ + 0x1B81B90533C6C879, 0xC2721BF457ACA835, + 0x516730CC1F0B4F25, 0xA7AAC6C567F35507, + 0x5AFBFCC69322C9CD, 0xB42D083AEDC88C42, + 0xFC8AB0D15E3E4C4A, 0x65B48E8F740F89BF, + } +) diff --git a/src/circl/dh/csidh/csidh.go b/src/circl/dh/csidh/csidh.go new file mode 100644 index 00000000000..2869edad7dd --- /dev/null +++ b/src/circl/dh/csidh/csidh.go @@ -0,0 +1,333 @@ +package csidh + +import ( + "io" +) + +// 511-bit number representing prime field element GF(p) +type fp [numWords]uint64 + +// Represents projective point on elliptic curve E over GF(p) +type point struct { + x fp + z fp +} + +// Curve coefficients +type coeff struct { + a fp + c fp +} + +type fpRngGen struct { + // working buffer needed to avoid memory allocation + wbuf [64]byte +} + +// Defines operations on public key +type PublicKey struct { + fpRngGen + // Montgomery coefficient A from GF(p) of the elliptic curve + // y^2 = x^3 + Ax^2 + x. + a fp +} + +// Defines operations on private key +type PrivateKey struct { + fpRngGen + // private key is a set of integers randomly + // each sampled from a range [-5, 5]. + e [PrivateKeySize]int8 +} + +// randFp generates random element from Fp. +func (s *fpRngGen) randFp(v *fp, rng io.Reader) { + mask := uint64(1<<(pbits%limbBitSize)) - 1 + for { + *v = fp{} + _, err := io.ReadFull(rng, s.wbuf[:]) + if err != nil { + panic("Can't read random number") + } + + for i := 0; i < len(s.wbuf); i++ { + j := i / limbByteSize + k := uint(i % 8) + v[j] |= uint64(s.wbuf[i]) << (8 * k) + } + + v[len(v)-1] &= mask + if isLess(v, &p) { + return + } + } +} + +// cofactorMul helper implements batch cofactor multiplication as described +// in the ia.cr/2018/383 (algo. 3). Returns tuple of two booleans, first indicates +// if function has finished successfully. In case first return value is true, +// second return value indicates if curve represented by coffactor 'a' is +// supersingular. +// Implementation uses divide-and-conquer strategy and recursion in order to +// speed up calculation of Q_i = [(p+1)/l_i] * P. +// Implementation is not constant time, but it operates on public data only. +func cofactorMul(p *point, a *coeff, halfL, halfR int, order *fp) (bool, bool) { + var Q point + var r1, d1, r2, d2 bool + if (halfR - halfL) == 1 { + // base case + if !p.z.isZero() { + var tmp = fp{primes[halfL]} + xMul(p, p, a, &tmp) + + if !p.z.isZero() { + // order does not divide p+1 -> ordinary curve + return true, false + } + + mul512(order, order, primes[halfL]) + if isLess(&fourSqrtP, order) { + // order > 4*sqrt(p) -> supersingular curve + return true, true + } + } + return false, false + } + + // perform another recursive step + mid := halfL + ((halfR - halfL + 1) / 2) + var mulL, mulR = fp{1}, fp{1} + // compute u = primes_1 * ... * primes_m + for i := halfL; i < mid; i++ { + mul512(&mulR, &mulR, primes[i]) + } + // compute v = primes_m+1 * ... * primes_n + for i := mid; i < halfR; i++ { + mul512(&mulL, &mulL, primes[i]) + } + + // calculate Q_i + xMul(&Q, p, a, &mulR) + xMul(p, p, a, &mulL) + + d1, r1 = cofactorMul(&Q, a, mid, halfR, order) + d2, r2 = cofactorMul(p, a, halfL, mid, order) + return d1 || d2, r1 || r2 +} + +// groupAction evaluates group action of prv.e on a Montgomery +// curve represented by coefficient pub.A. +// This is implementation of algorithm 2 from ia.cr/2018/383. +func groupAction(pub *PublicKey, prv *PrivateKey, rng io.Reader) { + var k [2]fp + var e [2][primeCount]uint8 + var done = [2]bool{false, false} + var A = coeff{a: pub.a, c: one} + + k[0][0] = 4 + k[1][0] = 4 + + for i, v := range primes { + t := (prv.e[uint(i)>>1] << ((uint(i) % 2) * 4)) >> 4 + if t > 0 { + e[0][i] = uint8(t) + e[1][i] = 0 + mul512(&k[1], &k[1], v) + } else if t < 0 { + e[1][i] = uint8(-t) + e[0][i] = 0 + mul512(&k[0], &k[0], v) + } else { + e[0][i] = 0 + e[1][i] = 0 + mul512(&k[0], &k[0], v) + mul512(&k[1], &k[1], v) + } + } + + for { + var P point + var rhs fp + prv.randFp(&P.x, rng) + P.z = one + montEval(&rhs, &A.a, &P.x) + sign := rhs.isNonQuadRes() + + if done[sign] { + continue + } + + xMul(&P, &P, &A, &k[sign]) + done[sign] = true + + for i, v := range primes { + if e[sign][i] != 0 { + var cof = fp{1} + var K point + + for j := i + 1; j < len(primes); j++ { + if e[sign][j] != 0 { + mul512(&cof, &cof, primes[j]) + } + } + + xMul(&K, &P, &A, &cof) + if !K.z.isZero() { + xIso(&P, &A, &K, v) + e[sign][i] = e[sign][i] - 1 + if e[sign][i] == 0 { + mul512(&k[sign], &k[sign], primes[i]) + } + } + } + done[sign] = done[sign] && (e[sign][i] == 0) + } + + modExpRdc512(&A.c, &A.c, &pMin1) + mulRdc(&A.a, &A.a, &A.c) + A.c = one + + if done[0] && done[1] { + break + } + } + pub.a = A.a +} + +// PrivateKey operations + +func (c *PrivateKey) Import(key []byte) bool { + if len(key) < len(c.e) { + return false + } + for i, v := range key { + c.e[i] = int8(v) + } + return true +} + +func (c PrivateKey) Export(out []byte) bool { + if len(out) < len(c.e) { + return false + } + for i, v := range c.e { + out[i] = byte(v) + } + return true +} + +func GeneratePrivateKey(key *PrivateKey, rng io.Reader) error { + for i := range key.e { + key.e[i] = 0 + } + + for i := 0; i < len(primes); { + _, err := io.ReadFull(rng, key.wbuf[:]) + if err != nil { + return err + } + + for j := range key.wbuf { + if int8(key.wbuf[j]) <= expMax && int8(key.wbuf[j]) >= -expMax { + key.e[i>>1] |= int8((key.wbuf[j] & 0xF) << uint((i%2)*4)) + i = i + 1 + if i == len(primes) { + break + } + } + } + } + return nil +} + +// Public key operations + +// reset removes key material from PublicKey. +func (c *PublicKey) reset() { + for i := range c.a { + c.a[i] = 0 + } +} + +// Assumes key is in Montgomery domain. +func (c *PublicKey) Import(key []byte) bool { + if len(key) != numWords*limbByteSize { + return false + } + for i := 0; i < len(key); i++ { + j := i / limbByteSize + k := uint64(i % 8) + c.a[j] |= uint64(key[i]) << (8 * k) + } + return true +} + +// Assumes key is exported as encoded in Montgomery domain. +func (c *PublicKey) Export(out []byte) bool { + if len(out) != numWords*limbByteSize { + return false + } + for i := 0; i < len(out); i++ { + j := i / limbByteSize + k := uint64(i % 8) + out[i] = byte(c.a[j] >> (8 * k)) + } + return true +} + +func GeneratePublicKey(pub *PublicKey, prv *PrivateKey, rng io.Reader) { + pub.reset() + groupAction(pub, prv, rng) +} + +// Validate returns true if 'pub' is a valid cSIDH public key, +// otherwise false. +// More precisely, the function verifies that curve +// y^2 = x^3 + pub.a * x^2 + x +// is supersingular. +func Validate(pub *PublicKey, rng io.Reader) bool { + // Check if in range + if !isLess(&pub.a, &p) { + return false + } + + // Check if pub represents a smooth Montgomery curve. + if pub.a.equal(&two) || pub.a.equal(&twoNeg) { + return false + } + + // Check if pub represents a supersingular curve. + for { + var P point + var A = point{pub.a, one} + + // Randomly chosen P must have big enough order to check + // supersingularity. Probability of random P having big + // enough order is very high, as proven by W.Castryck et + // al. (ia.cr/2018/383, ch 5) + pub.randFp(&P.x, rng) + P.z = one + + xDbl(&P, &P, &A) + xDbl(&P, &P, &A) + + done, res := cofactorMul(&P, &coeff{A.x, A.z}, 0, len(primes), &fp{1}) + if done { + return res + } + } +} + +// DeriveSecret computes a cSIDH shared secret. If successful, returns true +// and fills 'out' with shared secret. Function returns false in case 'pub' is invalid. +// More precisely, shared secret is a Montgomery coefficient A of a secret +// curve y^2 = x^3 + Ax^2 + x, computed by applying action of a prv.e +// on a curve represented by pub.a. +func DeriveSecret(out *[64]byte, pub *PublicKey, prv *PrivateKey, rng io.Reader) bool { + if !Validate(pub, rng) { + return false + } + groupAction(pub, prv, rng) + pub.Export(out[:]) + return true +} diff --git a/src/circl/dh/csidh/csidh_test.go b/src/circl/dh/csidh/csidh_test.go new file mode 100644 index 00000000000..64dca365077 --- /dev/null +++ b/src/circl/dh/csidh/csidh_test.go @@ -0,0 +1,360 @@ +package csidh + +import ( + "bytes" + "crypto/rand" + "encoding/binary" + "encoding/hex" + "encoding/json" + "os" + "testing" + + . "circl/internal/test" +) + +// Possible values for "Status" +const ( + Valid = iota // Indicates that shared secret must be agreed correctly + ValidPublicKey2 // Public key 2 must succeed validation + InvalidSharedSecret // Calculated shared secret must be different than test vector + InvalidPublicKey1 // Public key 1 generated from private key must be different than test vector + InvalidPublicKey2 // Public key 2 must fail validation +) + +var StatusValues = map[int]string{ + Valid: "valid", + ValidPublicKey2: "valid_public_key2", + InvalidSharedSecret: "invalid_shared_secret", + InvalidPublicKey1: "invalid_public_key1", + InvalidPublicKey2: "invalid_public_key2", +} + +var rng = rand.Reader + +type TestVector struct { + ID int `json:"Id"` + Pk1 string `json:"Pk1"` + Pr1 string `json:"Pr1"` + Pk2 string `json:"Pk2"` + Ss string `json:"Ss"` + Status string `json:"status"` +} + +type TestVectors struct { + Vectors []TestVector `json:"Vectors"` +} + +func TestCompare64(t *testing.T) { + const s uint64 = 0xFFFFFFFFFFFFFFFF + var val1 = fp{0, 2, 3, 4, 5, 6, 7, 8} + var val2 = fp{s, s, s, s, s, s, s, s} + var fp fp + + if !fp.isZero() { + t.Errorf("isZero returned true, where it should be false") + } + if val1.isZero() { + t.Errorf("isZero returned false, where it should be true") + } + if val2.isZero() { + t.Errorf("isZero returned false, where it should be true") + } +} + +func TestEphemeralKeyExchange(t *testing.T) { + var ss1, ss2 [64]byte + var prv1, prv2 PrivateKey + var pub1, pub2 PublicKey + + prvBytes1 := []byte{0xaa, 0x54, 0xe4, 0xd4, 0xd0, 0xbd, 0xee, 0xcb, 0xf4, 0xd0, 0xc2, 0xbc, 0x52, 0x44, 0x11, 0xee, 0xe1, 0x14, 0xd2, 0x24, 0xe5, 0x0, 0xcc, 0xf5, 0xc0, 0xe1, 0x1e, 0xb3, 0x43, 0x52, 0x45, 0xbe, 0xfb, 0x54, 0xc0, 0x55, 0xb2} + prv1.Import(prvBytes1) + GeneratePublicKey(&pub1, &prv1, rng) + + CheckNoErr(t, GeneratePrivateKey(&prv2, rng), "PrivateKey generation failed") + GeneratePublicKey(&pub2, &prv2, rng) + + CheckOk( + DeriveSecret(&ss1, &pub1, &prv2, rng), + "Derivation failed", t) + CheckOk( + DeriveSecret(&ss2, &pub2, &prv1, rng), + "Derivation failed", t) + + if !bytes.Equal(ss1[:], ss2[:]) { + t.Error("ss1 != ss2") + } +} + +func TestPrivateKeyExportImport(t *testing.T) { + var buf [37]byte + for i := 0; i < numIter; i++ { + var prv1, prv2 PrivateKey + CheckNoErr(t, GeneratePrivateKey(&prv1, rng), "PrivateKey generation failed") + prv1.Export(buf[:]) + prv2.Import(buf[:]) + + for i := 0; i < len(prv1.e); i++ { + if prv1.e[i] != prv2.e[i] { + t.Error("Error occurred when public key export/import") + } + } + } +} + +func TestValidateNegative(t *testing.T) { + pk := PublicKey{a: p} + pk.a[0]++ + if Validate(&pk, rng) { + t.Error("Public key > p has been validated") + } + + pk = PublicKey{a: p} + if Validate(&pk, rng) { + t.Error("Public key == p has been validated") + } + + pk = PublicKey{a: two} + if Validate(&pk, rng) { + t.Error("Public key == 2 has been validated") + } + + pk = PublicKey{a: twoNeg} + if Validate(&pk, rng) { + t.Error("Public key == -2 has been validated") + } +} + +func TestPublicKeyExportImport(t *testing.T) { + var buf [64]byte + eq64 := func(x, y []uint64) bool { + for i := range x { + if x[i] != y[i] { + return false + } + } + return true + } + + for i := 0; i < numIter; i++ { + var prv PrivateKey + var pub1, pub2 PublicKey + CheckNoErr(t, GeneratePrivateKey(&prv, rng), "PrivateKey generation failed") + GeneratePublicKey(&pub1, &prv, rng) + + pub1.Export(buf[:]) + pub2.Import(buf[:]) + + if !eq64(pub1.a[:], pub2.a[:]) { + t.Error("Error occurred when public key export/import") + } + } +} + +// Test vectors generated by reference implementation. +func TestKAT(t *testing.T) { + var tests TestVectors + // Helper checks if e==true and reports an error if not. + checkExpr := func(e bool, vec *TestVector, t *testing.T, msg string) { + t.Helper() + if !e { + t.Errorf("[Test ID=%d] "+msg, vec.ID) + } + } + // checkSharedSecret implements nominal case - imports asymmetric keys for + // both parties, derives secret key and compares it to value in test vector. + // Comparison must succeed in case status is "Valid" in any other case + // it must fail. + checkSharedSecret := func(vec *TestVector, t *testing.T, status int) { + var prv1 PrivateKey + var pub1, pub2 PublicKey + var ss [SharedSecretSize]byte + + prBuf, err := hex.DecodeString(vec.Pr1) + if err != nil { + t.Fatal(err) + } + checkExpr(prv1.Import(prBuf[:]), vec, t, "PrivateKey wrong") + pkBuf, err := hex.DecodeString(vec.Pk1) + if err != nil { + t.Fatal(err) + } + checkExpr(pub1.Import(pkBuf[:]), vec, t, "PublicKey 1 wrong") + pkBuf, err = hex.DecodeString(vec.Pk2) + if err != nil { + t.Fatal(err) + } + checkExpr(pub2.Import(pkBuf[:]), vec, t, "PublicKey 2 wrong") + checkExpr(DeriveSecret(&ss, &pub2, &prv1, rng), vec, t, "Error when deriving key") + ssExp, err := hex.DecodeString(vec.Ss) + if err != nil { + t.Fatal(err) + } + checkExpr(bytes.Equal(ss[:], ssExp) == (status == Valid), vec, t, "Unexpected value of shared secret") + } + // checkPublicKey1 imports public and private key for one party A + // and tries to generate public key for a private key. After that + // it compares generated key to a key from test vector. Comparison + // must fail. + checkPublicKey1 := func(vec *TestVector, t *testing.T) { + var prv PrivateKey + var pub PublicKey + var pubBytesGot [PublicKeySize]byte + + prBuf, err := hex.DecodeString(vec.Pr1) + if err != nil { + t.Fatal(err) + } + + pubBytesExp, err := hex.DecodeString(vec.Pk1) + if err != nil { + t.Fatal(err) + } + + checkExpr( + prv.Import(prBuf[:]), + vec, t, "PrivateKey wrong") + + // Generate public key + CheckNoErr(t, GeneratePrivateKey(&prv, rng), "PrivateKey generation failed") + pub.Export(pubBytesGot[:]) + + // pubBytesGot must be different than pubBytesExp + checkExpr( + !bytes.Equal(pubBytesGot[:], pubBytesExp), + vec, t, "Public key generated is the same as public key from the test vector") + } + // checkPublicKey2 the goal is to test key validation. Test tries to + // import public key for B and ensure that import succeeds in case + // status is "Valid" and fails otherwise. + checkPublicKey2 := func(vec *TestVector, t *testing.T, status int) { + var pub PublicKey + pubBytesExp, err := hex.DecodeString(vec.Pk2) + if err != nil { + t.Fatal(err) + } + // Import validates an input, so it must fail + pub.Import(pubBytesExp[:]) + checkExpr( + Validate(&pub, rng) == (status == Valid || status == ValidPublicKey2), + vec, t, "PublicKey has been validated correctly") + } + // Load test data + file, err := os.Open(katFile) + if err != nil { + t.Fatal(err.Error()) + } + err = json.NewDecoder(file).Decode(&tests) + if err != nil { + t.Fatal(err.Error()) + } + // Loop over numIter test cases + // The algorithm is relatively slow, so it tests a smaller number. + N := len(tests.Vectors) + var buf [2]byte + for i := 0; i < numIter; i++ { + _, _ = rand.Read(buf[:]) + idx := binary.LittleEndian.Uint16(buf[:]) % uint16(N) + test := tests.Vectors[idx] + switch test.Status { + case StatusValues[Valid]: + checkSharedSecret(&test, t, Valid) + checkPublicKey2(&test, t, Valid) + case StatusValues[InvalidSharedSecret]: + checkSharedSecret(&test, t, InvalidSharedSecret) + case StatusValues[InvalidPublicKey1]: + checkPublicKey1(&test, t) + case StatusValues[InvalidPublicKey2]: + checkPublicKey2(&test, t, InvalidPublicKey2) + case StatusValues[InvalidPublicKey2]: + checkPublicKey2(&test, t, InvalidPublicKey2) + case StatusValues[ValidPublicKey2]: + checkPublicKey2(&test, t, ValidPublicKey2) + } + } +} + +var prv1, prv2 PrivateKey +var pub1, pub2 PublicKey + +// Private key generation. +func BenchmarkGeneratePrivate(b *testing.B) { + for n := 0; n < b.N; n++ { + _ = GeneratePrivateKey(&prv1, rng) + } +} + +// Public key generation from private (group action on empty key). +func BenchmarkGenerateKeyPair(b *testing.B) { + for n := 0; n < b.N; n++ { + var pub PublicKey + _ = GeneratePrivateKey(&prv1, rng) + GeneratePublicKey(&pub, &prv1, rng) + } +} + +// Benchmark validation on same key multiple times. +func BenchmarkValidate(b *testing.B) { + prvBytes := []byte{0xaa, 0x54, 0xe4, 0xd4, 0xd0, 0xbd, 0xee, 0xcb, 0xf4, 0xd0, 0xc2, 0xbc, 0x52, 0x44, 0x11, 0xee, 0xe1, 0x14, 0xd2, 0x24, 0xe5, 0x0, 0xcc, 0xf5, 0xc0, 0xe1, 0x1e, 0xb3, 0x43, 0x52, 0x45, 0xbe, 0xfb, 0x54, 0xc0, 0x55, 0xb2} + prv1.Import(prvBytes) + + var pub PublicKey + GeneratePublicKey(&pub, &prv1, rng) + + for n := 0; n < b.N; n++ { + Validate(&pub, rng) + } +} + +// Benchmark validation on random (most probably wrong) key. +func BenchmarkValidateRandom(b *testing.B) { + var tmp [64]byte + var pub PublicKey + + // Initialize seed + for n := 0; n < b.N; n++ { + if _, err := rng.Read(tmp[:]); err != nil { + b.FailNow() + } + pub.Import(tmp[:]) + } +} + +// Benchmark validation on different keys. +func BenchmarkValidateGenerated(b *testing.B) { + for n := 0; n < b.N; n++ { + _ = GeneratePrivateKey(&prv1, rng) + GeneratePublicKey(&pub1, &prv1, rng) + Validate(&pub1, rng) + } +} + +// Generate some keys and benchmark derive. +func BenchmarkDerive(b *testing.B) { + var ss [64]byte + + _ = GeneratePrivateKey(&prv1, rng) + GeneratePublicKey(&pub1, &prv1, rng) + + _ = GeneratePrivateKey(&prv2, rng) + GeneratePublicKey(&pub2, &prv2, rng) + + b.ResetTimer() + for n := 0; n < b.N; n++ { + DeriveSecret(&ss, &pub2, &prv1, rng) + } +} + +// Benchmarks both - key generation and derivation. +func BenchmarkDeriveGenerated(b *testing.B) { + var ss [64]byte + + for n := 0; n < b.N; n++ { + _ = GeneratePrivateKey(&prv1, rng) + GeneratePublicKey(&pub1, &prv1, rng) + + _ = GeneratePrivateKey(&prv2, rng) + GeneratePublicKey(&pub2, &prv2, rng) + + DeriveSecret(&ss, &pub2, &prv1, rng) + } +} diff --git a/src/circl/dh/csidh/curve.go b/src/circl/dh/csidh/curve.go new file mode 100644 index 00000000000..2208726e688 --- /dev/null +++ b/src/circl/dh/csidh/curve.go @@ -0,0 +1,212 @@ +package csidh + +// xAdd implements differential arithmetic in P^1 for Montgomery +// curves E(x): x^3 + A*x^2 + x by using x-coordinate only arithmetic. +// x(PaQ) = x(P) + x(Q) by using x(P-Q) +// This algorithms is correctly defined only for cases when +// P!=inf, Q!=inf, P!=Q and P!=-Q. +func xAdd(PaQ, P, Q, PdQ *point) { + var t0, t1, t2, t3 fp + addRdc(&t0, &P.x, &P.z) + subRdc(&t1, &P.x, &P.z) + addRdc(&t2, &Q.x, &Q.z) + subRdc(&t3, &Q.x, &Q.z) + mulRdc(&t0, &t0, &t3) + mulRdc(&t1, &t1, &t2) + addRdc(&t2, &t0, &t1) + subRdc(&t3, &t0, &t1) + mulRdc(&t2, &t2, &t2) // sqr + mulRdc(&t3, &t3, &t3) // sqr + mulRdc(&PaQ.x, &PdQ.z, &t2) + mulRdc(&PaQ.z, &PdQ.x, &t3) +} + +// xDbl implements point doubling on a Montgomery curve +// E(x): x^3 + A*x^2 + x by using x-coordinate onlyh arithmetic. +// x(Q) = [2]*x(P) +// It is correctly defined for all P != inf. +func xDbl(Q, P, A *point) { + var t0, t1, t2 fp + addRdc(&t0, &P.x, &P.z) + mulRdc(&t0, &t0, &t0) // sqr + subRdc(&t1, &P.x, &P.z) + mulRdc(&t1, &t1, &t1) // sqr + subRdc(&t2, &t0, &t1) + mulRdc(&t1, &four, &t1) + mulRdc(&t1, &t1, &A.z) + mulRdc(&Q.x, &t0, &t1) + addRdc(&t0, &A.z, &A.z) + addRdc(&t0, &t0, &A.x) + mulRdc(&t0, &t0, &t2) + addRdc(&t0, &t0, &t1) + mulRdc(&Q.z, &t0, &t2) +} + +// xDblAdd implements combined doubling of point P +// and addition of points P and Q on a Montgomery curve +// E(x): x^3 + A*x^2 + x by using x-coordinate onlyh arithmetic. +// x(PaP) = x(2*P) +// x(PaQ) = x(P+Q) +func xDblAdd(PaP, PaQ, P, Q, PdQ *point, A24 *coeff) { + var t0, t1, t2 fp + + addRdc(&t0, &P.x, &P.z) + subRdc(&t1, &P.x, &P.z) + mulRdc(&PaP.x, &t0, &t0) + subRdc(&t2, &Q.x, &Q.z) + addRdc(&PaQ.x, &Q.x, &Q.z) + mulRdc(&t0, &t0, &t2) + mulRdc(&PaP.z, &t1, &t1) + mulRdc(&t1, &t1, &PaQ.x) + subRdc(&t2, &PaP.x, &PaP.z) + mulRdc(&PaP.z, &PaP.z, &A24.c) + mulRdc(&PaP.x, &PaP.x, &PaP.z) + mulRdc(&PaQ.x, &A24.a, &t2) + subRdc(&PaQ.z, &t0, &t1) + addRdc(&PaP.z, &PaP.z, &PaQ.x) + addRdc(&PaQ.x, &t0, &t1) + mulRdc(&PaP.z, &PaP.z, &t2) + mulRdc(&PaQ.z, &PaQ.z, &PaQ.z) + mulRdc(&PaQ.x, &PaQ.x, &PaQ.x) + mulRdc(&PaQ.z, &PaQ.z, &PdQ.x) + mulRdc(&PaQ.x, &PaQ.x, &PdQ.z) +} + +// cswappoint swaps P1 with P2 in constant time. The 'choice' +// parameter must have a value of either 1 (results +// in swap) or 0 (results in no-swap). +func cswappoint(P1, P2 *point, choice uint8) { + cswap512(&P1.x, &P2.x, choice) + cswap512(&P1.z, &P2.z, choice) +} + +// xMul implements point multiplication with left-to-right Montgomery +// adder. co is A coefficient of x^3 + A*x^2 + x curve. k must be > 0 +// +// Non-constant time! +func xMul(kP, P *point, co *coeff, k *fp) { + var A24 coeff + var Q point + var j uint + var A = point{x: co.a, z: co.c} + var R = *P + + // Precompyte A24 = (A+2C:4C) => (A24.x = A.x+2A.z; A24.z = 4*A.z) + addRdc(&A24.a, &co.c, &co.c) + addRdc(&A24.a, &A24.a, &co.a) + mulRdc(&A24.c, &co.c, &four) + + // Skip initial 0 bits. + for j = 511; j > 0; j-- { + // performance hit from making it constant-time is actually + // quite big, so... unsafe branch for now + if uint8(k[j>>6]>>(j&63)&1) != 0 { + break + } + } + + xDbl(&Q, P, &A) + prevBit := uint8(1) + for i := j; i > 0; { + i-- + bit := uint8(k[i>>6] >> (i & 63) & 1) + cswappoint(&Q, &R, prevBit^bit) + xDblAdd(&Q, &R, &Q, &R, P, &A24) + prevBit = bit + } + cswappoint(&Q, &R, uint8(k[0]&1)) + *kP = Q +} + +// xIso computes the isogeny with kernel point kern of a given order +// kernOrder. Returns the new curve coefficient co and the image img. +// +// During computation function switches between Montgomery and twisted +// Edwards curves in order to compute image curve parameters faster. +// This technique is described by Meyer and Reith in ia.cr/2018/782. +// +// Non-constant time. +func xIso(img *point, co *coeff, kern *point, kernOrder uint64) { + var t0, t1, t2, S, D fp + var Q, prod point + var coEd coeff + var M = [3]point{*kern} + + // Compute twisted Edwards coefficients + // coEd.a = co.a + 2*co.c + // coEd.c = co.a - 2*co.c + // coEd.a*X^2 + Y^2 = 1 + coEd.c*X^2*Y^2 + addRdc(&coEd.c, &co.c, &co.c) + addRdc(&coEd.a, &co.a, &coEd.c) + subRdc(&coEd.c, &co.a, &coEd.c) + + // Transfer point to twisted Edwards YZ-coordinates + // (X:Z)->(Y:Z) = (X-Z : X+Z) + addRdc(&S, &img.x, &img.z) + subRdc(&D, &img.x, &img.z) + + subRdc(&prod.x, &kern.x, &kern.z) + addRdc(&prod.z, &kern.x, &kern.z) + + mulRdc(&t1, &prod.x, &S) + mulRdc(&t0, &prod.z, &D) + addRdc(&Q.x, &t0, &t1) + subRdc(&Q.z, &t0, &t1) + + xDbl(&M[1], kern, &point{x: co.a, z: co.c}) + + // NOTE: Not constant time. + for i := uint64(1); i < kernOrder>>1; i++ { + if i >= 2 { + xAdd(&M[i%3], &M[(i-1)%3], kern, &M[(i-2)%3]) + } + subRdc(&t1, &M[i%3].x, &M[i%3].z) + addRdc(&t0, &M[i%3].x, &M[i%3].z) + mulRdc(&prod.x, &prod.x, &t1) + mulRdc(&prod.z, &prod.z, &t0) + mulRdc(&t1, &t1, &S) + mulRdc(&t0, &t0, &D) + addRdc(&t2, &t0, &t1) + mulRdc(&Q.x, &Q.x, &t2) + subRdc(&t2, &t0, &t1) + mulRdc(&Q.z, &Q.z, &t2) + } + + mulRdc(&Q.x, &Q.x, &Q.x) + mulRdc(&Q.z, &Q.z, &Q.z) + mulRdc(&img.x, &img.x, &Q.x) + mulRdc(&img.z, &img.z, &Q.z) + + // coEd.a^kernOrder and coEd.c^kernOrder + modExpRdc64(&coEd.a, &coEd.a, kernOrder) + modExpRdc64(&coEd.c, &coEd.c, kernOrder) + + // prod^8 + mulRdc(&prod.x, &prod.x, &prod.x) + mulRdc(&prod.x, &prod.x, &prod.x) + mulRdc(&prod.x, &prod.x, &prod.x) + mulRdc(&prod.z, &prod.z, &prod.z) + mulRdc(&prod.z, &prod.z, &prod.z) + mulRdc(&prod.z, &prod.z, &prod.z) + + // Compute image curve params + mulRdc(&coEd.c, &coEd.c, &prod.x) + mulRdc(&coEd.a, &coEd.a, &prod.z) + + // Convert curve coefficients back to Montgomery + addRdc(&co.a, &coEd.a, &coEd.c) + subRdc(&co.c, &coEd.a, &coEd.c) + addRdc(&co.a, &co.a, &co.a) +} + +// montEval evaluates x^3 + Ax^2 + x. +func montEval(res, A, x *fp) { + var t fp + + *res = *x + mulRdc(res, res, res) + mulRdc(&t, A, x) + addRdc(res, res, &t) + addRdc(res, res, &one) + mulRdc(res, res, x) +} diff --git a/src/circl/dh/csidh/curve_test.go b/src/circl/dh/csidh/curve_test.go new file mode 100644 index 00000000000..e933e794407 --- /dev/null +++ b/src/circl/dh/csidh/curve_test.go @@ -0,0 +1,371 @@ +package csidh + +import ( + "math/big" + "testing" +) + +// Actual test implementation. +func TestXAdd(t *testing.T) { + var P, Q, PdQ point + var PaQ point + var expPaQ big.Int + + // points from a Elliptic Curve defined in sage as follows: + // A = 0x6055947AAFEBF773CE912680A6A32656073233D2FD6FDF4A143BE82D25B44ECC0431DE564C0F0D6591ACC62D6876E86F5D06B68C9EAF20D0DB0A6B99ED558512 + // E = EllipticCurve(GF(p), [0, A, 0, 1, 0]) + // where p is CSIDH's 511-bit prime + + checkXAdd := func() { + xAdd(&PaQ, &P, &Q, &PdQ) + ret := toNormX(&PaQ) + if ret.Cmp(&expPaQ) != 0 { + t.Errorf("\nExp: %s\nGot: %s", expPaQ.Text(16), ret.Text(16)) + } + } + + expPaQ.SetString("0x41C98C5D7FF118B1A3987733581FD69C0CC27D7B63BCCA525106B9945869C6DAEDAA3D5D9D2679237EF0D013BE68EF12731DBFB26E12576BAD1E824C67ABD125", 0) + P.x = toFp("0x5840FD8E0165F7F474260F99337461AF195233F791FABE735EC2634B74A95559568B4CEB23959C8A01C5C57E215D22639868ED840D74FE2BAC04830CF75047AD") + P.z = toFp("1") + Q.x = toFp("0x3C1A003C71436698B4A181CEB12BA4B4D1FF7BB14AAAF6FBDA6957C4EBA20AD8E3893DF6F64E67E81163E024C19C7E975F3EC61862F75502C3ED802370E75A3F") + Q.z = toFp("1") + PdQ.x = toFp("0x519B1928F752B0B2143C1C23EB247B370DBB5B9C29B9A3A064D7FBC1B67FAC34B6D3DDA0F3CB87C387B425B36F31B93A8E73252BA701927B767A9DE89D5A92AE") + PdQ.z = toFp("1") + checkXAdd() + + expPaQ.SetString("0x5840FD8E0165F7F474260F99337461AF195233F791FABE735EC2634B74A95559568B4CEB23959C8A01C5C57E215D22639868ED840D74FE2BAC04830CF75047AD", 0) + P.x = toFp("0x5840FD8E0165F7F474260F99337461AF195233F791FABE735EC2634B74A95559568B4CEB23959C8A01C5C57E215D22639868ED840D74FE2BAC04830CF75047AD") + P.z = toFp("1") + Q.x = toFp("1") + Q.z = toFp("0x0") + PdQ.x = toFp(expPaQ.Text(10)) + PdQ.z = toFp("1") + checkXAdd() +} + +func TestXDbl(t *testing.T) { + var P, A point + var PaP point + var expPaP big.Int + + // points from a Elliptic Curve defined in sage as follows: + // A = 0x599841D7D1FCD92A85759B7A3D2D5E4C56EFB17F19F86EB70E121EA16305EDE45A55868BE069313F821F7D94069EC220A4AC3B85500376710538246E9B3BC138 + // E = EllipticCurve(GF(p), [0, A, 0, 1, 0]) + // where p is CSIDH's 511-bit prime + + expPaP.SetString("0x6115B5D8BB613D11BDFEA70D436D87C1515553F6A15061727B4001E0AF745AAA9F39EB9464982829D931F77DAB9D71B24FF0D1D34C347F2A51FD45821F2EA06F", 0) + P.x = toFp("0x6C5B4D4AB0765AAB23C10F8455BE522D3A5363324D7AD641CC67C0A52FC1FFE9F3F8EDFE641478CA93D4D0016D83F21487FD4AF4E02F8A2C237CF27C5604BCC") + P.z = toFp("1") + A.x = toFp("0x599841D7D1FCD92A85759B7A3D2D5E4C56EFB17F19F86EB70E121EA16305EDE45A55868BE069313F821F7D94069EC220A4AC3B85500376710538246E9B3BC138") + A.z = toFp("1") + + xDbl(&PaP, &P, &A) + ret := toNormX(&PaP) + if ret.Cmp(&expPaP) != 0 { + t.Errorf("\nExp: %s\nGot: %s", expPaP.Text(16), ret.Text(16)) + } +} + +func TestXDblAddNominal(t *testing.T) { + var P, Q, PdQ point + var PaP, PaQ point + var expPaP, expPaQ big.Int + var A coeff + + checkXDblAdd := func() { + var A24 coeff + + // A24.a = 2*A.z + A.a + addRdc(&A24.a, &A.c, &A.c) + addRdc(&A24.a, &A24.a, &A.a) + // A24.z = 4*A.z + mulRdc(&A24.c, &A.c, &four) + + // Additionally will check if input can be same as output + PaP = P + PaQ = Q + + xDblAdd(&PaP, &PaQ, &PaP, &PaQ, &PdQ, &A24) + retPaP := toNormX(&PaP) + retPaQ := toNormX(&PaQ) + if retPaP.Cmp(&expPaP) != 0 { + t.Errorf("\nExp: %s\nGot: %s", expPaP.Text(16), retPaP.Text(16)) + } + + if retPaQ.Cmp(&expPaQ) != 0 { + t.Errorf("\nExp: %s\nGot: %s", expPaQ.Text(16), retPaQ.Text(16)) + } + } + + // 2*P + expPaP.SetString("0x38F5B37271A3D8FA50107F88045D6F6B08355DD026C02E0306CE5875F47422736AD841B4122B2BD7DE6166BB6498F6A283378FF8250948E834F15CEA2D59A57B", 0) + // P+Q + expPaQ.SetString("0x53D9B44C5F61651612243CF7987F619FE6ACB5CF29538F96A63E7278E131F41A17D64388E31B028A5183EF9096AE82724BC34D8DDFD67AD68BD552A33C345B8C", 0) + P.x = toFp("0x4FE17B4CC66E85960F57033CD45996C99248DA09DF2E36F8840657B52F74ED8173E0D322FA57D7B4D0EE7F12967BBD59140B42F2626E29167D6419E851E5A4C9") + P.z = toFp("1") + Q.x = toFp("0x465047949CD6574FDBE00EA365CAF7A95DC9DEBE96A188823CA8C9DD9F527CF81290D49864F61DF0C08C1D6052139230735CA6CFDBDC1A8820610CCD71861176") + Q.z = toFp("1") + PdQ.x = toFp("0x49D3B999A0A020B34473568A8F75B5405F2D3BE5A006595015FC6DDC6BED8AB2A51A887B6DC62C64354466865FFD69E50AD37F6F4FBD74119EB65EBC9367B556") + PdQ.z = toFp("1") + A.a = toFp("0x118F955D498D902FD42E5B2926F297CC814CD7649EC5B070295622F97C4A0D9BD34058A7E0E00CB73ED32FCC237F9F6B7D2A15F5CC7C4EC61ECEF80ACBB0EFA4") + A.c = toFp("1") + checkXDblAdd() + + // Case P=value, Q=(x=1, z=0). In this case PaQ==P; PaP=2*P + expPaP.SetString("0x38F5B37271A3D8FA50107F88045D6F6B08355DD026C02E0306CE5875F47422736AD841B4122B2BD7DE6166BB6498F6A283378FF8250948E834F15CEA2D59A57B", 0) + expPaQ.SetString("0x4FE17B4CC66E85960F57033CD45996C99248DA09DF2E36F8840657B52F74ED8173E0D322FA57D7B4D0EE7F12967BBD59140B42F2626E29167D6419E851E5A4C9", 0) + P.x = toFp("0x4FE17B4CC66E85960F57033CD45996C99248DA09DF2E36F8840657B52F74ED8173E0D322FA57D7B4D0EE7F12967BBD59140B42F2626E29167D6419E851E5A4C9") + P.z = toFp("1") + Q.x = toFp("1") + Q.z = toFp("0") + PdQ.x = toFp("0x4FE17B4CC66E85960F57033CD45996C99248DA09DF2E36F8840657B52F74ED8173E0D322FA57D7B4D0EE7F12967BBD59140B42F2626E29167D6419E851E5A4C9") + PdQ.z = toFp("1") + A.a = toFp("0x118F955D498D902FD42E5B2926F297CC814CD7649EC5B070295622F97C4A0D9BD34058A7E0E00CB73ED32FCC237F9F6B7D2A15F5CC7C4EC61ECEF80ACBB0EFA4") + A.c = toFp("1") + checkXDblAdd() +} + +func TestXDblAddVSxDblxAdd(t *testing.T) { + var P, Q, PdQ point + var PaP1, PaQ1 point + var PaP2, PaQ2 point + var A point + var A24 coeff + + P.x = toFp("0x4FE17B4CC66E85960F57033CD45996C99248DA09DF2E36F8840657B52F74ED8173E0D322FA57D7B4D0EE7F12967BBD59140B42F2626E29167D6419E851E5A4C9") + P.z = toFp("1") + Q.x = toFp("0x465047949CD6574FDBE00EA365CAF7A95DC9DEBE96A188823CA8C9DD9F527CF81290D49864F61DF0C08C1D6052139230735CA6CFDBDC1A8820610CCD71861176") + Q.z = toFp("1") + PdQ.x = toFp("0x49D3B999A0A020B34473568A8F75B5405F2D3BE5A006595015FC6DDC6BED8AB2A51A887B6DC62C64354466865FFD69E50AD37F6F4FBD74119EB65EBC9367B556") + PdQ.z = toFp("1") + A.x = toFp("0x118F955D498D902FD42E5B2926F297CC814CD7649EC5B070295622F97C4A0D9BD34058A7E0E00CB73ED32FCC237F9F6B7D2A15F5CC7C4EC61ECEF80ACBB0EFA4") + A.z = toFp("1") + + // Precompute A24 for xDblAdd + // (A+2C:4C) => (A24.x = A.x+2A.z; A24.z = 4*A.z) + addRdc(&A24.a, &A.z, &A.z) + addRdc(&A24.a, &A24.a, &A.x) + mulRdc(&A24.c, &A.z, &four) + + for i := 0; i < numIter; i++ { + xAdd(&PaQ2, &P, &Q, &PdQ) + xDbl(&PaP2, &P, &A) + xDblAdd(&PaP1, &PaQ1, &P, &Q, &PdQ, &A24) + + if !ceqpoint(&PaQ1, &PaQ2) { + exp := toNormX(&PaQ1) + got := toNormX(&PaQ2) + t.Errorf("\nExp: \n\t%s\nGot from xAdd: \n\t%s", exp.Text(16), got.Text(16)) + } + + if !ceqpoint(&PaP1, &PaP2) { + exp := toNormX(&PaP1) + got := toNormX(&PaP2) + t.Errorf("\nExp: \n\t%s\nGot from xDbl: \n\t%s", exp.Text(16), got.Text(16)) + } + + // Swap values for next operation + PdQ = Q + Q = P + P = PaP1 + } +} + +func TestXMul(t *testing.T) { + var P point + var co coeff + var expKP big.Int + var k fp + + checkXMul := func() { + var kP point + + xMul(&kP, &P, &co, &k) + retKP := toNormX(&kP) + if expKP.Cmp(&retKP) != 0 { + t.Errorf("\nExp: %s\nGot: %s", expKP.Text(16), retKP.Text(16)) + } + + // Check if first and second argument can overlap + xMul(&P, &P, &co, &k) + retKP = toNormX(&P) + if expKP.Cmp(&retKP) != 0 { + t.Errorf("\nExp: %s\nGot: %s", expKP.Text(16), retKP.Text(16)) + } + } + + // Case C=1 + expKP.SetString("0x582B866603E6FBEBD21FE660FB34EF9466FDEC55FFBCE1073134CC557071147821BBAD225E30F7B2B6790B00ED9C39A29AA043F58AF995E440AFB13DA8E6D788", 0) + P.x = toFp("0x1C5CA539C1D5B52DE4750C390C24C05251E8B1D33E48971FA86F5ADDED2D06C8CD31E94887541468BB2925EBD693C9DDFF5BD9508430F25FE28EE30C0760C0FE") + P.z = toFp("1") + co.a = toFp("0x538F785D52996919C8D5C73D842A0249669B5B6BB05338B74EAE8094AE5009A3BA2D73730F527D7403E8184D9B1FA11C0C4C40E7B328A84874A6DBCE99E1DF92") + co.c = toFp("1") + k = fp{0x7A36C930A83EFBD5, 0xD0E80041ED0DDF9F, 0x5AA17134F1B8F877, 0x975711EC94168E51, 0xB3CAD962BED4BAC5, 0x3026DFDD7E4F5687, 0xE67F91AB8EC9C3AF, 0x34671D3FD8C317E7} + checkXMul() + + // Check if algorithms works correctly with k=1 + expKP.SetString("0x1C5CA539C1D5B52DE4750C390C24C05251E8B1D33E48971FA86F5ADDED2D06C8CD31E94887541468BB2925EBD693C9DDFF5BD9508430F25FE28EE30C0760C0FE", 0) + P.x = toFp("0x1C5CA539C1D5B52DE4750C390C24C05251E8B1D33E48971FA86F5ADDED2D06C8CD31E94887541468BB2925EBD693C9DDFF5BD9508430F25FE28EE30C0760C0FE") + P.z = toFp("1") + co.a = toFp("0x538F785D52996919C8D5C73D842A0249669B5B6BB05338B74EAE8094AE5009A3BA2D73730F527D7403E8184D9B1FA11C0C4C40E7B328A84874A6DBCE99E1DF92") + co.c = toFp("1") + k = fp{1, 0, 0, 0, 0, 0, 0, 0} + checkXMul() + + // Check if algorithms works correctly with value of k for which few small and high + // order bits are 0 (test for odd number of cswaps in xMul) + expKP.SetString("0x1925EDA0928C10F427B4E642E7E1481A670D1249956DED6A2292B9BAB841F6AA86A9F41459400845ED4A5E2531A14165F64FE4E43DBD85321B429C6DAE2E8987", 0) + P.x = toFp("0x4CE8603817B9BB06515E921AA201D26B31F3CE181D1E18CD5CD704708CCAD47546CEEAB42B98EE67925A5259E0684A0489F574A999DE127F708B849ACAA12A63") + P.z = toFp("1") + co.a = toFp("0x538F785D52996919C8D5C73D842A0249669B5B6BB05338B74EAE8094AE5009A3BA2D73730F527D7403E8184D9B1FA11C0C4C40E7B328A84874A6DBCE99E1DF92") + co.c = toFp("1") + k = fp{0, 7, 0, 0, 0, 0, 0, 0} + checkXMul() + + // Check if algorithms works correctly with value of k for which few small and high + // order bits are 0 (test for even number of cswaps in xMul) + expKP.SetString("0x30C02915C5967C3B6EB2196A934ADF38A183E9C7E814B54121F93048A8FC12D5036992FABF8D807581017A4C1F93D07352413F38F6A902FC76A8894FE8D94805", 0) + P.x = toFp("0x2DDD15ED7C169BE6D9EC02CFE3DC507EC4A7A4D96DE3FAAB9BFCEA1B047807EA301E89830F2FDD0E7E642A85E7ACDE16BAD76DF140F719C4A7AB85153E7D69DC") + P.z = toFp("1") + co.a = toFp("0x538F785D52996919C8D5C73D842A0249669B5B6BB05338B74EAE8094AE5009A3BA2D73730F527D7403E8184D9B1FA11C0C4C40E7B328A84874A6DBCE99E1DF92") + co.c = toFp("1") + k = fp{0, 15, 0, 0, 0, 0, 0, 0} + checkXMul() + + // xMul512 does NOT work correctly for k==0. In such case function will return 2*P. But + // thanks to that fact we don't need to handle k==0 case, we get some speedup. + expKP.SetString("0x6115B5D8BB613D11BDFEA70D436D87C1515553F6A15061727B4001E0AF745AAA9F39EB9464982829D931F77DAB9D71B24FF0D1D34C347F2A51FD45821F2EA06F", 0) + P.x = toFp("0x6C5B4D4AB0765AAB23C10F8455BE522D3A5363324D7AD641CC67C0A52FC1FFE9F3F8EDFE641478CA93D4D0016D83F21487FD4AF4E02F8A2C237CF27C5604BCC") + P.z = toFp("1") + co.a = toFp("0x599841D7D1FCD92A85759B7A3D2D5E4C56EFB17F19F86EB70E121EA16305EDE45A55868BE069313F821F7D94069EC220A4AC3B85500376710538246E9B3BC138") + co.c = toFp("1") + k = fp{0, 0, 0, 0, 0, 0, 0, 0} + checkXMul() +} + +func TestMappointHardcoded3(t *testing.T) { + var P = point{ + x: fp{0xca1a2fdec38c669b, 0xf2fe3678ebeb978b, 0xfda3e9a6f0c719d, 0x6f7bffa41772570b, 0x3d90cdd6283dc150, 0x21b55b738eb1ded9, 0x209515d0a9f41dd6, 0x5275cf397d154a12}, + z: fp{0x1fff8309761576e, 0xef239cbeda7c2ba1, 0x6136ae2d76e95873, 0x1f8f6ac909570cec, 0x780fdf0cc7d676d8, 0x548098fe92ed04e1, 0xb39da564701ef35d, 0x5fec19626df41306}} + var A = coeff{ + a: fp{0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0}, + c: fp{0xc8fc8df598726f0a, 0x7b1bc81750a6af95, 0x5d319e67c1e961b4, 0xb0aa7275301955f1, 0x4a080672d9ba6c64, 0x97a5ef8a246ee77b, 0x6ea9e5d4383676a, 0x3496e2e117e0ec80}} + var K = point{ + x: fp{0x597616608e291c6f, 0xd14230b008736798, 0xa63099b1ace67e6e, 0xe37c13afd768bcfa, 0xc6ef718894f08135, 0x53a4fd09091f3522, 0xc9a1f9f670645fe1, 0x628c4a8efd83e5f0}, + z: fp{0x8f18a654312ac1ad, 0xbc20a9b2472785c9, 0xdaf97c29bbf9e492, 0xf91a8c799e2f6119, 0xc8dc675cc8e528e6, 0x9a7b2c2f0df95171, 0x85629cd38cdd9fdb, 0x656d5253d3fd1a6e}} + var k uint64 = 3 + + var expA = coeff{ + a: fp{0x6fa92a66e77cfc1, 0x9efbfb7118f1832c, 0x441894cc5d1d24ae, 0x5a2f0fafa26761de, 0x8095c36d3a20a78a, 0xb22be0023612a135, 0x5eb844d06ef0f430, 0x52e53309d1c90cf8}, + c: fp{0x98173d5664a23e5c, 0xd8fe1c6306bbc11a, 0xa774fbc502648059, 0x766a0d839aa62c83, 0x4b074f9b93d1633d, 0xf306019dbf87f505, 0x77c720ca059234b0, 0x3d47ab65269c5908}} + var expP = point{ + x: fp{0x91aba9b39f280495, 0xfbd8ea69d2990aeb, 0xb03e1b8ed7fe3dba, 0x3d30a41499f08998, 0xb15a42630de9c606, 0xa7dd487fef16f5c8, 0x8673948afed8e968, 0x57ecc8710004cd4d}, + z: fp{0xce8819869a942526, 0xb98ca2ff79ef8969, 0xd49c9703743a1812, 0x21dbb090f9152e03, 0xbabdcac831b1adea, 0x8cee90762baa2ddd, 0xa0dd2ddcef809d96, 0x1de2a8887a32f19b}} + xIso(&P, &A, &K, k) + if !eqFp(&P.x, &expP.x) || !eqFp(&P.z, &expP.z) { + normP := toNormX(&P) + normPExp := toNormX(&expP) + t.Errorf("P != expP [\n %s != %s\n]", normP.Text(16), normPExp.Text(16)) + } + if !eqFp(&A.a, &expA.a) || !eqFp(&A.c, &expA.c) { + t.Errorf("A != expA %X %X", A.a[0], expA.a[0]) + } +} + +func TestMappointHardcoded5(t *testing.T) { + var P = point{ + x: fp{0xca1a2fdec38c669b, 0xf2fe3678ebeb978b, 0xfda3e9a6f0c719d, 0x6f7bffa41772570b, 0x3d90cdd6283dc150, 0x21b55b738eb1ded9, 0x209515d0a9f41dd6, 0x5275cf397d154a12}, + z: fp{0x1fff8309761576e, 0xef239cbeda7c2ba1, 0x6136ae2d76e95873, 0x1f8f6ac909570cec, 0x780fdf0cc7d676d8, 0x548098fe92ed04e1, 0xb39da564701ef35d, 0x5fec19626df41306}} + var A = coeff{ + a: fp{0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0}, + c: fp{0xc8fc8df598726f0a, 0x7b1bc81750a6af95, 0x5d319e67c1e961b4, 0xb0aa7275301955f1, 0x4a080672d9ba6c64, 0x97a5ef8a246ee77b, 0x6ea9e5d4383676a, 0x3496e2e117e0ec80}} + var K = point{ + x: fp{0x597616608e291c6f, 0xd14230b008736798, 0xa63099b1ace67e6e, 0xe37c13afd768bcfa, 0xc6ef718894f08135, 0x53a4fd09091f3522, 0xc9a1f9f670645fe1, 0x628c4a8efd83e5f0}, + z: fp{0x8f18a654312ac1ad, 0xbc20a9b2472785c9, 0xdaf97c29bbf9e492, 0xf91a8c799e2f6119, 0xc8dc675cc8e528e6, 0x9a7b2c2f0df95171, 0x85629cd38cdd9fdb, 0x656d5253d3fd1a6e}} + var k uint64 = 5 + + var expA = coeff{ + a: fp{0x32076f58298ed474, 0x5094a1fc8696d307, 0x82e510594157944a, 0xb60ce760f88c83a9, 0xae8a28c325186983, 0xe31d2446a4ad2f18, 0xb266c612b5f141c1, 0x64283e618db5a705}, + c: fp{0x4472b49b65272190, 0x2bd5919309778f56, 0x6132753691fe016c, 0x8f654849c09e6d34, 0xfa208dd9aea1ef12, 0xf7df0dd10071411a, 0x75afb7860500922c, 0x52fb7d34b129fb65}} + var expP = point{ + x: fp{0x3b75fc94b2a6df2d, 0x96d53dc9b0e867a0, 0x22e87202421d274e, 0x30a361440697ee1a, 0x8b52ee078bdbddcd, 0x64425d500e6b934d, 0xf47d1f568f6df391, 0x5d9d3607431395ab}, + z: fp{0x746e02dafa040976, 0xcd408f2cddbf3a8e, 0xf643354e0e13a93f, 0x7c39ed96ce9a5e29, 0xfcdf26f1a1a550ca, 0x2fc8aafc4ca0a559, 0x5d204a2b14cf19ba, 0xbd2c3406762f05d}} + + xIso(&P, &A, &K, k) + if !eqFp(&P.x, &expP.x) || !eqFp(&P.z, &expP.z) { + normP := toNormX(&P) + normPExp := toNormX(&expP) + t.Errorf("P != expP [\n %s != %s\n]", normP.Text(16), normPExp.Text(16)) + } + if !eqFp(&A.a, &expA.a) || !eqFp(&A.c, &expA.c) { + t.Errorf("A != expA %X %X", A.a[0], expA.a[0]) + } +} + +func BenchmarkXMul(b *testing.B) { + var kP, P point + var co coeff + var expKP big.Int + var k fp + + // Case C=1 + expKP.SetString("0x582B866603E6FBEBD21FE660FB34EF9466FDEC55FFBCE1073134CC557071147821BBAD225E30F7B2B6790B00ED9C39A29AA043F58AF995E440AFB13DA8E6D788", 0) + P.x = toFp("0x1C5CA539C1D5B52DE4750C390C24C05251E8B1D33E48971FA86F5ADDED2D06C8CD31E94887541468BB2925EBD693C9DDFF5BD9508430F25FE28EE30C0760C0FE") + P.z = toFp("1") + co.a = toFp("0x538F785D52996919C8D5C73D842A0249669B5B6BB05338B74EAE8094AE5009A3BA2D73730F527D7403E8184D9B1FA11C0C4C40E7B328A84874A6DBCE99E1DF92") + co.c = toFp("1") + k = fp{0x7A36C930A83EFBD5, 0xD0E80041ED0DDF9F, 0x5AA17134F1B8F877, 0x975711EC94168E51, 0xB3CAD962BED4BAC5, 0x3026DFDD7E4F5687, 0xE67F91AB8EC9C3AF, 0x34671D3FD8C317E7} + + for n := 0; n < b.N; n++ { + xMul(&kP, &P, &co, &k) + } +} + +func BenchmarkXAdd(b *testing.B) { + var P, Q, PdQ point + var PaQ point + + P.x = toFp("0x5840FD8E0165F7F474260F99337461AF195233F791FABE735EC2634B74A95559568B4CEB23959C8A01C5C57E215D22639868ED840D74FE2BAC04830CF75047AD") + P.z = toFp("1") + Q.x = toFp("0x3C1A003C71436698B4A181CEB12BA4B4D1FF7BB14AAAF6FBDA6957C4EBA20AD8E3893DF6F64E67E81163E024C19C7E975F3EC61862F75502C3ED802370E75A3F") + Q.z = toFp("1") + PdQ.x = toFp("0x519B1928F752B0B2143C1C23EB247B370DBB5B9C29B9A3A064D7FBC1B67FAC34B6D3DDA0F3CB87C387B425B36F31B93A8E73252BA701927B767A9DE89D5A92AE") + PdQ.z = toFp("1") + + for n := 0; n < b.N; n++ { + xAdd(&PaQ, &P, &Q, &PdQ) + } +} + +func BenchmarkXDbl(b *testing.B) { + var P, A point + var PaP point + + P.x = toFp("0x6C5B4D4AB0765AAB23C10F8455BE522D3A5363324D7AD641CC67C0A52FC1FFE9F3F8EDFE641478CA93D4D0016D83F21487FD4AF4E02F8A2C237CF27C5604BCC") + P.z = toFp("1") + A.x = toFp("0x599841D7D1FCD92A85759B7A3D2D5E4C56EFB17F19F86EB70E121EA16305EDE45A55868BE069313F821F7D94069EC220A4AC3B85500376710538246E9B3BC138") + A.z = toFp("1") + + for n := 0; n < b.N; n++ { + xDbl(&PaP, &P, &A) + } +} + +func BenchmarkIsom(b *testing.B) { + var P, kern point + var expPhiP big.Int + var co coeff + var k = uint64(2) + + expPhiP.SetString("0x5FEBD68F795F9AEB732ECF0D1507904922F2B0736704E0751EF242B4E191E6F630D83778B5E5681161FD071CDEF7DF4C3A41D0ECEB30E90B119C5BF86C5AB51A", 0) + P.x = toFp("0x5FD8D226C228FD6AA3CCDCAB931C5D3AA000A46B47041F59D9724E517594F696D38F2CB45C987ACF68BB1057D8D518F926D8F55171F337D05354E0022BC66B23") + P.z = toFp("1") + co.a = toFp("0x9E8DBC4914E3C4F080592642DD0B08B9564AB3ADF75EE9B58A685443BA6E39A1ACD1201B7F034077AF344123880AF9D8C77575E6E782E00186881ECE8B87CA3") + co.c = toFp("1") + kern.x = toFp("0x594F77A49EABBF2A12025BC00E1DBC119CDA674B9FE8A00791724B42FEB7D225C4C9940B01B09B8F00B30B0E961212FB63E42614814E38EC9E5E5B0FEBF98C58") + kern.z = toFp("1") + + for n := 0; n < b.N; n++ { + xIso(&P, &co, &kern, k) + } +} diff --git a/src/circl/dh/csidh/doc.go b/src/circl/dh/csidh/doc.go new file mode 100644 index 00000000000..9c87e534df2 --- /dev/null +++ b/src/circl/dh/csidh/doc.go @@ -0,0 +1,11 @@ +// Package csidh implements commutative supersingular isogeny-based Diffie-Hellman +// key exchange algorithm (CSIDH) resulting from the group action. Implementation +// uses prime field of a size 512-bits. +// This implementation is highly experimental work and currently it is not suitable +// for securing systems. +// +// References: +// - cSIDH: ia.cr/2018/383 +// - Faster cSIDH: ia.cr/2018/782 +// +package csidh diff --git a/src/circl/dh/csidh/fp511.go b/src/circl/dh/csidh/fp511.go new file mode 100644 index 00000000000..e537f60c3ac --- /dev/null +++ b/src/circl/dh/csidh/fp511.go @@ -0,0 +1,216 @@ +package csidh + +import ( + "math/bits" +) + +// Constant time select. +// if pick == 0xFF..FF (out = in1) +// if pick == 0 (out = in2) +// else out is undefined. +func ctPick64(which uint64, in1, in2 uint64) uint64 { + return (in1 & which) | (in2 & ^which) +} + +// ctIsNonZero64 returns 0 in case i == 0, otherwise it returns 1. +// Constant-time. +func ctIsNonZero64(i uint64) int { + // In case i==0 then i-1 will set MSB. Only in such case (i OR ~(i-1)) + // will result in MSB being not set (logical implication: (i-1)=>i is + // false iff (i-1)==0 and i==non-zero). In every other case MSB is + // set and hence function returns 1. + return int((i | (^(i - 1))) >> 63) +} + +// Returns result of x= 0; i-- { + v, c := bits.Sub64(y[i], x[i], 0) + if c != 0 { + return false + } + if v != 0 { + return true + } + } + // x == y + return false +} + +// r = x + y mod p. +func addRdc(r, x, y *fp) { + var c uint64 + var t fp + r[0], c = bits.Add64(x[0], y[0], 0) + r[1], c = bits.Add64(x[1], y[1], c) + r[2], c = bits.Add64(x[2], y[2], c) + r[3], c = bits.Add64(x[3], y[3], c) + r[4], c = bits.Add64(x[4], y[4], c) + r[5], c = bits.Add64(x[5], y[5], c) + r[6], c = bits.Add64(x[6], y[6], c) + r[7], _ = bits.Add64(x[7], y[7], c) + + t[0], c = bits.Sub64(r[0], p[0], 0) + t[1], c = bits.Sub64(r[1], p[1], c) + t[2], c = bits.Sub64(r[2], p[2], c) + t[3], c = bits.Sub64(r[3], p[3], c) + t[4], c = bits.Sub64(r[4], p[4], c) + t[5], c = bits.Sub64(r[5], p[5], c) + t[6], c = bits.Sub64(r[6], p[6], c) + t[7], c = bits.Sub64(r[7], p[7], c) + + var w = 0 - c + r[0] = ctPick64(w, r[0], t[0]) + r[1] = ctPick64(w, r[1], t[1]) + r[2] = ctPick64(w, r[2], t[2]) + r[3] = ctPick64(w, r[3], t[3]) + r[4] = ctPick64(w, r[4], t[4]) + r[5] = ctPick64(w, r[5], t[5]) + r[6] = ctPick64(w, r[6], t[6]) + r[7] = ctPick64(w, r[7], t[7]) +} + +// r = x - y. +func sub512(r, x, y *fp) uint64 { + var c uint64 + r[0], c = bits.Sub64(x[0], y[0], 0) + r[1], c = bits.Sub64(x[1], y[1], c) + r[2], c = bits.Sub64(x[2], y[2], c) + r[3], c = bits.Sub64(x[3], y[3], c) + r[4], c = bits.Sub64(x[4], y[4], c) + r[5], c = bits.Sub64(x[5], y[5], c) + r[6], c = bits.Sub64(x[6], y[6], c) + r[7], c = bits.Sub64(x[7], y[7], c) + return c +} + +// r = x - y mod p. +func subRdc(r, x, y *fp) { + var c uint64 + + // Same as sub512(r,x,y). Unfortunately + // compiler is not able to inline it. + r[0], c = bits.Sub64(x[0], y[0], 0) + r[1], c = bits.Sub64(x[1], y[1], c) + r[2], c = bits.Sub64(x[2], y[2], c) + r[3], c = bits.Sub64(x[3], y[3], c) + r[4], c = bits.Sub64(x[4], y[4], c) + r[5], c = bits.Sub64(x[5], y[5], c) + r[6], c = bits.Sub64(x[6], y[6], c) + r[7], c = bits.Sub64(x[7], y[7], c) + + // if x r=x-y+p + var w = 0 - c + r[0], c = bits.Add64(r[0], ctPick64(w, p[0], 0), 0) + r[1], c = bits.Add64(r[1], ctPick64(w, p[1], 0), c) + r[2], c = bits.Add64(r[2], ctPick64(w, p[2], 0), c) + r[3], c = bits.Add64(r[3], ctPick64(w, p[3], 0), c) + r[4], c = bits.Add64(r[4], ctPick64(w, p[4], 0), c) + r[5], c = bits.Add64(r[5], ctPick64(w, p[5], 0), c) + r[6], c = bits.Add64(r[6], ctPick64(w, p[6], 0), c) + r[7], _ = bits.Add64(r[7], ctPick64(w, p[7], 0), c) +} + +// Fixed-window mod exp for fpBitLen bit value with 4 bit window. Returned +// result is a number in montgomery domain. +// r = b ^ e (mod p). +// Constant time. +func modExpRdcCommon(r, b, e *fp, fpBitLen int) { + var precomp [16]fp + var t fp + var c uint64 + + // Precompute step, computes an array of small powers of 'b'. As this + // algorithm implements 4-bit window, we need 2^4=16 of such values. + // b^0 = 1, which is equal to R from REDC. + precomp[0] = one // b ^ 0 + precomp[1] = *b // b ^ 1 + for i := 2; i < 16; i = i + 2 { + // OPTIMIZE: implement fast squaring. Then interleaving fast squaring + // with multiplication should improve performance. + mulRdc(&precomp[i], &precomp[i/2], &precomp[i/2]) // sqr + mulRdc(&precomp[i+1], &precomp[i], b) + } + + *r = one + for i := fpBitLen/4 - 1; i >= 0; i-- { + for j := 0; j < 4; j++ { + mulRdc(r, r, r) + } + // note: non resistant to cache SCA + idx := (e[i/16] >> uint((i%16)*4)) & 15 + mulRdc(r, r, &precomp[idx]) + } + + // if p <= r < 2p then r = r-p + t[0], c = bits.Sub64(r[0], p[0], 0) + t[1], c = bits.Sub64(r[1], p[1], c) + t[2], c = bits.Sub64(r[2], p[2], c) + t[3], c = bits.Sub64(r[3], p[3], c) + t[4], c = bits.Sub64(r[4], p[4], c) + t[5], c = bits.Sub64(r[5], p[5], c) + t[6], c = bits.Sub64(r[6], p[6], c) + t[7], c = bits.Sub64(r[7], p[7], c) + + var w = 0 - c + r[0] = ctPick64(w, r[0], t[0]) + r[1] = ctPick64(w, r[1], t[1]) + r[2] = ctPick64(w, r[2], t[2]) + r[3] = ctPick64(w, r[3], t[3]) + r[4] = ctPick64(w, r[4], t[4]) + r[5] = ctPick64(w, r[5], t[5]) + r[6] = ctPick64(w, r[6], t[6]) + r[7] = ctPick64(w, r[7], t[7]) +} + +// modExpRdc does modular exponentiation of 512-bit number. +// Constant-time. +func modExpRdc512(r, b, e *fp) { + modExpRdcCommon(r, b, e, 512) +} + +// modExpRdc does modular exponentiation of 64-bit number. +// Constant-time. +func modExpRdc64(r, b *fp, e uint64) { + modExpRdcCommon(r, b, &fp{e}, 64) +} + +// isNonQuadRes checks whether value v is quadratic residue. +// Implementation uses Fermat's little theorem (or +// Euler's criterion) +// a^(p-1) == 1, hence +// (a^2) ((p-1)/2) == 1 +// Which means v is a quadratic residue iff v^((p-1)/2) == 1. +// Caller provided v must be in montgomery domain. +// Returns 0 in case v is quadratic residue or 1 in case +// v is quadratic non-residue. +func (v *fp) isNonQuadRes() int { + var res fp + var b uint64 + + modExpRdc512(&res, v, &pMin1By2) + for i := range res { + b |= res[i] ^ one[i] + } + + return ctIsNonZero64(b) +} + +// isZero returns false in case v is equal to 0, otherwise +// true. Constant time. +func (v *fp) isZero() bool { + var r uint64 + for i := 0; i < numWords; i++ { + r |= v[i] + } + return ctIsNonZero64(r) == 0 +} + +// equal checks if v is equal to in. Constant time. +func (v *fp) equal(in *fp) bool { + var r uint64 + for i := range v { + r |= v[i] ^ in[i] + } + return ctIsNonZero64(r) == 0 +} diff --git a/src/circl/dh/csidh/fp511_amd64.go b/src/circl/dh/csidh/fp511_amd64.go new file mode 100644 index 00000000000..98d01597e36 --- /dev/null +++ b/src/circl/dh/csidh/fp511_amd64.go @@ -0,0 +1,64 @@ +// +build amd64,!noasm + +package csidh + +import ( + "math/bits" + + "internal/cpu" +) + +var ( + // Signals support for BMI2 (MULX) + hasBMI2 = cpu.X86.HasBMI2 + // Signals support for ADX and BMI2 + hasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX +) + +var _ = hasBMI2 + +func mul512(r, m1 *fp, m2 uint64) { mul512Amd64(r, m1, m2) } +func cswap512(x, y *fp, choice uint8) { cswap512Amd64(x, y, choice) } +func mulRdc(r, x, y *fp) { mulRdcAmd64(r, x, y) } + +//go:noescape +func mul512Amd64(a, b *fp, c uint64) + +//go:noescape +func cswap512Amd64(x, y *fp, choice uint8) + +//go:noescape +func mulBmiAsm(res, x, y *fp) + +// mulRdc performs montgomery multiplication r = x * y mod P. +// Returned result r is already reduced and in Montgomery domain. +func mulRdcAmd64(r, x, y *fp) { + var t fp + var c uint64 + + if hasADXandBMI2 { + mulBmiAsm(r, x, y) + } else { + mulGeneric(r, x, y) + } + + // if p <= r < 2p then r = r-p + t[0], c = bits.Sub64(r[0], p[0], 0) + t[1], c = bits.Sub64(r[1], p[1], c) + t[2], c = bits.Sub64(r[2], p[2], c) + t[3], c = bits.Sub64(r[3], p[3], c) + t[4], c = bits.Sub64(r[4], p[4], c) + t[5], c = bits.Sub64(r[5], p[5], c) + t[6], c = bits.Sub64(r[6], p[6], c) + t[7], c = bits.Sub64(r[7], p[7], c) + + var w = 0 - c + r[0] = ctPick64(w, r[0], t[0]) + r[1] = ctPick64(w, r[1], t[1]) + r[2] = ctPick64(w, r[2], t[2]) + r[3] = ctPick64(w, r[3], t[3]) + r[4] = ctPick64(w, r[4], t[4]) + r[5] = ctPick64(w, r[5], t[5]) + r[6] = ctPick64(w, r[6], t[6]) + r[7] = ctPick64(w, r[7], t[7]) +} diff --git a/src/circl/dh/csidh/fp511_amd64.s b/src/circl/dh/csidh/fp511_amd64.s new file mode 100644 index 00000000000..c248c0a3a3f --- /dev/null +++ b/src/circl/dh/csidh/fp511_amd64.s @@ -0,0 +1,166 @@ +// +build amd64 + +#include "textflag.h" + +// Multiplies 512-bit value by 64-bit value. Uses MULQ instruction to +// multiply 2 64-bit values. +// +// Result: x = (y * z) mod 2^512 +// +// Registers used: AX, CX, DX, SI, DI, R8 +// +// func mul512Amd64(a, b *Fp, c uint64) +TEXT ·mul512Amd64(SB), NOSPLIT, $0-24 + MOVQ a+0(FP), DI // result + MOVQ b+8(FP), SI // multiplicand + + // Check whether to use optimized implementation + CMPB ·hasBMI2(SB), $1 + JE mul512_mulx + + MOVQ c+16(FP), R10 // 64 bit multiplier, used by MULQ + MOVQ R10, AX; MULQ 0(SI); MOVQ DX, R11; MOVQ AX, 0(DI) //x[0] + MOVQ R10, AX; MULQ 8(SI); ADDQ R11, AX; ADCQ $0, DX; MOVQ DX, R11; MOVQ AX, 8(DI) //x[1] + MOVQ R10, AX; MULQ 16(SI); ADDQ R11, AX; ADCQ $0, DX; MOVQ DX, R11; MOVQ AX, 16(DI) //x[2] + MOVQ R10, AX; MULQ 24(SI); ADDQ R11, AX; ADCQ $0, DX; MOVQ DX, R11; MOVQ AX, 24(DI) //x[3] + MOVQ R10, AX; MULQ 32(SI); ADDQ R11, AX; ADCQ $0, DX; MOVQ DX, R11; MOVQ AX, 32(DI) //x[4] + MOVQ R10, AX; MULQ 40(SI); ADDQ R11, AX; ADCQ $0, DX; MOVQ DX, R11; MOVQ AX, 40(DI) //x[5] + MOVQ R10, AX; MULQ 48(SI); ADDQ R11, AX; ADCQ $0, DX; MOVQ DX, R11; MOVQ AX, 48(DI) //x[6] + MOVQ R10, AX; MULQ 56(SI); ADDQ R11, AX; MOVQ AX, 56(DI) //x[7] + RET + +// Optimized for CPUs with BMI2 +mul512_mulx: + MOVQ c+16(FP), DX // 64 bit multiplier, used by MULX + MULXQ 0(SI), AX, R10; MOVQ AX, 0(DI) // x[0] + MULXQ 8(SI), AX, R11; ADDQ R10, AX; MOVQ AX, 8(DI) // x[1] + MULXQ 16(SI), AX, R10; ADCQ R11, AX; MOVQ AX, 16(DI) // x[2] + MULXQ 24(SI), AX, R11; ADCQ R10, AX; MOVQ AX, 24(DI) // x[3] + MULXQ 32(SI), AX, R10; ADCQ R11, AX; MOVQ AX, 32(DI) // x[4] + MULXQ 40(SI), AX, R11; ADCQ R10, AX; MOVQ AX, 40(DI) // x[5] + MULXQ 48(SI), AX, R10; ADCQ R11, AX; MOVQ AX, 48(DI) // x[6] + MULXQ 56(SI), AX, R11; ADCQ R10, AX; MOVQ AX, 56(DI) // x[7] + RET + +TEXT ·cswap512Amd64(SB),NOSPLIT,$0-17 + MOVQ x+0(FP), DI + MOVQ y+8(FP), SI + MOVBLZX choice+16(FP), AX // AL = 0 or 1 + + // Make AX, so that either all bits are set or non + // AX = 0 or 1 + NEGQ AX + + // Fill xmm15. After this step first half of XMM15 is + // just zeros and second half is whatever in AX + MOVQ AX, X15 + + // Copy lower double word everywhere else. So that + // XMM15=AL|AL|AL|AL. As AX has either all bits set + // or non result will be that XMM15 has also either + // all bits set or non of them. + PSHUFD $0, X15, X15 + +#ifndef CSWAP_BLOCK +#define CSWAP_BLOCK(idx) \ + MOVOU (idx*16)(DI), X0 \ + MOVOU (idx*16)(SI), X1 \ + \ // X2 = mask & (X0 ^ X1) + MOVO X1, X2 \ + PXOR X0, X2 \ + PAND X15, X2 \ + \ + PXOR X2, X0 \ + PXOR X2, X1 \ + \ + MOVOU X0, (idx*16)(DI) \ + MOVOU X1, (idx*16)(SI) +#endif + + CSWAP_BLOCK(0) + CSWAP_BLOCK(1) + CSWAP_BLOCK(2) + CSWAP_BLOCK(3) + + RET + +// mulAsm implements montgomery multiplication interleaved with +// montgomery reduction. It uses MULX and ADCX/ADOX instructions. +// Implementation specific to 511-bit prime 'p' +// +// func mulBmiAsm(res, x, y *fp) +TEXT ·mulBmiAsm(SB),NOSPLIT,$8-24 + + MOVQ x+8(FP), DI // multiplicand + MOVQ y+16(FP), SI // multiplier + + XORQ R8, R8 + XORQ R9, R9 + XORQ R10, R10 + XORQ R11, R11 + XORQ R12, R12 + XORQ R13, R13 + XORQ R14, R14 + XORQ R15, R15 + + MOVQ BP, 0(SP) // push: BP is Callee-save. + XORQ BP, BP + +// Uses BMI2 (MULX) +#ifdef MULS_MULX_512 +#undef MULS_MULX_512 +#endif +#define MULS_MULX_512(idx, r0, r1, r2, r3, r4, r5, r6, r7, r8) \ + \ // Reduction step + MOVQ ( 0)(SI), DX \ + MULXQ ( 8*idx)(DI), DX, CX \ + ADDQ r0, DX \ + MULXQ ·pNegInv(SB), DX, CX \ + \ + XORQ AX, AX \ + MULXQ ·p+ 0(SB), AX, BX; ; ADOXQ AX, r0 \ + MULXQ ·p+ 8(SB), AX, CX; ADCXQ BX, r1; ADOXQ AX, r1 \ + MULXQ ·p+16(SB), AX, BX; ADCXQ CX, r2; ADOXQ AX, r2 \ + MULXQ ·p+24(SB), AX, CX; ADCXQ BX, r3; ADOXQ AX, r3 \ + MULXQ ·p+32(SB), AX, BX; ADCXQ CX, r4; ADOXQ AX, r4 \ + MULXQ ·p+40(SB), AX, CX; ADCXQ BX, r5; ADOXQ AX, r5 \ + MULXQ ·p+48(SB), AX, BX; ADCXQ CX, r6; ADOXQ AX, r6 \ + MULXQ ·p+56(SB), AX, CX; ADCXQ BX, r7; ADOXQ AX, r7 \ + MOVQ $0, AX ; ADCXQ CX, r8; ADOXQ AX, r8 \ + \ // Multiplication step + MOVQ (8*idx)(DI), DX \ + \ + XORQ AX, AX \ + MULXQ ( 0)(SI), AX, BX; ADOXQ AX, r0 \ + MULXQ ( 8)(SI), AX, CX; ADCXQ BX, r1; ADOXQ AX, r1 \ + MULXQ (16)(SI), AX, BX; ADCXQ CX, r2; ADOXQ AX, r2 \ + MULXQ (24)(SI), AX, CX; ADCXQ BX, r3; ADOXQ AX, r3 \ + MULXQ (32)(SI), AX, BX; ADCXQ CX, r4; ADOXQ AX, r4 \ + MULXQ (40)(SI), AX, CX; ADCXQ BX, r5; ADOXQ AX, r5 \ + MULXQ (48)(SI), AX, BX; ADCXQ CX, r6; ADOXQ AX, r6 \ + MULXQ (56)(SI), AX, CX; ADCXQ BX, r7; ADOXQ AX, r7 \ + MOVQ $0, AX ; ADCXQ CX, r8; ADOXQ AX, r8 + + MULS_MULX_512(0, R8, R9, R10, R11, R12, R13, R14, R15, BP) + MULS_MULX_512(1, R9, R10, R11, R12, R13, R14, R15, BP, R8) + MULS_MULX_512(2, R10, R11, R12, R13, R14, R15, BP, R8, R9) + MULS_MULX_512(3, R11, R12, R13, R14, R15, BP, R8, R9, R10) + MULS_MULX_512(4, R12, R13, R14, R15, BP, R8, R9, R10, R11) + MULS_MULX_512(5, R13, R14, R15, BP, R8, R9, R10, R11, R12) + MULS_MULX_512(6, R14, R15, BP, R8, R9, R10, R11, R12, R13) + MULS_MULX_512(7, R15, BP, R8, R9, R10, R11, R12, R13, R14) +#undef MULS_MULX_512 + + MOVQ res+0(FP), DI + MOVQ BP, ( 0)(DI) + MOVQ R8, ( 8)(DI) + MOVQ R9, (16)(DI) + MOVQ R10, (24)(DI) + MOVQ R11, (32)(DI) + MOVQ R12, (40)(DI) + MOVQ R13, (48)(DI) + MOVQ R14, (56)(DI) + MOVQ 0(SP), BP // pop: BP is Callee-save. + + // NOW DI needs to be reduced if > p + RET diff --git a/src/circl/dh/csidh/fp511_generic.go b/src/circl/dh/csidh/fp511_generic.go new file mode 100644 index 00000000000..ceb819e7989 --- /dev/null +++ b/src/circl/dh/csidh/fp511_generic.go @@ -0,0 +1,180 @@ +package csidh + +import "math/bits" + +// mul576 implements schoolbook multiplication of +// 64x512-bit integer. Returns result modulo 2^512. +// r = m1*m2. +func mul512Generic(r, m1 *fp, m2 uint64) { + var c, h, l uint64 + + c, r[0] = bits.Mul64(m2, m1[0]) + + h, l = bits.Mul64(m2, m1[1]) + r[1], c = bits.Add64(l, c, 0) + c = h + c + + h, l = bits.Mul64(m2, m1[2]) + r[2], c = bits.Add64(l, c, 0) + c = h + c + + h, l = bits.Mul64(m2, m1[3]) + r[3], c = bits.Add64(l, c, 0) + c = h + c + + h, l = bits.Mul64(m2, m1[4]) + r[4], c = bits.Add64(l, c, 0) + c = h + c + + h, l = bits.Mul64(m2, m1[5]) + r[5], c = bits.Add64(l, c, 0) + c = h + c + + h, l = bits.Mul64(m2, m1[6]) + r[6], c = bits.Add64(l, c, 0) + c = h + c + + _, l = bits.Mul64(m2, m1[7]) + r[7], _ = bits.Add64(l, c, 0) +} + +// mul576 implements schoolbook multiplication of +// 64x512-bit integer. Returns 576-bit result of +// multiplication. +// r = m1*m2. +func mul576Generic(r *[9]uint64, m1 *fp, m2 uint64) { + var c, h, l uint64 + + c, r[0] = bits.Mul64(m2, m1[0]) + + h, l = bits.Mul64(m2, m1[1]) + r[1], c = bits.Add64(l, c, 0) + c = h + c + + h, l = bits.Mul64(m2, m1[2]) + r[2], c = bits.Add64(l, c, 0) + c = h + c + + h, l = bits.Mul64(m2, m1[3]) + r[3], c = bits.Add64(l, c, 0) + c = h + c + + h, l = bits.Mul64(m2, m1[4]) + r[4], c = bits.Add64(l, c, 0) + c = h + c + + h, l = bits.Mul64(m2, m1[5]) + r[5], c = bits.Add64(l, c, 0) + c = h + c + + h, l = bits.Mul64(m2, m1[6]) + r[6], c = bits.Add64(l, c, 0) + c = h + c + + h, l = bits.Mul64(m2, m1[7]) + r[7], c = bits.Add64(l, c, 0) + r[8], c = bits.Add64(h, c, 0) + r[8] += c +} + +// cswap512 implements constant time swap operation. +// If choice = 0, leave x,y unchanged. If choice = 1, set x,y = y,x. +// If choice is neither 0 nor 1 then behaviour is undefined. +func cswap512Generic(x, y *fp, choice uint8) { + var tmp uint64 + mask64 := 0 - uint64(choice) + + for i := 0; i < numWords; i++ { + tmp = mask64 & (x[i] ^ y[i]) + x[i] = tmp ^ x[i] + y[i] = tmp ^ y[i] + } +} + +// mulRdc performs montgomery multiplication r = x * y mod P. +// Returned result r is already reduced and in Montgomery domain. +func mulRdcGeneric(r, x, y *fp) { + var t fp + var c uint64 + + mulGeneric(r, x, y) + + // if p <= r < 2p then r = r-p + t[0], c = bits.Sub64(r[0], p[0], 0) + t[1], c = bits.Sub64(r[1], p[1], c) + t[2], c = bits.Sub64(r[2], p[2], c) + t[3], c = bits.Sub64(r[3], p[3], c) + t[4], c = bits.Sub64(r[4], p[4], c) + t[5], c = bits.Sub64(r[5], p[5], c) + t[6], c = bits.Sub64(r[6], p[6], c) + t[7], c = bits.Sub64(r[7], p[7], c) + + w := 0 - c + r[0] = ctPick64(w, r[0], t[0]) + r[1] = ctPick64(w, r[1], t[1]) + r[2] = ctPick64(w, r[2], t[2]) + r[3] = ctPick64(w, r[3], t[3]) + r[4] = ctPick64(w, r[4], t[4]) + r[5] = ctPick64(w, r[5], t[5]) + r[6] = ctPick64(w, r[6], t[6]) + r[7] = ctPick64(w, r[7], t[7]) +} + +func mulGeneric(r, x, y *fp) { + var s fp // keeps intermediate results + var t1, t2 [9]uint64 + var c, q uint64 + + for i := 0; i < numWords-1; i++ { + q = ((x[i] * y[0]) + s[0]) * pNegInv[0] + mul576Generic(&t1, &p, q) + mul576Generic(&t2, y, x[i]) + + // x[i]*y + q_i*p + t1[0], c = bits.Add64(t1[0], t2[0], 0) + t1[1], c = bits.Add64(t1[1], t2[1], c) + t1[2], c = bits.Add64(t1[2], t2[2], c) + t1[3], c = bits.Add64(t1[3], t2[3], c) + t1[4], c = bits.Add64(t1[4], t2[4], c) + t1[5], c = bits.Add64(t1[5], t2[5], c) + t1[6], c = bits.Add64(t1[6], t2[6], c) + t1[7], c = bits.Add64(t1[7], t2[7], c) + t1[8], _ = bits.Add64(t1[8], t2[8], c) + + // s = (s + x[i]*y + q_i * p) / R + _, c = bits.Add64(t1[0], s[0], 0) + s[0], c = bits.Add64(t1[1], s[1], c) + s[1], c = bits.Add64(t1[2], s[2], c) + s[2], c = bits.Add64(t1[3], s[3], c) + s[3], c = bits.Add64(t1[4], s[4], c) + s[4], c = bits.Add64(t1[5], s[5], c) + s[5], c = bits.Add64(t1[6], s[6], c) + s[6], c = bits.Add64(t1[7], s[7], c) + s[7], _ = bits.Add64(t1[8], 0, c) + } + + // last iteration stores result in r + q = ((x[numWords-1] * y[0]) + s[0]) * pNegInv[0] + mul576Generic(&t1, &p, q) + mul576Generic(&t2, y, x[numWords-1]) + + t1[0], c = bits.Add64(t1[0], t2[0], c) + t1[1], c = bits.Add64(t1[1], t2[1], c) + t1[2], c = bits.Add64(t1[2], t2[2], c) + t1[3], c = bits.Add64(t1[3], t2[3], c) + t1[4], c = bits.Add64(t1[4], t2[4], c) + t1[5], c = bits.Add64(t1[5], t2[5], c) + t1[6], c = bits.Add64(t1[6], t2[6], c) + t1[7], c = bits.Add64(t1[7], t2[7], c) + t1[8], _ = bits.Add64(t1[8], t2[8], c) + + _, c = bits.Add64(t1[0], s[0], 0) + r[0], c = bits.Add64(t1[1], s[1], c) + r[1], c = bits.Add64(t1[2], s[2], c) + r[2], c = bits.Add64(t1[3], s[3], c) + r[3], c = bits.Add64(t1[4], s[4], c) + r[4], c = bits.Add64(t1[5], s[5], c) + r[5], c = bits.Add64(t1[6], s[6], c) + r[6], c = bits.Add64(t1[7], s[7], c) + r[7], _ = bits.Add64(t1[8], 0, c) +} diff --git a/src/circl/dh/csidh/fp511_noasm.go b/src/circl/dh/csidh/fp511_noasm.go new file mode 100644 index 00000000000..10ece5df13f --- /dev/null +++ b/src/circl/dh/csidh/fp511_noasm.go @@ -0,0 +1,8 @@ +// +build !amd64 purego + +package csidh + +func mul512(r, m1 *fp, m2 uint64) { mul512Generic(r, m1, m2) } +func mul576(r *[9]uint64, m1 *fp, m2 uint64) { mul576Generic(r, m1, m2) } +func cswap512(x, y *fp, choice uint8) { cswap512Generic(x, y, choice) } +func mulRdc(r, x, y *fp) { mulRdcGeneric(r, x, y) } diff --git a/src/circl/dh/csidh/fp511_test.go b/src/circl/dh/csidh/fp511_test.go new file mode 100644 index 00000000000..c2920bacbd6 --- /dev/null +++ b/src/circl/dh/csidh/fp511_test.go @@ -0,0 +1,399 @@ +package csidh + +import ( + "crypto/rand" + "math/big" + "testing" + + "circl/internal/test" +) + +func testFp512Mul3Nominal(t *testing.T, f func(*fp, *fp, uint64)) { + var mod, two64 big.Int + + // modulus: 2^512 + mod.SetUint64(1).Lsh(&mod, 512) + two64.SetUint64(1).Lsh(&two64, 64) + + for i := 0; i < numIter; i++ { + multiplier64, _ := rand.Int(rand.Reader, &two64) + mul64 := multiplier64.Uint64() + + fV := randomFp() + exp, _ := new(big.Int).SetString(fp2S(fV), 16) + exp.Mul(exp, multiplier64) + // Truncate to 512 bits + exp.Mod(exp, &mod) + + f(&fV, &fV, mul64) + res, _ := new(big.Int).SetString(fp2S(fV), 16) + + if exp.Cmp(res) != 0 { + test.ReportError(t, exp, res, fV) + } + } +} + +// Check if mul512 produces result +// z = x*y mod 2^512. +func TestFp512Mul3_Nominal(t *testing.T) { + testFp512Mul3Nominal(t, mul512) + testFp512Mul3Nominal(t, mul512Generic) +} + +func TestAddRdcRandom(t *testing.T) { + for i := 0; i < numIter; i++ { + a := randomFp() + bigA, _ := new(big.Int).SetString(fp2S(a), 16) + bigA.Mod(bigA, modulus) + copy(a[:], intGetU64(bigA)) + + b := randomFp() + bigB, _ := new(big.Int).SetString(fp2S(b), 16) + bigB.Mod(bigB, modulus) + copy(b[:], intGetU64(bigB)) + + addRdc(&a, &a, &b) + bigRet, _ := new(big.Int).SetString(fp2S(a), 16) + + bigA.Add(bigA, bigB) + bigA.Mod(bigA, modulus) + + if bigRet.Cmp(bigA) != 0 { + test.ReportError(t, bigRet, bigA, a, b) + } + } +} + +func TestAddRdcNominal(t *testing.T) { + var res fp + + tmp := oneFp512 + addRdc(&res, &tmp, &p) + if !eqFp(&res, &tmp) { + t.Errorf("Wrong value\n%X", res) + } + + tmp = zeroFp512 + addRdc(&res, &p, &p) + if !eqFp(&res, &p) { + t.Errorf("Wrong value\n%X", res) + } + + tmp = fp{1, 1, 1, 1, 1, 1, 1, 1} + addRdc(&res, &p, &tmp) + if !eqFp(&res, &tmp) { + t.Errorf("Wrong value\n%X", res) + } + + tmp = fp{1, 1, 1, 1, 1, 1, 1, 1} + exp := fp{2, 2, 2, 2, 2, 2, 2, 2} + addRdc(&res, &tmp, &tmp) + if !eqFp(&res, &exp) { + t.Errorf("Wrong value\n%X", res) + } +} + +func TestFp512Sub3_Nominal(t *testing.T) { + var ret fp + var mod big.Int + // modulus: 2^512 + mod.SetUint64(1).Lsh(&mod, 512) + + for i := 0; i < numIter; i++ { + a := randomFp() + bigA, _ := new(big.Int).SetString(fp2S(a), 16) + b := randomFp() + bigB, _ := new(big.Int).SetString(fp2S(b), 16) + + sub512(&ret, &a, &b) + bigRet, _ := new(big.Int).SetString(fp2S(ret), 16) + bigA.Sub(bigA, bigB) + // Truncate to 512 bits + bigA.Mod(bigA, &mod) + + if bigRet.Cmp(bigA) != 0 { + test.ReportError(t, bigRet, bigA, a, b) + } + } +} + +func TestFp512Sub3_DoesntReturnCarry(t *testing.T) { + a := fp{} + b := fp{ + 0xFFFFFFFFFFFFFFFF, 1, + 0, 0, + 0, 0, + 0, 0} + c := fp{ + 0xFFFFFFFFFFFFFFFF, 2, + 0, 0, + 0, 0, + 0, 0} + + if sub512(&a, &b, &c) != 1 { + t.Error("Carry not returned") + } +} + +func TestFp512Sub3_ReturnsCarry(t *testing.T) { + a := fp{} + b := fp{ + 0xFFFFFFFFFFFFFFFF, 2, + 0, 0, + 0, 0, + 0, 0} + c := fp{ + 0xFFFFFFFFFFFFFFFF, 1, + 0, 0, + 0, 0, + 0, 0} + + if sub512(&a, &b, &c) != 0 { + t.Error("Carry not returned") + } +} + +func testCswap(t *testing.T, f func(*fp, *fp, uint8)) { + arg1 := randomFp() + arg2 := randomFp() + + arg1cpy := arg1 + f(&arg1, &arg2, 0) + if !eqFp(&arg1, &arg1cpy) { + t.Error("cswap swapped") + } + + arg1cpy = arg1 + f(&arg1, &arg2, 1) + if eqFp(&arg1, &arg1cpy) { + t.Error("cswap didn't swapped") + } + + arg1cpy = arg1 + f(&arg1, &arg2, 0xF2) + if eqFp(&arg1, &arg1cpy) { + t.Error("cswap didn't swapped") + } +} + +func TestCswap(t *testing.T) { + testCswap(t, cswap512Generic) + testCswap(t, cswap512) +} + +func TestSubRdc(t *testing.T) { + var res fp + + // 1 - 1 mod P + tmp := oneFp512 + subRdc(&res, &tmp, &tmp) + if !eqFp(&res, &zeroFp512) { + t.Errorf("Wrong value\n%X", res) + } + zero(&res) + + // 0 - 1 mod P + exp := p + exp[0]-- + + subRdc(&res, &zeroFp512, &oneFp512) + if !eqFp(&res, &exp) { + t.Errorf("Wrong value\n%X\n%X", res, exp) + } + zero(&res) + + // P - (P-1) + pMinusOne := p + pMinusOne[0]-- + subRdc(&res, &p, &pMinusOne) + if !eqFp(&res, &oneFp512) { + t.Errorf("Wrong value\n[%X != %X]", res, oneFp512) + } + zero(&res) + + subRdc(&res, &p, &oneFp512) + if !eqFp(&res, &pMinusOne) { + t.Errorf("Wrong value\n[%X != %X]", res, pMinusOne) + } +} + +func testMulRdc(t *testing.T, f func(*fp, *fp, *fp)) { + var res fp + var m1 = fp{ + 0x85E2579C786882D0, 0x4E3433657E18DA95, + 0x850AE5507965A0B3, 0xA15BC4E676475964} + var m2 = fp{ + 0x85E2579C786882CF, 0x4E3433657E18DA95, + 0x850AE5507965A0B3, 0xA15BC4E676475964} + + // Expected + var m1m1 = fp{ + 0xAEBF46E92C88A4B4, 0xCFE857977B946347, + 0xD3B264FF08493901, 0x6EEB3D23746B6C7C, + 0xC0CA874A349D64B4, 0x7AD4A38B406F8504, + 0x38B6B6CEB82472FB, 0x1587015FD7DDFC7D} + var m1m2 = fp{ + 0x51534771258C4624, 0x2BFEDE86504E2160, + 0xE8127D5E9329670B, 0x0C84DBD584491D75, + 0x656C73C68B16E38C, 0x01C0DA470B30B8DE, + 0x2532E3903EAA950B, 0x3F2C28EA97FE6FEC} + + // 0*0 + tmp := zeroFp512 + f(&res, &tmp, &tmp) + if !eqFp(&res, &tmp) { + t.Errorf("Wrong value\n%X", res) + } + + // 1*m1 == m1 + zero(&res) + f(&res, &m1, &one) + if !eqFp(&res, &m1) { + t.Errorf("Wrong value\n%X", res) + } + + // m1*m2 < p + zero(&res) + f(&res, &m1, &m2) + if !eqFp(&res, &m1m2) { + t.Errorf("Wrong value\n%X", res) + } + + // m1*m1 > p + zero(&res) + f(&res, &m1, &m1) + if !eqFp(&res, &m1m1) { + t.Errorf("Wrong value\n%X", res) + } +} + +func TestMulRdc(t *testing.T) { + testMulRdc(t, mulRdcGeneric) + testMulRdc(t, mulRdc) +} + +func TestModExp(t *testing.T) { + var resExp, base, exp big.Int + var baseFp, expFp, resFp, resFpExp fp + + for i := 0; i < numIter; i++ { + // Perform modexp with reference implementation + // in Montgomery domain + base.SetString(fp2S(randomFp()), 16) + exp.SetString(fp2S(randomFp()), 16) + resExp.Exp(&base, &exp, modulus) + toMont(&base, true) + toMont(&resExp, true) + + // Convert to fp + copy(baseFp[:], intGetU64(&base)) + copy(expFp[:], intGetU64(&exp)) + copy(resFpExp[:], intGetU64(&resExp)) + + // Perform modexp with our implementation + modExpRdc512(&resFp, &baseFp, &expFp) + + if !eqFp(&resFp, &resFpExp) { + test.ReportError(t, resFp, intGetU64(&resExp), base, exp) + } + } +} + +// Test uses Euler's Criterion. +func TestIsNonQuadRes(t *testing.T) { + var n, nMont big.Int + var pm1o2, rawP big.Int + var nMontFp fp + + // (p-1)/2 + pm1o2.SetString("0x32da4747ba07c4dffe455868af1f26255a16841d76e446212d7dfe63499164e6d3d56362b3f9aa83a8b398660f85a792e1390dfa2bd6541a8dc0dc8299e3643d", 0) + // modulus value (not in montgomery) + rawP.SetString("0x65b48e8f740f89bffc8ab0d15e3e4c4ab42d083aedc88c425afbfcc69322c9cda7aac6c567f35507516730cc1f0b4f25c2721bf457aca8351b81b90533c6c87b", 0) + + // There is 641 quadratic residues in this range + for i := uint64(1); i < uint64(numIter); i++ { + n.SetUint64(i) + n.Exp(&n, &pm1o2, &rawP) + // exp == 1 iff n is quadratic non-residue + exp := n.Cmp(big.NewInt(1)) + if exp < 0 { + panic("Should never happen") + } + + nMont.SetUint64(i) + toMont(&nMont, true) + copy(nMontFp[:], intGetU64(&nMont)) + ret := nMontFp.isNonQuadRes() + + if ret != exp { + toMont(&nMont, false) + t.Errorf("Test failed for value %s", nMont.Text(10)) + } + } +} + +func TestCheckSmaller(t *testing.T) { + // p-1 + var pMin1 = p + pMin1[0]-- + + // p-1 < p => 1 + if !isLess(&pMin1, &p) { + t.Error("pMin1>p") + } + + // p < p-1 => 0 + if isLess(&p, &pMin1) { + t.Error("p>pMin1") + } + + // p == p => 0 + if isLess(&p, &p) { + t.Error("p==p") + } +} + +func BenchmarkFp(b *testing.B) { + var res, arg1 fp + var two64 big.Int + two64.SetUint64(1).Lsh(&two64, 64) + n, _ := rand.Int(rand.Reader, &two64) + u64 := n.Uint64() + arg2, arg3 := randomFp(), randomFp() + b.Run("sub512", func(b *testing.B) { + for n := 0; n < b.N; n++ { + sub512(&arg1, &arg2, &arg3) + } + }) + b.Run("mul", func(b *testing.B) { + for n := 0; n < b.N; n++ { + mul512(&arg2, &arg3, u64) + } + }) + b.Run("cswap", func(b *testing.B) { + for n := 0; n < b.N; n++ { + cswap512(&arg1, &arg2, uint8(n%2)) + } + }) + b.Run("add", func(b *testing.B) { + for n := 0; n < b.N; n++ { + addRdc(&res, &arg1, &arg2) + } + }) + b.Run("sub", func(b *testing.B) { + for n := 0; n < b.N; n++ { + subRdc(&res, &arg1, &arg2) + } + }) + b.Run("mul", func(b *testing.B) { + for n := 0; n < b.N; n++ { + mulRdc(&res, &arg1, &arg2) + } + }) + b.Run("exp", func(b *testing.B) { + for n := 0; n < b.N; n++ { + modExpRdc512(&res, &arg1, &arg2) + } + }) +} diff --git a/src/circl/dh/csidh/testdata/csidh_testvectors.json b/src/circl/dh/csidh/testdata/csidh_testvectors.json new file mode 100644 index 00000000000..01cfec9a373 --- /dev/null +++ b/src/circl/dh/csidh/testdata/csidh_testvectors.json @@ -0,0 +1,2956 @@ +{ + "Vectors": [ + { + "Id": 0, + "Pk1": "2fd62ea1798c0839387d17587a22dcbb89c5797531bb38eff0cd505575c91c440a70e88aa4e67ad267460e40235076dec6ea6f7b60b59aed2a199cc1eb12123c", + "Pr1": "c4d4dccbfedd1b103c123ff2ed11345dfced1514decbc40cdee12e450fdb35fdb5b33ffb2d", + "Pk2": "895ee9f9e96aebf244c20171133aa0c2601b89f98b9c1f2eff7a44bbfc646a4ff5468775dde42d75803d5298eb5b6d27212d49bf59238c0ddea0eeae8bded937", + "Ss": "870ad67d9875cd535a8b4b5776c2eb59acaa872a5775231f75cef212449e40752ac557d12d556edcac68b1ee94a2a5ba6dce4f6bcb6e91c311d5759c83568e29", + "status": "valid", + "comment": "" + }, + { + "Id": 1, + "Pk1": "c017b2703feb1f429d7e101d34b52652a4dea6499c4731d494e1841c1d4333e8c3c6f986ea8e5a62b7943b61025fc273bce2e1c0430a69b78ec35141065de84e", + "Pr1": "0c323ecd4fbbbbd12ccd5eb41d5c1f420ebf330e1521fc21c104cf0db0f0cb0dd5d10225fe", + "Pk2": "9f189b6f09ec6ef686de1abc438e9708ceaac64cf01e9695c55e1997c5c13992f4e1c35e5c809af2d9be6ffad36e8966a94190f84962fd6e7f5fe9bbd7aee41f", + "Ss": "755e8a3e344b0ef2accd8855ac292cdf1dd3d0f9e7403464f85a0784351f0317caae5455d4f8c2a1666adb364e9dc4aff578f02a4bb3da031a5e5e1e30f5dd30", + "status": "valid", + "comment": "" + }, + { + "Id": 2, + "Pk1": "758baaa1d991fce063ff29b4192dba6c8d9b6620ef858fefe2e5218c1902dc0d84c81877f0eba7ba3346dc6a67c292e2f3ee0567b5ad4a285fab92bd43441305", + "Pr1": "3db1b323d054ec052201d02ff20103b250ceeeb243f40e5e24bf122ebfe30551e55ed0b1eb", + "Pk2": "41d8d0a352cbdeb2ea16733e83b6a6e222abfc2afafd76451ee4231c47d527a58956b69abcccdc582706d4aababbedf26c242c7c1192f43f5d465feb77d72f63", + "Ss": "b95b8b83f4fb3de618306608c5da7e774822f6e4e2f1e93eee0906f5a714c5d58d467cb9e5af617d0b9894dd5008f34fde855ac418b5460bc0109941b7f8151a", + "status": "valid", + "comment": "" + }, + { + "Id": 3, + "Pk1": "0cd103b51492be43c35c80523607142ae88f6896dc64e90bd710d6778688e2b3c2c6cd49d376d859d0ed84804d4584a1ac942cab87483c53bee22369aa0a0d65", + "Pr1": "bfffb01ceb01e2544e1de44e30c21effee3212f5ee534b4b30fffebefbe3e400ebf13e0b2d", + "Pk2": "5ec767260e61594ecf768cc0c3a381042184d58e4092c6c13eca657b2bceb1eb44275babf98741a64618b5c8998d18454c63e92ea0b7fdacdded1bedc44d4549", + "Ss": "c962080c5170ecd996c904b363c9034c49472e177523247029a7d85fd3aa01eb589e17bbec73196fa3835f7460a0bdd75bebb3cd53467cd2d1eec5906d21761a", + "status": "valid", + "comment": "" + }, + { + "Id": 4, + "Pk1": "111fd8d9e336cad4578179638cf3d1e64a5ddc51c1f8a5fcc8bf321563c410e7e0ee7531ac7595b2eb13eddcb70df6919848edbafb941142ae9cce03e47e2d4c", + "Pr1": "f00f025ec4feb142b2cd2e5d04ffc3b10ee4c1ec350ff41d553e1f0323efe305e24fc0f150", + "Pk2": "87d6effecd8ee94b6f84521637187dd9fc4d29100e0ee4b07516c9889acf5fdebe9881dfeb902efd354b367a3ddba3773991cb1cd52ca4f25a7d18f739272462", + "Ss": "20bfe627e1d0a6ff0ead98ab55049d190fb2a563f78b85b574d494c4760d8c567315f3ce7eec8852ae359f74d7b7f0c55ef24d72a285ab6b838f9b16d7cf8749", + "status": "valid", + "comment": "" + }, + { + "Id": 5, + "Pk1": "db8aa23c21ed69dd507048dd032050288f6330c97599d0b78f4091991d39f8b9ecc101d966d4049b38de7f21cb7dae42c02fb5f3d6323c74639f52cbcbf6553b", + "Pr1": "4c23dc513b1ddcbdd5f2fc25bf540b1215ece4f244e1222f44c01515ec0bed1d4b2fcdf234", + "Pk2": "d8d3bb64e2e354e0a4d209d05f39e7150f6dcd074cf5ac558706bc4428555e2c44dea6b036e5492cd5fe2e59e5bed9bde65aeccf8a47d6a28f8525283ec23a09", + "Ss": "af726b0535a37777c3790db3ddf8118c7f795366d51c77d2decab720c799248e34c4417d825a1b3bf3de814bf27c8917ba16e8a83b7117709cb455f34fd37328", + "status": "valid", + "comment": "" + }, + { + "Id": 6, + "Pk1": "c170985f761b9742950f27256f6e5fe63564ace2bb1c1240c87f915b0fe3761295d3c0f8344d78872706124ba6c01b9f460d683801563c7f333404017b8c874d", + "Pr1": "052dde3fcdfc0cd2efe2bd3512d1df32b304cbbbf4402e1cc55f00e3ec2cfdf4fc2c03cb0f", + "Pk2": "096a2838cb794731790b102549905ceda31a94b6951038e6a73483e035045b75917fc8acf982b161418a9a667a8c2afc184feb48462520cc0e85f64a114f0438", + "Ss": "80690d9623baf4e4881aa63f47f751ec88c9c099516a384f3c5d97179c8d33700679e28087f0318e51ed7839917c76dd0db74fc03e10fb1c539c92075368f85a", + "status": "valid", + "comment": "" + }, + { + "Id": 7, + "Pk1": "60270f86533c7394ba891009668d0c5f31dbdf22d6c74b8c1ffddc280d7a16a49797e14c9ae0b16cdaf337f718206d5dab380e345c2bcf9567e25c3eb757bd3f", + "Pr1": "5b224f4dd4501cb0f15b045dd154cd50b25bf52234fbd1cb4db3e50f3b404eb3e4fc1ee530", + "Pk2": "26dc974e40298a7a550d1d28f1eb9273bf16852327d2f2cfef768bda463b43346ec711bb3454bb5dd0a7778744bc6dab6de330f3024baaf249095ae916d87e43", + "Ss": 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"c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118e212f580562bf2b8f08701ef4245769dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 311, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f0e7f580562bf2b8f08701ef4245769dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 312, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f0127580562bf2b8f08701ef4245769dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 313, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f5d6562bf2b8f08701ef4245769dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 314, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f5807d2bf2b8f08701ef4245769dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 315, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f58056d9f2b8f08701ef4245769dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 316, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562b4ab8f08701ef4245769dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 317, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562bf248f08701ef4245769dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 318, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562bf2b8778701ef4245769dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 319, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562bf2b8f08601ef4245769dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 320, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562bf2b8f087eeef4245769dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 321, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562bf2b8f08701ad4245769dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 322, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562bf2b8f08701ef0745769dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 323, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562bf2b8f08701ef4233769dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 324, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562bf2b8f08701ef4245eb9dc460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 325, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562bf2b8f08701ef42457659c460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 326, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562bf2b8f08701ef4245769da460", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + }, + { + "Id": 327, + "Pk1": "49986cb4962be33fa910c08d866cf938f3cc157e1c665a679d0fd5038cf7bcb458cf58b850799492a82608995337bbb4f3b3841c8b3120bb8e88c9991989b625", + "Pr1": "c1331bb3d2d2e4de455344403edf143d01eccb5cd1edfc5fe0e1c0cc1edcfd43fccfd23110", + "Pk2": "b67e64c7535b3f6c0633c62c7f3e05eec88179d34cf0eac136d5c0e3bacb5bd509f9028bf188099489166b34e118f012f580562bf2b8f08701ef4245769dc4d6", + "Ss": "3954a50e07180680389550be867732f8284da03ab6f63d8bf22b2e225ac47fb973ee987b1a9db0d35d48c3267be0dfec2e5b136acdb8d6f58105a5961627ce52", + "status": "invalid_public_key2", + "comment": "" + } + ] +} \ No newline at end of file diff --git a/src/circl/dh/csidh/utils_test.go b/src/circl/dh/csidh/utils_test.go new file mode 100644 index 00000000000..08ecee5a2bd --- /dev/null +++ b/src/circl/dh/csidh/utils_test.go @@ -0,0 +1,132 @@ +package csidh + +import ( + "crypto/rand" + "encoding/binary" + "fmt" + "math/big" +) + +var ( + // Number of iterations + numIter = 10 + // Modulus + modulus, _ = new(big.Int).SetString(fp2S(p), 16) + // Zero in fp + zeroFp512 = fp{} + // One in fp + oneFp512 = fp{1, 0, 0, 0, 0, 0, 0, 0} + // file with KAT vectors + katFile = "testdata/csidh_testvectors.json" +) + +// Converts dst to Montgomery if "toMont==true" or from Montgomery domain otherwise. +func toMont(dst *big.Int, toMont bool) { + var bigP, bigR big.Int + + intSetU64(&bigP, p[:]) + bigR.SetUint64(1) + bigR.Lsh(&bigR, 512) + + if !toMont { + bigR.ModInverse(&bigR, &bigP) + } + dst.Mul(dst, &bigR) + dst.Mod(dst, &bigP) +} + +func fp2S(v fp) string { + var str string + for i := 0; i < 8; i++ { + str = fmt.Sprintf("%016x", v[i]) + str + } + return str +} + +// zeroize fp. +func zero(v *fp) { + for i := range *v { + v[i] = 0 + } +} + +// returns random value in a range (0,p). +func randomFp() (u fp) { + _ = binary.Read(rand.Reader, binary.LittleEndian, &u) + return +} + +// return x==y for fp. +func eqFp(l, r *fp) bool { + for idx := range l { + if l[idx] != r[idx] { + return false + } + } + return true +} + +// return x==y for point. +func ceqpoint(l, r *point) bool { + return eqFp(&l.x, &r.x) && eqFp(&l.z, &r.z) +} + +// Converts src to big.Int. Function assumes that src is a slice of uint64 +// values encoded in little-endian byte order. +func intSetU64(dst *big.Int, src []uint64) { + var tmp big.Int + + dst.SetUint64(0) + for i := range src { + tmp.SetUint64(src[i]) + tmp.Lsh(&tmp, uint(i*64)) + dst.Add(dst, &tmp) + } +} + +// Converts src to an array of uint64 values encoded in little-endian +// byte order. +func intGetU64(src *big.Int) []uint64 { + var tmp, mod big.Int + dst := make([]uint64, (src.BitLen()/64)+1) + + u64 := uint64(0) + u64-- + mod.SetUint64(u64) + for i := 0; i < (src.BitLen()/64)+1; i++ { + tmp.Set(src) + tmp.Rsh(&tmp, uint(i)*64) + tmp.And(&tmp, &mod) + dst[i] = tmp.Uint64() + } + return dst +} + +// Returns projective coordinate X of normalized EC 'point' (point.x / point.z). +func toNormX(point *point) big.Int { + var bigP, bigDnt, bigDor big.Int + + intSetU64(&bigP, p[:]) + intSetU64(&bigDnt, point.x[:]) + intSetU64(&bigDor, point.z[:]) + + bigDor.ModInverse(&bigDor, &bigP) + bigDnt.Mul(&bigDnt, &bigDor) + bigDnt.Mod(&bigDnt, &bigP) + return bigDnt +} + +// Converts string to fp element in Montgomery domain of cSIDH-512. +func toFp(num string) fp { + var tmp big.Int + var ok bool + var ret fp + + _, ok = tmp.SetString(num, 0) + if !ok { + panic("Can't parse a number") + } + toMont(&tmp, true) + copy(ret[:], intGetU64(&tmp)) + return ret +} diff --git a/src/circl/dh/curve4q/curve4Q.go b/src/circl/dh/curve4q/curve4Q.go new file mode 100644 index 00000000000..2af8616c322 --- /dev/null +++ b/src/circl/dh/curve4q/curve4Q.go @@ -0,0 +1,27 @@ +package curve4q + +import "circl/ecc/fourq" + +// Size is the size in bytes of keys. +const Size = 32 + +// Key represents a public or private key of FourQ. +type Key [Size]byte + +// KeyGen calculates a public key k from a secret key. +func KeyGen(public, secret *Key) { + var P fourq.Point + P.ScalarBaseMult((*[Size]byte)(secret)) + P.Marshal((*[Size]byte)(public)) +} + +// Shared calculates a shared key k from Alice's secret and Bob's public key. +// Returns true on success. +func Shared(shared, secret, public *Key) bool { + var P, Q fourq.Point + ok := P.Unmarshal((*[Size]byte)(public)) + Q.ScalarMult((*[Size]byte)(secret), &P) + Q.Marshal((*[Size]byte)(shared)) + ok = ok && Q.IsOnCurve() + return ok +} diff --git a/src/circl/dh/curve4q/curve4Q_test.go b/src/circl/dh/curve4q/curve4Q_test.go new file mode 100644 index 00000000000..923dab90b7f --- /dev/null +++ b/src/circl/dh/curve4q/curve4Q_test.go @@ -0,0 +1,78 @@ +package curve4q + +import ( + "bytes" + "crypto/rand" + "fmt" + "io" + "testing" + + "circl/internal/test" +) + +func TestDH(t *testing.T) { + var secretAlice, publicAlice, sharedAlice Key + var secretBob, publicBob, sharedBob Key + testTimes := 1 << 10 + + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(secretAlice[:]) + _, _ = rand.Read(secretBob[:]) + + KeyGen(&publicAlice, &secretAlice) + KeyGen(&publicBob, &secretBob) + + if ok := Shared(&sharedAlice, &secretAlice, &publicBob); !ok { + test.ReportError(t, ok, true, secretAlice, publicBob) + } + if ok := Shared(&sharedBob, &secretBob, &publicAlice); !ok { + test.ReportError(t, ok, true, secretBob, publicAlice) + } + + got := sharedAlice + want := sharedBob + if !bytes.Equal(got[:], want[:]) { + test.ReportError(t, got, want, secretAlice, secretBob) + } + } +} + +func BenchmarkDH(b *testing.B) { + var secret, public, shared Key + _, _ = rand.Read(secret[:]) + _, _ = rand.Read(public[:]) + + b.Run("keygen", func(b *testing.B) { + for i := 0; i < b.N; i++ { + KeyGen(&public, &secret) + } + }) + b.Run("shared", func(b *testing.B) { + for i := 0; i < b.N; i++ { + Shared(&shared, &secret, &public) + } + }) +} + +func ExampleKey() { + var AliceSecret, BobSecret, + AlicePublic, BobPublic, + AliceShared, BobShared Key + + // Generating Alice's secret and public keys + _, _ = io.ReadFull(rand.Reader, AliceSecret[:]) + KeyGen(&AlicePublic, &AliceSecret) + + // Generating Bob's secret and public keys + _, _ = io.ReadFull(rand.Reader, BobSecret[:]) + KeyGen(&BobPublic, &BobSecret) + + // Deriving Alice's shared key + Shared(&AliceShared, &AliceSecret, &BobPublic) + + // Deriving Bob's shared key + Shared(&BobShared, &BobSecret, &AlicePublic) + + fmt.Println(AliceShared == BobShared) + // Output: true +} diff --git a/src/circl/dh/curve4q/doc.go b/src/circl/dh/curve4q/doc.go new file mode 100644 index 00000000000..5e34f806e96 --- /dev/null +++ b/src/circl/dh/curve4q/doc.go @@ -0,0 +1,8 @@ +// Package curve4q implements Diffie-Hellman operations using the FourQ curve +// at the 128-bit security level. +// +// References: +// - https://eprint.iacr.org/2015/565 +// - https://tools.ietf.org/html/draft-ladd-cfrg-4q-01 +// +package curve4q diff --git a/src/circl/dh/doc.go b/src/circl/dh/doc.go new file mode 100644 index 00000000000..0ce65b7a153 --- /dev/null +++ b/src/circl/dh/doc.go @@ -0,0 +1,2 @@ +// Package dh provides variety of Diffie-Hellman key exchange methods. +package dh diff --git a/src/circl/dh/sidh/doc.go b/src/circl/dh/sidh/doc.go new file mode 100644 index 00000000000..ef8a6d2a8f6 --- /dev/null +++ b/src/circl/dh/sidh/doc.go @@ -0,0 +1,30 @@ +// Package sidh provides implementation of experimental post-quantum +// Supersingular Isogeny Diffie-Hellman (SIDH) as well as Supersingular +// Isogeny Key Encapsulation (SIKE). +// +// It comes with implementations of 2 different field arithmetic +// implementations sidh.Fp503 and sidh.Fp751. +// +// | Algorithm | Public Key Size | Shared Secret Size | Ciphertext Size | +// |-----------|-----------------|--------------------|-----------------| +// | SIDH/p503 | 376 | 126 | N/A | +// | SIDH/p751 | 564 | 188 | N/A | +// | SIKE/p503 | 376 | 16 | 402 | +// | SIKE/p751 | 564 | 24 | 596 | +// +// In order to instantiate SIKE/p751 KEM one needs to create a KEM object +// and allocate internal structures. This can be done with NewSike751 helper. +// After that kem can be used multiple times. +// +// var kem = sike.NewSike751(rand.Reader) +// kem.Encapsulate(ciphertext, sharedSecret, publicBob) +// kem.Decapsulate(sharedSecret, privateBob, PublicBob, ciphertext) +// +// Code is optimized for AMD64 and aarch64. Generic implementation +// is provided for other architectures. +// +// References: +// - [SIDH] https://eprint.iacr.org/2011/506 +// - [SIKE] http://www.sike.org/files/SIDH-spec.pdf +// +package sidh diff --git a/src/circl/dh/sidh/internal/common/doc.go b/src/circl/dh/sidh/internal/common/doc.go new file mode 100644 index 00000000000..f606f420a58 --- /dev/null +++ b/src/circl/dh/sidh/internal/common/doc.go @@ -0,0 +1,2 @@ +// Package common provides types, variables, constants and functions commonly used in SIDH or SIKE. +package common diff --git a/src/circl/dh/sidh/internal/common/params.go b/src/circl/dh/sidh/internal/common/params.go new file mode 100644 index 00000000000..fe06a41c88b --- /dev/null +++ b/src/circl/dh/sidh/internal/common/params.go @@ -0,0 +1,24 @@ +package common + +import "fmt" + +// Keeps mapping: SIDH prime field ID to domain parameters +var sidhParams = make(map[uint8]SidhParams) + +// Params returns domain parameters corresponding to finite field and identified by +// `id` provided by the caller. Function panics in case `id` wasn't registered earlier. +func Params(id uint8) *SidhParams { + if val, ok := sidhParams[id]; ok { + return &val + } + panic("sidh: SIDH Params ID unregistered") +} + +// Registers SIDH parameters for particular field. +func Register(id uint8, p *SidhParams) { + if _, ok := sidhParams[id]; ok { + msg := fmt.Sprintf("sidh: Field with id %d already registered", id) + panic(msg) + } + sidhParams[id] = *p +} diff --git a/src/circl/dh/sidh/internal/common/types.go b/src/circl/dh/sidh/internal/common/types.go new file mode 100644 index 00000000000..dc5499691ca --- /dev/null +++ b/src/circl/dh/sidh/internal/common/types.go @@ -0,0 +1,106 @@ +package common + +const ( + // corresponds to words in P751 + FpMaxWords = 12 + // corresponds to byte size of P751 SIDH private key for B + MaxSidhPrivateKeyBsz = 48 + // corresponds to byte size of P751 SIKE private key for B + MaxSikePrivateKeyBsz = MaxSidhPrivateKeyBsz + MaxMsgBsz + // corresponds to SIKE max length of 'n' (see 1.4 of SIKE spec in NIST PQC round 1) + MaxMsgBsz = 40 + // corresponds to byte size of shared secret generated by SIKEp751 + MaxSharedSecretBsz = 188 + // corresponds to by size of the P751 public key + MaxPublicKeySz = 3 * FpMaxWords * 64 + // corresponds to by size of the ciphertext produced by SIKE/P751 + MaxCiphertextBsz = MaxMsgBsz + MaxPublicKeySz +) + +// Id's correspond to bitlength of the prime field characteristic +// Currently Fp751 is the only one supported by this implementation +const ( + Fp503 uint8 = iota + Fp751 + Fp434 +) + +// Representation of an element of the base field F_p. +// +// No particular meaning is assigned to the representation -- it could represent +// an element in Montgomery form, or not. Tracking the meaning of the field +// element is left to higher types. +type Fp [FpMaxWords]uint64 + +// Represents an intermediate product of two elements of the base field F_p. +type FpX2 [2 * FpMaxWords]uint64 + +// Represents an element of the extended field Fp^2 = Fp(x+i) +type Fp2 struct { + A Fp + B Fp +} + +type DomainParams struct { + // P, Q and R=P-Q base points + AffineP, AffineQ, AffineR Fp2 + // Size of a computation strategy for x-torsion group + IsogenyStrategy []uint32 + // Max size of secret key for x-torsion group + SecretBitLen uint + // Max size of secret key for x-torsion group + SecretByteLen uint +} + +type SidhParams struct { + ID uint8 + // Bytelen of P + Bytelen int + // The public key size, in bytes. + PublicKeySize int + // The shared secret size, in bytes. + SharedSecretSize int + // 2- and 3-torsion group parameter definitions + A, B DomainParams + // Precomputed identity element in the Fp2 in Montgomery domain + OneFp2 Fp2 + // Precomputed 1/2 in the Fp2 in Montgomery domain + HalfFp2 Fp2 + // Length of SIKE secret message. Must be one of {24,32,40}, + // depending on size of prime field used (see [SIKE], 1.4 and 5.1) + MsgLen int + // Length of SIKE ephemeral KEM key (see [SIKE], 1.4 and 5.1) + KemSize int + // Byte size of ciphertext that KEM produces + CiphertextSize int + // Defines A,C constant for starting curve Cy^2 = x^3 + Ax^2 + x + InitCurve ProjectiveCurveParameters +} + +// Stores curve projective parameters equivalent to A/C. Meaning of the +// values depends on the context. When working with isogenies over +// subgroup that are powers of: +// * three then (A:C) ~ (A+2C:A-2C) +// * four then (A:C) ~ (A+2C: 4C) +// See Appendix A of SIKE for more details +type CurveCoefficientsEquiv struct { + A Fp2 + C Fp2 +} + +// A point on the projective line P^1(F_{p^2}). +// +// This represents a point on the Kummer line of a Montgomery curve. The +// curve is specified by a ProjectiveCurveParameters struct. +type ProjectivePoint struct { + X Fp2 + Z Fp2 +} + +// A point on the projective line P^1(F_{p^2}). +// +// This is used to work projectively with the curve coefficients. +type ProjectiveCurveParameters struct { + A Fp2 + C Fp2 +} diff --git a/src/circl/dh/sidh/internal/common/utils.go b/src/circl/dh/sidh/internal/common/utils.go new file mode 100644 index 00000000000..8db334b81cf --- /dev/null +++ b/src/circl/dh/sidh/internal/common/utils.go @@ -0,0 +1,50 @@ +package common + +import "encoding/binary" + +// Constant time select. +// if pick == 1 (out = in1) +// if pick == 0 (out = in2) +// else out is undefined. +func Cpick(pick int, out, in1, in2 []byte) { + var which = byte((int8(pick << 7)) >> 7) + for i := range out { + out[i] = (in1[i] & which) | (in2[i] & ^which) + } +} + +// Read 2*bytelen(p) bytes into the given ExtensionFieldElement. +// +// It is an error to call this function if the input byte slice is less than 2*bytelen(p) bytes long. +func BytesToFp2(fp2 *Fp2, input []byte, bytelen int) { + if len(input) < 2*bytelen { + panic("input byte slice too short") + } + numW64 := (bytelen*8 + 63) / 64 + a := make([]byte, 8*numW64) + b := make([]byte, 8*numW64) + copy(a[:bytelen], input[:bytelen]) + copy(b[:bytelen], input[bytelen:]) + for i := 0; i < numW64; i++ { + fp2.A[i] = binary.LittleEndian.Uint64(a[i*8 : (i+1)*8]) + fp2.B[i] = binary.LittleEndian.Uint64(b[i*8 : (i+1)*8]) + } +} + +// Convert the input to wire format. +// +// The output byte slice must be at least 2*bytelen(p) bytes long. +func Fp2ToBytes(output []byte, fp2 *Fp2, bytelen int) { + if len(output) < 2*bytelen { + panic("output byte slice too short") + } + numW64 := (bytelen*8 + 63) / 64 + a := make([]byte, 8*numW64) + b := make([]byte, 8*numW64) + for i := 0; i < numW64; i++ { + binary.LittleEndian.PutUint64(a[i*8:(i+1)*8], fp2.A[i]) + binary.LittleEndian.PutUint64(b[i*8:(i+1)*8], fp2.B[i]) + } + copy(output[:bytelen], a[:bytelen]) + copy(output[bytelen:], b[:bytelen]) +} diff --git a/src/circl/dh/sidh/internal/p434/arith_amd64.s b/src/circl/dh/sidh/internal/p434/arith_amd64.s new file mode 100644 index 00000000000..abdd504ea2a --- /dev/null +++ b/src/circl/dh/sidh/internal/p434/arith_amd64.s @@ -0,0 +1,1232 @@ +// +build amd64,!noasm + +#include "textflag.h" + +// p434 +#define P434_0 $0xFFFFFFFFFFFFFFFF +#define P434_3 $0xFDC1767AE2FFFFFF +#define P434_4 $0x7BC65C783158AEA3 +#define P434_5 $0x6CFC5FD681C52056 +#define P434_6 $0x0002341F27177344 + +// p434 x 2 +#define P434X2_0 $0xFFFFFFFFFFFFFFFE +#define P434X2_1 $0xFFFFFFFFFFFFFFFF +#define P434X2_3 $0xFB82ECF5C5FFFFFF +#define P434X2_4 $0xF78CB8F062B15D47 +#define P434X2_5 $0xD9F8BFAD038A40AC +#define P434X2_6 $0x0004683E4E2EE688 + +// Redefine P434p1Zeros +#define P434_P1_ZEROS 3 + +// Performs schoolbook multiplication of 128-bit with 256-bit +// number. Uses MULX, ADOX, ADCX instruction. +#define MULX128x256(IDX, M0, M1, T0, T1, T2, T3, T4, T5, T6) \ + XORQ AX, AX \ + MOVQ (IDX)(M0), DX \ + MULXQ M1+ 0(SB), T0, T1 \ // T0 <- C0 + MULXQ M1+ 8(SB), T4, T2 \ + MULXQ M1+16(SB), T5, T3 \ + ADOXQ T4, T1 \ // T1: interm1 + ADOXQ T5, T2 \ // T2: interm2 + \ + MULXQ M1+24(SB), T5, T4 \ + ADOXQ T5, T3 \ // T3: interm3 + ADOXQ AX, T4 \ // T4: interm4 + \ + XORQ AX, AX \ + MOVQ (IDX+8)(M0), DX \ + MULXQ M1+ 0(SB), T5, T6 \ + ADCXQ T5, T1 \ // T1 <- C1 + ADCXQ T6, T2 \ + \ + MULXQ M1+ 8(SB), T6, T5 \ + ADCXQ T5, T3 \ + ADOXQ T6, T2 \ // T2 <- C2 + \ + MULXQ M1+16(SB), T6, T5 \ + ADCXQ T5, T4 \ + ADOXQ T6, T3 \ // T3 <- C3 + \ + MULXQ M1+24(SB), T6, T5 \ + ADCXQ AX, T5 \ + ADOXQ T6, T4 \ // T4 <- C4 + ADOXQ AX, T5 // T5 <- C5 + +// Performs schoolbook multiplication of 64-bit with 256-bit +// number. Uses MULX and ADOX instructions. +// +// Uses registers: DX,AX +#define MULX64x256(IDX, M0, M1, T0, T1, T2, T3, T4, T5) \ + XORQ AX, AX \ + MOVQ (IDX)(M0), DX \ + MULXQ M1+ 0(SB), T0, T1 \ // T0 <- C0 + MULXQ M1+ 8(SB), T4, T2 \ + MULXQ M1+16(SB), T5, T3 \ + \ + ADOXQ T4, T1 \ // T1 <- C1 + ADOXQ T5, T2 \ // T2 <- C2 + \ + MULXQ M1+24(SB), T5, T4 \ + ADOXQ T5, T3 \ // T3 <- C3 + ADOXQ AX, T4 // T4 <- C4 + +// Performs schoolbook multiplication of two 192-bit numbers +// number. Uses MULX and ADOX instructions. +// +// Uses registers: DX,AX +#define MULX192(IM0,M0,IM1,M1,ID,MDST,T0,T1,T2,T3,T4,T5,T6) \ + MOVQ (0+IM0)(M0), DX \ + MULXQ (0+IM1)(M1), T1, T0 \ // T0:T1 = A0*B0 + MOVQ T1,(ID+0)(MDST) \ // MDST0 + MULXQ (IM1+ 8)(M1), T2, T1 \ // T1:T2 = A0*B1 + XORQ AX, AX \ + ADOXQ T2, T0 \ + MULXQ (IM1+16)(M1),T3, T2 \ // T2:T3 = A0*B2 + ADOXQ T3, T1 \ + \ + MOVQ (IM0+8)(M0), DX \ + MULXQ (IM1+0)(M1), T4, T3 \ // T3:T4 = A1*B0 + ADOXQ AX, T2 \ + XORQ AX, AX \ + \ + MULXQ (IM1+8)(M1), T6, T5 \ // T6:T7 = A1*B1 + ADOXQ T0, T4 \ + MOVQ T4,(ID+8)(MDST) \ // MDST1 + ADCXQ T6, T3 \ + \ + MULXQ (IM1+16)(M1),T0, T6 \ // T6:T0 = A1*B2 + ADOXQ T1, T3 \ + ADCXQ T0, T5 \ + ADCXQ AX, T6 \ + ADOXQ T2, T5 \ + \ + MOVQ (IM0+16)(M0),DX \ + MULXQ (IM1+ 0)(M1), T0, T1 \ // T1:T0 = A2*B0 + ADOXQ AX, T6 \ + XORQ AX, AX \ + \ + MULXQ (IM1+ 8)(M1), T2, T4 \ // T4:T2 = A2*B1 + ADOXQ T3, T0 \ + MOVQ T0, (ID+16)(MDST) \ // MDST2 + ADCXQ T5, T1 \ + \ + MULXQ (IM1+16)(M1),T3, T0 \ // T0:T3 = A2*B2 + ADCXQ T6, T4 \ + ADCXQ AX, T0 \ + ADOXQ T2, T1 \ + ADOXQ T4, T3 \ + ADOXQ AX, T0 \ + MOVQ T1, (ID+24)(MDST) \ // MDST3 + MOVQ T3, (ID+32)(MDST) \ // MDST4 + MOVQ T0, (ID+40)(MDST) // MDST5 + +// Performs schoolbook multiplication of 2 256-bit numbers. Uses +// MULX instruction. Result is stored in 256 bits pointed by $DST. +// +// Uses registers: DX,AX +#define MULX256(IM0,M0,IM1,M1,ID,MDST,T0,T1,T2,T3,T4,T5,T6,T7,T8,T9) \ + MOVQ (IM0+0)(M0), DX \ + MULXQ (IM1+0)(M1), T1, T0 \ // A0*B[0-3] + MOVQ T1, (ID+0)(MDST) \ + MULXQ (IM1+8)(M1), T2, T1 \ + XORQ AX, AX \ + ADOXQ T2, T0 \ + MULXQ (IM1+16)(M1),T3, T2 \ + ADOXQ T3, T1 \ + MULXQ (IM1+24)(M1),T4, T3 \ + ADOXQ T4, T2 \ + \ + MOVQ (IM0+8)(M0), DX \ + MULXQ (IM1+0)(M1), T4, T5 \ // A1*B[0-3] + ADOXQ AX, T3 \ + XORQ AX, AX \ + MULXQ (IM1+8)(M1), T7, T6 \ + ADOXQ T0, T4 \ + MOVQ T4, (ID+8)(MDST) \ + ADCXQ T7, T5 \ + MULXQ (IM1+16)(M1),T8, T7 \ + ADCXQ T8, T6 \ + ADOXQ T1, T5 \ + MULXQ (IM1+24)(M1),T9, T8 \ + ADCXQ T9, T7 \ + ADCXQ AX, T8 \ + ADOXQ T2, T6 \ + \ + MOVQ (IM0+16)(M0),DX \ // A2*B[0-3] + MULXQ (IM1+ 0)(M1), T0, T1 \ + ADOXQ T3, T7 \ + ADOXQ AX, T8 \ + XORQ AX, AX \ + MULXQ (IM1+8)(M1), T3, T2 \ + ADOXQ T5, T0 \ + MOVQ T0, (ID+16)(MDST) \ + ADCXQ T3, T1 \ + MULXQ (IM1+16)(M1),T4, T3 \ + ADCXQ T4, T2 \ + ADOXQ T6, T1 \ + MULXQ (IM1+24)(M1),T9, T4 \ + ADCXQ T9, T3 \ + ADCXQ AX, T4 \ + \ + ADOXQ T7, T2 \ + ADOXQ T8, T3 \ + ADOXQ AX, T4 \ + \ + MOVQ (IM0+24)(M0),DX \ + MULXQ (IM1+ 0)(M1), T0, T5\ // A3*B[0-3] + XORQ AX, AX \ + MULXQ (IM1+ 8)(M1), T7, T6\ + ADCXQ T7, T5 \ + ADOXQ T0, T1 \ + MULXQ (IM1+16)(M1), T8, T7 \ + ADCXQ T8, T6 \ + ADOXQ T5, T2 \ + MULXQ (IM1+24)(M1), T9, T8 \ + ADCXQ T9, T7 \ + ADCXQ AX, T8 \ + ADOXQ T6, T3 \ + ADOXQ T7, T4 \ + ADOXQ AX, T8 \ + MOVQ T1, (ID+24)(MDST) \ + MOVQ T2, (ID+32)(MDST) \ + MOVQ T3, (ID+40)(MDST) \ + MOVQ T4, (ID+48)(MDST) \ + MOVQ T8, (ID+56)(MDST) + +// Performs schoolbook multiplication of 64-bit with 256-bit +// number. +// +// Uses registers: DX, AX +#define MUL64x256(IDX,M0,M1,C0,C1,C2,C3,C4,T0) \ + MOVQ (IDX)(M0), T0 \ + \ + XORQ C2, C2 \ + MOVQ M1+0(SB), AX \ + MULQ T0 \ + MOVQ AX, C0 \ + MOVQ DX, C1 \ + \ + XORQ C3, C3 \ + MOVQ M1+8(SB), AX \ + MULQ T0 \ + ADDQ AX, C1 \ + ADCQ DX, C2 \ + \ + XORQ C4, C4 \ + MOVQ M1+16(SB), AX \ + MULQ T0 \ + ADDQ AX, C2 \ + ADCQ DX, C3 \ + \ + MOVQ M1+24(SB), AX \ + MULQ T0 \ + ADDQ AX, C3 \ + ADCQ DX, C4 + +// Performs schoolbook multiplication of 128-bit with 256-bit +// number. Destroys RAX and RDX +// +// Uses registers: DX, AX +#define MUL128x256(IDX,M0,M1,C0,C1,C2,C3,C4,C5,T0,T1) \ + \ // A0 x B0 + MOVQ (IDX+0)(M0), T0 \ + MOVQ M1+0(SB), AX \ + MULQ T0 \ + XORQ C2, C2 \ + MOVQ AX, C0 \ + MOVQ DX, C1 \ + \ // A0 x B1 + MOVQ M1+8(SB), AX \ + MULQ T0 \ + XORQ C3, C3 \ + ADDQ AX, C1 \ + ADCQ DX, C2 \ + \ // A1 x B0 + MOVQ (IDX+8)(M0), T1 \ + MOVQ M1+0(SB), AX \ + MULQ T1 \ + ADDQ AX, C1 \ + ADCQ DX, C2 \ + ADCQ $0, C3 \ + \ // A0 x B2 + XORQ C4, C4 \ + MOVQ M1+16(SB), AX \ + MULQ T0 \ + ADDQ AX, C2 \ + ADCQ DX, C3 \ + ADCQ $0, C4 \ + \ // A1 x B1 + MOVQ M1+8(SB), AX \ + MULQ T1 \ + ADDQ AX, C2 \ + ADCQ DX, C3 \ + ADCQ $0, C4 \ + \ // A0 x B3 + MOVQ M1+24(SB), AX \ + MULQ T0 \ + XORQ C5, C5 \ + ADDQ AX, C3 \ + ADCQ DX, C4 \ + ADCQ $0, C5 \ + \ // A1 x B2 + MOVQ M1+16(SB), AX \ + MULQ T1 \ + ADDQ AX, C3 \ + ADCQ DX, C4 \ + ADCQ $0, C5 \ + \ // A1 x B3 + MOVQ M1+24(SB), AX \ + MULQ T1 \ + ADDQ AX, C4 \ + ADCQ DX, C5 + +#define REDC_COMMON(MUL01, MUL23, MUL45, MUL67) \ + MUL01 \ + XORQ CX, CX \ + ADDQ 0x18(DI), R8 \ + ADCQ 0x20(DI), R9 \ + ADCQ 0x28(DI), R10 \ + ADCQ 0x30(DI), R11 \ + ADCQ 0x38(DI), R12 \ + ADCQ 0x40(DI), R13 \ + ADCQ 0x48(DI), CX \ + MOVQ R8, 0x18(DI) \ + MOVQ R9, 0x20(DI) \ + MOVQ R10, 0x28(DI) \ + MOVQ R11, 0x30(DI) \ + MOVQ R12, 0x38(DI) \ + MOVQ R13, 0x40(DI) \ + MOVQ CX, 0x48(DI) \ + MOVQ 0x50(DI), R8 \ + MOVQ 0x58(DI), R9 \ + MOVQ 0x60(DI), R10 \ + MOVQ 0x68(DI), R11 \ + ADCQ $0, R8 \ + ADCQ $0, R9 \ + ADCQ $0, R10 \ + ADCQ $0, R11 \ + MOVQ R8, 0x50(DI) \ + MOVQ R9, 0x58(DI) \ + MOVQ R10, 0x60(DI) \ + MOVQ R11, 0x68(DI) \ + \ + MUL23 \ + XORQ CX, CX \ + ADDQ 0x28(DI), R8 \ + ADCQ 0x30(DI), R9 \ + ADCQ 0x38(DI), R10 \ + ADCQ 0x40(DI), R11 \ + ADCQ 0x48(DI), R12 \ + ADCQ 0x50(DI), R13 \ + ADCQ 0x58(DI), CX \ + MOVQ R8, 0x28(DI) \ + MOVQ R9, 0x30(DI) \ + MOVQ R10, 0x38(DI) \ + MOVQ R11, 0x40(DI) \ + MOVQ R12, 0x48(DI) \ + MOVQ R13, 0x50(DI) \ + MOVQ CX, 0x58(DI) \ + MOVQ 0x60(DI), R8 \ + MOVQ 0x68(DI), R9 \ + ADCQ $0, R8 \ + ADCQ $0, R9 \ + MOVQ R8, 0x60(DI) \ + MOVQ R9, 0x68(DI) \ + \ + MUL45 \ + XORQ CX, CX \ + ADDQ 0x38(DI), R8 \ + ADCQ 0x40(DI), R9 \ + ADCQ 0x48(DI), R10 \ + ADCQ 0x50(DI), R11 \ + ADCQ 0x58(DI), R12 \ + ADCQ 0x60(DI), R13 \ + ADCQ 0x68(DI), CX \ + MOVQ R8, 0x0(SI) \ // OUT0 + MOVQ R9, 0x8(SI) \ // OUT1 + MOVQ R10, 0x48(DI) \ + MOVQ R11, 0x50(DI) \ + MOVQ R12, 0x58(DI) \ + MOVQ R13, 0x60(DI) \ + MOVQ CX, 0x68(DI) \ + \ + MUL67 \ + ADDQ 0x48(DI), R8 \ + ADCQ 0x50(DI), R9 \ + ADCQ 0x58(DI), R10 \ + ADCQ 0x60(DI), R11 \ + ADCQ 0x68(DI), R12 \ + MOVQ R8, 0x10(SI) \ // OUT2 + MOVQ R9, 0x18(SI) \ // OUT3 + MOVQ R10, 0x20(SI) \ // OUT4 + MOVQ R11, 0x28(SI) \ // OUT5 + MOVQ R12, 0x30(SI) // OUT6 + +TEXT ·cswapP434(SB),NOSPLIT,$0-17 + + MOVQ x+0(FP), DI + MOVQ y+8(FP), SI + MOVB choice+16(FP), AL // AL = 0 or 1 + MOVBLZX AL, AX // AX = 0 or 1 + NEGQ AX // AX = 0x00..00 or 0xff..ff +#ifndef CSWAP_BLOCK +#define CSWAP_BLOCK(idx) \ + MOVQ (idx*8)(DI), BX \ // BX = x[idx] + MOVQ (idx*8)(SI), CX \ // CX = y[idx] + MOVQ CX, DX \ // DX = y[idx] + XORQ BX, DX \ // DX = y[idx] ^ x[idx] + ANDQ AX, DX \ // DX = (y[idx] ^ x[idx]) & mask + XORQ DX, BX \ // BX = (y[idx] ^ x[idx]) & mask) ^ x[idx] = x[idx] or y[idx] + XORQ DX, CX \ // CX = (y[idx] ^ x[idx]) & mask) ^ y[idx] = y[idx] or x[idx] + MOVQ BX, (idx*8)(DI) \ + MOVQ CX, (idx*8)(SI) +#endif + CSWAP_BLOCK(0) + CSWAP_BLOCK(1) + CSWAP_BLOCK(2) + CSWAP_BLOCK(3) + CSWAP_BLOCK(4) + CSWAP_BLOCK(5) + CSWAP_BLOCK(6) +#ifdef CSWAP_BLOCK +#undef CSWAP_BLOCK +#endif + RET + +TEXT ·addP434(SB),NOSPLIT,$0-24 + MOVQ z+0(FP), DX + MOVQ x+8(FP), DI + MOVQ y+16(FP), SI + + // Used later to calculate a mask + XORQ CX, CX + + // [R8-R14]: z = x + y + MOVQ ( 0)(DI), R8; ADDQ ( 0)(SI), R8 + MOVQ ( 8)(DI), R9; ADCQ ( 8)(SI), R9 + MOVQ (16)(DI), R10; ADCQ (16)(SI), R10 + MOVQ (24)(DI), R11; ADCQ (24)(SI), R11 + MOVQ (32)(DI), R12; ADCQ (32)(SI), R12 + MOVQ (40)(DI), R13; ADCQ (40)(SI), R13 + MOVQ (48)(DI), R14; ADCQ (48)(SI), R14 + + XORQ DI, DI + + MOVQ P434X2_0, AX; SUBQ AX, R8 + MOVQ P434X2_1, AX; SBBQ AX, R9 + SBBQ AX, R10 + MOVQ P434X2_3, AX; SBBQ AX, R11 + MOVQ P434X2_4, AX; SBBQ AX, R12 + MOVQ P434X2_5, AX; SBBQ AX, R13 + MOVQ P434X2_6, AX; SBBQ AX, R14 + + // mask + SBBQ $0, CX + + // if z<0 add P434x2 back + MOVQ P434X2_0, R15; ANDQ CX, R15; + MOVQ P434X2_1, AX; ANDQ CX, AX; + + ADDQ R8, R15; MOVQ R15, ( 0)(DX) + ADCQ AX, R9; MOVQ R9, ( 8)(DX) + ADCQ AX, R10; MOVQ R10, (16)(DX) + + ADCQ $0, DI + MOVQ P434X2_3, R15; ANDQ CX, R15; + MOVQ P434X2_4, R8; ANDQ CX, R8; + MOVQ P434X2_5, R9; ANDQ CX, R9; + MOVQ P434X2_6, R10; ANDQ CX, R10; + BTQ $0, DI + + ADCQ R11, R15; MOVQ R15, (24)(DX) + ADCQ R12, R8; MOVQ R8, (32)(DX) + ADCQ R13, R9; MOVQ R9, (40)(DX) + ADCQ R14, R10; MOVQ R10, (48)(DX) + + RET + +TEXT ·adlP434(SB),NOSPLIT,$0-24 + MOVQ z+0(FP), DX + MOVQ x+8(FP), DI + MOVQ y+16(FP),SI + + MOVQ ( 0)(DI), R8 + ADDQ ( 0)(SI), R8 + MOVQ ( 8)(DI), R9 + ADCQ ( 8)(SI), R9 + MOVQ (16)(DI), R10 + ADCQ (16)(SI), R10 + MOVQ (24)(DI), R11 + ADCQ (24)(SI), R11 + MOVQ (32)(DI), R12 + ADCQ (32)(SI), R12 + MOVQ (40)(DI), R13 + ADCQ (40)(SI), R13 + MOVQ (48)(DI), R14 + ADCQ (48)(SI), R14 + MOVQ (56)(DI), R15 + ADCQ (56)(SI), R15 + MOVQ (64)(DI), AX + ADCQ (64)(SI), AX + MOVQ (72)(DI), BX + ADCQ (72)(SI), BX + MOVQ (80)(DI), CX + ADCQ (80)(SI), CX + + MOVQ R8, ( 0)(DX) + MOVQ R9, ( 8)(DX) + MOVQ R10,(16)(DX) + MOVQ R11,(24)(DX) + MOVQ R12,(32)(DX) + MOVQ R13,(40)(DX) + MOVQ R14,(48)(DX) + MOVQ R15,(56)(DX) + MOVQ AX, (64)(DX) + MOVQ BX, (72)(DX) + MOVQ CX, (80)(DX) + + MOVQ (88)(DI), R8 + ADCQ (88)(SI), R8 + MOVQ (96)(DI), R9 + ADCQ (96)(SI), R9 + MOVQ (104)(DI), R10 + ADCQ (104)(SI), R10 + + MOVQ R8, (88)(DX) + MOVQ R9, (96)(DX) + MOVQ R10,(104)(DX) + RET + +TEXT ·subP434(SB),NOSPLIT,$0-24 + MOVQ z+0(FP), DX + MOVQ x+8(FP), DI + MOVQ y+16(FP), SI + + // Used later to calculate a mask + XORQ CX, CX + + MOVQ ( 0)(DI), R8; SUBQ ( 0)(SI), R8 + MOVQ ( 8)(DI), R9; SBBQ ( 8)(SI), R9 + MOVQ (16)(DI), R10; SBBQ (16)(SI), R10 + MOVQ (24)(DI), R11; SBBQ (24)(SI), R11 + MOVQ (32)(DI), R12; SBBQ (32)(SI), R12 + MOVQ (40)(DI), R13; SBBQ (40)(SI), R13 + MOVQ (48)(DI), R14; SBBQ (48)(SI), R14 + + // mask + SBBQ $0, CX + XORQ R15, R15 + + // if z<0 add p434x2 back + MOVQ P434X2_0, DI; ANDQ CX, DI + MOVQ P434X2_1, SI; ANDQ CX, SI + MOVQ P434X2_3, AX; ANDQ CX, AX + + ADDQ DI, R8; MOVQ R8, ( 0)(DX) + ADCQ SI, R9; MOVQ R9, ( 8)(DX) + ADCQ SI, R10; MOVQ R10, (16)(DX) + ADCQ AX, R11; MOVQ R11, (24)(DX) + ADCQ $0, R15 + + MOVQ P434X2_4, R8; ANDQ CX, R8; + MOVQ P434X2_5, R9; ANDQ CX, R9; + MOVQ P434X2_6, R10; ANDQ CX, R10 + + BTQ $0, R15 + + ADCQ R8, R12; MOVQ R12, (32)(DX) + ADCQ R9, R13; MOVQ R13, (40)(DX) + ADCQ R10, R14; MOVQ R14, (48)(DX) + RET + +TEXT ·sulP434(SB),NOSPLIT,$0-24 + MOVQ z+0(FP), DX + MOVQ x+8(FP), DI + MOVQ y+16(FP), SI + + // Used later to store result of 0-borrow + XORQ CX, CX + + // SUBC for first 10 limbs + MOVQ ( 0)(DI), R8; SUBQ ( 0)(SI), R8 + MOVQ ( 8)(DI), R9; SBBQ ( 8)(SI), R9 + MOVQ (16)(DI), R10; SBBQ (16)(SI), R10 + MOVQ (24)(DI), R11; SBBQ (24)(SI), R11 + MOVQ (32)(DI), R12; SBBQ (32)(SI), R12 + MOVQ (40)(DI), R13; SBBQ (40)(SI), R13 + MOVQ (48)(DI), R14; SBBQ (48)(SI), R14 + MOVQ (56)(DI), R15; SBBQ (56)(SI), R15 + MOVQ (64)(DI), AX; SBBQ (64)(SI), AX + MOVQ (72)(DI), BX; SBBQ (72)(SI), BX + + MOVQ R8, ( 0)(DX) + MOVQ R9, ( 8)(DX) + MOVQ R10, (16)(DX) + MOVQ R11, (24)(DX) + MOVQ R12, (32)(DX) + MOVQ R13, (40)(DX) + MOVQ R14, (48)(DX) + MOVQ R15, (56)(DX) + MOVQ AX, (64)(DX) + MOVQ BX, (72)(DX) + + // SUBC for last 4 limbs + MOVQ ( 80)(DI), R8; SBBQ ( 80)(SI), R8 + MOVQ ( 88)(DI), R9; SBBQ ( 88)(SI), R9 + MOVQ ( 96)(DI), R10; SBBQ ( 96)(SI), R10 + MOVQ (104)(DI), R11; SBBQ (104)(SI), R11 + + // Store carry flag + SBBQ $0, CX + + MOVQ R8, ( 80)(DX) + MOVQ R9, ( 88)(DX) + MOVQ R10, ( 96)(DX) + MOVQ R11, (104)(DX) + + // Load p into registers: + MOVQ P434_0, R8; ANDQ CX, R8 + // P434_{1,2} = P434_0, so reuse R8 + MOVQ P434_3, R9; ANDQ CX, R9 + MOVQ P434_4, R10; ANDQ CX, R10 + MOVQ P434_5, R11; ANDQ CX, R11 + MOVQ P434_6, R12; ANDQ CX, R12 + + MOVQ (56 )(DX), AX; ADDQ R8, AX; MOVQ AX, (56 )(DX) + MOVQ (56+ 8)(DX), AX; ADCQ R8, AX; MOVQ AX, (56+ 8)(DX) + MOVQ (56+16)(DX), AX; ADCQ R8, AX; MOVQ AX, (56+16)(DX) + MOVQ (56+24)(DX), AX; ADCQ R9, AX; MOVQ AX, (56+24)(DX) + MOVQ (56+32)(DX), AX; ADCQ R10, AX; MOVQ AX, (56+32)(DX) + MOVQ (56+40)(DX), AX; ADCQ R11, AX; MOVQ AX, (56+40)(DX) + MOVQ (56+48)(DX), AX; ADCQ R12, AX; MOVQ AX, (56+48)(DX) + + RET + +TEXT ·modP434(SB),NOSPLIT,$0-8 + MOVQ x+0(FP), DI + + // Zero AX for later use: + XORQ AX, AX + + // Set x <- x - p + MOVQ P434_0, R8 + SUBQ R8, ( 0)(DI) + // P434_{1,2} = P434_0, so reuse R8 + MOVQ P434_3, R9 + SBBQ R8, ( 8)(DI) + SBBQ R8, (16)(DI) + MOVQ P434_4, R10 + SBBQ R9, (24)(DI) + MOVQ P434_5, R11 + SBBQ R10, (32)(DI) + MOVQ P434_6, R12 + SBBQ R11, (40)(DI) + SBBQ R12, (48)(DI) + + // save carry + SBBQ $0, AX + + // Conditionally add p to x if x-p < 0 + ANDQ AX, R8 + ANDQ AX, R9 + ANDQ AX, R10 + ANDQ AX, R11 + ANDQ AX, R12 + + ADDQ R8, ( 0)(DI) + ADCQ R8, ( 8)(DI) + ADCQ R8, (16)(DI) + ADCQ R9, (24)(DI) + ADCQ R10,(32)(DI) + ADCQ R11,(40)(DI) + ADCQ R12,(48)(DI) + RET + +// 434-bit multiplication using Karatsuba (one level), +// schoolbook (one level). +TEXT ·mulP434(SB),NOSPLIT,$112-24 + MOVQ z+0(FP), CX + MOVQ x+8(FP), DI + MOVQ y+16(FP), SI + + // Check whether to use optimized implementation + CMPB ·HasADXandBMI2(SB), $1 + JE mul_with_mulx_adcx_adox + + // rcx[0-3] <- AH+AL + XORQ AX, AX + MOVQ 0x20(DI), R8 + MOVQ 0x28(DI), R9 + MOVQ 0x30(DI), R10 + XORQ R11, R11 + ADDQ 0x0(DI), R8 + ADCQ 0x8(DI), R9 + ADCQ 0x10(DI), R10 + ADCQ 0x18(DI), R11 + // store AH+AL mask + SBBQ $0, AX + MOVQ AX, 0x40(SP) + // store AH+AL in 0-0x18(rcx) + MOVQ R8, 0x0(CX) + MOVQ R9, 0x8(CX) + MOVQ R10, 0x10(CX) + MOVQ R11, 0x18(CX) + + // r12-r15 <- BH+BL + XORQ DX, DX + MOVQ 0x20(SI), R12 + MOVQ 0x28(SI), R13 + MOVQ 0x30(SI), R14 + XORQ R15, R15 + ADDQ 0x0(SI), R12 + ADCQ 0x8(SI), R13 + ADCQ 0x10(SI), R14 + ADCQ 0x18(SI), R15 + SBBQ $0, DX + + // store BH+BL mask + MOVQ DX, 0x48(SP) + + // (rsp[0-0x38]) <- (AH+AL)*(BH+BL) + MOVQ (CX), AX + MULQ R12 + MOVQ AX, (SP) + MOVQ DX, R8 + + XORQ R9, R9 + MOVQ (CX), AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + + XORQ R10, R10 + MOVQ 0x8(CX), AX + MULQ R12 + ADDQ AX, R8 + MOVQ R8, 0x8(SP) + ADCQ DX, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ (CX), AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ 0x10(CX), AX + MULQ R12 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ 0x8(CX), AX + MULQ R13 + ADDQ AX, R9 + MOVQ R9, 0x10(SP) + ADCQ DX, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ (CX),AX + MULQ R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ 0x18(CX), AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ 0x8(CX), AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ 0x10(CX), AX + MULQ R13 + ADDQ AX, R10 + MOVQ R10, 0x18(SP) + ADCQ DX, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ 0x8(CX), AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ 0x18(CX), AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ 0x10(CX), AX + MULQ R14 + ADDQ AX, R8 + MOVQ R8, 0x20(SP) + ADCQ DX, R9 + ADCQ $0, R10 + + XORQ R11, R11 + MOVQ 0x10(CX), AX + MULQ R15 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R11 + + MOVQ 0x18(CX), AX + MULQ R14 + ADDQ AX, R9 + MOVQ R9, 0x28(SP) + ADCQ DX, R10 + ADCQ $0, R11 + + MOVQ 0x18(CX), AX + MULQ R15 + ADDQ AX, R10 + MOVQ R10, 0x30(SP) + ADCQ DX, R11 + MOVQ R11,0x38(SP) + + // r12-r15 <- masked (BH + BL) + MOVQ 0x40(SP), AX + ANDQ AX, R12 + ANDQ AX, R13 + ANDQ AX, R14 + ANDQ AX, R15 + + // r8-r11 <- masked (AH + AL) + MOVQ 0x48(SP), AX + MOVQ 0x00(CX), R8 + ANDQ AX, R8 + MOVQ 0x08(CX), R9 + ANDQ AX, R9 + MOVQ 0x10(CX), R10 + ANDQ AX, R10 + MOVQ 0x18(CX), R11 + ANDQ AX, R11 + + // r12-r15 <- masked (AH + AL) + masked (BH + BL) + ADDQ R8, R12 + ADCQ R9, R13 + ADCQ R10, R14 + ADCQ R11, R15 + + // rsp[0x20-0x38] <- (AH+AL) x (BH+BL) high + MOVQ 0x20(SP), AX + ADDQ AX, R12 + MOVQ 0x28(SP), AX + ADCQ AX, R13 + MOVQ 0x30(SP), AX + ADCQ AX, R14 + MOVQ 0x38(SP), AX + ADCQ AX, R15 + MOVQ R12, 0x50(SP) + MOVQ R13, 0x58(SP) + MOVQ R14, 0x60(SP) + MOVQ R15, 0x68(SP) + + // [rcx] <- CL = AL x BL + MOVQ (DI), R11 + MOVQ (SI), AX + MULQ R11 + XORQ R9, R9 + MOVQ AX, (CX) + MOVQ DX, R8 + + MOVQ 0x10(DI), R14 + MOVQ 0x8(SI), AX + MULQ R11 + XORQ R10, R10 + ADDQ AX, R8 + ADCQ DX, R9 + + MOVQ 0x8(DI), R12 + MOVQ (SI), AX + MULQ R12 + ADDQ AX, R8 + MOVQ R8, 0x8(CX) + ADCQ DX, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ 0x10(SI), AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (SI), R13 + MOVQ R14, AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ 0x8(SI), AX + MULQ R12 + ADDQ AX, R9 + MOVQ R9, 0x10(CX) + ADCQ DX, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ 0x18(SI), AX + MULQ R11 + MOVQ 0x18(DI), R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ R15, AX + MULQ R13 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ 0x10(SI), AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ 0x8(SI), AX + MULQ R14 + ADDQ AX, R10 + MOVQ R10, 0x18(CX) + ADCQ DX, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ 0x18(SI), AX + MULQ R12 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ 0x8(SI), AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ 0x10(SI), AX + MULQ R14 + ADDQ AX, R8 + MOVQ R8, 0x20(CX) + ADCQ DX, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ 0x18(SI), AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ 0x10(SI), AX + MULQ R15 + ADDQ AX, R9 + MOVQ R9, 0x28(CX) + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ 0x18(SI), AX + MULQ R15 + ADDQ AX, R10 + MOVQ R10, 0x30(CX) + ADCQ DX, R8 + MOVQ R8, 0x38(CX) + + // rcx[0x40-0x68] <- AH*BH + // multiplies 2 192-bit numbers A,B + MOVQ 0x20(DI), R11 + MOVQ 0x20(SI), AX + MULQ R11 + XORQ R9, R9 + MOVQ AX, 0x40(CX) + MOVQ DX, R8 + + MOVQ 0x30(DI), R14 + MOVQ 0x28(SI), AX + MULQ R11 + XORQ R10, R10 + ADDQ AX, R8 + ADCQ DX, R9 + + MOVQ 0x28(DI), R12 + MOVQ 0x20(SI), AX + MULQ R12 + ADDQ AX, R8 + MOVQ R8, 0x48(CX) + ADCQ DX, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ 0x30(SI), AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ 0x20(SI), R13 + MOVQ R14, AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ 0x28(SI), AX + MULQ R12 + ADDQ AX, R9 + MOVQ R9, 0x50(CX) + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ 0x30(SI), AX + MULQ R12 + XORQ R12, R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R12 + + MOVQ 0x28(SI), AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R12 + MOVQ R10, 0x58(CX) + + MOVQ 0x30(SI), AX + MULQ R14 + ADDQ AX, R8 + ADCQ $0, R12 + MOVQ R8, 0x60(CX) + + ADDQ R12, DX + + // [r8-r15] <- (AH+AL)x(BH+BL) - ALxBL + MOVQ 0x0(SP), R8 + SUBQ 0x0(CX), R8 + MOVQ 0x8(SP), R9 + SBBQ 0x8(CX), R9 + MOVQ 0x10(SP), R10 + SBBQ 0x10(CX), R10 + MOVQ 0x18(SP), R11 + SBBQ 0x18(CX), R11 + MOVQ 0x50(SP), R12 + SBBQ 0x20(CX), R12 + MOVQ 0x58(SP), R13 + SBBQ 0x28(CX), R13 + MOVQ 0x60(SP), R14 + SBBQ 0x30(CX), R14 + MOVQ 0x68(SP), R15 + SBBQ 0x38(CX), R15 + + // [r8-r15] <- (AH+AL) x (BH+BL) - ALxBL - AHxBH + MOVQ 0x40(CX), AX + SUBQ AX, R8 + MOVQ 0x48(CX), AX + SBBQ AX, R9 + MOVQ 0x50(CX), AX + SBBQ AX, R10 + MOVQ 0x58(CX), AX + SBBQ AX, R11 + MOVQ 0x60(CX), AX + SBBQ AX, R12 + SBBQ DX, R13 + SBBQ $0, R14 + SBBQ $0, R15 + + // Final result + ADDQ 0x20(CX), R8 + MOVQ R8, 0x20(CX) // OUT4 + ADCQ 0x28(CX), R9 + MOVQ R9, 0x28(CX) // OUT5 + ADCQ 0x30(CX), R10 + MOVQ R10, 0x30(CX) // OUT6 + ADCQ 0x38(CX), R11 + MOVQ R11, 0x38(CX) // OUT7 + ADCQ 0x40(CX), R12 + MOVQ R12, 0x40(CX) // OUT8 + ADCQ 0x48(CX), R13 + MOVQ R13, 0x48(CX) // OUT9 + ADCQ 0x50(CX), R14 + MOVQ R14, 0x50(CX) // OUT10 + ADCQ 0x58(CX), R15 + MOVQ R15, 0x58(CX) // OUT11 + MOVQ 0x60(CX), R12 + ADCQ $0, R12 + MOVQ R12, 0x60(CX) // OUT12 + ADCQ $0, DX + MOVQ DX, 0x68(CX) // OUT13 + RET + +mul_with_mulx_adcx_adox: + // Mul implementation for CPUs supporting two independent carry chain + // (ADOX/ADCX) instructions and carry-less MULX multiplier + XORQ AX, AX + MOVQ 0x0(DI), R8 + MOVQ 0x8(DI), R9 + MOVQ 0x10(DI), R10 + MOVQ 0x18(DI), R11 + + MOVQ BP, 0x70(SP) // push: BP is Callee-save. + + ADDQ 0x20(DI), R8 + ADCQ 0x28(DI), R9 + ADCQ 0x30(DI), R10 + ADCQ $0, R11 + SBBQ $0, AX + MOVQ R8, 0x0(SP) + MOVQ R9, 0x8(SP) + MOVQ R10, 0x10(SP) + MOVQ R11, 0x18(SP) + + // r12-r15 <- BH + BL, rbx <- mask + XORQ BX, BX + MOVQ 0x0(SI), R12 + MOVQ 0x8(SI), R13 + MOVQ 0x10(SI), R14 + MOVQ 0x18(SI), R15 + ADDQ 0x20(SI), R12 + ADCQ 0x28(SI), R13 + ADCQ 0x30(SI), R14 + ADCQ $0, R15 + SBBQ $0, BX + MOVQ R12, 0x20(SP) + MOVQ R13, 0x28(SP) + MOVQ R14, 0x30(SP) + MOVQ R15, 0x38(SP) + + // r12-r15 <- masked (BH + BL) + ANDQ AX, R12 + ANDQ AX, R13 + ANDQ AX, R14 + ANDQ AX, R15 + + // r8-r11 <- masked (AH + AL) + ANDQ BX, R8 + ANDQ BX, R9 + ANDQ BX, R10 + ANDQ BX, R11 + + // r8-r11 <- masked (AH + AL) + masked (BH + BL) + ADDQ R12, R8 + ADCQ R13, R9 + ADCQ R14, R10 + ADCQ R15, R11 + MOVQ R8, 0x40(SP) + MOVQ R9, 0x48(SP) + MOVQ R10, 0x50(SP) + MOVQ R11, 0x58(SP) + + // [rsp] <- CM = (AH+AL) x (BH+BL) + MULX256(0,SP,32,SP,0,SP,R8,R9,R10,R11,R12,R13,R14,R15,BX,BP) + // [rcx] <- CL = AL x BL (Result c0-c3) + MULX256(0,DI,0,SI,0,CX,R8,R9,R10,R11,R12,R13,R14,R15,BX,BP) + // [rcx+64] <- CH = AH x BH + MULX192(32,DI,32,SI,64,CX,R8,R9,R10,R11,R12,R13,R14) + + // r8-r11 <- (AH+AL) x (BH+BL), final step + MOVQ 0x40(SP), R8 + MOVQ 0x48(SP), R9 + MOVQ 0x50(SP), R10 + MOVQ 0x58(SP), R11 + + MOVQ 0x20(SP), AX + ADDQ AX, R8 + MOVQ 0x28(SP), AX + ADCQ AX, R9 + MOVQ 0x30(SP), AX + ADCQ AX, R10 + MOVQ 0x38(SP), AX + ADCQ AX, R11 + + // [rsp], x3-x5 <- (AH+AL) x (BH+BL) - ALxBL + MOVQ 0x0(SP), R12 + MOVQ 0x8(SP), R13 + MOVQ 0x10(SP), R14 + MOVQ 0x18(SP), R15 + SUBQ 0x0(CX), R12 + SBBQ 0x8(CX), R13 + SBBQ 0x10(CX), R14 + SBBQ 0x18(CX), R15 + SBBQ 0x20(CX), R8 + SBBQ 0x28(CX), R9 + SBBQ 0x30(CX), R10 + SBBQ 0x38(CX), R11 + + // r8-r15 <- (AH+AL) x (BH+BL) - ALxBL - AHxBH + SUBQ 0x40(CX), R12 + SBBQ 0x48(CX), R13 + SBBQ 0x50(CX), R14 + SBBQ 0x58(CX), R15 + SBBQ 0x60(CX), R8 + SBBQ 0x68(CX), R9 + SBBQ $0, R10 + SBBQ $0, R11 + + ADDQ 0x20(CX), R12 + MOVQ R12, 0x20(CX) // OUT4 + ADCQ 0x28(CX), R13 + MOVQ R13, 0x28(CX) // OUT5 + ADCQ 0x30(CX), R14 + MOVQ R14, 0x30(CX) // OUT6 + ADCQ 0x38(CX), R15 + MOVQ R15, 0x38(CX) // OUT7 + ADCQ 0x40(CX), R8 + MOVQ R8, 0x40(CX) // OUT8 + ADCQ 0x48(CX), R9 + MOVQ R9, 0x48(CX) // OUT9 + ADCQ 0x50(CX), R10 + MOVQ R10, 0x50(CX) // OUT10 + ADCQ 0x58(CX), R11 + MOVQ R11, 0x58(CX) // OUT11 + MOVQ 0x60(CX), R12 + ADCQ $0, R12 + MOVQ R12, 0x60(CX) // OUT12 + MOVQ 0x68(CX), R13 + ADCQ $0, R13 + MOVQ R13, 0x68(CX) // OUT13 + + MOVQ 0x70(SP), BP // pop: BP is Callee-save. + RET + +TEXT ·rdcP434(SB),$0-16 + MOVQ z+0(FP), SI + MOVQ x+8(FP), DI + CMPB ·HasADXandBMI2(SB), $1 + JE redc_bdw +#define MUL01 MUL128x256( 0,DI,·P434p1+(8*P434_P1_ZEROS),R8,R9,R10,R11,R12,R13,R14,CX) +#define MUL23 MUL128x256(16,DI,·P434p1+(8*P434_P1_ZEROS),R8,R9,R10,R11,R12,R13,R14,CX) +#define MUL45 MUL128x256(32,DI,·P434p1+(8*P434_P1_ZEROS),R8,R9,R10,R11,R12,R13,R14,CX) +#define MUL67 MUL64x256(48,DI,·P434p1+(8*P434_P1_ZEROS),R8,R9,R10,R11,R12,R13) + REDC_COMMON(MUL01, MUL23, MUL45, MUL67) +#undef MUL01 +#undef MUL23 +#undef MUL45 +#undef MUL67 + RET + +// 434-bit montgomery reduction Uses MULX/ADOX/ADCX instructions +// available on Broadwell micro-architectures and newer. +redc_bdw: +#define MULX01 MULX128x256( 0,DI,·P434p1+(8*P434_P1_ZEROS),R8,R9,R10,R11,R12,R13,CX) +#define MULX23 MULX128x256(16,DI,·P434p1+(8*P434_P1_ZEROS),R8,R9,R10,R11,R12,R13,CX) +#define MULX45 MULX128x256(32,DI,·P434p1+(8*P434_P1_ZEROS),R8,R9,R10,R11,R12,R13,CX) +#define MULX67 MULX64x256(48,DI,·P434p1+(8*P434_P1_ZEROS),R8,R9,R10,R11,R12,R13) + REDC_COMMON(MULX01, MULX23, MULX45, MULX67) +#undef MULX01 +#undef MULX23 +#undef MULX45 +#undef MULX67 + RET diff --git a/src/circl/dh/sidh/internal/p434/arith_amd64_test.go b/src/circl/dh/sidh/internal/p434/arith_amd64_test.go new file mode 100644 index 00000000000..e4a923cc8bc --- /dev/null +++ b/src/circl/dh/sidh/internal/p434/arith_amd64_test.go @@ -0,0 +1,96 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +// +build amd64,!noasm + +package p434 + +import ( + "reflect" + "testing" + "testing/quick" + + "circl/dh/sidh/internal/common" + "internal/cpu" +) + +type OptimFlag uint + +const ( + // Indicates that optimisation which uses MUL instruction should be used + kUse_MUL OptimFlag = 1 << 0 + // Indicates that optimisation which uses MULX, ADOX and ADCX instructions should be used + kUse_MULXandADxX = 1 << 1 +) + +func resetCpuFeatures() { + HasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX +} + +// Utility function used for testing Mul implementations. Tests caller provided +// mulFunc against mul() +func testMul(t *testing.T, f1, f2 OptimFlag) { + doMulTest := func(multiplier, multiplicant common.Fp) bool { + defer resetCpuFeatures() + var resMulRef, resMulOptim common.FpX2 + + // Compute multiplier*multiplicant with first implementation + HasADXandBMI2 = (kUse_MULXandADxX & f1) == kUse_MULXandADxX + mulP434(&resMulOptim, &multiplier, &multiplicant) + + // Compute multiplier*multiplicant with second implementation + HasADXandBMI2 = (kUse_MULXandADxX & f2) == kUse_MULXandADxX + mulP434(&resMulRef, &multiplier, &multiplicant) + + // Compare results + return reflect.DeepEqual(resMulRef, resMulOptim) + } + + if err := quick.Check(doMulTest, quickCheckConfig); err != nil { + t.Error(err) + } +} + +// Utility function used for testing REDC implementations. Tests caller provided +// redcFunc against redc() +func testRedc(t *testing.T, f1, f2 OptimFlag) { + doRedcTest := func(aRR common.FpX2) bool { + defer resetCpuFeatures() + var resRedcF1, resRedcF2 common.Fp + var aRRcpy = aRR + + // Compute redc with first implementation + HasADXandBMI2 = (kUse_MULXandADxX & f1) == kUse_MULXandADxX + rdcP434(&resRedcF1, &aRR) + + // Compute redc with second implementation + HasADXandBMI2 = (kUse_MULXandADxX & f2) == kUse_MULXandADxX + rdcP434(&resRedcF2, &aRRcpy) + + // Compare results + return reflect.DeepEqual(resRedcF2, resRedcF1) + } + + if err := quick.Check(doRedcTest, quickCheckConfig); err != nil { + t.Error(err) + } +} + +// Ensures correctness of implementation of mul operation which uses MULX and ADOX/ADCX +func TestMulWithMULXADxX(t *testing.T) { + defer resetCpuFeatures() + if !HasADXandBMI2 { + t.Skip("MULX, ADCX and ADOX not supported by the platform") + } + testMul(t, kUse_MULXandADxX, kUse_MUL) +} + +// Ensures correctness of Montgomery reduction implementation which uses MULX +// and ADCX/ADOX. +func TestRedcWithMULXADxX(t *testing.T) { + defer resetCpuFeatures() + if !HasADXandBMI2 { + t.Skip("MULX, ADCX and ADOX not supported by the platform") + } + testRedc(t, kUse_MULXandADxX, kUse_MUL) +} diff --git a/src/circl/dh/sidh/internal/p434/arith_decl.go b/src/circl/dh/sidh/internal/p434/arith_decl.go new file mode 100644 index 00000000000..ae15f64b40a --- /dev/null +++ b/src/circl/dh/sidh/internal/p434/arith_decl.go @@ -0,0 +1,45 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +// +build amd64,!noasm + +package p434 + +import ( + . "circl/dh/sidh/internal/common" +) + +// If choice = 0, leave x,y unchanged. If choice = 1, set x,y = y,x. +// If choice is neither 0 nor 1 then behaviour is undefined. +// This function executes in constant time. +//go:noescape +func cswapP434(x, y *Fp, choice uint8) + +// Compute z = x + y (mod p). +//go:noescape +func addP434(z, x, y *Fp) + +// Compute z = x - y (mod p). +//go:noescape +func subP434(z, x, y *Fp) + +// Compute z = x + y, without reducing mod p. +//go:noescape +func adlP434(z, x, y *FpX2) + +// Compute z = x - y, without reducing mod p. +//go:noescape +func sulP434(z, x, y *FpX2) + +// Reduce a field element in [0, 2*p) to one in [0,p). +//go:noescape +func modP434(x *Fp) + +// Computes z = x * y. +//go:noescape +func mulP434(z *FpX2, x, y *Fp) + +// Computes the Montgomery reduction z = x R^{-1} (mod 2*p). On return value +// of x may be changed. z=x not allowed. +//go:noescape +func rdcP434(z *Fp, x *FpX2) diff --git a/src/circl/dh/sidh/internal/p434/arith_generic.go b/src/circl/dh/sidh/internal/p434/arith_generic.go new file mode 100644 index 00000000000..08a76de8324 --- /dev/null +++ b/src/circl/dh/sidh/internal/p434/arith_generic.go @@ -0,0 +1,192 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +// +build noasm !amd64 + +package p434 + +import ( + "math/bits" + + "circl/dh/sidh/internal/common" +) + +// Compute z = x + y (mod p). +func addP434(z, x, y *common.Fp) { + var carry uint64 + + // z=x+y % P434 + for i := 0; i < FpWords; i++ { + z[i], carry = bits.Add64(x[i], y[i], carry) + } + + // z = z - P434x2 + carry = 0 + for i := 0; i < FpWords; i++ { + z[i], carry = bits.Sub64(z[i], P434x2[i], carry) + } + + // if z<0 add P434x2 back + mask := uint64(0 - carry) + carry = 0 + for i := 0; i < FpWords; i++ { + z[i], carry = bits.Add64(z[i], P434x2[i]&mask, carry) + } +} + +// Compute z = x - y (mod p). +func subP434(z, x, y *common.Fp) { + var borrow uint64 + + for i := 0; i < FpWords; i++ { + z[i], borrow = bits.Sub64(x[i], y[i], borrow) + } + + mask := uint64(0 - borrow) + borrow = 0 + + for i := 0; i < FpWords; i++ { + z[i], borrow = bits.Add64(z[i], P434x2[i]&mask, borrow) + } +} + +// Conditionally swaps bits in x and y in constant time. +// mask indicates bits to be swapped (set bits are swapped) +// For details see "Hackers Delight, 2.20" +// +// Implementation doesn't actually depend on a prime field. +func cswapP434(x, y *common.Fp, mask uint8) { + var tmp, mask64 uint64 + + mask64 = 0 - uint64(mask) + for i := 0; i < FpWords; i++ { + tmp = mask64 & (x[i] ^ y[i]) + x[i] = tmp ^ x[i] + y[i] = tmp ^ y[i] + } +} + +// Perform Montgomery reduction: set z = x R^{-1} (mod 2*p) +// with R=2^(FpWords*64). Destroys the input value. +func rdcP434(z *common.Fp, x *common.FpX2) { + var carry, t, u, v uint64 + var hi, lo uint64 + var count int + + count = P434p1Zeros + + for i := 0; i < FpWords; i++ { + for j := 0; j < i; j++ { + if j < (i - count + 1) { + hi, lo = bits.Mul64(z[j], P434p1[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + } + v, carry = bits.Add64(v, x[i], 0) + u, carry = bits.Add64(u, 0, carry) + t += carry + + z[i] = v + v = u + u = t + t = 0 + } + + for i := FpWords; i < 2*FpWords-1; i++ { + if count > 0 { + count-- + } + for j := i - FpWords + 1; j < FpWords; j++ { + if j < (FpWords - count) { + hi, lo = bits.Mul64(z[j], P434p1[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + } + v, carry = bits.Add64(v, x[i], 0) + u, carry = bits.Add64(u, 0, carry) + + t += carry + z[i-FpWords] = v + v = u + u = t + t = 0 + } + v, _ = bits.Add64(v, x[2*FpWords-1], 0) + z[FpWords-1] = v +} + +// Compute z = x * y. +func mulP434(z *common.FpX2, x, y *common.Fp) { + var u, v, t uint64 + var hi, lo uint64 + var carry uint64 + + for i := uint64(0); i < FpWords; i++ { + for j := uint64(0); j <= i; j++ { + hi, lo = bits.Mul64(x[j], y[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + z[i] = v + v = u + u = t + t = 0 + } + + for i := FpWords; i < (2*FpWords)-1; i++ { + for j := i - FpWords + 1; j < FpWords; j++ { + hi, lo = bits.Mul64(x[j], y[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + z[i] = v + v = u + u = t + t = 0 + } + z[2*FpWords-1] = v +} + +// Compute z = x + y, without reducing mod p. +func adlP434(z, x, y *common.FpX2) { + var carry uint64 + for i := 0; i < 2*FpWords; i++ { + z[i], carry = bits.Add64(x[i], y[i], carry) + } +} + +// Reduce a field element in [0, 2*p) to one in [0,p). +func modP434(x *common.Fp) { + var borrow, mask uint64 + for i := 0; i < FpWords; i++ { + x[i], borrow = bits.Sub64(x[i], P434[i], borrow) + } + + // Sets all bits if borrow = 1 + mask = 0 - borrow + borrow = 0 + for i := 0; i < FpWords; i++ { + x[i], borrow = bits.Add64(x[i], P434[i]&mask, borrow) + } +} + +// Compute z = x - y, without reducing mod p. +func sulP434(z, x, y *common.FpX2) { + var borrow, mask uint64 + for i := 0; i < 2*FpWords; i++ { + z[i], borrow = bits.Sub64(x[i], y[i], borrow) + } + + // Sets all bits if borrow = 1 + mask = 0 - borrow + borrow = 0 + for i := FpWords; i < 2*FpWords; i++ { + z[i], borrow = bits.Add64(z[i], P434[i-FpWords]&mask, borrow) + } +} diff --git a/src/circl/dh/sidh/internal/p434/arith_test.go b/src/circl/dh/sidh/internal/p434/arith_test.go new file mode 100644 index 00000000000..d6fe171bb81 --- /dev/null +++ b/src/circl/dh/sidh/internal/p434/arith_test.go @@ -0,0 +1,101 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p434 + +import ( + "testing" + + "circl/dh/sidh/internal/common" +) + +// Package-level storage for this field element is intended to deter +// compiler optimizations. +var ( + benchmarkFp common.Fp + benchmarkFpX2 common.FpX2 + bench_x = common.Fp{17026702066521327207, 5108203422050077993, 10225396685796065916, 11153620995215874678, 6531160855165088358, 15302925148404145445, 1248821577836769963, 9789766903037985294, 7493111552032041328, 10838999828319306046, 18103257655515297935, 27403304611634} + bench_y = common.Fp{4227467157325093378, 10699492810770426363, 13500940151395637365, 12966403950118934952, 16517692605450415877, 13647111148905630666, 14223628886152717087, 7167843152346903316, 15855377759596736571, 4300673881383687338, 6635288001920617779, 30486099554235} + bench_z = common.FpX2{1595347748594595712, 10854920567160033970, 16877102267020034574, 12435724995376660096, 3757940912203224231, 8251999420280413600, 3648859773438820227, 17622716832674727914, 11029567000887241528, 11216190007549447055, 17606662790980286987, 4720707159513626555, 12887743598335030915, 14954645239176589309, 14178817688915225254, 1191346797768989683, 12629157932334713723, 6348851952904485603, 16444232588597434895, 7809979927681678066, 14642637672942531613, 3092657597757640067, 10160361564485285723, 240071237} +) + +func TestFpCswap(t *testing.T) { + var one = common.Fp{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} + var two = common.Fp{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2} + + var x = one + var y = two + + cswapP434(&x, &y, 0) + for i := 0; i < FpWords; i++ { + if (x[i] != one[i]) || (y[i] != two[i]) { + t.Error("Found", x, "expected", two) + } + } + + cswapP434(&x, &y, 1) + for i := 0; i < FpWords; i++ { + if (x[i] != two[i]) || (y[i] != one[i]) { + t.Error("Found", x, "expected", two) + } + } +} + +// Benchmarking for field arithmetic +func BenchmarkMul(b *testing.B) { + for n := 0; n < b.N; n++ { + mulP434(&benchmarkFpX2, &bench_x, &bench_y) + } +} + +func BenchmarkRdc(b *testing.B) { + z := bench_z + + // This benchmark actually computes garbage, because + // rdcP434 mangles its input, but since it's + // constant-time that shouldn't matter for the benchmarks. + for n := 0; n < b.N; n++ { + rdcP434(&benchmarkFp, &z) + } +} + +func BenchmarkAdd(b *testing.B) { + for n := 0; n < b.N; n++ { + addP434(&benchmarkFp, &bench_x, &bench_y) + } +} + +func BenchmarkSub(b *testing.B) { + for n := 0; n < b.N; n++ { + subP434(&benchmarkFp, &bench_x, &bench_y) + } +} + +func BenchmarkCswap(b *testing.B) { + x, y := bench_x, bench_y + for n := 0; n < b.N; n++ { + cswapP434(&x, &y, 1) + cswapP434(&x, &y, 0) + } +} + +func BenchmarkMod(b *testing.B) { + x := bench_x + for n := 0; n < b.N; n++ { + modP434(&x) + } +} + +func BenchmarkX2AddLazy(b *testing.B) { + x, y, z := bench_z, bench_z, bench_z + for n := 0; n < b.N; n++ { + adlP434(&x, &y, &z) + } +} + +func BenchmarkX2SubLazy(b *testing.B) { + x, y, z := bench_z, bench_z, bench_z + for n := 0; n < b.N; n++ { + sulP434(&x, &y, &z) + } +} diff --git a/src/circl/dh/sidh/internal/p434/core.go b/src/circl/dh/sidh/internal/p434/core.go new file mode 100644 index 00000000000..f410d45ae67 --- /dev/null +++ b/src/circl/dh/sidh/internal/p434/core.go @@ -0,0 +1,282 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p434 + +import ( + . "circl/dh/sidh/internal/common" +) + +// ----------------------------------------------------------------------------- +// Functions for traversing isogeny trees acoording to strategy. Key type 'A' is +// + +// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed +// for public key generation. +func traverseTreePublicKeyA(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny4 + + cparam := CalcCurveParamsEquiv4(curve) + strat := params.A.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow2k(xR, &cparam, 2*k) + i += int(k) + } + cparam = phi.GenerateCurve(xR) + + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + *phiP = phi.EvaluatePoint(phiP) + *phiQ = phi.EvaluatePoint(phiQ) + *phiR = phi.EvaluatePoint(phiR) + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Traverses isogeny tree in order to compute xR needed +// for public key generation. +func traverseTreeSharedKeyA(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny4 + + cparam := CalcCurveParamsEquiv4(curve) + strat := params.A.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow2k(xR, &cparam, 2*k) + i += int(k) + } + cparam = phi.GenerateCurve(xR) + + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed +// for public key generation. +func traverseTreePublicKeyB(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny3 + + cparam := CalcCurveParamsEquiv3(curve) + strat := params.B.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow3k(xR, &cparam, k) + i += int(k) + } + + cparam = phi.GenerateCurve(xR) + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + + *phiP = phi.EvaluatePoint(phiP) + *phiQ = phi.EvaluatePoint(phiQ) + *phiR = phi.EvaluatePoint(phiR) + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed +// for public key generation. +func traverseTreeSharedKeyB(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny3 + + cparam := CalcCurveParamsEquiv3(curve) + strat := params.B.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow3k(xR, &cparam, k) + i += int(k) + } + + cparam = phi.GenerateCurve(xR) + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Generate a public key in the 2-torsion group. Public key is a set +// of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) +func PublicKeyGenA(pub3Pt *[3]Fp2, prvBytes []byte) { + var xPA, xQA, xRA ProjectivePoint + var xPB, xQB, xRB, xR ProjectivePoint + var invZP, invZQ, invZR Fp2 + var phi isogeny4 + + // Load points for A + xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} + xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} + xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} + + // Load points for B + xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} + xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} + xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} + + // Find isogeny kernel + xR = ScalarMul3Pt(¶ms.InitCurve, &xPA, &xQA, &xRA, params.A.SecretBitLen, prvBytes) + traverseTreePublicKeyA(¶ms.InitCurve, &xR, &xPB, &xQB, &xRB) + + // Secret isogeny + phi.GenerateCurve(&xR) + xPA = phi.EvaluatePoint(&xPB) + xQA = phi.EvaluatePoint(&xQB) + xRA = phi.EvaluatePoint(&xRB) + Fp2Batch3Inv(&xPA.Z, &xQA.Z, &xRA.Z, &invZP, &invZQ, &invZR) + + mul(&pub3Pt[0], &xPA.X, &invZP) + mul(&pub3Pt[1], &xQA.X, &invZQ) + mul(&pub3Pt[2], &xRA.X, &invZR) +} + +// Generate a public key in the 2-torsion group. Public key is a set +// of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) +func PublicKeyGenB(pub3Pt *[3]Fp2, prvBytes []byte) { + var xPB, xQB, xRB, xR ProjectivePoint + var xPA, xQA, xRA ProjectivePoint + var invZP, invZQ, invZR Fp2 + var phi isogeny3 + + // Load points for B + xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} + xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} + xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} + + // Load points for A + xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} + xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} + xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} + + // Find isogeny kernel + xR = ScalarMul3Pt(¶ms.InitCurve, &xPB, &xQB, &xRB, params.B.SecretBitLen, prvBytes) + traverseTreePublicKeyB(¶ms.InitCurve, &xR, &xPA, &xQA, &xRA) + + phi.GenerateCurve(&xR) + xPB = phi.EvaluatePoint(&xPA) + xQB = phi.EvaluatePoint(&xQA) + xRB = phi.EvaluatePoint(&xRA) + Fp2Batch3Inv(&xPB.Z, &xQB.Z, &xRB.Z, &invZP, &invZQ, &invZR) + + mul(&pub3Pt[0], &xPB.X, &invZP) + mul(&pub3Pt[1], &xQB.X, &invZQ) + mul(&pub3Pt[2], &xRB.X, &invZR) +} + +// ----------------------------------------------------------------------------- +// Key agreement functions +// + +// Establishing shared keys in in 2-torsion group +func DeriveSecretA(ss, prv []byte, pub3Pt *[3]Fp2) { + var xP, xQ, xQmP ProjectivePoint + var xR ProjectivePoint + var phi isogeny4 + var jInv Fp2 + + // Recover curve coefficients + cparam := params.InitCurve + RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) + + // Find kernel of the morphism + xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} + xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} + xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} + xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.A.SecretBitLen, prv) + + // Traverse isogeny tree + traverseTreeSharedKeyA(&cparam, &xR) + + // Calculate j-invariant on isogeneus curve + c := phi.GenerateCurve(&xR) + RecoverCurveCoefficients4(&cparam, &c) + Jinvariant(&cparam, &jInv) + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(ss, &jInv, params.Bytelen) +} + +// Establishing shared keys in in 3-torsion group +func DeriveSecretB(ss, prv []byte, pub3Pt *[3]Fp2) { + var xP, xQ, xQmP ProjectivePoint + var xR ProjectivePoint + var phi isogeny3 + var jInv Fp2 + + // Recover curve coefficients + cparam := params.InitCurve + RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) + + // Find kernel of the morphism + xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} + xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} + xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} + xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.B.SecretBitLen, prv) + + // Traverse isogeny tree + traverseTreeSharedKeyB(&cparam, &xR) + + // Calculate j-invariant on isogeneus curve + c := phi.GenerateCurve(&xR) + RecoverCurveCoefficients3(&cparam, &c) + Jinvariant(&cparam, &jInv) + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(ss, &jInv, params.Bytelen) +} diff --git a/src/circl/dh/sidh/internal/p434/curve.go b/src/circl/dh/sidh/internal/p434/curve.go new file mode 100644 index 00000000000..94476d5f9db --- /dev/null +++ b/src/circl/dh/sidh/internal/p434/curve.go @@ -0,0 +1,362 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p434 + +import ( + . "circl/dh/sidh/internal/common" +) + +// Stores isogeny 3 curve constants +type isogeny3 struct { + K1 Fp2 + K2 Fp2 +} + +// Stores isogeny 4 curve constants +type isogeny4 struct { + isogeny3 + K3 Fp2 +} + +// Computes j-invariant for a curve y2=x3+A/Cx+x with A,C in F_(p^2). Result +// is returned in jBytes buffer, encoded in little-endian format. Caller +// provided jBytes buffer has to be big enough to j-invariant value. In case +// of SIDH, buffer size must be at least size of shared secret. +// Implementation corresponds to Algorithm 9 from SIKE. +func Jinvariant(cparams *ProjectiveCurveParameters, j *Fp2) { + var t0, t1 Fp2 + + sqr(j, &cparams.A) // j = A^2 + sqr(&t1, &cparams.C) // t1 = C^2 + add(&t0, &t1, &t1) // t0 = t1 + t1 + sub(&t0, j, &t0) // t0 = j - t0 + sub(&t0, &t0, &t1) // t0 = t0 - t1 + sub(j, &t0, &t1) // t0 = t0 - t1 + sqr(&t1, &t1) // t1 = t1^2 + mul(j, j, &t1) // j = j * t1 + add(&t0, &t0, &t0) // t0 = t0 + t0 + add(&t0, &t0, &t0) // t0 = t0 + t0 + sqr(&t1, &t0) // t1 = t0^2 + mul(&t0, &t0, &t1) // t0 = t0 * t1 + add(&t0, &t0, &t0) // t0 = t0 + t0 + add(&t0, &t0, &t0) // t0 = t0 + t0 + inv(j, j) // j = 1/j + mul(j, &t0, j) // j = t0 * j +} + +// Given affine points x(P), x(Q) and x(Q-P) in a extension field F_{p^2}, function +// recorvers projective coordinate A of a curve. This is Algorithm 10 from SIKE. +func RecoverCoordinateA(curve *ProjectiveCurveParameters, xp, xq, xr *Fp2) { + var t0, t1 Fp2 + + add(&t1, xp, xq) // t1 = Xp + Xq + mul(&t0, xp, xq) // t0 = Xp * Xq + mul(&curve.A, xr, &t1) // A = X(q-p) * t1 + add(&curve.A, &curve.A, &t0) // A = A + t0 + mul(&t0, &t0, xr) // t0 = t0 * X(q-p) + sub(&curve.A, &curve.A, ¶ms.OneFp2) // A = A - 1 + add(&t0, &t0, &t0) // t0 = t0 + t0 + add(&t1, &t1, xr) // t1 = t1 + X(q-p) + add(&t0, &t0, &t0) // t0 = t0 + t0 + sqr(&curve.A, &curve.A) // A = A^2 + inv(&t0, &t0) // t0 = 1/t0 + mul(&curve.A, &curve.A, &t0) // A = A * t0 + sub(&curve.A, &curve.A, &t1) // A = A - t1 +} + +// Computes equivalence (A:C) ~ (A+2C : A-2C) +func CalcCurveParamsEquiv3(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { + var coef CurveCoefficientsEquiv + var c2 Fp2 + + add(&c2, &cparams.C, &cparams.C) + // A24p = A+2*C + add(&coef.A, &cparams.A, &c2) + // A24m = A-2*C + sub(&coef.C, &cparams.A, &c2) + return coef +} + +// Computes equivalence (A:C) ~ (A+2C : 4C) +func CalcCurveParamsEquiv4(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { + var coefEq CurveCoefficientsEquiv + + add(&coefEq.C, &cparams.C, &cparams.C) + // A24p = A+2C + add(&coefEq.A, &cparams.A, &coefEq.C) + // C24 = 4*C + add(&coefEq.C, &coefEq.C, &coefEq.C) + return coefEq +} + +// Helper function for RightToLeftLadder(). Returns A+2C / 4. +func CalcAplus2Over4(cparams *ProjectiveCurveParameters) (ret Fp2) { + var tmp Fp2 + + // 2C + add(&tmp, &cparams.C, &cparams.C) + // A+2C + add(&ret, &cparams.A, &tmp) + // 1/4C + add(&tmp, &tmp, &tmp) + inv(&tmp, &tmp) + // A+2C/4C + mul(&ret, &ret, &tmp) + return +} + +// Recovers (A:C) curve parameters from projectively equivalent (A+2C:A-2C). +func RecoverCurveCoefficients3(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { + add(&cparams.A, &coefEq.A, &coefEq.C) + // cparams.A = 2*(A+2C+A-2C) = 4A + add(&cparams.A, &cparams.A, &cparams.A) + // cparams.C = (A+2C-A+2C) = 4C + sub(&cparams.C, &coefEq.A, &coefEq.C) + return +} + +// Recovers (A:C) curve parameters from projectively equivalent (A+2C:4C). +func RecoverCurveCoefficients4(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { + // cparams.C = (4C)*1/2=2C + mul(&cparams.C, &coefEq.C, ¶ms.HalfFp2) + // cparams.A = A+2C - 2C = A + sub(&cparams.A, &coefEq.A, &cparams.C) + // cparams.C = 2C * 1/2 = C + mul(&cparams.C, &cparams.C, ¶ms.HalfFp2) +} + +// Combined coordinate doubling and differential addition. Takes projective points +// P,Q,Q-P and (A+2C)/4C curve E coefficient. Returns 2*P and P+Q calculated on E. +// Function is used only by RightToLeftLadder. Corresponds to Algorithm 5 of SIKE +func xDbladd(P, Q, QmP *ProjectivePoint, a24 *Fp2) (dblP, PaQ ProjectivePoint) { + var t0, t1, t2 Fp2 + + xQmP, zQmP := &QmP.X, &QmP.Z + xPaQ, zPaQ := &PaQ.X, &PaQ.Z + x2P, z2P := &dblP.X, &dblP.Z + xP, zP := &P.X, &P.Z + xQ, zQ := &Q.X, &Q.Z + + add(&t0, xP, zP) // t0 = Xp+Zp + sub(&t1, xP, zP) // t1 = Xp-Zp + sqr(x2P, &t0) // 2P.X = t0^2 + sub(&t2, xQ, zQ) // t2 = Xq-Zq + add(xPaQ, xQ, zQ) // Xp+q = Xq+Zq + mul(&t0, &t0, &t2) // t0 = t0 * t2 + mul(z2P, &t1, &t1) // 2P.Z = t1 * t1 + mul(&t1, &t1, xPaQ) // t1 = t1 * Xp+q + sub(&t2, x2P, z2P) // t2 = 2P.X - 2P.Z + mul(x2P, x2P, z2P) // 2P.X = 2P.X * 2P.Z + mul(xPaQ, a24, &t2) // Xp+q = A24 * t2 + sub(zPaQ, &t0, &t1) // Zp+q = t0 - t1 + add(z2P, xPaQ, z2P) // 2P.Z = Xp+q + 2P.Z + add(xPaQ, &t0, &t1) // Xp+q = t0 + t1 + mul(z2P, z2P, &t2) // 2P.Z = 2P.Z * t2 + sqr(zPaQ, zPaQ) // Zp+q = Zp+q ^ 2 + sqr(xPaQ, xPaQ) // Xp+q = Xp+q ^ 2 + mul(zPaQ, xQmP, zPaQ) // Zp+q = Xq-p * Zp+q + mul(xPaQ, zQmP, xPaQ) // Xp+q = Zq-p * Xp+q + return +} + +// Given the curve parameters, xP = x(P), computes xP = x([2^k]P) +// Safe to overlap xP, x2P. +func Pow2k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { + var t0, t1 Fp2 + + x, z := &xP.X, &xP.Z + for i := uint32(0); i < k; i++ { + sub(&t0, x, z) // t0 = Xp - Zp + add(&t1, x, z) // t1 = Xp + Zp + sqr(&t0, &t0) // t0 = t0 ^ 2 + sqr(&t1, &t1) // t1 = t1 ^ 2 + mul(z, ¶ms.C, &t0) // Z2p = C24 * t0 + mul(x, z, &t1) // X2p = Z2p * t1 + sub(&t1, &t1, &t0) // t1 = t1 - t0 + mul(&t0, ¶ms.A, &t1) // t0 = A24+ * t1 + add(z, z, &t0) // Z2p = Z2p + t0 + mul(z, z, &t1) // Zp = Z2p * t1 + } +} + +// Given the curve parameters, xP = x(P), and k >= 0, compute xP = x([3^k]P). +// +// Safe to overlap xP, xR. +func Pow3k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { + var t0, t1, t2, t3, t4, t5, t6 Fp2 + + x, z := &xP.X, &xP.Z + for i := uint32(0); i < k; i++ { + sub(&t0, x, z) // t0 = Xp - Zp + sqr(&t2, &t0) // t2 = t0^2 + add(&t1, x, z) // t1 = Xp + Zp + sqr(&t3, &t1) // t3 = t1^2 + add(&t4, &t1, &t0) // t4 = t1 + t0 + sub(&t0, &t1, &t0) // t0 = t1 - t0 + sqr(&t1, &t4) // t1 = t4^2 + sub(&t1, &t1, &t3) // t1 = t1 - t3 + sub(&t1, &t1, &t2) // t1 = t1 - t2 + mul(&t5, &t3, ¶ms.A) // t5 = t3 * A24+ + mul(&t3, &t3, &t5) // t3 = t5 * t3 + mul(&t6, &t2, ¶ms.C) // t6 = t2 * A24- + mul(&t2, &t2, &t6) // t2 = t2 * t6 + sub(&t3, &t2, &t3) // t3 = t2 - t3 + sub(&t2, &t5, &t6) // t2 = t5 - t6 + mul(&t1, &t2, &t1) // t1 = t2 * t1 + add(&t2, &t3, &t1) // t2 = t3 + t1 + sqr(&t2, &t2) // t2 = t2^2 + mul(x, &t2, &t4) // X3p = t2 * t4 + sub(&t1, &t3, &t1) // t1 = t3 - t1 + sqr(&t1, &t1) // t1 = t1^2 + mul(z, &t1, &t0) // Z3p = t1 * t0 + } +} + +// Set (y1, y2, y3) = (1/x1, 1/x2, 1/x3). +// +// All xi, yi must be distinct. +func Fp2Batch3Inv(x1, x2, x3, y1, y2, y3 *Fp2) { + var x1x2, t Fp2 + + mul(&x1x2, x1, x2) // x1*x2 + mul(&t, &x1x2, x3) // 1/(x1*x2*x3) + inv(&t, &t) + mul(y1, &t, x2) // 1/x1 + mul(y1, y1, x3) + mul(y2, &t, x1) // 1/x2 + mul(y2, y2, x3) + mul(y3, &t, &x1x2) // 1/x3 +} + +// Scalarmul3Pt is a right-to-left point multiplication that given the +// x-coordinate of P, Q and P-Q calculates the x-coordinate of R=Q+[scalar]P. +// nbits must be smaller or equal to len(scalar). +func ScalarMul3Pt(cparams *ProjectiveCurveParameters, P, Q, PmQ *ProjectivePoint, nbits uint, scalar []uint8) ProjectivePoint { + var R0, R2, R1 ProjectivePoint + aPlus2Over4 := CalcAplus2Over4(cparams) + R1 = *P + R2 = *PmQ + R0 = *Q + + // Iterate over the bits of the scalar, bottom to top + prevBit := uint8(0) + for i := uint(0); i < nbits; i++ { + bit := (scalar[i>>3] >> (i & 7) & 1) + swap := prevBit ^ bit + prevBit = bit + cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, swap) + R0, R2 = xDbladd(&R0, &R2, &R1, &aPlus2Over4) + } + cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, prevBit) + return R1 +} + +// Given a three-torsion point p = x(PB) on the curve E_(A:C), construct the +// three-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). +// +// Input: (XP_3: ZP_3), where P_3 has exact order 3 on E_A/C +// Output: * Curve coordinates (A' + 2C', A' - 2C') corresponding to E_A'/C' = A_E/C/ +// * Isogeny phi with constants in F_p^2 +func (phi *isogeny3) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { + var t0, t1, t2, t3, t4 Fp2 + var coefEq CurveCoefficientsEquiv + var K1, K2 = &phi.K1, &phi.K2 + + sub(K1, &p.X, &p.Z) // K1 = XP3 - ZP3 + sqr(&t0, K1) // t0 = K1^2 + add(K2, &p.X, &p.Z) // K2 = XP3 + ZP3 + sqr(&t1, K2) // t1 = K2^2 + add(&t2, &t0, &t1) // t2 = t0 + t1 + add(&t3, K1, K2) // t3 = K1 + K2 + sqr(&t3, &t3) // t3 = t3^2 + sub(&t3, &t3, &t2) // t3 = t3 - t2 + add(&t2, &t1, &t3) // t2 = t1 + t3 + add(&t3, &t3, &t0) // t3 = t3 + t0 + add(&t4, &t3, &t0) // t4 = t3 + t0 + add(&t4, &t4, &t4) // t4 = t4 + t4 + add(&t4, &t1, &t4) // t4 = t1 + t4 + mul(&coefEq.C, &t2, &t4) // A24m = t2 * t4 + add(&t4, &t1, &t2) // t4 = t1 + t2 + add(&t4, &t4, &t4) // t4 = t4 + t4 + add(&t4, &t0, &t4) // t4 = t0 + t4 + mul(&t4, &t3, &t4) // t4 = t3 * t4 + sub(&t0, &t4, &coefEq.C) // t0 = t4 - A24m + add(&coefEq.A, &coefEq.C, &t0) // A24p = A24m + t0 + return coefEq +} + +// Given a 3-isogeny phi and a point pB = x(PB), compute x(QB), the x-coordinate +// of the image QB = phi(PB) of PB under phi : E_(A:C) -> E_(A':C'). +// +// The output xQ = x(Q) is then a point on the curve E_(A':C'); the curve +// parameters are returned by the GenerateCurve function used to construct phi. +func (phi *isogeny3) EvaluatePoint(p *ProjectivePoint) ProjectivePoint { + var t0, t1, t2 Fp2 + var q ProjectivePoint + var K1, K2 = &phi.K1, &phi.K2 + var px, pz = &p.X, &p.Z + + add(&t0, px, pz) // t0 = XQ + ZQ + sub(&t1, px, pz) // t1 = XQ - ZQ + mul(&t0, K1, &t0) // t2 = K1 * t0 + mul(&t1, K2, &t1) // t1 = K2 * t1 + add(&t2, &t0, &t1) // t2 = t0 + t1 + sub(&t0, &t1, &t0) // t0 = t1 - t0 + sqr(&t2, &t2) // t2 = t2 ^ 2 + sqr(&t0, &t0) // t0 = t0 ^ 2 + mul(&q.X, px, &t2) // XQ'= XQ * t2 + mul(&q.Z, pz, &t0) // ZQ'= ZQ * t0 + return q +} + +// Given a four-torsion point p = x(PB) on the curve E_(A:C), construct the +// four-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). +// +// Input: (XP_4: ZP_4), where P_4 has exact order 4 on E_A/C +// Output: * Curve coordinates (A' + 2C', 4C') corresponding to E_A'/C' = A_E/C/ +// * Isogeny phi with constants in F_p^2 +func (phi *isogeny4) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { + var coefEq CurveCoefficientsEquiv + var xp4, zp4 = &p.X, &p.Z + var K1, K2, K3 = &phi.K1, &phi.K2, &phi.K3 + + sub(K2, xp4, zp4) + add(K3, xp4, zp4) + sqr(K1, zp4) + add(K1, K1, K1) + sqr(&coefEq.C, K1) + add(K1, K1, K1) + sqr(&coefEq.A, xp4) + add(&coefEq.A, &coefEq.A, &coefEq.A) + sqr(&coefEq.A, &coefEq.A) + return coefEq +} + +// Given a 4-isogeny phi and a point xP = x(P), compute x(Q), the x-coordinate +// of the image Q = phi(P) of P under phi : E_(A:C) -> E_(A':C'). +// +// Input: Isogeny returned by GenerateCurve and point q=(Qx,Qz) from E0_A/C +// Output: Corresponding point q from E1_A'/C', where E1 is 4-isogenous to E0 +func (phi *isogeny4) EvaluatePoint(p *ProjectivePoint) ProjectivePoint { + var t0, t1 Fp2 + var q = *p + var xq, zq = &q.X, &q.Z + var K1, K2, K3 = &phi.K1, &phi.K2, &phi.K3 + + add(&t0, xq, zq) + sub(&t1, xq, zq) + mul(xq, &t0, K2) + mul(zq, &t1, K3) + mul(&t0, &t0, &t1) + mul(&t0, &t0, K1) + add(&t1, xq, zq) + sub(zq, xq, zq) + sqr(&t1, &t1) + sqr(zq, zq) + add(xq, &t0, &t1) + sub(&t0, zq, &t0) + mul(xq, xq, &t1) + mul(zq, zq, &t0) + return q +} diff --git a/src/circl/dh/sidh/internal/p434/curve_test.go b/src/circl/dh/sidh/internal/p434/curve_test.go new file mode 100644 index 00000000000..d054f9ca1ca --- /dev/null +++ b/src/circl/dh/sidh/internal/p434/curve_test.go @@ -0,0 +1,100 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p434 + +import ( + "bytes" + "testing" + + . "circl/dh/sidh/internal/common" +) + +func vartimeEqProjFp2(lhs, rhs *ProjectivePoint) bool { + var t0, t1 Fp2 + mul(&t0, &lhs.X, &rhs.Z) + mul(&t1, &lhs.Z, &rhs.X) + return vartimeEqFp2(&t0, &t1) +} + +func toAffine(point *ProjectivePoint) *Fp2 { + var affineX Fp2 + inv(&affineX, &point.Z) + mul(&affineX, &affineX, &point.X) + return &affineX +} + +func Test_jInvariant(t *testing.T) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + var jbufRes = make([]byte, params.SharedSecretSize) + var jbufExp = make([]byte, params.SharedSecretSize) + var jInv Fp2 + + Jinvariant(&curve, &jInv) + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(jbufRes, &jInv, params.Bytelen) + + jInv = expectedJ + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(jbufExp, &jInv, params.Bytelen) + + if !bytes.Equal(jbufRes[:], jbufExp[:]) { + t.Error("Computed incorrect j-invariant: found\n", jbufRes, "\nexpected\n", jbufExp) + } +} + +func TestProjectivePointVartimeEq(t *testing.T) { + var xP ProjectivePoint + + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + xQ := xP + + // Scale xQ, which results in the same projective point + mul(&xQ.X, &xQ.X, &curveA) + mul(&xQ.Z, &xQ.Z, &curveA) + if !vartimeEqProjFp2(&xP, &xQ) { + t.Error("Expected the scaled point to be equal to the original") + } +} + +func TestPointMulVersusSage(t *testing.T) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + var cparams = CalcCurveParamsEquiv4(&curve) + var xP ProjectivePoint + + // x 2 + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + Pow2k(&xP, &cparams, 1) + afxQ := toAffine(&xP) + if !vartimeEqFp2(afxQ, &affineXP2) { + t.Error("\nExpected\n", affineXP2, "\nfound\n", afxQ) + } + + // x 4 + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + Pow2k(&xP, &cparams, 2) + afxQ = toAffine(&xP) + if !vartimeEqFp2(afxQ, &affineXP4) { + t.Error("\nExpected\n", affineXP4, "\nfound\n", afxQ) + } +} + +func TestPointMul9VersusSage(t *testing.T) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + var cparams = CalcCurveParamsEquiv3(&curve) + var xP ProjectivePoint + + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + Pow3k(&xP, &cparams, 2) + afxQ := toAffine(&xP) + if !vartimeEqFp2(afxQ, &affineXP9) { + t.Error("\nExpected\n", affineXP9, "\nfound\n", afxQ) + } +} + +func BenchmarkThreePointLadder(b *testing.B) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + for n := 0; n < b.N; n++ { + ScalarMul3Pt(&curve, &threePointLadderInputs[0], &threePointLadderInputs[1], &threePointLadderInputs[2], uint(len(scalar3Pt)*8), scalar3Pt[:]) + } +} diff --git a/src/circl/dh/sidh/internal/p434/fp2.go b/src/circl/dh/sidh/internal/p434/fp2.go new file mode 100644 index 00000000000..911fe3b4000 --- /dev/null +++ b/src/circl/dh/sidh/internal/p434/fp2.go @@ -0,0 +1,195 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p434 + +import ( + "circl/dh/sidh/internal/common" +) + +// Montgomery multiplication. Input values must be already +// in Montgomery domain. +func mulP(dest, lhs, rhs *common.Fp) { + var ab common.FpX2 + mulP434(&ab, lhs, rhs) // = a*b*R*R + rdcP434(dest, &ab) // = a*b*R mod p +} + +// Set dest = x^((p-3)/4). If x is square, this is 1/sqrt(x). +// Uses variation of sliding-window algorithm from with window size +// of 5 and least to most significant bit sliding (left-to-right) +// See HAC 14.85 for general description. +// +// Allowed to overlap x with dest. +// All values in Montgomery domains +// Set dest = x^(2^k), for k >= 1, by repeated squarings. +func p34(dest, x *common.Fp) { + var lookup [16]common.Fp + + // This performs sum(powStrategy) + 1 squarings and len(lookup) + len(mulStrategy) + // multiplications. + powStrategy := []uint8{3, 10, 7, 5, 6, 5, 3, 8, 4, 7, 5, 6, 4, 5, 9, 6, 3, 11, 5, 5, 2, 8, 4, 7, 7, 8, 5, 6, 4, 8, 5, 2, 10, 6, 5, 4, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1} + mulStrategy := []uint8{2, 15, 9, 8, 14, 12, 2, 8, 5, 15, 8, 15, 6, 6, 3, 2, 0, 10, 9, 13, 1, 12, 3, 7, 1, 10, 8, 11, 2, 15, 14, 1, 11, 12, 14, 3, 11, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0} + initialMul := uint8(8) + + // Precompute lookup table of odd multiples of x for window + // size k=5. + var xx common.Fp + mulP(&xx, x, x) + lookup[0] = *x + for i := 1; i < 16; i++ { + mulP(&lookup[i], &lookup[i-1], &xx) + } + + // Now lookup = {x, x^3, x^5, ... } + // so that lookup[i] = x^{2*i + 1} + // so that lookup[k/2] = x^k, for odd k + *dest = lookup[initialMul] + for i := uint8(0); i < uint8(len(powStrategy)); i++ { + mulP(dest, dest, dest) + for j := uint8(1); j < powStrategy[i]; j++ { + mulP(dest, dest, dest) + } + mulP(dest, dest, &lookup[mulStrategy[i]]) + } +} + +func add(dest, lhs, rhs *common.Fp2) { + addP434(&dest.A, &lhs.A, &rhs.A) + addP434(&dest.B, &lhs.B, &rhs.B) +} + +func sub(dest, lhs, rhs *common.Fp2) { + subP434(&dest.A, &lhs.A, &rhs.A) + subP434(&dest.B, &lhs.B, &rhs.B) +} + +func mul(dest, lhs, rhs *common.Fp2) { + var bMinA, cMinD common.Fp + var ac, bd common.FpX2 + var adPlusBc common.FpX2 + var acMinBd common.FpX2 + + // Let (a,b,c,d) = (lhs.a,lhs.b,rhs.a,rhs.b). + // + // (a + bi)*(c + di) = (a*c - b*d) + (a*d + b*c)i + // + // Use Karatsuba's trick: note that + // + // (b - a)*(c - d) = (b*c + a*d) - a*c - b*d + // + // so (a*d + b*c) = (b-a)*(c-d) + a*c + b*d. + mulP434(&ac, &lhs.A, &rhs.A) // = a*c*R*R + mulP434(&bd, &lhs.B, &rhs.B) // = b*d*R*R + subP434(&bMinA, &lhs.B, &lhs.A) // = (b-a)*R + subP434(&cMinD, &rhs.A, &rhs.B) // = (c-d)*R + mulP434(&adPlusBc, &bMinA, &cMinD) // = (b-a)*(c-d)*R*R + adlP434(&adPlusBc, &adPlusBc, &ac) // = ((b-a)*(c-d) + a*c)*R*R + adlP434(&adPlusBc, &adPlusBc, &bd) // = ((b-a)*(c-d) + a*c + b*d)*R*R + rdcP434(&dest.B, &adPlusBc) // = (a*d + b*c)*R mod p + sulP434(&acMinBd, &ac, &bd) // = (a*c - b*d)*R*R + rdcP434(&dest.A, &acMinBd) // = (a*c - b*d)*R mod p +} + +// Set dest = 1/x +// +// Allowed to overlap dest with x. +// +// Returns dest to allow chaining operations. +func inv(dest, x *common.Fp2) { + var e1, e2 common.FpX2 + var f1, f2 common.Fp + + // We want to compute + // + // 1 1 (a - bi) (a - bi) + // -------- = -------- -------- = ----------- + // (a + bi) (a + bi) (a - bi) (a^2 + b^2) + // + // Letting c = 1/(a^2 + b^2), this is + // + // 1/(a+bi) = a*c - b*ci. + + mulP434(&e1, &x.A, &x.A) // = a*a*R*R + mulP434(&e2, &x.B, &x.B) // = b*b*R*R + adlP434(&e1, &e1, &e2) // = (a^2 + b^2)*R*R + rdcP434(&f1, &e1) // = (a^2 + b^2)*R mod p + // Now f1 = a^2 + b^2 + + mulP(&f2, &f1, &f1) + p34(&f2, &f2) + mulP(&f2, &f2, &f2) + mulP(&f2, &f2, &f1) + + mulP434(&e1, &x.A, &f2) + rdcP434(&dest.A, &e1) + + subP434(&f1, &common.Fp{}, &x.B) + mulP434(&e1, &f1, &f2) + rdcP434(&dest.B, &e1) +} + +func sqr(dest, x *common.Fp2) { + var a2, aPlusB, aMinusB common.Fp + var a2MinB2, ab2 common.FpX2 + + a := &x.A + b := &x.B + + // (a + bi)*(a + bi) = (a^2 - b^2) + 2abi. + addP434(&a2, a, a) // = a*R + a*R = 2*a*R + addP434(&aPlusB, a, b) // = a*R + b*R = (a+b)*R + subP434(&aMinusB, a, b) // = a*R - b*R = (a-b)*R + mulP434(&a2MinB2, &aPlusB, &aMinusB) // = (a+b)*(a-b)*R*R = (a^2 - b^2)*R*R + mulP434(&ab2, &a2, b) // = 2*a*b*R*R + rdcP434(&dest.A, &a2MinB2) // = (a^2 - b^2)*R mod p + rdcP434(&dest.B, &ab2) // = 2*a*b*R mod p +} + +// In case choice == 1, performs following swap in constant time: +// xPx <-> xQx +// xPz <-> xQz +// Otherwise returns xPx, xPz, xQx, xQz unchanged +func cswap(xPx, xPz, xQx, xQz *common.Fp2, choice uint8) { + cswapP434(&xPx.A, &xQx.A, choice) + cswapP434(&xPx.B, &xQx.B, choice) + cswapP434(&xPz.A, &xQz.A, choice) + cswapP434(&xPz.B, &xQz.B, choice) +} + +// Converts in.A and in.B to Montgomery domain and stores +// in 'out' +// out.A = in.A * R mod p +// out.B = in.B * R mod p +// Performs v = v*R^2*R^(-1) mod p, for both in.A and in.B +func ToMontgomery(out, in *common.Fp2) { + var aRR common.FpX2 + + // a*R*R + mulP434(&aRR, &in.A, &P434R2) + // a*R mod p + rdcP434(&out.A, &aRR) + mulP434(&aRR, &in.B, &P434R2) + rdcP434(&out.B, &aRR) +} + +// Converts in.A and in.B from Montgomery domain and stores +// in 'out' +// out.A = in.A mod p +// out.B = in.B mod p +// +// After returning from the call 'in' is not modified. +func FromMontgomery(out, in *common.Fp2) { + var aR common.FpX2 + + // convert from montgomery domain + copy(aR[:], in.A[:]) + rdcP434(&out.A, &aR) // = a mod p in [0, 2p) + modP434(&out.A) // = a mod p in [0, p) + for i := range aR { + aR[i] = 0 + } + copy(aR[:], in.B[:]) + rdcP434(&out.B, &aR) + modP434(&out.B) +} diff --git a/src/circl/dh/sidh/internal/p434/fp2_test.go b/src/circl/dh/sidh/internal/p434/fp2_test.go new file mode 100644 index 00000000000..e3107330b37 --- /dev/null +++ b/src/circl/dh/sidh/internal/p434/fp2_test.go @@ -0,0 +1,245 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p434 + +import ( + "math/rand" + "reflect" + "testing" + "testing/quick" + + "circl/dh/sidh/internal/common" +) + +type testParams struct { + Point common.ProjectivePoint + Cparam common.ProjectiveCurveParameters + ExtElem common.Fp2 +} + +// Returns true if lhs = rhs. Takes variable time. +func vartimeEqFp2(lhs, rhs *common.Fp2) bool { + a := *lhs + b := *rhs + + modP434(&a.A) + modP434(&a.B) + modP434(&b.A) + modP434(&b.B) + + eq := true + for i := 0; i < FpWords && eq; i++ { + eq = eq && (a.A[i] == b.A[i]) + eq = eq && (a.B[i] == b.B[i]) + } + return eq +} + +func (testParams) generateFp2(rand *rand.Rand) common.Fp2 { + // Generation strategy: low limbs taken from [0,2^64); high limb + // taken from smaller range + // + // Size hint is ignored since all elements are fixed size. + // + // Field elements taken in range [0,2p). Emulate this by capping + // the high limb by the top digit of 2*p-1: + // + // sage: (2*p-1).digits(2^64)[-1] + // + // This still allows generating values >= 2p, but hopefully that + // excess is OK (and if it's not, we'll find out, because it's for + // testing...) + highLimb := rand.Uint64() % P434x2[FpWords-1] + fpElementGen := func() (fp common.Fp) { + for i := 0; i < (FpWords - 1); i++ { + fp[i] = rand.Uint64() + } + fp[FpWords-1] = highLimb + return fp + } + return common.Fp2{A: fpElementGen(), B: fpElementGen()} +} + +func (c testParams) Generate(rand *rand.Rand, size int) reflect.Value { + return reflect.ValueOf( + testParams{ + common.ProjectivePoint{ + X: c.generateFp2(rand), + Z: c.generateFp2(rand), + }, + common.ProjectiveCurveParameters{ + A: c.generateFp2(rand), + C: c.generateFp2(rand), + }, + c.generateFp2(rand), + }) +} + +func TestOne(t *testing.T) { + var tmp common.Fp2 + + mul(&tmp, ¶ms.OneFp2, ¶ms.A.AffineP) + if !vartimeEqFp2(&tmp, ¶ms.A.AffineP) { + t.Error("Not equal 1") + } +} + +func TestFp2ToBytesRoundTrip(t *testing.T) { + roundTrips := func(x testParams) bool { + var xBytes = make([]byte, 2*params.Bytelen) + var xPrime common.Fp2 + + common.Fp2ToBytes(xBytes[:], &x.ExtElem, params.Bytelen) + common.BytesToFp2(&xPrime, xBytes[:], params.Bytelen) + return vartimeEqFp2(&xPrime, &x.ExtElem) + } + + if err := quick.Check(roundTrips, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2MulDistributesOverAdd(t *testing.T) { + mulDistributesOverAdd := func(x, y, z testParams) bool { + // Compute t1 = (x+y)*z + t1 := new(common.Fp2) + add(t1, &x.ExtElem, &y.ExtElem) + mul(t1, t1, &z.ExtElem) + + // Compute t2 = x*z + y*z + t2 := new(common.Fp2) + t3 := new(common.Fp2) + mul(t2, &x.ExtElem, &z.ExtElem) + mul(t3, &y.ExtElem, &z.ExtElem) + add(t2, t2, t3) + + return vartimeEqFp2(t1, t2) + } + + if err := quick.Check(mulDistributesOverAdd, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2MulIsAssociative(t *testing.T) { + isAssociative := func(x, y, z testParams) bool { + // Compute t1 = (x*y)*z + t1 := new(common.Fp2) + mul(t1, &x.ExtElem, &y.ExtElem) + mul(t1, t1, &z.ExtElem) + + // Compute t2 = (y*z)*x + t2 := new(common.Fp2) + mul(t2, &y.ExtElem, &z.ExtElem) + mul(t2, t2, &x.ExtElem) + + return vartimeEqFp2(t1, t2) + } + + if err := quick.Check(isAssociative, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2SquareMatchesMul(t *testing.T) { + sqrMatchesMul := func(x testParams) bool { + // Compute t1 = (x*x) + t1 := new(common.Fp2) + mul(t1, &x.ExtElem, &x.ExtElem) + + // Compute t2 = x^2 + t2 := new(common.Fp2) + sqr(t2, &x.ExtElem) + + return vartimeEqFp2(t1, t2) + } + + if err := quick.Check(sqrMatchesMul, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2Inv(t *testing.T) { + inverseIsCorrect := func(x testParams) bool { + z := new(common.Fp2) + inv(z, &x.ExtElem) + + // Now z = (1/x), so (z * x) * x == x + mul(z, z, &x.ExtElem) + mul(z, z, &x.ExtElem) + + return vartimeEqFp2(z, &x.ExtElem) + } + + // This is more expensive; run fewer tests + var quickCheckConfig = &quick.Config{MaxCount: (1 << 11)} + if err := quick.Check(inverseIsCorrect, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2Batch3Inv(t *testing.T) { + batchInverseIsCorrect := func(x1, x2, x3 testParams) bool { + var x1Inv, x2Inv, x3Inv common.Fp2 + inv(&x1Inv, &x1.ExtElem) + inv(&x2Inv, &x2.ExtElem) + inv(&x3Inv, &x3.ExtElem) + + var y1, y2, y3 common.Fp2 + Fp2Batch3Inv(&x1.ExtElem, &x2.ExtElem, &x3.ExtElem, &y1, &y2, &y3) + + return (vartimeEqFp2(&x1Inv, &y1) && vartimeEqFp2(&x2Inv, &y2) && vartimeEqFp2(&x3Inv, &y3)) + } + + // This is more expensive; run fewer tests + var quickCheckConfig = &quick.Config{MaxCount: (1 << 8)} + if err := quick.Check(batchInverseIsCorrect, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func BenchmarkFp2Mul(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + mul(w, z, z) + } +} + +func BenchmarkFp2Inv(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + inv(w, z) + } +} + +func BenchmarkFp2Square(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + sqr(w, z) + } +} + +func BenchmarkFp2Add(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + add(w, z, z) + } +} + +func BenchmarkFp2Sub(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + sub(w, z, z) + } +} diff --git a/src/circl/dh/sidh/internal/p434/params.go b/src/circl/dh/sidh/internal/p434/params.go new file mode 100644 index 00000000000..a383ca49997 --- /dev/null +++ b/src/circl/dh/sidh/internal/p434/params.go @@ -0,0 +1,197 @@ +package p434 + +//go:generate go run ../templates/gen.go P434 + +import ( + "circl/dh/sidh/internal/common" + "internal/cpu" +) + +const ( + // Number of uint64 limbs used to store field element + FpWords = 7 +) + +var ( + // HasADXandBMI2 signals support for ADX and BMI2 + HasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX + + // P434 is a prime used by field Fp434 + P434 = common.Fp{ + 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFDC1767AE2FFFFFF, + 0x7BC65C783158AEA3, 0x6CFC5FD681C52056, 0x2341F27177344, + } + + // P434x2 = 2*p434 - 1 + P434x2 = common.Fp{ + 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFB82ECF5C5FFFFFF, + 0xF78CB8F062B15D47, 0xD9F8BFAD038A40AC, 0x4683E4E2EE688, + } + + // P434p1 = p434 + 1 + P434p1 = common.Fp{ + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xFDC1767AE3000000, + 0x7BC65C783158AEA3, 0x6CFC5FD681C52056, 0x0002341F27177344, + } + + // P434R2 = (2^448)^2 mod p + P434R2 = common.Fp{ + 0x28E55B65DCD69B30, 0xACEC7367768798C2, 0xAB27973F8311688D, 0x175CC6AF8D6C7C0B, + 0xABCD92BF2DDE347E, 0x69E16A61C7686D9A, 0x000025A89BCDD12A, + } + + // 1/2 * R mod p + half = common.Fp2{ + A: common.Fp{ + 0x0000000000003A16, 0x0000000000000000, 0x0000000000000000, 0x5C87FA027E000000, + 0x6C00D27DAACFD66A, 0x74992A2A2FBBA086, 0x0000767753DE976D}, + } + + // 1*R mod p + one = common.Fp2{ + A: common.Fp{ + 0x000000000000742C, 0x0000000000000000, 0x0000000000000000, 0xB90FF404FC000000, + 0xD801A4FB559FACD4, 0xE93254545F77410C, 0x0000ECEEA7BD2EDA}, + } + + // 6*R mod p + six = common.Fp2{ + A: common.Fp{ + 0x000000000002B90A, 0x0000000000000000, 0x0000000000000000, 0x5ADCCB2822000000, + 0x187D24F39F0CAFB4, 0x9D353A4D394145A0, 0x00012559A0403298}, + } + + P434p1Zeros = 3 + + params = common.SidhParams{ + ID: common.Fp434, + // SIDH public key byte size. + PublicKeySize: 330, + // SIDH shared secret byte size. + SharedSecretSize: 110, + InitCurve: common.ProjectiveCurveParameters{ + A: six, + C: one, + }, + A: common.DomainParams{ + // The x-coordinate of PA + AffineP: common.Fp2{ + A: common.Fp{ + 0x05ADF455C5C345BF, 0x91935C5CC767AC2B, 0xAFE4E879951F0257, 0x70E792DC89FA27B1, + 0xF797F526BB48C8CD, 0x2181DB6131AF621F, 0x00000A1C08B1ECC4, + }, + B: common.Fp{ + 0x74840EB87CDA7788, 0x2971AA0ECF9F9D0B, 0xCB5732BDF41715D5, 0x8CD8E51F7AACFFAA, + 0xA7F424730D7E419F, 0xD671EB919A179E8C, 0x0000FFA26C5A924A, + }, + }, + // The x-coordinate of QA + AffineQ: common.Fp2{ + A: common.Fp{ + 0xFEC6E64588B7273B, 0xD2A626D74CBBF1C6, 0xF8F58F07A78098C7, 0xE23941F470841B03, + 0x1B63EDA2045538DD, 0x735CFEB0FFD49215, 0x0001C4CB77542876, + }, + B: common.Fp{ + 0xADB0F733C17FFDD6, 0x6AFFBD037DA0A050, 0x680EC43DB144E02F, 0x1E2E5D5FF524E374, + 0xE2DDA115260E2995, 0xA6E4B552E2EDE508, 0x00018ECCDDF4B53E, + }, + }, + + // The x-coordinate of RA = PA-QA + AffineR: common.Fp2{ + A: common.Fp{ + 0x01BA4DB518CD6C7D, 0x2CB0251FE3CC0611, 0x259B0C6949A9121B, 0x60E17AC16D2F82AD, + 0x3AA41F1CE175D92D, 0x413FBE6A9B9BC4F3, 0x00022A81D8D55643, + }, + B: common.Fp{ + 0xB8ADBC70FC82E54A, 0xEF9CDDB0D5FADDED, 0x5820C734C80096A0, 0x7799994BAA96E0E4, + 0x044961599E379AF8, 0xDB2B94FBF09F27E2, 0x0000B87FC716C0C6, + }, + }, + // Max size of secret key for 2-torsion group, corresponds to 2^e2 - 1 + SecretBitLen: 216, + // SecretBitLen in bytes. + SecretByteLen: 28, + // 2-torsion group computation strategy + IsogenyStrategy: []uint32{ + 0x30, 0x1C, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, + 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, + 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, + 0x02, 0x01, 0x01, 0x0D, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, + 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x04, + 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, + 0x15, 0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, + 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01, + 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05, 0x03, + 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, + 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01}, + }, + B: common.DomainParams{ + // The x-coordinate of PB + AffineP: common.Fp2{ + A: common.Fp{ + 0x6E5497556EDD48A3, 0x2A61B501546F1C05, 0xEB919446D049887D, 0x5864A4A69D450C4F, + 0xB883F276A6490D2B, 0x22CC287022D5F5B9, 0x0001BED4772E551F, + }, + B: common.Fp{ + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + }, + }, + // The x-coordinate of QB + AffineQ: common.Fp2{ + A: common.Fp{ + 0xFAE2A3F93D8B6B8E, 0x494871F51700FE1C, 0xEF1A94228413C27C, 0x498FF4A4AF60BD62, + 0xB00AD2A708267E8A, 0xF4328294E017837F, 0x000034080181D8AE, + }, + B: common.Fp{ + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + }, + }, + // The x-coordinate of RB = PB - QB + AffineR: common.Fp2{ + A: common.Fp{ + 0x283B34FAFEFDC8E4, 0x9208F44977C3E647, 0x7DEAE962816F4E9A, 0x68A2BA8AA262EC9D, + 0x8176F112EA43F45B, 0x02106D022634F504, 0x00007E8A50F02E37, + }, + B: common.Fp{ + 0xB378B7C1DA22CCB1, 0x6D089C99AD1D9230, 0xEBE15711813E2369, 0x2B35A68239D48A53, + 0x445F6FD138407C93, 0xBEF93B29A3F6B54B, 0x000173FA910377D3, + }, + }, + // Size of secret key for 3-torsion group, corresponds to log_2(3^e3) - 1. + SecretBitLen: 217, + // SecretBitLen in bytes. + SecretByteLen: 28, + // 3-torsion group computation strategy + IsogenyStrategy: []uint32{ + 0x42, 0x21, 0x11, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, + 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, + 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, + 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x10, + 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, + 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, + 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, + 0x01, 0x20, 0x10, 0x08, 0x04, 0x03, 0x01, 0x01, 0x01, 0x01, + 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, + 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, + 0x01, 0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, + 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, + 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, + 0x02, 0x01, 0x01, 0x02, 0x01, 0x01}, + }, + OneFp2: one, + HalfFp2: half, + MsgLen: 16, + // SIKEp434 provides 192 bit of classical security ([SIKE], 5.1) + KemSize: 16, + // ceil(434+7/8) + Bytelen: 55, + CiphertextSize: 16 + 330, + } +) + +func init() { + common.Register(common.Fp434, ¶ms) +} diff --git a/src/circl/dh/sidh/internal/p434/params_test.go b/src/circl/dh/sidh/internal/p434/params_test.go new file mode 100644 index 00000000000..e001ce84462 --- /dev/null +++ b/src/circl/dh/sidh/internal/p434/params_test.go @@ -0,0 +1,69 @@ +package p434 + +// Contains values used by tests +import ( + "testing/quick" + + . "circl/dh/sidh/internal/common" +) + +// Values computed using Sage +var ( + expectedJ = Fp2{ + A: Fp{0x38ECC0A0F53BACB4, 0xF987759E90A6C0DD, 0xC3007B353AE699F6, 0xB2B7E62A4F182414, 0xA65A854B34034F1B, 0xC71EAD20BE427422, 0xFC94F0D8DD51}, + B: Fp{0xFC3B47615764A089, 0x9D32DF1BA8CF22E5, 0x7B895EF92F44C690, 0xE83667F85BBFA475, 0xD44627DCF539CA71, 0x9619A0E7D6657401, 0x4BC5BF1D9B01}} + + curveA = Fp2{ + A: Fp{0x13A5A42C36E5E170, 0xC801DC4104E2C1DC, 0xB102AE39A7E24F31, 0x2FB616EA2E824C97, 0xB97073B55448AA67, 0x607266F7204D90DA, 0x1E98FE9739F27}, + B: Fp{0x000000000000742C, 0x0000000000000000, 0x0000000000000000, 0xB90FF404FC000000, 0xD801A4FB559FACD4, 0xE93254545F77410C, 0x0ECEEA7BD2EDA}} + + curveC = Fp2{ + A: Fp{0x8CBBA3505E5EDAB2, 0xB1DE7B91FBB77718, 0x6957392BFDC9BEB0, 0xC258E527E05FDDDE, 0x8C5FC7ADF5E50AE9, 0x1B2149FBEC2F4D18, 0x19FC2A5C79942}, + B: Fp{0x000000000000E858, 0x0000000000000000, 0x0000000000000000, 0x721FE809F8000000, 0xB00349F6AB3F59A9, 0xD264A8A8BEEE8219, 0x1D9DD4F7A5DB5}} + + affineXP = Fp2{ + A: Fp{0x775C29CA29E5FC3F, 0xCAB15BD1A1AB2754, 0x2C7F5B5DC58096EB, 0x2EE7B0B5A789355A, 0xBBD7BC749FF4D74E, 0x1373A265C9A9D58B, 0x5C183CE99B13}, + B: Fp{0x38CDA704EB4D517C, 0x2F8BA33C91C147D4, 0x4D17E97F04A8D431, 0x5DB8F238AE1B099F, 0x44DC758CE879824C, 0x7E95F1151F6DFA3C, 0xB59F64352B87}} + + affineXP2 = Fp2{ + A: Fp{0x2A5C658FD540804D, 0xA27CDB81FA7C6A5C, 0x6C36B6EB38B1B562, 0xC08642D636AF9A51, 0x36B2323A1279F346, 0x530BF3E8726D8B71, 0x61E38F638919}, + B: Fp{0x5D835C52A68FC93D, 0x9E8FAF973A68306C, 0xB3C28FE9D155F61C, 0xCCE6FA22BC1A1FBF, 0xEAB44D8952802BA5, 0xEAAC0F259AAC3A8F, 0x959B242CE01A}} + + affineXP4 = Fp2{ + A: Fp{0xF824931762C6DC4A, 0xA9B0FD30136F4B50, 0xAF041BBAB14DC6B1, 0x0AD52F55527A9BA2, 0x282B236D61F08C59, 0x5D3D7EC0C5EB9DCB, 0x10BBDDEA44BF7}, + B: Fp{0x77D92493AF97245B, 0xD717FEC838D464C6, 0xCAACD67DB3BF965D, 0x82D59FB89CDC0711, 0xF13CAE433F39CDE1, 0x9B55DFB11A585FFA, 0x0DC8BA1C054D3}} + + affineXP9 = Fp2{ + A: Fp{0x1F6F0785353A02C0, 0xCCB1B8524A63E37F, 0xB283C636B1FDD74C, 0xB76DBFF592DE6FF5, 0x15750EE706F18226, 0x50791362F26E459C, 0x1EA2A9074423}, + B: Fp{0x945C6909DA5039A3, 0x349CFD24FD84FDAF, 0x2FD2F391F2E26E75, 0xEF73E8A634EBDC76, 0x59DDA2622AC22A6C, 0xE0370B80E15F61F4, 0xB302956A0276}} + + // Inputs for testing 3-point-ladder + threePointLadderInputs = []ProjectivePoint{ + // x(P) + { + X: Fp2{ + A: Fp{0x43941FA9244C059E, 0xD1F337D076941189, 0x6B6A8B3A8763C96A, 0x6DF569708D6C9482, 0x487EE5707A52F4AA, 0xDE396F6E2559689E, 0xE5EE3895A8991469, 0x2B0946695790A8}, + B: Fp{0xAB552C0FDAED092E, 0x7DF895E43E7DCB1C, 0x35C700E761920C4B, 0xCC5807DD70DC117A, 0x0884039A5A8DB18A, 0xD04620B3D0738052, 0xA200835605138F10, 0x3FF2E59B2FDC6A}}, + Z: params.OneFp2, + }, + // x(Q) + { + X: Fp2{ + A: Fp{0x77015826982BA1FD, 0x44024489673471E4, 0x1CAA2A5F4D5DA63B, 0xA183C07E50738C01, 0x8B97782D4E1A0DE6, 0x9B819522FBC38280, 0x0BDA46A937FB7B8A, 0x3B3614305914DF}, + B: Fp{0xBF0366E97B3168D9, 0xAA522AC3879CEF0F, 0x0AF5EC975BD035C8, 0x1F26FEE7BBAC165C, 0xA0EE6A637724A6AB, 0xFB52101E36BA3A38, 0xD29CF5E376E17376, 0x1374A50DF57071}}, + Z: params.OneFp2, + }, + // x(P-Q) + { + X: Fp2{ + A: Fp{0xD99279BBD41EA559, 0x35CF18E72F578214, 0x90473B1DC77F73E8, 0xBFFEA930B25D7F66, 0xFD558EA177B900B2, 0x7CFAD273A782A23E, 0x6B1F610822E0F611, 0x26D2D2EF9619B5}, + B: Fp{0x534F83651CBCC75D, 0x591FB4757AED5D08, 0x0B04353D40BED542, 0x829A94703AAC9139, 0x0F9C2E6D7663EB5B, 0x5D2D0F90C283F746, 0x34C872AA12A7676E, 0x0ECDB605FBFA16}}, + Z: params.OneFp2, + }, + } + scalar3Pt = [...]uint8{0x9f, 0x3b, 0xe7, 0xf9, 0xf4, 0x7c, 0xe6, 0xce, 0x79, 0x3e, 0x3d, 0x9f, 0x9f, 0x3b, 0xe7, 0xf9, 0xf4, 0x7c, 0xe6, 0xce, 0x79, 0x3e, 0x3d, 0x9f} +) + +var quickCheckConfig = &quick.Config{ + MaxCount: (1 << 15), +} diff --git a/src/circl/dh/sidh/internal/p503/arith_amd64.s b/src/circl/dh/sidh/internal/p503/arith_amd64.s new file mode 100644 index 00000000000..cef846a6823 --- /dev/null +++ b/src/circl/dh/sidh/internal/p503/arith_amd64.s @@ -0,0 +1,1673 @@ +// +build amd64,!noasm + +#include "textflag.h" + +// p503 +#define P503_0 $0xFFFFFFFFFFFFFFFF +#define P503_1 $0xFFFFFFFFFFFFFFFF +#define P503_2 $0xFFFFFFFFFFFFFFFF +#define P503_3 $0xABFFFFFFFFFFFFFF +#define P503_4 $0x13085BDA2211E7A0 +#define P503_5 $0x1B9BF6C87B7E7DAF +#define P503_6 $0x6045C6BDDA77A4D0 +#define P503_7 $0x004066F541811E1E + +// p503+1 +#define P503P1_3 $0xAC00000000000000 +#define P503P1_4 $0x13085BDA2211E7A0 +#define P503P1_5 $0x1B9BF6C87B7E7DAF +#define P503P1_6 $0x6045C6BDDA77A4D0 +#define P503P1_7 $0x004066F541811E1E + +// p503x2 +#define P503X2_0 $0xFFFFFFFFFFFFFFFE +#define P503X2_1 $0xFFFFFFFFFFFFFFFF +#define P503X2_2 $0xFFFFFFFFFFFFFFFF +#define P503X2_3 $0x57FFFFFFFFFFFFFF +#define P503X2_4 $0x2610B7B44423CF41 +#define P503X2_5 $0x3737ED90F6FCFB5E +#define P503X2_6 $0xC08B8D7BB4EF49A0 +#define P503X2_7 $0x0080CDEA83023C3C + +#define REG_P1 DI +#define REG_P2 SI +#define REG_P3 DX + +// Performs schoolbook multiplication of 2 256-bit numbers. This optimized version +// uses MULX instruction. Macro smashes value in DX. +// Input: I0 and I1. +// Output: O +// All the other arguments are registers, used for storing temporary values +#define MULS256_MULX(O, I0, I1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9) \ + MOVQ I0, DX \ + MULXQ I1, T1, T0 \ // T0:T1 = A0*B0 + MOVQ T1, O \ // O[0] + MULXQ 8+I1, T2, T1 \ // T1:T2 = U0*V1 + ADDQ T2, T0 \ + MULXQ 16+I1, T3, T2 \ // T2:T3 = U0*V2 + ADCQ T3, T1 \ + MULXQ 24+I1, T4, T3 \ // T3:T4 = U0*V3 + ADCQ T4, T2 \ + \ // Column U1 + MOVQ 8+I0, DX \ + ADCQ $0, T3 \ + MULXQ 0+I1, T4, T5 \ // T5:T4 = U1*V0 + MULXQ 8+I1, T7, T6 \ // T6:T7 = U1*V1 + ADDQ T7, T5 \ + MULXQ 16+I1, T8, T7 \ // T7:T8 = U1*V2 + ADCQ T8, T6 \ + MULXQ 24+I1, T9, T8 \ // T8:T9 = U1*V3 + ADCQ T9, T7 \ + ADCQ $0, T8 \ + ADDQ T0, T4 \ + MOVQ T4, 8+O \ // O[1] + ADCQ T1, T5 \ + ADCQ T2, T6 \ + ADCQ T3, T7 \ + \ // Column U2 + MOVQ 16+I0, DX \ + ADCQ $0, T8 \ + MULXQ 0+I1, T0, T1 \ // T1:T0 = U2*V0 + MULXQ 8+I1, T3, T2 \ // T2:T3 = U2*V1 + ADDQ T3, T1 \ + MULXQ 16+I1, T4, T3 \ // T3:T4 = U2*V2 + ADCQ T4, T2 \ + MULXQ 24+I1, T9, T4 \ // T4:T9 = U2*V3 + ADCQ T9, T3 \ + \ // Column U3 + MOVQ 24+I0, DX \ + ADCQ $0, T4 \ + ADDQ T5, T0 \ + MOVQ T0, 16+O \ // O[2] + ADCQ T6, T1 \ + ADCQ T7, T2 \ + ADCQ T8, T3 \ + ADCQ $0, T4 \ + MULXQ 0+I1, T0, T5 \ // T5:T0 = U3*V0 + MULXQ 8+I1, T7, T6 \ // T6:T7 = U3*V1 + ADDQ T7, T5 \ + MULXQ 16+I1, T8, T7 \ // T7:T8 = U3*V2 + ADCQ T8, T6 \ + MULXQ 24+I1, T9, T8 \ // T8:T9 = U3*V3 + ADCQ T9, T7 \ + ADCQ $0, T8 \ + \ // Add values in remaining columns + ADDQ T0, T1 \ + MOVQ T1, 24+O \ // O[3] + ADCQ T5, T2 \ + MOVQ T2, 32+O \ // O[4] + ADCQ T6, T3 \ + MOVQ T3, 40+O \ // O[5] + ADCQ T7, T4 \ + MOVQ T4, 48+O \ // O[6] + ADCQ $0, T8 \ // O[7] + MOVQ T8, 56+O + +// Performs schoolbook multiplication of 2 256-bit numbers. This optimized version +// uses ADOX, ADCX and MULX instructions. Macro smashes values in AX and DX. +// Input: I0 and I1. +// Output: O +// All the other arguments registers are used for storing temporary values +#define MULS256_MULX_ADCX_ADOX(O, I0, I1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9) \ + \ // U0[0] + MOVQ 0+I0, DX \ // MULX requires multiplayer in DX + \ // T0:T1 = I1*DX + MULXQ I1, T1, T0 \ // T0:T1 = U0*V0 (low:high) + MOVQ T1, O \ // O0[0] + MULXQ 8+I1, T2, T1 \ // T2:T1 = U0*V1 + XORQ AX, AX \ + ADOXQ T2, T0 \ + MULXQ 16+I1, T3, T2 \ // T2:T3 = U0*V2 + ADOXQ T3, T1 \ + MULXQ 24+I1, T4, T3 \ // T3:T4 = U0*V3 + ADOXQ T4, T2 \ + \ // Column U1 + MOVQ 8+I0, DX \ + MULXQ I1, T4, T5 \ // T5:T4 = U1*V0 + ADOXQ AX, T3 \ + XORQ AX, AX \ + MULXQ 8+I1, T7, T6 \ // T6:T7 = U1*V1 + ADOXQ T0, T4 \ + MOVQ T4, 8+O \ // O[1] + ADCXQ T7, T5 \ + MULXQ 16+I1, T8, T7 \ // T7:T8 = U1*V2 + ADCXQ T8, T6 \ + ADOXQ T1, T5 \ + MULXQ 24+I1, T9, T8 \ // T8:T9 = U1*V3 + ADCXQ T9, T7 \ + ADCXQ AX, T8 \ + ADOXQ T2, T6 \ + \ // Column U2 + MOVQ 16+I0, DX \ + MULXQ I1, T0, T1 \ // T1:T0 = U2*V0 + ADOXQ T3, T7 \ + ADOXQ AX, T8 \ + XORQ AX, AX \ + MULXQ 8+I1, T3, T2 \ // T2:T3 = U2*V1 + ADOXQ T5, T0 \ + MOVQ T0, 16+O \ // O[2] + ADCXQ T3, T1 \ + MULXQ 16+I1, T4, T3 \ // T3:T4 = U2*V2 + ADCXQ T4, T2 \ + ADOXQ T6, T1 \ + MULXQ 24+I1, T9, T4 \ // T9:T4 = U2*V3 + ADCXQ T9, T3 \ + MOVQ 24+I0, DX \ + ADCXQ AX, T4 \ + \ + ADOXQ T7, T2 \ + ADOXQ T8, T3 \ + ADOXQ AX, T4 \ + \ // Column U3 + MULXQ I1, T0, T5 \ // T5:T0 = U3*B0 + XORQ AX, AX \ + MULXQ 8+I1, T7, T6 \ // T6:T7 = U3*B1 + ADCXQ T7, T5 \ + ADOXQ T0, T1 \ + MULXQ 16+I1, T8, T7 \ // T7:T8 = U3*V2 + ADCXQ T8, T6 \ + ADOXQ T5, T2 \ + MULXQ 24+I1, T9, T8 \ // T8:T9 = U3*V3 + ADCXQ T9, T7 \ + ADCXQ AX, T8 \ + \ + ADOXQ T6, T3 \ + ADOXQ T7, T4 \ + ADOXQ AX, T8 \ + MOVQ T1, 24+O \ // O[3] + MOVQ T2, 32+O \ // O[4] + MOVQ T3, 40+O \ // O[5] + MOVQ T4, 48+O \ // O[6] and O[7] below + MOVQ T8, 56+O + +// Template of a macro that performs schoolbook multiplication of 128-bit with 320-bit +// number. It uses MULX instruction This template must be customized with functions +// performing ADD (add1, add2) and ADD-with-carry (adc1, adc2). addX/adcX may or may +// not be instructions that use two independent carry chains. +// Input: +// * I0 128-bit number +// * I1 320-bit number +// * add1, add2: instruction performing integer addition and starting carry chain +// * adc1, adc2: instruction performing integer addition with carry +// Output: T[0-6] registers +#define MULS_128x320(I0, I1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, add1, add2, adc1, adc2) \ + \ // Column 0 + MOVQ I0, DX \ + MULXQ I1+24(SB), T0, T1 \ + MULXQ I1+32(SB), T4, T2 \ + XORQ AX, AX \ + MULXQ I1+40(SB), T5, T3 \ + add1 T4, T1 \ + adc1 T5, T2 \ + MULXQ I1+48(SB), T7, T4 \ + adc1 T7, T3 \ + MULXQ I1+56(SB), T6, T5 \ + adc1 T6, T4 \ + adc1 AX, T5 \ + \ // Column 1 + MOVQ 8+I0, DX \ + MULXQ I1+24(SB), T6, T7 \ + add2 T6, T1 \ + adc2 T7, T2 \ + MULXQ I1+32(SB), T8, T6 \ + adc2 T6, T3 \ + MULXQ I1+40(SB), T7, T9 \ + adc2 T9, T4 \ + MULXQ I1+48(SB), T9, T6 \ + adc2 T6, T5 \ + MULXQ I1+56(SB), DX, T6 \ + adc2 AX, T6 \ + \ // Output + XORQ AX, AX \ + add1 T8, T2 \ + adc1 T7, T3 \ + adc1 T9, T4 \ + adc1 DX, T5 \ + adc1 AX, T6 + +// Multiplies 128-bit with 320-bit integer. Optimized with MULX instruction. +#define MULS_128x320_MULX(I0, I1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9) \ + MULS_128x320(I0, I1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, ADDQ, ADDQ, ADCQ, ADCQ) + +// Multiplies 128-bit with 320-bit integer. Optimized with MULX, ADOX and ADCX instructions +#define MULS_128x320_MULX_ADCX_ADOX(I0, I1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9) \ + MULS_128x320(I0, I1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, ADOXQ, ADCXQ, ADOXQ, ADCXQ) + +// Template of a macro performing multiplication of two 512-bit numbers. It uses one +// level of Karatsuba and one level of schoolbook multiplication. Template must be +// customized with macro performing schoolbook multiplication. +// Input: +// * I0, I1 - two 512-bit numbers +// * MULS - either MULS256_MULX or MULS256_MULX_ADCX_ADOX +// Output: OUT - 1024-bit long +#define MUL(OUT, I0, I1, MULS) \ + \ // R[8-11]: U1+U0 + XORQ AX, AX \ + MOVQ ( 0)(I0), R8 \ + MOVQ ( 8)(I0), R9 \ + MOVQ (16)(I0), R10 \ + MOVQ (24)(I0), R11 \ + ADDQ (32)(I0), R8 \ + ADCQ (40)(I0), R9 \ + ADCQ (48)(I0), R10 \ + ADCQ (56)(I0), R11 \ + SBBQ $0, AX \ // store mask + MOVQ R8, ( 0)(SP) \ + MOVQ R9, ( 8)(SP) \ + MOVQ R10, (16)(SP) \ + MOVQ R11, (24)(SP) \ + \ + \ // R[12-15]: V1+V0 + XORQ BX, BX \ + MOVQ ( 0)(I1), R12 \ + MOVQ ( 8)(I1), R13 \ + MOVQ (16)(I1), R14 \ + MOVQ (24)(I1), R15 \ + ADDQ (32)(I1), R12 \ + ADCQ (40)(I1), R13 \ + ADCQ (48)(I1), R14 \ + ADCQ (56)(I1), R15 \ + SBBQ $0, BX \ // store mask + MOVQ R12, (32)(SP) \ + MOVQ R13, (40)(SP) \ + MOVQ R14, (48)(SP) \ + MOVQ R15, (56)(SP) \ + \ // Prepare mask for U0+U1 (U1+U0 mod 256^4 if U1+U0 sets carry flag, otherwise 0) + ANDQ AX, R12 \ + ANDQ AX, R13 \ + ANDQ AX, R14 \ + ANDQ AX, R15 \ + \ // Prepare mask for V0+V1 (V1+V0 mod 256^4 if U1+U0 sets carry flag, otherwise 0) + ANDQ BX, R8 \ + ANDQ BX, R9 \ + ANDQ BX, R10 \ + ANDQ BX, R11 \ + \ // res = masked(U0+U1) + masked(V0 + V1) + ADDQ R12, R8 \ + ADCQ R13, R9 \ + ADCQ R14, R10 \ + ADCQ R15, R11 \ + \ // SP[64-96] <- res + MOVQ R8, (64)(SP) \ + MOVQ R9, (72)(SP) \ + MOVQ R10, (80)(SP) \ + MOVQ R11, (88)(SP) \ + \ // BP will be used for schoolbook multiplication below + MOVQ BP, 96(SP) \ // push: BP is Callee-save. + \ // (U1+U0)*(V1+V0) + MULS((64)(OUT), 0(SP), 32(SP), R8, R9, R10, R11, R12, R13, R14, R15, BX, BP) \ + \ // U0 x V0 + MULS(0(OUT), 0(I0), 0(I1), R8, R9, R10, R11, R12, R13, R14, R15, BX, BP) \ + \ // U1 x V1 + MULS(0(SP), 32(I0), 32(I1), R8, R9, R10, R11, R12, R13, R14, R15, BX, BP) \ + \ // Recover BP + MOVQ 96(SP), BP \ // pop: BP is Callee-save. + \ // Final part of schoolbook multiplication; R[8-11] = (U0+U1) x (V0+V1) + MOVQ (64)(SP), R8 \ + MOVQ (72)(SP), R9 \ + MOVQ (80)(SP), R10 \ + MOVQ (88)(SP), R11 \ + MOVQ (96)(OUT), AX \ + ADDQ AX, R8 \ + MOVQ (104)(OUT), AX \ + ADCQ AX, R9 \ + MOVQ (112)(OUT), AX \ + ADCQ AX, R10 \ + MOVQ (120)(OUT), AX \ + ADCQ AX, R11 \ + \ // R[12-15, 8-11] = (U0+U1) x (V0+V1) - U0xV0 + MOVQ (64)(OUT), R12 \ + MOVQ (72)(OUT), R13 \ + MOVQ (80)(OUT), R14 \ + MOVQ (88)(OUT), R15 \ + SUBQ ( 0)(OUT), R12 \ + SBBQ ( 8)(OUT), R13 \ + SBBQ (16)(OUT), R14 \ + SBBQ (24)(OUT), R15 \ + SBBQ (32)(OUT), R8 \ + SBBQ (40)(OUT), R9 \ + SBBQ (48)(OUT), R10 \ + SBBQ (56)(OUT), R11 \ + \ // r8-r15 <- (U0+U1) x (V0+V1) - U0xV0 - U1xV1 + SUBQ ( 0)(SP), R12 \ + SBBQ ( 8)(SP), R13 \ + SBBQ (16)(SP), R14 \ + SBBQ (24)(SP), R15 \ + SBBQ (32)(SP), R8 \ + SBBQ (40)(SP), R9 \ + SBBQ (48)(SP), R10 \ + SBBQ (56)(SP), R11 \ + \ + ; ADDQ (32)(OUT), R12; MOVQ R12, ( 32)(OUT) \ + ; ADCQ (40)(OUT), R13; MOVQ R13, ( 40)(OUT) \ + ; ADCQ (48)(OUT), R14; MOVQ R14, ( 48)(OUT) \ + ; ADCQ (56)(OUT), R15; MOVQ R15, ( 56)(OUT) \ + MOVQ ( 0)(SP), AX; ADCQ AX, R8; MOVQ R8, ( 64)(OUT) \ + MOVQ ( 8)(SP), AX; ADCQ AX, R9; MOVQ R9, ( 72)(OUT) \ + MOVQ (16)(SP), AX; ADCQ AX, R10; MOVQ R10, ( 80)(OUT) \ + MOVQ (24)(SP), AX; ADCQ AX, R11; MOVQ R11, ( 88)(OUT) \ + MOVQ (32)(SP), R12; ADCQ $0, R12; MOVQ R12, ( 96)(OUT) \ + MOVQ (40)(SP), R13; ADCQ $0, R13; MOVQ R13, (104)(OUT) \ + MOVQ (48)(SP), R14; ADCQ $0, R14; MOVQ R14, (112)(OUT) \ + MOVQ (56)(SP), R15; ADCQ $0, R15; MOVQ R15, (120)(OUT) + +// Template for calculating the Montgomery reduction algorithm described in +// section 5.2.3 of https://eprint.iacr.org/2017/1015.pdf. Template must be +// customized with schoolbook multiplication for 128 x 320-bit number. +// This macro reuses memory of IN value and *changes* it. Smashes registers +// R[8-15], BX, CX +// Input: +// * IN: 1024-bit number to be reduced +// * MULS: either MULS_128x320_MULX or MULS_128x320_MULX_ADCX_ADOX +// Output: OUT 512-bit +#define REDC(OUT, IN, MULS) \ + MULS(0(IN), ·P503p1, R8, R9, R10, R11, R12, R13, R14, BX, CX, R15) \ + XORQ R15, R15 \ + ADDQ (24)(IN), R8 \ + ADCQ (32)(IN), R9 \ + ADCQ (40)(IN), R10 \ + ADCQ (48)(IN), R11 \ + ADCQ (56)(IN), R12 \ + ADCQ (64)(IN), R13 \ + ADCQ (72)(IN), R14 \ + ADCQ (80)(IN), R15 \ + MOVQ R8, (24)(IN) \ + MOVQ R9, (32)(IN) \ + MOVQ R10, (40)(IN) \ + MOVQ R11, (48)(IN) \ + MOVQ R12, (56)(IN) \ + MOVQ R13, (64)(IN) \ + MOVQ R14, (72)(IN) \ + MOVQ R15, (80)(IN) \ + MOVQ (88)(IN), R8 \ + MOVQ (96)(IN), R9 \ + MOVQ (104)(IN), R10 \ + MOVQ (112)(IN), R11 \ + MOVQ (120)(IN), R12 \ + ADCQ $0, R8 \ + ADCQ $0, R9 \ + ADCQ $0, R10 \ + ADCQ $0, R11 \ + ADCQ $0, R12 \ + MOVQ R8, (88)(IN) \ + MOVQ R9, (96)(IN) \ + MOVQ R10, (104)(IN) \ + MOVQ R11, (112)(IN) \ + MOVQ R12, (120)(IN) \ + \ + MULS(16(IN), ·P503p1, R8, R9, R10, R11, R12, R13, R14, BX, CX, R15) \ + XORQ R15, R15 \ + ADDQ (40)(IN), R8 \ + ADCQ (48)(IN), R9 \ + ADCQ (56)(IN), R10 \ + ADCQ (64)(IN), R11 \ + ADCQ (72)(IN), R12 \ + ADCQ (80)(IN), R13 \ + ADCQ (88)(IN), R14 \ + ADCQ (96)(IN), R15 \ + MOVQ R8, (40)(IN) \ + MOVQ R9, (48)(IN) \ + MOVQ R10, (56)(IN) \ + MOVQ R11, (64)(IN) \ + MOVQ R12, (72)(IN) \ + MOVQ R13, (80)(IN) \ + MOVQ R14, (88)(IN) \ + MOVQ R15, (96)(IN) \ + MOVQ (104)(IN), R8 \ + MOVQ (112)(IN), R9 \ + MOVQ (120)(IN), R10 \ + ADCQ $0, R8 \ + ADCQ $0, R9 \ + ADCQ $0, R10 \ + MOVQ R8, (104)(IN) \ + MOVQ R9, (112)(IN) \ + MOVQ R10, (120)(IN) \ + \ + MULS(32(IN), ·P503p1, R8, R9, R10, R11, R12, R13, R14, BX, CX, R15) \ + XORQ R15, R15 \ + XORQ BX, BX \ + ADDQ ( 56)(IN), R8 \ + ADCQ ( 64)(IN), R9 \ + ADCQ ( 72)(IN), R10 \ + ADCQ ( 80)(IN), R11 \ + ADCQ ( 88)(IN), R12 \ + ADCQ ( 96)(IN), R13 \ + ADCQ (104)(IN), R14 \ + ADCQ (112)(IN), R15 \ + ADCQ (120)(IN), BX \ + MOVQ R8, ( 56)(IN) \ + MOVQ R10, ( 72)(IN) \ + MOVQ R11, ( 80)(IN) \ + MOVQ R12, ( 88)(IN) \ + MOVQ R13, ( 96)(IN) \ + MOVQ R14, (104)(IN) \ + MOVQ R15, (112)(IN) \ + MOVQ BX, (120)(IN) \ + MOVQ R9, ( 0)(OUT) \ // Result: OUT[0] + \ + MULS(48(IN), ·P503p1, R8, R9, R10, R11, R12, R13, R14, BX, CX, R15) \ + ADDQ ( 72)(IN), R8 \ + ADCQ ( 80)(IN), R9 \ + ADCQ ( 88)(IN), R10 \ + ADCQ ( 96)(IN), R11 \ + ADCQ (104)(IN), R12 \ + ADCQ (112)(IN), R13 \ + ADCQ (120)(IN), R14 \ + MOVQ R8, ( 8)(OUT) \ // Result: OUT[1] + MOVQ R9, (16)(OUT) \ // Result: OUT[2] + MOVQ R10, (24)(OUT) \ // Result: OUT[3] + MOVQ R11, (32)(OUT) \ // Result: OUT[4] + MOVQ R12, (40)(OUT) \ // Result: OUT[5] + MOVQ R13, (48)(OUT) \ // Result: OUT[6] and OUT[7] + MOVQ R14, (56)(OUT) + +TEXT ·modP503(SB), NOSPLIT, $0-8 + MOVQ x+0(FP), REG_P1 + + // Zero AX for later use: + XORQ AX, AX + + // Load p into registers: + MOVQ P503_0, R8 + // P503_{1,2} = P503_0, so reuse R8 + MOVQ P503_3, R9 + MOVQ P503_4, R10 + MOVQ P503_5, R11 + MOVQ P503_6, R12 + MOVQ P503_7, R13 + + // Set x <- x - p + SUBQ R8, ( 0)(REG_P1) + SBBQ R8, ( 8)(REG_P1) + SBBQ R8, (16)(REG_P1) + SBBQ R9, (24)(REG_P1) + SBBQ R10, (32)(REG_P1) + SBBQ R11, (40)(REG_P1) + SBBQ R12, (48)(REG_P1) + SBBQ R13, (56)(REG_P1) + + // Save carry flag indicating x-p < 0 as a mask + SBBQ $0, AX + + // Conditionally add p to x if x-p < 0 + ANDQ AX, R8 + ANDQ AX, R9 + ANDQ AX, R10 + ANDQ AX, R11 + ANDQ AX, R12 + ANDQ AX, R13 + + ADDQ R8, ( 0)(REG_P1) + ADCQ R8, ( 8)(REG_P1) + ADCQ R8, (16)(REG_P1) + ADCQ R9, (24)(REG_P1) + ADCQ R10,(32)(REG_P1) + ADCQ R11,(40)(REG_P1) + ADCQ R12,(48)(REG_P1) + ADCQ R13,(56)(REG_P1) + + RET + +TEXT ·cswapP503(SB),NOSPLIT,$0-17 + + MOVQ x+0(FP), REG_P1 + MOVQ y+8(FP), REG_P2 + MOVB choice+16(FP), AL // AL = 0 or 1 + MOVBLZX AL, AX // AX = 0 or 1 + NEGQ AX // AX = 0x00..00 or 0xff..ff + +#ifndef CSWAP_BLOCK +#define CSWAP_BLOCK(idx) \ + MOVQ (idx*8)(REG_P1), BX \ // BX = x[idx] + MOVQ (idx*8)(REG_P2), CX \ // CX = y[idx] + MOVQ CX, DX \ // DX = y[idx] + XORQ BX, DX \ // DX = y[idx] ^ x[idx] + ANDQ AX, DX \ // DX = (y[idx] ^ x[idx]) & mask + XORQ DX, BX \ // BX = (y[idx] ^ x[idx]) & mask) ^ x[idx] = x[idx] or y[idx] + XORQ DX, CX \ // CX = (y[idx] ^ x[idx]) & mask) ^ y[idx] = y[idx] or x[idx] + MOVQ BX, (idx*8)(REG_P1) \ + MOVQ CX, (idx*8)(REG_P2) +#endif + + CSWAP_BLOCK(0) + CSWAP_BLOCK(1) + CSWAP_BLOCK(2) + CSWAP_BLOCK(3) + CSWAP_BLOCK(4) + CSWAP_BLOCK(5) + CSWAP_BLOCK(6) + CSWAP_BLOCK(7) + +#ifdef CSWAP_BLOCK +#undef CSWAP_BLOCK +#endif + + RET + +TEXT ·addP503(SB),NOSPLIT,$0-24 + + MOVQ z+0(FP), REG_P3 + MOVQ x+8(FP), REG_P1 + MOVQ y+16(FP), REG_P2 + + // Used later to calculate a mask + XORQ CX, CX + + // [R8-R15]: z = x + y + MOVQ ( 0)(REG_P1), R8 + MOVQ ( 8)(REG_P1), R9 + MOVQ (16)(REG_P1), R10 + MOVQ (24)(REG_P1), R11 + MOVQ (32)(REG_P1), R12 + MOVQ (40)(REG_P1), R13 + MOVQ (48)(REG_P1), R14 + MOVQ (56)(REG_P1), R15 + ADDQ ( 0)(REG_P2), R8 + ADCQ ( 8)(REG_P2), R9 + ADCQ (16)(REG_P2), R10 + ADCQ (24)(REG_P2), R11 + ADCQ (32)(REG_P2), R12 + ADCQ (40)(REG_P2), R13 + ADCQ (48)(REG_P2), R14 + ADCQ (56)(REG_P2), R15 + + MOVQ P503X2_0, AX + SUBQ AX, R8 + MOVQ P503X2_1, AX + SBBQ AX, R9 + SBBQ AX, R10 + MOVQ P503X2_3, AX + SBBQ AX, R11 + MOVQ P503X2_4, AX + SBBQ AX, R12 + MOVQ P503X2_5, AX + SBBQ AX, R13 + MOVQ P503X2_6, AX + SBBQ AX, R14 + MOVQ P503X2_7, AX + SBBQ AX, R15 + + // mask + SBBQ $0, CX + + // move z to REG_P3 + MOVQ R8, ( 0)(REG_P3) + MOVQ R9, ( 8)(REG_P3) + MOVQ R10, (16)(REG_P3) + MOVQ R11, (24)(REG_P3) + MOVQ R12, (32)(REG_P3) + MOVQ R13, (40)(REG_P3) + MOVQ R14, (48)(REG_P3) + MOVQ R15, (56)(REG_P3) + + // if z<0 add p503x2 back + MOVQ P503X2_0, R8 + MOVQ P503X2_1, R9 + MOVQ P503X2_3, R10 + MOVQ P503X2_4, R11 + MOVQ P503X2_5, R12 + MOVQ P503X2_6, R13 + MOVQ P503X2_7, R14 + ANDQ CX, R8 + ANDQ CX, R9 + ANDQ CX, R10 + ANDQ CX, R11 + ANDQ CX, R12 + ANDQ CX, R13 + ANDQ CX, R14 + MOVQ ( 0)(REG_P3), AX; ADDQ R8, AX; MOVQ AX, ( 0)(REG_P3) + MOVQ ( 8)(REG_P3), AX; ADCQ R9, AX; MOVQ AX, ( 8)(REG_P3) + MOVQ (16)(REG_P3), AX; ADCQ R9, AX; MOVQ AX, (16)(REG_P3) + MOVQ (24)(REG_P3), AX; ADCQ R10, AX; MOVQ AX, (24)(REG_P3) + MOVQ (32)(REG_P3), AX; ADCQ R11, AX; MOVQ AX, (32)(REG_P3) + MOVQ (40)(REG_P3), AX; ADCQ R12, AX; MOVQ AX, (40)(REG_P3) + MOVQ (48)(REG_P3), AX; ADCQ R13, AX; MOVQ AX, (48)(REG_P3) + MOVQ (56)(REG_P3), AX; ADCQ R14, AX; MOVQ AX, (56)(REG_P3) + RET + +TEXT ·subP503(SB), NOSPLIT, $0-24 + + MOVQ z+0(FP), REG_P3 + MOVQ x+8(FP), REG_P1 + MOVQ y+16(FP), REG_P2 + + // Used later to calculate a mask + XORQ CX, CX + + MOVQ ( 0)(REG_P1), R8 + MOVQ ( 8)(REG_P1), R9 + MOVQ (16)(REG_P1), R10 + MOVQ (24)(REG_P1), R11 + MOVQ (32)(REG_P1), R12 + MOVQ (40)(REG_P1), R13 + MOVQ (48)(REG_P1), R14 + MOVQ (56)(REG_P1), R15 + + SUBQ ( 0)(REG_P2), R8 + SBBQ ( 8)(REG_P2), R9 + SBBQ (16)(REG_P2), R10 + SBBQ (24)(REG_P2), R11 + SBBQ (32)(REG_P2), R12 + SBBQ (40)(REG_P2), R13 + SBBQ (48)(REG_P2), R14 + SBBQ (56)(REG_P2), R15 + + // mask + SBBQ $0, CX + + // store x-y in REG_P3 + MOVQ R8, ( 0)(REG_P3) + MOVQ R9, ( 8)(REG_P3) + MOVQ R10, (16)(REG_P3) + MOVQ R11, (24)(REG_P3) + MOVQ R12, (32)(REG_P3) + MOVQ R13, (40)(REG_P3) + MOVQ R14, (48)(REG_P3) + MOVQ R15, (56)(REG_P3) + + // if z<0 add p503x2 back + MOVQ P503X2_0, R8 + MOVQ P503X2_1, R9 + MOVQ P503X2_3, R10 + MOVQ P503X2_4, R11 + MOVQ P503X2_5, R12 + MOVQ P503X2_6, R13 + MOVQ P503X2_7, R14 + ANDQ CX, R8 + ANDQ CX, R9 + ANDQ CX, R10 + ANDQ CX, R11 + ANDQ CX, R12 + ANDQ CX, R13 + ANDQ CX, R14 + MOVQ ( 0)(REG_P3), AX; ADDQ R8, AX; MOVQ AX, ( 0)(REG_P3) + MOVQ ( 8)(REG_P3), AX; ADCQ R9, AX; MOVQ AX, ( 8)(REG_P3) + MOVQ (16)(REG_P3), AX; ADCQ R9, AX; MOVQ AX, (16)(REG_P3) + MOVQ (24)(REG_P3), AX; ADCQ R10, AX; MOVQ AX, (24)(REG_P3) + MOVQ (32)(REG_P3), AX; ADCQ R11, AX; MOVQ AX, (32)(REG_P3) + MOVQ (40)(REG_P3), AX; ADCQ R12, AX; MOVQ AX, (40)(REG_P3) + MOVQ (48)(REG_P3), AX; ADCQ R13, AX; MOVQ AX, (48)(REG_P3) + MOVQ (56)(REG_P3), AX; ADCQ R14, AX; MOVQ AX, (56)(REG_P3) + + RET + +TEXT ·mulP503(SB), NOSPLIT, $104-24 + MOVQ z+0(FP), CX + MOVQ x+8(FP), REG_P1 + MOVQ y+16(FP), REG_P2 + + // Check whether to use optimized implementation + CMPB ·HasADXandBMI2(SB), $1 + JE mul_with_mulx_adcx_adox + CMPB ·HasBMI2(SB), $1 + JE mul_with_mulx + + // Generic x86 implementation (below) uses variant of Karatsuba method. + // + // Here we store the destination in CX instead of in REG_P3 because the + // multiplication instructions use DX as an implicit destination + // operand: MULQ $REG sets DX:AX <-- AX * $REG. + + // RAX and RDX will be used for a mask (0-borrow) + XORQ AX, AX + + // RCX[0-3]: U1+U0 + MOVQ (32)(REG_P1), R8 + MOVQ (40)(REG_P1), R9 + MOVQ (48)(REG_P1), R10 + MOVQ (56)(REG_P1), R11 + ADDQ ( 0)(REG_P1), R8 + ADCQ ( 8)(REG_P1), R9 + ADCQ (16)(REG_P1), R10 + ADCQ (24)(REG_P1), R11 + MOVQ R8, ( 0)(CX) + MOVQ R9, ( 8)(CX) + MOVQ R10, (16)(CX) + MOVQ R11, (24)(CX) + + SBBQ $0, AX + + // R12-R15: V1+V0 + XORQ DX, DX + MOVQ (32)(REG_P2), R12 + MOVQ (40)(REG_P2), R13 + MOVQ (48)(REG_P2), R14 + MOVQ (56)(REG_P2), R15 + ADDQ ( 0)(REG_P2), R12 + ADCQ ( 8)(REG_P2), R13 + ADCQ (16)(REG_P2), R14 + ADCQ (24)(REG_P2), R15 + + SBBQ $0, DX + + // Store carries on stack + MOVQ AX, (64)(SP) + MOVQ DX, (72)(SP) + + // (SP[0-3],R8,R9,R10,R11) <- (U0+U1)*(V0+V1). + // MUL using comba; In comments below U=U0+U1 V=V0+V1 + + // U0*V0 + MOVQ (CX), AX + MULQ R12 + MOVQ AX, (SP) // C0 + MOVQ DX, R8 + + // U0*V1 + XORQ R9, R9 + MOVQ (CX), AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + + // U1*V0 + XORQ R10, R10 + MOVQ (8)(CX), AX + MULQ R12 + ADDQ AX, R8 + MOVQ R8, (8)(SP) // C1 + ADCQ DX, R9 + ADCQ $0, R10 + + // U0*V2 + XORQ R8, R8 + MOVQ (CX), AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + // U2*V0 + MOVQ (16)(CX), AX + MULQ R12 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + // U1*V1 + MOVQ (8)(CX), AX + MULQ R13 + ADDQ AX, R9 + MOVQ R9, (16)(SP) // C2 + ADCQ DX, R10 + ADCQ $0, R8 + + // U0*V3 + XORQ R9, R9 + MOVQ (CX), AX + MULQ R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + // U3*V0 + MOVQ (24)(CX), AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + // U1*V2 + MOVQ (8)(CX), AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + // U2*V1 + MOVQ (16)(CX), AX + MULQ R13 + ADDQ AX, R10 + MOVQ R10, (24)(SP) // C3 + ADCQ DX, R8 + ADCQ $0, R9 + + // U1*V3 + XORQ R10, R10 + MOVQ (8)(CX), AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + // U3*V1 + MOVQ (24)(CX), AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + // U2*V2 + MOVQ (16)(CX), AX + MULQ R14 + ADDQ AX, R8 + MOVQ R8, (32)(SP) // C4 + ADCQ DX, R9 + ADCQ $0, R10 + + // U2*V3 + XORQ R11, R11 + MOVQ (16)(CX), AX + MULQ R15 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R11 + + // U3*V2 + MOVQ (24)(CX), AX + MULQ R14 + ADDQ AX, R9 // C5 + ADCQ DX, R10 + ADCQ $0, R11 + + // U3*V3 + MOVQ (24)(CX), AX + MULQ R15 + ADDQ AX, R10 // C6 + ADCQ DX, R11 // C7 + + MOVQ (64)(SP), AX + ANDQ AX, R12 + ANDQ AX, R13 + ANDQ AX, R14 + ANDQ AX, R15 + ADDQ R8, R12 + ADCQ R9, R13 + ADCQ R10, R14 + ADCQ R11, R15 + + MOVQ (72)(SP), AX + MOVQ (CX), R8 + MOVQ (8)(CX), R9 + MOVQ (16)(CX), R10 + MOVQ (24)(CX), R11 + ANDQ AX, R8 + ANDQ AX, R9 + ANDQ AX, R10 + ANDQ AX, R11 + ADDQ R12, R8 + ADCQ R13, R9 + ADCQ R14, R10 + ADCQ R15, R11 + MOVQ R8, (32)(SP) + MOVQ R9, (40)(SP) + MOVQ R10, (48)(SP) + MOVQ R11, (56)(SP) + + // CX[0-7] <- AL*BL + + // U0*V0 + MOVQ (REG_P1), R11 + MOVQ (REG_P2), AX + MULQ R11 + XORQ R9, R9 + MOVQ AX, (CX) // C0 + MOVQ DX, R8 + + // U0*V1 + MOVQ (16)(REG_P1), R14 + MOVQ (8)(REG_P2), AX + MULQ R11 + XORQ R10, R10 + ADDQ AX, R8 + ADCQ DX, R9 + + // U1*V0 + MOVQ (8)(REG_P1), R12 + MOVQ (REG_P2), AX + MULQ R12 + ADDQ AX, R8 + MOVQ R8, (8)(CX) // C1 + ADCQ DX, R9 + ADCQ $0, R10 + + // U0*V2 + XORQ R8, R8 + MOVQ (16)(REG_P2), AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + // U2*V0 + MOVQ (REG_P2), R13 + MOVQ R14, AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + // U1*V1 + MOVQ (8)(REG_P2), AX + MULQ R12 + ADDQ AX, R9 + MOVQ R9, (16)(CX) // C2 + ADCQ DX, R10 + ADCQ $0, R8 + + // U0*V3 + XORQ R9, R9 + MOVQ (24)(REG_P2), AX + MULQ R11 + MOVQ (24)(REG_P1), R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + // U3*V1 + MOVQ R15, AX + MULQ R13 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + // U2*V2 + MOVQ (16)(REG_P2), AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + // U2*V3 + MOVQ (8)(REG_P2), AX + MULQ R14 + ADDQ AX, R10 + MOVQ R10, (24)(CX) // C3 + ADCQ DX, R8 + ADCQ $0, R9 + + // U3*V2 + XORQ R10, R10 + MOVQ (24)(REG_P2), AX + MULQ R12 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + // U3*V1 + MOVQ (8)(REG_P2), AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + // U2*V2 + MOVQ (16)(REG_P2), AX + MULQ R14 + ADDQ AX, R8 + MOVQ R8, (32)(CX) // C4 + ADCQ DX, R9 + ADCQ $0, R10 + + // U2*V3 + XORQ R8, R8 + MOVQ (24)(REG_P2), AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + // U3*V2 + MOVQ (16)(REG_P2), AX + MULQ R15 + ADDQ AX, R9 + MOVQ R9, (40)(CX) // C5 + ADCQ DX, R10 + ADCQ $0, R8 + + // U3*V3 + MOVQ (24)(REG_P2), AX + MULQ R15 + ADDQ AX, R10 + MOVQ R10, (48)(CX) // C6 + ADCQ DX, R8 + MOVQ R8, (56)(CX) // C7 + + // CX[8-15] <- U1*V1 + MOVQ (32)(REG_P1), R11 + MOVQ (32)(REG_P2), AX + MULQ R11 + XORQ R9, R9 + MOVQ AX, (64)(CX) // C0 + MOVQ DX, R8 + + MOVQ (48)(REG_P1), R14 + MOVQ (40)(REG_P2), AX + MULQ R11 + XORQ R10, R10 + ADDQ AX, R8 + ADCQ DX, R9 + + MOVQ (40)(REG_P1), R12 + MOVQ (32)(REG_P2), AX + MULQ R12 + ADDQ AX, R8 + MOVQ R8, (72)(CX) // C1 + ADCQ DX, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ (48)(REG_P2), AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (32)(REG_P2), R13 + MOVQ R14, AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (40)(REG_P2), AX + MULQ R12 + ADDQ AX, R9 + MOVQ R9, (80)(CX) // C2 + ADCQ DX, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ (56)(REG_P2), AX + MULQ R11 + MOVQ (56)(REG_P1), R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ R15, AX + MULQ R13 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (48)(REG_P2), AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (40)(REG_P2), AX + MULQ R14 + ADDQ AX, R10 + MOVQ R10, (88)(CX) // C3 + ADCQ DX, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ (56)(REG_P2), AX + MULQ R12 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (40)(REG_P2), AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (48)(REG_P2), AX + MULQ R14 + ADDQ AX, R8 + MOVQ R8, (96)(CX) // C4 + ADCQ DX, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ (56)(REG_P2), AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (48)(REG_P2), AX + MULQ R15 + ADDQ AX, R9 + MOVQ R9, (104)(CX) // C5 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (56)(REG_P2), AX + MULQ R15 + ADDQ AX, R10 + MOVQ R10, (112)(CX) // C6 + ADCQ DX, R8 + MOVQ R8, (120)(CX) // C7 + + // [R8-R15] <- (U0+U1)*(V0+V1) - U1*V1 + MOVQ (SP), R8 + SUBQ (CX), R8 + MOVQ (8)(SP), R9 + SBBQ (8)(CX), R9 + MOVQ (16)(SP), R10 + SBBQ (16)(CX), R10 + MOVQ (24)(SP), R11 + SBBQ (24)(CX), R11 + MOVQ (32)(SP), R12 + SBBQ (32)(CX), R12 + MOVQ (40)(SP), R13 + SBBQ (40)(CX), R13 + MOVQ (48)(SP), R14 + SBBQ (48)(CX), R14 + MOVQ (56)(SP), R15 + SBBQ (56)(CX), R15 + + // [R8-R15] <- (U0+U1)*(V0+V1) - U1*V0 - U0*U1 + MOVQ ( 64)(CX), AX; SUBQ AX, R8 + MOVQ ( 72)(CX), AX; SBBQ AX, R9 + MOVQ ( 80)(CX), AX; SBBQ AX, R10 + MOVQ ( 88)(CX), AX; SBBQ AX, R11 + MOVQ ( 96)(CX), AX; SBBQ AX, R12 + MOVQ (104)(CX), DX; SBBQ DX, R13 + MOVQ (112)(CX), DI; SBBQ DI, R14 + MOVQ (120)(CX), SI; SBBQ SI, R15 + + // Final result + ADDQ (32)(CX), R8; MOVQ R8, (32)(CX) + ADCQ (40)(CX), R9; MOVQ R9, (40)(CX) + ADCQ (48)(CX), R10; MOVQ R10, (48)(CX) + ADCQ (56)(CX), R11; MOVQ R11, (56)(CX) + ADCQ (64)(CX), R12; MOVQ R12, (64)(CX) + ADCQ (72)(CX), R13; MOVQ R13, (72)(CX) + ADCQ (80)(CX), R14; MOVQ R14, (80)(CX) + ADCQ (88)(CX), R15; MOVQ R15, (88)(CX) + ADCQ $0, AX; MOVQ AX, (96)(CX) + ADCQ $0, DX; MOVQ DX, (104)(CX) + ADCQ $0, DI; MOVQ DI, (112)(CX) + ADCQ $0, SI; MOVQ SI, (120)(CX) + RET + +mul_with_mulx_adcx_adox: + // Mul implementation for CPUs supporting two independent carry chain + // (ADOX/ADCX) instructions and carry-less MULX multiplier + MUL(CX, REG_P1, REG_P2, MULS256_MULX_ADCX_ADOX) + RET + +mul_with_mulx: + // Mul implementation for CPUs supporting carry-less MULX multiplier. + MUL(CX, REG_P1, REG_P2, MULS256_MULX) + RET + +TEXT ·rdcP503(SB), $0-16 + MOVQ z+0(FP), REG_P2 + MOVQ x+8(FP), REG_P1 + + // Check whether to use optimized implementation + CMPB ·HasADXandBMI2(SB), $1 + JE redc_with_mulx_adcx_adox + CMPB ·HasBMI2(SB), $1 + JE redc_with_mulx + + MOVQ (REG_P1), R11 + MOVQ P503P1_3, AX + MULQ R11 + XORQ R8, R8 + ADDQ (24)(REG_P1), AX + MOVQ AX, (24)(REG_P2) + ADCQ DX, R8 + + XORQ R9, R9 + MOVQ P503P1_4, AX + MULQ R11 + XORQ R10, R10 + ADDQ AX, R8 + ADCQ DX, R9 + + MOVQ (8)(REG_P1), R12 + MOVQ P503P1_3, AX + MULQ R12 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + ADDQ (32)(REG_P1), R8 + MOVQ R8, (32)(REG_P2) // Z4 + ADCQ $0, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ P503P1_5, AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P503P1_4, AX + MULQ R12 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (16)(REG_P1), R13 + MOVQ P503P1_3, AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + ADDQ (40)(REG_P1), R9 + MOVQ R9, (40)(REG_P2) // Z5 + ADCQ $0, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ P503P1_6, AX + MULQ R11 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P503P1_5, AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P503P1_4, AX + MULQ R13 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (24)(REG_P2), R14 + MOVQ P503P1_3, AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + ADDQ (48)(REG_P1), R10 + MOVQ R10, (48)(REG_P2) // Z6 + ADCQ $0, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ P503P1_7, AX + MULQ R11 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P503P1_6, AX + MULQ R12 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P503P1_5, AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P503P1_4, AX + MULQ R14 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (32)(REG_P2), R15 + MOVQ P503P1_3, AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + ADDQ (56)(REG_P1), R8 + MOVQ R8, (56)(REG_P2) // Z7 + ADCQ $0, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ P503P1_7, AX + MULQ R12 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P503P1_6, AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P503P1_5, AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P503P1_4, AX + MULQ R15 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (40)(REG_P2), CX + MOVQ P503P1_3, AX + MULQ CX + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + ADDQ (64)(REG_P1), R9 + MOVQ R9, (REG_P2) // Z0 + ADCQ $0, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ P503P1_7, AX + MULQ R13 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P503P1_6, AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P503P1_5, AX + MULQ R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P503P1_4, AX + MULQ CX + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (48)(REG_P2), R13 + MOVQ P503P1_3, AX + MULQ R13 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + ADDQ (72)(REG_P1), R10 + MOVQ R10, (8)(REG_P2) // Z1 + ADCQ $0, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ P503P1_7, AX + MULQ R14 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P503P1_6, AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P503P1_5, AX + MULQ CX + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P503P1_4, AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (56)(REG_P2), R14 + MOVQ P503P1_3, AX + MULQ R14 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + ADDQ (80)(REG_P1), R8 + MOVQ R8, (16)(REG_P2) // Z2 + ADCQ $0, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ P503P1_7, AX + MULQ R15 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P503P1_6, AX + MULQ CX + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P503P1_5, AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P503P1_4, AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + ADDQ (88)(REG_P1), R9 + MOVQ R9, (24)(REG_P2) // Z3 + ADCQ $0, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ P503P1_7, AX + MULQ CX + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P503P1_6, AX + MULQ R13 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P503P1_5, AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + ADDQ (96)(REG_P1), R10 + MOVQ R10, (32)(REG_P2) // Z4 + ADCQ $0, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ P503P1_7, AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P503P1_6, AX + MULQ R14 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + ADDQ (104)(REG_P1), R8 // Z5 + MOVQ R8, (40)(REG_P2) // Z5 + ADCQ $0, R9 + ADCQ $0, R10 + + MOVQ P503P1_7, AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADDQ (112)(REG_P1), R9 // Z6 + MOVQ R9, (48)(REG_P2) // Z6 + ADCQ $0, R10 + ADDQ (120)(REG_P1), R10 // Z7 + MOVQ R10, (56)(REG_P2) // Z7 + RET + +redc_with_mulx_adcx_adox: + // Implementation of the Montgomery reduction for CPUs + // supporting two independent carry chain (ADOX/ADCX) + // instructions and carry-less MULX multiplier + REDC(REG_P2, REG_P1, MULS_128x320_MULX_ADCX_ADOX) + RET + +redc_with_mulx: + // Implementation of the Montgomery reduction for CPUs + // supporting carry-less MULX multiplier. + REDC(REG_P2, REG_P1, MULS_128x320_MULX) + RET + +TEXT ·adlP503(SB), NOSPLIT, $0-24 + + MOVQ z+0(FP), REG_P3 + MOVQ x+8(FP), REG_P1 + MOVQ y+16(FP), REG_P2 + + MOVQ (REG_P1), R8 + MOVQ (8)(REG_P1), R9 + MOVQ (16)(REG_P1), R10 + MOVQ (24)(REG_P1), R11 + MOVQ (32)(REG_P1), R12 + MOVQ (40)(REG_P1), R13 + MOVQ (48)(REG_P1), R14 + MOVQ (56)(REG_P1), R15 + MOVQ (64)(REG_P1), AX + MOVQ (72)(REG_P1), BX + MOVQ (80)(REG_P1), CX + + ADDQ (REG_P2), R8 + ADCQ (8)(REG_P2), R9 + ADCQ (16)(REG_P2), R10 + ADCQ (24)(REG_P2), R11 + ADCQ (32)(REG_P2), R12 + ADCQ (40)(REG_P2), R13 + ADCQ (48)(REG_P2), R14 + ADCQ (56)(REG_P2), R15 + ADCQ (64)(REG_P2), AX + ADCQ (72)(REG_P2), BX + ADCQ (80)(REG_P2), CX + + MOVQ R8, (REG_P3) + MOVQ R9, (8)(REG_P3) + MOVQ R10, (16)(REG_P3) + MOVQ R11, (24)(REG_P3) + MOVQ R12, (32)(REG_P3) + MOVQ R13, (40)(REG_P3) + MOVQ R14, (48)(REG_P3) + MOVQ R15, (56)(REG_P3) + MOVQ AX, (64)(REG_P3) + MOVQ BX, (72)(REG_P3) + MOVQ CX, (80)(REG_P3) + + MOVQ (88)(REG_P1), R8 + MOVQ (96)(REG_P1), R9 + MOVQ (104)(REG_P1), R10 + MOVQ (112)(REG_P1), R11 + MOVQ (120)(REG_P1), R12 + + ADCQ (88)(REG_P2), R8 + ADCQ (96)(REG_P2), R9 + ADCQ (104)(REG_P2), R10 + ADCQ (112)(REG_P2), R11 + ADCQ (120)(REG_P2), R12 + + MOVQ R8, (88)(REG_P3) + MOVQ R9, (96)(REG_P3) + MOVQ R10, (104)(REG_P3) + MOVQ R11, (112)(REG_P3) + MOVQ R12, (120)(REG_P3) + + RET + +TEXT ·sulP503(SB), NOSPLIT, $0-24 + + MOVQ z+0(FP), REG_P3 + MOVQ x+8(FP), REG_P1 + MOVQ y+16(FP), REG_P2 + // Used later to store result of 0-borrow + XORQ CX, CX + + // SUBC for first 11 limbs + MOVQ (REG_P1), R8 + MOVQ (8)(REG_P1), R9 + MOVQ (16)(REG_P1), R10 + MOVQ (24)(REG_P1), R11 + MOVQ (32)(REG_P1), R12 + MOVQ (40)(REG_P1), R13 + MOVQ (48)(REG_P1), R14 + MOVQ (56)(REG_P1), R15 + MOVQ (64)(REG_P1), AX + MOVQ (72)(REG_P1), BX + + SUBQ (REG_P2), R8 + SBBQ (8)(REG_P2), R9 + SBBQ (16)(REG_P2), R10 + SBBQ (24)(REG_P2), R11 + SBBQ (32)(REG_P2), R12 + SBBQ (40)(REG_P2), R13 + SBBQ (48)(REG_P2), R14 + SBBQ (56)(REG_P2), R15 + SBBQ (64)(REG_P2), AX + SBBQ (72)(REG_P2), BX + + MOVQ R8, (REG_P3) + MOVQ R9, (8)(REG_P3) + MOVQ R10, (16)(REG_P3) + MOVQ R11, (24)(REG_P3) + MOVQ R12, (32)(REG_P3) + MOVQ R13, (40)(REG_P3) + MOVQ R14, (48)(REG_P3) + MOVQ R15, (56)(REG_P3) + MOVQ AX, (64)(REG_P3) + MOVQ BX, (72)(REG_P3) + + // SUBC for last 5 limbs + MOVQ (80)(REG_P1), R8 + MOVQ (88)(REG_P1), R9 + MOVQ (96)(REG_P1), R10 + MOVQ (104)(REG_P1), R11 + MOVQ (112)(REG_P1), R12 + MOVQ (120)(REG_P1), R13 + + SBBQ (80)(REG_P2), R8 + SBBQ (88)(REG_P2), R9 + SBBQ (96)(REG_P2), R10 + SBBQ (104)(REG_P2), R11 + SBBQ (112)(REG_P2), R12 + SBBQ (120)(REG_P2), R13 + + MOVQ R8, (80)(REG_P3) + MOVQ R9, (88)(REG_P3) + MOVQ R10, (96)(REG_P3) + MOVQ R11, (104)(REG_P3) + MOVQ R12, (112)(REG_P3) + MOVQ R13, (120)(REG_P3) + + // Now the carry flag is 1 if x-y < 0. If so, add p*2^512. + SBBQ $0, CX + + // Load p into registers: + MOVQ P503_0, R8 + // P503_{1,2} = P503_0, so reuse R8 + MOVQ P503_3, R9 + MOVQ P503_4, R10 + MOVQ P503_5, R11 + MOVQ P503_6, R12 + MOVQ P503_7, R13 + + ANDQ CX, R8 + ANDQ CX, R9 + ANDQ CX, R10 + ANDQ CX, R11 + ANDQ CX, R12 + ANDQ CX, R13 + + MOVQ (64 )(REG_P3), AX; ADDQ R8, AX; MOVQ AX, (64 )(REG_P3) + MOVQ (64+ 8)(REG_P3), AX; ADCQ R8, AX; MOVQ AX, (64+ 8)(REG_P3) + MOVQ (64+16)(REG_P3), AX; ADCQ R8, AX; MOVQ AX, (64+16)(REG_P3) + MOVQ (64+24)(REG_P3), AX; ADCQ R9, AX; MOVQ AX, (64+24)(REG_P3) + MOVQ (64+32)(REG_P3), AX; ADCQ R10, AX; MOVQ AX, (64+32)(REG_P3) + MOVQ (64+40)(REG_P3), AX; ADCQ R11, AX; MOVQ AX, (64+40)(REG_P3) + MOVQ (64+48)(REG_P3), AX; ADCQ R12, AX; MOVQ AX, (64+48)(REG_P3) + MOVQ (64+56)(REG_P3), AX; ADCQ R13, AX; MOVQ AX, (64+56)(REG_P3) + + RET diff --git a/src/circl/dh/sidh/internal/p503/arith_amd64_test.go b/src/circl/dh/sidh/internal/p503/arith_amd64_test.go new file mode 100644 index 00000000000..bfe4226ba66 --- /dev/null +++ b/src/circl/dh/sidh/internal/p503/arith_amd64_test.go @@ -0,0 +1,140 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +// +build amd64,!noasm + +package p503 + +import ( + "reflect" + "testing" + "testing/quick" + + "circl/dh/sidh/internal/common" + "internal/cpu" +) + +type OptimFlag uint + +const ( + // Indicates that optimisation which uses MUL instruction should be used + kUse_MUL OptimFlag = 1 << 0 + // Indicates that optimisation which uses MULX instruction should be used + kUse_MULX = 1 << 1 + // Indicates that optimisation which uses MULX, ADOX and ADCX instructions should be used + kUse_MULXandADxX = 1 << 2 +) + +func resetCpuFeatures() { + HasBMI2 = cpu.X86.HasBMI2 + HasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX +} + +// Utility function used for testing Mul implementations. Tests caller provided +// mulFunc against mul() +func testMul(t *testing.T, f1, f2 OptimFlag) { + doMulTest := func(multiplier, multiplicant common.Fp) bool { + defer resetCpuFeatures() + var resMulRef, resMulOptim common.FpX2 + + // Compute multiplier*multiplicant with first implementation + HasBMI2 = (kUse_MULX & f1) == kUse_MULX + HasADXandBMI2 = (kUse_MULXandADxX & f1) == kUse_MULXandADxX + mulP503(&resMulOptim, &multiplier, &multiplicant) + + // Compute multiplier*multiplicant with second implementation + HasBMI2 = (kUse_MULX & f2) == kUse_MULX + HasADXandBMI2 = (kUse_MULXandADxX & f2) == kUse_MULXandADxX + mulP503(&resMulRef, &multiplier, &multiplicant) + + // Compare results + return reflect.DeepEqual(resMulRef, resMulOptim) + } + + if err := quick.Check(doMulTest, quickCheckConfig); err != nil { + t.Error(err) + } +} + +// Utility function used for testing REDC implementations. Tests caller provided +// redcFunc against redc() +func testRedc(t *testing.T, f1, f2 OptimFlag) { + doRedcTest := func(aRR common.FpX2) bool { + defer resetCpuFeatures() + var resRedcF1, resRedcF2 common.Fp + var aRRcpy = aRR + + // Compute redc with first implementation + HasBMI2 = (kUse_MULX & f1) == kUse_MULX + HasADXandBMI2 = (kUse_MULXandADxX & f1) == kUse_MULXandADxX + rdcP503(&resRedcF1, &aRR) + + // Compute redc with second implementation + HasBMI2 = (kUse_MULX & f2) == kUse_MULX + HasADXandBMI2 = (kUse_MULXandADxX & f2) == kUse_MULXandADxX + rdcP503(&resRedcF2, &aRRcpy) + + // Compare results + return reflect.DeepEqual(resRedcF2, resRedcF1) + } + + if err := quick.Check(doRedcTest, quickCheckConfig); err != nil { + t.Error(err) + } +} + +// Ensures correctness of implementation of mul operation which uses MULX +func TestMulWithMULX(t *testing.T) { + defer resetCpuFeatures() + if !HasBMI2 { + t.Skip("MULX not supported by the platform") + } + testMul(t, kUse_MULX, kUse_MUL) +} + +// Ensures correctness of implementation of mul operation which uses MULX and ADOX/ADCX +func TestMulWithMULXADxX(t *testing.T) { + defer resetCpuFeatures() + if !HasADXandBMI2 { + t.Skip("MULX, ADCX and ADOX not supported by the platform") + } + testMul(t, kUse_MULXandADxX, kUse_MUL) +} + +// Ensures correctness of implementation of mul operation which uses MULX and ADOX/ADCX +func TestMulWithMULXADxXAgainstMULX(t *testing.T) { + defer resetCpuFeatures() + if !HasADXandBMI2 { + t.Skip("MULX, ADCX and ADOX not supported by the platform") + } + testMul(t, kUse_MULX, kUse_MULXandADxX) +} + +// Ensures correctness of Montgomery reduction implementation which uses MULX +func TestRedcWithMULX(t *testing.T) { + defer resetCpuFeatures() + if !HasBMI2 { + t.Skip("MULX not supported by the platform") + } + testRedc(t, kUse_MULX, kUse_MUL) +} + +// Ensures correctness of Montgomery reduction implementation which uses MULX +// and ADCX/ADOX. +func TestRedcWithMULXADxX(t *testing.T) { + defer resetCpuFeatures() + if !HasADXandBMI2 { + t.Skip("MULX, ADCX and ADOX not supported by the platform") + } + testRedc(t, kUse_MULXandADxX, kUse_MUL) +} + +// Ensures correctness of Montgomery reduction implementation which uses MULX +// and ADCX/ADOX. +func TestRedcWithMULXADxXAgainstMULX(t *testing.T) { + defer resetCpuFeatures() + if !HasADXandBMI2 { + t.Skip("MULX, ADCX and ADOX not supported by the platform") + } + testRedc(t, kUse_MULXandADxX, kUse_MULX) +} diff --git a/src/circl/dh/sidh/internal/p503/arith_arm64.s b/src/circl/dh/sidh/internal/p503/arith_arm64.s new file mode 100644 index 00000000000..a393670e656 --- /dev/null +++ b/src/circl/dh/sidh/internal/p503/arith_arm64.s @@ -0,0 +1,769 @@ +// +build arm64,!noasm + +#include "textflag.h" + +TEXT ·cswapP503(SB), NOSPLIT, $0-17 + MOVD x+0(FP), R0 + MOVD y+8(FP), R1 + MOVB choice+16(FP), R2 + + // Set flags + // If choice is not 0 or 1, this implementation will swap completely + CMP $0, R2 + + LDP 0(R0), (R3, R4) + LDP 0(R1), (R5, R6) + CSEL EQ, R3, R5, R7 + CSEL EQ, R4, R6, R8 + STP (R7, R8), 0(R0) + CSEL NE, R3, R5, R9 + CSEL NE, R4, R6, R10 + STP (R9, R10), 0(R1) + + LDP 16(R0), (R3, R4) + LDP 16(R1), (R5, R6) + CSEL EQ, R3, R5, R7 + CSEL EQ, R4, R6, R8 + STP (R7, R8), 16(R0) + CSEL NE, R3, R5, R9 + CSEL NE, R4, R6, R10 + STP (R9, R10), 16(R1) + + LDP 32(R0), (R3, R4) + LDP 32(R1), (R5, R6) + CSEL EQ, R3, R5, R7 + CSEL EQ, R4, R6, R8 + STP (R7, R8), 32(R0) + CSEL NE, R3, R5, R9 + CSEL NE, R4, R6, R10 + STP (R9, R10), 32(R1) + + LDP 48(R0), (R3, R4) + LDP 48(R1), (R5, R6) + CSEL EQ, R3, R5, R7 + CSEL EQ, R4, R6, R8 + STP (R7, R8), 48(R0) + CSEL NE, R3, R5, R9 + CSEL NE, R4, R6, R10 + STP (R9, R10), 48(R1) + + RET + +TEXT ·addP503(SB), NOSPLIT, $0-24 + MOVD z+0(FP), R2 + MOVD x+8(FP), R0 + MOVD y+16(FP), R1 + + // Load first summand into R3-R10 + // Add first summand and second summand and store result in R3-R10 + LDP 0(R0), (R3, R4) + LDP 0(R1), (R11, R12) + LDP 16(R0), (R5, R6) + LDP 16(R1), (R13, R14) + ADDS R11, R3 + ADCS R12, R4 + ADCS R13, R5 + ADCS R14, R6 + + LDP 32(R0), (R7, R8) + LDP 32(R1), (R11, R12) + LDP 48(R0), (R9, R10) + LDP 48(R1), (R13, R14) + ADCS R11, R7 + ADCS R12, R8 + ADCS R13, R9 + ADC R14, R10 + + // Subtract 2 * p503 in R11-R17 from the result in R3-R10 + LDP ·P503x2+0(SB), (R11, R12) + LDP ·P503x2+24(SB), (R13, R14) + SUBS R11, R3 + SBCS R12, R4 + LDP ·P503x2+40(SB), (R15, R16) + SBCS R12, R5 + SBCS R13, R6 + MOVD ·P503x2+56(SB), R17 + SBCS R14, R7 + SBCS R15, R8 + SBCS R16, R9 + SBCS R17, R10 + SBC ZR, ZR, R19 + + // If x + y - 2 * p503 < 0, R19 is 1 and 2 * p503 should be added + AND R19, R11 + AND R19, R12 + AND R19, R13 + AND R19, R14 + AND R19, R15 + AND R19, R16 + AND R19, R17 + + ADDS R11, R3 + ADCS R12, R4 + STP (R3, R4), 0(R2) + ADCS R12, R5 + ADCS R13, R6 + STP (R5, R6), 16(R2) + ADCS R14, R7 + ADCS R15, R8 + STP (R7, R8), 32(R2) + ADCS R16, R9 + ADC R17, R10 + STP (R9, R10), 48(R2) + + RET + +TEXT ·subP503(SB), NOSPLIT, $0-24 + MOVD z+0(FP), R2 + MOVD x+8(FP), R0 + MOVD y+16(FP), R1 + + // Load x into R3-R10 + // Subtract y from x and store result in R3-R10 + LDP 0(R0), (R3, R4) + LDP 0(R1), (R11, R12) + LDP 16(R0), (R5, R6) + LDP 16(R1), (R13, R14) + SUBS R11, R3 + SBCS R12, R4 + SBCS R13, R5 + SBCS R14, R6 + + LDP 32(R0), (R7, R8) + LDP 32(R1), (R11, R12) + LDP 48(R0), (R9, R10) + LDP 48(R1), (R13, R14) + SBCS R11, R7 + SBCS R12, R8 + SBCS R13, R9 + SBCS R14, R10 + SBC ZR, ZR, R19 + + // If x - y < 0, R19 is 1 and 2 * p503 should be added + LDP ·P503x2+0(SB), (R11, R12) + LDP ·P503x2+24(SB), (R13, R14) + AND R19, R11 + AND R19, R12 + LDP ·P503x2+40(SB), (R15, R16) + AND R19, R13 + AND R19, R14 + MOVD ·P503x2+56(SB), R17 + AND R19, R15 + AND R19, R16 + AND R19, R17 + + ADDS R11, R3 + ADCS R12, R4 + STP (R3, R4), 0(R2) + ADCS R12, R5 + ADCS R13, R6 + STP (R5, R6), 16(R2) + ADCS R14, R7 + ADCS R15, R8 + STP (R7, R8), 32(R2) + ADCS R16, R9 + ADC R17, R10 + STP (R9, R10), 48(R2) + + RET + +TEXT ·adlP503(SB), NOSPLIT, $0-24 + MOVD z+0(FP), R2 + MOVD x+8(FP), R0 + MOVD y+16(FP), R1 + + LDP 0(R0), (R3, R4) + LDP 0(R1), (R11, R12) + LDP 16(R0), (R5, R6) + LDP 16(R1), (R13, R14) + ADDS R11, R3 + ADCS R12, R4 + STP (R3, R4), 0(R2) + ADCS R13, R5 + ADCS R14, R6 + STP (R5, R6), 16(R2) + + LDP 32(R0), (R7, R8) + LDP 32(R1), (R11, R12) + LDP 48(R0), (R9, R10) + LDP 48(R1), (R13, R14) + ADCS R11, R7 + ADCS R12, R8 + STP (R7, R8), 32(R2) + ADCS R13, R9 + ADCS R14, R10 + STP (R9, R10), 48(R2) + + LDP 64(R0), (R3, R4) + LDP 64(R1), (R11, R12) + LDP 80(R0), (R5, R6) + LDP 80(R1), (R13, R14) + ADCS R11, R3 + ADCS R12, R4 + STP (R3, R4), 64(R2) + ADCS R13, R5 + ADCS R14, R6 + STP (R5, R6), 80(R2) + + LDP 96(R0), (R7, R8) + LDP 96(R1), (R11, R12) + LDP 112(R0), (R9, R10) + LDP 112(R1), (R13, R14) + ADCS R11, R7 + ADCS R12, R8 + STP (R7, R8), 96(R2) + ADCS R13, R9 + ADC R14, R10 + STP (R9, R10), 112(R2) + + RET + +TEXT ·sulP503(SB), NOSPLIT, $0-24 + MOVD z+0(FP), R2 + MOVD x+8(FP), R0 + MOVD y+16(FP), R1 + + LDP 0(R0), (R3, R4) + LDP 0(R1), (R11, R12) + LDP 16(R0), (R5, R6) + LDP 16(R1), (R13, R14) + SUBS R11, R3 + SBCS R12, R4 + STP (R3, R4), 0(R2) + SBCS R13, R5 + SBCS R14, R6 + STP (R5, R6), 16(R2) + + LDP 32(R0), (R7, R8) + LDP 32(R1), (R11, R12) + LDP 48(R0), (R9, R10) + LDP 48(R1), (R13, R14) + SBCS R11, R7 + SBCS R12, R8 + STP (R7, R8), 32(R2) + SBCS R13, R9 + SBCS R14, R10 + STP (R9, R10), 48(R2) + + LDP 64(R0), (R3, R4) + LDP 64(R1), (R11, R12) + LDP 80(R0), (R5, R6) + LDP 80(R1), (R13, R14) + SBCS R11, R3 + SBCS R12, R4 + SBCS R13, R5 + SBCS R14, R6 + + LDP 96(R0), (R7, R8) + LDP 96(R1), (R11, R12) + LDP 112(R0), (R9, R10) + LDP 112(R1), (R13, R14) + SBCS R11, R7 + SBCS R12, R8 + SBCS R13, R9 + SBCS R14, R10 + SBC ZR, ZR, R15 + + // If x - y < 0, R15 is 1 and p503 should be added + LDP ·P503+16(SB), (R16, R17) + LDP ·P503+32(SB), (R19, R20) + AND R15, R16 + AND R15, R17 + LDP ·P503+48(SB), (R21, R22) + AND R15, R19 + AND R15, R20 + AND R15, R21 + AND R15, R22 + + ADDS R16, R3 + ADCS R16, R4 + STP (R3, R4), 64(R2) + ADCS R16, R5 + ADCS R17, R6 + STP (R5, R6), 80(R2) + ADCS R19, R7 + ADCS R20, R8 + STP (R7, R8), 96(R2) + ADCS R21, R9 + ADC R22, R10 + STP (R9, R10), 112(R2) + + RET + +// Expects that X0*Y0 is already in Z0(low),Z3(high) and X0*Y1 in Z1(low),Z2(high) +// Z0 is not actually touched +// Result of (X0-X1) * (Y0-Y1) will be in Z0-Z3 +// Inputs get overwritten, except for X1 +#define mul128x128comba(X0, X1, Y0, Y1, Z0, Z1, Z2, Z3, T0) \ + MUL X1, Y0, X0 \ + UMULH X1, Y0, Y0 \ + ADDS Z3, Z1 \ + ADC ZR, Z2 \ + \ + MUL Y1, X1, T0 \ + UMULH Y1, X1, Y1 \ + ADDS X0, Z1 \ + ADCS Y0, Z2 \ + ADC ZR, ZR, Z3 \ + \ + ADDS T0, Z2 \ + ADC Y1, Z3 + +// Expects that X points to (X0-X1) +// Result of (X0-X3) * (Y0-Y3) will be in Z0-Z7 +// Inputs get overwritten, except X2-X3 and Y2-Y3 +#define mul256x256karatsuba(X, X0, X1, X2, X3, Y0, Y1, Y2, Y3, Z0, Z1, Z2, Z3, Z4, Z5, Z6, Z7, T0, T1)\ + ADDS X2, X0 \ // xH + xL, destroys xL + ADCS X3, X1 \ + ADCS ZR, ZR, T0 \ + \ + ADDS Y2, Y0, Z6 \ // yH + yL + ADCS Y3, Y1, T1 \ + ADC ZR, ZR, Z7 \ + \ + SUB T0, ZR, Z2 \ + SUB Z7, ZR, Z3 \ + AND Z7, T0 \ // combined carry + \ + AND Z2, Z6, Z0 \ // masked(yH + yL) + AND Z2, T1, Z1 \ + \ + AND Z3, X0, Z4 \ // masked(xH + xL) + AND Z3, X1, Z5 \ + \ + MUL Z6, X0, Z2 \ + MUL T1, X0, Z3 \ + \ + ADDS Z4, Z0 \ + UMULH T1, X0, Z4 \ + ADCS Z5, Z1 \ + UMULH Z6, X0, Z5 \ + ADC ZR, T0 \ + \ // (xH + xL) * (yH + yL) + mul128x128comba(X0, X1, Z6, T1, Z2, Z3, Z4, Z5, Z7)\ + \ + LDP 0+X, (X0, X1) \ + \ + ADDS Z0, Z4 \ + UMULH Y0, X0, Z7 \ + UMULH Y1, X0, T1 \ + ADCS Z1, Z5 \ + MUL Y0, X0, Z0 \ + MUL Y1, X0, Z1 \ + ADC ZR, T0 \ + \ // xL * yL + mul128x128comba(X0, X1, Y0, Y1, Z0, Z1, T1, Z7, Z6)\ + \ + MUL Y2, X2, X0 \ + UMULH Y2, X2, Y0 \ + SUBS Z0, Z2 \ // (xH + xL) * (yH + yL) - xL * yL + SBCS Z1, Z3 \ + SBCS T1, Z4 \ + MUL Y3, X2, X1 \ + UMULH Y3, X2, Z6 \ + SBCS Z7, Z5 \ + SBCS ZR, T0 \ + \ // xH * yH + mul128x128comba(X2, X3, Y2, Y3, X0, X1, Z6, Y0, Y1)\ + \ + SUBS X0, Z2 \ // (xH + xL) * (yH + yL) - xL * yL - xH * yH + SBCS X1, Z3 \ + SBCS Z6, Z4 \ + SBCS Y0, Z5 \ + SBCS ZR, T0 \ + \ + ADDS T1, Z2 \ // (xH * yH) * 2^256 + ((xH + xL) * (yH + yL) - xL * yL - xH * yH) * 2^128 + xL * yL + ADCS Z7, Z3 \ + ADCS X0, Z4 \ + ADCS X1, Z5 \ + ADCS T0, Z6 \ + ADC Y0, ZR, Z7 + + +// This implements two-level Karatsuba with a 128x128 Comba multiplier +// at the bottom +TEXT ·mulP503(SB), NOSPLIT, $0-24 + MOVD z+0(FP), R2 + MOVD x+8(FP), R0 + MOVD y+16(FP), R1 + + // Load xL in R3-R6, xH in R7-R10 + // (xH + xL) in R25-R29 + LDP 0(R0), (R3, R4) + LDP 32(R0), (R7, R8) + ADDS R3, R7, R25 + ADCS R4, R8, R26 + LDP 16(R0), (R5, R6) + LDP 48(R0), (R9, R10) + ADCS R5, R9, R27 + ADCS R6, R10, R29 + ADC ZR, ZR, R7 + + // Load yL in R11-R14, yH in R15-19 + // (yH + yL) in R11-R14, destroys yL + LDP 0(R1), (R11, R12) + LDP 32(R1), (R15, R16) + ADDS R15, R11 + ADCS R16, R12 + LDP 16(R1), (R13, R14) + LDP 48(R1), (R17, R19) + ADCS R17, R13 + ADCS R19, R14 + ADC ZR, ZR, R8 + + // Compute masks and combined carry + SUB R7, ZR, R9 + SUB R8, ZR, R10 + AND R8, R7 + + // masked(yH + yL) + AND R9, R11, R15 + AND R9, R12, R16 + AND R9, R13, R17 + AND R9, R14, R19 + + // masked(xH + xL) + AND R10, R25, R20 + AND R10, R26, R21 + AND R10, R27, R22 + AND R10, R29, R23 + + // masked(xH + xL) + masked(yH + yL) in R15-R19 + ADDS R20, R15 + ADCS R21, R16 + ADCS R22, R17 + ADCS R23, R19 + ADC ZR, R7 + + // Use z as temporary storage + STP (R25, R26), 0(R2) + + // (xH + xL) * (yH + yL) + mul256x256karatsuba(0(R2), R25, R26, R27, R29, R11, R12, R13, R14, R8, R9, R10, R20, R21, R22, R23, R24, R0, R1) + + MOVD x+8(FP), R0 + MOVD y+16(FP), R1 + + ADDS R21, R15 + ADCS R22, R16 + ADCS R23, R17 + ADCS R24, R19 + ADC ZR, R7 + + // Load yL in R11-R14 + LDP 0(R1), (R11, R12) + LDP 16(R1), (R13, R14) + + // xL * yL + mul256x256karatsuba(0(R0), R3, R4, R5, R6, R11, R12, R13, R14, R21, R22, R23, R24, R25, R26, R27, R29, R1, R2) + + MOVD z+0(FP), R2 + MOVD y+16(FP), R1 + + // (xH + xL) * (yH + yL) - xL * yL + SUBS R21, R8 + SBCS R22, R9 + STP (R21, R22), 0(R2) + SBCS R23, R10 + SBCS R24, R20 + STP (R23, R24), 16(R2) + SBCS R25, R15 + SBCS R26, R16 + SBCS R27, R17 + SBCS R29, R19 + SBC ZR, R7 + + // Load xH in R3-R6, yH in R11-R14 + LDP 32(R0), (R3, R4) + LDP 48(R0), (R5, R6) + LDP 32(R1), (R11, R12) + LDP 48(R1), (R13, R14) + + ADDS R25, R8 + ADCS R26, R9 + ADCS R27, R10 + ADCS R29, R20 + ADC ZR, ZR, R1 + + MOVD R20, 32(R2) + + // xH * yH + mul256x256karatsuba(32(R0), R3, R4, R5, R6, R11, R12, R13, R14, R21, R22, R23, R24, R25, R26, R27, R29, R2, R20) + NEG R1, R1 + + MOVD z+0(FP), R2 + MOVD 32(R2), R20 + + // (xH + xL) * (yH + yL) - xL * yL - xH * yH in R8-R10,R20,R15-R19 + // Store lower half in z, that's done + SUBS R21, R8 + SBCS R22, R9 + STP (R8, R9), 32(R2) + SBCS R23, R10 + SBCS R24, R20 + STP (R10, R20), 48(R2) + SBCS R25, R15 + SBCS R26, R16 + SBCS R27, R17 + SBCS R29, R19 + SBC ZR, R7 + + // (xH * yH) * 2^512 + ((xH + xL) * (yH + yL) - xL * yL - xH * yH) * 2^256 + xL * yL + // Store remaining limbs in z + ADDS $1, R1 + ADCS R21, R15 + ADCS R22, R16 + STP (R15, R16), 64(R2) + ADCS R23, R17 + ADCS R24, R19 + STP (R17, R19), 80(R2) + ADCS R7, R25 + ADCS ZR, R26 + STP (R25, R26), 96(R2) + ADCS ZR, R27 + ADC ZR, R29 + STP (R27, R29), 112(R2) + + RET + +// Expects that X0*Y0 is already in Z0(low),Z3(high) and X0*Y1 in Z1(low),Z2(high) +// Z0 is not actually touched +// Result of (X0-X1) * (Y0-Y3) will be in Z0-Z5 +// Inputs remain intact +#define mul128x256comba(X0, X1, Y0, Y1, Y2, Y3, Z0, Z1, Z2, Z3, Z4, Z5, T0, T1, T2, T3)\ + MUL X1, Y0, T0 \ + UMULH X1, Y0, T1 \ + ADDS Z3, Z1 \ + ADC ZR, Z2 \ + \ + MUL X0, Y2, T2 \ + UMULH X0, Y2, T3 \ + ADDS T0, Z1 \ + ADCS T1, Z2 \ + ADC ZR, ZR, Z3 \ + \ + MUL X1, Y1, T0 \ + UMULH X1, Y1, T1 \ + ADDS T2, Z2 \ + ADCS T3, Z3 \ + ADC ZR, ZR, Z4 \ + \ + MUL X0, Y3, T2 \ + UMULH X0, Y3, T3 \ + ADDS T0, Z2 \ + ADCS T1, Z3 \ + ADC ZR, Z4 \ + \ + MUL X1, Y2, T0 \ + UMULH X1, Y2, T1 \ + ADDS T2, Z3 \ + ADCS T3, Z4 \ + ADC ZR, ZR, Z5 \ + \ + MUL X1, Y3, T2 \ + UMULH X1, Y3, T3 \ + ADDS T0, Z3 \ + ADCS T1, Z4 \ + ADC ZR, Z5 \ + ADDS T2, Z4 \ + ADC T3, Z5 + +// This implements the shifted 2^(B*w) Montgomery reduction from +// https://eprint.iacr.org/2016/986.pdf with B = 4, w = 64 +TEXT ·rdcP503(SB), NOSPLIT, $0-16 + MOVD x+8(FP), R0 + + // Load x0-x1 + LDP 0(R0), (R2, R3) + + // Load the prime constant in R25-R29 + LDP ·P503p1s8+32(SB), (R25, R26) + LDP ·P503p1s8+48(SB), (R27, R29) + + // [x0,x1] * p503p1s8 to R4-R9 + MUL R2, R25, R4 // x0 * p503p1s8[0] + UMULH R2, R25, R7 + MUL R2, R26, R5 // x0 * p503p1s8[1] + UMULH R2, R26, R6 + + mul128x256comba(R2, R3, R25, R26, R27, R29, R4, R5, R6, R7, R8, R9, R10, R11, R12, R13) + + LDP 16(R0), (R3, R11) // x2 + LDP 32(R0), (R12, R13) + LDP 48(R0), (R14, R15) + + // Left-shift result in R4-R9 by 56 to R4-R10 + ORR R9>>8, ZR, R10 + LSL $56, R9 + ORR R8>>8, R9 + LSL $56, R8 + ORR R7>>8, R8 + LSL $56, R7 + ORR R6>>8, R7 + LSL $56, R6 + ORR R5>>8, R6 + LSL $56, R5 + ORR R4>>8, R5 + LSL $56, R4 + + ADDS R4, R11 // x3 + ADCS R5, R12 // x4 + ADCS R6, R13 + ADCS R7, R14 + ADCS R8, R15 + LDP 64(R0), (R16, R17) + LDP 80(R0), (R19, R20) + MUL R3, R25, R4 // x2 * p503p1s8[0] + UMULH R3, R25, R7 + ADCS R9, R16 + ADCS R10, R17 + ADCS ZR, R19 + ADCS ZR, R20 + LDP 96(R0), (R21, R22) + LDP 112(R0), (R23, R24) + MUL R3, R26, R5 // x2 * p503p1s8[1] + UMULH R3, R26, R6 + ADCS ZR, R21 + ADCS ZR, R22 + ADCS ZR, R23 + ADC ZR, R24 + + // [x2,x3] * p503p1s8 to R4-R9 + mul128x256comba(R3, R11, R25, R26, R27, R29, R4, R5, R6, R7, R8, R9, R10, R0, R1, R2) + + ORR R9>>8, ZR, R10 + LSL $56, R9 + ORR R8>>8, R9 + LSL $56, R8 + ORR R7>>8, R8 + LSL $56, R7 + ORR R6>>8, R7 + LSL $56, R6 + ORR R5>>8, R6 + LSL $56, R5 + ORR R4>>8, R5 + LSL $56, R4 + + ADDS R4, R13 // x5 + ADCS R5, R14 // x6 + ADCS R6, R15 + ADCS R7, R16 + MUL R12, R25, R4 // x4 * p503p1s8[0] + UMULH R12, R25, R7 + ADCS R8, R17 + ADCS R9, R19 + ADCS R10, R20 + ADCS ZR, R21 + MUL R12, R26, R5 // x4 * p503p1s8[1] + UMULH R12, R26, R6 + ADCS ZR, R22 + ADCS ZR, R23 + ADC ZR, R24 + + // [x4,x5] * p503p1s8 to R4-R9 + mul128x256comba(R12, R13, R25, R26, R27, R29, R4, R5, R6, R7, R8, R9, R10, R0, R1, R2) + + ORR R9>>8, ZR, R10 + LSL $56, R9 + ORR R8>>8, R9 + LSL $56, R8 + ORR R7>>8, R8 + LSL $56, R7 + ORR R6>>8, R7 + LSL $56, R6 + ORR R5>>8, R6 + LSL $56, R5 + ORR R4>>8, R5 + LSL $56, R4 + + ADDS R4, R15 // x7 + ADCS R5, R16 // x8 + ADCS R6, R17 + ADCS R7, R19 + MUL R14, R25, R4 // x6 * p503p1s8[0] + UMULH R14, R25, R7 + ADCS R8, R20 + ADCS R9, R21 + ADCS R10, R22 + MUL R14, R26, R5 // x6 * p503p1s8[1] + UMULH R14, R26, R6 + ADCS ZR, R23 + ADC ZR, R24 + + // [x6,x7] * p503p1s8 to R4-R9 + mul128x256comba(R14, R15, R25, R26, R27, R29, R4, R5, R6, R7, R8, R9, R10, R0, R1, R2) + + ORR R9>>8, ZR, R10 + LSL $56, R9 + ORR R8>>8, R9 + LSL $56, R8 + ORR R7>>8, R8 + LSL $56, R7 + ORR R6>>8, R7 + LSL $56, R6 + ORR R5>>8, R6 + LSL $56, R5 + ORR R4>>8, R5 + LSL $56, R4 + + MOVD z+0(FP), R0 + ADDS R4, R17 + ADCS R5, R19 + STP (R16, R17), 0(R0) // Store final result to z + ADCS R6, R20 + ADCS R7, R21 + STP (R19, R20), 16(R0) + ADCS R8, R22 + ADCS R9, R23 + STP (R21, R22), 32(R0) + ADC R10, R24 + STP (R23, R24), 48(R0) + + RET + +TEXT ·modP503(SB), NOSPLIT, $0-8 + MOVD x+0(FP), R0 + + // Keep x in R1-R8, p503 in R9-R14, subtract to R1-R8 + LDP ·P503+16(SB), (R9, R10) + LDP 0(R0), (R1, R2) + LDP 16(R0), (R3, R4) + SUBS R9, R1 + SBCS R9, R2 + + LDP 32(R0), (R5, R6) + LDP ·P503+32(SB), (R11, R12) + SBCS R9, R3 + SBCS R10, R4 + + LDP 48(R0), (R7, R8) + LDP ·P503+48(SB), (R13, R14) + SBCS R11, R5 + SBCS R12, R6 + + SBCS R13, R7 + SBCS R14, R8 + SBC ZR, ZR, R15 + + // Mask with the borrow and add p503 + AND R15, R9 + AND R15, R10 + AND R15, R11 + AND R15, R12 + AND R15, R13 + AND R15, R14 + + ADDS R9, R1 + ADCS R9, R2 + STP (R1, R2), 0(R0) + ADCS R9, R3 + ADCS R10, R4 + STP (R3, R4), 16(R0) + ADCS R11, R5 + ADCS R12, R6 + STP (R5, R6), 32(R0) + ADCS R13, R7 + ADCS R14, R8 + STP (R7, R8), 48(R0) + + RET diff --git a/src/circl/dh/sidh/internal/p503/arith_decl.go b/src/circl/dh/sidh/internal/p503/arith_decl.go new file mode 100644 index 00000000000..a8a466e94af --- /dev/null +++ b/src/circl/dh/sidh/internal/p503/arith_decl.go @@ -0,0 +1,45 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +// +build amd64,!noasm arm64,!noasm + +package p503 + +import ( + . "circl/dh/sidh/internal/common" +) + +// If choice = 0, leave x,y unchanged. If choice = 1, set x,y = y,x. +// If choice is neither 0 nor 1 then behaviour is undefined. +// This function executes in constant time. +//go:noescape +func cswapP503(x, y *Fp, choice uint8) + +// Compute z = x + y (mod p). +//go:noescape +func addP503(z, x, y *Fp) + +// Compute z = x - y (mod p). +//go:noescape +func subP503(z, x, y *Fp) + +// Compute z = x + y, without reducing mod p. +//go:noescape +func adlP503(z, x, y *FpX2) + +// Compute z = x - y, without reducing mod p. +//go:noescape +func sulP503(z, x, y *FpX2) + +// Reduce a field element in [0, 2*p) to one in [0,p). +//go:noescape +func modP503(x *Fp) + +// Computes z = x * y. +//go:noescape +func mulP503(z *FpX2, x, y *Fp) + +// Computes the Montgomery reduction z = x R^{-1} (mod 2*p). On return value +// of x may be changed. z=x not allowed. +//go:noescape +func rdcP503(z *Fp, x *FpX2) diff --git a/src/circl/dh/sidh/internal/p503/arith_generic.go b/src/circl/dh/sidh/internal/p503/arith_generic.go new file mode 100644 index 00000000000..3c288c24aa5 --- /dev/null +++ b/src/circl/dh/sidh/internal/p503/arith_generic.go @@ -0,0 +1,192 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +// +build noasm !amd64,!arm64 + +package p503 + +import ( + "math/bits" + + "circl/dh/sidh/internal/common" +) + +// Compute z = x + y (mod p). +func addP503(z, x, y *common.Fp) { + var carry uint64 + + // z=x+y % P503 + for i := 0; i < FpWords; i++ { + z[i], carry = bits.Add64(x[i], y[i], carry) + } + + // z = z - P503x2 + carry = 0 + for i := 0; i < FpWords; i++ { + z[i], carry = bits.Sub64(z[i], P503x2[i], carry) + } + + // if z<0 add P503x2 back + mask := uint64(0 - carry) + carry = 0 + for i := 0; i < FpWords; i++ { + z[i], carry = bits.Add64(z[i], P503x2[i]&mask, carry) + } +} + +// Compute z = x - y (mod p). +func subP503(z, x, y *common.Fp) { + var borrow uint64 + + for i := 0; i < FpWords; i++ { + z[i], borrow = bits.Sub64(x[i], y[i], borrow) + } + + mask := uint64(0 - borrow) + borrow = 0 + + for i := 0; i < FpWords; i++ { + z[i], borrow = bits.Add64(z[i], P503x2[i]&mask, borrow) + } +} + +// Conditionally swaps bits in x and y in constant time. +// mask indicates bits to be swapped (set bits are swapped) +// For details see "Hackers Delight, 2.20" +// +// Implementation doesn't actually depend on a prime field. +func cswapP503(x, y *common.Fp, mask uint8) { + var tmp, mask64 uint64 + + mask64 = 0 - uint64(mask) + for i := 0; i < FpWords; i++ { + tmp = mask64 & (x[i] ^ y[i]) + x[i] = tmp ^ x[i] + y[i] = tmp ^ y[i] + } +} + +// Perform Montgomery reduction: set z = x R^{-1} (mod 2*p) +// with R=2^(FpWords*64). Destroys the input value. +func rdcP503(z *common.Fp, x *common.FpX2) { + var carry, t, u, v uint64 + var hi, lo uint64 + var count int + + count = P503p1Zeros + + for i := 0; i < FpWords; i++ { + for j := 0; j < i; j++ { + if j < (i - count + 1) { + hi, lo = bits.Mul64(z[j], P503p1[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + } + v, carry = bits.Add64(v, x[i], 0) + u, carry = bits.Add64(u, 0, carry) + t += carry + + z[i] = v + v = u + u = t + t = 0 + } + + for i := FpWords; i < 2*FpWords-1; i++ { + if count > 0 { + count-- + } + for j := i - FpWords + 1; j < FpWords; j++ { + if j < (FpWords - count) { + hi, lo = bits.Mul64(z[j], P503p1[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + } + v, carry = bits.Add64(v, x[i], 0) + u, carry = bits.Add64(u, 0, carry) + + t += carry + z[i-FpWords] = v + v = u + u = t + t = 0 + } + v, _ = bits.Add64(v, x[2*FpWords-1], 0) + z[FpWords-1] = v +} + +// Compute z = x * y. +func mulP503(z *common.FpX2, x, y *common.Fp) { + var u, v, t uint64 + var hi, lo uint64 + var carry uint64 + + for i := uint64(0); i < FpWords; i++ { + for j := uint64(0); j <= i; j++ { + hi, lo = bits.Mul64(x[j], y[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + z[i] = v + v = u + u = t + t = 0 + } + + for i := FpWords; i < (2*FpWords)-1; i++ { + for j := i - FpWords + 1; j < FpWords; j++ { + hi, lo = bits.Mul64(x[j], y[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + z[i] = v + v = u + u = t + t = 0 + } + z[2*FpWords-1] = v +} + +// Compute z = x + y, without reducing mod p. +func adlP503(z, x, y *common.FpX2) { + var carry uint64 + for i := 0; i < 2*FpWords; i++ { + z[i], carry = bits.Add64(x[i], y[i], carry) + } +} + +// Reduce a field element in [0, 2*p) to one in [0,p). +func modP503(x *common.Fp) { + var borrow, mask uint64 + for i := 0; i < FpWords; i++ { + x[i], borrow = bits.Sub64(x[i], P503[i], borrow) + } + + // Sets all bits if borrow = 1 + mask = 0 - borrow + borrow = 0 + for i := 0; i < FpWords; i++ { + x[i], borrow = bits.Add64(x[i], P503[i]&mask, borrow) + } +} + +// Compute z = x - y, without reducing mod p. +func sulP503(z, x, y *common.FpX2) { + var borrow, mask uint64 + for i := 0; i < 2*FpWords; i++ { + z[i], borrow = bits.Sub64(x[i], y[i], borrow) + } + + // Sets all bits if borrow = 1 + mask = 0 - borrow + borrow = 0 + for i := FpWords; i < 2*FpWords; i++ { + z[i], borrow = bits.Add64(z[i], P503[i-FpWords]&mask, borrow) + } +} diff --git a/src/circl/dh/sidh/internal/p503/arith_test.go b/src/circl/dh/sidh/internal/p503/arith_test.go new file mode 100644 index 00000000000..c2ad848079b --- /dev/null +++ b/src/circl/dh/sidh/internal/p503/arith_test.go @@ -0,0 +1,101 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p503 + +import ( + "testing" + + "circl/dh/sidh/internal/common" +) + +// Package-level storage for this field element is intended to deter +// compiler optimizations. +var ( + benchmarkFp common.Fp + benchmarkFpX2 common.FpX2 + bench_x = common.Fp{17026702066521327207, 5108203422050077993, 10225396685796065916, 11153620995215874678, 6531160855165088358, 15302925148404145445, 1248821577836769963, 9789766903037985294, 7493111552032041328, 10838999828319306046, 18103257655515297935, 27403304611634} + bench_y = common.Fp{4227467157325093378, 10699492810770426363, 13500940151395637365, 12966403950118934952, 16517692605450415877, 13647111148905630666, 14223628886152717087, 7167843152346903316, 15855377759596736571, 4300673881383687338, 6635288001920617779, 30486099554235} + bench_z = common.FpX2{1595347748594595712, 10854920567160033970, 16877102267020034574, 12435724995376660096, 3757940912203224231, 8251999420280413600, 3648859773438820227, 17622716832674727914, 11029567000887241528, 11216190007549447055, 17606662790980286987, 4720707159513626555, 12887743598335030915, 14954645239176589309, 14178817688915225254, 1191346797768989683, 12629157932334713723, 6348851952904485603, 16444232588597434895, 7809979927681678066, 14642637672942531613, 3092657597757640067, 10160361564485285723, 240071237} +) + +func TestFpCswap(t *testing.T) { + var one = common.Fp{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} + var two = common.Fp{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2} + + var x = one + var y = two + + cswapP503(&x, &y, 0) + for i := 0; i < FpWords; i++ { + if (x[i] != one[i]) || (y[i] != two[i]) { + t.Error("Found", x, "expected", two) + } + } + + cswapP503(&x, &y, 1) + for i := 0; i < FpWords; i++ { + if (x[i] != two[i]) || (y[i] != one[i]) { + t.Error("Found", x, "expected", two) + } + } +} + +// Benchmarking for field arithmetic +func BenchmarkMul(b *testing.B) { + for n := 0; n < b.N; n++ { + mulP503(&benchmarkFpX2, &bench_x, &bench_y) + } +} + +func BenchmarkRdc(b *testing.B) { + z := bench_z + + // This benchmark actually computes garbage, because + // rdcP503 mangles its input, but since it's + // constant-time that shouldn't matter for the benchmarks. + for n := 0; n < b.N; n++ { + rdcP503(&benchmarkFp, &z) + } +} + +func BenchmarkAdd(b *testing.B) { + for n := 0; n < b.N; n++ { + addP503(&benchmarkFp, &bench_x, &bench_y) + } +} + +func BenchmarkSub(b *testing.B) { + for n := 0; n < b.N; n++ { + subP503(&benchmarkFp, &bench_x, &bench_y) + } +} + +func BenchmarkCswap(b *testing.B) { + x, y := bench_x, bench_y + for n := 0; n < b.N; n++ { + cswapP503(&x, &y, 1) + cswapP503(&x, &y, 0) + } +} + +func BenchmarkMod(b *testing.B) { + x := bench_x + for n := 0; n < b.N; n++ { + modP503(&x) + } +} + +func BenchmarkX2AddLazy(b *testing.B) { + x, y, z := bench_z, bench_z, bench_z + for n := 0; n < b.N; n++ { + adlP503(&x, &y, &z) + } +} + +func BenchmarkX2SubLazy(b *testing.B) { + x, y, z := bench_z, bench_z, bench_z + for n := 0; n < b.N; n++ { + sulP503(&x, &y, &z) + } +} diff --git a/src/circl/dh/sidh/internal/p503/core.go b/src/circl/dh/sidh/internal/p503/core.go new file mode 100644 index 00000000000..d4e6f679e44 --- /dev/null +++ b/src/circl/dh/sidh/internal/p503/core.go @@ -0,0 +1,282 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p503 + +import ( + . "circl/dh/sidh/internal/common" +) + +// ----------------------------------------------------------------------------- +// Functions for traversing isogeny trees acoording to strategy. Key type 'A' is +// + +// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed +// for public key generation. +func traverseTreePublicKeyA(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny4 + + cparam := CalcCurveParamsEquiv4(curve) + strat := params.A.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow2k(xR, &cparam, 2*k) + i += int(k) + } + cparam = phi.GenerateCurve(xR) + + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + *phiP = phi.EvaluatePoint(phiP) + *phiQ = phi.EvaluatePoint(phiQ) + *phiR = phi.EvaluatePoint(phiR) + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Traverses isogeny tree in order to compute xR needed +// for public key generation. +func traverseTreeSharedKeyA(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny4 + + cparam := CalcCurveParamsEquiv4(curve) + strat := params.A.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow2k(xR, &cparam, 2*k) + i += int(k) + } + cparam = phi.GenerateCurve(xR) + + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed +// for public key generation. +func traverseTreePublicKeyB(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny3 + + cparam := CalcCurveParamsEquiv3(curve) + strat := params.B.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow3k(xR, &cparam, k) + i += int(k) + } + + cparam = phi.GenerateCurve(xR) + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + + *phiP = phi.EvaluatePoint(phiP) + *phiQ = phi.EvaluatePoint(phiQ) + *phiR = phi.EvaluatePoint(phiR) + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed +// for public key generation. +func traverseTreeSharedKeyB(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny3 + + cparam := CalcCurveParamsEquiv3(curve) + strat := params.B.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow3k(xR, &cparam, k) + i += int(k) + } + + cparam = phi.GenerateCurve(xR) + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Generate a public key in the 2-torsion group. Public key is a set +// of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) +func PublicKeyGenA(pub3Pt *[3]Fp2, prvBytes []byte) { + var xPA, xQA, xRA ProjectivePoint + var xPB, xQB, xRB, xR ProjectivePoint + var invZP, invZQ, invZR Fp2 + var phi isogeny4 + + // Load points for A + xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} + xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} + xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} + + // Load points for B + xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} + xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} + xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} + + // Find isogeny kernel + xR = ScalarMul3Pt(¶ms.InitCurve, &xPA, &xQA, &xRA, params.A.SecretBitLen, prvBytes) + traverseTreePublicKeyA(¶ms.InitCurve, &xR, &xPB, &xQB, &xRB) + + // Secret isogeny + phi.GenerateCurve(&xR) + xPA = phi.EvaluatePoint(&xPB) + xQA = phi.EvaluatePoint(&xQB) + xRA = phi.EvaluatePoint(&xRB) + Fp2Batch3Inv(&xPA.Z, &xQA.Z, &xRA.Z, &invZP, &invZQ, &invZR) + + mul(&pub3Pt[0], &xPA.X, &invZP) + mul(&pub3Pt[1], &xQA.X, &invZQ) + mul(&pub3Pt[2], &xRA.X, &invZR) +} + +// Generate a public key in the 2-torsion group. Public key is a set +// of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) +func PublicKeyGenB(pub3Pt *[3]Fp2, prvBytes []byte) { + var xPB, xQB, xRB, xR ProjectivePoint + var xPA, xQA, xRA ProjectivePoint + var invZP, invZQ, invZR Fp2 + var phi isogeny3 + + // Load points for B + xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} + xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} + xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} + + // Load points for A + xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} + xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} + xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} + + // Find isogeny kernel + xR = ScalarMul3Pt(¶ms.InitCurve, &xPB, &xQB, &xRB, params.B.SecretBitLen, prvBytes) + traverseTreePublicKeyB(¶ms.InitCurve, &xR, &xPA, &xQA, &xRA) + + phi.GenerateCurve(&xR) + xPB = phi.EvaluatePoint(&xPA) + xQB = phi.EvaluatePoint(&xQA) + xRB = phi.EvaluatePoint(&xRA) + Fp2Batch3Inv(&xPB.Z, &xQB.Z, &xRB.Z, &invZP, &invZQ, &invZR) + + mul(&pub3Pt[0], &xPB.X, &invZP) + mul(&pub3Pt[1], &xQB.X, &invZQ) + mul(&pub3Pt[2], &xRB.X, &invZR) +} + +// ----------------------------------------------------------------------------- +// Key agreement functions +// + +// Establishing shared keys in in 2-torsion group +func DeriveSecretA(ss, prv []byte, pub3Pt *[3]Fp2) { + var xP, xQ, xQmP ProjectivePoint + var xR ProjectivePoint + var phi isogeny4 + var jInv Fp2 + + // Recover curve coefficients + cparam := params.InitCurve + RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) + + // Find kernel of the morphism + xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} + xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} + xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} + xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.A.SecretBitLen, prv) + + // Traverse isogeny tree + traverseTreeSharedKeyA(&cparam, &xR) + + // Calculate j-invariant on isogeneus curve + c := phi.GenerateCurve(&xR) + RecoverCurveCoefficients4(&cparam, &c) + Jinvariant(&cparam, &jInv) + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(ss, &jInv, params.Bytelen) +} + +// Establishing shared keys in in 3-torsion group +func DeriveSecretB(ss, prv []byte, pub3Pt *[3]Fp2) { + var xP, xQ, xQmP ProjectivePoint + var xR ProjectivePoint + var phi isogeny3 + var jInv Fp2 + + // Recover curve coefficients + cparam := params.InitCurve + RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) + + // Find kernel of the morphism + xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} + xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} + xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} + xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.B.SecretBitLen, prv) + + // Traverse isogeny tree + traverseTreeSharedKeyB(&cparam, &xR) + + // Calculate j-invariant on isogeneus curve + c := phi.GenerateCurve(&xR) + RecoverCurveCoefficients3(&cparam, &c) + Jinvariant(&cparam, &jInv) + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(ss, &jInv, params.Bytelen) +} diff --git a/src/circl/dh/sidh/internal/p503/curve.go b/src/circl/dh/sidh/internal/p503/curve.go new file mode 100644 index 00000000000..c250e6f0c0b --- /dev/null +++ b/src/circl/dh/sidh/internal/p503/curve.go @@ -0,0 +1,362 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p503 + +import ( + . "circl/dh/sidh/internal/common" +) + +// Stores isogeny 3 curve constants +type isogeny3 struct { + K1 Fp2 + K2 Fp2 +} + +// Stores isogeny 4 curve constants +type isogeny4 struct { + isogeny3 + K3 Fp2 +} + +// Computes j-invariant for a curve y2=x3+A/Cx+x with A,C in F_(p^2). Result +// is returned in jBytes buffer, encoded in little-endian format. Caller +// provided jBytes buffer has to be big enough to j-invariant value. In case +// of SIDH, buffer size must be at least size of shared secret. +// Implementation corresponds to Algorithm 9 from SIKE. +func Jinvariant(cparams *ProjectiveCurveParameters, j *Fp2) { + var t0, t1 Fp2 + + sqr(j, &cparams.A) // j = A^2 + sqr(&t1, &cparams.C) // t1 = C^2 + add(&t0, &t1, &t1) // t0 = t1 + t1 + sub(&t0, j, &t0) // t0 = j - t0 + sub(&t0, &t0, &t1) // t0 = t0 - t1 + sub(j, &t0, &t1) // t0 = t0 - t1 + sqr(&t1, &t1) // t1 = t1^2 + mul(j, j, &t1) // j = j * t1 + add(&t0, &t0, &t0) // t0 = t0 + t0 + add(&t0, &t0, &t0) // t0 = t0 + t0 + sqr(&t1, &t0) // t1 = t0^2 + mul(&t0, &t0, &t1) // t0 = t0 * t1 + add(&t0, &t0, &t0) // t0 = t0 + t0 + add(&t0, &t0, &t0) // t0 = t0 + t0 + inv(j, j) // j = 1/j + mul(j, &t0, j) // j = t0 * j +} + +// Given affine points x(P), x(Q) and x(Q-P) in a extension field F_{p^2}, function +// recorvers projective coordinate A of a curve. This is Algorithm 10 from SIKE. +func RecoverCoordinateA(curve *ProjectiveCurveParameters, xp, xq, xr *Fp2) { + var t0, t1 Fp2 + + add(&t1, xp, xq) // t1 = Xp + Xq + mul(&t0, xp, xq) // t0 = Xp * Xq + mul(&curve.A, xr, &t1) // A = X(q-p) * t1 + add(&curve.A, &curve.A, &t0) // A = A + t0 + mul(&t0, &t0, xr) // t0 = t0 * X(q-p) + sub(&curve.A, &curve.A, ¶ms.OneFp2) // A = A - 1 + add(&t0, &t0, &t0) // t0 = t0 + t0 + add(&t1, &t1, xr) // t1 = t1 + X(q-p) + add(&t0, &t0, &t0) // t0 = t0 + t0 + sqr(&curve.A, &curve.A) // A = A^2 + inv(&t0, &t0) // t0 = 1/t0 + mul(&curve.A, &curve.A, &t0) // A = A * t0 + sub(&curve.A, &curve.A, &t1) // A = A - t1 +} + +// Computes equivalence (A:C) ~ (A+2C : A-2C) +func CalcCurveParamsEquiv3(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { + var coef CurveCoefficientsEquiv + var c2 Fp2 + + add(&c2, &cparams.C, &cparams.C) + // A24p = A+2*C + add(&coef.A, &cparams.A, &c2) + // A24m = A-2*C + sub(&coef.C, &cparams.A, &c2) + return coef +} + +// Computes equivalence (A:C) ~ (A+2C : 4C) +func CalcCurveParamsEquiv4(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { + var coefEq CurveCoefficientsEquiv + + add(&coefEq.C, &cparams.C, &cparams.C) + // A24p = A+2C + add(&coefEq.A, &cparams.A, &coefEq.C) + // C24 = 4*C + add(&coefEq.C, &coefEq.C, &coefEq.C) + return coefEq +} + +// Helper function for RightToLeftLadder(). Returns A+2C / 4. +func CalcAplus2Over4(cparams *ProjectiveCurveParameters) (ret Fp2) { + var tmp Fp2 + + // 2C + add(&tmp, &cparams.C, &cparams.C) + // A+2C + add(&ret, &cparams.A, &tmp) + // 1/4C + add(&tmp, &tmp, &tmp) + inv(&tmp, &tmp) + // A+2C/4C + mul(&ret, &ret, &tmp) + return +} + +// Recovers (A:C) curve parameters from projectively equivalent (A+2C:A-2C). +func RecoverCurveCoefficients3(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { + add(&cparams.A, &coefEq.A, &coefEq.C) + // cparams.A = 2*(A+2C+A-2C) = 4A + add(&cparams.A, &cparams.A, &cparams.A) + // cparams.C = (A+2C-A+2C) = 4C + sub(&cparams.C, &coefEq.A, &coefEq.C) + return +} + +// Recovers (A:C) curve parameters from projectively equivalent (A+2C:4C). +func RecoverCurveCoefficients4(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { + // cparams.C = (4C)*1/2=2C + mul(&cparams.C, &coefEq.C, ¶ms.HalfFp2) + // cparams.A = A+2C - 2C = A + sub(&cparams.A, &coefEq.A, &cparams.C) + // cparams.C = 2C * 1/2 = C + mul(&cparams.C, &cparams.C, ¶ms.HalfFp2) +} + +// Combined coordinate doubling and differential addition. Takes projective points +// P,Q,Q-P and (A+2C)/4C curve E coefficient. Returns 2*P and P+Q calculated on E. +// Function is used only by RightToLeftLadder. Corresponds to Algorithm 5 of SIKE +func xDbladd(P, Q, QmP *ProjectivePoint, a24 *Fp2) (dblP, PaQ ProjectivePoint) { + var t0, t1, t2 Fp2 + + xQmP, zQmP := &QmP.X, &QmP.Z + xPaQ, zPaQ := &PaQ.X, &PaQ.Z + x2P, z2P := &dblP.X, &dblP.Z + xP, zP := &P.X, &P.Z + xQ, zQ := &Q.X, &Q.Z + + add(&t0, xP, zP) // t0 = Xp+Zp + sub(&t1, xP, zP) // t1 = Xp-Zp + sqr(x2P, &t0) // 2P.X = t0^2 + sub(&t2, xQ, zQ) // t2 = Xq-Zq + add(xPaQ, xQ, zQ) // Xp+q = Xq+Zq + mul(&t0, &t0, &t2) // t0 = t0 * t2 + mul(z2P, &t1, &t1) // 2P.Z = t1 * t1 + mul(&t1, &t1, xPaQ) // t1 = t1 * Xp+q + sub(&t2, x2P, z2P) // t2 = 2P.X - 2P.Z + mul(x2P, x2P, z2P) // 2P.X = 2P.X * 2P.Z + mul(xPaQ, a24, &t2) // Xp+q = A24 * t2 + sub(zPaQ, &t0, &t1) // Zp+q = t0 - t1 + add(z2P, xPaQ, z2P) // 2P.Z = Xp+q + 2P.Z + add(xPaQ, &t0, &t1) // Xp+q = t0 + t1 + mul(z2P, z2P, &t2) // 2P.Z = 2P.Z * t2 + sqr(zPaQ, zPaQ) // Zp+q = Zp+q ^ 2 + sqr(xPaQ, xPaQ) // Xp+q = Xp+q ^ 2 + mul(zPaQ, xQmP, zPaQ) // Zp+q = Xq-p * Zp+q + mul(xPaQ, zQmP, xPaQ) // Xp+q = Zq-p * Xp+q + return +} + +// Given the curve parameters, xP = x(P), computes xP = x([2^k]P) +// Safe to overlap xP, x2P. +func Pow2k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { + var t0, t1 Fp2 + + x, z := &xP.X, &xP.Z + for i := uint32(0); i < k; i++ { + sub(&t0, x, z) // t0 = Xp - Zp + add(&t1, x, z) // t1 = Xp + Zp + sqr(&t0, &t0) // t0 = t0 ^ 2 + sqr(&t1, &t1) // t1 = t1 ^ 2 + mul(z, ¶ms.C, &t0) // Z2p = C24 * t0 + mul(x, z, &t1) // X2p = Z2p * t1 + sub(&t1, &t1, &t0) // t1 = t1 - t0 + mul(&t0, ¶ms.A, &t1) // t0 = A24+ * t1 + add(z, z, &t0) // Z2p = Z2p + t0 + mul(z, z, &t1) // Zp = Z2p * t1 + } +} + +// Given the curve parameters, xP = x(P), and k >= 0, compute xP = x([3^k]P). +// +// Safe to overlap xP, xR. +func Pow3k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { + var t0, t1, t2, t3, t4, t5, t6 Fp2 + + x, z := &xP.X, &xP.Z + for i := uint32(0); i < k; i++ { + sub(&t0, x, z) // t0 = Xp - Zp + sqr(&t2, &t0) // t2 = t0^2 + add(&t1, x, z) // t1 = Xp + Zp + sqr(&t3, &t1) // t3 = t1^2 + add(&t4, &t1, &t0) // t4 = t1 + t0 + sub(&t0, &t1, &t0) // t0 = t1 - t0 + sqr(&t1, &t4) // t1 = t4^2 + sub(&t1, &t1, &t3) // t1 = t1 - t3 + sub(&t1, &t1, &t2) // t1 = t1 - t2 + mul(&t5, &t3, ¶ms.A) // t5 = t3 * A24+ + mul(&t3, &t3, &t5) // t3 = t5 * t3 + mul(&t6, &t2, ¶ms.C) // t6 = t2 * A24- + mul(&t2, &t2, &t6) // t2 = t2 * t6 + sub(&t3, &t2, &t3) // t3 = t2 - t3 + sub(&t2, &t5, &t6) // t2 = t5 - t6 + mul(&t1, &t2, &t1) // t1 = t2 * t1 + add(&t2, &t3, &t1) // t2 = t3 + t1 + sqr(&t2, &t2) // t2 = t2^2 + mul(x, &t2, &t4) // X3p = t2 * t4 + sub(&t1, &t3, &t1) // t1 = t3 - t1 + sqr(&t1, &t1) // t1 = t1^2 + mul(z, &t1, &t0) // Z3p = t1 * t0 + } +} + +// Set (y1, y2, y3) = (1/x1, 1/x2, 1/x3). +// +// All xi, yi must be distinct. +func Fp2Batch3Inv(x1, x2, x3, y1, y2, y3 *Fp2) { + var x1x2, t Fp2 + + mul(&x1x2, x1, x2) // x1*x2 + mul(&t, &x1x2, x3) // 1/(x1*x2*x3) + inv(&t, &t) + mul(y1, &t, x2) // 1/x1 + mul(y1, y1, x3) + mul(y2, &t, x1) // 1/x2 + mul(y2, y2, x3) + mul(y3, &t, &x1x2) // 1/x3 +} + +// Scalarmul3Pt is a right-to-left point multiplication that given the +// x-coordinate of P, Q and P-Q calculates the x-coordinate of R=Q+[scalar]P. +// nbits must be smaller or equal to len(scalar). +func ScalarMul3Pt(cparams *ProjectiveCurveParameters, P, Q, PmQ *ProjectivePoint, nbits uint, scalar []uint8) ProjectivePoint { + var R0, R2, R1 ProjectivePoint + aPlus2Over4 := CalcAplus2Over4(cparams) + R1 = *P + R2 = *PmQ + R0 = *Q + + // Iterate over the bits of the scalar, bottom to top + prevBit := uint8(0) + for i := uint(0); i < nbits; i++ { + bit := (scalar[i>>3] >> (i & 7) & 1) + swap := prevBit ^ bit + prevBit = bit + cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, swap) + R0, R2 = xDbladd(&R0, &R2, &R1, &aPlus2Over4) + } + cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, prevBit) + return R1 +} + +// Given a three-torsion point p = x(PB) on the curve E_(A:C), construct the +// three-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). +// +// Input: (XP_3: ZP_3), where P_3 has exact order 3 on E_A/C +// Output: * Curve coordinates (A' + 2C', A' - 2C') corresponding to E_A'/C' = A_E/C/ +// * Isogeny phi with constants in F_p^2 +func (phi *isogeny3) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { + var t0, t1, t2, t3, t4 Fp2 + var coefEq CurveCoefficientsEquiv + var K1, K2 = &phi.K1, &phi.K2 + + sub(K1, &p.X, &p.Z) // K1 = XP3 - ZP3 + sqr(&t0, K1) // t0 = K1^2 + add(K2, &p.X, &p.Z) // K2 = XP3 + ZP3 + sqr(&t1, K2) // t1 = K2^2 + add(&t2, &t0, &t1) // t2 = t0 + t1 + add(&t3, K1, K2) // t3 = K1 + K2 + sqr(&t3, &t3) // t3 = t3^2 + sub(&t3, &t3, &t2) // t3 = t3 - t2 + add(&t2, &t1, &t3) // t2 = t1 + t3 + add(&t3, &t3, &t0) // t3 = t3 + t0 + add(&t4, &t3, &t0) // t4 = t3 + t0 + add(&t4, &t4, &t4) // t4 = t4 + t4 + add(&t4, &t1, &t4) // t4 = t1 + t4 + mul(&coefEq.C, &t2, &t4) // A24m = t2 * t4 + add(&t4, &t1, &t2) // t4 = t1 + t2 + add(&t4, &t4, &t4) // t4 = t4 + t4 + add(&t4, &t0, &t4) // t4 = t0 + t4 + mul(&t4, &t3, &t4) // t4 = t3 * t4 + sub(&t0, &t4, &coefEq.C) // t0 = t4 - A24m + add(&coefEq.A, &coefEq.C, &t0) // A24p = A24m + t0 + return coefEq +} + +// Given a 3-isogeny phi and a point pB = x(PB), compute x(QB), the x-coordinate +// of the image QB = phi(PB) of PB under phi : E_(A:C) -> E_(A':C'). +// +// The output xQ = x(Q) is then a point on the curve E_(A':C'); the curve +// parameters are returned by the GenerateCurve function used to construct phi. +func (phi *isogeny3) EvaluatePoint(p *ProjectivePoint) ProjectivePoint { + var t0, t1, t2 Fp2 + var q ProjectivePoint + var K1, K2 = &phi.K1, &phi.K2 + var px, pz = &p.X, &p.Z + + add(&t0, px, pz) // t0 = XQ + ZQ + sub(&t1, px, pz) // t1 = XQ - ZQ + mul(&t0, K1, &t0) // t2 = K1 * t0 + mul(&t1, K2, &t1) // t1 = K2 * t1 + add(&t2, &t0, &t1) // t2 = t0 + t1 + sub(&t0, &t1, &t0) // t0 = t1 - t0 + sqr(&t2, &t2) // t2 = t2 ^ 2 + sqr(&t0, &t0) // t0 = t0 ^ 2 + mul(&q.X, px, &t2) // XQ'= XQ * t2 + mul(&q.Z, pz, &t0) // ZQ'= ZQ * t0 + return q +} + +// Given a four-torsion point p = x(PB) on the curve E_(A:C), construct the +// four-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). +// +// Input: (XP_4: ZP_4), where P_4 has exact order 4 on E_A/C +// Output: * Curve coordinates (A' + 2C', 4C') corresponding to E_A'/C' = A_E/C/ +// * Isogeny phi with constants in F_p^2 +func (phi *isogeny4) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { + var coefEq CurveCoefficientsEquiv + var xp4, zp4 = &p.X, &p.Z + var K1, K2, K3 = &phi.K1, &phi.K2, &phi.K3 + + sub(K2, xp4, zp4) + add(K3, xp4, zp4) + sqr(K1, zp4) + add(K1, K1, K1) + sqr(&coefEq.C, K1) + add(K1, K1, K1) + sqr(&coefEq.A, xp4) + add(&coefEq.A, &coefEq.A, &coefEq.A) + sqr(&coefEq.A, &coefEq.A) + return coefEq +} + +// Given a 4-isogeny phi and a point xP = x(P), compute x(Q), the x-coordinate +// of the image Q = phi(P) of P under phi : E_(A:C) -> E_(A':C'). +// +// Input: Isogeny returned by GenerateCurve and point q=(Qx,Qz) from E0_A/C +// Output: Corresponding point q from E1_A'/C', where E1 is 4-isogenous to E0 +func (phi *isogeny4) EvaluatePoint(p *ProjectivePoint) ProjectivePoint { + var t0, t1 Fp2 + var q = *p + var xq, zq = &q.X, &q.Z + var K1, K2, K3 = &phi.K1, &phi.K2, &phi.K3 + + add(&t0, xq, zq) + sub(&t1, xq, zq) + mul(xq, &t0, K2) + mul(zq, &t1, K3) + mul(&t0, &t0, &t1) + mul(&t0, &t0, K1) + add(&t1, xq, zq) + sub(zq, xq, zq) + sqr(&t1, &t1) + sqr(zq, zq) + add(xq, &t0, &t1) + sub(&t0, zq, &t0) + mul(xq, xq, &t1) + mul(zq, zq, &t0) + return q +} diff --git a/src/circl/dh/sidh/internal/p503/curve_test.go b/src/circl/dh/sidh/internal/p503/curve_test.go new file mode 100644 index 00000000000..9ed669e8a4f --- /dev/null +++ b/src/circl/dh/sidh/internal/p503/curve_test.go @@ -0,0 +1,100 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p503 + +import ( + "bytes" + "testing" + + . "circl/dh/sidh/internal/common" +) + +func vartimeEqProjFp2(lhs, rhs *ProjectivePoint) bool { + var t0, t1 Fp2 + mul(&t0, &lhs.X, &rhs.Z) + mul(&t1, &lhs.Z, &rhs.X) + return vartimeEqFp2(&t0, &t1) +} + +func toAffine(point *ProjectivePoint) *Fp2 { + var affineX Fp2 + inv(&affineX, &point.Z) + mul(&affineX, &affineX, &point.X) + return &affineX +} + +func Test_jInvariant(t *testing.T) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + var jbufRes = make([]byte, params.SharedSecretSize) + var jbufExp = make([]byte, params.SharedSecretSize) + var jInv Fp2 + + Jinvariant(&curve, &jInv) + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(jbufRes, &jInv, params.Bytelen) + + jInv = expectedJ + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(jbufExp, &jInv, params.Bytelen) + + if !bytes.Equal(jbufRes[:], jbufExp[:]) { + t.Error("Computed incorrect j-invariant: found\n", jbufRes, "\nexpected\n", jbufExp) + } +} + +func TestProjectivePointVartimeEq(t *testing.T) { + var xP ProjectivePoint + + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + xQ := xP + + // Scale xQ, which results in the same projective point + mul(&xQ.X, &xQ.X, &curveA) + mul(&xQ.Z, &xQ.Z, &curveA) + if !vartimeEqProjFp2(&xP, &xQ) { + t.Error("Expected the scaled point to be equal to the original") + } +} + +func TestPointMulVersusSage(t *testing.T) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + var cparams = CalcCurveParamsEquiv4(&curve) + var xP ProjectivePoint + + // x 2 + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + Pow2k(&xP, &cparams, 1) + afxQ := toAffine(&xP) + if !vartimeEqFp2(afxQ, &affineXP2) { + t.Error("\nExpected\n", affineXP2, "\nfound\n", afxQ) + } + + // x 4 + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + Pow2k(&xP, &cparams, 2) + afxQ = toAffine(&xP) + if !vartimeEqFp2(afxQ, &affineXP4) { + t.Error("\nExpected\n", affineXP4, "\nfound\n", afxQ) + } +} + +func TestPointMul9VersusSage(t *testing.T) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + var cparams = CalcCurveParamsEquiv3(&curve) + var xP ProjectivePoint + + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + Pow3k(&xP, &cparams, 2) + afxQ := toAffine(&xP) + if !vartimeEqFp2(afxQ, &affineXP9) { + t.Error("\nExpected\n", affineXP9, "\nfound\n", afxQ) + } +} + +func BenchmarkThreePointLadder(b *testing.B) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + for n := 0; n < b.N; n++ { + ScalarMul3Pt(&curve, &threePointLadderInputs[0], &threePointLadderInputs[1], &threePointLadderInputs[2], uint(len(scalar3Pt)*8), scalar3Pt[:]) + } +} diff --git a/src/circl/dh/sidh/internal/p503/doc.go b/src/circl/dh/sidh/internal/p503/doc.go new file mode 100644 index 00000000000..3541a440183 --- /dev/null +++ b/src/circl/dh/sidh/internal/p503/doc.go @@ -0,0 +1,2 @@ +// Package p503 provides implementation of field arithmetic used in SIDH and SIKE. +package p503 diff --git a/src/circl/dh/sidh/internal/p503/fp2.go b/src/circl/dh/sidh/internal/p503/fp2.go new file mode 100644 index 00000000000..69dca22f530 --- /dev/null +++ b/src/circl/dh/sidh/internal/p503/fp2.go @@ -0,0 +1,195 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p503 + +import ( + "circl/dh/sidh/internal/common" +) + +// Montgomery multiplication. Input values must be already +// in Montgomery domain. +func mulP(dest, lhs, rhs *common.Fp) { + var ab common.FpX2 + mulP503(&ab, lhs, rhs) // = a*b*R*R + rdcP503(dest, &ab) // = a*b*R mod p +} + +// Set dest = x^((p-3)/4). If x is square, this is 1/sqrt(x). +// Uses variation of sliding-window algorithm from with window size +// of 5 and least to most significant bit sliding (left-to-right) +// See HAC 14.85 for general description. +// +// Allowed to overlap x with dest. +// All values in Montgomery domains +// Set dest = x^(2^k), for k >= 1, by repeated squarings. +func p34(dest, x *common.Fp) { + var lookup [16]common.Fp + + // This performs sum(powStrategy) + 1 squarings and len(lookup) + len(mulStrategy) + // multiplications. + powStrategy := []uint8{12, 5, 5, 2, 7, 11, 3, 8, 4, 11, 4, 7, 5, 6, 3, 7, 5, 7, 2, 12, 5, 6, 4, 6, 8, 6, 4, 7, 5, 5, 8, 5, 8, 5, 5, 8, 9, 3, 6, 2, 10, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3} + mulStrategy := []uint8{12, 11, 10, 0, 1, 8, 3, 7, 1, 8, 3, 6, 7, 14, 2, 14, 14, 9, 0, 13, 9, 15, 5, 12, 7, 13, 7, 15, 6, 7, 9, 0, 5, 7, 6, 8, 8, 3, 7, 0, 10, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 3} + initialMul := uint8(0) + + // Precompute lookup table of odd multiples of x for window + // size k=5. + var xx common.Fp + mulP(&xx, x, x) + lookup[0] = *x + for i := 1; i < 16; i++ { + mulP(&lookup[i], &lookup[i-1], &xx) + } + + // Now lookup = {x, x^3, x^5, ... } + // so that lookup[i] = x^{2*i + 1} + // so that lookup[k/2] = x^k, for odd k + *dest = lookup[initialMul] + for i := uint8(0); i < uint8(len(powStrategy)); i++ { + mulP(dest, dest, dest) + for j := uint8(1); j < powStrategy[i]; j++ { + mulP(dest, dest, dest) + } + mulP(dest, dest, &lookup[mulStrategy[i]]) + } +} + +func add(dest, lhs, rhs *common.Fp2) { + addP503(&dest.A, &lhs.A, &rhs.A) + addP503(&dest.B, &lhs.B, &rhs.B) +} + +func sub(dest, lhs, rhs *common.Fp2) { + subP503(&dest.A, &lhs.A, &rhs.A) + subP503(&dest.B, &lhs.B, &rhs.B) +} + +func mul(dest, lhs, rhs *common.Fp2) { + var bMinA, cMinD common.Fp + var ac, bd common.FpX2 + var adPlusBc common.FpX2 + var acMinBd common.FpX2 + + // Let (a,b,c,d) = (lhs.a,lhs.b,rhs.a,rhs.b). + // + // (a + bi)*(c + di) = (a*c - b*d) + (a*d + b*c)i + // + // Use Karatsuba's trick: note that + // + // (b - a)*(c - d) = (b*c + a*d) - a*c - b*d + // + // so (a*d + b*c) = (b-a)*(c-d) + a*c + b*d. + mulP503(&ac, &lhs.A, &rhs.A) // = a*c*R*R + mulP503(&bd, &lhs.B, &rhs.B) // = b*d*R*R + subP503(&bMinA, &lhs.B, &lhs.A) // = (b-a)*R + subP503(&cMinD, &rhs.A, &rhs.B) // = (c-d)*R + mulP503(&adPlusBc, &bMinA, &cMinD) // = (b-a)*(c-d)*R*R + adlP503(&adPlusBc, &adPlusBc, &ac) // = ((b-a)*(c-d) + a*c)*R*R + adlP503(&adPlusBc, &adPlusBc, &bd) // = ((b-a)*(c-d) + a*c + b*d)*R*R + rdcP503(&dest.B, &adPlusBc) // = (a*d + b*c)*R mod p + sulP503(&acMinBd, &ac, &bd) // = (a*c - b*d)*R*R + rdcP503(&dest.A, &acMinBd) // = (a*c - b*d)*R mod p +} + +// Set dest = 1/x +// +// Allowed to overlap dest with x. +// +// Returns dest to allow chaining operations. +func inv(dest, x *common.Fp2) { + var e1, e2 common.FpX2 + var f1, f2 common.Fp + + // We want to compute + // + // 1 1 (a - bi) (a - bi) + // -------- = -------- -------- = ----------- + // (a + bi) (a + bi) (a - bi) (a^2 + b^2) + // + // Letting c = 1/(a^2 + b^2), this is + // + // 1/(a+bi) = a*c - b*ci. + + mulP503(&e1, &x.A, &x.A) // = a*a*R*R + mulP503(&e2, &x.B, &x.B) // = b*b*R*R + adlP503(&e1, &e1, &e2) // = (a^2 + b^2)*R*R + rdcP503(&f1, &e1) // = (a^2 + b^2)*R mod p + // Now f1 = a^2 + b^2 + + mulP(&f2, &f1, &f1) + p34(&f2, &f2) + mulP(&f2, &f2, &f2) + mulP(&f2, &f2, &f1) + + mulP503(&e1, &x.A, &f2) + rdcP503(&dest.A, &e1) + + subP503(&f1, &common.Fp{}, &x.B) + mulP503(&e1, &f1, &f2) + rdcP503(&dest.B, &e1) +} + +func sqr(dest, x *common.Fp2) { + var a2, aPlusB, aMinusB common.Fp + var a2MinB2, ab2 common.FpX2 + + a := &x.A + b := &x.B + + // (a + bi)*(a + bi) = (a^2 - b^2) + 2abi. + addP503(&a2, a, a) // = a*R + a*R = 2*a*R + addP503(&aPlusB, a, b) // = a*R + b*R = (a+b)*R + subP503(&aMinusB, a, b) // = a*R - b*R = (a-b)*R + mulP503(&a2MinB2, &aPlusB, &aMinusB) // = (a+b)*(a-b)*R*R = (a^2 - b^2)*R*R + mulP503(&ab2, &a2, b) // = 2*a*b*R*R + rdcP503(&dest.A, &a2MinB2) // = (a^2 - b^2)*R mod p + rdcP503(&dest.B, &ab2) // = 2*a*b*R mod p +} + +// In case choice == 1, performs following swap in constant time: +// xPx <-> xQx +// xPz <-> xQz +// Otherwise returns xPx, xPz, xQx, xQz unchanged +func cswap(xPx, xPz, xQx, xQz *common.Fp2, choice uint8) { + cswapP503(&xPx.A, &xQx.A, choice) + cswapP503(&xPx.B, &xQx.B, choice) + cswapP503(&xPz.A, &xQz.A, choice) + cswapP503(&xPz.B, &xQz.B, choice) +} + +// Converts in.A and in.B to Montgomery domain and stores +// in 'out' +// out.A = in.A * R mod p +// out.B = in.B * R mod p +// Performs v = v*R^2*R^(-1) mod p, for both in.A and in.B +func ToMontgomery(out, in *common.Fp2) { + var aRR common.FpX2 + + // a*R*R + mulP503(&aRR, &in.A, &P503R2) + // a*R mod p + rdcP503(&out.A, &aRR) + mulP503(&aRR, &in.B, &P503R2) + rdcP503(&out.B, &aRR) +} + +// Converts in.A and in.B from Montgomery domain and stores +// in 'out' +// out.A = in.A mod p +// out.B = in.B mod p +// +// After returning from the call 'in' is not modified. +func FromMontgomery(out, in *common.Fp2) { + var aR common.FpX2 + + // convert from montgomery domain + copy(aR[:], in.A[:]) + rdcP503(&out.A, &aR) // = a mod p in [0, 2p) + modP503(&out.A) // = a mod p in [0, p) + for i := range aR { + aR[i] = 0 + } + copy(aR[:], in.B[:]) + rdcP503(&out.B, &aR) + modP503(&out.B) +} diff --git a/src/circl/dh/sidh/internal/p503/fp2_test.go b/src/circl/dh/sidh/internal/p503/fp2_test.go new file mode 100644 index 00000000000..2f058ec6b7a --- /dev/null +++ b/src/circl/dh/sidh/internal/p503/fp2_test.go @@ -0,0 +1,245 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p503 + +import ( + "math/rand" + "reflect" + "testing" + "testing/quick" + + "circl/dh/sidh/internal/common" +) + +type testParams struct { + Point common.ProjectivePoint + Cparam common.ProjectiveCurveParameters + ExtElem common.Fp2 +} + +// Returns true if lhs = rhs. Takes variable time. +func vartimeEqFp2(lhs, rhs *common.Fp2) bool { + a := *lhs + b := *rhs + + modP503(&a.A) + modP503(&a.B) + modP503(&b.A) + modP503(&b.B) + + eq := true + for i := 0; i < FpWords && eq; i++ { + eq = eq && (a.A[i] == b.A[i]) + eq = eq && (a.B[i] == b.B[i]) + } + return eq +} + +func (testParams) generateFp2(rand *rand.Rand) common.Fp2 { + // Generation strategy: low limbs taken from [0,2^64); high limb + // taken from smaller range + // + // Size hint is ignored since all elements are fixed size. + // + // Field elements taken in range [0,2p). Emulate this by capping + // the high limb by the top digit of 2*p-1: + // + // sage: (2*p-1).digits(2^64)[-1] + // + // This still allows generating values >= 2p, but hopefully that + // excess is OK (and if it's not, we'll find out, because it's for + // testing...) + highLimb := rand.Uint64() % P503x2[FpWords-1] + fpElementGen := func() (fp common.Fp) { + for i := 0; i < (FpWords - 1); i++ { + fp[i] = rand.Uint64() + } + fp[FpWords-1] = highLimb + return fp + } + return common.Fp2{A: fpElementGen(), B: fpElementGen()} +} + +func (c testParams) Generate(rand *rand.Rand, size int) reflect.Value { + return reflect.ValueOf( + testParams{ + common.ProjectivePoint{ + X: c.generateFp2(rand), + Z: c.generateFp2(rand), + }, + common.ProjectiveCurveParameters{ + A: c.generateFp2(rand), + C: c.generateFp2(rand), + }, + c.generateFp2(rand), + }) +} + +func TestOne(t *testing.T) { + var tmp common.Fp2 + + mul(&tmp, ¶ms.OneFp2, ¶ms.A.AffineP) + if !vartimeEqFp2(&tmp, ¶ms.A.AffineP) { + t.Error("Not equal 1") + } +} + +func TestFp2ToBytesRoundTrip(t *testing.T) { + roundTrips := func(x testParams) bool { + var xBytes = make([]byte, 2*params.Bytelen) + var xPrime common.Fp2 + + common.Fp2ToBytes(xBytes[:], &x.ExtElem, params.Bytelen) + common.BytesToFp2(&xPrime, xBytes[:], params.Bytelen) + return vartimeEqFp2(&xPrime, &x.ExtElem) + } + + if err := quick.Check(roundTrips, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2MulDistributesOverAdd(t *testing.T) { + mulDistributesOverAdd := func(x, y, z testParams) bool { + // Compute t1 = (x+y)*z + t1 := new(common.Fp2) + add(t1, &x.ExtElem, &y.ExtElem) + mul(t1, t1, &z.ExtElem) + + // Compute t2 = x*z + y*z + t2 := new(common.Fp2) + t3 := new(common.Fp2) + mul(t2, &x.ExtElem, &z.ExtElem) + mul(t3, &y.ExtElem, &z.ExtElem) + add(t2, t2, t3) + + return vartimeEqFp2(t1, t2) + } + + if err := quick.Check(mulDistributesOverAdd, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2MulIsAssociative(t *testing.T) { + isAssociative := func(x, y, z testParams) bool { + // Compute t1 = (x*y)*z + t1 := new(common.Fp2) + mul(t1, &x.ExtElem, &y.ExtElem) + mul(t1, t1, &z.ExtElem) + + // Compute t2 = (y*z)*x + t2 := new(common.Fp2) + mul(t2, &y.ExtElem, &z.ExtElem) + mul(t2, t2, &x.ExtElem) + + return vartimeEqFp2(t1, t2) + } + + if err := quick.Check(isAssociative, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2SquareMatchesMul(t *testing.T) { + sqrMatchesMul := func(x testParams) bool { + // Compute t1 = (x*x) + t1 := new(common.Fp2) + mul(t1, &x.ExtElem, &x.ExtElem) + + // Compute t2 = x^2 + t2 := new(common.Fp2) + sqr(t2, &x.ExtElem) + + return vartimeEqFp2(t1, t2) + } + + if err := quick.Check(sqrMatchesMul, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2Inv(t *testing.T) { + inverseIsCorrect := func(x testParams) bool { + z := new(common.Fp2) + inv(z, &x.ExtElem) + + // Now z = (1/x), so (z * x) * x == x + mul(z, z, &x.ExtElem) + mul(z, z, &x.ExtElem) + + return vartimeEqFp2(z, &x.ExtElem) + } + + // This is more expensive; run fewer tests + var quickCheckConfig = &quick.Config{MaxCount: (1 << 11)} + if err := quick.Check(inverseIsCorrect, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2Batch3Inv(t *testing.T) { + batchInverseIsCorrect := func(x1, x2, x3 testParams) bool { + var x1Inv, x2Inv, x3Inv common.Fp2 + inv(&x1Inv, &x1.ExtElem) + inv(&x2Inv, &x2.ExtElem) + inv(&x3Inv, &x3.ExtElem) + + var y1, y2, y3 common.Fp2 + Fp2Batch3Inv(&x1.ExtElem, &x2.ExtElem, &x3.ExtElem, &y1, &y2, &y3) + + return (vartimeEqFp2(&x1Inv, &y1) && vartimeEqFp2(&x2Inv, &y2) && vartimeEqFp2(&x3Inv, &y3)) + } + + // This is more expensive; run fewer tests + var quickCheckConfig = &quick.Config{MaxCount: (1 << 8)} + if err := quick.Check(batchInverseIsCorrect, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func BenchmarkFp2Mul(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + mul(w, z, z) + } +} + +func BenchmarkFp2Inv(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + inv(w, z) + } +} + +func BenchmarkFp2Square(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + sqr(w, z) + } +} + +func BenchmarkFp2Add(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + add(w, z, z) + } +} + +func BenchmarkFp2Sub(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + sub(w, z, z) + } +} diff --git a/src/circl/dh/sidh/internal/p503/params.go b/src/circl/dh/sidh/internal/p503/params.go new file mode 100644 index 00000000000..4e95ab6032d --- /dev/null +++ b/src/circl/dh/sidh/internal/p503/params.go @@ -0,0 +1,203 @@ +package p503 + +//go:generate go run ../templates/gen.go P503 + +import ( + "circl/dh/sidh/internal/common" + "internal/cpu" +) + +const ( + // Number of uint64 limbs used to store field element + FpWords = 8 +) + +// P503 is a prime used by field Fp503 +var ( + // According to https://github.com/golang/go/issues/28230, + // variables referred from the assembly must be in the same package. + // HasBMI2 signals support for MULX which is in BMI2 + HasBMI2 = cpu.X86.HasBMI2 + // HasADXandBMI2 signals support for ADX and BMI2 + HasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX + + // P503 is a prime used by field Fp503 + P503 = common.Fp{ + 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xABFFFFFFFFFFFFFF, + 0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E, + } + + // P503x2 = 2*p503 - 1 + P503x2 = common.Fp{ + 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x57FFFFFFFFFFFFFF, + 0x2610B7B44423CF41, 0x3737ED90F6FCFB5E, 0xC08B8D7BB4EF49A0, 0x0080CDEA83023C3C, + } + + // P503p1 = p503 + 1 + P503p1 = common.Fp{ + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xAC00000000000000, + 0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E, + } + + // P503R2 = (2^512)^2 mod p + P503R2 = common.Fp{ + 0x5289A0CF641D011F, 0x9B88257189FED2B9, 0xA3B365D58DC8F17A, 0x5BC57AB6EFF168EC, + 0x9E51998BD84D4423, 0xBF8999CBAC3B5695, 0x46E9127BCE14CDB6, 0x003F6CFCE8B81771, + } + + // P503p1s8 = p503 + 1 left-shifted by 8, assuming little endianness + P503p1s8 = common.Fp{ + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + 0x085BDA2211E7A0AC, 0x9BF6C87B7E7DAF13, 0x45C6BDDA77A4D01B, 0x4066F541811E1E60, + } + + // P503p1Zeros number of 0 digits in the least significant part of P503+1 + P503p1Zeros = 3 + + // 1*R mod p + one = common.Fp2{ + A: common.Fp{ + 0x00000000000003F9, 0x0000000000000000, 0x0000000000000000, 0xB400000000000000, + 0x63CB1A6EA6DED2B4, 0x51689D8D667EB37D, 0x8ACD77C71AB24142, 0x0026FBAEC60F5953}, + } + // 1/2 * R mod p + half = common.Fp2{ + A: common.Fp{ + 0x00000000000001FC, 0x0000000000000000, 0x0000000000000000, 0xB000000000000000, + 0x3B69BB2464785D2A, 0x36824A2AF0FE9896, 0xF5899F427A94F309, 0x0033B15203C83BB8}, + } + // 6*R mod p + six = common.Fp2{ + A: common.Fp{ + 0x00000000000017D8, 0x0000000000000000, 0x0000000000000000, 0xE000000000000000, + 0x30B1E6E3A51520FA, 0xB13BC3BF6FFB3992, 0x8045412EEB3E3DED, 0x0069182E2159DBB8}, + } + + params = common.SidhParams{ + ID: common.Fp503, + // SIDH public key byte size. + PublicKeySize: 378, + // SIDH shared secret byte size. + SharedSecretSize: 126, + A: common.DomainParams{ + // The x-coordinate of PA + AffineP: common.Fp2{ + A: common.Fp{ + 0x5D083011589AD893, 0xADFD8D2CB67D0637, 0x330C9AC34FFB6361, 0xF0D47489A2E805A2, + 0x27E2789259C6B8DC, 0x63866A2C121931B9, 0x8D4C65A7137DCF44, 0x003A183AE5967B3F, + }, + B: common.Fp{ + 0x7E3541B8C96D1519, 0xD3ADAEEC0D61A26C, 0xC0A2219CE7703DD9, 0xFF3E46658FCDBC52, + 0xD5B38DEAE6E196FF, 0x1AAC826364956D58, 0xEC9F4875B9A5F27A, 0x001B0B475AB99843, + }, + }, + // The x-coordinate of QA + AffineQ: common.Fp2{ + A: common.Fp{ + 0x4D83695107D03BAD, 0x221F3299005E2FCF, 0x78E6AE22F30DECF2, 0x6D982DB5111253E4, + 0x504C80A8AB4526A8, 0xEFD0C3AA210BB024, 0xCB77483501DC6FCF, 0x001052544A96BDF3, + }, + B: common.Fp{ + 0x0D74FE3402BCAE47, 0xDF5B8CDA832D8AED, 0xB86BCF06E4BD837E, 0x892A2933A0FA1F63, + 0x9F88FC67B6CCB461, 0x822926EA9DDA3AC8, 0xEAC8DDE5855425ED, 0x000618FE6DA37A80, + }, + }, + + // The x-coordinate of RA = PA-QA + AffineR: common.Fp2{ + A: common.Fp{ + 0x1D9D32D2DC877C17, 0x5517CD8F71D5B02B, 0x395AFB8F6B60C117, 0x3AE31AC85F9098C8, + 0x5F5341C198450848, 0xF8C609DBEA435C6A, 0xD832BC7EDC7BA5E4, 0x002AD98AA6968BF5, + }, + B: common.Fp{ + 0xC466CAB0F73C2E5B, 0x7B1817148FB2CF9C, 0x873E87C099E470A0, 0xBB17AC6D17A7BAC1, + 0xA146FDCD0F2E2A58, 0x88B311E9CEAB6201, 0x37604CF5C7951757, 0x0006804071C74BF9, + }, + }, + // Max size of secret key for 2-torsion group, corresponds to 2^e2 - 1 + SecretBitLen: 250, + // SecretBitLen in bytes. + SecretByteLen: 32, + // 2-torsion group computation strategy + IsogenyStrategy: []uint32{ + 0x3D, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, + 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, + 0x01, 0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, + 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, + 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x1D, 0x10, 0x08, 0x04, 0x02, 0x01, + 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, + 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x0D, 0x08, + 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, + 0x05, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01}, + }, + B: common.DomainParams{ + // The x-coordinate of PB + AffineP: common.Fp2{ + A: common.Fp{ + 0xDF630FC5FB2468DB, 0xC30C5541C102040E, 0x3CDC9987B76511FC, 0xF54B5A09353D0CDD, + 0x3ADBA8E00703C42F, 0x8253F9303DDC95D0, 0x62D30778763ABFD7, 0x001CD00FB581CD55, + }, + B: common.Fp{ + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + }, + }, + // The x-coordinate of QB + AffineQ: common.Fp2{ + A: common.Fp{ + 0x2E3457A12B429261, 0x311F94E89627DCF8, 0x5B71C98FD1DB73F6, 0x3671DB7DCFC21541, + 0xB6D1484C9FE0CF4F, 0x19CD110717356E35, 0xF4F9FB00AC9919DF, 0x0035BC124D38A70B, + }, + B: common.Fp{ + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + }, + }, + // The x-coordinate of RB = PB - QB + AffineR: common.Fp2{ + A: common.Fp{ + 0x2E08BB99413D2952, 0xD3021467CD088D72, 0x21017AF859752245, 0x26314ED8FFD9DE5C, + 0x4AF43C73344B6686, 0xCFA1F91149DF0993, 0xF327A95365587A89, 0x000DBF54E03D3906, + }, + B: common.Fp{ + 0x03E03FF342F5F304, 0x993D604D7B4B6E56, 0x80412F4D9280E71F, 0x0FFDC9EF990B3982, + 0xE584E64C51604931, 0x1374F42AC8B0BBD7, 0x07D5BC37DFA41A5F, 0x00396CCFD61FD34C, + }, + }, + // Size of secret key for 3-torsion group, corresponds to log_2(3^e3) - 1. + SecretBitLen: 252, + // SecretBitLen in bytes. + SecretByteLen: 32, + // 3-torsion group computation strategy + IsogenyStrategy: []uint32{ + 0x47, 0x26, 0x15, 0x0D, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, + 0x01, 0x01, 0x02, 0x01, 0x01, 0x05, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x02, + 0x01, 0x01, 0x01, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, + 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x11, 0x09, 0x05, 0x03, 0x02, + 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, + 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, + 0x01, 0x02, 0x01, 0x01, 0x21, 0x11, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, + 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, + 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, + 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, + 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, + 0x01, 0x02, 0x01, 0x01}, + }, + OneFp2: one, + HalfFp2: half, + MsgLen: 24, + // SIKEp503 provides 192 bit of classical security ([SIKE], 5.1) + KemSize: 24, + // ceil(503+7/8) + Bytelen: 63, + CiphertextSize: 24 + 378, + InitCurve: common.ProjectiveCurveParameters{ + A: six, + C: one, + }, + } +) + +func init() { + common.Register(common.Fp503, ¶ms) +} diff --git a/src/circl/dh/sidh/internal/p503/params_test.go b/src/circl/dh/sidh/internal/p503/params_test.go new file mode 100644 index 00000000000..5550031d307 --- /dev/null +++ b/src/circl/dh/sidh/internal/p503/params_test.go @@ -0,0 +1,73 @@ +package p503 + +// Contains values used by tests +import ( + "testing/quick" + + . "circl/dh/sidh/internal/common" +) + +// Values computed using Sage +var ( + // j = 3674553797500778604587777859668542828244523188705960771798425843588160903687122861541242595678107095655647237100722594066610650373491179241544334443939077738732728884873568393760629500307797547379838602108296735640313894560419*i + 3127495302417548295242630557836520229396092255080675419212556702820583041296798857582303163183558315662015469648040494128968509467224910895884358424271180055990446576645240058960358037224785786494172548090318531038910933793845 + expectedJ = Fp2{ + A: Fp{0x2c441d03b72e27c, 0xf2c6748151dbf84, 0x3a774f6191070e, 0xa7c6212c9c800ba6, 0x23921b5cf09abc27, 0x9e1baefbb3cd4265, 0x8cd6a289f12e10dc, 0x3fa364128cf87e}, + B: Fp{0xe7497ac2bf6b0596, 0x629ee01ad23bd039, 0x95ee11587a119fa7, 0x572fb28a24772269, 0x3c00410b6c71567e, 0xe681e83a345f8a34, 0x65d21b1d96bd2d52, 0x7889a47e58901}, + } + + // A = 8752234765512331234913716743014562460822083005386252003333602919474238975785850965349950219277942402920758585086620525443539725921333735154674119646075*i + 6339624979889725406021454983012408976766782818694212228554611573314701271183857175866122275755278397694585249002282183018114967373119429936587424396917 + curveA = Fp2{ + A: Fp{0xd9816986a543095f, 0xa78cb1d7217bec21, 0x9595dc97b74ea70, 0x9120a1da6b42797d, 0x59ef9d903f74e47c, 0x4c58a4cdc45b6d0b, 0x816d5213aaf7ee6d, 0x3892fee6bb7343}, + B: Fp{0x28c5288acbedf11b, 0x2143a438c86f6c68, 0x7cb5c4ae9c4c8e34, 0xb478aea445eed48b, 0x24d5c175776db478, 0x234582f8676c0ebe, 0x56234267b625fb08, 0x2c6e58d84b1192}} + + // C = 10458464853790890798085664692909194316288127038910691163573355876336993883402795907795767791362493831987298578966325154262747805705783782806176495638177*i + 7770984753616185271325854825309278833018655051139367603077592443785629339985729818288672809062782315510526648882226172896710704020683893684611137718845 + curveC = Fp2{ + A: Fp{0xe05948236f2f913b, 0xc45da9ad1219a255, 0x7a568972a32fc1d0, 0x30f00bdd7071c3b1, 0x3b761b8dac2c98bc, 0x760f21b2179737b6, 0x13217e6656a13476, 0x2606b798e685aa}, + B: Fp{0x1c0171f78820052e, 0x440b7f7087e57140, 0xe0510c07b31b0e96, 0xd0cf489b2ac4aea9, 0x4fb328f1c1fdf783, 0xb3b4912342951cb7, 0x70a4b64e81961c42, 0x33eed63cf07181}} + // x(P) = 9720237205826983370867050298878715935679372786589878620121159082290288918688002583435964840822877971257659901481591644347943354235932355923042390796255*i + 634577413124118560098123299804750904956499531431297942628887930019161512075536652691244843248133437326050395005054997679717801535474938466995392156605 + affineXP = Fp2{ + A: Fp{0xb606d954d407faf2, 0x58a1ef6cd213a203, 0x9823b55033e62f7b, 0x59cafc060d5e25a1, 0x529685f1753526fc, 0xc2eac3d219989c7d, 0xc5e30c75dfd343a0, 0x378285adc968a0}, + B: Fp{0x6670f36db977b9da, 0xa07e2fdda5e1a7f0, 0xf367a7a722aed87d, 0x6c269e06d595cd10, 0x8379aa6092d87700, 0x57276ce3557ee7ae, 0xac8107bfbcd28993, 0x3d6f98869617a7}} + + affineXP2 = Fp2{ + A: Fp{0x4e1133c2b3855902, 0x875a775c67597fbb, 0xd17eb74254141abb, 0x1d5a464a4f3391f5, 0x24405c332811d007, 0x7e47e3eb489a7372, 0x65b130dfd9efe605, 0xfa69fac179803}, + B: Fp{0x329f5322e1be51ee, 0x9004dca8132ebd6f, 0x7cd87e447ca8a7b6, 0x10a6ec02c38ce69e, 0x8cef2ed7d112ac46, 0x5f385a9fc4b57cd7, 0x68a366354fe7a32e, 0x2223c1455486ac}} + + affineXP4 = Fp2{ + A: Fp{0x4eb695d34b46be8f, 0xfb5e76c58585f2d2, 0xa41f8aafa6dbb531, 0x4db82f5db5cfd144, 0x14dab0e3200cbba0, 0x430381706a279f81, 0xdf6707a57161f81, 0x44740f17197c3}, + B: Fp{0xa2473705cdb6d4e9, 0xfa3cd67b9c15502c, 0xf0928166d0c5cee1, 0x6150aba0c874faaa, 0x6c0b18d6d92f9034, 0xcff71d340fc1e72e, 0x19a47027af917587, 0x25ed4bad443b8f}} + + affineXP9 = Fp2{ + A: Fp{0x112da30e288217e0, 0x5b336d527320a5f7, 0xbbf4d9403b68e3c6, 0x55eccb31c40b359c, 0x8907129ab69b3203, 0x69cc8c750125a915, 0xa41a38e6f530c0e1, 0xbe68e23af1b8d}, + B: Fp{0x472c603765964213, 0xe4e64995b0769754, 0x4515583c74a6dd24, 0xff7c57f5818363a2, 0xbeaeb24662a92177, 0x8a54fa61fbf24c68, 0xa85542049eb45e12, 0x2b54caf655e285}} + + // Inputs for testing 3-point-ladder + threePointLadderInputs = []ProjectivePoint{ + // x(P) + { + X: Fp2{ + A: Fp{0x43941FA9244C059E, 0xD1F337D076941189, 0x6B6A8B3A8763C96A, 0x6DF569708D6C9482, 0x487EE5707A52F4AA, 0xDE396F6E2559689E, 0xE5EE3895A8991469, 0x2B0946695790A8}, + B: Fp{0xAB552C0FDAED092E, 0x7DF895E43E7DCB1C, 0x35C700E761920C4B, 0xCC5807DD70DC117A, 0x0884039A5A8DB18A, 0xD04620B3D0738052, 0xA200835605138F10, 0x3FF2E59B2FDC6A}}, + Z: params.OneFp2, + }, + // x(Q) + { + X: Fp2{ + A: Fp{0x77015826982BA1FD, 0x44024489673471E4, 0x1CAA2A5F4D5DA63B, 0xA183C07E50738C01, 0x8B97782D4E1A0DE6, 0x9B819522FBC38280, 0x0BDA46A937FB7B8A, 0x3B3614305914DF}, + B: Fp{0xBF0366E97B3168D9, 0xAA522AC3879CEF0F, 0x0AF5EC975BD035C8, 0x1F26FEE7BBAC165C, 0xA0EE6A637724A6AB, 0xFB52101E36BA3A38, 0xD29CF5E376E17376, 0x1374A50DF57071}}, + Z: params.OneFp2, + }, + // x(P-Q) + { + X: Fp2{ + A: Fp{0xD99279BBD41EA559, 0x35CF18E72F578214, 0x90473B1DC77F73E8, 0xBFFEA930B25D7F66, 0xFD558EA177B900B2, 0x7CFAD273A782A23E, 0x6B1F610822E0F611, 0x26D2D2EF9619B5}, + B: Fp{0x534F83651CBCC75D, 0x591FB4757AED5D08, 0x0B04353D40BED542, 0x829A94703AAC9139, 0x0F9C2E6D7663EB5B, 0x5D2D0F90C283F746, 0x34C872AA12A7676E, 0x0ECDB605FBFA16}}, + Z: params.OneFp2, + }, + } + scalar3Pt = [...]uint8{0x9f, 0x3b, 0xe7, 0xf9, 0xf4, 0x7c, 0xe6, 0xce, 0x79, 0x3e, 0x3d, 0x9f, 0x9f, 0x3b, 0xe7, 0xf9, 0xf4, 0x7c, 0xe6, 0xce, 0x79, 0x3e, 0x3d, 0x9f} +) + +var quickCheckConfig = &quick.Config{ + MaxCount: (1 << 15), +} diff --git a/src/circl/dh/sidh/internal/p751/arith_amd64.s b/src/circl/dh/sidh/internal/p751/arith_amd64.s new file mode 100644 index 00000000000..a20a9d9a2f2 --- /dev/null +++ b/src/circl/dh/sidh/internal/p751/arith_amd64.s @@ -0,0 +1,2577 @@ +// +build amd64,!noasm + +#include "textflag.h" + +// p751 + 1 +#define P751P1_5 $0xEEB0000000000000 +#define P751P1_6 $0xE3EC968549F878A8 +#define P751P1_7 $0xDA959B1A13F7CC76 +#define P751P1_8 $0x084E9867D6EBE876 +#define P751P1_9 $0x8562B5045CB25748 +#define P751P1_10 $0x0E12909F97BADC66 +#define P751P1_11 $0x00006FE5D541F71C + +#define P751_0 $0xFFFFFFFFFFFFFFFF +#define P751_5 $0xEEAFFFFFFFFFFFFF +#define P751_6 $0xE3EC968549F878A8 +#define P751_7 $0xDA959B1A13F7CC76 +#define P751_8 $0x084E9867D6EBE876 +#define P751_9 $0x8562B5045CB25748 +#define P751_10 $0x0E12909F97BADC66 +#define P751_11 $0x00006FE5D541F71C + +#define P751X2_0 $0xFFFFFFFFFFFFFFFE +#define P751X2_1 $0xFFFFFFFFFFFFFFFF +#define P751X2_5 $0xDD5FFFFFFFFFFFFF +#define P751X2_6 $0xC7D92D0A93F0F151 +#define P751X2_7 $0xB52B363427EF98ED +#define P751X2_8 $0x109D30CFADD7D0ED +#define P751X2_9 $0x0AC56A08B964AE90 +#define P751X2_10 $0x1C25213F2F75B8CD +#define P751X2_11 $0x0000DFCBAA83EE38 + +// The MSR code uses these registers for parameter passing. Keep using +// them to avoid significant code changes. This means that when the Go +// assembler does something strange, we can diff the machine code +// against a different assembler to find out what Go did. + +#define REG_P1 DI +#define REG_P2 SI +#define REG_P3 DX + +TEXT ·modP751(SB), NOSPLIT, $0-8 + MOVQ x+0(FP), REG_P1 + + // Zero AX for later use: + XORQ AX, AX + + // Load p into registers: + MOVQ P751_0, R8 + // P751_{1,2,3,4} = P751_0, so reuse R8 + MOVQ P751_5, R9 + MOVQ P751_6, R10 + MOVQ P751_7, R11 + MOVQ P751_8, R12 + MOVQ P751_9, R13 + MOVQ P751_10, R14 + MOVQ P751_11, R15 + + // Set x <- x - p + SUBQ R8, (REG_P1) + SBBQ R8, (8)(REG_P1) + SBBQ R8, (16)(REG_P1) + SBBQ R8, (24)(REG_P1) + SBBQ R8, (32)(REG_P1) + SBBQ R9, (40)(REG_P1) + SBBQ R10, (48)(REG_P1) + SBBQ R11, (56)(REG_P1) + SBBQ R12, (64)(REG_P1) + SBBQ R13, (72)(REG_P1) + SBBQ R14, (80)(REG_P1) + SBBQ R15, (88)(REG_P1) + + // Save carry flag indicating x-p < 0 as a mask in AX + SBBQ $0, AX + + // Conditionally add p to x if x-p < 0 + ANDQ AX, R8 + ANDQ AX, R9 + ANDQ AX, R10 + ANDQ AX, R11 + ANDQ AX, R12 + ANDQ AX, R13 + ANDQ AX, R14 + ANDQ AX, R15 + + ADDQ R8, (REG_P1) + ADCQ R8, (8)(REG_P1) + ADCQ R8, (16)(REG_P1) + ADCQ R8, (24)(REG_P1) + ADCQ R8, (32)(REG_P1) + ADCQ R9, (40)(REG_P1) + ADCQ R10, (48)(REG_P1) + ADCQ R11, (56)(REG_P1) + ADCQ R12, (64)(REG_P1) + ADCQ R13, (72)(REG_P1) + ADCQ R14, (80)(REG_P1) + ADCQ R15, (88)(REG_P1) + + RET + +TEXT ·cswapP751(SB), NOSPLIT, $0-17 + + MOVQ x+0(FP), REG_P1 + MOVQ y+8(FP), REG_P2 + MOVB choice+16(FP), AL // AL = 0 or 1 + MOVBLZX AL, AX // AX = 0 or 1 + NEGQ AX // RAX = 0x00..00 or 0xff..ff + + MOVQ (0*8)(REG_P1), BX // BX = x[0] + MOVQ (0*8)(REG_P2), CX // CX = y[0] + MOVQ CX, DX // DX = y[0] + XORQ BX, DX // DX = y[0] ^ x[0] + ANDQ AX, DX // DX = (y[0] ^ x[0]) & mask + XORQ DX, BX // BX = (y[0] ^ x[0]) & mask) ^ x[0] = x[0] or y[0] + XORQ DX, CX // CX = (y[0] ^ x[0]) & mask) ^ y[0] = y[0] or x[0] + MOVQ BX, (0*8)(REG_P1) + MOVQ CX, (0*8)(REG_P2) + + MOVQ (1*8)(REG_P1), BX + MOVQ (1*8)(REG_P2), CX + MOVQ CX, DX + XORQ BX, DX + ANDQ AX, DX + XORQ DX, BX + XORQ DX, CX + MOVQ BX, (1*8)(REG_P1) + MOVQ CX, (1*8)(REG_P2) + + MOVQ (2*8)(REG_P1), BX + MOVQ (2*8)(REG_P2), CX + MOVQ CX, DX + XORQ BX, DX + ANDQ AX, DX + XORQ DX, BX + XORQ DX, CX + MOVQ BX, (2*8)(REG_P1) + MOVQ CX, (2*8)(REG_P2) + + MOVQ (3*8)(REG_P1), BX + MOVQ (3*8)(REG_P2), CX + MOVQ CX, DX + XORQ BX, DX + ANDQ AX, DX + XORQ DX, BX + XORQ DX, CX + MOVQ BX, (3*8)(REG_P1) + MOVQ CX, (3*8)(REG_P2) + + MOVQ (4*8)(REG_P1), BX + MOVQ (4*8)(REG_P2), CX + MOVQ CX, DX + XORQ BX, DX + ANDQ AX, DX + XORQ DX, BX + XORQ DX, CX + MOVQ BX, (4*8)(REG_P1) + MOVQ CX, (4*8)(REG_P2) + + MOVQ (5*8)(REG_P1), BX + MOVQ (5*8)(REG_P2), CX + MOVQ CX, DX + XORQ BX, DX + ANDQ AX, DX + XORQ DX, BX + XORQ DX, CX + MOVQ BX, (5*8)(REG_P1) + MOVQ CX, (5*8)(REG_P2) + + MOVQ (6*8)(REG_P1), BX + MOVQ (6*8)(REG_P2), CX + MOVQ CX, DX + XORQ BX, DX + ANDQ AX, DX + XORQ DX, BX + XORQ DX, CX + MOVQ BX, (6*8)(REG_P1) + MOVQ CX, (6*8)(REG_P2) + + MOVQ (7*8)(REG_P1), BX + MOVQ (7*8)(REG_P2), CX + MOVQ CX, DX + XORQ BX, DX + ANDQ AX, DX + XORQ DX, BX + XORQ DX, CX + MOVQ BX, (7*8)(REG_P1) + MOVQ CX, (7*8)(REG_P2) + + MOVQ (8*8)(REG_P1), BX + MOVQ (8*8)(REG_P2), CX + MOVQ CX, DX + XORQ BX, DX + ANDQ AX, DX + XORQ DX, BX + XORQ DX, CX + MOVQ BX, (8*8)(REG_P1) + MOVQ CX, (8*8)(REG_P2) + + MOVQ (9*8)(REG_P1), BX + MOVQ (9*8)(REG_P2), CX + MOVQ CX, DX + XORQ BX, DX + ANDQ AX, DX + XORQ DX, BX + XORQ DX, CX + MOVQ BX, (9*8)(REG_P1) + MOVQ CX, (9*8)(REG_P2) + + MOVQ (10*8)(REG_P1), BX + MOVQ (10*8)(REG_P2), CX + MOVQ CX, DX + XORQ BX, DX + ANDQ AX, DX + XORQ DX, BX + XORQ DX, CX + MOVQ BX, (10*8)(REG_P1) + MOVQ CX, (10*8)(REG_P2) + + MOVQ (11*8)(REG_P1), BX + MOVQ (11*8)(REG_P2), CX + MOVQ CX, DX + XORQ BX, DX + ANDQ AX, DX + XORQ DX, BX + XORQ DX, CX + MOVQ BX, (11*8)(REG_P1) + MOVQ CX, (11*8)(REG_P2) + + RET + +TEXT ·addP751(SB), NOSPLIT, $0-24 + + MOVQ z+0(FP), REG_P3 + MOVQ x+8(FP), REG_P1 + MOVQ y+16(FP), REG_P2 + + MOVQ (REG_P1), R8 + MOVQ (8)(REG_P1), R9 + MOVQ (16)(REG_P1), R10 + MOVQ (24)(REG_P1), R11 + MOVQ (32)(REG_P1), R12 + MOVQ (40)(REG_P1), R13 + MOVQ (48)(REG_P1), R14 + MOVQ (56)(REG_P1), R15 + MOVQ (64)(REG_P1), CX + ADDQ (REG_P2), R8 + ADCQ (8)(REG_P2), R9 + ADCQ (16)(REG_P2), R10 + ADCQ (24)(REG_P2), R11 + ADCQ (32)(REG_P2), R12 + ADCQ (40)(REG_P2), R13 + ADCQ (48)(REG_P2), R14 + ADCQ (56)(REG_P2), R15 + ADCQ (64)(REG_P2), CX + MOVQ (72)(REG_P1), AX + ADCQ (72)(REG_P2), AX + MOVQ AX, (72)(REG_P3) + MOVQ (80)(REG_P1), AX + ADCQ (80)(REG_P2), AX + MOVQ AX, (80)(REG_P3) + MOVQ (88)(REG_P1), AX + ADCQ (88)(REG_P2), AX + MOVQ AX, (88)(REG_P3) + + MOVQ P751X2_0, AX + SUBQ AX, R8 + MOVQ P751X2_1, AX + SBBQ AX, R9 + SBBQ AX, R10 + SBBQ AX, R11 + SBBQ AX, R12 + MOVQ P751X2_5, AX + SBBQ AX, R13 + MOVQ P751X2_6, AX + SBBQ AX, R14 + MOVQ P751X2_7, AX + SBBQ AX, R15 + MOVQ P751X2_8, AX + SBBQ AX, CX + MOVQ R8, (REG_P3) + MOVQ R9, (8)(REG_P3) + MOVQ R10, (16)(REG_P3) + MOVQ R11, (24)(REG_P3) + MOVQ R12, (32)(REG_P3) + MOVQ R13, (40)(REG_P3) + MOVQ R14, (48)(REG_P3) + MOVQ R15, (56)(REG_P3) + MOVQ CX, (64)(REG_P3) + MOVQ (72)(REG_P3), R8 + MOVQ (80)(REG_P3), R9 + MOVQ (88)(REG_P3), R10 + MOVQ P751X2_9, AX + SBBQ AX, R8 + MOVQ P751X2_10, AX + SBBQ AX, R9 + MOVQ P751X2_11, AX + SBBQ AX, R10 + MOVQ R8, (72)(REG_P3) + MOVQ R9, (80)(REG_P3) + MOVQ R10, (88)(REG_P3) + MOVQ $0, AX + SBBQ $0, AX + + MOVQ P751X2_0, SI + ANDQ AX, SI + MOVQ P751X2_1, R8 + ANDQ AX, R8 + MOVQ P751X2_5, R9 + ANDQ AX, R9 + MOVQ P751X2_6, R10 + ANDQ AX, R10 + MOVQ P751X2_7, R11 + ANDQ AX, R11 + MOVQ P751X2_8, R12 + ANDQ AX, R12 + MOVQ P751X2_9, R13 + ANDQ AX, R13 + MOVQ P751X2_10, R14 + ANDQ AX, R14 + MOVQ P751X2_11, R15 + ANDQ AX, R15 + + MOVQ (REG_P3), AX + ADDQ SI, AX + MOVQ AX, (REG_P3) + MOVQ (8)(REG_P3), AX + ADCQ R8, AX + MOVQ AX, (8)(REG_P3) + MOVQ (16)(REG_P3), AX + ADCQ R8, AX + MOVQ AX, (16)(REG_P3) + MOVQ (24)(REG_P3), AX + ADCQ R8, AX + MOVQ AX, (24)(REG_P3) + MOVQ (32)(REG_P3), AX + ADCQ R8, AX + MOVQ AX, (32)(REG_P3) + MOVQ (40)(REG_P3), AX + ADCQ R9, AX + MOVQ AX, (40)(REG_P3) + MOVQ (48)(REG_P3), AX + ADCQ R10, AX + MOVQ AX, (48)(REG_P3) + MOVQ (56)(REG_P3), AX + ADCQ R11, AX + MOVQ AX, (56)(REG_P3) + MOVQ (64)(REG_P3), AX + ADCQ R12, AX + MOVQ AX, (64)(REG_P3) + MOVQ (72)(REG_P3), AX + ADCQ R13, AX + MOVQ AX, (72)(REG_P3) + MOVQ (80)(REG_P3), AX + ADCQ R14, AX + MOVQ AX, (80)(REG_P3) + MOVQ (88)(REG_P3), AX + ADCQ R15, AX + MOVQ AX, (88)(REG_P3) + + RET + +TEXT ·subP751(SB), NOSPLIT, $0-24 + + MOVQ z+0(FP), REG_P3 + MOVQ x+8(FP), REG_P1 + MOVQ y+16(FP), REG_P2 + + MOVQ (REG_P1), R8 + MOVQ (8)(REG_P1), R9 + MOVQ (16)(REG_P1), R10 + MOVQ (24)(REG_P1), R11 + MOVQ (32)(REG_P1), R12 + MOVQ (40)(REG_P1), R13 + MOVQ (48)(REG_P1), R14 + MOVQ (56)(REG_P1), R15 + MOVQ (64)(REG_P1), CX + SUBQ (REG_P2), R8 + SBBQ (8)(REG_P2), R9 + SBBQ (16)(REG_P2), R10 + SBBQ (24)(REG_P2), R11 + SBBQ (32)(REG_P2), R12 + SBBQ (40)(REG_P2), R13 + SBBQ (48)(REG_P2), R14 + SBBQ (56)(REG_P2), R15 + SBBQ (64)(REG_P2), CX + MOVQ R8, (REG_P3) + MOVQ R9, (8)(REG_P3) + MOVQ R10, (16)(REG_P3) + MOVQ R11, (24)(REG_P3) + MOVQ R12, (32)(REG_P3) + MOVQ R13, (40)(REG_P3) + MOVQ R14, (48)(REG_P3) + MOVQ R15, (56)(REG_P3) + MOVQ CX, (64)(REG_P3) + MOVQ (72)(REG_P1), AX + SBBQ (72)(REG_P2), AX + MOVQ AX, (72)(REG_P3) + MOVQ (80)(REG_P1), AX + SBBQ (80)(REG_P2), AX + MOVQ AX, (80)(REG_P3) + MOVQ (88)(REG_P1), AX + SBBQ (88)(REG_P2), AX + MOVQ AX, (88)(REG_P3) + MOVQ $0, AX + SBBQ $0, AX + + MOVQ P751X2_0, SI + ANDQ AX, SI + MOVQ P751X2_1, R8 + ANDQ AX, R8 + MOVQ P751X2_5, R9 + ANDQ AX, R9 + MOVQ P751X2_6, R10 + ANDQ AX, R10 + MOVQ P751X2_7, R11 + ANDQ AX, R11 + MOVQ P751X2_8, R12 + ANDQ AX, R12 + MOVQ P751X2_9, R13 + ANDQ AX, R13 + MOVQ P751X2_10, R14 + ANDQ AX, R14 + MOVQ P751X2_11, R15 + ANDQ AX, R15 + + MOVQ (REG_P3), AX + ADDQ SI, AX + MOVQ AX, (REG_P3) + MOVQ (8)(REG_P3), AX + ADCQ R8, AX + MOVQ AX, (8)(REG_P3) + MOVQ (16)(REG_P3), AX + ADCQ R8, AX + MOVQ AX, (16)(REG_P3) + MOVQ (24)(REG_P3), AX + ADCQ R8, AX + MOVQ AX, (24)(REG_P3) + MOVQ (32)(REG_P3), AX + ADCQ R8, AX + MOVQ AX, (32)(REG_P3) + MOVQ (40)(REG_P3), AX + ADCQ R9, AX + MOVQ AX, (40)(REG_P3) + MOVQ (48)(REG_P3), AX + ADCQ R10, AX + MOVQ AX, (48)(REG_P3) + MOVQ (56)(REG_P3), AX + ADCQ R11, AX + MOVQ AX, (56)(REG_P3) + MOVQ (64)(REG_P3), AX + ADCQ R12, AX + MOVQ AX, (64)(REG_P3) + MOVQ (72)(REG_P3), AX + ADCQ R13, AX + MOVQ AX, (72)(REG_P3) + MOVQ (80)(REG_P3), AX + ADCQ R14, AX + MOVQ AX, (80)(REG_P3) + MOVQ (88)(REG_P3), AX + ADCQ R15, AX + MOVQ AX, (88)(REG_P3) + + RET + +TEXT ·mulP751(SB), $96-24 + + // Here we store the destination in CX instead of in REG_P3 because the + // multiplication instructions use DX as an implicit destination + // operand: MULQ $REG sets DX:AX <-- AX * $REG. + + MOVQ z+0(FP), CX + MOVQ x+8(FP), REG_P1 + MOVQ y+16(FP), REG_P2 + + XORQ AX, AX + MOVQ (48)(REG_P1), R8 + MOVQ (56)(REG_P1), R9 + MOVQ (64)(REG_P1), R10 + MOVQ (72)(REG_P1), R11 + MOVQ (80)(REG_P1), R12 + MOVQ (88)(REG_P1), R13 + ADDQ (REG_P1), R8 + ADCQ (8)(REG_P1), R9 + ADCQ (16)(REG_P1), R10 + ADCQ (24)(REG_P1), R11 + ADCQ (32)(REG_P1), R12 + ADCQ (40)(REG_P1), R13 + MOVQ R8, (CX) + MOVQ R9, (8)(CX) + MOVQ R10, (16)(CX) + MOVQ R11, (24)(CX) + MOVQ R12, (32)(CX) + MOVQ R13, (40)(CX) + SBBQ $0, AX + + XORQ DX, DX + MOVQ (48)(REG_P2), R8 + MOVQ (56)(REG_P2), R9 + MOVQ (64)(REG_P2), R10 + MOVQ (72)(REG_P2), R11 + MOVQ (80)(REG_P2), R12 + MOVQ (88)(REG_P2), R13 + ADDQ (REG_P2), R8 + ADCQ (8)(REG_P2), R9 + ADCQ (16)(REG_P2), R10 + ADCQ (24)(REG_P2), R11 + ADCQ (32)(REG_P2), R12 + ADCQ (40)(REG_P2), R13 + MOVQ R8, (48)(CX) + MOVQ R9, (56)(CX) + MOVQ R10, (64)(CX) + MOVQ R11, (72)(CX) + MOVQ R12, (80)(CX) + MOVQ R13, (88)(CX) + SBBQ $0, DX + MOVQ AX, (80)(SP) + MOVQ DX, (88)(SP) + + // (SP[0-8],R10,R8,R9) <- (AH+AL)*(BH+BL) + + MOVQ (CX), R11 + MOVQ R8, AX + MULQ R11 + MOVQ AX, (SP) // c0 + MOVQ DX, R14 + + XORQ R15, R15 + MOVQ R9, AX + MULQ R11 + XORQ R9, R9 + ADDQ AX, R14 + ADCQ DX, R9 + + MOVQ (8)(CX), R12 + MOVQ R8, AX + MULQ R12 + ADDQ AX, R14 + MOVQ R14, (8)(SP) // c1 + ADCQ DX, R9 + ADCQ $0, R15 + + XORQ R8, R8 + MOVQ R10, AX + MULQ R11 + ADDQ AX, R9 + MOVQ (48)(CX), R13 + ADCQ DX, R15 + ADCQ $0, R8 + + MOVQ (16)(CX), AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R15 + MOVQ (56)(CX), AX + ADCQ $0, R8 + + MULQ R12 + ADDQ AX, R9 + MOVQ R9, (16)(SP) // c2 + ADCQ DX, R15 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ (72)(CX), AX + MULQ R11 + ADDQ AX, R15 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (24)(CX), AX + MULQ R13 + ADDQ AX, R15 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ R10, AX + MULQ R12 + ADDQ AX, R15 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (16)(CX), R14 + MOVQ (56)(CX), AX + MULQ R14 + ADDQ AX, R15 + MOVQ R15, (24)(SP) // c3 + ADCQ DX, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ (80)(CX), AX + MULQ R11 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (64)(CX), AX + MULQ R14 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (48)(CX), R15 + MOVQ (32)(CX), AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (72)(CX), AX + MULQ R12 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (24)(CX), R13 + MOVQ (56)(CX), AX + MULQ R13 + ADDQ AX, R8 + MOVQ R8, (32)(SP) // c4 + ADCQ DX, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ (88)(CX), AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (64)(CX), AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (72)(CX), AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (40)(CX), AX + MULQ R15 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (80)(CX), AX + MULQ R12 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (32)(CX), R15 + MOVQ (56)(CX), AX + MULQ R15 + ADDQ AX, R9 + MOVQ R9, (40)(SP) // c5 + ADCQ DX, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ (64)(CX), AX + MULQ R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (88)(CX), AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (80)(CX), AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (40)(CX), R11 + MOVQ (56)(CX), AX + MULQ R11 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (72)(CX), AX + MULQ R13 + ADDQ AX, R10 + MOVQ R10, (48)(SP) // c6 + ADCQ DX, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ (88)(CX), AX + MULQ R14 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (64)(CX), AX + MULQ R11 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (80)(CX), AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (72)(CX), AX + MULQ R15 + ADDQ AX, R8 + MOVQ R8, (56)(SP) // c7 + ADCQ DX, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ (72)(CX), AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (80)(CX), AX + MULQ R15 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (88)(CX), AX + MULQ R13 + ADDQ AX, R9 + MOVQ R9, (64)(SP) // c8 + ADCQ DX, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ (88)(CX), AX + MULQ R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (80)(CX), AX + MULQ R11 + ADDQ AX, R10 // c9 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (88)(CX), AX + MULQ R11 + ADDQ AX, R8 // c10 + ADCQ DX, R9 // c11 + + MOVQ (88)(SP), AX + MOVQ (CX), DX + ANDQ AX, R12 + ANDQ AX, R14 + ANDQ AX, DX + ANDQ AX, R13 + ANDQ AX, R15 + ANDQ AX, R11 + MOVQ (48)(SP), AX + ADDQ AX, DX + MOVQ (56)(SP), AX + ADCQ AX, R12 + MOVQ (64)(SP), AX + ADCQ AX, R14 + ADCQ R10, R13 + ADCQ R8, R15 + ADCQ R9, R11 + MOVQ (80)(SP), AX + MOVQ DX, (48)(SP) + MOVQ R12, (56)(SP) + MOVQ R14, (64)(SP) + MOVQ R13, (72)(SP) + MOVQ R15, (80)(SP) + MOVQ R11, (88)(SP) + + MOVQ (48)(CX), R8 + MOVQ (56)(CX), R9 + MOVQ (64)(CX), R10 + MOVQ (72)(CX), R11 + MOVQ (80)(CX), R12 + MOVQ (88)(CX), R13 + ANDQ AX, R8 + ANDQ AX, R9 + ANDQ AX, R10 + ANDQ AX, R11 + ANDQ AX, R12 + ANDQ AX, R13 + MOVQ (48)(SP), AX + ADDQ AX, R8 + MOVQ (56)(SP), AX + ADCQ AX, R9 + MOVQ (64)(SP), AX + ADCQ AX, R10 + MOVQ (72)(SP), AX + ADCQ AX, R11 + MOVQ (80)(SP), AX + ADCQ AX, R12 + MOVQ (88)(SP), AX + ADCQ AX, R13 + MOVQ R8, (48)(SP) + MOVQ R9, (56)(SP) + MOVQ R11, (72)(SP) + + // CX[0-11] <- AL*BL + MOVQ (REG_P1), R11 + MOVQ (REG_P2), AX + MULQ R11 + XORQ R9, R9 + MOVQ AX, (CX) // c0 + MOVQ R10, (64)(SP) + MOVQ DX, R8 + + MOVQ (8)(REG_P2), AX + MULQ R11 + XORQ R10, R10 + ADDQ AX, R8 + MOVQ R12, (80)(SP) + ADCQ DX, R9 + + MOVQ (8)(REG_P1), R12 + MOVQ (REG_P2), AX + MULQ R12 + ADDQ AX, R8 + MOVQ R8, (8)(CX) // c1 + ADCQ DX, R9 + MOVQ R13, (88)(SP) + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ (16)(REG_P2), AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (REG_P2), R13 + MOVQ (16)(REG_P1), AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (8)(REG_P2), AX + MULQ R12 + ADDQ AX, R9 + MOVQ R9, (16)(CX) // c2 + ADCQ DX, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ (24)(REG_P2), AX + MULQ R11 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (24)(REG_P1), AX + MULQ R13 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (16)(REG_P2), AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (16)(REG_P1), R14 + MOVQ (8)(REG_P2), AX + MULQ R14 + ADDQ AX, R10 + MOVQ R10, (24)(CX) // c3 + ADCQ DX, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ (32)(REG_P2), AX + MULQ R11 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (16)(REG_P2), AX + MULQ R14 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (32)(REG_P1), AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (24)(REG_P2), AX + MULQ R12 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (24)(REG_P1), R13 + MOVQ (8)(REG_P2), AX + MULQ R13 + ADDQ AX, R8 + MOVQ R8, (32)(CX) // c4 + ADCQ DX, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ (40)(REG_P2), AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (16)(REG_P2), AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (24)(REG_P2), AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (40)(REG_P1), R11 + MOVQ (REG_P2), AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (32)(REG_P2), AX + MULQ R12 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (32)(REG_P1), R15 + MOVQ (8)(REG_P2), AX + MULQ R15 + ADDQ AX, R9 + MOVQ R9, (40)(CX) //c5 + ADCQ DX, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ (16)(REG_P2), AX + MULQ R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (40)(REG_P2), AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (32)(REG_P2), AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (8)(REG_P2), AX + MULQ R11 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (24)(REG_P2), AX + MULQ R13 + ADDQ AX, R10 + MOVQ R10, (48)(CX) // c6 + ADCQ DX, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ (40)(REG_P2), AX + MULQ R14 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (16)(REG_P2), AX + MULQ R11 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (32)(REG_P2), AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (24)(REG_P2), AX + MULQ R15 + ADDQ AX, R8 + MOVQ R8, (56)(CX) // c7 + ADCQ DX, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ (24)(REG_P2), AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (32)(REG_P2), AX + MULQ R15 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (40)(REG_P2), AX + MULQ R13 + ADDQ AX, R9 + MOVQ R9, (64)(CX) // c8 + ADCQ DX, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ (40)(REG_P2), AX + MULQ R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (32)(REG_P2), AX + MULQ R11 + ADDQ AX, R10 + MOVQ R10, (72)(CX) // c9 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (40)(REG_P2), AX + MULQ R11 + ADDQ AX, R8 + MOVQ R8, (80)(CX) // c10 + ADCQ DX, R9 + MOVQ R9, (88)(CX) // c11 + + // CX[12-23] <- AH*BH + MOVQ (48)(REG_P1), R11 + MOVQ (48)(REG_P2), AX + MULQ R11 + XORQ R9, R9 + MOVQ AX, (96)(CX) // c0 + MOVQ DX, R8 + + MOVQ (56)(REG_P2), AX + MULQ R11 + XORQ R10, R10 + ADDQ AX, R8 + ADCQ DX, R9 + + MOVQ (56)(REG_P1), R12 + MOVQ (48)(REG_P2), AX + MULQ R12 + ADDQ AX, R8 + MOVQ R8, (104)(CX) // c1 + ADCQ DX, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ (64)(REG_P2), AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (48)(REG_P2), R13 + MOVQ (64)(REG_P1), AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (56)(REG_P2), AX + MULQ R12 + ADDQ AX, R9 + MOVQ R9, (112)(CX) // c2 + ADCQ DX, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ (72)(REG_P2), AX + MULQ R11 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (72)(REG_P1), AX + MULQ R13 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (64)(REG_P2), AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (64)(REG_P1), R14 + MOVQ (56)(REG_P2), AX + MULQ R14 + ADDQ AX, R10 + MOVQ R10, (120)(CX) // c3 + ADCQ DX, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ (80)(REG_P2), AX + MULQ R11 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (64)(REG_P2), AX + MULQ R14 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (80)(REG_P1), R15 + MOVQ R13, AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (72)(REG_P2), AX + MULQ R12 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (72)(REG_P1), R13 + MOVQ (56)(REG_P2), AX + MULQ R13 + ADDQ AX, R8 + MOVQ R8, (128)(CX) // c4 + ADCQ DX, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ (88)(REG_P2), AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (64)(REG_P2), AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (72)(REG_P2), AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (88)(REG_P1), R11 + MOVQ (48)(REG_P2), AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (80)(REG_P2), AX + MULQ R12 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (56)(REG_P2), AX + MULQ R15 + ADDQ AX, R9 + MOVQ R9, (136)(CX) // c5 + ADCQ DX, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ (64)(REG_P2), AX + MULQ R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (88)(REG_P2), AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (80)(REG_P2), AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (56)(REG_P2), AX + MULQ R11 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (72)(REG_P2), AX + MULQ R13 + ADDQ AX, R10 + MOVQ R10, (144)(CX) // c6 + ADCQ DX, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ (88)(REG_P2), AX + MULQ R14 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (64)(REG_P2), AX + MULQ R11 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (80)(REG_P2), AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (72)(REG_P2), AX + MULQ R15 + ADDQ AX, R8 + MOVQ R8, (152)(CX) // c7 + ADCQ DX, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ (72)(REG_P2), AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (80)(REG_P2), AX + MULQ R15 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (88)(REG_P2), AX + MULQ R13 + ADDQ AX, R9 + MOVQ R9, (160)(CX) // c8 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (88)(REG_P2), AX + MULQ R15 + ADDQ AX, R10 + ADCQ DX, R8 + + MOVQ (80)(REG_P2), AX + MULQ R11 + ADDQ AX, R10 + MOVQ R10, (168)(CX) // c9 + ADCQ DX, R8 + + MOVQ (88)(REG_P2), AX + MULQ R11 + ADDQ AX, R8 + MOVQ R8, (176)(CX) // c10 + ADCQ $0, DX + MOVQ DX, (184)(CX) // c11 + + // [R8-R15,AX,DX,DI,(SP)] <- (AH+AL)*(BH+BL)-AL*BL + MOVQ (SP), R8 + SUBQ (CX), R8 + MOVQ (8)(SP), R9 + SBBQ (8)(CX), R9 + MOVQ (16)(SP), R10 + SBBQ (16)(CX), R10 + MOVQ (24)(SP), R11 + SBBQ (24)(CX), R11 + MOVQ (32)(SP), R12 + SBBQ (32)(CX), R12 + MOVQ (40)(SP), R13 + SBBQ (40)(CX), R13 + MOVQ (48)(SP), R14 + SBBQ (48)(CX), R14 + MOVQ (56)(SP), R15 + SBBQ (56)(CX), R15 + MOVQ (64)(SP), AX + SBBQ (64)(CX), AX + MOVQ (72)(SP), DX + SBBQ (72)(CX), DX + MOVQ (80)(SP), DI + SBBQ (80)(CX), DI + MOVQ (88)(SP), SI + SBBQ (88)(CX), SI + MOVQ SI, (SP) + + // [R8-R15,AX,DX,DI,(SP)] <- (AH+AL)*(BH+BL) - AL*BL - AH*BH + MOVQ (96)(CX), SI + SUBQ SI, R8 + MOVQ (104)(CX), SI + SBBQ SI, R9 + MOVQ (112)(CX), SI + SBBQ SI, R10 + MOVQ (120)(CX), SI + SBBQ SI, R11 + MOVQ (128)(CX), SI + SBBQ SI, R12 + MOVQ (136)(CX), SI + SBBQ SI, R13 + MOVQ (144)(CX), SI + SBBQ SI, R14 + MOVQ (152)(CX), SI + SBBQ SI, R15 + MOVQ (160)(CX), SI + SBBQ SI, AX + MOVQ (168)(CX), SI + SBBQ SI, DX + MOVQ (176)(CX), SI + SBBQ SI, DI + MOVQ (SP), SI + SBBQ (184)(CX), SI + + // FINAL RESULT + ADDQ (48)(CX), R8 + MOVQ R8, (48)(CX) + ADCQ (56)(CX), R9 + MOVQ R9, (56)(CX) + ADCQ (64)(CX), R10 + MOVQ R10, (64)(CX) + ADCQ (72)(CX), R11 + MOVQ R11, (72)(CX) + ADCQ (80)(CX), R12 + MOVQ R12, (80)(CX) + ADCQ (88)(CX), R13 + MOVQ R13, (88)(CX) + ADCQ (96)(CX), R14 + MOVQ R14, (96)(CX) + ADCQ (104)(CX), R15 + MOVQ R15, (104)(CX) + ADCQ (112)(CX), AX + MOVQ AX, (112)(CX) + ADCQ (120)(CX), DX + MOVQ DX, (120)(CX) + ADCQ (128)(CX), DI + MOVQ DI, (128)(CX) + ADCQ (136)(CX), SI + MOVQ SI, (136)(CX) + MOVQ (144)(CX), AX + ADCQ $0, AX + MOVQ AX, (144)(CX) + MOVQ (152)(CX), AX + ADCQ $0, AX + MOVQ AX, (152)(CX) + MOVQ (160)(CX), AX + ADCQ $0, AX + MOVQ AX, (160)(CX) + MOVQ (168)(CX), AX + ADCQ $0, AX + MOVQ AX, (168)(CX) + MOVQ (176)(CX), AX + ADCQ $0, AX + MOVQ AX, (176)(CX) + MOVQ (184)(CX), AX + ADCQ $0, AX + MOVQ AX, (184)(CX) + + RET + +// This multiplies a 256-bit number pointed to by M0 with p751+1. +// It is assumed that M1 points to p751+1 stored as a 768-bit Fp751Element. +// C points to the place to store the result and should be at least 192 bits. +// This should only be used when the BMI2 and ADX instruction set extensions +// are available. +#define mul256x448bmi2adx(M0, M1, C, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, T10) \ + MOVQ 0+M0, DX \ + MULXQ M1+40(SB), T1, T0 \ + MULXQ M1+48(SB), T3, T2 \ + MOVQ T1, 0+C \ // C0_final + XORQ AX, AX \ + MULXQ M1+56(SB), T5, T4 \ + ADOXQ T3, T0 \ + ADOXQ T5, T2 \ + MULXQ M1+64(SB), T3, T1 \ + ADOXQ T3, T4 \ + MULXQ M1+72(SB), T6, T5 \ + ADOXQ T6, T1 \ + MULXQ M1+80(SB), T7, T3 \ + ADOXQ T7, T5 \ + MULXQ M1+88(SB), T8, T6 \ + ADOXQ T8, T3 \ + ADOXQ AX, T6 \ + \ + MOVQ 8+M0, DX \ + MULXQ M1+40(SB), T7, T8 \ + XORQ AX, AX \ + ADCXQ T7, T0 \ + MOVQ T0, 8+C \ // C1_final + ADCXQ T8, T2 \ + MULXQ M1+48(SB), T8, T7 \ + ADOXQ T8, T2 \ + ADCXQ T7, T4 \ + MULXQ M1+56(SB), T8, T0 \ + ADOXQ T8, T4 \ + ADCXQ T1, T0 \ + MULXQ M1+64(SB), T7, T1 \ + ADCXQ T5, T1 \ + MULXQ M1+72(SB), T8, T5 \ + ADCXQ T5, T3 \ + MULXQ M1+80(SB), T9, T5 \ + ADCXQ T5, T6 \ + MULXQ M1+88(SB), DX, T5 \ + ADCXQ AX, T5 \ + \ + ADOXQ T7, T0 \ + ADOXQ T8, T1 \ + ADOXQ T9, T3 \ + ADOXQ DX, T6 \ + ADOXQ AX, T5 \ + \ + MOVQ 16+M0, DX \ + MULXQ M1+40(SB), T7, T8 \ + XORQ AX, AX \ + ADCXQ T7, T2 \ + MOVQ T2, 16+C \ // C2_final + ADCXQ T8, T4 \ + MULXQ M1+48(SB), T7, T8 \ + ADOXQ T7, T4 \ + ADCXQ T8, T0 \ + MULXQ M1+56(SB), T8, T2 \ + ADOXQ T8, T0 \ + ADCXQ T2, T1 \ + MULXQ M1+64(SB), T7, T2 \ + ADCXQ T2, T3 \ + MULXQ M1+72(SB), T8, T2 \ + ADCXQ T2, T6 \ + MULXQ M1+80(SB), T9, T2 \ + ADCXQ T2, T5 \ + MULXQ M1+88(SB), DX, T2 \ + ADCXQ AX, T2 \ + \ + ADOXQ T7, T1 \ + ADOXQ T8, T3 \ + ADOXQ T9, T6 \ + ADOXQ DX, T5 \ + ADOXQ AX, T2 \ + \ + MOVQ 24+M0, DX \ + MULXQ M1+40(SB), T7, T8 \ + XORQ AX, AX \ + ADCXQ T4, T7 \ + ADCXQ T8, T0 \ + MULXQ M1+48(SB), T10, T8 \ + ADOXQ T10, T0 \ + ADCXQ T8, T1 \ + MULXQ M1+56(SB), T8, T4 \ + ADOXQ T8, T1 \ + ADCXQ T4, T3 \ + MULXQ M1+64(SB), T10, T4 \ + ADCXQ T4, T6 \ + MULXQ M1+72(SB), T8, T4 \ + ADCXQ T4, T5 \ + MULXQ M1+80(SB), T9, T4 \ + ADCXQ T4, T2 \ + MULXQ M1+88(SB), DX, T4 \ + ADCXQ AX, T4 \ + \ + ADOXQ T10, T3 \ + ADOXQ T8, T6 \ + ADOXQ T9, T5 \ + ADOXQ DX, T2 \ + ADOXQ AX, T4 + +// This multiplies a 256-bit number pointed to by M0 with p751+1. +// It is assumed that M1 points to p751+1 stored as a 768-bit Fp751Element. +// C points to the place to store the result and should be at least 192 bits. +// This should only be used when the BMI2 instruction set extension is +// available. +#define mul256x448bmi2(M0, M1, C, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, T10) \ + MOVQ 0+M0, DX \ + MULXQ M1+40(SB), T1, T0 \ + MULXQ M1+48(SB), T3, T2 \ + MOVQ T1, 0+C \ // C0_final + XORQ AX, AX \ + MULXQ M1+56(SB), T5, T4 \ + ADDQ T3, T0 \ + ADCQ T5, T2 \ + MULXQ M1+64(SB), T3, T1 \ + ADCQ T3, T4 \ + MULXQ M1+72(SB), T6, T5 \ + ADCQ T6, T1 \ + MULXQ M1+80(SB), T7, T3 \ + ADCQ T7, T5 \ + MULXQ M1+88(SB), T8, T6 \ + ADCQ T8, T3 \ + ADCQ AX, T6 \ + \ + MOVQ 8+M0, DX \ + MULXQ M1+40(SB), T7, T8 \ + ADDQ T7, T0 \ + MOVQ T0, 8+C \ // C1_final + ADCQ T8, T2 \ + MULXQ M1+48(SB), T8, T7 \ + MOVQ T8, 32+C \ + ADCQ T7, T4 \ + MULXQ M1+56(SB), T8, T0 \ + MOVQ T8, 40+C \ + ADCQ T1, T0 \ + MULXQ M1+64(SB), T7, T1 \ + ADCQ T5, T1 \ + MULXQ M1+72(SB), T8, T5 \ + ADCQ T5, T3 \ + MULXQ M1+80(SB), T9, T5 \ + ADCQ T5, T6 \ + MULXQ M1+88(SB), DX, T5 \ + ADCQ AX, T5 \ + \ + XORQ AX, AX \ + ADDQ 32+C, T2 \ + ADCQ 40+C, T4 \ + ADCQ T7, T0 \ + ADCQ T8, T1 \ + ADCQ T9, T3 \ + ADCQ DX, T6 \ + ADCQ AX, T5 \ + \ + MOVQ 16+M0, DX \ + MULXQ M1+40(SB), T7, T8 \ + ADDQ T7, T2 \ + MOVQ T2, 16+C \ // C2_final + ADCQ T8, T4 \ + MULXQ M1+48(SB), T7, T8 \ + MOVQ T7, 32+C \ + ADCQ T8, T0 \ + MULXQ M1+56(SB), T8, T2 \ + MOVQ T8, 40+C \ + ADCQ T2, T1 \ + MULXQ M1+64(SB), T7, T2 \ + ADCQ T2, T3 \ + MULXQ M1+72(SB), T8, T2 \ + ADCQ T2, T6 \ + MULXQ M1+80(SB), T9, T2 \ + ADCQ T2, T5 \ + MULXQ M1+88(SB), DX, T2 \ + ADCQ AX, T2 \ + \ + XORQ AX, AX \ + ADDQ 32+C, T4 \ + ADCQ 40+C, T0 \ + ADCQ T7, T1 \ + ADCQ T8, T3 \ + ADCQ T9, T6 \ + ADCQ DX, T5 \ + ADCQ AX, T2 \ + \ + MOVQ 24+M0, DX \ + MULXQ M1+40(SB), T7, T8 \ + ADDQ T4, T7 \ + ADCQ T8, T0 \ + MULXQ M1+48(SB), T10, T8 \ + MOVQ T10, 32+C \ + ADCQ T8, T1 \ + MULXQ M1+56(SB), T8, T4 \ + MOVQ T8, 40+C \ + ADCQ T4, T3 \ + MULXQ M1+64(SB), T10, T4 \ + ADCQ T4, T6 \ + MULXQ M1+72(SB), T8, T4 \ + ADCQ T4, T5 \ + MULXQ M1+80(SB), T9, T4 \ + ADCQ T4, T2 \ + MULXQ M1+88(SB), DX, T4 \ + ADCQ AX, T4 \ + \ + XORQ AX, AX \ + ADDQ 32+C, T0 \ + ADCQ 40+C, T1 \ + ADCQ T10, T3 \ + ADCQ T8, T6 \ + ADCQ T9, T5 \ + ADCQ DX, T2 \ + ADCQ AX, T4 + +// Template for calculating the Montgomery reduction algorithm described in +// section 5.2.3 of https://eprint.iacr.org/2017/1015.pdf. Template must be +// customized with schoolbook multiplication for 256 x 448-bit number. +// This macro reuses memory of IN value and *changes* it. Smashes registers +// R[8-15], AX, BX, CX, DX, BP. +// Input: +// * M0: 1536-bit number to be reduced +// * C : either mul256x448bmi2 or mul256x448bmi2adx +// Output: OUT 768-bit +#define REDC(C, M0, MULS) \ + \ // a[0-3] x p751p1_nz --> result: [reg_p2+48], [reg_p2+56], [reg_p2+64], and rbp, r8:r14 + MULS(M0, ·P751p1, 48+C, R8, R9, R13, R10, R14, R12, R11, BP, BX, CX, R15) \ + XORQ R15, R15 \ + MOVQ 48+C, AX \ + MOVQ 56+C, DX \ + MOVQ 64+C, BX \ + ADDQ 40+M0, AX \ + ADCQ 48+M0, DX \ + ADCQ 56+M0, BX \ + MOVQ AX, 40+M0 \ + MOVQ DX, 48+M0 \ + MOVQ BX, 56+M0 \ + ADCQ 64+M0, BP \ + ADCQ 72+M0, R8 \ + ADCQ 80+M0, R9 \ + ADCQ 88+M0, R10 \ + ADCQ 96+M0, R11 \ + ADCQ 104+M0, R12 \ + ADCQ 112+M0, R13 \ + ADCQ 120+M0, R14 \ + ADCQ 128+M0, R15 \ + MOVQ BP, 64+M0 \ + MOVQ R8, 72+M0 \ + MOVQ R9, 80+M0 \ + MOVQ R10, 88+M0 \ + MOVQ R11, 96+M0 \ + MOVQ R12, 104+M0 \ + MOVQ R13, 112+M0 \ + MOVQ R14, 120+M0 \ + MOVQ R15, 128+M0 \ + MOVQ 136+M0, R8 \ + MOVQ 144+M0, R9 \ + MOVQ 152+M0, R10 \ + MOVQ 160+M0, R11 \ + MOVQ 168+M0, R12 \ + MOVQ 176+M0, R13 \ + MOVQ 184+M0, R14 \ + ADCQ $0, R8 \ + ADCQ $0, R9 \ + ADCQ $0, R10 \ + ADCQ $0, R11 \ + ADCQ $0, R12 \ + ADCQ $0, R13 \ + ADCQ $0, R14 \ + MOVQ R8, 136+M0 \ + MOVQ R9, 144+M0 \ + MOVQ R10, 152+M0 \ + MOVQ R11, 160+M0 \ + MOVQ R12, 168+M0 \ + MOVQ R13, 176+M0 \ + MOVQ R14, 184+M0 \ + \ // a[4-7] x p751p1_nz --> result: [reg_p2+48], [reg_p2+56], [reg_p2+64], and rbp, r8:r14 + MULS(32+M0, ·P751p1, 48+C, R8, R9, R13, R10, R14, R12, R11, BP, BX, CX, R15) \ + XORQ R15, R15 \ + MOVQ 48+C, AX \ + MOVQ 56+C, DX \ + MOVQ 64+C, BX \ + ADDQ 72+M0, AX \ + ADCQ 80+M0, DX \ + ADCQ 88+M0, BX \ + MOVQ AX, 72+M0 \ + MOVQ DX, 80+M0 \ + MOVQ BX, 88+M0 \ + ADCQ 96+M0, BP \ + ADCQ 104+M0, R8 \ + ADCQ 112+M0, R9 \ + ADCQ 120+M0, R10 \ + ADCQ 128+M0, R11 \ + ADCQ 136+M0, R12 \ + ADCQ 144+M0, R13 \ + ADCQ 152+M0, R14 \ + ADCQ 160+M0, R15 \ + MOVQ BP, 0+C \ // Final result c0 + MOVQ R8, 104+M0 \ + MOVQ R9, 112+M0 \ + MOVQ R10, 120+M0 \ + MOVQ R11, 128+M0 \ + MOVQ R12, 136+M0 \ + MOVQ R13, 144+M0 \ + MOVQ R14, 152+M0 \ + MOVQ R15, 160+M0 \ + MOVQ 168+M0, R12 \ + MOVQ 176+M0, R13 \ + MOVQ 184+M0, R14 \ + ADCQ $0, R12 \ + ADCQ $0, R13 \ + ADCQ $0, R14 \ + MOVQ R12, 168+M0 \ + MOVQ R13, 176+M0 \ + MOVQ R14, 184+M0 \ + \ // a[8-11] x p751p1_nz --> result: [reg_p2+48], [reg_p2+56], [reg_p2+64], and rbp, r8:r14 + MULS(64+M0, ·P751p1, 48+C, R8, R9, R13, R10, R14, R12, R11, BP, BX, CX, R15) \ + MOVQ 48+C, AX \ // Final result c1:c11 + MOVQ 56+C, DX \ + MOVQ 64+C, BX \ + ADDQ 104+M0, AX \ + ADCQ 112+M0, DX \ + ADCQ 120+M0, BX \ + MOVQ AX, 8+C \ + MOVQ DX, 16+C \ + MOVQ BX, 24+C \ + ADCQ 128+M0, BP \ + ADCQ 136+M0, R8 \ + ADCQ 144+M0, R9 \ + ADCQ 152+M0, R10 \ + ADCQ 160+M0, R11 \ + ADCQ 168+M0, R12 \ + ADCQ 176+M0, R13 \ + ADCQ 184+M0, R14 \ + MOVQ BP, 32+C \ + MOVQ R8, 40+C \ + MOVQ R9, 48+C \ + MOVQ R10, 56+C \ + MOVQ R11, 64+C \ + MOVQ R12, 72+C \ + MOVQ R13, 80+C \ + MOVQ R14, 88+C + +TEXT ·rdcP751(SB), $8-16 + MOVQ z+0(FP), REG_P2 + MOVQ x+8(FP), REG_P1 + + // Check whether to use optimized implementation + CMPB ·HasADXandBMI2(SB), $1 + JE redc_with_mulx_adcx_adox + CMPB ·HasBMI2(SB), $1 + JE redc_with_mulx + + MOVQ (REG_P1), R11 + MOVQ P751P1_5, AX + MULQ R11 + XORQ R8, R8 + ADDQ (40)(REG_P1), AX + MOVQ AX, (40)(REG_P2) // Z5 + ADCQ DX, R8 + + XORQ R9, R9 + MOVQ P751P1_6, AX + MULQ R11 + XORQ R10, R10 + ADDQ AX, R8 + ADCQ DX, R9 + + MOVQ (8)(REG_P1), R12 + MOVQ P751P1_5, AX + MULQ R12 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + ADDQ (48)(REG_P1), R8 + MOVQ R8, (48)(REG_P2) // Z6 + ADCQ $0, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ P751P1_7, AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_6, AX + MULQ R12 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (16)(REG_P1), R13 + MOVQ P751P1_5, AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + ADDQ (56)(REG_P1), R9 + MOVQ R9, (56)(REG_P2) // Z7 + ADCQ $0, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ P751P1_8, AX + MULQ R11 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_7, AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_6, AX + MULQ R13 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (24)(REG_P1), R14 + MOVQ P751P1_5, AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + ADDQ (64)(REG_P1), R10 + MOVQ R10, (64)(REG_P2) // Z8 + ADCQ $0, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ P751P1_9, AX + MULQ R11 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_8, AX + MULQ R12 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_7, AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_6, AX + MULQ R14 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (32)(REG_P1), R15 + MOVQ P751P1_5, AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + ADDQ (72)(REG_P1), R8 + MOVQ R8, (72)(REG_P2) // Z9 + ADCQ $0, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ P751P1_10, AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_9, AX + MULQ R12 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_8, AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_7, AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_6, AX + MULQ R15 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (40)(REG_P2), CX + MOVQ P751P1_5, AX + MULQ CX + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + ADDQ (80)(REG_P1), R9 + MOVQ R9, (80)(REG_P2) // Z10 + ADCQ $0, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ P751P1_11, AX + MULQ R11 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_10, AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_9, AX + MULQ R13 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_8, AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_7, AX + MULQ R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_6, AX + MULQ CX + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (48)(REG_P2), R11 + MOVQ P751P1_5, AX + MULQ R11 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + ADDQ (88)(REG_P1), R10 + MOVQ R10, (88)(REG_P2) // Z11 + ADCQ $0, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ P751P1_11, AX + MULQ R12 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_10, AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_9, AX + MULQ R14 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_8, AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_7, AX + MULQ CX + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_6, AX + MULQ R11 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (56)(REG_P2), R12 + MOVQ P751P1_5, AX + MULQ R12 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + ADDQ (96)(REG_P1), R8 + MOVQ R8, (REG_P2) // Z0 + ADCQ $0, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ P751P1_11, AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_10, AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_9, AX + MULQ R15 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_8, AX + MULQ CX + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_7, AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_6, AX + MULQ R12 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (64)(REG_P2), R13 + MOVQ P751P1_5, AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + ADDQ (104)(REG_P1), R9 + MOVQ R9, (8)(REG_P2) // Z1 + ADCQ $0, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ P751P1_11, AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_10, AX + MULQ R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_9, AX + MULQ CX + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_8, AX + MULQ R11 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_7, AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_6, AX + MULQ R13 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ (72)(REG_P2), R14 + MOVQ P751P1_5, AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + ADDQ (112)(REG_P1), R10 + MOVQ R10, (16)(REG_P2) // Z2 + ADCQ $0, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ P751P1_11, AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_10, AX + MULQ CX + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_9, AX + MULQ R11 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_8, AX + MULQ R12 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_7, AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_6, AX + MULQ R14 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ (80)(REG_P2), R15 + MOVQ P751P1_5, AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + ADDQ (120)(REG_P1), R8 + MOVQ R8, (24)(REG_P2) // Z3 + ADCQ $0, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ P751P1_11, AX + MULQ CX + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_10, AX + MULQ R11 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_9, AX + MULQ R12 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_8, AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_7, AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_6, AX + MULQ R15 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ (88)(REG_P2), CX + MOVQ P751P1_5, AX + MULQ CX + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + ADDQ (128)(REG_P1), R9 + MOVQ R9, (32)(REG_P2) // Z4 + ADCQ $0, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ P751P1_11, AX + MULQ R11 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_10, AX + MULQ R12 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_9, AX + MULQ R13 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_8, AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_7, AX + MULQ R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_6, AX + MULQ CX + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + ADDQ (136)(REG_P1), R10 + MOVQ R10, (40)(REG_P2) // Z5 + ADCQ $0, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ P751P1_11, AX + MULQ R12 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_10, AX + MULQ R13 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_9, AX + MULQ R14 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_8, AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_7, AX + MULQ CX + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + ADDQ (144)(REG_P1), R8 + MOVQ R8, (48)(REG_P2) // Z6 + ADCQ $0, R9 + ADCQ $0, R10 + + XORQ R8, R8 + MOVQ P751P1_11, AX + MULQ R13 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_10, AX + MULQ R14 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_9, AX + MULQ R15 + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + + MOVQ P751P1_8, AX + MULQ CX + ADDQ AX, R9 + ADCQ DX, R10 + ADCQ $0, R8 + ADDQ (152)(REG_P1), R9 + MOVQ R9, (56)(REG_P2) // Z7 + ADCQ $0, R10 + ADCQ $0, R8 + + XORQ R9, R9 + MOVQ P751P1_11, AX + MULQ R14 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_10, AX + MULQ R15 + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + + MOVQ P751P1_9, AX + MULQ CX + ADDQ AX, R10 + ADCQ DX, R8 + ADCQ $0, R9 + ADDQ (160)(REG_P1), R10 + MOVQ R10, (64)(REG_P2) // Z8 + ADCQ $0, R8 + ADCQ $0, R9 + + XORQ R10, R10 + MOVQ P751P1_11, AX + MULQ R15 + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + + MOVQ P751P1_10, AX + MULQ CX + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, R10 + ADDQ (168)(REG_P1), R8 // Z9 + MOVQ R8, (72)(REG_P2) // Z9 + ADCQ $0, R9 + ADCQ $0, R10 + + MOVQ P751P1_11, AX + MULQ CX + ADDQ AX, R9 + ADCQ DX, R10 + ADDQ (176)(REG_P1), R9 // Z10 + MOVQ R9, (80)(REG_P2) // Z10 + ADCQ $0, R10 + ADDQ (184)(REG_P1), R10 // Z11 + MOVQ R10, (88)(REG_P2) // Z11 + RET + +redc_with_mulx_adcx_adox: + // This implements the Montgomery reduction algorithm described in + // section 5.2.3 of https://eprint.iacr.org/2017/1015.pdf. + // This assumes that the BMI2 and ADX instruction set extensions are available. + MOVQ BP, 0(SP) // push: BP is Callee-save. + REDC(0(REG_P2), 0(REG_P1), mul256x448bmi2adx) + MOVQ 0(SP), BP // pop: BP is Callee-save. + RET + +redc_with_mulx: + // This implements the Montgomery reduction algorithm described in + // section 5.2.3 of https://eprint.iacr.org/2017/1015.pdf. + // This assumes that the BMI2 instruction set extension is available. + MOVQ BP, 0(SP) // push: BP is Callee-save. + REDC(0(REG_P2), 0(REG_P1), mul256x448bmi2) + MOVQ 0(SP), BP // pop: BP is Callee-save. + RET + +TEXT ·adlP751(SB), NOSPLIT, $0-24 + + MOVQ z+0(FP), REG_P3 + MOVQ x+8(FP), REG_P1 + MOVQ y+16(FP), REG_P2 + + MOVQ (REG_P1), R8 + MOVQ (8)(REG_P1), R9 + MOVQ (16)(REG_P1), R10 + MOVQ (24)(REG_P1), R11 + MOVQ (32)(REG_P1), R12 + MOVQ (40)(REG_P1), R13 + MOVQ (48)(REG_P1), R14 + MOVQ (56)(REG_P1), R15 + MOVQ (64)(REG_P1), AX + MOVQ (72)(REG_P1), BX + MOVQ (80)(REG_P1), CX + + ADDQ (REG_P2), R8 + ADCQ (8)(REG_P2), R9 + ADCQ (16)(REG_P2), R10 + ADCQ (24)(REG_P2), R11 + ADCQ (32)(REG_P2), R12 + ADCQ (40)(REG_P2), R13 + ADCQ (48)(REG_P2), R14 + ADCQ (56)(REG_P2), R15 + ADCQ (64)(REG_P2), AX + ADCQ (72)(REG_P2), BX + ADCQ (80)(REG_P2), CX + + MOVQ R8, (REG_P3) + MOVQ R9, (8)(REG_P3) + MOVQ R10, (16)(REG_P3) + MOVQ R11, (24)(REG_P3) + MOVQ R12, (32)(REG_P3) + MOVQ R13, (40)(REG_P3) + MOVQ R14, (48)(REG_P3) + MOVQ R15, (56)(REG_P3) + MOVQ AX, (64)(REG_P3) + MOVQ BX, (72)(REG_P3) + MOVQ CX, (80)(REG_P3) + MOVQ (88)(REG_P1), AX + ADCQ (88)(REG_P2), AX + MOVQ AX, (88)(REG_P3) + + MOVQ (96)(REG_P1), R8 + MOVQ (104)(REG_P1), R9 + MOVQ (112)(REG_P1), R10 + MOVQ (120)(REG_P1), R11 + MOVQ (128)(REG_P1), R12 + MOVQ (136)(REG_P1), R13 + MOVQ (144)(REG_P1), R14 + MOVQ (152)(REG_P1), R15 + MOVQ (160)(REG_P1), AX + MOVQ (168)(REG_P1), BX + MOVQ (176)(REG_P1), CX + MOVQ (184)(REG_P1), DI + + ADCQ (96)(REG_P2), R8 + ADCQ (104)(REG_P2), R9 + ADCQ (112)(REG_P2), R10 + ADCQ (120)(REG_P2), R11 + ADCQ (128)(REG_P2), R12 + ADCQ (136)(REG_P2), R13 + ADCQ (144)(REG_P2), R14 + ADCQ (152)(REG_P2), R15 + ADCQ (160)(REG_P2), AX + ADCQ (168)(REG_P2), BX + ADCQ (176)(REG_P2), CX + ADCQ (184)(REG_P2), DI + + MOVQ R8, (96)(REG_P3) + MOVQ R9, (104)(REG_P3) + MOVQ R10, (112)(REG_P3) + MOVQ R11, (120)(REG_P3) + MOVQ R12, (128)(REG_P3) + MOVQ R13, (136)(REG_P3) + MOVQ R14, (144)(REG_P3) + MOVQ R15, (152)(REG_P3) + MOVQ AX, (160)(REG_P3) + MOVQ BX, (168)(REG_P3) + MOVQ CX, (176)(REG_P3) + MOVQ DI, (184)(REG_P3) + + RET + + +TEXT ·sulP751(SB), NOSPLIT, $0-24 + + MOVQ z+0(FP), REG_P3 + MOVQ x+8(FP), REG_P1 + MOVQ y+16(FP), REG_P2 + + MOVQ (REG_P1), R8 + MOVQ (8)(REG_P1), R9 + MOVQ (16)(REG_P1), R10 + MOVQ (24)(REG_P1), R11 + MOVQ (32)(REG_P1), R12 + MOVQ (40)(REG_P1), R13 + MOVQ (48)(REG_P1), R14 + MOVQ (56)(REG_P1), R15 + MOVQ (64)(REG_P1), AX + MOVQ (72)(REG_P1), BX + MOVQ (80)(REG_P1), CX + + SUBQ (REG_P2), R8 + SBBQ (8)(REG_P2), R9 + SBBQ (16)(REG_P2), R10 + SBBQ (24)(REG_P2), R11 + SBBQ (32)(REG_P2), R12 + SBBQ (40)(REG_P2), R13 + SBBQ (48)(REG_P2), R14 + SBBQ (56)(REG_P2), R15 + SBBQ (64)(REG_P2), AX + SBBQ (72)(REG_P2), BX + SBBQ (80)(REG_P2), CX + + MOVQ R8, (REG_P3) + MOVQ R9, (8)(REG_P3) + MOVQ R10, (16)(REG_P3) + MOVQ R11, (24)(REG_P3) + MOVQ R12, (32)(REG_P3) + MOVQ R13, (40)(REG_P3) + MOVQ R14, (48)(REG_P3) + MOVQ R15, (56)(REG_P3) + MOVQ AX, (64)(REG_P3) + MOVQ BX, (72)(REG_P3) + MOVQ CX, (80)(REG_P3) + MOVQ (88)(REG_P1), AX + SBBQ (88)(REG_P2), AX + MOVQ AX, (88)(REG_P3) + + MOVQ (96)(REG_P1), R8 + MOVQ (104)(REG_P1), R9 + MOVQ (112)(REG_P1), R10 + MOVQ (120)(REG_P1), R11 + MOVQ (128)(REG_P1), R12 + MOVQ (136)(REG_P1), R13 + MOVQ (144)(REG_P1), R14 + MOVQ (152)(REG_P1), R15 + MOVQ (160)(REG_P1), AX + MOVQ (168)(REG_P1), BX + MOVQ (176)(REG_P1), CX + MOVQ (184)(REG_P1), DI + + SBBQ (96)(REG_P2), R8 + SBBQ (104)(REG_P2), R9 + SBBQ (112)(REG_P2), R10 + SBBQ (120)(REG_P2), R11 + SBBQ (128)(REG_P2), R12 + SBBQ (136)(REG_P2), R13 + SBBQ (144)(REG_P2), R14 + SBBQ (152)(REG_P2), R15 + SBBQ (160)(REG_P2), AX + SBBQ (168)(REG_P2), BX + SBBQ (176)(REG_P2), CX + SBBQ (184)(REG_P2), DI + + MOVQ R8, (96)(REG_P3) + MOVQ R9, (104)(REG_P3) + MOVQ R10, (112)(REG_P3) + MOVQ R11, (120)(REG_P3) + MOVQ R12, (128)(REG_P3) + MOVQ R13, (136)(REG_P3) + MOVQ R14, (144)(REG_P3) + MOVQ R15, (152)(REG_P3) + MOVQ AX, (160)(REG_P3) + MOVQ BX, (168)(REG_P3) + MOVQ CX, (176)(REG_P3) + MOVQ DI, (184)(REG_P3) + + // Now the carry flag is 1 if x-y < 0. If so, add p*2^768. + MOVQ $0, AX + SBBQ $0, AX + + // Load p into registers: + MOVQ P751_0, R8 + // P751_{1,2,3,4} = P751_0, so reuse R8 + MOVQ P751_5, R9 + MOVQ P751_6, R10 + MOVQ P751_7, R11 + MOVQ P751_8, R12 + MOVQ P751_9, R13 + MOVQ P751_10, R14 + MOVQ P751_11, R15 + + ANDQ AX, R8 + ANDQ AX, R9 + ANDQ AX, R10 + ANDQ AX, R11 + ANDQ AX, R12 + ANDQ AX, R13 + ANDQ AX, R14 + ANDQ AX, R15 + + ADDQ R8, (96 )(REG_P3) + ADCQ R8, (96+ 8)(REG_P3) + ADCQ R8, (96+16)(REG_P3) + ADCQ R8, (96+24)(REG_P3) + ADCQ R8, (96+32)(REG_P3) + ADCQ R9, (96+40)(REG_P3) + ADCQ R10, (96+48)(REG_P3) + ADCQ R11, (96+56)(REG_P3) + ADCQ R12, (96+64)(REG_P3) + ADCQ R13, (96+72)(REG_P3) + ADCQ R14, (96+80)(REG_P3) + ADCQ R15, (96+88)(REG_P3) + + RET + diff --git a/src/circl/dh/sidh/internal/p751/arith_amd64_test.go b/src/circl/dh/sidh/internal/p751/arith_amd64_test.go new file mode 100644 index 00000000000..b87b4ebe338 --- /dev/null +++ b/src/circl/dh/sidh/internal/p751/arith_amd64_test.go @@ -0,0 +1,140 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +// +build amd64,!noasm + +package p751 + +import ( + "reflect" + "testing" + "testing/quick" + + "circl/dh/sidh/internal/common" + "internal/cpu" +) + +type OptimFlag uint + +const ( + // Indicates that optimisation which uses MUL instruction should be used + kUse_MUL OptimFlag = 1 << 0 + // Indicates that optimisation which uses MULX instruction should be used + kUse_MULX = 1 << 1 + // Indicates that optimisation which uses MULX, ADOX and ADCX instructions should be used + kUse_MULXandADxX = 1 << 2 +) + +func resetCpuFeatures() { + HasBMI2 = cpu.X86.HasBMI2 + HasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX +} + +// Utility function used for testing Mul implementations. Tests caller provided +// mulFunc against mul() +func testMul(t *testing.T, f1, f2 OptimFlag) { + doMulTest := func(multiplier, multiplicant common.Fp) bool { + defer resetCpuFeatures() + var resMulRef, resMulOptim common.FpX2 + + // Compute multiplier*multiplicant with first implementation + HasBMI2 = (kUse_MULX & f1) == kUse_MULX + HasADXandBMI2 = (kUse_MULXandADxX & f1) == kUse_MULXandADxX + mulP751(&resMulOptim, &multiplier, &multiplicant) + + // Compute multiplier*multiplicant with second implementation + HasBMI2 = (kUse_MULX & f2) == kUse_MULX + HasADXandBMI2 = (kUse_MULXandADxX & f2) == kUse_MULXandADxX + mulP751(&resMulRef, &multiplier, &multiplicant) + + // Compare results + return reflect.DeepEqual(resMulRef, resMulOptim) + } + + if err := quick.Check(doMulTest, quickCheckConfig); err != nil { + t.Error(err) + } +} + +// Utility function used for testing REDC implementations. Tests caller provided +// redcFunc against redc() +func testRedc(t *testing.T, f1, f2 OptimFlag) { + doRedcTest := func(aRR common.FpX2) bool { + defer resetCpuFeatures() + var resRedcF1, resRedcF2 common.Fp + var aRRcpy = aRR + + // Compute redc with first implementation + HasBMI2 = (kUse_MULX & f1) == kUse_MULX + HasADXandBMI2 = (kUse_MULXandADxX & f1) == kUse_MULXandADxX + rdcP751(&resRedcF1, &aRR) + + // Compute redc with second implementation + HasBMI2 = (kUse_MULX & f2) == kUse_MULX + HasADXandBMI2 = (kUse_MULXandADxX & f2) == kUse_MULXandADxX + rdcP751(&resRedcF2, &aRRcpy) + + // Compare results + return reflect.DeepEqual(resRedcF2, resRedcF1) + } + + if err := quick.Check(doRedcTest, quickCheckConfig); err != nil { + t.Error(err) + } +} + +// Ensures correctness of implementation of mul operation which uses MULX +func TestMulWithMULX(t *testing.T) { + defer resetCpuFeatures() + if !HasBMI2 { + t.Skip("MULX not supported by the platform") + } + testMul(t, kUse_MULX, kUse_MUL) +} + +// Ensures correctness of implementation of mul operation which uses MULX and ADOX/ADCX +func TestMulWithMULXADxX(t *testing.T) { + defer resetCpuFeatures() + if !HasADXandBMI2 { + t.Skip("MULX, ADCX and ADOX not supported by the platform") + } + testMul(t, kUse_MULXandADxX, kUse_MUL) +} + +// Ensures correctness of implementation of mul operation which uses MULX and ADOX/ADCX +func TestMulWithMULXADxXAgainstMULX(t *testing.T) { + defer resetCpuFeatures() + if !HasADXandBMI2 { + t.Skip("MULX, ADCX and ADOX not supported by the platform") + } + testMul(t, kUse_MULX, kUse_MULXandADxX) +} + +// Ensures correctness of Montgomery reduction implementation which uses MULX +func TestRedcWithMULX(t *testing.T) { + defer resetCpuFeatures() + if !HasBMI2 { + t.Skip("MULX not supported by the platform") + } + testRedc(t, kUse_MULX, kUse_MUL) +} + +// Ensures correctness of Montgomery reduction implementation which uses MULX +// and ADCX/ADOX. +func TestRedcWithMULXADxX(t *testing.T) { + defer resetCpuFeatures() + if !HasADXandBMI2 { + t.Skip("MULX, ADCX and ADOX not supported by the platform") + } + testRedc(t, kUse_MULXandADxX, kUse_MUL) +} + +// Ensures correctness of Montgomery reduction implementation which uses MULX +// and ADCX/ADOX. +func TestRedcWithMULXADxXAgainstMULX(t *testing.T) { + defer resetCpuFeatures() + if !HasADXandBMI2 { + t.Skip("MULX, ADCX and ADOX not supported by the platform") + } + testRedc(t, kUse_MULXandADxX, kUse_MULX) +} diff --git a/src/circl/dh/sidh/internal/p751/arith_arm64.s b/src/circl/dh/sidh/internal/p751/arith_arm64.s new file mode 100644 index 00000000000..2c564f91a5f --- /dev/null +++ b/src/circl/dh/sidh/internal/p751/arith_arm64.s @@ -0,0 +1,1478 @@ +// +build arm64,!noasm + +#include "textflag.h" + +TEXT ·cswapP751(SB), NOSPLIT, $0-17 + MOVD x+0(FP), R0 + MOVD y+8(FP), R1 + MOVB choice+16(FP), R2 + + // Set flags + // If choice is not 0 or 1, this implementation will swap completely + CMP $0, R2 + + LDP 0(R0), (R3, R4) + LDP 0(R1), (R5, R6) + CSEL EQ, R3, R5, R7 + CSEL EQ, R4, R6, R8 + STP (R7, R8), 0(R0) + CSEL NE, R3, R5, R9 + CSEL NE, R4, R6, R10 + STP (R9, R10), 0(R1) + + LDP 16(R0), (R3, R4) + LDP 16(R1), (R5, R6) + CSEL EQ, R3, R5, R7 + CSEL EQ, R4, R6, R8 + STP (R7, R8), 16(R0) + CSEL NE, R3, R5, R9 + CSEL NE, R4, R6, R10 + STP (R9, R10), 16(R1) + + LDP 32(R0), (R3, R4) + LDP 32(R1), (R5, R6) + CSEL EQ, R3, R5, R7 + CSEL EQ, R4, R6, R8 + STP (R7, R8), 32(R0) + CSEL NE, R3, R5, R9 + CSEL NE, R4, R6, R10 + STP (R9, R10), 32(R1) + + LDP 48(R0), (R3, R4) + LDP 48(R1), (R5, R6) + CSEL EQ, R3, R5, R7 + CSEL EQ, R4, R6, R8 + STP (R7, R8), 48(R0) + CSEL NE, R3, R5, R9 + CSEL NE, R4, R6, R10 + STP (R9, R10), 48(R1) + + LDP 64(R0), (R3, R4) + LDP 64(R1), (R5, R6) + CSEL EQ, R3, R5, R7 + CSEL EQ, R4, R6, R8 + STP (R7, R8), 64(R0) + CSEL NE, R3, R5, R9 + CSEL NE, R4, R6, R10 + STP (R9, R10), 64(R1) + + LDP 80(R0), (R3, R4) + LDP 80(R1), (R5, R6) + CSEL EQ, R3, R5, R7 + CSEL EQ, R4, R6, R8 + STP (R7, R8), 80(R0) + CSEL NE, R3, R5, R9 + CSEL NE, R4, R6, R10 + STP (R9, R10), 80(R1) + + RET + +TEXT ·addP751(SB), NOSPLIT, $0-24 + MOVD z+0(FP), R2 + MOVD x+8(FP), R0 + MOVD y+16(FP), R1 + + // Load first summand into R3-R14 + // Add first summand and second summand and store result in R3-R14 + LDP 0(R0), (R3, R4) + LDP 0(R1), (R15, R16) + LDP 16(R0), (R5, R6) + LDP 16(R1), (R17, R19) + ADDS R15, R3 + ADCS R16, R4 + ADCS R17, R5 + ADCS R19, R6 + + LDP 32(R0), (R7, R8) + LDP 32(R1), (R15, R16) + LDP 48(R0), (R9, R10) + LDP 48(R1), (R17, R19) + ADCS R15, R7 + ADCS R16, R8 + ADCS R17, R9 + ADCS R19, R10 + + LDP 64(R0), (R11, R12) + LDP 64(R1), (R15, R16) + LDP 80(R0), (R13, R14) + LDP 80(R1), (R17, R19) + ADCS R15, R11 + ADCS R16, R12 + ADCS R17, R13 + ADC R19, R14 + + // Subtract 2 * p751 in R15-R24 from the result in R3-R14 + LDP ·P751x2+0(SB), (R15, R16) + SUBS R15, R3 + SBCS R16, R4 + LDP ·P751x2+40(SB), (R17, R19) + SBCS R16, R5 + SBCS R16, R6 + SBCS R16, R7 + LDP ·P751x2+56(SB), (R20, R21) + SBCS R17, R8 + SBCS R19, R9 + LDP ·P751x2+72(SB), (R22, R23) + SBCS R20, R10 + SBCS R21, R11 + MOVD ·P751x2+88(SB), R24 + SBCS R22, R12 + SBCS R23, R13 + SBCS R24, R14 + SBC ZR, ZR, R25 + + // If x + y - 2 * p751 < 0, R25 is 1 and 2 * p751 should be added + AND R25, R15 + AND R25, R16 + AND R25, R17 + AND R25, R19 + AND R25, R20 + AND R25, R21 + AND R25, R22 + AND R25, R23 + AND R25, R24 + + ADDS R15, R3 + ADCS R16, R4 + STP (R3, R4), 0(R2) + ADCS R16, R5 + ADCS R16, R6 + STP (R5, R6), 16(R2) + ADCS R16, R7 + ADCS R17, R8 + STP (R7, R8), 32(R2) + ADCS R19, R9 + ADCS R20, R10 + STP (R9, R10), 48(R2) + ADCS R21, R11 + ADCS R22, R12 + STP (R11, R12), 64(R2) + ADCS R23, R13 + ADC R24, R14 + STP (R13, R14), 80(R2) + + RET + +TEXT ·subP751(SB), NOSPLIT, $0-24 + MOVD z+0(FP), R2 + MOVD x+8(FP), R0 + MOVD y+16(FP), R1 + + // Load x into R3-R14 + // Subtract y from x and store result in R3-R14 + LDP 0(R0), (R3, R4) + LDP 0(R1), (R15, R16) + LDP 16(R0), (R5, R6) + LDP 16(R1), (R17, R19) + SUBS R15, R3 + SBCS R16, R4 + SBCS R17, R5 + SBCS R19, R6 + + LDP 32(R0), (R7, R8) + LDP 32(R1), (R15, R16) + LDP 48(R0), (R9, R10) + LDP 48(R1), (R17, R19) + SBCS R15, R7 + SBCS R16, R8 + SBCS R17, R9 + SBCS R19, R10 + + LDP 64(R0), (R11, R12) + LDP 64(R1), (R15, R16) + LDP 80(R0), (R13, R14) + LDP 80(R1), (R17, R19) + SBCS R15, R11 + SBCS R16, R12 + SBCS R17, R13 + SBCS R19, R14 + SBC ZR, ZR, R15 + + // If x - y < 0, R15 is 1 and 2 * p751 should be added + LDP ·P751x2+0(SB), (R16, R17) + AND R15, R16 + AND R15, R17 + LDP ·P751x2+40(SB), (R19, R20) + AND R15, R19 + AND R15, R20 + + ADDS R16, R3 + ADCS R17, R4 + STP (R3, R4), 0(R2) + ADCS R17, R5 + ADCS R17, R6 + STP (R5, R6), 16(R2) + ADCS R17, R7 + ADCS R19, R8 + STP (R7, R8), 32(R2) + ADCS R20, R9 + + LDP ·P751x2+56(SB), (R16, R17) + AND R15, R16 + AND R15, R17 + LDP ·P751x2+72(SB), (R19, R20) + AND R15, R19 + AND R15, R20 + + ADCS R16, R10 + STP (R9, R10), 48(R2) + ADCS R17, R11 + ADCS R19, R12 + STP (R11, R12), 64(R2) + ADCS R20, R13 + + MOVD ·P751x2+88(SB), R16 + AND R15, R16 + ADC R16, R14 + STP (R13, R14), 80(R2) + + RET + +TEXT ·adlP751(SB), NOSPLIT, $0-24 + MOVD z+0(FP), R2 + MOVD x+8(FP), R0 + MOVD y+16(FP), R1 + + LDP 0(R0), (R3, R4) + LDP 0(R1), (R15, R16) + LDP 16(R0), (R5, R6) + LDP 16(R1), (R17, R19) + ADDS R15, R3 + ADCS R16, R4 + STP (R3, R4), 0(R2) + ADCS R17, R5 + ADCS R19, R6 + STP (R5, R6), 16(R2) + + LDP 32(R0), (R7, R8) + LDP 32(R1), (R15, R16) + LDP 48(R0), (R9, R10) + LDP 48(R1), (R17, R19) + ADCS R15, R7 + ADCS R16, R8 + STP (R7, R8), 32(R2) + ADCS R17, R9 + ADCS R19, R10 + STP (R9, R10), 48(R2) + + LDP 64(R0), (R11, R12) + LDP 64(R1), (R15, R16) + LDP 80(R0), (R13, R14) + LDP 80(R1), (R17, R19) + ADCS R15, R11 + ADCS R16, R12 + STP (R11, R12), 64(R2) + ADCS R17, R13 + ADCS R19, R14 + STP (R13, R14), 80(R2) + + LDP 96(R0), (R3, R4) + LDP 96(R1), (R15, R16) + LDP 112(R0), (R5, R6) + LDP 112(R1), (R17, R19) + ADCS R15, R3 + ADCS R16, R4 + STP (R3, R4), 96(R2) + ADCS R17, R5 + ADCS R19, R6 + STP (R5, R6), 112(R2) + + LDP 128(R0), (R7, R8) + LDP 128(R1), (R15, R16) + LDP 144(R0), (R9, R10) + LDP 144(R1), (R17, R19) + ADCS R15, R7 + ADCS R16, R8 + STP (R7, R8), 128(R2) + ADCS R17, R9 + ADCS R19, R10 + STP (R9, R10), 144(R2) + + LDP 160(R0), (R11, R12) + LDP 160(R1), (R15, R16) + LDP 176(R0), (R13, R14) + LDP 176(R1), (R17, R19) + ADCS R15, R11 + ADCS R16, R12 + STP (R11, R12), 160(R2) + ADCS R17, R13 + ADC R19, R14 + STP (R13, R14), 176(R2) + + RET + +TEXT ·sulP751(SB), NOSPLIT, $0-24 + MOVD z+0(FP), R2 + MOVD x+8(FP), R0 + MOVD y+16(FP), R1 + + LDP 0(R0), (R3, R4) + LDP 0(R1), (R15, R16) + LDP 16(R0), (R5, R6) + LDP 16(R1), (R17, R19) + SUBS R15, R3 + SBCS R16, R4 + STP (R3, R4), 0(R2) + SBCS R17, R5 + SBCS R19, R6 + STP (R5, R6), 16(R2) + + LDP 32(R0), (R7, R8) + LDP 32(R1), (R15, R16) + LDP 48(R0), (R9, R10) + LDP 48(R1), (R17, R19) + SBCS R15, R7 + SBCS R16, R8 + STP (R7, R8), 32(R2) + SBCS R17, R9 + SBCS R19, R10 + STP (R9, R10), 48(R2) + + LDP 64(R0), (R11, R12) + LDP 64(R1), (R15, R16) + LDP 80(R0), (R13, R14) + LDP 80(R1), (R17, R19) + SBCS R15, R11 + SBCS R16, R12 + STP (R11, R12), 64(R2) + SBCS R17, R13 + SBCS R19, R14 + STP (R13, R14), 80(R2) + + LDP 96(R0), (R3, R4) + LDP 96(R1), (R15, R16) + LDP 112(R0), (R5, R6) + LDP 112(R1), (R17, R19) + SBCS R15, R3 + SBCS R16, R4 + SBCS R17, R5 + SBCS R19, R6 + + LDP 128(R0), (R7, R8) + LDP 128(R1), (R15, R16) + LDP 144(R0), (R9, R10) + LDP 144(R1), (R17, R19) + SBCS R15, R7 + SBCS R16, R8 + SBCS R17, R9 + SBCS R19, R10 + + LDP 160(R0), (R11, R12) + LDP 160(R1), (R15, R16) + LDP 176(R0), (R13, R14) + LDP 176(R1), (R17, R19) + SBCS R15, R11 + SBCS R16, R12 + SBCS R17, R13 + SBCS R19, R14 + SBC ZR, ZR, R15 + + // If x - y < 0, R15 is 1 and p751 should be added + MOVD ·P751+0(SB), R20 + AND R15, R20 + LDP ·P751+40(SB), (R16, R17) + ADDS R20, R3 + ADCS R20, R4 + STP (R3, R4), 96(R2) + ADCS R20, R5 + ADCS R20, R6 + STP (R5, R6), 112(R2) + ADCS R20, R7 + + LDP ·P751+56(SB), (R19, R20) + AND R15, R16 + AND R15, R17 + ADCS R16, R8 + STP (R7, R8), 128(R2) + ADCS R17, R9 + + LDP ·P751+72(SB), (R16, R17) + AND R15, R19 + AND R15, R20 + ADCS R19, R10 + STP (R9, R10), 144(R2) + ADCS R20, R11 + + MOVD ·P751+88(SB), R19 + AND R15, R16 + AND R15, R17 + ADCS R16, R12 + STP (R11, R12), 160(R2) + ADCS R17, R13 + + AND R15, R19 + ADC R19, R14 + STP (R13, R14), 176(R2) + + RET + +// Expects that X0*Y0 is already in Z0(low),Z3(high) and X0*Y1 in Z1(low),Z2(high) +// Z0 is not actually touched +// Result of (X0-X2) * (Y0-Y2) will be in Z0-Z5 +// Inputs remain intact +#define mul192x192comba(X0, X1, X2, Y0, Y1, Y2, Z0, Z1, Z2, Z3, Z4, Z5, T0, T1, T2, T3) \ + MUL X1, Y0, T2 \ + UMULH X1, Y0, T3 \ + \ + ADDS Z3, Z1 \ + ADCS ZR, Z2 \ + ADC ZR, ZR, Z3 \ + \ + MUL X0, Y2, T0 \ + UMULH X0, Y2, T1 \ + \ + ADDS T2, Z1 \ + ADCS T3, Z2 \ + ADC ZR, Z3 \ + \ + MUL X1, Y1, T2 \ + UMULH X1, Y1, T3 \ + \ + ADDS T0, Z2 \ + ADCS T1, Z3 \ + ADC ZR, ZR, Z4 \ + \ + MUL X2, Y0, T0 \ + UMULH X2, Y0, T1 \ + \ + ADDS T2, Z2 \ + ADCS T3, Z3 \ + ADC ZR, Z4 \ + \ + MUL X1, Y2, T2 \ + UMULH X1, Y2, T3 \ + \ + ADDS T0, Z2 \ + ADCS T1, Z3 \ + ADC ZR, Z4 \ + \ + MUL X2, Y1, T0 \ + UMULH X2, Y1, T1 \ + \ + ADDS T2, Z3 \ + ADCS T3, Z4 \ + ADC ZR, ZR, Z5 \ + \ + MUL X2, Y2, T2 \ + UMULH X2, Y2, T3 \ + \ + ADDS T0, Z3 \ + ADCS T1, Z4 \ + ADC ZR, Z5 \ + \ + ADDS T2, Z4 \ + ADC T3, Z5 + +// Expects that X points to (X4-X6), Y to (Y4-Y6) +// Result of (X0-X5) * (Y0-Y5) will be in (0(Z), 8(Z), 16(Z), T0-T8) +// Inputs get overwritten +#define mul384x384karatsuba(X, Y, Z, X0, X1, X2, X3, X4, X5, Y0, Y1, Y2, Y3, Y4, Y5, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, T10)\ + ADDS X0, X3 \ // xH + xL, destroys xH + ADCS X1, X4 \ + ADCS X2, X5 \ + ADC ZR, ZR, T10 \ + \ + ADDS Y0, Y3 \ // yH + yL, destroys yH + ADCS Y1, Y4 \ + ADCS Y2, Y5 \ + ADC ZR, ZR, T6 \ + \ + SUB T10, ZR, T7 \ + SUB T6, ZR, T8 \ + AND T6, T10 \ // combined carry + \ + AND T7, Y3, T0 \ // masked(yH + yL) + AND T7, Y4, T1 \ + AND T7, Y5, T2 \ + \ + AND T8, X3, T3 \ // masked(xH + xL) + AND T8, X4, T4 \ + AND T8, X5, T5 \ + \ + ADDS T3, T0 \ + ADCS T4, T1 \ + STP (T0, T1), 0+Z \ + \ + MUL X3, Y3, T0 \ + MUL X3, Y4, T1 \ + \ + ADCS T5, T2 \ + MOVD T2, 16+Z \ + \ + UMULH X3, Y4, T2 \ + UMULH X3, Y3, T3 \ + \ + ADC ZR, T10 \ + \ // (xH + xL) * (yH + yL) + mul192x192comba(X3, X4, X5, Y3, Y4, Y5, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9)\ + \ + MUL X0, Y0, X3 \ + LDP 0+Z, (T6, T7) \ + MOVD 16+Z, T8 \ + \ + UMULH X0, Y0, Y3 \ + ADDS T6, T3 \ + ADCS T7, T4 \ + MUL X0, Y1, X4 \ + ADCS T8, T5 \ + ADC ZR, T10 \ + UMULH X0, Y1, X5 \ + \ // xL * yL + mul192x192comba(X0, X1, X2, Y0, Y1, Y2, X3, X4, X5, Y3, Y4, Y5, T6, T7, T8, T9)\ + \ + STP (X3, X4), 0+Z \ + MOVD X5, 16+Z \ + \ + SUBS X3, T0 \ // (xH + xL) * (yH + yL) - xL * yL + SBCS X4, T1 \ + LDP 0+X, (X3, X4) \ + SBCS X5, T2 \ + MOVD 16+X, X5 \ + SBCS Y3, T3 \ + SBCS Y4, T4 \ + SBCS Y5, T5 \ + SBC ZR, T10 \ + \ + ADDS Y3, T0 \ // ((xH + xL) * (yH + yL) - xL * yL) * 2^192 + xL * yL + ADCS Y4, T1 \ + LDP 0+Y, (Y3, Y4) \ + MUL X3, Y3, X0 \ + ADCS Y5, T2 \ + UMULH X3, Y3, Y0 \ + MOVD 16+Y, Y5 \ + MUL X3, Y4, X1 \ + ADCS ZR, T3 \ + UMULH X3, Y4, X2 \ + ADCS ZR, T4 \ + ADCS ZR, T5 \ + ADC ZR, T10 \ + \ // xH * yH, overwrite xLow, yLow + mul192x192comba(X3, X4, X5, Y3, Y4, Y5, X0, X1, X2, Y0, Y1, Y2, T6, T7, T8, T9)\ + \ + SUBS X0, T0 \ // ((xH + xL) * (yH + yL) - xL * yL - xH * yH) + SBCS X1, T1 \ + SBCS X2, T2 \ + SBCS Y0, T3 \ + SBCS Y1, T4 \ + SBCS Y2, T5 \ + SBC ZR, T10 \ + \ + ADDS X0, T3 \ + ADCS X1, T4 \ + ADCS X2, T5 \ + ADCS T10, Y0, T6 \ + ADCS ZR, Y1, T7 \ + ADC ZR, Y2, T8 + + +TEXT ·mulP751(SB), NOSPLIT, $0-24 + MOVD z+0(FP), R2 + MOVD x+8(FP), R0 + MOVD y+16(FP), R1 + + // Load xL in R3-R8, xH in R9-R14 + // (xH + xL) in R3-R8, destroys xH + LDP 0(R0), (R3, R4) + LDP 48(R0), (R9, R10) + ADDS R9, R3 + ADCS R10, R4 + LDP 16(R0), (R5, R6) + LDP 64(R0), (R11, R12) + ADCS R11, R5 + ADCS R12, R6 + LDP 32(R0), (R7, R8) + LDP 80(R0), (R13, R14) + ADCS R13, R7 + ADCS R14, R8 + ADC ZR, ZR, R22 + + // Load yL in R9-R14, yH in R15-21 + // (yH + yL) in R9-R14, destroys yH + LDP 0(R1), (R9, R10) + LDP 48(R1), (R15, R16) + ADDS R15, R9 + ADCS R16, R10 + LDP 16(R1), (R11, R12) + LDP 64(R1), (R17, R19) + ADCS R17, R11 + ADCS R19, R12 + LDP 32(R1), (R13, R14) + LDP 80(R1), (R20, R21) + ADCS R20, R13 + ADCS R21, R14 + ADC ZR, ZR, R23 + + // Compute masks and combined carry + SUB R22, ZR, R24 + SUB R23, ZR, R25 + AND R23, R22 + + // Store xH, yH in z so mul384x384karatsuba can retrieve them from memory + // It doesn't have enough registers + // Meanwhile computed masked(xH + xL) in R15-R21 + STP (R6, R7), 0(R2) + AND R25, R3, R15 + AND R25, R4, R16 + STP (R8, R12), 16(R2) + AND R25, R5, R17 + AND R25, R6, R19 + STP (R13, R14), 32(R2) + AND R25, R7, R20 + AND R25, R8, R21 + + // Masked(xH + xL) + masked(yH + yL) in R15-R21 + // Store intermediate values in z + AND R24, R9, R25 + AND R24, R10, R26 + ADDS R25, R15 + ADCS R26, R16 + STP (R15, R16), 96(R2) + AND R24, R11, R25 + AND R24, R12, R26 + ADCS R25, R17 + ADCS R26, R19 + STP (R17, R19), 112(R2) + AND R24, R13, R25 + AND R24, R14, R26 + ADCS R25, R20 + ADCS R26, R21 + STP (R20, R21), 128(R2) + // Store carry in R29 so it can remain there + ADC ZR, R22, R29 + + // (xH + xL) * (yH + yL) + mul384x384karatsuba(0(R2), 24(R2), 48(R2), R3, R4, R5, R6, R7, R8, R9, R10, R11, R12, R13, R14, R15, R16, R17, R19, R20, R21, R22, R23, R24, R25, R26) + + // Load masked(xH + xL) + masked(yH + yL) and add that to its top half + // Store the result back in z + STP (R15, R16), 72(R2) + LDP 96(R2), (R3, R4) + ADDS R3, R19 + STP (R17, R19), 88(R2) + ADCS R4, R20 + LDP 112(R2), (R5, R6) + ADCS R5, R21 + STP (R20, R21), 104(R2) + ADCS R6, R22 + LDP 128(R2), (R7, R8) + ADCS R7, R23 + STP (R22, R23), 120(R2) + ADCS R8, R24 + MOVD R24, 136(R2) + ADC ZR, R29 + + // Load xL, yL + LDP 0(R0), (R3, R4) + LDP 16(R0), (R5, R6) + LDP 32(R0), (R7, R8) + LDP 0(R1), (R9, R10) + LDP 16(R1), (R11, R12) + LDP 32(R1), (R13, R14) + + // xL * yL + mul384x384karatsuba(24(R0), 24(R1), 0(R2), R3, R4, R5, R6, R7, R8, R9, R10, R11, R12, R13, R14, R15, R16, R17, R19, R20, R21, R22, R23, R24, R25, R26) + + // (xH + xL) * (yH + yL) - xL * yL in R3-R14 + LDP 0(R2), (R12, R13) + LDP 48(R2), (R3, R4) + SUBS R12, R3 + LDP 64(R2), (R5, R6) + MOVD 16(R2), R14 + SBCS R13, R4 + SBCS R14, R5 + LDP 80(R2), (R7, R8) + SBCS R15, R6 + SBCS R16, R7 + LDP 96(R2), (R9, R10) + SBCS R17, R8 + SBCS R19, R9 + LDP 112(R2), (R11, R12) + SBCS R20, R10 + SBCS R21, R11 + LDP 128(R2), (R13, R14) + SBCS R22, R12 + SBCS R23, R13 + SBCS R24, R14 + SBC ZR, R29 + + STP (R15, R16), 24(R2) + MOVD R17, 40(R2) + + // ((xH + xL) * (yH + yL) - xL * yL) * 2^384 + xL * yL and store back in z + ADDS R19, R3 + ADCS R20, R4 + STP (R3, R4), 48(R2) + ADCS R21, R5 + ADCS R22, R6 + STP (R5, R6), 64(R2) + ADCS R23, R7 + ADCS R24, R8 + STP (R7, R8), 80(R2) + ADCS ZR, R9 + ADCS ZR, R10 + STP (R9, R10), 96(R2) + ADCS ZR, R11 + ADCS ZR, R12 + STP (R11, R12), 112(R2) + ADCS ZR, R13 + ADCS ZR, R14 + STP (R13, R14), 128(R2) + ADC ZR, R29 + + // Load xH, yH + LDP 48(R0), (R3, R4) + LDP 64(R0), (R5, R6) + LDP 80(R0), (R7, R8) + LDP 48(R1), (R9, R10) + LDP 64(R1), (R11, R12) + LDP 80(R1), (R13, R14) + + // xH * yH + mul384x384karatsuba(72(R0), 72(R1), 144(R2), R3, R4, R5, R6, R7, R8, R9, R10, R11, R12, R13, R14, R15, R16, R17, R19, R20, R21, R22, R23, R24, R25, R26) + + LDP 144(R2), (R12, R13) + MOVD 160(R2), R14 + + // (xH + xL) * (yH + yL) - xL * yL - xH * yH in R3-R14 + // Store lower half in z, that's done + LDP 48(R2), (R3, R4) + SUBS R12, R3 + LDP 64(R2), (R5, R6) + SBCS R13, R4 + SBCS R14, R5 + LDP 80(R2), (R7, R8) + SBCS R15, R6 + SBCS R16, R7 + LDP 96(R2), (R9, R10) + SBCS R17, R8 + SBCS R19, R9 + LDP 112(R2), (R11, R12) + SBCS R20, R10 + SBCS R21, R11 + LDP 128(R2), (R13, R14) + SBCS R22, R12 + SBCS R23, R13 + STP (R3, R4), 48(R2) + SBCS R24, R14 + STP (R5, R6), 64(R2) + SBC ZR, R29 + STP (R7, R8), 80(R2) + + // (xH * yH) * 2^768 + ((xH + xL) * (yH + yL) - xL * yL - xH * yH) * 2^384 + xL * yL + // Store remaining limbs in z + LDP 144(R2), (R3, R4) + MOVD 160(R2), R5 + + ADDS R3, R9 + ADCS R4, R10 + STP (R9, R10), 96(R2) + ADCS R5, R11 + ADCS R15, R12 + STP (R11, R12), 112(R2) + ADCS R16, R13 + ADCS R17, R14 + STP (R13, R14), 128(R2) + + ADCS R29, R19 + ADCS ZR, R20 + STP (R19, R20), 144(R2) + ADCS ZR, R21 + ADCS ZR, R22 + STP (R21, R22), 160(R2) + ADCS ZR, R23 + ADC ZR, R24 + STP (R23, R24), 176(R2) + + RET + +TEXT ·rdcP751(SB), NOSPLIT, $0-16 + MOVD z+0(FP), R0 + MOVD x+8(FP), R1 + + // Load p751+1 in R14-R17, R29, R19-R20, spread over arithmetic + LDP ·P751p1+40(SB), (R14, R15) + // z0-z11 will be R2-R13 + // Load x0-x4 to z0-z4 and x5, spread over arithmetic + LDP 0(R1), (R2, R3) + + // x5 iteration + MUL R2, R14, R22 + LDP 32(R1), (R6, R21) + UMULH R2, R14, R23 + ADDS R21, R22, R7 // Set z5 + ADC ZR, R23, R25 + + // x6 iteration + MUL R2, R15, R22 + MOVD 48(R1), R21 + UMULH R2, R15, R23 + ADDS R22, R25 + ADC R23, ZR, R26 + + MUL R3, R14, R22 + LDP ·P751p1+56(SB), (R16, R17) + UMULH R3, R14, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, ZR, R24 + + ADDS R21, R25, R8 // Set z6 + ADCS ZR, R26 + ADC ZR, R24 + + // x7 iteration + MUL R2, R16, R22 + MOVD 56(R1), R21 + UMULH R2, R16, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, ZR, R25 + + MUL R3, R15, R22 + LDP 16(R1), (R4, R5) + UMULH R3, R15, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R4, R14, R22 + LDP ·P751p1+72(SB), (R29, R19) + UMULH R4, R14, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + ADDS R21, R26, R9 // Set z7 + ADCS ZR, R24 + ADC ZR, R25 + + // x8 iteration + MUL R2, R17, R22 + MOVD 64(R1), R21 + UMULH R2, R17, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, ZR, R26 + + MUL R3, R16, R22 + MOVD ·P751p1+88(SB), R20 + UMULH R3, R16, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R4, R15, R22 + UMULH R4, R15, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R5, R14, R22 + UMULH R5, R14, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + ADDS R24, R21, R10 // Set z8 + ADCS ZR, R25 + ADC ZR, R26 + + // x9 iteration + MUL R2, R29, R22 + MOVD 72(R1), R21 + UMULH R2, R29, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, ZR, R24 + + MUL R3, R17, R22 + UMULH R3, R17, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R4, R16, R22 + UMULH R4, R16, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R5, R15, R22 + UMULH R5, R15, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R6, R14, R22 + UMULH R6, R14, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + ADDS R21, R25, R11 // Set z9 + ADCS ZR, R26 + ADC ZR, R24 + + // x10 iteration + MUL R2, R19, R22 + MOVD 80(R1), R21 + UMULH R2, R19, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, ZR, R25 + + MUL R3, R29, R22 + UMULH R3, R29, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R4, R17, R22 + UMULH R4, R17, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R5, R16, R22 + UMULH R5, R16, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R6, R15, R22 + UMULH R6, R15, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R7, R14, R22 + UMULH R7, R14, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + ADDS R21, R26, R12 // Set z10 + ADCS ZR, R24 + ADC ZR, R25 + + // x11 iteration + MUL R2, R20, R22 + MOVD 88(R1), R21 + UMULH R2, R20, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, ZR, R26 + + MUL R3, R19, R22 + UMULH R3, R19, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R4, R29, R22 + UMULH R4, R29, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R5, R17, R22 + UMULH R5, R17, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R6, R16, R22 + UMULH R6, R16, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R7, R15, R22 + UMULH R7, R15, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R8, R14, R22 + UMULH R8, R14, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + ADDS R21, R24, R13 // Set z11 + ADCS ZR, R25 + ADC ZR, R26 + + // x12 iteration + MUL R3, R20, R22 + MOVD 96(R1), R21 + UMULH R3, R20, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, ZR, R24 + + MUL R4, R19, R22 + UMULH R4, R19, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R5, R29, R22 + UMULH R5, R29, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R6, R17, R22 + UMULH R6, R17, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R7, R16, R22 + UMULH R7, R16, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R8, R15, R22 + UMULH R8, R15, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R9, R14, R22 + UMULH R9, R14, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + ADDS R21, R25, R2 // Set z0 + ADCS ZR, R26 + ADC ZR, R24 + + // x13 iteration + MUL R4, R20, R22 + MOVD 104(R1), R21 + UMULH R4, R20, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, ZR, R25 + + MUL R5, R19, R22 + UMULH R5, R19, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R6, R29, R22 + UMULH R6, R29, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R7, R17, R22 + UMULH R7, R17, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R8, R16, R22 + UMULH R8, R16, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R9, R15, R22 + UMULH R9, R15, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R10, R14, R22 + UMULH R10, R14, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + ADDS R21, R26, R3 // Set z1 + STP (R2, R3), 0(R0) + ADCS ZR, R24 + ADC ZR, R25 + + // x14 iteration + MUL R5, R20, R22 + MOVD 112(R1), R21 + UMULH R5, R20, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, ZR, R26 + + MUL R6, R19, R22 + UMULH R6, R19, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R7, R29, R22 + UMULH R7, R29, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R8, R17, R22 + UMULH R8, R17, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R9, R16, R22 + UMULH R9, R16, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R10, R15, R22 + UMULH R10, R15, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R11, R14, R22 + UMULH R11, R14, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + ADDS R21, R24, R4 // Set z2 + ADCS ZR, R25 + ADC ZR, R26 + + // x15 iteration + MUL R6, R20, R22 + MOVD 120(R1), R21 + UMULH R6, R20, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, ZR, R24 + + MUL R7, R19, R22 + UMULH R7, R19, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R8, R29, R22 + UMULH R8, R29, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R9, R17, R22 + UMULH R9, R17, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R10, R16, R22 + UMULH R10, R16, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R11, R15, R22 + UMULH R11, R15, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R12, R14, R22 + UMULH R12, R14, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + ADDS R21, R25, R5 // Set z3 + STP (R4, R5), 16(R0) + ADCS ZR, R26 + ADC ZR, R24 + + // x16 iteration + MUL R7, R20, R22 + MOVD 128(R1), R21 + UMULH R7, R20, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, ZR, R25 + + MUL R8, R19, R22 + UMULH R8, R19, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R9, R29, R22 + UMULH R9, R29, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R10, R17, R22 + UMULH R10, R17, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R11, R16, R22 + UMULH R11, R16, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R12, R15, R22 + UMULH R12, R15, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R13, R14, R22 + UMULH R13, R14, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + ADDS R21, R26, R6 // Set z4 + ADCS ZR, R24 + ADC ZR, R25 + + // x17 iteration + MUL R8, R20, R22 + MOVD 136(R1), R21 + UMULH R8, R20, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, ZR, R26 + + MUL R9, R19, R22 + UMULH R9, R19, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R10, R29, R22 + UMULH R10, R29, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R11, R17, R22 + UMULH R11, R17, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R12, R16, R22 + UMULH R12, R16, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R13, R15, R22 + UMULH R13, R15, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + ADDS R21, R24, R7 // Set z5 + STP (R6, R7), 32(R0) + ADCS ZR, R25 + ADC ZR, R26 + + // x18 iteration + MUL R9, R20, R22 + MOVD 144(R1), R21 + UMULH R9, R20, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, ZR, R24 + + MUL R10, R19, R22 + UMULH R10, R19, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R11, R29, R22 + UMULH R11, R29, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R12, R17, R22 + UMULH R12, R17, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + MUL R13, R16, R22 + UMULH R13, R16, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + ADDS R21, R25, R8 // Set z6 + ADCS ZR, R26 + ADC ZR, R24 + + // x19 iteration + MUL R10, R20, R22 + MOVD 152(R1), R21 + UMULH R10, R20, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, ZR, R25 + + MUL R11, R19, R22 + UMULH R11, R19, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R12, R29, R22 + UMULH R12, R29, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + MUL R13, R17, R22 + UMULH R13, R17, R23 + ADDS R22, R26 + ADCS R23, R24 + ADC ZR, R25 + + ADDS R21, R26, R9 // Set z7 + STP (R8, R9), 48(R0) + ADCS ZR, R24 + ADC ZR, R25 + + // x20 iteration + MUL R11, R20, R22 + MOVD 160(R1), R21 + UMULH R11, R20, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, ZR, R26 + + MUL R12, R19, R22 + UMULH R12, R19, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + MUL R13, R29, R22 + UMULH R13, R29, R23 + ADDS R22, R24 + ADCS R23, R25 + ADC ZR, R26 + + ADDS R21, R24, R10 // Set z8 + ADCS ZR, R25 + ADC ZR, R26 + + // x21 iteration + MUL R12, R20, R22 + MOVD 168(R1), R21 + UMULH R12, R20, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, ZR, R24 + + MUL R13, R19, R22 + UMULH R13, R19, R23 + ADDS R22, R25 + ADCS R23, R26 + ADC ZR, R24 + + ADDS R21, R25, R11 // Set z9 + STP (R10, R11), 64(R0) + ADCS ZR, R26 + ADC ZR, R24 + + // x22 iteration + MUL R13, R20, R22 + MOVD 176(R1), R21 + UMULH R13, R20, R23 + ADDS R22, R26 + ADC R23, R24 + ADDS R21, R26, R12 // Set z10 + + MOVD 184(R1), R21 + ADC R21, R24, R13 // Set z11 + STP (R12, R13), 80(R0) + + RET + +TEXT ·modP751(SB), NOSPLIT, $0-8 + MOVD x+0(FP), R0 + + // Keep x in R1-R12, p751 in R13-R21, subtract to R1-R12 + MOVD ·P751+0(SB), R13 + LDP 0(R0), (R1, R2) + LDP 16(R0), (R3, R4) + SUBS R13, R1 + SBCS R13, R2 + + LDP 32(R0), (R5, R6) + LDP ·P751+40(SB), (R14, R15) + SBCS R13, R3 + SBCS R13, R4 + + LDP 48(R0), (R7, R8) + LDP ·P751+56(SB), (R16, R17) + SBCS R13, R5 + SBCS R14, R6 + + LDP 64(R0), (R9, R10) + LDP ·P751+72(SB), (R19, R20) + SBCS R15, R7 + SBCS R16, R8 + + LDP 80(R0), (R11, R12) + MOVD ·P751+88(SB), R21 + SBCS R17, R9 + SBCS R19, R10 + + SBCS R20, R11 + SBCS R21, R12 + SBC ZR, ZR, R22 + + // Mask with the borrow and add p751 + AND R22, R13 + AND R22, R14 + AND R22, R15 + AND R22, R16 + AND R22, R17 + AND R22, R19 + AND R22, R20 + AND R22, R21 + + ADDS R13, R1 + ADCS R13, R2 + STP (R1, R2), 0(R0) + ADCS R13, R3 + ADCS R13, R4 + STP (R3, R4), 16(R0) + ADCS R13, R5 + ADCS R14, R6 + STP (R5, R6), 32(R0) + ADCS R15, R7 + ADCS R16, R8 + STP (R7, R8), 48(R0) + ADCS R17, R9 + ADCS R19, R10 + STP (R9, R10), 64(R0) + ADCS R20, R11 + ADC R21, R12 + STP (R11, R12), 80(R0) + + RET diff --git a/src/circl/dh/sidh/internal/p751/arith_decl.go b/src/circl/dh/sidh/internal/p751/arith_decl.go new file mode 100644 index 00000000000..1cc19624bf5 --- /dev/null +++ b/src/circl/dh/sidh/internal/p751/arith_decl.go @@ -0,0 +1,45 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +// +build amd64,!noasm arm64,!noasm + +package p751 + +import ( + . "circl/dh/sidh/internal/common" +) + +// If choice = 0, leave x,y unchanged. If choice = 1, set x,y = y,x. +// If choice is neither 0 nor 1 then behaviour is undefined. +// This function executes in constant time. +//go:noescape +func cswapP751(x, y *Fp, choice uint8) + +// Compute z = x + y (mod p). +//go:noescape +func addP751(z, x, y *Fp) + +// Compute z = x - y (mod p). +//go:noescape +func subP751(z, x, y *Fp) + +// Compute z = x + y, without reducing mod p. +//go:noescape +func adlP751(z, x, y *FpX2) + +// Compute z = x - y, without reducing mod p. +//go:noescape +func sulP751(z, x, y *FpX2) + +// Reduce a field element in [0, 2*p) to one in [0,p). +//go:noescape +func modP751(x *Fp) + +// Computes z = x * y. +//go:noescape +func mulP751(z *FpX2, x, y *Fp) + +// Computes the Montgomery reduction z = x R^{-1} (mod 2*p). On return value +// of x may be changed. z=x not allowed. +//go:noescape +func rdcP751(z *Fp, x *FpX2) diff --git a/src/circl/dh/sidh/internal/p751/arith_generic.go b/src/circl/dh/sidh/internal/p751/arith_generic.go new file mode 100644 index 00000000000..d4a31841b75 --- /dev/null +++ b/src/circl/dh/sidh/internal/p751/arith_generic.go @@ -0,0 +1,192 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +// +build noasm !amd64,!arm64 + +package p751 + +import ( + "math/bits" + + "circl/dh/sidh/internal/common" +) + +// Compute z = x + y (mod p). +func addP751(z, x, y *common.Fp) { + var carry uint64 + + // z=x+y % P751 + for i := 0; i < FpWords; i++ { + z[i], carry = bits.Add64(x[i], y[i], carry) + } + + // z = z - P751x2 + carry = 0 + for i := 0; i < FpWords; i++ { + z[i], carry = bits.Sub64(z[i], P751x2[i], carry) + } + + // if z<0 add P751x2 back + mask := uint64(0 - carry) + carry = 0 + for i := 0; i < FpWords; i++ { + z[i], carry = bits.Add64(z[i], P751x2[i]&mask, carry) + } +} + +// Compute z = x - y (mod p). +func subP751(z, x, y *common.Fp) { + var borrow uint64 + + for i := 0; i < FpWords; i++ { + z[i], borrow = bits.Sub64(x[i], y[i], borrow) + } + + mask := uint64(0 - borrow) + borrow = 0 + + for i := 0; i < FpWords; i++ { + z[i], borrow = bits.Add64(z[i], P751x2[i]&mask, borrow) + } +} + +// Conditionally swaps bits in x and y in constant time. +// mask indicates bits to be swapped (set bits are swapped) +// For details see "Hackers Delight, 2.20" +// +// Implementation doesn't actually depend on a prime field. +func cswapP751(x, y *common.Fp, mask uint8) { + var tmp, mask64 uint64 + + mask64 = 0 - uint64(mask) + for i := 0; i < FpWords; i++ { + tmp = mask64 & (x[i] ^ y[i]) + x[i] = tmp ^ x[i] + y[i] = tmp ^ y[i] + } +} + +// Perform Montgomery reduction: set z = x R^{-1} (mod 2*p) +// with R=2^(FpWords*64). Destroys the input value. +func rdcP751(z *common.Fp, x *common.FpX2) { + var carry, t, u, v uint64 + var hi, lo uint64 + var count int + + count = P751p1Zeros + + for i := 0; i < FpWords; i++ { + for j := 0; j < i; j++ { + if j < (i - count + 1) { + hi, lo = bits.Mul64(z[j], P751p1[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + } + v, carry = bits.Add64(v, x[i], 0) + u, carry = bits.Add64(u, 0, carry) + t += carry + + z[i] = v + v = u + u = t + t = 0 + } + + for i := FpWords; i < 2*FpWords-1; i++ { + if count > 0 { + count-- + } + for j := i - FpWords + 1; j < FpWords; j++ { + if j < (FpWords - count) { + hi, lo = bits.Mul64(z[j], P751p1[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + } + v, carry = bits.Add64(v, x[i], 0) + u, carry = bits.Add64(u, 0, carry) + + t += carry + z[i-FpWords] = v + v = u + u = t + t = 0 + } + v, _ = bits.Add64(v, x[2*FpWords-1], 0) + z[FpWords-1] = v +} + +// Compute z = x * y. +func mulP751(z *common.FpX2, x, y *common.Fp) { + var u, v, t uint64 + var hi, lo uint64 + var carry uint64 + + for i := uint64(0); i < FpWords; i++ { + for j := uint64(0); j <= i; j++ { + hi, lo = bits.Mul64(x[j], y[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + z[i] = v + v = u + u = t + t = 0 + } + + for i := FpWords; i < (2*FpWords)-1; i++ { + for j := i - FpWords + 1; j < FpWords; j++ { + hi, lo = bits.Mul64(x[j], y[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + z[i] = v + v = u + u = t + t = 0 + } + z[2*FpWords-1] = v +} + +// Compute z = x + y, without reducing mod p. +func adlP751(z, x, y *common.FpX2) { + var carry uint64 + for i := 0; i < 2*FpWords; i++ { + z[i], carry = bits.Add64(x[i], y[i], carry) + } +} + +// Reduce a field element in [0, 2*p) to one in [0,p). +func modP751(x *common.Fp) { + var borrow, mask uint64 + for i := 0; i < FpWords; i++ { + x[i], borrow = bits.Sub64(x[i], P751[i], borrow) + } + + // Sets all bits if borrow = 1 + mask = 0 - borrow + borrow = 0 + for i := 0; i < FpWords; i++ { + x[i], borrow = bits.Add64(x[i], P751[i]&mask, borrow) + } +} + +// Compute z = x - y, without reducing mod p. +func sulP751(z, x, y *common.FpX2) { + var borrow, mask uint64 + for i := 0; i < 2*FpWords; i++ { + z[i], borrow = bits.Sub64(x[i], y[i], borrow) + } + + // Sets all bits if borrow = 1 + mask = 0 - borrow + borrow = 0 + for i := FpWords; i < 2*FpWords; i++ { + z[i], borrow = bits.Add64(z[i], P751[i-FpWords]&mask, borrow) + } +} diff --git a/src/circl/dh/sidh/internal/p751/arith_test.go b/src/circl/dh/sidh/internal/p751/arith_test.go new file mode 100644 index 00000000000..49b11654eb3 --- /dev/null +++ b/src/circl/dh/sidh/internal/p751/arith_test.go @@ -0,0 +1,101 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p751 + +import ( + "testing" + + "circl/dh/sidh/internal/common" +) + +// Package-level storage for this field element is intended to deter +// compiler optimizations. +var ( + benchmarkFp common.Fp + benchmarkFpX2 common.FpX2 + bench_x = common.Fp{17026702066521327207, 5108203422050077993, 10225396685796065916, 11153620995215874678, 6531160855165088358, 15302925148404145445, 1248821577836769963, 9789766903037985294, 7493111552032041328, 10838999828319306046, 18103257655515297935, 27403304611634} + bench_y = common.Fp{4227467157325093378, 10699492810770426363, 13500940151395637365, 12966403950118934952, 16517692605450415877, 13647111148905630666, 14223628886152717087, 7167843152346903316, 15855377759596736571, 4300673881383687338, 6635288001920617779, 30486099554235} + bench_z = common.FpX2{1595347748594595712, 10854920567160033970, 16877102267020034574, 12435724995376660096, 3757940912203224231, 8251999420280413600, 3648859773438820227, 17622716832674727914, 11029567000887241528, 11216190007549447055, 17606662790980286987, 4720707159513626555, 12887743598335030915, 14954645239176589309, 14178817688915225254, 1191346797768989683, 12629157932334713723, 6348851952904485603, 16444232588597434895, 7809979927681678066, 14642637672942531613, 3092657597757640067, 10160361564485285723, 240071237} +) + +func TestFpCswap(t *testing.T) { + var one = common.Fp{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} + var two = common.Fp{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2} + + var x = one + var y = two + + cswapP751(&x, &y, 0) + for i := 0; i < FpWords; i++ { + if (x[i] != one[i]) || (y[i] != two[i]) { + t.Error("Found", x, "expected", two) + } + } + + cswapP751(&x, &y, 1) + for i := 0; i < FpWords; i++ { + if (x[i] != two[i]) || (y[i] != one[i]) { + t.Error("Found", x, "expected", two) + } + } +} + +// Benchmarking for field arithmetic +func BenchmarkMul(b *testing.B) { + for n := 0; n < b.N; n++ { + mulP751(&benchmarkFpX2, &bench_x, &bench_y) + } +} + +func BenchmarkRdc(b *testing.B) { + z := bench_z + + // This benchmark actually computes garbage, because + // rdcP751 mangles its input, but since it's + // constant-time that shouldn't matter for the benchmarks. + for n := 0; n < b.N; n++ { + rdcP751(&benchmarkFp, &z) + } +} + +func BenchmarkAdd(b *testing.B) { + for n := 0; n < b.N; n++ { + addP751(&benchmarkFp, &bench_x, &bench_y) + } +} + +func BenchmarkSub(b *testing.B) { + for n := 0; n < b.N; n++ { + subP751(&benchmarkFp, &bench_x, &bench_y) + } +} + +func BenchmarkCswap(b *testing.B) { + x, y := bench_x, bench_y + for n := 0; n < b.N; n++ { + cswapP751(&x, &y, 1) + cswapP751(&x, &y, 0) + } +} + +func BenchmarkMod(b *testing.B) { + x := bench_x + for n := 0; n < b.N; n++ { + modP751(&x) + } +} + +func BenchmarkX2AddLazy(b *testing.B) { + x, y, z := bench_z, bench_z, bench_z + for n := 0; n < b.N; n++ { + adlP751(&x, &y, &z) + } +} + +func BenchmarkX2SubLazy(b *testing.B) { + x, y, z := bench_z, bench_z, bench_z + for n := 0; n < b.N; n++ { + sulP751(&x, &y, &z) + } +} diff --git a/src/circl/dh/sidh/internal/p751/core.go b/src/circl/dh/sidh/internal/p751/core.go new file mode 100644 index 00000000000..03c15d4725f --- /dev/null +++ b/src/circl/dh/sidh/internal/p751/core.go @@ -0,0 +1,282 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p751 + +import ( + . "circl/dh/sidh/internal/common" +) + +// ----------------------------------------------------------------------------- +// Functions for traversing isogeny trees acoording to strategy. Key type 'A' is +// + +// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed +// for public key generation. +func traverseTreePublicKeyA(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny4 + + cparam := CalcCurveParamsEquiv4(curve) + strat := params.A.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow2k(xR, &cparam, 2*k) + i += int(k) + } + cparam = phi.GenerateCurve(xR) + + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + *phiP = phi.EvaluatePoint(phiP) + *phiQ = phi.EvaluatePoint(phiQ) + *phiR = phi.EvaluatePoint(phiR) + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Traverses isogeny tree in order to compute xR needed +// for public key generation. +func traverseTreeSharedKeyA(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny4 + + cparam := CalcCurveParamsEquiv4(curve) + strat := params.A.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow2k(xR, &cparam, 2*k) + i += int(k) + } + cparam = phi.GenerateCurve(xR) + + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed +// for public key generation. +func traverseTreePublicKeyB(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny3 + + cparam := CalcCurveParamsEquiv3(curve) + strat := params.B.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow3k(xR, &cparam, k) + i += int(k) + } + + cparam = phi.GenerateCurve(xR) + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + + *phiP = phi.EvaluatePoint(phiP) + *phiQ = phi.EvaluatePoint(phiQ) + *phiR = phi.EvaluatePoint(phiR) + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed +// for public key generation. +func traverseTreeSharedKeyB(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny3 + + cparam := CalcCurveParamsEquiv3(curve) + strat := params.B.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow3k(xR, &cparam, k) + i += int(k) + } + + cparam = phi.GenerateCurve(xR) + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Generate a public key in the 2-torsion group. Public key is a set +// of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) +func PublicKeyGenA(pub3Pt *[3]Fp2, prvBytes []byte) { + var xPA, xQA, xRA ProjectivePoint + var xPB, xQB, xRB, xR ProjectivePoint + var invZP, invZQ, invZR Fp2 + var phi isogeny4 + + // Load points for A + xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} + xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} + xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} + + // Load points for B + xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} + xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} + xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} + + // Find isogeny kernel + xR = ScalarMul3Pt(¶ms.InitCurve, &xPA, &xQA, &xRA, params.A.SecretBitLen, prvBytes) + traverseTreePublicKeyA(¶ms.InitCurve, &xR, &xPB, &xQB, &xRB) + + // Secret isogeny + phi.GenerateCurve(&xR) + xPA = phi.EvaluatePoint(&xPB) + xQA = phi.EvaluatePoint(&xQB) + xRA = phi.EvaluatePoint(&xRB) + Fp2Batch3Inv(&xPA.Z, &xQA.Z, &xRA.Z, &invZP, &invZQ, &invZR) + + mul(&pub3Pt[0], &xPA.X, &invZP) + mul(&pub3Pt[1], &xQA.X, &invZQ) + mul(&pub3Pt[2], &xRA.X, &invZR) +} + +// Generate a public key in the 2-torsion group. Public key is a set +// of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) +func PublicKeyGenB(pub3Pt *[3]Fp2, prvBytes []byte) { + var xPB, xQB, xRB, xR ProjectivePoint + var xPA, xQA, xRA ProjectivePoint + var invZP, invZQ, invZR Fp2 + var phi isogeny3 + + // Load points for B + xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} + xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} + xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} + + // Load points for A + xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} + xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} + xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} + + // Find isogeny kernel + xR = ScalarMul3Pt(¶ms.InitCurve, &xPB, &xQB, &xRB, params.B.SecretBitLen, prvBytes) + traverseTreePublicKeyB(¶ms.InitCurve, &xR, &xPA, &xQA, &xRA) + + phi.GenerateCurve(&xR) + xPB = phi.EvaluatePoint(&xPA) + xQB = phi.EvaluatePoint(&xQA) + xRB = phi.EvaluatePoint(&xRA) + Fp2Batch3Inv(&xPB.Z, &xQB.Z, &xRB.Z, &invZP, &invZQ, &invZR) + + mul(&pub3Pt[0], &xPB.X, &invZP) + mul(&pub3Pt[1], &xQB.X, &invZQ) + mul(&pub3Pt[2], &xRB.X, &invZR) +} + +// ----------------------------------------------------------------------------- +// Key agreement functions +// + +// Establishing shared keys in in 2-torsion group +func DeriveSecretA(ss, prv []byte, pub3Pt *[3]Fp2) { + var xP, xQ, xQmP ProjectivePoint + var xR ProjectivePoint + var phi isogeny4 + var jInv Fp2 + + // Recover curve coefficients + cparam := params.InitCurve + RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) + + // Find kernel of the morphism + xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} + xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} + xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} + xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.A.SecretBitLen, prv) + + // Traverse isogeny tree + traverseTreeSharedKeyA(&cparam, &xR) + + // Calculate j-invariant on isogeneus curve + c := phi.GenerateCurve(&xR) + RecoverCurveCoefficients4(&cparam, &c) + Jinvariant(&cparam, &jInv) + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(ss, &jInv, params.Bytelen) +} + +// Establishing shared keys in in 3-torsion group +func DeriveSecretB(ss, prv []byte, pub3Pt *[3]Fp2) { + var xP, xQ, xQmP ProjectivePoint + var xR ProjectivePoint + var phi isogeny3 + var jInv Fp2 + + // Recover curve coefficients + cparam := params.InitCurve + RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) + + // Find kernel of the morphism + xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} + xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} + xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} + xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.B.SecretBitLen, prv) + + // Traverse isogeny tree + traverseTreeSharedKeyB(&cparam, &xR) + + // Calculate j-invariant on isogeneus curve + c := phi.GenerateCurve(&xR) + RecoverCurveCoefficients3(&cparam, &c) + Jinvariant(&cparam, &jInv) + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(ss, &jInv, params.Bytelen) +} diff --git a/src/circl/dh/sidh/internal/p751/curve.go b/src/circl/dh/sidh/internal/p751/curve.go new file mode 100644 index 00000000000..d773427e3ed --- /dev/null +++ b/src/circl/dh/sidh/internal/p751/curve.go @@ -0,0 +1,362 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p751 + +import ( + . "circl/dh/sidh/internal/common" +) + +// Stores isogeny 3 curve constants +type isogeny3 struct { + K1 Fp2 + K2 Fp2 +} + +// Stores isogeny 4 curve constants +type isogeny4 struct { + isogeny3 + K3 Fp2 +} + +// Computes j-invariant for a curve y2=x3+A/Cx+x with A,C in F_(p^2). Result +// is returned in jBytes buffer, encoded in little-endian format. Caller +// provided jBytes buffer has to be big enough to j-invariant value. In case +// of SIDH, buffer size must be at least size of shared secret. +// Implementation corresponds to Algorithm 9 from SIKE. +func Jinvariant(cparams *ProjectiveCurveParameters, j *Fp2) { + var t0, t1 Fp2 + + sqr(j, &cparams.A) // j = A^2 + sqr(&t1, &cparams.C) // t1 = C^2 + add(&t0, &t1, &t1) // t0 = t1 + t1 + sub(&t0, j, &t0) // t0 = j - t0 + sub(&t0, &t0, &t1) // t0 = t0 - t1 + sub(j, &t0, &t1) // t0 = t0 - t1 + sqr(&t1, &t1) // t1 = t1^2 + mul(j, j, &t1) // j = j * t1 + add(&t0, &t0, &t0) // t0 = t0 + t0 + add(&t0, &t0, &t0) // t0 = t0 + t0 + sqr(&t1, &t0) // t1 = t0^2 + mul(&t0, &t0, &t1) // t0 = t0 * t1 + add(&t0, &t0, &t0) // t0 = t0 + t0 + add(&t0, &t0, &t0) // t0 = t0 + t0 + inv(j, j) // j = 1/j + mul(j, &t0, j) // j = t0 * j +} + +// Given affine points x(P), x(Q) and x(Q-P) in a extension field F_{p^2}, function +// recorvers projective coordinate A of a curve. This is Algorithm 10 from SIKE. +func RecoverCoordinateA(curve *ProjectiveCurveParameters, xp, xq, xr *Fp2) { + var t0, t1 Fp2 + + add(&t1, xp, xq) // t1 = Xp + Xq + mul(&t0, xp, xq) // t0 = Xp * Xq + mul(&curve.A, xr, &t1) // A = X(q-p) * t1 + add(&curve.A, &curve.A, &t0) // A = A + t0 + mul(&t0, &t0, xr) // t0 = t0 * X(q-p) + sub(&curve.A, &curve.A, ¶ms.OneFp2) // A = A - 1 + add(&t0, &t0, &t0) // t0 = t0 + t0 + add(&t1, &t1, xr) // t1 = t1 + X(q-p) + add(&t0, &t0, &t0) // t0 = t0 + t0 + sqr(&curve.A, &curve.A) // A = A^2 + inv(&t0, &t0) // t0 = 1/t0 + mul(&curve.A, &curve.A, &t0) // A = A * t0 + sub(&curve.A, &curve.A, &t1) // A = A - t1 +} + +// Computes equivalence (A:C) ~ (A+2C : A-2C) +func CalcCurveParamsEquiv3(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { + var coef CurveCoefficientsEquiv + var c2 Fp2 + + add(&c2, &cparams.C, &cparams.C) + // A24p = A+2*C + add(&coef.A, &cparams.A, &c2) + // A24m = A-2*C + sub(&coef.C, &cparams.A, &c2) + return coef +} + +// Computes equivalence (A:C) ~ (A+2C : 4C) +func CalcCurveParamsEquiv4(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { + var coefEq CurveCoefficientsEquiv + + add(&coefEq.C, &cparams.C, &cparams.C) + // A24p = A+2C + add(&coefEq.A, &cparams.A, &coefEq.C) + // C24 = 4*C + add(&coefEq.C, &coefEq.C, &coefEq.C) + return coefEq +} + +// Helper function for RightToLeftLadder(). Returns A+2C / 4. +func CalcAplus2Over4(cparams *ProjectiveCurveParameters) (ret Fp2) { + var tmp Fp2 + + // 2C + add(&tmp, &cparams.C, &cparams.C) + // A+2C + add(&ret, &cparams.A, &tmp) + // 1/4C + add(&tmp, &tmp, &tmp) + inv(&tmp, &tmp) + // A+2C/4C + mul(&ret, &ret, &tmp) + return +} + +// Recovers (A:C) curve parameters from projectively equivalent (A+2C:A-2C). +func RecoverCurveCoefficients3(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { + add(&cparams.A, &coefEq.A, &coefEq.C) + // cparams.A = 2*(A+2C+A-2C) = 4A + add(&cparams.A, &cparams.A, &cparams.A) + // cparams.C = (A+2C-A+2C) = 4C + sub(&cparams.C, &coefEq.A, &coefEq.C) + return +} + +// Recovers (A:C) curve parameters from projectively equivalent (A+2C:4C). +func RecoverCurveCoefficients4(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { + // cparams.C = (4C)*1/2=2C + mul(&cparams.C, &coefEq.C, ¶ms.HalfFp2) + // cparams.A = A+2C - 2C = A + sub(&cparams.A, &coefEq.A, &cparams.C) + // cparams.C = 2C * 1/2 = C + mul(&cparams.C, &cparams.C, ¶ms.HalfFp2) +} + +// Combined coordinate doubling and differential addition. Takes projective points +// P,Q,Q-P and (A+2C)/4C curve E coefficient. Returns 2*P and P+Q calculated on E. +// Function is used only by RightToLeftLadder. Corresponds to Algorithm 5 of SIKE +func xDbladd(P, Q, QmP *ProjectivePoint, a24 *Fp2) (dblP, PaQ ProjectivePoint) { + var t0, t1, t2 Fp2 + + xQmP, zQmP := &QmP.X, &QmP.Z + xPaQ, zPaQ := &PaQ.X, &PaQ.Z + x2P, z2P := &dblP.X, &dblP.Z + xP, zP := &P.X, &P.Z + xQ, zQ := &Q.X, &Q.Z + + add(&t0, xP, zP) // t0 = Xp+Zp + sub(&t1, xP, zP) // t1 = Xp-Zp + sqr(x2P, &t0) // 2P.X = t0^2 + sub(&t2, xQ, zQ) // t2 = Xq-Zq + add(xPaQ, xQ, zQ) // Xp+q = Xq+Zq + mul(&t0, &t0, &t2) // t0 = t0 * t2 + mul(z2P, &t1, &t1) // 2P.Z = t1 * t1 + mul(&t1, &t1, xPaQ) // t1 = t1 * Xp+q + sub(&t2, x2P, z2P) // t2 = 2P.X - 2P.Z + mul(x2P, x2P, z2P) // 2P.X = 2P.X * 2P.Z + mul(xPaQ, a24, &t2) // Xp+q = A24 * t2 + sub(zPaQ, &t0, &t1) // Zp+q = t0 - t1 + add(z2P, xPaQ, z2P) // 2P.Z = Xp+q + 2P.Z + add(xPaQ, &t0, &t1) // Xp+q = t0 + t1 + mul(z2P, z2P, &t2) // 2P.Z = 2P.Z * t2 + sqr(zPaQ, zPaQ) // Zp+q = Zp+q ^ 2 + sqr(xPaQ, xPaQ) // Xp+q = Xp+q ^ 2 + mul(zPaQ, xQmP, zPaQ) // Zp+q = Xq-p * Zp+q + mul(xPaQ, zQmP, xPaQ) // Xp+q = Zq-p * Xp+q + return +} + +// Given the curve parameters, xP = x(P), computes xP = x([2^k]P) +// Safe to overlap xP, x2P. +func Pow2k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { + var t0, t1 Fp2 + + x, z := &xP.X, &xP.Z + for i := uint32(0); i < k; i++ { + sub(&t0, x, z) // t0 = Xp - Zp + add(&t1, x, z) // t1 = Xp + Zp + sqr(&t0, &t0) // t0 = t0 ^ 2 + sqr(&t1, &t1) // t1 = t1 ^ 2 + mul(z, ¶ms.C, &t0) // Z2p = C24 * t0 + mul(x, z, &t1) // X2p = Z2p * t1 + sub(&t1, &t1, &t0) // t1 = t1 - t0 + mul(&t0, ¶ms.A, &t1) // t0 = A24+ * t1 + add(z, z, &t0) // Z2p = Z2p + t0 + mul(z, z, &t1) // Zp = Z2p * t1 + } +} + +// Given the curve parameters, xP = x(P), and k >= 0, compute xP = x([3^k]P). +// +// Safe to overlap xP, xR. +func Pow3k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { + var t0, t1, t2, t3, t4, t5, t6 Fp2 + + x, z := &xP.X, &xP.Z + for i := uint32(0); i < k; i++ { + sub(&t0, x, z) // t0 = Xp - Zp + sqr(&t2, &t0) // t2 = t0^2 + add(&t1, x, z) // t1 = Xp + Zp + sqr(&t3, &t1) // t3 = t1^2 + add(&t4, &t1, &t0) // t4 = t1 + t0 + sub(&t0, &t1, &t0) // t0 = t1 - t0 + sqr(&t1, &t4) // t1 = t4^2 + sub(&t1, &t1, &t3) // t1 = t1 - t3 + sub(&t1, &t1, &t2) // t1 = t1 - t2 + mul(&t5, &t3, ¶ms.A) // t5 = t3 * A24+ + mul(&t3, &t3, &t5) // t3 = t5 * t3 + mul(&t6, &t2, ¶ms.C) // t6 = t2 * A24- + mul(&t2, &t2, &t6) // t2 = t2 * t6 + sub(&t3, &t2, &t3) // t3 = t2 - t3 + sub(&t2, &t5, &t6) // t2 = t5 - t6 + mul(&t1, &t2, &t1) // t1 = t2 * t1 + add(&t2, &t3, &t1) // t2 = t3 + t1 + sqr(&t2, &t2) // t2 = t2^2 + mul(x, &t2, &t4) // X3p = t2 * t4 + sub(&t1, &t3, &t1) // t1 = t3 - t1 + sqr(&t1, &t1) // t1 = t1^2 + mul(z, &t1, &t0) // Z3p = t1 * t0 + } +} + +// Set (y1, y2, y3) = (1/x1, 1/x2, 1/x3). +// +// All xi, yi must be distinct. +func Fp2Batch3Inv(x1, x2, x3, y1, y2, y3 *Fp2) { + var x1x2, t Fp2 + + mul(&x1x2, x1, x2) // x1*x2 + mul(&t, &x1x2, x3) // 1/(x1*x2*x3) + inv(&t, &t) + mul(y1, &t, x2) // 1/x1 + mul(y1, y1, x3) + mul(y2, &t, x1) // 1/x2 + mul(y2, y2, x3) + mul(y3, &t, &x1x2) // 1/x3 +} + +// Scalarmul3Pt is a right-to-left point multiplication that given the +// x-coordinate of P, Q and P-Q calculates the x-coordinate of R=Q+[scalar]P. +// nbits must be smaller or equal to len(scalar). +func ScalarMul3Pt(cparams *ProjectiveCurveParameters, P, Q, PmQ *ProjectivePoint, nbits uint, scalar []uint8) ProjectivePoint { + var R0, R2, R1 ProjectivePoint + aPlus2Over4 := CalcAplus2Over4(cparams) + R1 = *P + R2 = *PmQ + R0 = *Q + + // Iterate over the bits of the scalar, bottom to top + prevBit := uint8(0) + for i := uint(0); i < nbits; i++ { + bit := (scalar[i>>3] >> (i & 7) & 1) + swap := prevBit ^ bit + prevBit = bit + cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, swap) + R0, R2 = xDbladd(&R0, &R2, &R1, &aPlus2Over4) + } + cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, prevBit) + return R1 +} + +// Given a three-torsion point p = x(PB) on the curve E_(A:C), construct the +// three-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). +// +// Input: (XP_3: ZP_3), where P_3 has exact order 3 on E_A/C +// Output: * Curve coordinates (A' + 2C', A' - 2C') corresponding to E_A'/C' = A_E/C/ +// * Isogeny phi with constants in F_p^2 +func (phi *isogeny3) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { + var t0, t1, t2, t3, t4 Fp2 + var coefEq CurveCoefficientsEquiv + var K1, K2 = &phi.K1, &phi.K2 + + sub(K1, &p.X, &p.Z) // K1 = XP3 - ZP3 + sqr(&t0, K1) // t0 = K1^2 + add(K2, &p.X, &p.Z) // K2 = XP3 + ZP3 + sqr(&t1, K2) // t1 = K2^2 + add(&t2, &t0, &t1) // t2 = t0 + t1 + add(&t3, K1, K2) // t3 = K1 + K2 + sqr(&t3, &t3) // t3 = t3^2 + sub(&t3, &t3, &t2) // t3 = t3 - t2 + add(&t2, &t1, &t3) // t2 = t1 + t3 + add(&t3, &t3, &t0) // t3 = t3 + t0 + add(&t4, &t3, &t0) // t4 = t3 + t0 + add(&t4, &t4, &t4) // t4 = t4 + t4 + add(&t4, &t1, &t4) // t4 = t1 + t4 + mul(&coefEq.C, &t2, &t4) // A24m = t2 * t4 + add(&t4, &t1, &t2) // t4 = t1 + t2 + add(&t4, &t4, &t4) // t4 = t4 + t4 + add(&t4, &t0, &t4) // t4 = t0 + t4 + mul(&t4, &t3, &t4) // t4 = t3 * t4 + sub(&t0, &t4, &coefEq.C) // t0 = t4 - A24m + add(&coefEq.A, &coefEq.C, &t0) // A24p = A24m + t0 + return coefEq +} + +// Given a 3-isogeny phi and a point pB = x(PB), compute x(QB), the x-coordinate +// of the image QB = phi(PB) of PB under phi : E_(A:C) -> E_(A':C'). +// +// The output xQ = x(Q) is then a point on the curve E_(A':C'); the curve +// parameters are returned by the GenerateCurve function used to construct phi. +func (phi *isogeny3) EvaluatePoint(p *ProjectivePoint) ProjectivePoint { + var t0, t1, t2 Fp2 + var q ProjectivePoint + var K1, K2 = &phi.K1, &phi.K2 + var px, pz = &p.X, &p.Z + + add(&t0, px, pz) // t0 = XQ + ZQ + sub(&t1, px, pz) // t1 = XQ - ZQ + mul(&t0, K1, &t0) // t2 = K1 * t0 + mul(&t1, K2, &t1) // t1 = K2 * t1 + add(&t2, &t0, &t1) // t2 = t0 + t1 + sub(&t0, &t1, &t0) // t0 = t1 - t0 + sqr(&t2, &t2) // t2 = t2 ^ 2 + sqr(&t0, &t0) // t0 = t0 ^ 2 + mul(&q.X, px, &t2) // XQ'= XQ * t2 + mul(&q.Z, pz, &t0) // ZQ'= ZQ * t0 + return q +} + +// Given a four-torsion point p = x(PB) on the curve E_(A:C), construct the +// four-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). +// +// Input: (XP_4: ZP_4), where P_4 has exact order 4 on E_A/C +// Output: * Curve coordinates (A' + 2C', 4C') corresponding to E_A'/C' = A_E/C/ +// * Isogeny phi with constants in F_p^2 +func (phi *isogeny4) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { + var coefEq CurveCoefficientsEquiv + var xp4, zp4 = &p.X, &p.Z + var K1, K2, K3 = &phi.K1, &phi.K2, &phi.K3 + + sub(K2, xp4, zp4) + add(K3, xp4, zp4) + sqr(K1, zp4) + add(K1, K1, K1) + sqr(&coefEq.C, K1) + add(K1, K1, K1) + sqr(&coefEq.A, xp4) + add(&coefEq.A, &coefEq.A, &coefEq.A) + sqr(&coefEq.A, &coefEq.A) + return coefEq +} + +// Given a 4-isogeny phi and a point xP = x(P), compute x(Q), the x-coordinate +// of the image Q = phi(P) of P under phi : E_(A:C) -> E_(A':C'). +// +// Input: Isogeny returned by GenerateCurve and point q=(Qx,Qz) from E0_A/C +// Output: Corresponding point q from E1_A'/C', where E1 is 4-isogenous to E0 +func (phi *isogeny4) EvaluatePoint(p *ProjectivePoint) ProjectivePoint { + var t0, t1 Fp2 + var q = *p + var xq, zq = &q.X, &q.Z + var K1, K2, K3 = &phi.K1, &phi.K2, &phi.K3 + + add(&t0, xq, zq) + sub(&t1, xq, zq) + mul(xq, &t0, K2) + mul(zq, &t1, K3) + mul(&t0, &t0, &t1) + mul(&t0, &t0, K1) + add(&t1, xq, zq) + sub(zq, xq, zq) + sqr(&t1, &t1) + sqr(zq, zq) + add(xq, &t0, &t1) + sub(&t0, zq, &t0) + mul(xq, xq, &t1) + mul(zq, zq, &t0) + return q +} diff --git a/src/circl/dh/sidh/internal/p751/curve_test.go b/src/circl/dh/sidh/internal/p751/curve_test.go new file mode 100644 index 00000000000..8ea423258e6 --- /dev/null +++ b/src/circl/dh/sidh/internal/p751/curve_test.go @@ -0,0 +1,100 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p751 + +import ( + "bytes" + "testing" + + . "circl/dh/sidh/internal/common" +) + +func vartimeEqProjFp2(lhs, rhs *ProjectivePoint) bool { + var t0, t1 Fp2 + mul(&t0, &lhs.X, &rhs.Z) + mul(&t1, &lhs.Z, &rhs.X) + return vartimeEqFp2(&t0, &t1) +} + +func toAffine(point *ProjectivePoint) *Fp2 { + var affineX Fp2 + inv(&affineX, &point.Z) + mul(&affineX, &affineX, &point.X) + return &affineX +} + +func Test_jInvariant(t *testing.T) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + var jbufRes = make([]byte, params.SharedSecretSize) + var jbufExp = make([]byte, params.SharedSecretSize) + var jInv Fp2 + + Jinvariant(&curve, &jInv) + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(jbufRes, &jInv, params.Bytelen) + + jInv = expectedJ + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(jbufExp, &jInv, params.Bytelen) + + if !bytes.Equal(jbufRes[:], jbufExp[:]) { + t.Error("Computed incorrect j-invariant: found\n", jbufRes, "\nexpected\n", jbufExp) + } +} + +func TestProjectivePointVartimeEq(t *testing.T) { + var xP ProjectivePoint + + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + xQ := xP + + // Scale xQ, which results in the same projective point + mul(&xQ.X, &xQ.X, &curveA) + mul(&xQ.Z, &xQ.Z, &curveA) + if !vartimeEqProjFp2(&xP, &xQ) { + t.Error("Expected the scaled point to be equal to the original") + } +} + +func TestPointMulVersusSage(t *testing.T) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + var cparams = CalcCurveParamsEquiv4(&curve) + var xP ProjectivePoint + + // x 2 + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + Pow2k(&xP, &cparams, 1) + afxQ := toAffine(&xP) + if !vartimeEqFp2(afxQ, &affineXP2) { + t.Error("\nExpected\n", affineXP2, "\nfound\n", afxQ) + } + + // x 4 + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + Pow2k(&xP, &cparams, 2) + afxQ = toAffine(&xP) + if !vartimeEqFp2(afxQ, &affineXP4) { + t.Error("\nExpected\n", affineXP4, "\nfound\n", afxQ) + } +} + +func TestPointMul9VersusSage(t *testing.T) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + var cparams = CalcCurveParamsEquiv3(&curve) + var xP ProjectivePoint + + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + Pow3k(&xP, &cparams, 2) + afxQ := toAffine(&xP) + if !vartimeEqFp2(afxQ, &affineXP9) { + t.Error("\nExpected\n", affineXP9, "\nfound\n", afxQ) + } +} + +func BenchmarkThreePointLadder(b *testing.B) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + for n := 0; n < b.N; n++ { + ScalarMul3Pt(&curve, &threePointLadderInputs[0], &threePointLadderInputs[1], &threePointLadderInputs[2], uint(len(scalar3Pt)*8), scalar3Pt[:]) + } +} diff --git a/src/circl/dh/sidh/internal/p751/doc.go b/src/circl/dh/sidh/internal/p751/doc.go new file mode 100644 index 00000000000..fb774fec9fc --- /dev/null +++ b/src/circl/dh/sidh/internal/p751/doc.go @@ -0,0 +1,2 @@ +// Package p751 provides implementation of field arithmetic used in SIDH and SIKE. +package p751 diff --git a/src/circl/dh/sidh/internal/p751/fp2.go b/src/circl/dh/sidh/internal/p751/fp2.go new file mode 100644 index 00000000000..d9f19bcb3b0 --- /dev/null +++ b/src/circl/dh/sidh/internal/p751/fp2.go @@ -0,0 +1,195 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p751 + +import ( + "circl/dh/sidh/internal/common" +) + +// Montgomery multiplication. Input values must be already +// in Montgomery domain. +func mulP(dest, lhs, rhs *common.Fp) { + var ab common.FpX2 + mulP751(&ab, lhs, rhs) // = a*b*R*R + rdcP751(dest, &ab) // = a*b*R mod p +} + +// Set dest = x^((p-3)/4). If x is square, this is 1/sqrt(x). +// Uses variation of sliding-window algorithm from with window size +// of 5 and least to most significant bit sliding (left-to-right) +// See HAC 14.85 for general description. +// +// Allowed to overlap x with dest. +// All values in Montgomery domains +// Set dest = x^(2^k), for k >= 1, by repeated squarings. +func p34(dest, x *common.Fp) { + var lookup [16]common.Fp + + // This performs sum(powStrategy) + 1 squarings and len(lookup) + len(mulStrategy) + // multiplications. + powStrategy := []uint8{5, 7, 6, 2, 10, 4, 6, 9, 8, 5, 9, 4, 7, 5, 5, 4, 8, 3, 9, 5, 5, 4, 10, 4, 6, 6, 6, 5, 8, 9, 3, 4, 9, 4, 5, 6, 6, 2, 9, 4, 5, 5, 5, 7, 7, 9, 4, 6, 4, 8, 5, 8, 6, 6, 2, 9, 7, 4, 8, 8, 8, 4, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2} + mulStrategy := []uint8{15, 11, 10, 0, 15, 3, 3, 3, 4, 4, 9, 7, 11, 11, 5, 3, 12, 2, 10, 8, 5, 2, 8, 3, 5, 4, 11, 4, 0, 9, 2, 1, 12, 7, 5, 14, 15, 0, 14, 5, 6, 4, 5, 13, 6, 9, 7, 15, 1, 14, 11, 15, 12, 5, 0, 10, 9, 7, 7, 10, 14, 6, 11, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 1} + initialMul := uint8(13) + + // Precompute lookup table of odd multiples of x for window + // size k=5. + var xx common.Fp + mulP(&xx, x, x) + lookup[0] = *x + for i := 1; i < 16; i++ { + mulP(&lookup[i], &lookup[i-1], &xx) + } + + // Now lookup = {x, x^3, x^5, ... } + // so that lookup[i] = x^{2*i + 1} + // so that lookup[k/2] = x^k, for odd k + *dest = lookup[initialMul] + for i := uint8(0); i < uint8(len(powStrategy)); i++ { + mulP(dest, dest, dest) + for j := uint8(1); j < powStrategy[i]; j++ { + mulP(dest, dest, dest) + } + mulP(dest, dest, &lookup[mulStrategy[i]]) + } +} + +func add(dest, lhs, rhs *common.Fp2) { + addP751(&dest.A, &lhs.A, &rhs.A) + addP751(&dest.B, &lhs.B, &rhs.B) +} + +func sub(dest, lhs, rhs *common.Fp2) { + subP751(&dest.A, &lhs.A, &rhs.A) + subP751(&dest.B, &lhs.B, &rhs.B) +} + +func mul(dest, lhs, rhs *common.Fp2) { + var bMinA, cMinD common.Fp + var ac, bd common.FpX2 + var adPlusBc common.FpX2 + var acMinBd common.FpX2 + + // Let (a,b,c,d) = (lhs.a,lhs.b,rhs.a,rhs.b). + // + // (a + bi)*(c + di) = (a*c - b*d) + (a*d + b*c)i + // + // Use Karatsuba's trick: note that + // + // (b - a)*(c - d) = (b*c + a*d) - a*c - b*d + // + // so (a*d + b*c) = (b-a)*(c-d) + a*c + b*d. + mulP751(&ac, &lhs.A, &rhs.A) // = a*c*R*R + mulP751(&bd, &lhs.B, &rhs.B) // = b*d*R*R + subP751(&bMinA, &lhs.B, &lhs.A) // = (b-a)*R + subP751(&cMinD, &rhs.A, &rhs.B) // = (c-d)*R + mulP751(&adPlusBc, &bMinA, &cMinD) // = (b-a)*(c-d)*R*R + adlP751(&adPlusBc, &adPlusBc, &ac) // = ((b-a)*(c-d) + a*c)*R*R + adlP751(&adPlusBc, &adPlusBc, &bd) // = ((b-a)*(c-d) + a*c + b*d)*R*R + rdcP751(&dest.B, &adPlusBc) // = (a*d + b*c)*R mod p + sulP751(&acMinBd, &ac, &bd) // = (a*c - b*d)*R*R + rdcP751(&dest.A, &acMinBd) // = (a*c - b*d)*R mod p +} + +// Set dest = 1/x +// +// Allowed to overlap dest with x. +// +// Returns dest to allow chaining operations. +func inv(dest, x *common.Fp2) { + var e1, e2 common.FpX2 + var f1, f2 common.Fp + + // We want to compute + // + // 1 1 (a - bi) (a - bi) + // -------- = -------- -------- = ----------- + // (a + bi) (a + bi) (a - bi) (a^2 + b^2) + // + // Letting c = 1/(a^2 + b^2), this is + // + // 1/(a+bi) = a*c - b*ci. + + mulP751(&e1, &x.A, &x.A) // = a*a*R*R + mulP751(&e2, &x.B, &x.B) // = b*b*R*R + adlP751(&e1, &e1, &e2) // = (a^2 + b^2)*R*R + rdcP751(&f1, &e1) // = (a^2 + b^2)*R mod p + // Now f1 = a^2 + b^2 + + mulP(&f2, &f1, &f1) + p34(&f2, &f2) + mulP(&f2, &f2, &f2) + mulP(&f2, &f2, &f1) + + mulP751(&e1, &x.A, &f2) + rdcP751(&dest.A, &e1) + + subP751(&f1, &common.Fp{}, &x.B) + mulP751(&e1, &f1, &f2) + rdcP751(&dest.B, &e1) +} + +func sqr(dest, x *common.Fp2) { + var a2, aPlusB, aMinusB common.Fp + var a2MinB2, ab2 common.FpX2 + + a := &x.A + b := &x.B + + // (a + bi)*(a + bi) = (a^2 - b^2) + 2abi. + addP751(&a2, a, a) // = a*R + a*R = 2*a*R + addP751(&aPlusB, a, b) // = a*R + b*R = (a+b)*R + subP751(&aMinusB, a, b) // = a*R - b*R = (a-b)*R + mulP751(&a2MinB2, &aPlusB, &aMinusB) // = (a+b)*(a-b)*R*R = (a^2 - b^2)*R*R + mulP751(&ab2, &a2, b) // = 2*a*b*R*R + rdcP751(&dest.A, &a2MinB2) // = (a^2 - b^2)*R mod p + rdcP751(&dest.B, &ab2) // = 2*a*b*R mod p +} + +// In case choice == 1, performs following swap in constant time: +// xPx <-> xQx +// xPz <-> xQz +// Otherwise returns xPx, xPz, xQx, xQz unchanged +func cswap(xPx, xPz, xQx, xQz *common.Fp2, choice uint8) { + cswapP751(&xPx.A, &xQx.A, choice) + cswapP751(&xPx.B, &xQx.B, choice) + cswapP751(&xPz.A, &xQz.A, choice) + cswapP751(&xPz.B, &xQz.B, choice) +} + +// Converts in.A and in.B to Montgomery domain and stores +// in 'out' +// out.A = in.A * R mod p +// out.B = in.B * R mod p +// Performs v = v*R^2*R^(-1) mod p, for both in.A and in.B +func ToMontgomery(out, in *common.Fp2) { + var aRR common.FpX2 + + // a*R*R + mulP751(&aRR, &in.A, &P751R2) + // a*R mod p + rdcP751(&out.A, &aRR) + mulP751(&aRR, &in.B, &P751R2) + rdcP751(&out.B, &aRR) +} + +// Converts in.A and in.B from Montgomery domain and stores +// in 'out' +// out.A = in.A mod p +// out.B = in.B mod p +// +// After returning from the call 'in' is not modified. +func FromMontgomery(out, in *common.Fp2) { + var aR common.FpX2 + + // convert from montgomery domain + copy(aR[:], in.A[:]) + rdcP751(&out.A, &aR) // = a mod p in [0, 2p) + modP751(&out.A) // = a mod p in [0, p) + for i := range aR { + aR[i] = 0 + } + copy(aR[:], in.B[:]) + rdcP751(&out.B, &aR) + modP751(&out.B) +} diff --git a/src/circl/dh/sidh/internal/p751/fp2_test.go b/src/circl/dh/sidh/internal/p751/fp2_test.go new file mode 100644 index 00000000000..466e118e954 --- /dev/null +++ b/src/circl/dh/sidh/internal/p751/fp2_test.go @@ -0,0 +1,245 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package p751 + +import ( + "math/rand" + "reflect" + "testing" + "testing/quick" + + "circl/dh/sidh/internal/common" +) + +type testParams struct { + Point common.ProjectivePoint + Cparam common.ProjectiveCurveParameters + ExtElem common.Fp2 +} + +// Returns true if lhs = rhs. Takes variable time. +func vartimeEqFp2(lhs, rhs *common.Fp2) bool { + a := *lhs + b := *rhs + + modP751(&a.A) + modP751(&a.B) + modP751(&b.A) + modP751(&b.B) + + eq := true + for i := 0; i < FpWords && eq; i++ { + eq = eq && (a.A[i] == b.A[i]) + eq = eq && (a.B[i] == b.B[i]) + } + return eq +} + +func (testParams) generateFp2(rand *rand.Rand) common.Fp2 { + // Generation strategy: low limbs taken from [0,2^64); high limb + // taken from smaller range + // + // Size hint is ignored since all elements are fixed size. + // + // Field elements taken in range [0,2p). Emulate this by capping + // the high limb by the top digit of 2*p-1: + // + // sage: (2*p-1).digits(2^64)[-1] + // + // This still allows generating values >= 2p, but hopefully that + // excess is OK (and if it's not, we'll find out, because it's for + // testing...) + highLimb := rand.Uint64() % P751x2[FpWords-1] + fpElementGen := func() (fp common.Fp) { + for i := 0; i < (FpWords - 1); i++ { + fp[i] = rand.Uint64() + } + fp[FpWords-1] = highLimb + return fp + } + return common.Fp2{A: fpElementGen(), B: fpElementGen()} +} + +func (c testParams) Generate(rand *rand.Rand, size int) reflect.Value { + return reflect.ValueOf( + testParams{ + common.ProjectivePoint{ + X: c.generateFp2(rand), + Z: c.generateFp2(rand), + }, + common.ProjectiveCurveParameters{ + A: c.generateFp2(rand), + C: c.generateFp2(rand), + }, + c.generateFp2(rand), + }) +} + +func TestOne(t *testing.T) { + var tmp common.Fp2 + + mul(&tmp, ¶ms.OneFp2, ¶ms.A.AffineP) + if !vartimeEqFp2(&tmp, ¶ms.A.AffineP) { + t.Error("Not equal 1") + } +} + +func TestFp2ToBytesRoundTrip(t *testing.T) { + roundTrips := func(x testParams) bool { + var xBytes = make([]byte, 2*params.Bytelen) + var xPrime common.Fp2 + + common.Fp2ToBytes(xBytes[:], &x.ExtElem, params.Bytelen) + common.BytesToFp2(&xPrime, xBytes[:], params.Bytelen) + return vartimeEqFp2(&xPrime, &x.ExtElem) + } + + if err := quick.Check(roundTrips, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2MulDistributesOverAdd(t *testing.T) { + mulDistributesOverAdd := func(x, y, z testParams) bool { + // Compute t1 = (x+y)*z + t1 := new(common.Fp2) + add(t1, &x.ExtElem, &y.ExtElem) + mul(t1, t1, &z.ExtElem) + + // Compute t2 = x*z + y*z + t2 := new(common.Fp2) + t3 := new(common.Fp2) + mul(t2, &x.ExtElem, &z.ExtElem) + mul(t3, &y.ExtElem, &z.ExtElem) + add(t2, t2, t3) + + return vartimeEqFp2(t1, t2) + } + + if err := quick.Check(mulDistributesOverAdd, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2MulIsAssociative(t *testing.T) { + isAssociative := func(x, y, z testParams) bool { + // Compute t1 = (x*y)*z + t1 := new(common.Fp2) + mul(t1, &x.ExtElem, &y.ExtElem) + mul(t1, t1, &z.ExtElem) + + // Compute t2 = (y*z)*x + t2 := new(common.Fp2) + mul(t2, &y.ExtElem, &z.ExtElem) + mul(t2, t2, &x.ExtElem) + + return vartimeEqFp2(t1, t2) + } + + if err := quick.Check(isAssociative, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2SquareMatchesMul(t *testing.T) { + sqrMatchesMul := func(x testParams) bool { + // Compute t1 = (x*x) + t1 := new(common.Fp2) + mul(t1, &x.ExtElem, &x.ExtElem) + + // Compute t2 = x^2 + t2 := new(common.Fp2) + sqr(t2, &x.ExtElem) + + return vartimeEqFp2(t1, t2) + } + + if err := quick.Check(sqrMatchesMul, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2Inv(t *testing.T) { + inverseIsCorrect := func(x testParams) bool { + z := new(common.Fp2) + inv(z, &x.ExtElem) + + // Now z = (1/x), so (z * x) * x == x + mul(z, z, &x.ExtElem) + mul(z, z, &x.ExtElem) + + return vartimeEqFp2(z, &x.ExtElem) + } + + // This is more expensive; run fewer tests + var quickCheckConfig = &quick.Config{MaxCount: (1 << 11)} + if err := quick.Check(inverseIsCorrect, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2Batch3Inv(t *testing.T) { + batchInverseIsCorrect := func(x1, x2, x3 testParams) bool { + var x1Inv, x2Inv, x3Inv common.Fp2 + inv(&x1Inv, &x1.ExtElem) + inv(&x2Inv, &x2.ExtElem) + inv(&x3Inv, &x3.ExtElem) + + var y1, y2, y3 common.Fp2 + Fp2Batch3Inv(&x1.ExtElem, &x2.ExtElem, &x3.ExtElem, &y1, &y2, &y3) + + return (vartimeEqFp2(&x1Inv, &y1) && vartimeEqFp2(&x2Inv, &y2) && vartimeEqFp2(&x3Inv, &y3)) + } + + // This is more expensive; run fewer tests + var quickCheckConfig = &quick.Config{MaxCount: (1 << 8)} + if err := quick.Check(batchInverseIsCorrect, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func BenchmarkFp2Mul(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + mul(w, z, z) + } +} + +func BenchmarkFp2Inv(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + inv(w, z) + } +} + +func BenchmarkFp2Square(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + sqr(w, z) + } +} + +func BenchmarkFp2Add(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + add(w, z, z) + } +} + +func BenchmarkFp2Sub(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + sub(w, z, z) + } +} diff --git a/src/circl/dh/sidh/internal/p751/params.go b/src/circl/dh/sidh/internal/p751/params.go new file mode 100644 index 00000000000..29ab8b4d383 --- /dev/null +++ b/src/circl/dh/sidh/internal/p751/params.go @@ -0,0 +1,249 @@ +package p751 + +//go:generate go run ../templates/gen.go P751 + +import ( + "circl/dh/sidh/internal/common" + "internal/cpu" +) + +const ( + // Number of uint64 limbs used to store field element + FpWords = 12 +) + +var ( + // HasBMI2 signals support for MULX which is in BMI2 + HasBMI2 = cpu.X86.HasBMI2 + // HasADXandBMI2 signals support for ADX and BMI2 + HasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX + // P751 is a prime used by field Fp751 + P751 = common.Fp{ + 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, + 0xffffffffffffffff, 0xffffffffffffffff, 0xeeafffffffffffff, + 0xe3ec968549f878a8, 0xda959b1a13f7cc76, 0x084e9867d6ebe876, + 0x8562b5045cb25748, 0x0e12909f97badc66, 0x00006fe5d541f71c} + + // P751x2 = 2*p751 - 1 + P751x2 = common.Fp{ + 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, + 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xDD5FFFFFFFFFFFFF, + 0xC7D92D0A93F0F151, 0xB52B363427EF98ED, 0x109D30CFADD7D0ED, + 0x0AC56A08B964AE90, 0x1C25213F2F75B8CD, 0x0000DFCBAA83EE38} + + // P751p1 = p751 + 1 + P751p1 = common.Fp{ + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + 0x0000000000000000, 0x0000000000000000, 0xeeb0000000000000, + 0xe3ec968549f878a8, 0xda959b1a13f7cc76, 0x084e9867d6ebe876, + 0x8562b5045cb25748, 0x0e12909f97badc66, 0x00006fe5d541f71c} + + // P751R2 = (2^768)^2 mod p + P751R2 = common.Fp{ + 0x233046449DAD4058, 0xDB010161A696452A, 0x5E36941472E3FD8E, + 0xF40BFE2082A2E706, 0x4932CCA8904F8751, 0x1F735F1F1EE7FC81, + 0xA24F4D80C1048E18, 0xB56C383CCDB607C5, 0x441DD47B735F9C90, + 0x5673ED2C6A6AC82A, 0x06C905261132294B, 0x000041AD830F1F35} + + // P751p1Zeros number of 0 digits in the least significant part of P751+1 + P751p1Zeros = 5 + + // 1*R mod p + one = common.Fp2{ + A: common.Fp{ + 0x00000000000249ad, 0x0000000000000000, 0x0000000000000000, + 0x0000000000000000, 0x0000000000000000, 0x8310000000000000, + 0x5527b1e4375c6c66, 0x697797bf3f4f24d0, 0xc89db7b2ac5c4e2e, + 0x4ca4b439d2076956, 0x10f7926c7512c7e9, 0x00002d5b24bce5e2}, + } + // 1/2 * R mod p + half = common.Fp2{ + A: common.Fp{ + 0x00000000000124D6, 0x0000000000000000, 0x0000000000000000, + 0x0000000000000000, 0x0000000000000000, 0xB8E0000000000000, + 0x9C8A2434C0AA7287, 0xA206996CA9A378A3, 0x6876280D41A41B52, + 0xE903B49F175CE04F, 0x0F8511860666D227, 0x00004EA07CFF6E7F}, + } + // 6*R mod p + six = common.Fp2{ + A: common.Fp{ + 0x00000000000DBA10, 0x0000000000000000, 0x0000000000000000, + 0x0000000000000000, 0x0000000000000000, 0x3500000000000000, + 0x3714FE4EB8399915, 0xC3A2584753EB43F4, 0xA3151D605C520428, + 0xC116CF5232C7C978, 0x49A84D4B8EFAF6AA, 0x0000305731E97514}, + } + + params = common.SidhParams{ + ID: common.Fp751, + // SIDH public key byte size. + PublicKeySize: 564, + // SIDH shared secret byte size. + SharedSecretSize: 188, + A: common.DomainParams{ + // The x-coordinate of PA + AffineP: common.Fp2{ + A: common.Fp{ + 0x884F46B74000BAA8, 0xBA52630F939DEC20, 0xC16FB97BA714A04D, + 0x082536745B1AB3DB, 0x1117157F446F9E82, 0xD2F27D621A018490, + 0x6B24AB523D544BCD, 0x9307D6AA2EA85C94, 0xE1A096729528F20F, + 0x896446F868F3255C, 0x2401D996B1BFF8A5, 0x00000EF8786A5C0A, + }, + B: common.Fp{ + 0xAEB78B3B96F59394, 0xAB26681E29C90B74, 0xE520AC30FDC4ACF1, + 0x870AAAE3A4B8111B, 0xF875BDB738D64EFF, 0x50109A7ECD7ED6BC, + 0x4CC64848FF0C56FB, 0xE617CB6C519102C9, 0x9C74B3835921E609, + 0xC91DDAE4A35A7146, 0x7FC82A155C1B9129, 0x0000214FA6B980B3, + }, + }, + // The x-coordinate of QA + AffineQ: common.Fp2{ + A: common.Fp{ + 0x0F93CC38680A8CA9, 0x762E733822E7FED7, 0xE549F005AC0ADB67, + 0x94A71FDD2C43A4ED, 0xD48645C2B04721C5, 0x432DA1FE4D4CA4DC, + 0xBC99655FAA7A80E8, 0xB2C6D502BCFD4823, 0xEE92F40CA2EC8BDB, + 0x7B074132EFB6D16C, 0x3340B46FA38A7633, 0x0000215749657F6C, + }, + B: common.Fp{ + 0xECFF375BF3079F4C, 0xFBFE74B043E80EF3, 0x17376CBE3C5C7AD1, + 0xC06327A7E29CDBF2, 0x2111649C438BF3D4, 0xC1F9298261BA2E97, + 0x1F9FECE869CFD1C2, 0x01A39B4FC9346D62, 0x147CD1D3E82A3C9F, + 0xDE84E9D249E533EE, 0x1C48A5ADFB7C578D, 0x000061ACA0B82E1D, + }, + }, + // The x-coordinate of RA = PA-QA + AffineR: common.Fp2{ + A: common.Fp{ + 0x1600C525D41059F1, 0xA596899A0A1D83F7, 0x6BFDEED6D2B23F35, + 0x5C7E707270C23910, 0x276CA1A4E8369411, 0xB193651A602925A0, + 0x243D239F1CA1F04A, 0x543DC6DA457860AD, 0xCDA590F325181DE9, + 0xD3AB7ACFDA80B395, 0x6C97468580FDDF7B, 0x0000352A3E5C4C77, + }, + B: common.Fp{ + 0x9B794F9FD1CC3EE8, 0xDB32E40A9B2FD23E, 0x26192A2542E42B67, + 0xA18E94FCA045BCE7, 0x96DC1BC38E7CDA2D, 0x9A1D91B752487DE2, + 0xCC63763987436DA3, 0x1316717AACCC551D, 0xC4C368A4632AFE72, + 0x4B6EA85C9CCD5710, 0x7A12CAD582C7BC9A, 0x00001C7E240149BF, + }, + }, + // Max size of secret key for 2-torsion group, corresponds to 2^e2 - 1 + SecretBitLen: 372, + // SecretBitLen in bytes. + SecretByteLen: 47, + // 2-torsion group computation strategy + IsogenyStrategy: []uint32{ + 0x50, 0x30, 0x1B, 0x0F, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, + 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x07, + 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, + 0x01, 0x01, 0x01, 0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, + 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03, + 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x15, + 0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, + 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01, 0x01, + 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05, 0x03, 0x02, + 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, + 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x21, 0x14, 0x0C, 0x07, + 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, + 0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, + 0x02, 0x01, 0x01, 0x01, 0x08, 0x05, 0x03, 0x02, 0x01, 0x01, + 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, + 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, + 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, + 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, + 0x01, 0x01, 0x02, 0x01, 0x01}, + }, + B: common.DomainParams{ + // The x-coordinate of PB + AffineP: common.Fp2{ + A: common.Fp{ + 0x85691AAF4015F88C, 0x7478C5B8C36E9631, 0x7EF2A185DE4DD6E2, + 0x943BBEE46BEB9DC7, 0x1A3EC62798792D22, 0x791BC4B084B31D69, + 0x03DBE6522CEA17C4, 0x04749AA65D665D83, 0x3D52B5C45EF450F3, + 0x0B4219848E36947D, 0xA4CF7070466BDE27, 0x0000334B1FA6D193, + }, + B: common.Fp{ + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + }, + }, + // The x-coordinate of QB + AffineQ: common.Fp2{ + A: common.Fp{ + 0x8E7CB3FA53211340, 0xD67CE54F7A05EEE0, 0xFDDC2C8BCE46FC38, + 0x08587FAE3110DF1E, 0xD6B8246FA22B058B, 0x4DAC3ACC905A5DBD, + 0x51D0BF2FADCED3E8, 0xE5A2406DF6484425, 0x907F177584F671B8, + 0x4738A2FFCCED051C, 0x2B0067B4177E4853, 0x00002806AC948D3D, + }, + B: common.Fp{ + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, + }, + }, + // The x-coordinate of RB = PB - QB + AffineR: common.Fp2{ + A: common.Fp{ + 0xB56457016D1D6D1C, 0x03DECCB38F39C491, 0xDFB910AC8A559452, + 0xA9D0F17D1FF24883, 0x8562BBAF515C248C, 0x249B2A6DDB1CB67D, + 0x3131AF96FB46835C, 0xE10258398480C3E1, 0xEAB5E2B872D4FAB1, + 0xB71E63875FAEB1DF, 0xF8384D4F13757CF6, 0x0000361EC9B09912, + }, + B: common.Fp{ + 0x58C967899ED16EF4, 0x81998376DC622A4B, 0x3D1C1DCFE0B12681, + 0x9347DEBB953E1730, 0x9ABB344D3A82C2D7, 0xE4881BD2820552B2, + 0x0037247923D90266, 0x2E3156EDB157E5A5, 0xF86A46A7506823F7, + 0x8FE5523A7B7F1CFC, 0xFA3CFFA38372F67B, 0x0000692DCE85FFBD, + }, + }, + // Size of secret key for 3-torsion group, corresponds to log_2(3^e3) - 1. + SecretBitLen: 378, + // SecretBitLen in bytes. + SecretByteLen: 48, + // 3-torsion group computation strategy + IsogenyStrategy: []uint32{ + 0x70, 0x3F, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, + 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, + 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, + 0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, + 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, + 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, + 0x01, 0x01, 0x02, 0x01, 0x01, 0x1F, 0x10, 0x08, 0x04, 0x02, + 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, + 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, + 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x0F, 0x08, 0x04, + 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, + 0x02, 0x01, 0x01, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, + 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x31, 0x1F, 0x10, + 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, + 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, + 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, + 0x0F, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, + 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x07, 0x04, 0x02, 0x01, + 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, + 0x15, 0x0C, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, + 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x05, 0x03, 0x02, + 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05, + 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, + 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01}, + }, + OneFp2: one, + HalfFp2: half, + + MsgLen: 32, + // SIKEp751 provides 128 bit of classical security ([SIKE], 5.1) + KemSize: 32, + // ceil(751+7/8) + Bytelen: 94, + CiphertextSize: 32 + 564, + InitCurve: common.ProjectiveCurveParameters{ + A: six, + C: one, + }, + } +) + +func init() { + common.Register(common.Fp751, ¶ms) +} diff --git a/src/circl/dh/sidh/internal/p751/params_test.go b/src/circl/dh/sidh/internal/p751/params_test.go new file mode 100644 index 00000000000..c258552cc23 --- /dev/null +++ b/src/circl/dh/sidh/internal/p751/params_test.go @@ -0,0 +1,74 @@ +package p751 + +// Contains values used by tests +import ( + "testing/quick" + + . "circl/dh/sidh/internal/common" +) + +var ( + expectedJ = Fp2{ + A: Fp{0xc7a8921c1fb23993, 0xa20aea321327620b, 0xf1caa17ed9676fa8, 0x61b780e6b1a04037, 0x47784af4c24acc7a, 0x83926e2e300b9adf, 0xcd891d56fae5b66, 0x49b66985beb733bc, 0xd4bcd2a473d518f, 0xe242239991abe224, 0xa8af5b20f98672f8, 0x139e4d4e4d98}, + B: Fp{0xb5b52a21f81f359, 0x715e3a865db6d920, 0x9bac2f9d8911978b, 0xef14acd8ac4c1e3d, 0xe81aacd90cfb09c8, 0xaf898288de4a09d9, 0xb85a7fb88c5c4601, 0x2c37c3f1dd303387, 0x7ad3277fe332367c, 0xd4cbee7f25a8e6f8, 0x36eacbe979eaeffa, 0x59eb5a13ac33}, + } + // A = 4385300808024233870220415655826946795549183378139271271040522089756750951667981765872679172832050962894122367066234419550072004266298327417513857609747116903999863022476533671840646615759860564818837299058134292387429068536219*i + 1408083354499944307008104531475821995920666351413327060806684084512082259107262519686546161682384352696826343970108773343853651664489352092568012759783386151707999371397181344707721407830640876552312524779901115054295865393760 + curveA = Fp2{ + A: Fp{0x8319eb18ca2c435e, 0x3a93beae72cd0267, 0x5e465e1f72fd5a84, 0x8617fa4150aa7272, 0x887da24799d62a13, 0xb079b31b3c7667fe, 0xc4661b150fa14f2e, 0xd4d2b2967bc6efd6, 0x854215a8b7239003, 0x61c5302ccba656c2, 0xf93194a27d6f97a2, 0x1ed9532bca75}, + B: Fp{0xb6f541040e8c7db6, 0x99403e7365342e15, 0x457e9cee7c29cced, 0x8ece72dc073b1d67, 0x6e73cef17ad28d28, 0x7aed836ca317472, 0x89e1de9454263b54, 0x745329277aa0071b, 0xf623dfc73bc86b9b, 0xb8e3c1d8a9245882, 0x6ad0b3d317770bec, 0x5b406e8d502b}} + + // C = 933177602672972392833143808100058748100491911694554386487433154761658932801917030685312352302083870852688835968069519091048283111836766101703759957146191882367397129269726925521881467635358356591977198680477382414690421049768*i + 9088894745865170214288643088620446862479558967886622582768682946704447519087179261631044546285104919696820250567182021319063155067584445633834024992188567423889559216759336548208016316396859149888322907914724065641454773776307 + curveC = Fp2{ + A: Fp{0x4fb2358bbf723107, 0x3a791521ac79e240, 0x283e24ef7c4c922f, 0xc89baa1205e33cc, 0x3031be81cff6fee1, 0xaf7a494a2f6a95c4, 0x248d251eaac83a1d, 0xc122fca1e2550c88, 0xbc0451b11b6cfd3d, 0x9c0a114ab046222c, 0x43b957b32f21f6ea, 0x5b9c87fa61de}, + B: Fp{0xacf142afaac15ec6, 0xfd1322a504a071d5, 0x56bb205e10f6c5c6, 0xe204d2849a97b9bd, 0x40b0122202fe7f2e, 0xecf72c6fafacf2cb, 0x45dfc681f869f60a, 0x11814c9aff4af66c, 0x9278b0c4eea54fe7, 0x9a633d5baf7f2e2e, 0x69a329e6f1a05112, 0x1d874ace23e4}} + + // x(P) = 8172151271761071554796221948801462094972242987811852753144865524899433583596839357223411088919388342364651632180452081960511516040935428737829624206426287774255114241789158000915683252363913079335550843837650671094705509470594*i + 9326574858039944121604015439381720195556183422719505497448541073272720545047742235526963773359004021838961919129020087515274115525812121436661025030481584576474033630899768377131534320053412545346268645085054880212827284581557 + affineXP = Fp2{ + A: Fp{0xe8d05f30aac47247, 0x576ec00c55441de7, 0xbf1a8ec5fe558518, 0xd77cb17f77515881, 0x8e9852837ee73ec4, 0x8159634ad4f44a6b, 0x2e4eb5533a798c5, 0x9be8c4354d5bc849, 0xf47dc61806496b84, 0x25d0e130295120e0, 0xdbef54095f8139e3, 0x5a724f20862c}, + B: Fp{0x3ca30d7623602e30, 0xfb281eddf45f07b7, 0xd2bf62d5901a45bc, 0xc67c9baf86306dd2, 0x4e2bd93093f538ca, 0xcfd92075c25b9cbe, 0xceafe9a3095bcbab, 0x7d928ad380c85414, 0x37c5f38b2afdc095, 0x75325899a7b779f4, 0xf130568249f20fdd, 0x178f264767d1}} + + // x([2]P) = 1476586462090705633631615225226507185986710728845281579274759750260315746890216330325246185232948298241128541272709769576682305216876843626191069809810990267291824247158062860010264352034514805065784938198193493333201179504845*i + 3623708673253635214546781153561465284135688791018117615357700171724097420944592557655719832228709144190233454198555848137097153934561706150196041331832421059972652530564323645509890008896574678228045006354394485640545367112224 + affineXP2 = Fp2{ + A: Fp{0x2a77afa8576ce979, 0xab1360e69b0aeba0, 0xd79e3e3cbffad660, 0x5fd0175aa10f106b, 0x1800ebafce9fbdbc, 0x228fc9142bdd6166, 0x867cf907314e34c3, 0xa58d18c94c13c31c, 0x699a5bc78b11499f, 0xa29fc29a01f7ccf1, 0x6c69c0c5347eebce, 0x38ecee0cc57}, + B: Fp{0x43607fd5f4837da0, 0x560bad4ce27f8f4a, 0x2164927f8495b4dd, 0x621103fdb831a997, 0xad740c4eea7db2db, 0x2cde0442205096cd, 0x2af51a70ede8324e, 0x41a4e680b9f3466, 0x5481f74660b8f476, 0xfcb2f3e656ff4d18, 0x42e3ce0837171acc, 0x44238c30530c}} + + // x([2^2]P) = 441719501189485559222919502512761433931671682884872259563221427434901842337947564993718830905758163254463901652874331063768876314142359813382575876106725244985607032091781306919778265250690045578695338669105227100119314831452*i + 6961734028200975729170216310486458180126343885294922940439352055937945948015840788921225114530454649744697857047401608073256634790353321931728699534700109268264491160589480994022419317695690866764726967221310990488404411684053 + affineXP4 = Fp2{ + A: Fp{0x6f9dbe4c39175153, 0xf2fec757eb99e88, 0x43d7361a93733d91, 0x3abd10ed19c85a3d, 0xc4de9ab9c5ef7181, 0x53e375901684c900, 0x68ffc3e7d71c41ff, 0x47adab62c8d942fe, 0x226a33fd6fbb381d, 0x87ef4c8fdd83309a, 0xaca1cf44c5fa8799, 0x6cbae86c755f}, + B: Fp{0x4c80c37fe68282a7, 0xbd8b9d7248bf553a, 0x1fb0e8e74d5e1762, 0xb63fa0e4e5f91482, 0xc675ab8a45a1439, 0xdfa6772deace7820, 0xf0d813d71d9a9255, 0x53a1a58c634534bd, 0x4ebfc6485fdfd888, 0x6991fe4358bcf169, 0xc0547bdaca85b6fd, 0xf461548d632}} + + // x([3^2]P) = 3957171963425208493644602380039721164492341594850197356580248639045894821895524981729970650520936632013218950972842867220898274664982599375786979902471523505057611521217523103474682939638645404445093536997296151472632038973463*i + 1357869545269286021642168835877253886774707209614159162748874474269328421720121175566245719916322684751967981171882659798149072149161259103020057556362998810229937432814792024248155991141511691087135859252304684633946087474060 + affineXP9 = Fp2{ + A: Fp{0x7c0daa0f04ded4e0, 0x52dc4f883d85e065, 0x91afbdc2c1714d0b, 0xb7b3db8e658cfeba, 0x43d4e72a692882f3, 0x535c56d83753da30, 0xc8a58724433cbf5d, 0x351153c0a5e74219, 0x2c81827d19f93dd5, 0x26ef8aca3370ea1a, 0x1cf939a6dd225dec, 0x3403cb28ad41}, + B: Fp{0x93e7bc373a9ff7b, 0x57b8cc47635ebc0f, 0x92eab55689106cf3, 0x93643111d421f24c, 0x1c58b519506f6b7a, 0xebd409fb998faa13, 0x5c86ed799d09d80e, 0xd9a1d764d6363562, 0xf95e87f92fb0c4cc, 0x6b2bbaf5632a5609, 0x2d9b6a809dfaff7f, 0x29c0460348b}} + + // Inputs for testing 3-point-ladder + threePointLadderInputs = []ProjectivePoint{ + // x(P) + { + X: Fp2{ + A: Fp{0xe8d05f30aac47247, 0x576ec00c55441de7, 0xbf1a8ec5fe558518, 0xd77cb17f77515881, 0x8e9852837ee73ec4, 0x8159634ad4f44a6b, 0x2e4eb5533a798c5, 0x9be8c4354d5bc849, 0xf47dc61806496b84, 0x25d0e130295120e0, 0xdbef54095f8139e3, 0x5a724f20862c}, + B: Fp{0x3ca30d7623602e30, 0xfb281eddf45f07b7, 0xd2bf62d5901a45bc, 0xc67c9baf86306dd2, 0x4e2bd93093f538ca, 0xcfd92075c25b9cbe, 0xceafe9a3095bcbab, 0x7d928ad380c85414, 0x37c5f38b2afdc095, 0x75325899a7b779f4, 0xf130568249f20fdd, 0x178f264767d1}}, + Z: params.OneFp2, + }, + // x(Q) + { + X: Fp2{ + A: Fp{0x2b71a2a93ad1e10e, 0xf0b9842a92cfb333, 0xae17373615a27f5c, 0x3039239f428330c4, 0xa0c4b735ed7dcf98, 0x6e359771ddf6af6a, 0xe986e4cac4584651, 0x8233a2b622d5518, 0xbfd67bf5f06b818b, 0xdffe38d0f5b966a6, 0xa86b36a3272ee00a, 0x193e2ea4f68f}, + B: Fp{0x5a0f396459d9d998, 0x479f42250b1b7dda, 0x4016b57e2a15bf75, 0xc59f915203fa3749, 0xd5f90257399cf8da, 0x1fb2dadfd86dcef4, 0x600f20e6429021dc, 0x17e347d380c57581, 0xc1b0d5fa8fe3e440, 0xbcf035330ac20e8, 0x50c2eb5f6a4f03e6, 0x86b7c4571}}, + Z: params.OneFp2, + }, + // x(P-Q) + { + X: Fp2{ + A: Fp{0x4aafa9f378f7b5ff, 0x1172a683aa8eee0, 0xea518d8cbec2c1de, 0xe191bcbb63674557, 0x97bc19637b259011, 0xdbeae5c9f4a2e454, 0x78f64d1b72a42f95, 0xe71cb4ea7e181e54, 0xe4169d4c48543994, 0x6198c2286a98730f, 0xd21d675bbab1afa5, 0x2e7269fce391}, + B: Fp{0x23355783ce1d0450, 0x683164cf4ce3d93f, 0xae6d1c4d25970fd8, 0x7807007fb80b48cf, 0xa005a62ec2bbb8a2, 0x6b5649bd016004cb, 0xbb1a13fa1330176b, 0xbf38e51087660461, 0xe577fddc5dd7b930, 0x5f38116f56947cd3, 0x3124f30b98c36fde, 0x4ca9b6e6db37}}, + Z: params.OneFp2, + }, + } + scalar3Pt = [...]uint8{84, 222, 146, 63, 85, 18, 173, 162, 167, 38, 10, 8, 143, 176, 93, 228, 247, 128, 50, 128, 205, 42, 15, 137, 119, 67, 43, 3, 61, 91, 237, 24, 235, 12, 53, 96, 186, 164, 232, 223, 197, 224, 64, 109, 137, 63, 246, 4} +) + +var quickCheckConfig = &quick.Config{ + MaxCount: (1 << 15), +} diff --git a/src/circl/dh/sidh/internal/templates/arith_decl.gotemp b/src/circl/dh/sidh/internal/templates/arith_decl.gotemp new file mode 100644 index 00000000000..c7be93f42b8 --- /dev/null +++ b/src/circl/dh/sidh/internal/templates/arith_decl.gotemp @@ -0,0 +1,45 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +// +build amd64,!noasm{{if .OPT_ARM}} arm64,!noasm{{end}} + +package {{ .PACKAGE}} + +import ( + . "circl/dh/sidh/internal/common" +) + +// If choice = 0, leave x,y unchanged. If choice = 1, set x,y = y,x. +// If choice is neither 0 nor 1 then behaviour is undefined. +// This function executes in constant time. +//go:noescape +func cswap{{ .FIELD}}(x, y *Fp, choice uint8) + +// Compute z = x + y (mod p). +//go:noescape +func add{{ .FIELD}}(z, x, y *Fp) + +// Compute z = x - y (mod p). +//go:noescape +func sub{{ .FIELD}}(z, x, y *Fp) + +// Compute z = x + y, without reducing mod p. +//go:noescape +func adl{{ .FIELD}}(z, x, y *FpX2) + +// Compute z = x - y, without reducing mod p. +//go:noescape +func sul{{ .FIELD}}(z, x, y *FpX2) + +// Reduce a field element in [0, 2*p) to one in [0,p). +//go:noescape +func mod{{ .FIELD}}(x *Fp) + +// Computes z = x * y. +//go:noescape +func mul{{ .FIELD}}(z *FpX2, x, y *Fp) + +// Computes the Montgomery reduction z = x R^{-1} (mod 2*p). On return value +// of x may be changed. z=x not allowed. +//go:noescape +func rdc{{ .FIELD}}(z *Fp, x *FpX2) diff --git a/src/circl/dh/sidh/internal/templates/arith_generic.gotemp b/src/circl/dh/sidh/internal/templates/arith_generic.gotemp new file mode 100644 index 00000000000..f82ca3b6547 --- /dev/null +++ b/src/circl/dh/sidh/internal/templates/arith_generic.gotemp @@ -0,0 +1,192 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +// +build {{if .OPT_ARM}}noasm !amd64,!arm64{{else}}noasm !amd64{{end}} + +package {{ .PACKAGE}} + +import ( + "math/bits" + + "circl/dh/sidh/internal/common" +) + +// Compute z = x + y (mod p). +func add{{ .FIELD }}(z, x, y *common.Fp) { + var carry uint64 + + // z=x+y % {{ .FIELD }} + for i := 0; i < FpWords; i++ { + z[i], carry = bits.Add64(x[i], y[i], carry) + } + + // z = z - {{ .FIELD}}x2 + carry = 0 + for i := 0; i < FpWords; i++ { + z[i], carry = bits.Sub64(z[i], {{ .FIELD}}x2[i], carry) + } + + // if z<0 add {{ .FIELD}}x2 back + mask := uint64(0 - carry) + carry = 0 + for i := 0; i < FpWords; i++ { + z[i], carry = bits.Add64(z[i], {{ .FIELD}}x2[i]&mask, carry) + } +} + +// Compute z = x - y (mod p). +func sub{{ .FIELD }}(z, x, y *common.Fp) { + var borrow uint64 + + for i := 0; i < FpWords; i++ { + z[i], borrow = bits.Sub64(x[i], y[i], borrow) + } + + mask := uint64(0 - borrow) + borrow = 0 + + for i := 0; i < FpWords; i++ { + z[i], borrow = bits.Add64(z[i], {{ .FIELD}}x2[i]&mask, borrow) + } +} + +// Conditionally swaps bits in x and y in constant time. +// mask indicates bits to be swapped (set bits are swapped) +// For details see "Hackers Delight, 2.20" +// +// Implementation doesn't actually depend on a prime field. +func cswap{{ .FIELD }}(x, y *common.Fp, mask uint8) { + var tmp, mask64 uint64 + + mask64 = 0 - uint64(mask) + for i := 0; i < FpWords; i++ { + tmp = mask64 & (x[i] ^ y[i]) + x[i] = tmp ^ x[i] + y[i] = tmp ^ y[i] + } +} + +// Perform Montgomery reduction: set z = x R^{-1} (mod 2*p) +// with R=2^(FpWords*64). Destroys the input value. +func rdc{{ .FIELD }}(z *common.Fp, x *common.FpX2) { + var carry, t, u, v uint64 + var hi, lo uint64 + var count int + + count = {{ .FIELD}}p1Zeros + + for i := 0; i < FpWords; i++ { + for j := 0; j < i; j++ { + if j < (i - count + 1) { + hi, lo = bits.Mul64(z[j], {{ .FIELD }}p1[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + } + v, carry = bits.Add64(v, x[i], 0) + u, carry = bits.Add64(u, 0, carry) + t += carry + + z[i] = v + v = u + u = t + t = 0 + } + + for i := FpWords; i < 2*FpWords-1; i++ { + if count > 0 { + count-- + } + for j := i - FpWords + 1; j < FpWords; j++ { + if j < (FpWords - count) { + hi, lo = bits.Mul64(z[j], {{ .FIELD }}p1[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + } + v, carry = bits.Add64(v, x[i], 0) + u, carry = bits.Add64(u, 0, carry) + + t += carry + z[i-FpWords] = v + v = u + u = t + t = 0 + } + v, _ = bits.Add64(v, x[2*FpWords-1], 0) + z[FpWords-1] = v +} + +// Compute z = x * y. +func mul{{ .FIELD }}(z *common.FpX2, x, y *common.Fp) { + var u, v, t uint64 + var hi, lo uint64 + var carry uint64 + + for i := uint64(0); i < FpWords; i++ { + for j := uint64(0); j <= i; j++ { + hi, lo = bits.Mul64(x[j], y[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + z[i] = v + v = u + u = t + t = 0 + } + + for i := FpWords; i < (2*FpWords)-1; i++ { + for j := i - FpWords + 1; j < FpWords; j++ { + hi, lo = bits.Mul64(x[j], y[i-j]) + v, carry = bits.Add64(lo, v, 0) + u, carry = bits.Add64(hi, u, carry) + t += carry + } + z[i] = v + v = u + u = t + t = 0 + } + z[2*FpWords-1] = v +} + +// Compute z = x + y, without reducing mod p. +func adl{{ .FIELD }}(z, x, y *common.FpX2) { + var carry uint64 + for i := 0; i < 2*FpWords; i++ { + z[i], carry = bits.Add64(x[i], y[i], carry) + } +} + +// Reduce a field element in [0, 2*p) to one in [0,p). +func mod{{ .FIELD }}(x *common.Fp) { + var borrow, mask uint64 + for i := 0; i < FpWords; i++ { + x[i], borrow = bits.Sub64(x[i], {{ .FIELD }}[i], borrow) + } + + // Sets all bits if borrow = 1 + mask = 0 - borrow + borrow = 0 + for i := 0; i < FpWords; i++ { + x[i], borrow = bits.Add64(x[i], {{ .FIELD }}[i]&mask, borrow) + } +} + +// Compute z = x - y, without reducing mod p. +func sul{{ .FIELD }}(z, x, y *common.FpX2) { + var borrow, mask uint64 + for i := 0; i < 2*FpWords; i++ { + z[i], borrow = bits.Sub64(x[i], y[i], borrow) + } + + // Sets all bits if borrow = 1 + mask = 0 - borrow + borrow = 0 + for i := FpWords; i < 2*FpWords; i++ { + z[i], borrow = bits.Add64(z[i], {{ .FIELD }}[i-FpWords]&mask, borrow) + } +} diff --git a/src/circl/dh/sidh/internal/templates/arith_test.gotemp b/src/circl/dh/sidh/internal/templates/arith_test.gotemp new file mode 100644 index 00000000000..07d051aae25 --- /dev/null +++ b/src/circl/dh/sidh/internal/templates/arith_test.gotemp @@ -0,0 +1,101 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package {{ .PACKAGE}} + +import ( + "testing" + + "circl/dh/sidh/internal/common" +) + +// Package-level storage for this field element is intended to deter +// compiler optimizations. +var ( + benchmarkFp common.Fp + benchmarkFpX2 common.FpX2 + bench_x = common.Fp{17026702066521327207, 5108203422050077993, 10225396685796065916, 11153620995215874678, 6531160855165088358, 15302925148404145445, 1248821577836769963, 9789766903037985294, 7493111552032041328, 10838999828319306046, 18103257655515297935, 27403304611634} + bench_y = common.Fp{4227467157325093378, 10699492810770426363, 13500940151395637365, 12966403950118934952, 16517692605450415877, 13647111148905630666, 14223628886152717087, 7167843152346903316, 15855377759596736571, 4300673881383687338, 6635288001920617779, 30486099554235} + bench_z = common.FpX2{1595347748594595712, 10854920567160033970, 16877102267020034574, 12435724995376660096, 3757940912203224231, 8251999420280413600, 3648859773438820227, 17622716832674727914, 11029567000887241528, 11216190007549447055, 17606662790980286987, 4720707159513626555, 12887743598335030915, 14954645239176589309, 14178817688915225254, 1191346797768989683, 12629157932334713723, 6348851952904485603, 16444232588597434895, 7809979927681678066, 14642637672942531613, 3092657597757640067, 10160361564485285723, 240071237} +) + +func TestFpCswap(t *testing.T) { + var one = common.Fp{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} + var two = common.Fp{2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2} + + var x = one + var y = two + + cswap{{ .FIELD}}(&x, &y, 0) + for i := 0; i < FpWords; i++ { + if (x[i] != one[i]) || (y[i] != two[i]) { + t.Error("Found", x, "expected", two) + } + } + + cswap{{ .FIELD}}(&x, &y, 1) + for i := 0; i < FpWords; i++ { + if (x[i] != two[i]) || (y[i] != one[i]) { + t.Error("Found", x, "expected", two) + } + } +} + +// Benchmarking for field arithmetic +func BenchmarkMul(b *testing.B) { + for n := 0; n < b.N; n++ { + mul{{ .FIELD}}(&benchmarkFpX2, &bench_x, &bench_y) + } +} + +func BenchmarkRdc(b *testing.B) { + z := bench_z + + // This benchmark actually computes garbage, because + // rdc{{ .FIELD}} mangles its input, but since it's + // constant-time that shouldn't matter for the benchmarks. + for n := 0; n < b.N; n++ { + rdc{{ .FIELD}}(&benchmarkFp, &z) + } +} + +func BenchmarkAdd(b *testing.B) { + for n := 0; n < b.N; n++ { + add{{ .FIELD}}(&benchmarkFp, &bench_x, &bench_y) + } +} + +func BenchmarkSub(b *testing.B) { + for n := 0; n < b.N; n++ { + sub{{ .FIELD}}(&benchmarkFp, &bench_x, &bench_y) + } +} + +func BenchmarkCswap(b *testing.B) { + x, y := bench_x, bench_y + for n := 0; n < b.N; n++ { + cswap{{ .FIELD}}(&x, &y, 1) + cswap{{ .FIELD}}(&x, &y, 0) + } +} + +func BenchmarkMod(b *testing.B) { + x := bench_x + for n := 0; n < b.N; n++ { + mod{{ .FIELD}}(&x) + } +} + +func BenchmarkX2AddLazy(b *testing.B) { + x, y, z := bench_z, bench_z, bench_z + for n := 0; n < b.N; n++ { + adl{{ .FIELD}}(&x, &y, &z) + } +} + +func BenchmarkX2SubLazy(b *testing.B) { + x, y, z := bench_z, bench_z, bench_z + for n := 0; n < b.N; n++ { + sul{{ .FIELD}}(&x, &y, &z) + } +} diff --git a/src/circl/dh/sidh/internal/templates/core.gotemp b/src/circl/dh/sidh/internal/templates/core.gotemp new file mode 100644 index 00000000000..a1ce27a3a6e --- /dev/null +++ b/src/circl/dh/sidh/internal/templates/core.gotemp @@ -0,0 +1,282 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package {{ .PACKAGE}} + +import ( + . "circl/dh/sidh/internal/common" +) + +// ----------------------------------------------------------------------------- +// Functions for traversing isogeny trees acoording to strategy. Key type 'A' is +// + +// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed +// for public key generation. +func traverseTreePublicKeyA(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny4 + + cparam := CalcCurveParamsEquiv4(curve) + strat := params.A.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow2k(xR, &cparam, 2*k) + i += int(k) + } + cparam = phi.GenerateCurve(xR) + + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + *phiP = phi.EvaluatePoint(phiP) + *phiQ = phi.EvaluatePoint(phiQ) + *phiR = phi.EvaluatePoint(phiR) + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Traverses isogeny tree in order to compute xR needed +// for public key generation. +func traverseTreeSharedKeyA(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny4 + + cparam := CalcCurveParamsEquiv4(curve) + strat := params.A.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow2k(xR, &cparam, 2*k) + i += int(k) + } + cparam = phi.GenerateCurve(xR) + + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed +// for public key generation. +func traverseTreePublicKeyB(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny3 + + cparam := CalcCurveParamsEquiv3(curve) + strat := params.B.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow3k(xR, &cparam, k) + i += int(k) + } + + cparam = phi.GenerateCurve(xR) + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + + *phiP = phi.EvaluatePoint(phiP) + *phiQ = phi.EvaluatePoint(phiQ) + *phiR = phi.EvaluatePoint(phiR) + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed +// for public key generation. +func traverseTreeSharedKeyB(curve *ProjectiveCurveParameters, xR *ProjectivePoint) { + var points = make([]ProjectivePoint, 0, 8) + var indices = make([]int, 0, 8) + var i, sIdx int + var phi isogeny3 + + cparam := CalcCurveParamsEquiv3(curve) + strat := params.B.IsogenyStrategy + stratSz := len(strat) + + for j := 1; j <= stratSz; j++ { + for i <= stratSz-j { + points = append(points, *xR) + indices = append(indices, i) + + k := strat[sIdx] + sIdx++ + Pow3k(xR, &cparam, k) + i += int(k) + } + + cparam = phi.GenerateCurve(xR) + for k := 0; k < len(points); k++ { + points[k] = phi.EvaluatePoint(&points[k]) + } + + // pop xR from points + *xR, points = points[len(points)-1], points[:len(points)-1] + i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1] + } +} + +// Generate a public key in the 2-torsion group. Public key is a set +// of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) +func PublicKeyGenA(pub3Pt *[3]Fp2, prvBytes []byte) { + var xPA, xQA, xRA ProjectivePoint + var xPB, xQB, xRB, xR ProjectivePoint + var invZP, invZQ, invZR Fp2 + var phi isogeny4 + + // Load points for A + xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} + xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} + xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} + + // Load points for B + xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} + xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} + xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} + + // Find isogeny kernel + xR = ScalarMul3Pt(¶ms.InitCurve, &xPA, &xQA, &xRA, params.A.SecretBitLen, prvBytes) + traverseTreePublicKeyA(¶ms.InitCurve, &xR, &xPB, &xQB, &xRB) + + // Secret isogeny + phi.GenerateCurve(&xR) + xPA = phi.EvaluatePoint(&xPB) + xQA = phi.EvaluatePoint(&xQB) + xRA = phi.EvaluatePoint(&xRB) + Fp2Batch3Inv(&xPA.Z, &xQA.Z, &xRA.Z, &invZP, &invZQ, &invZR) + + mul(&pub3Pt[0], &xPA.X, &invZP) + mul(&pub3Pt[1], &xQA.X, &invZQ) + mul(&pub3Pt[2], &xRA.X, &invZR) +} + +// Generate a public key in the 2-torsion group. Public key is a set +// of three x-coordinates: xP,xQ,x(P-Q), where P,Q are points on E_a(Fp2) +func PublicKeyGenB(pub3Pt *[3]Fp2, prvBytes []byte) { + var xPB, xQB, xRB, xR ProjectivePoint + var xPA, xQA, xRA ProjectivePoint + var invZP, invZQ, invZR Fp2 + var phi isogeny3 + + // Load points for B + xRB = ProjectivePoint{X: params.B.AffineR, Z: params.OneFp2} + xQB = ProjectivePoint{X: params.B.AffineQ, Z: params.OneFp2} + xPB = ProjectivePoint{X: params.B.AffineP, Z: params.OneFp2} + + // Load points for A + xPA = ProjectivePoint{X: params.A.AffineP, Z: params.OneFp2} + xQA = ProjectivePoint{X: params.A.AffineQ, Z: params.OneFp2} + xRA = ProjectivePoint{X: params.A.AffineR, Z: params.OneFp2} + + // Find isogeny kernel + xR = ScalarMul3Pt(¶ms.InitCurve, &xPB, &xQB, &xRB, params.B.SecretBitLen, prvBytes) + traverseTreePublicKeyB(¶ms.InitCurve, &xR, &xPA, &xQA, &xRA) + + phi.GenerateCurve(&xR) + xPB = phi.EvaluatePoint(&xPA) + xQB = phi.EvaluatePoint(&xQA) + xRB = phi.EvaluatePoint(&xRA) + Fp2Batch3Inv(&xPB.Z, &xQB.Z, &xRB.Z, &invZP, &invZQ, &invZR) + + mul(&pub3Pt[0], &xPB.X, &invZP) + mul(&pub3Pt[1], &xQB.X, &invZQ) + mul(&pub3Pt[2], &xRB.X, &invZR) +} + +// ----------------------------------------------------------------------------- +// Key agreement functions +// + +// Establishing shared keys in in 2-torsion group +func DeriveSecretA(ss, prv []byte, pub3Pt *[3]Fp2) { + var xP, xQ, xQmP ProjectivePoint + var xR ProjectivePoint + var phi isogeny4 + var jInv Fp2 + + // Recover curve coefficients + cparam := params.InitCurve + RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) + + // Find kernel of the morphism + xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} + xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} + xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} + xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.A.SecretBitLen, prv) + + // Traverse isogeny tree + traverseTreeSharedKeyA(&cparam, &xR) + + // Calculate j-invariant on isogeneus curve + c := phi.GenerateCurve(&xR) + RecoverCurveCoefficients4(&cparam, &c) + Jinvariant(&cparam, &jInv) + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(ss, &jInv, params.Bytelen) +} + +// Establishing shared keys in in 3-torsion group +func DeriveSecretB(ss, prv []byte, pub3Pt *[3]Fp2) { + var xP, xQ, xQmP ProjectivePoint + var xR ProjectivePoint + var phi isogeny3 + var jInv Fp2 + + // Recover curve coefficients + cparam := params.InitCurve + RecoverCoordinateA(&cparam, &pub3Pt[0], &pub3Pt[1], &pub3Pt[2]) + + // Find kernel of the morphism + xP = ProjectivePoint{X: pub3Pt[0], Z: params.OneFp2} + xQ = ProjectivePoint{X: pub3Pt[1], Z: params.OneFp2} + xQmP = ProjectivePoint{X: pub3Pt[2], Z: params.OneFp2} + xR = ScalarMul3Pt(&cparam, &xP, &xQ, &xQmP, params.B.SecretBitLen, prv) + + // Traverse isogeny tree + traverseTreeSharedKeyB(&cparam, &xR) + + // Calculate j-invariant on isogeneus curve + c := phi.GenerateCurve(&xR) + RecoverCurveCoefficients3(&cparam, &c) + Jinvariant(&cparam, &jInv) + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(ss, &jInv, params.Bytelen) +} diff --git a/src/circl/dh/sidh/internal/templates/curve.gotemp b/src/circl/dh/sidh/internal/templates/curve.gotemp new file mode 100644 index 00000000000..e272804db83 --- /dev/null +++ b/src/circl/dh/sidh/internal/templates/curve.gotemp @@ -0,0 +1,362 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package {{ .PACKAGE}} + +import ( + . "circl/dh/sidh/internal/common" +) + +// Stores isogeny 3 curve constants +type isogeny3 struct { + K1 Fp2 + K2 Fp2 +} + +// Stores isogeny 4 curve constants +type isogeny4 struct { + isogeny3 + K3 Fp2 +} + +// Computes j-invariant for a curve y2=x3+A/Cx+x with A,C in F_(p^2). Result +// is returned in jBytes buffer, encoded in little-endian format. Caller +// provided jBytes buffer has to be big enough to j-invariant value. In case +// of SIDH, buffer size must be at least size of shared secret. +// Implementation corresponds to Algorithm 9 from SIKE. +func Jinvariant(cparams *ProjectiveCurveParameters, j *Fp2) { + var t0, t1 Fp2 + + sqr(j, &cparams.A) // j = A^2 + sqr(&t1, &cparams.C) // t1 = C^2 + add(&t0, &t1, &t1) // t0 = t1 + t1 + sub(&t0, j, &t0) // t0 = j - t0 + sub(&t0, &t0, &t1) // t0 = t0 - t1 + sub(j, &t0, &t1) // t0 = t0 - t1 + sqr(&t1, &t1) // t1 = t1^2 + mul(j, j, &t1) // j = j * t1 + add(&t0, &t0, &t0) // t0 = t0 + t0 + add(&t0, &t0, &t0) // t0 = t0 + t0 + sqr(&t1, &t0) // t1 = t0^2 + mul(&t0, &t0, &t1) // t0 = t0 * t1 + add(&t0, &t0, &t0) // t0 = t0 + t0 + add(&t0, &t0, &t0) // t0 = t0 + t0 + inv(j, j) // j = 1/j + mul(j, &t0, j) // j = t0 * j +} + +// Given affine points x(P), x(Q) and x(Q-P) in a extension field F_{p^2}, function +// recorvers projective coordinate A of a curve. This is Algorithm 10 from SIKE. +func RecoverCoordinateA(curve *ProjectiveCurveParameters, xp, xq, xr *Fp2) { + var t0, t1 Fp2 + + add(&t1, xp, xq) // t1 = Xp + Xq + mul(&t0, xp, xq) // t0 = Xp * Xq + mul(&curve.A, xr, &t1) // A = X(q-p) * t1 + add(&curve.A, &curve.A, &t0) // A = A + t0 + mul(&t0, &t0, xr) // t0 = t0 * X(q-p) + sub(&curve.A, &curve.A, ¶ms.OneFp2) // A = A - 1 + add(&t0, &t0, &t0) // t0 = t0 + t0 + add(&t1, &t1, xr) // t1 = t1 + X(q-p) + add(&t0, &t0, &t0) // t0 = t0 + t0 + sqr(&curve.A, &curve.A) // A = A^2 + inv(&t0, &t0) // t0 = 1/t0 + mul(&curve.A, &curve.A, &t0) // A = A * t0 + sub(&curve.A, &curve.A, &t1) // A = A - t1 +} + +// Computes equivalence (A:C) ~ (A+2C : A-2C) +func CalcCurveParamsEquiv3(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { + var coef CurveCoefficientsEquiv + var c2 Fp2 + + add(&c2, &cparams.C, &cparams.C) + // A24p = A+2*C + add(&coef.A, &cparams.A, &c2) + // A24m = A-2*C + sub(&coef.C, &cparams.A, &c2) + return coef +} + +// Computes equivalence (A:C) ~ (A+2C : 4C) +func CalcCurveParamsEquiv4(cparams *ProjectiveCurveParameters) CurveCoefficientsEquiv { + var coefEq CurveCoefficientsEquiv + + add(&coefEq.C, &cparams.C, &cparams.C) + // A24p = A+2C + add(&coefEq.A, &cparams.A, &coefEq.C) + // C24 = 4*C + add(&coefEq.C, &coefEq.C, &coefEq.C) + return coefEq +} + +// Helper function for RightToLeftLadder(). Returns A+2C / 4. +func CalcAplus2Over4(cparams *ProjectiveCurveParameters) (ret Fp2) { + var tmp Fp2 + + // 2C + add(&tmp, &cparams.C, &cparams.C) + // A+2C + add(&ret, &cparams.A, &tmp) + // 1/4C + add(&tmp, &tmp, &tmp) + inv(&tmp, &tmp) + // A+2C/4C + mul(&ret, &ret, &tmp) + return +} + +// Recovers (A:C) curve parameters from projectively equivalent (A+2C:A-2C). +func RecoverCurveCoefficients3(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { + add(&cparams.A, &coefEq.A, &coefEq.C) + // cparams.A = 2*(A+2C+A-2C) = 4A + add(&cparams.A, &cparams.A, &cparams.A) + // cparams.C = (A+2C-A+2C) = 4C + sub(&cparams.C, &coefEq.A, &coefEq.C) + return +} + +// Recovers (A:C) curve parameters from projectively equivalent (A+2C:4C). +func RecoverCurveCoefficients4(cparams *ProjectiveCurveParameters, coefEq *CurveCoefficientsEquiv) { + // cparams.C = (4C)*1/2=2C + mul(&cparams.C, &coefEq.C, ¶ms.HalfFp2) + // cparams.A = A+2C - 2C = A + sub(&cparams.A, &coefEq.A, &cparams.C) + // cparams.C = 2C * 1/2 = C + mul(&cparams.C, &cparams.C, ¶ms.HalfFp2) +} + +// Combined coordinate doubling and differential addition. Takes projective points +// P,Q,Q-P and (A+2C)/4C curve E coefficient. Returns 2*P and P+Q calculated on E. +// Function is used only by RightToLeftLadder. Corresponds to Algorithm 5 of SIKE +func xDbladd(P, Q, QmP *ProjectivePoint, a24 *Fp2) (dblP, PaQ ProjectivePoint) { + var t0, t1, t2 Fp2 + + xQmP, zQmP := &QmP.X, &QmP.Z + xPaQ, zPaQ := &PaQ.X, &PaQ.Z + x2P, z2P := &dblP.X, &dblP.Z + xP, zP := &P.X, &P.Z + xQ, zQ := &Q.X, &Q.Z + + add(&t0, xP, zP) // t0 = Xp+Zp + sub(&t1, xP, zP) // t1 = Xp-Zp + sqr(x2P, &t0) // 2P.X = t0^2 + sub(&t2, xQ, zQ) // t2 = Xq-Zq + add(xPaQ, xQ, zQ) // Xp+q = Xq+Zq + mul(&t0, &t0, &t2) // t0 = t0 * t2 + mul(z2P, &t1, &t1) // 2P.Z = t1 * t1 + mul(&t1, &t1, xPaQ) // t1 = t1 * Xp+q + sub(&t2, x2P, z2P) // t2 = 2P.X - 2P.Z + mul(x2P, x2P, z2P) // 2P.X = 2P.X * 2P.Z + mul(xPaQ, a24, &t2) // Xp+q = A24 * t2 + sub(zPaQ, &t0, &t1) // Zp+q = t0 - t1 + add(z2P, xPaQ, z2P) // 2P.Z = Xp+q + 2P.Z + add(xPaQ, &t0, &t1) // Xp+q = t0 + t1 + mul(z2P, z2P, &t2) // 2P.Z = 2P.Z * t2 + sqr(zPaQ, zPaQ) // Zp+q = Zp+q ^ 2 + sqr(xPaQ, xPaQ) // Xp+q = Xp+q ^ 2 + mul(zPaQ, xQmP, zPaQ) // Zp+q = Xq-p * Zp+q + mul(xPaQ, zQmP, xPaQ) // Xp+q = Zq-p * Xp+q + return +} + +// Given the curve parameters, xP = x(P), computes xP = x([2^k]P) +// Safe to overlap xP, x2P. +func Pow2k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { + var t0, t1 Fp2 + + x, z := &xP.X, &xP.Z + for i := uint32(0); i < k; i++ { + sub(&t0, x, z) // t0 = Xp - Zp + add(&t1, x, z) // t1 = Xp + Zp + sqr(&t0, &t0) // t0 = t0 ^ 2 + sqr(&t1, &t1) // t1 = t1 ^ 2 + mul(z, ¶ms.C, &t0) // Z2p = C24 * t0 + mul(x, z, &t1) // X2p = Z2p * t1 + sub(&t1, &t1, &t0) // t1 = t1 - t0 + mul(&t0, ¶ms.A, &t1) // t0 = A24+ * t1 + add(z, z, &t0) // Z2p = Z2p + t0 + mul(z, z, &t1) // Zp = Z2p * t1 + } +} + +// Given the curve parameters, xP = x(P), and k >= 0, compute xP = x([3^k]P). +// +// Safe to overlap xP, xR. +func Pow3k(xP *ProjectivePoint, params *CurveCoefficientsEquiv, k uint32) { + var t0, t1, t2, t3, t4, t5, t6 Fp2 + + x, z := &xP.X, &xP.Z + for i := uint32(0); i < k; i++ { + sub(&t0, x, z) // t0 = Xp - Zp + sqr(&t2, &t0) // t2 = t0^2 + add(&t1, x, z) // t1 = Xp + Zp + sqr(&t3, &t1) // t3 = t1^2 + add(&t4, &t1, &t0) // t4 = t1 + t0 + sub(&t0, &t1, &t0) // t0 = t1 - t0 + sqr(&t1, &t4) // t1 = t4^2 + sub(&t1, &t1, &t3) // t1 = t1 - t3 + sub(&t1, &t1, &t2) // t1 = t1 - t2 + mul(&t5, &t3, ¶ms.A) // t5 = t3 * A24+ + mul(&t3, &t3, &t5) // t3 = t5 * t3 + mul(&t6, &t2, ¶ms.C) // t6 = t2 * A24- + mul(&t2, &t2, &t6) // t2 = t2 * t6 + sub(&t3, &t2, &t3) // t3 = t2 - t3 + sub(&t2, &t5, &t6) // t2 = t5 - t6 + mul(&t1, &t2, &t1) // t1 = t2 * t1 + add(&t2, &t3, &t1) // t2 = t3 + t1 + sqr(&t2, &t2) // t2 = t2^2 + mul(x, &t2, &t4) // X3p = t2 * t4 + sub(&t1, &t3, &t1) // t1 = t3 - t1 + sqr(&t1, &t1) // t1 = t1^2 + mul(z, &t1, &t0) // Z3p = t1 * t0 + } +} + +// Set (y1, y2, y3) = (1/x1, 1/x2, 1/x3). +// +// All xi, yi must be distinct. +func Fp2Batch3Inv(x1, x2, x3, y1, y2, y3 *Fp2) { + var x1x2, t Fp2 + + mul(&x1x2, x1, x2) // x1*x2 + mul(&t, &x1x2, x3) // 1/(x1*x2*x3) + inv(&t, &t) + mul(y1, &t, x2) // 1/x1 + mul(y1, y1, x3) + mul(y2, &t, x1) // 1/x2 + mul(y2, y2, x3) + mul(y3, &t, &x1x2) // 1/x3 +} + +// Scalarmul3Pt is a right-to-left point multiplication that given the +// x-coordinate of P, Q and P-Q calculates the x-coordinate of R=Q+[scalar]P. +// nbits must be smaller or equal to len(scalar). +func ScalarMul3Pt(cparams *ProjectiveCurveParameters, P, Q, PmQ *ProjectivePoint, nbits uint, scalar []uint8) ProjectivePoint { + var R0, R2, R1 ProjectivePoint + aPlus2Over4 := CalcAplus2Over4(cparams) + R1 = *P + R2 = *PmQ + R0 = *Q + + // Iterate over the bits of the scalar, bottom to top + prevBit := uint8(0) + for i := uint(0); i < nbits; i++ { + bit := (scalar[i>>3] >> (i & 7) & 1) + swap := prevBit ^ bit + prevBit = bit + cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, swap) + R0, R2 = xDbladd(&R0, &R2, &R1, &aPlus2Over4) + } + cswap(&R1.X, &R1.Z, &R2.X, &R2.Z, prevBit) + return R1 +} + +// Given a three-torsion point p = x(PB) on the curve E_(A:C), construct the +// three-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). +// +// Input: (XP_3: ZP_3), where P_3 has exact order 3 on E_A/C +// Output: * Curve coordinates (A' + 2C', A' - 2C') corresponding to E_A'/C' = A_E/C/ +// * Isogeny phi with constants in F_p^2 +func (phi *isogeny3) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { + var t0, t1, t2, t3, t4 Fp2 + var coefEq CurveCoefficientsEquiv + var K1, K2 = &phi.K1, &phi.K2 + + sub(K1, &p.X, &p.Z) // K1 = XP3 - ZP3 + sqr(&t0, K1) // t0 = K1^2 + add(K2, &p.X, &p.Z) // K2 = XP3 + ZP3 + sqr(&t1, K2) // t1 = K2^2 + add(&t2, &t0, &t1) // t2 = t0 + t1 + add(&t3, K1, K2) // t3 = K1 + K2 + sqr(&t3, &t3) // t3 = t3^2 + sub(&t3, &t3, &t2) // t3 = t3 - t2 + add(&t2, &t1, &t3) // t2 = t1 + t3 + add(&t3, &t3, &t0) // t3 = t3 + t0 + add(&t4, &t3, &t0) // t4 = t3 + t0 + add(&t4, &t4, &t4) // t4 = t4 + t4 + add(&t4, &t1, &t4) // t4 = t1 + t4 + mul(&coefEq.C, &t2, &t4) // A24m = t2 * t4 + add(&t4, &t1, &t2) // t4 = t1 + t2 + add(&t4, &t4, &t4) // t4 = t4 + t4 + add(&t4, &t0, &t4) // t4 = t0 + t4 + mul(&t4, &t3, &t4) // t4 = t3 * t4 + sub(&t0, &t4, &coefEq.C) // t0 = t4 - A24m + add(&coefEq.A, &coefEq.C, &t0) // A24p = A24m + t0 + return coefEq +} + +// Given a 3-isogeny phi and a point pB = x(PB), compute x(QB), the x-coordinate +// of the image QB = phi(PB) of PB under phi : E_(A:C) -> E_(A':C'). +// +// The output xQ = x(Q) is then a point on the curve E_(A':C'); the curve +// parameters are returned by the GenerateCurve function used to construct phi. +func (phi *isogeny3) EvaluatePoint(p *ProjectivePoint) ProjectivePoint { + var t0, t1, t2 Fp2 + var q ProjectivePoint + var K1, K2 = &phi.K1, &phi.K2 + var px, pz = &p.X, &p.Z + + add(&t0, px, pz) // t0 = XQ + ZQ + sub(&t1, px, pz) // t1 = XQ - ZQ + mul(&t0, K1, &t0) // t2 = K1 * t0 + mul(&t1, K2, &t1) // t1 = K2 * t1 + add(&t2, &t0, &t1) // t2 = t0 + t1 + sub(&t0, &t1, &t0) // t0 = t1 - t0 + sqr(&t2, &t2) // t2 = t2 ^ 2 + sqr(&t0, &t0) // t0 = t0 ^ 2 + mul(&q.X, px, &t2) // XQ'= XQ * t2 + mul(&q.Z, pz, &t0) // ZQ'= ZQ * t0 + return q +} + +// Given a four-torsion point p = x(PB) on the curve E_(A:C), construct the +// four-isogeny phi : E_(A:C) -> E_(A:C)/ = E_(A':C'). +// +// Input: (XP_4: ZP_4), where P_4 has exact order 4 on E_A/C +// Output: * Curve coordinates (A' + 2C', 4C') corresponding to E_A'/C' = A_E/C/ +// * Isogeny phi with constants in F_p^2 +func (phi *isogeny4) GenerateCurve(p *ProjectivePoint) CurveCoefficientsEquiv { + var coefEq CurveCoefficientsEquiv + var xp4, zp4 = &p.X, &p.Z + var K1, K2, K3 = &phi.K1, &phi.K2, &phi.K3 + + sub(K2, xp4, zp4) + add(K3, xp4, zp4) + sqr(K1, zp4) + add(K1, K1, K1) + sqr(&coefEq.C, K1) + add(K1, K1, K1) + sqr(&coefEq.A, xp4) + add(&coefEq.A, &coefEq.A, &coefEq.A) + sqr(&coefEq.A, &coefEq.A) + return coefEq +} + +// Given a 4-isogeny phi and a point xP = x(P), compute x(Q), the x-coordinate +// of the image Q = phi(P) of P under phi : E_(A:C) -> E_(A':C'). +// +// Input: Isogeny returned by GenerateCurve and point q=(Qx,Qz) from E0_A/C +// Output: Corresponding point q from E1_A'/C', where E1 is 4-isogenous to E0 +func (phi *isogeny4) EvaluatePoint(p *ProjectivePoint) ProjectivePoint { + var t0, t1 Fp2 + var q = *p + var xq, zq = &q.X, &q.Z + var K1, K2, K3 = &phi.K1, &phi.K2, &phi.K3 + + add(&t0, xq, zq) + sub(&t1, xq, zq) + mul(xq, &t0, K2) + mul(zq, &t1, K3) + mul(&t0, &t0, &t1) + mul(&t0, &t0, K1) + add(&t1, xq, zq) + sub(zq, xq, zq) + sqr(&t1, &t1) + sqr(zq, zq) + add(xq, &t0, &t1) + sub(&t0, zq, &t0) + mul(xq, xq, &t1) + mul(zq, zq, &t0) + return q +} diff --git a/src/circl/dh/sidh/internal/templates/curve_test.gotemp b/src/circl/dh/sidh/internal/templates/curve_test.gotemp new file mode 100644 index 00000000000..487c13b774a --- /dev/null +++ b/src/circl/dh/sidh/internal/templates/curve_test.gotemp @@ -0,0 +1,100 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package {{ .PACKAGE}} + +import ( + "bytes" + "testing" + + . "circl/dh/sidh/internal/common" +) + +func vartimeEqProjFp2(lhs, rhs *ProjectivePoint) bool { + var t0, t1 Fp2 + mul(&t0, &lhs.X, &rhs.Z) + mul(&t1, &lhs.Z, &rhs.X) + return vartimeEqFp2(&t0, &t1) +} + +func toAffine(point *ProjectivePoint) *Fp2 { + var affineX Fp2 + inv(&affineX, &point.Z) + mul(&affineX, &affineX, &point.X) + return &affineX +} + +func Test_jInvariant(t *testing.T) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + var jbufRes = make([]byte, params.SharedSecretSize) + var jbufExp = make([]byte, params.SharedSecretSize) + var jInv Fp2 + + Jinvariant(&curve, &jInv) + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(jbufRes, &jInv, params.Bytelen) + + jInv = expectedJ + FromMontgomery(&jInv, &jInv) + Fp2ToBytes(jbufExp, &jInv, params.Bytelen) + + if !bytes.Equal(jbufRes[:], jbufExp[:]) { + t.Error("Computed incorrect j-invariant: found\n", jbufRes, "\nexpected\n", jbufExp) + } +} + +func TestProjectivePointVartimeEq(t *testing.T) { + var xP ProjectivePoint + + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + xQ := xP + + // Scale xQ, which results in the same projective point + mul(&xQ.X, &xQ.X, &curveA) + mul(&xQ.Z, &xQ.Z, &curveA) + if !vartimeEqProjFp2(&xP, &xQ) { + t.Error("Expected the scaled point to be equal to the original") + } +} + +func TestPointMulVersusSage(t *testing.T) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + var cparams = CalcCurveParamsEquiv4(&curve) + var xP ProjectivePoint + + // x 2 + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + Pow2k(&xP, &cparams, 1) + afxQ := toAffine(&xP) + if !vartimeEqFp2(afxQ, &affineXP2) { + t.Error("\nExpected\n", affineXP2, "\nfound\n", afxQ) + } + + // x 4 + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + Pow2k(&xP, &cparams, 2) + afxQ = toAffine(&xP) + if !vartimeEqFp2(afxQ, &affineXP4) { + t.Error("\nExpected\n", affineXP4, "\nfound\n", afxQ) + } +} + +func TestPointMul9VersusSage(t *testing.T) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + var cparams = CalcCurveParamsEquiv3(&curve) + var xP ProjectivePoint + + xP = ProjectivePoint{X: affineXP, Z: params.OneFp2} + Pow3k(&xP, &cparams, 2) + afxQ := toAffine(&xP) + if !vartimeEqFp2(afxQ, &affineXP9) { + t.Error("\nExpected\n", affineXP9, "\nfound\n", afxQ) + } +} + +func BenchmarkThreePointLadder(b *testing.B) { + var curve = ProjectiveCurveParameters{A: curveA, C: curveC} + for n := 0; n < b.N; n++ { + ScalarMul3Pt(&curve, &threePointLadderInputs[0], &threePointLadderInputs[1], &threePointLadderInputs[2], uint(len(scalar3Pt)*8), scalar3Pt[:]) + } +} diff --git a/src/circl/dh/sidh/internal/templates/fp2.gotemp b/src/circl/dh/sidh/internal/templates/fp2.gotemp new file mode 100644 index 00000000000..1f9e612b1f1 --- /dev/null +++ b/src/circl/dh/sidh/internal/templates/fp2.gotemp @@ -0,0 +1,195 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package {{ .PACKAGE}} + +import ( + "circl/dh/sidh/internal/common" +) + +// Montgomery multiplication. Input values must be already +// in Montgomery domain. +func mulP(dest, lhs, rhs *common.Fp) { + var ab common.FpX2 + mul{{ .FIELD}}(&ab, lhs, rhs) // = a*b*R*R + rdc{{ .FIELD}}(dest, &ab) // = a*b*R mod p +} + +// Set dest = x^((p-3)/4). If x is square, this is 1/sqrt(x). +// Uses variation of sliding-window algorithm from with window size +// of 5 and least to most significant bit sliding (left-to-right) +// See HAC 14.85 for general description. +// +// Allowed to overlap x with dest. +// All values in Montgomery domains +// Set dest = x^(2^k), for k >= 1, by repeated squarings. +func p34(dest, x *common.Fp) { + var lookup [16]common.Fp + + // This performs sum(powStrategy) + 1 squarings and len(lookup) + len(mulStrategy) + // multiplications. + powStrategy := {{ .P34_POW_STRATEGY}} + mulStrategy := {{ .P34_MUL_STRATEGY}} + initialMul := uint8({{ .P34_INITIAL_MUL}}) + + // Precompute lookup table of odd multiples of x for window + // size k=5. + var xx common.Fp + mulP(&xx, x, x) + lookup[0] = *x + for i := 1; i < 16; i++ { + mulP(&lookup[i], &lookup[i-1], &xx) + } + + // Now lookup = {x, x^3, x^5, ... } + // so that lookup[i] = x^{2*i + 1} + // so that lookup[k/2] = x^k, for odd k + *dest = lookup[initialMul] + for i := uint8(0); i < uint8(len(powStrategy)); i++ { + mulP(dest, dest, dest) + for j := uint8(1); j < powStrategy[i]; j++ { + mulP(dest, dest, dest) + } + mulP(dest, dest, &lookup[mulStrategy[i]]) + } +} + +func add(dest, lhs, rhs *common.Fp2) { + add{{ .FIELD}}(&dest.A, &lhs.A, &rhs.A) + add{{ .FIELD}}(&dest.B, &lhs.B, &rhs.B) +} + +func sub(dest, lhs, rhs *common.Fp2) { + sub{{ .FIELD}}(&dest.A, &lhs.A, &rhs.A) + sub{{ .FIELD}}(&dest.B, &lhs.B, &rhs.B) +} + +func mul(dest, lhs, rhs *common.Fp2) { + var bMinA, cMinD common.Fp + var ac, bd common.FpX2 + var adPlusBc common.FpX2 + var acMinBd common.FpX2 + + // Let (a,b,c,d) = (lhs.a,lhs.b,rhs.a,rhs.b). + // + // (a + bi)*(c + di) = (a*c - b*d) + (a*d + b*c)i + // + // Use Karatsuba's trick: note that + // + // (b - a)*(c - d) = (b*c + a*d) - a*c - b*d + // + // so (a*d + b*c) = (b-a)*(c-d) + a*c + b*d. + mul{{ .FIELD}}(&ac, &lhs.A, &rhs.A) // = a*c*R*R + mul{{ .FIELD}}(&bd, &lhs.B, &rhs.B) // = b*d*R*R + sub{{ .FIELD}}(&bMinA, &lhs.B, &lhs.A) // = (b-a)*R + sub{{ .FIELD}}(&cMinD, &rhs.A, &rhs.B) // = (c-d)*R + mul{{ .FIELD}}(&adPlusBc, &bMinA, &cMinD) // = (b-a)*(c-d)*R*R + adl{{ .FIELD}}(&adPlusBc, &adPlusBc, &ac) // = ((b-a)*(c-d) + a*c)*R*R + adl{{ .FIELD}}(&adPlusBc, &adPlusBc, &bd) // = ((b-a)*(c-d) + a*c + b*d)*R*R + rdc{{ .FIELD}}(&dest.B, &adPlusBc) // = (a*d + b*c)*R mod p + sul{{ .FIELD}}(&acMinBd, &ac, &bd) // = (a*c - b*d)*R*R + rdc{{ .FIELD}}(&dest.A, &acMinBd) // = (a*c - b*d)*R mod p +} + +// Set dest = 1/x +// +// Allowed to overlap dest with x. +// +// Returns dest to allow chaining operations. +func inv(dest, x *common.Fp2) { + var e1, e2 common.FpX2 + var f1, f2 common.Fp + + // We want to compute + // + // 1 1 (a - bi) (a - bi) + // -------- = -------- -------- = ----------- + // (a + bi) (a + bi) (a - bi) (a^2 + b^2) + // + // Letting c = 1/(a^2 + b^2), this is + // + // 1/(a+bi) = a*c - b*ci. + + mul{{ .FIELD}}(&e1, &x.A, &x.A) // = a*a*R*R + mul{{ .FIELD}}(&e2, &x.B, &x.B) // = b*b*R*R + adl{{ .FIELD}}(&e1, &e1, &e2) // = (a^2 + b^2)*R*R + rdc{{ .FIELD}}(&f1, &e1) // = (a^2 + b^2)*R mod p + // Now f1 = a^2 + b^2 + + mulP(&f2, &f1, &f1) + p34(&f2, &f2) + mulP(&f2, &f2, &f2) + mulP(&f2, &f2, &f1) + + mul{{ .FIELD}}(&e1, &x.A, &f2) + rdc{{ .FIELD}}(&dest.A, &e1) + + sub{{ .FIELD}}(&f1, &common.Fp{}, &x.B) + mul{{ .FIELD}}(&e1, &f1, &f2) + rdc{{ .FIELD}}(&dest.B, &e1) +} + +func sqr(dest, x *common.Fp2) { + var a2, aPlusB, aMinusB common.Fp + var a2MinB2, ab2 common.FpX2 + + a := &x.A + b := &x.B + + // (a + bi)*(a + bi) = (a^2 - b^2) + 2abi. + add{{ .FIELD}}(&a2, a, a) // = a*R + a*R = 2*a*R + add{{ .FIELD}}(&aPlusB, a, b) // = a*R + b*R = (a+b)*R + sub{{ .FIELD}}(&aMinusB, a, b) // = a*R - b*R = (a-b)*R + mul{{ .FIELD}}(&a2MinB2, &aPlusB, &aMinusB) // = (a+b)*(a-b)*R*R = (a^2 - b^2)*R*R + mul{{ .FIELD}}(&ab2, &a2, b) // = 2*a*b*R*R + rdc{{ .FIELD}}(&dest.A, &a2MinB2) // = (a^2 - b^2)*R mod p + rdc{{ .FIELD}}(&dest.B, &ab2) // = 2*a*b*R mod p +} + +// In case choice == 1, performs following swap in constant time: +// xPx <-> xQx +// xPz <-> xQz +// Otherwise returns xPx, xPz, xQx, xQz unchanged +func cswap(xPx, xPz, xQx, xQz *common.Fp2, choice uint8) { + cswap{{ .FIELD}}(&xPx.A, &xQx.A, choice) + cswap{{ .FIELD}}(&xPx.B, &xQx.B, choice) + cswap{{ .FIELD}}(&xPz.A, &xQz.A, choice) + cswap{{ .FIELD}}(&xPz.B, &xQz.B, choice) +} + +// Converts in.A and in.B to Montgomery domain and stores +// in 'out' +// out.A = in.A * R mod p +// out.B = in.B * R mod p +// Performs v = v*R^2*R^(-1) mod p, for both in.A and in.B +func ToMontgomery(out, in *common.Fp2) { + var aRR common.FpX2 + + // a*R*R + mul{{ .FIELD}}(&aRR, &in.A, &{{ .FIELD}}R2) + // a*R mod p + rdc{{ .FIELD}}(&out.A, &aRR) + mul{{ .FIELD}}(&aRR, &in.B, &{{ .FIELD}}R2) + rdc{{ .FIELD}}(&out.B, &aRR) +} + +// Converts in.A and in.B from Montgomery domain and stores +// in 'out' +// out.A = in.A mod p +// out.B = in.B mod p +// +// After returning from the call 'in' is not modified. +func FromMontgomery(out, in *common.Fp2) { + var aR common.FpX2 + + // convert from montgomery domain + copy(aR[:], in.A[:]) + rdc{{ .FIELD}}(&out.A, &aR) // = a mod p in [0, 2p) + mod{{ .FIELD}}(&out.A) // = a mod p in [0, p) + for i := range aR { + aR[i] = 0 + } + copy(aR[:], in.B[:]) + rdc{{ .FIELD}}(&out.B, &aR) + mod{{ .FIELD}}(&out.B) +} diff --git a/src/circl/dh/sidh/internal/templates/fp2_test.gotemp b/src/circl/dh/sidh/internal/templates/fp2_test.gotemp new file mode 100644 index 00000000000..3bab4442e47 --- /dev/null +++ b/src/circl/dh/sidh/internal/templates/fp2_test.gotemp @@ -0,0 +1,245 @@ +// Code generated by go generate; DO NOT EDIT. +// This file was generated by robots. + +package {{ .PACKAGE}} + +import ( + "math/rand" + "reflect" + "testing" + "testing/quick" + + "circl/dh/sidh/internal/common" +) + +type testParams struct { + Point common.ProjectivePoint + Cparam common.ProjectiveCurveParameters + ExtElem common.Fp2 +} + +// Returns true if lhs = rhs. Takes variable time. +func vartimeEqFp2(lhs, rhs *common.Fp2) bool { + a := *lhs + b := *rhs + + mod{{ .FIELD}}(&a.A) + mod{{ .FIELD}}(&a.B) + mod{{ .FIELD}}(&b.A) + mod{{ .FIELD}}(&b.B) + + eq := true + for i := 0; i < FpWords && eq; i++ { + eq = eq && (a.A[i] == b.A[i]) + eq = eq && (a.B[i] == b.B[i]) + } + return eq +} + +func (testParams) generateFp2(rand *rand.Rand) common.Fp2 { + // Generation strategy: low limbs taken from [0,2^64); high limb + // taken from smaller range + // + // Size hint is ignored since all elements are fixed size. + // + // Field elements taken in range [0,2p). Emulate this by capping + // the high limb by the top digit of 2*p-1: + // + // sage: (2*p-1).digits(2^64)[-1] + // + // This still allows generating values >= 2p, but hopefully that + // excess is OK (and if it's not, we'll find out, because it's for + // testing...) + highLimb := rand.Uint64() % {{ .FIELD}}x2[FpWords-1] + fpElementGen := func() (fp common.Fp) { + for i := 0; i < (FpWords - 1); i++ { + fp[i] = rand.Uint64() + } + fp[FpWords-1] = highLimb + return fp + } + return common.Fp2{A: fpElementGen(), B: fpElementGen()} +} + +func (c testParams) Generate(rand *rand.Rand, size int) reflect.Value { + return reflect.ValueOf( + testParams{ + common.ProjectivePoint{ + X: c.generateFp2(rand), + Z: c.generateFp2(rand), + }, + common.ProjectiveCurveParameters{ + A: c.generateFp2(rand), + C: c.generateFp2(rand), + }, + c.generateFp2(rand), + }) +} + +func TestOne(t *testing.T) { + var tmp common.Fp2 + + mul(&tmp, ¶ms.OneFp2, ¶ms.A.AffineP) + if !vartimeEqFp2(&tmp, ¶ms.A.AffineP) { + t.Error("Not equal 1") + } +} + +func TestFp2ToBytesRoundTrip(t *testing.T) { + roundTrips := func(x testParams) bool { + var xBytes = make([]byte, 2*params.Bytelen) + var xPrime common.Fp2 + + common.Fp2ToBytes(xBytes[:], &x.ExtElem, params.Bytelen) + common.BytesToFp2(&xPrime, xBytes[:], params.Bytelen) + return vartimeEqFp2(&xPrime, &x.ExtElem) + } + + if err := quick.Check(roundTrips, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2MulDistributesOverAdd(t *testing.T) { + mulDistributesOverAdd := func(x, y, z testParams) bool { + // Compute t1 = (x+y)*z + t1 := new(common.Fp2) + add(t1, &x.ExtElem, &y.ExtElem) + mul(t1, t1, &z.ExtElem) + + // Compute t2 = x*z + y*z + t2 := new(common.Fp2) + t3 := new(common.Fp2) + mul(t2, &x.ExtElem, &z.ExtElem) + mul(t3, &y.ExtElem, &z.ExtElem) + add(t2, t2, t3) + + return vartimeEqFp2(t1, t2) + } + + if err := quick.Check(mulDistributesOverAdd, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2MulIsAssociative(t *testing.T) { + isAssociative := func(x, y, z testParams) bool { + // Compute t1 = (x*y)*z + t1 := new(common.Fp2) + mul(t1, &x.ExtElem, &y.ExtElem) + mul(t1, t1, &z.ExtElem) + + // Compute t2 = (y*z)*x + t2 := new(common.Fp2) + mul(t2, &y.ExtElem, &z.ExtElem) + mul(t2, t2, &x.ExtElem) + + return vartimeEqFp2(t1, t2) + } + + if err := quick.Check(isAssociative, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2SquareMatchesMul(t *testing.T) { + sqrMatchesMul := func(x testParams) bool { + // Compute t1 = (x*x) + t1 := new(common.Fp2) + mul(t1, &x.ExtElem, &x.ExtElem) + + // Compute t2 = x^2 + t2 := new(common.Fp2) + sqr(t2, &x.ExtElem) + + return vartimeEqFp2(t1, t2) + } + + if err := quick.Check(sqrMatchesMul, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2Inv(t *testing.T) { + inverseIsCorrect := func(x testParams) bool { + z := new(common.Fp2) + inv(z, &x.ExtElem) + + // Now z = (1/x), so (z * x) * x == x + mul(z, z, &x.ExtElem) + mul(z, z, &x.ExtElem) + + return vartimeEqFp2(z, &x.ExtElem) + } + + // This is more expensive; run fewer tests + var quickCheckConfig = &quick.Config{MaxCount: (1 << 11)} + if err := quick.Check(inverseIsCorrect, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func TestFp2Batch3Inv(t *testing.T) { + batchInverseIsCorrect := func(x1, x2, x3 testParams) bool { + var x1Inv, x2Inv, x3Inv common.Fp2 + inv(&x1Inv, &x1.ExtElem) + inv(&x2Inv, &x2.ExtElem) + inv(&x3Inv, &x3.ExtElem) + + var y1, y2, y3 common.Fp2 + Fp2Batch3Inv(&x1.ExtElem, &x2.ExtElem, &x3.ExtElem, &y1, &y2, &y3) + + return (vartimeEqFp2(&x1Inv, &y1) && vartimeEqFp2(&x2Inv, &y2) && vartimeEqFp2(&x3Inv, &y3)) + } + + // This is more expensive; run fewer tests + var quickCheckConfig = &quick.Config{MaxCount: (1 << 8)} + if err := quick.Check(batchInverseIsCorrect, quickCheckConfig); err != nil { + t.Error(err) + } +} + +func BenchmarkFp2Mul(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + mul(w, z, z) + } +} + +func BenchmarkFp2Inv(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + inv(w, z) + } +} + +func BenchmarkFp2Square(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + sqr(w, z) + } +} + +func BenchmarkFp2Add(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + add(w, z, z) + } +} + +func BenchmarkFp2Sub(b *testing.B) { + z := &common.Fp2{A: bench_x, B: bench_y} + w := new(common.Fp2) + + for n := 0; n < b.N; n++ { + sub(w, z, z) + } +} diff --git a/src/circl/dh/sidh/internal/templates/gen.go b/src/circl/dh/sidh/internal/templates/gen.go new file mode 100644 index 00000000000..bfb9974527c --- /dev/null +++ b/src/circl/dh/sidh/internal/templates/gen.go @@ -0,0 +1,106 @@ +// The following directive is necessary to make the package coherent: + +// +build ignore + +// This program generates contributors.go. It can be invoked by running +// go generate +package main + +import ( + "fmt" + "os" + "strings" + "text/template" +) + +var p34 = map[string]struct { + pow_strategy string + mul_strategy string + mul_initial int +}{ + "P434": { + pow_strategy: "[]uint8{3, 10, 7, 5, 6, 5, 3, 8, 4, 7, 5, 6, 4, 5, 9, 6, 3, 11, 5, 5, 2, 8, 4, 7, 7, 8, 5, 6, 4, 8, 5, 2, 10, 6, 5, 4, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1}", + mul_strategy: "[]uint8{2, 15, 9, 8, 14, 12, 2, 8, 5, 15, 8, 15, 6, 6, 3, 2, 0, 10, 9, 13, 1, 12, 3, 7, 1, 10, 8, 11, 2, 15, 14, 1, 11, 12, 14, 3, 11, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0}", + mul_initial: 8, + }, + "P503": { + pow_strategy: "[]uint8{12, 5, 5, 2, 7, 11, 3, 8, 4, 11, 4, 7, 5, 6, 3, 7, 5, 7, 2, 12, 5, 6, 4, 6, 8, 6, 4, 7, 5, 5, 8, 5, 8, 5, 5, 8, 9, 3, 6, 2, 10, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3}", + mul_strategy: "[]uint8{12, 11, 10, 0, 1, 8, 3, 7, 1, 8, 3, 6, 7, 14, 2, 14, 14, 9, 0, 13, 9, 15, 5, 12, 7, 13, 7, 15, 6, 7, 9, 0, 5, 7, 6, 8, 8, 3, 7, 0, 10, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 3}", + mul_initial: 0, + }, + "P751": { + pow_strategy: "[]uint8{5, 7, 6, 2, 10, 4, 6, 9, 8, 5, 9, 4, 7, 5, 5, 4, 8, 3, 9, 5, 5, 4, 10, 4, 6, 6, 6, 5, 8, 9, 3, 4, 9, 4, 5, 6, 6, 2, 9, 4, 5, 5, 5, 7, 7, 9, 4, 6, 4, 8, 5, 8, 6, 6, 2, 9, 7, 4, 8, 8, 8, 4, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2}", + mul_strategy: "[]uint8{15, 11, 10, 0, 15, 3, 3, 3, 4, 4, 9, 7, 11, 11, 5, 3, 12, 2, 10, 8, 5, 2, 8, 3, 5, 4, 11, 4, 0, 9, 2, 1, 12, 7, 5, 14, 15, 0, 14, 5, 6, 4, 5, 13, 6, 9, 7, 15, 1, 14, 11, 15, 12, 5, 0, 10, 9, 7, 7, 10, 14, 6, 11, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 1}", + mul_initial: 13, + }, +} + +// P434 optimized implementation for +// ARM64 is not ported yet +var opt_arm = map[string]bool{ + "P434": false, + "P503": true, + "P751": true, +} + +// Generates an 'fileNameBase.go' from 'fileNameBase.gotemp' file +// for a given finite 'field'. Maps placeholders to 'values'. +func gen(field, fileNameBase string, values interface{}) { + // name of the output .go file + outFileName := fileNameBase + ".go" + out, err := os.Create(outFileName) + if err != nil { + panic("Cannot open file") + } + + // Template files are located in ../templates and have + // extension .gotemp + templateFile := "../templates/" + fileNameBase + ".gotemp" + t, err := template.ParseFiles(templateFile) + if err != nil { + panic(fmt.Sprintf("Cannot open template file %s", templateFile)) + } + + t.Execute(out, values) + err = out.Close() + if err != nil { + panic("Cant close generated file") + } +} + +func main() { + field := os.Args[1] + + s := struct { + FIELD string + PACKAGE string + P34_POW_STRATEGY string + P34_MUL_STRATEGY string + P34_INITIAL_MUL int + OPT_ARM bool + }{ + FIELD: field, + PACKAGE: strings.ToLower(field), + P34_POW_STRATEGY: p34[field].pow_strategy, + P34_MUL_STRATEGY: p34[field].mul_strategy, + P34_INITIAL_MUL: p34[field].mul_initial, + OPT_ARM: opt_arm[field], + } + + targets := map[string]interface{}{ + "arith_decl": s, + "arith_generic": s, + "curve": s, + "fp2": s, + "core": s, + + // tests + "arith_test": s, + "fp2_test": s, + "curve_test": s, + } + + for v, s := range targets { + gen(field, v, s) + } +} diff --git a/src/circl/dh/sidh/sidh.go b/src/circl/dh/sidh/sidh.go new file mode 100644 index 00000000000..ad911d86e11 --- /dev/null +++ b/src/circl/dh/sidh/sidh.go @@ -0,0 +1,289 @@ +package sidh + +import ( + "errors" + "io" + + "circl/dh/sidh/internal/common" + "circl/dh/sidh/internal/p434" + "circl/dh/sidh/internal/p503" + "circl/dh/sidh/internal/p751" +) + +// I keep it bool in order to be able to apply logical NOT. +type KeyVariant uint + +// Base type for public and private key. Used mainly to carry domain +// parameters. +type key struct { + // Domain parameters of the algorithm to be used with a key + params *common.SidhParams + // Flag indicates whether corresponds to 2-, 3-torsion group or SIKE + keyVariant KeyVariant +} + +// Defines operations on public key +type PublicKey struct { + key + // x-coordinates of P,Q,P-Q in this exact order + affine3Pt [3]common.Fp2 +} + +// Defines operations on private key +type PrivateKey struct { + key + // Secret key + Scalar []byte + // Used only by KEM + S []byte +} + +// Id's correspond to bitlength of the prime field characteristic +// Currently Fp751 is the only one supported by this implementation +const ( + Fp434 = common.Fp434 + Fp503 = common.Fp503 + Fp751 = common.Fp751 +) + +const ( + // First 2 bits identify SIDH variant third bit indicates + // whether key is a SIKE variant (set) or SIDH (not set) + + // 001 - SIDH: corresponds to 2-torsion group + KeyVariantSidhA KeyVariant = 1 << 0 + // 010 - SIDH: corresponds to 3-torsion group + KeyVariantSidhB = 1 << 1 + // 110 - SIKE + KeyVariantSike = 1<<2 | KeyVariantSidhB +) + +// Accessor to key variant. +func (key *key) Variant() KeyVariant { + return key.keyVariant +} + +// NewPublicKey initializes public key. +// Usage of this function guarantees that the object is correctly initialized. +func NewPublicKey(id uint8, v KeyVariant) *PublicKey { + return &PublicKey{key: key{params: common.Params(id), keyVariant: v}} +} + +// Import clears content of the public key currently stored in the structure +// and imports key stored in the byte string. Returns error in case byte string +// size is wrong. Doesn't perform any validation. +func (pub *PublicKey) Import(input []byte) error { + if len(input) != pub.Size() { + return errors.New("sidh: input to short") + } + ssSz := pub.params.SharedSecretSize + common.BytesToFp2(&pub.affine3Pt[0], input[0:ssSz], pub.params.Bytelen) + common.BytesToFp2(&pub.affine3Pt[1], input[ssSz:2*ssSz], pub.params.Bytelen) + common.BytesToFp2(&pub.affine3Pt[2], input[2*ssSz:3*ssSz], pub.params.Bytelen) + switch pub.params.ID { + case Fp434: + p434.ToMontgomery(&pub.affine3Pt[0], &pub.affine3Pt[0]) + p434.ToMontgomery(&pub.affine3Pt[1], &pub.affine3Pt[1]) + p434.ToMontgomery(&pub.affine3Pt[2], &pub.affine3Pt[2]) + case Fp503: + p503.ToMontgomery(&pub.affine3Pt[0], &pub.affine3Pt[0]) + p503.ToMontgomery(&pub.affine3Pt[1], &pub.affine3Pt[1]) + p503.ToMontgomery(&pub.affine3Pt[2], &pub.affine3Pt[2]) + case Fp751: + p751.ToMontgomery(&pub.affine3Pt[0], &pub.affine3Pt[0]) + p751.ToMontgomery(&pub.affine3Pt[1], &pub.affine3Pt[1]) + p751.ToMontgomery(&pub.affine3Pt[2], &pub.affine3Pt[2]) + default: + panic("Unsupported key") + } + return nil +} + +// Exports currently stored key. In case structure hasn't been filled with key data +// returned byte string is filled with zeros. +func (pub *PublicKey) Export(out []byte) { + var feTmp [3]common.Fp2 + ssSz := pub.params.SharedSecretSize + switch pub.params.ID { + case Fp434: + p434.FromMontgomery(&feTmp[0], &pub.affine3Pt[0]) + p434.FromMontgomery(&feTmp[1], &pub.affine3Pt[1]) + p434.FromMontgomery(&feTmp[2], &pub.affine3Pt[2]) + case Fp503: + p503.FromMontgomery(&feTmp[0], &pub.affine3Pt[0]) + p503.FromMontgomery(&feTmp[1], &pub.affine3Pt[1]) + p503.FromMontgomery(&feTmp[2], &pub.affine3Pt[2]) + case Fp751: + p751.FromMontgomery(&feTmp[0], &pub.affine3Pt[0]) + p751.FromMontgomery(&feTmp[1], &pub.affine3Pt[1]) + p751.FromMontgomery(&feTmp[2], &pub.affine3Pt[2]) + default: + panic("Unsupported key") + } + common.Fp2ToBytes(out[0:ssSz], &feTmp[0], pub.params.Bytelen) + common.Fp2ToBytes(out[ssSz:2*ssSz], &feTmp[1], pub.params.Bytelen) + common.Fp2ToBytes(out[2*ssSz:3*ssSz], &feTmp[2], pub.params.Bytelen) +} + +// Size returns size of the public key in bytes. +func (pub *PublicKey) Size() int { + return pub.params.PublicKeySize +} + +// NewPrivateKey initializes private key. +// Usage of this function guarantees that the object is correctly initialized. +func NewPrivateKey(id uint8, v KeyVariant) *PrivateKey { + prv := &PrivateKey{key: key{params: common.Params(id), keyVariant: v}} + if (v & KeyVariantSidhA) == KeyVariantSidhA { + prv.Scalar = make([]byte, prv.params.A.SecretByteLen) + } else { + prv.Scalar = make([]byte, prv.params.B.SecretByteLen) + } + if v == KeyVariantSike { + prv.S = make([]byte, prv.params.MsgLen) + } + return prv +} + +// Exports currently stored key. In case structure hasn't been filled with key data +// returned byte string is filled with zeros. +func (prv *PrivateKey) Export(out []byte) { + copy(out, prv.S) + copy(out[len(prv.S):], prv.Scalar) +} + +// Size returns size of the private key in bytes. +func (prv *PrivateKey) Size() int { + tmp := len(prv.Scalar) + if prv.Variant() == KeyVariantSike { + tmp += prv.params.MsgLen + } + return tmp +} + +// Size returns size of the shared secret. +func (prv *PrivateKey) SharedSecretSize() int { + return prv.params.SharedSecretSize +} + +// Import clears content of the private key currently stored in the structure +// and imports key from octet string. In case of SIKE, the random value 'S' +// must be prepended to the value of actual private key (see SIKE spec for details). +// Function doesn't import public key value to PrivateKey object. +func (prv *PrivateKey) Import(input []byte) error { + if len(input) != prv.Size() { + return errors.New("sidh: input to short") + } + copy(prv.S, input[:len(prv.S)]) + copy(prv.Scalar, input[len(prv.S):]) + return nil +} + +// Generates random private key for SIDH or SIKE. Generated value is +// formed as little-endian integer from key-space <2^(e2-1)..2^e2 - 1> +// for KeyVariant_A or <2^(s-1)..2^s - 1>, where s = floor(log_2(3^e3)), +// for KeyVariant_B. +// +// Returns error in case user provided RNG fails. +func (prv *PrivateKey) Generate(rand io.Reader) error { + var dp *common.DomainParams + + if (prv.keyVariant & KeyVariantSidhA) == KeyVariantSidhA { + dp = &prv.params.A + } else { + dp = &prv.params.B + } + + if prv.keyVariant == KeyVariantSike { + if _, err := io.ReadFull(rand, prv.S); err != nil { + return err + } + } + + // Private key generation takes advantage of the fact that keyspace for secret + // key is (0, 2^x - 1), for some positive value of 'x' (see SIKE, 1.3.8). + // It means that all bytes in the secret key, but the last one, can take any + // value between <0x00,0xFF>. Similarly for the last byte, but generation + // needs to chop off some bits, to make sure generated value is an element of + // a key-space. + if _, err := io.ReadFull(rand, prv.Scalar); err != nil { + return err + } + + prv.Scalar[len(prv.Scalar)-1] &= (1 << (dp.SecretBitLen % 8)) - 1 + // Make sure scalar is SecretBitLen long. SIKE spec says that key + // space starts from 0, but I'm not comfortable with having low + // value scalars used for private keys. It is still secure as per + // table 5.1 in [SIKE]. + prv.Scalar[len(prv.Scalar)-1] |= 1 << ((dp.SecretBitLen % 8) - 1) + + return nil +} + +// Generates public key. +func (prv *PrivateKey) GeneratePublicKey(pub *PublicKey) { + var isA = (prv.keyVariant & KeyVariantSidhA) == KeyVariantSidhA + + if (pub.keyVariant != prv.keyVariant) || (pub.params.ID != prv.params.ID) { + panic("sidh: incompatible public key") + } + + switch prv.params.ID { + case Fp434: + if isA { + p434.PublicKeyGenA(&pub.affine3Pt, prv.Scalar) + } else { + p434.PublicKeyGenB(&pub.affine3Pt, prv.Scalar) + } + case Fp503: + if isA { + p503.PublicKeyGenA(&pub.affine3Pt, prv.Scalar) + } else { + p503.PublicKeyGenB(&pub.affine3Pt, prv.Scalar) + } + case Fp751: + if isA { + p751.PublicKeyGenA(&pub.affine3Pt, prv.Scalar) + } else { + p751.PublicKeyGenB(&pub.affine3Pt, prv.Scalar) + } + default: + panic("Field not supported") + } +} + +// Computes a SIDH shared secret. Function requires that pub has different +// KeyVariant than prv. Length of returned output is 2*ceil(log_2 P)/8), +// where P is a prime defining finite field. +// +// Caller must make sure key SIDH key pair is not used more than once. +func (prv *PrivateKey) DeriveSecret(ss []byte, pub *PublicKey) { + var isA = (prv.keyVariant & KeyVariantSidhA) == KeyVariantSidhA + + if (pub.keyVariant == prv.keyVariant) || (pub.params.ID != prv.params.ID) { + panic("sidh: public and private are incompatible") + } + + switch prv.params.ID { + case Fp434: + if isA { + p434.DeriveSecretA(ss, prv.Scalar, &pub.affine3Pt) + } else { + p434.DeriveSecretB(ss, prv.Scalar, &pub.affine3Pt) + } + case Fp503: + if isA { + p503.DeriveSecretA(ss, prv.Scalar, &pub.affine3Pt) + } else { + p503.DeriveSecretB(ss, prv.Scalar, &pub.affine3Pt) + } + case Fp751: + if isA { + p751.DeriveSecretA(ss, prv.Scalar, &pub.affine3Pt) + } else { + p751.DeriveSecretB(ss, prv.Scalar, &pub.affine3Pt) + } + default: + panic("Field not supported") + } +} diff --git a/src/circl/dh/sidh/sidh_test.go b/src/circl/dh/sidh/sidh_test.go new file mode 100644 index 00000000000..9f1e821965c --- /dev/null +++ b/src/circl/dh/sidh/sidh_test.go @@ -0,0 +1,613 @@ +package sidh + +import ( + "bytes" + "crypto/rand" + "encoding/hex" + "fmt" + "math/big" + "testing" + + "circl/dh/sidh/internal/common" + . "circl/internal/test" +) + +/* ------------------------------------------------------------------------- + Test data + -------------------------------------------------------------------------*/ +type sidhVec struct { + id uint8 + name string + PkA string + PrA string + PkB string + PrB string +} + +var tdataSidh = map[uint8]sidhVec{ + Fp434: { + id: Fp434, + name: "P-434", + PrA: "3A727E04EA9B7E2A766A6F846489E7E7B915263BCEED308BB10FC900", + PrB: "E37BFE55B43B32448F375903D8D226EC94ADBFEA1D2B3536EB987001", + PkA: "9E668D1E6750ED4B91EE052C32839CA9DD2E56D52BC24DECC950AAAD" + + "24CEED3F9049C77FE80F0B9B01E7F8DAD7833EEC2286544D6380009C" + + "379CDD3E7517CEF5E20EB01F8231D52FC30DC61D2F63FB357F85DC63" + + "96E8A95DB9740BD3A972C8DB7901B31F074CD3E45345CA78F9008171" + + "30E688A29A7CF0073B5C00FF2C65FBE776918EF9BD8E75B29EF7FAB7" + + "91969B60B0C5B37A8992EDEF95FA7BAC40A95DAFE02E237301FEE9A7" + + "A43FD0B73477E8035DD12B73FAFEF18D39904DDE3653A754F36BE188" + + "8F6607C6A7951349A414352CF31A29F2C40302DB406C48018C905EB9" + + "DC46AFBF42A9187A9BB9E51B587622A2862DC7D5CC598BF38ED6320F" + + "B51D8697AD3D7A72ABCC32A393F0133DA8DF5E253D9E00B760B2DF34" + + "2FCE974DCFE946CFE4727783531882800F9E5DD594D6D5A6275EEFEF" + + "9713ED838F4A06BB34D7B8D46E0B385AAEA1C7963601", + PkB: "C9F73E4497AAA3FDF9EB688135866A8A83934BA10E273B8CC3808CF0" + + "C1F5FAB3E9BB295885881B73DEBC875670C0F51C4BB40DF5FEDE01B8" + + "AF32D1BF10508B8C17B2734EB93B2B7F5D84A4A0F2F816E9E2C32AC2" + + "53C0B6025B124D05A87A9E2A8567930F44BAA14219B941B6B400B4AE" + + "D1D796DA12A5A9F0B8F3F5EE9DD43F64CB24A3B1719DF278ADF56B5F" + + "3395187829DA2319DEABF6BBD6EDA244DE2B62CC5AC250C1009DD1CD" + + "4712B0B37406612AD002B5E51A62B51AC9C0374D143ABBBD58275FAF" + + "C4A5E959C54838C2D6D9FB43B7B2609061267B6A2E6C6D01D295C422" + + "3E0D3D7A4CDCFB28A7818A737935279751A6DD8290FD498D1F6AD5F4" + + "FFF6BDFA536713F509DCE8047252F1E7D0DD9FCC414C0070B5DCCE36" + + "65A21A032D7FBE749181032183AFAD240B7E671E87FBBEC3A8CA4C11" + + "AA7A9A23AC69AE2ACF54B664DECD27753D63508F1B02", + }, + Fp503: { + id: Fp503, + name: "P-503", + PrA: "D5B94224FA1AD1701EC277FDA83462D09E87181C2E583C5F09FD446A43F25103", + PrB: "FF0EF91753D71D83D912656856086007AD2CF3B2A979B2BD63E5313BFD276506", + PkA: "FFB9A589DBB3975A20373F1AD3B449880E1DA47916FCD7C751A019AAA8E95A03" + + "4ADA1AE8BFCF6FBF70F323713318E25315DE865B29C9124982594BF78CD61C09" + + "B98C22307DFD4FC0958C58EC0D144828006E510FA4072D721B48D1A3CFEA02F6" + + "062324FE1B68F457CF29BD4EB1FB68D0684EE69F53A3FAC327404341BB39365B" + + "5DE885034C9A6DD6798CB08126183C696D0302730D489584AC8D6BCADF3AB4DE" + + "FFC227D3B1701462DA15BF68EF2B07C44712DB5429B74063202F43DC0EA7919D" + + "B95025B2B03E5A3EBF57FF37E21838CE8F5531F491315E576A260DC2F515DDF2" + + "4DEDE54CA69737CE6442B4219CD472D9CCCF8AF12B5C5B23ACB9C22929924ABA" + + "52C820932C82435518B920AFC43F2041263AE98D29E58B73F33A5DD42AAC7533" + + "404B4AC2B83DD2C7BEA7676930B6007CC185C264672B75F5332C18429BBC7B0F" + + "2EA3F746995A298E7443FFB0C1B27DCA7D19635064AF3B87938960587F56B724" + + "C1EF1FF012B056D7301F8713295B7734563542D4259B8BEA260C", + PkB: "AA3303F79FCE4855DE125B239D10BEC3B7082E55B08C769A9765F1BF41A31210" + + "66382D6BF2857D85138CC17D69593B8FC7703D22C553FB077DFB3AC577CF1E55" + + "2AED6DC0368123E01DDD70059A47E31E06423D2F697A3DA5D621EB5FF2A52EE7" + + "CA7D3BD01B427AC14CB6099E03C6639A3BAC9B939297CEB10F276F93CF16A1EE" + + "1B8085DE3DA037C911491B145B034A47B42A996A61C2313FEF166FD3665B0AE8" + + "C201A268DA01AB52E4759ACCC1DD09685A17CDA5D44AF847931ABB221D62E241" + + "2329394445ADFD662C77472A9268F40AB540177C0E6F1D59026E595C46FBED2F" + + "703838C5F3D7A811B500237596C5E960AA1F2989C5F17DD60D8A752569DBF250" + + "E01C63C9790D014CE05A9D8683814A320E30185E478AF9ABD761DADDA8DE7E3E" + + "A53C224AC8313C176D14BD0F04AB09A9D0D0302ACBF768EB4DB03681EAE3BC10" + + "21CAA429A1490AE1D6E0CA9D6BC4BCD14B1CFE694226D03E8731E9E0B3760877" + + "7D56630B31298CC05B6FF6C1A08935312D8E95B8056AD7831A22", + }, + Fp751: { + id: Fp751, + name: "P-751", + // PrA - Alice's Private Key: 2*randint(0,2^371) + PrA: "B1937F2B009FD9F785C5AD899F5ED2FD064218C07A76798D1433336E093DF184CA0CAF6E7C92B320E89632A7765F0B", + // PrB - Bob's Private Key: 3*randint(0,3^238) + PrB: "54DB4380D4134E187F5793FA82A4F18B39CA2F8F1C145FFB040FC917E2F41542037FF227F3A4AAFB17A6983AA88B4403", + PkA: "2B53BB7C002A9D18B077D068C38353ADFD57A3CA0E431D92CCB8060D41A83A09" + + "C1500BEE63FB07DA1DBEDB4AF145F22C2D8152B07B7E124F06643C7AB5B1C48D" + + "581FC4C6FB7FC165F6E02F40B47D81400B84B6288DEAB38DE795B51486430974" + + "788377770D46B0ABC1F3F7C3647A0E38ACED475EA8EE990F3C5A7668452478C1" + + "975993E126B405E476AD6A10E9DD4E135ADA910BE41A8F93331268791F7B958A" + + "0888052D1CF7B9128058A258002F22AC48E2C296E3935033139D336FDEB33E9B" + + "8713663B1705B566AC4F4455FD0E710A5236C18011EA971DDD18633F9022C432" + + "B225EC401FCD4C233B8BF91BE5944D1A657516CE4B844D0BC6049478046B60B6" + + "BE163E41CCE743054806B13FAC0A1FA393C866D74A5A93A938209287324FAB46" + + "295F5B271C9D8CFEE17868599202D7AEF1A67EBE2FA2A27AD9E0991CEDEE270D" + + "1E7639425D94A0F0A2EFDE90B86D5D7F03F3CF97D30415CAA661F865ADB788E6" + + "3F79EE2FE8637D9DCAF3BCD5C42AE499688048BBB49F216B4714675FD87F7CCC" + + "37A0C2EA56BB53675584F7648BA052F963C35387ECC4DDED4F8076934FF32D5D" + + "77B5D3C57553757A4CB9588C4575D4CC4CA8280370041A6FF03007C31D0712E8" + + "327CC5BC9885F896904FAB4EE167745260D331C3E85E8A32FCCD23093F2C55A9" + + "EA8D7BECEFC3564D3C3D4CE585B62785773B2228742185C97D6F51CD3E3CF885" + + "5CF37F305734E97A86479580FDB9983DDCAE9D0F1B125523DB2FE58339240A58" + + "131D0EFD14A560A6F7EDE774F6C3C54F46DD0830", + PkB: "E93E4E2B0E7348C088FD91F8E3B17CC52B55C5E8933B6D00B3757E5347C5A0AE" + + "5F1A6051C32FB20A41013A244484C8D0501B6A3516A634581E08C907F29D651C" + + "BCC5B6CA6BAC4DCC980CD36155B60A2108134D3F78ED19ADA2B8B20184302FD7" + + "47E096B01ABB33CB76B115D673B00F76913281CF7A0B44FF5CF1A256B8138FE6" + + "77AB8D22FEBBCB10EB46E442D0AD96A126DD24E941280C7AB3F9FAC2832A149C" + + "AD93D221EDCB406303F5A1B38F43F310244D766239A7F4D89EED4C6FD272BC4F" + + "F7C4E34F3E5E77BFF59D6FE5C0D3937F574ABE81C2FC1FEDD98F43323F8F2D7C" + + "154DCEBF410FCF698A4E6506D6FD6E4A861395F75698C810A527E00ADC118C90" + + "9CDE7729B24C6E7DE9C92CFB592CB9A4BAC54DB468AA52724452CC7A7B40509B" + + "B7894ACCF2C7933537FD52DB312D7FBC4FDE01AC2350CD25ABDD5E6F3AEF87BA" + + "1BE23691544EB6A4F8FA9CF2BE70B9665EA479B44DC3C61D4651CDDB53656B6F" + + "3A2D139EC6BE8550B8A623CCA30EB5374F70C67A932712002006F3D73190384F" + + "6D3BEC9DB9F46E9B7AE2891E615752E74DC112579CF43283E8B6EBEF4C802BD6" + + "700A97B9739E8694B48D8CB9C8ABBC915A834FF1DBF2C823B3E156D0A415C558" + + "71B719BD9DD215F57C8D19A6B4F8CD93283D6EBD135347DAAF4F20C54D24017F" + + "5E6AF400AB6DC98AD2D5810E59360DF64503599FAF6FBAB720CC557DEEF0F528" + + "249DEB530C8F310465E0BE2B4041C24DAF783BC4EE71D27C760FA7CFD4A9A691" + + "70BCBA465CA242961671DF0C53A8112CCD708D58", + }, +} + +/* ------------------------------------------------------------------------- + Helpers + -------------------------------------------------------------------------*/ +// Converts string to private key. +func convToPrv(s string, v KeyVariant, id uint8) *PrivateKey { + key := NewPrivateKey(id, v) + hex, e := hex.DecodeString(s) + if e != nil { + panic("non-hex number provided") + } + e = key.Import(hex) + if e != nil { + panic("Can't import private key") + } + return key +} + +// Converts string to public key. +func convToPub(s string, v KeyVariant, id uint8) *PublicKey { + key := NewPublicKey(id, v) + hex, e := hex.DecodeString(s) + if e != nil { + panic("non-hex number provided") + } + e = key.Import(hex) + if e != nil { + panic("Can't import public key") + } + return key +} + +/* Unit tests */ + +func testKeygen(t *testing.T, v sidhVec) { + pubA := NewPublicKey(v.id, KeyVariantSidhA) + pubB := NewPublicKey(v.id, KeyVariantSidhB) + alicePrivate := convToPrv(v.PrA, KeyVariantSidhA, v.id) + bobPrivate := convToPrv(v.PrB, KeyVariantSidhB, v.id) + expPubA := convToPub(v.PkA, KeyVariantSidhA, v.id) + expPubB := convToPub(v.PkB, KeyVariantSidhB, v.id) + + alicePrivate.GeneratePublicKey(pubA) + bobPrivate.GeneratePublicKey(pubB) + + got := make([]byte, expPubA.Size()) + exp := make([]byte, expPubA.Size()) + pubA.Export(got) + expPubA.Export(exp) + if !bytes.Equal(got, exp) { + t.Fatalf("unexpected value of public key A\ngot [%X]\nexp [%X]", got, exp) + } + + got = make([]byte, expPubB.Size()) + exp = make([]byte, expPubB.Size()) + pubB.Export(got) + expPubB.Export(exp) + if !bytes.Equal(got, exp) { + t.Fatalf("unexpected value of public key B\ngot [%X]\nexp [%X]", got, exp) + } +} + +func testRoundtrip(t *testing.T, v sidhVec) { + var err error + pubA := NewPublicKey(v.id, KeyVariantSidhA) + pubB := NewPublicKey(v.id, KeyVariantSidhB) + prvA := NewPrivateKey(v.id, KeyVariantSidhA) + prvB := NewPrivateKey(v.id, KeyVariantSidhB) + s1 := make([]byte, common.Params(v.id).SharedSecretSize) + s2 := make([]byte, common.Params(v.id).SharedSecretSize) + + // Generate private keys + err = prvA.Generate(rand.Reader) + CheckNoErr(t, err, "key generation failed") + err = prvB.Generate(rand.Reader) + CheckNoErr(t, err, "key generation failed") + + // Generate public keys + prvA.GeneratePublicKey(pubA) + prvB.GeneratePublicKey(pubB) + + // Derive shared secret + prvB.DeriveSecret(s1, pubA) + prvA.DeriveSecret(s2, pubB) + + if !bytes.Equal(s1[:], s2[:]) { + t.Fatalf("Two shared keys do not match:\ns1 [%X]\ns2 [%X]", s1, s2) + } +} + +func testKeyAgreement(t *testing.T, v sidhVec) { + var err error + s1 := make([]byte, common.Params(v.id).SharedSecretSize) + s2 := make([]byte, common.Params(v.id).SharedSecretSize) + + // KeyPairs + alicePublic := convToPub(v.PkA, KeyVariantSidhA, v.id) + bobPublic := convToPub(v.PkB, KeyVariantSidhB, v.id) + alicePrivate := convToPrv(v.PrA, KeyVariantSidhA, v.id) + bobPrivate := convToPrv(v.PrB, KeyVariantSidhB, v.id) + + // Do actual test + bobPrivate.DeriveSecret(s1, alicePublic) + alicePrivate.DeriveSecret(s2, bobPublic) + + if !bytes.Equal(s1[:], s2[:]) { + t.Fatalf("two shared keys do not match\ngot [%X]\nexp [%X]", s1, s2) + } + + // Negative case + dec, err := hex.DecodeString(v.PkA) + CheckNoErr(t, err, "decoding failed") + + dec[0] = ^dec[0] + err = alicePublic.Import(dec) + CheckNoErr(t, err, "import failed") + + bobPrivate.DeriveSecret(s1, alicePublic) + alicePrivate.DeriveSecret(s2, bobPublic) + if bytes.Equal(s1[:], s2[:]) { + t.Fatalf("DeriveSecret produces wrong results. The two shared keys match, but they shouldn't") + } +} + +func testImportExport(t *testing.T, v sidhVec) { + var err error + a := NewPublicKey(v.id, KeyVariantSidhA) + b := NewPublicKey(v.id, KeyVariantSidhB) + + // Import keys + aHex, err := hex.DecodeString(v.PkA) + CheckNoErr(t, err, "invalid hex-number provided") + + err = a.Import(aHex) + CheckNoErr(t, err, "import failed") + + bHex, err := hex.DecodeString(v.PkB) + CheckNoErr(t, err, "invalid hex-number provided") + + err = b.Import(bHex) + CheckNoErr(t, err, "import failed") + + aBytes := make([]byte, a.Size()) + bBytes := make([]byte, b.Size()) + a.Export(aBytes) + b.Export(bBytes) + + // Export and check if same + if !bytes.Equal(bBytes, bHex) || !bytes.Equal(aBytes, aHex) { + t.Fatalf("export/import failed") + } + + if (len(bBytes) != b.Size()) || (len(aBytes) != a.Size()) { + t.Fatalf("wrong size of exported keys") + } + + // Ensure that public key is unchanged after it is exported + aBytes2 := make([]byte, a.Size()) + bBytes2 := make([]byte, b.Size()) + a.Export(aBytes2) + b.Export(bBytes2) + if !bytes.Equal(aBytes, aBytes2) || !bytes.Equal(bBytes, bBytes2) { + t.Fatalf("Second export doesn't match first export") + } +} + +func testPrivateKeyBelowMax(t *testing.T, vec sidhVec) { + for variant, keySz := range map[KeyVariant]*common.DomainParams{ + KeyVariantSidhA: &common.Params(vec.id).A, + KeyVariantSidhB: &common.Params(vec.id).B} { + func(v KeyVariant, dp *common.DomainParams) { + var blen = int(dp.SecretByteLen) + var prv = NewPrivateKey(vec.id, v) + var secretBytes = make([]byte, prv.Size()) + + // Calculate either (2^e2 - 1) or (2^s - 1); where s=ceil(log_2(3^e3))) + maxSecretVal := big.NewInt(int64(dp.SecretBitLen)) + maxSecretVal.Exp(big.NewInt(int64(2)), maxSecretVal, nil) + maxSecretVal.Sub(maxSecretVal, big.NewInt(1)) + + // Do same test 1000 times + for i := 0; i < 1000; i++ { + err := prv.Generate(rand.Reader) + CheckNoErr(t, err, "Private key generation") + + // Convert to big-endian, as that's what expected by (*Int)SetBytes() + prv.Export(secretBytes) + for i := 0; i < blen/2; i++ { + tmp := secretBytes[i] ^ secretBytes[blen-i-1] + secretBytes[i] = tmp ^ secretBytes[i] + secretBytes[blen-i-1] = tmp ^ secretBytes[blen-i-1] + } + prvBig := new(big.Int).SetBytes(secretBytes) + // Check if generated key is bigger then acceptable + if prvBig.Cmp(maxSecretVal) == 1 { + t.Error("Generated private key is wrong") + } + } + }(variant, keySz) + } +} + +func TestKeyAgreementP751_AliceEvenNumber(t *testing.T) { + // even alice + v := tdataSidh[Fp751] + v.PkA = "FDED78E9F490CB518BD6357E18FEEB63FFEFEBE907338B3ABCA74A7E590DBF79" + + "0C732AB9E3778244608CD563064BDF6AAEF511CEAF07C702309ADAA7EBEBC6B3" + + "D7B00F5C02FB2FEDA763B2D695FD27F93F45D3AC58C2F0524A942D6DE407B651" + + "1854A1D974F11A8686CF8AD675A081F4B668F3C6617029AA33FD597C8910AB37" + + "F71DBE004A3FF8442C4B65DE51201DFAE6F9DC20FDE5B998D19C23589437229D" + + "724B4378602321F247276E7B4E441383C9BE6D277A127362D9C9FB68A41C5F5B" + + "9D2BA63FA790D62315DECF5049F0476A43D30BC1E8A36047C8EE0DA9E0A3937E" + + "BDF52A91BC53266A82CBF2CEAB227CB6D5075B486679CA7701F6F35C53499B45" + + "A451CE37C57B9BB1276142F495B83D987BD4B62E78E3084DCF3EB906D19DFA8F" + + "819DFC7FDF104C1A01CCF8D933B91EBD72CDE83A502B1FB0A5DF782BC7085766" + + "AE795123903A2D30F0F79073D27CF71BA4C9D3CA86512842AA8B5AEB729C78B1" + + "E15392E20A6043C05F88F6F412C3C9FE14F8FAAE8B8482514822162F93E81615" + + "BDD77363F872D0506FFDC1809C165A5C8A19F8EA0254D73E08202A6FF3AF43CF" + + "A7EC9B137AE003A19440DCE2EF3CFC99080F75E683AF6D0E25DF55C60B2A8013" + + "FA3D59828D31C2360DF83E202FB48AFAA65AF7279137E827B80E761FA49B842A" + + "A70FD4E77B284A14B8E28C8B11B389E1160DD9877C8D5A5A1471E605F1848369" + + "3F7578B3733DDEE117227E35B1765FEBB765B340A084E8D99176C0837099C864" + + "C71C864842D3E9B58CB870AD45F3B6BE476FEB6D" + v.PrA = "C09957CC83045FB4C3726384D784476ACB6FFD92E5B15B3C2D451BA063F1BD4CE" + + "D8FBCF682A98DD0954D37BCAF730F" + testKeyAgreement(t, v) +} + +/* ------------------------------------------------------------------------- + Wrappers for 'testing' SIDH + -------------------------------------------------------------------------*/ +func testSidhVec(t *testing.T, m *map[uint8]sidhVec, f func(t *testing.T, v sidhVec)) { + for i := range *m { + v := (*m)[i] + t.Run(v.name, func(t *testing.T) { f(t, v) }) + } +} +func TestKeygen(t *testing.T) { testSidhVec(t, &tdataSidh, testKeygen) } +func TestRoundtrip(t *testing.T) { testSidhVec(t, &tdataSidh, testRoundtrip) } +func TestImportExport(t *testing.T) { testSidhVec(t, &tdataSidh, testImportExport) } +func TestKeyAgreement(t *testing.T) { testSidhVec(t, &tdataSidh, testKeyAgreement) } +func TestPrivateKeyBelowMax(t *testing.T) { testSidhVec(t, &tdataSidh, testPrivateKeyBelowMax) } + +/* ------------------------------------------------------------------------- + Benchmarking + -------------------------------------------------------------------------*/ +func BenchmarkSidhKeyAgreementP751(b *testing.B) { + // KeyPairs + alicePublic := convToPub(tdataSidh[Fp751].PkA, KeyVariantSidhA, Fp751) + bobPublic := convToPub(tdataSidh[Fp751].PkB, KeyVariantSidhB, Fp751) + alicePrivate := convToPrv(tdataSidh[Fp751].PrA, KeyVariantSidhA, Fp751) + bobPrivate := convToPrv(tdataSidh[Fp751].PrB, KeyVariantSidhB, Fp751) + var ss [2 * 94]byte + + for i := 0; i < b.N; i++ { + // Derive shared secret + bobPrivate.DeriveSecret(ss[:], alicePublic) + alicePrivate.DeriveSecret(ss[:], bobPublic) + } +} + +func BenchmarkSidhKeyAgreementP503(b *testing.B) { + // KeyPairs + alicePublic := convToPub(tdataSidh[Fp503].PkA, KeyVariantSidhA, Fp503) + bobPublic := convToPub(tdataSidh[Fp503].PkB, KeyVariantSidhB, Fp503) + alicePrivate := convToPrv(tdataSidh[Fp503].PrA, KeyVariantSidhA, Fp503) + bobPrivate := convToPrv(tdataSidh[Fp503].PrB, KeyVariantSidhB, Fp503) + var ss [2 * 63]byte + + for i := 0; i < b.N; i++ { + // Derive shared secret + bobPrivate.DeriveSecret(ss[:], alicePublic) + alicePrivate.DeriveSecret(ss[:], bobPublic) + } +} + +func BenchmarkSidhKeyAgreementP434(b *testing.B) { + // KeyPairs + alicePublic := convToPub(tdataSidh[Fp434].PkA, KeyVariantSidhA, Fp434) + bobPublic := convToPub(tdataSidh[Fp434].PkB, KeyVariantSidhB, Fp434) + alicePrivate := convToPrv(tdataSidh[Fp434].PrA, KeyVariantSidhA, Fp434) + bobPrivate := convToPrv(tdataSidh[Fp434].PrB, KeyVariantSidhB, Fp434) + var ss [2 * 63]byte + + for i := 0; i < b.N; i++ { + // Derive shared secret + bobPrivate.DeriveSecret(ss[:], alicePublic) + alicePrivate.DeriveSecret(ss[:], bobPublic) + } +} + +func BenchmarkAliceKeyGenPrvP751(b *testing.B) { + prv := NewPrivateKey(Fp751, KeyVariantSidhA) + for n := 0; n < b.N; n++ { + _ = prv.Generate(rand.Reader) + } +} + +func BenchmarkAliceKeyGenPrvP503(b *testing.B) { + prv := NewPrivateKey(Fp503, KeyVariantSidhA) + for n := 0; n < b.N; n++ { + _ = prv.Generate(rand.Reader) + } +} + +func BenchmarkAliceKeyGenPrvP434(b *testing.B) { + prv := NewPrivateKey(Fp434, KeyVariantSidhA) + for n := 0; n < b.N; n++ { + _ = prv.Generate(rand.Reader) + } +} + +func BenchmarkBobKeyGenPrvP751(b *testing.B) { + prv := NewPrivateKey(Fp751, KeyVariantSidhB) + for n := 0; n < b.N; n++ { + _ = prv.Generate(rand.Reader) + } +} + +func BenchmarkBobKeyGenPrvP503(b *testing.B) { + prv := NewPrivateKey(Fp503, KeyVariantSidhB) + for n := 0; n < b.N; n++ { + _ = prv.Generate(rand.Reader) + } +} + +func BenchmarkBobKeyGenPrvP434(b *testing.B) { + prv := NewPrivateKey(Fp434, KeyVariantSidhB) + for n := 0; n < b.N; n++ { + _ = prv.Generate(rand.Reader) + } +} + +func BenchmarkAliceKeyGenPubP751(b *testing.B) { + prv := NewPrivateKey(Fp751, KeyVariantSidhA) + pub := NewPublicKey(Fp751, KeyVariantSidhA) + _ = prv.Generate(rand.Reader) + for n := 0; n < b.N; n++ { + prv.GeneratePublicKey(pub) + } +} + +func BenchmarkAliceKeyGenPubP503(b *testing.B) { + prv := NewPrivateKey(Fp503, KeyVariantSidhA) + pub := NewPublicKey(Fp503, KeyVariantSidhA) + _ = prv.Generate(rand.Reader) + for n := 0; n < b.N; n++ { + prv.GeneratePublicKey(pub) + } +} + +func BenchmarkAliceKeyGenPubP434(b *testing.B) { + prv := NewPrivateKey(Fp434, KeyVariantSidhA) + pub := NewPublicKey(Fp434, KeyVariantSidhA) + _ = prv.Generate(rand.Reader) + for n := 0; n < b.N; n++ { + prv.GeneratePublicKey(pub) + } +} + +func BenchmarkBobKeyGenPubP751(b *testing.B) { + prv := NewPrivateKey(Fp751, KeyVariantSidhB) + pub := NewPublicKey(Fp751, KeyVariantSidhB) + _ = prv.Generate(rand.Reader) + for n := 0; n < b.N; n++ { + prv.GeneratePublicKey(pub) + } +} + +func BenchmarkBobKeyGenPubP503(b *testing.B) { + prv := NewPrivateKey(Fp503, KeyVariantSidhB) + pub := NewPublicKey(Fp503, KeyVariantSidhB) + _ = prv.Generate(rand.Reader) + for n := 0; n < b.N; n++ { + prv.GeneratePublicKey(pub) + } +} + +func BenchmarkBobKeyGenPubP434(b *testing.B) { + prv := NewPrivateKey(Fp434, KeyVariantSidhB) + pub := NewPublicKey(Fp434, KeyVariantSidhB) + _ = prv.Generate(rand.Reader) + for n := 0; n < b.N; n++ { + prv.GeneratePublicKey(pub) + } +} + +func BenchmarkSharedSecretAliceP751(b *testing.B) { + aPr := convToPrv(tdataSidh[Fp751].PrA, KeyVariantSidhA, Fp751) + bPk := convToPub(tdataSidh[Fp751].PkB, KeyVariantSidhB, Fp751) + var ss [2 * 94]byte + for n := 0; n < b.N; n++ { + aPr.DeriveSecret(ss[:], bPk) + } +} + +func BenchmarkSharedSecretAliceP503(b *testing.B) { + aPr := convToPrv(tdataSidh[Fp503].PrA, KeyVariantSidhA, Fp503) + bPk := convToPub(tdataSidh[Fp503].PkB, KeyVariantSidhB, Fp503) + var ss [2 * 63]byte + for n := 0; n < b.N; n++ { + aPr.DeriveSecret(ss[:], bPk) + } +} + +func BenchmarkSharedSecretAliceP434(b *testing.B) { + aPr := convToPrv(tdataSidh[Fp434].PrA, KeyVariantSidhA, Fp434) + bPk := convToPub(tdataSidh[Fp434].PkB, KeyVariantSidhB, Fp434) + var ss [2 * 63]byte + for n := 0; n < b.N; n++ { + aPr.DeriveSecret(ss[:], bPk) + } +} + +func BenchmarkSharedSecretBobP751(b *testing.B) { + // m_B = 3*randint(0,3^238) + aPk := convToPub(tdataSidh[Fp751].PkA, KeyVariantSidhA, Fp751) + bPr := convToPrv(tdataSidh[Fp751].PrB, KeyVariantSidhB, Fp751) + var ss [2 * 94]byte + for n := 0; n < b.N; n++ { + bPr.DeriveSecret(ss[:], aPk) + } +} + +func BenchmarkSharedSecretBobP503(b *testing.B) { + // m_B = 3*randint(0,3^238) + aPk := convToPub(tdataSidh[Fp503].PkA, KeyVariantSidhA, Fp503) + bPr := convToPrv(tdataSidh[Fp503].PrB, KeyVariantSidhB, Fp503) + var ss [2 * 63]byte + for n := 0; n < b.N; n++ { + bPr.DeriveSecret(ss[:], aPk) + } +} + +func BenchmarkSharedSecretBobP434(b *testing.B) { + // m_B = 3*randint(0,3^238) + aPk := convToPub(tdataSidh[Fp434].PkA, KeyVariantSidhA, Fp434) + bPr := convToPrv(tdataSidh[Fp434].PrB, KeyVariantSidhB, Fp434) + var ss [2 * 63]byte + for n := 0; n < b.N; n++ { + bPr.DeriveSecret(ss[:], aPk) + } +} + +// Examples + +func ExamplePrivateKey() { + // import "circl/dh/sidh" + + // Allice's key pair + prvA := NewPrivateKey(Fp503, KeyVariantSidhA) + pubA := NewPublicKey(Fp503, KeyVariantSidhA) + // Bob's key pair + prvB := NewPrivateKey(Fp503, KeyVariantSidhB) + pubB := NewPublicKey(Fp503, KeyVariantSidhB) + // Generate keypair for Allice + err := prvA.Generate(rand.Reader) + if err != nil { + fmt.Print(err) + } + prvA.GeneratePublicKey(pubA) + // Generate keypair for Bob + err = prvB.Generate(rand.Reader) + if err != nil { + fmt.Print(err) + } + prvB.GeneratePublicKey(pubB) + // Buffers storing shared secret + ssA := make([]byte, prvA.SharedSecretSize()) + ssB := make([]byte, prvA.SharedSecretSize()) + // Allice calculates shared secret with hers private + // key and Bob's public key + prvA.DeriveSecret(ssA[:], pubB) + // Bob calculates shared secret with hers private + // key and Allice's public key + prvB.DeriveSecret(ssB[:], pubA) + // Check if ssA == ssB + fmt.Printf("%t\n", bytes.Equal(ssA, ssB)) + // Output: + // true +} diff --git a/src/circl/dh/sidh/sike.go b/src/circl/dh/sidh/sike.go new file mode 100644 index 00000000000..8281a6f2d27 --- /dev/null +++ b/src/circl/dh/sidh/sike.go @@ -0,0 +1,272 @@ +package sidh + +import ( + "crypto/subtle" + "errors" + "io" + + "circl/dh/sidh/internal/common" + "circl/internal/sha3" +) + +// SIKE KEM interface. +type KEM struct { + allocated bool + rng io.Reader + msg []byte + secretBytes []byte + params *common.SidhParams + shake sha3.State +} + +// NewSike434 instantiates SIKE/p434 KEM. +func NewSike434(rng io.Reader) *KEM { + var c KEM + c.Allocate(Fp434, rng) + return &c +} + +// NewSike503 instantiates SIKE/p503 KEM. +func NewSike503(rng io.Reader) *KEM { + var c KEM + c.Allocate(Fp503, rng) + return &c +} + +// NewSike751 instantiates SIKE/p751 KEM. +func NewSike751(rng io.Reader) *KEM { + var c KEM + c.Allocate(Fp751, rng) + return &c +} + +// Allocate allocates KEM object for multiple SIKE operations. The rng +// must be cryptographically secure PRNG. +func (c *KEM) Allocate(id uint8, rng io.Reader) { + c.rng = rng + c.params = common.Params(id) + c.msg = make([]byte, c.params.MsgLen) + c.secretBytes = make([]byte, c.params.A.SecretByteLen) + c.shake = sha3.NewShake256() + c.allocated = true +} + +// Encapsulate receives the public key and generates SIKE ciphertext and shared secret. +// The generated ciphertext is used for authentication. +// Error is returned in case PRNG fails. Function panics in case wrongly formatted +// input was provided. +func (c *KEM) Encapsulate(ciphertext, secret []byte, pub *PublicKey) error { + if !c.allocated { + panic("KEM unallocated") + } + + if KeyVariantSike != pub.keyVariant { + panic("Wrong type of public key") + } + + if len(secret) < c.SharedSecretSize() { + panic("shared secret buffer to small") + } + + if len(ciphertext) < c.CiphertextSize() { + panic("ciphertext buffer to small") + } + + // Generate ephemeral value + _, err := io.ReadFull(c.rng, c.msg[:]) + if err != nil { + return err + } + + var buf [3 * common.MaxSharedSecretBsz]byte + var skA = PrivateKey{ + key: key{ + params: c.params, + keyVariant: KeyVariantSidhA}, + Scalar: c.secretBytes} + var pkA = NewPublicKey(c.params.ID, KeyVariantSidhA) + + pub.Export(buf[:]) + c.shake.Reset() + _, _ = c.shake.Write(c.msg) + _, _ = c.shake.Write(buf[:3*c.params.SharedSecretSize]) + _, _ = c.shake.Read(skA.Scalar) + + // Ensure bitlength is not bigger then to 2^e2-1 + skA.Scalar[len(skA.Scalar)-1] &= (1 << (c.params.A.SecretBitLen % 8)) - 1 + skA.GeneratePublicKey(pkA) + c.generateCiphertext(ciphertext, &skA, pkA, pub, c.msg[:]) + + // K = H(msg||(c0||c1)) + c.shake.Reset() + _, _ = c.shake.Write(c.msg) + _, _ = c.shake.Write(ciphertext) + _, _ = c.shake.Read(secret[:c.SharedSecretSize()]) + return nil +} + +// Decapsulate given the keypair and ciphertext as inputs, Decapsulate outputs a shared +// secret if plaintext verifies correctly, otherwise function outputs random value. +// Decapsulation may panic in case input is wrongly formatted, in particular, size of +// the 'ciphertext' must be exactly equal to c.CiphertextSize(). +func (c *KEM) Decapsulate(secret []byte, prv *PrivateKey, pub *PublicKey, ciphertext []byte) error { + if !c.allocated { + panic("KEM unallocated") + } + + if KeyVariantSike != pub.keyVariant { + panic("Wrong type of public key") + } + + if pub.keyVariant != prv.keyVariant { + panic("Public and private key are of different type") + } + + if len(secret) < c.SharedSecretSize() { + panic("shared secret buffer to small") + } + + if len(ciphertext) != c.CiphertextSize() { + panic("ciphertext buffer to small") + } + + var m [common.MaxMsgBsz]byte + var r [common.MaxSidhPrivateKeyBsz]byte + var pkBytes [3 * common.MaxSharedSecretBsz]byte + var skA = PrivateKey{ + key: key{ + params: c.params, + keyVariant: KeyVariantSidhA}, + Scalar: c.secretBytes} + var pkA = NewPublicKey(c.params.ID, KeyVariantSidhA) + c1Len, err := c.decrypt(m[:], prv, ciphertext) + if err != nil { + return err + } + + // r' = G(m'||pub) + pub.Export(pkBytes[:]) + c.shake.Reset() + _, _ = c.shake.Write(m[:c1Len]) + _, _ = c.shake.Write(pkBytes[:3*c.params.SharedSecretSize]) + _, _ = c.shake.Read(r[:c.params.A.SecretByteLen]) + // Ensure bitlength is not bigger than 2^e2-1 + r[c.params.A.SecretByteLen-1] &= (1 << (c.params.A.SecretBitLen % 8)) - 1 + + err = skA.Import(r[:c.params.A.SecretByteLen]) + if err != nil { + return err + } + skA.GeneratePublicKey(pkA) + pkA.Export(pkBytes[:]) + + // S is chosen at random when generating a key and unknown to other party. It is + // important that S is unpredictable to the other party. Without this check, would + // be possible to recover a secret, by providing series of invalid ciphertexts. + // + // See more details in "On the security of supersingular isogeny cryptosystems" + // (S. Galbraith, et al., 2016, ePrint #859). + mask := subtle.ConstantTimeCompare(pkBytes[:c.params.PublicKeySize], ciphertext[:pub.params.PublicKeySize]) + common.Cpick(mask, m[:c1Len], m[:c1Len], prv.S) + c.shake.Reset() + _, _ = c.shake.Write(m[:c1Len]) + _, _ = c.shake.Write(ciphertext) + _, _ = c.shake.Read(secret[:c.SharedSecretSize()]) + return nil +} + +// Resets internal state of KEM. Function should be used +// after Allocate and between subsequent calls to Encapsulate +// and/or Decapsulate. +func (c *KEM) Reset() { + for i := range c.msg { + c.msg[i] = 0 + } + + for i := range c.secretBytes { + c.secretBytes[i] = 0 + } +} + +// Returns size of resulting ciphertext. +func (c *KEM) CiphertextSize() int { + return c.params.CiphertextSize +} + +// Returns size of resulting shared secret. +func (c *KEM) SharedSecretSize() int { + return c.params.KemSize +} + +// PublicKeySize returns size of the public key in bytes. +func (c *KEM) PublicKeySize() int { + return c.params.PublicKeySize +} + +// Size returns size of the private key in bytes. +func (c *KEM) PrivateKeySize() int { + return int(c.params.B.SecretByteLen) + c.params.MsgLen +} + +func (c *KEM) generateCiphertext(ctext []byte, skA *PrivateKey, pkA, pkB *PublicKey, ptext []byte) { + var n [common.MaxMsgBsz]byte + var j [common.MaxSharedSecretBsz]byte + var ptextLen = skA.params.MsgLen + + skA.DeriveSecret(j[:], pkB) + c.shake.Reset() + _, _ = c.shake.Write(j[:skA.params.SharedSecretSize]) + _, _ = c.shake.Read(n[:ptextLen]) + for i := range ptext { + n[i] ^= ptext[i] + } + + pkA.Export(ctext) + copy(ctext[pkA.Size():], n[:ptextLen]) +} + +// encrypt uses SIKE public key to encrypt plaintext. Requires cryptographically secure +// PRNG. Returns ciphertext in case encryption succeeds. Returns error in case PRNG fails +// or wrongly formated input was provided. +func (c *KEM) encrypt(ctext []byte, rng io.Reader, pub *PublicKey, ptext []byte) error { + var ptextLen = len(ptext) + // c1 must be security level + 64 bits (see [SIKE] 1.4 and 4.3.3) + if ptextLen != pub.params.KemSize { + return errors.New("unsupported message length") + } + + skA := NewPrivateKey(pub.params.ID, KeyVariantSidhA) + pkA := NewPublicKey(pub.params.ID, KeyVariantSidhA) + err := skA.Generate(rng) + if err != nil { + return err + } + + skA.GeneratePublicKey(pkA) + c.generateCiphertext(ctext, skA, pkA, pub, ptext) + return nil +} + +// decrypt uses SIKE private key to decrypt ciphertext. Returns plaintext in case +// decryption succeeds or error in case unexpected input was provided. +// Constant time. +func (c *KEM) decrypt(n []byte, prv *PrivateKey, ctext []byte) (int, error) { + var c1Len int + var j [common.MaxSharedSecretBsz]byte + var pkLen = prv.params.PublicKeySize + + // ctext is a concatenation of (ciphertext = pubkey_A || c1) + // it must be security level + 64 bits (see [SIKE] 1.4 and 4.3.3) + // Lengths has been already checked by Decapsulate() + c1Len = len(ctext) - pkLen + c0 := NewPublicKey(prv.params.ID, KeyVariantSidhA) + err := c0.Import(ctext[:pkLen]) + prv.DeriveSecret(j[:], c0) + c.shake.Reset() + _, _ = c.shake.Write(j[:prv.params.SharedSecretSize]) + _, _ = c.shake.Read(n[:c1Len]) + for i := range n[:c1Len] { + n[i] ^= ctext[pkLen+i] + } + return c1Len, err +} diff --git a/src/circl/dh/sidh/sike_test.go b/src/circl/dh/sidh/sike_test.go new file mode 100644 index 00000000000..099d41d5a4d --- /dev/null +++ b/src/circl/dh/sidh/sike_test.go @@ -0,0 +1,579 @@ +package sidh + +import ( + "bufio" + "bytes" + "crypto/rand" + "encoding/hex" + "fmt" + "io" + "os" + "strings" + "testing" + + "circl/dh/sidh/internal/common" + . "circl/internal/test" +) + +type sikeVec struct { + id uint8 + name string + kem *KEM + KatFile string + PkB string + PrB string +} + +var tdataSike = map[uint8]sikeVec{ + Fp434: { + Fp434, "P-434", NewSike434(rand.Reader), + "testdata/PQCkemKAT_374.rsp", + "1BD0A2E81307B6F96461317DDF535ACC0E59C742627BAE60D27605E10FAF722D" + + "22A73E184CB572A12E79DCD58C6B54FB01442114CBE9010B6CAEC25D04C16C5E" + + "42540C1524C545B8C67614ED4183C9FA5BD0BE45A7F89FBC770EE8E7E5E391C7" + + "EE6F35F74C29E6D9E35B1663DA01E48E9DEB2347512D366FDE505161677055E3" + + "EF23054D276E817E2C57025DA1C10D2461F68617F2D11256EEE4E2D7DBDF6C8E" + + "34F3A0FD00C625428CB41857002159DAB94267ABE42D630C6AAA91AF837C7A67" + + "40754EA6634C45454C51B0BB4D44C3CCCCE4B32C00901CF69C008D013348379B" + + "2F9837F428A01B6173584691F2A6F3A3C4CF487D20D261B36C8CDB1BC158E2A5" + + "162A9DA4F7A97AA0879B9897E2B6891B672201F9AEFBF799C27B2587120AC586" + + "A511360926FB7DA8EBF5CB5272F396AE06608422BE9792E2CE9BEF21BF55B7EF" + + "F8DC7EC8C99910D3F800", + "4B622DE1350119C45A9F2E2EF3DC5DF56A27FCDFCDDAF58CD69B903752D68C20" + + "0934E160B234E49EDE247601"}, + Fp503: { + Fp503, "P-503", NewSike503(rand.Reader), + "testdata/PQCkemKAT_434.rsp", + "4032A90B6C036B7D2A83878AD116641AD319E420235A505F3F5C3DEC27C87A6C" + + "BA0792201D6E7B196C582D43CAF86CB2C7DEFA6598B543C946CDDF62EF9A328C" + + "8719B66BA5052231DAE13AF7D9CDEBB4ED327773C7AE0818F41AF1D28CD78B16" + + "C996232528235C8392B8FCFD925CB311B2A801B0402A90E527261EA32F2BEF67" + + "7C544908D5509B8AB7D7BF20456727AD358AD585306A0B28F6B2AA583CE8A3E0" + + "BB92D8CD55347D39D4E3C30D3D0F96EABB721A6968CDD143FE9227643CF697FB" + + "2DF0B71322B5EA1505D0DDBF70A2FD1193011F3BC18AA1E127C614B76969DCDA" + + "45A2072B519A1074FDA49F5C828450C6A007BF8D7CDDD5D2FC112119C679CA3A" + + "B16C6960B25F6C681A7DCED0F0E3901740D3DBF3A33011EB7DA460E8ADA80EE3" + + "45B2B71420950A9A803E4F11330EB91CCABB1EEE4D875A109D7724ABD201272C" + + "0B4981BDCDFA70F3430A89D2A88EEED474CF0CFAC65CE883F44B4722FA280C6F" + + "A9C4724D414B35AF69D6ECB21BFDA23BFF6B66C22C2451DC8E1C", + "7BF6938C975658AEB8B4D37CFFBDE25D97E561F36C219A0E8FE645816DBBC7ED7B57" + + "7700AE8DC3138E97A0C3F6F002065C92A0B1B8180208"}, + Fp751: { + Fp751, "P-751", NewSike751(rand.Reader), + "testdata/PQCkemKAT_644.rsp", + "E1A758EC0D418BFE86D8077B5BB169133C06C1F2A067D8B202D9D058FFC51F63" + + "FD26155A6577C74BA7F1A27E7BA51982517B923615DEB00BE408920A07831DF5" + + "978CFDDD0BF690A264353A4A16B666F90586D7F89A193CE09375D389C1379A7A" + + "528581C3ACB002CD2DC4F0FD672568FF9050BA8365C7FEFC5E6ED089B921DE68" + + "04091A0744DE3EB14D426A3F7DA215C50312617C1C2697243980D06056F2CCE8" + + "8AE7AE73C7343C0B7104C9F2870A94FED744CF6E94630514B6CEAB0E64733BB6" + + "FA67B931E5D8206010475CBE8BC587248D65D89D8CD9C8BBFA93E8B5F9EB9130" + + "773DED665D52ABBD91C4C8C255F73C0FC82501AE33330E9F308DE7177CBF83E4" + + "E26E334D7CB09019E638147FC58ED372AF660F14C194BC80E9666325C98E0F80" + + "877271D4A6BF514F603703D8A697874CD50A34D92F5AAEA84633CCF96801BD51" + + "7BF425DEE4A32AAF06684052473EA14643C3D535440FB2240A988D09F297C5A3" + + "88CB3DE60ED943F124034B90EFF611221F80F78EC124956338A105F6636B063D" + + "7E48BFBD5D614310FB97D86F122E4AE6F9DDF4977A93ED7D0CE2A94E346A1A03" + + "D3219CF21907B85A5BCDC713F93A4406A22E03B1655A66E1F6741A2F953E6FE0" + + "868B2614BABEF1943BBBCB1B66D3E7017E533EA84F291240B56AB33EF1DC3F3D" + + "E99DBF9E8BE51A0076E462BCDD825EA96D7F63C99177C305C257B31461F4C23D" + + "43115F0220409E8880BBB2468586D03461E807BE824B693874911B2B52AF06FD" + + "BDC47F5A0159729641A7C950AB9E03F2DC045135", + "0001020304050607080900010203040506070809000102030405060708090102" + + "8626ED79D451140800E03B59B956F8210E556067407D13DC90FA9E8B872BFB8F" + + "AB0A7289852106E40538D3575C500201"}, +} + +// Encrypt, Decrypt, check if input/output plaintext is the same. +func testPKERoundTrip(t *testing.T, v sikeVec) { + // Message to be encrypted + var pt [common.MaxMsgBsz]byte + var params = common.Params(v.id) + var ct = make([]byte, v.kem.CiphertextSize()) + var msg = make([]byte, params.MsgLen) + for i := range msg { + msg[i] = byte(i) + } + + // Import keys + pkB := NewPublicKey(params.ID, KeyVariantSike) + skB := NewPrivateKey(params.ID, KeyVariantSike) + pkHex, err := hex.DecodeString(v.PkB) + CheckNoErr(t, err, "Test vector wrong") + skHex, err := hex.DecodeString(v.PrB) + CheckNoErr(t, err, "Test vector wrong") + err = pkB.Import(pkHex) + CheckNoErr(t, err, "Public key import failed") + err = skB.Import(skHex) + CheckNoErr(t, err, "Private key import failed") + err = v.kem.encrypt(ct, rand.Reader, pkB, msg[:]) + CheckNoErr(t, err, "PKE roundtrip - encryption failed") + ptLen, err := v.kem.decrypt(pt[:], skB, ct) + CheckNoErr(t, err, "PKE roundtrip - description failed") + + if !bytes.Equal(pt[:ptLen], msg[:]) { + t.Errorf("Decryption failed \n got : %X\n exp : %X", pt[:ptLen], msg) + } +} + +// Generate key and check if can encrypt. +func testPKEKeyGeneration(t *testing.T, v sikeVec) { + var err error + var params = common.Params(v.id) + var pt [common.MaxMsgBsz]byte + var msg = make([]byte, params.MsgLen) + var ct = make([]byte, v.kem.CiphertextSize()) + // static buffer to ensure no overrides + var pk = NewPublicKey(v.id, KeyVariantSike) + var sk = NewPrivateKey(v.id, KeyVariantSike) + + for i := range msg { + msg[i] = byte(i) + } + + err = sk.Generate(rand.Reader) + CheckNoErr(t, err, "PKE key generation") + sk.GeneratePublicKey(pk) + + err = v.kem.encrypt(ct, rand.Reader, pk, msg[:]) + CheckNoErr(t, err, "PKE encryption") + ptLen, err := v.kem.decrypt(pt[:], sk, ct) + CheckNoErr(t, err, "PKE key decryption") + + if !bytes.Equal(pt[:ptLen], msg[:]) { + t.Fatalf("Decryption failed \n got : %X\n exp : %X", pt, msg) + } +} + +func testNegativePKE(t *testing.T, v sikeVec) { + var err error + var msg [common.MaxMsgBsz]byte + var ct = make([]byte, v.kem.CiphertextSize()) + var pk = NewPublicKey(v.id, KeyVariantSike) + var sk = NewPrivateKey(v.id, KeyVariantSike) + + // Generate key + err = sk.Generate(rand.Reader) + CheckNoErr(t, err, "key generation") + sk.GeneratePublicKey(pk) + + // bytelen(msg) - 1 + err = v.kem.encrypt(ct, rand.Reader, pk, msg[:v.kem.params.KemSize+8-1]) + CheckIsErr(t, err, "PKE encryption doesn't fail") + for _, v := range ct { + if v != 0 { + t.Fatal("Returned ciphertext must be not changed") + } + } +} + +func testKEMRoundTrip(t *testing.T, pkB, skB []byte, v sikeVec) { + // Import keys + var err error + var ssE [common.MaxSharedSecretBsz]byte + var ssD [common.MaxSharedSecretBsz]byte + var pk = NewPublicKey(v.id, KeyVariantSike) + var sk = NewPrivateKey(v.id, KeyVariantSike) + var ct = make([]byte, v.kem.CiphertextSize()) + var ssBsz = v.kem.SharedSecretSize() + + err = pk.Import(pkB) + CheckNoErr(t, err, "Public key import failed") + err = sk.Import(skB) + CheckNoErr(t, err, "Private key import failed") + + v.kem.Reset() + err = v.kem.Encapsulate(ct, ssE[:], pk) + CheckNoErr(t, err, "Encapsulation failed") + v.kem.Reset() + err = v.kem.Decapsulate(ssD[:ssBsz], sk, pk, ct) + CheckNoErr(t, err, "Decapsulation failed") + + if !bytes.Equal(ssE[:v.kem.SharedSecretSize()], ssD[:v.kem.SharedSecretSize()]) { + t.Errorf("Shared secrets from decapsulation and encapsulation differ [%s]", v.name) + } +} + +func testKEMKeyGeneration(t *testing.T, v sikeVec) { + var ssE [common.MaxSharedSecretBsz]byte + var ssD [common.MaxSharedSecretBsz]byte + var ct = make([]byte, v.kem.CiphertextSize()) + + sk := NewPrivateKey(v.id, KeyVariantSike) + pk := NewPublicKey(v.id, KeyVariantSike) + CheckNoErr(t, sk.Generate(rand.Reader), "error: key generation") + sk.GeneratePublicKey(pk) + + // calculated shared secret + v.kem.Reset() + err := v.kem.Encapsulate(ct, ssE[:], pk) + CheckNoErr(t, err, "encapsulation failed") + v.kem.Reset() + err = v.kem.Decapsulate(ssD[:v.kem.SharedSecretSize()], sk, pk, ct) + CheckNoErr(t, err, "decapsulation failed") + + if !bytes.Equal(ssE[:], ssD[:]) { + t.Fatalf("KEM failed \n encapsulated: %X\n decapsulated: %X", ssD[:], ssE[:]) + } +} + +func testNegativeKEM(t *testing.T, v sikeVec) { + var ssE [common.MaxSharedSecretBsz]byte + var ssD [common.MaxSharedSecretBsz]byte + var ssTmp [common.MaxSharedSecretBsz]byte + var ct = make([]byte, v.kem.CiphertextSize()) + var ssBsz = v.kem.SharedSecretSize() + + sk := NewPrivateKey(v.id, KeyVariantSike) + pk := NewPublicKey(v.id, KeyVariantSike) + CheckNoErr(t, sk.Generate(rand.Reader), "error: key generation") + sk.GeneratePublicKey(pk) + + v.kem.Reset() + err := v.kem.Encapsulate(ct, ssE[:], pk) + CheckNoErr(t, err, "pre-requisite for a test failed") + + // Try decapsulate too small ciphertext + v.kem.Reset() + CheckNoErr( + t, + CheckPanic(func() { _ = v.kem.Decapsulate(ssTmp[:ssBsz], sk, pk, ct[:len(ct)-2]) }), + "Decapsulation must panic if ciphertext is too small") + + ctTmp := make([]byte, len(ct)+1) + // Try decapsulate too big ciphertext + v.kem.Reset() + CheckNoErr( + t, + CheckPanic(func() { _ = v.kem.Decapsulate(ssTmp[:ssBsz], sk, pk, ctTmp) }), + "Decapsulation must panic if ciphertext is too big") + + // Change ciphertext + ct[0] = ct[0] - 1 + v.kem.Reset() + err = v.kem.Decapsulate(ssD[:ssBsz], sk, pk, ct) + CheckNoErr(t, err, "decapsulation returns error when invalid ciphertext provided") + + if bytes.Equal(ssE[:], ssD[:]) { + // no idea how this could ever happen, but it would be very bad + t.Error("critical error") + } + + // Try encapsulating with SIDH key + pkSidh := NewPublicKey(v.id, KeyVariantSidhB) + prSidh := NewPrivateKey(v.id, KeyVariantSidhB) + v.kem.Reset() + CheckNoErr( + t, + CheckPanic(func() { _ = v.kem.Encapsulate(ct, ssE[:], pkSidh) }), + "encapsulation accepts SIDH public key") + + // Try decapsulating with SIDH key + v.kem.Reset() + CheckNoErr( + t, + CheckPanic(func() { _ = v.kem.Decapsulate(ssD[:ssBsz], prSidh, pk, ct) }), + "encapsulation accepts SIDH public key") +} + +// In case invalid ciphertext is provided, SIKE's decapsulation must +// return same (but unpredictable) result for a given key. +func testNegativeKEMSameWrongResult(t *testing.T, v sikeVec) { + var ssE [common.MaxSharedSecretBsz]byte + var ssD1 [common.MaxSharedSecretBsz]byte + var ssD2 [common.MaxSharedSecretBsz]byte + var ct = make([]byte, v.kem.CiphertextSize()) + var ssBsz = v.kem.SharedSecretSize() + + sk := NewPrivateKey(v.id, KeyVariantSike) + pk := NewPublicKey(v.id, KeyVariantSike) + CheckNoErr(t, sk.Generate(rand.Reader), "error: key generation") + sk.GeneratePublicKey(pk) + + v.kem.Reset() + err := v.kem.Encapsulate(ct, ssE[:], pk) + CheckNoErr(t, err, "pre-requisite for a test failed") + + // make ciphertext wrong + ct[0] = ct[0] - 1 + v.kem.Reset() + err = v.kem.Decapsulate(ssD1[:ssBsz], sk, pk, ct) + CheckNoErr(t, err, "pre-requisite for a test failed") + + // change secret keysecond decapsulation must be done with same, but imported private key + var expSk [common.MaxSikePrivateKeyBsz]byte + sk.Export(expSk[:]) + + // create new private key + sk = NewPrivateKey(v.id, KeyVariantSike) + CheckNoErr(t, sk.Import(expSk[:sk.Size()]), "import failed") + + // try decapsulating again. + v.kem.Reset() + err = v.kem.Decapsulate(ssD2[:ssBsz], sk, pk, ct) + CheckNoErr(t, err, "pre-requisite for a test failed") + + // ssD1 must be same as ssD2 + if !bytes.Equal(ssD1[:], ssD2[:]) { + t.Error("decapsulation is insecure") + } + + // ssD1 and ssD2 must be different than ssE + if bytes.Equal(ssE[:], ssD1[:]) || bytes.Equal(ssE[:], ssD2[:]) { + // this test requires that decapsulation returns wrong result + t.Errorf("test implementation error") + } +} + +func testKAT(t *testing.T, v sikeVec) { + ssGot := make([]byte, v.kem.SharedSecretSize()) + testDecapsulation := func(pk, sk, ct, ssExpected []byte) { + var pubKey = NewPublicKey(v.id, KeyVariantSike) + var prvKey = NewPrivateKey(v.id, KeyVariantSike) + if pubKey.Import(pk) != nil || prvKey.Import(sk) != nil { + panic("sike test: can't load KAT") + } + + err := v.kem.Decapsulate(ssGot, prvKey, pubKey, ct) + CheckNoErr(t, err, "sike test: can't perform degcapsulation KAT") + if !bytes.Equal(ssGot, ssExpected) { + t.Fatalf("KAT decapsulation failed\n") + } + } + + readAndCheckLine := func(r *bufio.Reader) []byte { + // Read next line from buffer + line, isPrefix, err := r.ReadLine() + if err != nil || isPrefix { + panic("Wrong format of input file") + } + + // Function expects that line is in format "KEY = HEX_VALUE". Get + // value, which should be a hex string + hexst := strings.Split(string(line), "=")[1] + hexst = strings.TrimSpace(hexst) + // Convert value to byte string + ret, err := hex.DecodeString(hexst) + if err != nil { + panic("Wrong format of input file") + } + return ret + } + + testKeygen := func(pk, sk []byte) bool { + // Import provided private key + var prvKey = NewPrivateKey(v.id, KeyVariantSike) + var pubKey = NewPublicKey(v.id, KeyVariantSike) + var pubKeyBytes = make([]byte, pubKey.Size()) + CheckNoErr(t, prvKey.Import(sk), "Can't load KAT") + + // Generate public key + prvKey.GeneratePublicKey(pubKey) + pubKey.Export(pubKeyBytes) + return bytes.Equal(pubKeyBytes, pk) + } + + f, err := os.Open(v.KatFile) + if err != nil { + t.Fatal(err) + } + + r := bufio.NewReader(f) + for { + line, isPrefix, err := r.ReadLine() + if err != nil || isPrefix { + if err == io.EOF { + break + } else { + t.Fatal(err) + } + } + if len(strings.TrimSpace(string(line))) == 0 || line[0] == '#' { + continue + } + + // count + _ = strings.Split(string(line), "=")[1] + // seed + _ = readAndCheckLine(r) + // pk + pk := readAndCheckLine(r) + // sk (secret key in test vector is concatenation of + // MSG + SECRET_BOB_KEY + PUBLIC_BOB_KEY. We use only MSG+SECRET_BOB_KEY + sk := readAndCheckLine(r) + sk = sk[:v.kem.params.MsgLen+int(v.kem.params.B.SecretByteLen)] + // ct + ct := readAndCheckLine(r) + // ss + ss := readAndCheckLine(r) + + testKeygen(pk, sk) + testDecapsulation(pk, sk, ct, ss) + testKEMRoundTrip(t, pk, sk, v) + } +} + +// Interface to "testing" + +/* ------------------------------------------------------------------------- + Wrappers for 'testing' SIDH + -------------------------------------------------------------------------*/ +func testSike(t *testing.T, m *map[uint8]sikeVec, f func(*testing.T, sikeVec)) { + for i := range *m { + v := (*m)[i] + t.Run(v.name, func(t *testing.T) { f(t, v) }) + } +} + +func TestPKERoundTrip(t *testing.T) { testSike(t, &tdataSike, testPKERoundTrip) } +func TestPKEKeyGeneration(t *testing.T) { testSike(t, &tdataSike, testPKEKeyGeneration) } +func TestNegativePKE(t *testing.T) { testSike(t, &tdataSike, testNegativePKE) } +func TestKEMKeyGeneration(t *testing.T) { testSike(t, &tdataSike, testKEMKeyGeneration) } +func TestNegativeKEM(t *testing.T) { testSike(t, &tdataSike, testNegativeKEM) } +func TestKAT(t *testing.T) { testSike(t, &tdataSike, testKAT) } +func TestNegativeKEMSameWrongResult(t *testing.T) { + testSike(t, &tdataSike, testNegativeKEMSameWrongResult) +} + +func TestKEMRoundTrip(t *testing.T) { + for _, val := range tdataSike { + // fmt.Printf("\tTesting: %s\n", val.name) + pk, err := hex.DecodeString(val.PkB) + CheckNoErr(t, err, "public key B not a number") + sk, err := hex.DecodeString(val.PrB) + CheckNoErr(t, err, "private key B not a number") + testKEMRoundTrip(t, pk, sk, val) + } +} + +/* ------------------------------------------------------------------------- + Benchmarking + -------------------------------------------------------------------------*/ + +func benchSike(t *testing.B, m *map[uint8]sikeVec, f func(*testing.B, sikeVec)) { + for i := range *m { + v := (*m)[i] + t.Run(v.name, func(t *testing.B) { f(t, v) }) + } +} + +func benchKeygen(b *testing.B, v sikeVec) { + pub := NewPublicKey(v.id, KeyVariantSike) + prv := NewPrivateKey(v.id, KeyVariantSike) + _ = prv.Generate(rand.Reader) + + b.ResetTimer() + for n := 0; n < b.N; n++ { + prv.GeneratePublicKey(pub) + } +} + +func benchmarkEncaps(b *testing.B, v sikeVec) { + pub := NewPublicKey(v.id, KeyVariantSike) + prv := NewPrivateKey(v.id, KeyVariantSike) + + if prv.Generate(rand.Reader) != nil { + b.FailNow() + } + prv.GeneratePublicKey(pub) + + var ct [common.MaxCiphertextBsz]byte + var ss [common.MaxSharedSecretBsz]byte + + b.ResetTimer() + for n := 0; n < b.N; n++ { + v.kem.Reset() + _ = v.kem.Encapsulate(ct[:], ss[:], pub) + } +} + +func benchmarkDecaps(b *testing.B, v sikeVec) { + var ct [common.MaxCiphertextBsz]byte + var ss [common.MaxSharedSecretBsz]byte + var ssBsz = v.kem.SharedSecretSize() + + pkA := NewPublicKey(v.id, KeyVariantSike) + prvA := NewPrivateKey(v.id, KeyVariantSike) + pkB := NewPublicKey(v.id, KeyVariantSike) + prvB := NewPrivateKey(v.id, KeyVariantSike) + + if prvA.Generate(rand.Reader) != nil || prvB.Generate(rand.Reader) != nil { + b.FailNow() + } + + prvA.GeneratePublicKey(pkA) + prvB.GeneratePublicKey(pkB) + + v.kem.Reset() + err := v.kem.Encapsulate(ct[:], ss[:], pkA) + if err != nil { + b.FailNow() + } + + ctSlc := ct[:v.kem.CiphertextSize()] + + b.ResetTimer() + for n := 0; n < b.N; n++ { + v.kem.Reset() + _ = v.kem.Decapsulate(ss[:ssBsz], prvA, pkB, ctSlc) + } +} + +func BenchmarkKeygen(b *testing.B) { benchSike(b, &tdataSike, benchKeygen) } +func BenchmarkEncaps(b *testing.B) { benchSike(b, &tdataSike, benchmarkEncaps) } +func BenchmarkDecaps(b *testing.B) { benchSike(b, &tdataSike, benchmarkDecaps) } + +func ExampleKEM() { + // Allice's key pair + prvA := NewPrivateKey(Fp503, KeyVariantSike) + pubA := NewPublicKey(Fp503, KeyVariantSike) + // Bob's key pair + prvB := NewPrivateKey(Fp503, KeyVariantSike) + pubB := NewPublicKey(Fp503, KeyVariantSike) + // Generate keypair for Allice + err := prvA.Generate(rand.Reader) + if err != nil { + panic(err) + } + prvA.GeneratePublicKey(pubA) + // Generate keypair for Bob + err = prvB.Generate(rand.Reader) + if err != nil { + panic(err) + } + prvB.GeneratePublicKey(pubB) + // Initialize internal KEM structures + var kem = NewSike503(rand.Reader) + // Create buffers for ciphertext, shared secret received + // from encapsulation and shared secret from decapsulation + ct := make([]byte, kem.CiphertextSize()) + ssE := make([]byte, kem.SharedSecretSize()) + ssD := make([]byte, kem.SharedSecretSize()) + // Allice performs encapsulation with Bob's public key + err = kem.Encapsulate(ct, ssE, pubB) + if err != nil { + panic(err) + } + // Bob performs decapsulation with his key pair + err = kem.Decapsulate(ssD, prvB, pubB, ct) + if err != nil { + panic(err) + } + fmt.Printf("%t\n", bytes.Equal(ssE, ssD)) + + // Bob performs encapsulation with Allices's public key + err = kem.Encapsulate(ct, ssE, pubA) + if err != nil { + panic(err) + } + // Allice performs decapsulation with hers key pair + err = kem.Decapsulate(ssD, prvA, pubA, ct) + if err != nil { + panic(err) + } + fmt.Printf("%t\n", bytes.Equal(ssE, ssD)) + + // Output: + // true + // true +} diff --git a/src/circl/dh/sidh/testdata/PQCkemKAT_374.rsp b/src/circl/dh/sidh/testdata/PQCkemKAT_374.rsp new file mode 100644 index 00000000000..8498b26dcb8 --- /dev/null +++ b/src/circl/dh/sidh/testdata/PQCkemKAT_374.rsp @@ -0,0 +1,702 @@ +# SIKEp434 + +count = 0 +seed = 061550234D158C5EC95595FE04EF7A25767F2E24CC2BC479D09D86DC9ABCFDE7056A8C266F9EF97ED08541DBD2E1FFA1 +pk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sk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ct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ss = 35F7F8FF388714DEDC41F139078CEDC9 + +count = 1 +seed = D81C4D8D734FCBFBEADE3D3F8A039FAA2A2C9957E835AD55B22E75BF57BB556AC81ADDE6AEEB4A5A875C3BFCADFA958F +pk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sk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ct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ss = 9D7EDCCC78E60EFDDD75D585AD920730 + +count = 2 +seed = 64335BF29E5DE62842C941766BA129B0643B5E7121CA26CFC190EC7DC3543830557FDD5C03CF123A456D48EFEA43C868 +pk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sk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ct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ss = 68C17AB42604D799578D835DC7256001 + +count = 3 +seed = 225D5CE2CEAC61930A07503FB59F7C2F936A3E075481DA3CA299A80F8C5DF9223A073E7B90E02EBF98CA2227EBA38C1A +pk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sk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ct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ss = E0BD6870B0308BACBDA1061628CE8F0D + +count = 4 +seed = EDC76E7C1523E3862552133FEA4D2AB05C69FB54A9354F0846456A2A407E071DF4650EC0E0A5666A52CD09462DBC51F9 +pk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sk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ct = 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ss = 377A154FEDAC0A7DF1DFB1409D34F568 + +count = 6 +seed = 2E014DC7C2696B9F6D4AF555CBA4B931B34863FF60E2341D4FDFE472FEF2FE2C33E0813FC5CAFDE4E30277FE522A9049 +pk = 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ss = CBC8B73A7F31E6E4B909DF774D17E1A2 + +count = 8 +seed = CBE5161E8DE02DDA7DE204AEB0FBB4CA81344BA8C30FE357A4664E5D2988A03B64184D7DC69F8D367550E5FEA0876D41 +pk = 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ss = B49ABAAE30A790FECE54A3F113FD575B + +count = 11 +seed = 6C029462CA42ED520F10A579F52687101105E0B90C6E7BFA582A4C112B579D5AD0A0ABD38F72ABCFDCAAF5893A112BDC +pk = 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ss = A663DA396F96655AED1602ACFB1C83B3 + +count = 12 +seed = DB00120937570D62331F4C3F19A10465231EFF46465CDEE336A0D46AA1E7493DF80F18617F9FFD0476CF7784A403EF4F +pk = 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ss = 897ECF117CAD056AA7607F485F5EDBBD + +count = 14 +seed = E2819EF86853BCA1B9DEE7EE1C1619988964F9A913E635AACF0D96CA6E0300D084329DABD8F149E24176D22757404260 +pk = 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46722EFE47F4BFDC5B36F8FDC92336C965669E48B6A1018E88B4AFAF4EC7765AF9ACD146F2D0DD800BBC15B8A79043E74DBA8372DA5E0157635F4C61FEA89934E5948B39B2C4833DF9BBD41A92E87D2EAA03F892FBE46D5A3DED0474FD123B6BC29A6D451F0C4CCD913994BD1900E3164E578A596DD8E7B0C6EB7A2485113A8AD5770BEECEA55E302039658E234E918495E0EEAFED4FB8AE8FDB0CE0EB926075C4E5EB4B00B57C1643BD1B4166191A35C0DCC839FEBB8B4BE072452C5BF0E901D34A71350BAA7EC471780306856FE952C97668E94EACDF943047870093BCF560CE4A01C0F26C9B4ADC2B7EFE2C97D9FA8C38FA193A61D50DC4DC4CFD09EE9F3D4025F51231CDEF2D1229B4995274B3EBDD5B01849C10CF45ED4C2EC1BCA8C03A0F0619FEE9FA84095D9A95CDC957450BCB5B3639076A6D6117922D8998BA479026F050C1A9923FEFBD009C4DF016F2395F2C7EFC8203AAF18A58 +ss = B58E59F4A05558B84AE4851836CC49B2 + +count = 39 +seed = CF520B92A2E3677AFD003EC1EC6EF136A709D78F828C9C0DD4946EFBD451C5FAABFC83CA66F9D3D17EE4220553B7A69F +pk = 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ss = B899E849D60739D059CF343F459E7230 + +count = 41 +seed = F170583CB451D8A45D105457C02C01A33A40350616ED8515BD49067142F61EFB00F07857E4FFF3FE11E7164C648C76ED +pk = 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ss = A3ABAE416B3EFD3FA907D5C21E9B8F51 + +count = 55 +seed = 467F6158CB86B724039FF18C47950AE5C49170163C910FC9A9B30141F86E9C06EBCEC91497BCD156D95758C9F0C6EF91 +pk = 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ss = A5611782265E1932DF3B7E736F40BA3A + +count = 59 +seed = A0264C58AB1F2CBCB212077FD378D340307ACCB31F1312137CF84E3D3135044D4EAE8BD38BC3E540A0C14D46458F6179 +pk = 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ss = BBA5BD08A7BD6DB8620A1C1149B00D03 + +count = 60 +seed = 99A9CDBFC674AB3FF2C64CDED7D697A6E27A767434A47AFF7C3FBF3C6A22D6043D27868955286A13EFE3DE36D22EC48E +pk = 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3613BFD6D40D49A140CDE59FF2AFF193B5C6A5E5699E25AB2FE0FD4A495B68E3FBF4C3FF92440462C3881D533D289619D63D7F48F05400F70F1977A6EDAC7BDBA93E629032B0BF5501B7BF17FD2B3C1BF2A2273498F1A96620730CC4EE61E76CF0680B52DC49BFC4CAF155FB9C00AFED4CDB9DCEEA14389E1E6A174A8D23E863380E06B3DDBE07BF19CC88005C2A68F82CA2462FEC058D11F7C44811363E7945705C3E710085443A799503AF24CC49688C6D8900E27577E9ACFB18601F383E36143C36CF7F013F97024598B64B3EB1AA60738AF99D00FDDD66105D0114932A2E7F50C4A38269C81C97574A43821FF7F53655F1264281FFDEF023D4398D56084958C27B8EB72729C0CFAC6FEA68618683CF6C00D9C8A17F50184135053706013D0FAB0B11E3CBCFF39ECA75A02980A178800A730AD15308714481FD9BCF733408B17EDF38661432F48101430614AC37977237A2E574DC450EC6C4 +ss = E72DEB6A7678A71CC4986737F98204E5 + +count = 61 +seed = C799D57B41F28C5C446DFC58A5AC6499C4BCF3C162AFD2B09A16549826EC2A6F689E44BAFC4ACC82F5D6AEC23F4A3993 +pk = 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703BB1DD130A7087003CD296E13FFA7CE1AB2EFA024EB02ECBB6054C2DA0537317614E1D075F1F0A03A289B48212EFA3E0FCFD6D00DF009E6D779B03BC0EFE5C1FC44327E710FAB872A967B5A53D129AF3336FBFD92BEB7361DFBB019DC19630D756D7888095DB3396DF579D200064B53C4DC5DE29A5535E77B5C5BACF30373F2D85E29FEB60ECBDF46ECE95DAEFF20D1331DEF5F53AD0004385275C206A1AF5BF46914D00BB9D1D4C631000C5FDB4ECA685E0C14FA07CA70795798B801CB05658615A9B11B953519A6A15E7BE7A9D24665F3D0146215A3451BCA000E1FF18EFAC26EAA35A084C4D4644DA52D3E69357C3E51A6C3DB78B968A2046DC7727BB115B24C92D63D1E0DBE440F96B1E3428BA3A7801F4190D85804D261D1613A361F529FDFA77579CA65586E7E6DD91E9F0B7B376597745BA0821176F66B1613B84B973D0B9EF62E41741C6013AFCE7D7BCFAB307E3543041847B858B +ss = 14E0D35F4EEF91D784C700B5C9E99296 + +count = 62 +seed = F7AE036A0176A9DE9A036A542DD2840033277C44AE936D10B768566216DE9D4395CD42B116873B69D9804BA6CCBC05D5 +pk = 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ss = D229BBB3CA9080B96B26D87F2FBFCC26 + +count = 75 +seed = 8E2995F1B3E43853B18916BB1212ACEB05898E2B177A87ABEB928AD7184E59695C56B2CCCF5DB80853C28A525E327D13 +pk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sk = 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ss = C96B986298CC6BFDA4253200192D1573 + +count = 76 +seed = 9218943C51FD2DE47E509AAC67EFF176795102F37D7A2017E3AFD768FCDA7877AF38739B00FCDF227C2FD62EB635942C +pk = 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ss = B1466D6C93EDFD9DDA1805592F90690D + +count = 77 +seed = 542E20078ADD5296050AF150360F057F6B9AB3BA835589DD56987DE805F900B906505B5390A0D86CBA28038992DFC59A +pk = 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ct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ss = 8C41BCA14516014306BE132DC6EFDDDA + +count = 96 +seed = B3AC6503206ACCC2A92CBC210D020A2654726911D11CE676AA04FEAA08AF1D20C654E4105883AE470EC3AB299075D420 +pk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sk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ct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ss = A6DB9C606E364AECDF4AC552B41757DE + +count = 97 +seed = 59EFF60B1EF6185DB34EE1E3B1DD2F159106CECEAA79BEB74923B4F5623D5BC52DBF5D2594A1F7C6C64D12CF144E9ED4 +pk = 39261E697967B0BB7EE0AD5621B7C62179401C8FCCB5BDA55776AF330E450DAE2E5B7241E9CEC5A2C09514CB96CA35A7BCACEB781E6500D62CF7ACEE028461D8A542F5FA2B7FA25147D62AD481F97C4E2AAE52C6B8AF0D5CEFB771E4E42FD707FEC2B9BE61E403D211DA70AC6801BD0472EDAFAF17A0DD1D772D3B39FCE955FD37648EDE750AE8B707AF6747A1EB53A91EC66C25F30DDB3171C8D83A8114DE7F722460BD017811EF82DF92339BAF90291CB3B37879D4795FAC777793F2DE1FA2724DF4EBE6CB6C0EA6BD6D9548D3AF8701E21292B6791D2A9B0E2901A45B0C8CACE6E2F70172B04128CAE55DCE6B0A2EE31013D6765E7C027A6985DEC8F02ACD09D4BCA7F79516D4F3F4965EB572717CB3BB01FA8871B8D508B9DD59342A43AEAEBEDF788AB4A64585C0C0CB33E1DFB3063566F3B549F4E801AEF11420094EF1143F2D9C84DFBE574301 +sk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ct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ss = F68927D6306B93CC1F822E2CBB5C43B3 + +count = 98 +seed = DDDCA9DC31BEA737D3F474E7560B37FACB2F53C803E768FFAADE7669FF94B1D4FBD17068CFFD5DFDD24AADADA4EF6B12 +pk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sk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ct = CA1221AE3B6D2227DBEB2D3366A6FF04D4CEAFD8A87A646A0E69C17DE92A65FE381542CCC3DF59EE06EDD5589252CE0154D00CB22BDE00426BA25F63E4D80872B0369562226670F392ABC3EE8254B777AFA9818DA03201D927C6A44A798C4E8101DF0A4532439592FF6219230500C7BA12B97300F7E8251A15508E61299AC293EE92F07C720E5647590A445C11B746402E7722B801ED9D237C5E11F40EAC9F518BB17D2C014A45AAC78605365D21191A0176DA1EA59002F6552A84B34E9CD87099A4C92682510E0F306DB57F65A8B22BB4835EA77F71345041451402F7C5B8C5254F64ECB9E70694D6942986AB2CE261E8BCE34DBAC5BC35AEDAAF97F4638468E81A58A86762F3C7DC33BFE134F7EBBA728301704D894ED7B1E1EE9B56FDC3BC28C991337265D84811A47351F6AB7B7DC13F5903CE4C8533E67EB4562BAD582B6F37A1E43FE31420F901E066D6103DB5DDEE5402CBBCA607DBDC +ss = ABB141C9189DD1D2F5BCD86C02037C36 + +count = 99 +seed = 2A6F7386B815366F572AEB6C79E272CC21B7095FE09575F18072C9D677DA23BC9C8A4BC393B7524604D299BEDD260C8B +pk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sk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ct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ss = DA40C7AB4E2ED76E4A3BDB509B806E5C + diff --git a/src/circl/dh/sidh/testdata/PQCkemKAT_434.rsp b/src/circl/dh/sidh/testdata/PQCkemKAT_434.rsp new file mode 100644 index 00000000000..5f969bb0b11 --- /dev/null +++ b/src/circl/dh/sidh/testdata/PQCkemKAT_434.rsp @@ -0,0 +1,702 @@ +# SIKEp503 + +count = 0 +seed = 061550234D158C5EC95595FE04EF7A25767F2E24CC2BC479D09D86DC9ABCFDE7056A8C266F9EF97ED08541DBD2E1FFA1 +pk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sk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ct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ss = AF1280151C2C59B4D4150B18BA7F71590523CEA83C9BDDDA + +count = 1 +seed = D81C4D8D734FCBFBEADE3D3F8A039FAA2A2C9957E835AD55B22E75BF57BB556AC81ADDE6AEEB4A5A875C3BFCADFA958F +pk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sk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ct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ss = 810D3549BEB3DD6E45EEADBB75386F6A63FF3330ECB04C22 + +count = 2 +seed = 64335BF29E5DE62842C941766BA129B0643B5E7121CA26CFC190EC7DC3543830557FDD5C03CF123A456D48EFEA43C868 +pk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sk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ct = 4BF036711DD1C3B4C941967D4F63A35C4EBBF45E4601573CF33D49921D95F17792674F7C18E455D8C7F1BEF479BB91D5B22E2EC955988C70DFFAC371BFB41AB81252F22949685E78E055E7495D82AE77006B1D05015F149D9EA4F927096500C8FCB583452C2E20E0C55B4AB18F801E570E5A8BBC56273902279B2B4C3C1DB0DF7811617694C1DE0117A9E112FA58EA523F8A40A749184DC9F9EF44E09BF372EDB9D55A4C7DB348EC971185EBE8CD005A73008ED74131AB939083813129086BBC1EA1DD04A3D5D844F901DC9FDF089A2504F1D32C61EAFFB0B0B66445856AA5359D49DD737B01A6235B2A35E29154AC71229F93DD4C9CD3DCA2C3621158F11EC6895D5C57A6E2FDCD0DCABB4E150DB2ADF9F5F16320BCE723220522E05B196AFBDEC21FF14E53FE9EF054639FC98D637FEF20FA0149709517BB3521C787B9F377857DE2B41F4FCF60113DE4E0488EFAF0A536E8C46B34E41D8DB237AD704CE981D15CD8765084B35983BD35E172ED977F9B43F8D9273B915D8639F91164642199EFC3F90B43017D1D46BB68ABF28A7EA1D471 +ss = 68CFB6A6E01FB2FFD8707C8278D705E0DCB53A502BFAD6B4 + +count = 3 +seed = 225D5CE2CEAC61930A07503FB59F7C2F936A3E075481DA3CA299A80F8C5DF9223A073E7B90E02EBF98CA2227EBA38C1A +pk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sk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ct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ss = 6CB10B8CF5C9E4D96562A962E5C1B0553799BCE28197C48B + +count = 4 +seed = EDC76E7C1523E3862552133FEA4D2AB05C69FB54A9354F0846456A2A407E071DF4650EC0E0A5666A52CD09462DBC51F9 +pk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sk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ct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ss = 815FA89CD9C0C6DEBD6D4C3F4B38FDBA423C8AE4555C6939 + +count = 5 +seed = AA93649193C2C5985ACF8F9E6AC50C36AE16A2526D7C684F7A3BB4ABCD7B6FF790E82BADCE89BC7380D66251F97AAAAA +pk = 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ss = 4668C26A46478B62B40E5BED0BF71492A7FDB443FC010AB2 + +count = 6 +seed = 2E014DC7C2696B9F6D4AF555CBA4B931B34863FF60E2341D4FDFE472FEF2FE2C33E0813FC5CAFDE4E30277FE522A9049 +pk = 4B8C0E0261C43AE34A19A0C61C63C333C8CC58E415944FDEFED6A7AF831740BEB8BA07E79C806CF4DA9A1DE9448F657F71E0A05C0AE67C0243E36BB4A0560F0F08BC79BC60A32E66B84D9C8D3BA2AE66B7B6DB17584647D9B412DD25219D3F52CD939E8B29FE13458460A22D9EF857DBCE1C41E84796BE1B5653DD37660F57C76419688DA976A1D42D53357F42A80BE16B74F289C1EA06D9410A3E4AC94FABF1A05FB87CD0E3233B469E32CF98500C8FB92C52743A4923D83370AE8509ED2C24F05A3B03EAB4D6AA7795EB3AF2F907E06CF0EFCEB2019C6B6544F0E9B075C438BB0433669B5EAC9010733ABB675ACBA6A3DB1E0EDE690DCD3CDE4E2B17BE9C0B26411E9CD7C5C06B18150DAB03D7C38CE09B4FBFB64827FAFE6C7E62E19C9477F73E1CA00B0A737F3A8CCF6D669979DAAEE8B445372C147790D420DD53630B87676B53FFF90242D834125A1A369975EB3475716CC7B9E168C4A9560B364F164E6EDFE67DDC1967C16496C339789D22C757934980C39752E10E1D +sk = 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ss = F9CDF2C113564143F3CF1EF59E20785D99974121A6832AEC + +count = 7 +seed = AEFB28FDD34E0AB403A703B535296E3A545CA479C1D8148E2D501B3C8DD8B1034BD986F13F1A7B4671BE769359FD2AAB +pk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sk = 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ss = 7D5AFA784F3C460498AAA1782428C25E4C3DC97B6F7D3125 + +count = 8 +seed = CBE5161E8DE02DDA7DE204AEB0FBB4CA81344BA8C30FE357A4664E5D2988A03B64184D7DC69F8D367550E5FEA0876D41 +pk = 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ss = 25356B80E1208646C29DBA5EF1348D3265E8FF9E767C4465 + +count = 24 +seed = 7E87FB886BC3C7C9FC12569F465D2ECD12532E76CC27C65644C8D3DD603B0CB2D036C5974E675058F271D5C82AD7A813 +pk = 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ss = 55501CE296D88A5A9C9C962B05C7562B8924ACF2128AB352 + +count = 45 +seed = D3C9EBBA6EB03CCB5C9B9D2C8D7F0CFBBF50841E24396CDDF0E56525B38918C2FBE6C34CC1B93F7BCD4F4D5777E1A488 +pk = 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55F3EAAB473FEBF0CAA4B5C5EB737BBFEC56D4E1CB64899E1FC60BD392ECAA345D84D73F1896527F79E966F5EA58C683B43386AEE0B98CF745365DFC0F2525BC5E692947E7257585DD766E6BC9FE0104F8FCC402F947AE491437A797FC7BCCF6BA7447ABB15A0DBD80E11E419C617B2DFDD231A2C39ACF734BB9D2713D17975C78F8255F7CE70BE77ACF8B364A29600A419542A74DF74F037824CB73BF62070BB7D9AE6967D0F4363544312006F0C9A26C3ABD7B421C8B481F47B2A01FC04DACC9915CD373F4CF9A823A5E3B0D8125E4D8F2576536739D5348EA9E30E03C5F3B9B115B9B36DDCE3AA2C8EEAAC1743000041C0CE97F4F9A630726B713F72339E81E36C0EAE60434DE616CC0E2738B6090CCE6EC0D1F3C7F9E95D66BBEB87218F9580A236824C292FA312AE85C9F67A5C45393781870B5C08F6F5209C2DE8B1DF17E8309CA1C0E0DBC981F2FC3911F054497F9E507A5E9708C3F964E16678D943425162892D882C5D7E8B218EB69FA71CD4F61FE7EE8EB5A8F512815829B4A6BBE3D27AA1E48F570EED41B68EAE8E2FDD03499 +ss = 6611465188E82C488DAA81274C8E37E2B3C93A885D9009A7 + +count = 53 +seed = D71729DCBB27D7CB39E9E905025D3E55C8602EFBCC483C9B866EBF82326157833169243C14550AD728BD1470F39C642E +pk = 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40650D6491686A9501CE92B7847D910B2590FED52A4B4DADFD286BB8E88714E7D8324C7169BE8BA591A15D6C65610B784589A46E69A5A20565FDDE9B49941C05C17D040ECC38020CC574F83EF9D8B94EBC42CFA36991EB3955081EFF82D6A398F2B67D84F87B71D51939074B1A7E7562A53CDF71F427BF536E92D26C610A2FCEC7E861C33EA1D5069C136CA9EB2855C5451158A60E02A8B35F0C3BB45A4214E9167EA81CFE6FADCA48A1EDE89AECEA213B6A312E21E6E2A8D981148B3E4A7CD7FA6F9BF9857B96DCA7EB2A48638DE84BAB37646D9F90DF16CC82AC9D873D00FE36B9213ABCC19BB6AE8533AB4903D99B768FA42B89C79A6B66DA8D06D4116CDFB2AC643560023C0234D4296C9D5BD1A6E4C6994C900EEE0A136F0E19919857D8F7CF6AD147DDDD436B7998D4617A1B58D3FBC5BE78DEC37A722D07519A1ED6995C45AF687619BD0D00E1D20E6EC9EC83CF6319CA30564974143E0AAED1B8DF4A4970AC33CE3B0738AC522078BDCE647804A10C6DF5BD1BB276004745252BB9270F325196904B9F71F7A84E5E447E78F54BA5 +ss = 3F068357967BF2EA7A4C4A1C3A7DCDEAB3690623416DDAA9 + +count = 54 +seed = A7C2C8EDB3601396BEB2DF0657EC82FD5780A2723581A9E03DEE1CDB018440439BB1142CAB0487C5D136E9AF46338AB7 +pk = 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5A229B3C3524E57838F0079074FC2D9D527890DFCBC6E5F83DB85CF3752B67F30E363EEBBC4DCDB0536FAC2D240BE47426D0D4779AAE1305664DBF4A57110A664F8B2B49EEB39974294E455099EC98E5E972240AB6521075B05ED8AF8B0BDB1AF92353F353EDBDDAF04996B6CC83D3E89B2855981EB895EA04F11DC3870CE71AA30076AA72EA9EBB686E4E2E45F489E67C9CB6CF22B1D8BEF243F97E41ADF7CAB8293FD2E950E1F9B3014531B8E4F8DDFD74B7688D03502C32B12CA317518E28A30A713CEA817C32101906D0EAC55DD243642E47606B63885F1CE6E1EF76AA7FCFDB11376E4ACC386A1FF95CE8454481081431AD785CA58C013709172DB03666EBA3F858C750E33067290AAFEE066A1F9B24EFFB14DCD26BFB9D86F6217D217E8C7A5951A2EAAF963D3824E9C44285CA799A4DCFFD9CBA1920A016FBD40E1449E6EF636D91421465A2F3A15ED829D1BE2DC988FDB8F8E92CCCD5BAF6C93084E2BE6F361DA62D63E7D942A4FDFCFD4F8B978714E310565F1C99115F71C71CE99642BAC7DEF32438E45F65BD4E7B1D32E92750 +ss = DE7DC467814DC94405A38C45B0E6FA2984DCC97598D75874 + +count = 55 +seed = 467F6158CB86B724039FF18C47950AE5C49170163C910FC9A9B30141F86E9C06EBCEC91497BCD156D95758C9F0C6EF91 +pk = 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ct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ss = EABE408DD38AB61A83E0E1515ED453208B6C687EFD749C02 + +count = 56 +seed = 687C02DE1041ABAC7B2C1E6EC2A7C3375552ED5EDB10E3A8139C24CC76BDA44D719D8121A81D47A0B762B4E9EEB85235 +pk = 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ss = 15ADDD6F14BF3F56D5EC1747A00A4BDEB6E01EB242D939FD + +count = 58 +seed = BD334D7B7EB14E00E68863F2E5551A095F8AF10681C28353FD19B9A7E70B8BFE266840860609008A567ABC66316C77CE +pk = 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ss = DC5408384C412EFE0E18E8BDCF488CF5D0534867A416A697 + +count = 60 +seed = 99A9CDBFC674AB3FF2C64CDED7D697A6E27A767434A47AFF7C3FBF3C6A22D6043D27868955286A13EFE3DE36D22EC48E +pk = 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ss = 74900EF600281F369AA1B1D1472FBE03D608C826E33CACDB + +count = 62 +seed = F7AE036A0176A9DE9A036A542DD2840033277C44AE936D10B768566216DE9D4395CD42B116873B69D9804BA6CCBC05D5 +pk = 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ss = 45EFF041C387924E111B34C419C409635FB2F40B78F975BA + +count = 63 +seed = D995D38F934B6E1A7CA77C9522E3D037676CC939B0C8BD4B84394B3DC91A791F09D2D97199258C9943DA955E7F7B26FC +pk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sk = 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ss = 6709B260549C1BBAFB6A97C9034D8F67ED3F62BB1BC80C1F + +count = 64 +seed = 5929F02A271725CB40200DE32D9D03D8BEA53B53AC83186C42C7F565CCB1CA508305D470850CF86E9B2C61A5B8CA1C93 +pk = 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ss = 0B6B8EC0C8CFB0ED111785D7CBDE0162A44C96D58772E5C8 + +count = 79 +seed = 7F4A56EDA151E7B097CFB8EF980440FFF707AFFBA91867C89522CED6C5FF3BD7F5F00BB49DDD615D9361A7E4EFA42851 +pk = 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ss = C506F215F739D554DA46B2C9FA8F98DA69B52E1FE7BC5574 + +count = 80 +seed = 09FC004519BCF85B20D25D314A0DFC79E00CB6262A7DDDF9C52473641AFB8CFA0F5DD5F53558184CAAE9EC34B459E98E +pk = 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ss = 8E29194E92798F63A56372A284CBA20051D66FCE75098C33 + +count = 81 +seed = E3C41CCA6F04CFE7732FD54DE30CC5CAAC93E2F80E76AED7D24A962A3969C1B6A311459A3EC3E510E3E9B1E4291D4D7D +pk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sk = 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ss = 78B38CCB78A36C6AC719A53A4A571DF65F7021AC114D0742 + +count = 82 +seed = 373FDDE922CFC416ED96B444E445BDD0962E8989F6C50ADF9912A89937C57217D3600B06C95440448E3F601AE69CA5BE +pk = 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sk = 9D405D3EBDAF35FA8722DE431B669722ACAAEA2FD10B81436CEB14F7662BE0C42779459F69A145C0E2CE9F0BD9A0CD1BF32ED5694CC9AE026C9B4D10DFB63EA98D6C89B8C03E969D11A5C764E25A01C952A304530CC58CE0216B09D2AC98F2DF4837EDD028BCD1BB3FDF2D2E033F1A333D52B200007B2DF201C71B1FA6B0DA29C7BCBF9AFD6A3E918BDC76122936041458257BED2383C8646A6B44D8B47E4FC2671C4745D4940D94D797D9D7A1A2683BB13D46064D00D458C927E6562A263DE32C07984411D50658F125A5153F2CA9D85F10BA4FB71123DF5669913D2F40C8E5DD67CC5EA2F96B1A138D9D860FECE2ED479F3DC03F1EB14A87347F5122245CD8587442BC0FB15D514E083487AE1F1177857A30C67F12996DD22511CE1848F10C17FA6FD3BA67E78F17C647889A55EBC7F9509D23A89E7D06CFA009BCBAE53BE32AFAF6606E56E2FC699DEF55EA5EC3F038A9F5305374698F2AD822B521147A40F78B2A5049494467EC77224073409E79A19F3DAF98FC285FF9FA6DB77C6F59A4F94ED206AF00E9DC5B7B329FD047820CDF8D174C785236C40F7849640A829E4CBC09910289F5CC12076286A1E819A05A3C22 +ct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ss = 37BBC45B6B83CDB5B8E1E01B05C8DCCA445E9362D853C869 + +count = 84 +seed = D0611F9AE5BE4DA5D7EADC9109944348E716CB3DAEE545721EEA8C892E7831CF2E54603146454CBFD92387739E9A78D8 +pk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sk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ct = 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243848C51898581160FF5A4F7C1A9EE24408CAE8004289892445CA11F8BBFF9011231C55A6C659913A39B9D7BB4E427554E4E52CCFA982153C6DDD1665352A0C8874FCF42C5896DC0AB029407C3BDF96D0BE6C7A70DB404E3F4AF8D23CADE2B1D809C8FFC17B4B70FCBB109002468C7F2D5F84E26D120FFA40162D4A95017BB9B5879961C7906BB703342EB6A58EEE1919E8A3AE3965EEC40D6BFF8D1FE260B45309EF2F6D4B9ABD181F04A11ACEF6FAADF3922C427B06BAA9F1AE770C6EB8F7890BD663D8B474BAFB866C7C03657DF4AF1C6965534653E4924B632A972DA493AA48A81A862ACE5715BB43814329302EDC0627EA11A5019141EB1F17927FB006C8EA0CF965B004CAB36FB22FD519E027A7B13426DC233E1A848A2D99F3D0260F34ECC063B253F0DF3E35C5D6F0CC7C0887957BB638B26A55CD20369474A42647BFD37A30BD1868C90A34D507D13C6A1F5E171A673134E67B6B1C1D189B931B3B3C8181F9710698733E2B99D4F58BFC884CDF6C7550E9CD08AD3B +sk = 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ss = 32F85E3ABC134C88F5994A0C9EE049FE07AF4D7EE67F12C6 + +count = 86 +seed = 1722219CB5DB47374EB0AF0232C856A57F026F1CB09E5A5799F4C333DD422FF6A0A67C4DA502FAAE727FB2D45DAFCF35 +pk = 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ss = 44F2C67406C5E032106545CC7118D8F3FC0A0FF6C1EA93BC + +count = 88 +seed = CC7152849C98D5FED2813275D32069E44824ECB14EAEF425CE017448CD9A401C91C06D0F7EED6D22B7BBE8BA6C429EC3 +pk = 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AFEA78B52C993F7EA0E94272E89052424B908ACFC5D8C50041724FBE6E2AE3AAD10619F3B6593D3831A0CCC7D089D21600D458707C7EA1CE924F634297C7026C4461C00B07BF8401231FCDD9DC9FB7ECAEACB78055ADB4D5D55035879522E70C28775A45C96C8D439B8EC5DC7C18C1C25A03F33093AB91BD83463A16CB1BD2672A6A8259DA43F8C9E44DB7B5E81E8328AFEEC6203DFFEC1F9BF0F2F2B0958FD5AC4B37D5CDEFC1056B63B875981AAB4A857ADC087F70C9ED53DBF5F627383D8E2FCDEFBF75AB63F181B14F35B70C0D1ADDE6B696CA8BC31F6B363902DFF19712E80ACD1B891E623C5400F44CC1E98181C4894DFE658A1C6FAB305C0EAAE225E87A76E9D596D91D6B338E65A3C31E32C42F7A9941B2BD32240A3681C092C53EFEA96EFE67E583283BF6E1B4E4EAEC38E3EB3ECAD8A15735908EF30824DD0DC83E4B7F5EECBE27BBDEF9F01C2EF578A20148C1B6A0C7E69983142735C5095D09109C0A14FB83AAFC693F982FAE602C97642B32B19C17EA1B281A04D878341C564BDCAA064F242E9CD87F69629138265328EE88 +ss = 4E77D3896C5494B0B06FEACB1DB71A345638B0D8BB0908DB + +count = 89 +seed = 96D9A06F88FF2C2036FA8E914B89C765E4A510B468DEE40F914F78858C811857EFE9FD0E17C0048E7389E8D996B7E2B0 +pk = 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ss = B41F3712746A65094FDC479A3AC76C79E7516AC03C6EF8F4 + +count = 90 +seed = D26CE360D399BF7B89DC364AA7AC06BB513EAB8F527383E93E30727EDC3F22C262AA0EC70257B39EDFF0630DCDC1B79A +pk = 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sk = 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ss = EB336F774D19B142F59AD745419C288CD4876C478F8D923F + +count = 96 +seed = B3AC6503206ACCC2A92CBC210D020A2654726911D11CE676AA04FEAA08AF1D20C654E4105883AE470EC3AB299075D420 +pk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sk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ct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ss = 9C09F9F457B9A961DDAD79027B92AB15257CDD6FEB7E91BB + +count = 97 +seed = 59EFF60B1EF6185DB34EE1E3B1DD2F159106CECEAA79BEB74923B4F5623D5BC52DBF5D2594A1F7C6C64D12CF144E9ED4 +pk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sk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ct = 1D355B433C42B27B5B46FC1D40B1B8439FCA38C18ACEAB23DA86FA9F33F154EAFF88A2B270D922630B3A28835AE6722FA08172ABBA60D61DB6CF3588AE8B0BC632E0F0A5EB0AEE43C2872EBB70B356D2C9962844BCD5B010253405F1E5AC6E9BF170C936344569E65A0C04EC2C992E0165D414C9484F781F28BE22A5EC21FD2C4F30C4E531BA3FC4B81BCD7DD93CA46BEF434FC0D04CD9DFA50394F343EA6A0BED874404AE3B0EFF4F4A66AFD548A3D31E05254586908BE12080FA533A13C0CE2B5D7756E2D78338913EEEB2A2DA35E8C9C0A4DD3F4D060DAD4BA7971171D12EEF9BEC8FA4C03BAE2BD5E1F829AEADAB640525F4C11E1B81AB8A5C003E25E5399F622DEDD6BA00451153AC42C15A38CA9E0F9A0B6B495AE28318951911D799A1DE8FF73370364BDBBC50929BF744062B9066D1713CC401C62E3340882556F096AC3F238069AC636548D9427B7688E211D4E51DB474EB726E3E02878B82C565E5B932B35A9AFBB7E4ACEFE3650A6C2BA1D1CD76B8216588EC5A24508323642EE2E92A996AE6C443F5D5E7E9D426B46C478E3A +ss = 3C988FB8F65F3CCF385CEDC792AFE350C019C819A697FC47 + +count = 98 +seed = DDDCA9DC31BEA737D3F474E7560B37FACB2F53C803E768FFAADE7669FF94B1D4FBD17068CFFD5DFDD24AADADA4EF6B12 +pk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sk = AA6DD1E5799CDF7AF9C4FC632B3EB9D51D66E85C8E0A21ECFDA268813EFAB5204EFA60F78BF81D320D01AC09AC06244F7AFBD2D80FD35609FAE47FF12AD9BCD71917E48A3C8860DF4DC91E065C98D7823783244BF9345D602E13653FA41844307BF4528E88FDA69C3385C1F76BB7FC1AAE417923BF153D27145FE6B6C70240DBB6C8B01F5526E883AC30F07C99BCABF4C8B4F41C0178F34929583CCD0ACB8CCFD63126752FE9FB1EC25575ED8E92767C8FA5EF7C4F1D1A117DB9ABD1D85A1635F3EFB549BCBD4211FB451D97F880518A3130F45B6D3E2883871E2A8C5C357A5B8F2452AAA23B27B2774230F54164BA07C634C74C0930A84340F4DB33A27A81B80261AD1CA2A59A0245162E1CAAC2B227934B5DB5CB2E7FEC62BEECBD00A5D2A5C7DC2181B56979798AE0B60AFCF1D006B9BE1A0083E70171E6141BF2D0C4437428CFC3F9B3BED38DBFCA73EBCA52BB1325E177E97089DB31A4094FB33FF9EBF50ABFBB859B4208FD6540E17E869C248513741AB3F8BA290853804B383082769CBE70E14417F9372931B128D61B7C2202C5F9C3F1CA67FA960B079932EEB32AC9C8105E1E6E8F877D881193C7A0A450A4CE3F +ct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ss = 1CB460A2C31B62A729B4D0E781498CE4C4C8B6819CFD3F3A + +count = 99 +seed = 2A6F7386B815366F572AEB6C79E272CC21B7095FE09575F18072C9D677DA23BC9C8A4BC393B7524604D299BEDD260C8B +pk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sk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ct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ss = A047B7E873C8EA4ECE4B143C3E0896E9E9C7863511508292 + diff --git a/src/circl/dh/sidh/testdata/PQCkemKAT_644.rsp b/src/circl/dh/sidh/testdata/PQCkemKAT_644.rsp new file mode 100644 index 00000000000..9788a3153ed --- /dev/null +++ b/src/circl/dh/sidh/testdata/PQCkemKAT_644.rsp @@ -0,0 +1,702 @@ +# SIKEp751 + +count = 0 +seed = 061550234D158C5EC95595FE04EF7A25767F2E24CC2BC479D09D86DC9ABCFDE7056A8C266F9EF97ED08541DBD2E1FFA1 +pk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sk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ct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ss = FEE94595E8A05C50113C044D4D8558DA101035EBBF604AA41D0AAA75B8A7F786 + +count = 1 +seed = D81C4D8D734FCBFBEADE3D3F8A039FAA2A2C9957E835AD55B22E75BF57BB556AC81ADDE6AEEB4A5A875C3BFCADFA958F +pk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sk = D60B93492A1D8C1C7BA6FC0B733137F3406CEE8110A93F170E7A78658AF326D9003271531CF27285B8721ED5CB46853043B346A66CBA6CF765F1B0EAA40BF6723F327918FF97790AF87AD7C2F6030303EBE0D12301E2BA26D6666163DD18BA35392D8F9A4BC87B938A29C3DE7E309FDAF243191766729BDF54CE21C2A0939B61B4E456F2A2CA440F7B0618302EE6895B3C154DBC94FCC6BC2A11B11A67481718CF6CDCA734E40E80E41F2322DA4DE1C73F6EF21410B36975A44CF62325CF7F47117D10F3923B8C6DAFA48CE7B7913D8A31F3F881D2CE867AC0684760CBAF822B969690EE28914D466B1B171DDD41299E1C6E8ABFA7843136D05FC86E64D7FD996A8469164093AF569C6B582E67962FA687AFA2B1A0B506834159469C6DAC216C0970D255D0CE9A729A2107A66383107BC0C11CBC21764CDB48BEDC9903C7B194DA03743940904D6EEF6A8D7065A0E1C907E62EB5B5E7E4138ED239F3B6654F092F14069311A49DD7FD586E499AC7D23C2F5B84B805E0CCC4247F8FBA8DB2F09F1E95EB6E02758E5A9C5DF6FEA7BF0338E7B0AC40139405168BCC4FF5965FE78B3F7C58076ADB7EEA556B18DF2317153C88F7B1BE544373571F78E3FA7737F6E96BF68737A7D095503F5E374D03B5A03F9468AA71D604549CEAC13C7395D09430B82CE860D9B8117F5AFB52823B0272000A1E28AD78358A2415FC9A996092CDE52192145F89E6D3F5017F396A01CC4CB6402CBB46DE99D870C5CF1A4E4D7720A7CA3BE066C60144BC90E937DEE815230943E3B6CC3D5E4B0A2B4136B9B34BF73F38A704D4B986D14D901E72C94B256D9CCEB468A043822465D263F8581713D27966D7D5611615983EDDE4FAED6A4F1B1AE8385808405C78394E8DCAEC922B7E504C82575B +ct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ss = A8F68D31099FD86235B5A72D9DB689F25AE6FD1EDF0765744F83A6A6577EC0BC + +count = 2 +seed = 64335BF29E5DE62842C941766BA129B0643B5E7121CA26CFC190EC7DC3543830557FDD5C03CF123A456D48EFEA43C868 +pk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sk = 4B622DE1350119C45A9F2E2EF3DC5DF50A759D138CDFBD64C81CC7CC2F513345E82FCC97CA60CCB27BF6938C975658AEB8B4D37CFFBDE25D97E561F36C219ADEF716FB6E3CCBFD9ACEED34DB628D4201F84DCAE8F838C1F89B17F6C5E159E7AC16C87B99154EC9D00EA0F1E99BDFB70C7A82E2C7262907C70D3E6003460902618494AD5C19690F26758A800C41095430EF2AA4B1D677A4D9DEF977412349F9DDB745CD75268C9E5929FB669F6B6E710B4B03F57C2DD2E9DF2ECAAC84C59A6D99B13DB3BDB9AFB138783E21D443A5700FB1FECB24DDCEAF55B7E12EF2C68A992B7308A09360EB924A6F1C82FD39FADA40972776941FC9FE0262661D547713E96926203BD8FFC822E742A8303EE377A08716EC15840BA178DECB4CE11AF6A06D302F60F003F61E5BC2E4204F9A88A0EA17C765B38CA497D11FECDFD56E83BAC72D1A34998D055393AC0B98333E385F7AC2E84334B370A5A18D52A054F018B33D5B61999AF114B0C3D1F1623C4EB6027784927839D1985BE4F4E54E09E63BD4BDC088B41C0E9D0227FE669D5827F643CDCE7831DC1567BC78AC056E0F7B5A1F6A5D9F54BF2F2CB88D091EF9F5DBAE3EA4473C4891FC76D85F7B04E777AC222BF1F382E0D2825EF19C33FF25D430610381A0A0013B338972E9448C95FC820F87CDFA77DDAC7F8284FAF7D21641BF26D6000FFC7D4D5F1B9596F209B8DE93EC9DEF1360455D1AD235D3B60D8B3EFD9D6E621E775C594D65D58AF65E9DA578B2F414D5CB47F5B8932BE8497543FBECB12D93DF4AA7C46DA0BD0FBDA4CBF542D69D204908DCCBFFDEDD92753B09411062089A035E59C3280A72DBA84D0C2407B59A18E5A75D29F2130A26607D45D1230AD7CCD496B8FFAB71F1A990EE575FD5546D47190CA3C91C +ct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ss = 52FBD8CC39FC5F77D544B9613452B8361BFF5EA79268331B02FF7F0EE145F54F + +count = 3 +seed = 225D5CE2CEAC61930A07503FB59F7C2F936A3E075481DA3CA299A80F8C5DF9223A073E7B90E02EBF98CA2227EBA38C1A +pk = 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ct = AC7AFED8D2BE5EAB4E7B5633FB14658ADECC8AE41A84266051E3CFF903E976A3C9D23BE318F885BEFDBA1C41A32D0DF059D9CED6139A1D39452A5601F359A71E2F69CB0CA2AD2E3BA48F77E65E2EFF98A47E2525F4B98A232F076A99BF2A4A86C51EFFA3AA036784CAA79D170481B437781D5169DA7579207CBA22CBA467F6C717FE4FADE74EAACEB0404B18DD410A49ECCEDF1187A9E37917B199A86C7DD9479D969F5BA07DAD4AED185DEED28689EA464B0B61DEA2DAD807F1056088E2A294D603D209B6DFC48ACFAD3DB08ED047D7BE8751AEC02674E0A170AFB7BBA4B7623C1F526C347A994E2ABDBF990AC4A1A93516208577353BFB27DCE8C72A1A7D5DE92FE1D3720C3AB4DBC1E4FF67128989F937A7C639A9B46E884F72C175A3CA3E052E1E7EA9D41A74450C0211C4032A41AC92594F2BBD4C30274A0CF0FF1535DAB024ECEB3118B695EB2ED71A7C00CF89A3471DB9757680B0946D6D1959064EDEC78E1C95D8265791F876183B27CD906CC228593EB250745436FBF49ADB1460B6D54F596B00F942856792C1E0A867601EE288068132D3DA8D4E9C980FB3E4594EB7E22C3717A97364DE6612F68464E9CF85AABFE50BFE2A20910C624A10CF3E6E45377CB91780E9B6C00B1B6326E9BA5B3C6E0098CB03B946711E814854EB78792DBA97EFD0C7EBA16D345422FC5A2E2C6D4C3F41C138CFF3360FA45348BA7A955E80A2F2338F2A9EF8489FDB45EE5E50C6F9807C0B2DB80BEB37B719FCD1212C8AF9A798BF6A34DEE56FAF929F6720F95E68581F5FDE76F5E4004ED19B000F8DE5E8C97996223D5B9380E60A5167433B77C125F8 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+sk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ct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+sk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ct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sk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ct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ss = 83C18909FD73AD3732ED11B61AADFC25867E17CE0900C7F001293770325169E0 + +count = 7 +seed = AEFB28FDD34E0AB403A703B535296E3A545CA479C1D8148E2D501B3C8DD8B1034BD986F13F1A7B4671BE769359FD2AAB +pk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sk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ct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ss = 600D281AA7B4FD07967253C51C8628F082C0DC380246C5BEC4105483E2B6D62D + +count = 8 +seed = CBE5161E8DE02DDA7DE204AEB0FBB4CA81344BA8C30FE357A4664E5D2988A03B64184D7DC69F8D367550E5FEA0876D41 +pk = 71FA1AD2142E2FCEC33D9509FF702675060031F94EDA26BA7922F1333E131F5D7754D0E528C8ACCEE369774210D880A1C2ABC415720940B418C001BC7761FBE7AE1D7E6BA935874DB0559CC7EDFBAA42A21E7E0188DFE3D771B7D20C4B453E32A82262DE27827061845BEBF92568A5A62F45F09061146CE8A9D67933EBF098C00D12E00ED492B74D70EED721F85D8E6ECC8F3995FFBE17FA28B8E22DB2CA688698C5D95CE900A09CE156A7EF258E13BF79C17AD1CFEF24EAC664CD574AD17470D221FB7A4579499E2532AC28CA62954E2E8CE236C40FFB2B51B78BC988B53C726775360992F1E232DD7E5280863046DD10FDE7C5EB9C3A5DAF50976E810562AD60B37FB357770CBCFC2316D8682B3C904924540640A9C5CF2B1729C4FA3DFF4C2573108FA20448A565B19386021CD51C2761FFAF4D3F125CAA2A71D3247FCFE00EEB5EC7F32958CBA0F757A32B9B7D3A6C4151CC2BBC7D39D329340A03E553A540FCF6F64CC1EE9C2EB8BB00910F2A75470772D3A3565210D70782C1DBAF9AAF1C34026D78E51F626102133F2C35CDC7A859A1305AADFC8582BC5A2049835282056CA2BA3EBD610A758EE2082A0277512ED2ADD2DC648D66F52B0FF85283E2528342A64EAF56720E33A556D05BB1AE14463A7746BE66896C350776CEFAD010F923D345D18E952AC5EF8B06D000AF47862F394E5586C3A94BA38FB0E2B98313793720B062EFE94A98C2EDB5A17BF1E9E429EA5F6D6FE1DEF27A94EFB232A810056000CFADB12FABDCCAB978E9D7B058B25459454D +sk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ct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sk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ct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ss = 0AC4196CED9103213B8ADEA333A872DFB2B029B1B9095E32BC24D30441DC4E8C + +count = 10 +seed = 980D0BA7C8F8B23D0E948A6029FF2659810EA1360064663A8994D0333C8543EE5FF5D6D5C9ACF446E61DC464F792B9D3 +pk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sk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ct = 8728390D12B3761658764AC25BB768F2C95E5BD30BE9A81CE2F05BCDBEE0394BE1DF656F677719CFDC5096BEAB8C6C4FDB3BCC2135B92D51149C23ED1AF5239905EE00EC794BDF794C02F92ECA364D265E84F5D1E6AE0B759AB842D64341FCA42BCE2927863D5211FA9ED8B01EA91DC5644C13AC8B3A1FCF0F8CA5929F3E44FA43311F56FF8536DEA3027DC8CA0D238651C794D35447B3D9C490D2362F04F534CA0D6135C1E4E84327EA8681A2A67E535A300711B222D6EE761D683E0F96D65BCD2CC488058224CCD2D04946A183EC318A96D4D950BF1807FB925FCB60D06D55778F8C7F53F1A162193D3E03A9DC31FDD83FF6E19D43EDA1E7C643E1CF8315BEBE65B14827E38BC5AF6D2D55EE9FCD32915B26C4EFE1C5DE7654F7B975F91CD32B79AE9E7AD21DAF08F5AFC8161CC04885C550735CB9F9708FF0A5DE87DBAF6C913460A91D76F2A6B1052A06F0235355DFEEB4A93D73F2125EC3DB6B240116C4424FB6C9CD78192B57B2F2AEBEBFFC900BB2DC21D51ACA4489917CF8AE2676145D8F24A5F520A50A8B52E0603B3210A19A25AFB61DB6C98E5F5F2272E668C3F95773DCB822D97976E2704509D1E660BDB88E670BF2B055E0934F8F14541286CF79A6EDDCAC2FCB493D15D5677951850FAF4A9958EA53D7C5A9EA744BB286A03BA3B54E4627C4180E78C50F54AA5A4A5A5E5C8CD37EFD673091528F3195A070DF45BABF46FA4A328A5678F06F6B09F6D0F9712F0DBCA121587D3463BFDDF8E6086732450AF060B248AEC59005D1471B15CD0CC131DB732F1678297A5A536B79AD05099BD3B5108281657A31A48F71AEBE1448D67D +ss = FE8CF769164A3ACB29D531BB06E430386CFA36FEDC4D2DFE4769D738BD0F776F + +count = 11 +seed = 6C029462CA42ED520F10A579F52687101105E0B90C6E7BFA582A4C112B579D5AD0A0ABD38F72ABCFDCAAF5893A112BDC +pk = C0E1706227AAA182687BB5FE51FE72CA158C4263AC370CF176570CAB238A3B8F029EA62E965A00F49EBD9F8577B941E14BA57D8307173F3E526191694A81A25A87332BC44A488C6156EFE40593CE23387EC7BEE5B6617AE9A3AC4000314CFB47A4B52F2582176C74F64EBB6ED24DE7F66ECBB5E76015F92A90D5D318FF1DD442E28D45FAAFB0065636CEDD488DB8346AD39CF56616890FF71178415A050BDA4147270EC989402CA1A21A83492889F6A668BE6E723C00E7E038C1733FFB7ACE332C730BB287898AC6F8BAE8223854FBC2F1501864F23F947218BAABFF0BF2D4044CC52CCEA2D8B97A211F031D87A0AA11B99BC612BB7513575884A04E79C946A3CB1FCD35560EDD3045F7702BD230926951FE7EDA9F131193E824E9591B04DB227F9F16F85DD9EB645A5A9BF68E6A76DD350FC854FF1A29F29D323ABD5CD4A380A688F2907B8CB78FB223C4BD881C9765427612FD8827856FDFBDEFDB665AD56C70744A2D2153F1CC23E927CBD78568292CE1993B7205BC0783EFECB8B3B3C70FB7138050B5CB64001FF924627A219BFC3B467740F62F94847304AF81A8D8FC7752E40868A50F977B22AF37411971AC8F7FFB956669AF0747371075479DBF4431C50C2BAA08A6BB763E2C81335F9D095F4AAF9E76C841461C5A2C67698EF36FCBBD4E78CDC45643CCC79C291B96F338BB365C37B3BF32C64FDEFAC37CAE1FDB949A5F26EA3626305D1FBE7A8424DF624BC9D5FB22711B5DF438403316962CE07D8439196FD53575EB8B405E826AE2E6F85BE88F3E +sk = 31BEDA3462627F601CBC56F3DDF4424E1529C04737EF0EF2AF6D7401F653B8A1812083BFA3B670E3EAF9B443702FB6DB16AC1197656BBD61A8E25ED523B8D1E5D2331859E2A7B4F3F9858D9D97F7C703C0E1706227AAA182687BB5FE51FE72CA158C4263AC370CF176570CAB238A3B8F029EA62E965A00F49EBD9F8577B941E14BA57D8307173F3E526191694A81A25A87332BC44A488C6156EFE40593CE23387EC7BEE5B6617AE9A3AC4000314CFB47A4B52F2582176C74F64EBB6ED24DE7F66ECBB5E76015F92A90D5D318FF1DD442E28D45FAAFB0065636CEDD488DB8346AD39CF56616890FF71178415A050BDA4147270EC989402CA1A21A83492889F6A668BE6E723C00E7E038C1733FFB7ACE332C730BB287898AC6F8BAE8223854FBC2F1501864F23F947218BAABFF0BF2D4044CC52CCEA2D8B97A211F031D87A0AA11B99BC612BB7513575884A04E79C946A3CB1FCD35560EDD3045F7702BD230926951FE7EDA9F131193E824E9591B04DB227F9F16F85DD9EB645A5A9BF68E6A76DD350FC854FF1A29F29D323ABD5CD4A380A688F2907B8CB78FB223C4BD881C9765427612FD8827856FDFBDEFDB665AD56C70744A2D2153F1CC23E927CBD78568292CE1993B7205BC0783EFECB8B3B3C70FB7138050B5CB64001FF924627A219BFC3B467740F62F94847304AF81A8D8FC7752E40868A50F977B22AF37411971AC8F7FFB956669AF0747371075479DBF4431C50C2BAA08A6BB763E2C81335F9D095F4AAF9E76C841461C5A2C67698EF36FCBBD4E78CDC45643CCC79C291B96F338BB365C37B3BF32C64FDEFAC37CAE1FDB949A5F26EA3626305D1FBE7A8424DF624BC9D5FB22711B5DF438403316962CE07D8439196FD53575EB8B405E826AE2E6F85BE88F3E +ct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ct = 06A4254ECD625472935428F20886535A261AC3278760F234033AD2D1C6FA509680C34C0560F4A34B979BDB611B55B4850A2D979CF0B3C87626EC20908162A315D261904C39C5E87651AF92E2771A81C80236D3C30FC333C8545C64CD0437460BEA0E558E43055A6E183D05208FF7AE18EC69220F6585EA9C5EAEBB764A22DC50FE36457793FBB844FC7436D4EE663CA0CECB97215D4D7C89A7CE53073DAEAA0A8B496EEC4F41148EB00E9AAED85BD69CD763B50CC9A7C0B5F4E5BA2DB0625DD9CEC5DE46EB4C2EC829E596F395B1A51CBCEEF2256A84208405648E3B8C1319D2DD25E55BD4CF89D1D5D5F11C025B9EC94A23EA2E702458BD4E1EC5A0EA1620CC7E6F033F72E69112021F9701CDB54987EF40EB211CFE5CD1D4684E6C4583A3E8E30411E4B44941295E1D1B67CB332A86358734E38B53BAFF7F8B8BCBCCCE8E62584DAF92F8ECDF6C2CC72EF897A2DCFF4C5AB0F4C3E026E6EA76E898E46D4F424AC6973DAAB4A7D837AD9115A4371E886FCB6B3BD94FB45DB3A6FD6AF491072DE556774F3D01C600AB91EEE07ABFF7D983F60E76782795FF035D219387089D1A17C1704241373E1BA0B0DFBC057CE3DB4CF1C2C414E76D81CC12D6A6DEB8CC7E5BA041B8B62AEDD88A403B945E96CFE81E219DFEB46E580C5FC9B5684BC73D57A7C0DD442FD3FE2135DABE8B8E7ACBACF05DE15654BB6B1AF6DB46AC039FBB594AD09F9944F66A08B9576B9C58DCBE0BB16EA90D5A5A4084A483869EC2B43B2153A5EE679C0A4E23713E329090F58ED4F29F2A3CCBF17E7C55692AD4ACFEB89B4CF909645DAE5BF0091A9A162B9E1A86C328CA39 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+sk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ct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sk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ct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ct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sk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ct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+sk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ct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+sk = 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+ct = 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ct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+sk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ct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sk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ct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ct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+sk = 74D87C7556F2671F2D666854A4D6E073E69F35421E6E1A428CCCEA49C37F972CE1FB7456AC0AA1B97068F452CBA64EBDC138BCF5D36B0A0FADA2A3B374141EB99850E03CA7F436DEDA9D54E13BBA0203C0CCA24B8A8C6256DC1BC41FC92DBF1B188B1975D39702A5999F3738EB97EAABFDA9A4FFC18A9656405E4232E2E226A133A9129E0D8010D4DE0B373C6286528F305571109D898DC9E03C978DC95466076754A80DE2967B708369FA3907243B32C79127E41E20DDA5380DBD14BF26813D5B3E80D1009B304E7BD901E0AA3E17E09F8F2E21A7095F9BC07CAAC305CDF89DCCBC50A55A30952AED77DD1175648318D180D4B623777A0E7F5AF486BD315F728CEC92C50AD030BC0496264D2E9BFFC2026413A3C120EF43C70C432E3EB7D0A567E766D21AA6D325F431E060CD419110EEBAA157AF0479B5C9DF1B3EDBF773C24E383019B8FA76A2EA018CAF390C21C379DDB058440146F989A50933CFEBBF5ED487313719F7D5F0286D34D55C953A08D957482253E4E44ABD3B8748F28F2409C6DBD032A28A17C3E5A81998387684804EA64625B6D514E7C87109A4BAA29B2DFD456170956D16B01C25A5F63658C57ABA6C9950C89DDF7F22CF922E14FDFAF5E0D7F6ED4D88E515492A82E85CFE881B95A22F5C8F6DB5B0E9464279DACD0C1B1F0E67AD17752675E5D68F398CD1FACE3C4FEFBE1AC6DD1AAADAF6F006BC0FBD00E23893BAF397C3E66DA18A9D57F7DCB25F929326D2D23F5277F2A8E71FE3648C739CB0A162AAD21810E7E86230D166941CDC73AA6804F15DD2268BE9C623455BEE7B06623C9917E68C4F0E1504C8379AEE8339617752DFFF3542E724AC08728796A2728B7DA41A1DFE30D1C4BFE5D4984FB008641F299ABCAEC46E9418181A1FE6146C +ct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sk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ct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ct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ct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ct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ss = 4D99061B6937AA37901AAED330B5ADB04694E8FCCE7D4347B75436827F2B250D + +count = 31 +seed = AD540A9CE816D6FB1661E5483C44F6FDD00C9E7BD1A8CEDA4B4C4D3697D4F78ED0A56954996CCB7DA96ECB8F5CB15809 +pk = 5035B9E8338D6017DA3C6A052F61A5E6B3B4DC71AC0E7C34709DB3C4CDDAC1E593B032F90926BBED53218D8DC76E32DF426C7E14A17A8259045A112DAA10B8ACD65007BC4751138F83557DB665BB94B4ABA4E0BA3BC7E68867C4C603F04FE7EF10D9DB71249D2493E12A00EF6B745694B7C30EBF4454554BBC5089E095DE0338FA0DB77CB1657CB63478D06215D823A7C57D75CC9570E3780FA1B89A75632B2DAD28BFEF52B9177EDAB702D08CC73BB1B514840589B219D0DAFB3E6109A1EDA8FDD1FCC14B78A32A22DF8335D3553E53951EE545B56D46CA6EE9CBD96332B0A22DF3E164C3C2EB05B7A80755F11DC89C7E7DB6920D1204C9C20C6FB483068A8CB7FE2F6A79D4D3D59D3C700F0E1BDB5BBFD82A590F44C30F506C13F368D193DC54158F846F5FC128F6ED950A517C9EB3A61A3CBCB9827E269FC42E4D1AB310717FB944DE3931FBE8D7CE4A0254DDEE448E5449DAEC1FE41E50809D95FD6FC82FC2CE08E4217A19F8A0EC04B6A588B1E0D80C0BF173E3E45EB739A2D2AC897325C0A2B4E7EF2252126F82B65ADFEC99335643D7408F6E2AD111562C487D70D93A1F7ADC9E92CE38BF0C0833BDE1A2F58CC6724AE59FC5F36A3D8DF4961D7D6C05EE1E2C8A3D793B7B3D5C9FC96632DA38936E72392D19EB89336D38C116D38F2BAB0CA7B8855C17A0CA1BD961AACF43E82C0002986C94443F029CB60279D020A273E29E70ACD6DA51F95B8608C11A53A167CF5FE198E1EC981FBEB68D8DBF540501F3BFDFE0DFD3CF82BB60FDA0663ABFFA41EF13 +sk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ct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ss = 3A328629E9EA491DD8FC925AE18FFF3E9C2CB62291FF4AFC4D4812D08A4CB508 + +count = 32 +seed = 288A5F2684D862A86D2790AFDDDDBAC6FDA934EE7D2E6DA1508BB550838609E8107312B28E00A6C01706374CCD3AEFA7 +pk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sk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ct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sk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ct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ss = 78696DC7DCF46923FBEC1AED5FD2EF9DC4FFB8045BCCADEA8D7557BC301E756C + +count = 34 +seed = 5DA2C51B4ACF488C8BDED5E985CC4702E4A7BCB248B5AC18AABA529F7F9CBF30EFA776E99F76D5C1686E94F50FB57DAE +pk = 9FCBC1354A4B69594486DBE040223865771590D6E5EF60FFB247E737F14DD39CE54764A4CFBD72A23415AFC4CCACC6135E5BDFEFE50EF0A5F8AF2F5DE204C2AD40F606B24D97CFC9E326A20CB982A6317A74B99CE71BF5A09C0E6B35CD2F2E3A645F7C5E94BAD3302C3587D28CC75AAB87D5D13F523B7754F9FADA02173979FEA05509E3EAAA9FDE220C57A03B7FCC0035D9D642C622FE547E7C7E43B337751766534A8D6F70AD32EDF9951395BEDE1EF9523DDEEA7008AB4B05826D38C22B82E9729647496E98C57BA2898C83C293F92D88FEDD26736F4B054DAA45F1C65883AF372719132B66627FB146A544AAC83F2EA4E5CEAA25BE93660F1F11F91B86BBD34DD5F412C64CFF65B8972240DDCB1147C35FEAA292DD5CA720F055121BD74F71820E7726C728DDABC4E4A29C825FF4FC7C7FFBD5B06BD871E9B133CF8FCC5F8E83C1BE3D3F29272B200A1382D1DBD5D156739BCBD8B67C06C5309CED5FF7D79648B93EB9A735C6389D50B021A36E91818C75789A33E844BDAFEF0ED9BC8DF791AC66DDC768B608556D3B8B68177A36D040CA2A492E048AAAA85E948396E4BF008145B328CA22E00F259B472437E89AE56CEF085D15FCE059698F290363600EB4BC375CD8A94D957612F1B9630A28A0B462144CDB47D52905F1A8CEA02EA532267FE003A8E4685F4716ED14A401A72CE2253B480A55852618FAF3E1FCBF37063AC8AF7E6819260AC93C5B18675DF45AC0648FDD805FB8C1BB9BCC81B223FDD8E75A02D8858B4FBD1544E2CB48D13BFFBAAA420B +sk = D76B3573F596EB286AB5231FEEC7499686B13021BE36CB126C7EBEB9D7030DAF248C0A21EA0BB6D6F56F12300E8584D8E9A34E0E6F52227281151AE4C305FB8FB2894654A15EBA3520C53320159D1C039FCBC1354A4B69594486DBE040223865771590D6E5EF60FFB247E737F14DD39CE54764A4CFBD72A23415AFC4CCACC6135E5BDFEFE50EF0A5F8AF2F5DE204C2AD40F606B24D97CFC9E326A20CB982A6317A74B99CE71BF5A09C0E6B35CD2F2E3A645F7C5E94BAD3302C3587D28CC75AAB87D5D13F523B7754F9FADA02173979FEA05509E3EAAA9FDE220C57A03B7FCC0035D9D642C622FE547E7C7E43B337751766534A8D6F70AD32EDF9951395BEDE1EF9523DDEEA7008AB4B05826D38C22B82E9729647496E98C57BA2898C83C293F92D88FEDD26736F4B054DAA45F1C65883AF372719132B66627FB146A544AAC83F2EA4E5CEAA25BE93660F1F11F91B86BBD34DD5F412C64CFF65B8972240DDCB1147C35FEAA292DD5CA720F055121BD74F71820E7726C728DDABC4E4A29C825FF4FC7C7FFBD5B06BD871E9B133CF8FCC5F8E83C1BE3D3F29272B200A1382D1DBD5D156739BCBD8B67C06C5309CED5FF7D79648B93EB9A735C6389D50B021A36E91818C75789A33E844BDAFEF0ED9BC8DF791AC66DDC768B608556D3B8B68177A36D040CA2A492E048AAAA85E948396E4BF008145B328CA22E00F259B472437E89AE56CEF085D15FCE059698F290363600EB4BC375CD8A94D957612F1B9630A28A0B462144CDB47D52905F1A8CEA02EA532267FE003A8E4685F4716ED14A401A72CE2253B480A55852618FAF3E1FCBF37063AC8AF7E6819260AC93C5B18675DF45AC0648FDD805FB8C1BB9BCC81B223FDD8E75A02D8858B4FBD1544E2CB48D13BFFBAAA420B +ct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ss = 41F998F447908AD3448A348F8E73441FBA26717A83C1306C22BD8BCD4F8A525D + +count = 35 +seed = 4D2239E84B052109A78DBAB6D80C51A86D38248105970476B74A0B78B9CFAB6283E30D5A406FAE1C7F54F8BAE1110EE4 +pk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sk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ct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ss = A03F8B99F2B60AE8EC6679DB247508197CD8AC61735605BACDBEB15A320BFFAC + +count = 36 +seed = EE762F5C9021C36446706A88EF16312F4A12C725CD7AFFF1484337C91EDA8E89F7007F3705747D29907B3FB7500E5074 +pk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sk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ct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sk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ct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ss = 1A8218B58D3BE190E1050D633BB557DCD7C0C697BADF63E85B1D9355818DC3E7 + +count = 38 +seed = 6C3AFF39F5D097096D882F24717718C8A702382DC4AAFFD7629763FDA73C163CF084807BBB0C9F600CD31A7135F48AEC +pk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sk = 952B49C803D6D6FBA69F4375ADCE8594847A00BCAE2179DA49AF2AED0423250262D7033947AE42CA53522A65FBAFE18D3BC3E0CB66164E9A094FE4B44D8977EDC0D0914DABB32055DA762B4A61FCD0036DDDE835276822FDBD716BB7D7E873907629B3204EE71D97422265F89643E113C8C3E2AEABD36C92CADAF72FA3EF06627A038C10F008E75E1DD399514493ACAC5D603F1961DA64A529DD27506F8DFA5ADCF3C9564A7986D48A609A9AAF66CCF61A07940845A26F6E3942E252BBF5CC435481C2C330DC654619A7E43CA1CB03DDCD6659DC2BDC11D03F924443B689CED46174E43E2BF4B2F6EBA0B197918EE81B30ECB26AC536988F59DCBFFF94804C64F91EA6FE96344F9AE86F955C80F76C7BC3AF45BE9A36C3D5C4B489B44412011251BD1E9BC382D7E4A9E3547301ECF530F1CEE2C8302E29AD551363ED8B267F1150EFC056831BD7F85D64E1C9E1B2A114FAB4301B725965FB2660C030A8D5694D5C74279EB7D9FE52B014AC00664ED8B469C03A4C7EA384A319BFB5A5690AE3423F9FD85E370D053D0699B3CA19388F8034C1BBDC975753BD78894D1D87C5201AFBE216CC19AB9E8F9A4C58569F1B86750DD115CCD3DA5A5D50318EC3EAEE5524F7AA62BDD7EEE714BCB4B08BB2D1FEF2904E9A974B00383BE2435E465779C5A372CDB280B2D2EB968F037F2B668ED61C6701461F2B9D0539892D8C53908E3B6AD1747DA642BA258C2C57DF23741AA576E79B385083048357238A7208CBE4D5DF641D27CDA94B82315629E769289C53DA9FD6EB1F6D8051FEAA62874B230748F2DF135D0891921D0A5E53625DA6B4AF155D16F50A1E285BBD6DA2A2C464FDEB38CB508BB06751EB49025A54A65C95605D2F2A1DAFE3A01805552C166044244527CAEF2700 +ct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ct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+sk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ct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ss = E168D04F9EF20435AAEEB03FA2A556CD628F309F512994AC8D45C5BD9A4C7CEB + +count = 41 +seed = F170583CB451D8A45D105457C02C01A33A40350616ED8515BD49067142F61EFB00F07857E4FFF3FE11E7164C648C76ED +pk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sk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ct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ct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sk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ct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sk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ct = E08C30A230761F7D5A0DB8BA11E6804BA59048565ACE3DE0910A7B85ACD41C3E915E73C841FA52C8957A8BD82A06576161D81D838B504C1A8D95641927A346A0D2FBE493686650EFC2065B8BFC71ED4D0E7DE066B804FC467A3F3F9E24598BE2CD520B9DAC1B1BB5A28D5D2A35F824F563ED31E4FB5754C6DF8C9E1D9CB5B363537BAE541BE3AA88079ADC9C2AD9F6BB83A05E0E769E17C674B7F640A96C4AC5FB6344BC235402512918252C6F262DE4FD978E61BC6A676E4E655364814933F15C004323DCF82AA080716F6B3F0ABF53CBB186B15338537DFC72DD578AFF245F2C6C97625596C6BCA51461D0DA7B0C494F63AAD043DE99B51745C98E0610ACDE3BBC09A4552ED9D4B404C5FCB1C27C1A7D2B58BC633531286D3AE6EB9BB968B3D3190E1A5B3287129C4ACB8CE6E55B394CA79465866BFCA12E41A34B273ABFFD822E6A49D3B68CC8A94142E25F514C7541DA6A66C761808200DE9634733C7AEEB5781401FFAD17A9ABB9C6B299950ED57D4572697FCAF33CFABBD7BB00E59E6FBE64AC7140AA7B7D42E19FDC95F4ED1CA1B35C76837163B536AD0C083983687836E70BFA0CACF73F5FCA7A34A51BCDB5E6ADDE9123372A501A0339D29F36E3CD4416C8DAD39606249C5819E6C846B9D4755D46A0DB425BEE19EDAA540FCC6B877E0CD91B47CF3546872C01565B9717AAAFFBAA3B42BAEC0A089BEF595C3D7090F0A0C61EBF2F6CC23F6D2205956FAB63AE05978600CBB74750A3413030AFD7B0082C27729A475A7EA91B5643B34BAC4BA22269638573A07371D1606D0143A030FCAC21D53655A4826A60274C1A3C2FD68D357F1C 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ct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ct = 239DF62F111BE10BF18B9EF4E48305D5AE432D1CE0FEECF460642DC903265959C02DBCD1AC282A583B7E47152B343E88C9F70E1D43D6DC1CA2D393CD6AE517C4396F91F31F3DB0B5876B2D367424AEE12D3C3F9AD89C7180FA57069D9F2B7C5D661A5B0086016E1FE746FD2879B67EC02BE0D32DEACE1E284CBB6C70B0CEC6904FCFDC0691404A345947A8A7A118A8AAB9A85F7ED6689B62A03950D4EF1E87B5F7ACD312CA1404755C4749711A66E2E066B9D07202FE195859FAB437D2393B4827353207F40D2BCA1FA2904A857248D2E1175535D99EB09DA68B128374BACBC770799108600D7D23E564DF16B40EB4089FDD137D5D7CA3C015BC8710629E16DC7F9F71BFF7BABC765EB2D341CB1F7951B0427C9C6F13BB286B1F790BEFE6AA53BAB8271EDB84F404E47C797D74F244DD4159C79AFBD94D639C81F8CAE7E0773B90AC4ACE1249E1BA1E8C2B308F129C88758DCAC77198415B1F5CEF77F7938B0744FC7CAC9E6F98CCC8542ABC78A24E36361D32165D716A57D66B7B3DEC8D03CBF93D641738EC876293B7C38EB1FFEC78AB4F5C3985294E3E396D5FC751D39B59C2BA4DA72E258B0C87AFD64E4B41E7C65F0FF0B173D8813666FA3681A095AA5BC780C772D083E6AE14F9FEDA0F08C91ACC0F1D488C2B0F4AD1CFC3F0C6BE3DB3580A7234107055DB881AE938B4CA3FA40128FBE5B778B6508106C4D0501B82F74B4A8A01B4F9759A941E03A0229A50E42405CC2BD72B1C5767DDA57DB96CD1572F0275A8FAFAF18E33FC1D8F1009322D98ACD929A5D52A6B0EAB98837ED67FB808423631948C9273D532BA36ABDDD142277EFBCD 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sk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ct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sk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ct = FF5180A00E8D3999AF930DC3FE565C73CD76E1429BCBDF600D3A80D268DC86764BE58CBA103F6D4C3808B0A8D1229E29FB245A3F36B80108854E845E26544D14AAA77F378F9C045FBED6F1CA39F9A613B2BC17C867AA07F194CC61BB5D30556508157617232E70644908CE2D0EE75D18A82B331F573543E63904DC4217A21EA9ED279B1EB6A272E69B639DEF9D50035384B49B4D5738BCF12E7D6B431BC60EF4AF8809C370F8C36773CD1ECF4AC7EA7A2F016D64AC1FE6AA98211123BED06FC0DEC213929D85C4609BE6E57F2A2EB908C389CE11986C50CA487404958B858D36D94A152886D9184E76057D4DCA954577BA2E0B9B8E5168F4076561134D4C4482873C6A8EE6778544A2285F444625B93820F0288221B6688BD2313C6136433FF4ACEB3B84BA04AA0BDFF5534A11522FB960C5E6D9BA27BA153B009D7024C746C8521DC4E935B72732BB7BDDBDF0D65124EB08E47D47BAAE9B030989D8C939CB5443D2EBFC9C2149E19CDBD80CA40C5F74B07BE5BF1B941F59598AF769B8E97BD971C0342F578B07D32AD30CCF6BF6BD09DB1CE2392B5FE73BEC2E030374F8794D79331969DF21E07312CC562BF3E2281B439F7877601E5BEA2180DC681EAFB233372293F0F2784AE50D4A82DB455F4E622749C7B22B47DF45542C24DA3C4C7E050B73E403D1ED3D39806F4C5BA8FA2439D815E26127B2DF3D8768D900488E2BE98E88A9EE9E8A96DF26FAAEC5B9680175B05BE43254158D4A8463F74913D5E6D5C09F0542B2C77A32D5C92AD68555EB90CC040A6E0C818B83606A4F4AF9E645817AAD4B7EF6FEFE423C394B38D82CF14E1AB6EB5F +ss = 4ACEF422DBB0D1F49DD4367046C29FC7CA96FBD872A025D000DEE4CCBA6B8951 + +count = 49 +seed = 1853E72329353B3F89AE6A1B1EF700DA8ED3C10D19F9E61EE9252E28EBB0E15802EE43083A12A0B7527088832605E3AB +pk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sk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ct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ss = C54E70E7194F597FCEE8B17013B77285223253A43FB6EA82D32C532ED4E4F41C + +count = 50 +seed = 027C3D5847ED4470931141104F25B19AE76117CBB64B224EE424FFB782E9A0E988839E0BDED0DF666FE8E5FCBB5DBC09 +pk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sk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ct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ct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ss = 2798DC47E7CE8E60B363CA03CFF8B45F2EA8A302D781EA9E441E7643D0446DAE + +count = 52 +seed = 5DE720F2D152BF4E1F96A61E7AE5F1BED6B8548E32638C2CCEC9F43B87D1BB43DFCF334F0582984D27E440D519AB662F +pk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sk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ct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ss = A9CC3793476808A1248911D3B0D7DCDB32CF92575AF827FF5E71DC9FDE6033AA + +count = 53 +seed = D71729DCBB27D7CB39E9E905025D3E55C8602EFBCC483C9B866EBF82326157833169243C14550AD728BD1470F39C642E +pk = C63CCFC7C0BA0DEFDA9D496A9945355E042274F18BF9B607FA693609B58BCBAAE001071C7916FFE11D517BA54C5FCE7605C7F4BC1588CC1FECF4603F1E67A26BF4FDA95E06640E3CF774E5C13EFDCC21ED11EDB22FB3F503BDAD1938002284C9FF3E6EC928E2B440727E68B88CE804E828A4DE577D626EF6F5D2D6A1174F4CA6C243D46B47BF93780060399530A4685D41D1450399C94654B2E0E2AC1DF7FACDDC78E25BAD03BA413C6545FA427DF909BB1506AB4EB13E0C79F2CF3224869FE5806BB4C5665113DB87251759C1917FD1F3F40BD8C027D4CDF3C140CB6BB6CCF62624B0FF309E9AB19A216B57893F3D4C952B4FFBFE1415901865220CDFE5B42D278F22E0DC858D06499817319C9F016B188489DAD2CF61732F25BBACD99A96BF5CAB58EB2825B7A6100657113B44705C667BD9E48EBFC5EDFD80363A5BEC321D8971CB64FD133E5F7612F2AC7C4B355F5E423F05B64FE135B88CB9A4C3910C3629FAFE612C45517807A91AED59607B05EAEE8C7213E8FA019E7FB2960F221371B6D24CFFEFC714B1686633E68CF19B6E00FD9078007E9E6519D42D4D77DC28A4B9E75632E4265847DF24A365E93173A9F292D5FA4398F320D94C4B14BAC06A1C6F0AEC970C6CF053E7F8C720CFE5D5BB52DC4EFB9415AF80B83314DEA25395F1C4ECFDEE494190FA2017C2FD0ADBE22B47AD7F8DE55EC41E8B7A4B815659F1C11929E03E361B0E813A8EB6CE47FABF9FBC39B513A1C895632AE480BC8A73816CB3BD70F7B9365F7D5995E06E2FC356420407DF56 +sk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ct = 6D5DBED9942D879727D6EE76540F024BD4090082CB4B0BB4F28F469E940CBE52FBC44DC2B16E0274715EB71C132B150ED1AB88DA13507BBF4469524C98E9261D363DBA0C1ED1A86D9642093A875C94DB40812E0ED7FBDB99C0D758D3511D3DBC0E4540267DFCE4F17179ED1EBEE904F77C7993467703291E00039E1FABF3DD3852837B63DBFB0519D597E210EDB8C13BF795A8927F062245D740C521E5E0FC518D8341247AEE37860802D171739B9244081D6F3AFC51EF7C3C532C5DE2C99EEE949F7B7375DFE3D2B5C675B8FE4827C8181F0C6B1D3A7BD5A31ABD448EA30CD3EAC27CA1E11B6ACEBFD4825460ED1F8C01117FEF1EE358C43AD763DE5C8037BDA1F7DC6F302735E0BAEF030A6D63DE20DB8DC12F14CEBE4216540D061007A7812F56607D22A73C0727DD149E70956F4B7AF6261069FFE5C0C68F847C1D2293021EEB23DD64D37DF276B6EBA3972A8BDD69ECBCB94B81AA199C9FF6434BE90EC41D72A525238C26B4E916AC5DF6A4379C0E48D2E417EA7E4CC0298D037EBF1D4464A37332D12354B840C1F7023673FBBBF6A7FBC1D9CFDA31E98FD34A1060762C71E158280AE31E5FCE62FC65AE16033299AE9302693BCBC067C4422E631F7B4B2B5343DAFFC590F5ECA4C82F82C6C4B447526CD1DB28D7F008534D1045E022FDF64C615661BA0DD833889F5717BBA9860134C033014D169CCE2C901AA01777474F538A0796CDE025B63E30FBB0BC1FFB9A0492871F1375F650608F0E9184A747E49DC50C49F56AAFF1A175BCFB19B88F6312933FD9F648D3D921961B94769EB44E6FAE55C83A38573CE243418593A05182E92A3A 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sk = 6C8C53ED6F65E6B2E324B84364E10DE42D1C26A106D4D1C99EEE79C78586FB55B9402BF02481CE4B27A52E87FEB92C4399C7F2988D40E942E7496AD15AD2AA8841AC9E53A84C4F6E854A8394306D42019097AD9405F24E53BE449D3285650E59CE88CF4412468D1D1A4B922EACA855DBAFE948FCFCD35301CE1346AAB3017CA19A01C052FF6A697813F8347C16CB04F7CFC18E44B57E650E3BDE360985EBB10ACFCF4ACD17E9D569E525F05DF32CB882B4AF59A8FD754C90569F5557B47727C9A380BEFD94F2F98F3EF172681F808AC68CF2EAD954AE209E9320E6B228C98D7832BD8326FC49F3056B2AF74A4E01EFB8E131F845347D9CD6A623BBD1857E5721509BDD80DC83A6BE6C8ABF634B71D9DC92687CB8FF94ECF19276B82A1D12F1AB81BDDC361BFE65795F4ED2C31F202D9887B376B61D13BF8D17DB3B8B7AC839925BCB06CE63A030F7EA5556BCB9D2C624DE325577A4478E943C7BB658FD9B5B537B1B9C7CCD3DBD5C38585434CC60C44785AF06B5B660451DEA0DECB5857E26B471DD1960A7E052205D249A41CCB15A42894369EE608BA01C9082BD45206AADC172254AF6DA920BF0E72CF9C7A187CB1D1F19598F254D07277CE1CD319CF8F8B3605FA0BDDFF6400A7FB53524D990B4097252F3610CC34F374641E977304A7AFA008E2B3195656CD4C11D85D716A690FD989879565786D6DD44B61D4103CFE38DAAFCF14D5980BF98083D9CE534B93F6F55B5907EAB7A7D6725B14858C5F3B4D9C83EF4235D4967D28E7144BDA6534E7AB92F82A599AA127226FDE2AA4060A863E9FB46571C5626E79DC3842DB53DED492B990C55EB595788B7438CCAF5E1F87406E37614A3EE8B9891EE26BABBBFFFDC137B456C597D525A8E103B16C99C714D8D7C1244 +ct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sk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ct = AD6DC098D3843B70817652D1DE6E1C58B868AF65F1BCD11E1BD05A72A047B26AD655CFFA19FAE7B6930F6ABCE65B781C2B5494262EEB51AC09EB9C381246D124905825623000EAD81C890D4FB007C30BEFDAE7436B3A7FBB37527BBDD944832F1F44C327D1787B775A4AA2AC19FE86025AD6C06CAD0868158AB916A4A9C14CDA40B9BFF9ABC943AEB97CEB1CF062EBF81A89C8891E6B30AC015A206D0EAC2000510784D969838F2B1A6453F562E439D97856756CFAE5D002CD9DB73B859B997FA5B8EC9AEB7902B974495F84447E4C1D1218C21C942B39CC87D3E1A927498A43B2CEFD74BE1D45DF6F53C1D1C657A68F1577EDD154B33D89EDC0229482CDEABB796E2EA5B25CC13F3654BE6AA0530D6217DD40FCC2E4F966281ACAD739874F4D274CD11BE31DF811CC45B16B35B881C46E824DB2132F2D0EA4A484BDC671FA217CBC9DF80AA8BCDE64F5FF2F9379ECE900D4AB4AAC7F1B4AC5985B9C4B30DF71C76958BB542D817A7D564D4569E668B676667B6FE1D8606645D3FB46D95DAC76798DB21874D1CE9E1C9BEF9BD1DC373220D08D3B789BC4EE3864CB9158F7F084D4FC1E623003D555903B5DDB8624FC6E1B6A2EB4678D37D5B1585F1C080418DB92D1470651934AD819BA4E4114BAE4C1B7D57500DC3A0DA478A932BE68205B95431BD519A73ED746E984634DE656F190E7D31F3293F79AD5661D114144BC373EC5384B1AAE61ED63BB74AE099868E00BD529875D7FAF22819EE4ADAD1E68254D856EC5D6751574A1488B5AE54D40815D565A9B55AB7725335187ABB0F674AED93D659BDF2683F7819BDBBD6BD758695FE0BEF4D4 +ss = 8C5FA3CE335959851C3C06CAFD39CDB9E1848E8D4F72128FD9842AB5BF244F17 + +count = 56 +seed = 687C02DE1041ABAC7B2C1E6EC2A7C3375552ED5EDB10E3A8139C24CC76BDA44D719D8121A81D47A0B762B4E9EEB85235 +pk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sk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ct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6A1AEE5E708C1B47F02BDACCE4F56C860F74FC7CFEC1EF3B58285B1C8AD7FEC2230E05B7114FF0395CC6634DB1EAE8258072D09C09F291E92D6620B177DC50D7B992373F9086C7AFDBF4B44A96BBA802AF164FD987430A7901D7896A23A68E506844813955D965761C1DA2BE415C039B497753E5FC91CEBD75956708A4AD9DBB90B62E157DC0A965CC350A523C01F2A2CF53E5C5677E792BD7E2DAE32A83D329779DB1E5ACE7BBEE7C3C272C214DFAC2D9AF2472F82981B525128E48523207D9B62220B89623BC8206BC21F5A3AC2F406988B402E3E187A11E689143D45A4D405BA00C760ACC0D7FED7807479A84FD781C385AED31AA100ACF88F9EB79737C43D9B6F78BEF6F897425A4AD6A8CD55FB6B68E6199581C9E9F601829FFDF9DBBFD7245C713EA9B6AFD5DE268A21CEC23140C6418F3B29EE7B9BA388BD97D0DC2A31DC191EEDD09FCBEBBCC2F5972A20369BCB7E86DDE8842A5B745CDBE0F3481CD0C5225989D2F8CF6BE261F5DACB1ECA74E2F777C2654AA0F45EEB2CBB51C739D1E30D60233C3E68F97970ECEFD7B1959903191D53FA218E07582B0D36F3888F1FAF700F885659690B120F1CD211F90E03C1CBACCA3362AB6073C9857397541785DD16C2B467831339D4ACB8A913776D0D6E81EA6910E007D532FDDC4C41B6AEEBACA86694E53B4F1EAFF28883C22D5C6F72714F24EFD55DF7034B6D64C83027791AE32375CF54A21D366E783B2ECD7120B9B85C84D8396EE5FE1DF376820C34069A9B3D43A6665ED8AACB4D5E2E48A0FA32B8AF2EAE4574650828C541BAED27F6315836A2CBC3C0442B19F64012542A6ACE9FB98CB6A18B49E56AD7A692340D0D3D60799C406E8E5473A43893C0D23A7CEDD99FEAEDAB114B6B372E6794AF6FD7CAD6A1E +ct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+sk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ct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+sk = A453BCACDD2B0D4646009E5ED451C3C45F08FB827EF733DB3C517A9DC1AF93E67A3CC8AA3239D4C52CE4C95AFDEFF6EFBFACAC10D294EDC0E7CF4535059BFDBABFF7698FF728119CEFE3FA1A6BB2F800F2CD33D0403CC1FE95410E1E9312CC7B2601ACB189BF030DADA92A539016451D574EF10F336480F29D31403F863CE4BC69FBC915BDB8A1766C0BE74B61DCC2D57D6F79541096E12A1D14DACF5D45098BA3CEE8739355B5084F9BE5FA273E6ADF284FDDD5A7D3FCBE00105441ACCEB1AC821B77156A8479B15087332989BAD6EE4FCBF3DB10E3C690B8797467DD715F0AF1CB98AED9F5EB1AA35DA482C4DD9C9095EB96BDBCF6900C54466C5B29316B06B91B64725CB6AD6F1A56253088C182909246CBD4EEA14623DD1E76E827E7A86A71A4CAABE2CC10C65455539F3E47778C48038FD98FF23ED294EFBA9148D3CD189AD5387922E16C3779B16FD482F8B015ACF7730176C0480859EE10D0E51EB8EDD9F8BE3746841CA02C2D81591E08434FD99CE87EC0E41B81CEECF9DAE3752B819185672DC6DC844F8B64B76B9EEB61EF012017BC379D3A7061B23F54388AAAC75050694CA7375B18A4E6A18E213C7AAC8FB0BC3A8C46805E18D362A793724E47CFFFBD9C8814E34D1057A0031074D475D44D05653BE73D937CB024D958A57903B588FD82184FA97C04FF6999EC7F84E871B4BCC839E4CE42D2B2AE9E3239A0C5F8BDF230ACD82B3044394BF67AC3CF124695A4EBAC4C8AECDD850766317838FAFB5BBCA0C4258ED985A79B49E42CDEC7CE08CB503A8EFA7E2B598A955CF1C50D2A1FB339BB30187D6450C3A98A3DBD8D2C721F200FB616AD3672E83BE1C66600630FEC9E903E1E56AC88937FF968C858A6878FDB998F2C61DE6C8E50A784257ED9351E42 +ct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sk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ct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ss = BC6C4B7FB37F8074CED5D09537104E7D2F8A25020E28E13D63D86E9A5619C784 + +count = 61 +seed = C799D57B41F28C5C446DFC58A5AC6499C4BCF3C162AFD2B09A16549826EC2A6F689E44BAFC4ACC82F5D6AEC23F4A3993 +pk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sk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ct = 0ACCF97C1A2AD0EBCBD00B1FAFA60AC76ABF5165EBFFB6D5B5BD5CC5F481F153E917383B8DD08C1ACDA5FF2471357B0C6EE67A32AC00D16A8A7ABA2EE590EC6553F70CDDF6E61F95FDB88846E64AF4722F2A868065957A06C84891F9E3011B1168244EA46D2463788453AB79B819547704A3099DB704A075635594585F4F27A91CC5063D5E66C7D57F25ABF2349F495A10DB2355C3F1D1FBDAC0DFBCB7762BF7C988C57CA84ABCF652EC38F1A0DFAF5FE58FE14302EBA8B3AF7C7201F53D56AF03A17CC8C3E4DF1B826F810623446BDB7A74FB76C5724642B3E707DDDFBD484831F53ABFD399E59DD52ECCCB1BFB114EC7B67DE37A262474D8668ABFDE025EBF0D76823CCEDA5D85E7C45C3C5E15F911351C70EDB03F4151F350894DCB6742F3AE01EB24F79ECC82D907C0524C900FF3C8137B4A1C31F491654E7DDBECEB6CBFDE04AE5BFD57C3C8B6CF66E3A727C9AC68D1EE16495D867085B6A98B1D4CBBAA1E524BFA3549C3EBDCB68C6D2E17A33D3AB53AF60D374D2D56633B4D6104D9AA23B079D95F50E67BB49E0FF4084180C80DCFE60D2A084B3BCD2D5F67A21F303225A16FB28A237395CB42B64EB2B612EF47E6B5693139708736B5E5929CA13C9D6ABCF6F5185D68FCD3521D539116446A007AB5F21D6A5F43D4C9997553CC904C20A55FA3BE59ADF6C8BBEBC80B3BFF2783F5199643FA5D95ED7D204DEC3F11FCDF002B7E5ADC22376435B496F0688997FBC7D75A080B21A6C4C14047EDA8DBE73590FC1A2F73F8A5F2EF76231F49F80FCD0C1C2A08045BF2035403A9D408AAA1E6E525A24C59AB839E1AEC8253C582D66117D4C7 +ss = 54DF5956155EB8EC96F4BF24A1E85984B2376FB0CADC4A51DC5B15B78B91C7B9 + +count = 62 +seed = F7AE036A0176A9DE9A036A542DD2840033277C44AE936D10B768566216DE9D4395CD42B116873B69D9804BA6CCBC05D5 +pk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sk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ct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ss = 1BEA35EECCA0EB3A88C2E9366E1AFE6E263921F4973F8A69E37E2ED15621FA92 + +count = 63 +seed = D995D38F934B6E1A7CA77C9522E3D037676CC939B0C8BD4B84394B3DC91A791F09D2D97199258C9943DA955E7F7B26FC +pk = 106DCA703C5EED03312712347F2B74EC3AA978045200AC5D569D5335DD8AB19A77D469EEEC95DB59DBF748C5EBC592A9A1975F4A2160369B48589A6A7FED06AAF12A3E7D51BC07281F99F05A4B2E76CDD81FA339B3CEB9253051425B9F4796CC9C4D4DE3B5502939323A199888D3307544907941186C994CB55197CABA62CE95CFED06F5399A06279AE1CC2652789F287268B6B72DFC7E112005FE943850A43A64BD8758DFBDE892C09058D90D36E799450CD067D53EB30310A02C269B0DEC00A6D96E9D85D4628C538BA89E164C7ECC09B7959ABE550F3ADA0C05F7666076D7A1BFE924CF64830E4F16E39E00FE2465A2D9B3BB82D369AD4D5C45C089A28351A28079344210CBD6FCC2B90865253B1282319A7A950920CCFB15F105AB559EE4C312D005B1DE64A932FE524376A5D163F442F2F4D5A6E73C8515E23601EF4F9631CF25F1F7B211CB2D60208EE1F762EA39AC8F71141A36BB66007D9E066C76DEB9DD870D7ED9E55DA515A75093B044E3B7B642B50743E510CFFD343913B86F54809658E8098BCCA42BDAD4F386D3E532DCFD29664B2F486A62181CFEFF0A68E756D2D348DE56EE251FA1634D285E49130582001D7A5B8E8AB5760AC6249961501FA2A0452E49798FE005721A5F24DE1311EC59F6A1594D36439EDB21EBA0BBAAE9ED5F6746D695ED0DF54891E9CF1D1795DE86FFDAE8ECCA8AB91E4D89512F7E9B3BB3432544219AA57D66486AA21DC9F2886BBD7B618AC61674B908A356E7DE5C2048E26BAF6AF82D231DADD61B5EA6C9310D4F +sk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ct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ss = 0C77A265D4D025CF8A1234D18336AA4E635A7D5F52C058AEED0A100656D701B3 + +count = 64 +seed = 5929F02A271725CB40200DE32D9D03D8BEA53B53AC83186C42C7F565CCB1CA508305D470850CF86E9B2C61A5B8CA1C93 +pk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sk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ct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ss = 643DF928F7681C94AFC18C6CC19F2FA446FAF7D7F38111D42C4BB3EB3F09292E + +count = 65 +seed = 905074033D7B75DEB2D06A2F29144EB377B452534C5710632989F02D45312D156557E96D4486020826DB200153BC4A8B +pk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sk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ct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ss = E39C1892E0D8EBCA1E85DB794E65C5F5954FD6929E64FDCAE0E5B47EF2B46A5B + +count = 66 +seed = A3E2E511AFA7BB560446BDADF67D2EE2E16FFC7BAEAE7EFB8C5455068BBD4E91BF9BE9D98B280072FABA7712C75B26D4 +pk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ct = EE8DD7AD12C06F3791A8E4283721BA9EA832D3A8FAAB16992DB5D6BED2A628B9C0E59D80B5E854529FE4714F11FF4C7B79C293A9703177A883802E88A772E12D535AF1568C608D53F132FC61A705681E1E6D16EB8BECC8A7592F8B04DA28C3C19FD760768394C3AE0DAD21A8256BDB1572DBDD8CAFC7B5A4C60F8DCD7841CA146B89543FAAE8447C6FFB6F57D10BE110DBADD5AF6CD13E83D27193787E7D431B0DFE03148601859C75F02782CDD8F28A01178EB19B3B55816C5E01140DDCB74A9C77DC1BAECD7F00F256DD6F81120595B6C3F86C64B2318DAB1DA67FAB1D821548863B441924539F16A832D734963B344B610C336CBF3494AF8A32B9920294598BCEDBE354D3172B2D53B4C18F4E95DEE8787D9AC6083B77970D99E12AAA4C922DD38F2C9732ECDBF4CB92ABCAF61544FC2998CF5008C7B512FA8952D91A24FB57D90E76EFA99DAFA191A530846214F81CABD8884B56C4774592E29737008FF1D808EEDA323988494884E67E44F5D16C9D09DCEF91BDCA305189F73D1D8C702FA07697FCB09EDDB8EC7618AF6350E21BD952B4492423787597AD94BF1F6FCA465FA2770BB300E56573BDD8DF8100352ACC0BA9F1AE227644F0D4038CD31D97BAB544583E986E01C646EF95A31455E4741DB7E48DD1639BF7C16376777273F3F9B370790CDF16B15B52082FE1E6345E076BFA068050AA0BEEFBB157ACFE8D71D213CF69604047BFAC9B23BF18FE36CBC8F8C899329A548FB1E9C815DC440431F6916D300504489EF3F1812C872C65A778A201F90762DA8C2EFDE53B04B0EED1B5173A9DD2E03C8F85CC7E0B70EAACAED18B0E7EEB 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+sk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ct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+sk = 6995143E8EB8A6E93840F76EEC844F67D2B5F75B1839A5040337E61F9806764A0F4DFF8E56F68440836A072412A30D851ACE2C7C6F02D60E7A8420001A63E6C6289AD9FBE5D49083E7078F73238A2402F028C7EFEAC23F7A9B7EE50C73D3041011862083518CA731D6496AEC46BD8A938F5C9BEA5EF04573DD4806BBF1EF8025E74255AB8FEC9A705BC373438D1F43E79FEADAA60CF5E138A54B96862ABE4B21994A4921C53400E856BEA19E5C58DB0812DA8EF2FF7722667D49F0D8A03B462CE8F7E94A2CF99597A5866C82F0A4E50756238EF872741229B52975E5F2B7946502F6F7D39584FADA259533F148B2E2F1E89CF06CA0099B4D25853B9F4F9084CA57927274C095DAA5AE4527269FB200A42F26A6997FAE385FD7162A341B2C8D86796287ABCE75DC9D3B3BA775FBF818F0A08FE774E7D0387021C5CC83D99BCE441BE8345A3741AC15B68265E50A4C9EE9715FFE494A23ACF7A2744768E6E2543B9556D0A230CF6A50F86D6B722272CA5AB49BD0221F4BBA4F6B353317B2BF9640F6F36AA798BD2A61FE0A62BC12D5064F483A833FD203A00058F8A9273E2AE281FC2ACCB443CF5F0F6F9CA03AF90ACFC4045271BA0C79B672CF871F61E49388555E02F3B03865634423B623A61D73A7FB8821996139BC2079C1FBF6036A40EAD5C14A3E0DD35F97E7388380AECC41F3F16513071F10407805F9AC44BFF51B676A2503CA16FCC9ABD340EF3209D3AFB6A09E1098B2C0EEABF1F22F02C32A7363D8A76DB2381565D1B13CE39735129BADC8D97BD2AC18FD3EDE3DDEE362489079B78CE0E28EE620C9A38706A16D4BAC64A6B7141A87C31CC17EAE37DDF77997084431201E353C1A2A03BEF410C607DAD61590C9691143E2E9B5261A515C59771C67F244B60C +ct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ct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+sk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ct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+sk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ct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sk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ct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+sk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ct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ss = 3BC6E89EB86810163951340118ED66AD0B8B84EA6021DF32384D9EE2ED438716 + +count = 74 +seed = DEB963F8B1D8FBDF499D564BA8D2D47915BB402DA02F17031B37B4039A842AFB9B7E48F37200605992BD2429427A7A4E +pk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sk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ct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ss = 9C96C97D3032D9A7283A9F4488D291CC7484F8F6DCA8B17419B04DDBFD9A12E1 + +count = 75 +seed = 8E2995F1B3E43853B18916BB1212ACEB05898E2B177A87ABEB928AD7184E59695C56B2CCCF5DB80853C28A525E327D13 +pk = 077E537B7271895348293B7C34EF117FD286DF34F0E07BC89FD344DB8D1E5D8CF0E7D41F1A7C22BE01B3A3AC8FD919C68E936E4F66F543F365E199C41BAA599D49CE23FA772975E225F2AC3969FDFB32BF4A2F26B388E9C51377EB778159112730151F4F3EDF3197713424588F1BB3B2782FFC9200279B11FBEB4D7204C4504C246DA183F1E15B9C7B89B39FCA508755865B8EABF1D363D279B0F38D8CAE0EDA7926F370BC66F67C31BFDB44DC9CF2B28F9DEC21520DE58B8811161BD33E14E41E13EECF0CB587158CC5661BC79B43EF41AF9CB3F6D3A006FACFFED78B2A8BC6CCACC4694B2D470480D698508016333BE798457F632BE1A79AA2ADBB165CC5CD3020A7AAE9FDC2157B6196836D48709E1F0AD5318BD31531450EC3FBDBC1D00286823EB7FD00B08935E2E6CBC1104803D154DFABF848418147F0429B7CF7A3F532917989106E96A7161E3444712AF249216B01D7C2BA97361FF9B3B3518C0D57B5D1A4023F88EF69640E63BABF6DE29536BFE39E4B28CD08CA1AE6C9DFD9D2080DB9A7AABAC74E103F6AEFB7447C36EE43C91F2A8042B96D33F7922543B88D5E8D78D5B9277986A52FFF1C51EF03B33CB7AF137645D78B05F9ABE26EC423472B168ADC67CBDF8777AC8F3EBC2ABAD44F40C03A00F01C8D1B961242D29B70B4C45A32F6D6463C4720F98C7A9C95C74E037E15A22FB769A8D3F45F93687BCAC6493171E15D0E919AADAC8906FF2E80C3212E02CB9041228E4C94F692E266191C16AC895DE4F7045CEDC85F29C41B24A845DB9D4B2A +sk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ct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ss = 2193074EA86C6435F13AAF99E488F9CD34049D64EDE5A0DE7A84F5DB6474CF2D + +count = 76 +seed = 9218943C51FD2DE47E509AAC67EFF176795102F37D7A2017E3AFD768FCDA7877AF38739B00FCDF227C2FD62EB635942C +pk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sk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ct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ss = B22BAE3C5A03DB642A25672388E7735BF8E23AD6814CFA72F7B9E5F62614F7B4 + +count = 77 +seed = 542E20078ADD5296050AF150360F057F6B9AB3BA835589DD56987DE805F900B906505B5390A0D86CBA28038992DFC59A +pk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sk = 241191401A63AFA750F05662E354DDDBC683C776CE3222BEB83E3CF913D7ED7CA59B3BD23B49A95BC1FAD20070FEC930B6060BD827D742B077092E422268E15D85112C0C2683DE1DFA7719ED7F49880249EBB990C7F8408519C13A9C6CEF765C21C156D224C818BF2895E94B55F8806E0339839AB1A8B7A9F8A9CCAD5EBB16650EC8164AFCA022E094E01765FF49DDE35468755EC176EE6D35C692E848975225F22131172E1AECF4F51CABBD3A5CC73B517A61DA7F3466E2F53849B81BB5D6EE2BA91BDABBE6E2B6FA731F40950237FDA8F0205232810813593722270BC1D9180C10E1526BCADF15B30244B216EA5E311DE6F2344FBC85F1CE38A24DE9977441534D2F79B3FA1317CF509C46458EFA7EED6FA51171BEFA4D6946FFA61F091AC3446DFCDB1D9E7C29884E4758F805CFB54FAE8706C9A28A1F76536E1AC9929DCF70A0A59BD2CDB34D0A82E71FB0005EDCE388FB0F8241A9B2200E8CE97C381EF0B9427727A91A5C26B13B95789DC4A002C19FC15B7E7210F5D7CEB4DADE023FE5DE7A70F63218AFB8ACD717AB3D6864C2B773F45C59171D44B48D8662C3981E629286CD2D9C232A0B738B76B616E1BB955DEC5115810BA52C190C21BB02A6FD3F43EEAA713294DB5E58FFCFE6F53601C2F2DB38EC1FD8651DD7ED702B70F6C9375E4C4A51D79E3C0DE28A5B6801AB8F7BCFF099E77672360FE7B1A036B36A7843A14B7F085004C9F83529F448C61AABE105C281F3E504A64BF40E3909B619997B080DBAF3621ADC5B9464BCFDFA850DAB77A3C676D2BB8537EAD3AF16ED2FED11B61846A622AB1A5FD14BBE9C1F5D862BCE653CCF007E552E418C3D9D3B18CBE1AE95E413E032ECED079AD01F98226067D6551DB612DCDF2017D1502D55EB888BD93F1514 +ct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+sk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ct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ct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sk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ct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ss = 8C46A9F4111F3A275FAFCE4FCF0BBCF828A0A9006D0A9C632F1B5B8E669D23C4 + +count = 82 +seed = 373FDDE922CFC416ED96B444E445BDD0962E8989F6C50ADF9912A89937C57217D3600B06C95440448E3F601AE69CA5BE +pk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sk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ct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ss = 60F62850F54096EF4D8AB44D5050086D48889FEF1D2523B2BAFF585D2E4BDACC + +count = 83 +seed = 16BEF67F7AC3A755C59C816478B75FCC16CE5844DB537791ACCD1EBD49D2824B105FD2E970F728C8F0CF16E439A9AE2F +pk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sk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ct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ss = 4EEA80450240413B5947E8CC918E91C4F1662655FBBBB2EEDBA9D802B76835F9 + +count = 84 +seed = D0611F9AE5BE4DA5D7EADC9109944348E716CB3DAEE545721EEA8C892E7831CF2E54603146454CBFD92387739E9A78D8 +pk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ct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ss = A6AA55F4F84ACE96FCCFD113B3B77E885748F05E84A0F8BB68B5B59AB3813116 + +count = 85 +seed = FBC38D7614D7718E931EDB850D2C6F0C5EEA9EE889B3E25BD69AC255D5B91E885D93E808E66BF9C88C655DC594DA5792 +pk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sk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ct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ss = B51F055A645FAE20F634F62243B398358544C00F2E93DBF55FA69EA82C00B43A + +count = 86 +seed = 1722219CB5DB47374EB0AF0232C856A57F026F1CB09E5A5799F4C333DD422FF6A0A67C4DA502FAAE727FB2D45DAFCF35 +pk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sk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ct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ct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ct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sk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ct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ct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ss = F0072B8ABE7D3C6B1686702E58B9C9F15D91B3765954B237D851F441E976A94E + +count = 91 +seed = C5856298C3CB6AC9787A0F30938537AB2635B96F6D19CC9522063360E7A5C88E644929D2879180E3E5BCAD2422B7CFC3 +pk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sk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ct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ss = A70CA9CADC09966C85907688FA6AECC1C0AE83FF905770A34FC6E2B3F8287AB3 + +count = 92 +seed = A28EAD0A08E7228AEFF602B16A1E752278B8ED1E91DAC67994F5ADC372E1D82F95CC390CD97AB9212275E0566C833FD8 +pk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sk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ct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+sk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ct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sk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ct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FC37F83331A63916EC11797513CA32F0A6549012F07BEE7162C4A06352885C0F8A56F74745CCCE89E027C8466DEA7EDB747D8EF60FDFB90EAECBBDCF41D14EF9EA8C70FE436A85126735DC0277E0EC30E84D1844D930BA32BEB3EAA9122E327B5AEF76F277DC00AD148DE1072C6FD51F7CB68589893E97257390FD78FA65502A7F47C952DFFA97CA51B8406DD949C94EB133154A6029CCCBB3966F8271F61B06CAF6A446C66EB872503111AFCCCD966BDDE520E4B537619399FB2C10208936A201C0084341A2E505F0712BAB7683EB9A0E521A8F34BD16C2B11A5C0E12A5B49E038059E14A573B032E923E46C8A667845821F4B7AB1124C441FDE54F7F85B9E7322B3BD9590D09820E9670B94304330D6AFC31C70D35525A8E6BA0238376B04A2F245FB1D02A3A7DFAC6280706E049DA5ABF9F8C07ED31E5DBC9AB4C38D6954C206361722E63D2EC91DE02C3BE2454D36E214F3068F4C37172528EC610E7D5DCF6092456E289BC924CCB6ED489B45964E0F03524CE97F315B41BBFDB1F0916EF321C84D8AF4A9CEB6B5CD0D9369A616B12678FCBA937F805D06AEA6F46C6C7EE51068DBEF43D4CA27D3C68C514307898F5A20E509E8898F803384B5E11B99B8944BD1CD14154A02A4DFA89F7663ABF612B8E0DFADF2BF1ABF09F761620D73B079AF8C83772A675325640849341B389A0AEE65FAA87FE883759C50AF8699347CB0B6D9C69F82247FDD0EE2F5FF08D9309BBB8CDFEBD255AFE6866AF77D21C98B942370DE12462886C95271FF18CF274398329D022 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ct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ss = 6D33FE9327795188EF4404E03A913F58918AE8A29C34B28C9124B4689E2E63A7 + +count = 97 +seed = 59EFF60B1EF6185DB34EE1E3B1DD2F159106CECEAA79BEB74923B4F5623D5BC52DBF5D2594A1F7C6C64D12CF144E9ED4 +pk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sk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ct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ss = 864742A6F00FCB874217B6159D2090F8C7F45092337EEB3D9185C72429CDD5F5 + +count = 98 +seed = DDDCA9DC31BEA737D3F474E7560B37FACB2F53C803E768FFAADE7669FF94B1D4FBD17068CFFD5DFDD24AADADA4EF6B12 +pk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sk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ct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ss = 5CA7F1A531AA82BBF918A7C07F7F155D83E94EFBF4ED58EE7C0E89ED6C80F2C0 + +count = 99 +seed = 2A6F7386B815366F572AEB6C79E272CC21B7095FE09575F18072C9D677DA23BC9C8A4BC393B7524604D299BEDD260C8B +pk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sk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ct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ss = 8ABCE489762C5BBC4C2326539BDA39B08CDE688D81EC4F75F11946550E603D57 + diff --git a/src/circl/dh/x25519/curve.go b/src/circl/dh/x25519/curve.go new file mode 100644 index 00000000000..af2ccc40a94 --- /dev/null +++ b/src/circl/dh/x25519/curve.go @@ -0,0 +1,96 @@ +package x25519 + +import ( + fp "circl/math/fp25519" +) + +// ladderJoye calculates a fixed-point multiplication with the generator point. +// The algorithm is the right-to-left Joye's ladder as described +// in "How to precompute a ladder" in SAC'2017. +func ladderJoye(k *Key) { + w := [5]fp.Elt{} // [mu,x1,z1,x2,z2] order must be preserved. + fp.SetOne(&w[1]) // x1 = 1 + fp.SetOne(&w[2]) // z1 = 1 + w[3] = fp.Elt{ // x2 = G-S + 0xbd, 0xaa, 0x2f, 0xc8, 0xfe, 0xe1, 0x94, 0x7e, + 0xf8, 0xed, 0xb2, 0x14, 0xae, 0x95, 0xf0, 0xbb, + 0xe2, 0x48, 0x5d, 0x23, 0xb9, 0xa0, 0xc7, 0xad, + 0x34, 0xab, 0x7c, 0xe2, 0xee, 0xcd, 0xae, 0x1e, + } + fp.SetOne(&w[4]) // z2 = 1 + + const n = 255 + const h = 3 + swap := uint(1) + for s := 0; s < n-h; s++ { + i := (s + h) / 8 + j := (s + h) % 8 + bit := uint((k[i] >> uint(j)) & 1) + copy(w[0][:], tableGenerator[s*Size:(s+1)*Size]) + diffAdd(&w, swap^bit) + swap = bit + } + for s := 0; s < h; s++ { + double(&w[1], &w[2]) + } + toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) +} + +// ladderMontgomery calculates a generic scalar point multiplication +// The algorithm implemented is the left-to-right Montgomery's ladder. +func ladderMontgomery(k, xP *Key) { + w := [5]fp.Elt{} // [x1, x2, z2, x3, z3] order must be preserved. + w[0] = *(*fp.Elt)(xP) // x1 = xP + fp.SetOne(&w[1]) // x2 = 1 + w[3] = *(*fp.Elt)(xP) // x3 = xP + fp.SetOne(&w[4]) // z3 = 1 + + move := uint(0) + for s := 255 - 1; s >= 0; s-- { + i := s / 8 + j := s % 8 + bit := uint((k[i] >> uint(j)) & 1) + ladderStep(&w, move^bit) + move = bit + } + toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) +} + +func toAffine(k *[fp.Size]byte, x, z *fp.Elt) { + fp.Inv(z, z) + fp.Mul(x, x, z) + _ = fp.ToBytes(k[:], x) +} + +var lowOrderPoints = [5]fp.Elt{ + { /* (0,_,1) point of order 2 on Curve25519 */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + { /* (1,_,1) point of order 4 on Curve25519 */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + { /* (x,_,1) first point of order 8 on Curve25519 */ + 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae, + 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a, + 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd, + 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00, + }, + { /* (x,_,1) second point of order 8 on Curve25519 */ + 0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24, + 0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b, + 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86, + 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57, + }, + { /* (-1,_,1) a point of order 4 on the twist of Curve25519 */ + 0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, + }, +} diff --git a/src/circl/dh/x25519/curve_amd64.go b/src/circl/dh/x25519/curve_amd64.go new file mode 100644 index 00000000000..46711e0648d --- /dev/null +++ b/src/circl/dh/x25519/curve_amd64.go @@ -0,0 +1,30 @@ +// +build amd64,!purego + +package x25519 + +import ( + "internal/cpu" + + fp "circl/math/fp25519" +) + +var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX + +var _ = hasBmi2Adx + +func double(x, z *fp.Elt) { doubleAmd64(x, z) } +func diffAdd(w *[5]fp.Elt, b uint) { diffAddAmd64(w, b) } +func ladderStep(w *[5]fp.Elt, b uint) { ladderStepAmd64(w, b) } +func mulA24(z, x *fp.Elt) { mulA24Amd64(z, x) } + +//go:noescape +func ladderStepAmd64(w *[5]fp.Elt, b uint) + +//go:noescape +func diffAddAmd64(w *[5]fp.Elt, b uint) + +//go:noescape +func doubleAmd64(x, z *fp.Elt) + +//go:noescape +func mulA24Amd64(z, x *fp.Elt) diff --git a/src/circl/dh/x25519/curve_amd64.h b/src/circl/dh/x25519/curve_amd64.h new file mode 100644 index 00000000000..8c1ae4d0fbb --- /dev/null +++ b/src/circl/dh/x25519/curve_amd64.h @@ -0,0 +1,111 @@ +#define ladderStepLeg \ + addSub(x2,z2) \ + addSub(x3,z3) \ + integerMulLeg(b0,x2,z3) \ + integerMulLeg(b1,x3,z2) \ + reduceFromDoubleLeg(t0,b0) \ + reduceFromDoubleLeg(t1,b1) \ + addSub(t0,t1) \ + cselect(x2,x3,regMove) \ + cselect(z2,z3,regMove) \ + integerSqrLeg(b0,t0) \ + integerSqrLeg(b1,t1) \ + reduceFromDoubleLeg(x3,b0) \ + reduceFromDoubleLeg(z3,b1) \ + integerMulLeg(b0,x1,z3) \ + reduceFromDoubleLeg(z3,b0) \ + integerSqrLeg(b0,x2) \ + integerSqrLeg(b1,z2) \ + reduceFromDoubleLeg(x2,b0) \ + reduceFromDoubleLeg(z2,b1) \ + subtraction(t0,x2,z2) \ + multiplyA24Leg(t1,t0) \ + additionLeg(t1,t1,z2) \ + integerMulLeg(b0,x2,z2) \ + integerMulLeg(b1,t0,t1) \ + reduceFromDoubleLeg(x2,b0) \ + reduceFromDoubleLeg(z2,b1) + +#define ladderStepBmi2Adx \ + addSub(x2,z2) \ + addSub(x3,z3) \ + integerMulAdx(b0,x2,z3) \ + integerMulAdx(b1,x3,z2) \ + reduceFromDoubleAdx(t0,b0) \ + reduceFromDoubleAdx(t1,b1) \ + addSub(t0,t1) \ + cselect(x2,x3,regMove) \ + cselect(z2,z3,regMove) \ + integerSqrAdx(b0,t0) \ + integerSqrAdx(b1,t1) \ + reduceFromDoubleAdx(x3,b0) \ + reduceFromDoubleAdx(z3,b1) \ + integerMulAdx(b0,x1,z3) \ + reduceFromDoubleAdx(z3,b0) \ + integerSqrAdx(b0,x2) \ + integerSqrAdx(b1,z2) \ + reduceFromDoubleAdx(x2,b0) \ + reduceFromDoubleAdx(z2,b1) \ + subtraction(t0,x2,z2) \ + multiplyA24Adx(t1,t0) \ + additionAdx(t1,t1,z2) \ + integerMulAdx(b0,x2,z2) \ + integerMulAdx(b1,t0,t1) \ + reduceFromDoubleAdx(x2,b0) \ + reduceFromDoubleAdx(z2,b1) + +#define difAddLeg \ + addSub(x1,z1) \ + integerMulLeg(b0,z1,ui) \ + reduceFromDoubleLeg(z1,b0) \ + addSub(x1,z1) \ + integerSqrLeg(b0,x1) \ + integerSqrLeg(b1,z1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) \ + integerMulLeg(b0,x1,z2) \ + integerMulLeg(b1,z1,x2) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) + +#define difAddBmi2Adx \ + addSub(x1,z1) \ + integerMulAdx(b0,z1,ui) \ + reduceFromDoubleAdx(z1,b0) \ + addSub(x1,z1) \ + integerSqrAdx(b0,x1) \ + integerSqrAdx(b1,z1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) \ + integerMulAdx(b0,x1,z2) \ + integerMulAdx(b1,z1,x2) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) + +#define doubleLeg \ + addSub(x1,z1) \ + integerSqrLeg(b0,x1) \ + integerSqrLeg(b1,z1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) \ + subtraction(t0,x1,z1) \ + multiplyA24Leg(t1,t0) \ + additionLeg(t1,t1,z1) \ + integerMulLeg(b0,x1,z1) \ + integerMulLeg(b1,t0,t1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) + +#define doubleBmi2Adx \ + addSub(x1,z1) \ + integerSqrAdx(b0,x1) \ + integerSqrAdx(b1,z1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) \ + subtraction(t0,x1,z1) \ + multiplyA24Adx(t1,t0) \ + additionAdx(t1,t1,z1) \ + integerMulAdx(b0,x1,z1) \ + integerMulAdx(b1,t0,t1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) diff --git a/src/circl/dh/x25519/curve_amd64.s b/src/circl/dh/x25519/curve_amd64.s new file mode 100644 index 00000000000..b7723185b61 --- /dev/null +++ b/src/circl/dh/x25519/curve_amd64.s @@ -0,0 +1,156 @@ +// +build amd64 + +#include "textflag.h" + +// Depends on circl/math/fp25519 package +#include "../../math/fp25519/fp_amd64.h" +#include "curve_amd64.h" + +// CTE_A24 is (A+2)/4 from Curve25519 +#define CTE_A24 121666 + +#define Size 32 + +// multiplyA24Leg multiplies x times CTE_A24 and stores in z +// Uses: AX, DX, R8-R13, FLAGS +// Instr: x86_64, cmov +#define multiplyA24Leg(z,x) \ + MOVL $CTE_A24, AX; MULQ 0+x; MOVQ AX, R8; MOVQ DX, R9; \ + MOVL $CTE_A24, AX; MULQ 8+x; MOVQ AX, R12; MOVQ DX, R10; \ + MOVL $CTE_A24, AX; MULQ 16+x; MOVQ AX, R13; MOVQ DX, R11; \ + MOVL $CTE_A24, AX; MULQ 24+x; \ + ADDQ R12, R9; \ + ADCQ R13, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + MOVL $38, AX; /* 2*C = 38 = 2^256 MOD 2^255-19*/ \ + IMULQ AX, DX; \ + ADDQ DX, R8; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ $0, R11; MOVQ R11, 24+z; \ + MOVQ $0, DX; \ + CMOVQCS AX, DX; \ + ADDQ DX, R8; MOVQ R8, 0+z; + +// multiplyA24Adx multiplies x times CTE_A24 and stores in z +// Uses: AX, DX, R8-R12, FLAGS +// Instr: x86_64, cmov, bmi2 +#define multiplyA24Adx(z,x) \ + MOVQ $CTE_A24, DX; \ + MULXQ 0+x, R8, R10; \ + MULXQ 8+x, R9, R11; ADDQ R10, R9; \ + MULXQ 16+x, R10, AX; ADCQ R11, R10; \ + MULXQ 24+x, R11, R12; ADCQ AX, R11; \ + ;;;;;;;;;;;;;;;;;;;;; ADCQ $0, R12; \ + MOVL $38, DX; /* 2*C = 38 = 2^256 MOD 2^255-19*/ \ + IMULQ DX, R12; \ + ADDQ R12, R8; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ $0, R11; MOVQ R11, 24+z; \ + MOVQ $0, R12; \ + CMOVQCS DX, R12; \ + ADDQ R12, R8; MOVQ R8, 0+z; + +#define mulA24Legacy \ + multiplyA24Leg(0(DI),0(SI)) +#define mulA24Bmi2Adx \ + multiplyA24Adx(0(DI),0(SI)) + +// func mulA24Amd64(z, x *fp255.Elt) +TEXT ·mulA24Amd64(SB),NOSPLIT,$0-16 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + CHECK_BMI2ADX(LMA24, mulA24Legacy, mulA24Bmi2Adx) + + +// func ladderStepAmd64(w *[5]fp255.Elt, b uint) +// ladderStepAmd64 calculates a point addition and doubling as follows: +// (x2,z2) = 2*(x2,z2) and (x3,z3) = (x2,z2)+(x3,z3) using as a difference (x1,-). +// work = (x1,x2,z2,x3,z3) are five fp255.Elt of 32 bytes. +// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and +// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·ladderStepAmd64(SB),NOSPLIT,$192-16 + // Parameters + #define regWork DI + #define regMove SI + #define x1 0*Size(regWork) + #define x2 1*Size(regWork) + #define z2 2*Size(regWork) + #define x3 3*Size(regWork) + #define z3 4*Size(regWork) + // Local variables + #define t0 0*Size(SP) + #define t1 1*Size(SP) + #define b0 2*Size(SP) + #define b1 4*Size(SP) + MOVQ w+0(FP), regWork + MOVQ b+8(FP), regMove + CHECK_BMI2ADX(LLADSTEP, ladderStepLeg, ladderStepBmi2Adx) + #undef regWork + #undef regMove + #undef x1 + #undef x2 + #undef z2 + #undef x3 + #undef z3 + #undef t0 + #undef t1 + #undef b0 + #undef b1 + +// func diffAddAmd64(w *[5]fp255.Elt, b uint) +// diffAddAmd64 calculates a differential point addition using a precomputed point. +// (x1,z1) = (x1,z1)+(mu) using a difference point (x2,z2) +// w = (mu,x1,z1,x2,z2) are five fp.Elt, and +// stack = (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·diffAddAmd64(SB),NOSPLIT,$128-16 + // Parameters + #define regWork DI + #define regSwap SI + #define ui 0*Size(regWork) + #define x1 1*Size(regWork) + #define z1 2*Size(regWork) + #define x2 3*Size(regWork) + #define z2 4*Size(regWork) + // Local variables + #define b0 0*Size(SP) + #define b1 2*Size(SP) + MOVQ w+0(FP), regWork + MOVQ b+8(FP), regSwap + cswap(x1,x2,regSwap) + cswap(z1,z2,regSwap) + CHECK_BMI2ADX(LDIFADD, difAddLeg, difAddBmi2Adx) + #undef regWork + #undef regSwap + #undef ui + #undef x1 + #undef z1 + #undef x2 + #undef z2 + #undef b0 + #undef b1 + +// func doubleAmd64(x, z *fp255.Elt) +// doubleAmd64 calculates a point doubling (x1,z1) = 2*(x1,z1). +// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and +// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·doubleAmd64(SB),NOSPLIT,$192-16 + // Parameters + #define x1 0(DI) + #define z1 0(SI) + // Local variables + #define t0 0*Size(SP) + #define t1 1*Size(SP) + #define b0 2*Size(SP) + #define b1 4*Size(SP) + MOVQ x+0(FP), DI + MOVQ z+8(FP), SI + CHECK_BMI2ADX(LDOUB,doubleLeg,doubleBmi2Adx) + #undef x1 + #undef z1 + #undef t0 + #undef t1 + #undef b0 + #undef b1 diff --git a/src/circl/dh/x25519/curve_generic.go b/src/circl/dh/x25519/curve_generic.go new file mode 100644 index 00000000000..2d59187f9e2 --- /dev/null +++ b/src/circl/dh/x25519/curve_generic.go @@ -0,0 +1,85 @@ +package x25519 + +import ( + "encoding/binary" + "math/bits" + + fp "circl/math/fp25519" +) + +func doubleGeneric(x, z *fp.Elt) { + t0, t1 := &fp.Elt{}, &fp.Elt{} + fp.AddSub(x, z) + fp.Sqr(x, x) + fp.Sqr(z, z) + fp.Sub(t0, x, z) + mulA24Generic(t1, t0) + fp.Add(t1, t1, z) + fp.Mul(x, x, z) + fp.Mul(z, t0, t1) +} + +func diffAddGeneric(w *[5]fp.Elt, b uint) { + mu, x1, z1, x2, z2 := &w[0], &w[1], &w[2], &w[3], &w[4] + fp.Cswap(x1, x2, b) + fp.Cswap(z1, z2, b) + fp.AddSub(x1, z1) + fp.Mul(z1, z1, mu) + fp.AddSub(x1, z1) + fp.Sqr(x1, x1) + fp.Sqr(z1, z1) + fp.Mul(x1, x1, z2) + fp.Mul(z1, z1, x2) +} + +func ladderStepGeneric(w *[5]fp.Elt, b uint) { + x1, x2, z2, x3, z3 := &w[0], &w[1], &w[2], &w[3], &w[4] + t0 := &fp.Elt{} + t1 := &fp.Elt{} + fp.AddSub(x2, z2) + fp.AddSub(x3, z3) + fp.Mul(t0, x2, z3) + fp.Mul(t1, x3, z2) + fp.AddSub(t0, t1) + fp.Cmov(x2, x3, b) + fp.Cmov(z2, z3, b) + fp.Sqr(x3, t0) + fp.Sqr(z3, t1) + fp.Mul(z3, x1, z3) + fp.Sqr(x2, x2) + fp.Sqr(z2, z2) + fp.Sub(t0, x2, z2) + mulA24Generic(t1, t0) + fp.Add(t1, t1, z2) + fp.Mul(x2, x2, z2) + fp.Mul(z2, t0, t1) +} + +func mulA24Generic(z, x *fp.Elt) { + const A24 = 121666 + const n = 8 + var xx [4]uint64 + for i := range xx { + xx[i] = binary.LittleEndian.Uint64(x[i*n : (i+1)*n]) + } + + h0, l0 := bits.Mul64(xx[0], A24) + h1, l1 := bits.Mul64(xx[1], A24) + h2, l2 := bits.Mul64(xx[2], A24) + h3, l3 := bits.Mul64(xx[3], A24) + + var c3 uint64 + l1, c0 := bits.Add64(h0, l1, 0) + l2, c1 := bits.Add64(h1, l2, c0) + l3, c2 := bits.Add64(h2, l3, c1) + l4, _ := bits.Add64(h3, 0, c2) + _, l4 = bits.Mul64(l4, 38) + l0, c0 = bits.Add64(l0, l4, 0) + xx[1], c1 = bits.Add64(l1, 0, c0) + xx[2], c2 = bits.Add64(l2, 0, c1) + xx[3], c3 = bits.Add64(l3, 0, c2) + xx[0], _ = bits.Add64(l0, (-c3)&38, 0) + for i := range xx { + binary.LittleEndian.PutUint64(z[i*n:(i+1)*n], xx[i]) + } +} diff --git a/src/circl/dh/x25519/curve_noasm.go b/src/circl/dh/x25519/curve_noasm.go new file mode 100644 index 00000000000..67349cf935a --- /dev/null +++ b/src/circl/dh/x25519/curve_noasm.go @@ -0,0 +1,10 @@ +// +build !amd64 purego + +package x25519 + +import fp "circl/math/fp25519" + +func double(x, z *fp.Elt) { doubleGeneric(x, z) } +func diffAdd(w *[5]fp.Elt, b uint) { diffAddGeneric(w, b) } +func ladderStep(w *[5]fp.Elt, b uint) { ladderStepGeneric(w, b) } +func mulA24(z, x *fp.Elt) { mulA24Generic(z, x) } diff --git a/src/circl/dh/x25519/curve_test.go b/src/circl/dh/x25519/curve_test.go new file mode 100644 index 00000000000..d3381b7e7e5 --- /dev/null +++ b/src/circl/dh/x25519/curve_test.go @@ -0,0 +1,206 @@ +package x25519 + +import ( + "crypto/rand" + "math/big" + "testing" + + "circl/internal/conv" + "circl/internal/test" + fp "circl/math/fp25519" +) + +func getModulus() *big.Int { + p := big.NewInt(1) + p.Lsh(p, 255).Sub(p, big.NewInt(19)) + return p +} + +func doubleBig(x1, z1, p *big.Int) { + // Montgomery point doubling in projective (X:Z) coordinates. + A24 := big.NewInt(121666) + A, B, C := big.NewInt(0), big.NewInt(0), big.NewInt(0) + A.Add(x1, z1).Mod(A, p) + B.Sub(x1, z1).Mod(B, p) + A.Mul(A, A) + B.Mul(B, B) + C.Sub(A, B) + x1.Mul(A, B).Mod(x1, p) + z1.Mul(C, A24).Add(z1, B).Mul(z1, C).Mod(z1, p) +} + +func diffAddBig(work [5]*big.Int, p *big.Int, b uint) { + // Equation 7 at https://eprint.iacr.org/2017/264 + mu, x1, z1, x2, z2 := work[0], work[1], work[2], work[3], work[4] + A, B := big.NewInt(0), big.NewInt(0) + if b != 0 { + t := new(big.Int) + t.Set(x1) + x1.Set(x2) + x2.Set(t) + t.Set(z1) + z1.Set(z2) + z2.Set(t) + } + A.Add(x1, z1) + B.Sub(x1, z1) + B.Mul(B, mu).Mod(B, p) + x1.Add(A, B).Mod(x1, p) + z1.Sub(A, B).Mod(z1, p) + x1.Mul(x1, x1).Mul(x1, z2).Mod(x1, p) + z1.Mul(z1, z1).Mul(z1, x2).Mod(z1, p) + mu.Mod(mu, p) + x2.Mod(x2, p) + z2.Mod(z2, p) +} + +func ladderStepBig(work [5]*big.Int, p *big.Int, b uint) { + A24 := big.NewInt(121666) + x1 := work[0] + x2, z2 := work[1], work[2] + x3, z3 := work[3], work[4] + A, B, C, D := big.NewInt(0), big.NewInt(0), big.NewInt(0), big.NewInt(0) + DA, CB, E := big.NewInt(0), big.NewInt(0), big.NewInt(0) + A.Add(x2, z2).Mod(A, p) + B.Sub(x2, z2).Mod(B, p) + C.Add(x3, z3).Mod(C, p) + D.Sub(x3, z3).Mod(D, p) + DA.Mul(D, A).Mod(DA, p) + CB.Mul(C, B).Mod(CB, p) + if b != 0 { + t := new(big.Int) + t.Set(A) + A.Set(C) + C.Set(t) + t.Set(B) + B.Set(D) + D.Set(t) + } + AA := A.Mul(A, A).Mod(A, p) + BB := B.Mul(B, B).Mod(B, p) + E.Sub(AA, BB) + x1.Mod(x1, p) + x2.Mul(AA, BB).Mod(x2, p) + z2.Mul(E, A24).Add(z2, BB).Mul(z2, E).Mod(z2, p) + x3.Add(DA, CB) + z3.Sub(DA, CB) + x3.Mul(x3, x3).Mod(x3, p) + z3.Mul(z3, z3).Mul(z3, x1).Mod(z3, p) +} + +func testMulA24(t *testing.T, f func(z, x *fp.Elt)) { + const numTests = 1 << 9 + var x, z fp.Elt + p := getModulus() + A24 := big.NewInt(121666) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + bigX := conv.BytesLe2BigInt(x[:]) + f(&z, &x) + got := conv.BytesLe2BigInt(z[:]) + got.Mod(got, p) + + want := bigX.Mul(bigX, A24).Mod(bigX, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } +} + +func testDouble(t *testing.T, f func(x, z *fp.Elt)) { + const numTests = 1 << 9 + var x, z fp.Elt + p := getModulus() + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(z[:]) + + bigX := conv.BytesLe2BigInt(x[:]) + bigZ := conv.BytesLe2BigInt(z[:]) + f(&x, &z) + got0 := conv.BytesLe2BigInt(x[:]) + got1 := conv.BytesLe2BigInt(z[:]) + got0.Mod(got0, p) + got1.Mod(got1, p) + + doubleBig(bigX, bigZ, p) + want0 := bigX + want1 := bigZ + + if got0.Cmp(want0) != 0 { + test.ReportError(t, got0, want0, x, z) + } + if got1.Cmp(want1) != 0 { + test.ReportError(t, got1, want1, x, z) + } + } +} + +func testDiffAdd(t *testing.T, f func(w *[5]fp.Elt, b uint)) { + const numTests = 1 << 9 + p := getModulus() + var w [5]fp.Elt + bigWork := [5]*big.Int{} + for i := 0; i < numTests; i++ { + for j := range w { + _, _ = rand.Read(w[j][:]) + bigWork[j] = conv.BytesLe2BigInt(w[j][:]) + } + b := uint(w[0][0] & 1) + + f(&w, b) + + diffAddBig(bigWork, p, b) + + for j := range w { + got := conv.BytesLe2BigInt(w[j][:]) + got.Mod(got, p) + want := bigWork[j] + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, w, b) + } + } + } +} + +func testLadderStep(t *testing.T, f func(w *[5]fp.Elt, b uint)) { + const numTests = 1 << 9 + var w [5]fp.Elt + bigWork := [5]*big.Int{} + p := getModulus() + for i := 0; i < numTests; i++ { + for j := range w { + _, _ = rand.Read(w[j][:]) + bigWork[j] = conv.BytesLe2BigInt(w[j][:]) + } + b := uint(w[0][0] & 1) + + f(&w, b) + + ladderStepBig(bigWork, p, b) + + for j := range bigWork { + got := conv.BytesLe2BigInt(w[j][:]) + got.Mod(got, p) + want := bigWork[j] + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, w, b) + } + } + } +} + +func TestGeneric(t *testing.T) { + t.Run("Double", func(t *testing.T) { testDouble(t, doubleGeneric) }) + t.Run("DiffAdd", func(t *testing.T) { testDiffAdd(t, diffAddGeneric) }) + t.Run("LadderStep", func(t *testing.T) { testLadderStep(t, ladderStepGeneric) }) + t.Run("MulA24", func(t *testing.T) { testMulA24(t, mulA24Generic) }) +} + +func TestNative(t *testing.T) { + t.Run("Double", func(t *testing.T) { testDouble(t, double) }) + t.Run("DiffAdd", func(t *testing.T) { testDiffAdd(t, diffAdd) }) + t.Run("LadderStep", func(t *testing.T) { testLadderStep(t, ladderStep) }) + t.Run("MulA24", func(t *testing.T) { testMulA24(t, mulA24) }) +} diff --git a/src/circl/dh/x25519/doc.go b/src/circl/dh/x25519/doc.go new file mode 100644 index 00000000000..e8feed56947 --- /dev/null +++ b/src/circl/dh/x25519/doc.go @@ -0,0 +1,20 @@ +/* +Package x25519 provides Diffie-Hellman functions as specified in RFC-7748. + +Validation of public keys. + +The Diffie-Hellman function, as described in RFC-7748 [1], works for any +public key. However, if a different protocol requires contributory +behaviour [2,3], then the public keys must be validated against low-order +points [3,4]. To do that, the Shared function performs this validation +internally and returns false when the public key is invalid (i.e., it +is a low-order point). + +References: + - [1] RFC7748 by Langley, Hamburg, Turner (https://rfc-editor.org/rfc/rfc7748.txt) + - [2] Curve25519 by Bernstein (https://cr.yp.to/ecdh.html) + - [3] Bernstein (https://cr.yp.to/ecdh.html#validate) + - [4] Cremers&Jackson (https://eprint.iacr.org/2019/526) + +*/ +package x25519 diff --git a/src/circl/dh/x25519/key.go b/src/circl/dh/x25519/key.go new file mode 100644 index 00000000000..35573e469ef --- /dev/null +++ b/src/circl/dh/x25519/key.go @@ -0,0 +1,47 @@ +package x25519 + +import ( + "crypto/subtle" + + fp "circl/math/fp25519" +) + +// Size is the length in bytes of a X25519 key. +const Size = 32 + +// Key represents a X25519 key. +type Key [Size]byte + +func (k *Key) clamp(in *Key) *Key { + *k = *in + k[0] &= 248 + k[31] = (k[31] & 127) | 64 + return k +} + +// isValidPubKey verifies if the public key is not a low-order point. +func (k *Key) isValidPubKey() bool { + fp.Modp((*fp.Elt)(k)) + isLowOrder := false + for _, P := range lowOrderPoints { + isLowOrder = isLowOrder || subtle.ConstantTimeCompare(P[:], k[:]) != 0 + } + return !isLowOrder +} + +// KeyGen obtains a public key given a secret key. +func KeyGen(public, secret *Key) { + ladderJoye(public.clamp(secret)) +} + +// Shared calculates Alice's shared key from Alice's secret key and Bob's +// public key returning true on success. A failure case happens when the public +// key is a low-order point, thus the shared key is all-zeros and the function +// returns false. +func Shared(shared, secret, public *Key) bool { + validPk := *public + validPk[31] &= (1 << (255 % 8)) - 1 + ok := validPk.isValidPubKey() + ladderMontgomery(shared.clamp(secret), &validPk) + return ok +} diff --git a/src/circl/dh/x25519/key_test.go b/src/circl/dh/x25519/key_test.go new file mode 100644 index 00000000000..a254a85b81d --- /dev/null +++ b/src/circl/dh/x25519/key_test.go @@ -0,0 +1,199 @@ +package x25519 + +import ( + "crypto/rand" + "encoding/hex" + "encoding/json" + "flag" + "fmt" + "io" + "io/ioutil" + "os" + "testing" + + "circl/internal/test" +) + +func hexStr2Key(k *Key, s string) { + b, err := hex.DecodeString(s) + if err != nil { + panic("Can't convert string to key") + } + copy(k[:], b) +} + +// Indicates whether long tests should be run +var runLongTest = flag.Bool("long", false, "runs longer tests") + +type katVector struct { + Public string `json:"input"` + Shared string `json:"output"` + Private string `json:"scalar"` +} + +func TestRFC7748Kat(t *testing.T) { + const nameFile = "testdata/rfc7748_kat_test.json" + var kat []katVector + + jsonFile, err := os.Open(nameFile) + if err != nil { + t.Fatalf("File %v can not be opened. Error: %v", nameFile, err) + } + defer jsonFile.Close() + input, _ := ioutil.ReadAll(jsonFile) + + err = json.Unmarshal(input, &kat) + if err != nil { + t.Fatalf("File %v can not be loaded. Error: %v", nameFile, err) + } + + var priv, pub, got, want Key + for _, v := range kat { + hexStr2Key(&pub, v.Public) + hexStr2Key(&priv, v.Private) + Shared(&got, &priv, &pub) + hexStr2Key(&want, v.Shared) + if got != want { + test.ReportError(t, got, want, v) + } + } +} + +type katTimes struct { + Times uint32 `json:"times"` + Key string `json:"key"` +} + +func TestRFC7748Times(t *testing.T) { + const nameFile = "testdata/rfc7748_times_test.json" + jsonFile, err := os.Open(nameFile) + if err != nil { + t.Fatalf("File %v can not be opened. Error: %v", nameFile, err) + } + defer jsonFile.Close() + input, _ := ioutil.ReadAll(jsonFile) + + var kat []katTimes + err = json.Unmarshal(input, &kat) + if err != nil { + t.Fatalf("File %v can not be loaded. Error: %v", nameFile, err) + } + + var got, want Key + for _, v := range kat { + if !*runLongTest && v.Times == uint32(1000000) { + t.Log("Skipped one long test, add -long flag to run longer tests") + continue + } + u := Key{9} + k := u + r := u + for i := uint32(0); i < v.Times; i++ { + Shared(&r, &k, &u) + u = k + k = r + } + got = k + hexStr2Key(&want, v.Key) + + if got != want { + test.ReportError(t, got, want, v.Times) + } + } +} + +func TestBase(t *testing.T) { + testTimes := 1 << 10 + var got, want, secret Key + gen := Key{9} + for i := 0; i < testTimes; i++ { + _, _ = io.ReadFull(rand.Reader, secret[:]) + KeyGen(&got, &secret) + Shared(&want, &secret, &gen) + if got != want { + test.ReportError(t, got, want, secret) + } + } +} + +func TestWycheproof(t *testing.T) { + // Test vectors from Wycheproof v0.4.12 + const nameFile = "testdata/wycheproof_kat.json" + jsonFile, err := os.Open(nameFile) + if err != nil { + t.Fatalf("File %v can not be opened. Error: %v", nameFile, err) + } + defer jsonFile.Close() + + input, _ := ioutil.ReadAll(jsonFile) + var vecRaw []struct { + TcID int `json:"tcId"` + Comment string `json:"comment"` + Curve string `json:"curve"` + Public string `json:"public"` + Private string `json:"private"` + Shared string `json:"shared"` + Result string `json:"result"` + Flags []string `json:"flags"` + } + + err = json.Unmarshal(input, &vecRaw) + if err != nil { + t.Fatalf("File %v can not be loaded. Error: %v", nameFile, err) + } + var got, want, priv, pub Key + for _, v := range vecRaw { + hexStr2Key(&pub, v.Public) + hexStr2Key(&priv, v.Private) + hexStr2Key(&want, v.Shared) + ok := Shared(&got, &priv, &pub) + if got != want { + test.ReportError(t, got, want, v.TcID, priv, pub) + } + if !ok && v.Result != "acceptable" { + test.ReportError(t, got, want, v.TcID, priv, pub) + } + } +} + +func BenchmarkX25519(b *testing.B) { + var x, y, z Key + + _, _ = io.ReadFull(rand.Reader, x[:]) + _, _ = io.ReadFull(rand.Reader, y[:]) + _, _ = io.ReadFull(rand.Reader, z[:]) + + b.Run("KeyGen", func(b *testing.B) { + for i := 0; i < b.N; i++ { + KeyGen(&x, &y) + } + }) + b.Run("Shared", func(b *testing.B) { + for i := 0; i < b.N; i++ { + Shared(&z, &x, &y) + } + }) +} + +func Example_x25519() { + var AliceSecret, BobSecret, + AlicePublic, BobPublic, + AliceShared, BobShared Key + + // Generating Alice's secret and public keys + _, _ = io.ReadFull(rand.Reader, AliceSecret[:]) + KeyGen(&AlicePublic, &AliceSecret) + + // Generating Bob's secret and public keys + _, _ = io.ReadFull(rand.Reader, BobSecret[:]) + KeyGen(&BobPublic, &BobSecret) + + // Deriving Alice's shared key + okA := Shared(&AliceShared, &AliceSecret, &BobPublic) + + // Deriving Bob's shared key + okB := Shared(&BobShared, &BobSecret, &AlicePublic) + + fmt.Println(AliceShared == BobShared && okA && okB) + // Output: true +} diff --git a/src/circl/dh/x25519/table.go b/src/circl/dh/x25519/table.go new file mode 100644 index 00000000000..34c4552dc3d --- /dev/null +++ b/src/circl/dh/x25519/table.go @@ -0,0 +1,266 @@ +package x25519 + +import "circl/math/fp25519" + +// tableGenerator contains the set of points: +// t[i] = (xi+1)/(xi-1), +// where (xi,yi) = 2^iG and G is the generator point +// Size = (256)*(256/8) = 8192 bytes. +var tableGenerator = [256 * fp25519.Size]byte{ + /* (2^ 0)P */ 0xf3, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x5f, + /* (2^ 1)P */ 0x96, 0xfe, 0xaa, 0x16, 0xf4, 0x20, 0x82, 0x6b, 0x34, 0x6a, 0x56, 0x4f, 0x2b, 0xeb, 0xeb, 0x82, 0x0f, 0x95, 0xa5, 0x75, 0xb0, 0xa5, 0xa9, 0xd5, 0xf4, 0x88, 0x24, 0x4b, 0xcf, 0xb2, 0x42, 0x51, + /* (2^ 2)P */ 0x0c, 0x68, 0x69, 0x00, 0x75, 0xbc, 0xae, 0x6a, 0x41, 0x9c, 0xf9, 0xa0, 0x20, 0x78, 0xcf, 0x89, 0xf4, 0xd0, 0x56, 0x3b, 0x18, 0xd9, 0x58, 0x2a, 0xa4, 0x11, 0x60, 0xe3, 0x80, 0xca, 0x5a, 0x4b, + /* (2^ 3)P */ 0x5d, 0x74, 0x29, 0x8c, 0x34, 0x32, 0x91, 0x32, 0xd7, 0x2f, 0x64, 0xe1, 0x16, 0xe6, 0xa2, 0xf4, 0x34, 0xbc, 0x67, 0xff, 0x03, 0xbb, 0x45, 0x1e, 0x4a, 0x9b, 0x2a, 0xf4, 0xd0, 0x12, 0x69, 0x30, + /* (2^ 4)P */ 0x54, 0x71, 0xaf, 0xe6, 0x07, 0x65, 0x88, 0xff, 0x2f, 0xc8, 0xee, 0xdf, 0x13, 0x0e, 0xf5, 0x04, 0xce, 0xb5, 0xba, 0x2a, 0xe8, 0x2f, 0x51, 0xaa, 0x22, 0xf2, 0xd5, 0x68, 0x1a, 0x25, 0x4e, 0x17, + /* (2^ 5)P */ 0x98, 0x88, 0x02, 0x82, 0x0d, 0x70, 0x96, 0xcf, 0xc5, 0x02, 0x2c, 0x0a, 0x37, 0xe3, 0x43, 0x17, 0xaa, 0x6e, 0xe8, 0xb4, 0x98, 0xec, 0x9e, 0x37, 0x2e, 0x48, 0xe0, 0x51, 0x8a, 0x88, 0x59, 0x0c, + /* (2^ 6)P */ 0x89, 0xd1, 0xb5, 0x99, 0xd6, 0xf1, 0xcb, 0xfb, 0x84, 0xdc, 0x9f, 0x8e, 0xd5, 0xf0, 0xae, 0xac, 0x14, 0x76, 0x1f, 0x23, 0x06, 0x0d, 0xc2, 0xc1, 0x72, 0xf9, 0x74, 0xa2, 0x8d, 0x21, 0x38, 0x29, + /* (2^ 7)P */ 0x18, 0x7f, 0x1d, 0xff, 0xbe, 0x49, 0xaf, 0xf6, 0xc2, 0xc9, 0x7a, 0x38, 0x22, 0x1c, 0x54, 0xcc, 0x6b, 0xc5, 0x15, 0x40, 0xef, 0xc9, 0xfc, 0x96, 0xa9, 0x13, 0x09, 0x69, 0x7c, 0x62, 0xc1, 0x69, + /* (2^ 8)P */ 0x0e, 0xdb, 0x33, 0x47, 0x2f, 0xfd, 0x86, 0x7a, 0xe9, 0x7d, 0x08, 0x9e, 0xf2, 0xc4, 0xb8, 0xfd, 0x29, 0xa2, 0xa2, 0x8e, 0x1a, 0x4b, 0x5e, 0x09, 0x79, 0x7a, 0xb3, 0x29, 0xc8, 0xa7, 0xd7, 0x1a, + /* (2^ 9)P */ 0xc0, 0xa0, 0x7e, 0xd1, 0xca, 0x89, 0x2d, 0x34, 0x51, 0x20, 0xed, 0xcc, 0xa6, 0xdd, 0xbe, 0x67, 0x74, 0x2f, 0xb4, 0x2b, 0xbf, 0x31, 0xca, 0x19, 0xbb, 0xac, 0x80, 0x49, 0xc8, 0xb4, 0xf7, 0x3d, + /* (2^ 10)P */ 0x83, 0xd8, 0x0a, 0xc8, 0x4d, 0x44, 0xc6, 0xa8, 0x85, 0xab, 0xe3, 0x66, 0x03, 0x44, 0x1e, 0xb9, 0xd8, 0xf6, 0x64, 0x01, 0xa0, 0xcd, 0x15, 0xc2, 0x68, 0xe6, 0x47, 0xf2, 0x6e, 0x7c, 0x86, 0x3d, + /* (2^ 11)P */ 0x8c, 0x65, 0x3e, 0xcc, 0x2b, 0x58, 0xdd, 0xc7, 0x28, 0x55, 0x0e, 0xee, 0x48, 0x47, 0x2c, 0xfd, 0x71, 0x4f, 0x9f, 0xcc, 0x95, 0x9b, 0xfd, 0xa0, 0xdf, 0x5d, 0x67, 0xb0, 0x71, 0xd8, 0x29, 0x75, + /* (2^ 12)P */ 0x78, 0xbd, 0x3c, 0x2d, 0xb4, 0x68, 0xf5, 0xb8, 0x82, 0xda, 0xf3, 0x91, 0x1b, 0x01, 0x33, 0x12, 0x62, 0x3b, 0x7c, 0x4a, 0xcd, 0x6c, 0xce, 0x2d, 0x03, 0x86, 0x49, 0x9e, 0x8e, 0xfc, 0xe7, 0x75, + /* (2^ 13)P */ 0xec, 0xb6, 0xd0, 0xfc, 0xf1, 0x13, 0x4f, 0x2f, 0x45, 0x7a, 0xff, 0x29, 0x1f, 0xca, 0xa8, 0xf1, 0x9b, 0xe2, 0x81, 0x29, 0xa7, 0xc1, 0x49, 0xc2, 0x6a, 0xb5, 0x83, 0x8c, 0xbb, 0x0d, 0xbe, 0x6e, + /* (2^ 14)P */ 0x22, 0xb2, 0x0b, 0x17, 0x8d, 0xfa, 0x14, 0x71, 0x5f, 0x93, 0x93, 0xbf, 0xd5, 0xdc, 0xa2, 0x65, 0x9a, 0x97, 0x9c, 0xb5, 0x68, 0x1f, 0xc4, 0xbd, 0x89, 0x92, 0xce, 0xa2, 0x79, 0xef, 0x0e, 0x2f, + /* (2^ 15)P */ 0xce, 0x37, 0x3c, 0x08, 0x0c, 0xbf, 0xec, 0x42, 0x22, 0x63, 0x49, 0xec, 0x09, 0xbc, 0x30, 0x29, 0x0d, 0xac, 0xfe, 0x9c, 0xc1, 0xb0, 0x94, 0xf2, 0x80, 0xbb, 0xfa, 0xed, 0x4b, 0xaa, 0x80, 0x37, + /* (2^ 16)P */ 0x29, 0xd9, 0xea, 0x7c, 0x3e, 0x7d, 0xc1, 0x56, 0xc5, 0x22, 0x57, 0x2e, 0xeb, 0x4b, 0xcb, 0xe7, 0x5a, 0xe1, 0xbf, 0x2d, 0x73, 0x31, 0xe9, 0x0c, 0xf8, 0x52, 0x10, 0x62, 0xc7, 0x83, 0xb8, 0x41, + /* (2^ 17)P */ 0x50, 0x53, 0xd2, 0xc3, 0xa0, 0x5c, 0xf7, 0xdb, 0x51, 0xe3, 0xb1, 0x6e, 0x08, 0xbe, 0x36, 0x29, 0x12, 0xb2, 0xa9, 0xb4, 0x3c, 0xe0, 0x36, 0xc9, 0xaa, 0x25, 0x22, 0x32, 0x82, 0xbf, 0x45, 0x1d, + /* (2^ 18)P */ 0xc5, 0x4c, 0x02, 0x6a, 0x03, 0xb1, 0x1a, 0xe8, 0x72, 0x9a, 0x4c, 0x30, 0x1c, 0x20, 0x12, 0xe2, 0xfc, 0xb1, 0x32, 0x68, 0xba, 0x3f, 0xd7, 0xc5, 0x81, 0x95, 0x83, 0x4d, 0x5a, 0xdb, 0xff, 0x20, + /* (2^ 19)P */ 0xad, 0x0f, 0x5d, 0xbe, 0x67, 0xd3, 0x83, 0xa2, 0x75, 0x44, 0x16, 0x8b, 0xca, 0x25, 0x2b, 0x6c, 0x2e, 0xf2, 0xaa, 0x7c, 0x46, 0x35, 0x49, 0x9d, 0x49, 0xff, 0x85, 0xee, 0x8e, 0x40, 0x66, 0x51, + /* (2^ 20)P */ 0x61, 0xe3, 0xb4, 0xfa, 0xa2, 0xba, 0x67, 0x3c, 0xef, 0x5c, 0xf3, 0x7e, 0xc6, 0x33, 0xe4, 0xb3, 0x1c, 0x9b, 0x15, 0x41, 0x92, 0x72, 0x59, 0x52, 0x33, 0xab, 0xb0, 0xd5, 0x92, 0x18, 0x62, 0x6a, + /* (2^ 21)P */ 0xcb, 0xcd, 0x55, 0x75, 0x38, 0x4a, 0xb7, 0x20, 0x3f, 0x92, 0x08, 0x12, 0x0e, 0xa1, 0x2a, 0x53, 0xd1, 0x1d, 0x28, 0x62, 0x77, 0x7b, 0xa1, 0xea, 0xbf, 0x44, 0x5c, 0xf0, 0x43, 0x34, 0xab, 0x61, + /* (2^ 22)P */ 0xf8, 0xde, 0x24, 0x23, 0x42, 0x6c, 0x7a, 0x25, 0x7f, 0xcf, 0xe3, 0x17, 0x10, 0x6c, 0x1c, 0x13, 0x57, 0xa2, 0x30, 0xf6, 0x39, 0x87, 0x75, 0x23, 0x80, 0x85, 0xa7, 0x01, 0x7a, 0x40, 0x5a, 0x29, + /* (2^ 23)P */ 0xd9, 0xa8, 0x5d, 0x6d, 0x24, 0x43, 0xc4, 0xf8, 0x5d, 0xfa, 0x52, 0x0c, 0x45, 0x75, 0xd7, 0x19, 0x3d, 0xf8, 0x1b, 0x73, 0x92, 0xfc, 0xfc, 0x2a, 0x00, 0x47, 0x2b, 0x1b, 0xe8, 0xc8, 0x10, 0x7d, + /* (2^ 24)P */ 0x0b, 0xa2, 0xba, 0x70, 0x1f, 0x27, 0xe0, 0xc8, 0x57, 0x39, 0xa6, 0x7c, 0x86, 0x48, 0x37, 0x99, 0xbb, 0xd4, 0x7e, 0xcb, 0xb3, 0xef, 0x12, 0x54, 0x75, 0x29, 0xe6, 0x73, 0x61, 0xd3, 0x96, 0x31, + /* (2^ 25)P */ 0xfc, 0xdf, 0xc7, 0x41, 0xd1, 0xca, 0x5b, 0xde, 0x48, 0xc8, 0x95, 0xb3, 0xd2, 0x8c, 0xcc, 0x47, 0xcb, 0xf3, 0x1a, 0xe1, 0x42, 0xd9, 0x4c, 0xa3, 0xc2, 0xce, 0x4e, 0xd0, 0xf2, 0xdb, 0x56, 0x02, + /* (2^ 26)P */ 0x7f, 0x66, 0x0e, 0x4b, 0xe9, 0xb7, 0x5a, 0x87, 0x10, 0x0d, 0x85, 0xc0, 0x83, 0xdd, 0xd4, 0xca, 0x9f, 0xc7, 0x72, 0x4e, 0x8f, 0x2e, 0xf1, 0x47, 0x9b, 0xb1, 0x85, 0x8c, 0xbb, 0x87, 0x1a, 0x5f, + /* (2^ 27)P */ 0xb8, 0x51, 0x7f, 0x43, 0xb6, 0xd0, 0xe9, 0x7a, 0x65, 0x90, 0x87, 0x18, 0x55, 0xce, 0xc7, 0x12, 0xee, 0x7a, 0xf7, 0x5c, 0xfe, 0x09, 0xde, 0x2a, 0x27, 0x56, 0x2c, 0x7d, 0x2f, 0x5a, 0xa0, 0x23, + /* (2^ 28)P */ 0x9a, 0x16, 0x7c, 0xf1, 0x28, 0xe1, 0x08, 0x59, 0x2d, 0x85, 0xd0, 0x8a, 0xdd, 0x98, 0x74, 0xf7, 0x64, 0x2f, 0x10, 0xab, 0xce, 0xc4, 0xb4, 0x74, 0x45, 0x98, 0x13, 0x10, 0xdd, 0xba, 0x3a, 0x18, + /* (2^ 29)P */ 0xac, 0xaa, 0x92, 0xaa, 0x8d, 0xba, 0x65, 0xb1, 0x05, 0x67, 0x38, 0x99, 0x95, 0xef, 0xc5, 0xd5, 0xd1, 0x40, 0xfc, 0xf8, 0x0c, 0x8f, 0x2f, 0xbe, 0x14, 0x45, 0x20, 0xee, 0x35, 0xe6, 0x01, 0x27, + /* (2^ 30)P */ 0x14, 0x65, 0x15, 0x20, 0x00, 0xa8, 0x9f, 0x62, 0xce, 0xc1, 0xa8, 0x64, 0x87, 0x86, 0x23, 0xf2, 0x0e, 0x06, 0x3f, 0x0b, 0xff, 0x4f, 0x89, 0x5b, 0xfa, 0xa3, 0x08, 0xf7, 0x4c, 0x94, 0xd9, 0x60, + /* (2^ 31)P */ 0x1f, 0x20, 0x7a, 0x1c, 0x1a, 0x00, 0xea, 0xae, 0x63, 0xce, 0xe2, 0x3e, 0x63, 0x6a, 0xf1, 0xeb, 0xe1, 0x07, 0x7a, 0x4c, 0x59, 0x09, 0x77, 0x6f, 0xcb, 0x08, 0x02, 0x0d, 0x15, 0x58, 0xb9, 0x79, + /* (2^ 32)P */ 0xe7, 0x10, 0xd4, 0x01, 0x53, 0x5e, 0xb5, 0x24, 0x4d, 0xc8, 0xfd, 0xf3, 0xdf, 0x4e, 0xa3, 0xe3, 0xd8, 0x32, 0x40, 0x90, 0xe4, 0x68, 0x87, 0xd8, 0xec, 0xae, 0x3a, 0x7b, 0x42, 0x84, 0x13, 0x13, + /* (2^ 33)P */ 0x14, 0x4f, 0x23, 0x86, 0x12, 0xe5, 0x05, 0x84, 0x29, 0xc5, 0xb4, 0xad, 0x39, 0x47, 0xdc, 0x14, 0xfd, 0x4f, 0x63, 0x50, 0xb2, 0xb5, 0xa2, 0xb8, 0x93, 0xff, 0xa7, 0xd8, 0x4a, 0xa9, 0xe2, 0x2f, + /* (2^ 34)P */ 0xdd, 0xfa, 0x43, 0xe8, 0xef, 0x57, 0x5c, 0xec, 0x18, 0x99, 0xbb, 0xf0, 0x40, 0xce, 0x43, 0x28, 0x05, 0x63, 0x3d, 0xcf, 0xd6, 0x61, 0xb5, 0xa4, 0x7e, 0x77, 0xfb, 0xe8, 0xbd, 0x29, 0x36, 0x74, + /* (2^ 35)P */ 0x8f, 0x73, 0xaf, 0xbb, 0x46, 0xdd, 0x3e, 0x34, 0x51, 0xa6, 0x01, 0xb1, 0x28, 0x18, 0x98, 0xed, 0x7a, 0x79, 0x2c, 0x88, 0x0b, 0x76, 0x01, 0xa4, 0x30, 0x87, 0xc8, 0x8d, 0xe2, 0x23, 0xc2, 0x1f, + /* (2^ 36)P */ 0x0e, 0xba, 0x0f, 0xfc, 0x91, 0x4e, 0x60, 0x48, 0xa4, 0x6f, 0x2c, 0x05, 0x8f, 0xf7, 0x37, 0xb6, 0x9c, 0x23, 0xe9, 0x09, 0x3d, 0xac, 0xcc, 0x91, 0x7c, 0x68, 0x7a, 0x43, 0xd4, 0xee, 0xf7, 0x23, + /* (2^ 37)P */ 0x00, 0xd8, 0x9b, 0x8d, 0x11, 0xb1, 0x73, 0x51, 0xa7, 0xd4, 0x89, 0x31, 0xb6, 0x41, 0xd6, 0x29, 0x86, 0xc5, 0xbb, 0x88, 0x79, 0x17, 0xbf, 0xfd, 0xf5, 0x1d, 0xd8, 0xca, 0x4f, 0x89, 0x59, 0x29, + /* (2^ 38)P */ 0x99, 0xc8, 0xbb, 0xb4, 0xf3, 0x8e, 0xbc, 0xae, 0xb9, 0x92, 0x69, 0xb2, 0x5a, 0x99, 0x48, 0x41, 0xfb, 0x2c, 0xf9, 0x34, 0x01, 0x0b, 0xe2, 0x24, 0xe8, 0xde, 0x05, 0x4a, 0x89, 0x58, 0xd1, 0x40, + /* (2^ 39)P */ 0xf6, 0x76, 0xaf, 0x85, 0x11, 0x0b, 0xb0, 0x46, 0x79, 0x7a, 0x18, 0x73, 0x78, 0xc7, 0xba, 0x26, 0x5f, 0xff, 0x8f, 0xab, 0x95, 0xbf, 0xc0, 0x3d, 0xd7, 0x24, 0x55, 0x94, 0xd8, 0x8b, 0x60, 0x2a, + /* (2^ 40)P */ 0x02, 0x63, 0x44, 0xbd, 0x88, 0x95, 0x44, 0x26, 0x9c, 0x43, 0x88, 0x03, 0x1c, 0xc2, 0x4b, 0x7c, 0xb2, 0x11, 0xbd, 0x83, 0xf3, 0xa4, 0x98, 0x8e, 0xb9, 0x76, 0xd8, 0xc9, 0x7b, 0x8d, 0x21, 0x26, + /* (2^ 41)P */ 0x8a, 0x17, 0x7c, 0x99, 0x42, 0x15, 0x08, 0xe3, 0x6f, 0x60, 0xb6, 0x6f, 0xa8, 0x29, 0x2d, 0x3c, 0x74, 0x93, 0x27, 0xfa, 0x36, 0x77, 0x21, 0x5c, 0xfa, 0xb1, 0xfe, 0x4a, 0x73, 0x05, 0xde, 0x7d, + /* (2^ 42)P */ 0xab, 0x2b, 0xd4, 0x06, 0x39, 0x0e, 0xf1, 0x3b, 0x9c, 0x64, 0x80, 0x19, 0x3e, 0x80, 0xf7, 0xe4, 0x7a, 0xbf, 0x95, 0x95, 0xf8, 0x3b, 0x05, 0xe6, 0x30, 0x55, 0x24, 0xda, 0x38, 0xaf, 0x4f, 0x39, + /* (2^ 43)P */ 0xf4, 0x28, 0x69, 0x89, 0x58, 0xfb, 0x8e, 0x7a, 0x3c, 0x11, 0x6a, 0xcc, 0xe9, 0x78, 0xc7, 0xfb, 0x6f, 0x59, 0xaf, 0x30, 0xe3, 0x0c, 0x67, 0x72, 0xf7, 0x6c, 0x3d, 0x1d, 0xa8, 0x22, 0xf2, 0x48, + /* (2^ 44)P */ 0xa7, 0xca, 0x72, 0x0d, 0x41, 0xce, 0x1f, 0xf0, 0x95, 0x55, 0x3b, 0x21, 0xc7, 0xec, 0x20, 0x5a, 0x83, 0x14, 0xfa, 0xc1, 0x65, 0x11, 0xc2, 0x7b, 0x41, 0xa7, 0xa8, 0x1d, 0xe3, 0x9a, 0xf8, 0x07, + /* (2^ 45)P */ 0xf9, 0x0f, 0x83, 0xc6, 0xb4, 0xc2, 0xd2, 0x05, 0x93, 0x62, 0x31, 0xc6, 0x0f, 0x33, 0x3e, 0xd4, 0x04, 0xa9, 0xd3, 0x96, 0x0a, 0x59, 0xa5, 0xa5, 0xb6, 0x33, 0x53, 0xa6, 0x91, 0xdb, 0x5e, 0x70, + /* (2^ 46)P */ 0xf7, 0xa5, 0xb9, 0x0b, 0x5e, 0xe1, 0x8e, 0x04, 0x5d, 0xaf, 0x0a, 0x9e, 0xca, 0xcf, 0x40, 0x32, 0x0b, 0xa4, 0xc4, 0xed, 0xce, 0x71, 0x4b, 0x8f, 0x6d, 0x4a, 0x54, 0xde, 0xa3, 0x0d, 0x1c, 0x62, + /* (2^ 47)P */ 0x91, 0x40, 0x8c, 0xa0, 0x36, 0x28, 0x87, 0x92, 0x45, 0x14, 0xc9, 0x10, 0xb0, 0x75, 0x83, 0xce, 0x94, 0x63, 0x27, 0x4f, 0x52, 0xeb, 0x72, 0x8a, 0x35, 0x36, 0xc8, 0x7e, 0xfa, 0xfc, 0x67, 0x26, + /* (2^ 48)P */ 0x2a, 0x75, 0xe8, 0x45, 0x33, 0x17, 0x4c, 0x7f, 0xa5, 0x79, 0x70, 0xee, 0xfe, 0x47, 0x1b, 0x06, 0x34, 0xff, 0x86, 0x9f, 0xfa, 0x9a, 0xdd, 0x25, 0x9c, 0xc8, 0x5d, 0x42, 0xf5, 0xce, 0x80, 0x37, + /* (2^ 49)P */ 0xe9, 0xb4, 0x3b, 0x51, 0x5a, 0x03, 0x46, 0x1a, 0xda, 0x5a, 0x57, 0xac, 0x79, 0xf3, 0x1e, 0x3e, 0x50, 0x4b, 0xa2, 0x5f, 0x1c, 0x5f, 0x8c, 0xc7, 0x22, 0x9f, 0xfd, 0x34, 0x76, 0x96, 0x1a, 0x32, + /* (2^ 50)P */ 0xfa, 0x27, 0x6e, 0x82, 0xb8, 0x07, 0x67, 0x94, 0xd0, 0x6f, 0x50, 0x4c, 0xd6, 0x84, 0xca, 0x3d, 0x36, 0x14, 0xe9, 0x75, 0x80, 0x21, 0x89, 0xc1, 0x84, 0x84, 0x3b, 0x9b, 0x16, 0x84, 0x92, 0x6d, + /* (2^ 51)P */ 0xdf, 0x2d, 0x3f, 0x38, 0x40, 0xe8, 0x67, 0x3a, 0x75, 0x9b, 0x4f, 0x0c, 0xa3, 0xc9, 0xee, 0x33, 0x47, 0xef, 0x83, 0xa7, 0x6f, 0xc8, 0xc7, 0x3e, 0xc4, 0xfb, 0xc9, 0xba, 0x9f, 0x44, 0xec, 0x26, + /* (2^ 52)P */ 0x7d, 0x9e, 0x9b, 0xa0, 0xcb, 0x38, 0x0f, 0x5c, 0x8c, 0x47, 0xa3, 0x62, 0xc7, 0x8c, 0x16, 0x81, 0x1c, 0x12, 0xfc, 0x06, 0xd3, 0xb0, 0x23, 0x3e, 0xdd, 0xdc, 0xef, 0xa5, 0xa0, 0x8a, 0x23, 0x5a, + /* (2^ 53)P */ 0xff, 0x43, 0xea, 0xc4, 0x21, 0x61, 0xa2, 0x1b, 0xb5, 0x32, 0x88, 0x7c, 0x7f, 0xc7, 0xf8, 0x36, 0x9a, 0xf9, 0xdc, 0x0a, 0x0b, 0xea, 0xfb, 0x88, 0xf9, 0xeb, 0x5b, 0xc2, 0x8e, 0x93, 0xa9, 0x5c, + /* (2^ 54)P */ 0xa0, 0xcd, 0xfc, 0x51, 0x5e, 0x6a, 0x43, 0xd5, 0x3b, 0x89, 0xcd, 0xc2, 0x97, 0x47, 0xbc, 0x1d, 0x08, 0x4a, 0x22, 0xd3, 0x65, 0x6a, 0x34, 0x19, 0x66, 0xf4, 0x9a, 0x9b, 0xe4, 0x34, 0x50, 0x0f, + /* (2^ 55)P */ 0x6e, 0xb9, 0xe0, 0xa1, 0x67, 0x39, 0x3c, 0xf2, 0x88, 0x4d, 0x7a, 0x86, 0xfa, 0x08, 0x8b, 0xe5, 0x79, 0x16, 0x34, 0xa7, 0xc6, 0xab, 0x2f, 0xfb, 0x46, 0x69, 0x02, 0xb6, 0x1e, 0x38, 0x75, 0x2a, + /* (2^ 56)P */ 0xac, 0x20, 0x94, 0xc1, 0xe4, 0x3b, 0x0a, 0xc8, 0xdc, 0xb6, 0xf2, 0x81, 0xc6, 0xf6, 0xb1, 0x66, 0x88, 0x33, 0xe9, 0x61, 0x67, 0x03, 0xf7, 0x7c, 0xc4, 0xa4, 0x60, 0xa6, 0xd8, 0xbb, 0xab, 0x25, + /* (2^ 57)P */ 0x98, 0x51, 0xfd, 0x14, 0xba, 0x12, 0xea, 0x91, 0xa9, 0xff, 0x3c, 0x4a, 0xfc, 0x50, 0x49, 0x68, 0x28, 0xad, 0xf5, 0x30, 0x21, 0x84, 0x26, 0xf8, 0x41, 0xa4, 0x01, 0x53, 0xf7, 0x88, 0xa9, 0x3e, + /* (2^ 58)P */ 0x6f, 0x8c, 0x5f, 0x69, 0x9a, 0x10, 0x78, 0xc9, 0xf3, 0xc3, 0x30, 0x05, 0x4a, 0xeb, 0x46, 0x17, 0x95, 0x99, 0x45, 0xb4, 0x77, 0x6d, 0x4d, 0x44, 0xc7, 0x5c, 0x4e, 0x05, 0x8c, 0x2b, 0x95, 0x75, + /* (2^ 59)P */ 0xaa, 0xd6, 0xf4, 0x15, 0x79, 0x3f, 0x70, 0xa3, 0xd8, 0x47, 0x26, 0x2f, 0x20, 0x46, 0xc3, 0x66, 0x4b, 0x64, 0x1d, 0x81, 0xdf, 0x69, 0x14, 0xd0, 0x1f, 0xd7, 0xa5, 0x81, 0x7d, 0xa4, 0xfe, 0x77, + /* (2^ 60)P */ 0x81, 0xa3, 0x7c, 0xf5, 0x9e, 0x52, 0xe9, 0xc5, 0x1a, 0x88, 0x2f, 0xce, 0xb9, 0xb4, 0xee, 0x6e, 0xd6, 0x9b, 0x00, 0xe8, 0x28, 0x1a, 0xe9, 0xb6, 0xec, 0x3f, 0xfc, 0x9a, 0x3e, 0xbe, 0x80, 0x4b, + /* (2^ 61)P */ 0xc5, 0xd2, 0xae, 0x26, 0xc5, 0x73, 0x37, 0x7e, 0x9d, 0xa4, 0xc9, 0x53, 0xb4, 0xfc, 0x4a, 0x1b, 0x4d, 0xb2, 0xff, 0xba, 0xd7, 0xbd, 0x20, 0xa9, 0x0e, 0x40, 0x2d, 0x12, 0x9f, 0x69, 0x54, 0x7c, + /* (2^ 62)P */ 0xc8, 0x4b, 0xa9, 0x4f, 0xe1, 0xc8, 0x46, 0xef, 0x5e, 0xed, 0x52, 0x29, 0xce, 0x74, 0xb0, 0xe0, 0xd5, 0x85, 0xd8, 0xdb, 0xe1, 0x50, 0xa4, 0xbe, 0x2c, 0x71, 0x0f, 0x32, 0x49, 0x86, 0xb6, 0x61, + /* (2^ 63)P */ 0xd1, 0xbd, 0xcc, 0x09, 0x73, 0x5f, 0x48, 0x8a, 0x2d, 0x1a, 0x4d, 0x7d, 0x0d, 0x32, 0x06, 0xbd, 0xf4, 0xbe, 0x2d, 0x32, 0x73, 0x29, 0x23, 0x25, 0x70, 0xf7, 0x17, 0x8c, 0x75, 0xc4, 0x5d, 0x44, + /* (2^ 64)P */ 0x3c, 0x93, 0xc8, 0x7c, 0x17, 0x34, 0x04, 0xdb, 0x9f, 0x05, 0xea, 0x75, 0x21, 0xe8, 0x6f, 0xed, 0x34, 0xdb, 0x53, 0xc0, 0xfd, 0xbe, 0xfe, 0x1e, 0x99, 0xaf, 0x5d, 0xc6, 0x67, 0xe8, 0xdb, 0x4a, + /* (2^ 65)P */ 0xdf, 0x09, 0x06, 0xa9, 0xa2, 0x71, 0xcd, 0x3a, 0x50, 0x40, 0xd0, 0x6d, 0x85, 0x91, 0xe9, 0xe5, 0x3c, 0xc2, 0x57, 0x81, 0x68, 0x9b, 0xc6, 0x1e, 0x4d, 0xfe, 0x5c, 0x88, 0xf6, 0x27, 0x74, 0x69, + /* (2^ 66)P */ 0x51, 0xa8, 0xe1, 0x65, 0x9b, 0x7b, 0xbe, 0xd7, 0xdd, 0x36, 0xc5, 0x22, 0xd5, 0x28, 0x3d, 0xa0, 0x45, 0xb6, 0xd2, 0x8f, 0x65, 0x9d, 0x39, 0x28, 0xe1, 0x41, 0x26, 0x7c, 0xe1, 0xb7, 0xe5, 0x49, + /* (2^ 67)P */ 0xa4, 0x57, 0x04, 0x70, 0x98, 0x3a, 0x8c, 0x6f, 0x78, 0x67, 0xbb, 0x5e, 0xa2, 0xf0, 0x78, 0x50, 0x0f, 0x96, 0x82, 0xc3, 0xcb, 0x3c, 0x3c, 0xd1, 0xb1, 0x84, 0xdf, 0xa7, 0x58, 0x32, 0x00, 0x2e, + /* (2^ 68)P */ 0x1c, 0x6a, 0x29, 0xe6, 0x9b, 0xf3, 0xd1, 0x8a, 0xb2, 0xbf, 0x5f, 0x2a, 0x65, 0xaa, 0xee, 0xc1, 0xcb, 0xf3, 0x26, 0xfd, 0x73, 0x06, 0xee, 0x33, 0xcc, 0x2c, 0x9d, 0xa6, 0x73, 0x61, 0x25, 0x59, + /* (2^ 69)P */ 0x41, 0xfc, 0x18, 0x4e, 0xaa, 0x07, 0xea, 0x41, 0x1e, 0xa5, 0x87, 0x7c, 0x52, 0x19, 0xfc, 0xd9, 0x6f, 0xca, 0x31, 0x58, 0x80, 0xcb, 0xaa, 0xbd, 0x4f, 0x69, 0x16, 0xc9, 0x2d, 0x65, 0x5b, 0x44, + /* (2^ 70)P */ 0x15, 0x23, 0x17, 0xf2, 0xa7, 0xa3, 0x92, 0xce, 0x64, 0x99, 0x1b, 0xe1, 0x2d, 0x28, 0xdc, 0x1e, 0x4a, 0x31, 0x4c, 0xe0, 0xaf, 0x3a, 0x82, 0xa1, 0x86, 0xf5, 0x7c, 0x43, 0x94, 0x2d, 0x0a, 0x79, + /* (2^ 71)P */ 0x09, 0xe0, 0xf6, 0x93, 0xfb, 0x47, 0xc4, 0x71, 0x76, 0x52, 0x84, 0x22, 0x67, 0xa5, 0x22, 0x89, 0x69, 0x51, 0x4f, 0x20, 0x3b, 0x90, 0x70, 0xbf, 0xfe, 0x19, 0xa3, 0x1b, 0x89, 0x89, 0x7a, 0x2f, + /* (2^ 72)P */ 0x0c, 0x14, 0xe2, 0x77, 0xb5, 0x8e, 0xa0, 0x02, 0xf4, 0xdc, 0x7b, 0x42, 0xd4, 0x4e, 0x9a, 0xed, 0xd1, 0x3c, 0x32, 0xe4, 0x44, 0xec, 0x53, 0x52, 0x5b, 0x35, 0xe9, 0x14, 0x3c, 0x36, 0x88, 0x3e, + /* (2^ 73)P */ 0x8c, 0x0b, 0x11, 0x77, 0x42, 0xc1, 0x66, 0xaa, 0x90, 0x33, 0xa2, 0x10, 0x16, 0x39, 0xe0, 0x1a, 0xa2, 0xc2, 0x3f, 0xc9, 0x12, 0xbd, 0x30, 0x20, 0xab, 0xc7, 0x55, 0x95, 0x57, 0x41, 0xe1, 0x3e, + /* (2^ 74)P */ 0x41, 0x7d, 0x6e, 0x6d, 0x3a, 0xde, 0x14, 0x92, 0xfe, 0x7e, 0xf1, 0x07, 0x86, 0xd8, 0xcd, 0x3c, 0x17, 0x12, 0xe1, 0xf8, 0x88, 0x12, 0x4f, 0x67, 0xd0, 0x93, 0x9f, 0x32, 0x0f, 0x25, 0x82, 0x56, + /* (2^ 75)P */ 0x6e, 0x39, 0x2e, 0x6d, 0x13, 0x0b, 0xf0, 0x6c, 0xbf, 0xde, 0x14, 0x10, 0x6f, 0xf8, 0x4c, 0x6e, 0x83, 0x4e, 0xcc, 0xbf, 0xb5, 0xb1, 0x30, 0x59, 0xb6, 0x16, 0xba, 0x8a, 0xb4, 0x69, 0x70, 0x04, + /* (2^ 76)P */ 0x93, 0x07, 0xb2, 0x69, 0xab, 0xe4, 0x4c, 0x0d, 0x9e, 0xfb, 0xd0, 0x97, 0x1a, 0xb9, 0x4d, 0xb2, 0x1d, 0xd0, 0x00, 0x4e, 0xf5, 0x50, 0xfa, 0xcd, 0xb5, 0xdd, 0x8b, 0x36, 0x85, 0x10, 0x1b, 0x22, + /* (2^ 77)P */ 0xd2, 0xd8, 0xe3, 0xb1, 0x68, 0x94, 0xe5, 0xe7, 0x93, 0x2f, 0x12, 0xbd, 0x63, 0x65, 0xc5, 0x53, 0x09, 0x3f, 0x66, 0xe0, 0x03, 0xa9, 0xe8, 0xee, 0x42, 0x3d, 0xbe, 0xcb, 0x62, 0xa6, 0xef, 0x61, + /* (2^ 78)P */ 0x2a, 0xab, 0x6e, 0xde, 0xdd, 0xdd, 0xf8, 0x2c, 0x31, 0xf2, 0x35, 0x14, 0xd5, 0x0a, 0xf8, 0x9b, 0x73, 0x49, 0xf0, 0xc9, 0xce, 0xda, 0xea, 0x5d, 0x27, 0x9b, 0xd2, 0x41, 0x5d, 0x5b, 0x27, 0x29, + /* (2^ 79)P */ 0x4f, 0xf1, 0xeb, 0x95, 0x08, 0x0f, 0xde, 0xcf, 0xa7, 0x05, 0x49, 0x05, 0x6b, 0xb9, 0xaa, 0xb9, 0xfd, 0x20, 0xc4, 0xa1, 0xd9, 0x0d, 0xe8, 0xca, 0xc7, 0xbb, 0x73, 0x16, 0x2f, 0xbf, 0x63, 0x0a, + /* (2^ 80)P */ 0x8c, 0xbc, 0x8f, 0x95, 0x11, 0x6e, 0x2f, 0x09, 0xad, 0x2f, 0x82, 0x04, 0xe8, 0x81, 0x2a, 0x67, 0x17, 0x25, 0xd5, 0x60, 0x15, 0x35, 0xc8, 0xca, 0xf8, 0x92, 0xf1, 0xc8, 0x22, 0x77, 0x3f, 0x6f, + /* (2^ 81)P */ 0xb7, 0x94, 0xe8, 0xc2, 0xcc, 0x90, 0xba, 0xf8, 0x0d, 0x9f, 0xff, 0x38, 0xa4, 0x57, 0x75, 0x2c, 0x59, 0x23, 0xe5, 0x5a, 0x85, 0x1d, 0x4d, 0x89, 0x69, 0x3d, 0x74, 0x7b, 0x15, 0x22, 0xe1, 0x68, + /* (2^ 82)P */ 0xf3, 0x19, 0xb9, 0xcf, 0x70, 0x55, 0x7e, 0xd8, 0xb9, 0x8d, 0x79, 0x95, 0xcd, 0xde, 0x2c, 0x3f, 0xce, 0xa2, 0xc0, 0x10, 0x47, 0x15, 0x21, 0x21, 0xb2, 0xc5, 0x6d, 0x24, 0x15, 0xa1, 0x66, 0x3c, + /* (2^ 83)P */ 0x72, 0xcb, 0x4e, 0x29, 0x62, 0xc5, 0xed, 0xcb, 0x16, 0x0b, 0x28, 0x6a, 0xc3, 0x43, 0x71, 0xba, 0x67, 0x8b, 0x07, 0xd4, 0xef, 0xc2, 0x10, 0x96, 0x1e, 0x4b, 0x6a, 0x94, 0x5d, 0x73, 0x44, 0x61, + /* (2^ 84)P */ 0x50, 0x33, 0x5b, 0xd7, 0x1e, 0x11, 0x6f, 0x53, 0x1b, 0xd8, 0x41, 0x20, 0x8c, 0xdb, 0x11, 0x02, 0x3c, 0x41, 0x10, 0x0e, 0x00, 0xb1, 0x3c, 0xf9, 0x76, 0x88, 0x9e, 0x03, 0x3c, 0xfd, 0x9d, 0x14, + /* (2^ 85)P */ 0x5b, 0x15, 0x63, 0x6b, 0xe4, 0xdd, 0x79, 0xd4, 0x76, 0x79, 0x83, 0x3c, 0xe9, 0x15, 0x6e, 0xb6, 0x38, 0xe0, 0x13, 0x1f, 0x3b, 0xe4, 0xfd, 0xda, 0x35, 0x0b, 0x4b, 0x2e, 0x1a, 0xda, 0xaf, 0x5f, + /* (2^ 86)P */ 0x81, 0x75, 0x19, 0x17, 0xdf, 0xbb, 0x00, 0x36, 0xc2, 0xd2, 0x3c, 0xbe, 0x0b, 0x05, 0x72, 0x39, 0x86, 0xbe, 0xd5, 0xbd, 0x6d, 0x90, 0x38, 0x59, 0x0f, 0x86, 0x9b, 0x3f, 0xe4, 0xe5, 0xfc, 0x34, + /* (2^ 87)P */ 0x02, 0x4d, 0xd1, 0x42, 0xcd, 0xa4, 0xa8, 0x75, 0x65, 0xdf, 0x41, 0x34, 0xc5, 0xab, 0x8d, 0x82, 0xd3, 0x31, 0xe1, 0xd2, 0xed, 0xab, 0xdc, 0x33, 0x5f, 0xd2, 0x14, 0xb8, 0x6f, 0xd7, 0xba, 0x3e, + /* (2^ 88)P */ 0x0f, 0xe1, 0x70, 0x6f, 0x56, 0x6f, 0x90, 0xd4, 0x5a, 0x0f, 0x69, 0x51, 0xaa, 0xf7, 0x12, 0x5d, 0xf2, 0xfc, 0xce, 0x76, 0x6e, 0xb1, 0xad, 0x45, 0x99, 0x29, 0x23, 0xad, 0xae, 0x68, 0xf7, 0x01, + /* (2^ 89)P */ 0xbd, 0xfe, 0x48, 0x62, 0x7b, 0xc7, 0x6c, 0x2b, 0xfd, 0xaf, 0x3a, 0xec, 0x28, 0x06, 0xd3, 0x3c, 0x6a, 0x48, 0xef, 0xd4, 0x80, 0x0b, 0x1c, 0xce, 0x23, 0x6c, 0xf6, 0xa6, 0x2e, 0xff, 0x3b, 0x4c, + /* (2^ 90)P */ 0x5f, 0xeb, 0xea, 0x4a, 0x09, 0xc4, 0x2e, 0x3f, 0xa7, 0x2c, 0x37, 0x6e, 0x28, 0x9b, 0xb1, 0x61, 0x1d, 0x70, 0x2a, 0xde, 0x66, 0xa9, 0xef, 0x5e, 0xef, 0xe3, 0x55, 0xde, 0x65, 0x05, 0xb2, 0x23, + /* (2^ 91)P */ 0x57, 0x85, 0xd5, 0x79, 0x52, 0xca, 0x01, 0xe3, 0x4f, 0x87, 0xc2, 0x27, 0xce, 0xd4, 0xb2, 0x07, 0x67, 0x1d, 0xcf, 0x9d, 0x8a, 0xcd, 0x32, 0xa5, 0x56, 0xff, 0x2b, 0x3f, 0xe2, 0xfe, 0x52, 0x2a, + /* (2^ 92)P */ 0x3d, 0x66, 0xd8, 0x7c, 0xb3, 0xef, 0x24, 0x86, 0x94, 0x75, 0xbd, 0xff, 0x20, 0xac, 0xc7, 0xbb, 0x45, 0x74, 0xd3, 0x82, 0x9c, 0x5e, 0xb8, 0x57, 0x66, 0xec, 0xa6, 0x86, 0xcb, 0x52, 0x30, 0x7b, + /* (2^ 93)P */ 0x1e, 0xe9, 0x25, 0x25, 0xad, 0xf0, 0x82, 0x34, 0xa0, 0xdc, 0x8e, 0xd2, 0x43, 0x80, 0xb6, 0x2c, 0x3a, 0x00, 0x1b, 0x2e, 0x05, 0x6d, 0x4f, 0xaf, 0x0a, 0x1b, 0x78, 0x29, 0x25, 0x8c, 0x5f, 0x18, + /* (2^ 94)P */ 0xd6, 0xe0, 0x0c, 0xd8, 0x5b, 0xde, 0x41, 0xaa, 0xd6, 0xe9, 0x53, 0x68, 0x41, 0xb2, 0x07, 0x94, 0x3a, 0x4c, 0x7f, 0x35, 0x6e, 0xc3, 0x3e, 0x56, 0xce, 0x7b, 0x29, 0x0e, 0xdd, 0xb8, 0xc4, 0x4c, + /* (2^ 95)P */ 0x0e, 0x73, 0xb8, 0xff, 0x52, 0x1a, 0xfc, 0xa2, 0x37, 0x8e, 0x05, 0x67, 0x6e, 0xf1, 0x11, 0x18, 0xe1, 0x4e, 0xdf, 0xcd, 0x66, 0xa3, 0xf9, 0x10, 0x99, 0xf0, 0xb9, 0xa0, 0xc4, 0xa0, 0xf4, 0x72, + /* (2^ 96)P */ 0xa7, 0x4e, 0x3f, 0x66, 0x6f, 0xc0, 0x16, 0x8c, 0xba, 0x0f, 0x97, 0x4e, 0xf7, 0x3a, 0x3b, 0x69, 0x45, 0xc3, 0x9e, 0xd6, 0xf1, 0xe7, 0x02, 0x21, 0x89, 0x80, 0x8a, 0x96, 0xbc, 0x3c, 0xa5, 0x0b, + /* (2^ 97)P */ 0x37, 0x55, 0xa1, 0xfe, 0xc7, 0x9d, 0x3d, 0xca, 0x93, 0x64, 0x53, 0x51, 0xbb, 0x24, 0x68, 0x4c, 0xb1, 0x06, 0x40, 0x84, 0x14, 0x63, 0x88, 0xb9, 0x60, 0xcc, 0x54, 0xb4, 0x2a, 0xa7, 0xd2, 0x40, + /* (2^ 98)P */ 0x75, 0x09, 0x57, 0x12, 0xb7, 0xa1, 0x36, 0x59, 0x57, 0xa6, 0xbd, 0xde, 0x48, 0xd6, 0xb9, 0x91, 0xea, 0x30, 0x43, 0xb6, 0x4b, 0x09, 0x44, 0x33, 0xd0, 0x51, 0xee, 0x12, 0x0d, 0xa1, 0x6b, 0x00, + /* (2^ 99)P */ 0x58, 0x5d, 0xde, 0xf5, 0x68, 0x84, 0x22, 0x19, 0xb0, 0x05, 0xcc, 0x38, 0x4c, 0x2f, 0xb1, 0x0e, 0x90, 0x19, 0x60, 0xd5, 0x9d, 0x9f, 0x03, 0xa1, 0x0b, 0x0e, 0xff, 0x4f, 0xce, 0xd4, 0x02, 0x45, + /* (2^100)P */ 0x89, 0xc1, 0x37, 0x68, 0x10, 0x54, 0x20, 0xeb, 0x3c, 0xb9, 0xd3, 0x6d, 0x4c, 0x54, 0xf6, 0xd0, 0x4f, 0xd7, 0x16, 0xc4, 0x64, 0x70, 0x72, 0x40, 0xf0, 0x2e, 0x50, 0x4b, 0x11, 0xc6, 0x15, 0x6e, + /* (2^101)P */ 0x6b, 0xa7, 0xb1, 0xcf, 0x98, 0xa3, 0xf2, 0x4d, 0xb1, 0xf6, 0xf2, 0x19, 0x74, 0x6c, 0x25, 0x11, 0x43, 0x60, 0x6e, 0x06, 0x62, 0x79, 0x49, 0x4a, 0x44, 0x5b, 0x35, 0x41, 0xab, 0x3a, 0x5b, 0x70, + /* (2^102)P */ 0xd8, 0xb1, 0x97, 0xd7, 0x36, 0xf5, 0x5e, 0x36, 0xdb, 0xf0, 0xdd, 0x22, 0xd6, 0x6b, 0x07, 0x00, 0x88, 0x5a, 0x57, 0xe0, 0xb0, 0x33, 0xbf, 0x3b, 0x4d, 0xca, 0xe4, 0xc8, 0x05, 0xaa, 0x77, 0x37, + /* (2^103)P */ 0x5f, 0xdb, 0x78, 0x55, 0xc8, 0x45, 0x27, 0x39, 0xe2, 0x5a, 0xae, 0xdb, 0x49, 0x41, 0xda, 0x6f, 0x67, 0x98, 0xdc, 0x8a, 0x0b, 0xb0, 0xf0, 0xb1, 0xa3, 0x1d, 0x6f, 0xd3, 0x37, 0x34, 0x96, 0x09, + /* (2^104)P */ 0x53, 0x38, 0xdc, 0xa5, 0x90, 0x4e, 0x82, 0x7e, 0xbd, 0x5c, 0x13, 0x1f, 0x64, 0xf6, 0xb5, 0xcc, 0xcc, 0x8f, 0xce, 0x87, 0x6c, 0xd8, 0x36, 0x67, 0x9f, 0x24, 0x04, 0x66, 0xe2, 0x3c, 0x5f, 0x62, + /* (2^105)P */ 0x3f, 0xf6, 0x02, 0x95, 0x05, 0xc8, 0x8a, 0xaf, 0x69, 0x14, 0x35, 0x2e, 0x0a, 0xe7, 0x05, 0x0c, 0x05, 0x63, 0x4b, 0x76, 0x9c, 0x2e, 0x29, 0x35, 0xc3, 0x3a, 0xe2, 0xc7, 0x60, 0x43, 0x39, 0x1a, + /* (2^106)P */ 0x64, 0x32, 0x18, 0x51, 0x32, 0xd5, 0xc6, 0xd5, 0x4f, 0xb7, 0xc2, 0x43, 0xbd, 0x5a, 0x06, 0x62, 0x9b, 0x3f, 0x97, 0x3b, 0xd0, 0xf5, 0xfb, 0xb5, 0x5e, 0x6e, 0x20, 0x61, 0x36, 0xda, 0xa3, 0x13, + /* (2^107)P */ 0xe5, 0x94, 0x5d, 0x72, 0x37, 0x58, 0xbd, 0xc6, 0xc5, 0x16, 0x50, 0x20, 0x12, 0x09, 0xe3, 0x18, 0x68, 0x3c, 0x03, 0x70, 0x15, 0xce, 0x88, 0x20, 0x87, 0x79, 0x83, 0x5c, 0x49, 0x1f, 0xba, 0x7f, + /* (2^108)P */ 0x9d, 0x07, 0xf9, 0xf2, 0x23, 0x74, 0x8c, 0x5a, 0xc5, 0x3f, 0x02, 0x34, 0x7b, 0x15, 0x35, 0x17, 0x51, 0xb3, 0xfa, 0xd2, 0x9a, 0xb4, 0xf9, 0xe4, 0x3c, 0xe3, 0x78, 0xc8, 0x72, 0xff, 0x91, 0x66, + /* (2^109)P */ 0x3e, 0xff, 0x5e, 0xdc, 0xde, 0x2a, 0x2c, 0x12, 0xf4, 0x6c, 0x95, 0xd8, 0xf1, 0x4b, 0xdd, 0xf8, 0xda, 0x5b, 0x9e, 0x9e, 0x5d, 0x20, 0x86, 0xeb, 0x43, 0xc7, 0x75, 0xd9, 0xb9, 0x92, 0x9b, 0x04, + /* (2^110)P */ 0x5a, 0xc0, 0xf6, 0xb0, 0x30, 0x97, 0x37, 0xa5, 0x53, 0xa5, 0xf3, 0xc6, 0xac, 0xff, 0xa0, 0x72, 0x6d, 0xcd, 0x0d, 0xb2, 0x34, 0x2c, 0x03, 0xb0, 0x4a, 0x16, 0xd5, 0x88, 0xbc, 0x9d, 0x0e, 0x47, + /* (2^111)P */ 0x47, 0xc0, 0x37, 0xa2, 0x0c, 0xf1, 0x9c, 0xb1, 0xa2, 0x81, 0x6c, 0x1f, 0x71, 0x66, 0x54, 0xb6, 0x43, 0x0b, 0xd8, 0x6d, 0xd1, 0x1b, 0x32, 0xb3, 0x8e, 0xbe, 0x5f, 0x0c, 0x60, 0x4f, 0xc1, 0x48, + /* (2^112)P */ 0x03, 0xc8, 0xa6, 0x4a, 0x26, 0x1c, 0x45, 0x66, 0xa6, 0x7d, 0xfa, 0xa4, 0x04, 0x39, 0x6e, 0xb6, 0x95, 0x83, 0x12, 0xb3, 0xb0, 0x19, 0x5f, 0xd4, 0x10, 0xbc, 0xc9, 0xc3, 0x27, 0x26, 0x60, 0x31, + /* (2^113)P */ 0x0d, 0xe1, 0xe4, 0x32, 0x48, 0xdc, 0x20, 0x31, 0xf7, 0x17, 0xc7, 0x56, 0x67, 0xc4, 0x20, 0xeb, 0x94, 0x02, 0x28, 0x67, 0x3f, 0x2e, 0xf5, 0x00, 0x09, 0xc5, 0x30, 0x47, 0xc1, 0x4f, 0x6d, 0x56, + /* (2^114)P */ 0x06, 0x72, 0x83, 0xfd, 0x40, 0x5d, 0x3a, 0x7e, 0x7a, 0x54, 0x59, 0x71, 0xdc, 0x26, 0xe9, 0xc1, 0x95, 0x60, 0x8d, 0xa6, 0xfb, 0x30, 0x67, 0x21, 0xa7, 0xce, 0x69, 0x3f, 0x84, 0xc3, 0xe8, 0x22, + /* (2^115)P */ 0x2b, 0x4b, 0x0e, 0x93, 0xe8, 0x74, 0xd0, 0x33, 0x16, 0x58, 0xd1, 0x84, 0x0e, 0x35, 0xe4, 0xb6, 0x65, 0x23, 0xba, 0xd6, 0x6a, 0xc2, 0x34, 0x55, 0xf3, 0xf3, 0xf1, 0x89, 0x2f, 0xc1, 0x73, 0x77, + /* (2^116)P */ 0xaa, 0x62, 0x79, 0xa5, 0x4d, 0x40, 0xba, 0x8c, 0x56, 0xce, 0x99, 0x19, 0xa8, 0x97, 0x98, 0x5b, 0xfc, 0x92, 0x16, 0x12, 0x2f, 0x86, 0x8e, 0x50, 0x91, 0xc2, 0x93, 0xa0, 0x7f, 0x90, 0x81, 0x3a, + /* (2^117)P */ 0x10, 0xa5, 0x25, 0x47, 0xff, 0xd0, 0xde, 0x0d, 0x03, 0xc5, 0x3f, 0x67, 0x10, 0xcc, 0xd8, 0x10, 0x89, 0x4e, 0x1f, 0x9f, 0x1c, 0x15, 0x9d, 0x5b, 0x4c, 0xa4, 0x09, 0xcb, 0xd5, 0xc1, 0xa5, 0x32, + /* (2^118)P */ 0xfb, 0x41, 0x05, 0xb9, 0x42, 0xa4, 0x0a, 0x1e, 0xdb, 0x85, 0xb4, 0xc1, 0x7c, 0xeb, 0x85, 0x5f, 0xe5, 0xf2, 0x9d, 0x8a, 0xce, 0x95, 0xe5, 0xbe, 0x36, 0x22, 0x42, 0x22, 0xc7, 0x96, 0xe4, 0x25, + /* (2^119)P */ 0xb9, 0xe5, 0x0f, 0xcd, 0x46, 0x3c, 0xdf, 0x5e, 0x88, 0x33, 0xa4, 0xd2, 0x7e, 0x5a, 0xe7, 0x34, 0x52, 0xe3, 0x61, 0xd7, 0x11, 0xde, 0x88, 0xe4, 0x5c, 0x54, 0x85, 0xa0, 0x01, 0x8a, 0x87, 0x0e, + /* (2^120)P */ 0x04, 0xbb, 0x21, 0xe0, 0x77, 0x3c, 0x49, 0xba, 0x9a, 0x89, 0xdf, 0xc7, 0x43, 0x18, 0x4d, 0x2b, 0x67, 0x0d, 0xe8, 0x7a, 0x48, 0x7a, 0xa3, 0x9e, 0x94, 0x17, 0xe4, 0x11, 0x80, 0x95, 0xa9, 0x67, + /* (2^121)P */ 0x65, 0xb0, 0x97, 0x66, 0x1a, 0x05, 0x58, 0x4b, 0xd4, 0xa6, 0x6b, 0x8d, 0x7d, 0x3f, 0xe3, 0x47, 0xc1, 0x46, 0xca, 0x83, 0xd4, 0xa8, 0x4d, 0xbb, 0x0d, 0xdb, 0xc2, 0x81, 0xa1, 0xca, 0xbe, 0x68, + /* (2^122)P */ 0xa5, 0x9a, 0x98, 0x0b, 0xe9, 0x80, 0x89, 0x8d, 0x9b, 0xc9, 0x93, 0x2c, 0x4a, 0xb1, 0x5e, 0xf9, 0xa2, 0x73, 0x6e, 0x79, 0xc4, 0xc7, 0xc6, 0x51, 0x69, 0xb5, 0xef, 0xb5, 0x63, 0x83, 0x22, 0x6e, + /* (2^123)P */ 0xc8, 0x24, 0xd6, 0x2d, 0xb0, 0xc0, 0xbb, 0xc6, 0xee, 0x70, 0x81, 0xec, 0x7d, 0xb4, 0x7e, 0x77, 0xa9, 0xaf, 0xcf, 0x04, 0xa0, 0x15, 0xde, 0x3c, 0x9b, 0xbf, 0x60, 0x71, 0x08, 0xbc, 0xc6, 0x1d, + /* (2^124)P */ 0x02, 0x40, 0xc3, 0xee, 0x43, 0xe0, 0x07, 0x2e, 0x7f, 0xdc, 0x68, 0x7a, 0x67, 0xfc, 0xe9, 0x18, 0x9a, 0x5b, 0xd1, 0x8b, 0x18, 0x03, 0xda, 0xd8, 0x53, 0x82, 0x56, 0x00, 0xbb, 0xc3, 0xfb, 0x48, + /* (2^125)P */ 0xe1, 0x4c, 0x65, 0xfb, 0x4c, 0x7d, 0x54, 0x57, 0xad, 0xe2, 0x58, 0xa0, 0x82, 0x5b, 0x56, 0xd3, 0x78, 0x44, 0x15, 0xbf, 0x0b, 0xaf, 0x3e, 0xf6, 0x18, 0xbb, 0xdf, 0x14, 0xf1, 0x1e, 0x53, 0x47, + /* (2^126)P */ 0x87, 0xc5, 0x78, 0x42, 0x0a, 0x63, 0xec, 0xe1, 0xf3, 0x83, 0x8e, 0xca, 0x46, 0xd5, 0x07, 0x55, 0x2b, 0x0c, 0xdc, 0x3a, 0xc6, 0x35, 0xe1, 0x85, 0x4e, 0x84, 0x82, 0x56, 0xa8, 0xef, 0xa7, 0x0a, + /* (2^127)P */ 0x15, 0xf6, 0xe1, 0xb3, 0xa8, 0x1b, 0x69, 0x72, 0xfa, 0x3f, 0xbe, 0x1f, 0x70, 0xe9, 0xb4, 0x32, 0x68, 0x78, 0xbb, 0x39, 0x2e, 0xd9, 0xb6, 0x97, 0xe8, 0x39, 0x2e, 0xa0, 0xde, 0x53, 0xfe, 0x2c, + /* (2^128)P */ 0xb0, 0x52, 0xcd, 0x85, 0xcd, 0x92, 0x73, 0x68, 0x31, 0x98, 0xe2, 0x10, 0xc9, 0x66, 0xff, 0x27, 0x06, 0x2d, 0x83, 0xa9, 0x56, 0x45, 0x13, 0x97, 0xa0, 0xf8, 0x84, 0x0a, 0x36, 0xb0, 0x9b, 0x26, + /* (2^129)P */ 0x5c, 0xf8, 0x43, 0x76, 0x45, 0x55, 0x6e, 0x70, 0x1b, 0x7d, 0x59, 0x9b, 0x8c, 0xa4, 0x34, 0x37, 0x72, 0xa4, 0xef, 0xc6, 0xe8, 0x91, 0xee, 0x7a, 0xe0, 0xd9, 0xa9, 0x98, 0xc1, 0xab, 0xd6, 0x5c, + /* (2^130)P */ 0x1a, 0xe4, 0x3c, 0xcb, 0x06, 0xde, 0x04, 0x0e, 0x38, 0xe1, 0x02, 0x34, 0x89, 0xeb, 0xc6, 0xd8, 0x72, 0x37, 0x6e, 0x68, 0xbb, 0x59, 0x46, 0x90, 0xc8, 0xa8, 0x6b, 0x74, 0x71, 0xc3, 0x15, 0x72, + /* (2^131)P */ 0xd9, 0xa2, 0xe4, 0xea, 0x7e, 0xa9, 0x12, 0xfd, 0xc5, 0xf2, 0x94, 0x63, 0x51, 0xb7, 0x14, 0x95, 0x94, 0xf2, 0x08, 0x92, 0x80, 0xd5, 0x6f, 0x26, 0xb9, 0x26, 0x9a, 0x61, 0x85, 0x70, 0x84, 0x5c, + /* (2^132)P */ 0xea, 0x94, 0xd6, 0xfe, 0x10, 0x54, 0x98, 0x52, 0x54, 0xd2, 0x2e, 0x4a, 0x93, 0x5b, 0x90, 0x3c, 0x67, 0xe4, 0x3b, 0x2d, 0x69, 0x47, 0xbb, 0x10, 0xe1, 0xe9, 0xe5, 0x69, 0x2d, 0x3d, 0x3b, 0x06, + /* (2^133)P */ 0xeb, 0x7d, 0xa5, 0xdd, 0xee, 0x26, 0x27, 0x47, 0x91, 0x18, 0xf4, 0x10, 0xae, 0xc4, 0xb6, 0xef, 0x14, 0x76, 0x30, 0x7b, 0x91, 0x41, 0x16, 0x2b, 0x7c, 0x5b, 0xf4, 0xc4, 0x4f, 0x55, 0x7c, 0x11, + /* (2^134)P */ 0x12, 0x88, 0x9d, 0x8f, 0x11, 0xf3, 0x7c, 0xc0, 0x39, 0x79, 0x01, 0x50, 0x20, 0xd8, 0xdb, 0x01, 0x27, 0x28, 0x1b, 0x17, 0xf4, 0x03, 0xe8, 0xd7, 0xea, 0x25, 0xd2, 0x87, 0x74, 0xe8, 0x15, 0x10, + /* (2^135)P */ 0x4d, 0xcc, 0x3a, 0xd2, 0xfe, 0xe3, 0x8d, 0xc5, 0x2d, 0xbe, 0xa7, 0x94, 0xc2, 0x91, 0xdb, 0x50, 0x57, 0xf4, 0x9c, 0x1c, 0x3d, 0xd4, 0x94, 0x0b, 0x4a, 0x52, 0x37, 0x6e, 0xfa, 0x40, 0x16, 0x6b, + /* (2^136)P */ 0x09, 0x0d, 0xda, 0x5f, 0x6c, 0x34, 0x2f, 0x69, 0x51, 0x31, 0x4d, 0xfa, 0x59, 0x1c, 0x0b, 0x20, 0x96, 0xa2, 0x77, 0x07, 0x76, 0x6f, 0xc4, 0xb8, 0xcf, 0xfb, 0xfd, 0x3f, 0x5f, 0x39, 0x38, 0x4b, + /* (2^137)P */ 0x71, 0xd6, 0x54, 0xbe, 0x00, 0x5e, 0xd2, 0x18, 0xa6, 0xab, 0xc8, 0xbe, 0x82, 0x05, 0xd5, 0x60, 0x82, 0xb9, 0x78, 0x3b, 0x26, 0x8f, 0xad, 0x87, 0x32, 0x04, 0xda, 0x9c, 0x4e, 0xf6, 0xfd, 0x50, + /* (2^138)P */ 0xf0, 0xdc, 0x78, 0xc5, 0xaa, 0x67, 0xf5, 0x90, 0x3b, 0x13, 0xa3, 0xf2, 0x0e, 0x9b, 0x1e, 0xef, 0x71, 0xde, 0xd9, 0x42, 0x92, 0xba, 0xeb, 0x0e, 0xc7, 0x01, 0x31, 0xf0, 0x9b, 0x3c, 0x47, 0x15, + /* (2^139)P */ 0x95, 0x80, 0xb7, 0x56, 0xae, 0xe8, 0x77, 0x7c, 0x8e, 0x07, 0x6f, 0x6e, 0x66, 0xe7, 0x78, 0xb6, 0x1f, 0xba, 0x48, 0x53, 0x61, 0xb9, 0xa0, 0x2d, 0x0b, 0x3f, 0x73, 0xff, 0xc1, 0x31, 0xf9, 0x7c, + /* (2^140)P */ 0x6c, 0x36, 0x0a, 0x0a, 0xf5, 0x57, 0xb3, 0x26, 0x32, 0xd7, 0x87, 0x2b, 0xf4, 0x8c, 0x70, 0xe9, 0xc0, 0xb2, 0x1c, 0xf9, 0xa5, 0xee, 0x3a, 0xc1, 0x4c, 0xbb, 0x43, 0x11, 0x99, 0x0c, 0xd9, 0x35, + /* (2^141)P */ 0xdc, 0xd9, 0xa0, 0xa9, 0x04, 0xc4, 0xc1, 0x47, 0x51, 0xd2, 0x72, 0x19, 0x45, 0x58, 0x9e, 0x65, 0x31, 0x8c, 0xb3, 0x73, 0xc4, 0xa8, 0x75, 0x38, 0x24, 0x1f, 0x56, 0x79, 0xd3, 0x9e, 0xbd, 0x1f, + /* (2^142)P */ 0x8d, 0xc2, 0x1e, 0xd4, 0x6f, 0xbc, 0xfa, 0x11, 0xca, 0x2d, 0x2a, 0xcd, 0xe3, 0xdf, 0xf8, 0x7e, 0x95, 0x45, 0x40, 0x8c, 0x5d, 0x3b, 0xe7, 0x72, 0x27, 0x2f, 0xb7, 0x54, 0x49, 0xfa, 0x35, 0x61, + /* (2^143)P */ 0x9c, 0xb6, 0x24, 0xde, 0xa2, 0x32, 0xfc, 0xcc, 0x88, 0x5d, 0x09, 0x1f, 0x8c, 0x69, 0x55, 0x3f, 0x29, 0xf9, 0xc3, 0x5a, 0xed, 0x50, 0x33, 0xbe, 0xeb, 0x7e, 0x47, 0xca, 0x06, 0xf8, 0x9b, 0x5e, + /* (2^144)P */ 0x68, 0x9f, 0x30, 0x3c, 0xb6, 0x8f, 0xce, 0xe9, 0xf4, 0xf9, 0xe1, 0x65, 0x35, 0xf6, 0x76, 0x53, 0xf1, 0x93, 0x63, 0x5a, 0xb3, 0xcf, 0xaf, 0xd1, 0x06, 0x35, 0x62, 0xe5, 0xed, 0xa1, 0x32, 0x66, + /* (2^145)P */ 0x4c, 0xed, 0x2d, 0x0c, 0x39, 0x6c, 0x7d, 0x0b, 0x1f, 0xcb, 0x04, 0xdf, 0x81, 0x32, 0xcb, 0x56, 0xc7, 0xc3, 0xec, 0x49, 0x12, 0x5a, 0x30, 0x66, 0x2a, 0xa7, 0x8c, 0xa3, 0x60, 0x8b, 0x58, 0x5d, + /* (2^146)P */ 0x2d, 0xf4, 0xe5, 0xe8, 0x78, 0xbf, 0xec, 0xa6, 0xec, 0x3e, 0x8a, 0x3c, 0x4b, 0xb4, 0xee, 0x86, 0x04, 0x16, 0xd2, 0xfb, 0x48, 0x9c, 0x21, 0xec, 0x31, 0x67, 0xc3, 0x17, 0xf5, 0x1a, 0xaf, 0x1a, + /* (2^147)P */ 0xe7, 0xbd, 0x69, 0x67, 0x83, 0xa2, 0x06, 0xc3, 0xdb, 0x2a, 0x1e, 0x2b, 0x62, 0x80, 0x82, 0x20, 0xa6, 0x94, 0xff, 0xfb, 0x1f, 0xf5, 0x27, 0x80, 0x6b, 0xf2, 0x24, 0x11, 0xce, 0xa1, 0xcf, 0x76, + /* (2^148)P */ 0xb6, 0xab, 0x22, 0x24, 0x56, 0x00, 0xeb, 0x18, 0xc3, 0x29, 0x8c, 0x8f, 0xd5, 0xc4, 0x77, 0xf3, 0x1a, 0x56, 0x31, 0xf5, 0x07, 0xc2, 0xbb, 0x4d, 0x27, 0x8a, 0x12, 0x82, 0xf0, 0xb7, 0x53, 0x02, + /* (2^149)P */ 0xe0, 0x17, 0x2c, 0xb6, 0x1c, 0x09, 0x1f, 0x3d, 0xa9, 0x28, 0x46, 0xd6, 0xab, 0xe1, 0x60, 0x48, 0x53, 0x42, 0x9d, 0x30, 0x36, 0x74, 0xd1, 0x52, 0x76, 0xe5, 0xfa, 0x3e, 0xe1, 0x97, 0x6f, 0x35, + /* (2^150)P */ 0x5b, 0x53, 0x50, 0xa1, 0x1a, 0xe1, 0x51, 0xd3, 0xcc, 0x78, 0xd8, 0x1d, 0xbb, 0x45, 0x6b, 0x3e, 0x98, 0x2c, 0xd9, 0xbe, 0x28, 0x61, 0x77, 0x0c, 0xb8, 0x85, 0x28, 0x03, 0x93, 0xae, 0x34, 0x1d, + /* (2^151)P */ 0xc3, 0xa4, 0x5b, 0xa8, 0x8c, 0x48, 0xa0, 0x4b, 0xce, 0xe6, 0x9c, 0x3c, 0xc3, 0x48, 0x53, 0x98, 0x70, 0xa7, 0xbd, 0x97, 0x6f, 0x4c, 0x12, 0x66, 0x4a, 0x12, 0x54, 0x06, 0x29, 0xa0, 0x81, 0x0f, + /* (2^152)P */ 0xfd, 0x86, 0x9b, 0x56, 0xa6, 0x9c, 0xd0, 0x9e, 0x2d, 0x9a, 0xaf, 0x18, 0xfd, 0x09, 0x10, 0x81, 0x0a, 0xc2, 0xd8, 0x93, 0x3f, 0xd0, 0x08, 0xff, 0x6b, 0xf2, 0xae, 0x9f, 0x19, 0x48, 0xa1, 0x52, + /* (2^153)P */ 0x73, 0x1b, 0x8d, 0x2d, 0xdc, 0xf9, 0x03, 0x3e, 0x70, 0x1a, 0x96, 0x73, 0x18, 0x80, 0x05, 0x42, 0x70, 0x59, 0xa3, 0x41, 0xf0, 0x87, 0xd9, 0xc0, 0x49, 0xd5, 0xc0, 0xa1, 0x15, 0x1f, 0xaa, 0x07, + /* (2^154)P */ 0x24, 0x72, 0xd2, 0x8c, 0xe0, 0x6c, 0xd4, 0xdf, 0x39, 0x42, 0x4e, 0x93, 0x4f, 0x02, 0x0a, 0x6d, 0x59, 0x7b, 0x89, 0x99, 0x63, 0x7a, 0x8a, 0x80, 0xa2, 0x95, 0x3d, 0xe1, 0xe9, 0x56, 0x45, 0x0a, + /* (2^155)P */ 0x45, 0x30, 0xc1, 0xe9, 0x1f, 0x99, 0x1a, 0xd2, 0xb8, 0x51, 0x77, 0xfe, 0x48, 0x85, 0x0e, 0x9b, 0x35, 0x00, 0xf3, 0x4b, 0xcb, 0x43, 0xa6, 0x5d, 0x21, 0xf7, 0x40, 0x39, 0xd6, 0x28, 0xdb, 0x77, + /* (2^156)P */ 0x11, 0x90, 0xdc, 0x4a, 0x61, 0xeb, 0x5e, 0xfc, 0xeb, 0x11, 0xc4, 0xe8, 0x9a, 0x41, 0x29, 0x52, 0x74, 0xcf, 0x1d, 0x7d, 0x78, 0xe7, 0xc3, 0x9e, 0xb5, 0x4c, 0x6e, 0x21, 0x3e, 0x05, 0x0d, 0x34, + /* (2^157)P */ 0xb4, 0xf2, 0x8d, 0xb4, 0x39, 0xaf, 0xc7, 0xca, 0x94, 0x0a, 0xa1, 0x71, 0x28, 0xec, 0xfa, 0xc0, 0xed, 0x75, 0xa5, 0x5c, 0x24, 0x69, 0x0a, 0x14, 0x4c, 0x3a, 0x27, 0x34, 0x71, 0xc3, 0xf1, 0x0c, + /* (2^158)P */ 0xa5, 0xb8, 0x24, 0xc2, 0x6a, 0x30, 0xee, 0xc8, 0xb0, 0x30, 0x49, 0xcb, 0x7c, 0xee, 0xea, 0x57, 0x4f, 0xe7, 0xcb, 0xaa, 0xbd, 0x06, 0xe8, 0xa1, 0x7d, 0x65, 0xeb, 0x2e, 0x74, 0x62, 0x9a, 0x7d, + /* (2^159)P */ 0x30, 0x48, 0x6c, 0x54, 0xef, 0xb6, 0xb6, 0x9e, 0x2e, 0x6e, 0xb3, 0xdd, 0x1f, 0xca, 0x5c, 0x88, 0x05, 0x71, 0x0d, 0xef, 0x83, 0xf3, 0xb9, 0xe6, 0x12, 0x04, 0x2e, 0x9d, 0xef, 0x4f, 0x65, 0x58, + /* (2^160)P */ 0x26, 0x8e, 0x0e, 0xbe, 0xff, 0xc4, 0x05, 0xa9, 0x6e, 0x81, 0x31, 0x9b, 0xdf, 0xe5, 0x2d, 0x94, 0xe1, 0x88, 0x2e, 0x80, 0x3f, 0x72, 0x7d, 0x49, 0x8d, 0x40, 0x2f, 0x60, 0xea, 0x4d, 0x68, 0x30, + /* (2^161)P */ 0x34, 0xcb, 0xe6, 0xa3, 0x78, 0xa2, 0xe5, 0x21, 0xc4, 0x1d, 0x15, 0x5b, 0x6f, 0x6e, 0xfb, 0xae, 0x15, 0xca, 0x77, 0x9d, 0x04, 0x8e, 0x0b, 0xb3, 0x81, 0x89, 0xb9, 0x53, 0xcf, 0xc9, 0xc3, 0x28, + /* (2^162)P */ 0x2a, 0xdd, 0x6c, 0x55, 0x21, 0xb7, 0x7f, 0x28, 0x74, 0x22, 0x02, 0x97, 0xa8, 0x7c, 0x31, 0x0d, 0x58, 0x32, 0x54, 0x3a, 0x42, 0xc7, 0x68, 0x74, 0x2f, 0x64, 0xb5, 0x4e, 0x46, 0x11, 0x7f, 0x4a, + /* (2^163)P */ 0xa6, 0x3a, 0x19, 0x4d, 0x77, 0xa4, 0x37, 0xa2, 0xa1, 0x29, 0x21, 0xa9, 0x6e, 0x98, 0x65, 0xd8, 0x88, 0x1a, 0x7c, 0xf8, 0xec, 0x15, 0xc5, 0x24, 0xeb, 0xf5, 0x39, 0x5f, 0x57, 0x03, 0x40, 0x60, + /* (2^164)P */ 0x27, 0x9b, 0x0a, 0x57, 0x89, 0xf1, 0xb9, 0x47, 0x78, 0x4b, 0x5e, 0x46, 0xde, 0xce, 0x98, 0x2b, 0x20, 0x5c, 0xb8, 0xdb, 0x51, 0xf5, 0x6d, 0x02, 0x01, 0x19, 0xe2, 0x47, 0x10, 0xd9, 0xfc, 0x74, + /* (2^165)P */ 0xa3, 0xbf, 0xc1, 0x23, 0x0a, 0xa9, 0xe2, 0x13, 0xf6, 0x19, 0x85, 0x47, 0x4e, 0x07, 0xb0, 0x0c, 0x44, 0xcf, 0xf6, 0x3a, 0xbe, 0xcb, 0xf1, 0x5f, 0xbe, 0x2d, 0x81, 0xbe, 0x38, 0x54, 0xfe, 0x67, + /* (2^166)P */ 0xb0, 0x05, 0x0f, 0xa4, 0x4f, 0xf6, 0x3c, 0xd1, 0x87, 0x37, 0x28, 0x32, 0x2f, 0xfb, 0x4d, 0x05, 0xea, 0x2a, 0x0d, 0x7f, 0x5b, 0x91, 0x73, 0x41, 0x4e, 0x0d, 0x61, 0x1f, 0x4f, 0x14, 0x2f, 0x48, + /* (2^167)P */ 0x34, 0x82, 0x7f, 0xb4, 0x01, 0x02, 0x21, 0xf6, 0x90, 0xb9, 0x70, 0x9e, 0x92, 0xe1, 0x0a, 0x5d, 0x7c, 0x56, 0x49, 0xb0, 0x55, 0xf4, 0xd7, 0xdc, 0x01, 0x6f, 0x91, 0xf0, 0xf1, 0xd0, 0x93, 0x7e, + /* (2^168)P */ 0xfa, 0xb4, 0x7d, 0x8a, 0xf1, 0xcb, 0x79, 0xdd, 0x2f, 0xc6, 0x74, 0x6f, 0xbf, 0x91, 0x83, 0xbe, 0xbd, 0x91, 0x82, 0x4b, 0xd1, 0x45, 0x71, 0x02, 0x05, 0x17, 0xbf, 0x2c, 0xea, 0x73, 0x5a, 0x58, + /* (2^169)P */ 0xb2, 0x0d, 0x8a, 0x92, 0x3e, 0xa0, 0x5c, 0x48, 0xe7, 0x57, 0x28, 0x74, 0xa5, 0x01, 0xfc, 0x10, 0xa7, 0x51, 0xd5, 0xd6, 0xdb, 0x2e, 0x48, 0x2f, 0x8a, 0xdb, 0x8f, 0x04, 0xb5, 0x33, 0x04, 0x0f, + /* (2^170)P */ 0x47, 0x62, 0xdc, 0xd7, 0x8d, 0x2e, 0xda, 0x60, 0x9a, 0x81, 0xd4, 0x8c, 0xd3, 0xc9, 0xb4, 0x88, 0x97, 0x66, 0xf6, 0x01, 0xc0, 0x3a, 0x03, 0x13, 0x75, 0x7d, 0x36, 0x3b, 0xfe, 0x24, 0x3b, 0x27, + /* (2^171)P */ 0xd4, 0xb9, 0xb3, 0x31, 0x6a, 0xf6, 0xe8, 0xc6, 0xd5, 0x49, 0xdf, 0x94, 0xa4, 0x14, 0x15, 0x28, 0xa7, 0x3d, 0xb2, 0xc8, 0xdf, 0x6f, 0x72, 0xd1, 0x48, 0xe5, 0xde, 0x03, 0xd1, 0xe7, 0x3a, 0x4b, + /* (2^172)P */ 0x7e, 0x9d, 0x4b, 0xce, 0x19, 0x6e, 0x25, 0xc6, 0x1c, 0xc6, 0xe3, 0x86, 0xf1, 0x5c, 0x5c, 0xff, 0x45, 0xc1, 0x8e, 0x4b, 0xa3, 0x3c, 0xc6, 0xac, 0x74, 0x65, 0xe6, 0xfe, 0x88, 0x18, 0x62, 0x74, + /* (2^173)P */ 0x1e, 0x0a, 0x29, 0x45, 0x96, 0x40, 0x6f, 0x95, 0x2e, 0x96, 0x3a, 0x26, 0xe3, 0xf8, 0x0b, 0xef, 0x7b, 0x64, 0xc2, 0x5e, 0xeb, 0x50, 0x6a, 0xed, 0x02, 0x75, 0xca, 0x9d, 0x3a, 0x28, 0x94, 0x06, + /* (2^174)P */ 0xd1, 0xdc, 0xa2, 0x43, 0x36, 0x96, 0x9b, 0x76, 0x53, 0x53, 0xfc, 0x09, 0xea, 0xc8, 0xb7, 0x42, 0xab, 0x7e, 0x39, 0x13, 0xee, 0x2a, 0x00, 0x4f, 0x3a, 0xd6, 0xb7, 0x19, 0x2c, 0x5e, 0x00, 0x63, + /* (2^175)P */ 0xea, 0x3b, 0x02, 0x63, 0xda, 0x36, 0x67, 0xca, 0xb7, 0x99, 0x2a, 0xb1, 0x6d, 0x7f, 0x6c, 0x96, 0xe1, 0xc5, 0x37, 0xc5, 0x90, 0x93, 0xe0, 0xac, 0xee, 0x89, 0xaa, 0xa1, 0x63, 0x60, 0x69, 0x0b, + /* (2^176)P */ 0xe5, 0x56, 0x8c, 0x28, 0x97, 0x3e, 0xb0, 0xeb, 0xe8, 0x8b, 0x8c, 0x93, 0x9f, 0x9f, 0x2a, 0x43, 0x71, 0x7f, 0x71, 0x5b, 0x3d, 0xa9, 0xa5, 0xa6, 0x97, 0x9d, 0x8f, 0xe1, 0xc3, 0xb4, 0x5f, 0x1a, + /* (2^177)P */ 0xce, 0xcd, 0x60, 0x1c, 0xad, 0xe7, 0x94, 0x1c, 0xa0, 0xc4, 0x02, 0xfc, 0x43, 0x2a, 0x20, 0xee, 0x20, 0x6a, 0xc4, 0x67, 0xd8, 0xe4, 0xaf, 0x8d, 0x58, 0x7b, 0xc2, 0x8a, 0x3c, 0x26, 0x10, 0x0a, + /* (2^178)P */ 0x4a, 0x2a, 0x43, 0xe4, 0xdf, 0xa9, 0xde, 0xd0, 0xc5, 0x77, 0x92, 0xbe, 0x7b, 0xf8, 0x6a, 0x85, 0x1a, 0xc7, 0x12, 0xc2, 0xac, 0x72, 0x84, 0xce, 0x91, 0x1e, 0xbb, 0x9b, 0x6d, 0x1b, 0x15, 0x6f, + /* (2^179)P */ 0x6a, 0xd5, 0xee, 0x7c, 0x52, 0x6c, 0x77, 0x26, 0xec, 0xfa, 0xf8, 0xfb, 0xb7, 0x1c, 0x21, 0x7d, 0xcc, 0x09, 0x46, 0xfd, 0xa6, 0x66, 0xae, 0x37, 0x42, 0x0c, 0x77, 0xd2, 0x02, 0xb7, 0x81, 0x1f, + /* (2^180)P */ 0x92, 0x83, 0xc5, 0xea, 0x57, 0xb0, 0xb0, 0x2f, 0x9d, 0x4e, 0x74, 0x29, 0xfe, 0x89, 0xdd, 0xe1, 0xf8, 0xb4, 0xbe, 0x17, 0xeb, 0xf8, 0x64, 0xc9, 0x1e, 0xd4, 0xa2, 0xc9, 0x73, 0x10, 0x57, 0x29, + /* (2^181)P */ 0x54, 0xe2, 0xc0, 0x81, 0x89, 0xa1, 0x48, 0xa9, 0x30, 0x28, 0xb2, 0x65, 0x9b, 0x36, 0xf6, 0x2d, 0xc6, 0xd3, 0xcf, 0x5f, 0xd7, 0xb2, 0x3e, 0xa3, 0x1f, 0xa0, 0x99, 0x41, 0xec, 0xd6, 0x8c, 0x07, + /* (2^182)P */ 0x2f, 0x0d, 0x90, 0xad, 0x41, 0x4a, 0x58, 0x4a, 0x52, 0x4c, 0xc7, 0xe2, 0x78, 0x2b, 0x14, 0x32, 0x78, 0xc9, 0x31, 0x84, 0x33, 0xe8, 0xc4, 0x68, 0xc2, 0x9f, 0x68, 0x08, 0x90, 0xea, 0x69, 0x7f, + /* (2^183)P */ 0x65, 0x82, 0xa3, 0x46, 0x1e, 0xc8, 0xf2, 0x52, 0xfd, 0x32, 0xa8, 0x04, 0x2d, 0x07, 0x78, 0xfd, 0x94, 0x9e, 0x35, 0x25, 0xfa, 0xd5, 0xd7, 0x8c, 0xd2, 0x29, 0xcc, 0x54, 0x74, 0x1b, 0xe7, 0x4d, + /* (2^184)P */ 0xc9, 0x6a, 0xda, 0x1e, 0xad, 0x60, 0xeb, 0x42, 0x3a, 0x9c, 0xc0, 0xdb, 0xdf, 0x37, 0xad, 0x0a, 0x91, 0xc1, 0x3c, 0xe3, 0x71, 0x4b, 0x00, 0x81, 0x3c, 0x80, 0x22, 0x51, 0x34, 0xbe, 0xe6, 0x44, + /* (2^185)P */ 0xdb, 0x20, 0x19, 0xba, 0x88, 0x83, 0xfe, 0x03, 0x08, 0xb0, 0x0d, 0x15, 0x32, 0x7c, 0xd5, 0xf5, 0x29, 0x0c, 0xf6, 0x1a, 0x28, 0xc4, 0xc8, 0x49, 0xee, 0x1a, 0x70, 0xde, 0x18, 0xb5, 0xed, 0x21, + /* (2^186)P */ 0x99, 0xdc, 0x06, 0x8f, 0x41, 0x3e, 0xb6, 0x7f, 0xb8, 0xd7, 0x66, 0xc1, 0x99, 0x0d, 0x46, 0xa4, 0x83, 0x0a, 0x52, 0xce, 0x48, 0x52, 0xdd, 0x24, 0x58, 0x83, 0x92, 0x2b, 0x71, 0xad, 0xc3, 0x5e, + /* (2^187)P */ 0x0f, 0x93, 0x17, 0xbd, 0x5f, 0x2a, 0x02, 0x15, 0xe3, 0x70, 0x25, 0xd8, 0x77, 0x4a, 0xf6, 0xa4, 0x12, 0x37, 0x78, 0x15, 0x69, 0x8d, 0xbc, 0x12, 0xbb, 0x0a, 0x62, 0xfc, 0xc0, 0x94, 0x81, 0x49, + /* (2^188)P */ 0x82, 0x6c, 0x68, 0x55, 0xd2, 0xd9, 0xa2, 0x38, 0xf0, 0x21, 0x3e, 0x19, 0xd9, 0x6b, 0x5c, 0x78, 0x84, 0x54, 0x4a, 0xb2, 0x1a, 0xc8, 0xd5, 0xe4, 0x89, 0x09, 0xe2, 0xb2, 0x60, 0x78, 0x30, 0x56, + /* (2^189)P */ 0xc4, 0x74, 0x4d, 0x8b, 0xf7, 0x55, 0x9d, 0x42, 0x31, 0x01, 0x35, 0x43, 0x46, 0x83, 0xf1, 0x22, 0xff, 0x1f, 0xc7, 0x98, 0x45, 0xc2, 0x60, 0x1e, 0xef, 0x83, 0x99, 0x97, 0x14, 0xf0, 0xf2, 0x59, + /* (2^190)P */ 0x44, 0x4a, 0x49, 0xeb, 0x56, 0x7d, 0xa4, 0x46, 0x8e, 0xa1, 0x36, 0xd6, 0x54, 0xa8, 0x22, 0x3e, 0x3b, 0x1c, 0x49, 0x74, 0x52, 0xe1, 0x46, 0xb3, 0xe7, 0xcd, 0x90, 0x53, 0x4e, 0xfd, 0xea, 0x2c, + /* (2^191)P */ 0x75, 0x66, 0x0d, 0xbe, 0x38, 0x85, 0x8a, 0xba, 0x23, 0x8e, 0x81, 0x50, 0xbb, 0x74, 0x90, 0x4b, 0xc3, 0x04, 0xd3, 0x85, 0x90, 0xb8, 0xda, 0xcb, 0xc4, 0x92, 0x61, 0xe5, 0xe0, 0x4f, 0xa2, 0x61, + /* (2^192)P */ 0xcb, 0x5b, 0x52, 0xdb, 0xe6, 0x15, 0x76, 0xcb, 0xca, 0xe4, 0x67, 0xa5, 0x35, 0x8c, 0x7d, 0xdd, 0x69, 0xdd, 0xfc, 0xca, 0x3a, 0x15, 0xb4, 0xe6, 0x66, 0x97, 0x3c, 0x7f, 0x09, 0x8e, 0x66, 0x2d, + /* (2^193)P */ 0xf0, 0x5e, 0xe5, 0x5c, 0x26, 0x7e, 0x7e, 0xa5, 0x67, 0xb9, 0xd4, 0x7c, 0x52, 0x4e, 0x9f, 0x5d, 0xe5, 0xd1, 0x2f, 0x49, 0x06, 0x36, 0xc8, 0xfb, 0xae, 0xf7, 0xc3, 0xb7, 0xbe, 0x52, 0x0d, 0x09, + /* (2^194)P */ 0x7c, 0x4d, 0x7b, 0x1e, 0x5a, 0x51, 0xb9, 0x09, 0xc0, 0x44, 0xda, 0x99, 0x25, 0x6a, 0x26, 0x1f, 0x04, 0x55, 0xc5, 0xe2, 0x48, 0x95, 0xc4, 0xa1, 0xcc, 0x15, 0x6f, 0x12, 0x87, 0x42, 0xf0, 0x7e, + /* (2^195)P */ 0x15, 0xef, 0x30, 0xbd, 0x9d, 0x65, 0xd1, 0xfe, 0x7b, 0x27, 0xe0, 0xc4, 0xee, 0xb9, 0x4a, 0x8b, 0x91, 0x32, 0xdf, 0xa5, 0x36, 0x62, 0x4d, 0x88, 0x88, 0xf7, 0x5c, 0xbf, 0xa6, 0x6e, 0xd9, 0x1f, + /* (2^196)P */ 0x9a, 0x0d, 0x19, 0x1f, 0x98, 0x61, 0xa1, 0x42, 0xc1, 0x52, 0x60, 0x7e, 0x50, 0x49, 0xd8, 0x61, 0xd5, 0x2c, 0x5a, 0x28, 0xbf, 0x13, 0xe1, 0x9f, 0xd8, 0x85, 0xad, 0xdb, 0x76, 0xd6, 0x22, 0x7c, + /* (2^197)P */ 0x7d, 0xd2, 0xfb, 0x2b, 0xed, 0x70, 0xe7, 0x82, 0xa5, 0xf5, 0x96, 0xe9, 0xec, 0xb2, 0x05, 0x4c, 0x50, 0x01, 0x90, 0xb0, 0xc2, 0xa9, 0x40, 0xcd, 0x64, 0xbf, 0xd9, 0x13, 0x92, 0x31, 0x95, 0x58, + /* (2^198)P */ 0x08, 0x2e, 0xea, 0x3f, 0x70, 0x5d, 0xcc, 0xe7, 0x8c, 0x18, 0xe2, 0x58, 0x12, 0x49, 0x0c, 0xb5, 0xf0, 0x5b, 0x20, 0x48, 0xaa, 0x0b, 0xe3, 0xcc, 0x62, 0x2d, 0xa3, 0xcf, 0x9c, 0x65, 0x7c, 0x53, + /* (2^199)P */ 0x88, 0xc0, 0xcf, 0x98, 0x3a, 0x62, 0xb6, 0x37, 0xa4, 0xac, 0xd6, 0xa4, 0x1f, 0xed, 0x9b, 0xfe, 0xb0, 0xd1, 0xa8, 0x56, 0x8e, 0x9b, 0xd2, 0x04, 0x75, 0x95, 0x51, 0x0b, 0xc4, 0x71, 0x5f, 0x72, + /* (2^200)P */ 0xe6, 0x9c, 0x33, 0xd0, 0x9c, 0xf8, 0xc7, 0x28, 0x8b, 0xc1, 0xdd, 0x69, 0x44, 0xb1, 0x67, 0x83, 0x2c, 0x65, 0xa1, 0xa6, 0x83, 0xda, 0x3a, 0x88, 0x17, 0x6c, 0x4d, 0x03, 0x74, 0x19, 0x5f, 0x58, + /* (2^201)P */ 0x88, 0x91, 0xb1, 0xf1, 0x66, 0xb2, 0xcf, 0x89, 0x17, 0x52, 0xc3, 0xe7, 0x63, 0x48, 0x3b, 0xe6, 0x6a, 0x52, 0xc0, 0xb4, 0xa6, 0x9d, 0x8c, 0xd8, 0x35, 0x46, 0x95, 0xf0, 0x9d, 0x5c, 0x03, 0x3e, + /* (2^202)P */ 0x9d, 0xde, 0x45, 0xfb, 0x12, 0x54, 0x9d, 0xdd, 0x0d, 0xf4, 0xcf, 0xe4, 0x32, 0x45, 0x68, 0xdd, 0x1c, 0x67, 0x1d, 0x15, 0x9b, 0x99, 0x5c, 0x4b, 0x90, 0xf6, 0xe7, 0x11, 0xc8, 0x2c, 0x8c, 0x2d, + /* (2^203)P */ 0x40, 0x5d, 0x05, 0x90, 0x1d, 0xbe, 0x54, 0x7f, 0x40, 0xaf, 0x4a, 0x46, 0xdf, 0xc5, 0x64, 0xa4, 0xbe, 0x17, 0xe9, 0xf0, 0x24, 0x96, 0x97, 0x33, 0x30, 0x6b, 0x35, 0x27, 0xc5, 0x8d, 0x01, 0x2c, + /* (2^204)P */ 0xd4, 0xb3, 0x30, 0xe3, 0x24, 0x50, 0x41, 0xa5, 0xd3, 0x52, 0x16, 0x69, 0x96, 0x3d, 0xff, 0x73, 0xf1, 0x59, 0x9b, 0xef, 0xc4, 0x42, 0xec, 0x94, 0x5a, 0x8e, 0xd0, 0x18, 0x16, 0x20, 0x47, 0x07, + /* (2^205)P */ 0x53, 0x1c, 0x41, 0xca, 0x8a, 0xa4, 0x6c, 0x4d, 0x19, 0x61, 0xa6, 0xcf, 0x2f, 0x5f, 0x41, 0x66, 0xff, 0x27, 0xe2, 0x51, 0x00, 0xd4, 0x4d, 0x9c, 0xeb, 0xf7, 0x02, 0x9a, 0xc0, 0x0b, 0x81, 0x59, + /* (2^206)P */ 0x1d, 0x10, 0xdc, 0xb3, 0x71, 0xb1, 0x7e, 0x2a, 0x8e, 0xf6, 0xfe, 0x9f, 0xb9, 0x5a, 0x1c, 0x44, 0xea, 0x59, 0xb3, 0x93, 0x9b, 0x5c, 0x02, 0x32, 0x2f, 0x11, 0x9d, 0x1e, 0xa7, 0xe0, 0x8c, 0x5e, + /* (2^207)P */ 0xfd, 0x03, 0x95, 0x42, 0x92, 0xcb, 0xcc, 0xbf, 0x55, 0x5d, 0x09, 0x2f, 0x75, 0xba, 0x71, 0xd2, 0x1e, 0x09, 0x2d, 0x97, 0x5e, 0xad, 0x5e, 0x34, 0xba, 0x03, 0x31, 0xa8, 0x11, 0xdf, 0xc8, 0x18, + /* (2^208)P */ 0x4c, 0x0f, 0xed, 0x9a, 0x9a, 0x94, 0xcd, 0x90, 0x7e, 0xe3, 0x60, 0x66, 0xcb, 0xf4, 0xd1, 0xc5, 0x0b, 0x2e, 0xc5, 0x56, 0x2d, 0xc5, 0xca, 0xb8, 0x0d, 0x8e, 0x80, 0xc5, 0x00, 0xe4, 0x42, 0x6e, + /* (2^209)P */ 0x23, 0xfd, 0xae, 0xee, 0x66, 0x69, 0xb4, 0xa3, 0xca, 0xcd, 0x9e, 0xe3, 0x0b, 0x1f, 0x4f, 0x0c, 0x1d, 0xa5, 0x83, 0xd6, 0xc9, 0xc8, 0x9d, 0x18, 0x1b, 0x35, 0x09, 0x4c, 0x05, 0x7f, 0xf2, 0x51, + /* (2^210)P */ 0x82, 0x06, 0x32, 0x2a, 0xcd, 0x7c, 0x48, 0x4c, 0x96, 0x1c, 0xdf, 0xb3, 0x5b, 0xa9, 0x7e, 0x58, 0xe8, 0xb8, 0x5c, 0x55, 0x9e, 0xf7, 0xcc, 0xc8, 0x3d, 0xd7, 0x06, 0xa2, 0x29, 0xc8, 0x7d, 0x54, + /* (2^211)P */ 0x06, 0x9b, 0xc3, 0x80, 0xcd, 0xa6, 0x22, 0xb8, 0xc6, 0xd4, 0x00, 0x20, 0x73, 0x54, 0x6d, 0xe9, 0x4d, 0x3b, 0x46, 0x91, 0x6f, 0x5b, 0x53, 0x28, 0x1d, 0x6e, 0x48, 0xe2, 0x60, 0x46, 0x8f, 0x22, + /* (2^212)P */ 0xbf, 0x3a, 0x8d, 0xde, 0x38, 0x95, 0x79, 0x98, 0x6e, 0xca, 0xeb, 0x45, 0x00, 0x33, 0xd8, 0x8c, 0x38, 0xe7, 0x21, 0x82, 0x00, 0x2a, 0x95, 0x79, 0xbb, 0xd2, 0x5c, 0x53, 0xa7, 0xe1, 0x22, 0x43, + /* (2^213)P */ 0x1c, 0x80, 0xd1, 0x19, 0x18, 0xc1, 0x14, 0xb1, 0xc7, 0x5e, 0x3f, 0x4f, 0xd8, 0xe4, 0x16, 0x20, 0x4c, 0x0f, 0x26, 0x09, 0xf4, 0x2d, 0x0e, 0xdd, 0x66, 0x72, 0x5f, 0xae, 0xc0, 0x62, 0xc3, 0x5e, + /* (2^214)P */ 0xee, 0xb4, 0xb2, 0xb8, 0x18, 0x2b, 0x46, 0xc0, 0xfb, 0x1a, 0x4d, 0x27, 0x50, 0xd9, 0xc8, 0x7c, 0xd2, 0x02, 0x6b, 0x43, 0x05, 0x71, 0x5f, 0xf2, 0xd3, 0xcc, 0xf9, 0xbf, 0xdc, 0xf8, 0xbb, 0x43, + /* (2^215)P */ 0xdf, 0xe9, 0x39, 0xa0, 0x67, 0x17, 0xad, 0xb6, 0x83, 0x35, 0x9d, 0xf6, 0xa8, 0x4d, 0x71, 0xb0, 0xf5, 0x31, 0x29, 0xb4, 0x18, 0xfa, 0x55, 0x5e, 0x61, 0x09, 0xc6, 0x33, 0x8f, 0x55, 0xd5, 0x4e, + /* (2^216)P */ 0xdd, 0xa5, 0x47, 0xc6, 0x01, 0x79, 0xe3, 0x1f, 0x57, 0xd3, 0x81, 0x80, 0x1f, 0xdf, 0x3d, 0x59, 0xa6, 0xd7, 0x3f, 0x81, 0xfd, 0xa4, 0x49, 0x02, 0x61, 0xaf, 0x9c, 0x4e, 0x27, 0xca, 0xac, 0x69, + /* (2^217)P */ 0xc9, 0x21, 0x07, 0x33, 0xea, 0xa3, 0x7b, 0x04, 0xa0, 0x1e, 0x7e, 0x0e, 0xc2, 0x3f, 0x42, 0x83, 0x60, 0x4a, 0x31, 0x01, 0xaf, 0xc0, 0xf4, 0x1d, 0x27, 0x95, 0x28, 0x89, 0xab, 0x2d, 0xa6, 0x09, + /* (2^218)P */ 0x00, 0xcb, 0xc6, 0x9c, 0xa4, 0x25, 0xb3, 0xa5, 0xb6, 0x6c, 0xb5, 0x54, 0xc6, 0x5d, 0x4b, 0xe9, 0xa0, 0x94, 0xc9, 0xad, 0x79, 0x87, 0xe2, 0x3b, 0xad, 0x4a, 0x3a, 0xba, 0xf8, 0xe8, 0x96, 0x42, + /* (2^219)P */ 0xab, 0x1e, 0x45, 0x1e, 0x76, 0x89, 0x86, 0x32, 0x4a, 0x59, 0x59, 0xff, 0x8b, 0x59, 0x4d, 0x2e, 0x4a, 0x08, 0xa7, 0xd7, 0x53, 0x68, 0xb9, 0x49, 0xa8, 0x20, 0x14, 0x60, 0x19, 0xa3, 0x80, 0x49, + /* (2^220)P */ 0x42, 0x2c, 0x55, 0x2f, 0xe1, 0xb9, 0x65, 0x95, 0x96, 0xfe, 0x00, 0x71, 0xdb, 0x18, 0x53, 0x8a, 0xd7, 0xd0, 0xad, 0x43, 0x4d, 0x0b, 0xc9, 0x05, 0xda, 0x4e, 0x5d, 0x6a, 0xd6, 0x4c, 0x8b, 0x53, + /* (2^221)P */ 0x9f, 0x03, 0x9f, 0xe8, 0xc3, 0x4f, 0xe9, 0xf4, 0x45, 0x80, 0x61, 0x6f, 0xf2, 0x9a, 0x2c, 0x59, 0x50, 0x95, 0x4b, 0xfd, 0xb5, 0x6e, 0xa3, 0x08, 0x19, 0x14, 0xed, 0xc2, 0xf6, 0xfa, 0xff, 0x25, + /* (2^222)P */ 0x54, 0xd3, 0x79, 0xcc, 0x59, 0x44, 0x43, 0x34, 0x6b, 0x47, 0xd5, 0xb1, 0xb4, 0xbf, 0xec, 0xee, 0x99, 0x5d, 0x61, 0x61, 0xa0, 0x34, 0xeb, 0xdd, 0x73, 0xb7, 0x64, 0xeb, 0xcc, 0xce, 0x29, 0x51, + /* (2^223)P */ 0x20, 0x35, 0x99, 0x94, 0x58, 0x21, 0x43, 0xee, 0x3b, 0x0b, 0x4c, 0xf1, 0x7c, 0x9c, 0x2f, 0x77, 0xd5, 0xda, 0xbe, 0x06, 0xe3, 0xfc, 0xe2, 0xd2, 0x97, 0x6a, 0xf0, 0x46, 0xb5, 0x42, 0x5f, 0x71, + /* (2^224)P */ 0x1a, 0x5f, 0x5b, 0xda, 0xce, 0xcd, 0x4e, 0x43, 0xa9, 0x41, 0x97, 0xa4, 0x15, 0x71, 0xa1, 0x0d, 0x2e, 0xad, 0xed, 0x73, 0x7c, 0xd7, 0x0b, 0x68, 0x41, 0x90, 0xdd, 0x4e, 0x35, 0x02, 0x7c, 0x48, + /* (2^225)P */ 0xc4, 0xd9, 0x0e, 0xa7, 0xf3, 0xef, 0xef, 0xb8, 0x02, 0xe3, 0x57, 0xe8, 0xa3, 0x2a, 0xa3, 0x56, 0xa0, 0xa5, 0xa2, 0x48, 0xbd, 0x68, 0x3a, 0xdf, 0x44, 0xc4, 0x76, 0x31, 0xb7, 0x50, 0xf6, 0x07, + /* (2^226)P */ 0xb1, 0xcc, 0xe0, 0x26, 0x16, 0x9b, 0x8b, 0xe3, 0x36, 0xfb, 0x09, 0x8b, 0xc1, 0x53, 0xe0, 0x79, 0x64, 0x49, 0xf9, 0xc9, 0x19, 0x03, 0xd9, 0x56, 0xc4, 0xf5, 0x9f, 0xac, 0xe7, 0x41, 0xa9, 0x1c, + /* (2^227)P */ 0xbb, 0xa0, 0x2f, 0x16, 0x29, 0xdf, 0xc4, 0x49, 0x05, 0x33, 0xb3, 0x82, 0x32, 0xcf, 0x88, 0x84, 0x7d, 0x43, 0xbb, 0xca, 0x14, 0xda, 0xdf, 0x95, 0x86, 0xad, 0xd5, 0x64, 0x82, 0xf7, 0x91, 0x33, + /* (2^228)P */ 0x5d, 0x09, 0xb5, 0xe2, 0x6a, 0xe0, 0x9a, 0x72, 0x46, 0xa9, 0x59, 0x32, 0xd7, 0x58, 0x8a, 0xd5, 0xed, 0x21, 0x39, 0xd1, 0x62, 0x42, 0x83, 0xe9, 0x92, 0xb5, 0x4b, 0xa5, 0xfa, 0xda, 0xfe, 0x27, + /* (2^229)P */ 0xbb, 0x48, 0xad, 0x29, 0xb8, 0xc5, 0x9d, 0xa9, 0x60, 0xe2, 0x9e, 0x49, 0x42, 0x57, 0x02, 0x5f, 0xfd, 0x13, 0x75, 0x5d, 0xcd, 0x8e, 0x2c, 0x80, 0x38, 0xd9, 0x6d, 0x3f, 0xef, 0xb3, 0xce, 0x78, + /* (2^230)P */ 0x94, 0x5d, 0x13, 0x8a, 0x4f, 0xf4, 0x42, 0xc3, 0xa3, 0xdd, 0x8c, 0x82, 0x44, 0xdb, 0x9e, 0x7b, 0xe7, 0xcf, 0x37, 0x05, 0x1a, 0xd1, 0x36, 0x94, 0xc8, 0xb4, 0x1a, 0xec, 0x64, 0xb1, 0x64, 0x50, + /* (2^231)P */ 0xfc, 0xb2, 0x7e, 0xd3, 0xcf, 0xec, 0x20, 0x70, 0xfc, 0x25, 0x0d, 0xd9, 0x3e, 0xea, 0x31, 0x1f, 0x34, 0xbb, 0xa1, 0xdf, 0x7b, 0x0d, 0x93, 0x1b, 0x44, 0x30, 0x11, 0x48, 0x7a, 0x46, 0x44, 0x53, + /* (2^232)P */ 0xfb, 0x6d, 0x5e, 0xf2, 0x70, 0x31, 0x07, 0x70, 0xc8, 0x4c, 0x11, 0x50, 0x1a, 0xdc, 0x85, 0xe3, 0x00, 0x4f, 0xfc, 0xc8, 0x8a, 0x69, 0x48, 0x23, 0xd8, 0x40, 0xdd, 0x84, 0x52, 0xa5, 0x77, 0x2a, + /* (2^233)P */ 0xe4, 0x6c, 0x8c, 0xc9, 0xe0, 0xaf, 0x06, 0xfe, 0xe4, 0xd6, 0xdf, 0xdd, 0x96, 0xdf, 0x35, 0xc2, 0xd3, 0x1e, 0xbf, 0x33, 0x1e, 0xd0, 0x28, 0x14, 0xaf, 0xbd, 0x00, 0x93, 0xec, 0x68, 0x57, 0x78, + /* (2^234)P */ 0x3b, 0xb6, 0xde, 0x91, 0x7a, 0xe5, 0x02, 0x97, 0x80, 0x8b, 0xce, 0xe5, 0xbf, 0xb8, 0xbd, 0x61, 0xac, 0x58, 0x1d, 0x3d, 0x6f, 0x42, 0x5b, 0x64, 0xbc, 0x57, 0xa5, 0x27, 0x22, 0xa8, 0x04, 0x48, + /* (2^235)P */ 0x01, 0x26, 0x4d, 0xb4, 0x8a, 0x04, 0x57, 0x8e, 0x35, 0x69, 0x3a, 0x4b, 0x1a, 0x50, 0xd6, 0x68, 0x93, 0xc2, 0xe1, 0xf9, 0xc3, 0x9e, 0x9c, 0xc3, 0xe2, 0x63, 0xde, 0xd4, 0x57, 0xf2, 0x72, 0x41, + /* (2^236)P */ 0x01, 0x64, 0x0c, 0x33, 0x50, 0xb4, 0x68, 0xd3, 0x91, 0x23, 0x8f, 0x41, 0x17, 0x30, 0x0d, 0x04, 0x0d, 0xd9, 0xb7, 0x90, 0x60, 0xbb, 0x34, 0x2c, 0x1f, 0xd5, 0xdf, 0x8f, 0x22, 0x49, 0xf6, 0x16, + /* (2^237)P */ 0xf5, 0x8e, 0x92, 0x2b, 0x8e, 0x81, 0xa6, 0xbe, 0x72, 0x1e, 0xc1, 0xcd, 0x91, 0xcf, 0x8c, 0xe2, 0xcd, 0x36, 0x7a, 0xe7, 0x68, 0xaa, 0x4a, 0x59, 0x0f, 0xfd, 0x7f, 0x6c, 0x80, 0x34, 0x30, 0x31, + /* (2^238)P */ 0x65, 0xbd, 0x49, 0x22, 0xac, 0x27, 0x9d, 0x8a, 0x12, 0x95, 0x8e, 0x01, 0x64, 0xb4, 0xa3, 0x19, 0xc7, 0x7e, 0xb3, 0x52, 0xf3, 0xcf, 0x6c, 0xc2, 0x21, 0x7b, 0x79, 0x1d, 0x34, 0x68, 0x6f, 0x05, + /* (2^239)P */ 0x27, 0x23, 0xfd, 0x7e, 0x75, 0xd6, 0x79, 0x5e, 0x15, 0xfe, 0x3a, 0x55, 0xb6, 0xbc, 0xbd, 0xfa, 0x60, 0x5a, 0xaf, 0x6e, 0x2c, 0x22, 0xe7, 0xd3, 0x3b, 0x74, 0xae, 0x4d, 0x6d, 0xc7, 0x46, 0x70, + /* (2^240)P */ 0x55, 0x4a, 0x8d, 0xb1, 0x72, 0xe8, 0x0b, 0x66, 0x96, 0x14, 0x4e, 0x57, 0x18, 0x25, 0x99, 0x19, 0xbb, 0xdc, 0x2b, 0x30, 0x3a, 0x05, 0x03, 0xc1, 0x8e, 0x8e, 0x21, 0x0b, 0x80, 0xe9, 0xd8, 0x3e, + /* (2^241)P */ 0x3e, 0xe0, 0x75, 0xfa, 0x39, 0x92, 0x0b, 0x7b, 0x83, 0xc0, 0x33, 0x46, 0x68, 0xfb, 0xe9, 0xef, 0x93, 0x77, 0x1a, 0x39, 0xbe, 0x5f, 0xa3, 0x98, 0x34, 0xfe, 0xd0, 0xe2, 0x0f, 0x51, 0x65, 0x60, + /* (2^242)P */ 0x0c, 0xad, 0xab, 0x48, 0x85, 0x66, 0xcb, 0x55, 0x27, 0xe5, 0x87, 0xda, 0x48, 0x45, 0x58, 0xb4, 0xdd, 0xc1, 0x07, 0x01, 0xea, 0xec, 0x43, 0x2c, 0x35, 0xde, 0x72, 0x93, 0x80, 0x28, 0x60, 0x52, + /* (2^243)P */ 0x1f, 0x3b, 0x21, 0xf9, 0x6a, 0xc5, 0x15, 0x34, 0xdb, 0x98, 0x7e, 0x01, 0x4d, 0x1a, 0xee, 0x5b, 0x9b, 0x70, 0xcf, 0xb5, 0x05, 0xb1, 0xf6, 0x13, 0xb6, 0x9a, 0xb2, 0x82, 0x34, 0x0e, 0xf2, 0x5f, + /* (2^244)P */ 0x90, 0x6c, 0x2e, 0xcc, 0x75, 0x9c, 0xa2, 0x0a, 0x06, 0xe2, 0x70, 0x3a, 0xca, 0x73, 0x7d, 0xfc, 0x15, 0xc5, 0xb5, 0xc4, 0x8f, 0xc3, 0x9f, 0x89, 0x07, 0xc2, 0xff, 0x24, 0xb1, 0x86, 0x03, 0x25, + /* (2^245)P */ 0x56, 0x2b, 0x3d, 0xae, 0xd5, 0x28, 0xea, 0x54, 0xce, 0x60, 0xde, 0xd6, 0x9d, 0x14, 0x13, 0x99, 0xc1, 0xd6, 0x06, 0x8f, 0xc5, 0x4f, 0x69, 0x16, 0xc7, 0x8f, 0x01, 0xeb, 0x75, 0x39, 0xb2, 0x46, + /* (2^246)P */ 0xe2, 0xb4, 0xb7, 0xb4, 0x0f, 0x6a, 0x0a, 0x47, 0xde, 0x53, 0x72, 0x8f, 0x5a, 0x47, 0x92, 0x5d, 0xdb, 0x3a, 0xbd, 0x2f, 0xb5, 0xe5, 0xee, 0xab, 0x68, 0x69, 0x80, 0xa0, 0x01, 0x08, 0xa2, 0x7f, + /* (2^247)P */ 0xd2, 0x14, 0x77, 0x9f, 0xf1, 0xfa, 0xf3, 0x76, 0xc3, 0x60, 0x46, 0x2f, 0xc1, 0x40, 0xe8, 0xb3, 0x4e, 0x74, 0x12, 0xf2, 0x8d, 0xcd, 0xb4, 0x0f, 0xd2, 0x2d, 0x3a, 0x1d, 0x25, 0x5a, 0x06, 0x4b, + /* (2^248)P */ 0x4a, 0xcd, 0x77, 0x3d, 0x38, 0xde, 0xeb, 0x5c, 0xb1, 0x9c, 0x2c, 0x88, 0xdf, 0x39, 0xdf, 0x6a, 0x59, 0xf7, 0x9a, 0xb0, 0x2e, 0x24, 0xdd, 0xa2, 0x22, 0x64, 0x5f, 0x0e, 0xe5, 0xc0, 0x47, 0x31, + /* (2^249)P */ 0xdb, 0x50, 0x13, 0x1d, 0x10, 0xa5, 0x4c, 0x16, 0x62, 0xc9, 0x3f, 0xc3, 0x79, 0x34, 0xd1, 0xf8, 0x08, 0xda, 0xe5, 0x13, 0x4d, 0xce, 0x40, 0xe6, 0xba, 0xf8, 0x61, 0x50, 0xc4, 0xe0, 0xde, 0x4b, + /* (2^250)P */ 0xc9, 0xb1, 0xed, 0xa4, 0xc1, 0x6d, 0xc4, 0xd7, 0x8a, 0xd9, 0x7f, 0x43, 0xb6, 0xd7, 0x14, 0x55, 0x0b, 0xc0, 0xa1, 0xb2, 0x6b, 0x2f, 0x94, 0x58, 0x0e, 0x71, 0x70, 0x1d, 0xab, 0xb2, 0xff, 0x2d, + /* (2^251)P */ 0x68, 0x6d, 0x8b, 0xc1, 0x2f, 0xcf, 0xdf, 0xcc, 0x67, 0x61, 0x80, 0xb7, 0xa8, 0xcb, 0xeb, 0xa8, 0xe3, 0x37, 0x29, 0x5e, 0xf9, 0x97, 0x06, 0x98, 0x8c, 0x6e, 0x12, 0xd0, 0x1c, 0xba, 0xfb, 0x02, + /* (2^252)P */ 0x65, 0x45, 0xff, 0xad, 0x60, 0xc3, 0x98, 0xcb, 0x19, 0x15, 0xdb, 0x4b, 0xd2, 0x01, 0x71, 0x44, 0xd5, 0x15, 0xfb, 0x75, 0x74, 0xc8, 0xc4, 0x98, 0x7d, 0xa2, 0x22, 0x6e, 0x6d, 0xc7, 0xf8, 0x05, + /* (2^253)P */ 0x94, 0xf4, 0xb9, 0xfe, 0xdf, 0xe5, 0x69, 0xab, 0x75, 0x6b, 0x40, 0x18, 0x9d, 0xc7, 0x09, 0xae, 0x1d, 0x2d, 0xa4, 0x94, 0xfb, 0x45, 0x9b, 0x19, 0x84, 0xfa, 0x2a, 0xae, 0xeb, 0x0a, 0x71, 0x79, + /* (2^254)P */ 0xdf, 0xd2, 0x34, 0xf3, 0xa7, 0xed, 0xad, 0xa6, 0xb4, 0x57, 0x2a, 0xaf, 0x51, 0x9c, 0xde, 0x7b, 0xa8, 0xea, 0xdc, 0x86, 0x4f, 0xc6, 0x8f, 0xa9, 0x7b, 0xd0, 0x0e, 0xc2, 0x35, 0x03, 0xbe, 0x6b, + /* (2^255)P */ 0x44, 0x43, 0x98, 0x53, 0xbe, 0xdc, 0x7f, 0x66, 0xa8, 0x49, 0x59, 0x00, 0x1c, 0xbc, 0x72, 0x07, 0x8e, 0xd6, 0xbe, 0x4e, 0x9f, 0xa4, 0x07, 0xba, 0xbf, 0x30, 0xdf, 0xba, 0x85, 0xb0, 0xa7, 0x1f, +} diff --git a/src/circl/dh/x25519/testdata/rfc7748_kat_test.json b/src/circl/dh/x25519/testdata/rfc7748_kat_test.json new file mode 100644 index 00000000000..c77f8658977 --- /dev/null +++ b/src/circl/dh/x25519/testdata/rfc7748_kat_test.json @@ -0,0 +1,32 @@ +[ + { + "input": "e6db6867583030db3594c1a424b15f7c726624ec26b3353b10a903a6d0ab1c4c", + "output": "c3da55379de9c6908e94ea4df28d084f32eccf03491c71f754b4075577a28552", + "scalar": "a546e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449ac4" + }, + { + "input": "e5210f12786811d3f4b7959d0538ae2c31dbe7106fc03c3efc4cd549c715a493", + "output": "95cbde9476e8907d7aade45cb4b873f88b595a68799fa152e6f8f7647aac7957", + "scalar": "4b66e9d4d1b4673c5ad22691957d6af5c11b6421e0ea01d42ca4169e7918ba0d" + }, + { + "input": "0900000000000000000000000000000000000000000000000000000000000000", + "output": "8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4e6a", + "scalar": "77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a" + }, + { + "input": "0900000000000000000000000000000000000000000000000000000000000000", + "output": "de9edb7d7b7dc1b4d35b61c2ece435373f8343c85b78674dadfc7e146f882b4f", + "scalar": "5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb" + }, + { + "input": "de9edb7d7b7dc1b4d35b61c2ece435373f8343c85b78674dadfc7e146f882b4f", + "output": "4a5d9d5ba4ce2de1728e3bf480350f25e07e21c947d19e3376f09b3c1e161742", + "scalar": "77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a" + }, + { + "input": "8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4e6a", + "output": "4a5d9d5ba4ce2de1728e3bf480350f25e07e21c947d19e3376f09b3c1e161742", + "scalar": "5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb" + } +] diff --git a/src/circl/dh/x25519/testdata/rfc7748_times_test.json b/src/circl/dh/x25519/testdata/rfc7748_times_test.json new file mode 100644 index 00000000000..7c26881886e --- /dev/null +++ b/src/circl/dh/x25519/testdata/rfc7748_times_test.json @@ -0,0 +1,14 @@ +[ + { + "times": 1, + "key": "422c8e7a6227d7bca1350b3e2bb7279f7897b87bb6854b783c60e80311ae3079" + }, + { + "times": 1000, + "key": "684cf59ba83309552800ef566f2f4d3c1c3887c49360e3875f2eb94d99532c51" + }, + { + "times": 1000000, + "key": "7c3911e0ab2586fd864497297e575e6f3bc601c0883c30df5f4dd2d24f665424" + } +] diff --git a/src/circl/dh/x25519/testdata/wycheproof_kat.json b/src/circl/dh/x25519/testdata/wycheproof_kat.json new file mode 100644 index 00000000000..b80b2bc7707 --- /dev/null +++ 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"shared":"54c9a1ed95e546d27822a360931dda60a1df049da6f904253c0612bbdc087476", + "result":"acceptable", + "flags":[ + + ] + }, + { + "tcId":56, + "comment":"public key >= p", + "curve":"curve25519", + "public":"daffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", + "private":"f8f707b7999b18cb0d6b96124f2045972ca274bfc154ad0c87038c24c6d0d4b2", + "shared":"cc1f40d743cdc2230e1043daba8b75e810f1fbab7f255269bd9ebb29e6bf494f", + "result":"acceptable", + "flags":[ + + ] + }, + { + "tcId":57, + "comment":"public key >= p", + "curve":"curve25519", + "public":"dbffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", + "private":"a034f684fa631e1a348118c1ce4c98231f2d9eec9ba5365b4a05d69a785b0796", + "shared":"54998ee43a5b007bf499f078e736524400a8b5c7e9b9b43771748c7cdf880412", + "result":"acceptable", + "flags":[ + + ] + }, + { + "tcId":58, + "comment":"public key >= p", + "curve":"curve25519", + "public":"dcffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", + "private":"30b6c6a0f2ffa680768f992ba89e152d5bc9893d38c9119be4f767bfab6e0ca5", + "shared":"ead9b38efdd723637934e55ab717a7ae09eb86a21dc36a3feeb88b759e391e09", + "result":"acceptable", + "flags":[ + + ] + }, + { + "tcId":59, + "comment":"public key >= p", + "curve":"curve25519", + "public":"eaffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", + "private":"901b9dcf881e01e027575035d40b43bdc1c5242e030847495b0c7286469b6591", + "shared":"602ff40789b54b41805915fe2a6221f07a50ffc2c3fc94cf61f13d7904e88e0e", + "result":"acceptable", + "flags":[ + + ] + }, + { + "tcId":60, + "comment":"public key >= p", + "curve":"curve25519", + "public":"ebffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", + "private":"8046677c28fd82c9a1bdb71a1a1a34faba1225e2507fe3f54d10bd5b0d865f8e", + "shared":"e00ae8b143471247ba24f12c885536c3cb981b58e1e56b2baf35c12ae1f79c26", + "result":"acceptable", + "flags":[ + + ] + }, + { + "tcId":61, + "comment":"public key >= p", + "curve":"curve25519", + "public":"efffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", + "private":"602f7e2f68a846b82cc269b1d48e939886ae54fd636c1fe074d710127d472491", + "shared":"98cb9b50dd3fc2b0d4f2d2bf7c5cfdd10c8fcd31fc40af1ad44f47c131376362", + "result":"acceptable", + "flags":[ + + ] + }, + { + "tcId":62, + "comment":"public key >= p", + "curve":"curve25519", + "public":"f0ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", + "private":"60887b3dc72443026ebedbbbb70665f42b87add1440e7768fbd7e8e2ce5f639d", + "shared":"38d6304c4a7e6d9f7959334fb5245bd2c754525d4c91db950206926234c1f633", + "result":"acceptable", + "flags":[ + + ] + }, + { + "tcId":63, + "comment":"public key >= p", + "curve":"curve25519", + "public":"f1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", + "private":"78d31dfa854497d72d8def8a1b7fb006cec2d8c4924647c93814ae56faeda495", + "shared":"786cd54996f014a5a031ec14db812ed08355061fdb5de680a800ac521f318e23", + "result":"acceptable", + "flags":[ + + ] + }, + { + "tcId":64, + "comment":"public key >= p", + "curve":"curve25519", + "public":"ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", + "private":"c04c5baefa8302ddded6a4bb957761b4eb97aefa4fc3b8043085f96a5659b3a5", + "shared":"29ae8bc73e9b10a08b4f681c43c3e0ac1a171d31b38f1a48efba29ae639ea134", + "result":"acceptable", + "flags":[ + + ] + }, + { + "tcId":65, + "comment":"RFC 7748", + "curve":"curve25519", + "public":"e6db6867583030db3594c1a424b15f7c726624ec26b3353b10a903a6d0ab1c4c", + "private":"a046e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449a44", + "shared":"c3da55379de9c6908e94ea4df28d084f32eccf03491c71f754b4075577a28552", + "result":"valid", + "flags":[ + + ] + }, + { + "tcId":66, + "comment":"RFC 7748", + "curve":"curve25519", + "public":"e5210f12786811d3f4b7959d0538ae2c31dbe7106fc03c3efc4cd549c715a413", + "private":"4866e9d4d1b4673c5ad22691957d6af5c11b6421e0ea01d42ca4169e7918ba4d", + "shared":"95cbde9476e8907d7aade45cb4b873f88b595a68799fa152e6f8f7647aac7957", + "result":"valid", + "flags":[ + + ] + }, + { + "tcId":67, + "comment":"edge case for shared secret", + "curve":"curve25519", + "public":"0ab4e76380d84dde4f6833c58f2a9fb8f83bb0169b172be4b6e0592887741a36", + "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", + "shared":"0200000000000000000000000000000000000000000000000000000000000000", + "result":"acceptable", + "flags":[ + "Twist" + ] + }, + { + "tcId":68, + "comment":"edge case for shared secret", + "curve":"curve25519", + "public":"89e10d5701b4337d2d032181538b1064bd4084401ceca1fd12663a1959388000", + "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", + "shared":"0900000000000000000000000000000000000000000000000000000000000000", + "result":"valid", + "flags":[ + + ] + }, + { + "tcId":69, + "comment":"edge case for shared secret", + "curve":"curve25519", + "public":"2b55d3aa4a8f80c8c0b2ae5f933e85af49beac36c2fa7394bab76c8933f8f81d", + "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", + "shared":"1000000000000000000000000000000000000000000000000000000000000000", + "result":"valid", + "flags":[ + + ] + }, + { + "tcId":70, + "comment":"edge case for shared secret", + "curve":"curve25519", + "public":"63e5b1fe9601fe84385d8866b0421262f78fbfa5aff9585e626679b18547d959", + "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", + "shared":"feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff3f", + "result":"acceptable", + "flags":[ + "Twist" + ] + }, + { + "tcId":71, + "comment":"edge case for shared secret", + "curve":"curve25519", + "public":"e428f3dac17809f827a522ce32355058d07369364aa78902ee10139b9f9dd653", + "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", + "shared":"fcffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff3f", + "result":"valid", + "flags":[ + + ] + }, + { + "tcId":72, + "comment":"edge case for shared secret", + "curve":"curve25519", + "public":"b3b50e3ed3a407b95de942ef74575b5ab8a10c09ee103544d60bdfed8138ab2b", + "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", + "shared":"f9ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff3f", + "result":"acceptable", + "flags":[ + "Twist" + ] + }, + { + "tcId":73, + "comment":"edge case for shared secret", + "curve":"curve25519", + "public":"213fffe93d5ea8cd242e462844029922c43c77c9e3e42f562f485d24c501a20b", + "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", + "shared":"f3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff3f", + "result":"valid", + "flags":[ + + ] + }, + { + "tcId":74, + "comment":"edge case for shared secret", + "curve":"curve25519", + "public":"91b232a178b3cd530932441e6139418f72172292f1da4c1834fc5ebfefb51e3f", + "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", + "shared":"ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff03", + "result":"valid", + "flags":[ + + ] + }, + { + "tcId":75, + "comment":"edge case for shared secret", + "curve":"curve25519", + "public":"045c6e11c5d332556c7822fe94ebf89b56a3878dc27ca079103058849fabcb4f", + "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", + "shared":"e5ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", + "result":"acceptable", + "flags":[ + "Twist" + ] + }, + { + "tcId":76, + "comment":"edge case for shared secret", + "curve":"curve25519", + "public":"1ca2190b71163539063c35773bda0c9c928e9136f0620aeb093f099197b7f74e", + "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", + "shared":"e3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", + "result":"acceptable", + "flags":[ + "Twist" + ] + }, + { + "tcId":77, + "comment":"edge case for shared secret", + "curve":"curve25519", + "public":"f76e9010ac33c5043b2d3b76a842171000c4916222e9e85897a0aec7f6350b3c", + "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", + "shared":"ddffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", + "result":"valid", + "flags":[ + + ] + }, + { + "tcId":78, + "comment":"edge case for shared secret", + "curve":"curve25519", + "public":"bb72688d8f8aa7a39cd6060cd5c8093cdec6fe341937c3886a99346cd07faa55", + "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", + "shared":"dbffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", + "result":"acceptable", + "flags":[ + "Twist" + ] + }, + { + "tcId":79, + "comment":"edge case for shared secret", + "curve":"curve25519", + "public":"88fddea193391c6a5933ef9b71901549447205aae9da928a6b91a352ba10f41f", + "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", + "shared":"0000000000000000000000000000000000000000000000000000000000000002", + "result":"acceptable", + "flags":[ + "Twist" + ] + }, + { + "tcId":80, + "comment":"edge case for shared secret", + "curve":"curve25519", + "public":"303b392f153116cad9cc682a00ccc44c95ff0d3bbe568beb6c4e739bafdc2c68", + "private":"a0a4f130b98a5be4b1cedb7cb85584a3520e142d474dc9ccb909a073a976bf63", + "shared":"0000000000000000000000000000000000000000000000000000000000008000", + "result":"acceptable", + "flags":[ + "Twist" + ] + }, + { + "tcId":81, + "comment":"checking for overflow", + "curve":"curve25519", + "public":"fd300aeb40e1fa582518412b49b208a7842b1e1f056a040178ea4141534f652d", + "private":"c81724704000b26d31703cc97e3a378d56fad8219361c88cca8bd7c5719b12b2", + "shared":"b734105dc257585d73b566ccb76f062795ccbec89128e52b02f3e59639f13c46", + "result":"valid", + "flags":[ + + ] + }, + { + "tcId":82, + "comment":"checking for overflow", + "curve":"curve25519", + "public":"c8ef79b514d7682677bc7931e06ee5c27c9b392b4ae9484473f554e6678ecc2e", + "private":"c81724704000b26d31703cc97e3a378d56fad8219361c88cca8bd7c5719b12b2", + "shared":"647a46b6fc3f40d62141ee3cee706b4d7a9271593a7b143e8e2e2279883e4550", + "result":"valid", + "flags":[ + + ] + }, + { + "tcId":83, + "comment":"checking for overflow", + "curve":"curve25519", + "public":"64aeac2504144861532b7bbcb6c87d67dd4c1f07ebc2e06effb95aecc6170b2c", + "private":"c81724704000b26d31703cc97e3a378d56fad8219361c88cca8bd7c5719b12b2", + "shared":"4ff03d5fb43cd8657a3cf37c138cadcecce509e4eba089d0ef40b4e4fb946155", + "result":"valid", + "flags":[ + + ] + }, + { + "tcId":84, + "comment":"checking for overflow", + "curve":"curve25519", + "public":"bf68e35e9bdb7eee1b50570221860f5dcdad8acbab031b14974cc49013c49831", + "private":"c81724704000b26d31703cc97e3a378d56fad8219361c88cca8bd7c5719b12b2", + "shared":"21cee52efdbc812e1d021a4af1e1d8bc4db3c400e4d2a2c56a3926db4d99c65b", + "result":"valid", + "flags":[ + + ] + }, + { + "tcId":85, + "comment":"checking for overflow", + "curve":"curve25519", + "public":"5347c491331a64b43ddc683034e677f53dc32b52a52a577c15a83bf298e99f19", + "private":"c81724704000b26d31703cc97e3a378d56fad8219361c88cca8bd7c5719b12b2", + "shared":"18cb89e4e20c0c2bd324305245266c9327690bbe79acb88f5b8fb3f74eca3e52", + "result":"valid", + "flags":[ + + ] + }, + { + "tcId":86, + "comment":"private key == -1 (mod order)", + "curve":"curve25519", + "public":"258e04523b8d253ee65719fc6906c657192d80717edc828fa0af21686e2faa75", + "private":"a023cdd083ef5bb82f10d62e59e15a6800000000000000000000000000000050", + "shared":"258e04523b8d253ee65719fc6906c657192d80717edc828fa0af21686e2faa75", + "result":"valid", + "flags":[ + + ] + }, + { + "tcId":87, + "comment":"private key == 1 (mod order) on twist", + "curve":"curve25519", + "public":"2eae5ec3dd494e9f2d37d258f873a8e6e9d0dbd1e383ef64d98bb91b3e0be035", + "private":"58083dd261ad91eff952322ec824c682ffffffffffffffffffffffffffffff5f", + "shared":"2eae5ec3dd494e9f2d37d258f873a8e6e9d0dbd1e383ef64d98bb91b3e0be035", + "result":"acceptable", + "flags":[ + + ] + } +] diff --git a/src/circl/dh/x448/curve.go b/src/circl/dh/x448/curve.go new file mode 100644 index 00000000000..b7582d732cb --- /dev/null +++ b/src/circl/dh/x448/curve.go @@ -0,0 +1,104 @@ +package x448 + +import ( + fp "circl/math/fp448" +) + +// ladderJoye calculates a fixed-point multiplication with the generator point. +// The algorithm is the right-to-left Joye's ladder as described +// in "How to precompute a ladder" in SAC'2017. +func ladderJoye(k *Key) { + w := [5]fp.Elt{} // [mu,x1,z1,x2,z2] order must be preserved. + w[1] = fp.Elt{ // x1 = S + 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + } + fp.SetOne(&w[2]) // z1 = 1 + w[3] = fp.Elt{ // x2 = G-S + 0x20, 0x27, 0x9d, 0xc9, 0x7d, 0x19, 0xb1, 0xac, + 0xf8, 0xba, 0x69, 0x1c, 0xff, 0x33, 0xac, 0x23, + 0x51, 0x1b, 0xce, 0x3a, 0x64, 0x65, 0xbd, 0xf1, + 0x23, 0xf8, 0xc1, 0x84, 0x9d, 0x45, 0x54, 0x29, + 0x67, 0xb9, 0x81, 0x1c, 0x03, 0xd1, 0xcd, 0xda, + 0x7b, 0xeb, 0xff, 0x1a, 0x88, 0x03, 0xcf, 0x3a, + 0x42, 0x44, 0x32, 0x01, 0x25, 0xb7, 0xfa, 0xf0, + } + fp.SetOne(&w[4]) // z2 = 1 + + const n = 448 + const h = 2 + swap := uint(1) + for s := 0; s < n-h; s++ { + i := (s + h) / 8 + j := (s + h) % 8 + bit := uint((k[i] >> uint(j)) & 1) + copy(w[0][:], tableGenerator[s*Size:(s+1)*Size]) + diffAdd(&w, swap^bit) + swap = bit + } + for s := 0; s < h; s++ { + double(&w[1], &w[2]) + } + toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) +} + +// ladderMontgomery calculates a generic scalar point multiplication +// The algorithm implemented is the left-to-right Montgomery's ladder. +func ladderMontgomery(k, xP *Key) { + w := [5]fp.Elt{} // [x1, x2, z2, x3, z3] order must be preserved. + w[0] = *(*fp.Elt)(xP) // x1 = xP + fp.SetOne(&w[1]) // x2 = 1 + w[3] = *(*fp.Elt)(xP) // x3 = xP + fp.SetOne(&w[4]) // z3 = 1 + + move := uint(0) + for s := 448 - 1; s >= 0; s-- { + i := s / 8 + j := s % 8 + bit := uint((k[i] >> uint(j)) & 1) + ladderStep(&w, move^bit) + move = bit + } + toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) +} + +func toAffine(k *[fp.Size]byte, x, z *fp.Elt) { + fp.Inv(z, z) + fp.Mul(x, x, z) + _ = fp.ToBytes(k[:], x) +} + +var lowOrderPoints = [3]fp.Elt{ + { /* (0,_,1) point of order 2 on Curve448 */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + { /* (1,_,1) a point of order 4 on the twist of Curve448 */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + { /* (-1,_,1) point of order 4 on Curve448 */ + 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + }, +} diff --git a/src/circl/dh/x448/curve_amd64.go b/src/circl/dh/x448/curve_amd64.go new file mode 100644 index 00000000000..4bdc230e331 --- /dev/null +++ b/src/circl/dh/x448/curve_amd64.go @@ -0,0 +1,30 @@ +// +build amd64,!purego + +package x448 + +import ( + "internal/cpu" + + fp "circl/math/fp448" +) + +var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX + +var _ = hasBmi2Adx + +func double(x, z *fp.Elt) { doubleAmd64(x, z) } +func diffAdd(w *[5]fp.Elt, b uint) { diffAddAmd64(w, b) } +func ladderStep(w *[5]fp.Elt, b uint) { ladderStepAmd64(w, b) } +func mulA24(z, x *fp.Elt) { mulA24Amd64(z, x) } + +//go:noescape +func doubleAmd64(x, z *fp.Elt) + +//go:noescape +func diffAddAmd64(w *[5]fp.Elt, b uint) + +//go:noescape +func ladderStepAmd64(w *[5]fp.Elt, b uint) + +//go:noescape +func mulA24Amd64(z, x *fp.Elt) diff --git a/src/circl/dh/x448/curve_amd64.h b/src/circl/dh/x448/curve_amd64.h new file mode 100644 index 00000000000..8c1ae4d0fbb --- /dev/null +++ b/src/circl/dh/x448/curve_amd64.h @@ -0,0 +1,111 @@ +#define ladderStepLeg \ + addSub(x2,z2) \ + addSub(x3,z3) \ + integerMulLeg(b0,x2,z3) \ + integerMulLeg(b1,x3,z2) \ + reduceFromDoubleLeg(t0,b0) \ + reduceFromDoubleLeg(t1,b1) \ + addSub(t0,t1) \ + cselect(x2,x3,regMove) \ + cselect(z2,z3,regMove) \ + integerSqrLeg(b0,t0) \ + integerSqrLeg(b1,t1) \ + reduceFromDoubleLeg(x3,b0) \ + reduceFromDoubleLeg(z3,b1) \ + integerMulLeg(b0,x1,z3) \ + reduceFromDoubleLeg(z3,b0) \ + integerSqrLeg(b0,x2) \ + integerSqrLeg(b1,z2) \ + reduceFromDoubleLeg(x2,b0) \ + reduceFromDoubleLeg(z2,b1) \ + subtraction(t0,x2,z2) \ + multiplyA24Leg(t1,t0) \ + additionLeg(t1,t1,z2) \ + integerMulLeg(b0,x2,z2) \ + integerMulLeg(b1,t0,t1) \ + reduceFromDoubleLeg(x2,b0) \ + reduceFromDoubleLeg(z2,b1) + +#define ladderStepBmi2Adx \ + addSub(x2,z2) \ + addSub(x3,z3) \ + integerMulAdx(b0,x2,z3) \ + integerMulAdx(b1,x3,z2) \ + reduceFromDoubleAdx(t0,b0) \ + reduceFromDoubleAdx(t1,b1) \ + addSub(t0,t1) \ + cselect(x2,x3,regMove) \ + cselect(z2,z3,regMove) \ + integerSqrAdx(b0,t0) \ + integerSqrAdx(b1,t1) \ + reduceFromDoubleAdx(x3,b0) \ + reduceFromDoubleAdx(z3,b1) \ + integerMulAdx(b0,x1,z3) \ + reduceFromDoubleAdx(z3,b0) \ + integerSqrAdx(b0,x2) \ + integerSqrAdx(b1,z2) \ + reduceFromDoubleAdx(x2,b0) \ + reduceFromDoubleAdx(z2,b1) \ + subtraction(t0,x2,z2) \ + multiplyA24Adx(t1,t0) \ + additionAdx(t1,t1,z2) \ + integerMulAdx(b0,x2,z2) \ + integerMulAdx(b1,t0,t1) \ + reduceFromDoubleAdx(x2,b0) \ + reduceFromDoubleAdx(z2,b1) + +#define difAddLeg \ + addSub(x1,z1) \ + integerMulLeg(b0,z1,ui) \ + reduceFromDoubleLeg(z1,b0) \ + addSub(x1,z1) \ + integerSqrLeg(b0,x1) \ + integerSqrLeg(b1,z1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) \ + integerMulLeg(b0,x1,z2) \ + integerMulLeg(b1,z1,x2) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) + +#define difAddBmi2Adx \ + addSub(x1,z1) \ + integerMulAdx(b0,z1,ui) \ + reduceFromDoubleAdx(z1,b0) \ + addSub(x1,z1) \ + integerSqrAdx(b0,x1) \ + integerSqrAdx(b1,z1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) \ + integerMulAdx(b0,x1,z2) \ + integerMulAdx(b1,z1,x2) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) + +#define doubleLeg \ + addSub(x1,z1) \ + integerSqrLeg(b0,x1) \ + integerSqrLeg(b1,z1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) \ + subtraction(t0,x1,z1) \ + multiplyA24Leg(t1,t0) \ + additionLeg(t1,t1,z1) \ + integerMulLeg(b0,x1,z1) \ + integerMulLeg(b1,t0,t1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) + +#define doubleBmi2Adx \ + addSub(x1,z1) \ + integerSqrAdx(b0,x1) \ + integerSqrAdx(b1,z1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) \ + subtraction(t0,x1,z1) \ + multiplyA24Adx(t1,t0) \ + additionAdx(t1,t1,z1) \ + integerMulAdx(b0,x1,z1) \ + integerMulAdx(b1,t0,t1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) diff --git a/src/circl/dh/x448/curve_amd64.s b/src/circl/dh/x448/curve_amd64.s new file mode 100644 index 00000000000..810aa9e6481 --- /dev/null +++ b/src/circl/dh/x448/curve_amd64.s @@ -0,0 +1,193 @@ +// +build amd64 + +#include "textflag.h" + +// Depends on circl/math/fp448 package +#include "../../math/fp448/fp_amd64.h" +#include "curve_amd64.h" + +// CTE_A24 is (A+2)/4 from Curve448 +#define CTE_A24 39082 + +#define Size 56 + +// multiplyA24Leg multiplies x times CTE_A24 and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64, cmov, adx +#define multiplyA24Leg(z,x) \ + MOVQ $CTE_A24, R15; \ + MOVQ 0+x, AX; MULQ R15; MOVQ AX, R8; ;;;;;;;;;;;; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R15; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R15; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R15; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; \ + MOVQ 32+x, AX; MULQ R15; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; \ + MOVQ 40+x, AX; MULQ R15; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX, R14; \ + MOVQ 48+x, AX; MULQ R15; ADDQ AX, R14; ADCQ $0, DX; \ + MOVQ DX, AX; \ + SHLQ $32, AX; \ + ADDQ DX, R8; MOVQ $0, DX; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ AX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + ADCQ $0, DX; \ + MOVQ DX, AX; \ + SHLQ $32, AX; \ + ADDQ DX, R8; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ AX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + MOVQ R8, 0+z; \ + MOVQ R9, 8+z; \ + MOVQ R10, 16+z; \ + MOVQ R11, 24+z; \ + MOVQ R12, 32+z; \ + MOVQ R13, 40+z; \ + MOVQ R14, 48+z; + +// multiplyA24Adx multiplies x times CTE_A24 and stores in z +// Uses: AX, DX, R8-R14, FLAGS +// Instr: x86_64, bmi2 +#define multiplyA24Adx(z,x) \ + MOVQ $CTE_A24, DX; \ + MULXQ 0+x, R8, R9; \ + MULXQ 8+x, AX, R10; ADDQ AX, R9; \ + MULXQ 16+x, AX, R11; ADCQ AX, R10; \ + MULXQ 24+x, AX, R12; ADCQ AX, R11; \ + MULXQ 32+x, AX, R13; ADCQ AX, R12; \ + MULXQ 40+x, AX, R14; ADCQ AX, R13; \ + MULXQ 48+x, AX, DX; ADCQ AX, R14; \ + ;;;;;;;;;;;;;;;;;;;; ADCQ $0, DX; \ + MOVQ DX, AX; \ + SHLQ $32, AX; \ + ADDQ DX, R8; MOVQ $0, DX; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ AX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + ADCQ $0, DX; \ + MOVQ DX, AX; \ + SHLQ $32, AX; \ + ADDQ DX, R8; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ AX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + MOVQ R8, 0+z; \ + MOVQ R9, 8+z; \ + MOVQ R10, 16+z; \ + MOVQ R11, 24+z; \ + MOVQ R12, 32+z; \ + MOVQ R13, 40+z; \ + MOVQ R14, 48+z; + +#define mulA24Legacy \ + multiplyA24Leg(0(DI),0(SI)) +#define mulA24Bmi2Adx \ + multiplyA24Adx(0(DI),0(SI)) + +// func mulA24Amd64(z, x *fp448.Elt) +TEXT ·mulA24Amd64(SB),NOSPLIT,$0-16 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + CHECK_BMI2ADX(LMA24, mulA24Legacy, mulA24Bmi2Adx) + +// func ladderStepAmd64(w *[5]fp448.Elt, b uint) +// ladderStepAmd64 calculates a point addition and doubling as follows: +// (x2,z2) = 2*(x2,z2) and (x3,z3) = (x2,z2)+(x3,z3) using as a difference (x1,-). +// w = {x1,x2,z2,x3,z4} are five fp255.Elt of 56 bytes. +// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and +// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·ladderStepAmd64(SB),NOSPLIT,$336-16 + // Parameters + #define regWork DI + #define regMove SI + #define x1 0*Size(regWork) + #define x2 1*Size(regWork) + #define z2 2*Size(regWork) + #define x3 3*Size(regWork) + #define z3 4*Size(regWork) + // Local variables + #define t0 0*Size(SP) + #define t1 1*Size(SP) + #define b0 2*Size(SP) + #define b1 4*Size(SP) + MOVQ w+0(FP), regWork + MOVQ b+8(FP), regMove + CHECK_BMI2ADX(LLADSTEP, ladderStepLeg, ladderStepBmi2Adx) + #undef regWork + #undef regMove + #undef x1 + #undef x2 + #undef z2 + #undef x3 + #undef z3 + #undef t0 + #undef t1 + #undef b0 + #undef b1 + +// func diffAddAmd64(work *[5]fp.Elt, swap uint) +// diffAddAmd64 calculates a differential point addition using a precomputed point. +// (x1,z1) = (x1,z1)+(mu) using a difference point (x2,z2) +// work = {mu,x1,z1,x2,z2} are five fp448.Elt of 56 bytes, and +// stack = (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +// This is Equation 7 at https://eprint.iacr.org/2017/264. +TEXT ·diffAddAmd64(SB),NOSPLIT,$224-16 + // Parameters + #define regWork DI + #define regSwap SI + #define ui 0*Size(regWork) + #define x1 1*Size(regWork) + #define z1 2*Size(regWork) + #define x2 3*Size(regWork) + #define z2 4*Size(regWork) + // Local variables + #define b0 0*Size(SP) + #define b1 2*Size(SP) + MOVQ w+0(FP), regWork + MOVQ b+8(FP), regSwap + cswap(x1,x2,regSwap) + cswap(z1,z2,regSwap) + CHECK_BMI2ADX(LDIFADD, difAddLeg, difAddBmi2Adx) + #undef regWork + #undef regSwap + #undef ui + #undef x1 + #undef z1 + #undef x2 + #undef z2 + #undef b0 + #undef b1 + +// func doubleAmd64(x, z *fp448.Elt) +// doubleAmd64 calculates a point doubling (x1,z1) = 2*(x1,z1). +// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and +// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·doubleAmd64(SB),NOSPLIT,$336-16 + // Parameters + #define x1 0(DI) + #define z1 0(SI) + // Local variables + #define t0 0*Size(SP) + #define t1 1*Size(SP) + #define b0 2*Size(SP) + #define b1 4*Size(SP) + MOVQ x+0(FP), DI + MOVQ z+8(FP), SI + CHECK_BMI2ADX(LDOUB,doubleLeg,doubleBmi2Adx) + #undef x1 + #undef z1 + #undef t0 + #undef t1 + #undef b0 + #undef b1 diff --git a/src/circl/dh/x448/curve_generic.go b/src/circl/dh/x448/curve_generic.go new file mode 100644 index 00000000000..af9d2388ee1 --- /dev/null +++ b/src/circl/dh/x448/curve_generic.go @@ -0,0 +1,97 @@ +package x448 + +import ( + "encoding/binary" + "math/bits" + + "circl/math/fp448" +) + +func doubleGeneric(x, z *fp448.Elt) { + t0, t1 := &fp448.Elt{}, &fp448.Elt{} + fp448.AddSub(x, z) + fp448.Sqr(x, x) + fp448.Sqr(z, z) + fp448.Sub(t0, x, z) + mulA24Generic(t1, t0) + fp448.Add(t1, t1, z) + fp448.Mul(x, x, z) + fp448.Mul(z, t0, t1) +} +func diffAddGeneric(w *[5]fp448.Elt, b uint) { + mu, x1, z1, x2, z2 := &w[0], &w[1], &w[2], &w[3], &w[4] + fp448.Cswap(x1, x2, b) + fp448.Cswap(z1, z2, b) + fp448.AddSub(x1, z1) + fp448.Mul(z1, z1, mu) + fp448.AddSub(x1, z1) + fp448.Sqr(x1, x1) + fp448.Sqr(z1, z1) + fp448.Mul(x1, x1, z2) + fp448.Mul(z1, z1, x2) +} +func ladderStepGeneric(w *[5]fp448.Elt, b uint) { + x1, x2, z2, x3, z3 := &w[0], &w[1], &w[2], &w[3], &w[4] + t0 := &fp448.Elt{} + t1 := &fp448.Elt{} + fp448.AddSub(x2, z2) + fp448.AddSub(x3, z3) + fp448.Mul(t0, x2, z3) + fp448.Mul(t1, x3, z2) + fp448.AddSub(t0, t1) + fp448.Cmov(x2, x3, b) + fp448.Cmov(z2, z3, b) + fp448.Sqr(x3, t0) + fp448.Sqr(z3, t1) + fp448.Mul(z3, x1, z3) + fp448.Sqr(x2, x2) + fp448.Sqr(z2, z2) + fp448.Sub(t0, x2, z2) + mulA24Generic(t1, t0) + fp448.Add(t1, t1, z2) + fp448.Mul(x2, x2, z2) + fp448.Mul(z2, t0, t1) +} +func mulA24Generic(z, x *fp448.Elt) { + const A24 = 39082 + const n = 8 + var xx [7]uint64 + for i := range xx { + xx[i] = binary.LittleEndian.Uint64(x[i*n : (i+1)*n]) + } + h0, l0 := bits.Mul64(xx[0], A24) + h1, l1 := bits.Mul64(xx[1], A24) + h2, l2 := bits.Mul64(xx[2], A24) + h3, l3 := bits.Mul64(xx[3], A24) + h4, l4 := bits.Mul64(xx[4], A24) + h5, l5 := bits.Mul64(xx[5], A24) + h6, l6 := bits.Mul64(xx[6], A24) + + l1, c0 := bits.Add64(h0, l1, 0) + l2, c1 := bits.Add64(h1, l2, c0) + l3, c2 := bits.Add64(h2, l3, c1) + l4, c3 := bits.Add64(h3, l4, c2) + l5, c4 := bits.Add64(h4, l5, c3) + l6, c5 := bits.Add64(h5, l6, c4) + l7, _ := bits.Add64(h6, 0, c5) + + l0, c0 = bits.Add64(l0, l7, 0) + l1, c1 = bits.Add64(l1, 0, c0) + l2, c2 = bits.Add64(l2, 0, c1) + l3, c3 = bits.Add64(l3, l7<<32, c2) + l4, c4 = bits.Add64(l4, 0, c3) + l5, c5 = bits.Add64(l5, 0, c4) + l6, l7 = bits.Add64(l6, 0, c5) + + xx[0], c0 = bits.Add64(l0, l7, 0) + xx[1], c1 = bits.Add64(l1, 0, c0) + xx[2], c2 = bits.Add64(l2, 0, c1) + xx[3], c3 = bits.Add64(l3, l7<<32, c2) + xx[4], c4 = bits.Add64(l4, 0, c3) + xx[5], c5 = bits.Add64(l5, 0, c4) + xx[6], _ = bits.Add64(l6, 0, c5) + + for i := range xx { + binary.LittleEndian.PutUint64(z[i*n:(i+1)*n], xx[i]) + } +} diff --git a/src/circl/dh/x448/curve_noasm.go b/src/circl/dh/x448/curve_noasm.go new file mode 100644 index 00000000000..cd4bd55c804 --- /dev/null +++ b/src/circl/dh/x448/curve_noasm.go @@ -0,0 +1,10 @@ +// +build !amd64 purego + +package x448 + +import fp "circl/math/fp448" + +func double(x, z *fp.Elt) { doubleGeneric(x, z) } +func diffAdd(w *[5]fp.Elt, b uint) { diffAddGeneric(w, b) } +func ladderStep(w *[5]fp.Elt, b uint) { ladderStepGeneric(w, b) } +func mulA24(z, x *fp.Elt) { mulA24Generic(z, x) } diff --git a/src/circl/dh/x448/curve_test.go b/src/circl/dh/x448/curve_test.go new file mode 100644 index 00000000000..84aef014b26 --- /dev/null +++ b/src/circl/dh/x448/curve_test.go @@ -0,0 +1,214 @@ +package x448 + +import ( + "crypto/rand" + "math/big" + "testing" + + "circl/internal/conv" + "circl/internal/test" + fp "circl/math/fp448" +) + +func getModulus() *big.Int { + p := big.NewInt(1) + p.Lsh(p, 224) + p.Sub(p, new(big.Int).SetInt64(1)) + p.Lsh(p, 224) + p.Sub(p, new(big.Int).SetInt64(1)) + return p +} + +func doubleBig(x1, z1, p *big.Int) { + // Montgomery point doubling in projective (X:Z) coordinates. + A24 := big.NewInt(39082) + A, B, C := big.NewInt(0), big.NewInt(0), big.NewInt(0) + A.Add(x1, z1).Mod(A, p) + B.Sub(x1, z1).Mod(B, p) + A.Mul(A, A) + B.Mul(B, B) + C.Sub(A, B) + x1.Mul(A, B).Mod(x1, p) + z1.Mul(C, A24).Add(z1, B).Mul(z1, C).Mod(z1, p) +} + +// Equation 7 at https://eprint.iacr.org/2017/264 +func diffAddBig(work [5]*big.Int, p *big.Int, b uint) { + mu, x1, z1, x2, z2 := work[0], work[1], work[2], work[3], work[4] + A, B := big.NewInt(0), big.NewInt(0) + if b != 0 { + t := new(big.Int) + t.Set(x1) + x1.Set(x2) + x2.Set(t) + t.Set(z1) + z1.Set(z2) + z2.Set(t) + } + A.Add(x1, z1) + B.Sub(x1, z1) + B.Mul(B, mu).Mod(B, p) + x1.Add(A, B).Mod(x1, p) + z1.Sub(A, B).Mod(z1, p) + x1.Mul(x1, x1).Mul(x1, z2).Mod(x1, p) + z1.Mul(z1, z1).Mul(z1, x2).Mod(z1, p) + mu.Mod(mu, p) + x2.Mod(x2, p) + z2.Mod(z2, p) +} + +func ladderStepBig(work [5]*big.Int, p *big.Int, b uint) { + A24 := big.NewInt(39082) + x1 := work[0] + x2, z2 := work[1], work[2] + x3, z3 := work[3], work[4] + A, B, C, D := big.NewInt(0), big.NewInt(0), big.NewInt(0), big.NewInt(0) + DA, CB, E := big.NewInt(0), big.NewInt(0), big.NewInt(0) + A.Add(x2, z2).Mod(A, p) + B.Sub(x2, z2).Mod(B, p) + C.Add(x3, z3).Mod(C, p) + D.Sub(x3, z3).Mod(D, p) + DA.Mul(D, A).Mod(DA, p) + CB.Mul(C, B).Mod(CB, p) + if b != 0 { + t := new(big.Int) + t.Set(A) + A.Set(C) + C.Set(t) + t.Set(B) + B.Set(D) + D.Set(t) + } + AA := A.Mul(A, A).Mod(A, p) + BB := B.Mul(B, B).Mod(B, p) + E.Sub(AA, BB) + x1.Mod(x1, p) + x2.Mul(AA, BB).Mod(x2, p) + z2.Mul(E, A24).Add(z2, BB).Mul(z2, E).Mod(z2, p) + x3.Add(DA, CB) + z3.Sub(DA, CB) + x3.Mul(x3, x3).Mod(x3, p) + z3.Mul(z3, z3).Mul(z3, x1).Mod(z3, p) +} + +type tDouble func(x, z *fp.Elt) +type tDiffAdd func(w *[5]fp.Elt, b uint) +type tLadderStep func(w *[5]fp.Elt, b uint) +type tMulA24 func(z, x *fp.Elt) + +func TestGeneric(t *testing.T) { + testDouble(t, doubleGeneric) + testDiffAdd(t, diffAddGeneric) + testLadderStep(t, ladderStepGeneric) + testMulA24(t, mulA24Generic) +} + +func TestNative(t *testing.T) { + testDouble(t, double) + testDiffAdd(t, diffAdd) + testLadderStep(t, ladderStep) + testMulA24(t, mulA24) +} + +func testMulA24(t *testing.T, f tMulA24) { + const numTests = 1 << 9 + var x, z fp.Elt + p := getModulus() + A24 := big.NewInt(39082) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + bigX := conv.BytesLe2BigInt(x[:]) + f(&z, &x) + got := conv.BytesLe2BigInt(z[:]) + got.Mod(got, p) + + want := bigX.Mul(bigX, A24).Mod(bigX, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } +} + +func testDouble(t *testing.T, f tDouble) { + const numTests = 1 << 9 + var x, z fp.Elt + p := getModulus() + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(z[:]) + + bigX := conv.BytesLe2BigInt(x[:]) + bigZ := conv.BytesLe2BigInt(z[:]) + f(&x, &z) + got0 := conv.BytesLe2BigInt(x[:]) + got1 := conv.BytesLe2BigInt(z[:]) + got0.Mod(got0, p) + got1.Mod(got1, p) + + doubleBig(bigX, bigZ, p) + want0 := bigX + want1 := bigZ + + if got0.Cmp(want0) != 0 { + test.ReportError(t, got0, want0, x, z) + } + if got1.Cmp(want1) != 0 { + test.ReportError(t, got1, want1, x, z) + } + } +} + +func testDiffAdd(t *testing.T, f tDiffAdd) { + const numTests = 1 << 9 + var w [5]fp.Elt + bigWork := [5]*big.Int{} + p := getModulus() + for i := 0; i < numTests; i++ { + for j := range w { + _, _ = rand.Read(w[j][:]) + bigWork[j] = conv.BytesLe2BigInt(w[j][:]) + } + b := uint(w[0][0] & 1) + + f(&w, b) + + diffAddBig(bigWork, p, b) + + for j := range bigWork { + got := conv.BytesLe2BigInt(w[j][:]) + got.Mod(got, p) + want := bigWork[j] + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, w, b) + } + } + } +} + +func testLadderStep(t *testing.T, f tLadderStep) { + const numTests = 1 << 9 + var w [5]fp.Elt + bigWork := [5]*big.Int{} + p := getModulus() + for i := 0; i < numTests; i++ { + for j := range w { + _, _ = rand.Read(w[j][:]) + bigWork[j] = conv.BytesLe2BigInt(w[j][:]) + } + b := uint(w[0][0] & 1) + + f(&w, b) + + ladderStepBig(bigWork, p, b) + + for j := range bigWork { + got := conv.BytesLe2BigInt(w[j][:]) + got.Mod(got, p) + want := bigWork[j] + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, w, b) + } + } + } +} diff --git a/src/circl/dh/x448/doc.go b/src/circl/dh/x448/doc.go new file mode 100644 index 00000000000..8b9279cba2e --- /dev/null +++ b/src/circl/dh/x448/doc.go @@ -0,0 +1,20 @@ +/* +Package x448 provides Diffie-Hellman functions as specified in RFC-7748. + +Validation of public keys. + +The Diffie-Hellman function, as described in RFC-7748 [1], works for any +public key. However, if a different protocol requires contributory +behaviour [2,3], then the public keys must be validated against low-order +points [3,4]. To do that, the Shared function performs this validation +internally and returns false when the public key is invalid (i.e., it +is a low-order point). + +References: + - [1] RFC7748 by Langley, Hamburg, Turner (https://rfc-editor.org/rfc/rfc7748.txt) + - [2] Curve25519 by Bernstein (https://cr.yp.to/ecdh.html) + - [3] Bernstein (https://cr.yp.to/ecdh.html#validate) + - [4] Cremers&Jackson (https://eprint.iacr.org/2019/526) + +*/ +package x448 diff --git a/src/circl/dh/x448/key.go b/src/circl/dh/x448/key.go new file mode 100644 index 00000000000..3c7967dd381 --- /dev/null +++ b/src/circl/dh/x448/key.go @@ -0,0 +1,46 @@ +package x448 + +import ( + "crypto/subtle" + + fp "circl/math/fp448" +) + +// Size is the length in bytes of a X448 key. +const Size = 56 + +// Key represents a X448 key. +type Key [Size]byte + +func (k *Key) clamp(in *Key) *Key { + *k = *in + k[0] &= 252 + k[55] |= 128 + return k +} + +// isValidPubKey verifies if the public key is not a low-order point. +func (k *Key) isValidPubKey() bool { + fp.Modp((*fp.Elt)(k)) + isLowOrder := false + for _, P := range lowOrderPoints { + isLowOrder = isLowOrder || subtle.ConstantTimeCompare(P[:], k[:]) != 0 + } + return !isLowOrder +} + +// KeyGen obtains a public key given a secret key. +func KeyGen(public, secret *Key) { + ladderJoye(public.clamp(secret)) +} + +// Shared calculates Alice's shared key from Alice's secret key and Bob's +// public key returning true on success. A failure case happens when the public +// key is a low-order point, thus the shared key is all-zeros and the function +// returns false. +func Shared(shared, secret, public *Key) bool { + validPk := *public + ok := validPk.isValidPubKey() + ladderMontgomery(shared.clamp(secret), &validPk) + return ok +} diff --git a/src/circl/dh/x448/key_test.go b/src/circl/dh/x448/key_test.go new file mode 100644 index 00000000000..370d73b35c5 --- /dev/null +++ b/src/circl/dh/x448/key_test.go @@ -0,0 +1,156 @@ +package x448 + +import ( + "crypto/rand" + "encoding/hex" + "encoding/json" + "flag" + "fmt" + "io" + "io/ioutil" + "os" + "testing" + + "circl/internal/test" +) + +func hexStr2Key(k *Key, s string) { + b, err := hex.DecodeString(s) + if err != nil { + panic("Can't convert string to key") + } + copy(k[:], b) +} + +// Indicates whether long tests should be run +var runLongTest = flag.Bool("long", false, "runs longer tests") + +type katVector struct { + Public string `json:"input"` + Shared string `json:"output"` + Private string `json:"scalar"` +} + +func TestRFC7748Kat(t *testing.T) { + const nameFile = "testdata/rfc7748_kat_test.json" + var kat []katVector + + jsonFile, err := os.Open(nameFile) + if err != nil { + t.Fatalf("File %v can not be opened. Error: %v", nameFile, err) + } + defer jsonFile.Close() + input, _ := ioutil.ReadAll(jsonFile) + + err = json.Unmarshal(input, &kat) + if err != nil { + t.Fatalf("File %v can not be loaded. Error: %v", nameFile, err) + } + var priv, pub, got, want Key + for _, v := range kat { + hexStr2Key(&pub, v.Public) + hexStr2Key(&priv, v.Private) + Shared(&got, &priv, &pub) + hexStr2Key(&want, v.Shared) + if got != want { + test.ReportError(t, got, want, v) + } + } +} + +type katTimes struct { + Times uint32 `json:"times"` + Key string `json:"key"` +} + +func TestRFC7748Times(t *testing.T) { + const nameFile = "testdata/rfc7748_times_test.json" + jsonFile, err := os.Open(nameFile) + if err != nil { + t.Fatalf("File %v can not be opened. Error: %v", nameFile, err) + } + defer jsonFile.Close() + input, _ := ioutil.ReadAll(jsonFile) + + var kat []katTimes + err = json.Unmarshal(input, &kat) + if err != nil { + t.Fatalf("File %v can not be loaded. Error: %v", nameFile, err) + } + var got, want Key + for _, v := range kat { + if !*runLongTest && v.Times == uint32(1000000) { + t.Log("Skipped one long test, add -long flag to run longer tests") + continue + } + u := Key{5} + k := u + r := u + for i := uint32(0); i < v.Times; i++ { + Shared(&r, &k, &u) + u = k + k = r + } + got = k + hexStr2Key(&want, v.Key) + + if got != want { + test.ReportError(t, got, want, v.Times) + } + } +} + +func TestBase(t *testing.T) { + testTimes := 1 << 10 + var got, want, secret Key + gen := Key{5} + for i := 0; i < testTimes; i++ { + _, _ = io.ReadFull(rand.Reader, secret[:]) + KeyGen(&got, &secret) + Shared(&want, &secret, &gen) + if got != want { + test.ReportError(t, got, want, secret) + } + } +} + +func BenchmarkX448(b *testing.B) { + var x, y, z Key + _, _ = io.ReadFull(rand.Reader, x[:]) + _, _ = io.ReadFull(rand.Reader, y[:]) + _, _ = io.ReadFull(rand.Reader, z[:]) + + b.Run("KeyGen", func(b *testing.B) { + for i := 0; i < b.N; i++ { + KeyGen(&x, &y) + } + }) + b.Run("Shared", func(b *testing.B) { + for i := 0; i < b.N; i++ { + Shared(&z, &x, &y) + } + }) +} + +func Example_x448() { + var AliceSecret, BobSecret, + AlicePublic, BobPublic, + AliceShared, BobShared Key + + // Generating Alice's secret and public keys + _, _ = io.ReadFull(rand.Reader, AliceSecret[:]) + KeyGen(&AlicePublic, &AliceSecret) + + // Generating Bob's secret and public keys + _, _ = io.ReadFull(rand.Reader, BobSecret[:]) + KeyGen(&BobPublic, &BobSecret) + + // Deriving Alice's shared key + okA := Shared(&AliceShared, &AliceSecret, &BobPublic) + + // Deriving Bob's shared key + okB := Shared(&BobShared, &BobSecret, &AlicePublic) + + fmt.Println(AliceShared == BobShared && okA && okB) + // Output: true +} diff --git a/src/circl/dh/x448/table.go b/src/circl/dh/x448/table.go new file mode 100644 index 00000000000..3d55292e454 --- /dev/null +++ b/src/circl/dh/x448/table.go @@ -0,0 +1,458 @@ +package x448 + +import fp "circl/math/fp448" + +// tableGenerator contains the set of points: +// t[i] = (xi+1)/(xi-1), +// where (xi,yi) = 2^iG and G is the generator point +// Size = (448)*(448/8) = 25088 bytes. +var tableGenerator = [448 * fp.Size]byte{ + /* (2^ 0)P */ 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, + /* (2^ 1)P */ 0x37, 0xfa, 0xaa, 0x0d, 0x86, 0xa6, 0x24, 0xe9, 0x6c, 0x95, 0x08, 0x34, 0xba, 0x1a, 0x81, 0x3a, 0xae, 0x01, 0xa5, 0xa7, 0x05, 0x85, 0x96, 0x00, 0x06, 0x5a, 0xd7, 0xff, 0xee, 0x8e, 0x8f, 0x94, 0xd2, 0xdc, 0xd7, 0xfc, 0xe7, 0xe5, 0x99, 0x1d, 0x05, 0x46, 0x43, 0xe8, 0xbc, 0x12, 0xb7, 0xeb, 0x30, 0x5e, 0x7a, 0x85, 0x68, 0xed, 0x9d, 0x28, + /* (2^ 2)P */ 0xf1, 0x7d, 0x08, 0x2b, 0x32, 0x4a, 0x62, 0x80, 0x36, 0xe7, 0xa4, 0x76, 0x5a, 0x2a, 0x1e, 0xf7, 0x9e, 0x3c, 0x40, 0x46, 0x9a, 0x1b, 0x61, 0xc1, 0xbf, 0x1a, 0x1b, 0xae, 0x91, 0x80, 0xa3, 0x76, 0x6c, 0xd4, 0x8f, 0xa4, 0xee, 0x26, 0x39, 0x23, 0xa4, 0x80, 0xf4, 0x66, 0x92, 0xe4, 0xe1, 0x18, 0x76, 0xc5, 0xe2, 0x19, 0x87, 0xd5, 0xc3, 0xe8, + /* (2^ 3)P */ 0xfb, 0xc9, 0xf0, 0x07, 0xf2, 0x93, 0xd8, 0x50, 0x36, 0xed, 0xfb, 0xbd, 0xb2, 0xd3, 0xfc, 0xdf, 0xd5, 0x2a, 0x6e, 0x26, 0x09, 0xce, 0xd4, 0x07, 0x64, 0x9f, 0x40, 0x74, 0xad, 0x98, 0x2f, 0x1c, 0xb6, 0xdc, 0x2d, 0x42, 0xff, 0xbf, 0x97, 0xd8, 0xdb, 0xef, 0x99, 0xca, 0x73, 0x99, 0x1a, 0x04, 0x3b, 0x56, 0x2c, 0x1f, 0x87, 0x9d, 0x9f, 0x03, + /* (2^ 4)P */ 0x4c, 0x35, 0x97, 0xf7, 0x81, 0x2c, 0x84, 0xa6, 0xe0, 0xcb, 0xce, 0x37, 0x4c, 0x21, 0x1c, 0x67, 0xfa, 0xab, 0x18, 0x4d, 0xef, 0xd0, 0xf0, 0x44, 0xa9, 0xfb, 0xc0, 0x8e, 0xda, 0x57, 0xa1, 0xd8, 0xeb, 0x87, 0xf4, 0x17, 0xea, 0x66, 0x0f, 0x16, 0xea, 0xcd, 0x5f, 0x3e, 0x88, 0xea, 0x09, 0x68, 0x40, 0xdf, 0x43, 0xcc, 0x54, 0x61, 0x58, 0xaa, + /* (2^ 5)P */ 0x8d, 0xe7, 0x59, 0xd7, 0x5e, 0x63, 0x37, 0xa7, 0x3f, 0xd1, 0x49, 0x85, 0x01, 0xdd, 0x5e, 0xb3, 0xe6, 0x29, 0xcb, 0x25, 0x93, 0xdd, 0x08, 0x96, 0x83, 0x52, 0x76, 0x85, 0xf5, 0x5d, 0x02, 0xbf, 0xe9, 0x6d, 0x15, 0x27, 0xc1, 0x09, 0xd1, 0x14, 0x4d, 0x6e, 0xe8, 0xaf, 0x59, 0x58, 0x34, 0x9d, 0x2a, 0x99, 0x85, 0x26, 0xbe, 0x4b, 0x1e, 0xb9, + /* (2^ 6)P */ 0x8d, 0xce, 0x94, 0xe2, 0x18, 0x56, 0x0d, 0x82, 0x8e, 0xdf, 0x85, 0x01, 0x8f, 0x93, 0x3c, 0xc6, 0xbd, 0x61, 0xfb, 0xf4, 0x22, 0xc5, 0x16, 0x87, 0xd1, 0xb1, 0x9e, 0x09, 0xc5, 0x83, 0x2e, 0x4a, 0x07, 0x88, 0xee, 0xe0, 0x29, 0x8d, 0x2e, 0x1f, 0x88, 0xad, 0xfd, 0x18, 0x93, 0xb7, 0xed, 0x42, 0x86, 0x78, 0xf0, 0xb8, 0x70, 0xbe, 0x01, 0x67, + /* (2^ 7)P */ 0xdf, 0x62, 0x2d, 0x94, 0xc7, 0x35, 0x23, 0xda, 0x27, 0xbb, 0x2b, 0xdb, 0x30, 0x80, 0x68, 0x16, 0xa3, 0xae, 0xd7, 0xd2, 0xa7, 0x7c, 0xbf, 0x6a, 0x1d, 0x83, 0xde, 0x96, 0x0a, 0x43, 0xb6, 0x30, 0x37, 0xd6, 0xee, 0x63, 0x59, 0x9a, 0xbf, 0xa3, 0x30, 0x6c, 0xaf, 0x0c, 0xee, 0x3d, 0xcb, 0x35, 0x4b, 0x55, 0x5f, 0x84, 0x85, 0xcb, 0x4f, 0x1e, + /* (2^ 8)P */ 0x9d, 0x04, 0x68, 0x89, 0xa4, 0xa9, 0x0d, 0x87, 0xc1, 0x70, 0xf1, 0xeb, 0xfb, 0x47, 0x0a, 0xf0, 0xde, 0x67, 0xb7, 0x94, 0xcd, 0x36, 0x43, 0xa5, 0x49, 0x43, 0x67, 0xc3, 0xee, 0x3c, 0x6b, 0xec, 0xd0, 0x1a, 0xf4, 0xad, 0xef, 0x06, 0x4a, 0xe8, 0x46, 0x24, 0xd7, 0x93, 0xbf, 0xf0, 0xe3, 0x81, 0x61, 0xec, 0xea, 0x64, 0xfe, 0x67, 0xeb, 0xc7, + /* (2^ 9)P */ 0x95, 0x45, 0x79, 0xcf, 0x2c, 0xfd, 0x9b, 0xfe, 0x84, 0x46, 0x4b, 0x8f, 0xa1, 0xcf, 0xc3, 0x04, 0x94, 0x78, 0xdb, 0xc9, 0xa6, 0x01, 0x75, 0xa4, 0xb4, 0x93, 0x72, 0x43, 0xa7, 0x7d, 0xda, 0x31, 0x38, 0x54, 0xab, 0x4e, 0x3f, 0x89, 0xa6, 0xab, 0x57, 0xc0, 0x16, 0x65, 0xdb, 0x92, 0x96, 0xe4, 0xc8, 0xae, 0xe7, 0x4c, 0x7a, 0xeb, 0xbb, 0x5a, + /* (2^ 10)P */ 0xbe, 0xfe, 0x86, 0xc3, 0x97, 0xe0, 0x6a, 0x18, 0x20, 0x21, 0xca, 0x22, 0x55, 0xa1, 0xeb, 0xf5, 0x74, 0xe5, 0xc9, 0x59, 0xa7, 0x92, 0x65, 0x15, 0x08, 0x71, 0xd1, 0x09, 0x7e, 0x83, 0xfc, 0xbc, 0x5a, 0x93, 0x38, 0x0d, 0x43, 0x42, 0xfd, 0x76, 0x30, 0xe8, 0x63, 0x60, 0x09, 0x8d, 0x6c, 0xd3, 0xf8, 0x56, 0x3d, 0x68, 0x47, 0xab, 0xa0, 0x1d, + /* (2^ 11)P */ 0x38, 0x50, 0x1c, 0xb1, 0xac, 0x88, 0x8f, 0x38, 0xe3, 0x69, 0xe6, 0xfc, 0x4f, 0x8f, 0xe1, 0x9b, 0xb1, 0x1a, 0x09, 0x39, 0x19, 0xdf, 0xcd, 0x98, 0x7b, 0x64, 0x42, 0xf6, 0x11, 0xea, 0xc7, 0xe8, 0x92, 0x65, 0x00, 0x2c, 0x75, 0xb5, 0x94, 0x1e, 0x5b, 0xa6, 0x66, 0x81, 0x77, 0xf3, 0x39, 0x94, 0xac, 0xbd, 0xe4, 0x2a, 0x66, 0x84, 0x9c, 0x60, + /* (2^ 12)P */ 0xb5, 0xb6, 0xd9, 0x03, 0x67, 0xa4, 0xa8, 0x0a, 0x4a, 0x2b, 0x9d, 0xfa, 0x13, 0xe1, 0x99, 0x25, 0x4a, 0x5c, 0x67, 0xb9, 0xb2, 0xb7, 0xdd, 0x1e, 0xaf, 0xeb, 0x63, 0x41, 0xb6, 0xb9, 0xa0, 0x87, 0x0a, 0xe0, 0x06, 0x07, 0xaa, 0x97, 0xf8, 0xf9, 0x38, 0x4f, 0xdf, 0x0c, 0x40, 0x7c, 0xc3, 0x98, 0xa9, 0x74, 0xf1, 0x5d, 0xda, 0xd1, 0xc0, 0x0a, + /* (2^ 13)P */ 0xf2, 0x0a, 0xab, 0xab, 0x94, 0x50, 0xf0, 0xa3, 0x6f, 0xc6, 0x66, 0xba, 0xa6, 0xdc, 0x44, 0xdd, 0xd6, 0x08, 0xf4, 0xd3, 0xed, 0xb1, 0x40, 0x93, 0xee, 0xf6, 0xb8, 0x8e, 0xb4, 0x7c, 0xb9, 0x82, 0xc9, 0x9d, 0x45, 0x3b, 0x8e, 0x10, 0xcb, 0x70, 0x1e, 0xba, 0x3c, 0x62, 0x50, 0xda, 0xa9, 0x93, 0xb5, 0xd7, 0xd0, 0x6f, 0x29, 0x52, 0x95, 0xae, + /* (2^ 14)P */ 0x14, 0x68, 0x69, 0x23, 0xa8, 0x44, 0x87, 0x9e, 0x22, 0x91, 0xe8, 0x92, 0xdf, 0xf7, 0xae, 0xba, 0x1c, 0x96, 0xe1, 0xc3, 0x94, 0xed, 0x6c, 0x95, 0xae, 0x96, 0xa7, 0x15, 0x9f, 0xf1, 0x17, 0x11, 0x92, 0x42, 0xd5, 0xcd, 0x18, 0xe7, 0xa9, 0xb5, 0x2f, 0xcd, 0xde, 0x6c, 0xc9, 0x7d, 0xfc, 0x7e, 0xbd, 0x7f, 0x10, 0x3d, 0x01, 0x00, 0x8d, 0x95, + /* (2^ 15)P */ 0x3b, 0x76, 0x72, 0xae, 0xaf, 0x84, 0xf2, 0xf7, 0xd1, 0x6d, 0x13, 0x9c, 0x47, 0xe1, 0xb7, 0xa3, 0x19, 0x16, 0xee, 0x75, 0x45, 0xf6, 0x1a, 0x7b, 0x78, 0x49, 0x79, 0x05, 0x86, 0xf0, 0x7f, 0x9f, 0xfc, 0xc4, 0xbd, 0x86, 0xf3, 0x41, 0xa7, 0xfe, 0x01, 0xd5, 0x67, 0x16, 0x10, 0x5b, 0xa5, 0x16, 0xf3, 0x7f, 0x60, 0xce, 0xd2, 0x0c, 0x8e, 0x4b, + /* (2^ 16)P */ 0x4a, 0x07, 0x99, 0x4a, 0x0f, 0x74, 0x91, 0x14, 0x68, 0xb9, 0x48, 0xb7, 0x44, 0x77, 0x9b, 0x4a, 0xe0, 0x68, 0x0e, 0x43, 0x4d, 0x98, 0x98, 0xbf, 0xa8, 0x3a, 0xb7, 0x6d, 0x2a, 0x9a, 0x77, 0x5f, 0x62, 0xf5, 0x6b, 0x4a, 0xb7, 0x7d, 0xe5, 0x09, 0x6b, 0xc0, 0x8b, 0x9c, 0x88, 0x37, 0x33, 0xf2, 0x41, 0xac, 0x22, 0x1f, 0xcf, 0x3b, 0x82, 0x34, + /* (2^ 17)P */ 0x00, 0xc3, 0x78, 0x42, 0x32, 0x2e, 0xdc, 0xda, 0xb1, 0x96, 0x21, 0xa4, 0xe4, 0xbb, 0xe9, 0x9d, 0xbb, 0x0f, 0x93, 0xed, 0x26, 0x3d, 0xb5, 0xdb, 0x94, 0x31, 0x37, 0x07, 0xa2, 0xb2, 0xd5, 0x99, 0x0d, 0x93, 0xe1, 0xce, 0x3f, 0x0b, 0x96, 0x82, 0x47, 0xfe, 0x60, 0x6f, 0x8f, 0x61, 0x88, 0xd7, 0x05, 0x95, 0x0b, 0x46, 0x06, 0xb7, 0x32, 0x06, + /* (2^ 18)P */ 0x44, 0xf5, 0x34, 0xdf, 0x2f, 0x9c, 0x5d, 0x9f, 0x53, 0x5c, 0x42, 0x8f, 0xc9, 0xdc, 0xd8, 0x40, 0xa2, 0xe7, 0x6a, 0x4a, 0x05, 0xf7, 0x86, 0x77, 0x2b, 0xae, 0x37, 0xed, 0x48, 0xfb, 0xf7, 0x62, 0x7c, 0x17, 0x59, 0x92, 0x41, 0x61, 0x93, 0x38, 0x30, 0xd1, 0xef, 0x54, 0x54, 0x03, 0x17, 0x57, 0x91, 0x15, 0x11, 0x33, 0xb5, 0xfa, 0xfb, 0x17, + /* (2^ 19)P */ 0x29, 0xbb, 0xd4, 0xb4, 0x9c, 0xf1, 0x72, 0x94, 0xce, 0x6a, 0x29, 0xa8, 0x89, 0x18, 0x19, 0xf7, 0xb7, 0xcc, 0xee, 0x9a, 0x02, 0xe3, 0xc0, 0xb1, 0xe0, 0xee, 0x83, 0x78, 0xb4, 0x9e, 0x07, 0x87, 0xdf, 0xb0, 0x82, 0x26, 0x4e, 0xa4, 0x0c, 0x33, 0xaf, 0x40, 0x59, 0xb6, 0xdd, 0x52, 0x45, 0xf0, 0xb4, 0xf6, 0xe8, 0x4e, 0x4e, 0x79, 0x1a, 0x5d, + /* (2^ 20)P */ 0x27, 0x33, 0x4d, 0x4c, 0x6b, 0x4f, 0x75, 0xb1, 0xbc, 0x1f, 0xab, 0x5b, 0x2b, 0xf0, 0x1c, 0x57, 0x86, 0xdd, 0xfd, 0x60, 0xb0, 0x8c, 0xe7, 0x9a, 0xe5, 0x5c, 0xeb, 0x11, 0x3a, 0xda, 0x22, 0x25, 0x99, 0x06, 0x8d, 0xf4, 0xaf, 0x29, 0x7a, 0xc9, 0xe5, 0xd2, 0x16, 0x9e, 0xd4, 0x63, 0x1d, 0x64, 0xa6, 0x47, 0x96, 0x37, 0x6f, 0x93, 0x2c, 0xcc, + /* (2^ 21)P */ 0xc1, 0x94, 0x74, 0x86, 0x75, 0xf2, 0x91, 0x58, 0x23, 0x85, 0x63, 0x76, 0x54, 0xc7, 0xb4, 0x8c, 0xbc, 0x4e, 0xc4, 0xa7, 0xba, 0xa0, 0x55, 0x26, 0x71, 0xd5, 0x33, 0x72, 0xc9, 0xad, 0x1e, 0xf9, 0x5d, 0x78, 0x70, 0x93, 0x4e, 0x85, 0xfc, 0x39, 0x06, 0x73, 0x76, 0xff, 0xe8, 0x64, 0x69, 0x42, 0x45, 0xb2, 0x69, 0xb5, 0x32, 0xe7, 0x2c, 0xde, + /* (2^ 22)P */ 0xde, 0x16, 0xd8, 0x33, 0x49, 0x32, 0xe9, 0x0e, 0x3a, 0x60, 0xee, 0x2e, 0x24, 0x75, 0xe3, 0x9c, 0x92, 0x07, 0xdb, 0xad, 0x92, 0xf5, 0x11, 0xdf, 0xdb, 0xb0, 0x17, 0x5c, 0xd6, 0x1a, 0x70, 0x00, 0xb7, 0xe2, 0x18, 0xec, 0xdc, 0xc2, 0x02, 0x93, 0xb3, 0xc8, 0x3f, 0x4f, 0x1b, 0x96, 0xe6, 0x33, 0x8c, 0xfb, 0xcc, 0xa5, 0x4e, 0xe8, 0xe7, 0x11, + /* (2^ 23)P */ 0x05, 0x7a, 0x74, 0x52, 0xf8, 0xdf, 0x0d, 0x7c, 0x6a, 0x1a, 0x4e, 0x9a, 0x02, 0x1d, 0xae, 0x77, 0xf8, 0x8e, 0xf9, 0xa2, 0x38, 0x54, 0x50, 0xb2, 0x2c, 0x08, 0x9d, 0x9b, 0x9f, 0xfb, 0x2b, 0x06, 0xde, 0x9d, 0xc2, 0x03, 0x0b, 0x22, 0x2b, 0x10, 0x5b, 0x3a, 0x73, 0x29, 0x8e, 0x3e, 0x37, 0x08, 0x2c, 0x3b, 0xf8, 0x80, 0xc1, 0x66, 0x1e, 0x98, + /* (2^ 24)P */ 0xd8, 0xd6, 0x3e, 0xcd, 0x63, 0x8c, 0x2b, 0x41, 0x81, 0xc0, 0x0c, 0x06, 0x87, 0xd6, 0xe7, 0x92, 0xfe, 0xf1, 0x0c, 0x4a, 0x84, 0x5b, 0xaf, 0x40, 0x53, 0x6f, 0x60, 0xd6, 0x6b, 0x76, 0x4b, 0xc2, 0xad, 0xc9, 0xb6, 0xb6, 0x6a, 0xa2, 0xb3, 0xf5, 0xf5, 0xc2, 0x55, 0x83, 0xb2, 0xd3, 0xe9, 0x41, 0x6c, 0x63, 0x51, 0xb8, 0x81, 0x74, 0xc8, 0x2c, + /* (2^ 25)P */ 0xb2, 0xaf, 0x1c, 0xee, 0x07, 0xb0, 0x58, 0xa8, 0x2c, 0x6a, 0xc9, 0x2d, 0x62, 0x28, 0x75, 0x0c, 0x40, 0xb6, 0x11, 0x33, 0x96, 0x80, 0x28, 0x6d, 0xd5, 0x9e, 0x87, 0x90, 0x01, 0x66, 0x1d, 0x1c, 0xf8, 0xb4, 0x92, 0xac, 0x38, 0x18, 0x05, 0xc2, 0x4c, 0x4b, 0x54, 0x7d, 0x80, 0x46, 0x87, 0x2d, 0x99, 0x8e, 0x70, 0x80, 0x69, 0x71, 0x8b, 0xed, + /* (2^ 26)P */ 0x37, 0xa7, 0x6b, 0x71, 0x36, 0x75, 0x8e, 0xff, 0x0f, 0x42, 0xda, 0x5a, 0x46, 0xa6, 0x97, 0x79, 0x7e, 0x30, 0xb3, 0x8f, 0xc7, 0x3a, 0xa0, 0xcb, 0x1d, 0x9c, 0x78, 0x77, 0x36, 0xc2, 0xe7, 0xf4, 0x2f, 0x29, 0x07, 0xb1, 0x07, 0xfd, 0xed, 0x1b, 0x39, 0x77, 0x06, 0x38, 0x77, 0x0f, 0x50, 0x31, 0x12, 0xbf, 0x92, 0xbf, 0x72, 0x79, 0x54, 0xa9, + /* (2^ 27)P */ 0xbd, 0x4d, 0x46, 0x6b, 0x1a, 0x80, 0x46, 0x2d, 0xed, 0xfd, 0x64, 0x6d, 0x94, 0xbc, 0x4a, 0x6e, 0x0c, 0x12, 0xf6, 0x12, 0xab, 0x54, 0x88, 0xd3, 0x85, 0xac, 0x51, 0xae, 0x6f, 0xca, 0xc4, 0xb7, 0xec, 0x22, 0x54, 0x6d, 0x80, 0xb2, 0x1c, 0x63, 0x33, 0x76, 0x6b, 0x8e, 0x6d, 0x59, 0xcd, 0x73, 0x92, 0x5f, 0xff, 0xad, 0x10, 0x35, 0x70, 0x5f, + /* (2^ 28)P */ 0xb3, 0x84, 0xde, 0xc8, 0x04, 0x43, 0x63, 0xfa, 0x29, 0xd9, 0xf0, 0x69, 0x65, 0x5a, 0x0c, 0xe8, 0x2e, 0x0b, 0xfe, 0xb0, 0x7a, 0x42, 0xb3, 0xc3, 0xfc, 0xe6, 0xb8, 0x92, 0x29, 0xae, 0xed, 0xec, 0xd5, 0xe8, 0x4a, 0xa1, 0xbd, 0x3b, 0xd3, 0xc0, 0x07, 0xab, 0x65, 0x65, 0x35, 0x9a, 0xa6, 0x5e, 0x78, 0x18, 0x76, 0x1c, 0x15, 0x49, 0xe6, 0x75, + /* (2^ 29)P */ 0x45, 0xb3, 0x92, 0xa9, 0xc3, 0xb8, 0x11, 0x68, 0x64, 0x3a, 0x83, 0x5d, 0xa8, 0x94, 0x6a, 0x9d, 0xaa, 0x27, 0x9f, 0x98, 0x5d, 0xc0, 0x29, 0xf0, 0xc0, 0x4b, 0x14, 0x3c, 0x05, 0xe7, 0xf8, 0xbd, 0x38, 0x22, 0x96, 0x75, 0x65, 0x5e, 0x0d, 0x3f, 0xbb, 0x6f, 0xe8, 0x3f, 0x96, 0x76, 0x9f, 0xba, 0xd9, 0x44, 0x92, 0x96, 0x22, 0xe7, 0x52, 0xe7, + /* (2^ 30)P */ 0xf4, 0xa3, 0x95, 0x90, 0x47, 0xdf, 0x7d, 0xdc, 0xf4, 0x13, 0x87, 0x67, 0x7d, 0x4f, 0x9d, 0xa0, 0x00, 0x46, 0x72, 0x08, 0xc3, 0xa2, 0x7a, 0x3e, 0xe7, 0x6d, 0x52, 0x7c, 0x11, 0x36, 0x50, 0x83, 0x89, 0x64, 0xcb, 0x1f, 0x08, 0x83, 0x46, 0xcb, 0xac, 0xa6, 0xd8, 0x9c, 0x1b, 0xe8, 0x05, 0x47, 0xc7, 0x26, 0x06, 0x83, 0x39, 0xe9, 0xb1, 0x1c, + /* (2^ 31)P */ 0x11, 0xe8, 0xc8, 0x42, 0xbf, 0x30, 0x9c, 0xa3, 0xf1, 0x85, 0x96, 0x95, 0x4f, 0x4f, 0x52, 0xa2, 0xf5, 0x8b, 0x68, 0x24, 0x16, 0xac, 0x9b, 0xa9, 0x27, 0x28, 0x0e, 0x84, 0x03, 0x46, 0x22, 0x5f, 0xf7, 0x0d, 0xa6, 0x85, 0x88, 0xc1, 0x45, 0x4b, 0x85, 0x1a, 0x10, 0x7f, 0xc9, 0x94, 0x20, 0xb0, 0x04, 0x28, 0x12, 0x30, 0xb9, 0xe6, 0x40, 0x6b, + /* (2^ 32)P */ 0xac, 0x1b, 0x57, 0xb6, 0x42, 0xdb, 0x81, 0x8d, 0x76, 0xfd, 0x9b, 0x1c, 0x29, 0x30, 0xd5, 0x3a, 0xcc, 0x53, 0xd9, 0x26, 0x7a, 0x0f, 0x9c, 0x2e, 0x79, 0xf5, 0x62, 0xeb, 0x61, 0x9d, 0x9b, 0x80, 0x39, 0xcd, 0x60, 0x2e, 0x1f, 0x08, 0x22, 0xbc, 0x19, 0xb3, 0x2a, 0x43, 0x44, 0xf2, 0x4e, 0x66, 0xf4, 0x36, 0xa6, 0xa7, 0xbc, 0xa4, 0x15, 0x7e, + /* (2^ 33)P */ 0xc1, 0x90, 0x8a, 0xde, 0xff, 0x78, 0xc3, 0x73, 0x16, 0xee, 0x76, 0xa0, 0x84, 0x60, 0x8d, 0xe6, 0x82, 0x0f, 0xde, 0x4e, 0xc5, 0x99, 0x34, 0x06, 0x90, 0x44, 0x55, 0xf8, 0x91, 0xd8, 0xe1, 0xe4, 0x2c, 0x8a, 0xde, 0x94, 0x1e, 0x78, 0x25, 0x3d, 0xfd, 0xd8, 0x59, 0x7d, 0xaf, 0x6e, 0xbe, 0x96, 0xbe, 0x3c, 0x16, 0x23, 0x0f, 0x4c, 0xa4, 0x28, + /* (2^ 34)P */ 0xba, 0x11, 0x35, 0x57, 0x03, 0xb6, 0xf4, 0x24, 0x89, 0xb8, 0x5a, 0x0d, 0x50, 0x9c, 0xaa, 0x51, 0x7f, 0xa4, 0x0e, 0xfc, 0x71, 0xb3, 0x3b, 0xf1, 0x96, 0x50, 0x23, 0x15, 0xf5, 0xf5, 0xd4, 0x23, 0xdc, 0x8b, 0x26, 0x9e, 0xae, 0xb7, 0x50, 0xcd, 0xc4, 0x25, 0xf6, 0x75, 0x40, 0x9c, 0x37, 0x79, 0x33, 0x60, 0xd4, 0x4b, 0x13, 0x32, 0xee, 0xe2, + /* (2^ 35)P */ 0x43, 0xb8, 0x56, 0x59, 0xf0, 0x68, 0x23, 0xb3, 0xea, 0x70, 0x58, 0x4c, 0x1e, 0x5a, 0x16, 0x54, 0x03, 0xb2, 0xf4, 0x73, 0xb6, 0xd9, 0x5c, 0x9c, 0x6f, 0xcf, 0x82, 0x2e, 0x54, 0x15, 0x46, 0x2c, 0xa3, 0xda, 0x4e, 0x87, 0xf5, 0x2b, 0xba, 0x91, 0xa3, 0xa0, 0x89, 0xba, 0x48, 0x2b, 0xfa, 0x64, 0x02, 0x7f, 0x78, 0x03, 0xd1, 0xe8, 0x3b, 0xe9, + /* (2^ 36)P */ 0x15, 0xa4, 0x71, 0xd4, 0x0c, 0x24, 0xe9, 0x07, 0xa1, 0x43, 0xf4, 0x7f, 0xbb, 0xa2, 0xa6, 0x6b, 0xfa, 0xb7, 0xea, 0x58, 0xd1, 0x96, 0xb0, 0x24, 0x5c, 0xc7, 0x37, 0x4e, 0x60, 0x0f, 0x40, 0xf2, 0x2f, 0x44, 0x70, 0xea, 0x80, 0x63, 0xfe, 0xfc, 0x46, 0x59, 0x12, 0x27, 0xb5, 0x27, 0xfd, 0xb7, 0x73, 0x0b, 0xca, 0x8b, 0xc2, 0xd3, 0x71, 0x08, + /* (2^ 37)P */ 0x26, 0x0e, 0xd7, 0x52, 0x6f, 0xf1, 0xf2, 0x9d, 0xb8, 0x3d, 0xbd, 0xd4, 0x75, 0x97, 0xd8, 0xbf, 0xa8, 0x86, 0x96, 0xa5, 0x80, 0xa0, 0x45, 0x75, 0xf6, 0x77, 0x71, 0xdb, 0x77, 0x96, 0x55, 0x99, 0x31, 0xd0, 0x4f, 0x34, 0xf4, 0x35, 0x39, 0x41, 0xd3, 0x7d, 0xf7, 0xe2, 0x74, 0xde, 0xbe, 0x5b, 0x1f, 0x39, 0x10, 0x21, 0xa3, 0x4d, 0x3b, 0xc8, + /* (2^ 38)P */ 0x04, 0x00, 0x2a, 0x45, 0xb2, 0xaf, 0x9b, 0x18, 0x6a, 0xeb, 0x96, 0x28, 0xa4, 0x77, 0xd0, 0x13, 0xcf, 0x17, 0x65, 0xe8, 0xc5, 0x81, 0x28, 0xad, 0x39, 0x7a, 0x0b, 0xaa, 0x55, 0x2b, 0xf3, 0xfc, 0x86, 0x40, 0xad, 0x0d, 0x1e, 0x28, 0xa2, 0x2d, 0xc5, 0xd6, 0x04, 0x15, 0xa2, 0x30, 0x3d, 0x12, 0x8e, 0xd6, 0xb5, 0xf7, 0x69, 0xbb, 0x84, 0x20, + /* (2^ 39)P */ 0xd7, 0x7a, 0x77, 0x2c, 0xfb, 0x81, 0x80, 0xe9, 0x1e, 0xc6, 0x36, 0x31, 0x79, 0xc3, 0x7c, 0xa9, 0x57, 0x6b, 0xb5, 0x70, 0xfb, 0xe4, 0xa1, 0xff, 0xfd, 0x21, 0xa5, 0x7c, 0xfa, 0x44, 0xba, 0x0d, 0x96, 0x3d, 0xc4, 0x5c, 0x39, 0x52, 0x87, 0xd7, 0x22, 0x0f, 0x52, 0x88, 0x91, 0x87, 0x96, 0xac, 0xfa, 0x3b, 0xdf, 0xdc, 0x83, 0x8c, 0x99, 0x29, + /* (2^ 40)P */ 0x98, 0x6b, 0x3a, 0x8d, 0x83, 0x17, 0xe1, 0x62, 0xd8, 0x80, 0x4c, 0x97, 0xce, 0x6b, 0xaa, 0x10, 0xa7, 0xc4, 0xe9, 0xeb, 0xa5, 0xfb, 0xc9, 0xdd, 0x2d, 0xeb, 0xfc, 0x9a, 0x71, 0xcd, 0x68, 0x6e, 0xc0, 0x35, 0x64, 0x62, 0x1b, 0x95, 0x12, 0xe8, 0x53, 0xec, 0xf0, 0xf4, 0x86, 0x86, 0x78, 0x18, 0xc4, 0xc6, 0xbc, 0x5a, 0x59, 0x8f, 0x7c, 0x7e, + /* (2^ 41)P */ 0x7f, 0xd7, 0x1e, 0xc5, 0x83, 0xdc, 0x1f, 0xbe, 0x0b, 0xcf, 0x2e, 0x01, 0x01, 0xed, 0xac, 0x17, 0x3b, 0xed, 0xa4, 0x30, 0x96, 0x0e, 0x14, 0x7e, 0x19, 0x2b, 0xa5, 0x67, 0x1e, 0xb3, 0x34, 0x03, 0xa8, 0xbb, 0x0a, 0x7d, 0x08, 0x2d, 0xd5, 0x53, 0x19, 0x6f, 0x13, 0xd5, 0xc0, 0x90, 0x8a, 0xcc, 0xc9, 0x5c, 0xab, 0x24, 0xd7, 0x03, 0xf6, 0x57, + /* (2^ 42)P */ 0x49, 0xcb, 0xb4, 0x96, 0x5f, 0xa6, 0xf8, 0x71, 0x6f, 0x59, 0xad, 0x05, 0x24, 0x2d, 0xaf, 0x67, 0xa8, 0xbe, 0x95, 0xdf, 0x0d, 0x28, 0x5a, 0x7f, 0x6e, 0x87, 0x8c, 0x6e, 0x67, 0x0c, 0xf4, 0xe0, 0x1c, 0x30, 0xc2, 0x66, 0xae, 0x20, 0xa1, 0x34, 0xec, 0x9c, 0xbc, 0xae, 0x3d, 0xa1, 0x28, 0x28, 0x95, 0x1d, 0xc9, 0x3a, 0xa8, 0xfd, 0xfc, 0xa1, + /* (2^ 43)P */ 0xe2, 0x2b, 0x9d, 0xed, 0x02, 0x99, 0x67, 0xbb, 0x2e, 0x16, 0x62, 0x05, 0x70, 0xc7, 0x27, 0xb9, 0x1c, 0x3f, 0xf2, 0x11, 0x01, 0xd8, 0x51, 0xa4, 0x18, 0x92, 0xa9, 0x5d, 0xfb, 0xa9, 0xe4, 0x42, 0xba, 0x38, 0x34, 0x1a, 0x4a, 0xc5, 0x6a, 0x37, 0xde, 0xa7, 0x0c, 0xb4, 0x7e, 0x7f, 0xde, 0xa6, 0xee, 0xcd, 0x55, 0x57, 0x05, 0x06, 0xfd, 0x5d, + /* (2^ 44)P */ 0x2f, 0x32, 0xcf, 0x2e, 0x2c, 0x7b, 0xbe, 0x9a, 0x0c, 0x57, 0x35, 0xf8, 0x87, 0xda, 0x9c, 0xec, 0x48, 0xf2, 0xbb, 0xe2, 0xda, 0x10, 0x58, 0x20, 0xc6, 0xd3, 0x87, 0xe9, 0xc7, 0x26, 0xd1, 0x9a, 0x46, 0x87, 0x90, 0xda, 0xdc, 0xde, 0xc3, 0xb3, 0xf2, 0xe8, 0x6f, 0x4a, 0xe6, 0xe8, 0x9d, 0x98, 0x36, 0x20, 0x03, 0x47, 0x15, 0x3f, 0x64, 0x59, + /* (2^ 45)P */ 0xd4, 0x71, 0x49, 0x0a, 0x67, 0x97, 0xaa, 0x3f, 0xf4, 0x1b, 0x3a, 0x6e, 0x5e, 0x17, 0xcc, 0x0a, 0x8f, 0x81, 0x6a, 0x41, 0x38, 0x77, 0x40, 0x8a, 0x11, 0x42, 0x62, 0xd2, 0x50, 0x32, 0x79, 0x78, 0x28, 0xc2, 0x2e, 0x10, 0x01, 0x94, 0x30, 0x4f, 0x7f, 0x18, 0x17, 0x56, 0x85, 0x4e, 0xad, 0xf7, 0xcb, 0x87, 0x3c, 0x3f, 0x50, 0x2c, 0xc0, 0xba, + /* (2^ 46)P */ 0xbc, 0x30, 0x8e, 0x65, 0x8e, 0x57, 0x5b, 0x38, 0x7a, 0xd4, 0x95, 0x52, 0x7a, 0x32, 0x59, 0x69, 0xcd, 0x9d, 0x47, 0x34, 0x5b, 0x55, 0xa5, 0x24, 0x60, 0xdd, 0xc0, 0xc1, 0x62, 0x73, 0x44, 0xae, 0x4c, 0x9c, 0x65, 0x55, 0x1b, 0x9d, 0x8a, 0x29, 0xb0, 0x1a, 0x52, 0xa8, 0xf1, 0xe6, 0x9a, 0xb3, 0xf6, 0xa3, 0xc9, 0x0a, 0x70, 0x7d, 0x0f, 0xee, + /* (2^ 47)P */ 0x77, 0xd3, 0xe5, 0x8e, 0xfa, 0x00, 0xeb, 0x1b, 0x7f, 0xdc, 0x68, 0x3f, 0x92, 0xbd, 0xb7, 0x0b, 0xb7, 0xb5, 0x24, 0xdf, 0xc5, 0x67, 0x53, 0xd4, 0x36, 0x79, 0xc4, 0x7b, 0x57, 0xbc, 0x99, 0x97, 0x60, 0xef, 0xe4, 0x01, 0xa1, 0xa7, 0xaa, 0x12, 0x36, 0x29, 0xb1, 0x03, 0xc2, 0x83, 0x1c, 0x2b, 0x83, 0xef, 0x2e, 0x2c, 0x23, 0x92, 0xfd, 0xd1, + /* (2^ 48)P */ 0x94, 0xef, 0x03, 0x59, 0xfa, 0x8a, 0x18, 0x76, 0xee, 0x58, 0x08, 0x4d, 0x44, 0xce, 0xf1, 0x52, 0x33, 0x49, 0xf6, 0x69, 0x71, 0xe3, 0xa9, 0xbc, 0x86, 0xe3, 0x43, 0xde, 0x33, 0x7b, 0x90, 0x8b, 0x3e, 0x7d, 0xd5, 0x4a, 0xf0, 0x23, 0x99, 0xa6, 0xea, 0x5f, 0x08, 0xe5, 0xb9, 0x49, 0x8b, 0x0d, 0x6a, 0x21, 0xab, 0x07, 0x62, 0xcd, 0xc4, 0xbe, + /* (2^ 49)P */ 0x61, 0xbf, 0x70, 0x14, 0xfa, 0x4e, 0x9e, 0x7c, 0x0c, 0xf8, 0xb2, 0x48, 0x71, 0x62, 0x83, 0xd6, 0xd1, 0xdc, 0x9c, 0x29, 0x66, 0xb1, 0x34, 0x9c, 0x8d, 0xe6, 0x88, 0xaf, 0xbe, 0xdc, 0x4d, 0xeb, 0xb0, 0xe7, 0x28, 0xae, 0xb2, 0x05, 0x56, 0xc6, 0x0e, 0x10, 0x26, 0xab, 0x2c, 0x59, 0x72, 0x03, 0x66, 0xfe, 0x8f, 0x2c, 0x51, 0x2d, 0xdc, 0xae, + /* (2^ 50)P */ 0xdc, 0x63, 0xf1, 0x8b, 0x5c, 0x65, 0x0b, 0xf1, 0xa6, 0x22, 0xe2, 0xd9, 0xdb, 0x49, 0xb1, 0x3c, 0x47, 0xc2, 0xfe, 0xac, 0x86, 0x07, 0x52, 0xec, 0xb0, 0x08, 0x69, 0xfb, 0xd1, 0x06, 0xdc, 0x48, 0x5c, 0x3d, 0xb2, 0x4d, 0xb8, 0x1a, 0x4e, 0xda, 0xb9, 0xc1, 0x2b, 0xab, 0x4b, 0x62, 0x81, 0x21, 0x9a, 0xfc, 0x3d, 0x39, 0x83, 0x11, 0x36, 0xeb, + /* (2^ 51)P */ 0x94, 0xf3, 0x17, 0xef, 0xf9, 0x60, 0x54, 0xc3, 0xd7, 0x27, 0x35, 0xc5, 0x98, 0x5e, 0xf6, 0x63, 0x6c, 0xa0, 0x4a, 0xd3, 0xa3, 0x98, 0xd9, 0x42, 0xe3, 0xf1, 0xf8, 0x81, 0x96, 0xa9, 0xea, 0x6d, 0x4b, 0x8e, 0x33, 0xca, 0x94, 0x0d, 0xa0, 0xf7, 0xbb, 0x64, 0xa3, 0x36, 0x6f, 0xdc, 0x5a, 0x94, 0x42, 0xca, 0x06, 0xb2, 0x2b, 0x9a, 0x9f, 0x71, + /* (2^ 52)P */ 0xec, 0xdb, 0xa6, 0x1f, 0xdf, 0x15, 0x36, 0xa3, 0xda, 0x8a, 0x7a, 0xb6, 0xa7, 0xe3, 0xaf, 0x52, 0xe0, 0x8d, 0xe8, 0xf2, 0x44, 0x20, 0xeb, 0xa1, 0x20, 0xc4, 0x65, 0x3c, 0x7c, 0x6c, 0x49, 0xed, 0x2f, 0x66, 0x23, 0x68, 0x61, 0x91, 0x40, 0x9f, 0x50, 0x19, 0xd1, 0x84, 0xa7, 0xe2, 0xed, 0x34, 0x37, 0xe3, 0xe4, 0x11, 0x7f, 0x87, 0x55, 0x0f, + /* (2^ 53)P */ 0xb3, 0xa1, 0x0f, 0xb0, 0x48, 0xc0, 0x4d, 0x96, 0xa7, 0xcf, 0x5a, 0x81, 0xb8, 0x4a, 0x46, 0xef, 0x0a, 0xd3, 0x40, 0x7e, 0x02, 0xe3, 0x63, 0xaa, 0x50, 0xd1, 0x2a, 0x37, 0x22, 0x4a, 0x7f, 0x4f, 0xb6, 0xf9, 0x01, 0x82, 0x78, 0x3d, 0x93, 0x14, 0x11, 0x8a, 0x90, 0x60, 0xcd, 0x45, 0x4e, 0x7b, 0x42, 0xb9, 0x3e, 0x6e, 0x68, 0x1f, 0x36, 0x41, + /* (2^ 54)P */ 0x13, 0x73, 0x0e, 0x4f, 0x79, 0x93, 0x9e, 0x29, 0x70, 0x7b, 0x4a, 0x59, 0x1a, 0x9a, 0xf4, 0x55, 0x08, 0xf0, 0xdb, 0x17, 0x58, 0xec, 0x64, 0xad, 0x7f, 0x29, 0xeb, 0x3f, 0x85, 0x4e, 0x60, 0x28, 0x98, 0x1f, 0x73, 0x4e, 0xe6, 0xa8, 0xab, 0xd5, 0xd6, 0xfc, 0xa1, 0x36, 0x6d, 0x15, 0xc6, 0x13, 0x83, 0xa0, 0xc2, 0x6e, 0xd9, 0xdb, 0xc9, 0xcc, + /* (2^ 55)P */ 0xff, 0xd8, 0x52, 0xa3, 0xdc, 0x99, 0xcf, 0x3e, 0x19, 0xb3, 0x68, 0xd0, 0xb5, 0x0d, 0xb8, 0xee, 0x3f, 0xef, 0x6e, 0xc0, 0x38, 0x28, 0x44, 0x92, 0x78, 0x91, 0x1a, 0x08, 0x78, 0x6c, 0x65, 0x24, 0xf3, 0xa2, 0x3d, 0xf2, 0xe5, 0x79, 0x62, 0x69, 0x29, 0xf4, 0x22, 0xc5, 0xdb, 0x6a, 0xae, 0xf4, 0x44, 0xa3, 0x6f, 0xc7, 0x86, 0xab, 0xef, 0xef, + /* (2^ 56)P */ 0xbf, 0x54, 0x9a, 0x09, 0x5d, 0x17, 0xd0, 0xde, 0xfb, 0xf5, 0xca, 0xff, 0x13, 0x20, 0x88, 0x82, 0x3a, 0xe2, 0xd0, 0x3b, 0xfb, 0x05, 0x76, 0xd1, 0xc0, 0x02, 0x71, 0x3b, 0x94, 0xe8, 0xc9, 0x84, 0xcf, 0xa4, 0xe9, 0x28, 0x7b, 0xf5, 0x09, 0xc3, 0x2b, 0x22, 0x40, 0xf1, 0x68, 0x24, 0x24, 0x7d, 0x9f, 0x6e, 0xcd, 0xfe, 0xb0, 0x19, 0x61, 0xf5, + /* (2^ 57)P */ 0xe8, 0x63, 0x51, 0xb3, 0x95, 0x6b, 0x7b, 0x74, 0x92, 0x52, 0x45, 0xa4, 0xed, 0xea, 0x0e, 0x0d, 0x2b, 0x01, 0x1e, 0x2c, 0xbc, 0x91, 0x06, 0x69, 0xdb, 0x1f, 0xb5, 0x77, 0x1d, 0x56, 0xf5, 0xb4, 0x02, 0x80, 0x49, 0x56, 0x12, 0xce, 0x86, 0x05, 0xc9, 0xd9, 0xae, 0xf3, 0x6d, 0xe6, 0x3f, 0x40, 0x52, 0xe9, 0x49, 0x2b, 0x31, 0x06, 0x86, 0x14, + /* (2^ 58)P */ 0xf5, 0x09, 0x3b, 0xd2, 0xff, 0xdf, 0x11, 0xa5, 0x1c, 0x99, 0xe8, 0x1b, 0xa4, 0x2c, 0x7d, 0x8e, 0xc8, 0xf7, 0x03, 0x46, 0xfa, 0xb6, 0xde, 0x73, 0x91, 0x7e, 0x5a, 0x7a, 0xd7, 0x9a, 0x5b, 0x80, 0x24, 0x62, 0x5e, 0x92, 0xf1, 0xa3, 0x45, 0xa3, 0x43, 0x92, 0x8a, 0x2a, 0x5b, 0x0c, 0xb4, 0xc8, 0xad, 0x1c, 0xb6, 0x6c, 0x5e, 0x81, 0x18, 0x91, + /* (2^ 59)P */ 0x96, 0xb3, 0xca, 0x2b, 0xe3, 0x7a, 0x59, 0x72, 0x17, 0x74, 0x29, 0x21, 0xe7, 0x78, 0x07, 0xad, 0xda, 0xb6, 0xcd, 0xf9, 0x27, 0x4d, 0xc8, 0xf2, 0x98, 0x22, 0xca, 0xf2, 0x33, 0x74, 0x7a, 0xdd, 0x1e, 0x71, 0xec, 0xe3, 0x3f, 0xe2, 0xa2, 0xd2, 0x38, 0x75, 0xb0, 0xd0, 0x0a, 0xcf, 0x7d, 0x36, 0xdc, 0x49, 0x38, 0x25, 0x34, 0x4f, 0x20, 0x9a, + /* (2^ 60)P */ 0x2b, 0x6e, 0x04, 0x0d, 0x4f, 0x3d, 0x3b, 0x24, 0xf6, 0x4e, 0x5e, 0x0a, 0xbd, 0x48, 0x96, 0xba, 0x81, 0x8f, 0x39, 0x82, 0x13, 0xe6, 0x72, 0xf3, 0x0f, 0xb6, 0x94, 0xf4, 0xc5, 0x90, 0x74, 0x91, 0xa8, 0xf2, 0xc9, 0xca, 0x9a, 0x4d, 0x98, 0xf2, 0xdf, 0x52, 0x4e, 0x97, 0x2f, 0xeb, 0x84, 0xd3, 0xaf, 0xc2, 0xcc, 0xfb, 0x4c, 0x26, 0x4b, 0xe4, + /* (2^ 61)P */ 0x12, 0x9e, 0xfb, 0x9d, 0x78, 0x79, 0x99, 0xdd, 0xb3, 0x0b, 0x2e, 0x56, 0x41, 0x8e, 0x3f, 0x39, 0xb8, 0x97, 0x89, 0x53, 0x9b, 0x8a, 0x3c, 0x40, 0x9d, 0xa4, 0x6c, 0x2e, 0x31, 0x71, 0xc6, 0x0a, 0x41, 0xd4, 0x95, 0x06, 0x5e, 0xc1, 0xab, 0xc2, 0x14, 0xc4, 0xc7, 0x15, 0x08, 0x3a, 0xad, 0x7a, 0xb4, 0x62, 0xa3, 0x0c, 0x90, 0xf4, 0x47, 0x08, + /* (2^ 62)P */ 0x7f, 0xec, 0x09, 0x82, 0xf5, 0x94, 0x09, 0x93, 0x32, 0xd3, 0xdc, 0x56, 0x80, 0x7b, 0x5b, 0x22, 0x80, 0x6a, 0x96, 0x72, 0xb1, 0xc2, 0xd9, 0xa1, 0x8b, 0x66, 0x42, 0x16, 0xe2, 0x07, 0xb3, 0x2d, 0xf1, 0x75, 0x35, 0x72, 0xc7, 0x98, 0xbe, 0x63, 0x3b, 0x20, 0x75, 0x05, 0xc1, 0x3e, 0x31, 0x5a, 0xf7, 0xaa, 0xae, 0x4b, 0xdb, 0x1d, 0xd0, 0x74, + /* (2^ 63)P */ 0x36, 0x5c, 0x74, 0xe6, 0x5d, 0x59, 0x3f, 0x15, 0x4b, 0x4d, 0x4e, 0x67, 0x41, 0xfe, 0x98, 0x1f, 0x49, 0x76, 0x91, 0x0f, 0x9b, 0xf4, 0xaf, 0x86, 0xaf, 0x66, 0x19, 0xed, 0x46, 0xf1, 0x05, 0x9a, 0xcc, 0xd1, 0x14, 0x1f, 0x82, 0x12, 0x8e, 0xe6, 0xf4, 0xc3, 0x42, 0x5c, 0x4e, 0x33, 0x93, 0xbe, 0x30, 0xe7, 0x64, 0xa9, 0x35, 0x00, 0x4d, 0xf9, + /* (2^ 64)P */ 0x1f, 0xc1, 0x1e, 0xb7, 0xe3, 0x7c, 0xfa, 0xa3, 0x6b, 0x76, 0xaf, 0x9c, 0x05, 0x85, 0x4a, 0xa9, 0xfb, 0xe3, 0x7e, 0xf2, 0x49, 0x56, 0xdc, 0x2f, 0x57, 0x10, 0xba, 0x37, 0xb2, 0x62, 0xf5, 0x6b, 0xe5, 0x8f, 0x0a, 0x87, 0xd1, 0x6a, 0xcb, 0x9d, 0x07, 0xd0, 0xf6, 0x38, 0x99, 0x2c, 0x61, 0x4a, 0x4e, 0xd8, 0xd2, 0x88, 0x29, 0x99, 0x11, 0x95, + /* (2^ 65)P */ 0x6f, 0xdc, 0xd5, 0xd6, 0xd6, 0xa7, 0x4c, 0x46, 0x93, 0x65, 0x62, 0x23, 0x95, 0x32, 0x9c, 0xde, 0x40, 0x41, 0x68, 0x2c, 0x18, 0x4e, 0x5a, 0x8c, 0xc0, 0xc5, 0xc5, 0xea, 0x5c, 0x45, 0x0f, 0x60, 0x78, 0x39, 0xb6, 0x36, 0x23, 0x12, 0xbc, 0x21, 0x9a, 0xf8, 0x91, 0xac, 0xc4, 0x70, 0xdf, 0x85, 0x8e, 0x3c, 0xec, 0x22, 0x04, 0x98, 0xa8, 0xaa, + /* (2^ 66)P */ 0xcc, 0x52, 0x10, 0x5b, 0x4b, 0x6c, 0xc5, 0xfa, 0x3e, 0xd4, 0xf8, 0x1c, 0x04, 0x14, 0x48, 0x33, 0xd9, 0xfc, 0x5f, 0xb0, 0xa5, 0x48, 0x8c, 0x45, 0x8a, 0xee, 0x3e, 0xa7, 0xc1, 0x2e, 0x34, 0xca, 0xf6, 0xc9, 0xeb, 0x10, 0xbb, 0xe1, 0x59, 0x84, 0x25, 0xe8, 0x81, 0x70, 0xc0, 0x09, 0x42, 0xa7, 0x3b, 0x0d, 0x33, 0x00, 0xb5, 0x77, 0xbe, 0x25, + /* (2^ 67)P */ 0xcd, 0x1f, 0xbc, 0x7d, 0xef, 0xe5, 0xca, 0x91, 0xaf, 0xa9, 0x59, 0x6a, 0x09, 0xca, 0xd6, 0x1b, 0x3d, 0x55, 0xde, 0xa2, 0x6a, 0x80, 0xd6, 0x95, 0x47, 0xe4, 0x5f, 0x68, 0x54, 0x08, 0xdf, 0x29, 0xba, 0x2a, 0x02, 0x84, 0xe8, 0xe9, 0x00, 0x77, 0x99, 0x36, 0x03, 0xf6, 0x4a, 0x3e, 0x21, 0x81, 0x7d, 0xb8, 0xa4, 0x8a, 0xa2, 0x05, 0xef, 0xbc, + /* (2^ 68)P */ 0x7c, 0x59, 0x5f, 0x66, 0xd9, 0xb7, 0x83, 0x43, 0x8a, 0xa1, 0x8d, 0x51, 0x70, 0xba, 0xf2, 0x9b, 0x95, 0xc0, 0x4b, 0x4c, 0xa0, 0x14, 0xd3, 0xa4, 0x5d, 0x4a, 0x37, 0x36, 0x97, 0x31, 0x1e, 0x12, 0xe7, 0xbb, 0x08, 0x67, 0xa5, 0x23, 0xd7, 0xfb, 0x97, 0xd8, 0x6a, 0x03, 0xb1, 0xf8, 0x7f, 0xda, 0x58, 0xd9, 0x3f, 0x73, 0x4a, 0x53, 0xe1, 0x7b, + /* (2^ 69)P */ 0x55, 0x83, 0x98, 0x78, 0x6c, 0x56, 0x5e, 0xed, 0xf7, 0x23, 0x3e, 0x4c, 0x7d, 0x09, 0x2d, 0x09, 0x9c, 0x58, 0x8b, 0x32, 0xca, 0xfe, 0xbf, 0x47, 0x03, 0xeb, 0x4d, 0xe7, 0xeb, 0x9c, 0x83, 0x05, 0x68, 0xaa, 0x80, 0x89, 0x44, 0xf9, 0xd4, 0xdc, 0xdb, 0xb1, 0xdb, 0x77, 0xac, 0xf9, 0x2a, 0xae, 0x35, 0xac, 0x74, 0xb5, 0x95, 0x62, 0x18, 0x85, + /* (2^ 70)P */ 0xab, 0x82, 0x7e, 0x10, 0xd7, 0xe6, 0x57, 0xd1, 0x66, 0x12, 0x31, 0x9c, 0x9c, 0xa6, 0x27, 0x59, 0x71, 0x2e, 0xeb, 0xa0, 0x68, 0xc5, 0x87, 0x51, 0xf4, 0xca, 0x3f, 0x98, 0x56, 0xb0, 0x89, 0xb1, 0xc7, 0x7b, 0x46, 0xb3, 0xae, 0x36, 0xf2, 0xee, 0x15, 0x1a, 0x60, 0xf4, 0x50, 0x76, 0x4f, 0xc4, 0x53, 0x0d, 0x36, 0x4d, 0x31, 0xb1, 0x20, 0x51, + /* (2^ 71)P */ 0xf7, 0x1d, 0x8c, 0x1b, 0x5e, 0xe5, 0x02, 0x6f, 0xc5, 0xa5, 0xe0, 0x5f, 0xc6, 0xb6, 0x63, 0x43, 0xaf, 0x3c, 0x19, 0x6c, 0xf4, 0xaf, 0xa4, 0x33, 0xb1, 0x0a, 0x37, 0x3d, 0xd9, 0x4d, 0xe2, 0x29, 0x24, 0x26, 0x94, 0x7c, 0x02, 0xe4, 0xe2, 0xf2, 0xbe, 0xbd, 0xac, 0x1b, 0x48, 0xb8, 0xdd, 0xe9, 0x0d, 0x9a, 0x50, 0x1a, 0x98, 0x71, 0x6e, 0xdc, + /* (2^ 72)P */ 0x9f, 0x40, 0xb1, 0xb3, 0x66, 0x28, 0x6c, 0xfe, 0xa6, 0x7d, 0xf8, 0x3e, 0xb8, 0xf3, 0xde, 0x52, 0x76, 0x52, 0xa3, 0x92, 0x98, 0x23, 0xab, 0x4f, 0x88, 0x97, 0xfc, 0x22, 0xe1, 0x6b, 0x67, 0xcd, 0x13, 0x95, 0xda, 0x65, 0xdd, 0x3b, 0x67, 0x3f, 0x5f, 0x4c, 0xf2, 0x8a, 0xad, 0x98, 0xa7, 0x94, 0x24, 0x45, 0x87, 0x11, 0x7c, 0x75, 0x79, 0x85, + /* (2^ 73)P */ 0x70, 0xbf, 0xf9, 0x3b, 0xa9, 0x44, 0x57, 0x72, 0x96, 0xc9, 0xa4, 0x98, 0x65, 0xbf, 0x87, 0xb3, 0x3a, 0x39, 0x12, 0xde, 0xe5, 0x39, 0x01, 0x4f, 0xf7, 0xc0, 0x71, 0x52, 0x36, 0x85, 0xb3, 0x18, 0xf8, 0x14, 0xc0, 0x6d, 0xae, 0x9e, 0x4f, 0xb0, 0x72, 0x87, 0xac, 0x5c, 0xd1, 0x6c, 0x41, 0x6c, 0x90, 0x9d, 0x22, 0x81, 0xe4, 0x2b, 0xea, 0xe5, + /* (2^ 74)P */ 0xfc, 0xea, 0x1a, 0x65, 0xd9, 0x49, 0x6a, 0x39, 0xb5, 0x96, 0x72, 0x7b, 0x32, 0xf1, 0xd0, 0xe9, 0x45, 0xd9, 0x31, 0x55, 0xc7, 0x34, 0xe9, 0x5a, 0xec, 0x73, 0x0b, 0x03, 0xc4, 0xb3, 0xe6, 0xc9, 0x5e, 0x0a, 0x17, 0xfe, 0x53, 0x66, 0x7f, 0x21, 0x18, 0x74, 0x54, 0x1b, 0xc9, 0x49, 0x16, 0xd2, 0x48, 0xaf, 0x5b, 0x47, 0x7b, 0xeb, 0xaa, 0xc9, + /* (2^ 75)P */ 0x47, 0x04, 0xf5, 0x5a, 0x87, 0x77, 0x9e, 0x21, 0x34, 0x4e, 0x83, 0x88, 0xaf, 0x02, 0x1d, 0xb0, 0x5a, 0x1d, 0x1d, 0x7d, 0x8d, 0x2c, 0xd3, 0x8d, 0x63, 0xa9, 0x45, 0xfb, 0x15, 0x6d, 0x86, 0x45, 0xcd, 0x38, 0x0e, 0xf7, 0x37, 0x79, 0xed, 0x6d, 0x5a, 0xbc, 0x32, 0xcc, 0x66, 0xf1, 0x3a, 0xb2, 0x87, 0x6f, 0x70, 0x71, 0xd9, 0xf2, 0xfa, 0x7b, + /* (2^ 76)P */ 0x68, 0x07, 0xdc, 0x61, 0x40, 0xe4, 0xec, 0x32, 0xc8, 0xbe, 0x66, 0x30, 0x54, 0x80, 0xfd, 0x13, 0x7a, 0xef, 0xae, 0xed, 0x2e, 0x00, 0x6d, 0x3f, 0xbd, 0xfc, 0x91, 0x24, 0x53, 0x7f, 0x63, 0x9d, 0x2e, 0xe3, 0x76, 0xe0, 0xf3, 0xe1, 0x8f, 0x7a, 0xc4, 0x77, 0x0c, 0x91, 0xc0, 0xc2, 0x18, 0x6b, 0x04, 0xad, 0xb6, 0x70, 0x9a, 0x64, 0xc5, 0x82, + /* (2^ 77)P */ 0x7f, 0xea, 0x13, 0xd8, 0x9e, 0xfc, 0x5b, 0x06, 0xb5, 0x4f, 0xda, 0x38, 0xe0, 0x9c, 0xd2, 0x3a, 0xc1, 0x1c, 0x62, 0x70, 0x7f, 0xc6, 0x24, 0x0a, 0x47, 0x04, 0x01, 0xc4, 0x55, 0x09, 0xd1, 0x7a, 0x07, 0xba, 0xa3, 0x80, 0x4f, 0xc1, 0x65, 0x36, 0x6d, 0xc0, 0x10, 0xcf, 0x94, 0xa9, 0xa2, 0x01, 0x44, 0xd1, 0xf9, 0x1c, 0x4c, 0xfb, 0xf8, 0x99, + /* (2^ 78)P */ 0x6c, 0xb9, 0x6b, 0xee, 0x43, 0x5b, 0xb9, 0xbb, 0xee, 0x2e, 0x52, 0xc1, 0xc6, 0xb9, 0x61, 0xd2, 0x93, 0xa5, 0xaf, 0x52, 0xf4, 0xa4, 0x1a, 0x51, 0x61, 0xa7, 0xcb, 0x9e, 0xbb, 0x56, 0x65, 0xe2, 0xbf, 0x75, 0xb9, 0x9c, 0x50, 0x96, 0x60, 0x81, 0x74, 0x47, 0xc0, 0x04, 0x88, 0x71, 0x76, 0x39, 0x9a, 0xa7, 0xb1, 0x4e, 0x43, 0x15, 0xe0, 0xbb, + /* (2^ 79)P */ 0xbb, 0xce, 0xe2, 0xbb, 0xf9, 0x17, 0x0f, 0x82, 0x40, 0xad, 0x73, 0xe3, 0xeb, 0x3b, 0x06, 0x1a, 0xcf, 0x8e, 0x6e, 0x28, 0xb8, 0x26, 0xd9, 0x5b, 0xb7, 0xb3, 0xcf, 0xb4, 0x6a, 0x1c, 0xbf, 0x7f, 0xb8, 0xb5, 0x79, 0xcf, 0x45, 0x68, 0x7d, 0xc5, 0xeb, 0xf3, 0xbe, 0x39, 0x40, 0xfc, 0x07, 0x90, 0x7a, 0x62, 0xad, 0x86, 0x08, 0x71, 0x25, 0xe1, + /* (2^ 80)P */ 0x9b, 0x46, 0xac, 0xef, 0xc1, 0x4e, 0xa1, 0x97, 0x95, 0x76, 0xf9, 0x1b, 0xc2, 0xb2, 0x6a, 0x41, 0xea, 0x80, 0x3d, 0xe9, 0x08, 0x52, 0x5a, 0xe3, 0xf2, 0x08, 0xc5, 0xea, 0x39, 0x3f, 0x44, 0x71, 0x4d, 0xea, 0x0d, 0x05, 0x23, 0xe4, 0x2e, 0x3c, 0x89, 0xfe, 0x12, 0x8a, 0x95, 0x42, 0x0a, 0x68, 0xea, 0x5a, 0x28, 0x06, 0x9e, 0xe3, 0x5f, 0xe0, + /* (2^ 81)P */ 0x00, 0x61, 0x6c, 0x98, 0x9b, 0xe7, 0xb9, 0x06, 0x1c, 0xc5, 0x1b, 0xed, 0xbe, 0xc8, 0xb3, 0xea, 0x87, 0xf0, 0xc4, 0x24, 0x7d, 0xbb, 0x5d, 0xa4, 0x1d, 0x7a, 0x16, 0x00, 0x55, 0x94, 0x67, 0x78, 0xbd, 0x58, 0x02, 0x82, 0x90, 0x53, 0x76, 0xd4, 0x72, 0x99, 0x51, 0x6f, 0x7b, 0xcf, 0x80, 0x30, 0x31, 0x3b, 0x01, 0xc7, 0xc1, 0xef, 0xe6, 0x42, + /* (2^ 82)P */ 0xe2, 0x35, 0xaf, 0x4b, 0x79, 0xc6, 0x12, 0x24, 0x99, 0xc0, 0x68, 0xb0, 0x43, 0x3e, 0xe5, 0xef, 0xe2, 0x29, 0xea, 0xb8, 0xb3, 0xbc, 0x6a, 0x53, 0x2c, 0x69, 0x18, 0x5a, 0xf9, 0x15, 0xae, 0x66, 0x58, 0x18, 0xd3, 0x2d, 0x4b, 0x00, 0xfd, 0x84, 0xab, 0x4f, 0xae, 0x70, 0x6b, 0x9e, 0x9a, 0xdf, 0x83, 0xfd, 0x2e, 0x3c, 0xcf, 0xf8, 0x88, 0x5b, + /* (2^ 83)P */ 0xa4, 0x90, 0x31, 0x85, 0x13, 0xcd, 0xdf, 0x64, 0xc9, 0xa1, 0x0b, 0xe7, 0xb6, 0x73, 0x8a, 0x1b, 0x22, 0x78, 0x4c, 0xd4, 0xae, 0x48, 0x18, 0x00, 0x00, 0xa8, 0x9f, 0x06, 0xf9, 0xfb, 0x2d, 0xc3, 0xb1, 0x2a, 0xbc, 0x13, 0x99, 0x57, 0xaf, 0xf0, 0x8d, 0x61, 0x54, 0x29, 0xd5, 0xf2, 0x72, 0x00, 0x96, 0xd1, 0x85, 0x12, 0x8a, 0xf0, 0x23, 0xfb, + /* (2^ 84)P */ 0x69, 0xc7, 0xdb, 0xd9, 0x92, 0x75, 0x08, 0x9b, 0xeb, 0xa5, 0x93, 0xd1, 0x1a, 0xf4, 0xf5, 0xaf, 0xe6, 0xc4, 0x4a, 0x0d, 0x35, 0x26, 0x39, 0x9d, 0xd3, 0x17, 0x3e, 0xae, 0x2d, 0xbf, 0x73, 0x9f, 0xb7, 0x74, 0x91, 0xd1, 0xd8, 0x5c, 0x14, 0xf9, 0x75, 0xdf, 0xeb, 0xc2, 0x22, 0xd8, 0x14, 0x8d, 0x86, 0x23, 0x4d, 0xd1, 0x2d, 0xdb, 0x6b, 0x42, + /* (2^ 85)P */ 0x8c, 0xda, 0xc6, 0xf8, 0x71, 0xba, 0x2b, 0x06, 0x78, 0xae, 0xcc, 0x3a, 0xe3, 0xe3, 0xa1, 0x8b, 0xe2, 0x34, 0x6d, 0x28, 0x9e, 0x46, 0x13, 0x4d, 0x9e, 0xa6, 0x73, 0x49, 0x65, 0x79, 0x88, 0xb9, 0x3a, 0xd1, 0x6d, 0x2f, 0x48, 0x2b, 0x0a, 0x7f, 0x58, 0x20, 0x37, 0xf4, 0x0e, 0xbb, 0x4a, 0x95, 0x58, 0x0c, 0x88, 0x30, 0xc4, 0x74, 0xdd, 0xfd, + /* (2^ 86)P */ 0x6d, 0x13, 0x4e, 0x89, 0x2d, 0xa9, 0xa3, 0xed, 0x09, 0xe3, 0x0e, 0x71, 0x3e, 0x4a, 0xab, 0x90, 0xde, 0x03, 0xeb, 0x56, 0x46, 0x60, 0x06, 0xf5, 0x71, 0xe5, 0xee, 0x9b, 0xef, 0xff, 0xc4, 0x2c, 0x9f, 0x37, 0x48, 0x45, 0x94, 0x12, 0x41, 0x81, 0x15, 0x70, 0x91, 0x99, 0x5e, 0x56, 0x6b, 0xf4, 0xa6, 0xc9, 0xf5, 0x69, 0x9d, 0x78, 0x37, 0x57, + /* (2^ 87)P */ 0xf3, 0x51, 0x57, 0x7e, 0x43, 0x6f, 0xc6, 0x67, 0x59, 0x0c, 0xcf, 0x94, 0xe6, 0x3d, 0xb5, 0x07, 0xc9, 0x77, 0x48, 0xc9, 0x68, 0x0d, 0x98, 0x36, 0x62, 0x35, 0x38, 0x1c, 0xf5, 0xc5, 0xec, 0x66, 0x78, 0xfe, 0x47, 0xab, 0x26, 0xd6, 0x44, 0xb6, 0x06, 0x0f, 0x89, 0xe3, 0x19, 0x40, 0x1a, 0xe7, 0xd8, 0x65, 0x55, 0xf7, 0x1a, 0xfc, 0xa3, 0x0e, + /* (2^ 88)P */ 0x0e, 0x30, 0xa6, 0xb7, 0x58, 0x60, 0x62, 0x2a, 0x6c, 0x13, 0xa8, 0x14, 0x9b, 0xb8, 0xf2, 0x70, 0xd8, 0xb1, 0x71, 0x88, 0x8c, 0x18, 0x31, 0x25, 0x93, 0x90, 0xb4, 0xc7, 0x49, 0xd8, 0xd4, 0xdb, 0x1e, 0x1e, 0x7f, 0xaa, 0xba, 0xc9, 0xf2, 0x5d, 0xa9, 0x3a, 0x43, 0xb4, 0x5c, 0xee, 0x7b, 0xc7, 0x97, 0xb7, 0x66, 0xd7, 0x23, 0xd9, 0x22, 0x59, + /* (2^ 89)P */ 0x28, 0x19, 0xa6, 0xf9, 0x89, 0x20, 0x78, 0xd4, 0x6d, 0xcb, 0x79, 0x8f, 0x61, 0x6f, 0xb2, 0x5c, 0x4f, 0xa6, 0x54, 0x84, 0x95, 0x24, 0x36, 0x64, 0xcb, 0x39, 0xe7, 0x8f, 0x97, 0x9c, 0x5c, 0x3c, 0xfb, 0x51, 0x11, 0x01, 0x17, 0xdb, 0xc9, 0x9b, 0x51, 0x03, 0x9a, 0xe9, 0xe5, 0x24, 0x1e, 0xf5, 0xda, 0xe0, 0x48, 0x02, 0x23, 0xd0, 0x2c, 0x81, + /* (2^ 90)P */ 0x42, 0x1b, 0xe4, 0x91, 0x85, 0x2a, 0x0c, 0xd2, 0x28, 0x66, 0x57, 0x9e, 0x33, 0x8d, 0x25, 0x71, 0x10, 0x65, 0x76, 0xa2, 0x8c, 0x21, 0x86, 0x81, 0x15, 0xc2, 0x27, 0xeb, 0x54, 0x2d, 0x4f, 0x6c, 0xe6, 0xd6, 0x24, 0x9c, 0x1a, 0x12, 0xb8, 0x81, 0xe2, 0x0a, 0xf3, 0xd3, 0xf0, 0xd3, 0xe1, 0x74, 0x1f, 0x9b, 0x11, 0x47, 0xd0, 0xcf, 0xb6, 0x54, + /* (2^ 91)P */ 0x26, 0x45, 0xa2, 0x10, 0xd4, 0x2d, 0xae, 0xc0, 0xb0, 0xe8, 0x86, 0xb3, 0xc7, 0xea, 0x70, 0x87, 0x61, 0xb5, 0xa5, 0x55, 0xbe, 0x88, 0x1d, 0x7a, 0xd9, 0x6f, 0xeb, 0x83, 0xe2, 0x44, 0x7f, 0x98, 0x04, 0xd6, 0x50, 0x9d, 0xa7, 0x86, 0x66, 0x09, 0x63, 0xe1, 0xed, 0x72, 0xb1, 0xe4, 0x1d, 0x3a, 0xfd, 0x47, 0xce, 0x1c, 0xaa, 0x3b, 0x8f, 0x1b, + /* (2^ 92)P */ 0xf4, 0x3c, 0x4a, 0xb6, 0xc2, 0x9c, 0xe0, 0x2e, 0xb7, 0x38, 0xea, 0x61, 0x35, 0x97, 0x10, 0x90, 0xae, 0x22, 0x48, 0xb3, 0xa9, 0xc6, 0x7a, 0xbb, 0x23, 0xf2, 0xf8, 0x1b, 0xa7, 0xa1, 0x79, 0xcc, 0xc4, 0xf8, 0x08, 0x76, 0x8a, 0x5a, 0x1c, 0x1b, 0xc5, 0x33, 0x91, 0xa9, 0xb8, 0xb9, 0xd3, 0xf8, 0x49, 0xcd, 0xe5, 0x82, 0x43, 0xf7, 0xca, 0x68, + /* (2^ 93)P */ 0x38, 0xba, 0xae, 0x44, 0xfe, 0x57, 0x64, 0x56, 0x7c, 0x0e, 0x9c, 0xca, 0xff, 0xa9, 0x82, 0xbb, 0x38, 0x4a, 0xa7, 0xf7, 0x47, 0xab, 0xbe, 0x6d, 0x23, 0x0b, 0x8a, 0xed, 0xc2, 0xb9, 0x8f, 0xf1, 0xec, 0x91, 0x44, 0x73, 0x64, 0xba, 0xd5, 0x8f, 0x37, 0x38, 0x0d, 0xd5, 0xf8, 0x73, 0x57, 0xb6, 0xc2, 0x45, 0xdc, 0x25, 0xb2, 0xb6, 0xea, 0xd9, + /* (2^ 94)P */ 0xbf, 0xe9, 0x1a, 0x40, 0x4d, 0xcc, 0xe6, 0x1d, 0x70, 0x1a, 0x65, 0xcc, 0x34, 0x2c, 0x37, 0x2c, 0x2d, 0x6b, 0x6d, 0xe5, 0x2f, 0x19, 0x9e, 0xe4, 0xe1, 0xaa, 0xd4, 0xab, 0x54, 0xf4, 0xa8, 0xe4, 0x69, 0x2d, 0x8e, 0x4d, 0xd7, 0xac, 0xb0, 0x5b, 0xfe, 0xe3, 0x26, 0x07, 0xc3, 0xf8, 0x1b, 0x43, 0xa8, 0x1d, 0x64, 0xa5, 0x25, 0x88, 0xbb, 0x77, + /* (2^ 95)P */ 0x92, 0xcd, 0x6e, 0xa0, 0x79, 0x04, 0x18, 0xf4, 0x11, 0x58, 0x48, 0xb5, 0x3c, 0x7b, 0xd1, 0xcc, 0xd3, 0x14, 0x2c, 0xa0, 0xdd, 0x04, 0x44, 0x11, 0xb3, 0x6d, 0x2f, 0x0d, 0xf5, 0x2a, 0x75, 0x5d, 0x1d, 0xda, 0x86, 0x8d, 0x7d, 0x6b, 0x32, 0x68, 0xb6, 0x6c, 0x64, 0x9e, 0xde, 0x80, 0x88, 0xce, 0x08, 0xbf, 0x0b, 0xe5, 0x8e, 0x4f, 0x1d, 0xfb, + /* (2^ 96)P */ 0xaf, 0xe8, 0x85, 0xbf, 0x7f, 0x37, 0x8d, 0x66, 0x7c, 0xd5, 0xd3, 0x96, 0xa5, 0x81, 0x67, 0x95, 0xff, 0x48, 0xde, 0xde, 0xd7, 0x7a, 0x46, 0x34, 0xb1, 0x13, 0x70, 0x29, 0xed, 0x87, 0x90, 0xb0, 0x40, 0x2c, 0xa6, 0x43, 0x6e, 0xb6, 0xbc, 0x48, 0x8a, 0xc1, 0xae, 0xb8, 0xd4, 0xe2, 0xc0, 0x32, 0xb2, 0xa6, 0x2a, 0x8f, 0xb5, 0x16, 0x9e, 0xc3, + /* (2^ 97)P */ 0xff, 0x4d, 0xd2, 0xd6, 0x74, 0xef, 0x2c, 0x96, 0xc1, 0x11, 0xa8, 0xb8, 0xfe, 0x94, 0x87, 0x3e, 0xa0, 0xfb, 0x57, 0xa3, 0xfc, 0x7a, 0x7e, 0x6a, 0x59, 0x6c, 0x54, 0xbb, 0xbb, 0xa2, 0x25, 0x38, 0x1b, 0xdf, 0x5d, 0x7b, 0x94, 0x14, 0xde, 0x07, 0x6e, 0xd3, 0xab, 0x02, 0x26, 0x74, 0x16, 0x12, 0xdf, 0x2e, 0x2a, 0xa7, 0xb0, 0xe8, 0x29, 0xc0, + /* (2^ 98)P */ 0x6a, 0x38, 0x0b, 0xd3, 0xba, 0x45, 0x23, 0xe0, 0x04, 0x3b, 0x83, 0x39, 0xc5, 0x11, 0xe6, 0xcf, 0x39, 0x0a, 0xb3, 0xb0, 0x3b, 0x27, 0x29, 0x63, 0x1c, 0xf3, 0x00, 0xe6, 0xd2, 0x55, 0x21, 0x1f, 0x84, 0x97, 0x9f, 0x01, 0x49, 0x43, 0x30, 0x5f, 0xe0, 0x1d, 0x24, 0xc4, 0x4e, 0xa0, 0x2b, 0x0b, 0x12, 0x55, 0xc3, 0x27, 0xae, 0x08, 0x83, 0x7c, + /* (2^ 99)P */ 0x5d, 0x1a, 0xb7, 0xa9, 0xf5, 0xfd, 0xec, 0xad, 0xb7, 0x87, 0x02, 0x5f, 0x0d, 0x30, 0x4d, 0xe2, 0x65, 0x87, 0xa4, 0x41, 0x45, 0x1d, 0x67, 0xe0, 0x30, 0x5c, 0x13, 0x87, 0xf6, 0x2e, 0x08, 0xc1, 0xc7, 0x12, 0x45, 0xc8, 0x9b, 0xad, 0xb8, 0xd5, 0x57, 0xbb, 0x5c, 0x48, 0x3a, 0xe1, 0x91, 0x5e, 0xf6, 0x4d, 0x8a, 0x63, 0x75, 0x69, 0x0c, 0x01, + /* (2^100)P */ 0x8f, 0x53, 0x2d, 0xa0, 0x71, 0x3d, 0xfc, 0x45, 0x10, 0x96, 0xcf, 0x56, 0xf9, 0xbb, 0x40, 0x3c, 0x86, 0x52, 0x76, 0xbe, 0x84, 0xf9, 0xa6, 0x9d, 0x3d, 0x27, 0xbe, 0xb4, 0x00, 0x49, 0x94, 0xf5, 0x5d, 0xe1, 0x62, 0x85, 0x66, 0xe5, 0xb8, 0x20, 0x2c, 0x09, 0x7d, 0x9d, 0x3d, 0x6e, 0x74, 0x39, 0xab, 0xad, 0xa0, 0x90, 0x97, 0x5f, 0xbb, 0xa7, + /* (2^101)P */ 0xdb, 0x2d, 0x99, 0x08, 0x16, 0x46, 0x83, 0x7a, 0xa8, 0xea, 0x3d, 0x28, 0x5b, 0x49, 0xfc, 0xb9, 0x6d, 0x00, 0x9e, 0x54, 0x4f, 0x47, 0x64, 0x9b, 0x58, 0x4d, 0x07, 0x0c, 0x6f, 0x29, 0x56, 0x0b, 0x00, 0x14, 0x85, 0x96, 0x41, 0x04, 0xb9, 0x5c, 0xa4, 0xf6, 0x16, 0x73, 0x6a, 0xc7, 0x62, 0x0c, 0x65, 0x2f, 0x93, 0xbf, 0xf7, 0xb9, 0xb7, 0xf1, + /* (2^102)P */ 0xeb, 0x6d, 0xb3, 0x46, 0x32, 0xd2, 0xcb, 0x08, 0x94, 0x14, 0xbf, 0x3f, 0xc5, 0xcb, 0x5f, 0x9f, 0x8a, 0x89, 0x0c, 0x1b, 0x45, 0xad, 0x4c, 0x50, 0xb4, 0xe1, 0xa0, 0x6b, 0x11, 0x92, 0xaf, 0x1f, 0x00, 0xcc, 0xe5, 0x13, 0x7e, 0xe4, 0x2e, 0xa0, 0x57, 0xf3, 0xa7, 0x84, 0x79, 0x7a, 0xc2, 0xb7, 0xb7, 0xfc, 0x5d, 0xa5, 0xa9, 0x64, 0xcc, 0xd8, + /* (2^103)P */ 0xa9, 0xc4, 0x12, 0x8b, 0x34, 0x78, 0x3e, 0x38, 0xfd, 0x3f, 0x87, 0xfa, 0x88, 0x94, 0xd5, 0xd9, 0x7f, 0xeb, 0x58, 0xff, 0xb9, 0x45, 0xdb, 0xa1, 0xed, 0x22, 0x28, 0x1d, 0x00, 0x6d, 0x79, 0x85, 0x7a, 0x75, 0x5d, 0xf0, 0xb1, 0x9e, 0x47, 0x28, 0x8c, 0x62, 0xdf, 0xfb, 0x4c, 0x7b, 0xc5, 0x1a, 0x42, 0x95, 0xef, 0x9a, 0xb7, 0x27, 0x7e, 0xda, + /* (2^104)P */ 0xca, 0xd5, 0xc0, 0x17, 0xa1, 0x66, 0x79, 0x9c, 0x2a, 0xb7, 0x0a, 0xfe, 0x62, 0xe4, 0x26, 0x78, 0x90, 0xa7, 0xcb, 0xb0, 0x4f, 0x6d, 0xf9, 0x8f, 0xf7, 0x7d, 0xac, 0xb8, 0x78, 0x1f, 0x41, 0xea, 0x97, 0x1e, 0x62, 0x97, 0x43, 0x80, 0x58, 0x80, 0xb6, 0x69, 0x7d, 0xee, 0x16, 0xd2, 0xa1, 0x81, 0xd7, 0xb1, 0x27, 0x03, 0x48, 0xda, 0xab, 0xec, + /* (2^105)P */ 0x5b, 0xed, 0x40, 0x8e, 0x8c, 0xc1, 0x66, 0x90, 0x7f, 0x0c, 0xb2, 0xfc, 0xbd, 0x16, 0xac, 0x7d, 0x4c, 0x6a, 0xf9, 0xae, 0xe7, 0x4e, 0x11, 0x12, 0xe9, 0xbe, 0x17, 0x09, 0xc6, 0xc1, 0x5e, 0xb5, 0x7b, 0x50, 0x5c, 0x27, 0xfb, 0x80, 0xab, 0x01, 0xfa, 0x5b, 0x9b, 0x75, 0x16, 0x6e, 0xb2, 0x5c, 0x8c, 0x2f, 0xa5, 0x6a, 0x1a, 0x68, 0xa6, 0x90, + /* (2^106)P */ 0x75, 0xfe, 0xb6, 0x96, 0x96, 0x87, 0x4c, 0x12, 0xa9, 0xd1, 0xd8, 0x03, 0xa3, 0xc1, 0x15, 0x96, 0xe8, 0xa0, 0x75, 0x82, 0xa0, 0x6d, 0xea, 0x54, 0xdc, 0x5f, 0x0d, 0x7e, 0xf6, 0x70, 0xb5, 0xdc, 0x7a, 0xf6, 0xc4, 0xd4, 0x21, 0x49, 0xf5, 0xd4, 0x14, 0x6d, 0x48, 0x1d, 0x7c, 0x99, 0x42, 0xdf, 0x78, 0x6b, 0x9d, 0xb9, 0x30, 0x3c, 0xd0, 0x29, + /* (2^107)P */ 0x85, 0xd6, 0xd8, 0xf3, 0x91, 0x74, 0xdd, 0xbd, 0x72, 0x96, 0x10, 0xe4, 0x76, 0x02, 0x5a, 0x72, 0x67, 0xd3, 0x17, 0x72, 0x14, 0x9a, 0x20, 0x5b, 0x0f, 0x8d, 0xed, 0x6d, 0x4e, 0xe3, 0xd9, 0x82, 0xc2, 0x99, 0xee, 0x39, 0x61, 0x69, 0x8a, 0x24, 0x01, 0x92, 0x15, 0xe7, 0xfc, 0xf9, 0x4d, 0xac, 0xf1, 0x30, 0x49, 0x01, 0x0b, 0x6e, 0x0f, 0x20, + /* (2^108)P */ 0xd8, 0x25, 0x94, 0x5e, 0x43, 0x29, 0xf5, 0xcc, 0xe8, 0xe3, 0x55, 0x41, 0x3c, 0x9f, 0x58, 0x5b, 0x00, 0xeb, 0xc5, 0xdf, 0xcf, 0xfb, 0xfd, 0x6e, 0x92, 0xec, 0x99, 0x30, 0xd6, 0x05, 0xdd, 0x80, 0x7a, 0x5d, 0x6d, 0x16, 0x85, 0xd8, 0x9d, 0x43, 0x65, 0xd8, 0x2c, 0x33, 0x2f, 0x5c, 0x41, 0xea, 0xb7, 0x95, 0x77, 0xf2, 0x9e, 0x59, 0x09, 0xe8, + /* (2^109)P */ 0x00, 0xa0, 0x03, 0x80, 0xcd, 0x60, 0xe5, 0x17, 0xd4, 0x15, 0x99, 0xdd, 0x4f, 0xbf, 0x66, 0xb8, 0xc0, 0xf5, 0xf9, 0xfc, 0x6d, 0x42, 0x18, 0x34, 0x1c, 0x7d, 0x5b, 0xb5, 0x09, 0xd0, 0x99, 0x57, 0x81, 0x0b, 0x62, 0xb3, 0xa2, 0xf9, 0x0b, 0xae, 0x95, 0xb8, 0xc2, 0x3b, 0x0d, 0x5b, 0x00, 0xf1, 0xed, 0xbc, 0x05, 0x9d, 0x61, 0xbc, 0x73, 0x9d, + /* (2^110)P */ 0xd4, 0xdb, 0x29, 0xe5, 0x85, 0xe9, 0xc6, 0x89, 0x2a, 0xa8, 0x54, 0xab, 0xb3, 0x7f, 0x88, 0xc0, 0x4d, 0xe0, 0xd1, 0x74, 0x6e, 0xa3, 0xa7, 0x39, 0xd5, 0xcc, 0xa1, 0x8a, 0xcb, 0x5b, 0x34, 0xad, 0x92, 0xb4, 0xd8, 0xd5, 0x17, 0xf6, 0x77, 0x18, 0x9e, 0xaf, 0x45, 0x3b, 0x03, 0xe2, 0xf8, 0x52, 0x60, 0xdc, 0x15, 0x20, 0x9e, 0xdf, 0xd8, 0x5d, + /* (2^111)P */ 0x02, 0xc1, 0xac, 0x1a, 0x15, 0x8e, 0x6c, 0xf5, 0x1e, 0x1e, 0xba, 0x7e, 0xc2, 0xda, 0x7d, 0x02, 0xda, 0x43, 0xae, 0x04, 0x70, 0x28, 0x54, 0x78, 0x94, 0xf5, 0x4f, 0x07, 0x84, 0x8f, 0xed, 0xaa, 0xc0, 0xb8, 0xcd, 0x7f, 0x7e, 0x33, 0xa3, 0xbe, 0x21, 0x29, 0xc8, 0x56, 0x34, 0xc0, 0x76, 0x87, 0x8f, 0xc7, 0x73, 0x58, 0x90, 0x16, 0xfc, 0xd6, + /* (2^112)P */ 0xb8, 0x3f, 0xe1, 0xdf, 0x3a, 0x91, 0x25, 0x0c, 0xf6, 0x47, 0xa8, 0x89, 0xc4, 0xc6, 0x61, 0xec, 0x86, 0x2c, 0xfd, 0xbe, 0xa4, 0x6f, 0xc2, 0xd4, 0x46, 0x19, 0x70, 0x5d, 0x09, 0x02, 0x86, 0xd3, 0x4b, 0xe9, 0x16, 0x7b, 0xf0, 0x0d, 0x6c, 0xff, 0x91, 0x05, 0xbf, 0x55, 0xb4, 0x00, 0x8d, 0xe5, 0x6d, 0x68, 0x20, 0x90, 0x12, 0xb5, 0x5c, 0x32, + /* (2^113)P */ 0x80, 0x45, 0xc8, 0x51, 0x87, 0xba, 0x1c, 0x5c, 0xcf, 0x5f, 0x4b, 0x3c, 0x9e, 0x3b, 0x36, 0xd2, 0x26, 0xa2, 0x7f, 0xab, 0xb7, 0xbf, 0xda, 0x68, 0x23, 0x8f, 0xc3, 0xa0, 0xfd, 0xad, 0xf1, 0x56, 0x3b, 0xd0, 0x75, 0x2b, 0x44, 0x61, 0xd8, 0xf4, 0xf1, 0x05, 0x49, 0x53, 0x07, 0xee, 0x47, 0xef, 0xc0, 0x7c, 0x9d, 0xe4, 0x15, 0x88, 0xc5, 0x47, + /* (2^114)P */ 0x2d, 0xb5, 0x09, 0x80, 0xb9, 0xd3, 0xd8, 0xfe, 0x4c, 0xd2, 0xa6, 0x6e, 0xd3, 0x75, 0xcf, 0xb0, 0x99, 0xcb, 0x50, 0x8d, 0xe9, 0x67, 0x9b, 0x20, 0xe8, 0x57, 0xd8, 0x14, 0x85, 0x73, 0x6a, 0x74, 0xe0, 0x99, 0xf0, 0x6b, 0x6e, 0x59, 0x30, 0x31, 0x33, 0x96, 0x5f, 0xa1, 0x0c, 0x1b, 0xf4, 0xca, 0x09, 0xe1, 0x9b, 0xb5, 0xcf, 0x6d, 0x0b, 0xeb, + /* (2^115)P */ 0x1a, 0xde, 0x50, 0xa9, 0xac, 0x3e, 0x10, 0x43, 0x4f, 0x82, 0x4f, 0xc0, 0xfe, 0x3f, 0x33, 0xd2, 0x64, 0x86, 0x50, 0xa9, 0x51, 0x76, 0x5e, 0x50, 0x97, 0x6c, 0x73, 0x8d, 0x77, 0xa3, 0x75, 0x03, 0xbc, 0xc9, 0xfb, 0x50, 0xd9, 0x6d, 0x16, 0xad, 0x5d, 0x32, 0x3d, 0xac, 0x44, 0xdf, 0x51, 0xf7, 0x19, 0xd4, 0x0b, 0x57, 0x78, 0x0b, 0x81, 0x4e, + /* (2^116)P */ 0x32, 0x24, 0xf1, 0x6c, 0x55, 0x62, 0x1d, 0xb3, 0x1f, 0xda, 0xfa, 0x6a, 0x8f, 0x98, 0x01, 0x16, 0xde, 0x44, 0x50, 0x0d, 0x2e, 0x6c, 0x0b, 0xa2, 0xd3, 0x74, 0x0e, 0xa9, 0xbf, 0x8d, 0xa9, 0xc8, 0xc8, 0x2f, 0x62, 0xc1, 0x35, 0x5e, 0xfd, 0x3a, 0xb3, 0x83, 0x2d, 0xee, 0x4e, 0xfd, 0x5c, 0x5e, 0xad, 0x85, 0xa5, 0x10, 0xb5, 0x4f, 0x34, 0xa7, + /* (2^117)P */ 0xd1, 0x58, 0x6f, 0xe6, 0x54, 0x2c, 0xc2, 0xcd, 0xcf, 0x83, 0xdc, 0x88, 0x0c, 0xb9, 0xb4, 0x62, 0x18, 0x89, 0x65, 0x28, 0xe9, 0x72, 0x4b, 0x65, 0xcf, 0xd6, 0x90, 0x88, 0xd7, 0x76, 0x17, 0x4f, 0x74, 0x64, 0x1e, 0xcb, 0xd3, 0xf5, 0x4b, 0xaa, 0x2e, 0x4d, 0x2d, 0x7c, 0x13, 0x1f, 0xfd, 0xd9, 0x60, 0x83, 0x7e, 0xda, 0x64, 0x1c, 0xdc, 0x9f, + /* (2^118)P */ 0xad, 0xef, 0xac, 0x1b, 0xc1, 0x30, 0x5a, 0x15, 0xc9, 0x1f, 0xac, 0xf1, 0xca, 0x44, 0x95, 0x95, 0xea, 0xf2, 0x22, 0xe7, 0x8d, 0x25, 0xf0, 0xff, 0xd8, 0x71, 0xf7, 0xf8, 0x8f, 0x8f, 0xcd, 0xf4, 0x1e, 0xfe, 0x6c, 0x68, 0x04, 0xb8, 0x78, 0xa1, 0x5f, 0xa6, 0x5d, 0x5e, 0xf9, 0x8d, 0xea, 0x80, 0xcb, 0xf3, 0x17, 0xa6, 0x03, 0xc9, 0x38, 0xd5, + /* (2^119)P */ 0x79, 0x14, 0x31, 0xc3, 0x38, 0xe5, 0xaa, 0xbf, 0x17, 0xa3, 0x04, 0x4e, 0x80, 0x59, 0x9c, 0x9f, 0x19, 0x39, 0xe4, 0x2d, 0x23, 0x54, 0x4a, 0x7f, 0x3e, 0xf3, 0xd9, 0xc7, 0xba, 0x6c, 0x8f, 0x6b, 0xfa, 0x34, 0xb5, 0x23, 0x17, 0x1d, 0xff, 0x1d, 0xea, 0x1f, 0xd7, 0xba, 0x61, 0xb2, 0xe0, 0x38, 0x6a, 0xe9, 0xcf, 0x48, 0x5d, 0x6a, 0x10, 0x9c, + /* (2^120)P */ 0xc8, 0xbb, 0x13, 0x1c, 0x3f, 0x3c, 0x34, 0xfd, 0xac, 0x37, 0x52, 0x44, 0x25, 0xa8, 0xde, 0x1d, 0x63, 0xf4, 0x81, 0x9a, 0xbe, 0x0b, 0x74, 0x2e, 0xc8, 0x51, 0x16, 0xd3, 0xac, 0x4a, 0xaf, 0xe2, 0x5f, 0x3a, 0x89, 0x32, 0xd1, 0x9b, 0x7c, 0x90, 0x0d, 0xac, 0xdc, 0x8b, 0x73, 0x45, 0x45, 0x97, 0xb1, 0x90, 0x2c, 0x1b, 0x31, 0xca, 0xb1, 0x94, + /* (2^121)P */ 0x07, 0x28, 0xdd, 0x10, 0x14, 0xa5, 0x95, 0x7e, 0xf3, 0xe4, 0xd4, 0x14, 0xb4, 0x7e, 0x76, 0xdb, 0x42, 0xd6, 0x94, 0x3e, 0xeb, 0x44, 0x64, 0x88, 0x0d, 0xec, 0xc1, 0x21, 0xf0, 0x79, 0xe0, 0x83, 0x67, 0x55, 0x53, 0xc2, 0xf6, 0xc5, 0xc5, 0x89, 0x39, 0xe8, 0x42, 0xd0, 0x17, 0xbd, 0xff, 0x35, 0x59, 0x0e, 0xc3, 0x06, 0x86, 0xd4, 0x64, 0xcf, + /* (2^122)P */ 0x91, 0xa8, 0xdb, 0x57, 0x9b, 0xe2, 0x96, 0x31, 0x10, 0x6e, 0xd7, 0x9a, 0x97, 0xb3, 0xab, 0xb5, 0x15, 0x66, 0xbe, 0xcc, 0x6d, 0x9a, 0xac, 0x06, 0xb3, 0x0d, 0xaa, 0x4b, 0x9c, 0x96, 0x79, 0x6c, 0x34, 0xee, 0x9e, 0x53, 0x4d, 0x6e, 0xbd, 0x88, 0x02, 0xbf, 0x50, 0x54, 0x12, 0x5d, 0x01, 0x02, 0x46, 0xc6, 0x74, 0x02, 0x8c, 0x24, 0xae, 0xb1, + /* (2^123)P */ 0xf5, 0x22, 0xea, 0xac, 0x7d, 0x9c, 0x33, 0x8a, 0xa5, 0x36, 0x79, 0x6a, 0x4f, 0xa4, 0xdc, 0xa5, 0x73, 0x64, 0xc4, 0x6f, 0x43, 0x02, 0x3b, 0x94, 0x66, 0xd2, 0x4b, 0x4f, 0xf6, 0x45, 0x33, 0x5d, 0x10, 0x33, 0x18, 0x1e, 0xa3, 0xfc, 0xf7, 0xd2, 0xb8, 0xc8, 0xa7, 0xe0, 0x76, 0x8a, 0xcd, 0xff, 0x4f, 0x99, 0x34, 0x47, 0x84, 0x91, 0x96, 0x9f, + /* (2^124)P */ 0x8a, 0x48, 0x3b, 0x48, 0x4a, 0xbc, 0xac, 0xe2, 0x80, 0xd6, 0xd2, 0x35, 0xde, 0xd0, 0x56, 0x42, 0x33, 0xb3, 0x56, 0x5a, 0xcd, 0xb8, 0x3d, 0xb5, 0x25, 0xc1, 0xed, 0xff, 0x87, 0x0b, 0x79, 0xff, 0xf2, 0x62, 0xe1, 0x76, 0xc6, 0xa2, 0x0f, 0xa8, 0x9b, 0x0d, 0xcc, 0x3f, 0x3d, 0x35, 0x27, 0x8d, 0x0b, 0x74, 0xb0, 0xc3, 0x78, 0x8c, 0xcc, 0xc8, + /* (2^125)P */ 0xfc, 0x9a, 0x0c, 0xa8, 0x49, 0x42, 0xb8, 0xdf, 0xcf, 0xb3, 0x19, 0xa6, 0x64, 0x57, 0xfe, 0xe8, 0xf8, 0xa6, 0x4b, 0x86, 0xa1, 0xd5, 0x83, 0x7f, 0x14, 0x99, 0x18, 0x0c, 0x7d, 0x5b, 0xf7, 0x3d, 0xf9, 0x4b, 0x79, 0xb1, 0x86, 0x30, 0xb4, 0x5e, 0x6a, 0xe8, 0x9d, 0xfa, 0x8a, 0x41, 0xc4, 0x30, 0xfc, 0x56, 0x74, 0x14, 0x42, 0xc8, 0x96, 0x0e, + /* (2^126)P */ 0xdf, 0x66, 0xec, 0xbc, 0x44, 0xdb, 0x19, 0xce, 0xd4, 0xb5, 0x49, 0x40, 0x07, 0x49, 0xe0, 0x3a, 0x61, 0x10, 0xfb, 0x7d, 0xba, 0xb1, 0xe0, 0x28, 0x5b, 0x99, 0x59, 0x96, 0xa2, 0xee, 0xe0, 0x23, 0x37, 0x39, 0x1f, 0xe6, 0x57, 0x9f, 0xf8, 0xf8, 0xdc, 0x74, 0xf6, 0x8f, 0x4f, 0x5e, 0x51, 0xa4, 0x12, 0xac, 0xbe, 0xe4, 0xf3, 0xd1, 0xf0, 0x24, + /* (2^127)P */ 0x1e, 0x3e, 0x9a, 0x5f, 0xdf, 0x9f, 0xd6, 0x4e, 0x8a, 0x28, 0xc3, 0xcd, 0x96, 0x9d, 0x57, 0xc7, 0x61, 0x81, 0x90, 0xff, 0xae, 0xb1, 0x4f, 0xc2, 0x96, 0x8b, 0x1a, 0x18, 0xf4, 0x50, 0xcb, 0x31, 0xe1, 0x57, 0xf4, 0x90, 0xa8, 0xea, 0xac, 0xe7, 0x61, 0x98, 0xb6, 0x15, 0xc1, 0x7b, 0x29, 0xa4, 0xc3, 0x18, 0xef, 0xb9, 0xd8, 0xdf, 0xf6, 0xac, + /* (2^128)P */ 0xca, 0xa8, 0x6c, 0xf1, 0xb4, 0xca, 0xfe, 0x31, 0xee, 0x48, 0x38, 0x8b, 0x0e, 0xbb, 0x7a, 0x30, 0xaa, 0xf9, 0xee, 0x27, 0x53, 0x24, 0xdc, 0x2e, 0x15, 0xa6, 0x48, 0x8f, 0xa0, 0x7e, 0xf1, 0xdc, 0x93, 0x87, 0x39, 0xeb, 0x7f, 0x38, 0x92, 0x92, 0x4c, 0x29, 0xe9, 0x57, 0xd8, 0x59, 0xfc, 0xe9, 0x9c, 0x44, 0xc0, 0x65, 0xcf, 0xac, 0x4b, 0xdc, + /* (2^129)P */ 0xa3, 0xd0, 0x37, 0x8f, 0x86, 0x2f, 0xc6, 0x47, 0x55, 0x46, 0x65, 0x26, 0x4b, 0x91, 0xe2, 0x18, 0x5c, 0x4f, 0x23, 0xc1, 0x37, 0x29, 0xb9, 0xc1, 0x27, 0xc5, 0x3c, 0xbf, 0x7e, 0x23, 0xdb, 0x73, 0x99, 0xbd, 0x1b, 0xb2, 0x31, 0x68, 0x3a, 0xad, 0xb7, 0xb0, 0x10, 0xc5, 0xe5, 0x11, 0x51, 0xba, 0xa7, 0x60, 0x66, 0x54, 0xf0, 0x08, 0xd7, 0x69, + /* (2^130)P */ 0x89, 0x41, 0x79, 0xcc, 0xeb, 0x0a, 0xf5, 0x4b, 0xa3, 0x4c, 0xce, 0x52, 0xb0, 0xa7, 0xe4, 0x41, 0x75, 0x7d, 0x04, 0xbb, 0x09, 0x4c, 0x50, 0x9f, 0xdf, 0xea, 0x74, 0x61, 0x02, 0xad, 0xb4, 0x9d, 0xb7, 0x05, 0xb9, 0xea, 0xeb, 0x91, 0x35, 0xe7, 0x49, 0xea, 0xd3, 0x4f, 0x3c, 0x60, 0x21, 0x7a, 0xde, 0xc7, 0xe2, 0x5a, 0xee, 0x8e, 0x93, 0xc7, + /* (2^131)P */ 0x00, 0xe8, 0xed, 0xd0, 0xb3, 0x0d, 0xaf, 0xb2, 0xde, 0x2c, 0xf6, 0x00, 0xe2, 0xea, 0x6d, 0xf8, 0x0e, 0xd9, 0x67, 0x59, 0xa9, 0x50, 0xbb, 0x17, 0x8f, 0xff, 0xb1, 0x9f, 0x17, 0xb6, 0xf2, 0xb5, 0xba, 0x80, 0xf7, 0x0f, 0xba, 0xd5, 0x09, 0x43, 0xaa, 0x4e, 0x3a, 0x67, 0x6a, 0x89, 0x9b, 0x18, 0x65, 0x35, 0xf8, 0x3a, 0x49, 0x91, 0x30, 0x51, + /* (2^132)P */ 0x8d, 0x25, 0xe9, 0x0e, 0x7d, 0x50, 0x76, 0xe4, 0x58, 0x7e, 0xb9, 0x33, 0xe6, 0x65, 0x90, 0xc2, 0x50, 0x9d, 0x50, 0x2e, 0x11, 0xad, 0xd5, 0x43, 0x52, 0x32, 0x41, 0x4f, 0x7b, 0xb6, 0xa0, 0xec, 0x81, 0x75, 0x36, 0x7c, 0x77, 0x85, 0x59, 0x70, 0xe4, 0xf9, 0xef, 0x66, 0x8d, 0x35, 0xc8, 0x2a, 0x6e, 0x5b, 0xc6, 0x0d, 0x0b, 0x29, 0x60, 0x68, + /* (2^133)P */ 0xf8, 0xce, 0xb0, 0x3a, 0x56, 0x7d, 0x51, 0x9a, 0x25, 0x73, 0xea, 0xdd, 0xe4, 0xe0, 0x0e, 0xf0, 0x07, 0xc0, 0x31, 0x00, 0x73, 0x35, 0xd0, 0x39, 0xc4, 0x9b, 0xb7, 0x95, 0xe0, 0x62, 0x70, 0x36, 0x0b, 0xcb, 0xa0, 0x42, 0xde, 0x51, 0xcf, 0x41, 0xe0, 0xb8, 0xb4, 0xc0, 0xe5, 0x46, 0x99, 0x9f, 0x02, 0x7f, 0x14, 0x8c, 0xc1, 0x4e, 0xef, 0xe8, + /* (2^134)P */ 0x10, 0x01, 0x57, 0x0a, 0xbe, 0x8b, 0x18, 0xc8, 0xca, 0x00, 0x28, 0x77, 0x4a, 0x9a, 0xc7, 0x55, 0x2a, 0xcc, 0x0c, 0x7b, 0xb9, 0xe9, 0xc8, 0x97, 0x7c, 0x02, 0xe3, 0x09, 0x2f, 0x62, 0x30, 0xb8, 0x40, 0x09, 0x65, 0xe9, 0x55, 0x63, 0xb5, 0x07, 0xca, 0x9f, 0x00, 0xdf, 0x9d, 0x5c, 0xc7, 0xee, 0x57, 0xa5, 0x90, 0x15, 0x1e, 0x22, 0xa0, 0x12, + /* (2^135)P */ 0x71, 0x2d, 0xc9, 0xef, 0x27, 0xb9, 0xd8, 0x12, 0x43, 0x6b, 0xa8, 0xce, 0x3b, 0x6d, 0x6e, 0x91, 0x43, 0x23, 0xbc, 0x32, 0xb3, 0xbf, 0xe1, 0xc7, 0x39, 0xcf, 0x7c, 0x42, 0x4c, 0xb1, 0x30, 0xe2, 0xdd, 0x69, 0x06, 0xe5, 0xea, 0xf0, 0x2a, 0x16, 0x50, 0x71, 0xca, 0x92, 0xdf, 0xc1, 0xcc, 0xec, 0xe6, 0x54, 0x07, 0xf3, 0x18, 0x8d, 0xd8, 0x29, + /* (2^136)P */ 0x98, 0x51, 0x48, 0x8f, 0xfa, 0x2e, 0x5e, 0x67, 0xb0, 0xc6, 0x17, 0x12, 0xb6, 0x7d, 0xc9, 0xad, 0x81, 0x11, 0xad, 0x0c, 0x1c, 0x2d, 0x45, 0xdf, 0xac, 0x66, 0xbd, 0x08, 0x6f, 0x7c, 0xc7, 0x06, 0x6e, 0x19, 0x08, 0x39, 0x64, 0xd7, 0xe4, 0xd1, 0x11, 0x5f, 0x1c, 0xf4, 0x67, 0xc3, 0x88, 0x6a, 0xe6, 0x07, 0xa3, 0x83, 0xd7, 0xfd, 0x2a, 0xf9, + /* (2^137)P */ 0x87, 0xed, 0xeb, 0xd9, 0xdf, 0xff, 0x43, 0x8b, 0xaa, 0x20, 0x58, 0xb0, 0xb4, 0x6b, 0x14, 0xb8, 0x02, 0xc5, 0x40, 0x20, 0x22, 0xbb, 0xf7, 0xb4, 0xf3, 0x05, 0x1e, 0x4d, 0x94, 0xff, 0xe3, 0xc5, 0x22, 0x82, 0xfe, 0xaf, 0x90, 0x42, 0x98, 0x6b, 0x76, 0x8b, 0x3e, 0x89, 0x3f, 0x42, 0x2a, 0xa7, 0x26, 0x00, 0xda, 0x5c, 0xa2, 0x2b, 0xec, 0xdd, + /* (2^138)P */ 0x5c, 0x21, 0x16, 0x0d, 0x46, 0xb8, 0xd0, 0xa7, 0x88, 0xe7, 0x25, 0xcb, 0x3e, 0x50, 0x73, 0x61, 0xe7, 0xaf, 0x5a, 0x3f, 0x47, 0x8b, 0x3d, 0x97, 0x79, 0x2c, 0xe6, 0x6d, 0x95, 0x74, 0x65, 0x70, 0x36, 0xfd, 0xd1, 0x9e, 0x13, 0x18, 0x63, 0xb1, 0x2d, 0x0b, 0xb5, 0x36, 0x3e, 0xe7, 0x35, 0x42, 0x3b, 0xe6, 0x1f, 0x4d, 0x9d, 0x59, 0xa2, 0x43, + /* (2^139)P */ 0x8c, 0x0c, 0x7c, 0x24, 0x9e, 0xe0, 0xf8, 0x05, 0x1c, 0x9e, 0x1f, 0x31, 0xc0, 0x70, 0xb3, 0xfb, 0x4e, 0xf8, 0x0a, 0x57, 0xb7, 0x49, 0xb5, 0x73, 0xa1, 0x5f, 0x9b, 0x6a, 0x07, 0x6c, 0x87, 0x71, 0x87, 0xd4, 0xbe, 0x98, 0x1e, 0x98, 0xee, 0x52, 0xc1, 0x7b, 0x95, 0x0f, 0x28, 0x32, 0x36, 0x28, 0xd0, 0x3a, 0x0f, 0x7d, 0x2a, 0xa9, 0x62, 0xb9, + /* (2^140)P */ 0x97, 0xe6, 0x18, 0x77, 0xf9, 0x34, 0xac, 0xbc, 0xe0, 0x62, 0x9f, 0x42, 0xde, 0xbd, 0x2f, 0xf7, 0x1f, 0xb7, 0x14, 0x52, 0x8a, 0x79, 0xb2, 0x3f, 0xd2, 0x95, 0x71, 0x01, 0xe8, 0xaf, 0x8c, 0xa4, 0xa4, 0xa7, 0x27, 0xf3, 0x5c, 0xdf, 0x3e, 0x57, 0x7a, 0xf1, 0x76, 0x49, 0xe6, 0x42, 0x3f, 0x8f, 0x1e, 0x63, 0x4a, 0x65, 0xb5, 0x41, 0xf5, 0x02, + /* (2^141)P */ 0x72, 0x85, 0xc5, 0x0b, 0xe1, 0x47, 0x64, 0x02, 0xc5, 0x4d, 0x81, 0x69, 0xb2, 0xcf, 0x0f, 0x6c, 0xd4, 0x6d, 0xd0, 0xc7, 0xb4, 0x1c, 0xd0, 0x32, 0x59, 0x89, 0xe2, 0xe0, 0x96, 0x8b, 0x12, 0x98, 0xbf, 0x63, 0x7a, 0x4c, 0x76, 0x7e, 0x58, 0x17, 0x8f, 0x5b, 0x0a, 0x59, 0x65, 0x75, 0xbc, 0x61, 0x1f, 0xbe, 0xc5, 0x6e, 0x0a, 0x57, 0x52, 0x70, + /* (2^142)P */ 0x92, 0x1c, 0x77, 0xbb, 0x62, 0x02, 0x6c, 0x25, 0x9c, 0x66, 0x07, 0x83, 0xab, 0xcc, 0x80, 0x5d, 0xd2, 0x76, 0x0c, 0xa4, 0xc5, 0xb4, 0x8a, 0x68, 0x23, 0x31, 0x32, 0x29, 0x8a, 0x47, 0x92, 0x12, 0x80, 0xb3, 0xfa, 0x18, 0xe4, 0x8d, 0xc0, 0x4d, 0xfe, 0x97, 0x5f, 0x72, 0x41, 0xb5, 0x5c, 0x7a, 0xbd, 0xf0, 0xcf, 0x5e, 0x97, 0xaa, 0x64, 0x32, + /* (2^143)P */ 0x35, 0x3f, 0x75, 0xc1, 0x7a, 0x75, 0x7e, 0xa9, 0xc6, 0x0b, 0x4e, 0x32, 0x62, 0xec, 0xe3, 0x5c, 0xfb, 0x01, 0x43, 0xb6, 0xd4, 0x5b, 0x75, 0xd2, 0xee, 0x7f, 0x5d, 0x23, 0x2b, 0xb3, 0x54, 0x34, 0x4c, 0xd3, 0xb4, 0x32, 0x84, 0x81, 0xb5, 0x09, 0x76, 0x19, 0xda, 0x58, 0xda, 0x7c, 0xdb, 0x2e, 0xdd, 0x4c, 0x8e, 0xdd, 0x5d, 0x89, 0x10, 0x10, + /* (2^144)P */ 0x57, 0x25, 0x6a, 0x08, 0x37, 0x92, 0xa8, 0xdf, 0x24, 0xef, 0x8f, 0x33, 0x34, 0x52, 0xa4, 0x4c, 0xf0, 0x77, 0x9f, 0x69, 0x77, 0xd5, 0x8f, 0xd2, 0x9a, 0xb3, 0xb6, 0x1d, 0x2d, 0xa6, 0xf7, 0x1f, 0xda, 0xd7, 0xcb, 0x75, 0x11, 0xc3, 0x6b, 0xc0, 0x38, 0xb1, 0xd5, 0x2d, 0x96, 0x84, 0x16, 0xfa, 0x26, 0xb9, 0xcc, 0x3f, 0x16, 0x47, 0x23, 0x74, + /* (2^145)P */ 0x9b, 0x61, 0x2a, 0x1c, 0xdd, 0x39, 0xa5, 0xfa, 0x1c, 0x7d, 0x63, 0x50, 0xca, 0xe6, 0x9d, 0xfa, 0xb7, 0xc4, 0x4c, 0x6a, 0x97, 0x5f, 0x36, 0x4e, 0x47, 0xdd, 0x17, 0xf7, 0xf9, 0x19, 0xce, 0x75, 0x17, 0xad, 0xce, 0x2a, 0xf3, 0xfe, 0x27, 0x8f, 0x3e, 0x48, 0xc0, 0x60, 0x87, 0x24, 0x19, 0xae, 0x59, 0xe4, 0x5a, 0x00, 0x2a, 0xba, 0xa2, 0x1f, + /* (2^146)P */ 0x26, 0x88, 0x42, 0x60, 0x9f, 0x6e, 0x2c, 0x7c, 0x39, 0x0f, 0x47, 0x6a, 0x0e, 0x02, 0xbb, 0x4b, 0x34, 0x29, 0x55, 0x18, 0x36, 0xcf, 0x3b, 0x47, 0xf1, 0x2e, 0xfc, 0x6e, 0x94, 0xff, 0xe8, 0x6b, 0x06, 0xd2, 0xba, 0x77, 0x5e, 0x60, 0xd7, 0x19, 0xef, 0x02, 0x9d, 0x3a, 0xc2, 0xb7, 0xa9, 0xd8, 0x57, 0xee, 0x7e, 0x2b, 0xf2, 0x6d, 0x28, 0xda, + /* (2^147)P */ 0xdf, 0xd9, 0x92, 0x11, 0x98, 0x23, 0xe2, 0x45, 0x2f, 0x74, 0x70, 0xee, 0x0e, 0x55, 0x65, 0x79, 0x86, 0x38, 0x17, 0x92, 0x85, 0x87, 0x99, 0x50, 0xd9, 0x7c, 0xdb, 0xa1, 0x10, 0xec, 0x30, 0xb7, 0x40, 0xa3, 0x23, 0x9b, 0x0e, 0x27, 0x49, 0x29, 0x03, 0x94, 0xff, 0x53, 0xdc, 0xd7, 0xed, 0x49, 0xa9, 0x5a, 0x3b, 0xee, 0xd7, 0xc7, 0x65, 0xaf, + /* (2^148)P */ 0xa0, 0xbd, 0xbe, 0x03, 0xee, 0x0c, 0xbe, 0x32, 0x00, 0x7b, 0x52, 0xcb, 0x92, 0x29, 0xbf, 0xa0, 0xc6, 0xd9, 0xd2, 0xd6, 0x15, 0xe8, 0x3a, 0x75, 0x61, 0x65, 0x56, 0xae, 0xad, 0x3c, 0x2a, 0x64, 0x14, 0x3f, 0x8e, 0xc1, 0x2d, 0x0c, 0x8d, 0x20, 0xdb, 0x58, 0x4b, 0xe5, 0x40, 0x15, 0x4b, 0xdc, 0xa8, 0xbd, 0xef, 0x08, 0xa7, 0xd1, 0xf4, 0xb0, + /* (2^149)P */ 0xa9, 0x0f, 0x05, 0x94, 0x66, 0xac, 0x1f, 0x65, 0x3f, 0xe1, 0xb8, 0xe1, 0x34, 0x5e, 0x1d, 0x8f, 0xe3, 0x93, 0x03, 0x15, 0xff, 0xb6, 0x65, 0xb6, 0x6e, 0xc0, 0x2f, 0xd4, 0x2e, 0xb9, 0x2c, 0x13, 0x3c, 0x99, 0x1c, 0xb5, 0x87, 0xba, 0x79, 0xcb, 0xf0, 0x18, 0x06, 0x86, 0x04, 0x14, 0x25, 0x09, 0xcd, 0x1c, 0x14, 0xda, 0x35, 0xd0, 0x38, 0x3b, + /* (2^150)P */ 0x1b, 0x04, 0xa3, 0x27, 0xb4, 0xd3, 0x37, 0x48, 0x1e, 0x8f, 0x69, 0xd3, 0x5a, 0x2f, 0x20, 0x02, 0x36, 0xbe, 0x06, 0x7b, 0x6b, 0x6c, 0x12, 0x5b, 0x80, 0x74, 0x44, 0xe6, 0xf8, 0xf5, 0x95, 0x59, 0x29, 0xab, 0x51, 0x47, 0x83, 0x28, 0xe0, 0xad, 0xde, 0xaa, 0xd3, 0xb1, 0x1a, 0xcb, 0xa3, 0xcd, 0x8b, 0x6a, 0xb1, 0xa7, 0x0a, 0xd1, 0xf9, 0xbe, + /* (2^151)P */ 0xce, 0x2f, 0x85, 0xca, 0x74, 0x6d, 0x49, 0xb8, 0xce, 0x80, 0x44, 0xe0, 0xda, 0x5b, 0xcf, 0x2f, 0x79, 0x74, 0xfe, 0xb4, 0x2c, 0x99, 0x20, 0x6e, 0x09, 0x04, 0xfb, 0x6d, 0x57, 0x5b, 0x95, 0x0c, 0x45, 0xda, 0x4f, 0x7f, 0x63, 0xcc, 0x85, 0x5a, 0x67, 0x50, 0x68, 0x71, 0xb4, 0x67, 0xb1, 0x2e, 0xc1, 0x1c, 0xdc, 0xff, 0x2a, 0x7c, 0x10, 0x5e, + /* (2^152)P */ 0xa6, 0xde, 0xf3, 0xd4, 0x22, 0x30, 0x24, 0x9e, 0x0b, 0x30, 0x54, 0x59, 0x7e, 0xa2, 0xeb, 0x89, 0x54, 0x65, 0x3e, 0x40, 0xd1, 0xde, 0xe6, 0xee, 0x4d, 0xbf, 0x5e, 0x40, 0x1d, 0xee, 0x4f, 0x68, 0xd9, 0xa7, 0x2f, 0xb3, 0x64, 0xb3, 0xf5, 0xc8, 0xd3, 0xaa, 0x70, 0x70, 0x3d, 0xef, 0xd3, 0x95, 0x54, 0xdb, 0x3e, 0x94, 0x95, 0x92, 0x1f, 0x45, + /* (2^153)P */ 0x22, 0x80, 0x1d, 0x9d, 0x96, 0xa5, 0x78, 0x6f, 0xe0, 0x1e, 0x1b, 0x66, 0x42, 0xc8, 0xae, 0x9e, 0x46, 0x45, 0x08, 0x41, 0xdf, 0x80, 0xae, 0x6f, 0xdb, 0x15, 0x5a, 0x21, 0x31, 0x7a, 0xd0, 0xf2, 0x54, 0x15, 0x88, 0xd3, 0x0f, 0x7f, 0x14, 0x5a, 0x14, 0x97, 0xab, 0xf4, 0x58, 0x6a, 0x9f, 0xea, 0x74, 0xe5, 0x6b, 0x90, 0x59, 0x2b, 0x48, 0xd9, + /* (2^154)P */ 0x12, 0x24, 0x04, 0xf5, 0x50, 0xc2, 0x8c, 0xb0, 0x7c, 0x46, 0x98, 0xd5, 0x24, 0xad, 0xf6, 0x72, 0xdc, 0x82, 0x1a, 0x60, 0xc1, 0xeb, 0x48, 0xef, 0x7f, 0x6e, 0xe6, 0xcc, 0xdb, 0x7b, 0xae, 0xbe, 0x5e, 0x1e, 0x5c, 0xe6, 0x0a, 0x70, 0xdf, 0xa4, 0xa3, 0x85, 0x1b, 0x1b, 0x7f, 0x72, 0xb9, 0x96, 0x6f, 0xdc, 0x03, 0x76, 0x66, 0xfb, 0xa0, 0x33, + /* (2^155)P */ 0x37, 0x40, 0xbb, 0xbc, 0x68, 0x58, 0x86, 0xca, 0xbb, 0xa5, 0x24, 0x76, 0x3d, 0x48, 0xd1, 0xad, 0xb4, 0xa8, 0xcf, 0xc3, 0xb6, 0xa8, 0xba, 0x1a, 0x3a, 0xbe, 0x33, 0x75, 0x04, 0x5c, 0x13, 0x8c, 0x0d, 0x70, 0x8d, 0xa6, 0x4e, 0x2a, 0xeb, 0x17, 0x3c, 0x22, 0xdd, 0x3e, 0x96, 0x40, 0x11, 0x9e, 0x4e, 0xae, 0x3d, 0xf8, 0x91, 0xd7, 0x50, 0xc8, + /* (2^156)P */ 0xd8, 0xca, 0xde, 0x19, 0xcf, 0x00, 0xe4, 0x73, 0x18, 0x7f, 0x9b, 0x9f, 0xf4, 0x5b, 0x49, 0x49, 0x99, 0xdc, 0xa4, 0x46, 0x21, 0xb5, 0xd7, 0x3e, 0xb7, 0x47, 0x1b, 0xa9, 0x9f, 0x4c, 0x69, 0x7d, 0xec, 0x33, 0xd6, 0x1c, 0x51, 0x7f, 0x47, 0x74, 0x7a, 0x6c, 0xf3, 0xd2, 0x2e, 0xbf, 0xdf, 0x6c, 0x9e, 0x77, 0x3b, 0x34, 0xf6, 0x73, 0x80, 0xed, + /* (2^157)P */ 0x16, 0xfb, 0x16, 0xc3, 0xc2, 0x83, 0xe4, 0xf4, 0x03, 0x7f, 0x52, 0xb0, 0x67, 0x51, 0x7b, 0x24, 0x5a, 0x51, 0xd3, 0xb6, 0x4e, 0x59, 0x76, 0xcd, 0x08, 0x7b, 0x1d, 0x7a, 0x9c, 0x65, 0xae, 0xce, 0xaa, 0xd2, 0x1c, 0x85, 0x66, 0x68, 0x06, 0x15, 0xa8, 0x06, 0xe6, 0x16, 0x37, 0xf4, 0x49, 0x9e, 0x0f, 0x50, 0x37, 0xb1, 0xb2, 0x93, 0x70, 0x43, + /* (2^158)P */ 0x18, 0x3a, 0x16, 0xe5, 0x8d, 0xc8, 0x35, 0xd6, 0x7b, 0x09, 0xec, 0x61, 0x5f, 0x5c, 0x2a, 0x19, 0x96, 0x2e, 0xc3, 0xfd, 0xab, 0xe6, 0x23, 0xae, 0xab, 0xc5, 0xcb, 0xb9, 0x7b, 0x2d, 0x34, 0x51, 0xb9, 0x41, 0x9e, 0x7d, 0xca, 0xda, 0x25, 0x45, 0x14, 0xb0, 0xc7, 0x4d, 0x26, 0x2b, 0xfe, 0x43, 0xb0, 0x21, 0x5e, 0xfa, 0xdc, 0x7c, 0xf9, 0x5a, + /* (2^159)P */ 0x94, 0xad, 0x42, 0x17, 0xf5, 0xcd, 0x1c, 0x0d, 0xf6, 0x41, 0xd2, 0x55, 0xbb, 0x50, 0xf1, 0xc6, 0xbc, 0xa6, 0xc5, 0x3a, 0xfd, 0x9b, 0x75, 0x3e, 0xf6, 0x1a, 0xa7, 0xb2, 0x6e, 0x64, 0x12, 0xdc, 0x3c, 0xe5, 0xf6, 0xfc, 0x3b, 0xfa, 0x43, 0x81, 0xd4, 0xa5, 0xee, 0xf5, 0x9c, 0x47, 0x2f, 0xd0, 0x9c, 0xde, 0xa1, 0x48, 0x91, 0x9a, 0x34, 0xc1, + /* (2^160)P */ 0x37, 0x1b, 0xb3, 0x88, 0xc9, 0x98, 0x4e, 0xfb, 0x84, 0x4f, 0x2b, 0x0a, 0xb6, 0x8f, 0x35, 0x15, 0xcd, 0x61, 0x7a, 0x5f, 0x5c, 0xa0, 0xca, 0x23, 0xa0, 0x93, 0x1f, 0xcc, 0x3c, 0x39, 0x3a, 0x24, 0xa7, 0x49, 0xad, 0x8d, 0x59, 0xcc, 0x94, 0x5a, 0x16, 0xf5, 0x70, 0xe8, 0x52, 0x1e, 0xee, 0x20, 0x30, 0x17, 0x7e, 0xf0, 0x4c, 0x93, 0x06, 0x5a, + /* (2^161)P */ 0x81, 0xba, 0x3b, 0xd7, 0x3e, 0xb4, 0x32, 0x3a, 0x22, 0x39, 0x2a, 0xfc, 0x19, 0xd9, 0xd2, 0xf6, 0xc5, 0x79, 0x6c, 0x0e, 0xde, 0xda, 0x01, 0xff, 0x52, 0xfb, 0xb6, 0x95, 0x4e, 0x7a, 0x10, 0xb8, 0x06, 0x86, 0x3c, 0xcd, 0x56, 0xd6, 0x15, 0xbf, 0x6e, 0x3e, 0x4f, 0x35, 0x5e, 0xca, 0xbc, 0xa5, 0x95, 0xa2, 0xdf, 0x2d, 0x1d, 0xaf, 0x59, 0xf9, + /* (2^162)P */ 0x69, 0xe5, 0xe2, 0xfa, 0xc9, 0x7f, 0xdd, 0x09, 0xf5, 0x6b, 0x4e, 0x2e, 0xbe, 0xb4, 0xbf, 0x3e, 0xb2, 0xf2, 0x81, 0x30, 0xe1, 0x07, 0xa8, 0x0d, 0x2b, 0xd2, 0x5a, 0x55, 0xbe, 0x4b, 0x86, 0x5d, 0xb0, 0x5e, 0x7c, 0x8f, 0xc1, 0x3c, 0x81, 0x4c, 0xf7, 0x6d, 0x7d, 0xe6, 0x4f, 0x8a, 0x85, 0xc2, 0x2f, 0x28, 0xef, 0x8c, 0x69, 0xc2, 0xc2, 0x1a, + /* (2^163)P */ 0xd9, 0xe4, 0x0e, 0x1e, 0xc2, 0xf7, 0x2f, 0x9f, 0xa1, 0x40, 0xfe, 0x46, 0x16, 0xaf, 0x2e, 0xd1, 0xec, 0x15, 0x9b, 0x61, 0x92, 0xce, 0xfc, 0x10, 0x43, 0x1d, 0x00, 0xf6, 0xbe, 0x20, 0x80, 0x80, 0x6f, 0x3c, 0x16, 0x94, 0x59, 0xba, 0x03, 0x53, 0x6e, 0xb6, 0xdd, 0x25, 0x7b, 0x86, 0xbf, 0x96, 0xf4, 0x2f, 0xa1, 0x96, 0x8d, 0xf9, 0xb3, 0x29, + /* (2^164)P */ 0x3b, 0x04, 0x60, 0x6e, 0xce, 0xab, 0xd2, 0x63, 0x18, 0x53, 0x88, 0x16, 0x4a, 0x6a, 0xab, 0x72, 0x03, 0x68, 0xa5, 0xd4, 0x0d, 0xb2, 0x82, 0x81, 0x1f, 0x2b, 0x5c, 0x75, 0xe8, 0xd2, 0x1d, 0x7f, 0xe7, 0x1b, 0x35, 0x02, 0xde, 0xec, 0xbd, 0xcb, 0xc7, 0x01, 0xd3, 0x95, 0x61, 0xfe, 0xb2, 0x7a, 0x66, 0x09, 0x4c, 0x6d, 0xfd, 0x39, 0xf7, 0x52, + /* (2^165)P */ 0x42, 0xc1, 0x5f, 0xf8, 0x35, 0x52, 0xc1, 0xfe, 0xc5, 0x11, 0x80, 0x1c, 0x11, 0x46, 0x31, 0x11, 0xbe, 0xd0, 0xc4, 0xb6, 0x07, 0x13, 0x38, 0xa0, 0x8d, 0x65, 0xf0, 0x56, 0x9e, 0x16, 0xbf, 0x9d, 0xcd, 0x51, 0x34, 0xf9, 0x08, 0x48, 0x7b, 0x76, 0x0c, 0x7b, 0x30, 0x07, 0xa8, 0x76, 0xaf, 0xa3, 0x29, 0x38, 0xb0, 0x58, 0xde, 0x72, 0x4b, 0x45, + /* (2^166)P */ 0xd4, 0x16, 0xa7, 0xc0, 0xb4, 0x9f, 0xdf, 0x1a, 0x37, 0xc8, 0x35, 0xed, 0xc5, 0x85, 0x74, 0x64, 0x09, 0x22, 0xef, 0xe9, 0x0c, 0xaf, 0x12, 0x4c, 0x9e, 0xf8, 0x47, 0x56, 0xe0, 0x7f, 0x4e, 0x24, 0x6b, 0x0c, 0xe7, 0xad, 0xc6, 0x47, 0x1d, 0xa4, 0x0d, 0x86, 0x89, 0x65, 0xe8, 0x5f, 0x71, 0xc7, 0xe9, 0xcd, 0xec, 0x6c, 0x62, 0xc7, 0xe3, 0xb3, + /* (2^167)P */ 0xb5, 0xea, 0x86, 0xe3, 0x15, 0x18, 0x3f, 0x6d, 0x7b, 0x05, 0x95, 0x15, 0x53, 0x26, 0x1c, 0xeb, 0xbe, 0x7e, 0x16, 0x42, 0x4b, 0xa2, 0x3d, 0xdd, 0x0e, 0xff, 0xba, 0x67, 0xb5, 0xae, 0x7a, 0x17, 0xde, 0x23, 0xad, 0x14, 0xcc, 0xd7, 0xaf, 0x57, 0x01, 0xe0, 0xdd, 0x48, 0xdd, 0xd7, 0xe3, 0xdf, 0xe9, 0x2d, 0xda, 0x67, 0xa4, 0x9f, 0x29, 0x04, + /* (2^168)P */ 0x16, 0x53, 0xe6, 0x9c, 0x4e, 0xe5, 0x1e, 0x70, 0x81, 0x25, 0x02, 0x9b, 0x47, 0x6d, 0xd2, 0x08, 0x73, 0xbe, 0x0a, 0xf1, 0x7b, 0xeb, 0x24, 0xeb, 0x38, 0x23, 0x5c, 0xb6, 0x3e, 0xce, 0x1e, 0xe3, 0xbc, 0x82, 0x35, 0x1f, 0xaf, 0x3a, 0x3a, 0xe5, 0x4e, 0xc1, 0xca, 0xbf, 0x47, 0xb4, 0xbb, 0xbc, 0x5f, 0xea, 0xc6, 0xca, 0xf3, 0xa0, 0xa2, 0x73, + /* (2^169)P */ 0xef, 0xa4, 0x7a, 0x4e, 0xe4, 0xc7, 0xb6, 0x43, 0x2e, 0xa5, 0xe4, 0xa5, 0xba, 0x1e, 0xa5, 0xfe, 0x9e, 0xce, 0xa9, 0x80, 0x04, 0xcb, 0x4f, 0xd8, 0x74, 0x05, 0x48, 0xfa, 0x99, 0x11, 0x5d, 0x97, 0x3b, 0x07, 0x0d, 0xdd, 0xe6, 0xb1, 0x74, 0x87, 0x1a, 0xd3, 0x26, 0xb7, 0x8f, 0xe1, 0x63, 0x3d, 0xec, 0x53, 0x93, 0xb0, 0x81, 0x78, 0x34, 0xa4, + /* (2^170)P */ 0xe1, 0xe7, 0xd4, 0x58, 0x9d, 0x0e, 0x8b, 0x65, 0x66, 0x37, 0x16, 0x48, 0x6f, 0xaa, 0x42, 0x37, 0x77, 0xad, 0xb1, 0x56, 0x48, 0xdf, 0x65, 0x36, 0x30, 0xb8, 0x00, 0x12, 0xd8, 0x32, 0x28, 0x7f, 0xc1, 0x71, 0xeb, 0x93, 0x0f, 0x48, 0x04, 0xe1, 0x5a, 0x6a, 0x96, 0xc1, 0xca, 0x89, 0x6d, 0x1b, 0x82, 0x4c, 0x18, 0x6d, 0x55, 0x4b, 0xea, 0xfd, + /* (2^171)P */ 0x62, 0x1a, 0x53, 0xb4, 0xb1, 0xbe, 0x6f, 0x15, 0x18, 0x88, 0xd4, 0x66, 0x61, 0xc7, 0x12, 0x69, 0x02, 0xbd, 0x03, 0x23, 0x2b, 0xef, 0xf9, 0x54, 0xa4, 0x85, 0xa8, 0xe3, 0xb7, 0xbd, 0xa9, 0xa3, 0xf3, 0x2a, 0xdd, 0xf1, 0xd4, 0x03, 0x0f, 0xa9, 0xa1, 0xd8, 0xa3, 0xcd, 0xb2, 0x71, 0x90, 0x4b, 0x35, 0x62, 0xf2, 0x2f, 0xce, 0x67, 0x1f, 0xaa, + /* (2^172)P */ 0x9e, 0x1e, 0xcd, 0x43, 0x7e, 0x87, 0x37, 0x94, 0x3a, 0x97, 0x4c, 0x7e, 0xee, 0xc9, 0x37, 0x85, 0xf1, 0xd9, 0x4f, 0xbf, 0xf9, 0x6f, 0x39, 0x9a, 0x39, 0x87, 0x2e, 0x25, 0x84, 0x42, 0xc3, 0x80, 0xcb, 0x07, 0x22, 0xae, 0x30, 0xd5, 0x50, 0xa1, 0x23, 0xcc, 0x31, 0x81, 0x9d, 0xf1, 0x30, 0xd9, 0x2b, 0x73, 0x41, 0x16, 0x50, 0xab, 0x2d, 0xa2, + /* (2^173)P */ 0xa4, 0x69, 0x4f, 0xa1, 0x4e, 0xb9, 0xbf, 0x14, 0xe8, 0x2b, 0x04, 0x93, 0xb7, 0x6e, 0x9f, 0x7d, 0x73, 0x0a, 0xc5, 0x14, 0xb8, 0xde, 0x8c, 0xc1, 0xfe, 0xc0, 0xa7, 0xa4, 0xcc, 0x42, 0x42, 0x81, 0x15, 0x65, 0x8a, 0x80, 0xb9, 0xde, 0x1f, 0x60, 0x33, 0x0e, 0xcb, 0xfc, 0xe0, 0xdb, 0x83, 0xa1, 0xe5, 0xd0, 0x16, 0x86, 0x2c, 0xe2, 0x87, 0xed, + /* (2^174)P */ 0x7a, 0xc0, 0xeb, 0x6b, 0xf6, 0x0d, 0x4c, 0x6d, 0x1e, 0xdb, 0xab, 0xe7, 0x19, 0x45, 0xc6, 0xe3, 0xb2, 0x06, 0xbb, 0xbc, 0x70, 0x99, 0x83, 0x33, 0xeb, 0x28, 0xc8, 0x77, 0xf6, 0x4d, 0x01, 0xb7, 0x59, 0xa0, 0xd2, 0xb3, 0x2a, 0x72, 0x30, 0xe7, 0x11, 0x39, 0xb6, 0x41, 0x29, 0x65, 0x5a, 0x14, 0xb9, 0x86, 0x08, 0xe0, 0x7d, 0x32, 0x8c, 0xf0, + /* (2^175)P */ 0x5c, 0x11, 0x30, 0x9e, 0x05, 0x27, 0xf5, 0x45, 0x0f, 0xb3, 0xc9, 0x75, 0xc3, 0xd7, 0xe1, 0x82, 0x3b, 0x8e, 0x87, 0x23, 0x00, 0x15, 0x19, 0x07, 0xd9, 0x21, 0x53, 0xc7, 0xf1, 0xa3, 0xbf, 0x70, 0x64, 0x15, 0x18, 0xca, 0x23, 0x9e, 0xd3, 0x08, 0xc3, 0x2a, 0x8b, 0xe5, 0x83, 0x04, 0x89, 0x14, 0xfd, 0x28, 0x25, 0x1c, 0xe3, 0x26, 0xa7, 0x22, + /* (2^176)P */ 0xdc, 0xd4, 0x75, 0x60, 0x99, 0x94, 0xea, 0x09, 0x8e, 0x8a, 0x3c, 0x1b, 0xf9, 0xbd, 0x33, 0x0d, 0x51, 0x3d, 0x12, 0x6f, 0x4e, 0x72, 0xe0, 0x17, 0x20, 0xe9, 0x75, 0xe6, 0x3a, 0xb2, 0x13, 0x83, 0x4e, 0x7a, 0x08, 0x9e, 0xd1, 0x04, 0x5f, 0x6b, 0x42, 0x0b, 0x76, 0x2a, 0x2d, 0x77, 0x53, 0x6c, 0x65, 0x6d, 0x8e, 0x25, 0x3c, 0xb6, 0x8b, 0x69, + /* (2^177)P */ 0xb9, 0x49, 0x28, 0xd0, 0xdc, 0x6c, 0x8f, 0x4c, 0xc9, 0x14, 0x8a, 0x38, 0xa3, 0xcb, 0xc4, 0x9d, 0x53, 0xcf, 0xe9, 0xe3, 0xcf, 0xe0, 0xb1, 0xf2, 0x1b, 0x4c, 0x7f, 0x83, 0x2a, 0x7a, 0xe9, 0x8b, 0x3b, 0x86, 0x61, 0x30, 0xe9, 0x99, 0xbd, 0xba, 0x19, 0x6e, 0x65, 0x2a, 0x12, 0x3e, 0x9c, 0xa8, 0xaf, 0xc3, 0xcf, 0xf8, 0x1f, 0x77, 0x86, 0xea, + /* (2^178)P */ 0x30, 0xde, 0xe7, 0xff, 0x54, 0xf7, 0xa2, 0x59, 0xf6, 0x0b, 0xfb, 0x7a, 0xf2, 0x39, 0xf0, 0xdb, 0x39, 0xbc, 0xf0, 0xfa, 0x60, 0xeb, 0x6b, 0x4f, 0x47, 0x17, 0xc8, 0x00, 0x65, 0x6d, 0x25, 0x1c, 0xd0, 0x48, 0x56, 0x53, 0x45, 0x11, 0x30, 0x02, 0x49, 0x20, 0x27, 0xac, 0xf2, 0x4c, 0xac, 0x64, 0x3d, 0x52, 0xb8, 0x89, 0xe0, 0x93, 0x16, 0x0f, + /* (2^179)P */ 0x84, 0x09, 0xba, 0x40, 0xb2, 0x2f, 0xa3, 0xa8, 0xc2, 0xba, 0x46, 0x33, 0x05, 0x9d, 0x62, 0xad, 0xa1, 0x3c, 0x33, 0xef, 0x0d, 0xeb, 0xf0, 0x77, 0x11, 0x5a, 0xb0, 0x21, 0x9c, 0xdf, 0x55, 0x24, 0x25, 0x35, 0x51, 0x61, 0x92, 0xf0, 0xb1, 0xce, 0xf5, 0xd4, 0x7b, 0x6c, 0x21, 0x9d, 0x56, 0x52, 0xf8, 0xa1, 0x4c, 0xe9, 0x27, 0x55, 0xac, 0x91, + /* (2^180)P */ 0x03, 0x3e, 0x30, 0xd2, 0x0a, 0xfa, 0x7d, 0x82, 0x3d, 0x1f, 0x8b, 0xcb, 0xb6, 0x04, 0x5c, 0xcc, 0x8b, 0xda, 0xe2, 0x68, 0x74, 0x08, 0x8c, 0x44, 0x83, 0x57, 0x6d, 0x6f, 0x80, 0xb0, 0x7e, 0xa9, 0x82, 0x91, 0x7b, 0x4c, 0x37, 0x97, 0xd1, 0x63, 0xd1, 0xbd, 0x45, 0xe6, 0x8a, 0x86, 0xd6, 0x89, 0x54, 0xfd, 0xd2, 0xb1, 0xd7, 0x54, 0xad, 0xaf, + /* (2^181)P */ 0x8b, 0x33, 0x62, 0x49, 0x9f, 0x63, 0xf9, 0x87, 0x42, 0x58, 0xbf, 0xb3, 0xe6, 0x68, 0x02, 0x60, 0x5c, 0x76, 0x62, 0xf7, 0x61, 0xd7, 0x36, 0x31, 0xf7, 0x9c, 0xb5, 0xe5, 0x13, 0x6c, 0xea, 0x78, 0xae, 0xcf, 0xde, 0xbf, 0xb6, 0xeb, 0x4f, 0xc8, 0x2a, 0xb4, 0x9a, 0x9f, 0xf3, 0xd1, 0x6a, 0xec, 0x0c, 0xbd, 0x85, 0x98, 0x40, 0x06, 0x1c, 0x2a, + /* (2^182)P */ 0x74, 0x3b, 0xe7, 0x81, 0xd5, 0xae, 0x54, 0x56, 0x03, 0xe8, 0x97, 0x16, 0x76, 0xcf, 0x24, 0x96, 0x96, 0x5b, 0xcc, 0x09, 0xab, 0x23, 0x6f, 0x54, 0xae, 0x8f, 0xe4, 0x12, 0xcb, 0xfd, 0xbc, 0xac, 0x93, 0x45, 0x3d, 0x68, 0x08, 0x22, 0x59, 0xc6, 0xf0, 0x47, 0x19, 0x8c, 0x79, 0x93, 0x1e, 0x0e, 0x30, 0xb0, 0x94, 0xfb, 0x17, 0x1d, 0x5a, 0x12, + /* (2^183)P */ 0x85, 0xff, 0x40, 0x18, 0x85, 0xff, 0x44, 0x37, 0x69, 0x23, 0x4d, 0x34, 0xe1, 0xeb, 0xa3, 0x1b, 0x55, 0x40, 0xc1, 0x64, 0xf4, 0xd4, 0x13, 0x0a, 0x9f, 0xb9, 0x19, 0xfc, 0x88, 0x7d, 0xc0, 0x72, 0xcf, 0x69, 0x2f, 0xd2, 0x0c, 0x82, 0x0f, 0xda, 0x08, 0xba, 0x0f, 0xaa, 0x3b, 0xe9, 0xe5, 0x83, 0x7a, 0x06, 0xe8, 0x1b, 0x38, 0x43, 0xc3, 0x54, + /* (2^184)P */ 0x14, 0xaa, 0xb3, 0x6e, 0xe6, 0x28, 0xee, 0xc5, 0x22, 0x6c, 0x7c, 0xf9, 0xa8, 0x71, 0xcc, 0xfe, 0x68, 0x7e, 0xd3, 0xb8, 0x37, 0x96, 0xca, 0x0b, 0xd9, 0xb6, 0x06, 0xa9, 0xf6, 0x71, 0xe8, 0x31, 0xf7, 0xd8, 0xf1, 0x5d, 0xab, 0xb9, 0xf0, 0x5c, 0x98, 0xcf, 0x22, 0xa2, 0x2a, 0xf6, 0xd0, 0x59, 0xf0, 0x9d, 0xd9, 0x6a, 0x4f, 0x59, 0x57, 0xad, + /* (2^185)P */ 0xd7, 0x2b, 0x3d, 0x38, 0x4c, 0x2e, 0x23, 0x4d, 0x49, 0xa2, 0x62, 0x62, 0xf9, 0x0f, 0xde, 0x08, 0xf3, 0x86, 0x71, 0xb6, 0xc7, 0xf9, 0x85, 0x9c, 0x33, 0xa1, 0xcf, 0x16, 0xaa, 0x60, 0xb9, 0xb7, 0xea, 0xed, 0x01, 0x1c, 0x59, 0xdb, 0x3f, 0x3f, 0x97, 0x2e, 0xf0, 0x09, 0x9f, 0x10, 0x85, 0x5f, 0x53, 0x39, 0xf3, 0x13, 0x40, 0x56, 0x95, 0xf9, + /* (2^186)P */ 0xb4, 0xe3, 0xda, 0xc6, 0x1f, 0x78, 0x8e, 0xac, 0xd4, 0x20, 0x1d, 0xa0, 0xbf, 0x4c, 0x09, 0x16, 0xa7, 0x30, 0xb5, 0x8d, 0x9e, 0xa1, 0x5f, 0x6d, 0x52, 0xf4, 0x71, 0xb6, 0x32, 0x2d, 0x21, 0x51, 0xc6, 0xfc, 0x2f, 0x08, 0xf4, 0x13, 0x6c, 0x55, 0xba, 0x72, 0x81, 0x24, 0x49, 0x0e, 0x4f, 0x06, 0x36, 0x39, 0x6a, 0xc5, 0x81, 0xfc, 0xeb, 0xb2, + /* (2^187)P */ 0x7d, 0x8d, 0xc8, 0x6c, 0xea, 0xb4, 0xb9, 0xe8, 0x40, 0xc9, 0x69, 0xc9, 0x30, 0x05, 0xfd, 0x34, 0x46, 0xfd, 0x94, 0x05, 0x16, 0xf5, 0x4b, 0x13, 0x3d, 0x24, 0x1a, 0xd6, 0x64, 0x2b, 0x9c, 0xe2, 0xa5, 0xd9, 0x98, 0xe0, 0xe8, 0xf4, 0xbc, 0x2c, 0xbd, 0xa2, 0x56, 0xe3, 0x9e, 0x14, 0xdb, 0xbf, 0x05, 0xbf, 0x9a, 0x13, 0x5d, 0xf7, 0x91, 0xa3, + /* (2^188)P */ 0x8b, 0xcb, 0x27, 0xf3, 0x15, 0x26, 0x05, 0x40, 0x0f, 0xa6, 0x15, 0x13, 0x71, 0x95, 0xa2, 0xc6, 0x38, 0x04, 0x67, 0xf8, 0x9a, 0x83, 0x06, 0xaa, 0x25, 0x36, 0x72, 0x01, 0x6f, 0x74, 0x5f, 0xe5, 0x6e, 0x44, 0x99, 0xce, 0x13, 0xbc, 0x82, 0xc2, 0x0d, 0xa4, 0x98, 0x50, 0x38, 0xf3, 0xa2, 0xc5, 0xe5, 0x24, 0x1f, 0x6f, 0x56, 0x3e, 0x07, 0xb2, + /* (2^189)P */ 0xbd, 0x0f, 0x32, 0x60, 0x07, 0xb1, 0xd7, 0x0b, 0x11, 0x07, 0x57, 0x02, 0x89, 0xe8, 0x8b, 0xe8, 0x5a, 0x1f, 0xee, 0x54, 0x6b, 0xff, 0xb3, 0x04, 0x07, 0x57, 0x13, 0x0b, 0x94, 0xa8, 0x4d, 0x81, 0xe2, 0x17, 0x16, 0x45, 0xd4, 0x4b, 0xf7, 0x7e, 0x64, 0x66, 0x20, 0xe8, 0x0b, 0x26, 0xfd, 0xa9, 0x8a, 0x47, 0x52, 0x89, 0x14, 0xd0, 0xd1, 0xa1, + /* (2^190)P */ 0xdc, 0x03, 0xe6, 0x20, 0x44, 0x47, 0x8f, 0x04, 0x16, 0x24, 0x22, 0xc1, 0x55, 0x5c, 0xbe, 0x43, 0xc3, 0x92, 0xc5, 0x54, 0x3d, 0x5d, 0xd1, 0x05, 0x9c, 0xc6, 0x7c, 0xbf, 0x23, 0x84, 0x1a, 0xba, 0x4f, 0x1f, 0xfc, 0xa1, 0xae, 0x1a, 0x64, 0x02, 0x51, 0xf1, 0xcb, 0x7a, 0x20, 0xce, 0xb2, 0x34, 0x3c, 0xca, 0xe0, 0xe4, 0xba, 0x22, 0xd4, 0x7b, + /* (2^191)P */ 0xca, 0xfd, 0xca, 0xd7, 0xde, 0x61, 0xae, 0xf0, 0x79, 0x0c, 0x20, 0xab, 0xbc, 0x6f, 0x4d, 0x61, 0xf0, 0xc7, 0x9c, 0x8d, 0x4b, 0x52, 0xf3, 0xb9, 0x48, 0x63, 0x0b, 0xb6, 0xd2, 0x25, 0x9a, 0x96, 0x72, 0xc1, 0x6b, 0x0c, 0xb5, 0xfb, 0x71, 0xaa, 0xad, 0x47, 0x5b, 0xe7, 0xc0, 0x0a, 0x55, 0xb2, 0xd4, 0x16, 0x2f, 0xb1, 0x01, 0xfd, 0xce, 0x27, + /* (2^192)P */ 0x64, 0x11, 0x4b, 0xab, 0x57, 0x09, 0xc6, 0x49, 0x4a, 0x37, 0xc3, 0x36, 0xc4, 0x7b, 0x81, 0x1f, 0x42, 0xed, 0xbb, 0xe0, 0xa0, 0x8d, 0x51, 0xe6, 0xca, 0x8b, 0xb9, 0xcd, 0x99, 0x2d, 0x91, 0x53, 0xa9, 0x47, 0xcb, 0x32, 0xc7, 0xa4, 0x92, 0xec, 0x46, 0x74, 0x44, 0x6d, 0x71, 0x9f, 0x6d, 0x0c, 0x69, 0xa4, 0xf8, 0xbe, 0x9f, 0x7f, 0xa0, 0xd7, + /* (2^193)P */ 0x5f, 0x33, 0xb6, 0x91, 0xc8, 0xa5, 0x3f, 0x5d, 0x7f, 0x38, 0x6e, 0x74, 0x20, 0x4a, 0xd6, 0x2b, 0x98, 0x2a, 0x41, 0x4b, 0x83, 0x64, 0x0b, 0x92, 0x7a, 0x06, 0x1e, 0xc6, 0x2c, 0xf6, 0xe4, 0x91, 0xe5, 0xb1, 0x2e, 0x6e, 0x4e, 0xa8, 0xc8, 0x14, 0x32, 0x57, 0x44, 0x1c, 0xe4, 0xb9, 0x7f, 0x54, 0x51, 0x08, 0x81, 0xaa, 0x4e, 0xce, 0xa1, 0x5d, + /* (2^194)P */ 0x5c, 0xd5, 0x9b, 0x5e, 0x7c, 0xb5, 0xb1, 0x52, 0x73, 0x00, 0x41, 0x56, 0x79, 0x08, 0x7e, 0x07, 0x28, 0x06, 0xa6, 0xfb, 0x7f, 0x69, 0xbd, 0x7a, 0x3c, 0xae, 0x9f, 0x39, 0xbb, 0x54, 0xa2, 0x79, 0xb9, 0x0e, 0x7f, 0xbb, 0xe0, 0xe6, 0xb7, 0x27, 0x64, 0x38, 0x45, 0xdb, 0x84, 0xe4, 0x61, 0x72, 0x3f, 0xe2, 0x24, 0xfe, 0x7a, 0x31, 0x9a, 0xc9, + /* (2^195)P */ 0xa1, 0xd2, 0xa4, 0xee, 0x24, 0x96, 0xe5, 0x5b, 0x79, 0x78, 0x3c, 0x7b, 0x82, 0x3b, 0x8b, 0x58, 0x0b, 0xa3, 0x63, 0x2d, 0xbc, 0x75, 0x46, 0xe8, 0x83, 0x1a, 0xc0, 0x2a, 0x92, 0x61, 0xa8, 0x75, 0x37, 0x3c, 0xbf, 0x0f, 0xef, 0x8f, 0x6c, 0x97, 0x75, 0x10, 0x05, 0x7a, 0xde, 0x23, 0xe8, 0x2a, 0x35, 0xeb, 0x41, 0x64, 0x7d, 0xcf, 0xe0, 0x52, + /* (2^196)P */ 0x4a, 0xd0, 0x49, 0x93, 0xae, 0xf3, 0x24, 0x8c, 0xe1, 0x09, 0x98, 0x45, 0xd8, 0xb9, 0xfe, 0x8e, 0x8c, 0xa8, 0x2c, 0xc9, 0x9f, 0xce, 0x01, 0xdc, 0x38, 0x11, 0xab, 0x85, 0xb9, 0xe8, 0x00, 0x51, 0xfd, 0x82, 0xe1, 0x9b, 0x4e, 0xfc, 0xb5, 0x2a, 0x0f, 0x8b, 0xda, 0x4e, 0x02, 0xca, 0xcc, 0xe3, 0x91, 0xc4, 0xe0, 0xcf, 0x7b, 0xd6, 0xe6, 0x6a, + /* (2^197)P */ 0xfe, 0x11, 0xd7, 0xaa, 0xe3, 0x0c, 0x52, 0x2e, 0x04, 0xe0, 0xe0, 0x61, 0xc8, 0x05, 0xd7, 0x31, 0x4c, 0xc3, 0x9b, 0x2d, 0xce, 0x59, 0xbe, 0x12, 0xb7, 0x30, 0x21, 0xfc, 0x81, 0xb8, 0x5e, 0x57, 0x73, 0xd0, 0xad, 0x8e, 0x9e, 0xe4, 0xeb, 0xcd, 0xcf, 0xd2, 0x0f, 0x01, 0x35, 0x16, 0xed, 0x7a, 0x43, 0x8e, 0x42, 0xdc, 0xea, 0x4c, 0xa8, 0x7c, + /* (2^198)P */ 0x37, 0x26, 0xcc, 0x76, 0x0b, 0xe5, 0x76, 0xdd, 0x3e, 0x19, 0x3c, 0xc4, 0x6c, 0x7f, 0xd0, 0x03, 0xc1, 0xb8, 0x59, 0x82, 0xca, 0x36, 0xc1, 0xe4, 0xc8, 0xb2, 0x83, 0x69, 0x9c, 0xc5, 0x9d, 0x12, 0x82, 0x1c, 0xea, 0xb2, 0x84, 0x9f, 0xf3, 0x52, 0x6b, 0xbb, 0xd8, 0x81, 0x56, 0x83, 0x04, 0x66, 0x05, 0x22, 0x49, 0x37, 0x93, 0xb1, 0xfd, 0xd5, + /* (2^199)P */ 0xaf, 0x96, 0xbf, 0x03, 0xbe, 0xe6, 0x5d, 0x78, 0x19, 0xba, 0x37, 0x46, 0x0a, 0x2b, 0x52, 0x7c, 0xd8, 0x51, 0x9e, 0x3d, 0x29, 0x42, 0xdb, 0x0e, 0x31, 0x20, 0x94, 0xf8, 0x43, 0x9a, 0x2d, 0x22, 0xd3, 0xe3, 0xa1, 0x79, 0x68, 0xfb, 0x2d, 0x7e, 0xd6, 0x79, 0xda, 0x0b, 0xc6, 0x5b, 0x76, 0x68, 0xf0, 0xfe, 0x72, 0x59, 0xbb, 0xa1, 0x9c, 0x74, + /* (2^200)P */ 0x0a, 0xd9, 0xec, 0xc5, 0xbd, 0xf0, 0xda, 0xcf, 0x82, 0xab, 0x46, 0xc5, 0x32, 0x13, 0xdc, 0x5b, 0xac, 0xc3, 0x53, 0x9a, 0x7f, 0xef, 0xa5, 0x40, 0x5a, 0x1f, 0xc1, 0x12, 0x91, 0x54, 0x83, 0x6a, 0xb0, 0x9a, 0x85, 0x4d, 0xbf, 0x36, 0x8e, 0xd3, 0xa2, 0x2b, 0xe5, 0xd6, 0xc6, 0xe1, 0x58, 0x5b, 0x82, 0x9b, 0xc8, 0xf2, 0x03, 0xba, 0xf5, 0x92, + /* (2^201)P */ 0xfb, 0x21, 0x7e, 0xde, 0xe7, 0xb4, 0xc0, 0x56, 0x86, 0x3a, 0x5b, 0x78, 0xf8, 0xf0, 0xf4, 0xe7, 0x5c, 0x00, 0xd2, 0xd7, 0xd6, 0xf8, 0x75, 0x5e, 0x0f, 0x3e, 0xd1, 0x4b, 0x77, 0xd8, 0xad, 0xb0, 0xc9, 0x8b, 0x59, 0x7d, 0x30, 0x76, 0x64, 0x7a, 0x76, 0xd9, 0x51, 0x69, 0xfc, 0xbd, 0x8e, 0xb5, 0x55, 0xe0, 0xd2, 0x07, 0x15, 0xa9, 0xf7, 0xa4, + /* (2^202)P */ 0xaa, 0x2d, 0x2f, 0x2b, 0x3c, 0x15, 0xdd, 0xcd, 0xe9, 0x28, 0x82, 0x4f, 0xa2, 0xaa, 0x31, 0x48, 0xcc, 0xfa, 0x07, 0x73, 0x8a, 0x34, 0x74, 0x0d, 0xab, 0x1a, 0xca, 0xd2, 0xbf, 0x3a, 0xdb, 0x1a, 0x5f, 0x50, 0x62, 0xf4, 0x6b, 0x83, 0x38, 0x43, 0x96, 0xee, 0x6b, 0x39, 0x1e, 0xf0, 0x17, 0x80, 0x1e, 0x9b, 0xed, 0x2b, 0x2f, 0xcc, 0x65, 0xf7, + /* (2^203)P */ 0x03, 0xb3, 0x23, 0x9c, 0x0d, 0xd1, 0xeb, 0x7e, 0x34, 0x17, 0x8a, 0x4c, 0xde, 0x54, 0x39, 0xc4, 0x11, 0x82, 0xd3, 0xa4, 0x00, 0x32, 0x95, 0x9c, 0xa6, 0x64, 0x76, 0x6e, 0xd6, 0x53, 0x27, 0xb4, 0x6a, 0x14, 0x8c, 0x54, 0xf6, 0x58, 0x9e, 0x22, 0x4a, 0x55, 0x18, 0x77, 0xd0, 0x08, 0x6b, 0x19, 0x8a, 0xb5, 0xe7, 0x19, 0xb8, 0x60, 0x92, 0xb1, + /* (2^204)P */ 0x66, 0xec, 0xf3, 0x12, 0xde, 0x67, 0x7f, 0xd4, 0x5b, 0xf6, 0x70, 0x64, 0x0a, 0xb5, 0xc2, 0xf9, 0xb3, 0x64, 0xab, 0x56, 0x46, 0xc7, 0x93, 0xc2, 0x8b, 0x2d, 0xd0, 0xd6, 0x39, 0x3b, 0x1f, 0xcd, 0xb3, 0xac, 0xcc, 0x2c, 0x27, 0x6a, 0xbc, 0xb3, 0x4b, 0xa8, 0x3c, 0x69, 0x20, 0xe2, 0x18, 0x35, 0x17, 0xe1, 0x8a, 0xd3, 0x11, 0x74, 0xaa, 0x4d, + /* (2^205)P */ 0x96, 0xc4, 0x16, 0x7e, 0xfd, 0xf5, 0xd0, 0x7d, 0x1f, 0x32, 0x1b, 0xdb, 0xa6, 0xfd, 0x51, 0x75, 0x4d, 0xd7, 0x00, 0xe5, 0x7f, 0x58, 0x5b, 0xeb, 0x4b, 0x6a, 0x78, 0xfe, 0xe5, 0xd6, 0x8f, 0x99, 0x17, 0xca, 0x96, 0x45, 0xf7, 0x52, 0xdf, 0x84, 0x06, 0x77, 0xb9, 0x05, 0x63, 0x5d, 0xe9, 0x91, 0xb1, 0x4b, 0x82, 0x5a, 0xdb, 0xd7, 0xca, 0x69, + /* (2^206)P */ 0x02, 0xd3, 0x38, 0x38, 0x87, 0xea, 0xbd, 0x9f, 0x11, 0xca, 0xf3, 0x21, 0xf1, 0x9b, 0x35, 0x97, 0x98, 0xff, 0x8e, 0x6d, 0x3d, 0xd6, 0xb2, 0xfa, 0x68, 0xcb, 0x7e, 0x62, 0x85, 0xbb, 0xc7, 0x5d, 0xee, 0x32, 0x30, 0x2e, 0x71, 0x96, 0x63, 0x43, 0x98, 0xc4, 0xa7, 0xde, 0x60, 0xb2, 0xd9, 0x43, 0x4a, 0xfa, 0x97, 0x2d, 0x5f, 0x21, 0xd4, 0xfe, + /* (2^207)P */ 0x3b, 0x20, 0x29, 0x07, 0x07, 0xb5, 0x78, 0xc3, 0xc7, 0xab, 0x56, 0xba, 0x40, 0xde, 0x1d, 0xcf, 0xc3, 0x00, 0x56, 0x21, 0x0c, 0xc8, 0x42, 0xd9, 0x0e, 0xcd, 0x02, 0x7c, 0x07, 0xb9, 0x11, 0xd7, 0x96, 0xaf, 0xff, 0xad, 0xc5, 0xba, 0x30, 0x6d, 0x82, 0x3a, 0xbf, 0xef, 0x7b, 0xf7, 0x0a, 0x74, 0xbd, 0x31, 0x0c, 0xe4, 0xec, 0x1a, 0xe5, 0xc5, + /* (2^208)P */ 0xcc, 0xf2, 0x28, 0x16, 0x12, 0xbf, 0xef, 0x85, 0xbc, 0xf7, 0xcb, 0x9f, 0xdb, 0xa8, 0xb2, 0x49, 0x53, 0x48, 0xa8, 0x24, 0xa8, 0x68, 0x8d, 0xbb, 0x21, 0x0a, 0x5a, 0xbd, 0xb2, 0x91, 0x61, 0x47, 0xc4, 0x43, 0x08, 0xa6, 0x19, 0xef, 0x8e, 0x88, 0x39, 0xc6, 0x33, 0x30, 0xf3, 0x0e, 0xc5, 0x92, 0x66, 0xd6, 0xfe, 0xc5, 0x12, 0xd9, 0x4c, 0x2d, + /* (2^209)P */ 0x30, 0x34, 0x07, 0xbf, 0x9c, 0x5a, 0x4e, 0x65, 0xf1, 0x39, 0x35, 0x38, 0xae, 0x7b, 0x55, 0xac, 0x6a, 0x92, 0x24, 0x7e, 0x50, 0xd3, 0xba, 0x78, 0x51, 0xfe, 0x4d, 0x32, 0x05, 0x11, 0xf5, 0x52, 0xf1, 0x31, 0x45, 0x39, 0x98, 0x7b, 0x28, 0x56, 0xc3, 0x5d, 0x4f, 0x07, 0x6f, 0x84, 0xb8, 0x1a, 0x58, 0x0b, 0xc4, 0x7c, 0xc4, 0x8d, 0x32, 0x8e, + /* (2^210)P */ 0x7e, 0xaf, 0x98, 0xce, 0xc5, 0x2b, 0x9d, 0xf6, 0xfa, 0x2c, 0xb6, 0x2a, 0x5a, 0x1d, 0xc0, 0x24, 0x8d, 0xa4, 0xce, 0xb1, 0x12, 0x01, 0xf9, 0x79, 0xc6, 0x79, 0x38, 0x0c, 0xd4, 0x07, 0xc9, 0xf7, 0x37, 0xa1, 0x0b, 0xfe, 0x72, 0xec, 0x5d, 0xd6, 0xb0, 0x1c, 0x70, 0xbe, 0x70, 0x01, 0x13, 0xe0, 0x86, 0x95, 0xc7, 0x2e, 0x12, 0x3b, 0xe6, 0xa6, + /* (2^211)P */ 0x24, 0x82, 0x67, 0xe0, 0x14, 0x7b, 0x56, 0x08, 0x38, 0x44, 0xdb, 0xa0, 0x3a, 0x05, 0x47, 0xb2, 0xc0, 0xac, 0xd1, 0xcc, 0x3f, 0x82, 0xb8, 0x8a, 0x88, 0xbc, 0xf5, 0x33, 0xa1, 0x35, 0x0f, 0xf6, 0xe2, 0xef, 0x6c, 0xf7, 0x37, 0x9e, 0xe8, 0x10, 0xca, 0xb0, 0x8e, 0x80, 0x86, 0x00, 0x23, 0xd0, 0x4a, 0x76, 0x9f, 0xf7, 0x2c, 0x52, 0x15, 0x0e, + /* (2^212)P */ 0x5e, 0x49, 0xe1, 0x2c, 0x9a, 0x01, 0x76, 0xa6, 0xb3, 0x07, 0x5b, 0xa4, 0x07, 0xef, 0x1d, 0xc3, 0x6a, 0xbb, 0x64, 0xbe, 0x71, 0x15, 0x6e, 0x32, 0x31, 0x46, 0x9a, 0x9e, 0x8f, 0x45, 0x73, 0xce, 0x0b, 0x94, 0x1a, 0x52, 0x07, 0xf4, 0x50, 0x30, 0x49, 0x53, 0x50, 0xfb, 0x71, 0x1f, 0x5a, 0x03, 0xa9, 0x76, 0xf2, 0x8f, 0x42, 0xff, 0xed, 0xed, + /* (2^213)P */ 0xed, 0x08, 0xdb, 0x91, 0x1c, 0xee, 0xa2, 0xb4, 0x47, 0xa2, 0xfa, 0xcb, 0x03, 0xd1, 0xff, 0x8c, 0xad, 0x64, 0x50, 0x61, 0xcd, 0xfc, 0x88, 0xa0, 0x31, 0x95, 0x30, 0xb9, 0x58, 0xdd, 0xd7, 0x43, 0xe4, 0x46, 0xc2, 0x16, 0xd9, 0x72, 0x4a, 0x56, 0x51, 0x70, 0x85, 0xf1, 0xa1, 0x80, 0x40, 0xd5, 0xba, 0x67, 0x81, 0xda, 0xcd, 0x03, 0xea, 0x51, + /* (2^214)P */ 0x42, 0x50, 0xf0, 0xef, 0x37, 0x61, 0x72, 0x85, 0xe1, 0xf1, 0xff, 0x6f, 0x3d, 0xe8, 0x7b, 0x21, 0x5c, 0xe5, 0x50, 0x03, 0xde, 0x00, 0xc1, 0xf7, 0x3a, 0x55, 0x12, 0x1c, 0x9e, 0x1e, 0xce, 0xd1, 0x2f, 0xaf, 0x05, 0x70, 0x5b, 0x47, 0xf2, 0x04, 0x7a, 0x89, 0xbc, 0x78, 0xa6, 0x65, 0x6c, 0xaa, 0x3c, 0xa2, 0x3c, 0x8b, 0x5c, 0xa9, 0x22, 0x48, + /* (2^215)P */ 0x7e, 0x8c, 0x8f, 0x2f, 0x60, 0xe3, 0x5a, 0x94, 0xd4, 0xce, 0xdd, 0x9d, 0x83, 0x3b, 0x77, 0x78, 0x43, 0x1d, 0xfd, 0x8f, 0xc8, 0xe8, 0x02, 0x90, 0xab, 0xf6, 0xc9, 0xfc, 0xf1, 0x63, 0xaa, 0x5f, 0x42, 0xf1, 0x78, 0x34, 0x64, 0x16, 0x75, 0x9c, 0x7d, 0xd0, 0xe4, 0x74, 0x5a, 0xa8, 0xfb, 0xcb, 0xac, 0x20, 0xa3, 0xc2, 0xa6, 0x20, 0xf8, 0x1b, + /* (2^216)P */ 0x00, 0x4f, 0x1e, 0x56, 0xb5, 0x34, 0xb2, 0x87, 0x31, 0xe5, 0xee, 0x8d, 0xf1, 0x41, 0x67, 0xb7, 0x67, 0x3a, 0x54, 0x86, 0x5c, 0xf0, 0x0b, 0x37, 0x2f, 0x1b, 0x92, 0x5d, 0x58, 0x93, 0xdc, 0xd8, 0x58, 0xcc, 0x9e, 0x67, 0xd0, 0x97, 0x3a, 0xaf, 0x49, 0x39, 0x2d, 0x3b, 0xd8, 0x98, 0xfb, 0x76, 0x6b, 0xe7, 0xaf, 0xc3, 0x45, 0x44, 0x53, 0x94, + /* (2^217)P */ 0x30, 0xbd, 0x90, 0x75, 0xd3, 0xbd, 0x3b, 0x58, 0x27, 0x14, 0x9f, 0x6b, 0xd4, 0x31, 0x99, 0xcd, 0xde, 0x3a, 0x21, 0x1e, 0xb4, 0x02, 0xe4, 0x33, 0x04, 0x02, 0xb0, 0x50, 0x66, 0x68, 0x90, 0xdd, 0x7b, 0x69, 0x31, 0xd9, 0xcf, 0x68, 0x73, 0xf1, 0x60, 0xdd, 0xc8, 0x1d, 0x5d, 0xe3, 0xd6, 0x5b, 0x2a, 0xa4, 0xea, 0xc4, 0x3f, 0x08, 0xcd, 0x9c, + /* (2^218)P */ 0x6b, 0x1a, 0xbf, 0x55, 0xc1, 0x1b, 0x0c, 0x05, 0x09, 0xdf, 0xf5, 0x5e, 0xa3, 0x77, 0x95, 0xe9, 0xdf, 0x19, 0xdd, 0xc7, 0x94, 0xcb, 0x06, 0x73, 0xd0, 0x88, 0x02, 0x33, 0x94, 0xca, 0x7a, 0x2f, 0x8e, 0x3d, 0x72, 0x61, 0x2d, 0x4d, 0xa6, 0x61, 0x1f, 0x32, 0x5e, 0x87, 0x53, 0x36, 0x11, 0x15, 0x20, 0xb3, 0x5a, 0x57, 0x51, 0x93, 0x20, 0xd8, + /* (2^219)P */ 0xb7, 0x56, 0xf4, 0xab, 0x7d, 0x0c, 0xfb, 0x99, 0x1a, 0x30, 0x29, 0xb0, 0x75, 0x2a, 0xf8, 0x53, 0x71, 0x23, 0xbd, 0xa7, 0xd8, 0x0a, 0xe2, 0x27, 0x65, 0xe9, 0x74, 0x26, 0x98, 0x4a, 0x69, 0x19, 0xb2, 0x4d, 0x0a, 0x17, 0x98, 0xb2, 0xa9, 0x57, 0x4e, 0xf6, 0x86, 0xc8, 0x01, 0xa4, 0xc6, 0x98, 0xad, 0x5a, 0x90, 0x2c, 0x05, 0x46, 0x64, 0xb7, + /* (2^220)P */ 0x7b, 0x91, 0xdf, 0xfc, 0xf8, 0x1c, 0x8c, 0x15, 0x9e, 0xf7, 0xd5, 0xa8, 0xe8, 0xe7, 0xe3, 0xa3, 0xb0, 0x04, 0x74, 0xfa, 0x78, 0xfb, 0x26, 0xbf, 0x67, 0x42, 0xf9, 0x8c, 0x9b, 0xb4, 0x69, 0x5b, 0x02, 0x13, 0x6d, 0x09, 0x6c, 0xd6, 0x99, 0x61, 0x7b, 0x89, 0x4a, 0x67, 0x75, 0xa3, 0x98, 0x13, 0x23, 0x1d, 0x18, 0x24, 0x0e, 0xef, 0x41, 0x79, + /* (2^221)P */ 0x86, 0x33, 0xab, 0x08, 0xcb, 0xbf, 0x1e, 0x76, 0x3c, 0x0b, 0xbd, 0x30, 0xdb, 0xe9, 0xa3, 0x35, 0x87, 0x1b, 0xe9, 0x07, 0x00, 0x66, 0x7f, 0x3b, 0x35, 0x0c, 0x8a, 0x3f, 0x61, 0xbc, 0xe0, 0xae, 0xf6, 0xcc, 0x54, 0xe1, 0x72, 0x36, 0x2d, 0xee, 0x93, 0x24, 0xf8, 0xd7, 0xc5, 0xf9, 0xcb, 0xb0, 0xe5, 0x88, 0x0d, 0x23, 0x4b, 0x76, 0x15, 0xa2, + /* (2^222)P */ 0x37, 0xdb, 0x83, 0xd5, 0x6d, 0x06, 0x24, 0x37, 0x1b, 0x15, 0x85, 0x15, 0xe2, 0xc0, 0x4e, 0x02, 0xa9, 0x6d, 0x0a, 0x3a, 0x94, 0x4a, 0x6f, 0x49, 0x00, 0x01, 0x72, 0xbb, 0x60, 0x14, 0x35, 0xae, 0xb4, 0xc6, 0x01, 0x0a, 0x00, 0x9e, 0xc3, 0x58, 0xc5, 0xd1, 0x5e, 0x30, 0x73, 0x96, 0x24, 0x85, 0x9d, 0xf0, 0xf9, 0xec, 0x09, 0xd3, 0xe7, 0x70, + /* (2^223)P */ 0xf3, 0xbd, 0x96, 0x87, 0xe9, 0x71, 0xbd, 0xd6, 0xa2, 0x45, 0xeb, 0x0a, 0xcd, 0x2c, 0xf1, 0x72, 0xa6, 0x31, 0xa9, 0x6f, 0x09, 0xa1, 0x5e, 0xdd, 0xc8, 0x8d, 0x0d, 0xbc, 0x5a, 0x8d, 0xb1, 0x2c, 0x9a, 0xcc, 0x37, 0x74, 0xc2, 0xa9, 0x4e, 0xd6, 0xc0, 0x3c, 0xa0, 0x23, 0xb0, 0xa0, 0x77, 0x14, 0x80, 0x45, 0x71, 0x6a, 0x2d, 0x41, 0xc3, 0x82, + /* (2^224)P */ 0x37, 0x44, 0xec, 0x8a, 0x3e, 0xc1, 0x0c, 0xa9, 0x12, 0x9c, 0x08, 0x88, 0xcb, 0xd9, 0xf8, 0xba, 0x00, 0xd6, 0xc3, 0xdf, 0xef, 0x7a, 0x44, 0x7e, 0x25, 0x69, 0xc9, 0xc1, 0x46, 0xe5, 0x20, 0x9e, 0xcc, 0x0b, 0x05, 0x3e, 0xf4, 0x78, 0x43, 0x0c, 0xa6, 0x2f, 0xc1, 0xfa, 0x70, 0xb2, 0x3c, 0x31, 0x7a, 0x63, 0x58, 0xab, 0x17, 0xcf, 0x4c, 0x4f, + /* (2^225)P */ 0x2b, 0x08, 0x31, 0x59, 0x75, 0x8b, 0xec, 0x0a, 0xa9, 0x79, 0x70, 0xdd, 0xf1, 0x11, 0xc3, 0x11, 0x1f, 0xab, 0x37, 0xaa, 0x26, 0xea, 0x53, 0xc4, 0x79, 0xa7, 0x91, 0x00, 0xaa, 0x08, 0x42, 0xeb, 0x8b, 0x8b, 0xe8, 0xc3, 0x2f, 0xb8, 0x78, 0x90, 0x38, 0x0e, 0x8a, 0x42, 0x0c, 0x0f, 0xbf, 0x3e, 0xf8, 0xd8, 0x07, 0xcf, 0x6a, 0x34, 0xc9, 0xfa, + /* (2^226)P */ 0x11, 0xe0, 0x76, 0x4d, 0x23, 0xc5, 0xa6, 0xcc, 0x9f, 0x9a, 0x2a, 0xde, 0x3a, 0xb5, 0x92, 0x39, 0x19, 0x8a, 0xf1, 0x8d, 0xf9, 0x4d, 0xc9, 0xb4, 0x39, 0x9f, 0x57, 0xd8, 0x72, 0xab, 0x1d, 0x61, 0x6a, 0xb2, 0xff, 0x52, 0xba, 0x54, 0x0e, 0xfb, 0x83, 0x30, 0x8a, 0xf7, 0x3b, 0xf4, 0xd8, 0xae, 0x1a, 0x94, 0x3a, 0xec, 0x63, 0xfe, 0x6e, 0x7c, + /* (2^227)P */ 0xdc, 0x70, 0x8e, 0x55, 0x44, 0xbf, 0xd2, 0x6a, 0xa0, 0x14, 0x61, 0x89, 0xd5, 0x55, 0x45, 0x3c, 0xf6, 0x40, 0x0d, 0x83, 0x85, 0x44, 0xb4, 0x62, 0x56, 0xfe, 0x60, 0xd7, 0x07, 0x1d, 0x47, 0x30, 0x3b, 0x73, 0xa4, 0xb5, 0xb7, 0xea, 0xac, 0xda, 0xf1, 0x17, 0xaa, 0x60, 0xdf, 0xe9, 0x84, 0xda, 0x31, 0x32, 0x61, 0xbf, 0xd0, 0x7e, 0x8a, 0x02, + /* (2^228)P */ 0xb9, 0x51, 0xb3, 0x89, 0x21, 0x5d, 0xa2, 0xfe, 0x79, 0x2a, 0xb3, 0x2a, 0x3b, 0xe6, 0x6f, 0x2b, 0x22, 0x03, 0xea, 0x7b, 0x1f, 0xaf, 0x85, 0xc3, 0x38, 0x55, 0x5b, 0x8e, 0xb4, 0xaa, 0x77, 0xfe, 0x03, 0x6e, 0xda, 0x91, 0x24, 0x0c, 0x48, 0x39, 0x27, 0x43, 0x16, 0xd2, 0x0a, 0x0d, 0x43, 0xa3, 0x0e, 0xca, 0x45, 0xd1, 0x7f, 0xf5, 0xd3, 0x16, + /* (2^229)P */ 0x3d, 0x32, 0x9b, 0x38, 0xf8, 0x06, 0x93, 0x78, 0x5b, 0x50, 0x2b, 0x06, 0xd8, 0x66, 0xfe, 0xab, 0x9b, 0x58, 0xc7, 0xd1, 0x4d, 0xd5, 0xf8, 0x3b, 0x10, 0x7e, 0x85, 0xde, 0x58, 0x4e, 0xdf, 0x53, 0xd9, 0x58, 0xe0, 0x15, 0x81, 0x9f, 0x1a, 0x78, 0xfc, 0x9f, 0x10, 0xc2, 0x23, 0xd6, 0x78, 0xd1, 0x9d, 0xd2, 0xd5, 0x1c, 0x53, 0xe2, 0xc9, 0x76, + /* (2^230)P */ 0x98, 0x1e, 0x38, 0x7b, 0x71, 0x18, 0x4b, 0x15, 0xaf, 0xa1, 0xa6, 0x98, 0xcb, 0x26, 0xa3, 0xc8, 0x07, 0x46, 0xda, 0x3b, 0x70, 0x65, 0xec, 0x7a, 0x2b, 0x34, 0x94, 0xa8, 0xb6, 0x14, 0xf8, 0x1a, 0xce, 0xf7, 0xc8, 0x60, 0xf3, 0x88, 0xf4, 0x33, 0x60, 0x7b, 0xd1, 0x02, 0xe7, 0xda, 0x00, 0x4a, 0xea, 0xd2, 0xfd, 0x88, 0xd2, 0x99, 0x28, 0xf3, + /* (2^231)P */ 0x28, 0x24, 0x1d, 0x26, 0xc2, 0xeb, 0x8b, 0x3b, 0xb4, 0x6b, 0xbe, 0x6b, 0x77, 0xff, 0xf3, 0x21, 0x3b, 0x26, 0x6a, 0x8c, 0x8e, 0x2a, 0x44, 0xa8, 0x01, 0x2b, 0x71, 0xea, 0x64, 0x30, 0xfd, 0xfd, 0x95, 0xcb, 0x39, 0x38, 0x48, 0xfa, 0x96, 0x97, 0x8c, 0x2f, 0x33, 0xca, 0x03, 0xe6, 0xd7, 0x94, 0x55, 0x6c, 0xc3, 0xb3, 0xa8, 0xf7, 0xae, 0x8c, + /* (2^232)P */ 0xea, 0x62, 0x8a, 0xb4, 0xeb, 0x74, 0xf7, 0xb8, 0xae, 0xc5, 0x20, 0x71, 0x06, 0xd6, 0x7c, 0x62, 0x9b, 0x69, 0x74, 0xef, 0xa7, 0x6d, 0xd6, 0x8c, 0x37, 0xb9, 0xbf, 0xcf, 0xeb, 0xe4, 0x2f, 0x04, 0x02, 0x21, 0x7d, 0x75, 0x6b, 0x92, 0x48, 0xf8, 0x70, 0xad, 0x69, 0xe2, 0xea, 0x0e, 0x88, 0x67, 0x72, 0xcc, 0x2d, 0x10, 0xce, 0x2d, 0xcf, 0x65, + /* (2^233)P */ 0x49, 0xf3, 0x57, 0x64, 0xe5, 0x5c, 0xc5, 0x65, 0x49, 0x97, 0xc4, 0x8a, 0xcc, 0xa9, 0xca, 0x94, 0x7b, 0x86, 0x88, 0xb6, 0x51, 0x27, 0x69, 0xa5, 0x0f, 0x8b, 0x06, 0x59, 0xa0, 0x94, 0xef, 0x63, 0x1a, 0x01, 0x9e, 0x4f, 0xd2, 0x5a, 0x93, 0xc0, 0x7c, 0xe6, 0x61, 0x77, 0xb6, 0xf5, 0x40, 0xd9, 0x98, 0x43, 0x5b, 0x56, 0x68, 0xe9, 0x37, 0x8f, + /* (2^234)P */ 0xee, 0x87, 0xd2, 0x05, 0x1b, 0x39, 0x89, 0x10, 0x07, 0x6d, 0xe8, 0xfd, 0x8b, 0x4d, 0xb2, 0xa7, 0x7b, 0x1e, 0xa0, 0x6c, 0x0d, 0x3d, 0x3d, 0x49, 0xba, 0x61, 0x36, 0x1f, 0xc2, 0x84, 0x4a, 0xcc, 0x87, 0xa9, 0x1b, 0x23, 0x04, 0xe2, 0x3e, 0x97, 0xe1, 0xdb, 0xd5, 0x5a, 0xe8, 0x41, 0x6b, 0xe5, 0x5a, 0xa1, 0x99, 0xe5, 0x7b, 0xa7, 0xe0, 0x3b, + /* (2^235)P */ 0xea, 0xa3, 0x6a, 0xdd, 0x77, 0x7f, 0x77, 0x41, 0xc5, 0x6a, 0xe4, 0xaf, 0x11, 0x5f, 0x88, 0xa5, 0x10, 0xee, 0xd0, 0x8c, 0x0c, 0xb4, 0xa5, 0x2a, 0xd0, 0xd8, 0x1d, 0x47, 0x06, 0xc0, 0xd5, 0xce, 0x51, 0x54, 0x9b, 0x2b, 0xe6, 0x2f, 0xe7, 0xe7, 0x31, 0x5f, 0x5c, 0x23, 0x81, 0x3e, 0x03, 0x93, 0xaa, 0x2d, 0x71, 0x84, 0xa0, 0x89, 0x32, 0xa6, + /* (2^236)P */ 0x55, 0xa3, 0x13, 0x92, 0x4e, 0x93, 0x7d, 0xec, 0xca, 0x57, 0xfb, 0x37, 0xae, 0xd2, 0x18, 0x2e, 0x54, 0x05, 0x6c, 0xd1, 0x28, 0xca, 0x90, 0x40, 0x82, 0x2e, 0x79, 0xc6, 0x5a, 0xc7, 0xdd, 0x84, 0x93, 0xdf, 0x15, 0xb8, 0x1f, 0xb1, 0xf9, 0xaf, 0x2c, 0xe5, 0x32, 0xcd, 0xc2, 0x99, 0x6d, 0xac, 0x85, 0x5c, 0x63, 0xd3, 0xe2, 0xff, 0x24, 0xda, + /* (2^237)P */ 0x2d, 0x8d, 0xfd, 0x65, 0xcc, 0xe5, 0x02, 0xa0, 0xe5, 0xb9, 0xec, 0x59, 0x09, 0x50, 0x27, 0xb7, 0x3d, 0x2a, 0x79, 0xb2, 0x76, 0x5d, 0x64, 0x95, 0xf8, 0xc5, 0xaf, 0x8a, 0x62, 0x11, 0x5c, 0x56, 0x1c, 0x05, 0x64, 0x9e, 0x5e, 0xbd, 0x54, 0x04, 0xe6, 0x9e, 0xab, 0xe6, 0x22, 0x7e, 0x42, 0x54, 0xb5, 0xa5, 0xd0, 0x8d, 0x28, 0x6b, 0x0f, 0x0b, + /* (2^238)P */ 0x2d, 0xb2, 0x8c, 0x59, 0x10, 0x37, 0x84, 0x3b, 0x9b, 0x65, 0x1b, 0x0f, 0x10, 0xf9, 0xea, 0x60, 0x1b, 0x02, 0xf5, 0xee, 0x8b, 0xe6, 0x32, 0x7d, 0x10, 0x7f, 0x5f, 0x8c, 0x72, 0x09, 0x4e, 0x1f, 0x29, 0xff, 0x65, 0xcb, 0x3e, 0x3a, 0xd2, 0x96, 0x50, 0x1e, 0xea, 0x64, 0x99, 0xb5, 0x4c, 0x7a, 0x69, 0xb8, 0x95, 0xae, 0x48, 0xc0, 0x7c, 0xb1, + /* (2^239)P */ 0xcd, 0x7c, 0x4f, 0x3e, 0xea, 0xf3, 0x90, 0xcb, 0x12, 0x76, 0xd1, 0x17, 0xdc, 0x0d, 0x13, 0x0f, 0xfd, 0x4d, 0xb5, 0x1f, 0xe4, 0xdd, 0xf2, 0x4d, 0x58, 0xea, 0xa5, 0x66, 0x92, 0xcf, 0xe5, 0x54, 0xea, 0x9b, 0x35, 0x83, 0x1a, 0x44, 0x8e, 0x62, 0x73, 0x45, 0x98, 0xa3, 0x89, 0x95, 0x52, 0x93, 0x1a, 0x8d, 0x63, 0x0f, 0xc2, 0x57, 0x3c, 0xb1, + /* (2^240)P */ 0x72, 0xb4, 0xdf, 0x51, 0xb7, 0xf6, 0x52, 0xa2, 0x14, 0x56, 0xe5, 0x0a, 0x2e, 0x75, 0x81, 0x02, 0xee, 0x93, 0x48, 0x0a, 0x92, 0x4e, 0x0c, 0x0f, 0xdf, 0x09, 0x89, 0x99, 0xf6, 0xf9, 0x22, 0xa2, 0x32, 0xf8, 0xb0, 0x76, 0x0c, 0xb2, 0x4d, 0x6e, 0xbe, 0x83, 0x35, 0x61, 0x44, 0xd2, 0x58, 0xc7, 0xdd, 0x14, 0xcf, 0xc3, 0x4b, 0x7c, 0x07, 0xee, + /* (2^241)P */ 0x8b, 0x03, 0xee, 0xcb, 0xa7, 0x2e, 0x28, 0xbd, 0x97, 0xd1, 0x4c, 0x2b, 0xd1, 0x92, 0x67, 0x5b, 0x5a, 0x12, 0xbf, 0x29, 0x17, 0xfc, 0x50, 0x09, 0x74, 0x76, 0xa2, 0xd4, 0x82, 0xfd, 0x2c, 0x0c, 0x90, 0xf7, 0xe7, 0xe5, 0x9a, 0x2c, 0x16, 0x40, 0xb9, 0x6c, 0xd9, 0xe0, 0x22, 0x9e, 0xf8, 0xdd, 0x73, 0xe4, 0x7b, 0x9e, 0xbe, 0x4f, 0x66, 0x22, + /* (2^242)P */ 0xa4, 0x10, 0xbe, 0xb8, 0x83, 0x3a, 0x77, 0x8e, 0xea, 0x0a, 0xc4, 0x97, 0x3e, 0xb6, 0x6c, 0x81, 0xd7, 0x65, 0xd9, 0xf7, 0xae, 0xe6, 0xbe, 0xab, 0x59, 0x81, 0x29, 0x4b, 0xff, 0xe1, 0x0f, 0xc3, 0x2b, 0xad, 0x4b, 0xef, 0xc4, 0x50, 0x9f, 0x88, 0x31, 0xf2, 0xde, 0x80, 0xd6, 0xf4, 0x20, 0x9c, 0x77, 0x9b, 0xbe, 0xbe, 0x08, 0xf5, 0xf0, 0x95, + /* (2^243)P */ 0x0e, 0x7c, 0x7b, 0x7c, 0xb3, 0xd8, 0x83, 0xfc, 0x8c, 0x75, 0x51, 0x74, 0x1b, 0xe1, 0x6d, 0x11, 0x05, 0x46, 0x24, 0x0d, 0xa4, 0x2b, 0x32, 0xfd, 0x2c, 0x4e, 0x21, 0xdf, 0x39, 0x6b, 0x96, 0xfc, 0xff, 0x92, 0xfc, 0x35, 0x0d, 0x9a, 0x4b, 0xc0, 0x70, 0x46, 0x32, 0x7d, 0xc0, 0xc4, 0x04, 0xe0, 0x2d, 0x83, 0xa7, 0x00, 0xc7, 0xcb, 0xb4, 0x8f, + /* (2^244)P */ 0xa9, 0x5a, 0x7f, 0x0e, 0xdd, 0x2c, 0x85, 0xaa, 0x4d, 0xac, 0xde, 0xb3, 0xb6, 0xaf, 0xe6, 0xd1, 0x06, 0x7b, 0x2c, 0xa4, 0x01, 0x19, 0x22, 0x7d, 0x78, 0xf0, 0x3a, 0xea, 0x89, 0xfe, 0x21, 0x61, 0x6d, 0xb8, 0xfe, 0xa5, 0x2a, 0xab, 0x0d, 0x7b, 0x51, 0x39, 0xb6, 0xde, 0xbc, 0xf0, 0xc5, 0x48, 0xd7, 0x09, 0x82, 0x6e, 0x66, 0x75, 0xc5, 0xcd, + /* (2^245)P */ 0xee, 0xdf, 0x2b, 0x6c, 0xa8, 0xde, 0x61, 0xe1, 0x27, 0xfa, 0x2a, 0x0f, 0x68, 0xe7, 0x7a, 0x9b, 0x13, 0xe9, 0x56, 0xd2, 0x1c, 0x3d, 0x2f, 0x3c, 0x7a, 0xf6, 0x6f, 0x45, 0xee, 0xe8, 0xf4, 0xa0, 0xa6, 0xe8, 0xa5, 0x27, 0xee, 0xf2, 0x85, 0xa9, 0xd5, 0x0e, 0xa9, 0x26, 0x60, 0xfe, 0xee, 0xc7, 0x59, 0x99, 0x5e, 0xa3, 0xdf, 0x23, 0x36, 0xd5, + /* (2^246)P */ 0x15, 0x66, 0x6f, 0xd5, 0x78, 0xa4, 0x0a, 0xf7, 0xb1, 0xe8, 0x75, 0x6b, 0x48, 0x7d, 0xa6, 0x4d, 0x3d, 0x36, 0x9b, 0xc7, 0xcc, 0x68, 0x9a, 0xfe, 0x2f, 0x39, 0x2a, 0x51, 0x31, 0x39, 0x7d, 0x73, 0x6f, 0xc8, 0x74, 0x72, 0x6f, 0x6e, 0xda, 0x5f, 0xad, 0x48, 0xc8, 0x40, 0xe1, 0x06, 0x01, 0x36, 0xa1, 0x88, 0xc8, 0x99, 0x9c, 0xd1, 0x11, 0x8f, + /* (2^247)P */ 0xab, 0xc5, 0xcb, 0xcf, 0xbd, 0x73, 0x21, 0xd0, 0x82, 0xb1, 0x2e, 0x2d, 0xd4, 0x36, 0x1b, 0xed, 0xa9, 0x8a, 0x26, 0x79, 0xc4, 0x17, 0xae, 0xe5, 0x09, 0x0a, 0x0c, 0xa4, 0x21, 0xa0, 0x6e, 0xdd, 0x62, 0x8e, 0x44, 0x62, 0xcc, 0x50, 0xff, 0x93, 0xb3, 0x9a, 0x72, 0x8c, 0x3f, 0xa1, 0xa6, 0x4d, 0x87, 0xd5, 0x1c, 0x5a, 0xc0, 0x0b, 0x1a, 0xd6, + /* (2^248)P */ 0x67, 0x36, 0x6a, 0x1f, 0x96, 0xe5, 0x80, 0x20, 0xa9, 0xe8, 0x0b, 0x0e, 0x21, 0x29, 0x3f, 0xc8, 0x0a, 0x6d, 0x27, 0x47, 0xca, 0xd9, 0x05, 0x55, 0xbf, 0x11, 0xcf, 0x31, 0x7a, 0x37, 0xc7, 0x90, 0xa9, 0xf4, 0x07, 0x5e, 0xd5, 0xc3, 0x92, 0xaa, 0x95, 0xc8, 0x23, 0x2a, 0x53, 0x45, 0xe3, 0x3a, 0x24, 0xe9, 0x67, 0x97, 0x3a, 0x82, 0xf9, 0xa6, + /* (2^249)P */ 0x92, 0x9e, 0x6d, 0x82, 0x67, 0xe9, 0xf9, 0x17, 0x96, 0x2c, 0xa7, 0xd3, 0x89, 0xf9, 0xdb, 0xd8, 0x20, 0xc6, 0x2e, 0xec, 0x4a, 0x76, 0x64, 0xbf, 0x27, 0x40, 0xe2, 0xb4, 0xdf, 0x1f, 0xa0, 0xef, 0x07, 0x80, 0xfb, 0x8e, 0x12, 0xf8, 0xb8, 0xe1, 0xc6, 0xdf, 0x7c, 0x69, 0x35, 0x5a, 0xe1, 0x8e, 0x5d, 0x69, 0x84, 0x56, 0xb6, 0x31, 0x1c, 0x0b, + /* (2^250)P */ 0xd6, 0x94, 0x5c, 0xef, 0xbb, 0x46, 0x45, 0x44, 0x5b, 0xa1, 0xae, 0x03, 0x65, 0xdd, 0xb5, 0x66, 0x88, 0x35, 0x29, 0x95, 0x16, 0x54, 0xa6, 0xf5, 0xc9, 0x78, 0x34, 0xe6, 0x0f, 0xc4, 0x2b, 0x5b, 0x79, 0x51, 0x68, 0x48, 0x3a, 0x26, 0x87, 0x05, 0x70, 0xaf, 0x8b, 0xa6, 0xc7, 0x2e, 0xb3, 0xa9, 0x10, 0x01, 0xb0, 0xb9, 0x31, 0xfd, 0xdc, 0x80, + /* (2^251)P */ 0x25, 0xf2, 0xad, 0xd6, 0x75, 0xa3, 0x04, 0x05, 0x64, 0x8a, 0x97, 0x60, 0x27, 0x2a, 0xe5, 0x6d, 0xb0, 0x73, 0xf4, 0x07, 0x2a, 0x9d, 0xe9, 0x46, 0xb4, 0x1c, 0x51, 0xf8, 0x63, 0x98, 0x7e, 0xe5, 0x13, 0x51, 0xed, 0x98, 0x65, 0x98, 0x4f, 0x8f, 0xe7, 0x7e, 0x72, 0xd7, 0x64, 0x11, 0x2f, 0xcd, 0x12, 0xf8, 0xc4, 0x63, 0x52, 0x0f, 0x7f, 0xc4, + /* (2^252)P */ 0x5c, 0xd9, 0x85, 0x63, 0xc7, 0x8a, 0x65, 0x9a, 0x25, 0x83, 0x31, 0x73, 0x49, 0xf0, 0x93, 0x96, 0x70, 0x67, 0x6d, 0xb1, 0xff, 0x95, 0x54, 0xe4, 0xf8, 0x15, 0x6c, 0x5f, 0xbd, 0xf6, 0x0f, 0x38, 0x7b, 0x68, 0x7d, 0xd9, 0x3d, 0xf0, 0xa9, 0xa0, 0xe4, 0xd1, 0xb6, 0x34, 0x6d, 0x14, 0x16, 0xc2, 0x4c, 0x30, 0x0e, 0x67, 0xd3, 0xbe, 0x2e, 0xc0, + /* (2^253)P */ 0x06, 0x6b, 0x52, 0xc8, 0x14, 0xcd, 0xae, 0x03, 0x93, 0xea, 0xc1, 0xf2, 0xf6, 0x8b, 0xc5, 0xb6, 0xdc, 0x82, 0x42, 0x29, 0x94, 0xe0, 0x25, 0x6c, 0x3f, 0x9f, 0x5d, 0xe4, 0x96, 0xf6, 0x8e, 0x3f, 0xf9, 0x72, 0xc4, 0x77, 0x60, 0x8b, 0xa4, 0xf9, 0xa8, 0xc3, 0x0a, 0x81, 0xb1, 0x97, 0x70, 0x18, 0xab, 0xea, 0x37, 0x8a, 0x08, 0xc7, 0xe2, 0x95, + /* (2^254)P */ 0x94, 0x49, 0xd9, 0x5f, 0x76, 0x72, 0x82, 0xad, 0x2d, 0x50, 0x1a, 0x7a, 0x5b, 0xe6, 0x95, 0x1e, 0x95, 0x65, 0x87, 0x1c, 0x52, 0xd7, 0x44, 0xe6, 0x9b, 0x56, 0xcd, 0x6f, 0x05, 0xff, 0x67, 0xc5, 0xdb, 0xa2, 0xac, 0xe4, 0xa2, 0x28, 0x63, 0x5f, 0xfb, 0x0c, 0x3b, 0xf1, 0x87, 0xc3, 0x36, 0x78, 0x3f, 0x77, 0xfa, 0x50, 0x85, 0xf9, 0xd7, 0x82, + /* (2^255)P */ 0x64, 0xc0, 0xe0, 0xd8, 0x2d, 0xed, 0xcb, 0x6a, 0xfd, 0xcd, 0xbc, 0x7e, 0x9f, 0xc8, 0x85, 0xe9, 0xc1, 0x7c, 0x0f, 0xe5, 0x18, 0xea, 0xd4, 0x51, 0xad, 0x59, 0x13, 0x75, 0xd9, 0x3d, 0xd4, 0x8a, 0xb2, 0xbe, 0x78, 0x52, 0x2b, 0x52, 0x94, 0x37, 0x41, 0xd6, 0xb4, 0xb6, 0x45, 0x20, 0x76, 0xe0, 0x1f, 0x31, 0xdb, 0xb1, 0xa1, 0x43, 0xf0, 0x18, + /* (2^256)P */ 0x74, 0xa9, 0xa4, 0xa9, 0xdd, 0x6e, 0x3e, 0x68, 0xe5, 0xc3, 0x2e, 0x92, 0x17, 0xa4, 0xcb, 0x80, 0xb1, 0xf0, 0x06, 0x93, 0xef, 0xe6, 0x00, 0xe6, 0x3b, 0xb1, 0x32, 0x65, 0x7b, 0x83, 0xb6, 0x8a, 0x49, 0x1b, 0x14, 0x89, 0xee, 0xba, 0xf5, 0x6a, 0x8d, 0x36, 0xef, 0xb0, 0xd8, 0xb2, 0x16, 0x99, 0x17, 0x35, 0x02, 0x16, 0x55, 0x58, 0xdd, 0x82, + /* (2^257)P */ 0x36, 0x95, 0xe8, 0xf4, 0x36, 0x42, 0xbb, 0xc5, 0x3e, 0xfa, 0x30, 0x84, 0x9e, 0x59, 0xfd, 0xd2, 0x95, 0x42, 0xf8, 0x64, 0xd9, 0xb9, 0x0e, 0x9f, 0xfa, 0xd0, 0x7b, 0x20, 0x31, 0x77, 0x48, 0x29, 0x4d, 0xd0, 0x32, 0x57, 0x56, 0x30, 0xa6, 0x17, 0x53, 0x04, 0xbf, 0x08, 0x28, 0xec, 0xb8, 0x46, 0xc1, 0x03, 0x89, 0xdc, 0xed, 0xa0, 0x35, 0x53, + /* (2^258)P */ 0xc5, 0x7f, 0x9e, 0xd8, 0xc5, 0xba, 0x5f, 0x68, 0xc8, 0x23, 0x75, 0xea, 0x0d, 0xd9, 0x5a, 0xfd, 0x61, 0x1a, 0xa3, 0x2e, 0x45, 0x63, 0x14, 0x55, 0x86, 0x21, 0x29, 0xbe, 0xef, 0x5e, 0x50, 0xe5, 0x18, 0x59, 0xe7, 0xe3, 0xce, 0x4d, 0x8c, 0x15, 0x8f, 0x89, 0x66, 0x44, 0x52, 0x3d, 0xfa, 0xc7, 0x9a, 0x59, 0x90, 0x8e, 0xc0, 0x06, 0x3f, 0xc9, + /* (2^259)P */ 0x8e, 0x04, 0xd9, 0x16, 0x50, 0x1d, 0x8c, 0x9f, 0xd5, 0xe3, 0xce, 0xfd, 0x47, 0x04, 0x27, 0x4d, 0xc2, 0xfa, 0x71, 0xd9, 0x0b, 0xb8, 0x65, 0xf4, 0x11, 0xf3, 0x08, 0xee, 0x81, 0xc8, 0x67, 0x99, 0x0b, 0x8d, 0x77, 0xa3, 0x4f, 0xb5, 0x9b, 0xdb, 0x26, 0xf1, 0x97, 0xeb, 0x04, 0x54, 0xeb, 0x80, 0x08, 0x1d, 0x1d, 0xf6, 0x3d, 0x1f, 0x5a, 0xb8, + /* (2^260)P */ 0xb7, 0x9c, 0x9d, 0xee, 0xb9, 0x5c, 0xad, 0x0d, 0x9e, 0xfd, 0x60, 0x3c, 0x27, 0x4e, 0xa2, 0x95, 0xfb, 0x64, 0x7e, 0x79, 0x64, 0x87, 0x10, 0xb4, 0x73, 0xe0, 0x9d, 0x46, 0x4d, 0x3d, 0xee, 0x83, 0xe4, 0x16, 0x88, 0x97, 0xe6, 0x4d, 0xba, 0x70, 0xb6, 0x96, 0x7b, 0xff, 0x4b, 0xc8, 0xcf, 0x72, 0x83, 0x3e, 0x5b, 0x24, 0x2e, 0x57, 0xf1, 0x82, + /* (2^261)P */ 0x30, 0x71, 0x40, 0x51, 0x4f, 0x44, 0xbb, 0xc7, 0xf0, 0x54, 0x6e, 0x9d, 0xeb, 0x15, 0xad, 0xf8, 0x61, 0x43, 0x5a, 0xef, 0xc0, 0xb1, 0x57, 0xae, 0x03, 0x40, 0xe8, 0x68, 0x6f, 0x03, 0x20, 0x4f, 0x8a, 0x51, 0x2a, 0x9e, 0xd2, 0x45, 0xaf, 0xb4, 0xf5, 0xd4, 0x95, 0x7f, 0x3d, 0x3d, 0xb7, 0xb6, 0x28, 0xc5, 0x08, 0x8b, 0x44, 0xd6, 0x3f, 0xe7, + /* (2^262)P */ 0xa9, 0x52, 0x04, 0x67, 0xcb, 0x20, 0x63, 0xf8, 0x18, 0x01, 0x44, 0x21, 0x6a, 0x8a, 0x83, 0x48, 0xd4, 0xaf, 0x23, 0x0f, 0x35, 0x8d, 0xe5, 0x5a, 0xc4, 0x7c, 0x55, 0x46, 0x19, 0x5f, 0x35, 0xe0, 0x5d, 0x97, 0x4c, 0x2d, 0x04, 0xed, 0x59, 0xd4, 0xb0, 0xb2, 0xc6, 0xe3, 0x51, 0xe1, 0x38, 0xc6, 0x30, 0x49, 0x8f, 0xae, 0x61, 0x64, 0xce, 0xa8, + /* (2^263)P */ 0x9b, 0x64, 0x83, 0x3c, 0xd3, 0xdf, 0xb9, 0x27, 0xe7, 0x5b, 0x7f, 0xeb, 0xf3, 0x26, 0xcf, 0xb1, 0x8f, 0xaf, 0x26, 0xc8, 0x48, 0xce, 0xa1, 0xac, 0x7d, 0x10, 0x34, 0x28, 0xe1, 0x1f, 0x69, 0x03, 0x64, 0x77, 0x61, 0xdd, 0x4a, 0x9b, 0x18, 0x47, 0xf8, 0xca, 0x63, 0xc9, 0x03, 0x2d, 0x20, 0x2a, 0x69, 0x6e, 0x42, 0xd0, 0xe7, 0xaa, 0xb5, 0xf3, + /* (2^264)P */ 0xea, 0x31, 0x0c, 0x57, 0x0f, 0x3e, 0xe3, 0x35, 0xd8, 0x30, 0xa5, 0x6f, 0xdd, 0x95, 0x43, 0xc6, 0x66, 0x07, 0x4f, 0x34, 0xc3, 0x7e, 0x04, 0x10, 0x2d, 0xc4, 0x1c, 0x94, 0x52, 0x2e, 0x5b, 0x9a, 0x65, 0x2f, 0x91, 0xaa, 0x4f, 0x3c, 0xdc, 0x23, 0x18, 0xe1, 0x4f, 0x85, 0xcd, 0xf4, 0x8c, 0x51, 0xf7, 0xab, 0x4f, 0xdc, 0x15, 0x5c, 0x9e, 0xc5, + /* (2^265)P */ 0x54, 0x57, 0x23, 0x17, 0xe7, 0x82, 0x2f, 0x04, 0x7d, 0xfe, 0xe7, 0x1f, 0xa2, 0x57, 0x79, 0xe9, 0x58, 0x9b, 0xbe, 0xc6, 0x16, 0x4a, 0x17, 0x50, 0x90, 0x4a, 0x34, 0x70, 0x87, 0x37, 0x01, 0x26, 0xd8, 0xa3, 0x5f, 0x07, 0x7c, 0xd0, 0x7d, 0x05, 0x8a, 0x93, 0x51, 0x2f, 0x99, 0xea, 0xcf, 0x00, 0xd8, 0xc7, 0xe6, 0x9b, 0x8c, 0x62, 0x45, 0x87, + /* (2^266)P */ 0xc3, 0xfd, 0x29, 0x66, 0xe7, 0x30, 0x29, 0x77, 0xe0, 0x0d, 0x63, 0x5b, 0xe6, 0x90, 0x1a, 0x1e, 0x99, 0xc2, 0xa7, 0xab, 0xff, 0xa7, 0xbd, 0x79, 0x01, 0x97, 0xfd, 0x27, 0x1b, 0x43, 0x2b, 0xe6, 0xfe, 0x5e, 0xf1, 0xb9, 0x35, 0x38, 0x08, 0x25, 0x55, 0x90, 0x68, 0x2e, 0xc3, 0x67, 0x39, 0x9f, 0x2b, 0x2c, 0x70, 0x48, 0x8c, 0x47, 0xee, 0x56, + /* (2^267)P */ 0xf7, 0x32, 0x70, 0xb5, 0xe6, 0x42, 0xfd, 0x0a, 0x39, 0x9b, 0x07, 0xfe, 0x0e, 0xf4, 0x47, 0xba, 0x6a, 0x3f, 0xf5, 0x2c, 0x15, 0xf3, 0x60, 0x3f, 0xb1, 0x83, 0x7b, 0x2e, 0x34, 0x58, 0x1a, 0x6e, 0x4a, 0x49, 0x05, 0x45, 0xca, 0xdb, 0x00, 0x01, 0x0c, 0x42, 0x5e, 0x60, 0x40, 0x5f, 0xd9, 0xc7, 0x3a, 0x9e, 0x1c, 0x8d, 0xab, 0x11, 0x55, 0x65, + /* (2^268)P */ 0x87, 0x40, 0xb7, 0x0d, 0xaa, 0x34, 0x89, 0x90, 0x75, 0x6d, 0xa2, 0xfe, 0x3b, 0x6d, 0x5c, 0x39, 0x98, 0x10, 0x9e, 0x15, 0xc5, 0x35, 0xa2, 0x27, 0x23, 0x0a, 0x2d, 0x60, 0xe2, 0xa8, 0x7f, 0x3e, 0x77, 0x8f, 0xcc, 0x44, 0xcc, 0x30, 0x28, 0xe2, 0xf0, 0x04, 0x8c, 0xee, 0xe4, 0x5f, 0x68, 0x8c, 0xdf, 0x70, 0xbf, 0x31, 0xee, 0x2a, 0xfc, 0xce, + /* (2^269)P */ 0x92, 0xf2, 0xa0, 0xd9, 0x58, 0x3b, 0x7c, 0x1a, 0x99, 0x46, 0x59, 0x54, 0x60, 0x06, 0x8d, 0x5e, 0xf0, 0x22, 0xa1, 0xed, 0x92, 0x8a, 0x4d, 0x76, 0x95, 0x05, 0x0b, 0xff, 0xfc, 0x9a, 0xd1, 0xcc, 0x05, 0xb9, 0x5e, 0x99, 0xe8, 0x2a, 0x76, 0x7b, 0xfd, 0xa6, 0xe2, 0xd1, 0x1a, 0xd6, 0x76, 0x9f, 0x2f, 0x0e, 0xd1, 0xa8, 0x77, 0x5a, 0x40, 0x5a, + /* (2^270)P */ 0xff, 0xf9, 0x3f, 0xa9, 0xa6, 0x6c, 0x6d, 0x03, 0x8b, 0xa7, 0x10, 0x5d, 0x3f, 0xec, 0x3e, 0x1c, 0x0b, 0x6b, 0xa2, 0x6a, 0x22, 0xa9, 0x28, 0xd0, 0x66, 0xc9, 0xc2, 0x3d, 0x47, 0x20, 0x7d, 0xa6, 0x1d, 0xd8, 0x25, 0xb5, 0xf2, 0xf9, 0x70, 0x19, 0x6b, 0xf8, 0x43, 0x36, 0xc5, 0x1f, 0xe4, 0x5a, 0x4c, 0x13, 0xe4, 0x6d, 0x08, 0x0b, 0x1d, 0xb1, + /* (2^271)P */ 0x3f, 0x20, 0x9b, 0xfb, 0xec, 0x7d, 0x31, 0xc5, 0xfc, 0x88, 0x0b, 0x30, 0xed, 0x36, 0xc0, 0x63, 0xb1, 0x7d, 0x10, 0xda, 0xb6, 0x2e, 0xad, 0xf3, 0xec, 0x94, 0xe7, 0xec, 0xb5, 0x9c, 0xfe, 0xf5, 0x35, 0xf0, 0xa2, 0x2d, 0x7f, 0xca, 0x6b, 0x67, 0x1a, 0xf6, 0xb3, 0xda, 0x09, 0x2a, 0xaa, 0xdf, 0xb1, 0xca, 0x9b, 0xfb, 0xeb, 0xb3, 0xcd, 0xc0, + /* (2^272)P */ 0xcd, 0x4d, 0x89, 0x00, 0xa4, 0x3b, 0x48, 0xf0, 0x76, 0x91, 0x35, 0xa5, 0xf8, 0xc9, 0xb6, 0x46, 0xbc, 0xf6, 0x9a, 0x45, 0x47, 0x17, 0x96, 0x80, 0x5b, 0x3a, 0x28, 0x33, 0xf9, 0x5a, 0xef, 0x43, 0x07, 0xfe, 0x3b, 0xf4, 0x8e, 0x19, 0xce, 0xd2, 0x94, 0x4b, 0x6d, 0x8e, 0x67, 0x20, 0xc7, 0x4f, 0x2f, 0x59, 0x8e, 0xe1, 0xa1, 0xa9, 0xf9, 0x0e, + /* (2^273)P */ 0xdc, 0x7b, 0xb5, 0x50, 0x2e, 0xe9, 0x7e, 0x8b, 0x78, 0xa1, 0x38, 0x96, 0x22, 0xc3, 0x61, 0x67, 0x6d, 0xc8, 0x58, 0xed, 0x41, 0x1d, 0x5d, 0x86, 0x98, 0x7f, 0x2f, 0x1b, 0x8d, 0x3e, 0xaa, 0xc1, 0xd2, 0x0a, 0xf3, 0xbf, 0x95, 0x04, 0xf3, 0x10, 0x3c, 0x2b, 0x7f, 0x90, 0x46, 0x04, 0xaa, 0x6a, 0xa9, 0x35, 0x76, 0xac, 0x49, 0xb5, 0x00, 0x45, + /* (2^274)P */ 0xb1, 0x93, 0x79, 0x84, 0x4a, 0x2a, 0x30, 0x78, 0x16, 0xaa, 0xc5, 0x74, 0x06, 0xce, 0xa5, 0xa7, 0x32, 0x86, 0xe0, 0xf9, 0x10, 0xd2, 0x58, 0x76, 0xfb, 0x66, 0x49, 0x76, 0x3a, 0x90, 0xba, 0xb5, 0xcc, 0x99, 0xcd, 0x09, 0xc1, 0x9a, 0x74, 0x23, 0xdf, 0x0c, 0xfe, 0x99, 0x52, 0x80, 0xa3, 0x7c, 0x1c, 0x71, 0x5f, 0x2c, 0x49, 0x57, 0xf4, 0xf9, + /* (2^275)P */ 0x6d, 0xbf, 0x52, 0xe6, 0x25, 0x98, 0xed, 0xcf, 0xe3, 0xbc, 0x08, 0xa2, 0x1a, 0x90, 0xae, 0xa0, 0xbf, 0x07, 0x15, 0xad, 0x0a, 0x9f, 0x3e, 0x47, 0x44, 0xc2, 0x10, 0x46, 0xa6, 0x7a, 0x9e, 0x2f, 0x57, 0xbc, 0xe2, 0xf0, 0x1d, 0xd6, 0x9a, 0x06, 0xed, 0xfc, 0x54, 0x95, 0x92, 0x15, 0xa2, 0xf7, 0x8d, 0x6b, 0xef, 0xb2, 0x05, 0xed, 0x5c, 0x63, + /* (2^276)P */ 0xbc, 0x0b, 0x27, 0x3a, 0x3a, 0xf8, 0xe1, 0x48, 0x02, 0x7e, 0x27, 0xe6, 0x81, 0x62, 0x07, 0x73, 0x74, 0xe5, 0x52, 0xd7, 0xf8, 0x26, 0xca, 0x93, 0x4d, 0x3e, 0x9b, 0x55, 0x09, 0x8e, 0xe3, 0xd7, 0xa6, 0xe3, 0xb6, 0x2a, 0xa9, 0xb3, 0xb0, 0xa0, 0x8c, 0x01, 0xbb, 0x07, 0x90, 0x78, 0x6d, 0x6d, 0xe9, 0xf0, 0x7a, 0x90, 0xbd, 0xdc, 0x0c, 0x36, + /* (2^277)P */ 0x7f, 0x20, 0x12, 0x0f, 0x40, 0x00, 0x53, 0xd8, 0x0c, 0x27, 0x47, 0x47, 0x22, 0x80, 0xfb, 0x62, 0xe4, 0xa7, 0xf7, 0xbd, 0x42, 0xa5, 0xc3, 0x2b, 0xb2, 0x7f, 0x50, 0xcc, 0xe2, 0xfb, 0xd5, 0xc0, 0x63, 0xdd, 0x24, 0x5f, 0x7c, 0x08, 0x91, 0xbf, 0x6e, 0x47, 0x44, 0xd4, 0x6a, 0xc0, 0xc3, 0x09, 0x39, 0x27, 0xdd, 0xc7, 0xca, 0x06, 0x29, 0x55, + /* (2^278)P */ 0x76, 0x28, 0x58, 0xb0, 0xd2, 0xf3, 0x0f, 0x04, 0xe9, 0xc9, 0xab, 0x66, 0x5b, 0x75, 0x51, 0xdc, 0xe5, 0x8f, 0xe8, 0x1f, 0xdb, 0x03, 0x0f, 0xb0, 0x7d, 0xf9, 0x20, 0x64, 0x89, 0xe9, 0xdc, 0xe6, 0x24, 0xc3, 0xd5, 0xd2, 0x41, 0xa6, 0xe4, 0xe3, 0xc4, 0x79, 0x7c, 0x0f, 0xa1, 0x61, 0x2f, 0xda, 0xa4, 0xc9, 0xfd, 0xad, 0x5c, 0x65, 0x6a, 0xf3, + /* (2^279)P */ 0xd5, 0xab, 0x72, 0x7a, 0x3b, 0x59, 0xea, 0xcf, 0xd5, 0x17, 0xd2, 0xb2, 0x5f, 0x2d, 0xab, 0xad, 0x9e, 0x88, 0x64, 0x55, 0x96, 0x6e, 0xf3, 0x44, 0xa9, 0x11, 0xf5, 0xf8, 0x3a, 0xf1, 0xcd, 0x79, 0x4c, 0x99, 0x6d, 0x23, 0x6a, 0xa0, 0xc2, 0x1a, 0x19, 0x45, 0xb5, 0xd8, 0x95, 0x2f, 0x49, 0xe9, 0x46, 0x39, 0x26, 0x60, 0x04, 0x15, 0x8b, 0xcc, + /* (2^280)P */ 0x66, 0x0c, 0xf0, 0x54, 0x41, 0x02, 0x91, 0xab, 0xe5, 0x85, 0x8a, 0x44, 0xa6, 0x34, 0x96, 0x32, 0xc0, 0xdf, 0x6c, 0x41, 0x39, 0xd4, 0xc6, 0xe1, 0xe3, 0x81, 0xb0, 0x4c, 0x34, 0x4f, 0xe5, 0xf4, 0x35, 0x46, 0x1f, 0xeb, 0x75, 0xfd, 0x43, 0x37, 0x50, 0x99, 0xab, 0xad, 0xb7, 0x8c, 0xa1, 0x57, 0xcb, 0xe6, 0xce, 0x16, 0x2e, 0x85, 0xcc, 0xf9, + /* (2^281)P */ 0x63, 0xd1, 0x3f, 0x9e, 0xa2, 0x17, 0x2e, 0x1d, 0x3e, 0xce, 0x48, 0x2d, 0xbb, 0x8f, 0x69, 0xc9, 0xa6, 0x3d, 0x4e, 0xfe, 0x09, 0x56, 0xb3, 0x02, 0x5f, 0x99, 0x97, 0x0c, 0x54, 0xda, 0x32, 0x97, 0x9b, 0xf4, 0x95, 0xf1, 0xad, 0xe3, 0x2b, 0x04, 0xa7, 0x9b, 0x3f, 0xbb, 0xe7, 0x87, 0x2e, 0x1f, 0x8b, 0x4b, 0x7a, 0xa4, 0x43, 0x0c, 0x0f, 0x35, + /* (2^282)P */ 0x05, 0xdc, 0xe0, 0x2c, 0xa1, 0xc1, 0xd0, 0xf1, 0x1f, 0x4e, 0xc0, 0x6c, 0x35, 0x7b, 0xca, 0x8f, 0x8b, 0x02, 0xb1, 0xf7, 0xd6, 0x2e, 0xe7, 0x93, 0x80, 0x85, 0x18, 0x88, 0x19, 0xb9, 0xb4, 0x4a, 0xbc, 0xeb, 0x5a, 0x78, 0x38, 0xed, 0xc6, 0x27, 0x2a, 0x74, 0x76, 0xf0, 0x1b, 0x79, 0x92, 0x2f, 0xd2, 0x81, 0x98, 0xdf, 0xa9, 0x50, 0x19, 0xeb, + /* (2^283)P */ 0xb5, 0xe7, 0xb4, 0x11, 0x3a, 0x81, 0xb6, 0xb4, 0xf8, 0xa2, 0xb3, 0x6c, 0xfc, 0x9d, 0xe0, 0xc0, 0xe0, 0x59, 0x7f, 0x05, 0x37, 0xef, 0x2c, 0xa9, 0x3a, 0x24, 0xac, 0x7b, 0x25, 0xa0, 0x55, 0xd2, 0x44, 0x82, 0x82, 0x6e, 0x64, 0xa3, 0x58, 0xc8, 0x67, 0xae, 0x26, 0xa7, 0x0f, 0x42, 0x63, 0xe1, 0x93, 0x01, 0x52, 0x19, 0xaf, 0x49, 0x3e, 0x33, + /* (2^284)P */ 0x05, 0x85, 0xe6, 0x66, 0xaf, 0x5f, 0xdf, 0xbf, 0x9d, 0x24, 0x62, 0x60, 0x90, 0xe2, 0x4c, 0x7d, 0x4e, 0xc3, 0x74, 0x5d, 0x4f, 0x53, 0xf3, 0x63, 0x13, 0xf4, 0x74, 0x28, 0x6b, 0x7d, 0x57, 0x0c, 0x9d, 0x84, 0xa7, 0x1a, 0xff, 0xa0, 0x79, 0xdf, 0xfc, 0x65, 0x98, 0x8e, 0x22, 0x0d, 0x62, 0x7e, 0xf2, 0x34, 0x60, 0x83, 0x05, 0x14, 0xb1, 0xc1, + /* (2^285)P */ 0x64, 0x22, 0xcc, 0xdf, 0x5c, 0xbc, 0x88, 0x68, 0x4c, 0xd9, 0xbc, 0x0e, 0xc9, 0x8b, 0xb4, 0x23, 0x52, 0xad, 0xb0, 0xb3, 0xf1, 0x17, 0xd8, 0x15, 0x04, 0x6b, 0x99, 0xf0, 0xc4, 0x7d, 0x48, 0x22, 0x4a, 0xf8, 0x6f, 0xaa, 0x88, 0x0d, 0xc5, 0x5e, 0xa9, 0x1c, 0x61, 0x3d, 0x95, 0xa9, 0x7b, 0x6a, 0x79, 0x33, 0x0a, 0x2b, 0x99, 0xe3, 0x4e, 0x48, + /* (2^286)P */ 0x6b, 0x9b, 0x6a, 0x2a, 0xf1, 0x60, 0x31, 0xb4, 0x73, 0xd1, 0x87, 0x45, 0x9c, 0x15, 0x58, 0x4b, 0x91, 0x6d, 0x94, 0x1c, 0x41, 0x11, 0x4a, 0x83, 0xec, 0xaf, 0x65, 0xbc, 0x34, 0xaa, 0x26, 0xe2, 0xaf, 0xed, 0x46, 0x05, 0x4e, 0xdb, 0xc6, 0x4e, 0x10, 0x28, 0x4e, 0x72, 0xe5, 0x31, 0xa3, 0x20, 0xd7, 0xb1, 0x96, 0x64, 0xf6, 0xce, 0x08, 0x08, + /* (2^287)P */ 0x16, 0xa9, 0x5c, 0x9f, 0x9a, 0xb4, 0xb8, 0xc8, 0x32, 0x78, 0xc0, 0x3a, 0xd9, 0x5f, 0x94, 0xac, 0x3a, 0x42, 0x1f, 0x43, 0xd6, 0x80, 0x47, 0x2c, 0xdc, 0x76, 0x27, 0xfa, 0x50, 0xe5, 0xa1, 0xe4, 0xc3, 0xcb, 0x61, 0x31, 0xe1, 0x2e, 0xde, 0x81, 0x3b, 0x77, 0x1c, 0x39, 0x3c, 0xdb, 0xda, 0x87, 0x4b, 0x84, 0x12, 0xeb, 0xdd, 0x54, 0xbf, 0xe7, + /* (2^288)P */ 0xbf, 0xcb, 0x73, 0x21, 0x3d, 0x7e, 0x13, 0x8c, 0xa6, 0x34, 0x21, 0x2b, 0xa5, 0xe4, 0x9f, 0x8e, 0x9c, 0x01, 0x9c, 0x43, 0xd9, 0xc7, 0xb9, 0xf1, 0xbe, 0x7f, 0x45, 0x51, 0x97, 0xa1, 0x8e, 0x01, 0xf8, 0xbd, 0xd2, 0xbf, 0x81, 0x3a, 0x8b, 0xab, 0xe4, 0x89, 0xb7, 0xbd, 0xf2, 0xcd, 0xa9, 0x8a, 0x8a, 0xde, 0xfb, 0x8a, 0x55, 0x12, 0x7b, 0x17, + /* (2^289)P */ 0x1b, 0x95, 0x58, 0x4d, 0xe6, 0x51, 0x31, 0x52, 0x1c, 0xd8, 0x15, 0x84, 0xb1, 0x0d, 0x36, 0x25, 0x88, 0x91, 0x46, 0x71, 0x42, 0x56, 0xe2, 0x90, 0x08, 0x9e, 0x77, 0x1b, 0xee, 0x22, 0x3f, 0xec, 0xee, 0x8c, 0x7b, 0x2e, 0x79, 0xc4, 0x6c, 0x07, 0xa1, 0x7e, 0x52, 0xf5, 0x26, 0x5c, 0x84, 0x2a, 0x50, 0x6e, 0x82, 0xb3, 0x76, 0xda, 0x35, 0x16, + /* (2^290)P */ 0x0a, 0x6f, 0x99, 0x87, 0xc0, 0x7d, 0x8a, 0xb2, 0xca, 0xae, 0xe8, 0x65, 0x98, 0x0f, 0xb3, 0x44, 0xe1, 0xdc, 0x52, 0x79, 0x75, 0xec, 0x8f, 0x95, 0x87, 0x45, 0xd1, 0x32, 0x18, 0x55, 0x15, 0xce, 0x64, 0x9b, 0x08, 0x4f, 0x2c, 0xea, 0xba, 0x1c, 0x57, 0x06, 0x63, 0xc8, 0xb1, 0xfd, 0xc5, 0x67, 0xe7, 0x1f, 0x87, 0x9e, 0xde, 0x72, 0x7d, 0xec, + /* (2^291)P */ 0x36, 0x8b, 0x4d, 0x2c, 0xc2, 0x46, 0xe8, 0x96, 0xac, 0x0b, 0x8c, 0xc5, 0x09, 0x10, 0xfc, 0xf2, 0xda, 0xea, 0x22, 0xb2, 0xd3, 0x89, 0xeb, 0xb2, 0x85, 0x0f, 0xff, 0x59, 0x50, 0x2c, 0x99, 0x5a, 0x1f, 0xec, 0x2a, 0x6f, 0xec, 0xcf, 0xe9, 0xce, 0x12, 0x6b, 0x19, 0xd8, 0xde, 0x9b, 0xce, 0x0e, 0x6a, 0xaa, 0xe1, 0x32, 0xea, 0x4c, 0xfe, 0x92, + /* (2^292)P */ 0x5f, 0x17, 0x70, 0x53, 0x26, 0x03, 0x0b, 0xab, 0xd1, 0xc1, 0x42, 0x0b, 0xab, 0x2b, 0x3d, 0x31, 0xa4, 0xd5, 0x2b, 0x5e, 0x00, 0xd5, 0x9a, 0x22, 0x34, 0xe0, 0x53, 0x3f, 0x59, 0x7f, 0x2c, 0x6d, 0x72, 0x9a, 0xa4, 0xbe, 0x3d, 0x42, 0x05, 0x1b, 0xf2, 0x7f, 0x88, 0x56, 0xd1, 0x7c, 0x7d, 0x6b, 0x9f, 0x43, 0xfe, 0x65, 0x19, 0xae, 0x9c, 0x4c, + /* (2^293)P */ 0xf3, 0x7c, 0x20, 0xa9, 0xfc, 0xf2, 0xf2, 0x3b, 0x3c, 0x57, 0x41, 0x94, 0xe5, 0xcc, 0x6a, 0x37, 0x5d, 0x09, 0xf2, 0xab, 0xc2, 0xca, 0x60, 0x38, 0x6b, 0x7a, 0xe1, 0x78, 0x2b, 0xc1, 0x1d, 0xe8, 0xfd, 0xbc, 0x3d, 0x5c, 0xa2, 0xdb, 0x49, 0x20, 0x79, 0xe6, 0x1b, 0x9b, 0x65, 0xd9, 0x6d, 0xec, 0x57, 0x1d, 0xd2, 0xe9, 0x90, 0xeb, 0x43, 0x7b, + /* (2^294)P */ 0x2a, 0x8b, 0x2e, 0x19, 0x18, 0x10, 0xb8, 0x83, 0xe7, 0x7d, 0x2d, 0x9a, 0x3a, 0xe5, 0xd1, 0xe4, 0x7c, 0x38, 0xe5, 0x59, 0x2a, 0x6e, 0xd9, 0x01, 0x29, 0x3d, 0x23, 0xf7, 0x52, 0xba, 0x61, 0x04, 0x9a, 0xde, 0xc4, 0x31, 0x50, 0xeb, 0x1b, 0xaa, 0xde, 0x39, 0x58, 0xd8, 0x1b, 0x1e, 0xfc, 0x57, 0x9a, 0x28, 0x43, 0x9e, 0x97, 0x5e, 0xaa, 0xa3, + /* (2^295)P */ 0x97, 0x0a, 0x74, 0xc4, 0x39, 0x99, 0x6b, 0x40, 0xc7, 0x3e, 0x8c, 0xa7, 0xb1, 0x4e, 0x9a, 0x59, 0x6e, 0x1c, 0xfe, 0xfc, 0x2a, 0x5e, 0x73, 0x2b, 0x8c, 0xa9, 0x71, 0xf5, 0xda, 0x6b, 0x15, 0xab, 0xf7, 0xbe, 0x2a, 0x44, 0x5f, 0xba, 0xae, 0x67, 0x93, 0xc5, 0x86, 0xc1, 0xb8, 0xdf, 0xdc, 0xcb, 0xd7, 0xff, 0xb1, 0x71, 0x7c, 0x6f, 0x88, 0xf8, + /* (2^296)P */ 0x3f, 0x89, 0xb1, 0xbf, 0x24, 0x16, 0xac, 0x56, 0xfe, 0xdf, 0x94, 0x71, 0xbf, 0xd6, 0x57, 0x0c, 0xb4, 0x77, 0x37, 0xaa, 0x2a, 0x70, 0x76, 0x49, 0xaf, 0x0c, 0x97, 0x8e, 0x78, 0x2a, 0x67, 0xc9, 0x3b, 0x3d, 0x5b, 0x01, 0x2f, 0xda, 0xd5, 0xa8, 0xde, 0x02, 0xa9, 0xac, 0x76, 0x00, 0x0b, 0x46, 0xc6, 0x2d, 0xdc, 0x08, 0xf4, 0x10, 0x2c, 0xbe, + /* (2^297)P */ 0xcb, 0x07, 0xf9, 0x91, 0xc6, 0xd5, 0x3e, 0x54, 0x63, 0xae, 0xfc, 0x10, 0xbe, 0x3a, 0x20, 0x73, 0x4e, 0x65, 0x0e, 0x2d, 0x86, 0x77, 0x83, 0x9d, 0xe2, 0x0a, 0xe9, 0xac, 0x22, 0x52, 0x76, 0xd4, 0x6e, 0xfa, 0xe0, 0x09, 0xef, 0x78, 0x82, 0x9f, 0x26, 0xf9, 0x06, 0xb5, 0xe7, 0x05, 0x0e, 0xf2, 0x46, 0x72, 0x93, 0xd3, 0x24, 0xbd, 0x87, 0x60, + /* (2^298)P */ 0x14, 0x55, 0x84, 0x7b, 0x6c, 0x60, 0x80, 0x73, 0x8c, 0xbe, 0x2d, 0xd6, 0x69, 0xd6, 0x17, 0x26, 0x44, 0x9f, 0x88, 0xa2, 0x39, 0x7c, 0x89, 0xbc, 0x6d, 0x9e, 0x46, 0xb6, 0x68, 0x66, 0xea, 0xdc, 0x31, 0xd6, 0x21, 0x51, 0x9f, 0x28, 0x28, 0xaf, 0x9e, 0x47, 0x2c, 0x4c, 0x8f, 0xf3, 0xaf, 0x1f, 0xe4, 0xab, 0xac, 0xe9, 0x0c, 0x91, 0x3a, 0x61, + /* (2^299)P */ 0xb0, 0x37, 0x55, 0x4b, 0xe9, 0xc3, 0xb1, 0xce, 0x42, 0xe6, 0xc5, 0x11, 0x7f, 0x2c, 0x11, 0xfc, 0x4e, 0x71, 0x17, 0x00, 0x74, 0x7f, 0xbf, 0x07, 0x4d, 0xfd, 0x40, 0xb2, 0x87, 0xb0, 0xef, 0x1f, 0x35, 0x2c, 0x2d, 0xd7, 0xe1, 0xe4, 0xad, 0x0e, 0x7f, 0x63, 0x66, 0x62, 0x23, 0x41, 0xf6, 0xc1, 0x14, 0xa6, 0xd7, 0xa9, 0x11, 0x56, 0x9d, 0x1b, + /* (2^300)P */ 0x02, 0x82, 0x42, 0x18, 0x4f, 0x1b, 0xc9, 0x5d, 0x78, 0x5f, 0xee, 0xed, 0x01, 0x49, 0x8f, 0xf2, 0xa0, 0xe2, 0x6e, 0xbb, 0x6b, 0x04, 0x8d, 0xb2, 0x41, 0xae, 0xc8, 0x1b, 0x59, 0x34, 0xb8, 0x2a, 0xdb, 0x1f, 0xd2, 0x52, 0xdf, 0x3f, 0x35, 0x00, 0x8b, 0x61, 0xbc, 0x97, 0xa0, 0xc4, 0x77, 0xd1, 0xe4, 0x2c, 0x59, 0x68, 0xff, 0x30, 0xf2, 0xe2, + /* (2^301)P */ 0x79, 0x08, 0xb1, 0xdb, 0x55, 0xae, 0xd0, 0xed, 0xda, 0xa0, 0xec, 0x6c, 0xae, 0x68, 0xf2, 0x0b, 0x61, 0xb3, 0xf5, 0x21, 0x69, 0x87, 0x0b, 0x03, 0xea, 0x8a, 0x15, 0xd9, 0x7e, 0xca, 0xf7, 0xcd, 0xf3, 0x33, 0xb3, 0x4c, 0x5b, 0x23, 0x4e, 0x6f, 0x90, 0xad, 0x91, 0x4b, 0x4f, 0x46, 0x37, 0xe5, 0xe8, 0xb7, 0xeb, 0xd5, 0xca, 0x34, 0x4e, 0x23, + /* (2^302)P */ 0x09, 0x02, 0xdd, 0xfd, 0x70, 0xac, 0x56, 0x80, 0x36, 0x5e, 0x49, 0xd0, 0x3f, 0xc2, 0xe0, 0xba, 0x46, 0x7f, 0x5c, 0xf7, 0xc5, 0xbd, 0xd5, 0x55, 0x7d, 0x3f, 0xd5, 0x7d, 0x06, 0xdf, 0x27, 0x20, 0x4f, 0xe9, 0x30, 0xec, 0x1b, 0xa0, 0x0c, 0xd4, 0x2c, 0xe1, 0x2b, 0x65, 0x73, 0xea, 0x75, 0x35, 0xe8, 0xe6, 0x56, 0xd6, 0x07, 0x15, 0x99, 0xdf, + /* (2^303)P */ 0x4e, 0x10, 0xb7, 0xd0, 0x63, 0x8c, 0xcf, 0x16, 0x00, 0x7c, 0x58, 0xdf, 0x86, 0xdc, 0x4e, 0xca, 0x9c, 0x40, 0x5a, 0x42, 0xfd, 0xec, 0x98, 0xa4, 0x42, 0x53, 0xae, 0x16, 0x9d, 0xfd, 0x75, 0x5a, 0x12, 0x56, 0x1e, 0xc6, 0x57, 0xcc, 0x79, 0x27, 0x96, 0x00, 0xcf, 0x80, 0x4f, 0x8a, 0x36, 0x5c, 0xbb, 0xe9, 0x12, 0xdb, 0xb6, 0x2b, 0xad, 0x96, + /* (2^304)P */ 0x92, 0x32, 0x1f, 0xfd, 0xc6, 0x02, 0x94, 0x08, 0x1b, 0x60, 0x6a, 0x9f, 0x8b, 0xd6, 0xc8, 0xad, 0xd5, 0x1b, 0x27, 0x4e, 0xa4, 0x4d, 0x4a, 0x00, 0x10, 0x5f, 0x86, 0x11, 0xf5, 0xe3, 0x14, 0x32, 0x43, 0xee, 0xb9, 0xc7, 0xab, 0xf4, 0x6f, 0xe5, 0x66, 0x0c, 0x06, 0x0d, 0x96, 0x79, 0x28, 0xaf, 0x45, 0x2b, 0x56, 0xbe, 0xe4, 0x4a, 0x52, 0xd6, + /* (2^305)P */ 0x15, 0x16, 0x69, 0xef, 0x60, 0xca, 0x82, 0x25, 0x0f, 0xc6, 0x30, 0xa0, 0x0a, 0xd1, 0x83, 0x29, 0xcd, 0xb6, 0x89, 0x6c, 0xf5, 0xb2, 0x08, 0x38, 0xe6, 0xca, 0x6b, 0x19, 0x93, 0xc6, 0x5f, 0x75, 0x8e, 0x60, 0x34, 0x23, 0xc4, 0x13, 0x17, 0x69, 0x55, 0xcc, 0x72, 0x9c, 0x2b, 0x6c, 0x80, 0xf4, 0x4b, 0x8b, 0xb6, 0x97, 0x65, 0x07, 0xb6, 0xfb, + /* (2^306)P */ 0x01, 0x99, 0x74, 0x28, 0xa6, 0x67, 0xa3, 0xe5, 0x25, 0xfb, 0xdf, 0x82, 0x93, 0xe7, 0x35, 0x74, 0xce, 0xe3, 0x15, 0x1c, 0x1d, 0x79, 0x52, 0x84, 0x08, 0x04, 0x2f, 0x5c, 0xb8, 0xcd, 0x7f, 0x89, 0xb0, 0x39, 0x93, 0x63, 0xc9, 0x5d, 0x06, 0x01, 0x59, 0xf7, 0x7e, 0xf1, 0x4c, 0x3d, 0x12, 0x8d, 0x69, 0x1d, 0xb7, 0x21, 0x5e, 0x88, 0x82, 0xa2, + /* (2^307)P */ 0x8e, 0x69, 0xaf, 0x9a, 0x41, 0x0d, 0x9d, 0xcf, 0x8e, 0x8d, 0x5c, 0x51, 0x6e, 0xde, 0x0e, 0x48, 0x23, 0x89, 0xe5, 0x37, 0x80, 0xd6, 0x9d, 0x72, 0x32, 0x26, 0x38, 0x2d, 0x63, 0xa0, 0xfa, 0xd3, 0x40, 0xc0, 0x8c, 0x68, 0x6f, 0x2b, 0x1e, 0x9a, 0x39, 0x51, 0x78, 0x74, 0x9a, 0x7b, 0x4a, 0x8f, 0x0c, 0xa0, 0x88, 0x60, 0xa5, 0x21, 0xcd, 0xc7, + /* (2^308)P */ 0x3a, 0x7f, 0x73, 0x14, 0xbf, 0x89, 0x6a, 0x4c, 0x09, 0x5d, 0xf2, 0x93, 0x20, 0x2d, 0xc4, 0x29, 0x86, 0x06, 0x95, 0xab, 0x22, 0x76, 0x4c, 0x54, 0xe1, 0x7e, 0x80, 0x6d, 0xab, 0x29, 0x61, 0x87, 0x77, 0xf6, 0xc0, 0x3e, 0xda, 0xab, 0x65, 0x7e, 0x39, 0x12, 0xa1, 0x6b, 0x42, 0xf7, 0xc5, 0x97, 0x77, 0xec, 0x6f, 0x22, 0xbe, 0x44, 0xc7, 0x03, + /* (2^309)P */ 0xa5, 0x23, 0x90, 0x41, 0xa3, 0xc5, 0x3e, 0xe0, 0xa5, 0x32, 0x49, 0x1f, 0x39, 0x78, 0xb1, 0xd8, 0x24, 0xea, 0xd4, 0x87, 0x53, 0x42, 0x51, 0xf4, 0xd9, 0x46, 0x25, 0x2f, 0x62, 0xa9, 0x90, 0x9a, 0x4a, 0x25, 0x8a, 0xd2, 0x10, 0xe7, 0x3c, 0xbc, 0x58, 0x8d, 0x16, 0x14, 0x96, 0xa4, 0x6f, 0xf8, 0x12, 0x69, 0x91, 0x73, 0xe2, 0xfa, 0xf4, 0x57, + /* (2^310)P */ 0x51, 0x45, 0x3f, 0x96, 0xdc, 0x97, 0x38, 0xa6, 0x01, 0x63, 0x09, 0xea, 0xc2, 0x13, 0x30, 0xb0, 0x00, 0xb8, 0x0a, 0xce, 0xd1, 0x8f, 0x3e, 0x69, 0x62, 0x46, 0x33, 0x9c, 0xbf, 0x4b, 0xcb, 0x0c, 0x90, 0x1c, 0x45, 0xcf, 0x37, 0x5b, 0xf7, 0x4b, 0x5e, 0x95, 0xc3, 0x28, 0x9f, 0x08, 0x83, 0x53, 0x74, 0xab, 0x0c, 0xb4, 0xc0, 0xa1, 0xbc, 0x89, + /* (2^311)P */ 0x06, 0xb1, 0x51, 0x15, 0x65, 0x60, 0x21, 0x17, 0x7a, 0x20, 0x65, 0xee, 0x12, 0x35, 0x4d, 0x46, 0xf4, 0xf8, 0xd0, 0xb1, 0xca, 0x09, 0x30, 0x08, 0x89, 0x23, 0x3b, 0xe7, 0xab, 0x8b, 0x77, 0xa6, 0xad, 0x25, 0xdd, 0xea, 0x3c, 0x7d, 0xa5, 0x24, 0xb3, 0xe8, 0xfa, 0xfb, 0xc9, 0xf2, 0x71, 0xe9, 0xfa, 0xf2, 0xdc, 0x54, 0xdd, 0x55, 0x2e, 0x2f, + /* (2^312)P */ 0x7f, 0x96, 0x96, 0xfb, 0x52, 0x86, 0xcf, 0xea, 0x62, 0x18, 0xf1, 0x53, 0x1f, 0x61, 0x2a, 0x9f, 0x8c, 0x51, 0xca, 0x2c, 0xde, 0x6d, 0xce, 0xab, 0x58, 0x32, 0x0b, 0x33, 0x9b, 0x99, 0xb4, 0x5c, 0x88, 0x2a, 0x76, 0xcc, 0x3e, 0x54, 0x1e, 0x9d, 0xa2, 0x89, 0xe4, 0x19, 0xba, 0x80, 0xc8, 0x39, 0x32, 0x7f, 0x0f, 0xc7, 0x84, 0xbb, 0x43, 0x56, + /* (2^313)P */ 0x9b, 0x07, 0xb4, 0x42, 0xa9, 0xa0, 0x78, 0x4f, 0x28, 0x70, 0x2b, 0x7e, 0x61, 0xe0, 0xdd, 0x02, 0x98, 0xfc, 0xed, 0x31, 0x80, 0xf1, 0x15, 0x52, 0x89, 0x23, 0xcd, 0x5d, 0x2b, 0xc5, 0x19, 0x32, 0xfb, 0x70, 0x50, 0x7a, 0x97, 0x6b, 0x42, 0xdb, 0xca, 0xdb, 0xc4, 0x59, 0x99, 0xe0, 0x12, 0x1f, 0x17, 0xba, 0x8b, 0xf0, 0xc4, 0x38, 0x5d, 0x27, + /* (2^314)P */ 0x29, 0x1d, 0xdc, 0x2b, 0xf6, 0x5b, 0x04, 0x61, 0x36, 0x76, 0xa0, 0x56, 0x36, 0x6e, 0xd7, 0x24, 0x4d, 0xe7, 0xef, 0x44, 0xd2, 0xd5, 0x07, 0xcd, 0xc4, 0x9d, 0x80, 0x48, 0xc3, 0x38, 0xcf, 0xd8, 0xa3, 0xdd, 0xb2, 0x5e, 0xb5, 0x70, 0x15, 0xbb, 0x36, 0x85, 0x8a, 0xd7, 0xfb, 0x56, 0x94, 0x73, 0x9c, 0x81, 0xbe, 0xb1, 0x44, 0x28, 0xf1, 0x37, + /* (2^315)P */ 0xbf, 0xcf, 0x5c, 0xd2, 0xe2, 0xea, 0xc2, 0xcd, 0x70, 0x7a, 0x9d, 0xcb, 0x81, 0xc1, 0xe9, 0xf1, 0x56, 0x71, 0x52, 0xf7, 0x1b, 0x87, 0xc6, 0xd8, 0xcc, 0xb2, 0x69, 0xf3, 0xb0, 0xbd, 0xba, 0x83, 0x12, 0x26, 0xc4, 0xce, 0x72, 0xde, 0x3b, 0x21, 0x28, 0x9e, 0x5a, 0x94, 0xf5, 0x04, 0xa3, 0xc8, 0x0f, 0x5e, 0xbc, 0x71, 0xf9, 0x0d, 0xce, 0xf5, + /* (2^316)P */ 0x93, 0x97, 0x00, 0x85, 0xf4, 0xb4, 0x40, 0xec, 0xd9, 0x2b, 0x6c, 0xd6, 0x63, 0x9e, 0x93, 0x0a, 0x5a, 0xf4, 0xa7, 0x9a, 0xe3, 0x3c, 0xf0, 0x55, 0xd1, 0x96, 0x6c, 0xf5, 0x2a, 0xce, 0xd7, 0x95, 0x72, 0xbf, 0xc5, 0x0c, 0xce, 0x79, 0xa2, 0x0a, 0x78, 0xe0, 0x72, 0xd0, 0x66, 0x28, 0x05, 0x75, 0xd3, 0x23, 0x09, 0x91, 0xed, 0x7e, 0xc4, 0xbc, + /* (2^317)P */ 0x77, 0xc2, 0x9a, 0xf7, 0xa6, 0xe6, 0x18, 0xb4, 0xe7, 0xf6, 0xda, 0xec, 0x44, 0x6d, 0xfb, 0x08, 0xee, 0x65, 0xa8, 0x92, 0x85, 0x1f, 0xba, 0x38, 0x93, 0x20, 0x5c, 0x4d, 0xd2, 0x18, 0x0f, 0x24, 0xbe, 0x1a, 0x96, 0x44, 0x7d, 0xeb, 0xb3, 0xda, 0x95, 0xf4, 0xaf, 0x6c, 0x06, 0x0f, 0x47, 0x37, 0xc8, 0x77, 0x63, 0xe1, 0x29, 0xef, 0xff, 0xa5, + /* (2^318)P */ 0x16, 0x12, 0xd9, 0x47, 0x90, 0x22, 0x9b, 0x05, 0xf2, 0xa5, 0x9a, 0xae, 0x83, 0x98, 0xb5, 0xac, 0xab, 0x29, 0xaa, 0xdc, 0x5f, 0xde, 0xcd, 0xf7, 0x42, 0xad, 0x3b, 0x96, 0xd6, 0x3e, 0x6e, 0x52, 0x47, 0xb1, 0xab, 0x51, 0xde, 0x49, 0x7c, 0x87, 0x8d, 0x86, 0xe2, 0x70, 0x13, 0x21, 0x51, 0x1c, 0x0c, 0x25, 0xc1, 0xb0, 0xe6, 0x19, 0xcf, 0x12, + /* (2^319)P */ 0xf0, 0xbc, 0x97, 0x8f, 0x4b, 0x2f, 0xd1, 0x1f, 0x8c, 0x57, 0xed, 0x3c, 0xf4, 0x26, 0x19, 0xbb, 0x60, 0xca, 0x24, 0xc5, 0xd9, 0x97, 0xe2, 0x5f, 0x76, 0x49, 0x39, 0x7e, 0x2d, 0x12, 0x21, 0x98, 0xda, 0xe6, 0xdb, 0xd2, 0xd8, 0x9f, 0x18, 0xd8, 0x83, 0x6c, 0xba, 0x89, 0x8d, 0x29, 0xfa, 0x46, 0x33, 0x8c, 0x28, 0xdf, 0x6a, 0xb3, 0x69, 0x28, + /* (2^320)P */ 0x86, 0x17, 0xbc, 0xd6, 0x7c, 0xba, 0x1e, 0x83, 0xbb, 0x84, 0xb5, 0x8c, 0xad, 0xdf, 0xa1, 0x24, 0x81, 0x70, 0x40, 0x0f, 0xad, 0xad, 0x3b, 0x23, 0xd0, 0x93, 0xa0, 0x49, 0x5c, 0x4b, 0x51, 0xbe, 0x20, 0x49, 0x4e, 0xda, 0x2d, 0xd3, 0xad, 0x1b, 0x74, 0x08, 0x41, 0xf0, 0xef, 0x19, 0xe9, 0x45, 0x5d, 0x02, 0xae, 0x26, 0x25, 0xd9, 0xd1, 0xc2, + /* (2^321)P */ 0x48, 0x81, 0x3e, 0xb2, 0x83, 0xf8, 0x4d, 0xb3, 0xd0, 0x4c, 0x75, 0xb3, 0xa0, 0x52, 0x26, 0xf2, 0xaf, 0x5d, 0x36, 0x70, 0x72, 0xd6, 0xb7, 0x88, 0x08, 0x69, 0xbd, 0x15, 0x25, 0xb1, 0x45, 0x1b, 0xb7, 0x0b, 0x5f, 0x71, 0x5d, 0x83, 0x49, 0xb9, 0x84, 0x3b, 0x7c, 0xc1, 0x50, 0x93, 0x05, 0x53, 0xe0, 0x61, 0xea, 0xc1, 0xef, 0xdb, 0x82, 0x97, + /* (2^322)P */ 0x00, 0xd5, 0xc3, 0x3a, 0x4d, 0x8a, 0x23, 0x7a, 0xef, 0xff, 0x37, 0xef, 0xf3, 0xbc, 0xa9, 0xb6, 0xae, 0xd7, 0x3a, 0x7b, 0xfd, 0x3e, 0x8e, 0x9b, 0xab, 0x44, 0x54, 0x60, 0x28, 0x6c, 0xbf, 0x15, 0x24, 0x4a, 0x56, 0x60, 0x7f, 0xa9, 0x7a, 0x28, 0x59, 0x2c, 0x8a, 0xd1, 0x7d, 0x6b, 0x00, 0xfd, 0xa5, 0xad, 0xbc, 0x19, 0x3f, 0xcb, 0x73, 0xe0, + /* (2^323)P */ 0xcf, 0x9e, 0x66, 0x06, 0x4d, 0x2b, 0xf5, 0x9c, 0xc2, 0x9d, 0x9e, 0xed, 0x5a, 0x5c, 0x2d, 0x00, 0xbf, 0x29, 0x90, 0x88, 0xe4, 0x5d, 0xfd, 0xe2, 0xf0, 0x38, 0xec, 0x4d, 0x26, 0xea, 0x54, 0xf0, 0x3c, 0x84, 0x10, 0x6a, 0xf9, 0x66, 0x9c, 0xe7, 0x21, 0xfd, 0x0f, 0xc7, 0x13, 0x50, 0x81, 0xb6, 0x50, 0xf9, 0x04, 0x7f, 0xa4, 0x37, 0x85, 0x14, + /* (2^324)P */ 0xdb, 0x87, 0x49, 0xc7, 0xa8, 0x39, 0x0c, 0x32, 0x98, 0x0c, 0xb9, 0x1a, 0x1b, 0x4d, 0xe0, 0x8a, 0x9a, 0x8e, 0x8f, 0xab, 0x5a, 0x17, 0x3d, 0x04, 0x21, 0xce, 0x3e, 0x2c, 0xf9, 0xa3, 0x97, 0xe4, 0x77, 0x95, 0x0e, 0xb6, 0xa5, 0x15, 0xad, 0x3a, 0x1e, 0x46, 0x53, 0x17, 0x09, 0x83, 0x71, 0x4e, 0x86, 0x38, 0xd5, 0x23, 0x44, 0x16, 0x8d, 0xc8, + /* (2^325)P */ 0x05, 0x5e, 0x99, 0x08, 0xbb, 0xc3, 0xc0, 0xb7, 0x6c, 0x12, 0xf2, 0xf3, 0xf4, 0x7c, 0x6a, 0x4d, 0x9e, 0xeb, 0x3d, 0xb9, 0x63, 0x94, 0xce, 0x81, 0xd8, 0x11, 0xcb, 0x55, 0x69, 0x4a, 0x20, 0x0b, 0x4c, 0x2e, 0x14, 0xb8, 0xd4, 0x6a, 0x7c, 0xf0, 0xed, 0xfc, 0x8f, 0xef, 0xa0, 0xeb, 0x6c, 0x01, 0xe2, 0xdc, 0x10, 0x22, 0xa2, 0x01, 0x85, 0x64, + /* (2^326)P */ 0x58, 0xe1, 0x9c, 0x27, 0x55, 0xc6, 0x25, 0xa6, 0x7d, 0x67, 0x88, 0x65, 0x99, 0x6c, 0xcb, 0xdb, 0x27, 0x4f, 0x44, 0x29, 0xf5, 0x4a, 0x23, 0x10, 0xbc, 0x03, 0x3f, 0x36, 0x1e, 0xef, 0xb0, 0xba, 0x75, 0xe8, 0x74, 0x5f, 0x69, 0x3e, 0x26, 0x40, 0xb4, 0x2f, 0xdc, 0x43, 0xbf, 0xa1, 0x8b, 0xbd, 0xca, 0x6e, 0xc1, 0x6e, 0x21, 0x79, 0xa0, 0xd0, + /* (2^327)P */ 0x78, 0x93, 0x4a, 0x2d, 0x22, 0x6e, 0x6e, 0x7d, 0x74, 0xd2, 0x66, 0x58, 0xce, 0x7b, 0x1d, 0x97, 0xb1, 0xf2, 0xda, 0x1c, 0x79, 0xfb, 0xba, 0xd1, 0xc0, 0xc5, 0x6e, 0xc9, 0x11, 0x89, 0xd2, 0x41, 0x8d, 0x70, 0xb9, 0xcc, 0xea, 0x6a, 0xb3, 0x45, 0xb6, 0x05, 0x2e, 0xf2, 0x17, 0xf1, 0x27, 0xb8, 0xed, 0x06, 0x1f, 0xdb, 0x9d, 0x1f, 0x69, 0x28, + /* (2^328)P */ 0x93, 0x12, 0xa8, 0x11, 0xe1, 0x92, 0x30, 0x8d, 0xac, 0xe1, 0x1c, 0x60, 0x7c, 0xed, 0x2d, 0x2e, 0xd3, 0x03, 0x5c, 0x9c, 0xc5, 0xbd, 0x64, 0x4a, 0x8c, 0xba, 0x76, 0xfe, 0xc6, 0xc1, 0xea, 0xc2, 0x4f, 0xbe, 0x70, 0x3d, 0x64, 0xcf, 0x8e, 0x18, 0xcb, 0xcd, 0x57, 0xa7, 0xf7, 0x36, 0xa9, 0x6b, 0x3e, 0xb8, 0x69, 0xee, 0x47, 0xa2, 0x7e, 0xb2, + /* (2^329)P */ 0x96, 0xaf, 0x3a, 0xf5, 0xed, 0xcd, 0xaf, 0xf7, 0x82, 0xaf, 0x59, 0x62, 0x0b, 0x36, 0x85, 0xf9, 0xaf, 0xd6, 0x38, 0xff, 0x87, 0x2e, 0x1d, 0x6c, 0x8b, 0xaf, 0x3b, 0xdf, 0x28, 0xa2, 0xd6, 0x4d, 0x80, 0x92, 0xc3, 0x0f, 0x34, 0xa8, 0xae, 0x69, 0x5d, 0x7b, 0x9d, 0xbc, 0xf5, 0xfd, 0x1d, 0xb1, 0x96, 0x55, 0x86, 0xe1, 0x5c, 0xb6, 0xac, 0xb9, + /* (2^330)P */ 0x50, 0x9e, 0x37, 0x28, 0x7d, 0xa8, 0x33, 0x63, 0xda, 0x3f, 0x20, 0x98, 0x0e, 0x09, 0xa8, 0x77, 0x3b, 0x7a, 0xfc, 0x16, 0x85, 0x44, 0x64, 0x77, 0x65, 0x68, 0x92, 0x41, 0xc6, 0x1f, 0xdf, 0x27, 0xf9, 0xec, 0xa0, 0x61, 0x22, 0xea, 0x19, 0xe7, 0x75, 0x8b, 0x4e, 0xe5, 0x0f, 0xb7, 0xf7, 0xd2, 0x53, 0xf4, 0xdd, 0x4a, 0xaa, 0x78, 0x40, 0xb7, + /* (2^331)P */ 0xd4, 0x89, 0xe3, 0x79, 0xba, 0xb6, 0xc3, 0xda, 0xe6, 0x78, 0x65, 0x7d, 0x6e, 0x22, 0x62, 0xb1, 0x3d, 0xea, 0x90, 0x84, 0x30, 0x5e, 0xd4, 0x39, 0x84, 0x78, 0xd9, 0x75, 0xd6, 0xce, 0x2a, 0x11, 0x29, 0x69, 0xa4, 0x5e, 0xaa, 0x2a, 0x98, 0x5a, 0xe5, 0x91, 0x8f, 0xb2, 0xfb, 0xda, 0x97, 0xe8, 0x83, 0x6f, 0x04, 0xb9, 0x5d, 0xaf, 0xe1, 0x9b, + /* (2^332)P */ 0x8b, 0xe4, 0xe1, 0x48, 0x9c, 0xc4, 0x83, 0x89, 0xdf, 0x65, 0xd3, 0x35, 0x55, 0x13, 0xf4, 0x1f, 0x36, 0x92, 0x33, 0x38, 0xcb, 0xed, 0x15, 0xe6, 0x60, 0x2d, 0x25, 0xf5, 0x36, 0x60, 0x3a, 0x37, 0x9b, 0x71, 0x9d, 0x42, 0xb0, 0x14, 0xc8, 0xba, 0x62, 0xa3, 0x49, 0xb0, 0x88, 0xc1, 0x72, 0x73, 0xdd, 0x62, 0x40, 0xa9, 0x62, 0x88, 0x99, 0xca, + /* (2^333)P */ 0x47, 0x7b, 0xea, 0xda, 0x46, 0x2f, 0x45, 0xc6, 0xe3, 0xb4, 0x4d, 0x8d, 0xac, 0x0b, 0x54, 0x22, 0x06, 0x31, 0x16, 0x66, 0x3e, 0xe4, 0x38, 0x12, 0xcd, 0xf3, 0xe7, 0x99, 0x37, 0xd9, 0x62, 0x24, 0x4b, 0x05, 0xf2, 0x58, 0xe6, 0x29, 0x4b, 0x0d, 0xf6, 0xc1, 0xba, 0xa0, 0x1e, 0x0f, 0xcb, 0x1f, 0xc6, 0x2b, 0x19, 0xfc, 0x82, 0x01, 0xd0, 0x86, + /* (2^334)P */ 0xa2, 0xae, 0x77, 0x20, 0xfb, 0xa8, 0x18, 0xb4, 0x61, 0xef, 0xe8, 0x52, 0x79, 0xbb, 0x86, 0x90, 0x5d, 0x2e, 0x76, 0xed, 0x66, 0x60, 0x5d, 0x00, 0xb5, 0xa4, 0x00, 0x40, 0x89, 0xec, 0xd1, 0xd2, 0x0d, 0x26, 0xb9, 0x30, 0xb2, 0xd2, 0xb8, 0xe8, 0x0e, 0x56, 0xf9, 0x67, 0x94, 0x2e, 0x62, 0xe1, 0x79, 0x48, 0x2b, 0xa9, 0xfa, 0xea, 0xdb, 0x28, + /* (2^335)P */ 0x35, 0xf1, 0xb0, 0x43, 0xbd, 0x27, 0xef, 0x18, 0x44, 0xa2, 0x04, 0xb4, 0x69, 0xa1, 0x97, 0x1f, 0x8c, 0x04, 0x82, 0x9b, 0x00, 0x6d, 0xf8, 0xbf, 0x7d, 0xc1, 0x5b, 0xab, 0xe8, 0xb2, 0x34, 0xbd, 0xaf, 0x7f, 0xb2, 0x0d, 0xf3, 0xed, 0xfc, 0x5b, 0x50, 0xee, 0xe7, 0x4a, 0x20, 0xd9, 0xf5, 0xc6, 0x9a, 0x97, 0x6d, 0x07, 0x2f, 0xb9, 0x31, 0x02, + /* (2^336)P */ 0xf9, 0x54, 0x4a, 0xc5, 0x61, 0x7e, 0x1d, 0xa6, 0x0e, 0x1a, 0xa8, 0xd3, 0x8c, 0x36, 0x7d, 0xf1, 0x06, 0xb1, 0xac, 0x93, 0xcd, 0xe9, 0x8f, 0x61, 0x6c, 0x5d, 0x03, 0x23, 0xdf, 0x85, 0x53, 0x39, 0x63, 0x5e, 0xeb, 0xf3, 0xd3, 0xd3, 0x75, 0x97, 0x9b, 0x62, 0x9b, 0x01, 0xb3, 0x19, 0xd8, 0x2b, 0x36, 0xf2, 0x2c, 0x2c, 0x6f, 0x36, 0xc6, 0x3c, + /* (2^337)P */ 0x05, 0x74, 0x43, 0x10, 0xb6, 0xb0, 0xf8, 0xbf, 0x02, 0x46, 0x9a, 0xee, 0xc1, 0xaf, 0xc1, 0xe5, 0x5a, 0x2e, 0xbb, 0xe1, 0xdc, 0xc6, 0xce, 0x51, 0x29, 0x50, 0xbf, 0x1b, 0xde, 0xff, 0xba, 0x4d, 0x8d, 0x8b, 0x7e, 0xe7, 0xbd, 0x5b, 0x8f, 0xbe, 0xe3, 0x75, 0x71, 0xff, 0x37, 0x05, 0x5a, 0x10, 0xeb, 0x54, 0x7e, 0x44, 0x72, 0x2c, 0xd4, 0xfc, + /* (2^338)P */ 0x03, 0x12, 0x1c, 0xb2, 0x08, 0x90, 0xa1, 0x2d, 0x50, 0xa0, 0xad, 0x7f, 0x8d, 0xa6, 0x97, 0xc1, 0xbd, 0xdc, 0xc3, 0xa7, 0xad, 0x31, 0xdf, 0xb8, 0x03, 0x84, 0xc3, 0xb9, 0x29, 0x3d, 0x92, 0x2e, 0xc3, 0x90, 0x07, 0xe8, 0xa7, 0xc7, 0xbc, 0x61, 0xe9, 0x3e, 0xa0, 0x35, 0xda, 0x1d, 0xab, 0x48, 0xfe, 0x50, 0xc9, 0x25, 0x59, 0x23, 0x69, 0x3f, + /* (2^339)P */ 0x8e, 0x91, 0xab, 0x6b, 0x91, 0x4f, 0x89, 0x76, 0x67, 0xad, 0xb2, 0x65, 0x9d, 0xad, 0x02, 0x36, 0xdc, 0xac, 0x96, 0x93, 0x97, 0x21, 0x14, 0xd0, 0xe8, 0x11, 0x60, 0x1e, 0xeb, 0x96, 0x06, 0xf2, 0x53, 0xf2, 0x6d, 0xb7, 0x93, 0x6f, 0x26, 0x91, 0x23, 0xe3, 0x34, 0x04, 0x92, 0x91, 0x37, 0x08, 0x50, 0xd6, 0x28, 0x09, 0x27, 0xa1, 0x0c, 0x00, + /* (2^340)P */ 0x1f, 0xbb, 0x21, 0x26, 0x33, 0xcb, 0xa4, 0xd1, 0xee, 0x85, 0xf9, 0xd9, 0x3c, 0x90, 0xc3, 0xd1, 0x26, 0xa2, 0x25, 0x93, 0x43, 0x61, 0xed, 0x91, 0x6e, 0x54, 0x03, 0x2e, 0x42, 0x9d, 0xf7, 0xa6, 0x02, 0x0f, 0x2f, 0x9c, 0x7a, 0x8d, 0x12, 0xc2, 0x18, 0xfc, 0x41, 0xff, 0x85, 0x26, 0x1a, 0x44, 0x55, 0x0b, 0x89, 0xab, 0x6f, 0x62, 0x33, 0x8c, + /* (2^341)P */ 0xe0, 0x3c, 0x5d, 0x70, 0x64, 0x87, 0x81, 0x35, 0xf2, 0x37, 0xa6, 0x24, 0x3e, 0xe0, 0x62, 0xd5, 0x71, 0xe7, 0x93, 0xfb, 0xac, 0xc3, 0xe7, 0xc7, 0x04, 0xe2, 0x70, 0xd3, 0x29, 0x5b, 0x21, 0xbf, 0xf4, 0x26, 0x5d, 0xf3, 0x95, 0xb4, 0x2a, 0x6a, 0x07, 0x55, 0xa6, 0x4b, 0x3b, 0x15, 0xf2, 0x25, 0x8a, 0x95, 0x3f, 0x63, 0x2f, 0x7a, 0x23, 0x96, + /* (2^342)P */ 0x0d, 0x3d, 0xd9, 0x13, 0xa7, 0xb3, 0x5e, 0x67, 0xf7, 0x02, 0x23, 0xee, 0x84, 0xff, 0x99, 0xda, 0xb9, 0x53, 0xf8, 0xf0, 0x0e, 0x39, 0x2f, 0x3c, 0x64, 0x34, 0xe3, 0x09, 0xfd, 0x2b, 0x33, 0xc7, 0xfe, 0x62, 0x2b, 0x84, 0xdf, 0x2b, 0xd2, 0x7c, 0x26, 0x01, 0x70, 0x66, 0x5b, 0x85, 0xc2, 0xbe, 0x88, 0x37, 0xf1, 0x30, 0xac, 0xb8, 0x76, 0xa3, + /* (2^343)P */ 0x6e, 0x01, 0xf0, 0x55, 0x35, 0xe4, 0xbd, 0x43, 0x62, 0x9d, 0xd6, 0x11, 0xef, 0x6f, 0xb8, 0x8c, 0xaa, 0x98, 0x87, 0xc6, 0x6d, 0xc4, 0xcc, 0x74, 0x92, 0x53, 0x4a, 0xdf, 0xe4, 0x08, 0x89, 0x17, 0xd0, 0x0f, 0xf4, 0x00, 0x60, 0x78, 0x08, 0x44, 0xb5, 0xda, 0x18, 0xed, 0x98, 0xc8, 0x61, 0x3d, 0x39, 0xdb, 0xcf, 0x1d, 0x49, 0x40, 0x65, 0x75, + /* (2^344)P */ 0x8e, 0x10, 0xae, 0x5f, 0x06, 0xd2, 0x95, 0xfd, 0x20, 0x16, 0x49, 0x5b, 0x57, 0xbe, 0x22, 0x8b, 0x43, 0xfb, 0xe6, 0xcc, 0x26, 0xa5, 0x5d, 0xd3, 0x68, 0xc5, 0xf9, 0x5a, 0x86, 0x24, 0x87, 0x27, 0x05, 0xfd, 0xe2, 0xff, 0xb3, 0xa3, 0x7b, 0x37, 0x59, 0xc5, 0x4e, 0x14, 0x94, 0xf9, 0x3b, 0xcb, 0x7c, 0xed, 0xca, 0x1d, 0xb2, 0xac, 0x05, 0x4a, + /* (2^345)P */ 0xf4, 0xd1, 0x81, 0xeb, 0x89, 0xbf, 0xfe, 0x1e, 0x41, 0x92, 0x29, 0xee, 0xe1, 0x43, 0xf5, 0x86, 0x1d, 0x2f, 0xbb, 0x1e, 0x84, 0x5d, 0x7b, 0x8d, 0xd5, 0xda, 0xee, 0x1e, 0x8a, 0xd0, 0x27, 0xf2, 0x60, 0x51, 0x59, 0x82, 0xf4, 0x84, 0x2b, 0x5b, 0x14, 0x2d, 0x81, 0x82, 0x3e, 0x2b, 0xb4, 0x6d, 0x51, 0x4f, 0xc5, 0xcb, 0xbf, 0x74, 0xe3, 0xb4, + /* (2^346)P */ 0x19, 0x2f, 0x22, 0xb3, 0x04, 0x5f, 0x81, 0xca, 0x05, 0x60, 0xb9, 0xaa, 0xee, 0x0e, 0x2f, 0x48, 0x38, 0xf9, 0x91, 0xb4, 0x66, 0xe4, 0x57, 0x28, 0x54, 0x10, 0xe9, 0x61, 0x9d, 0xd4, 0x90, 0x75, 0xb1, 0x39, 0x23, 0xb6, 0xfc, 0x82, 0xe0, 0xfa, 0xbb, 0x5c, 0x6e, 0xc3, 0x44, 0x13, 0x00, 0x83, 0x55, 0x9e, 0x8e, 0x10, 0x61, 0x81, 0x91, 0x04, + /* (2^347)P */ 0x5f, 0x2a, 0xd7, 0x81, 0xd9, 0x9c, 0xbb, 0x79, 0xbc, 0x62, 0x56, 0x98, 0x03, 0x5a, 0x18, 0x85, 0x2a, 0x9c, 0xd0, 0xfb, 0xd2, 0xb1, 0xaf, 0xef, 0x0d, 0x24, 0xc5, 0xfa, 0x39, 0xbb, 0x6b, 0xed, 0xa4, 0xdf, 0xe4, 0x87, 0xcd, 0x41, 0xd3, 0x72, 0x32, 0xc6, 0x28, 0x21, 0xb1, 0xba, 0x8b, 0xa3, 0x91, 0x79, 0x76, 0x22, 0x25, 0x10, 0x61, 0xd1, + /* (2^348)P */ 0x73, 0xb5, 0x32, 0x97, 0xdd, 0xeb, 0xdd, 0x22, 0x22, 0xf1, 0x33, 0x3c, 0x77, 0x56, 0x7d, 0x6b, 0x48, 0x2b, 0x05, 0x81, 0x03, 0x03, 0x91, 0x9a, 0xe3, 0x5e, 0xd4, 0xee, 0x3f, 0xf8, 0xbb, 0x50, 0x21, 0x32, 0x4c, 0x4a, 0x58, 0x49, 0xde, 0x0c, 0xde, 0x30, 0x82, 0x3d, 0x92, 0xf0, 0x6c, 0xcc, 0x32, 0x3e, 0xd2, 0x78, 0x8a, 0x6e, 0x2c, 0xd0, + /* (2^349)P */ 0xf0, 0xf7, 0xa1, 0x0b, 0xc1, 0x74, 0x85, 0xa8, 0xe9, 0xdd, 0x48, 0xa1, 0xc0, 0x16, 0xd8, 0x2b, 0x61, 0x08, 0xc2, 0x2b, 0x30, 0x26, 0x79, 0xce, 0x9e, 0xfd, 0x39, 0xd7, 0x81, 0xa4, 0x63, 0x8c, 0xd5, 0x74, 0xa0, 0x88, 0xfa, 0x03, 0x30, 0xe9, 0x7f, 0x2b, 0xc6, 0x02, 0xc9, 0x5e, 0xe4, 0xd5, 0x4d, 0x92, 0xd0, 0xf6, 0xf2, 0x5b, 0x79, 0x08, + /* (2^350)P */ 0x34, 0x89, 0x81, 0x43, 0xd1, 0x94, 0x2c, 0x10, 0x54, 0x9b, 0xa0, 0xe5, 0x44, 0xe8, 0xc2, 0x2f, 0x3e, 0x0e, 0x74, 0xae, 0xba, 0xe2, 0xac, 0x85, 0x6b, 0xd3, 0x5c, 0x97, 0xf7, 0x90, 0xf1, 0x12, 0xc0, 0x03, 0xc8, 0x1f, 0x37, 0x72, 0x8c, 0x9b, 0x9c, 0x17, 0x96, 0x9d, 0xc7, 0xbf, 0xa3, 0x3f, 0x44, 0x3d, 0x87, 0x81, 0xbd, 0x81, 0xa6, 0x5f, + /* (2^351)P */ 0xe4, 0xff, 0x78, 0x62, 0x82, 0x5b, 0x76, 0x58, 0xf5, 0x5b, 0xa6, 0xc4, 0x53, 0x11, 0x3b, 0x7b, 0xaa, 0x67, 0xf8, 0xea, 0x3b, 0x5d, 0x9a, 0x2e, 0x04, 0xeb, 0x4a, 0x24, 0xfb, 0x56, 0xf0, 0xa8, 0xd4, 0x14, 0xed, 0x0f, 0xfd, 0xc5, 0x26, 0x17, 0x2a, 0xf0, 0xb9, 0x13, 0x8c, 0xbd, 0x65, 0x14, 0x24, 0x95, 0x27, 0x12, 0x63, 0x2a, 0x09, 0x18, + /* (2^352)P */ 0xe1, 0x5c, 0xe7, 0xe0, 0x00, 0x6a, 0x96, 0xf2, 0x49, 0x6a, 0x39, 0xa5, 0xe0, 0x17, 0x79, 0x4a, 0x63, 0x07, 0x62, 0x09, 0x61, 0x1b, 0x6e, 0xa9, 0xb5, 0x62, 0xb7, 0xde, 0xdf, 0x80, 0x4c, 0x5a, 0x99, 0x73, 0x59, 0x9d, 0xfb, 0xb1, 0x5e, 0xbe, 0xb8, 0xb7, 0x63, 0x93, 0xe8, 0xad, 0x5e, 0x1f, 0xae, 0x59, 0x1c, 0xcd, 0xb4, 0xc2, 0xb3, 0x8a, + /* (2^353)P */ 0x78, 0x53, 0xa1, 0x4c, 0x70, 0x9c, 0x63, 0x7e, 0xb3, 0x12, 0x40, 0x5f, 0xbb, 0x23, 0xa7, 0xf7, 0x77, 0x96, 0x5b, 0x4d, 0x91, 0x10, 0x52, 0x85, 0x9e, 0xa5, 0x38, 0x0b, 0xfd, 0x25, 0x01, 0x4b, 0xfa, 0x4d, 0xd3, 0x3f, 0x78, 0x74, 0x42, 0xff, 0x62, 0x2d, 0x27, 0xdc, 0x9d, 0xd1, 0x29, 0x76, 0x2e, 0x78, 0xb3, 0x35, 0xfa, 0x15, 0xd5, 0x38, + /* (2^354)P */ 0x8b, 0xc7, 0x43, 0xce, 0xf0, 0x5e, 0xf1, 0x0d, 0x02, 0x38, 0xe8, 0x82, 0xc9, 0x25, 0xad, 0x2d, 0x27, 0xa4, 0x54, 0x18, 0xb2, 0x30, 0x73, 0xa4, 0x41, 0x08, 0xe4, 0x86, 0xe6, 0x8c, 0xe9, 0x2a, 0x34, 0xb3, 0xd6, 0x61, 0x8f, 0x66, 0x26, 0x08, 0xb6, 0x06, 0x33, 0xaa, 0x12, 0xac, 0x72, 0xec, 0x2e, 0x52, 0xa3, 0x25, 0x3e, 0xd7, 0x62, 0xe8, + /* (2^355)P */ 0xc4, 0xbb, 0x89, 0xc8, 0x40, 0xcc, 0x84, 0xec, 0x4a, 0xd9, 0xc4, 0x55, 0x78, 0x00, 0xcf, 0xd8, 0xe9, 0x24, 0x59, 0xdc, 0x5e, 0xf0, 0x66, 0xa1, 0x83, 0xae, 0x97, 0x18, 0xc5, 0x54, 0x27, 0xa2, 0x21, 0x52, 0x03, 0x31, 0x5b, 0x11, 0x67, 0xf6, 0x12, 0x00, 0x87, 0x2f, 0xff, 0x59, 0x70, 0x8f, 0x6d, 0x71, 0xab, 0xab, 0x24, 0xb8, 0xba, 0x35, + /* (2^356)P */ 0x69, 0x43, 0xa7, 0x14, 0x06, 0x96, 0xe9, 0xc2, 0xe3, 0x2b, 0x45, 0x22, 0xc0, 0xd0, 0x2f, 0x34, 0xd1, 0x01, 0x99, 0xfc, 0x99, 0x38, 0xa1, 0x25, 0x2e, 0x59, 0x6c, 0x27, 0xc9, 0xeb, 0x7b, 0xdc, 0x4e, 0x26, 0x68, 0xba, 0xfa, 0xec, 0x02, 0x05, 0x64, 0x80, 0x30, 0x20, 0x5c, 0x26, 0x7f, 0xaf, 0x95, 0x17, 0x3d, 0x5c, 0x9e, 0x96, 0x96, 0xaf, + /* (2^357)P */ 0xa6, 0xba, 0x21, 0x29, 0x32, 0xe2, 0x98, 0xde, 0x9b, 0x6d, 0x0b, 0x44, 0x91, 0xa8, 0x3e, 0xd4, 0xb8, 0x04, 0x6c, 0xf6, 0x04, 0x39, 0xbd, 0x52, 0x05, 0x15, 0x27, 0x78, 0x8e, 0x55, 0xac, 0x79, 0xc5, 0xe6, 0x00, 0x7f, 0x90, 0xa2, 0xdd, 0x07, 0x13, 0xe0, 0x24, 0x70, 0x5c, 0x0f, 0x4d, 0xa9, 0xf9, 0xae, 0xcb, 0x34, 0x10, 0x9d, 0x89, 0x9d, + /* (2^358)P */ 0x12, 0xe0, 0xb3, 0x9f, 0xc4, 0x96, 0x1d, 0xcf, 0xed, 0x99, 0x64, 0x28, 0x8d, 0xc7, 0x31, 0x82, 0xee, 0x5e, 0x75, 0x48, 0xff, 0x3a, 0xf2, 0x09, 0x34, 0x03, 0x93, 0x52, 0x19, 0xb2, 0xc5, 0x81, 0x93, 0x45, 0x5e, 0x59, 0x21, 0x2b, 0xec, 0x89, 0xba, 0x36, 0x6e, 0xf9, 0x82, 0x75, 0x7e, 0x82, 0x3f, 0xaa, 0xe2, 0xe3, 0x3b, 0x94, 0xfd, 0x98, + /* (2^359)P */ 0x7c, 0xdb, 0x75, 0x31, 0x61, 0xfb, 0x15, 0x28, 0x94, 0xd7, 0xc3, 0x5a, 0xa9, 0xa1, 0x0a, 0x66, 0x0f, 0x2b, 0x13, 0x3e, 0x42, 0xb5, 0x28, 0x3a, 0xca, 0x83, 0xf3, 0x61, 0x22, 0xf4, 0x40, 0xc5, 0xdf, 0xe7, 0x31, 0x9f, 0x7e, 0x51, 0x75, 0x06, 0x9d, 0x51, 0xc8, 0xe7, 0x9f, 0xc3, 0x71, 0x4f, 0x3d, 0x5b, 0xfb, 0xe9, 0x8e, 0x08, 0x40, 0x8e, + /* (2^360)P */ 0xf7, 0x31, 0xad, 0x50, 0x5d, 0x25, 0x93, 0x73, 0x68, 0xf6, 0x7c, 0x89, 0x5a, 0x3d, 0x9f, 0x9b, 0x05, 0x82, 0xe7, 0x70, 0x4b, 0x19, 0xaa, 0xcf, 0xff, 0xde, 0x50, 0x8f, 0x2f, 0x69, 0xd3, 0xf0, 0x99, 0x51, 0x6b, 0x9d, 0xb6, 0x56, 0x6f, 0xf8, 0x4c, 0x74, 0x8b, 0x4c, 0x91, 0xf9, 0xa9, 0xb1, 0x3e, 0x07, 0xdf, 0x0b, 0x27, 0x8a, 0xb1, 0xed, + /* (2^361)P */ 0xfb, 0x67, 0xd9, 0x48, 0xd2, 0xe4, 0x44, 0x9b, 0x43, 0x15, 0x8a, 0xeb, 0x00, 0x53, 0xad, 0x25, 0xc7, 0x7e, 0x19, 0x30, 0x87, 0xb7, 0xd5, 0x5f, 0x04, 0xf8, 0xaa, 0xdd, 0x57, 0xae, 0x34, 0x75, 0xe2, 0x84, 0x4b, 0x54, 0x60, 0x37, 0x95, 0xe4, 0xd3, 0xec, 0xac, 0xef, 0x47, 0x31, 0xa3, 0xc8, 0x31, 0x22, 0xdb, 0x26, 0xe7, 0x6a, 0xb5, 0xad, + /* (2^362)P */ 0x44, 0x09, 0x5c, 0x95, 0xe4, 0x72, 0x3c, 0x1a, 0xd1, 0xac, 0x42, 0x51, 0x99, 0x6f, 0xfa, 0x1f, 0xf2, 0x22, 0xbe, 0xff, 0x7b, 0x66, 0xf5, 0x6c, 0xb3, 0x66, 0xc7, 0x4d, 0x78, 0x31, 0x83, 0x80, 0xf5, 0x41, 0xe9, 0x7f, 0xbe, 0xf7, 0x23, 0x49, 0x6b, 0x84, 0x4e, 0x7e, 0x47, 0x07, 0x6e, 0x74, 0xdf, 0xe5, 0x9d, 0x9e, 0x56, 0x2a, 0xc0, 0xbc, + /* (2^363)P */ 0xac, 0x10, 0x80, 0x8c, 0x7c, 0xfa, 0x83, 0xdf, 0xb3, 0xd0, 0xc4, 0xbe, 0xfb, 0x9f, 0xac, 0xc9, 0xc3, 0x40, 0x95, 0x0b, 0x09, 0x23, 0xda, 0x63, 0x67, 0xcf, 0xe7, 0x9f, 0x7d, 0x7b, 0x6b, 0xe2, 0xe6, 0x6d, 0xdb, 0x87, 0x9e, 0xa6, 0xff, 0x6d, 0xab, 0xbd, 0xfb, 0x54, 0x84, 0x68, 0xcf, 0x89, 0xf1, 0xd0, 0xe2, 0x85, 0x61, 0xdc, 0x22, 0xd1, + /* (2^364)P */ 0xa8, 0x48, 0xfb, 0x8c, 0x6a, 0x63, 0x01, 0x72, 0x43, 0x43, 0xeb, 0x21, 0xa3, 0x00, 0x8a, 0xc0, 0x87, 0x51, 0x9e, 0x86, 0x75, 0x16, 0x79, 0xf9, 0x6b, 0x11, 0x80, 0x62, 0xc2, 0x9d, 0xb8, 0x8c, 0x30, 0x8e, 0x8d, 0x03, 0x52, 0x7e, 0x31, 0x59, 0x38, 0xf9, 0x25, 0xc7, 0x0f, 0xc7, 0xa8, 0x2b, 0x5c, 0x80, 0xfa, 0x90, 0xa2, 0x63, 0xca, 0xe7, + /* (2^365)P */ 0xf1, 0x5d, 0xb5, 0xd9, 0x20, 0x10, 0x7d, 0x0f, 0xc5, 0x50, 0x46, 0x07, 0xff, 0x02, 0x75, 0x2b, 0x4a, 0xf3, 0x39, 0x91, 0x72, 0xb7, 0xd5, 0xcc, 0x38, 0xb8, 0xe7, 0x36, 0x26, 0x5e, 0x11, 0x97, 0x25, 0xfb, 0x49, 0x68, 0xdc, 0xb4, 0x46, 0x87, 0x5c, 0xc2, 0x7f, 0xaa, 0x7d, 0x36, 0x23, 0xa6, 0xc6, 0x53, 0xec, 0xbc, 0x57, 0x47, 0xc1, 0x2b, + /* (2^366)P */ 0x25, 0x5d, 0x7d, 0x95, 0xda, 0x0b, 0x8f, 0x78, 0x1e, 0x19, 0x09, 0xfa, 0x67, 0xe0, 0xa0, 0x17, 0x24, 0x76, 0x6c, 0x30, 0x1f, 0x62, 0x3d, 0xbe, 0x45, 0x70, 0xcc, 0xb6, 0x1e, 0x68, 0x06, 0x25, 0x68, 0x16, 0x1a, 0x33, 0x3f, 0x90, 0xc7, 0x78, 0x2d, 0x98, 0x3c, 0x2f, 0xb9, 0x2d, 0x94, 0x0b, 0xfb, 0x49, 0x56, 0x30, 0xd7, 0xc1, 0xe6, 0x48, + /* (2^367)P */ 0x7a, 0xd1, 0xe0, 0x8e, 0x67, 0xfc, 0x0b, 0x50, 0x1f, 0x84, 0x98, 0xfa, 0xaf, 0xae, 0x2e, 0x31, 0x27, 0xcf, 0x3f, 0xf2, 0x6e, 0x8d, 0x81, 0x8f, 0xd2, 0x5f, 0xde, 0xd3, 0x5e, 0xe9, 0xe7, 0x13, 0x48, 0x83, 0x5a, 0x4e, 0x84, 0xd1, 0x58, 0xcf, 0x6b, 0x84, 0xdf, 0x13, 0x1d, 0x91, 0x85, 0xe8, 0xcb, 0x29, 0x79, 0xd2, 0xca, 0xac, 0x6a, 0x93, + /* (2^368)P */ 0x53, 0x82, 0xce, 0x61, 0x96, 0x88, 0x6f, 0xe1, 0x4a, 0x4c, 0x1e, 0x30, 0x73, 0xe8, 0x74, 0xde, 0x40, 0x2b, 0xe0, 0xc4, 0xb5, 0xd8, 0x7c, 0x15, 0xe7, 0xe1, 0xb1, 0xe0, 0xd6, 0x88, 0xb1, 0x6a, 0x57, 0x19, 0x6a, 0x22, 0x66, 0x57, 0xf6, 0x8d, 0xfd, 0xc0, 0xf2, 0xa3, 0x03, 0x56, 0xfb, 0x2e, 0x75, 0x5e, 0xc7, 0x8e, 0x22, 0x96, 0x5c, 0x06, + /* (2^369)P */ 0x98, 0x7e, 0xbf, 0x3e, 0xbf, 0x24, 0x9d, 0x15, 0xd3, 0xf6, 0xd3, 0xd2, 0xf0, 0x11, 0xf2, 0xdb, 0x36, 0x23, 0x38, 0xf7, 0x1d, 0x71, 0x20, 0xd2, 0x54, 0x7f, 0x1e, 0x24, 0x8f, 0xe2, 0xaa, 0xf7, 0x3f, 0x6b, 0x41, 0x4e, 0xdc, 0x0e, 0xec, 0xe8, 0x35, 0x0a, 0x08, 0x6d, 0x89, 0x5b, 0x32, 0x91, 0x01, 0xb6, 0xe0, 0x2c, 0xc6, 0xa1, 0xbe, 0xb4, + /* (2^370)P */ 0x29, 0xf2, 0x1e, 0x1c, 0xdc, 0x68, 0x8a, 0x43, 0x87, 0x2c, 0x48, 0xb3, 0x9e, 0xed, 0xd2, 0x82, 0x46, 0xac, 0x2f, 0xef, 0x93, 0x34, 0x37, 0xca, 0x64, 0x8d, 0xc9, 0x06, 0x90, 0xbb, 0x78, 0x0a, 0x3c, 0x4c, 0xcf, 0x35, 0x7a, 0x0f, 0xf7, 0xa7, 0xf4, 0x2f, 0x45, 0x69, 0x3f, 0xa9, 0x5d, 0xce, 0x7b, 0x8a, 0x84, 0xc3, 0xae, 0xf4, 0xda, 0xd5, + /* (2^371)P */ 0xca, 0xba, 0x95, 0x43, 0x05, 0x7b, 0x06, 0xd9, 0x5c, 0x0a, 0x18, 0x5f, 0x6a, 0x6a, 0xce, 0xc0, 0x3d, 0x95, 0x51, 0x0e, 0x1a, 0xbe, 0x85, 0x7a, 0xf2, 0x69, 0xec, 0xc0, 0x8c, 0xca, 0xa3, 0x32, 0x0a, 0x76, 0x50, 0xc6, 0x76, 0x61, 0x00, 0x89, 0xbf, 0x6e, 0x0f, 0x48, 0x90, 0x31, 0x93, 0xec, 0x34, 0x70, 0xf0, 0xc3, 0x8d, 0xf0, 0x0f, 0xb5, + /* (2^372)P */ 0xbe, 0x23, 0xe2, 0x18, 0x99, 0xf1, 0xed, 0x8a, 0xf6, 0xc9, 0xac, 0xb8, 0x1e, 0x9a, 0x3c, 0x15, 0xae, 0xd7, 0x6d, 0xb3, 0x04, 0xee, 0x5b, 0x0d, 0x1e, 0x79, 0xb7, 0xf9, 0xf9, 0x8d, 0xad, 0xf9, 0x8f, 0x5a, 0x6a, 0x7b, 0xd7, 0x9b, 0xca, 0x62, 0xfe, 0x9c, 0xc0, 0x6f, 0x6d, 0x9d, 0x76, 0xa3, 0x69, 0xb9, 0x4c, 0xa1, 0xc4, 0x0c, 0x76, 0xaa, + /* (2^373)P */ 0x1c, 0x06, 0xfe, 0x3f, 0x45, 0x70, 0xcd, 0x97, 0xa9, 0xa2, 0xb1, 0xd3, 0xf2, 0xa5, 0x0c, 0x49, 0x2c, 0x75, 0x73, 0x1f, 0xcf, 0x00, 0xaf, 0xd5, 0x2e, 0xde, 0x0d, 0x8f, 0x8f, 0x7c, 0xc4, 0x58, 0xce, 0xd4, 0xf6, 0x24, 0x19, 0x2e, 0xd8, 0xc5, 0x1d, 0x1a, 0x3f, 0xb8, 0x4f, 0xbc, 0x7d, 0xbd, 0x68, 0xe3, 0x81, 0x98, 0x1b, 0xa8, 0xc9, 0xd9, + /* (2^374)P */ 0x39, 0x95, 0x78, 0x24, 0x6c, 0x38, 0xe4, 0xe7, 0xd0, 0x8d, 0xb9, 0x38, 0x71, 0x5e, 0xc1, 0x62, 0x80, 0xcc, 0xcb, 0x8c, 0x97, 0xca, 0xf8, 0xb9, 0xd9, 0x9c, 0xce, 0x72, 0x7b, 0x70, 0xee, 0x5f, 0xea, 0xa2, 0xdf, 0xa9, 0x14, 0x10, 0xf9, 0x6e, 0x59, 0x9f, 0x9c, 0xe0, 0x0c, 0xb2, 0x07, 0x97, 0xcd, 0xd2, 0x89, 0x16, 0xfd, 0x9c, 0xa8, 0xa5, + /* (2^375)P */ 0x5a, 0x61, 0xf1, 0x59, 0x7c, 0x38, 0xda, 0xe2, 0x85, 0x99, 0x68, 0xe9, 0xc9, 0xf7, 0x32, 0x7e, 0xc4, 0xca, 0xb7, 0x11, 0x08, 0x69, 0x2b, 0x66, 0x02, 0xf7, 0x2e, 0x18, 0xc3, 0x8e, 0xe1, 0xf9, 0xc5, 0x19, 0x9a, 0x0a, 0x9c, 0x07, 0xba, 0xc7, 0x9c, 0x03, 0x34, 0x89, 0x99, 0x67, 0x0b, 0x16, 0x4b, 0x07, 0x36, 0x16, 0x36, 0x2c, 0xe2, 0xa1, + /* (2^376)P */ 0x70, 0x10, 0x91, 0x27, 0xa8, 0x24, 0x8e, 0x29, 0x04, 0x6f, 0x79, 0x1f, 0xd3, 0xa5, 0x68, 0xd3, 0x0b, 0x7d, 0x56, 0x4d, 0x14, 0x57, 0x7b, 0x2e, 0x00, 0x9f, 0x9a, 0xfd, 0x6c, 0x63, 0x18, 0x81, 0xdb, 0x9d, 0xb7, 0xd7, 0xa4, 0x1e, 0xe8, 0x40, 0xf1, 0x4c, 0xa3, 0x01, 0xd5, 0x4b, 0x75, 0xea, 0xdd, 0x97, 0xfd, 0x5b, 0xb2, 0x66, 0x6a, 0x24, + /* (2^377)P */ 0x72, 0x11, 0xfe, 0x73, 0x1b, 0xd3, 0xea, 0x7f, 0x93, 0x15, 0x15, 0x05, 0xfe, 0x40, 0xe8, 0x28, 0xd8, 0x50, 0x47, 0x66, 0xfa, 0xb7, 0xb5, 0x04, 0xba, 0x35, 0x1e, 0x32, 0x9f, 0x5f, 0x32, 0xba, 0x3d, 0xd1, 0xed, 0x9a, 0x76, 0xca, 0xa3, 0x3e, 0x77, 0xd8, 0xd8, 0x7c, 0x5f, 0x68, 0x42, 0xb5, 0x86, 0x7f, 0x3b, 0xc9, 0xc1, 0x89, 0x64, 0xda, + /* (2^378)P */ 0xd5, 0xd4, 0x17, 0x31, 0xfc, 0x6a, 0xfd, 0xb8, 0xe8, 0xe5, 0x3e, 0x39, 0x06, 0xe4, 0xd1, 0x90, 0x2a, 0xca, 0xf6, 0x54, 0x6c, 0x1b, 0x2f, 0x49, 0x97, 0xb1, 0x2a, 0x82, 0x43, 0x3d, 0x1f, 0x8b, 0xe2, 0x47, 0xc5, 0x24, 0xa8, 0xd5, 0x53, 0x29, 0x7d, 0xc6, 0x87, 0xa6, 0x25, 0x3a, 0x64, 0xdd, 0x71, 0x08, 0x9e, 0xcd, 0xe9, 0x45, 0xc7, 0xba, + /* (2^379)P */ 0x37, 0x72, 0x6d, 0x13, 0x7a, 0x8d, 0x04, 0x31, 0xe6, 0xe3, 0x9e, 0x36, 0x71, 0x3e, 0xc0, 0x1e, 0xe3, 0x71, 0xd3, 0x49, 0x4e, 0x4a, 0x36, 0x42, 0x68, 0x68, 0x61, 0xc7, 0x3c, 0xdb, 0x81, 0x49, 0xf7, 0x91, 0x4d, 0xea, 0x4c, 0x4f, 0x98, 0xc6, 0x7e, 0x60, 0x84, 0x4b, 0x6a, 0x37, 0xbb, 0x52, 0xf7, 0xce, 0x02, 0xe4, 0xad, 0xd1, 0x3c, 0xa7, + /* (2^380)P */ 0x51, 0x06, 0x2d, 0xf8, 0x08, 0xe8, 0xf1, 0x0c, 0xe5, 0xa9, 0xac, 0x29, 0x73, 0x3b, 0xed, 0x98, 0x5f, 0x55, 0x08, 0x38, 0x51, 0x44, 0x36, 0x5d, 0xea, 0xc3, 0xb8, 0x0e, 0xa0, 0x4f, 0xd2, 0x79, 0xe9, 0x98, 0xc3, 0xf5, 0x00, 0xb9, 0x26, 0x27, 0x42, 0xa8, 0x07, 0xc1, 0x12, 0x31, 0xc1, 0xc3, 0x3c, 0x3b, 0x7a, 0x72, 0x97, 0xc2, 0x70, 0x3a, + /* (2^381)P */ 0xf4, 0xb2, 0xba, 0x32, 0xbc, 0xa9, 0x2f, 0x87, 0xc7, 0x3c, 0x45, 0xcd, 0xae, 0xe2, 0x13, 0x6d, 0x3a, 0xf2, 0xf5, 0x66, 0x97, 0x29, 0xaf, 0x53, 0x9f, 0xda, 0xea, 0x14, 0xdf, 0x04, 0x98, 0x19, 0x95, 0x9e, 0x2a, 0x00, 0x5c, 0x9d, 0x1d, 0xf0, 0x39, 0x23, 0xff, 0xfc, 0xca, 0x36, 0xb7, 0xde, 0xdf, 0x37, 0x78, 0x52, 0x21, 0xfa, 0x19, 0x10, + /* (2^382)P */ 0x50, 0x20, 0x73, 0x74, 0x62, 0x21, 0xf2, 0xf7, 0x9b, 0x66, 0x85, 0x34, 0x74, 0xd4, 0x9d, 0x60, 0xd7, 0xbc, 0xc8, 0x46, 0x3b, 0xb8, 0x80, 0x42, 0x15, 0x0a, 0x6c, 0x35, 0x1a, 0x69, 0xf0, 0x1d, 0x4b, 0x29, 0x54, 0x5a, 0x9a, 0x48, 0xec, 0x9f, 0x37, 0x74, 0x91, 0xd0, 0xd1, 0x9e, 0x00, 0xc2, 0x76, 0x56, 0xd6, 0xa0, 0x15, 0x14, 0x83, 0x59, + /* (2^383)P */ 0xc2, 0xf8, 0x22, 0x20, 0x23, 0x07, 0xbd, 0x1d, 0x6f, 0x1e, 0x8c, 0x56, 0x06, 0x6a, 0x4b, 0x9f, 0xe2, 0xa9, 0x92, 0x46, 0x4b, 0x46, 0x59, 0xd7, 0xe1, 0xda, 0x14, 0x98, 0x07, 0x65, 0x7e, 0x28, 0x20, 0xf2, 0x9d, 0x4f, 0x36, 0x5c, 0x92, 0xe0, 0x9d, 0xfe, 0x3e, 0xda, 0xe4, 0x47, 0x19, 0x3c, 0x00, 0x7f, 0x22, 0xf2, 0x9e, 0x51, 0xae, 0x4d, + /* (2^384)P */ 0xbe, 0x8c, 0x1b, 0x10, 0xb6, 0xad, 0xcc, 0xcc, 0xd8, 0x5e, 0x21, 0xa6, 0xfb, 0xf1, 0xf6, 0xbd, 0x0a, 0x24, 0x67, 0xb4, 0x57, 0x7a, 0xbc, 0xe8, 0xe9, 0xff, 0xee, 0x0a, 0x1f, 0xee, 0xbd, 0xc8, 0x44, 0xed, 0x2b, 0xbb, 0x55, 0x1f, 0xdd, 0x7c, 0xb3, 0xeb, 0x3f, 0x63, 0xa1, 0x28, 0x91, 0x21, 0xab, 0x71, 0xc6, 0x4c, 0xd0, 0xe9, 0xb0, 0x21, + /* (2^385)P */ 0xad, 0xc9, 0x77, 0x2b, 0xee, 0x89, 0xa4, 0x7b, 0xfd, 0xf9, 0xf6, 0x14, 0xe4, 0xed, 0x1a, 0x16, 0x9b, 0x78, 0x41, 0x43, 0xa8, 0x83, 0x72, 0x06, 0x2e, 0x7c, 0xdf, 0xeb, 0x7e, 0xdd, 0xd7, 0x8b, 0xea, 0x9a, 0x2b, 0x03, 0xba, 0x57, 0xf3, 0xf1, 0xd9, 0xe5, 0x09, 0xc5, 0x98, 0x61, 0x1c, 0x51, 0x6d, 0x5d, 0x6e, 0xfb, 0x5e, 0x95, 0x9f, 0xb5, + /* (2^386)P */ 0x23, 0xe2, 0x1e, 0x95, 0xa3, 0x5e, 0x42, 0x10, 0xc7, 0xc3, 0x70, 0xbf, 0x4b, 0x6b, 0x83, 0x36, 0x93, 0xb7, 0x68, 0x47, 0x88, 0x3a, 0x10, 0x88, 0x48, 0x7f, 0x8c, 0xae, 0x54, 0x10, 0x02, 0xa4, 0x52, 0x8f, 0x8d, 0xf7, 0x26, 0x4f, 0x50, 0xc3, 0x6a, 0xe2, 0x4e, 0x3b, 0x4c, 0xb9, 0x8a, 0x14, 0x15, 0x6d, 0x21, 0x29, 0xb3, 0x6e, 0x4e, 0xd0, + /* (2^387)P */ 0x4c, 0x8a, 0x18, 0x3f, 0xb7, 0x20, 0xfd, 0x3e, 0x54, 0xca, 0x68, 0x3c, 0xea, 0x6f, 0xf4, 0x6b, 0xa2, 0xbd, 0x01, 0xbd, 0xfe, 0x08, 0xa8, 0xd8, 0xc2, 0x20, 0x36, 0x05, 0xcd, 0xe9, 0xf3, 0x9e, 0xfa, 0x85, 0x66, 0x8f, 0x4b, 0x1d, 0x8c, 0x64, 0x4f, 0xb8, 0xc6, 0x0f, 0x5b, 0x57, 0xd8, 0x24, 0x19, 0x5a, 0x14, 0x4b, 0x92, 0xd3, 0x96, 0xbc, + /* (2^388)P */ 0xa9, 0x3f, 0xc9, 0x6c, 0xca, 0x64, 0x1e, 0x6f, 0xdf, 0x65, 0x7f, 0x9a, 0x47, 0x6b, 0x8a, 0x60, 0x31, 0xa6, 0x06, 0xac, 0x69, 0x30, 0xe6, 0xea, 0x63, 0x42, 0x26, 0x5f, 0xdb, 0xd0, 0xf2, 0x8e, 0x34, 0x0a, 0x3a, 0xeb, 0xf3, 0x79, 0xc8, 0xb7, 0x60, 0x56, 0x5c, 0x37, 0x95, 0x71, 0xf8, 0x7f, 0x49, 0x3e, 0x9e, 0x01, 0x26, 0x1e, 0x80, 0x9f, + /* (2^389)P */ 0xf8, 0x16, 0x9a, 0xaa, 0xb0, 0x28, 0xb5, 0x8e, 0xd0, 0x60, 0xe5, 0x26, 0xa9, 0x47, 0xc4, 0x5c, 0xa9, 0x39, 0xfe, 0x0a, 0xd8, 0x07, 0x2b, 0xb3, 0xce, 0xf1, 0xea, 0x1a, 0xf4, 0x7b, 0x98, 0x31, 0x3d, 0x13, 0x29, 0x80, 0xe8, 0x0d, 0xcf, 0x56, 0x39, 0x86, 0x50, 0x0c, 0xb3, 0x18, 0xf4, 0xc5, 0xca, 0xf2, 0x6f, 0xcd, 0x8d, 0xd5, 0x02, 0xb0, + /* (2^390)P */ 0xbf, 0x39, 0x3f, 0xac, 0x6d, 0x1a, 0x6a, 0xe4, 0x42, 0x24, 0xd6, 0x41, 0x9d, 0xb9, 0x5b, 0x46, 0x73, 0x93, 0x76, 0xaa, 0xb7, 0x37, 0x36, 0xa6, 0x09, 0xe5, 0x04, 0x3b, 0x66, 0xc4, 0x29, 0x3e, 0x41, 0xc2, 0xcb, 0xe5, 0x17, 0xd7, 0x34, 0x67, 0x1d, 0x2c, 0x12, 0xec, 0x24, 0x7a, 0x40, 0xa2, 0x45, 0x41, 0xf0, 0x75, 0xed, 0x43, 0x30, 0xc9, + /* (2^391)P */ 0x80, 0xf6, 0x47, 0x5b, 0xad, 0x54, 0x02, 0xbc, 0xdd, 0xa4, 0xb2, 0xd7, 0x42, 0x95, 0xf2, 0x0d, 0x1b, 0xef, 0x37, 0xa7, 0xb4, 0x34, 0x04, 0x08, 0x71, 0x1b, 0xd3, 0xdf, 0xa1, 0xf0, 0x2b, 0xfa, 0xc0, 0x1f, 0xf3, 0x44, 0xb5, 0xc6, 0x47, 0x3d, 0x65, 0x67, 0x45, 0x4d, 0x2f, 0xde, 0x52, 0x73, 0xfc, 0x30, 0x01, 0x6b, 0xc1, 0x03, 0xd8, 0xd7, + /* (2^392)P */ 0x1c, 0x67, 0x55, 0x3e, 0x01, 0x17, 0x0f, 0x3e, 0xe5, 0x34, 0x58, 0xfc, 0xcb, 0x71, 0x24, 0x74, 0x5d, 0x36, 0x1e, 0x89, 0x2a, 0x63, 0xf8, 0xf8, 0x9f, 0x50, 0x9f, 0x32, 0x92, 0x29, 0xd8, 0x1a, 0xec, 0x76, 0x57, 0x6c, 0x67, 0x12, 0x6a, 0x6e, 0xef, 0x97, 0x1f, 0xc3, 0x77, 0x60, 0x3c, 0x22, 0xcb, 0xc7, 0x04, 0x1a, 0x89, 0x2d, 0x10, 0xa6, + /* (2^393)P */ 0x12, 0xf5, 0xa9, 0x26, 0x16, 0xd9, 0x3c, 0x65, 0x5d, 0x83, 0xab, 0xd1, 0x70, 0x6b, 0x1c, 0xdb, 0xe7, 0x86, 0x0d, 0xfb, 0xe7, 0xf8, 0x2a, 0x58, 0x6e, 0x7a, 0x66, 0x13, 0x53, 0x3a, 0x6f, 0x8d, 0x43, 0x5f, 0x14, 0x23, 0x14, 0xff, 0x3d, 0x52, 0x7f, 0xee, 0xbd, 0x7a, 0x34, 0x8b, 0x35, 0x24, 0xc3, 0x7a, 0xdb, 0xcf, 0x22, 0x74, 0x9a, 0x8f, + /* (2^394)P */ 0xdb, 0x20, 0xfc, 0xe5, 0x39, 0x4e, 0x7d, 0x78, 0xee, 0x0b, 0xbf, 0x1d, 0x80, 0xd4, 0x05, 0x4f, 0xb9, 0xd7, 0x4e, 0x94, 0x88, 0x9a, 0x50, 0x78, 0x1a, 0x70, 0x8c, 0xcc, 0x25, 0xb6, 0x61, 0x09, 0xdc, 0x7b, 0xea, 0x3f, 0x7f, 0xea, 0x2a, 0x0d, 0x47, 0x1c, 0x8e, 0xa6, 0x5b, 0xd2, 0xa3, 0x61, 0x93, 0x3c, 0x68, 0x9f, 0x8b, 0xea, 0xb0, 0xcb, + /* (2^395)P */ 0xff, 0x54, 0x02, 0x19, 0xae, 0x8b, 0x4c, 0x2c, 0x3a, 0xe0, 0xe4, 0xac, 0x87, 0xf7, 0x51, 0x45, 0x41, 0x43, 0xdc, 0xaa, 0xcd, 0xcb, 0xdc, 0x40, 0xe3, 0x44, 0x3b, 0x1d, 0x9e, 0x3d, 0xb9, 0x82, 0xcc, 0x7a, 0xc5, 0x12, 0xf8, 0x1e, 0xdd, 0xdb, 0x8d, 0xb0, 0x2a, 0xe8, 0xe6, 0x6c, 0x94, 0x3b, 0xb7, 0x2d, 0xba, 0x79, 0x3b, 0xb5, 0x86, 0xfb, + /* (2^396)P */ 0x82, 0x88, 0x13, 0xdd, 0x6c, 0xcd, 0x85, 0x2b, 0x90, 0x86, 0xb7, 0xac, 0x16, 0xa6, 0x6e, 0x6a, 0x94, 0xd8, 0x1e, 0x4e, 0x41, 0x0f, 0xce, 0x81, 0x6a, 0xa8, 0x26, 0x56, 0x43, 0x52, 0x52, 0xe6, 0xff, 0x88, 0xcf, 0x47, 0x05, 0x1d, 0xff, 0xf3, 0xa0, 0x10, 0xb2, 0x97, 0x87, 0xeb, 0x47, 0xbb, 0xfa, 0x1f, 0xe8, 0x4c, 0xce, 0xc4, 0xcd, 0x93, + /* (2^397)P */ 0xf4, 0x11, 0xf5, 0x8d, 0x89, 0x29, 0x79, 0xb3, 0x59, 0x0b, 0x29, 0x7d, 0x9c, 0x12, 0x4a, 0x65, 0x72, 0x3a, 0xf9, 0xec, 0x37, 0x18, 0x86, 0xef, 0x44, 0x07, 0x25, 0x74, 0x76, 0x53, 0xed, 0x51, 0x01, 0xc6, 0x28, 0xc5, 0xc3, 0x4a, 0x0f, 0x99, 0xec, 0xc8, 0x40, 0x5a, 0x83, 0x30, 0x79, 0xa2, 0x3e, 0x63, 0x09, 0x2d, 0x6f, 0x23, 0x54, 0x1c, + /* (2^398)P */ 0x5c, 0x6f, 0x3b, 0x1c, 0x30, 0x77, 0x7e, 0x87, 0x66, 0x83, 0x2e, 0x7e, 0x85, 0x50, 0xfd, 0xa0, 0x7a, 0xc2, 0xf5, 0x0f, 0xc1, 0x64, 0xe7, 0x0b, 0xbd, 0x59, 0xa7, 0xe7, 0x65, 0x53, 0xc3, 0xf5, 0x55, 0x5b, 0xe1, 0x82, 0x30, 0x5a, 0x61, 0xcd, 0xa0, 0x89, 0x32, 0xdb, 0x87, 0xfc, 0x21, 0x8a, 0xab, 0x6d, 0x82, 0xa8, 0x42, 0x81, 0x4f, 0xf2, + /* (2^399)P */ 0xb3, 0xeb, 0x88, 0x18, 0xf6, 0x56, 0x96, 0xbf, 0xba, 0x5d, 0x71, 0xa1, 0x5a, 0xd1, 0x04, 0x7b, 0xd5, 0x46, 0x01, 0x74, 0xfe, 0x15, 0x25, 0xb7, 0xff, 0x0c, 0x24, 0x47, 0xac, 0xfd, 0xab, 0x47, 0x32, 0xe1, 0x6a, 0x4e, 0xca, 0xcf, 0x7f, 0xdd, 0xf8, 0xd2, 0x4b, 0x3b, 0xf5, 0x17, 0xba, 0xba, 0x8b, 0xa1, 0xec, 0x28, 0x3f, 0x97, 0xab, 0x2a, + /* (2^400)P */ 0x51, 0x38, 0xc9, 0x5e, 0xc6, 0xb3, 0x64, 0xf2, 0x24, 0x4d, 0x04, 0x7d, 0xc8, 0x39, 0x0c, 0x4a, 0xc9, 0x73, 0x74, 0x1b, 0x5c, 0xb2, 0xc5, 0x41, 0x62, 0xa0, 0x4c, 0x6d, 0x8d, 0x91, 0x9a, 0x7b, 0x88, 0xab, 0x9c, 0x7e, 0x23, 0xdb, 0x6f, 0xb5, 0x72, 0xd6, 0x47, 0x40, 0xef, 0x22, 0x58, 0x62, 0x19, 0x6c, 0x38, 0xba, 0x5b, 0x00, 0x30, 0x9f, + /* (2^401)P */ 0x65, 0xbb, 0x3b, 0x9b, 0xe9, 0xae, 0xbf, 0xbe, 0xe4, 0x13, 0x95, 0xf3, 0xe3, 0x77, 0xcb, 0xe4, 0x9a, 0x22, 0xb5, 0x4a, 0x08, 0x9d, 0xb3, 0x9e, 0x27, 0xe0, 0x15, 0x6c, 0x9f, 0x7e, 0x9a, 0x5e, 0x15, 0x45, 0x25, 0x8d, 0x01, 0x0a, 0xd2, 0x2b, 0xbd, 0x48, 0x06, 0x0d, 0x18, 0x97, 0x4b, 0xdc, 0xbc, 0xf0, 0xcd, 0xb2, 0x52, 0x3c, 0xac, 0xf5, + /* (2^402)P */ 0x3e, 0xed, 0x47, 0x6b, 0x5c, 0xf6, 0x76, 0xd0, 0xe9, 0x15, 0xa3, 0xcb, 0x36, 0x00, 0x21, 0xa3, 0x79, 0x20, 0xa5, 0x3e, 0x88, 0x03, 0xcb, 0x7e, 0x63, 0xbb, 0xed, 0xa9, 0x13, 0x35, 0x16, 0xaf, 0x2e, 0xb4, 0x70, 0x14, 0x93, 0xfb, 0xc4, 0x9b, 0xd8, 0xb1, 0xbe, 0x43, 0xd1, 0x85, 0xb8, 0x97, 0xef, 0xea, 0x88, 0xa1, 0x25, 0x52, 0x62, 0x75, + /* (2^403)P */ 0x8e, 0x4f, 0xaa, 0x23, 0x62, 0x7e, 0x2b, 0x37, 0x89, 0x00, 0x11, 0x30, 0xc5, 0x33, 0x4a, 0x89, 0x8a, 0xe2, 0xfc, 0x5c, 0x6a, 0x75, 0xe5, 0xf7, 0x02, 0x4a, 0x9b, 0xf7, 0xb5, 0x6a, 0x85, 0x31, 0xd3, 0x5a, 0xcf, 0xc3, 0xf8, 0xde, 0x2f, 0xcf, 0xb5, 0x24, 0xf4, 0xe3, 0xa1, 0xad, 0x42, 0xae, 0x09, 0xb9, 0x2e, 0x04, 0x2d, 0x01, 0x22, 0x3f, + /* (2^404)P */ 0x41, 0x16, 0xfb, 0x7d, 0x50, 0xfd, 0xb5, 0xba, 0x88, 0x24, 0xba, 0xfd, 0x3d, 0xb2, 0x90, 0x15, 0xb7, 0xfa, 0xa2, 0xe1, 0x4c, 0x7d, 0xb9, 0xc6, 0xff, 0x81, 0x57, 0xb6, 0xc2, 0x9e, 0xcb, 0xc4, 0x35, 0xbd, 0x01, 0xb7, 0xaa, 0xce, 0xd0, 0xe9, 0xb5, 0xd6, 0x72, 0xbf, 0xd2, 0xee, 0xc7, 0xac, 0x94, 0xff, 0x29, 0x57, 0x02, 0x49, 0x09, 0xad, + /* (2^405)P */ 0x27, 0xa5, 0x78, 0x1b, 0xbf, 0x6b, 0xaf, 0x0b, 0x8c, 0xd9, 0xa8, 0x37, 0xb0, 0x67, 0x18, 0xb6, 0xc7, 0x05, 0x8a, 0x67, 0x03, 0x30, 0x62, 0x6e, 0x56, 0x82, 0xa9, 0x54, 0x3e, 0x0c, 0x4e, 0x07, 0xe1, 0x5a, 0x38, 0xed, 0xfa, 0xc8, 0x55, 0x6b, 0x08, 0xa3, 0x6b, 0x64, 0x2a, 0x15, 0xd6, 0x39, 0x6f, 0x47, 0x99, 0x42, 0x3f, 0x33, 0x84, 0x8f, + /* (2^406)P */ 0xbc, 0x45, 0x29, 0x81, 0x0e, 0xa4, 0xc5, 0x72, 0x3a, 0x10, 0xe1, 0xc4, 0x1e, 0xda, 0xc3, 0xfe, 0xb0, 0xce, 0xd2, 0x13, 0x34, 0x67, 0x21, 0xc6, 0x7e, 0xf9, 0x8c, 0xff, 0x39, 0x50, 0xae, 0x92, 0x60, 0x35, 0x2f, 0x8b, 0x6e, 0xc9, 0xc1, 0x27, 0x3a, 0x94, 0x66, 0x3e, 0x26, 0x84, 0x93, 0xc8, 0x6c, 0xcf, 0xd2, 0x03, 0xa1, 0x10, 0xcf, 0xb7, + /* (2^407)P */ 0x64, 0xda, 0x19, 0xf6, 0xc5, 0x73, 0x17, 0x44, 0x88, 0x81, 0x07, 0x0d, 0x34, 0xb2, 0x75, 0xf9, 0xd9, 0xe2, 0xe0, 0x8b, 0x71, 0xcf, 0x72, 0x34, 0x83, 0xb4, 0xce, 0xfc, 0xd7, 0x29, 0x09, 0x5a, 0x98, 0xbf, 0x14, 0xac, 0x77, 0x55, 0x38, 0x47, 0x5b, 0x0f, 0x40, 0x24, 0xe5, 0xa5, 0xa6, 0xac, 0x2d, 0xa6, 0xff, 0x9c, 0x73, 0xfe, 0x5c, 0x7e, + /* (2^408)P */ 0x1e, 0x33, 0xcc, 0x68, 0xb2, 0xbc, 0x8c, 0x93, 0xaf, 0xcc, 0x38, 0xf8, 0xd9, 0x16, 0x72, 0x50, 0xac, 0xd9, 0xb5, 0x0b, 0x9a, 0xbe, 0x46, 0x7a, 0xf1, 0xee, 0xf1, 0xad, 0xec, 0x5b, 0x59, 0x27, 0x9c, 0x05, 0xa3, 0x87, 0xe0, 0x37, 0x2c, 0x83, 0xce, 0xb3, 0x65, 0x09, 0x8e, 0xc3, 0x9c, 0xbf, 0x6a, 0xa2, 0x00, 0xcc, 0x12, 0x36, 0xc5, 0x95, + /* (2^409)P */ 0x36, 0x11, 0x02, 0x14, 0x9c, 0x3c, 0xeb, 0x2f, 0x23, 0x5b, 0x6b, 0x2b, 0x08, 0x54, 0x53, 0xac, 0xb2, 0xa3, 0xe0, 0x26, 0x62, 0x3c, 0xe4, 0xe1, 0x81, 0xee, 0x13, 0x3e, 0xa4, 0x97, 0xef, 0xf9, 0x92, 0x27, 0x01, 0xce, 0x54, 0x8b, 0x3e, 0x31, 0xbe, 0xa7, 0x88, 0xcf, 0x47, 0x99, 0x3c, 0x10, 0x6f, 0x60, 0xb3, 0x06, 0x4e, 0xee, 0x1b, 0xf0, + /* (2^410)P */ 0x59, 0x49, 0x66, 0xcf, 0x22, 0xe6, 0xf6, 0x73, 0xfe, 0xa3, 0x1c, 0x09, 0xfa, 0x5f, 0x65, 0xa8, 0xf0, 0x82, 0xc2, 0xef, 0x16, 0x63, 0x6e, 0x79, 0x69, 0x51, 0x39, 0x07, 0x65, 0xc4, 0x81, 0xec, 0x73, 0x0f, 0x15, 0x93, 0xe1, 0x30, 0x33, 0xe9, 0x37, 0x86, 0x42, 0x4c, 0x1f, 0x9b, 0xad, 0xee, 0x3f, 0xf1, 0x2a, 0x8e, 0x6a, 0xa3, 0xc8, 0x35, + /* (2^411)P */ 0x1e, 0x49, 0xf1, 0xdd, 0xd2, 0x9c, 0x8e, 0x78, 0xb2, 0x06, 0xe4, 0x6a, 0xab, 0x3a, 0xdc, 0xcd, 0xf4, 0xeb, 0xe1, 0xe7, 0x2f, 0xaa, 0xeb, 0x40, 0x31, 0x9f, 0xb9, 0xab, 0x13, 0xa9, 0x78, 0xbf, 0x38, 0x89, 0x0e, 0x85, 0x14, 0x8b, 0x46, 0x76, 0x14, 0xda, 0xcf, 0x33, 0xc8, 0x79, 0xd3, 0xd5, 0xa3, 0x6a, 0x69, 0x45, 0x70, 0x34, 0xc3, 0xe9, + /* (2^412)P */ 0x5e, 0xe7, 0x78, 0xe9, 0x24, 0xcc, 0xe9, 0xf4, 0xc8, 0x6b, 0xe0, 0xfb, 0x3a, 0xbe, 0xcc, 0x42, 0x4a, 0x00, 0x22, 0xf8, 0xe6, 0x32, 0xbe, 0x6d, 0x18, 0x55, 0x60, 0xe9, 0x72, 0x69, 0x50, 0x56, 0xca, 0x04, 0x18, 0x38, 0xa1, 0xee, 0xd8, 0x38, 0x3c, 0xa7, 0x70, 0xe2, 0xb9, 0x4c, 0xa0, 0xc8, 0x89, 0x72, 0xcf, 0x49, 0x7f, 0xdf, 0xbc, 0x67, + /* (2^413)P */ 0x1d, 0x17, 0xcb, 0x0b, 0xbd, 0xb2, 0x36, 0xe3, 0xa8, 0x99, 0x31, 0xb6, 0x26, 0x9c, 0x0c, 0x74, 0xaf, 0x4d, 0x24, 0x61, 0xcf, 0x31, 0x7b, 0xed, 0xdd, 0xc3, 0xf6, 0x32, 0x70, 0xfe, 0x17, 0xf6, 0x51, 0x37, 0x65, 0xce, 0x5d, 0xaf, 0xa5, 0x2f, 0x2a, 0xfe, 0x00, 0x71, 0x7c, 0x50, 0xbe, 0x21, 0xc7, 0xed, 0xc6, 0xfc, 0x67, 0xcf, 0x9c, 0xdd, + /* (2^414)P */ 0x26, 0x3e, 0xf8, 0xbb, 0xd0, 0xb1, 0x01, 0xd8, 0xeb, 0x0b, 0x62, 0x87, 0x35, 0x4c, 0xde, 0xca, 0x99, 0x9c, 0x6d, 0xf7, 0xb6, 0xf0, 0x57, 0x0a, 0x52, 0x29, 0x6a, 0x3f, 0x26, 0x31, 0x04, 0x07, 0x2a, 0xc9, 0xfa, 0x9b, 0x0e, 0x62, 0x8e, 0x72, 0xf2, 0xad, 0xce, 0xb6, 0x35, 0x7a, 0xc1, 0xae, 0x35, 0xc7, 0xa3, 0x14, 0xcf, 0x0c, 0x28, 0xb7, + /* (2^415)P */ 0xa6, 0xf1, 0x32, 0x3a, 0x20, 0xd2, 0x24, 0x97, 0xcf, 0x5d, 0x37, 0x99, 0xaf, 0x33, 0x7a, 0x5b, 0x7a, 0xcc, 0x4e, 0x41, 0x38, 0xb1, 0x4e, 0xad, 0xc9, 0xd9, 0x71, 0x7e, 0xb2, 0xf5, 0xd5, 0x01, 0x6c, 0x4d, 0xfd, 0xa1, 0xda, 0x03, 0x38, 0x9b, 0x3d, 0x92, 0x92, 0xf2, 0xca, 0xbf, 0x1f, 0x24, 0xa4, 0xbb, 0x30, 0x6a, 0x74, 0x56, 0xc8, 0xce, + /* (2^416)P */ 0x27, 0xf4, 0xed, 0xc9, 0xc3, 0xb1, 0x79, 0x85, 0xbe, 0xf6, 0xeb, 0xf3, 0x55, 0xc7, 0xaa, 0xa6, 0xe9, 0x07, 0x5d, 0xf4, 0xeb, 0xa6, 0x81, 0xe3, 0x0e, 0xcf, 0xa3, 0xc1, 0xef, 0xe7, 0x34, 0xb2, 0x03, 0x73, 0x8a, 0x91, 0xf1, 0xad, 0x05, 0xc7, 0x0b, 0x43, 0x99, 0x12, 0x31, 0xc8, 0xc7, 0xc5, 0xa4, 0x3d, 0xcd, 0xe5, 0x4e, 0x6d, 0x24, 0xdd, + /* (2^417)P */ 0x61, 0x54, 0xd0, 0x95, 0x2c, 0x45, 0x75, 0xac, 0xb5, 0x1a, 0x9d, 0x11, 0xeb, 0xed, 0x6b, 0x57, 0xa3, 0xe6, 0xcd, 0x77, 0xd4, 0x83, 0x8e, 0x39, 0xf1, 0x0f, 0x98, 0xcb, 0x40, 0x02, 0x6e, 0x10, 0x82, 0x9e, 0xb4, 0x93, 0x76, 0xd7, 0x97, 0xa3, 0x53, 0x12, 0x86, 0xc6, 0x15, 0x78, 0x73, 0x93, 0xe7, 0x7f, 0xcf, 0x1f, 0xbf, 0xcd, 0xd2, 0x7a, + /* (2^418)P */ 0xc2, 0x21, 0xdc, 0xd5, 0x69, 0xff, 0xca, 0x49, 0x3a, 0xe1, 0xc3, 0x69, 0x41, 0x56, 0xc1, 0x76, 0x63, 0x24, 0xbd, 0x64, 0x1b, 0x3d, 0x92, 0xf9, 0x13, 0x04, 0x25, 0xeb, 0x27, 0xa6, 0xef, 0x39, 0x3a, 0x80, 0xe0, 0xf8, 0x27, 0xee, 0xc9, 0x49, 0x77, 0xef, 0x3f, 0x29, 0x3d, 0x5e, 0xe6, 0x66, 0x83, 0xd1, 0xf6, 0xfe, 0x9d, 0xbc, 0xf1, 0x96, + /* (2^419)P */ 0x6b, 0xc6, 0x99, 0x26, 0x3c, 0xf3, 0x63, 0xf9, 0xc7, 0x29, 0x8c, 0x52, 0x62, 0x2d, 0xdc, 0x8a, 0x66, 0xce, 0x2c, 0xa7, 0xe4, 0xf0, 0xd7, 0x37, 0x17, 0x1e, 0xe4, 0xa3, 0x53, 0x7b, 0x29, 0x8e, 0x60, 0x99, 0xf9, 0x0c, 0x7c, 0x6f, 0xa2, 0xcc, 0x9f, 0x80, 0xdd, 0x5e, 0x46, 0xaa, 0x0d, 0x6c, 0xc9, 0x6c, 0xf7, 0x78, 0x5b, 0x38, 0xe3, 0x24, + /* (2^420)P */ 0x4b, 0x75, 0x6a, 0x2f, 0x08, 0xe1, 0x72, 0x76, 0xab, 0x82, 0x96, 0xdf, 0x3b, 0x1f, 0x9b, 0xd8, 0xed, 0xdb, 0xcd, 0x15, 0x09, 0x5a, 0x1e, 0xb7, 0xc5, 0x26, 0x72, 0x07, 0x0c, 0x50, 0xcd, 0x3b, 0x4d, 0x3f, 0xa2, 0x67, 0xc2, 0x02, 0x61, 0x2e, 0x68, 0xe9, 0x6f, 0xf0, 0x21, 0x2a, 0xa7, 0x3b, 0x88, 0x04, 0x11, 0x64, 0x49, 0x0d, 0xb4, 0x46, + /* (2^421)P */ 0x63, 0x85, 0xf3, 0xc5, 0x2b, 0x5a, 0x9f, 0xf0, 0x17, 0xcb, 0x45, 0x0a, 0xf3, 0x6e, 0x7e, 0xb0, 0x7c, 0xbc, 0xf0, 0x4f, 0x3a, 0xb0, 0xbc, 0x36, 0x36, 0x52, 0x51, 0xcb, 0xfe, 0x9a, 0xcb, 0xe8, 0x7e, 0x4b, 0x06, 0x7f, 0xaa, 0x35, 0xc8, 0x0e, 0x7a, 0x30, 0xa3, 0xb1, 0x09, 0xbb, 0x86, 0x4c, 0xbe, 0xb8, 0xbd, 0xe0, 0x32, 0xa5, 0xd4, 0xf7, + /* (2^422)P */ 0x7d, 0x50, 0x37, 0x68, 0x4e, 0x22, 0xb2, 0x2c, 0xd5, 0x0f, 0x2b, 0x6d, 0xb1, 0x51, 0xf2, 0x82, 0xe9, 0x98, 0x7c, 0x50, 0xc7, 0x96, 0x7e, 0x0e, 0xdc, 0xb1, 0x0e, 0xb2, 0x63, 0x8c, 0x30, 0x37, 0x72, 0x21, 0x9c, 0x61, 0xc2, 0xa7, 0x33, 0xd9, 0xb2, 0x63, 0x93, 0xd1, 0x6b, 0x6a, 0x73, 0xa5, 0x58, 0x80, 0xff, 0x04, 0xc7, 0x83, 0x21, 0x29, + /* (2^423)P */ 0x29, 0x04, 0xbc, 0x99, 0x39, 0xc9, 0x58, 0xc9, 0x6b, 0x17, 0xe8, 0x90, 0xb3, 0xe6, 0xa9, 0xb6, 0x28, 0x9b, 0xcb, 0x3b, 0x28, 0x90, 0x68, 0x71, 0xff, 0xcf, 0x08, 0x78, 0xc9, 0x8d, 0xa8, 0x4e, 0x43, 0xd1, 0x1c, 0x9e, 0xa4, 0xe3, 0xdf, 0xbf, 0x92, 0xf4, 0xf9, 0x41, 0xba, 0x4d, 0x1c, 0xf9, 0xdd, 0x74, 0x76, 0x1c, 0x6e, 0x3e, 0x94, 0x87, + /* (2^424)P */ 0xe4, 0xda, 0xc5, 0xd7, 0xfb, 0x87, 0xc5, 0x4d, 0x6b, 0x19, 0xaa, 0xb9, 0xbc, 0x8c, 0xf2, 0x8a, 0xd8, 0x5d, 0xdb, 0x4d, 0xef, 0xa6, 0xf2, 0x65, 0xf1, 0x22, 0x9c, 0xf1, 0x46, 0x30, 0x71, 0x7c, 0xe4, 0x53, 0x8e, 0x55, 0x2e, 0x9c, 0x9a, 0x31, 0x2a, 0xc3, 0xab, 0x0f, 0xde, 0xe4, 0xbe, 0xd8, 0x96, 0x50, 0x6e, 0x0c, 0x54, 0x49, 0xe6, 0xec, + /* (2^425)P */ 0x3c, 0x1d, 0x5a, 0xa5, 0xda, 0xad, 0xdd, 0xc2, 0xae, 0xac, 0x6f, 0x86, 0x75, 0x31, 0x91, 0x64, 0x45, 0x9d, 0xa4, 0xf0, 0x81, 0xf1, 0x0e, 0xba, 0x74, 0xaf, 0x7b, 0xcd, 0x6f, 0xfe, 0xac, 0x4e, 0xdb, 0x4e, 0x45, 0x35, 0x36, 0xc5, 0xc0, 0x6c, 0x3d, 0x64, 0xf4, 0xd8, 0x07, 0x62, 0xd1, 0xec, 0xf3, 0xfc, 0x93, 0xc9, 0x28, 0x0c, 0x2c, 0xf3, + /* (2^426)P */ 0x0c, 0x69, 0x2b, 0x5c, 0xb6, 0x41, 0x69, 0xf1, 0xa4, 0xf1, 0x5b, 0x75, 0x4c, 0x42, 0x8b, 0x47, 0xeb, 0x69, 0xfb, 0xa8, 0xe6, 0xf9, 0x7b, 0x48, 0x50, 0xaf, 0xd3, 0xda, 0xb2, 0x35, 0x10, 0xb5, 0x5b, 0x40, 0x90, 0x39, 0xc9, 0x07, 0x06, 0x73, 0x26, 0x20, 0x95, 0x01, 0xa4, 0x2d, 0xf0, 0xe7, 0x2e, 0x00, 0x7d, 0x41, 0x09, 0x68, 0x13, 0xc4, + /* (2^427)P */ 0xbe, 0x38, 0x78, 0xcf, 0xc9, 0x4f, 0x36, 0xca, 0x09, 0x61, 0x31, 0x3c, 0x57, 0x2e, 0xec, 0x17, 0xa4, 0x7d, 0x19, 0x2b, 0x9b, 0x5b, 0xbe, 0x8f, 0xd6, 0xc5, 0x2f, 0x86, 0xf2, 0x64, 0x76, 0x17, 0x00, 0x6e, 0x1a, 0x8c, 0x67, 0x1b, 0x68, 0xeb, 0x15, 0xa2, 0xd6, 0x09, 0x91, 0xdd, 0x23, 0x0d, 0x98, 0xb2, 0x10, 0x19, 0x55, 0x9b, 0x63, 0xf2, + /* (2^428)P */ 0x51, 0x1f, 0x93, 0xea, 0x2a, 0x3a, 0xfa, 0x41, 0xc0, 0x57, 0xfb, 0x74, 0xa6, 0x65, 0x09, 0x56, 0x14, 0xb6, 0x12, 0xaa, 0xb3, 0x1a, 0x8d, 0x3b, 0x76, 0x91, 0x7a, 0x23, 0x56, 0x9c, 0x6a, 0xc0, 0xe0, 0x3c, 0x3f, 0xb5, 0x1a, 0xf4, 0x57, 0x71, 0x93, 0x2b, 0xb1, 0xa7, 0x70, 0x57, 0x22, 0x80, 0xf5, 0xb8, 0x07, 0x77, 0x87, 0x0c, 0xbe, 0x83, + /* (2^429)P */ 0x07, 0x9b, 0x0e, 0x52, 0x38, 0x63, 0x13, 0x86, 0x6a, 0xa6, 0xb4, 0xd2, 0x60, 0x68, 0x9a, 0x99, 0x82, 0x0a, 0x04, 0x5f, 0x89, 0x7a, 0x1a, 0x2a, 0xae, 0x2d, 0x35, 0x0c, 0x1e, 0xad, 0xef, 0x4f, 0x9a, 0xfc, 0xc8, 0xd9, 0xcf, 0x9d, 0x48, 0x71, 0xa5, 0x55, 0x79, 0x73, 0x39, 0x1b, 0xd8, 0x73, 0xec, 0x9b, 0x03, 0x16, 0xd8, 0x82, 0xf7, 0x67, + /* (2^430)P */ 0x52, 0x67, 0x42, 0x21, 0xc9, 0x40, 0x78, 0x82, 0x2b, 0x95, 0x2d, 0x20, 0x92, 0xd1, 0xe2, 0x61, 0x25, 0xb0, 0xc6, 0x9c, 0x20, 0x59, 0x8e, 0x28, 0x6f, 0xf3, 0xfd, 0xd3, 0xc1, 0x32, 0x43, 0xc9, 0xa6, 0x08, 0x7a, 0x77, 0x9c, 0x4c, 0x8c, 0x33, 0x71, 0x13, 0x69, 0xe3, 0x52, 0x30, 0xa7, 0xf5, 0x07, 0x67, 0xac, 0xad, 0x46, 0x8a, 0x26, 0x25, + /* (2^431)P */ 0xda, 0x86, 0xc4, 0xa2, 0x71, 0x56, 0xdd, 0xd2, 0x48, 0xd3, 0xde, 0x42, 0x63, 0x01, 0xa7, 0x2c, 0x92, 0x83, 0x6f, 0x2e, 0xd8, 0x1e, 0x3f, 0xc1, 0xc5, 0x42, 0x4e, 0x34, 0x19, 0x54, 0x6e, 0x35, 0x2c, 0x51, 0x2e, 0xfd, 0x0f, 0x9a, 0x45, 0x66, 0x5e, 0x4a, 0x83, 0xda, 0x0a, 0x53, 0x68, 0x63, 0xfa, 0xce, 0x47, 0x20, 0xd3, 0x34, 0xba, 0x0d, + /* (2^432)P */ 0xd0, 0xe9, 0x64, 0xa4, 0x61, 0x4b, 0x86, 0xe5, 0x93, 0x6f, 0xda, 0x0e, 0x31, 0x7e, 0x6e, 0xe3, 0xc6, 0x73, 0xd8, 0xa3, 0x08, 0x57, 0x52, 0xcd, 0x51, 0x63, 0x1d, 0x9f, 0x93, 0x00, 0x62, 0x91, 0x26, 0x21, 0xa7, 0xdd, 0x25, 0x0f, 0x09, 0x0d, 0x35, 0xad, 0xcf, 0x11, 0x8e, 0x6e, 0xe8, 0xae, 0x1d, 0x95, 0xcb, 0x88, 0xf8, 0x70, 0x7b, 0x91, + /* (2^433)P */ 0x0c, 0x19, 0x5c, 0xd9, 0x8d, 0xda, 0x9d, 0x2c, 0x90, 0x54, 0x65, 0xe8, 0xb6, 0x35, 0x50, 0xae, 0xea, 0xae, 0x43, 0xb7, 0x1e, 0x99, 0x8b, 0x4c, 0x36, 0x4e, 0xe4, 0x1e, 0xc4, 0x64, 0x43, 0xb6, 0xeb, 0xd4, 0xe9, 0x60, 0x22, 0xee, 0xcf, 0xb8, 0x52, 0x1b, 0xf0, 0x04, 0xce, 0xbc, 0x2b, 0xf0, 0xbe, 0xcd, 0x44, 0x74, 0x1e, 0x1f, 0x63, 0xf9, + /* (2^434)P */ 0xe1, 0x3f, 0x95, 0x94, 0xb2, 0xb6, 0x31, 0xa9, 0x1b, 0xdb, 0xfd, 0x0e, 0xdb, 0xdd, 0x1a, 0x22, 0x78, 0x60, 0x9f, 0x75, 0x5f, 0x93, 0x06, 0x0c, 0xd8, 0xbb, 0xa2, 0x85, 0x2b, 0x5e, 0xc0, 0x9b, 0xa8, 0x5d, 0xaf, 0x93, 0x91, 0x91, 0x47, 0x41, 0x1a, 0xfc, 0xb4, 0x51, 0x85, 0xad, 0x69, 0x4d, 0x73, 0x69, 0xd5, 0x4e, 0x82, 0xfb, 0x66, 0xcb, + /* (2^435)P */ 0x7c, 0xbe, 0xc7, 0x51, 0xc4, 0x74, 0x6e, 0xab, 0xfd, 0x41, 0x4f, 0x76, 0x4f, 0x24, 0x03, 0xd6, 0x2a, 0xb7, 0x42, 0xb4, 0xda, 0x41, 0x2c, 0x82, 0x48, 0x4c, 0x7f, 0x6f, 0x25, 0x5d, 0x36, 0xd4, 0x69, 0xf5, 0xef, 0x02, 0x81, 0xea, 0x6f, 0x19, 0x69, 0xe8, 0x6f, 0x5b, 0x2f, 0x14, 0x0e, 0x6f, 0x89, 0xb4, 0xb5, 0xd8, 0xae, 0xef, 0x7b, 0x87, + /* (2^436)P */ 0xe9, 0x91, 0xa0, 0x8b, 0xc9, 0xe0, 0x01, 0x90, 0x37, 0xc1, 0x6f, 0xdc, 0x5e, 0xf7, 0xbf, 0x43, 0x00, 0xaa, 0x10, 0x76, 0x76, 0x18, 0x6e, 0x19, 0x1e, 0x94, 0x50, 0x11, 0x0a, 0xd1, 0xe2, 0xdb, 0x08, 0x21, 0xa0, 0x1f, 0xdb, 0x54, 0xfe, 0xea, 0x6e, 0xa3, 0x68, 0x56, 0x87, 0x0b, 0x22, 0x4e, 0x66, 0xf3, 0x82, 0x82, 0x00, 0xcd, 0xd4, 0x12, + /* (2^437)P */ 0x25, 0x8e, 0x24, 0x77, 0x64, 0x4c, 0xe0, 0xf8, 0x18, 0xc0, 0xdc, 0xc7, 0x1b, 0x35, 0x65, 0xde, 0x67, 0x41, 0x5e, 0x6f, 0x90, 0x82, 0xa7, 0x2e, 0x6d, 0xf1, 0x47, 0xb4, 0x92, 0x9c, 0xfd, 0x6a, 0x9a, 0x41, 0x36, 0x20, 0x24, 0x58, 0xc3, 0x59, 0x07, 0x9a, 0xfa, 0x9f, 0x03, 0xcb, 0xc7, 0x69, 0x37, 0x60, 0xe1, 0xab, 0x13, 0x72, 0xee, 0xa2, + /* (2^438)P */ 0x74, 0x78, 0xfb, 0x13, 0xcb, 0x8e, 0x37, 0x1a, 0xf6, 0x1d, 0x17, 0x83, 0x06, 0xd4, 0x27, 0x06, 0x21, 0xe8, 0xda, 0xdf, 0x6b, 0xf3, 0x83, 0x6b, 0x34, 0x8a, 0x8c, 0xee, 0x01, 0x05, 0x5b, 0xed, 0xd3, 0x1b, 0xc9, 0x64, 0x83, 0xc9, 0x49, 0xc2, 0x57, 0x1b, 0xdd, 0xcf, 0xf1, 0x9d, 0x63, 0xee, 0x1c, 0x0d, 0xa0, 0x0a, 0x73, 0x1f, 0x5b, 0x32, + /* (2^439)P */ 0x29, 0xce, 0x1e, 0xc0, 0x6a, 0xf5, 0xeb, 0x99, 0x5a, 0x39, 0x23, 0xe9, 0xdd, 0xac, 0x44, 0x88, 0xbc, 0x80, 0x22, 0xde, 0x2c, 0xcb, 0xa8, 0x3b, 0xff, 0xf7, 0x6f, 0xc7, 0x71, 0x72, 0xa8, 0xa3, 0xf6, 0x4d, 0xc6, 0x75, 0xda, 0x80, 0xdc, 0xd9, 0x30, 0xd9, 0x07, 0x50, 0x5a, 0x54, 0x7d, 0xda, 0x39, 0x6f, 0x78, 0x94, 0xbf, 0x25, 0x98, 0xdc, + /* (2^440)P */ 0x01, 0x26, 0x62, 0x44, 0xfb, 0x0f, 0x11, 0x72, 0x73, 0x0a, 0x16, 0xc7, 0x16, 0x9c, 0x9b, 0x37, 0xd8, 0xff, 0x4f, 0xfe, 0x57, 0xdb, 0xae, 0xef, 0x7d, 0x94, 0x30, 0x04, 0x70, 0x83, 0xde, 0x3c, 0xd4, 0xb5, 0x70, 0xda, 0xa7, 0x55, 0xc8, 0x19, 0xe1, 0x36, 0x15, 0x61, 0xe7, 0x3b, 0x7d, 0x85, 0xbb, 0xf3, 0x42, 0x5a, 0x94, 0xf4, 0x53, 0x2a, + /* (2^441)P */ 0x14, 0x60, 0xa6, 0x0b, 0x83, 0xe1, 0x23, 0x77, 0xc0, 0xce, 0x50, 0xed, 0x35, 0x8d, 0x98, 0x99, 0x7d, 0xf5, 0x8d, 0xce, 0x94, 0x25, 0xc8, 0x0f, 0x6d, 0xfa, 0x4a, 0xa4, 0x3a, 0x1f, 0x66, 0xfb, 0x5a, 0x64, 0xaf, 0x8b, 0x54, 0x54, 0x44, 0x3f, 0x5b, 0x88, 0x61, 0xe4, 0x48, 0x45, 0x26, 0x20, 0xbe, 0x0d, 0x06, 0xbb, 0x65, 0x59, 0xe1, 0x36, + /* (2^442)P */ 0xb7, 0x98, 0xce, 0xa3, 0xe3, 0xee, 0x11, 0x1b, 0x9e, 0x24, 0x59, 0x75, 0x31, 0x37, 0x44, 0x6f, 0x6b, 0x9e, 0xec, 0xb7, 0x44, 0x01, 0x7e, 0xab, 0xbb, 0x69, 0x5d, 0x11, 0xb0, 0x30, 0x64, 0xea, 0x91, 0xb4, 0x7a, 0x8c, 0x02, 0x4c, 0xb9, 0x10, 0xa7, 0xc7, 0x79, 0xe6, 0xdc, 0x77, 0xe3, 0xc8, 0xef, 0x3e, 0xf9, 0x38, 0x81, 0xce, 0x9a, 0xb2, + /* (2^443)P */ 0x91, 0x12, 0x76, 0xd0, 0x10, 0xb4, 0xaf, 0xe1, 0x89, 0x3a, 0x93, 0x6b, 0x5c, 0x19, 0x5f, 0x24, 0xed, 0x04, 0x92, 0xc7, 0xf0, 0x00, 0x08, 0xc1, 0x92, 0xff, 0x90, 0xdb, 0xb2, 0xbf, 0xdf, 0x49, 0xcd, 0xbd, 0x5c, 0x6e, 0xbf, 0x16, 0xbb, 0x61, 0xf9, 0x20, 0x33, 0x35, 0x93, 0x11, 0xbc, 0x59, 0x69, 0xce, 0x18, 0x9f, 0xf8, 0x7b, 0xa1, 0x6e, + /* (2^444)P */ 0xa1, 0xf4, 0xaf, 0xad, 0xf8, 0xe6, 0x99, 0xd2, 0xa1, 0x4d, 0xde, 0x56, 0xc9, 0x7b, 0x0b, 0x11, 0x3e, 0xbf, 0x89, 0x1a, 0x9a, 0x90, 0xe5, 0xe2, 0xa6, 0x37, 0x88, 0xa1, 0x68, 0x59, 0xae, 0x8c, 0xec, 0x02, 0x14, 0x8d, 0xb7, 0x2e, 0x25, 0x75, 0x7f, 0x76, 0x1a, 0xd3, 0x4d, 0xad, 0x8a, 0x00, 0x6c, 0x96, 0x49, 0xa4, 0xc3, 0x2e, 0x5c, 0x7b, + /* (2^445)P */ 0x26, 0x53, 0xf7, 0xda, 0xa8, 0x01, 0x14, 0xb1, 0x63, 0xe3, 0xc3, 0x89, 0x88, 0xb0, 0x85, 0x40, 0x2b, 0x26, 0x9a, 0x10, 0x1a, 0x70, 0x33, 0xf4, 0x50, 0x9d, 0x4d, 0xd8, 0x64, 0xc6, 0x0f, 0xe1, 0x17, 0xc8, 0x10, 0x4b, 0xfc, 0xa0, 0xc9, 0xba, 0x2c, 0x98, 0x09, 0xf5, 0x84, 0xb6, 0x7c, 0x4e, 0xa3, 0xe3, 0x81, 0x1b, 0x32, 0x60, 0x02, 0xdd, + /* (2^446)P */ 0xa3, 0xe5, 0x86, 0xd4, 0x43, 0xa8, 0xd1, 0x98, 0x9d, 0x9d, 0xdb, 0x04, 0xcf, 0x6e, 0x35, 0x05, 0x30, 0x53, 0x3b, 0xbc, 0x90, 0x00, 0x4a, 0xc5, 0x40, 0x2a, 0x0f, 0xde, 0x1a, 0xd7, 0x36, 0x27, 0x44, 0x62, 0xa6, 0xac, 0x9d, 0xd2, 0x70, 0x69, 0x14, 0x39, 0x9b, 0xd1, 0xc3, 0x0a, 0x3a, 0x82, 0x0e, 0xf1, 0x94, 0xd7, 0x42, 0x94, 0xd5, 0x7d, + /* (2^447)P */ 0x04, 0xc0, 0x6e, 0x12, 0x90, 0x70, 0xf9, 0xdf, 0xf7, 0xc9, 0x86, 0xc0, 0xe6, 0x92, 0x8b, 0x0a, 0xa1, 0xc1, 0x3b, 0xcc, 0x33, 0xb7, 0xf0, 0xeb, 0x51, 0x50, 0x80, 0x20, 0x69, 0x1c, 0x4f, 0x89, 0x05, 0x1e, 0xe4, 0x7a, 0x0a, 0xc2, 0xf0, 0xf5, 0x78, 0x91, 0x76, 0x34, 0x45, 0xdc, 0x24, 0x53, 0x24, 0x98, 0xe2, 0x73, 0x6f, 0xe6, 0x46, 0x67, +} diff --git a/src/circl/dh/x448/testdata/rfc7748_kat_test.json b/src/circl/dh/x448/testdata/rfc7748_kat_test.json new file mode 100644 index 00000000000..782c85a0441 --- /dev/null +++ b/src/circl/dh/x448/testdata/rfc7748_kat_test.json @@ -0,0 +1,32 @@ +[ + { + "input": "06fce640fa3487bfda5f6cf2d5263f8aad88334cbd07437f020f08f9814dc031ddbdc38c19c6da2583fa5429db94ada18aa7a7fb4ef8a086", + "output": "ce3e4ff95a60dc6697da1db1d85e6afbdf79b50a2412d7546d5f239fe14fbaadeb445fc66a01b0779d98223961111e21766282f73dd96b6f", + "scalar": "3d262fddf9ec8e88495266fea19a34d28882acef045104d0d1aae121700a779c984c24f8cdd78fbff44943eba368f54b29259a4f1c600ad3" + }, + { + "input": "0fbcc2f993cd56d3305b0b7d9e55d4c1a8fb5dbb52f8e9a1e9b6201b165d015894e56c4d3570bee52fe205e28a78b91cdfbde71ce8d157db", + "output": "884a02576239ff7a2f2f63b2db6a9ff37047ac13568e1e30fe63c4a7ad1b3ee3a5700df34321d62077e63633c575c1c954514e99da7c179d", + "scalar": "203d494428b8399352665ddca42f9de8fef600908e0d461cb021f8c538345dd77c3e4806e25f46d3315c44e0a5b4371282dd2c8d5be3095f" + }, + { + "input": "0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "output": "9b08f7cc31b7e3e67d22d5aea121074a273bd2b83de09c63faa73d2c22c5d9bbc836647241d953d40c5b12da88120d53177f80e532c41fa0", + "scalar": "9a8f4925d1519f5775cf46b04b5800d4ee9ee8bae8bc5565d498c28dd9c9baf574a9419744897391006382a6f127ab1d9ac2d8c0a598726b" + }, + { + "input": "0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "output": "3eb7a829b0cd20f5bcfc0b599b6feccf6da4627107bdb0d4f345b43027d8b972fc3e34fb4232a13ca706dcb57aec3dae07bdc1c67bf33609", + "scalar": "1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d" + }, + { + "input": "3eb7a829b0cd20f5bcfc0b599b6feccf6da4627107bdb0d4f345b43027d8b972fc3e34fb4232a13ca706dcb57aec3dae07bdc1c67bf33609", + "output": "07fff4181ac6cc95ec1c16a94a0f74d12da232ce40a77552281d282bb60c0b56fd2464c335543936521c24403085d59a449a5037514a879d", + "scalar": "9a8f4925d1519f5775cf46b04b5800d4ee9ee8bae8bc5565d498c28dd9c9baf574a9419744897391006382a6f127ab1d9ac2d8c0a598726b" + }, + { + "input": "9b08f7cc31b7e3e67d22d5aea121074a273bd2b83de09c63faa73d2c22c5d9bbc836647241d953d40c5b12da88120d53177f80e532c41fa0", + "output": "07fff4181ac6cc95ec1c16a94a0f74d12da232ce40a77552281d282bb60c0b56fd2464c335543936521c24403085d59a449a5037514a879d", + "scalar": "1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d" + } +] diff --git a/src/circl/dh/x448/testdata/rfc7748_times_test.json b/src/circl/dh/x448/testdata/rfc7748_times_test.json new file mode 100644 index 00000000000..f55e7289ae2 --- /dev/null +++ b/src/circl/dh/x448/testdata/rfc7748_times_test.json @@ -0,0 +1,14 @@ +[ + { + "times": 1, + "key": "3f482c8a9f19b01e6c46ee9711d9dc14fd4bf67af30765c2ae2b846a4d23a8cd0db897086239492caf350b51f833868b9bc2b3bca9cf4113" + }, + { + "times": 1000, + "key": "aa3b4749d55b9daf1e5b00288826c467274ce3ebbdd5c17b975e09d4af6c67cf10d087202db88286e2b79fceea3ec353ef54faa26e219f38" + }, + { + "times": 1000000, + "key": "077f453681caca3693198420bbe515cae0002472519b3e67661a7e89cab94695c8f4bcd66e61b9b9c946da8d524de3d69bd9d9d66b997e37" + } +] diff --git a/src/circl/doc.go b/src/circl/doc.go new file mode 100644 index 00000000000..e31ac13b1ab --- /dev/null +++ b/src/circl/doc.go @@ -0,0 +1,8 @@ +// Package circl provides a collection of cryptographic primitives. The goal +// of this module is to be used as a tool for experimental deployment of +// cryptographic algorithms targeting Post-Quantum (PQ) and Elliptic +// Curve Cryptography (ECC). +// +// Following blog post describes ideas behind CIRCL in more details: +// https://blog.cloudflare.com/introducing-circl/ +package circl // circl diff --git a/src/circl/ecc/doc.go b/src/circl/ecc/doc.go new file mode 100644 index 00000000000..ab758514cec --- /dev/null +++ b/src/circl/ecc/doc.go @@ -0,0 +1,2 @@ +// Package ecc provides implementation of arithmetic on some elliptic curves. +package ecc diff --git a/src/circl/ecc/fourq/curve.go b/src/circl/ecc/fourq/curve.go new file mode 100644 index 00000000000..1a9e5af0802 --- /dev/null +++ b/src/circl/ecc/fourq/curve.go @@ -0,0 +1,96 @@ +package fourq + +import ( + "math/big" + + "circl/internal/conv" +) + +// Size of scalars used for point multiplication. +const Size = 32 + +// Point represents an affine point of the curve. The identity is (0,1). +type Point struct{ X, Y Fq } + +// CurveParams contains the parameters of the elliptic curve. +type CurveParams struct { + Name string // The canonical name of the curve. + P *big.Int // The order of the underlying field Fp. + N *big.Int // The order of the generator point. + G Point // This is the generator point. +} + +// Params returns the parameters for the curve. +func Params() *CurveParams { + params := CurveParams{Name: "FourQ"} + params.P = conv.Uint64Le2BigInt(prime[:]) + params.N = conv.Uint64Le2BigInt(orderGenerator[:]) + params.G.X = genX + params.G.Y = genY + return ¶ms +} + +// IsOnCurve reports whether the given P=(x,y) lies on the curve. +func (P *Point) IsOnCurve() bool { + var _P pointR1 + P.toR1(&_P) + return _P.IsOnCurve() +} + +// SetGenerator assigns to P the generator point G. +func (P *Point) SetGenerator() { P.X = genX; P.Y = genY } + +// SetIdentity assigns to P the identity element. +func (P *Point) SetIdentity() { + var _P pointR1 + _P.SetIdentity() + P.fromR1(&_P) +} + +// IsIdentity returns true if P is the identity element. +func (P *Point) IsIdentity() bool { + var _P pointR1 + P.toR1(&_P) + return _P.IsIdentity() +} + +// Add calculates a point addition P = Q + R. +func (P *Point) Add(Q, R *Point) { + var _Q, _R pointR1 + var _R2 pointR2 + Q.toR1(&_Q) + R.toR1(&_R) + _R2.FromR1(&_R) + _Q.add(&_R2) + P.fromR1(&_Q) +} + +// ScalarMult calculates P = k*Q, where Q is an N-torsion point. +func (P *Point) ScalarMult(k *[Size]byte, Q *Point) { + var _P, _Q pointR1 + Q.toR1(&_Q) + _Q.ClearCofactor() + _P.ScalarMult(k, &_Q) + P.fromR1(&_P) +} + +// ScalarBaseMult calculates P = k*G, where G is the generator point. +func (P *Point) ScalarBaseMult(k *[Size]byte) { + var _P pointR1 + _P.ScalarBaseMult(k) + P.fromR1(&_P) +} + +func (P *Point) fromR1(Q *pointR1) { + Q.ToAffine() + P.X = Q.X + P.Y = Q.Y +} + +func (P *Point) toR1(projP *pointR1) { + projP.X = P.X + projP.Y = P.Y + projP.Ta = P.X + projP.Tb = P.Y + projP.Z.setOne() +} diff --git a/src/circl/ecc/fourq/curve_test.go b/src/circl/ecc/fourq/curve_test.go new file mode 100644 index 00000000000..a574a95a07c --- /dev/null +++ b/src/circl/ecc/fourq/curve_test.go @@ -0,0 +1,108 @@ +package fourq + +import ( + "crypto/rand" + "testing" + + "circl/internal/conv" + "circl/internal/test" +) + +func (P *Point) random() { + var _P pointR1 + _P.random() + P.fromR1(&_P) +} + +func TestMarshal(t *testing.T) { + testTimes := 1 << 10 + var buf, k [Size]byte + var P, Q, R Point + t.Run("k*um(P)=kP", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + P.random() + _, _ = rand.Read(k[:]) + + P.Marshal(&buf) + if ok := Q.Unmarshal(&buf); !ok { + test.ReportError(t, ok, true) + } + Q.ScalarMult(&k, &Q) + R.ScalarMult(&k, &P) + + got := Q.X + want := R.X + if got != want { + test.ReportError(t, got, want, P, k) + } + got = Q.Y + want = R.Y + if got != want { + test.ReportError(t, got, want, P, k) + } + } + }) + t.Run("m(kP)~=m(-kP)", func(t *testing.T) { + c := Params() + var minusK, encQ, encR [Size]byte + for i := 0; i < testTimes; i++ { + P.random() + bigK, _ := rand.Int(rand.Reader, c.N) + conv.BigInt2BytesLe(k[:], bigK) + bigK.Neg(bigK).Mod(bigK, c.N) + conv.BigInt2BytesLe(minusK[:], bigK) + Q.ScalarMult(&k, &P) + R.ScalarMult(&minusK, &P) + Q.Marshal(&encQ) + R.Marshal(&encR) + + got := encQ[31] >> 7 + want := 1 - (encR[31] >> 7) + encQ[31] &= 0x7F + encR[31] &= 0x7F + + if encQ != encR { + test.ReportError(t, encQ, encR, P, k) + } + if got != want { + test.ReportError(t, got, want, P, k) + } + } + }) +} + +func BenchmarkCurve(b *testing.B) { + var P, Q, R Point + var k [32]byte + + _, _ = rand.Read(k[:]) + P.ScalarBaseMult(&k) + _, _ = rand.Read(k[:]) + Q.ScalarBaseMult(&k) + _, _ = rand.Read(k[:]) + R.ScalarBaseMult(&k) + + b.Run("Add", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.Add(&Q, &R) + } + }) + + b.Run("Double", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.Add(&Q, &Q) + } + }) + + b.Run("ScalarBaseMult", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.ScalarBaseMult(&k) + } + }) + + b.Run("ScalarMult", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.ScalarMult(&k, &Q) + } + }) +} diff --git a/src/circl/ecc/fourq/doc.go b/src/circl/ecc/fourq/doc.go new file mode 100644 index 00000000000..1d0c354de77 --- /dev/null +++ b/src/circl/ecc/fourq/doc.go @@ -0,0 +1,11 @@ +// Package fourq provides elliptic curve operations over FourQ curve. +// +// FourQ is a high-speed elliptic curve at the 128-bit security level. This package +// contains an AMD64-optimized implementation. In particular, this package does +// not implement FourQ's endomorphisms or lattice reduction techniques. +// +// +// References: +// - https://eprint.iacr.org/2015/565 +// +package fourq diff --git a/src/circl/ecc/fourq/fp.go b/src/circl/ecc/fourq/fp.go new file mode 100644 index 00000000000..8e0ff466437 --- /dev/null +++ b/src/circl/ecc/fourq/fp.go @@ -0,0 +1,112 @@ +package fourq + +import ( + "math/big" + + "circl/internal/conv" +) + +var modulusP = Fp{ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, +} + +// SizeFp is the length in bytes to represent an element in the base field. +const SizeFp = 16 + +// Fp is an element (in littleEndian order) of prime field GF(2^127-1). +type Fp [SizeFp]byte + +func (f *Fp) String() string { return conv.BytesLe2Hex(f[:]) } +func (f *Fp) isZero() bool { fpMod(f); return *f == Fp{} } +func (f *Fp) toBigInt() *big.Int { fpMod(f); return conv.BytesLe2BigInt(f[:]) } +func (f *Fp) setBigInt(b *big.Int) { conv.BigInt2BytesLe((*f)[:], b); fpMod(f) } +func (f *Fp) toBytes(buf []byte) { + if len(buf) == SizeFp { + fpMod(f) + copy(buf, f[:]) + } +} +func (f *Fp) fromBytes(buf []byte) bool { + if len(buf) == SizeFp { + if (buf[SizeFp-1] >> 7) == 0 { + copy(f[:], buf) + fpMod(f) + return true + } + } + return false +} +func fpNeg(c, a *Fp) { fpSub(c, &modulusP, a) } + +// fqSgn returns the sign of an element. +// +// -1 if x > (p+1)/2 +// 0 if x == 0 +// +1 if x > (p+1)/2. +func fpSgn(c *Fp) int { + s := 0 + if !c.isZero() { + b := int(c[SizeFp-1]>>6) & 0x1 + s = 1 - (b << 1) + } + return s +} + +// fpTwo1251 sets c = a^(2^125-1). +func fpTwo1251(c, a *Fp) { + t1, t2, t3, t4, t5 := &Fp{}, &Fp{}, &Fp{}, &Fp{}, &Fp{} + + fpSqr(t2, a) + fpMul(t2, t2, a) + fpSqr(t3, t2) + fpSqr(t3, t3) + fpMul(t3, t3, t2) + fpSqr(t4, t3) + fpSqr(t4, t4) + fpSqr(t4, t4) + fpSqr(t4, t4) + fpMul(t4, t4, t3) + fpSqr(t5, t4) + for i := 0; i < 7; i++ { + fpSqr(t5, t5) + } + fpMul(t5, t5, t4) + fpSqr(t2, t5) + for i := 0; i < 15; i++ { + fpSqr(t2, t2) + } + fpMul(t2, t2, t5) + fpSqr(t1, t2) + for i := 0; i < 31; i++ { + fpSqr(t1, t1) + } + fpMul(t1, t1, t2) + for i := 0; i < 32; i++ { + fpSqr(t1, t1) + } + fpMul(t1, t2, t1) + for i := 0; i < 16; i++ { + fpSqr(t1, t1) + } + fpMul(t1, t1, t5) + for i := 0; i < 8; i++ { + fpSqr(t1, t1) + } + fpMul(t1, t1, t4) + for i := 0; i < 4; i++ { + fpSqr(t1, t1) + } + fpMul(t1, t1, t3) + fpSqr(t1, t1) + fpMul(c, a, t1) +} + +// fpInv sets z to a^(-1) mod p. +func fpInv(z, a *Fp) { + t := &Fp{} + fpTwo1251(t, a) + fpSqr(t, t) + fpSqr(t, t) + fpMul(z, t, a) +} diff --git a/src/circl/ecc/fourq/fp_amd64.go b/src/circl/ecc/fourq/fp_amd64.go new file mode 100644 index 00000000000..601d3d6b1eb --- /dev/null +++ b/src/circl/ecc/fourq/fp_amd64.go @@ -0,0 +1,27 @@ +// +build amd64,!purego + +package fourq + +import ( + "internal/cpu" +) + +var hasBMI2 = cpu.X86.HasBMI2 //nolint + +//go:noescape +func fpMod(c *Fp) + +//go:noescape +func fpAdd(c, a, b *Fp) + +//go:noescape +func fpSub(c, a, b *Fp) + +//go:noescape +func fpMul(c, a, b *Fp) + +//go:noescape +func fpSqr(c, a *Fp) + +//go:noescape +func fpHlf(c, a *Fp) diff --git a/src/circl/ecc/fourq/fp_amd64.h b/src/circl/ecc/fourq/fp_amd64.h new file mode 100644 index 00000000000..17b5cf30613 --- /dev/null +++ b/src/circl/ecc/fourq/fp_amd64.h @@ -0,0 +1,85 @@ +// CHECK_BMI2 triggers bmi2 if supported, +// otherwise it fallbacks to legacy code. +#define CHECK_BMI2(label, legacy, bmi2) \ + CMPB ·hasBMI2(SB), $0 \ + JE label \ + bmi2 \ + RET \ + label: \ + legacy \ + RET + +#define _fpReduce(c0, c1) \ + BTRQ $63, c1 \ + ADCQ $0, c0 \ + ADCQ $0, c1 + +// _fpMod: c = c mod p +// Uses: AX, DX, FLAGS +// Instr: x86_64 +#define _fpMod(c) \ + MOVQ 0+c, AX \ + MOVQ 8+c, DX \ + SUBQ ·modulusP+0(SB), AX \ + SBBQ ·modulusP+8(SB), DX \ + BTRQ $63, DX \ + SBBQ $0, AX \ + SBBQ $0, DX \ + _fpReduce(AX, DX) \ + _fpReduce(AX, DX) \ + MOVQ AX, 0+c \ + MOVQ DX, 8+c + +// _fpAdd: c = a + b +// Uses: AX, DX, FLAGS +// Instr: x86_64 +#define _fpAdd(c,a,b) \ + MOVQ 0+a, AX \ + MOVQ 8+a, DX \ + ADDQ 0+b, AX \ + ADCQ 8+b, DX \ + _fpReduce(AX, DX) \ + MOVQ AX, 0+c \ + MOVQ DX, 8+c + +// _fpSub: c = a - b +// Uses: AX, DX, FLAGS +// Instr: x86_64 +#define _fpSub(c,a,b) \ + MOVQ 0+a, AX \ + MOVQ 8+a, DX \ + SUBQ 0+b, AX \ + SBBQ 8+b, DX \ + BTRQ $63, DX \ + SBBQ $0, AX \ + SBBQ $0, DX \ + MOVQ AX, 0+c \ + MOVQ DX, 8+c + +#define _fpMulLeg(C2, C1, C0, a, b) \ + MOVQ $0, C2 \ + MOVQ 0+b, CX \ + MOVQ 0+a, AX \ + MULQ CX \ + MOVQ AX, C0 \ + MOVQ DX, C1 \ + MOVQ 8+a, AX \ + MULQ CX \ + SHLQ $1,DX \ + ADDQ DX,C0 \ + ADCQ AX, C1 \ + ADCQ $0, C2 \ + MOVQ 8+b, CX \ + MOVQ 0+a, AX \ + MULQ CX \ + SHLQ $1,DX \ + ADDQ DX,C0 \ + ADCQ AX, C1 \ + ADCQ $0, C2 \ + MOVQ 8+a, AX \ + MULQ CX \ + SHLQ $1,AX,DX \ + SHLQ $1,AX \ + ADDQ AX,C0 \ + ADCQ DX, C1 \ + ADCQ $0, C2 diff --git a/src/circl/ecc/fourq/fp_amd64.s b/src/circl/ecc/fourq/fp_amd64.s new file mode 100644 index 00000000000..9543bd260e5 --- /dev/null +++ b/src/circl/ecc/fourq/fp_amd64.s @@ -0,0 +1,100 @@ +// +build amd64,!purego + +#include "textflag.h" +#include "fp_amd64.h" + +// fpModp sets e to zero if it is equal to p. This is the only case where c +// will not naturally be reduced to canonical form. +// func fpMod(c *fp) +TEXT ·fpMod(SB),0,$0-8 + MOVQ c+0(FP), DI + _fpMod(0(DI)) + RET + +// func fpAdd(c, a, b *fp) +TEXT ·fpAdd(SB),0,$0-24 + MOVQ c+0(FP), DI + MOVQ a+8(FP), SI + MOVQ b+16(FP), BX + _fpAdd(0(DI), 0(SI), 0(BX)) + RET + +// func fpSub(c, a, b *fp) +TEXT ·fpSub(SB),0,$0-24 + MOVQ c+0(FP), DI + MOVQ a+8(FP), SI + MOVQ b+16(FP), BX + _fpSub(0(DI), 0(SI), 0(BX)) + RET + +// func fpHlf(c, a *fp) +TEXT ·fpHlf(SB),0,$0-16 + MOVQ a+8(FP), DI + MOVQ 0(DI), AX + MOVQ 8(DI), BX + + SHLQ $1, BX + SHRQ $1, AX, BX + SHRQ $1, BX, AX + SHRQ $1, BX + + MOVQ c+0(FP), DI + MOVQ AX, 0(DI) + MOVQ BX, 8(DI) + RET + +// func fpMul(c, a, b *fp) +TEXT ·fpMul(SB),0,$0-24 + MOVQ a+8(FP), DI + MOVQ b+16(FP), SI + _fpMulLeg(R10, R9, R8, 0(DI), 0(SI)) + SHLQ $1, R10 + BTRQ $63, R9 + ADCQ R10, R8 + ADCQ $0, R9 + _fpReduce(R8, R9) + + MOVQ c+0(FP), DI + MOVQ R8, 0(DI) + MOVQ R9, 8(DI) + RET + +// func fpSqr(c, a *fp) +TEXT ·fpSqr(SB),0,$0-16 + MOVQ a+8(FP), DI + MOVQ $0, CX + + MOVQ 0(DI), AX + MULQ 0(DI) + MOVQ AX, R8 + MOVQ DX, R9 + + MOVQ 0(DI), AX + MULQ 8(DI) + SHLQ $1, DX + ADDQ DX, R8 + ADCQ AX, R9 + ADCQ $0, CX + ADDQ DX, R8 + ADCQ AX, R9 + ADCQ $0, CX + + MOVQ 8(DI), AX + MULQ 8(DI) + SHLQ $1, DX + SHLQ $1, AX + ADCQ $0, DX + ADDQ AX, R8 + ADCQ DX, R9 + ADCQ $0, CX + + SHLQ $1, CX + BTRQ $63, R9 + ADCQ CX, R8 + ADCQ $0, R9 + _fpReduce(R8, R9) + + MOVQ c+0(FP), DI + MOVQ R8, 0(DI) + MOVQ R9, 8(DI) + RET diff --git a/src/circl/ecc/fourq/fp_generic.go b/src/circl/ecc/fourq/fp_generic.go new file mode 100644 index 00000000000..4f644439412 --- /dev/null +++ b/src/circl/ecc/fourq/fp_generic.go @@ -0,0 +1,96 @@ +// +build go1.12 + +package fourq + +import ( + "encoding/binary" + "math/bits" +) + +func fpModGeneric(c *Fp) { fpSubGeneric(c, c, &modulusP) } + +func fpAddGeneric(c, a, b *Fp) { + a0 := binary.LittleEndian.Uint64(a[0*8 : 1*8]) + a1 := binary.LittleEndian.Uint64(a[1*8 : 2*8]) + + b0 := binary.LittleEndian.Uint64(b[0*8 : 1*8]) + b1 := binary.LittleEndian.Uint64(b[1*8 : 2*8]) + + c0, x := bits.Add64(a0, b0, 0) + c1, _ := bits.Add64(a1, b1, x) + c1, x = bits.Add64(c1, c1, 0) + c0, x = bits.Add64(c0, 0, x) + c1, _ = bits.Add64(c1>>1, 0, x) + + binary.LittleEndian.PutUint64(c[0*8:1*8], c0) + binary.LittleEndian.PutUint64(c[1*8:2*8], c1) +} + +func fpSubGeneric(c, a, b *Fp) { + a0 := binary.LittleEndian.Uint64(a[0*8 : 1*8]) + a1 := binary.LittleEndian.Uint64(a[1*8 : 2*8]) + + b0 := binary.LittleEndian.Uint64(b[0*8 : 1*8]) + b1 := binary.LittleEndian.Uint64(b[1*8 : 2*8]) + + c0, x := bits.Sub64(a0, b0, 0) + c1, _ := bits.Sub64(a1, b1, x) + c1, x = bits.Add64(c1, c1, 0) + c0, x = bits.Sub64(c0, 0, x) + c1, _ = bits.Sub64(c1>>1, 0, x) + + binary.LittleEndian.PutUint64(c[0*8:1*8], c0) + binary.LittleEndian.PutUint64(c[1*8:2*8], c1) +} + +func fpMulGeneric(c, a, b *Fp) { + a0 := binary.LittleEndian.Uint64(a[0*8 : 1*8]) + a1 := binary.LittleEndian.Uint64(a[1*8 : 2*8]) + + b0 := binary.LittleEndian.Uint64(b[0*8 : 1*8]) + b1 := binary.LittleEndian.Uint64(b[1*8 : 2*8]) + + c1, c0 := bits.Mul64(a0, b0) + hi, lo := bits.Mul64(a0, b1) + c0, x := bits.Add64(c0, hi<<1, 0) + c1, x = bits.Add64(c1, lo, x) + c2, _ := bits.Add64(0, 0, x) + + hi, lo = bits.Mul64(a1, b0) + c0, x = bits.Add64(c0, hi<<1, 0) + c1, x = bits.Add64(c1, lo, x) + c2, _ = bits.Add64(c2, 0, x) + + hi, lo = bits.Mul64(a1, b1) + lo, x = bits.Add64(lo, lo, 0) + hi, _ = bits.Add64(hi, hi, x) + + c0, x = bits.Add64(c0, lo, 0) + c1, x = bits.Add64(c1, hi, x) + c2, _ = bits.Add64(c2, 0, x) + + c1, x = bits.Add64(c1, c1, 0) + c0, x = bits.Add64(c0, c2<<1, x) + c1, _ = bits.Add64(c1>>1, 0, x) + + c1, x = bits.Add64(c1, c1, 0) + c0, x = bits.Add64(c0, 0, x) + c1, _ = bits.Add64(c1>>1, 0, x) + + binary.LittleEndian.PutUint64(c[0*8:1*8], c0) + binary.LittleEndian.PutUint64(c[1*8:2*8], c1) +} + +func fpSqrGeneric(c, a *Fp) { fpMulGeneric(c, a, a) } + +func fpHlfGeneric(c, a *Fp) { + a0 := binary.LittleEndian.Uint64(a[0*8 : 1*8]) + a1 := binary.LittleEndian.Uint64(a[1*8 : 2*8]) + + hlf := a0 & 0x1 + c0 := (a1 << 63) | (a0 >> 1) + c1 := (hlf << 62) | (a1 >> 1) + + binary.LittleEndian.PutUint64(c[0*8:1*8], c0) + binary.LittleEndian.PutUint64(c[1*8:2*8], c1) +} diff --git a/src/circl/ecc/fourq/fp_noasm.go b/src/circl/ecc/fourq/fp_noasm.go new file mode 100644 index 00000000000..5bc032e60af --- /dev/null +++ b/src/circl/ecc/fourq/fp_noasm.go @@ -0,0 +1,10 @@ +// +build !amd64 purego + +package fourq + +func fpMod(c *Fp) { fpModGeneric(c) } +func fpAdd(c, a, b *Fp) { fpAddGeneric(c, a, b) } +func fpSub(c, a, b *Fp) { fpSubGeneric(c, a, b) } +func fpMul(c, a, b *Fp) { fpMulGeneric(c, a, b) } +func fpSqr(c, a *Fp) { fpSqrGeneric(c, a) } +func fpHlf(c, a *Fp) { fpHlfGeneric(c, a) } diff --git a/src/circl/ecc/fourq/fp_test.go b/src/circl/ecc/fourq/fp_test.go new file mode 100644 index 00000000000..6d64ef4b8ba --- /dev/null +++ b/src/circl/ecc/fourq/fp_test.go @@ -0,0 +1,337 @@ +package fourq + +import ( + "crypto/rand" + "math/big" + "testing" + + "circl/internal/test" +) + +type tFpAdd = func(z, x, y *Fp) +type tFpSub = func(z, x, y *Fp) +type tFpMul = func(z, x, y *Fp) +type tFpSqr = func(z, x *Fp) +type tFpHlf = func(z, x *Fp) +type tFpModp = func(z *Fp) + +func getModulus() *big.Int { + p := big.NewInt(1) + return p.Lsh(p, 127).Sub(p, big.NewInt(1)) +} + +func TestFpSign(t *testing.T) { + const testTimes = 1 << 9 + P := getModulus() + x := &Fp{} + var P1div2 big.Int + P1div2.Add(P, big.NewInt(1)).Rsh(&P1div2, 1) // (p+1)/2 + + // Verifying Sign(0) = 0 + x.setBigInt(big.NewInt(0)) + got := fpSgn(x) + want := 0 + if got != want { + test.ReportError(t, got, want, x) + } + + // Verifying Sign(P) = 0 + x.setBigInt(P) + got = fpSgn(x) + want = 0 + if got != want { + test.ReportError(t, got, want, x) + } + + // Verifying Sign( (p+1)/2 ) = -1 + x.setBigInt(&P1div2) + got = fpSgn(x) + want = -1 + if got != want { + test.ReportError(t, got, want, x) + } + + // Verifying x be a non-zero positive + for i := 0; i < testTimes; i++ { + bigX, _ := rand.Int(rand.Reader, &P1div2) + x.setBigInt(bigX) + got = fpSgn(x) + want = 1 + if got != want { + test.ReportError(t, got, want, x) + } + } + // Verifying x be a non-zero negative + for i := 0; i < testTimes; i++ { + bigX, _ := rand.Int(rand.Reader, &P1div2) + bigX.Add(bigX, &P1div2) + x.setBigInt(bigX) + got = fpSgn(x) + want = -1 + if got != want { + test.ReportError(t, got, want, x) + } + } +} + +func TestFpIsZero(t *testing.T) { + P := getModulus() + x := &Fp{} + // Verifying x=0 + x.setBigInt(big.NewInt(0)) + got := x.isZero() + want := true + if got != want { + test.ReportError(t, got, want, x) + } + + // Verifying x=P goes to 0 + x.setBigInt(P) + got = x.isZero() + want = true + if got != want { + test.ReportError(t, got, want, x) + } + + // Verifying x!=0 + _, _ = rand.Read(x[:]) + got = x.isZero() + want = false + if got != want { + test.ReportError(t, got, want, x) + } +} + +func testFpModp(t *testing.T, f tFpModp) { + const testTimes = 1 << 9 + P := getModulus() + x := &Fp{} + var bigX big.Int + // Verifying x=P goes to 0 + bigX.Set(P) + x.setBigInt(&bigX) + f(x) + got := x.toBigInt() + want := big.NewInt(0) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + + // Verifying x=P+1 goes to 1 + bigX.Add(P, big.NewInt(1)) + x.setBigInt(&bigX) + f(x) + got = x.toBigInt() + want = big.NewInt(1) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(x[:]) + + bigX := x.toBigInt() + + fpMod(x) + got := x.toBigInt() + + want := bigX.Mod(bigX, P) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } +} + +func TestFpNeg(t *testing.T) { + const testTimes = 1 << 9 + P := getModulus() + x, z := &Fp{}, &Fp{} + for i := 0; i < testTimes; i++ { + bigX, _ := rand.Int(rand.Reader, P) + + x.setBigInt(bigX) + fpNeg(z, x) + got := z.toBigInt() + + want := bigX.Neg(bigX) + want = want.Mod(want, P) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } +} + +func testFpHlf(t *testing.T, f tFpHlf) { + const testTimes = 1 << 9 + P := getModulus() + x, z := &Fp{}, &Fp{} + invTwo := big.NewInt(2) + invTwo.ModInverse(invTwo, P) + for i := 0; i < testTimes; i++ { + bigX, _ := rand.Int(rand.Reader, P) + + x.setBigInt(bigX) + f(z, x) + got := z.toBigInt() + + want := bigX.Mul(bigX, invTwo) + want = want.Mod(want, P) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } +} + +func testFpAdd(t *testing.T, f tFpAdd) { + const testTimes = 1 << 9 + P := getModulus() + x, y, z := &Fp{}, &Fp{}, &Fp{} + for i := 0; i < testTimes; i++ { + bigX, _ := rand.Int(rand.Reader, P) + bigY, _ := rand.Int(rand.Reader, P) + + x.setBigInt(bigX) + y.setBigInt(bigY) + f(z, x, y) + got := z.toBigInt() + + want := bigX.Add(bigX, bigY) + want = want.Mod(want, P) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y) + } + } +} + +func testFpSub(t *testing.T, f tFpSub) { + const testTimes = 1 << 9 + P := getModulus() + x, y, z := &Fp{}, &Fp{}, &Fp{} + for i := 0; i < testTimes; i++ { + bigX, _ := rand.Int(rand.Reader, P) + bigY, _ := rand.Int(rand.Reader, P) + + x.setBigInt(bigX) + y.setBigInt(bigY) + f(z, x, y) + got := z.toBigInt() + + want := bigX.Sub(bigX, bigY) + want = want.Mod(want, P) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y) + } + } +} + +func testFpMul(t *testing.T, f tFpMul) { + const testTimes = 1 << 9 + P := getModulus() + x, y, z := &Fp{}, &Fp{}, &Fp{} + for i := 0; i < testTimes; i++ { + bigX, _ := rand.Int(rand.Reader, P) + bigY, _ := rand.Int(rand.Reader, P) + + x.setBigInt(bigX) + y.setBigInt(bigY) + f(z, x, y) + got := z.toBigInt() + + want := bigX.Mul(bigX, bigY) + want = want.Mod(want, P) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y) + } + } +} + +func testFpSqr(t *testing.T, f tFpSqr) { + const testTimes = 1 << 9 + P := getModulus() + x, z := &Fp{}, &Fp{} + for i := 0; i < testTimes; i++ { + bigX, _ := rand.Int(rand.Reader, P) + + x.setBigInt(bigX) + f(z, x) + got := z.toBigInt() + + want := bigX.Mul(bigX, bigX) + want = want.Mod(want, P) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } +} + +func TestFpInv(t *testing.T) { + const testTimes = 1 << 9 + P := getModulus() + x, z := &Fp{}, &Fp{} + for i := 0; i < testTimes; i++ { + bigX, _ := rand.Int(rand.Reader, P) + + x.setBigInt(bigX) + fpInv(z, x) + got := z.toBigInt() + + want := bigX.ModInverse(bigX, P) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } +} + +func TestFpGeneric(t *testing.T) { + t.Run("Add", func(t *testing.T) { testFpAdd(t, fpAddGeneric) }) + t.Run("Sub", func(t *testing.T) { testFpSub(t, fpSubGeneric) }) + t.Run("Mul", func(t *testing.T) { testFpMul(t, fpMulGeneric) }) + t.Run("Sqr", func(t *testing.T) { testFpSqr(t, fpSqrGeneric) }) + t.Run("Hlf", func(t *testing.T) { testFpHlf(t, fpHlfGeneric) }) + t.Run("Modp", func(t *testing.T) { testFpModp(t, fpModGeneric) }) +} + +func TestFpNative(t *testing.T) { + t.Run("Add", func(t *testing.T) { testFpAdd(t, fpAdd) }) + t.Run("Sub", func(t *testing.T) { testFpSub(t, fpSub) }) + t.Run("Mul", func(t *testing.T) { testFpMul(t, fpMul) }) + t.Run("Sqr", func(t *testing.T) { testFpSqr(t, fpSqr) }) + t.Run("Hlf", func(t *testing.T) { testFpHlf(t, fpHlf) }) + t.Run("Modp", func(t *testing.T) { testFpModp(t, fpMod) }) +} + +func BenchmarkFp(b *testing.B) { + x, y, z := &Fp{}, &Fp{}, &Fp{} + p := getModulus() + n, _ := rand.Int(rand.Reader, p) + x.setBigInt(n) + n, _ = rand.Int(rand.Reader, p) + y.setBigInt(n) + + b.Run("Add", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fpAdd(z, x, y) + } + }) + b.Run("Sub", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fpSub(z, x, y) + } + }) + b.Run("Mul", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fpMul(z, x, y) + } + }) + b.Run("Sqr", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fpSqr(z, x) + } + }) + b.Run("Inv", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fpInv(z, x) + } + }) +} diff --git a/src/circl/ecc/fourq/fq.go b/src/circl/ecc/fourq/fq.go new file mode 100644 index 00000000000..5456fc3b5c1 --- /dev/null +++ b/src/circl/ecc/fourq/fq.go @@ -0,0 +1,114 @@ +package fourq + +import ( + "crypto/subtle" + "math/big" +) + +// Fq implements operations of a field of size q=p^2 as a quadratic +// extension of the base field where i^2=-1. +// An element in Fq is represented as f[0]+f[1]*i, where f[0],f[1] are in Fp. +type Fq [2]Fp + +func (e *Fq) String() string { return e[1].String() + " *i+ " + e[0].String() } +func (e *Fq) toBigInt() (f0, f1 *big.Int) { return e[0].toBigInt(), e[1].toBigInt() } +func (e *Fq) setBigInt(f0, f1 *big.Int) { e[0].setBigInt(f0); e[1].setBigInt(f1) } +func (e *Fq) setZero() { var z Fp; e[0] = z; e[1] = z } +func (e *Fq) setOne() { e.setZero(); e[0][0] = 1 } +func (e *Fq) isZero() bool { return e[0].isZero() && e[1].isZero() } + +func (e *Fq) toBytes(buf []byte) { + if len(buf) == 2*SizeFp { + e[0].toBytes(buf[:SizeFp]) + e[1].toBytes(buf[SizeFp:]) + } +} +func (e *Fq) fromBytes(buf []byte) bool { + if len(buf) == 2*SizeFp { + return e[0].fromBytes(buf[:SizeFp]) && + e[1].fromBytes(buf[SizeFp:]) + } + return false +} + +func fqSgn(c *Fq) int { + s0 := fpSgn(&c[0]) + s1 := fpSgn(&c[1]) + return subtle.ConstantTimeSelect(s0&0x1, s0, s1) +} +func fqCopy(c, a *Fq) { *c = *a } +func fqNeg(c, a *Fq) { fpNeg(&c[0], &a[0]); fpNeg(&c[1], &a[1]) } + +// fqSqrt calculates c = sqrt(u/v) such that sgn(c)=s. +func fqSqrt(c, u, v *Fq, s int) { + t0, t1, t, r := &Fp{}, &Fp{}, &Fp{}, &Fp{} + a, b, g := &Fp{}, &Fp{}, &Fp{} + + // a = u0*v0 + u1*v1 + fpMul(a, &u[0], &v[0]) + fpMul(t0, &u[1], &v[1]) + fpAdd(a, a, t0) + + // b = v0^2 + v1^2 + fpSqr(b, &v[0]) + fpSqr(t0, &v[1]) + fpAdd(b, b, t0) + + // g = u1*v0 - u0*v1 + fpMul(g, &u[1], &v[0]) + fpMul(t0, &u[0], &v[1]) + fpSub(g, g, t0) + + // t = 2(a + sqrt(a^2+g^2)) = 2*(a + (a^2+g^2)^(2^125)) + // if t=0; then t = 2*(a - (a^2+g^2)^(2^125)) + fpSqr(t0, a) + fpSqr(t1, g) + fpAdd(t0, t0, t1) + for i := 0; i < 125; i++ { + fpSqr(t0, t0) + } + fpAdd(t, a, t0) + if t.isZero() { + fpSub(t, a, t0) + } + fpAdd(t, t, t) + + // r = (t*b^3)^(2^125-1) + fpSqr(r, b) + fpMul(r, r, b) + fpMul(r, r, t) + fpTwo1251(r, r) + + // x0 = (r*b*t)/2 + // x1 = (r*b*g) + fpMul(&c[1], r, b) + fpMul(&c[0], &c[1], t) + fpHlf(&c[0], &c[0]) + fpMul(&c[1], &c[1], g) + + // if b*(2*x0)^2 == t then (x0,x1) <- (x1,x0) + fpAdd(t0, &c[0], &c[0]) + fpSqr(t0, t0) + fpMul(t0, t0, b) + fpSub(t0, t0, t) + if !t0.isZero() { + *t0 = c[0] + c[0] = c[1] + c[1] = *t0 + } + + if fqSgn(c) != s { + fqNeg(c, c) + } +} + +func fqInv(c, a *Fq) { + t1, t2 := &Fp{}, &Fp{} + fpSqr(t1, &a[0]) + fpSqr(t2, &a[1]) + fpAdd(t1, t1, t2) + fpInv(t1, t1) + fpMul(&c[0], &a[0], t1) + fpNeg(t1, t1) + fpMul(&c[1], &a[1], t1) +} diff --git a/src/circl/ecc/fourq/fq_amd64.go b/src/circl/ecc/fourq/fq_amd64.go new file mode 100644 index 00000000000..e4d4810ab32 --- /dev/null +++ b/src/circl/ecc/fourq/fq_amd64.go @@ -0,0 +1,18 @@ +// +build amd64,!purego + +package fourq + +//go:noescape +func fqCmov(c, a *Fq, b int) + +//go:noescape +func fqAdd(c, a, b *Fq) + +//go:noescape +func fqSub(c, a, b *Fq) + +//go:noescape +func fqMul(c, a, b *Fq) + +//go:noescape +func fqSqr(c, a *Fq) diff --git a/src/circl/ecc/fourq/fq_amd64.h b/src/circl/ecc/fourq/fq_amd64.h new file mode 100644 index 00000000000..746a99979f3 --- /dev/null +++ b/src/circl/ecc/fourq/fq_amd64.h @@ -0,0 +1,216 @@ +#include "fp_amd64.h" + +#define _fqAdd(c,a,b) \ + _fpAdd( 0+c, 0+a, 0+b) \ + _fpAdd(16+c,16+a,16+b) + +#define _fqSub(c,a,b) \ + _fpSub( 0+c, 0+a, 0+b) \ + _fpSub(16+c,16+a,16+b) + +#define _fqMulBmi2(c, a, b) \ + \ // T0 = a0 * b0, R11:R10:R9:R8 <- 0+ra:8+ra * 0+rb:8+rb + MOVQ 0+b, DX \ + MULXQ 0+a, R8, R9 \ + MULXQ 8+a, R10, AX \ + ADDQ R10, R9 \ + MOVQ 8+b, DX \ + MULXQ 8+a, R10, R11 \ + ADCQ AX, R10 \ + MULXQ 0+a, DX, AX \ + ADCQ $0, R11 \ + ADDQ DX, R9 \ + \ + \ // T1 = a1 * b1, R15:R14:R13:R12 <- 16+ra:24+ra * 16+rb:24+rb + MOVQ 16+b, DX \ + MULXQ 16+a, R12, R13 \ + ADCQ AX, R10 \ + MULXQ 24+a, R14, AX \ + ADCQ $0, R11 \ + MOVQ 24+b, DX \ + ADDQ R14, R13 \ + MULXQ 24+a, R14, R15 \ + ADCQ AX, R14 \ + ADCQ $0, R15 \ + MULXQ 16+a, DX, AX \ + ADDQ DX, R13 \ + ADCQ AX, R14 \ + ADCQ $0, R15 \ + \ + \ // c0 = T0 - T1 = a0*b0 - a1*b1 + SUBQ R12, R8 \ + SBBQ R13, R9 \ + SBBQ R14, R10 \ + SBBQ R15, R11 \ + \ + SHLQ $1, R10, R11 \ + SHLQ $1, R9, R10 \ + MOVQ 16+b, DX \ + BTRQ $63, R9 \ + \ + \ // T0 = a0 * b1, R15:R14:R13:R12 <- 0+ra:8+ra * 16+rb:24+rb + MULXQ 0+a, R12, R13 \ + BTRQ $63, R11 \ + SBBQ $0, R10 \ + SBBQ $0, R11 \ + MULXQ 8+a, R14, AX \ + ADDQ R14, R13 \ + MOVQ 24+b, DX \ + MULXQ 8+a, R14, R15 \ + ADCQ AX, R14 \ + ADCQ $0, R15 \ + MULXQ 0+a, DX, AX \ + ADDQ DX, R13 \ + ADCQ AX, R14 \ + ADCQ $0, R15 \ + \ + \ // Reducing and storing c0 + ADDQ R8, R10 \ + ADCQ R9, R11 \ + BTRQ $63, R11 \ + ADCQ $0, R10 \ + ADCQ $0, R11 \ + \ + \ // T1 = a1 * b0, R12:R11:R10:R9 <- 16+ra:24+ra * 0+rb:8+rb + MOVQ 0+b, DX \ + MULXQ 16+a, R8, R9 \ + MOVQ R10, 0+c \ + MULXQ 24+a, R10, AX \ + ADDQ R10, R9 \ + MOVQ 8+b, DX \ + MOVQ R11, 8+c \ + MULXQ 24+a, R10, R11 \ + ADCQ AX, R10 \ + ADCQ $0, R11 \ + MULXQ 16+a, DX, AX \ + ADDQ DX, R9 \ + ADCQ AX, R10 \ + ADCQ $0, R11 \ + \ + \ // c1 = T0 + T1 = a0*b1 + a1*b0 + ADDQ R12, R8 \ + ADCQ R13, R9 \ + ADCQ R14, R10 \ + ADCQ R15, R11 \ + \ + \ // Reducing and storing c1 + SHLQ $1, R10, R11 \ + SHLQ $1, R9, R10 \ + BTRQ $63, R9 \ + BTRQ $63, R11 \ + ADCQ R10, R8 \ + ADCQ R11, R9 \ + BTRQ $63, R9 \ + ADCQ $0, R8 \ + ADCQ $0, R9 \ + MOVQ R8, 16+c \ + MOVQ R9, 24+c + +#define _fqMulLeg(c, a, b) \ + _fpMulLeg(R10, R9, R8, 0+a, 0+b) \ + _fpMulLeg(R13,R12,R11,16+a,16+b) \ + MOVQ $0,R14 \ + SUBQ R11, R8 \ + SBBQ R12, R9 \ + SBBQ R13,R10 \ + SBBQ $0,R14 \ + SHLQ $1,R10 \ + BTRQ $63, R9 \ + ADCQ R10, R8 \ + ADCQ R14, R9 \ + MOVQ R8, R14 \ + MOVQ R9, R15 \ + _fpMulLeg(R10, R9, R8, 0+a,16+b) \ + _fpMulLeg(R13,R12,R11,16+a, 0+b) \ + ADDQ R11, R8 \ + ADCQ R12, R9 \ + ADCQ R13,R10 \ + SHLQ $1,R10 \ + BTRQ $63, R9 \ + ADCQ R10, R8 \ + ADCQ $0, R9 \ + MOVQ R14, 0+c \ + MOVQ R15, 8+c \ + MOVQ R8,16+c \ + MOVQ R9,24+c + +#define _fqSqrBmi2(c,a) \ + \ // t0 = R9:R8 = a0 + a1, R14:CX = a1 + MOVQ 0+a, R10 \ + MOVQ 16+a, R14 \ + SUBQ R14, R10 \ + MOVQ 8+a, R11 \ + MOVQ 24+a, CX \ + SBBQ CX, R11 \ + \ + BTRQ $63, R11 \ + SBBQ $0, R10 \ + \ + \ // t1 = R11:R10 = a0 - a1 + MOVQ R10, DX \ + MOVQ 0+a, R8 \ + ADDQ R14, R8 \ + MOVQ 8+a, R9 \ + ADCQ CX, R9 \ + \ + \ // c0 = t0 * t1 = (a0 + a1)*(a0 - a1), CX:R14:R13:R12 <- R9:R8 * R11:R10 + MULXQ R8, R12, R13 \ + SBBQ $0, R11 \ + MULXQ R9, R14, AX \ + MOVQ R11, DX \ + ADDQ R14, R13 \ + MULXQ R9, R14, CX \ + MOVQ 8+a, R9 \ + ADCQ AX, R14 \ + ADCQ $0, CX \ + MULXQ R8, DX, AX \ + MOVQ 0+a, R8 \ + ADDQ DX, R13 \ + ADCQ AX, R14 \ + ADCQ $0, CX \ + \ + \ // t2 = R9:R8 = 2*a0 + ADDQ R8, R8 \ + ADCQ R9, R9 \ + \ + \ // Reducing and storing c0 + SHLQ $1, R14, CX \ + SHLQ $1, R13, R14 \ + BTRQ $63, R13 \ + BTRQ $63, CX \ + ADCQ R14, R12 \ + ADCQ CX, R13 \ + BTRQ $63, R13 \ + ADCQ $0, R12 \ + ADCQ $0, R13 \ + MOVQ R12, 0+c \ + MOVQ R13, 8+c \ + \ + \ // c1 = 2a0 * a1, CX:R14:R11:R10 <- R9:R8 * 16+ra:24+ra + MOVQ 16+a, DX \ + MULXQ R8, R10, R11 \ + MULXQ R9, R14, AX \ + ADDQ R14, R11 \ + MOVQ 24+a, DX \ + MULXQ R9, R14, CX \ + ADCQ AX, R14 \ + ADCQ $0, CX \ + MULXQ R8, DX, AX \ + ADDQ DX, R11 \ + ADCQ AX, R14 \ + ADCQ $0, CX \ + \ + \ // Reduce and store c1 + SHLQ $1, R14, CX \ + SHLQ $1, R11, R14 \ + BTRQ $63, R11 \ + BTRQ $63, CX \ + ADCQ R14, R10 \ + ADCQ CX, R11 \ + BTRQ $63, R11 \ + ADCQ $0, R10 \ + ADCQ $0, R11 \ + MOVQ R10, 16+c \ + MOVQ R11, 24+c + +#define _fqSqrLeg(c,a) _fqMulLeg(c,a,a) diff --git a/src/circl/ecc/fourq/fq_amd64.s b/src/circl/ecc/fourq/fq_amd64.s new file mode 100644 index 00000000000..415fc135dc8 --- /dev/null +++ b/src/circl/ecc/fourq/fq_amd64.s @@ -0,0 +1,56 @@ +// +build amd64,!purego + +#include "fq_amd64.h" + +#define fqMulLegacy \ + _fqMulLeg(0(DI),0(SI),0(BX)) +#define fqMulBmi2 \ + _fqMulBmi2(0(DI),0(SI),0(BX)) + +#define fqSqrLegacy \ + _fqSqrLeg(0(DI),0(SI)) +#define fqSqrBmi2 \ + _fqSqrBmi2(0(DI),0(SI)) + +// func fqCmov(c, a *fq, b int) +TEXT ·fqCmov(SB),0,$0-24 + MOVQ c+0(FP), DI + MOVQ a+8(FP), SI + MOVQ b+16(FP), BX + TESTQ BX, BX + MOVQ 0(DI), AX; MOVQ 0(SI), DX; CMOVQNE DX, AX; MOVQ AX, 0(DI); + MOVQ 8(DI), AX; MOVQ 8(SI), DX; CMOVQNE DX, AX; MOVQ AX, 8(DI); + MOVQ 16(DI), AX; MOVQ 16(SI), DX; CMOVQNE DX, AX; MOVQ AX, 16(DI); + MOVQ 24(DI), AX; MOVQ 24(SI), DX; CMOVQNE DX, AX; MOVQ AX, 24(DI); + RET + +// func fqAdd(c, a, b *fq) +TEXT ·fqAdd(SB),0,$0-24 + MOVQ c+0(FP), DI + MOVQ a+8(FP), SI + MOVQ b+16(FP), BX + _fqAdd(0(DI), 0(SI), 0(BX)) + RET + +// func fqSub(c, a, b *fq) +TEXT ·fqSub(SB),0,$0-24 + MOVQ c+0(FP), DI + MOVQ a+8(FP), SI + MOVQ b+16(FP), BX + _fqSub(0(DI), 0(SI), 0(BX)) + RET + +// func fqMul(c, a, b *fq) +TEXT ·fqMul(SB),0,$0-24 + MOVQ c+0(FP), DI + MOVQ a+8(FP), SI + MOVQ b+16(FP), BX + CHECK_BMI2(LFQMUL, fqMulLegacy, fqMulBmi2) + RET + +// func fqSqr(c, a *fq) +TEXT ·fqSqr(SB),0,$0-16 + MOVQ c+0(FP), DI + MOVQ a+8(FP), SI + CHECK_BMI2(LFQSQR, fqSqrLegacy, fqSqrBmi2) + RET diff --git a/src/circl/ecc/fourq/fq_generic.go b/src/circl/ecc/fourq/fq_generic.go new file mode 100644 index 00000000000..9285e887d78 --- /dev/null +++ b/src/circl/ecc/fourq/fq_generic.go @@ -0,0 +1,30 @@ +package fourq + +func fqAddGeneric(c, a, b *Fq) { + fpAddGeneric(&c[0], &a[0], &b[0]) + fpAddGeneric(&c[1], &a[1], &b[1]) +} + +func fqSubGeneric(c, a, b *Fq) { + fpSubGeneric(&c[0], &a[0], &b[0]) + fpSubGeneric(&c[1], &a[1], &b[1]) +} + +func fqMulGeneric(c, a, b *Fq) { + var a0b0, a0b1, a1b0, a1b1 Fp + fpMulGeneric(&a0b0, &a[0], &b[0]) + fpMulGeneric(&a0b1, &a[0], &b[1]) + fpMulGeneric(&a1b0, &a[1], &b[0]) + fpMulGeneric(&a1b1, &a[1], &b[1]) + fpSubGeneric(&c[0], &a0b0, &a1b1) + fpAddGeneric(&c[1], &a0b1, &a1b0) +} + +func fqSqrGeneric(c, a *Fq) { + var aa0, a01, aa1 Fp + fpSqrGeneric(&aa0, &a[0]) + fpMulGeneric(&a01, &a[0], &a[1]) + fpSqrGeneric(&aa1, &a[1]) + fpSubGeneric(&c[0], &aa0, &aa1) + fpAddGeneric(&c[1], &a01, &a01) +} diff --git a/src/circl/ecc/fourq/fq_noasm.go b/src/circl/ecc/fourq/fq_noasm.go new file mode 100644 index 00000000000..12fc9d6feb4 --- /dev/null +++ b/src/circl/ecc/fourq/fq_noasm.go @@ -0,0 +1,14 @@ +// +build !amd64 purego + +package fourq + +import "crypto/subtle" + +func fqCmov(c, a *Fq, b int) { + subtle.ConstantTimeCopy(b, c[0][:], a[0][:]) + subtle.ConstantTimeCopy(b, c[1][:], a[1][:]) +} +func fqAdd(c, a, b *Fq) { fqAddGeneric(c, a, b) } +func fqSub(c, a, b *Fq) { fqSubGeneric(c, a, b) } +func fqMul(c, a, b *Fq) { fqMulGeneric(c, a, b) } +func fqSqr(c, a *Fq) { fqSqrGeneric(c, a) } diff --git a/src/circl/ecc/fourq/fq_test.go b/src/circl/ecc/fourq/fq_test.go new file mode 100644 index 00000000000..54587b067ea --- /dev/null +++ b/src/circl/ecc/fourq/fq_test.go @@ -0,0 +1,359 @@ +package fourq + +import ( + "crypto/rand" + "math/big" + "testing" + + "circl/internal/test" +) + +type tFqAdd = func(z, x, y *Fq) +type tFqSub = func(z, x, y *Fq) +type tFqMul = func(z, x, y *Fq) +type tFqSqr = func(z, x *Fq) + +func TestFqOne(t *testing.T) { + x := &Fq{} + x.setOne() + got0, got1 := x.toBigInt() + want0, want1 := big.NewInt(1), big.NewInt(0) + if got0.Cmp(want0) != 0 { + test.ReportError(t, got0, want0, x) + } + if got1.Cmp(want1) != 0 { + test.ReportError(t, got1, want1, x) + } +} + +func TestFqSign(t *testing.T) { + testTimes := 1 << 9 + x := &Fq{} + P := getModulus() + var P1div2 big.Int + P1div2.Add(P, big.NewInt(1)).Rsh(&P1div2, 1) // (p+1)/2 + + // Verifying Sign(0) = 0 + x.setBigInt(big.NewInt(0), big.NewInt(0)) + got := fqSgn(x) + want := 0 + if got != want { + test.ReportError(t, got, want, x) + } + + // Verifying Sign(P) = 0 + x.setBigInt(P, P) + got = fqSgn(x) + want = 0 + if got != want { + test.ReportError(t, got, want, x) + } + + // Verifying Sign( (p+1)/2 ) = -1 + x.setBigInt(&P1div2, &P1div2) + got = fqSgn(x) + want = -1 + if got != want { + test.ReportError(t, got, want, x) + } + + // Verifying x be a non-zero positive + for i := 0; i < testTimes; i++ { + bigX1, _ := rand.Int(rand.Reader, &P1div2) + x.setBigInt(P, bigX1) + got = fqSgn(x) + want = 1 + if got != want { + test.ReportError(t, got, want, x) + } + } + // Verifying x be a non-zero positive + for i := 0; i < testTimes; i++ { + bigX0, _ := rand.Int(rand.Reader, &P1div2) + bigX1, _ := rand.Int(rand.Reader, &P1div2) + x.setBigInt(bigX0, bigX1) + got = fqSgn(x) + want = 1 + if got != want { + test.ReportError(t, got, want, x) + } + } + // Verifying x be a non-zero negative + for i := 0; i < testTimes; i++ { + bigX1, _ := rand.Int(rand.Reader, &P1div2) + bigX1.Add(bigX1, &P1div2) + x.setBigInt(P, bigX1) + got = fqSgn(x) + want = -1 + if got != want { + test.ReportError(t, got, want, x) + } + } + // Verifying x be a non-zero negative + for i := 0; i < testTimes; i++ { + bigX0, _ := rand.Int(rand.Reader, &P1div2) + bigX1, _ := rand.Int(rand.Reader, &P1div2) + bigX0.Add(bigX0, &P1div2) + bigX1.Add(bigX1, &P1div2) + x.setBigInt(bigX0, bigX1) + got = fqSgn(x) + want = -1 + if got != want { + test.ReportError(t, got, want, x) + } + } +} + +func TestFqIsZero(t *testing.T) { + x := &Fq{} + P := getModulus() + // Verifying x=0 + x.setBigInt(big.NewInt(0), big.NewInt(0)) + got := x.isZero() + want := true + if got != want { + test.ReportError(t, got, want, x) + } + + // Verifying x=P goes to 0 + x.setBigInt(P, P) + got = x.isZero() + want = true + if got != want { + test.ReportError(t, got, want, x) + } + + // Verifying x!=0 + bigX0, _ := rand.Int(rand.Reader, P) + bigX1, _ := rand.Int(rand.Reader, P) + x.setBigInt(bigX0, bigX1) + got = x.isZero() + want = false + if got != want { + test.ReportError(t, got, want, x) + } +} + +func TestFqNeg(t *testing.T) { + testTimes := 1 << 9 + x, z := &Fq{}, &Fq{} + P := getModulus() + for i := 0; i < testTimes; i++ { + bigX0, _ := rand.Int(rand.Reader, P) + bigX1, _ := rand.Int(rand.Reader, P) + + x.setBigInt(bigX0, bigX1) + fqNeg(z, x) + got0, got1 := z.toBigInt() + + want0 := bigX0.Neg(bigX0) + want1 := bigX1.Neg(bigX1) + want0 = want0.Mod(want0, P) + want1 = want1.Mod(want1, P) + if got0.Cmp(want0) != 0 { + test.ReportError(t, got0, want0, x) + } + if got1.Cmp(want1) != 0 { + test.ReportError(t, got1, want1, x) + } + } +} + +func testFqAdd(t *testing.T, f tFqAdd) { + testTimes := 1 << 9 + x, y, z := &Fq{}, &Fq{}, &Fq{} + P := getModulus() + for i := 0; i < testTimes; i++ { + bigX0, _ := rand.Int(rand.Reader, P) + bigX1, _ := rand.Int(rand.Reader, P) + bigY0, _ := rand.Int(rand.Reader, P) + bigY1, _ := rand.Int(rand.Reader, P) + + x.setBigInt(bigX0, bigX1) + y.setBigInt(bigY0, bigY1) + f(z, x, y) + got0, got1 := z.toBigInt() + + want0 := bigX0.Add(bigX0, bigY0) + want1 := bigX1.Add(bigX1, bigY1) + want0 = want0.Mod(want0, P) + want1 = want1.Mod(want1, P) + + if got0.Cmp(want0) != 0 { + test.ReportError(t, got0, want0, x, y) + } + if got1.Cmp(want1) != 0 { + test.ReportError(t, got1, want1, x, y) + } + } +} + +func testFqSub(t *testing.T, f tFqSub) { + testTimes := 1 << 9 + x, y, z := &Fq{}, &Fq{}, &Fq{} + P := getModulus() + for i := 0; i < testTimes; i++ { + bigX0, _ := rand.Int(rand.Reader, P) + bigX1, _ := rand.Int(rand.Reader, P) + bigY0, _ := rand.Int(rand.Reader, P) + bigY1, _ := rand.Int(rand.Reader, P) + + x.setBigInt(bigX0, bigX1) + y.setBigInt(bigY0, bigY1) + f(z, x, y) + got0, got1 := z.toBigInt() + + want0 := bigX0.Sub(bigX0, bigY0) + want1 := bigX1.Sub(bigX1, bigY1) + want0 = want0.Mod(want0, P) + want1 = want1.Mod(want1, P) + + if got0.Cmp(want0) != 0 { + test.ReportError(t, got0, want0, x, y) + } + if got1.Cmp(want1) != 0 { + test.ReportError(t, got1, want1, x, y) + } + } +} + +func testFqMul(t *testing.T, f tFqMul) { + testTimes := 1 << 9 + x, y, z := &Fq{}, &Fq{}, &Fq{} + P := getModulus() + for i := 0; i < testTimes; i++ { + bigX0, _ := rand.Int(rand.Reader, P) + bigX1, _ := rand.Int(rand.Reader, P) + bigY0, _ := rand.Int(rand.Reader, P) + bigY1, _ := rand.Int(rand.Reader, P) + + x.setBigInt(bigX0, bigX1) + y.setBigInt(bigY0, bigY1) + f(z, x, y) + got0, got1 := z.toBigInt() + + x0y0 := new(big.Int).Mul(bigX0, bigY0) + x0y1 := new(big.Int).Mul(bigX0, bigY1) + x1y0 := new(big.Int).Mul(bigX1, bigY0) + x1y1 := new(big.Int).Mul(bigX1, bigY1) + want0 := x0y0.Sub(x0y0, x1y1) + want1 := x1y0.Add(x1y0, x0y1) + want0 = want0.Mod(want0, P) + want1 = want1.Mod(want1, P) + + if got0.Cmp(want0) != 0 { + test.ReportError(t, got0, want0, x, y) + } + if got1.Cmp(want1) != 0 { + test.ReportError(t, got1, want1, x, y) + } + } +} + +func testFqSqr(t *testing.T, f tFqSqr) { + testTimes := 1 << 9 + x, z := &Fq{}, &Fq{} + P := getModulus() + for i := 0; i < testTimes; i++ { + bigX0, _ := rand.Int(rand.Reader, P) + bigX1, _ := rand.Int(rand.Reader, P) + + x.setBigInt(bigX0, bigX1) + f(z, x) + got0, got1 := z.toBigInt() + + x0x0 := new(big.Int).Mul(bigX0, bigX0) + x0x1 := new(big.Int).Mul(bigX0, bigX1) + x1x1 := new(big.Int).Mul(bigX1, bigX1) + want0 := x0x0.Sub(x0x0, x1x1) + want1 := x0x1.Lsh(x0x1, 1) + want0 = want0.Mod(want0, P) + want1 = want1.Mod(want1, P) + + if got0.Cmp(want0) != 0 { + test.ReportError(t, got0, want0, x) + } + if got1.Cmp(want1) != 0 { + test.ReportError(t, got1, want1, x) + } + } +} + +func TestFqInv(t *testing.T) { + testTimes := 1 << 9 + x, z := &Fq{}, &Fq{} + P := getModulus() + for i := 0; i < testTimes; i++ { + bigX0, _ := rand.Int(rand.Reader, P) + bigX1, _ := rand.Int(rand.Reader, P) + + x.setBigInt(bigX0, bigX1) + fqInv(z, x) + got0, got1 := z.toBigInt() + + x0x0 := new(big.Int).Mul(bigX0, bigX0) + x1x1 := new(big.Int).Mul(bigX1, bigX1) + inv := x0x0.Add(x0x0, x1x1) + inv.ModInverse(inv, P) + want0 := bigX0.Mul(bigX0, inv) + want1 := bigX1.Mul(bigX1, inv).Neg(bigX1) + want0 = want0.Mod(want0, P) + want1 = want1.Mod(want1, P) + + if got0.Cmp(want0) != 0 { + test.ReportError(t, got0, want0, x) + } + if got1.Cmp(want1) != 0 { + test.ReportError(t, got1, want1, x) + } + } +} + +func TestFqGeneric(t *testing.T) { + t.Run("Add", func(t *testing.T) { testFqAdd(t, fqAddGeneric) }) + t.Run("Sub", func(t *testing.T) { testFqSub(t, fqSubGeneric) }) + t.Run("Mul", func(t *testing.T) { testFqMul(t, fqMulGeneric) }) + t.Run("Sqr", func(t *testing.T) { testFqSqr(t, fqSqrGeneric) }) +} + +func TestFqNative(t *testing.T) { + t.Run("Add", func(t *testing.T) { testFqAdd(t, fqAdd) }) + t.Run("Sub", func(t *testing.T) { testFqSub(t, fqSub) }) + t.Run("Mul", func(t *testing.T) { testFqMul(t, fqMul) }) + t.Run("Sqr", func(t *testing.T) { testFqSqr(t, fqSqr) }) +} + +func BenchmarkFq(b *testing.B) { + x, y, z := &Fq{}, &Fq{}, &Fq{} + + b.Run("Add", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fqAdd(z, x, y) + } + }) + b.Run("Sub", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fqSub(z, x, y) + } + }) + b.Run("Mul", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fqMul(z, x, y) + } + }) + b.Run("Sqr", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fqSqr(z, x) + } + }) + b.Run("Inv", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fqInv(z, x) + } + }) + b.Run("Sqrt", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fqSqrt(z, x, y, 1) + } + }) +} diff --git a/src/circl/ecc/fourq/params.go b/src/circl/ecc/fourq/params.go new file mode 100644 index 00000000000..d49d3f14ee8 --- /dev/null +++ b/src/circl/ecc/fourq/params.go @@ -0,0 +1,49 @@ +package fourq + +//All values in little endian +var ( + + // prime is the modulus 2^127-1 + prime = [2]uint64{ + 0xFFFFFFFFFFFFFFFF, 0x7FFFFFFFFFFFFFFF, + } + + // orderGenerator is the size of the largest subgroup. + orderGenerator = [4]uint64{ + 0x2fb2540ec7768ce7, 0xdfbd004dfe0f7999, + 0xf05397829cbc14e5, 0x0029cbc14e5e0a72, + } + + paramD = Fq{ + Fp{ + 0x42, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xe4, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + Fp{ + 0x8d, 0x0c, 0xfc, 0xf1, 0x88, 0x14, 0x82, 0xb3, + 0xfc, 0xe0, 0x57, 0x66, 0x84, 0x2f, 0x47, 0x5e, + }, + } + + genX = Fq{ + Fp{ + 0xaa, 0x33, 0x38, 0x7b, 0xad, 0x92, 0x65, 0x28, + 0x05, 0xb3, 0x2f, 0x7c, 0x23, 0x72, 0x34, 0x1a, + }, + Fp{ + 0xf6, 0x77, 0xac, 0x60, 0xb3, 0x9f, 0x86, 0x96, + 0x9c, 0xaa, 0x78, 0x28, 0x3f, 0x55, 0x1f, 0x1e, + }, + } + + genY = Fq{ + Fp{ + 0x87, 0xb2, 0xcb, 0x2b, 0x46, 0xa2, 0x24, 0xb9, + 0x5a, 0x78, 0x20, 0xa1, 0x9b, 0xee, 0x3f, 0x0e, + }, + Fp{ + 0x5c, 0x8b, 0x4c, 0x84, 0x44, 0xc3, 0xa7, 0x49, + 0x42, 0x02, 0x0e, 0x63, 0xf8, 0x4a, 0x1c, 0x6e, + }, + } +) diff --git a/src/circl/ecc/fourq/point.go b/src/circl/ecc/fourq/point.go new file mode 100644 index 00000000000..e82627098f5 --- /dev/null +++ b/src/circl/ecc/fourq/point.go @@ -0,0 +1,346 @@ +package fourq + +import ( + "crypto/subtle" + "encoding/binary" + "math/bits" +) + +type pointR1 struct { + X, Y, Z, Ta, Tb Fq // (x,y,z,t=ta*tb) +} +type pointR3 struct { + addYX Fq // y + x + subYX Fq // y - x + dt2 Fq // 2*d*t +} +type pointR2 struct { + pointR3 + z2 Fq // 2 * z +} + +// subYDiv16 update x = (x - y) / 16. +func subYDiv16(x *[5]uint64, y int64) { + s := uint64(y >> 63) + x0, b0 := bits.Sub64((*x)[0], uint64(y), 0) + x1, b1 := bits.Sub64((*x)[1], s, b0) + x2, b2 := bits.Sub64((*x)[2], s, b1) + x3, b3 := bits.Sub64((*x)[3], s, b2) + x4, _ := bits.Sub64((*x)[4], s, b3) + (*x)[0] = (x0 >> 4) | (x1 << 60) + (*x)[1] = (x1 >> 4) | (x2 << 60) + (*x)[2] = (x2 >> 4) | (x3 << 60) + (*x)[3] = (x3 >> 4) | (x4 << 60) + (*x)[4] = (x4 >> 4) +} + +// condAddOrderN updates x = x+order if x is even, otherwise x remains unchanged. +func condAddOrderN(x *[5]uint64) { + var o [4]uint64 + isOdd := (x[0] & 0x1) - 1 + for i := range orderGenerator { + o[i] = isOdd & orderGenerator[i] + } + x0, c0 := bits.Add64((*x)[0], o[0], 0) + x1, c1 := bits.Add64((*x)[1], o[1], c0) + x2, c2 := bits.Add64((*x)[2], o[2], c1) + x3, c3 := bits.Add64((*x)[3], o[3], c2) + x4, _ := bits.Add64((*x)[4], 0, c3) + (*x)[0] = x0 + (*x)[1] = x1 + (*x)[2] = x2 + (*x)[3] = x3 + (*x)[4] = x4 +} + +func recodeScalar(d *[65]int8, k *[32]byte) { + var m [5]uint64 + m[0] = binary.LittleEndian.Uint64(k[0:8]) + m[1] = binary.LittleEndian.Uint64(k[8:16]) + m[2] = binary.LittleEndian.Uint64(k[16:24]) + m[3] = binary.LittleEndian.Uint64(k[24:32]) + condAddOrderN(&m) + for i := 0; i < 64; i++ { + d[i] = int8((m[0] & 0x1f) - 16) + subYDiv16(&m, int64(d[i])) + } + d[64] = int8(m[0]) +} + +func (P *pointR1) oddMultiples(T *[8]pointR2) { + var _2P, R pointR1 + var _p2P pointR2 + _2P.copy(P) + _2P.double() + _p2P.FromR1(&_2P) + R.copy(P) + T[0].FromR1(P) + for i := 1; i < 8; i++ { + R.add(&_p2P) + T[i].FromR1(&R) + } +} + +// scalarMult calculates P = k*Q. +func (P *pointR1) ScalarMult(k *[32]byte, Q *pointR1) { + var TabQ [8]pointR2 + var S pointR2 + var d [65]int8 + Q.oddMultiples(&TabQ) + recodeScalar(&d, k) + P.SetIdentity() + for i := 64; i >= 0; i-- { + P.double() + P.double() + P.double() + P.double() + mask := d[i] >> 7 + absDi := (d[i] + mask) ^ mask + inx := int((absDi - 1) >> 1) + sig := int((d[i] >> 7) & 0x1) + for j := range TabQ { + S.cmov(&TabQ[j], int((uint64(uint32(inx^j))-1)>>63)) + } + S.cneg(sig) + P.add(&S) + } +} + +// absolute returns always a positive value. +func absolute(x int32) int32 { + mask := x >> 31 + return (x + mask) ^ mask +} + +// div2subY update x = (x/2) - y. +func div2subY(x *[5]uint64, y int64) { + s := uint64(y >> 63) + x0 := (*x)[0] + x1 := (*x)[1] + x2 := (*x)[2] + x3 := (*x)[3] + x0 = (x0 >> 1) | (x1 << 63) + x1 = (x1 >> 1) | (x2 << 63) + x2 = (x2 >> 1) | (x3 << 63) + x3 = (x3 >> 1) + + x0, b0 := bits.Sub64(x0, uint64(y), 0) + x1, b1 := bits.Sub64(x1, s, b0) + x2, b2 := bits.Sub64(x2, s, b1) + x3, _ = bits.Sub64(x3, s, b2) + (*x)[0] = x0 + (*x)[1] = x1 + (*x)[2] = x2 + (*x)[3] = x3 +} + +// mLSBRecoding is the odd-only modified LSB-set. +// +// Reference: +// "Efficient and secure algorithms for GLV-based scalar multiplication and +// their implementation on GLV–GLS curves" by (Faz-Hernandez et al.) +// http://doi.org/10.1007/s13389-014-0085-7. +func mLSBRecoding(L []int8, k []byte) { + const e = (fxT + fxW*fxV - 1) / (fxW * fxV) + const d = e * fxV + const l = d * fxW + if len(L) == (l + 1) { + var m [5]uint64 + m[0] = binary.LittleEndian.Uint64(k[0:8]) + m[1] = binary.LittleEndian.Uint64(k[8:16]) + m[2] = binary.LittleEndian.Uint64(k[16:24]) + m[3] = binary.LittleEndian.Uint64(k[24:32]) + condAddOrderN(&m) + + L[d-1] = 1 + for i := 0; i < d-1; i++ { + kip1 := (m[(i+1)/64] >> (uint(i+1) % 64)) & 0x1 + L[i] = int8(kip1<<1) - 1 + } + { // right-shift by d + const right = (d % 64) + const left = 64 - (d % 64) + const lim = (5*64 - d) / 64 + const j = d / 64 + for i := 0; i < lim; i++ { + m[i] = (m[i+j] >> right) | (m[i+j+1] << left) + } + m[lim] = m[lim+j] >> right + } + for i := d; i < l; i++ { + L[i] = L[i%d] * int8(m[0]&0x1) + div2subY(&m, int64(L[i]>>1)) + } + L[l] = int8(m[0]) + } +} + +func (P *pointR1) ScalarBaseMult(scalar *[Size]byte) { + var S pointR3 + const e = (fxT + fxW*fxV - 1) / (fxW * fxV) + const d = e * fxV + const l = d * fxW + + var L [l + 1]int8 + mLSBRecoding(L[:], scalar[:]) + P.SetIdentity() + for ii := e - 1; ii >= 0; ii-- { + P.double() + for j := 0; j < fxV; j++ { + dig := L[fxW*d-j*e+ii-e] + for i := (fxW-1)*d - j*e + ii - e; i >= (2*d - j*e + ii - e); i = i - d { + dig = 2*dig + L[i] + } + idx := absolute(int32(dig)) + sig := L[d-j*e+ii-e] + Tabj := &tableBaseFixed[fxV-j-1] + for k := 0; k < fx2w1; k++ { + S.cmov(&Tabj[k], subtle.ConstantTimeEq(int32(k), idx)) + } + S.cneg(subtle.ConstantTimeEq(int32(sig), -1)) + P.mixAdd(&S) + } + } +} + +func (P *pointR1) copy(Q *pointR1) { + fqCopy(&P.X, &Q.X) + fqCopy(&P.Y, &Q.Y) + fqCopy(&P.Ta, &Q.Ta) + fqCopy(&P.Tb, &Q.Tb) + fqCopy(&P.Z, &Q.Z) +} + +func (P *pointR1) SetIdentity() { + P.X.setZero() + P.Y.setOne() + P.Ta.setZero() + P.Tb.setZero() + P.Z.setOne() +} + +func (P *pointR1) IsIdentity() bool { + t0, t1 := &Fq{}, &Fq{} + fqMul(t0, &P.Ta, &P.Tb) + fqSub(t1, &P.Y, &P.Z) + return P.X.isZero() && t0.isZero() && t1.isZero() +} + +func (P *pointR1) ToAffine() { + fqInv(&P.Z, &P.Z) + fqMul(&P.X, &P.X, &P.Z) + fqMul(&P.Y, &P.Y, &P.Z) + fqMul(&P.Ta, &P.X, &P.Y) + P.Tb.setOne() + P.Z.setOne() +} + +// Marshal encodes a point P into out buffer. +func (P *Point) Marshal(out *[Size]byte) { + P.Y.toBytes(out[:]) + // b=0 if x is positive or zero + // b=1 if x is negative + b := (1 - fqSgn(&P.X)) >> 1 + out[Size-1] |= byte(b) << 7 +} + +// Unmarshal retrieves a point P from the input buffer. On success, returns true. +func (P *Point) Unmarshal(in *[Size]byte) bool { + s := in[Size-1] >> 7 + in[Size-1] &= 0x7F + if ok := P.Y.fromBytes(in[:]); !ok { + return ok + } + in[Size-1] |= s << 7 + + t0, t1, one := &Fq{}, &Fq{}, &Fq{} + one.setOne() + fqSqr(t0, &P.Y) // t0 = y^2 + fqMul(t1, t0, ¶mD) // t1 = d*y^2 + fqSub(t0, t0, one) // t0 = y^2 - 1 + fqAdd(t1, t1, one) // t1 = d*y^2 + 1 + fqSqrt(&P.X, t0, t1, 1-2*int(s)) // x = sqrt(t0/t1) + + if !P.IsOnCurve() { + fpNeg(&P.X[1], &P.X[1]) + } + return true +} + +func (P *pointR1) IsOnCurve() bool { + t0, lhs, rhs := &Fq{}, &Fq{}, &Fq{} + + fqAdd(t0, &P.Y, &P.X) // t0 = y + x + fqSub(lhs, &P.Y, &P.X) // lhs = y - x + fqMul(lhs, lhs, t0) // lhs = y^2 - x^2 + fqMul(rhs, &P.X, &P.Y) // rhs = xy + fqSqr(rhs, rhs) // rhs = x^2y^2 + fqMul(rhs, rhs, ¶mD) // rhs = dx^2y^2 + t0.setOne() // t0 = 1 + fqAdd(rhs, rhs, t0) // rhs = 1 + dx^2y^2 + fqSub(t0, lhs, rhs) // t0 = -x^2 + y^2 - (1 + dx^2y^2) + return t0.isZero() +} + +func (P *pointR1) isEqual(Q *pointR1) bool { + l, r := &Fq{}, &Fq{} + fqMul(l, &P.X, &Q.Z) + fqMul(r, &Q.X, &P.Z) + fqSub(l, l, r) + b := l.isZero() + fqMul(l, &P.Y, &Q.Z) + fqMul(r, &Q.Y, &P.Z) + fqSub(l, l, r) + b = b && l.isZero() + fqMul(l, &P.Ta, &P.Tb) + fqMul(l, l, &Q.Z) + fqMul(r, &Q.Ta, &Q.Tb) + fqMul(r, r, &P.Z) + fqSub(l, l, r) + b = b && l.isZero() + return b +} + +func (P *pointR1) ClearCofactor() { + var Q pointR2 + Q.FromR1(P) + P.double() + P.add(&Q) + P.double() + P.double() + P.double() + P.double() + P.add(&Q) + P.double() + P.double() + P.double() +} + +func (P *pointR2) FromR1(Q *pointR1) { + fqAdd(&P.addYX, &Q.Y, &Q.X) + fqSub(&P.subYX, &Q.Y, &Q.X) + fqAdd(&P.z2, &Q.Z, &Q.Z) + fqMul(&P.dt2, &Q.Ta, &Q.Tb) + fqMul(&P.dt2, &P.dt2, ¶mD) + fqAdd(&P.dt2, &P.dt2, &P.dt2) +} + +func (P *pointR2) cmov(Q *pointR2, b int) { + P.pointR3.cmov(&Q.pointR3, b) + fqCmov(&P.z2, &Q.z2, b) +} + +func (P *pointR3) cneg(b int) { + var t Fq + fqCopy(&t, &P.addYX) + fqCmov(&P.addYX, &P.subYX, b) + fqCmov(&P.subYX, &t, b) + fqNeg(&t, &P.dt2) + fqCmov(&P.dt2, &t, b) +} + +func (P *pointR3) cmov(Q *pointR3, b int) { + fqCmov(&P.addYX, &Q.addYX, b) + fqCmov(&P.subYX, &Q.subYX, b) + fqCmov(&P.dt2, &Q.dt2, b) +} diff --git a/src/circl/ecc/fourq/point_amd64.go b/src/circl/ecc/fourq/point_amd64.go new file mode 100644 index 00000000000..854f0c13ef3 --- /dev/null +++ b/src/circl/ecc/fourq/point_amd64.go @@ -0,0 +1,35 @@ +// +build amd64,!purego + +package fourq + +import "unsafe" + +const ( // constants used in assembly implementation + _x = unsafe.Offsetof(pointR1{}.X) + _y = unsafe.Offsetof(pointR1{}.Y) + _z = unsafe.Offsetof(pointR1{}.Z) + _ta = unsafe.Offsetof(pointR1{}.Ta) + _tb = unsafe.Offsetof(pointR1{}.Tb) + _addYXR2 = unsafe.Offsetof(pointR2{}.addYX) + _subYXR2 = unsafe.Offsetof(pointR2{}.subYX) + _z2R2 = unsafe.Offsetof(pointR2{}.z2) + _dt2R2 = unsafe.Offsetof(pointR2{}.dt2) + _addYXR3 = unsafe.Offsetof(pointR3{}.addYX) + _subYXR3 = unsafe.Offsetof(pointR3{}.subYX) + _dt2R3 = unsafe.Offsetof(pointR3{}.dt2) + _ = _x + _y + _z + _ta + _tb + _addYXR2 + _subYXR2 + + _z2R2 + _dt2R2 + _addYXR3 + _subYXR3 + _dt2R3 +) + +func (P *pointR1) double() { doubleAmd64(P) } +func (P *pointR1) add(Q *pointR2) { addAmd64(P, Q) } +func (P *pointR1) mixAdd(Q *pointR3) { mixAddAmd64(P, Q) } + +//go:noescape +func doubleAmd64(P *pointR1) + +//go:noescape +func addAmd64(P *pointR1, Q *pointR2) + +//go:noescape +func mixAddAmd64(P *pointR1, Q *pointR3) diff --git a/src/circl/ecc/fourq/point_amd64.h b/src/circl/ecc/fourq/point_amd64.h new file mode 100644 index 00000000000..b87c293894a --- /dev/null +++ b/src/circl/ecc/fourq/point_amd64.h @@ -0,0 +1,93 @@ +#define doubleLeg \ + _fqAdd(e,Px,Py) \ + _fqSqrLeg(a,Px) \ + _fqSqrLeg(b,Py) \ + _fqSqrLeg(c,Pz) \ + _fqAdd(c,c,c) \ + _fqAdd(d,a,b) \ + _fqSqrLeg(e,e) \ + _fqSub(e,e,d) \ + _fqSub(f,b,a) \ + _fqSub(g,c,f) \ + _fqMulLeg(Pz,f,g) \ + _fqMulLeg(Px,e,g) \ + _fqMulLeg(Py,d,f) + +#define doubleBmi2 \ + _fqAdd(e,Px,Py) \ + _fqSqrBmi2(a,Px) \ + _fqSqrBmi2(b,Py) \ + _fqSqrBmi2(c,Pz) \ + _fqAdd(c,c,c) \ + _fqAdd(d,a,b) \ + _fqSqrBmi2(e,e) \ + _fqSub(e,e,d) \ + _fqSub(f,b,a) \ + _fqSub(g,c,f) \ + _fqMulBmi2(Pz,f,g) \ + _fqMulBmi2(Px,e,g) \ + _fqMulBmi2(Py,d,f) + +#define addLeg \ + _fqMulLeg(c, Pta, Ptb) \ + _fqSub(h, b, a) \ + _fqAdd(b, b, a) \ + _fqMulLeg(a, h, subYX) \ + _fqMulLeg(b, b, addYX) \ + _fqSub(e, b, a) \ + _fqAdd(h, b, a) \ + _fqMulLeg(d, Pz, z2) \ + _fqMulLeg(c, c, dt2) \ + _fqSub(f, d, c) \ + _fqAdd(g, d, c) \ + _fqMulLeg(Pz, f, g) \ + _fqMulLeg(Px, e, f) \ + _fqMulLeg(Py, g, h) + +#define addBmi2 \ + _fqMulBmi2(c, Pta, Ptb) \ + _fqSub(h, b, a) \ + _fqAdd(b, b, a) \ + _fqMulBmi2(a, h, subYX) \ + _fqMulBmi2(b, b, addYX) \ + _fqSub(e, b, a) \ + _fqAdd(h, b, a) \ + _fqMulBmi2(d, Pz, z2) \ + _fqMulBmi2(c, c, dt2) \ + _fqSub(f, d, c) \ + _fqAdd(g, d, c) \ + _fqMulBmi2(Pz, f, g) \ + _fqMulBmi2(Px, e, f) \ + _fqMulBmi2(Py, g, h) + +#define mixAddLeg \ + _fqMulLeg(c, Pta, Ptb) \ + _fqSub(h, b, a) \ + _fqAdd(b, b, a) \ + _fqMulLeg(a, h, subYX) \ + _fqMulLeg(b, b, addYX) \ + _fqSub(e, b, a) \ + _fqAdd(h, b, a) \ + _fqAdd(d, Pz, Pz) \ + _fqMulLeg(c, c, dt2) \ + _fqSub(f, d, c) \ + _fqAdd(g, d, c) \ + _fqMulLeg(Pz, f, g) \ + _fqMulLeg(Px, e, f) \ + _fqMulLeg(Py, g, h) + +#define mixAddBmi2 \ + _fqMulBmi2(c, Pta, Ptb) \ + _fqSub(h, b, a) \ + _fqAdd(b, b, a) \ + _fqMulBmi2(a, h, subYX) \ + _fqMulBmi2(b, b, addYX) \ + _fqSub(e, b, a) \ + _fqAdd(h, b, a) \ + _fqAdd(d, Pz, Pz) \ + _fqMulBmi2(c, c, dt2) \ + _fqSub(f, d, c) \ + _fqAdd(g, d, c) \ + _fqMulBmi2(Pz, f, g) \ + _fqMulBmi2(Px, e, f) \ + _fqMulBmi2(Py, g, h) diff --git a/src/circl/ecc/fourq/point_amd64.s b/src/circl/ecc/fourq/point_amd64.s new file mode 100644 index 00000000000..f4dd5dd5e6a --- /dev/null +++ b/src/circl/ecc/fourq/point_amd64.s @@ -0,0 +1,112 @@ +// +build amd64,!purego + +#include "go_asm.h" +#include "fq_amd64.h" +#include "point_amd64.h" + +// func doubleAmd64(P *pointR1) +TEXT ·doubleAmd64(SB),0,$0-8 + MOVQ P+0(FP), DI + #define Px const__x +0(DI) + #define Py const__y +0(DI) + #define Pz const__z +0(DI) + #define Pta const__ta+0(DI) + #define Ptb const__tb+0(DI) + #define a Px + #define b Py + #define c Pz + #define d Pta + #define e Ptb + #define f b + #define g a + CHECK_BMI2(LDOUBLE, doubleLeg, doubleBmi2) + #undef Px + #undef Py + #undef Pz + #undef Pta + #undef Ptb + #undef a + #undef b + #undef c + #undef d + #undef e + #undef f + #undef g + +// func addAmd64(P *pointR1, R *pointR2) +TEXT ·addAmd64(SB),0,$32-16 + MOVQ P+0(FP), DI + MOVQ Q+8(FP), SI + #define addYX const__addYXR2+0(SI) + #define subYX const__subYXR2+0(SI) + #define z2 const__z2R2 +0(SI) + #define dt2 const__dt2R2 +0(SI) + #define Px const__x +0(DI) + #define Py const__y +0(DI) + #define Pz const__z +0(DI) + #define Pta const__ta+0(DI) + #define Ptb const__tb+0(DI) + #define a Px + #define b Py + #define c 0(SP) + #define d b + #define e Pta + #define f a + #define g b + #define h Ptb + CHECK_BMI2(LDADD, addLeg, addBmi2) + #undef addYX + #undef subYX + #undef z2 + #undef dt2 + #undef Px + #undef Py + #undef Pz + #undef Pta + #undef Ptb + #undef a + #undef b + #undef c + #undef d + #undef e + #undef f + #undef g + #undef h + +// func mixAddAmd64(P *pointR1, Q *pointR3) +TEXT ·mixAddAmd64(SB),0,$32-16 + MOVQ P+0(FP), DI + MOVQ Q+8(FP), SI + #define addYX const__addYXR3+0(SI) + #define subYX const__subYXR3+0(SI) + #define dt2 const__dt2R3 +0(SI) + #define Px const__x +0(DI) + #define Py const__y +0(DI) + #define Pz const__z +0(DI) + #define Pta const__ta+0(DI) + #define Ptb const__tb+0(DI) + #define a Px + #define b Py + #define c 0(SP) + #define d b + #define e Pta + #define f a + #define g b + #define h Ptb + CHECK_BMI2(LDMIXADD, mixAddLeg, mixAddBmi2) + #undef addYX + #undef subYX + #undef dt2 + #undef Px + #undef Py + #undef Pz + #undef Pta + #undef Ptb + #undef a + #undef b + #undef c + #undef d + #undef e + #undef f + #undef g + #undef h diff --git a/src/circl/ecc/fourq/point_generic.go b/src/circl/ecc/fourq/point_generic.go new file mode 100644 index 00000000000..0a0d455b546 --- /dev/null +++ b/src/circl/ecc/fourq/point_generic.go @@ -0,0 +1,98 @@ +// +build !amd64 purego + +package fourq + +func doubleGeneric(P *pointR1) { + var Px = &P.X + var Py = &P.Y + var Pz = &P.Z + var Pta = &P.Ta + var Ptb = &P.Tb + var a = Px + var b = Py + var c = Pz + var d = Pta + var e = Ptb + var f = b + var g = a + fqAdd(e, Px, Py) + fqSqr(a, Px) + fqSqr(b, Py) + fqSqr(c, Pz) + fqAdd(c, c, c) + fqAdd(d, a, b) + fqSqr(e, e) + fqSub(e, e, d) + fqSub(f, b, a) + fqSub(g, c, f) + fqMul(Pz, f, g) + fqMul(Px, e, g) + fqMul(Py, d, f) +} + +func addGeneric(P *pointR1, Q *pointR2) { + var addYX = &Q.addYX + var subYX = &Q.subYX + var z2 = &Q.z2 + var dt2 = &Q.dt2 + var Px = &P.X + var Py = &P.Y + var Pz = &P.Z + var Pta = &P.Ta + var Ptb = &P.Tb + var a = Px + var b = Py + var c = &Fq{} + var d = b + var e = Pta + var f = a + var g = b + var h = Ptb + fqMul(c, Pta, Ptb) + fqSub(h, b, a) + fqAdd(b, b, a) + fqMul(a, h, subYX) + fqMul(b, b, addYX) + fqSub(e, b, a) + fqAdd(h, b, a) + fqMul(d, Pz, z2) + fqMul(c, c, dt2) + fqSub(f, d, c) + fqAdd(g, d, c) + fqMul(Pz, f, g) + fqMul(Px, e, f) + fqMul(Py, g, h) +} + +func mixAddGeneric(P *pointR1, Q *pointR3) { + var addYX = &Q.addYX + var subYX = &Q.subYX + var dt2 = &Q.dt2 + var Px = &P.X + var Py = &P.Y + var Pz = &P.Z + var Pta = &P.Ta + var Ptb = &P.Tb + var a = Px + var b = Py + var c = &Fq{} + var d = b + var e = Pta + var f = a + var g = b + var h = Ptb + fqMul(c, Pta, Ptb) + fqSub(h, b, a) + fqAdd(b, b, a) + fqMul(a, h, subYX) + fqMul(b, b, addYX) + fqSub(e, b, a) + fqAdd(h, b, a) + fqAdd(d, Pz, Pz) + fqMul(c, c, dt2) + fqSub(f, d, c) + fqAdd(g, d, c) + fqMul(Pz, f, g) + fqMul(Px, e, f) + fqMul(Py, g, h) +} diff --git a/src/circl/ecc/fourq/point_noasm.go b/src/circl/ecc/fourq/point_noasm.go new file mode 100644 index 00000000000..cf7dff0a3a8 --- /dev/null +++ b/src/circl/ecc/fourq/point_noasm.go @@ -0,0 +1,7 @@ +// +build !amd64 purego + +package fourq + +func (P *pointR1) double() { doubleGeneric(P) } +func (P *pointR1) add(Q *pointR2) { addGeneric(P, Q) } +func (P *pointR1) mixAdd(Q *pointR3) { mixAddGeneric(P, Q) } diff --git a/src/circl/ecc/fourq/point_test.go b/src/circl/ecc/fourq/point_test.go new file mode 100644 index 00000000000..61506aa5126 --- /dev/null +++ b/src/circl/ecc/fourq/point_test.go @@ -0,0 +1,265 @@ +package fourq + +import ( + "crypto/rand" + "math/big" + "testing" + + "circl/internal/conv" + "circl/internal/test" +) + +func (P *pointR1) random() { + var k [Size]byte + _, _ = rand.Read(k[:]) + P.ScalarBaseMult(&k) +} + +func TestPointAddition(t *testing.T) { + const testTimes = 1 << 10 + var P, Q pointR1 + _16P := &pointR1{} + S := &pointR2{} + for i := 0; i < testTimes; i++ { + P.random() + _16P.copy(&P) + S.FromR1(&P) + // 16P = 2^4P + for j := 0; j < 4; j++ { + _16P.double() + } + // 16P = P+P...+P + Q.SetIdentity() + for j := 0; j < 16; j++ { + Q.add(S) + } + got := _16P.isEqual(&Q) + want := true + if got != want { + test.ReportError(t, got, want, P) + } + } +} + +func TestOddMultiples(t *testing.T) { + const testTimes = 1 << 10 + var P, Q, R pointR1 + var Tab [8]pointR2 + for i := 0; i < testTimes; i++ { + P.random() + // T = [1P, 3P, 5P, 7P, 9P, 11P, 13P, 15P] + P.oddMultiples(&Tab) + // Q = sum of all T[i] == 64P + Q.SetIdentity() + for j := range Tab { + Q.add(&Tab[j]) + } + // R = (2^6)P == 64P + for j := 0; j < 6; j++ { + R.double() + } + got := Q.isEqual(&R) + want := true + if got != want { + test.ReportError(t, got, want, P) + } + } +} + +func TestScalarMult(t *testing.T) { + const testTimes = 1 << 10 + var P, Q, G pointR1 + var k [Size]byte + + t.Run("0P=0", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + P.random() + Q.ScalarMult(&k, &P) + got := Q.IsIdentity() + want := true + if got != want { + test.ReportError(t, got, want, P) + } + } + }) + t.Run("order*P=0", func(t *testing.T) { + conv.BigInt2BytesLe(k[:], conv.Uint64Le2BigInt(orderGenerator[:])) + for i := 0; i < testTimes; i++ { + P.random() + Q.ScalarMult(&k, &P) + got := Q.IsIdentity() + want := true + if got != want { + test.ReportError(t, got, want, P) + } + } + }) + t.Run("cofactor*P=clear(P)", func(t *testing.T) { + conv.BigInt2BytesLe(k[:], big.NewInt(392)) + for i := 0; i < testTimes; i++ { + P.random() + Q.ScalarMult(&k, &P) + P.ClearCofactor() + got := Q.isEqual(&P) + want := true + if got != want { + test.ReportError(t, got, want, P) + } + } + }) + t.Run("mult", func(t *testing.T) { + G.X = genX + G.Y = genY + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(k[:]) + P.ScalarMult(&k, &G) + Q.ScalarBaseMult(&k) + got := Q.isEqual(&P) + want := true + if got != want { + test.ReportError(t, got, want, k) + } + } + }) +} + +func TestScalar(t *testing.T) { + const testTimes = 1 << 12 + var x, xx [5]uint64 + two256 := big.NewInt(1) + two256.Lsh(two256, 256) + two64 := big.NewInt(1) + two64.Lsh(two64, 64) + bigOrder := conv.Uint64Le2BigInt(orderGenerator[:]) + + t.Run("subYdiv16", func(t *testing.T) { + want := new(big.Int) + for i := 0; i < testTimes; i++ { + bigX, _ := rand.Int(rand.Reader, two256) + conv.BigInt2Uint64Le(xx[:], bigX) + for j := range xx { + x[j] = xx[j] + } + bigY, _ := rand.Int(rand.Reader, two64) + y := bigY.Int64() + bigY.SetInt64(y) + + subYDiv16(&x, y) + got := conv.Uint64Le2BigInt(x[:]) + + want.Sub(bigX, bigY).Rsh(want, 4) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, bigX, y) + } + } + }) + + t.Run("div2subY", func(t *testing.T) { + want := new(big.Int) + for i := 0; i < testTimes; i++ { + bigX, _ := rand.Int(rand.Reader, two256) + conv.BigInt2Uint64Le(xx[:], bigX) + for j := range xx { + x[j] = xx[j] + } + bigY, _ := rand.Int(rand.Reader, two64) + y := bigY.Int64() + bigY.SetInt64(y) + + div2subY(&x, y) + got := conv.Uint64Le2BigInt(x[:]) + + want.Rsh(bigX, 1).Sub(want, bigY) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, bigX, y) + } + } + }) + + t.Run("condAddOrderN", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + bigX, _ := rand.Int(rand.Reader, two256) + conv.BigInt2Uint64Le(xx[:], bigX) + for j := range xx { + x[j] = xx[j] + } + + condAddOrderN(&x) + got := conv.Uint64Le2BigInt(x[:]) + + want := bigX + if want.Bit(0) == 0 { + want.Add(want, bigOrder) + } + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } + }) + + t.Run("recode", func(t *testing.T) { + var k [32]byte + var d [65]int8 + got := new(big.Int) + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(k[:]) + + recodeScalar(&d, &k) + got.SetInt64(0) + for j := len(d) - 1; j >= 0; j-- { + got.Lsh(got, 4).Add(got, big.NewInt(int64(d[j]))) + } + + want := conv.BytesLe2BigInt(k[:]) + if want.Bit(0) == 0 { + want.Add(want, bigOrder) + } + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } + }) +} + +func BenchmarkPoint(b *testing.B) { + var P, R pointR1 + var Q pointR2 + var k [Size]byte + + _, _ = rand.Read(k[:]) + + P.random() + R.random() + Q.FromR1(&R) + R.random() + + b.Run("affine", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.ToAffine() + } + }) + b.Run("double", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.double() + } + }) + b.Run("add", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.add(&Q) + } + }) + b.Run("scmulBase", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.ScalarBaseMult(&k) + } + }) + b.Run("scmul", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.ScalarMult(&k, &R) + } + }) +} diff --git a/src/circl/ecc/fourq/tableBase.go b/src/circl/ecc/fourq/tableBase.go new file mode 100644 index 00000000000..34785d65596 --- /dev/null +++ b/src/circl/ecc/fourq/tableBase.go @@ -0,0 +1,131 @@ +package fourq + +const ( + // This is the size of the largest scalar k = 2^256 - 1 + order + fxT = 257 + // Number of tables + fxV = 2 + // Window size + fxW = 3 + // Number of points per table + fx2w1 = (1 << (uint(fxW) - 1)) +) + +var tableBaseFixed = [fxV][fx2w1]pointR3{ + { + { + addYX: Fq{ + [SizeFp]byte{0x31, 0xe6, 0x03, 0xa7, 0xf3, 0x34, 0x8a, 0xe1, 0x5f, 0x2b, 0x50, 0x1d, 0xbf, 0x60, 0x74, 0x28}, + [SizeFp]byte{0x53, 0x03, 0xf9, 0xe4, 0xf7, 0x62, 0x2e, 0xe0, 0xde, 0xac, 0x86, 0x8b, 0x37, 0xa0, 0x3b, 0x0c}, + }, + subYX: Fq{ + [SizeFp]byte{0xdc, 0x7e, 0x93, 0xb0, 0x98, 0x0f, 0xbf, 0x90, 0x55, 0xc5, 0xf0, 0x24, 0x78, 0x7c, 0x0b, 0x74}, + [SizeFp]byte{0x66, 0x13, 0xa0, 0x23, 0x91, 0x23, 0x21, 0xb3, 0xa5, 0x57, 0x95, 0x3a, 0xb9, 0xf5, 0xfc, 0x4f}, + }, + dt2: Fq{ + [SizeFp]byte{0xbb, 0x42, 0xda, 0xab, 0xcb, 0xfc, 0x7a, 0x29, 0xc6, 0x97, 0x6c, 0x55, 0x37, 0xd1, 0x48, 0x59}, + [SizeFp]byte{0x4c, 0x68, 0x30, 0x33, 0x39, 0x9a, 0x18, 0xa8, 0x27, 0x1f, 0x34, 0x0a, 0x72, 0x2b, 0xaf, 0x0c}, + }, + }, + { + addYX: Fq{ + [SizeFp]byte{0x6a, 0x23, 0x5d, 0xcf, 0x2e, 0xf2, 0x8b, 0x5f, 0x5a, 0x2a, 0x6f, 0xa0, 0xef, 0xa7, 0x76, 0x32}, + [SizeFp]byte{0x57, 0xad, 0x0b, 0x1a, 0x60, 0xc4, 0x43, 0xdf, 0x6a, 0xbc, 0x31, 0xe6, 0x55, 0xd5, 0xc4, 0x4b}, + }, + subYX: Fq{ + [SizeFp]byte{0xf7, 0xab, 0xbf, 0xd2, 0x55, 0x8c, 0x13, 0xfe, 0xca, 0x64, 0x65, 0x03, 0xa9, 0x93, 0x29, 0x64}, + [SizeFp]byte{0xb5, 0x9b, 0xdd, 0x17, 0xb1, 0x5a, 0x0e, 0xbc, 0x22, 0x41, 0x77, 0x11, 0x25, 0x6f, 0xa1, 0x68}, + }, + dt2: Fq{ + [SizeFp]byte{0xb6, 0x76, 0xfe, 0x14, 0xa1, 0x31, 0x4e, 0xc8, 0xc4, 0x5f, 0x2c, 0x8d, 0x05, 0x23, 0xa8, 0x16}, + [SizeFp]byte{0x9d, 0x45, 0x6d, 0x97, 0xd7, 0x0a, 0x22, 0x5a, 0x7a, 0x71, 0x2c, 0x06, 0x6d, 0xeb, 0x9a, 0x7d}, + }, + }, + { + addYX: Fq{ + [SizeFp]byte{0x46, 0x6b, 0x69, 0xeb, 0x7f, 0x13, 0x9a, 0x2b, 0x40, 0x0a, 0xc1, 0xdc, 0xfa, 0x66, 0xf0, 0x39}, + [SizeFp]byte{0x77, 0x9c, 0xd9, 0x0a, 0x0e, 0x65, 0xb3, 0xc6, 0xbd, 0x1d, 0x7f, 0xe0, 0xf8, 0x5a, 0x4f, 0x55}, + }, + subYX: Fq{ + [SizeFp]byte{0xc1, 0x88, 0xb5, 0x09, 0xd0, 0xc5, 0x63, 0x62, 0x8e, 0x0e, 0x6b, 0xeb, 0xfd, 0x49, 0x27, 0x7a}, + [SizeFp]byte{0x8c, 0x38, 0x5e, 0x06, 0x05, 0x17, 0x5e, 0xe4, 0x2f, 0xda, 0x4b, 0x9f, 0x94, 0x68, 0x4d, 0x5b}, + }, + dt2: Fq{ + [SizeFp]byte{0x6f, 0x84, 0xf3, 0x3f, 0x08, 0x26, 0x0c, 0xb4, 0xfa, 0xc7, 0x9e, 0xe6, 0x2f, 0xef, 0x3f, 0x53}, + [SizeFp]byte{0x47, 0xd1, 0x71, 0x88, 0x9d, 0x2e, 0xcd, 0x4e, 0x94, 0x03, 0x49, 0xbe, 0x0b, 0x1a, 0x91, 0x6d}, + }, + }, + { + addYX: Fq{ + [SizeFp]byte{0x73, 0x9b, 0x3b, 0x99, 0x69, 0x39, 0x8c, 0xda, 0xf2, 0x3d, 0xba, 0xad, 0x7c, 0x75, 0xeb, 0x26}, + [SizeFp]byte{0x18, 0x56, 0xe6, 0xa9, 0xa4, 0x10, 0xf3, 0x13, 0x33, 0x25, 0x04, 0x60, 0x2a, 0x00, 0x62, 0x18}, + }, + subYX: Fq{ + [SizeFp]byte{0x6d, 0xcd, 0x87, 0xca, 0xce, 0xd1, 0xda, 0xb4, 0x5f, 0xd9, 0x0c, 0x21, 0x45, 0x3d, 0xf4, 0x38}, + [SizeFp]byte{0xc1, 0xe5, 0x03, 0xa6, 0x64, 0x57, 0x30, 0x13, 0xc7, 0xf8, 0xaa, 0xf2, 0xcd, 0x8f, 0x57, 0x6e}, + }, + dt2: Fq{ + [SizeFp]byte{0x05, 0x02, 0xcb, 0x13, 0xd6, 0x24, 0xa0, 0x20, 0xa9, 0xe0, 0xe0, 0xdd, 0x90, 0x6f, 0xd0, 0x7c}, + [SizeFp]byte{0xfc, 0x91, 0x59, 0x14, 0x5b, 0xa4, 0x8e, 0xf5, 0xe1, 0xc0, 0x4c, 0x82, 0xce, 0xe2, 0xf6, 0x41}, + }, + }, + }, + { + { + addYX: Fq{ + [SizeFp]byte{0x60, 0x31, 0xb8, 0xc2, 0xb0, 0x7f, 0x36, 0xdb, 0x8c, 0xe8, 0xfc, 0x0a, 0x1b, 0xf3, 0x2e, 0x21}, + [SizeFp]byte{0x5e, 0x89, 0xd9, 0xf0, 0xfc, 0x47, 0xe5, 0x20, 0x10, 0xe6, 0x26, 0xf2, 0x67, 0xdb, 0xcc, 0x42}, + }, + subYX: Fq{ + [SizeFp]byte{0x0e, 0x3b, 0xad, 0x12, 0x15, 0xa3, 0x40, 0x9e, 0x73, 0x97, 0x99, 0x43, 0x28, 0x74, 0xfe, 0x6d}, + [SizeFp]byte{0x92, 0x93, 0x68, 0xe8, 0xf5, 0xaf, 0x70, 0x4f, 0x1b, 0x4a, 0x36, 0x13, 0x21, 0x89, 0xee, 0x5f}, + }, + dt2: Fq{ + [SizeFp]byte{0x41, 0xc5, 0x53, 0xc7, 0xf7, 0xa4, 0x99, 0x82, 0x00, 0x49, 0x7f, 0x5f, 0xbe, 0x40, 0xc2, 0x7f}, + [SizeFp]byte{0xa6, 0x22, 0xe3, 0x40, 0x6e, 0xc7, 0xee, 0x4c, 0xff, 0x36, 0xf4, 0x01, 0x4b, 0x52, 0x54, 0x77}, + }, + }, + { + addYX: Fq{ + [SizeFp]byte{0x35, 0x58, 0xef, 0x56, 0xbc, 0xbb, 0xdf, 0xf9, 0x59, 0x2e, 0xf2, 0x2f, 0x4d, 0x89, 0xd8, 0x1d}, + [SizeFp]byte{0x6c, 0xde, 0xe6, 0xde, 0x89, 0x39, 0x24, 0x3a, 0xce, 0x8e, 0xf5, 0x46, 0x33, 0x2b, 0xa8, 0x12}, + }, + subYX: Fq{ + [SizeFp]byte{0x60, 0x72, 0x41, 0xb1, 0x06, 0xaf, 0x7d, 0x08, 0x6e, 0xee, 0xb7, 0x5e, 0x23, 0x95, 0xbf, 0x79}, + [SizeFp]byte{0x34, 0x42, 0xdc, 0x3a, 0x73, 0x96, 0x94, 0xbe, 0xb9, 0x5d, 0xb4, 0x4b, 0x10, 0x48, 0x5e, 0x25}, + }, + dt2: Fq{ + [SizeFp]byte{0x44, 0xff, 0xf4, 0x38, 0x90, 0x9d, 0xf4, 0x14, 0x9f, 0x4d, 0x5c, 0xab, 0xee, 0x68, 0xba, 0x0d}, + [SizeFp]byte{0x45, 0x95, 0xe5, 0x91, 0x20, 0x15, 0x7b, 0xe8, 0x1f, 0x89, 0x12, 0x51, 0xd3, 0xfa, 0x82, 0x0d}, + }, + }, + { + addYX: Fq{ + [SizeFp]byte{0x0c, 0xa3, 0xf8, 0x33, 0x76, 0x28, 0x4f, 0x2d, 0x26, 0xcc, 0x29, 0x77, 0x1a, 0xb3, 0x6e, 0x41}, + [SizeFp]byte{0xef, 0xc8, 0x87, 0x5d, 0x26, 0x5d, 0x2f, 0xd1, 0x5c, 0xe0, 0x04, 0x58, 0x1c, 0xa9, 0x80, 0x4d}, + }, + subYX: Fq{ + [SizeFp]byte{0x0a, 0xff, 0x06, 0x42, 0xe4, 0x76, 0xc5, 0xfa, 0xcd, 0x2a, 0xfb, 0x4c, 0xfa, 0x22, 0x0a, 0x7d}, + [SizeFp]byte{0xd9, 0x5c, 0x89, 0x6d, 0x63, 0xe8, 0x0a, 0xb3, 0x29, 0xa4, 0xb9, 0x42, 0x12, 0x1d, 0xea, 0x00}, + }, + dt2: Fq{ + [SizeFp]byte{0xb3, 0x59, 0x9d, 0x40, 0xdb, 0x32, 0x11, 0x41, 0x10, 0xa1, 0xbf, 0xf1, 0x7a, 0xe3, 0xdd, 0x11}, + [SizeFp]byte{0x2c, 0xcc, 0x5c, 0x98, 0x1c, 0xd5, 0x95, 0xd2, 0x96, 0x51, 0xb1, 0x82, 0xb2, 0x7f, 0xe7, 0x6a}, + }, + }, + { + addYX: Fq{ + [SizeFp]byte{0x07, 0xe9, 0xb9, 0x83, 0xeb, 0xf2, 0x9f, 0xd7, 0x43, 0x7c, 0xc2, 0xb0, 0x32, 0x70, 0xd0, 0x52}, + [SizeFp]byte{0xf9, 0x70, 0x82, 0x31, 0x7a, 0x9a, 0x9f, 0x75, 0xe9, 0x6c, 0x87, 0x73, 0x97, 0x1a, 0x5a, 0x22}, + }, + subYX: Fq{ + [SizeFp]byte{0x0b, 0x3b, 0xe5, 0x98, 0xdc, 0xf6, 0xd1, 0xf5, 0xb7, 0x7e, 0x34, 0x22, 0x35, 0x60, 0x41, 0x53}, + [SizeFp]byte{0x1f, 0xf4, 0xcc, 0x56, 0xbb, 0x76, 0x3e, 0xd9, 0x3b, 0x63, 0x82, 0x25, 0x98, 0x12, 0x80, 0x02}, + }, + dt2: Fq{ + [SizeFp]byte{0xeb, 0xdc, 0x9a, 0x7a, 0x70, 0x61, 0x5d, 0x6e, 0x41, 0x05, 0xd4, 0x0b, 0x4a, 0x63, 0x2a, 0x3b}, + [SizeFp]byte{0xab, 0x52, 0xe0, 0xb1, 0x3f, 0x8a, 0xb0, 0x2d, 0x55, 0xf8, 0x1c, 0xeb, 0xc1, 0x1b, 0xc8, 0x35}, + }, + }, + }, +} diff --git a/src/circl/ecc/goldilocks/constants.go b/src/circl/ecc/goldilocks/constants.go new file mode 100644 index 00000000000..6b722140873 --- /dev/null +++ b/src/circl/ecc/goldilocks/constants.go @@ -0,0 +1,71 @@ +package goldilocks + +import fp "circl/math/fp448" + +var ( + // genX is the x-coordinate of the generator of Goldilocks curve. + genX = fp.Elt{ + 0x5e, 0xc0, 0x0c, 0xc7, 0x2b, 0xa8, 0x26, 0x26, + 0x8e, 0x93, 0x00, 0x8b, 0xe1, 0x80, 0x3b, 0x43, + 0x11, 0x65, 0xb6, 0x2a, 0xf7, 0x1a, 0xae, 0x12, + 0x64, 0xa4, 0xd3, 0xa3, 0x24, 0xe3, 0x6d, 0xea, + 0x67, 0x17, 0x0f, 0x47, 0x70, 0x65, 0x14, 0x9e, + 0xda, 0x36, 0xbf, 0x22, 0xa6, 0x15, 0x1d, 0x22, + 0xed, 0x0d, 0xed, 0x6b, 0xc6, 0x70, 0x19, 0x4f, + } + // genY is the y-coordinate of the generator of Goldilocks curve. + genY = fp.Elt{ + 0x14, 0xfa, 0x30, 0xf2, 0x5b, 0x79, 0x08, 0x98, + 0xad, 0xc8, 0xd7, 0x4e, 0x2c, 0x13, 0xbd, 0xfd, + 0xc4, 0x39, 0x7c, 0xe6, 0x1c, 0xff, 0xd3, 0x3a, + 0xd7, 0xc2, 0xa0, 0x05, 0x1e, 0x9c, 0x78, 0x87, + 0x40, 0x98, 0xa3, 0x6c, 0x73, 0x73, 0xea, 0x4b, + 0x62, 0xc7, 0xc9, 0x56, 0x37, 0x20, 0x76, 0x88, + 0x24, 0xbc, 0xb6, 0x6e, 0x71, 0x46, 0x3f, 0x69, + } + // paramD is -39081 in Fp. + paramD = fp.Elt{ + 0x56, 0x67, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + } + // order is 2^446-0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d, + // which is the number of points in the prime subgroup. + order = Scalar{ + 0xf3, 0x44, 0x58, 0xab, 0x92, 0xc2, 0x78, 0x23, + 0x55, 0x8f, 0xc5, 0x8d, 0x72, 0xc2, 0x6c, 0x21, + 0x90, 0x36, 0xd6, 0xae, 0x49, 0xdb, 0x4e, 0xc4, + 0xe9, 0x23, 0xca, 0x7c, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, + } + // residue448 is 2^448 mod order. + residue448 = [4]uint64{ + 0x721cf5b5529eec34, 0x7a4cf635c8e9c2ab, 0xeec492d944a725bf, 0x20cd77058, + } + // invFour is 1/4 mod order. + invFour = Scalar{ + 0x3d, 0x11, 0xd6, 0xaa, 0xa4, 0x30, 0xde, 0x48, + 0xd5, 0x63, 0x71, 0xa3, 0x9c, 0x30, 0x5b, 0x08, + 0xa4, 0x8d, 0xb5, 0x6b, 0xd2, 0xb6, 0x13, 0x71, + 0xfa, 0x88, 0x32, 0xdf, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, + } + // paramDTwist is -39082 in Fp. The D parameter of the twist curve. + paramDTwist = fp.Elt{ + 0x55, 0x67, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + } +) diff --git a/src/circl/ecc/goldilocks/curve.go b/src/circl/ecc/goldilocks/curve.go new file mode 100644 index 00000000000..736cb080220 --- /dev/null +++ b/src/circl/ecc/goldilocks/curve.go @@ -0,0 +1,80 @@ +// Package goldilocks provides elliptic curve operations over the goldilocks curve. +package goldilocks + +import fp "circl/math/fp448" + +// Curve is the Goldilocks curve x^2+y^2=z^2-39081x^2y^2. +type Curve struct{} + +// Identity returns the identity point. +func (Curve) Identity() *Point { + return &Point{ + y: fp.One(), + z: fp.One(), + } +} + +// IsOnCurve returns true if the point lies on the curve. +func (Curve) IsOnCurve(P *Point) bool { + x2, y2, t, t2, z2 := &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{} + rhs, lhs := &fp.Elt{}, &fp.Elt{} + fp.Mul(t, &P.ta, &P.tb) // t = ta*tb + fp.Sqr(x2, &P.x) // x^2 + fp.Sqr(y2, &P.y) // y^2 + fp.Sqr(z2, &P.z) // z^2 + fp.Sqr(t2, t) // t^2 + fp.Add(lhs, x2, y2) // x^2 + y^2 + fp.Mul(rhs, t2, ¶mD) // dt^2 + fp.Add(rhs, rhs, z2) // z^2 + dt^2 + fp.Sub(lhs, lhs, rhs) // x^2 + y^2 - (z^2 + dt^2) + eq0 := fp.IsZero(lhs) + + fp.Mul(lhs, &P.x, &P.y) // xy + fp.Mul(rhs, t, &P.z) // tz + fp.Sub(lhs, lhs, rhs) // xy - tz + eq1 := fp.IsZero(lhs) + return eq0 && eq1 +} + +// Generator returns the generator point. +func (Curve) Generator() *Point { + return &Point{ + x: genX, + y: genY, + z: fp.One(), + ta: genX, + tb: genY, + } +} + +// Order returns the number of points in the prime subgroup. +func (Curve) Order() Scalar { return order } + +// Double returns 2P. +func (Curve) Double(P *Point) *Point { R := *P; R.Double(); return &R } + +// Add returns P+Q. +func (Curve) Add(P, Q *Point) *Point { R := *P; R.Add(Q); return &R } + +// ScalarMult returns kP. This function runs in constant time. +func (e Curve) ScalarMult(k *Scalar, P *Point) *Point { + k4 := &Scalar{} + k4.divBy4(k) + return e.pull(twistCurve{}.ScalarMult(k4, e.push(P))) +} + +// ScalarBaseMult returns kG where G is the generator point. This function runs in constant time. +func (e Curve) ScalarBaseMult(k *Scalar) *Point { + k4 := &Scalar{} + k4.divBy4(k) + return e.pull(twistCurve{}.ScalarBaseMult(k4)) +} + +// CombinedMult returns mG+nP, where G is the generator point. This function is non-constant time. +func (e Curve) CombinedMult(m, n *Scalar, P *Point) *Point { + m4 := &Scalar{} + n4 := &Scalar{} + m4.divBy4(m) + n4.divBy4(n) + return e.pull(twistCurve{}.CombinedMult(m4, n4, twistCurve{}.pull(P))) +} diff --git a/src/circl/ecc/goldilocks/curve_test.go b/src/circl/ecc/goldilocks/curve_test.go new file mode 100644 index 00000000000..e95152daf67 --- /dev/null +++ b/src/circl/ecc/goldilocks/curve_test.go @@ -0,0 +1,113 @@ +package goldilocks_test + +import ( + "crypto/rand" + "testing" + + "circl/ecc/goldilocks" + "circl/internal/test" +) + +func TestScalarMult(t *testing.T) { + const testTimes = 1 << 8 + var e goldilocks.Curve + k := &goldilocks.Scalar{} + zero := &goldilocks.Scalar{} + + t.Run("rG=0", func(t *testing.T) { + order := e.Order() + for i := 0; i < testTimes; i++ { + got := e.ScalarBaseMult(&order) + got.ToAffine() + want := e.Identity() + + if !e.IsOnCurve(got) || !e.IsOnCurve(want) || !got.IsEqual(want) { + want.ToAffine() + test.ReportError(t, got, want) + } + } + }) + t.Run("rP=0", func(t *testing.T) { + order := e.Order() + for i := 0; i < testTimes; i++ { + P := randomPoint() + + got := e.ScalarMult(&order, P) + got.ToAffine() + want := e.Identity() + + if !e.IsOnCurve(got) || !e.IsOnCurve(want) || !got.IsEqual(want) { + want.ToAffine() + test.ReportError(t, got, want, P, order) + } + } + }) + t.Run("kG", func(t *testing.T) { + I := e.Identity() + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(k[:]) + + got := e.ScalarBaseMult(k) + want := e.CombinedMult(k, zero, I) // k*G + 0*I + + if !e.IsOnCurve(got) || !e.IsOnCurve(want) || !got.IsEqual(want) { + test.ReportError(t, got, want, k) + } + } + }) + t.Run("kP", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + P := randomPoint() + _, _ = rand.Read(k[:]) + + got := e.ScalarMult(k, P) + want := e.CombinedMult(zero, k, P) + + if !e.IsOnCurve(got) || !e.IsOnCurve(want) || !got.IsEqual(want) { + test.ReportError(t, got, want, P, k) + } + } + }) + t.Run("kG+lP", func(t *testing.T) { + G := e.Generator() + l := &goldilocks.Scalar{} + for i := 0; i < testTimes; i++ { + P := randomPoint() + _, _ = rand.Read(k[:]) + _, _ = rand.Read(l[:]) + + kG := e.ScalarMult(k, G) + lP := e.ScalarMult(l, P) + got := e.Add(kG, lP) + want := e.CombinedMult(k, l, P) + + if !e.IsOnCurve(got) || !e.IsOnCurve(want) || !got.IsEqual(want) { + test.ReportError(t, got, want, P, k, l) + } + } + }) +} + +func BenchmarkCurve(b *testing.B) { + var e goldilocks.Curve + var k, l goldilocks.Scalar + _, _ = rand.Read(k[:]) + _, _ = rand.Read(l[:]) + P := randomPoint() + + b.Run("ScalarMult", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P = e.ScalarMult(&k, P) + } + }) + b.Run("ScalarBaseMult", func(b *testing.B) { + for i := 0; i < b.N; i++ { + e.ScalarBaseMult(&k) + } + }) + b.Run("CombinedMult", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P = e.CombinedMult(&k, &l, P) + } + }) +} diff --git a/src/circl/ecc/goldilocks/isogeny.go b/src/circl/ecc/goldilocks/isogeny.go new file mode 100644 index 00000000000..9941924ed9f --- /dev/null +++ b/src/circl/ecc/goldilocks/isogeny.go @@ -0,0 +1,52 @@ +package goldilocks + +import fp "circl/math/fp448" + +func (Curve) pull(P *twistPoint) *Point { return twistCurve{}.push(P) } +func (twistCurve) pull(P *Point) *twistPoint { return Curve{}.push(P) } + +// push sends a point on the Goldilocks curve to a point on the twist curve. +func (Curve) push(P *Point) *twistPoint { + Q := &twistPoint{} + Px, Py, Pz := &P.x, &P.y, &P.z + a, b, c, d, e, f, g, h := &Q.x, &Q.y, &Q.z, &fp.Elt{}, &Q.ta, &Q.x, &Q.y, &Q.tb + fp.Add(e, Px, Py) // x+y + fp.Sqr(a, Px) // A = x^2 + fp.Sqr(b, Py) // B = y^2 + fp.Sqr(c, Pz) // z^2 + fp.Add(c, c, c) // C = 2*z^2 + *d = *a // D = A + fp.Sqr(e, e) // (x+y)^2 + fp.Sub(e, e, a) // (x+y)^2-A + fp.Sub(e, e, b) // E = (x+y)^2-A-B + fp.Add(h, b, d) // H = B+D + fp.Sub(g, b, d) // G = B-D + fp.Sub(f, c, h) // F = C-H + fp.Mul(&Q.z, f, g) // Z = F * G + fp.Mul(&Q.x, e, f) // X = E * F + fp.Mul(&Q.y, g, h) // Y = G * H, // T = E * H + return Q +} + +// push sends a point on the twist curve to a point on the Goldilocks curve. +func (twistCurve) push(P *twistPoint) *Point { + Q := &Point{} + Px, Py, Pz := &P.x, &P.y, &P.z + a, b, c, d, e, f, g, h := &Q.x, &Q.y, &Q.z, &fp.Elt{}, &Q.ta, &Q.x, &Q.y, &Q.tb + fp.Add(e, Px, Py) // x+y + fp.Sqr(a, Px) // A = x^2 + fp.Sqr(b, Py) // B = y^2 + fp.Sqr(c, Pz) // z^2 + fp.Add(c, c, c) // C = 2*z^2 + fp.Neg(d, a) // D = -A + fp.Sqr(e, e) // (x+y)^2 + fp.Sub(e, e, a) // (x+y)^2-A + fp.Sub(e, e, b) // E = (x+y)^2-A-B + fp.Add(h, b, d) // H = B+D + fp.Sub(g, b, d) // G = B-D + fp.Sub(f, c, h) // F = C-H + fp.Mul(&Q.z, f, g) // Z = F * G + fp.Mul(&Q.x, e, f) // X = E * F + fp.Mul(&Q.y, g, h) // Y = G * H, // T = E * H + return Q +} diff --git a/src/circl/ecc/goldilocks/isogeny_test.go b/src/circl/ecc/goldilocks/isogeny_test.go new file mode 100644 index 00000000000..ba03c8d9809 --- /dev/null +++ b/src/circl/ecc/goldilocks/isogeny_test.go @@ -0,0 +1,35 @@ +package goldilocks + +import ( + "crypto/rand" + "testing" + + "circl/internal/test" +) + +func randomPoint() *Point { + var k Scalar + _, _ = rand.Read(k[:]) + return Curve{}.ScalarBaseMult(&k) +} + +func TestIsogeny(t *testing.T) { + const testTimes = 1 << 10 + var gold Curve + var twist twistCurve + + for i := 0; i < testTimes; i++ { + P := randomPoint() + Q := gold.pull(gold.push(P)) // phi^-(phi^+(P)) + got := Q + want := gold.Double(gold.Double(P)) // 4P + if !got.IsEqual(want) { + test.ReportError(t, got, want, P) + } + got = twist.push(twist.pull(Q)) // phi^-(phi^+(Q)) + want = gold.Double(gold.Double(Q)) // 4Q + if !got.IsEqual(want) { + test.ReportError(t, got, want, P) + } + } +} diff --git a/src/circl/ecc/goldilocks/point.go b/src/circl/ecc/goldilocks/point.go new file mode 100644 index 00000000000..10ed9d7b670 --- /dev/null +++ b/src/circl/ecc/goldilocks/point.go @@ -0,0 +1,171 @@ +package goldilocks + +import ( + "errors" + "fmt" + + fp "circl/math/fp448" +) + +// Point is a point on the Goldilocks Curve. +type Point struct{ x, y, z, ta, tb fp.Elt } + +func (P Point) String() string { + return fmt.Sprintf("x: %v\ny: %v\nz: %v\nta: %v\ntb: %v", P.x, P.y, P.z, P.ta, P.tb) +} + +// FromAffine creates a point from affine coordinates. +func FromAffine(x, y *fp.Elt) (*Point, error) { + P := &Point{ + x: *x, + y: *y, + z: fp.One(), + ta: *x, + tb: *y, + } + if !(Curve{}).IsOnCurve(P) { + return P, errors.New("point not on curve") + } + return P, nil +} + +// isLessThan returns true if 0 <= x < y, and assumes that slices are of the +// same length and are interpreted in little-endian order. +func isLessThan(x, y []byte) bool { + i := len(x) - 1 + for i > 0 && x[i] == y[i] { + i-- + } + return x[i] < y[i] +} + +// FromBytes returns a point from the input buffer. +func FromBytes(in []byte) (*Point, error) { + if len(in) < fp.Size+1 { + return nil, errors.New("wrong input length") + } + var err = errors.New("invalid decoding") + P := &Point{} + signX := in[fp.Size] >> 7 + copy(P.y[:], in[:fp.Size]) + p := fp.P() + if !isLessThan(P.y[:], p[:]) { + return nil, err + } + + u, v := &fp.Elt{}, &fp.Elt{} + one := fp.One() + fp.Sqr(u, &P.y) // u = y^2 + fp.Mul(v, u, ¶mD) // v = dy^2 + fp.Sub(u, u, &one) // u = y^2-1 + fp.Sub(v, v, &one) // v = dy^2-1 + isQR := fp.InvSqrt(&P.x, u, v) // x = sqrt(u/v) + if !isQR { + return nil, err + } + fp.Modp(&P.x) // x = x mod p + if fp.IsZero(&P.x) && signX == 1 { + return nil, err + } + if signX != (P.x[0] & 1) { + fp.Neg(&P.x, &P.x) + } + P.ta = P.x + P.tb = P.y + P.z = fp.One() + return P, nil +} + +// IsIdentity returns true is P is the identity Point. +func (P *Point) IsIdentity() bool { + return fp.IsZero(&P.x) && !fp.IsZero(&P.y) && !fp.IsZero(&P.z) && P.y == P.z +} + +// IsEqual returns true if P is equivalent to Q. +func (P *Point) IsEqual(Q *Point) bool { + l, r := &fp.Elt{}, &fp.Elt{} + fp.Mul(l, &P.x, &Q.z) + fp.Mul(r, &Q.x, &P.z) + fp.Sub(l, l, r) + b := fp.IsZero(l) + fp.Mul(l, &P.y, &Q.z) + fp.Mul(r, &Q.y, &P.z) + fp.Sub(l, l, r) + b = b && fp.IsZero(l) + fp.Mul(l, &P.ta, &P.tb) + fp.Mul(l, l, &Q.z) + fp.Mul(r, &Q.ta, &Q.tb) + fp.Mul(r, r, &P.z) + fp.Sub(l, l, r) + b = b && fp.IsZero(l) + return b +} + +// Neg obtains the inverse of the Point. +func (P *Point) Neg() { fp.Neg(&P.x, &P.x); fp.Neg(&P.ta, &P.ta) } + +// ToAffine returns the x,y affine coordinates of P. +func (P *Point) ToAffine() (x, y fp.Elt) { + fp.Inv(&P.z, &P.z) // 1/z + fp.Mul(&P.x, &P.x, &P.z) // x/z + fp.Mul(&P.y, &P.y, &P.z) // y/z + fp.Modp(&P.x) + fp.Modp(&P.y) + fp.SetOne(&P.z) + P.ta = P.x + P.tb = P.y + return P.x, P.y +} + +// ToBytes stores P into a slice of bytes. +func (P *Point) ToBytes(out []byte) error { + if len(out) < fp.Size+1 { + return errors.New("invalid decoding") + } + x, y := P.ToAffine() + out[fp.Size] = (x[0] & 1) << 7 + return fp.ToBytes(out[:fp.Size], &y) +} + +// MarshalBinary encodes the receiver into a binary form and returns the result. +func (P *Point) MarshalBinary() (data []byte, err error) { + data = make([]byte, fp.Size+1) + err = P.ToBytes(data[:fp.Size+1]) + return data, err +} + +// UnmarshalBinary must be able to decode the form generated by MarshalBinary. +func (P *Point) UnmarshalBinary(data []byte) error { Q, err := FromBytes(data); *P = *Q; return err } + +// Double sets P = 2Q. +func (P *Point) Double() { P.Add(P) } + +// Add sets P =P+Q.. +func (P *Point) Add(Q *Point) { + // This is formula (5) from "Twisted Edwards Curves Revisited" by + // Hisil H., Wong K.KH., Carter G., Dawson E. (2008) + // https://doi.org/10.1007/978-3-540-89255-7_20 + x1, y1, z1, ta1, tb1 := &P.x, &P.y, &P.z, &P.ta, &P.tb + x2, y2, z2, ta2, tb2 := &Q.x, &Q.y, &Q.z, &Q.ta, &Q.tb + x3, y3, z3, E, H := &P.x, &P.y, &P.z, &P.ta, &P.tb + A, B, C, D := &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{} + t1, t2, F, G := C, D, &fp.Elt{}, &fp.Elt{} + fp.Mul(t1, ta1, tb1) // t1 = ta1*tb1 + fp.Mul(t2, ta2, tb2) // t2 = ta2*tb2 + fp.Mul(A, x1, x2) // A = x1*x2 + fp.Mul(B, y1, y2) // B = y1*y2 + fp.Mul(C, t1, t2) // t1*t2 + fp.Mul(C, C, ¶mD) // C = d*t1*t2 + fp.Mul(D, z1, z2) // D = z1*z2 + fp.Add(F, x1, y1) // x1+y1 + fp.Add(E, x2, y2) // x2+y2 + fp.Mul(E, E, F) // (x1+y1)*(x2+y2) + fp.Sub(E, E, A) // (x1+y1)*(x2+y2)-A + fp.Sub(E, E, B) // E = (x1+y1)*(x2+y2)-A-B + fp.Sub(F, D, C) // F = D-C + fp.Add(G, D, C) // G = D+C + fp.Sub(H, B, A) // H = B-A + fp.Mul(z3, F, G) // Z = F * G + fp.Mul(x3, E, F) // X = E * F + fp.Mul(y3, G, H) // Y = G * H, T = E * H +} diff --git a/src/circl/ecc/goldilocks/point_test.go b/src/circl/ecc/goldilocks/point_test.go new file mode 100644 index 00000000000..e1c171cac03 --- /dev/null +++ b/src/circl/ecc/goldilocks/point_test.go @@ -0,0 +1,101 @@ +package goldilocks_test + +import ( + "crypto/rand" + "encoding" + "testing" + + "circl/ecc/goldilocks" + "circl/internal/test" +) + +func randomPoint() *goldilocks.Point { + var k goldilocks.Scalar + _, _ = rand.Read(k[:]) + return goldilocks.Curve{}.ScalarBaseMult(&k) +} + +func TestPointAdd(t *testing.T) { + const testTimes = 1 << 10 + var e goldilocks.Curve + for i := 0; i < testTimes; i++ { + P := randomPoint() + // 16P = 2^4P + got := e.Double(e.Double(e.Double(e.Double(P)))) + // 16P = P+P...+P + Q := e.Identity() + for j := 0; j < 16; j++ { + Q = e.Add(Q, P) + } + want := Q + if !e.IsOnCurve(got) || !e.IsOnCurve(want) || !got.IsEqual(want) { + test.ReportError(t, got, want, P) + } + } +} + +func TestPointNeg(t *testing.T) { + const testTimes = 1 << 10 + var e goldilocks.Curve + for i := 0; i < testTimes; i++ { + P := randomPoint() + Q := *P + Q.Neg() + R := e.Add(P, &Q) + got := R.IsIdentity() + want := true + if got != want { + test.ReportError(t, got, want, P) + } + } +} + +func TestPointAffine(t *testing.T) { + const testTimes = 1 << 10 + for i := 0; i < testTimes; i++ { + got := randomPoint() + x, y := got.ToAffine() + want, err := goldilocks.FromAffine(&x, &y) + if !got.IsEqual(want) || err != nil { + test.ReportError(t, got, want) + } + } +} + +func TestPointMarshal(t *testing.T) { + const testTimes = 1 << 10 + var want error + for i := 0; i < testTimes; i++ { + var P interface{} = randomPoint() + mar, _ := P.(encoding.BinaryMarshaler) + data, got := mar.MarshalBinary() + if got != want { + test.ReportError(t, got, want, P) + } + unmar, _ := P.(encoding.BinaryUnmarshaler) + got = unmar.UnmarshalBinary(data) + if got != want { + test.ReportError(t, got, want, P) + } + } +} + +func BenchmarkPoint(b *testing.B) { + P := randomPoint() + Q := randomPoint() + b.Run("ToAffine", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.ToAffine() + } + }) + b.Run("Add", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.Add(Q) + } + }) + b.Run("Double", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.Double() + } + }) +} diff --git a/src/circl/ecc/goldilocks/scalar.go b/src/circl/ecc/goldilocks/scalar.go new file mode 100644 index 00000000000..852d74f3acd --- /dev/null +++ b/src/circl/ecc/goldilocks/scalar.go @@ -0,0 +1,203 @@ +package goldilocks + +import ( + "encoding/binary" + "math/bits" +) + +// ScalarSize is the size (in bytes) of scalars. +const ScalarSize = 56 // 448 / 8 + +//_N is the number of 64-bit words to store scalars. +const _N = 7 // 448 / 64 + +// Scalar represents a positive integer stored in little-endian order. +type Scalar [ScalarSize]byte + +type scalar64 [_N]uint64 + +func (z *scalar64) fromScalar(x *Scalar) { + z[0] = binary.LittleEndian.Uint64(x[0*8 : 1*8]) + z[1] = binary.LittleEndian.Uint64(x[1*8 : 2*8]) + z[2] = binary.LittleEndian.Uint64(x[2*8 : 3*8]) + z[3] = binary.LittleEndian.Uint64(x[3*8 : 4*8]) + z[4] = binary.LittleEndian.Uint64(x[4*8 : 5*8]) + z[5] = binary.LittleEndian.Uint64(x[5*8 : 6*8]) + z[6] = binary.LittleEndian.Uint64(x[6*8 : 7*8]) +} + +func (z *scalar64) toScalar(x *Scalar) { + binary.LittleEndian.PutUint64(x[0*8:1*8], z[0]) + binary.LittleEndian.PutUint64(x[1*8:2*8], z[1]) + binary.LittleEndian.PutUint64(x[2*8:3*8], z[2]) + binary.LittleEndian.PutUint64(x[3*8:4*8], z[3]) + binary.LittleEndian.PutUint64(x[4*8:5*8], z[4]) + binary.LittleEndian.PutUint64(x[5*8:6*8], z[5]) + binary.LittleEndian.PutUint64(x[6*8:7*8], z[6]) +} + +// add calculates z = x + y. Assumes len(z) > max(len(x),len(y)). +func add(z, x, y []uint64) uint64 { + l, L, zz := len(x), len(y), y + if l > L { + l, L, zz = L, l, x + } + c := uint64(0) + for i := 0; i < l; i++ { + z[i], c = bits.Add64(x[i], y[i], c) + } + for i := l; i < L; i++ { + z[i], c = bits.Add64(zz[i], 0, c) + } + return c +} + +// sub calculates z = x - y. Assumes len(z) > max(len(x),len(y)). +func sub(z, x, y []uint64) uint64 { + l, L, zz := len(x), len(y), y + if l > L { + l, L, zz = L, l, x + } + c := uint64(0) + for i := 0; i < l; i++ { + z[i], c = bits.Sub64(x[i], y[i], c) + } + for i := l; i < L; i++ { + z[i], c = bits.Sub64(zz[i], 0, c) + } + return c +} + +// mulWord calculates z = x * y. Assumes len(z) >= len(x)+1. +func mulWord(z, x []uint64, y uint64) { + for i := range z { + z[i] = 0 + } + carry := uint64(0) + for i := range x { + hi, lo := bits.Mul64(x[i], y) + lo, cc := bits.Add64(lo, z[i], 0) + hi, _ = bits.Add64(hi, 0, cc) + z[i], cc = bits.Add64(lo, carry, 0) + carry, _ = bits.Add64(hi, 0, cc) + } + z[len(x)] = carry +} + +// Cmov moves x into z if b=1. +func (z *scalar64) Cmov(b uint64, x *scalar64) { + m := uint64(0) - b + for i := range z { + z[i] = (z[i] &^ m) | (x[i] & m) + } +} + +// leftShift shifts to the left the words of z returning the more significant word. +func (z *scalar64) leftShift(low uint64) uint64 { + high := z[_N-1] + for i := _N - 1; i > 0; i-- { + z[i] = z[i-1] + } + z[0] = low + return high +} + +// reduceOneWord calculates z = z + 2^448*x such that the result fits in a Scalar. +func (z *scalar64) reduceOneWord(x uint64) { + prod := (&scalar64{})[:] + mulWord(prod, residue448[:], x) + cc := add(z[:], z[:], prod) + mulWord(prod, residue448[:], cc) + add(z[:], z[:], prod) +} + +// modOrder reduces z mod order. +func (z *scalar64) modOrder() { + var o64, x scalar64 + o64.fromScalar(&order) + // Performs: while (z >= order) { z = z-order } + // At most 8 (eight) iterations reduce 3 bits by subtracting. + for i := 0; i < 8; i++ { + c := sub(x[:], z[:], o64[:]) // (c || x) = z-order + z.Cmov(1-c, &x) // if c != 0 { z = x } + } +} + +// FromBytes stores z = x mod order, where x is a number stored in little-endian order. +func (z *Scalar) FromBytes(x []byte) { + n := len(x) + nCeil := (n + 7) >> 3 + for i := range z { + z[i] = 0 + } + if nCeil < _N { + copy(z[:], x) + return + } + copy(z[:], x[8*(nCeil-_N):]) + var z64 scalar64 + z64.fromScalar(z) + for i := nCeil - _N - 1; i >= 0; i-- { + low := binary.LittleEndian.Uint64(x[8*i:]) + high := z64.leftShift(low) + z64.reduceOneWord(high) + } + z64.modOrder() + z64.toScalar(z) +} + +// divBy4 calculates z = x/4 mod order. +func (z *Scalar) divBy4(x *Scalar) { z.Mul(x, &invFour) } + +// Red reduces z mod order. +func (z *Scalar) Red() { var t scalar64; t.fromScalar(z); t.modOrder(); t.toScalar(z) } + +// Neg calculates z = -z mod order. +func (z *Scalar) Neg() { z.Sub(&order, z) } + +// Add calculates z = x+y mod order. +func (z *Scalar) Add(x, y *Scalar) { + var z64, x64, y64, t scalar64 + x64.fromScalar(x) + y64.fromScalar(y) + c := add(z64[:], x64[:], y64[:]) + add(t[:], z64[:], residue448[:]) + z64.Cmov(c, &t) + z64.modOrder() + z64.toScalar(z) +} + +// Sub calculates z = x-y mod order. +func (z *Scalar) Sub(x, y *Scalar) { + var z64, x64, y64, t scalar64 + x64.fromScalar(x) + y64.fromScalar(y) + c := sub(z64[:], x64[:], y64[:]) + sub(t[:], z64[:], residue448[:]) + z64.Cmov(c, &t) + z64.modOrder() + z64.toScalar(z) +} + +// Mul calculates z = x*y mod order. +func (z *Scalar) Mul(x, y *Scalar) { + var z64, x64, y64 scalar64 + prod := (&[_N + 1]uint64{})[:] + x64.fromScalar(x) + y64.fromScalar(y) + mulWord(prod, x64[:], y64[_N-1]) + copy(z64[:], prod[:_N]) + z64.reduceOneWord(prod[_N]) + for i := _N - 2; i >= 0; i-- { + h := z64.leftShift(0) + z64.reduceOneWord(h) + mulWord(prod, x64[:], y64[i]) + c := add(z64[:], z64[:], prod[:_N]) + z64.reduceOneWord(prod[_N] + c) + } + z64.modOrder() + z64.toScalar(z) +} + +// IsZero returns true if z=0. +func (z *Scalar) IsZero() bool { z.Red(); return *z == Scalar{} } diff --git a/src/circl/ecc/goldilocks/scalar_test.go b/src/circl/ecc/goldilocks/scalar_test.go new file mode 100644 index 00000000000..bf0c9a53eac --- /dev/null +++ b/src/circl/ecc/goldilocks/scalar_test.go @@ -0,0 +1,107 @@ +package goldilocks_test + +import ( + "crypto/rand" + "encoding/binary" + "math/big" + "testing" + + "circl/ecc/goldilocks" + "circl/internal/conv" + "circl/internal/test" +) + +func TestReduceModOrder(t *testing.T) { + order := goldilocks.Curve{}.Order() + bigOrder := conv.BytesLe2BigInt(order[:]) + const max = 3*goldilocks.ScalarSize - 1 + var b [max]byte + _, _ = rand.Read(b[:]) + var z goldilocks.Scalar + for i := 0; i < max; i++ { + x := b[0:i] + bigX := conv.BytesLe2BigInt(x) + + z.FromBytes(x) + got := conv.BytesLe2BigInt(z[:]) + got.Mod(got, bigOrder) + + want := bigX.Mod(bigX, bigOrder) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, i) + } + } +} + +func testOp(t *testing.T, + f func(z, x, y *goldilocks.Scalar), + g func(z, x, y *big.Int)) { + const testTimes = 1 << 8 + var x, y, z goldilocks.Scalar + order := goldilocks.Curve{}.Order() + want := new(big.Int) + bigOrder := conv.BytesLe2BigInt(order[:]) + + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + bigX := conv.BytesLe2BigInt(x[:]) + bigY := conv.BytesLe2BigInt(y[:]) + + f(&z, &x, &y) + got := conv.BytesLe2BigInt(z[:]) + + g(want, bigX, bigY) + want.Mod(want, bigOrder) + if got.Cmp(want) != 0 { + test.ReportError(t, got.Text(16), want.Text(16), + conv.BytesLe2Hex(x[:]), + conv.BytesLe2Hex(y[:])) + } + } +} + +func TestScalar(t *testing.T) { + t.Run("Add", func(t *testing.T) { + testOp(t, + func(z, x, y *goldilocks.Scalar) { z.Add(x, y) }, + func(z, x, y *big.Int) { z.Add(x, y) }) + }) + t.Run("Sub", func(t *testing.T) { + testOp(t, + func(z, x, y *goldilocks.Scalar) { z.Sub(x, y) }, + func(z, x, y *big.Int) { z.Sub(x, y) }) + }) + t.Run("Mul", func(t *testing.T) { + testOp(t, + func(z, x, y *goldilocks.Scalar) { z.Mul(x, y) }, + func(z, x, y *big.Int) { z.Mul(x, y) }) + }) +} + +func BenchmarkScalar(b *testing.B) { + var k [2 * goldilocks.ScalarSize]byte + var x, y, z goldilocks.Scalar + _ = binary.Read(rand.Reader, binary.LittleEndian, x[:]) + b.Run("Add", func(b *testing.B) { + for i := 0; i < b.N; i++ { + z.Add(&x, &y) + } + }) + b.Run("Sub", func(b *testing.B) { + for i := 0; i < b.N; i++ { + z.Sub(&x, &y) + } + }) + b.Run("Mul", func(b *testing.B) { + for i := 0; i < b.N; i++ { + z.Mul(&x, &y) + } + }) + b.Run("Red", func(b *testing.B) { + for i := 0; i < b.N; i++ { + z.FromBytes(k[:]) + } + }) +} diff --git a/src/circl/ecc/goldilocks/twist.go b/src/circl/ecc/goldilocks/twist.go new file mode 100644 index 00000000000..e5b6ee0c42b --- /dev/null +++ b/src/circl/ecc/goldilocks/twist.go @@ -0,0 +1,138 @@ +package goldilocks + +import ( + "crypto/subtle" + "math/bits" + + "circl/internal/conv" + "circl/math" + fp "circl/math/fp448" +) + +// twistCurve is -x^2+y^2=1-39082x^2y^2 and is 4-isogeneous to Goldilocks. +type twistCurve struct{} + +// Identity returns the identity point. +func (twistCurve) Identity() *twistPoint { + return &twistPoint{ + y: fp.One(), + z: fp.One(), + } +} + +// subYDiv16 update x = (x - y) / 16. +func subYDiv16(x *scalar64, y int64) { + s := uint64(y >> 63) + x0, b0 := bits.Sub64((*x)[0], uint64(y), 0) + x1, b1 := bits.Sub64((*x)[1], s, b0) + x2, b2 := bits.Sub64((*x)[2], s, b1) + x3, b3 := bits.Sub64((*x)[3], s, b2) + x4, b4 := bits.Sub64((*x)[4], s, b3) + x5, b5 := bits.Sub64((*x)[5], s, b4) + x6, _ := bits.Sub64((*x)[6], s, b5) + x[0] = (x0 >> 4) | (x1 << 60) + x[1] = (x1 >> 4) | (x2 << 60) + x[2] = (x2 >> 4) | (x3 << 60) + x[3] = (x3 >> 4) | (x4 << 60) + x[4] = (x4 >> 4) | (x5 << 60) + x[5] = (x5 >> 4) | (x6 << 60) + x[6] = (x6 >> 4) +} + +func recodeScalar(d *[113]int8, k *Scalar) { + var k64 scalar64 + k64.fromScalar(k) + for i := 0; i < 112; i++ { + d[i] = int8((k64[0] & 0x1f) - 16) + subYDiv16(&k64, int64(d[i])) + } + d[112] = int8(k64[0]) +} + +// ScalarMult returns kP. +func (e twistCurve) ScalarMult(k *Scalar, P *twistPoint) *twistPoint { + var TabP [8]preTwistPointProy + var S preTwistPointProy + var d [113]int8 + + var isZero int + if k.IsZero() { + isZero = 1 + } + subtle.ConstantTimeCopy(isZero, k[:], order[:]) + + minusK := *k + isEven := 1 - int(k[0]&0x1) + minusK.Neg() + subtle.ConstantTimeCopy(isEven, k[:], minusK[:]) + recodeScalar(&d, k) + + P.oddMultiples(TabP[:]) + Q := e.Identity() + for i := 112; i >= 0; i-- { + Q.Double() + Q.Double() + Q.Double() + Q.Double() + mask := d[i] >> 7 + absDi := (d[i] + mask) ^ mask + inx := int32((absDi - 1) >> 1) + sig := int((d[i] >> 7) & 0x1) + for j := range TabP { + S.cmov(&TabP[j], uint(subtle.ConstantTimeEq(inx, int32(j)))) + } + S.cneg(sig) + Q.mixAdd(&S) + } + Q.cneg(uint(isEven)) + return Q +} + +const ( + omegaFix = 7 + omegaVar = 5 +) + +// CombinedMult returns mG+nP. +func (e twistCurve) CombinedMult(m, n *Scalar, P *twistPoint) *twistPoint { + nafFix := math.OmegaNAF(conv.BytesLe2BigInt(m[:]), omegaFix) + nafVar := math.OmegaNAF(conv.BytesLe2BigInt(n[:]), omegaVar) + + if len(nafFix) > len(nafVar) { + nafVar = append(nafVar, make([]int32, len(nafFix)-len(nafVar))...) + } else if len(nafFix) < len(nafVar) { + nafFix = append(nafFix, make([]int32, len(nafVar)-len(nafFix))...) + } + + var TabQ [1 << (omegaVar - 2)]preTwistPointProy + P.oddMultiples(TabQ[:]) + Q := e.Identity() + for i := len(nafFix) - 1; i >= 0; i-- { + Q.Double() + // Generator point + if nafFix[i] != 0 { + idxM := absolute(nafFix[i]) >> 1 + R := tabVerif[idxM] + if nafFix[i] < 0 { + R.neg() + } + Q.mixAddZ1(&R) + } + // Variable input point + if nafVar[i] != 0 { + idxN := absolute(nafVar[i]) >> 1 + S := TabQ[idxN] + if nafVar[i] < 0 { + S.neg() + } + Q.mixAdd(&S) + } + } + return Q +} + +// absolute returns always a positive value. +func absolute(x int32) int32 { + mask := x >> 31 + return (x + mask) ^ mask +} diff --git a/src/circl/ecc/goldilocks/twistPoint.go b/src/circl/ecc/goldilocks/twistPoint.go new file mode 100644 index 00000000000..9bf1aa40b31 --- /dev/null +++ b/src/circl/ecc/goldilocks/twistPoint.go @@ -0,0 +1,135 @@ +package goldilocks + +import ( + "fmt" + + fp "circl/math/fp448" +) + +type twistPoint struct{ x, y, z, ta, tb fp.Elt } + +type preTwistPointAffine struct{ addYX, subYX, dt2 fp.Elt } + +type preTwistPointProy struct { + preTwistPointAffine + z2 fp.Elt +} + +func (P *twistPoint) String() string { + return fmt.Sprintf("x: %v\ny: %v\nz: %v\nta: %v\ntb: %v", P.x, P.y, P.z, P.ta, P.tb) +} + +// cneg conditionally negates the point if b=1. +func (P *twistPoint) cneg(b uint) { + t := &fp.Elt{} + fp.Neg(t, &P.x) + fp.Cmov(&P.x, t, b) + fp.Neg(t, &P.ta) + fp.Cmov(&P.ta, t, b) +} + +// Double updates P with 2P. +func (P *twistPoint) Double() { + // This is formula (7) from "Twisted Edwards Curves Revisited" by + // Hisil H., Wong K.KH., Carter G., Dawson E. (2008) + // https://doi.org/10.1007/978-3-540-89255-7_20 + Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb + a, b, c, e, f, g, h := Px, Py, Pz, Pta, Px, Py, Ptb + fp.Add(e, Px, Py) // x+y + fp.Sqr(a, Px) // A = x^2 + fp.Sqr(b, Py) // B = y^2 + fp.Sqr(c, Pz) // z^2 + fp.Add(c, c, c) // C = 2*z^2 + fp.Add(h, a, b) // H = A+B + fp.Sqr(e, e) // (x+y)^2 + fp.Sub(e, e, h) // E = (x+y)^2-A-B + fp.Sub(g, b, a) // G = B-A + fp.Sub(f, c, g) // F = C-G + fp.Mul(Pz, f, g) // Z = F * G + fp.Mul(Px, e, f) // X = E * F + fp.Mul(Py, g, h) // Y = G * H, T = E * H +} + +// mixAdd calculates P= P+Q, where Q is a precomputed point with Z_Q = 1. +func (P *twistPoint) mixAddZ1(Q *preTwistPointAffine) { + fp.Add(&P.z, &P.z, &P.z) // D = 2*z1 (z2=1) + P.coreAddition(Q) +} + +// coreAddition calculates P=P+Q for curves with A=-1. +func (P *twistPoint) coreAddition(Q *preTwistPointAffine) { + // This is the formula following (5) from "Twisted Edwards Curves Revisited" by + // Hisil H., Wong K.KH., Carter G., Dawson E. (2008) + // https://doi.org/10.1007/978-3-540-89255-7_20 + Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb + addYX2, subYX2, dt2 := &Q.addYX, &Q.subYX, &Q.dt2 + a, b, c, d, e, f, g, h := Px, Py, &fp.Elt{}, Pz, Pta, Px, Py, Ptb + fp.Mul(c, Pta, Ptb) // t1 = ta*tb + fp.Sub(h, Py, Px) // y1-x1 + fp.Add(b, Py, Px) // y1+x1 + fp.Mul(a, h, subYX2) // A = (y1-x1)*(y2-x2) + fp.Mul(b, b, addYX2) // B = (y1+x1)*(y2+x2) + fp.Mul(c, c, dt2) // C = 2*D*t1*t2 + fp.Sub(e, b, a) // E = B-A + fp.Add(h, b, a) // H = B+A + fp.Sub(f, d, c) // F = D-C + fp.Add(g, d, c) // G = D+C + fp.Mul(Pz, f, g) // Z = F * G + fp.Mul(Px, e, f) // X = E * F + fp.Mul(Py, g, h) // Y = G * H, T = E * H +} + +func (P *preTwistPointAffine) neg() { + P.addYX, P.subYX = P.subYX, P.addYX + fp.Neg(&P.dt2, &P.dt2) +} + +func (P *preTwistPointAffine) cneg(b int) { + t := &fp.Elt{} + fp.Cswap(&P.addYX, &P.subYX, uint(b)) + fp.Neg(t, &P.dt2) + fp.Cmov(&P.dt2, t, uint(b)) +} + +func (P *preTwistPointAffine) cmov(Q *preTwistPointAffine, b uint) { + fp.Cmov(&P.addYX, &Q.addYX, b) + fp.Cmov(&P.subYX, &Q.subYX, b) + fp.Cmov(&P.dt2, &Q.dt2, b) +} + +// mixAdd calculates P= P+Q, where Q is a precomputed point with Z_Q != 1. +func (P *twistPoint) mixAdd(Q *preTwistPointProy) { + fp.Mul(&P.z, &P.z, &Q.z2) // D = 2*z1*z2 + P.coreAddition(&Q.preTwistPointAffine) +} + +// oddMultiples calculates T[i] = (2*i-1)P for 0 < i < len(T). +func (P *twistPoint) oddMultiples(T []preTwistPointProy) { + if n := len(T); n > 0 { + T[0].FromTwistPoint(P) + _2P := *P + _2P.Double() + R := &preTwistPointProy{} + R.FromTwistPoint(&_2P) + for i := 1; i < n; i++ { + P.mixAdd(R) + T[i].FromTwistPoint(P) + } + } +} + +// cmov conditionally moves Q into P if b=1. +func (P *preTwistPointProy) cmov(Q *preTwistPointProy, b uint) { + P.preTwistPointAffine.cmov(&Q.preTwistPointAffine, b) + fp.Cmov(&P.z2, &Q.z2, b) +} + +// FromTwistPoint precomputes some coordinates of Q for missed addition. +func (P *preTwistPointProy) FromTwistPoint(Q *twistPoint) { + fp.Add(&P.addYX, &Q.y, &Q.x) // addYX = X + Y + fp.Sub(&P.subYX, &Q.y, &Q.x) // subYX = Y - X + fp.Mul(&P.dt2, &Q.ta, &Q.tb) // T = ta*tb + fp.Mul(&P.dt2, &P.dt2, ¶mDTwist) // D*T + fp.Add(&P.dt2, &P.dt2, &P.dt2) // dt2 = 2*D*T + fp.Add(&P.z2, &Q.z, &Q.z) // z2 = 2*Z +} diff --git a/src/circl/ecc/goldilocks/twistTables.go b/src/circl/ecc/goldilocks/twistTables.go new file mode 100644 index 00000000000..d5a4df8b974 --- /dev/null +++ b/src/circl/ecc/goldilocks/twistTables.go @@ -0,0 +1,216 @@ +package goldilocks + +import fp "circl/math/fp448" + +var tabFixMult = [fxV][fx2w1]preTwistPointAffine{ + { + { + addYX: fp.Elt{0x65, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2b, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05}, + subYX: fp.Elt{0x64, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2d, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05}, + dt2: fp.Elt{0x1a, 0x33, 0xea, 0x64, 0x45, 0x1c, 0xdf, 0x17, 0x1d, 0x16, 0x34, 0x28, 0xd6, 0x61, 0x19, 0x67, 0x79, 0xb4, 0x13, 0xcf, 0x3e, 0x7c, 0x0e, 0x72, 0xda, 0xf1, 0x5f, 0xda, 0xe6, 0xcf, 0x42, 0xd3, 0xb6, 0x17, 0xc2, 0x68, 0x13, 0x2d, 0xd9, 0x60, 0x3e, 0xae, 0xf0, 0x5b, 0x96, 0xf0, 0xcd, 0xaf, 0xea, 0xb7, 0x0d, 0x59, 0x16, 0xa7, 0xff, 0x55}, + }, + { + addYX: fp.Elt{0xca, 0xd8, 0x7d, 0x86, 0x1a, 0xef, 0xad, 0x11, 0xe3, 0x27, 0x41, 0x7e, 0x7f, 0x3e, 0xa9, 0xd2, 0xb5, 0x4e, 0x50, 0xe0, 0x77, 0x91, 0xc2, 0x13, 0x52, 0x73, 0x41, 0x09, 0xa6, 0x57, 0x9a, 0xc8, 0xa8, 0x90, 0x9d, 0x26, 0x14, 0xbb, 0xa1, 0x2a, 0xf7, 0x45, 0x43, 0x4e, 0xea, 0x35, 0x62, 0xe1, 0x08, 0x85, 0x46, 0xb8, 0x24, 0x05, 0x2d, 0xab}, + subYX: fp.Elt{0x9b, 0xe6, 0xd3, 0xe5, 0xfe, 0x50, 0x36, 0x3c, 0x3c, 0x6d, 0x74, 0x1d, 0x74, 0xc0, 0xde, 0x5b, 0x45, 0x27, 0xe5, 0x12, 0xee, 0x63, 0x35, 0x6b, 0x13, 0xe2, 0x41, 0x6b, 0x3a, 0x05, 0x2b, 0xb1, 0x89, 0x26, 0xb6, 0xc6, 0xd1, 0x84, 0xff, 0x0e, 0x9b, 0xa3, 0xfb, 0x21, 0x36, 0x6b, 0x01, 0xf7, 0x9f, 0x7c, 0xeb, 0xf5, 0x18, 0x7a, 0x2a, 0x70}, + dt2: fp.Elt{0x09, 0xad, 0x99, 0x1a, 0x38, 0xd3, 0xdf, 0x22, 0x37, 0x32, 0x61, 0x8b, 0xf3, 0x19, 0x48, 0x08, 0xe8, 0x49, 0xb6, 0x4a, 0xa7, 0xed, 0xa4, 0xa2, 0xee, 0x86, 0xd7, 0x31, 0x5e, 0xce, 0x95, 0x76, 0x86, 0x42, 0x1c, 0x9d, 0x07, 0x14, 0x8c, 0x34, 0x18, 0x9c, 0x6d, 0x3a, 0xdf, 0xa9, 0xe8, 0x36, 0x7e, 0xe4, 0x95, 0xbe, 0xb5, 0x09, 0xf8, 0x9c}, + }, + { + addYX: fp.Elt{0x51, 0xdb, 0x49, 0xa8, 0x9f, 0xe3, 0xd7, 0xec, 0x0d, 0x0f, 0x49, 0xe8, 0xb6, 0xc5, 0x0f, 0x5a, 0x1c, 0xce, 0x54, 0x0d, 0xb1, 0x8d, 0x5b, 0xbf, 0xf4, 0xaa, 0x34, 0x77, 0xc4, 0x5d, 0x59, 0xb6, 0xc5, 0x0e, 0x5a, 0xd8, 0x5b, 0x30, 0xc2, 0x1d, 0xec, 0x85, 0x1c, 0x42, 0xbe, 0x24, 0x2e, 0x50, 0x55, 0x44, 0xb2, 0x3a, 0x01, 0xaa, 0x98, 0xfb}, + subYX: fp.Elt{0xe7, 0x29, 0xb7, 0xd0, 0xaa, 0x4f, 0x32, 0x53, 0x56, 0xde, 0xbc, 0xd1, 0x92, 0x5d, 0x19, 0xbe, 0xa3, 0xe3, 0x75, 0x48, 0xe0, 0x7a, 0x1b, 0x54, 0x7a, 0xb7, 0x41, 0x77, 0x84, 0x38, 0xdd, 0x14, 0x9f, 0xca, 0x3f, 0xa3, 0xc8, 0xa7, 0x04, 0x70, 0xf1, 0x4d, 0x3d, 0xb3, 0x84, 0x79, 0xcb, 0xdb, 0xe4, 0xc5, 0x42, 0x9b, 0x57, 0x19, 0xf1, 0x2d}, + dt2: fp.Elt{0x20, 0xb4, 0x94, 0x9e, 0xdf, 0x31, 0x44, 0x0b, 0xc9, 0x7b, 0x75, 0x40, 0x9d, 0xd1, 0x96, 0x39, 0x70, 0x71, 0x15, 0xc8, 0x93, 0xd5, 0xc5, 0xe5, 0xba, 0xfe, 0xee, 0x08, 0x6a, 0x98, 0x0a, 0x1b, 0xb2, 0xaa, 0x3a, 0xf4, 0xa4, 0x79, 0xf9, 0x8e, 0x4d, 0x65, 0x10, 0x9b, 0x3a, 0x6e, 0x7c, 0x87, 0x94, 0x92, 0x11, 0x65, 0xbf, 0x1a, 0x09, 0xde}, + }, + { + addYX: fp.Elt{0xf3, 0x84, 0x76, 0x77, 0xa5, 0x6b, 0x27, 0x3b, 0x83, 0x3d, 0xdf, 0xa0, 0xeb, 0x32, 0x6d, 0x58, 0x81, 0x57, 0x64, 0xc2, 0x21, 0x7c, 0x9b, 0xea, 0xe6, 0xb0, 0x93, 0xf9, 0xe7, 0xc3, 0xed, 0x5a, 0x8e, 0xe2, 0xb4, 0x72, 0x76, 0x66, 0x0f, 0x22, 0x29, 0x94, 0x3e, 0x63, 0x48, 0x5e, 0x80, 0xcb, 0xac, 0xfa, 0x95, 0xb6, 0x4b, 0xc4, 0x95, 0x33}, + subYX: fp.Elt{0x0c, 0x55, 0xd1, 0x5e, 0x5f, 0xbf, 0xbf, 0xe2, 0x4c, 0xfc, 0x37, 0x4a, 0xc4, 0xb1, 0xf4, 0x83, 0x61, 0x93, 0x60, 0x8e, 0x9f, 0x31, 0xf0, 0xa0, 0x41, 0xff, 0x1d, 0xe2, 0x7f, 0xca, 0x40, 0xd6, 0x88, 0xe8, 0x91, 0x61, 0xe2, 0x11, 0x18, 0x83, 0xf3, 0x25, 0x2f, 0x3f, 0x49, 0x40, 0xd4, 0x83, 0xe2, 0xd7, 0x74, 0x6a, 0x16, 0x86, 0x4e, 0xab}, + dt2: fp.Elt{0xdd, 0x58, 0x65, 0xd8, 0x9f, 0xdd, 0x70, 0x7f, 0x0f, 0xec, 0xbd, 0x5c, 0x5c, 0x9b, 0x7e, 0x1b, 0x9f, 0x79, 0x36, 0x1f, 0xfd, 0x79, 0x10, 0x1c, 0x52, 0xf3, 0x22, 0xa4, 0x1f, 0x71, 0x6e, 0x63, 0x14, 0xf4, 0xa7, 0x3e, 0xbe, 0xad, 0x43, 0x30, 0x38, 0x8c, 0x29, 0xc6, 0xcf, 0x50, 0x75, 0x21, 0xe5, 0x78, 0xfd, 0xb0, 0x9a, 0xc4, 0x6d, 0xd4}, + }, + }, + { + { + addYX: fp.Elt{0x7a, 0xa1, 0x38, 0xa6, 0xfd, 0x0e, 0x96, 0xd5, 0x26, 0x76, 0x86, 0x70, 0x80, 0x30, 0xa6, 0x67, 0xeb, 0xf4, 0x39, 0xdb, 0x22, 0xf5, 0x9f, 0x98, 0xe4, 0xb5, 0x3a, 0x0c, 0x59, 0xbf, 0x85, 0xc6, 0xf0, 0x0b, 0x1c, 0x41, 0x38, 0x09, 0x01, 0xdb, 0xd6, 0x3c, 0xb7, 0xf1, 0x08, 0x6b, 0x4b, 0x9e, 0x63, 0x53, 0x83, 0xd3, 0xab, 0xa3, 0x72, 0x0d}, + subYX: fp.Elt{0x84, 0x68, 0x25, 0xe8, 0xe9, 0x8f, 0x91, 0xbf, 0xf7, 0xa4, 0x30, 0xae, 0xea, 0x9f, 0xdd, 0x56, 0x64, 0x09, 0xc9, 0x54, 0x68, 0x4e, 0x33, 0xc5, 0x6f, 0x7b, 0x2d, 0x52, 0x2e, 0x42, 0xbe, 0xbe, 0xf5, 0x64, 0xbf, 0x77, 0x54, 0xdf, 0xb0, 0x10, 0xd2, 0x16, 0x5d, 0xce, 0xaf, 0x9f, 0xfb, 0xa3, 0x63, 0x50, 0xcb, 0xc0, 0xd0, 0x88, 0x44, 0xa3}, + dt2: fp.Elt{0xc3, 0x8b, 0xa5, 0xf1, 0x44, 0xe4, 0x41, 0xcd, 0x75, 0xe3, 0x17, 0x69, 0x5b, 0xb9, 0xbb, 0xee, 0x82, 0xbb, 0xce, 0x57, 0xdf, 0x2a, 0x9c, 0x12, 0xab, 0x66, 0x08, 0x68, 0x05, 0x1b, 0x87, 0xee, 0x5d, 0x1e, 0x18, 0x14, 0x22, 0x4b, 0x99, 0x61, 0x75, 0x28, 0xe7, 0x65, 0x1c, 0x36, 0xb6, 0x18, 0x09, 0xa8, 0xdf, 0xef, 0x30, 0x35, 0xbc, 0x58}, + }, + { + addYX: fp.Elt{0xc5, 0xd3, 0x0e, 0x6f, 0xaf, 0x06, 0x69, 0xc4, 0x07, 0x9e, 0x58, 0x6e, 0x3f, 0x49, 0xd9, 0x0a, 0x3c, 0x2c, 0x37, 0xcd, 0x27, 0x4d, 0x87, 0x91, 0x7a, 0xb0, 0x28, 0xad, 0x2f, 0x68, 0x92, 0x05, 0x97, 0xf1, 0x30, 0x5f, 0x4c, 0x10, 0x20, 0x30, 0xd3, 0x08, 0x3f, 0xc1, 0xc6, 0xb7, 0xb5, 0xd1, 0x71, 0x7b, 0xa8, 0x0a, 0xd8, 0xf5, 0x17, 0xcf}, + subYX: fp.Elt{0x64, 0xd4, 0x8f, 0x91, 0x40, 0xab, 0x6e, 0x1a, 0x62, 0x83, 0xdc, 0xd7, 0x30, 0x1a, 0x4a, 0x2a, 0x4c, 0x54, 0x86, 0x19, 0x81, 0x5d, 0x04, 0x52, 0xa3, 0xca, 0x82, 0x38, 0xdc, 0x1e, 0xf0, 0x7a, 0x78, 0x76, 0x49, 0x4f, 0x71, 0xc4, 0x74, 0x2f, 0xf0, 0x5b, 0x2e, 0x5e, 0xac, 0xef, 0x17, 0xe4, 0x8e, 0x6e, 0xed, 0x43, 0x23, 0x61, 0x99, 0x49}, + dt2: fp.Elt{0x64, 0x90, 0x72, 0x76, 0xf8, 0x2c, 0x7d, 0x57, 0xf9, 0x30, 0x5e, 0x7a, 0x10, 0x74, 0x19, 0x39, 0xd9, 0xaf, 0x0a, 0xf1, 0x43, 0xed, 0x88, 0x9c, 0x8b, 0xdc, 0x9b, 0x1c, 0x90, 0xe7, 0xf7, 0xa3, 0xa5, 0x0d, 0xc6, 0xbc, 0x30, 0xfb, 0x91, 0x1a, 0x51, 0xba, 0x2d, 0xbe, 0x89, 0xdf, 0x1d, 0xdc, 0x53, 0xa8, 0x82, 0x8a, 0xd3, 0x8d, 0x16, 0x68}, + }, + { + addYX: fp.Elt{0xef, 0x5c, 0xe3, 0x74, 0xbf, 0x13, 0x4a, 0xbf, 0x66, 0x73, 0x64, 0xb7, 0xd4, 0xce, 0x98, 0x82, 0x05, 0xfa, 0x98, 0x0c, 0x0a, 0xae, 0xe5, 0x6b, 0x9f, 0xac, 0xbb, 0x6e, 0x1f, 0xcf, 0xff, 0xa6, 0x71, 0x9a, 0xa8, 0x7a, 0x9e, 0x64, 0x1f, 0x20, 0x4a, 0x61, 0xa2, 0xd6, 0x50, 0xe3, 0xba, 0x81, 0x0c, 0x50, 0x59, 0x69, 0x59, 0x15, 0x55, 0xdb}, + subYX: fp.Elt{0xe8, 0x77, 0x4d, 0xe8, 0x66, 0x3d, 0xc1, 0x00, 0x3c, 0xf2, 0x25, 0x00, 0xdc, 0xb2, 0xe5, 0x9b, 0x12, 0x89, 0xf3, 0xd6, 0xea, 0x85, 0x60, 0xfe, 0x67, 0x91, 0xfd, 0x04, 0x7c, 0xe0, 0xf1, 0x86, 0x06, 0x11, 0x66, 0xee, 0xd4, 0xd5, 0xbe, 0x3b, 0x0f, 0xe3, 0x59, 0xb3, 0x4f, 0x00, 0xb6, 0xce, 0x80, 0xc1, 0x61, 0xf7, 0xaf, 0x04, 0x6a, 0x3c}, + dt2: fp.Elt{0x00, 0xd7, 0x32, 0x93, 0x67, 0x70, 0x6f, 0xd7, 0x69, 0xab, 0xb1, 0xd3, 0xdc, 0xd6, 0xa8, 0xdd, 0x35, 0x25, 0xca, 0xd3, 0x8a, 0x6d, 0xce, 0xfb, 0xfd, 0x2b, 0x83, 0xf0, 0xd4, 0xac, 0x66, 0xfb, 0x72, 0x87, 0x7e, 0x55, 0xb7, 0x91, 0x58, 0x10, 0xc3, 0x11, 0x7e, 0x15, 0xfe, 0x7c, 0x55, 0x90, 0xa3, 0x9e, 0xed, 0x9a, 0x7f, 0xa7, 0xb7, 0xeb}, + }, + { + addYX: fp.Elt{0x25, 0x0f, 0xc2, 0x09, 0x9c, 0x10, 0xc8, 0x7c, 0x93, 0xa7, 0xbe, 0xe9, 0x26, 0x25, 0x7c, 0x21, 0xfe, 0xe7, 0x5f, 0x3c, 0x02, 0x83, 0xa7, 0x9e, 0xdf, 0xc0, 0x94, 0x2b, 0x7d, 0x1a, 0xd0, 0x1d, 0xcc, 0x2e, 0x7d, 0xd4, 0x85, 0xe7, 0xc1, 0x15, 0x66, 0xd6, 0xd6, 0x32, 0xb8, 0xf7, 0x63, 0xaa, 0x3b, 0xa5, 0xea, 0x49, 0xad, 0x88, 0x9b, 0x66}, + subYX: fp.Elt{0x09, 0x97, 0x79, 0x36, 0x41, 0x56, 0x9b, 0xdf, 0x15, 0xd8, 0x43, 0x28, 0x17, 0x5b, 0x96, 0xc9, 0xcf, 0x39, 0x1f, 0x13, 0xf7, 0x4d, 0x1d, 0x1f, 0xda, 0x51, 0x56, 0xe7, 0x0a, 0x5a, 0x65, 0xb6, 0x2a, 0x87, 0x49, 0x86, 0xc2, 0x2b, 0xcd, 0xfe, 0x07, 0xf6, 0x4c, 0xe2, 0x1d, 0x9b, 0xd8, 0x82, 0x09, 0x5b, 0x11, 0x10, 0x62, 0x56, 0x89, 0xbd}, + dt2: fp.Elt{0xd9, 0x15, 0x73, 0xf2, 0x96, 0x35, 0x53, 0xb0, 0xe7, 0xa8, 0x0b, 0x93, 0x35, 0x0b, 0x3a, 0x00, 0xf5, 0x18, 0xb1, 0xc3, 0x12, 0x3f, 0x91, 0x17, 0xc1, 0x4c, 0x15, 0x5a, 0x86, 0x92, 0x11, 0xbd, 0x44, 0x40, 0x5a, 0x7b, 0x15, 0x89, 0xba, 0xc1, 0xc1, 0xbc, 0x43, 0x45, 0xe6, 0x52, 0x02, 0x73, 0x0a, 0xd0, 0x2a, 0x19, 0xda, 0x47, 0xa8, 0xff}, + }, + }, +} + +// tabVerif contains the odd multiples of P. The entry T[i] = (2i+1)P, where +// P = phi(G) and G is the generator of the Goldilocks curve, and phi is a +// 4-degree isogeny. +var tabVerif = [1 << (omegaFix - 2)]preTwistPointAffine{ + { /* 1P*/ + addYX: fp.Elt{0x65, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2b, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05}, + subYX: fp.Elt{0x64, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2d, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05}, + dt2: fp.Elt{0x1a, 0x33, 0xea, 0x64, 0x45, 0x1c, 0xdf, 0x17, 0x1d, 0x16, 0x34, 0x28, 0xd6, 0x61, 0x19, 0x67, 0x79, 0xb4, 0x13, 0xcf, 0x3e, 0x7c, 0x0e, 0x72, 0xda, 0xf1, 0x5f, 0xda, 0xe6, 0xcf, 0x42, 0xd3, 0xb6, 0x17, 0xc2, 0x68, 0x13, 0x2d, 0xd9, 0x60, 0x3e, 0xae, 0xf0, 0x5b, 0x96, 0xf0, 0xcd, 0xaf, 0xea, 0xb7, 0x0d, 0x59, 0x16, 0xa7, 0xff, 0x55}, + }, + { /* 3P*/ + addYX: fp.Elt{0xd1, 0xe9, 0xa8, 0x33, 0x20, 0x76, 0x18, 0x08, 0x45, 0x2a, 0xc9, 0x67, 0x2a, 0xc3, 0x15, 0x24, 0xf9, 0x74, 0x21, 0x30, 0x99, 0x59, 0x8b, 0xb2, 0xf0, 0xa4, 0x07, 0xe2, 0x6a, 0x36, 0x8d, 0xd9, 0xd2, 0x4a, 0x7f, 0x73, 0x50, 0x39, 0x3d, 0xaa, 0xa7, 0x51, 0x73, 0x0d, 0x2b, 0x8b, 0x96, 0x47, 0xac, 0x3c, 0x5d, 0xaa, 0x39, 0x9c, 0xcf, 0xd5}, + subYX: fp.Elt{0x6b, 0x11, 0x5d, 0x1a, 0xf9, 0x41, 0x9d, 0xc5, 0x30, 0x3e, 0xad, 0x25, 0x2c, 0x04, 0x45, 0xea, 0xcc, 0x67, 0x07, 0x85, 0xe9, 0xda, 0x0e, 0xb5, 0x40, 0xb7, 0x32, 0xb4, 0x49, 0xdd, 0xff, 0xaa, 0xfc, 0xbb, 0x19, 0xca, 0x8b, 0x79, 0x2b, 0x8f, 0x8d, 0x00, 0x33, 0xc2, 0xad, 0xe9, 0xd3, 0x12, 0xa8, 0xaa, 0x87, 0x62, 0xad, 0x2d, 0xff, 0xa4}, + dt2: fp.Elt{0xb0, 0xaf, 0x3b, 0xea, 0xf0, 0x42, 0x0b, 0x5e, 0x88, 0xd3, 0x98, 0x08, 0x87, 0x59, 0x72, 0x0a, 0xc2, 0xdf, 0xcb, 0x7f, 0x59, 0xb5, 0x4c, 0x63, 0x68, 0xe8, 0x41, 0x38, 0x67, 0x4f, 0xe9, 0xc6, 0xb2, 0x6b, 0x08, 0xa7, 0xf7, 0x0e, 0xcd, 0xea, 0xca, 0x3d, 0xaf, 0x8e, 0xda, 0x4b, 0x2e, 0xd2, 0x88, 0x64, 0x8d, 0xc5, 0x5f, 0x76, 0x0f, 0x3d}, + }, + { /* 5P*/ + addYX: fp.Elt{0xe5, 0x65, 0xc9, 0xe2, 0x75, 0xf0, 0x7d, 0x1a, 0xba, 0xa4, 0x40, 0x4b, 0x93, 0x12, 0xa2, 0x80, 0x95, 0x0d, 0x03, 0x93, 0xe8, 0xa5, 0x4d, 0xe2, 0x3d, 0x81, 0xf5, 0xce, 0xd4, 0x2d, 0x25, 0x59, 0x16, 0x5c, 0xe7, 0xda, 0xc7, 0x45, 0xd2, 0x7e, 0x2c, 0x38, 0xd4, 0x37, 0x64, 0xb2, 0xc2, 0x28, 0xc5, 0x72, 0x16, 0x32, 0x45, 0x36, 0x6f, 0x9f}, + subYX: fp.Elt{0x09, 0xf4, 0x7e, 0xbd, 0x89, 0xdb, 0x19, 0x58, 0xe1, 0x08, 0x00, 0x8a, 0xf4, 0x5f, 0x2a, 0x32, 0x40, 0xf0, 0x2c, 0x3f, 0x5d, 0xe4, 0xfc, 0x89, 0x11, 0x24, 0xb4, 0x2f, 0x97, 0xad, 0xac, 0x8f, 0x19, 0xab, 0xfa, 0x12, 0xe5, 0xf9, 0x50, 0x4e, 0x50, 0x6f, 0x32, 0x30, 0x88, 0xa6, 0xe5, 0x48, 0x28, 0xa2, 0x1b, 0x9f, 0xcd, 0xe2, 0x43, 0x38}, + dt2: fp.Elt{0xa9, 0xcc, 0x53, 0x39, 0x86, 0x02, 0x60, 0x75, 0x34, 0x99, 0x57, 0xbd, 0xfc, 0x5a, 0x8e, 0xce, 0x5e, 0x98, 0x22, 0xd0, 0xa5, 0x24, 0xff, 0x90, 0x28, 0x9f, 0x58, 0xf3, 0x39, 0xe9, 0xba, 0x36, 0x23, 0xfb, 0x7f, 0x41, 0xcc, 0x2b, 0x5a, 0x25, 0x3f, 0x4c, 0x2a, 0xf1, 0x52, 0x6f, 0x2f, 0x07, 0xe3, 0x88, 0x81, 0x77, 0xdd, 0x7c, 0x88, 0x82}, + }, + { /* 7P*/ + addYX: fp.Elt{0xf7, 0xee, 0x88, 0xfd, 0x3a, 0xbf, 0x7e, 0x28, 0x39, 0x23, 0x79, 0xe6, 0x5c, 0x56, 0xcb, 0xb5, 0x48, 0x6a, 0x80, 0x6d, 0x37, 0x60, 0x6c, 0x10, 0x35, 0x49, 0x4b, 0x46, 0x60, 0xd4, 0x79, 0xd4, 0x53, 0xd3, 0x67, 0x88, 0xd0, 0x41, 0xd5, 0x43, 0x85, 0xc8, 0x71, 0xe3, 0x1c, 0xb6, 0xda, 0x22, 0x64, 0x8f, 0x80, 0xac, 0xad, 0x7d, 0xd5, 0x82}, + subYX: fp.Elt{0x92, 0x40, 0xc1, 0x83, 0x21, 0x9b, 0xd5, 0x7d, 0x3f, 0x29, 0xb6, 0x26, 0xef, 0x12, 0xb9, 0x27, 0x39, 0x42, 0x37, 0x97, 0x09, 0x9a, 0x08, 0xe1, 0x68, 0xb6, 0x7a, 0x3f, 0x9f, 0x45, 0xf8, 0x37, 0x19, 0x83, 0x97, 0xe6, 0x73, 0x30, 0x32, 0x35, 0xcf, 0xae, 0x5c, 0x12, 0x68, 0xdf, 0x6e, 0x2b, 0xde, 0x83, 0xa0, 0x44, 0x74, 0x2e, 0x4a, 0xe9}, + dt2: fp.Elt{0xcb, 0x22, 0x0a, 0xda, 0x6b, 0xc1, 0x8a, 0x29, 0xa1, 0xac, 0x8b, 0x5b, 0x8b, 0x32, 0x20, 0xf2, 0x21, 0xae, 0x0c, 0x43, 0xc4, 0xd7, 0x19, 0x37, 0x3d, 0x79, 0x25, 0x98, 0x6c, 0x9c, 0x22, 0x31, 0x2a, 0x55, 0x9f, 0xda, 0x5e, 0xa8, 0x13, 0xdb, 0x8e, 0x2e, 0x16, 0x39, 0xf4, 0x91, 0x6f, 0xec, 0x71, 0x71, 0xc9, 0x10, 0xf2, 0xa4, 0x8f, 0x11}, + }, + { /* 9P*/ + addYX: fp.Elt{0x85, 0xdd, 0x37, 0x62, 0x74, 0x8e, 0x33, 0x5b, 0x25, 0x12, 0x1b, 0xe7, 0xdf, 0x47, 0xe5, 0x12, 0xfd, 0x3a, 0x3a, 0xf5, 0x5d, 0x4c, 0xa2, 0x29, 0x3c, 0x5c, 0x2f, 0xee, 0x18, 0x19, 0x0a, 0x2b, 0xef, 0x67, 0x50, 0x7a, 0x0d, 0x29, 0xae, 0x55, 0x82, 0xcd, 0xd6, 0x41, 0x90, 0xb4, 0x13, 0x31, 0x5d, 0x11, 0xb8, 0xaa, 0x12, 0x86, 0x08, 0xac}, + subYX: fp.Elt{0xcc, 0x37, 0x8d, 0x83, 0x5f, 0xfd, 0xde, 0xd5, 0xf7, 0xf1, 0xae, 0x0a, 0xa7, 0x0b, 0xeb, 0x6d, 0x19, 0x8a, 0xb6, 0x1a, 0x59, 0xd8, 0xff, 0x3c, 0xbc, 0xbc, 0xef, 0x9c, 0xda, 0x7b, 0x75, 0x12, 0xaf, 0x80, 0x8f, 0x2c, 0x3c, 0xaa, 0x0b, 0x17, 0x86, 0x36, 0x78, 0x18, 0xc8, 0x8a, 0xf6, 0xb8, 0x2c, 0x2f, 0x57, 0x2c, 0x62, 0x57, 0xf6, 0x90}, + dt2: fp.Elt{0x83, 0xbc, 0xa2, 0x07, 0xa5, 0x38, 0x96, 0xea, 0xfe, 0x11, 0x46, 0x1d, 0x3b, 0xcd, 0x42, 0xc5, 0xee, 0x67, 0x04, 0x72, 0x08, 0xd8, 0xd9, 0x96, 0x07, 0xf7, 0xac, 0xc3, 0x64, 0xf1, 0x98, 0x2c, 0x55, 0xd7, 0x7d, 0xc8, 0x6c, 0xbd, 0x2c, 0xff, 0x15, 0xd6, 0x6e, 0xb8, 0x17, 0x8e, 0xa8, 0x27, 0x66, 0xb1, 0x73, 0x79, 0x96, 0xff, 0x29, 0x10}, + }, + { /* 11P*/ + addYX: fp.Elt{0x76, 0xcb, 0x9b, 0x0c, 0x5b, 0xfe, 0xe1, 0x2a, 0xdd, 0x6f, 0x6c, 0xdd, 0x6f, 0xb4, 0xc0, 0xc2, 0x1b, 0x4b, 0x38, 0xe8, 0x66, 0x8c, 0x1e, 0x31, 0x63, 0xb9, 0x94, 0xcd, 0xc3, 0x8c, 0x44, 0x25, 0x7b, 0xd5, 0x39, 0x80, 0xfc, 0x01, 0xaa, 0xf7, 0x2a, 0x61, 0x8a, 0x25, 0xd2, 0x5f, 0xc5, 0x66, 0x38, 0xa4, 0x17, 0xcf, 0x3e, 0x11, 0x0f, 0xa3}, + subYX: fp.Elt{0xe0, 0xb6, 0xd1, 0x9c, 0x71, 0x49, 0x2e, 0x7b, 0xde, 0x00, 0xda, 0x6b, 0xf1, 0xec, 0xe6, 0x7a, 0x15, 0x38, 0x71, 0xe9, 0x7b, 0xdb, 0xf8, 0x98, 0xc0, 0x91, 0x2e, 0x53, 0xee, 0x92, 0x87, 0x25, 0xc9, 0xb0, 0xbb, 0x33, 0x15, 0x46, 0x7f, 0xfd, 0x4f, 0x8b, 0x77, 0x05, 0x96, 0xb6, 0xe2, 0x08, 0xdb, 0x0d, 0x09, 0xee, 0x5b, 0xd1, 0x2a, 0x63}, + dt2: fp.Elt{0x8f, 0x7b, 0x57, 0x8c, 0xbf, 0x06, 0x0d, 0x43, 0x21, 0x92, 0x94, 0x2d, 0x6a, 0x38, 0x07, 0x0f, 0xa0, 0xf1, 0xe3, 0xd8, 0x2a, 0xbf, 0x46, 0xc6, 0x9e, 0x1f, 0x8f, 0x2b, 0x46, 0x84, 0x0b, 0x74, 0xed, 0xff, 0xf8, 0xa5, 0x94, 0xae, 0xf1, 0x67, 0xb1, 0x9b, 0xdd, 0x4a, 0xd0, 0xdb, 0xc2, 0xb5, 0x58, 0x49, 0x0c, 0xa9, 0x1d, 0x7d, 0xa9, 0xd3}, + }, + { /* 13P*/ + addYX: fp.Elt{0x73, 0x84, 0x2e, 0x31, 0x1f, 0xdc, 0xed, 0x9f, 0x74, 0xfa, 0xe0, 0x35, 0xb1, 0x85, 0x6a, 0x8d, 0x86, 0xd0, 0xff, 0xd6, 0x08, 0x43, 0x73, 0x1a, 0xd5, 0xf8, 0x43, 0xd4, 0xb3, 0xe5, 0x3f, 0xa8, 0x84, 0x17, 0x59, 0x65, 0x4e, 0xe6, 0xee, 0x54, 0x9c, 0xda, 0x5e, 0x7e, 0x98, 0x29, 0x6d, 0x73, 0x34, 0x1f, 0x99, 0x80, 0x54, 0x54, 0x81, 0x0b}, + subYX: fp.Elt{0xb1, 0xe5, 0xbb, 0x80, 0x22, 0x9c, 0x81, 0x6d, 0xaf, 0x27, 0x65, 0x6f, 0x7e, 0x9c, 0xb6, 0x8d, 0x35, 0x5c, 0x2e, 0x20, 0x48, 0x7a, 0x28, 0xf0, 0x97, 0xfe, 0xb7, 0x71, 0xce, 0xd6, 0xad, 0x3a, 0x81, 0xf6, 0x74, 0x5e, 0xf3, 0xfd, 0x1b, 0xd4, 0x1e, 0x7c, 0xc2, 0xb7, 0xc8, 0xa6, 0xc9, 0x89, 0x03, 0x47, 0xec, 0x24, 0xd6, 0x0e, 0xec, 0x9c}, + dt2: fp.Elt{0x91, 0x0a, 0x43, 0x34, 0x20, 0xc2, 0x64, 0xf7, 0x4e, 0x48, 0xc8, 0xd2, 0x95, 0x83, 0xd1, 0xa4, 0xfb, 0x4e, 0x41, 0x3b, 0x0d, 0xd5, 0x07, 0xd9, 0xf1, 0x13, 0x16, 0x78, 0x54, 0x57, 0xd0, 0xf1, 0x4f, 0x20, 0xac, 0xcf, 0x9c, 0x3b, 0x33, 0x0b, 0x99, 0x54, 0xc3, 0x7f, 0x3e, 0x57, 0x26, 0x86, 0xd5, 0xa5, 0x2b, 0x8d, 0xe3, 0x19, 0x36, 0xf7}, + }, + { /* 15P*/ + addYX: fp.Elt{0x23, 0x69, 0x47, 0x14, 0xf9, 0x9a, 0x50, 0xff, 0x64, 0xd1, 0x50, 0x35, 0xc3, 0x11, 0xd3, 0x19, 0xcf, 0x87, 0xda, 0x30, 0x0b, 0x50, 0xda, 0xc0, 0xe0, 0x25, 0x00, 0xe5, 0x68, 0x93, 0x04, 0xc2, 0xaf, 0xbd, 0x2f, 0x36, 0x5f, 0x47, 0x96, 0x10, 0xa8, 0xbd, 0xe4, 0x88, 0xac, 0x80, 0x52, 0x61, 0x73, 0xe9, 0x63, 0xdd, 0x99, 0xad, 0x20, 0x5b}, + subYX: fp.Elt{0x1b, 0x5e, 0xa2, 0x2a, 0x25, 0x0f, 0x86, 0xc0, 0xb1, 0x2e, 0x0c, 0x13, 0x40, 0x8d, 0xf0, 0xe6, 0x00, 0x55, 0x08, 0xc5, 0x7d, 0xf4, 0xc9, 0x31, 0x25, 0x3a, 0x99, 0x69, 0xdd, 0x67, 0x63, 0x9a, 0xd6, 0x89, 0x2e, 0xa1, 0x19, 0xca, 0x2c, 0xd9, 0x59, 0x5f, 0x5d, 0xc3, 0x6e, 0x62, 0x36, 0x12, 0x59, 0x15, 0xe1, 0xdc, 0xa4, 0xad, 0xc9, 0xd0}, + dt2: fp.Elt{0xbc, 0xea, 0xfc, 0xaf, 0x66, 0x23, 0xb7, 0x39, 0x6b, 0x2a, 0x96, 0xa8, 0x54, 0x43, 0xe9, 0xaa, 0x32, 0x40, 0x63, 0x92, 0x5e, 0xdf, 0x35, 0xc2, 0x9f, 0x24, 0x0c, 0xed, 0xfc, 0xde, 0x73, 0x8f, 0xa7, 0xd5, 0xa3, 0x2b, 0x18, 0x1f, 0xb0, 0xf8, 0xeb, 0x55, 0xd9, 0xc3, 0xfd, 0x28, 0x7c, 0x4f, 0xce, 0x0d, 0xf7, 0xae, 0xc2, 0x83, 0xc3, 0x78}, + }, + { /* 17P*/ + addYX: fp.Elt{0x71, 0xe6, 0x60, 0x93, 0x37, 0xdb, 0x01, 0xa5, 0x4c, 0xba, 0xe8, 0x8e, 0xd5, 0xf9, 0xd3, 0x98, 0xe5, 0xeb, 0xab, 0x3a, 0x15, 0x8b, 0x35, 0x60, 0xbe, 0xe5, 0x9c, 0x2d, 0x10, 0x9b, 0x2e, 0xcf, 0x65, 0x64, 0xea, 0x8f, 0x72, 0xce, 0xf5, 0x18, 0xe5, 0xe2, 0xf0, 0x0e, 0xae, 0x04, 0xec, 0xa0, 0x20, 0x65, 0x63, 0x07, 0xb1, 0x9f, 0x03, 0x97}, + subYX: fp.Elt{0x9e, 0x41, 0x64, 0x30, 0x95, 0x7f, 0x3a, 0x89, 0x7b, 0x0a, 0x79, 0x59, 0x23, 0x9a, 0x3b, 0xfe, 0xa4, 0x13, 0x08, 0xb2, 0x2e, 0x04, 0x50, 0x10, 0x30, 0xcd, 0x2e, 0xa4, 0x91, 0x71, 0x50, 0x36, 0x4a, 0x02, 0xf4, 0x8d, 0xa3, 0x36, 0x1b, 0xf4, 0x52, 0xba, 0x15, 0x04, 0x8b, 0x80, 0x25, 0xd9, 0xae, 0x67, 0x20, 0xd9, 0x88, 0x8f, 0x97, 0xa6}, + dt2: fp.Elt{0xb5, 0xe7, 0x46, 0xbd, 0x55, 0x23, 0xa0, 0x68, 0xc0, 0x12, 0xd9, 0xf1, 0x0a, 0x75, 0xe2, 0xda, 0xf4, 0x6b, 0xca, 0x14, 0xe4, 0x9f, 0x0f, 0xb5, 0x3c, 0xa6, 0xa5, 0xa2, 0x63, 0x94, 0xd1, 0x1c, 0x39, 0x58, 0x57, 0x02, 0x27, 0x98, 0xb6, 0x47, 0xc6, 0x61, 0x4b, 0x5c, 0xab, 0x6f, 0x2d, 0xab, 0xe3, 0xc1, 0x69, 0xf9, 0x12, 0xb0, 0xc8, 0xd5}, + }, + { /* 19P*/ + addYX: fp.Elt{0x19, 0x7d, 0xd5, 0xac, 0x79, 0xa2, 0x82, 0x9b, 0x28, 0x31, 0x22, 0xc0, 0x73, 0x02, 0x76, 0x17, 0x10, 0x70, 0x79, 0x57, 0xc9, 0x84, 0x62, 0x8e, 0x04, 0x04, 0x61, 0x67, 0x08, 0x48, 0xb4, 0x4b, 0xde, 0x53, 0x8c, 0xff, 0x36, 0x1b, 0x62, 0x86, 0x5d, 0xe1, 0x9b, 0xb1, 0xe5, 0xe8, 0x44, 0x64, 0xa1, 0x68, 0x3f, 0xa8, 0x45, 0x52, 0x91, 0xed}, + subYX: fp.Elt{0x42, 0x1a, 0x36, 0x1f, 0x90, 0x15, 0x24, 0x8d, 0x24, 0x80, 0xe6, 0xfe, 0x1e, 0xf0, 0xad, 0xaf, 0x6a, 0x93, 0xf0, 0xa6, 0x0d, 0x5d, 0xea, 0xf6, 0x62, 0x96, 0x7a, 0x05, 0x76, 0x85, 0x74, 0x32, 0xc7, 0xc8, 0x64, 0x53, 0x62, 0xe7, 0x54, 0x84, 0xe0, 0x40, 0x66, 0x19, 0x70, 0x40, 0x95, 0x35, 0x68, 0x64, 0x43, 0xcd, 0xba, 0x29, 0x32, 0xa8}, + dt2: fp.Elt{0x3e, 0xf6, 0xd6, 0xe4, 0x99, 0xeb, 0x20, 0x66, 0x08, 0x2e, 0x26, 0x64, 0xd7, 0x76, 0xf3, 0xb4, 0xc5, 0xa4, 0x35, 0x92, 0xd2, 0x99, 0x70, 0x5a, 0x1a, 0xe9, 0xe9, 0x3d, 0x3b, 0xe1, 0xcd, 0x0e, 0xee, 0x24, 0x13, 0x03, 0x22, 0xd6, 0xd6, 0x72, 0x08, 0x2b, 0xde, 0xfd, 0x93, 0xed, 0x0c, 0x7f, 0x5e, 0x31, 0x22, 0x4d, 0x80, 0x78, 0xc0, 0x48}, + }, + { /* 21P*/ + addYX: fp.Elt{0x8f, 0x72, 0xd2, 0x9e, 0xc4, 0xcd, 0x2c, 0xbf, 0xa8, 0xd3, 0x24, 0x62, 0x28, 0xee, 0x39, 0x0a, 0x19, 0x3a, 0x58, 0xff, 0x21, 0x2e, 0x69, 0x6c, 0x6e, 0x18, 0xd0, 0xcd, 0x61, 0xc1, 0x18, 0x02, 0x5a, 0xe9, 0xe3, 0xef, 0x1f, 0x8e, 0x10, 0xe8, 0x90, 0x2b, 0x48, 0xcd, 0xee, 0x38, 0xbd, 0x3a, 0xca, 0xbc, 0x2d, 0xe2, 0x3a, 0x03, 0x71, 0x02}, + subYX: fp.Elt{0xf8, 0xa4, 0x32, 0x26, 0x66, 0xaf, 0x3b, 0x53, 0xe7, 0xb0, 0x91, 0x92, 0xf5, 0x3c, 0x74, 0xce, 0xf2, 0xdd, 0x68, 0xa9, 0xf4, 0xcd, 0x5f, 0x60, 0xab, 0x71, 0xdf, 0xcd, 0x5c, 0x5d, 0x51, 0x72, 0x3a, 0x96, 0xea, 0xd6, 0xde, 0x54, 0x8e, 0x55, 0x4c, 0x08, 0x4c, 0x60, 0xdd, 0x34, 0xa9, 0x6f, 0xf3, 0x04, 0x02, 0xa8, 0xa6, 0x4e, 0x4d, 0x62}, + dt2: fp.Elt{0x76, 0x4a, 0xae, 0x38, 0x62, 0x69, 0x72, 0xdc, 0xe8, 0x43, 0xbe, 0x1d, 0x61, 0xde, 0x31, 0xc3, 0x42, 0x8f, 0x33, 0x9d, 0xca, 0xc7, 0x9c, 0xec, 0x6a, 0xe2, 0xaa, 0x01, 0x49, 0x78, 0x8d, 0x72, 0x4f, 0x38, 0xea, 0x52, 0xc2, 0xd3, 0xc9, 0x39, 0x71, 0xba, 0xb9, 0x09, 0x9b, 0xa3, 0x7f, 0x45, 0x43, 0x65, 0x36, 0x29, 0xca, 0xe7, 0x5c, 0x5f}, + }, + { /* 23P*/ + addYX: fp.Elt{0x89, 0x42, 0x35, 0x48, 0x6d, 0x74, 0xe5, 0x1f, 0xc3, 0xdd, 0x28, 0x5b, 0x84, 0x41, 0x33, 0x9f, 0x42, 0xf3, 0x1d, 0x5d, 0x15, 0x6d, 0x76, 0x33, 0x36, 0xaf, 0xe9, 0xdd, 0xfa, 0x63, 0x4f, 0x7a, 0x9c, 0xeb, 0x1c, 0x4f, 0x34, 0x65, 0x07, 0x54, 0xbb, 0x4c, 0x8b, 0x62, 0x9d, 0xd0, 0x06, 0x99, 0xb3, 0xe9, 0xda, 0x85, 0x19, 0xb0, 0x3d, 0x3c}, + subYX: fp.Elt{0xbb, 0x99, 0xf6, 0xbf, 0xaf, 0x2c, 0x22, 0x0d, 0x7a, 0xaa, 0x98, 0x6f, 0x01, 0x82, 0x99, 0xcf, 0x88, 0xbd, 0x0e, 0x3a, 0x89, 0xe0, 0x9c, 0x8c, 0x17, 0x20, 0xc4, 0xe0, 0xcf, 0x43, 0x7a, 0xef, 0x0d, 0x9f, 0x87, 0xd4, 0xfb, 0xf2, 0x96, 0xb8, 0x03, 0xe8, 0xcb, 0x5c, 0xec, 0x65, 0x5f, 0x49, 0xa4, 0x7c, 0x85, 0xb4, 0xf6, 0xc7, 0xdb, 0xa3}, + dt2: fp.Elt{0x11, 0xf3, 0x32, 0xa3, 0xa7, 0xb2, 0x7d, 0x51, 0x82, 0x44, 0xeb, 0xa2, 0x7d, 0x72, 0xcb, 0xc6, 0xf6, 0xc7, 0xb2, 0x38, 0x0e, 0x0f, 0x4f, 0x29, 0x00, 0xe4, 0x5b, 0x94, 0x46, 0x86, 0x66, 0xa1, 0x83, 0xb3, 0xeb, 0x15, 0xb6, 0x31, 0x50, 0x28, 0xeb, 0xed, 0x0d, 0x32, 0x39, 0xe9, 0x23, 0x81, 0x99, 0x3e, 0xff, 0x17, 0x4c, 0x11, 0x43, 0xd1}, + }, + { /* 25P*/ + addYX: fp.Elt{0xce, 0xe7, 0xf8, 0x94, 0x8f, 0x96, 0xf8, 0x96, 0xe6, 0x72, 0x20, 0x44, 0x2c, 0xa7, 0xfc, 0xba, 0xc8, 0xe1, 0xbb, 0xc9, 0x16, 0x85, 0xcd, 0x0b, 0xe5, 0xb5, 0x5a, 0x7f, 0x51, 0x43, 0x63, 0x8b, 0x23, 0x8e, 0x1d, 0x31, 0xff, 0x46, 0x02, 0x66, 0xcc, 0x9e, 0x4d, 0xa2, 0xca, 0xe2, 0xc7, 0xfd, 0x22, 0xb1, 0xdb, 0xdf, 0x6f, 0xe6, 0xa5, 0x82}, + subYX: fp.Elt{0xd0, 0xf5, 0x65, 0x40, 0xec, 0x8e, 0x65, 0x42, 0x78, 0xc1, 0x65, 0xe4, 0x10, 0xc8, 0x0b, 0x1b, 0xdd, 0x96, 0x68, 0xce, 0xee, 0x45, 0x55, 0xd8, 0x6e, 0xd3, 0xe6, 0x77, 0x19, 0xae, 0xc2, 0x8d, 0x8d, 0x3e, 0x14, 0x3f, 0x6d, 0x00, 0x2f, 0x9b, 0xd1, 0x26, 0x60, 0x28, 0x0f, 0x3a, 0x47, 0xb3, 0xe6, 0x68, 0x28, 0x24, 0x25, 0xca, 0xc8, 0x06}, + dt2: fp.Elt{0x54, 0xbb, 0x60, 0x92, 0xdb, 0x8f, 0x0f, 0x38, 0xe0, 0xe6, 0xe4, 0xc9, 0xcc, 0x14, 0x62, 0x01, 0xc4, 0x2b, 0x0f, 0xcf, 0xed, 0x7d, 0x8e, 0xa4, 0xd9, 0x73, 0x0b, 0xba, 0x0c, 0xaf, 0x0c, 0xf9, 0xe2, 0xeb, 0x29, 0x2a, 0x53, 0xdf, 0x2c, 0x5a, 0xfa, 0x8f, 0xc1, 0x01, 0xd7, 0xb1, 0x45, 0x73, 0x92, 0x32, 0x83, 0x85, 0x12, 0x74, 0x89, 0x44}, + }, + { /* 27P*/ + addYX: fp.Elt{0x0b, 0x73, 0x3c, 0xc2, 0xb1, 0x2e, 0xe1, 0xa7, 0xf5, 0xc9, 0x7a, 0xfb, 0x3d, 0x2d, 0xac, 0x59, 0xdb, 0xfa, 0x36, 0x11, 0xd1, 0x13, 0x04, 0x51, 0x1d, 0xab, 0x9b, 0x6b, 0x93, 0xfe, 0xda, 0xb0, 0x8e, 0xb4, 0x79, 0x11, 0x21, 0x0f, 0x65, 0xb9, 0xbb, 0x79, 0x96, 0x2a, 0xfd, 0x30, 0xe0, 0xb4, 0x2d, 0x9a, 0x55, 0x25, 0x5d, 0xd4, 0xad, 0x2a}, + subYX: fp.Elt{0x9e, 0xc5, 0x04, 0xfe, 0xec, 0x3c, 0x64, 0x1c, 0xed, 0x95, 0xed, 0xae, 0xaf, 0x5c, 0x6e, 0x08, 0x9e, 0x02, 0x29, 0x59, 0x7e, 0x5f, 0xc4, 0x9a, 0xd5, 0x32, 0x72, 0x86, 0xe1, 0x4e, 0x3c, 0xce, 0x99, 0x69, 0x3b, 0xc4, 0xdd, 0x4d, 0xb7, 0xbb, 0xda, 0x3b, 0x1a, 0x99, 0xaa, 0x62, 0x15, 0xc1, 0xf0, 0xb6, 0x6c, 0xec, 0x56, 0xc1, 0xff, 0x0c}, + dt2: fp.Elt{0x2f, 0xf1, 0x3f, 0x7a, 0x2d, 0x56, 0x19, 0x7f, 0xea, 0xbe, 0x59, 0x2e, 0x13, 0x67, 0x81, 0xfb, 0xdb, 0xc8, 0xa3, 0x1d, 0xd5, 0xe9, 0x13, 0x8b, 0x29, 0xdf, 0xcf, 0x9f, 0xe7, 0xd9, 0x0b, 0x70, 0xd3, 0x15, 0x57, 0x4a, 0xe9, 0x50, 0x12, 0x1b, 0x81, 0x4b, 0x98, 0x98, 0xa8, 0x31, 0x1d, 0x27, 0x47, 0x38, 0xed, 0x57, 0x99, 0x26, 0xb2, 0xee}, + }, + { /* 29P*/ + addYX: fp.Elt{0x1c, 0xb2, 0xb2, 0x67, 0x3b, 0x8b, 0x3d, 0x5a, 0x30, 0x7e, 0x38, 0x7e, 0x3c, 0x3d, 0x28, 0x56, 0x59, 0xd8, 0x87, 0x53, 0x8b, 0xe6, 0x6c, 0x5d, 0xe5, 0x0a, 0x33, 0x10, 0xce, 0xa2, 0x17, 0x0d, 0xe8, 0x76, 0xee, 0x68, 0xa8, 0x72, 0x54, 0xbd, 0xa6, 0x24, 0x94, 0x6e, 0x77, 0xc7, 0x53, 0xb7, 0x89, 0x1c, 0x7a, 0xe9, 0x78, 0x9a, 0x74, 0x5f}, + subYX: fp.Elt{0x76, 0x96, 0x1c, 0xcf, 0x08, 0x55, 0xd8, 0x1e, 0x0d, 0xa3, 0x59, 0x95, 0x32, 0xf4, 0xc2, 0x8e, 0x84, 0x5e, 0x4b, 0x04, 0xda, 0x71, 0xc9, 0x78, 0x52, 0xde, 0x14, 0xb4, 0x31, 0xf4, 0xd4, 0xb8, 0x58, 0xc5, 0x20, 0xe8, 0xdd, 0x15, 0xb5, 0xee, 0xea, 0x61, 0xe0, 0xf5, 0xd6, 0xae, 0x55, 0x59, 0x05, 0x3e, 0xaf, 0x74, 0xac, 0x1f, 0x17, 0x82}, + dt2: fp.Elt{0x59, 0x24, 0xcd, 0xfc, 0x11, 0x7e, 0x85, 0x18, 0x3d, 0x69, 0xf7, 0x71, 0x31, 0x66, 0x98, 0x42, 0x95, 0x00, 0x8c, 0xb2, 0xae, 0x39, 0x7e, 0x85, 0xd6, 0xb0, 0x02, 0xec, 0xce, 0xfc, 0x25, 0xb2, 0xe3, 0x99, 0x8e, 0x5b, 0x61, 0x96, 0x2e, 0x6d, 0x96, 0x57, 0x71, 0xa5, 0x93, 0x41, 0x0e, 0x6f, 0xfd, 0x0a, 0xbf, 0xa9, 0xf7, 0x56, 0xa9, 0x3e}, + }, + { /* 31P*/ + addYX: fp.Elt{0xa2, 0x2e, 0x0c, 0x17, 0x4d, 0xcc, 0x85, 0x2c, 0x18, 0xa0, 0xd2, 0x08, 0xba, 0x11, 0xfa, 0x47, 0x71, 0x86, 0xaf, 0x36, 0x6a, 0xd7, 0xfe, 0xb9, 0xb0, 0x2f, 0x89, 0x98, 0x49, 0x69, 0xf8, 0x6a, 0xad, 0x27, 0x5e, 0x0a, 0x22, 0x60, 0x5e, 0x5d, 0xca, 0x06, 0x51, 0x27, 0x99, 0x29, 0x85, 0x68, 0x98, 0xe1, 0xc4, 0x21, 0x50, 0xa0, 0xe9, 0xc1}, + subYX: fp.Elt{0x4d, 0x70, 0xee, 0x91, 0x92, 0x3f, 0xb7, 0xd3, 0x1d, 0xdb, 0x8d, 0x6e, 0x16, 0xf5, 0x65, 0x7d, 0x5f, 0xb5, 0x6c, 0x59, 0x26, 0x70, 0x4b, 0xf2, 0xfc, 0xe7, 0xdf, 0x86, 0xfe, 0xa5, 0xa7, 0xa6, 0x5d, 0xfb, 0x06, 0xe9, 0xf9, 0xcc, 0xc0, 0x37, 0xcc, 0xd8, 0x09, 0x04, 0xd2, 0xa5, 0x1d, 0xd7, 0xb7, 0xce, 0x92, 0xac, 0x3c, 0xad, 0xfb, 0xae}, + dt2: fp.Elt{0x17, 0xa3, 0x9a, 0xc7, 0x86, 0x2a, 0x51, 0xf7, 0x96, 0x79, 0x49, 0x22, 0x2e, 0x5a, 0x01, 0x5c, 0xb5, 0x95, 0xd4, 0xe8, 0xcb, 0x00, 0xca, 0x2d, 0x55, 0xb6, 0x34, 0x36, 0x0b, 0x65, 0x46, 0xf0, 0x49, 0xfc, 0x87, 0x86, 0xe5, 0xc3, 0x15, 0xdb, 0x32, 0xcd, 0xf2, 0xd3, 0x82, 0x4c, 0xe6, 0x61, 0x8a, 0xaf, 0xd4, 0x9e, 0x0f, 0x5a, 0xf2, 0x81}, + }, + { /* 33P*/ + addYX: fp.Elt{0x88, 0x10, 0xc0, 0xcb, 0xf5, 0x77, 0xae, 0xa5, 0xbe, 0xf6, 0xcd, 0x2e, 0x8b, 0x7e, 0xbd, 0x79, 0x62, 0x4a, 0xeb, 0x69, 0xc3, 0x28, 0xaa, 0x72, 0x87, 0xa9, 0x25, 0x87, 0x46, 0xea, 0x0e, 0x62, 0xa3, 0x6a, 0x1a, 0xe2, 0xba, 0xdc, 0x81, 0x10, 0x33, 0x01, 0xf6, 0x16, 0x89, 0x80, 0xc6, 0xcd, 0xdb, 0xdc, 0xba, 0x0e, 0x09, 0x4a, 0x35, 0x4a}, + subYX: fp.Elt{0x86, 0xb2, 0x2b, 0xd0, 0xb8, 0x4a, 0x6d, 0x66, 0x7b, 0x32, 0xdf, 0x3b, 0x1a, 0x19, 0x1f, 0x63, 0xee, 0x1f, 0x3d, 0x1c, 0x5c, 0x14, 0x60, 0x5b, 0x72, 0x49, 0x07, 0xb1, 0x0d, 0x72, 0xc6, 0x35, 0xf0, 0xbc, 0x5e, 0xda, 0x80, 0x6b, 0x64, 0x5b, 0xe5, 0x34, 0x54, 0x39, 0xdd, 0xe6, 0x3c, 0xcb, 0xe5, 0x29, 0x32, 0x06, 0xc6, 0xb1, 0x96, 0x34}, + dt2: fp.Elt{0x85, 0x86, 0xf5, 0x84, 0x86, 0xe6, 0x77, 0x8a, 0x71, 0x85, 0x0c, 0x4f, 0x81, 0x5b, 0x29, 0x06, 0xb5, 0x2e, 0x26, 0x71, 0x07, 0x78, 0x07, 0xae, 0xbc, 0x95, 0x46, 0xc3, 0x65, 0xac, 0xe3, 0x76, 0x51, 0x7d, 0xd4, 0x85, 0x31, 0xe3, 0x43, 0xf3, 0x1b, 0x7c, 0xf7, 0x6b, 0x2c, 0xf8, 0x1c, 0xbb, 0x8d, 0xca, 0xab, 0x4b, 0xba, 0x7f, 0xa4, 0xe2}, + }, + { /* 35P*/ + addYX: fp.Elt{0x1a, 0xee, 0xe7, 0xa4, 0x8a, 0x9d, 0x53, 0x80, 0xc6, 0xb8, 0x4e, 0xdc, 0x89, 0xe0, 0xc4, 0x2b, 0x60, 0x52, 0x6f, 0xec, 0x81, 0xd2, 0x55, 0x6b, 0x1b, 0x6f, 0x17, 0x67, 0x8e, 0x42, 0x26, 0x4c, 0x65, 0x23, 0x29, 0xc6, 0x7b, 0xcd, 0x9f, 0xad, 0x4b, 0x42, 0xd3, 0x0c, 0x75, 0xc3, 0x8a, 0xf5, 0xbe, 0x9e, 0x55, 0xf7, 0x47, 0x5d, 0xbd, 0x3a}, + subYX: fp.Elt{0x0d, 0xa8, 0x3b, 0xf9, 0xc7, 0x7e, 0xc6, 0x86, 0x94, 0xc0, 0x01, 0xff, 0x27, 0xce, 0x43, 0xac, 0xe5, 0xe1, 0xd2, 0x8d, 0xc1, 0x22, 0x31, 0xbe, 0xe1, 0xaf, 0xf9, 0x4a, 0x78, 0xa1, 0x0c, 0xaa, 0xd4, 0x80, 0xe4, 0x09, 0x8d, 0xfb, 0x1d, 0x52, 0xc8, 0x60, 0x2d, 0xf2, 0xa2, 0x89, 0x02, 0x56, 0x3d, 0x56, 0x27, 0x85, 0xc7, 0xf0, 0x2b, 0x9a}, + dt2: fp.Elt{0x62, 0x7c, 0xc7, 0x6b, 0x2c, 0x9d, 0x0a, 0x7c, 0xe5, 0x50, 0x3c, 0xe6, 0x87, 0x1c, 0x82, 0x30, 0x67, 0x3c, 0x39, 0xb6, 0xa0, 0x31, 0xfb, 0x03, 0x7b, 0xa1, 0x58, 0xdf, 0x12, 0x76, 0x5d, 0x5d, 0x0a, 0x8f, 0x9b, 0x37, 0x32, 0xc3, 0x60, 0x33, 0xea, 0x9f, 0x0a, 0x99, 0xfa, 0x20, 0xd0, 0x33, 0x21, 0xc3, 0x94, 0xd4, 0x86, 0x49, 0x7c, 0x4e}, + }, + { /* 37P*/ + addYX: fp.Elt{0xc7, 0x0c, 0x71, 0xfe, 0x55, 0xd1, 0x95, 0x8f, 0x43, 0xbb, 0x6b, 0x74, 0x30, 0xbd, 0xe8, 0x6f, 0x1c, 0x1b, 0x06, 0x62, 0xf5, 0xfc, 0x65, 0xa0, 0xeb, 0x81, 0x12, 0xc9, 0x64, 0x66, 0x61, 0xde, 0xf3, 0x6d, 0xd4, 0xae, 0x8e, 0xb1, 0x72, 0xe0, 0xcd, 0x37, 0x01, 0x28, 0x52, 0xd7, 0x39, 0x46, 0x0c, 0x55, 0xcf, 0x47, 0x70, 0xef, 0xa1, 0x17}, + subYX: fp.Elt{0x8d, 0x58, 0xde, 0x83, 0x88, 0x16, 0x0e, 0x12, 0x42, 0x03, 0x50, 0x60, 0x4b, 0xdf, 0xbf, 0x95, 0xcc, 0x7d, 0x18, 0x17, 0x7e, 0x31, 0x5d, 0x8a, 0x66, 0xc1, 0xcf, 0x14, 0xea, 0xf4, 0xf4, 0xe5, 0x63, 0x2d, 0x32, 0x86, 0x9b, 0xed, 0x1f, 0x4f, 0x03, 0xaf, 0x33, 0x92, 0xcb, 0xaf, 0x9c, 0x05, 0x0d, 0x47, 0x1b, 0x42, 0xba, 0x13, 0x22, 0x98}, + dt2: fp.Elt{0xb5, 0x48, 0xeb, 0x7d, 0x3d, 0x10, 0x9f, 0x59, 0xde, 0xf8, 0x1c, 0x4f, 0x7d, 0x9d, 0x40, 0x4d, 0x9e, 0x13, 0x24, 0xb5, 0x21, 0x09, 0xb7, 0xee, 0x98, 0x5c, 0x56, 0xbc, 0x5e, 0x2b, 0x78, 0x38, 0x06, 0xac, 0xe3, 0xe0, 0xfa, 0x2e, 0xde, 0x4f, 0xd2, 0xb3, 0xfb, 0x2d, 0x71, 0x84, 0xd1, 0x9d, 0x12, 0x5b, 0x35, 0xc8, 0x03, 0x68, 0x67, 0xc7}, + }, + { /* 39P*/ + addYX: fp.Elt{0xb6, 0x65, 0xfb, 0xa7, 0x06, 0x35, 0xbb, 0xe0, 0x31, 0x8d, 0x91, 0x40, 0x98, 0xab, 0x30, 0xe4, 0xca, 0x12, 0x59, 0x89, 0xed, 0x65, 0x5d, 0x7f, 0xae, 0x69, 0xa0, 0xa4, 0xfa, 0x78, 0xb4, 0xf7, 0xed, 0xae, 0x86, 0x78, 0x79, 0x64, 0x24, 0xa6, 0xd4, 0xe1, 0xf6, 0xd3, 0xa0, 0x89, 0xba, 0x20, 0xf4, 0x54, 0x0d, 0x8f, 0xdb, 0x1a, 0x79, 0xdb}, + subYX: fp.Elt{0xe1, 0x82, 0x0c, 0x4d, 0xde, 0x9f, 0x40, 0xf0, 0xc1, 0xbd, 0x8b, 0xd3, 0x24, 0x03, 0xcd, 0xf2, 0x92, 0x7d, 0xe2, 0x68, 0x7f, 0xf1, 0xbe, 0x69, 0xde, 0x34, 0x67, 0x4c, 0x85, 0x3b, 0xec, 0x98, 0xcc, 0x4d, 0x3e, 0xc0, 0x96, 0x27, 0xe6, 0x75, 0xfc, 0xdf, 0x37, 0xc0, 0x1e, 0x27, 0xe0, 0xf6, 0xc2, 0xbd, 0xbc, 0x3d, 0x9b, 0x39, 0xdc, 0xe2}, + dt2: fp.Elt{0xd8, 0x29, 0xa7, 0x39, 0xe3, 0x9f, 0x2f, 0x0e, 0x4b, 0x24, 0x21, 0x70, 0xef, 0xfd, 0x91, 0xea, 0xbf, 0xe1, 0x72, 0x90, 0xcc, 0xc9, 0x84, 0x0e, 0xad, 0xd5, 0xe6, 0xbb, 0xc5, 0x99, 0x7f, 0xa4, 0xf0, 0x2e, 0xcc, 0x95, 0x64, 0x27, 0x19, 0xd8, 0x4c, 0x27, 0x0d, 0xff, 0xb6, 0x29, 0xe2, 0x6c, 0xfa, 0xbb, 0x4d, 0x9c, 0xbb, 0xaf, 0xa5, 0xec}, + }, + { /* 41P*/ + addYX: fp.Elt{0xd6, 0x33, 0x3f, 0x9f, 0xcf, 0xfd, 0x4c, 0xd1, 0xfe, 0xe5, 0xeb, 0x64, 0x27, 0xae, 0x7a, 0xa2, 0x82, 0x50, 0x6d, 0xaa, 0xe3, 0x5d, 0xe2, 0x48, 0x60, 0xb3, 0x76, 0x04, 0xd9, 0x19, 0xa7, 0xa1, 0x73, 0x8d, 0x38, 0xa9, 0xaf, 0x45, 0xb5, 0xb2, 0x62, 0x9b, 0xf1, 0x35, 0x7b, 0x84, 0x66, 0xeb, 0x06, 0xef, 0xf1, 0xb2, 0x2d, 0x6a, 0x61, 0x15}, + subYX: fp.Elt{0x86, 0x50, 0x42, 0xf7, 0xda, 0x59, 0xb2, 0xcf, 0x0d, 0x3d, 0xee, 0x8e, 0x53, 0x5d, 0xf7, 0x9e, 0x6a, 0x26, 0x2d, 0xc7, 0x8c, 0x8e, 0x18, 0x50, 0x6d, 0xb7, 0x51, 0x4c, 0xa7, 0x52, 0x6e, 0x0e, 0x0a, 0x16, 0x74, 0xb2, 0x81, 0x8b, 0x56, 0x27, 0x22, 0x84, 0xf4, 0x56, 0xc5, 0x06, 0xe1, 0x8b, 0xca, 0x2d, 0xdb, 0x9a, 0xf6, 0x10, 0x9c, 0x51}, + dt2: fp.Elt{0x1f, 0x16, 0xa2, 0x78, 0x96, 0x1b, 0x85, 0x9c, 0x76, 0x49, 0xd4, 0x0f, 0xac, 0xb0, 0xf4, 0xd0, 0x06, 0x2c, 0x7e, 0x6d, 0x6e, 0x8e, 0xc7, 0x9f, 0x18, 0xad, 0xfc, 0x88, 0x0c, 0x0c, 0x09, 0x05, 0x05, 0xa0, 0x79, 0x72, 0x32, 0x72, 0x87, 0x0f, 0x49, 0x87, 0x0c, 0xb4, 0x12, 0xc2, 0x09, 0xf8, 0x9f, 0x30, 0x72, 0xa9, 0x47, 0x13, 0x93, 0x49}, + }, + { /* 43P*/ + addYX: fp.Elt{0xcc, 0xb1, 0x4c, 0xd3, 0xc0, 0x9e, 0x9e, 0x4d, 0x6d, 0x28, 0x0b, 0xa5, 0x94, 0xa7, 0x2e, 0xc2, 0xc7, 0xaf, 0x29, 0x73, 0xc9, 0x68, 0xea, 0x0f, 0x34, 0x37, 0x8d, 0x96, 0x8f, 0x3a, 0x3d, 0x73, 0x1e, 0x6d, 0x9f, 0xcf, 0x8d, 0x83, 0xb5, 0x71, 0xb9, 0xe1, 0x4b, 0x67, 0x71, 0xea, 0xcf, 0x56, 0xe5, 0xeb, 0x72, 0x15, 0x2f, 0x9e, 0xa8, 0xaa}, + subYX: fp.Elt{0xf4, 0x3e, 0x85, 0x1c, 0x1a, 0xef, 0x50, 0xd1, 0xb4, 0x20, 0xb2, 0x60, 0x05, 0x98, 0xfe, 0x47, 0x3b, 0xc1, 0x76, 0xca, 0x2c, 0x4e, 0x5a, 0x42, 0xa3, 0xf7, 0x20, 0xaa, 0x57, 0x39, 0xee, 0x34, 0x1f, 0xe1, 0x68, 0xd3, 0x7e, 0x06, 0xc4, 0x6c, 0xc7, 0x76, 0x2b, 0xe4, 0x1c, 0x48, 0x44, 0xe6, 0xe5, 0x44, 0x24, 0x8d, 0xb3, 0xb6, 0x88, 0x32}, + dt2: fp.Elt{0x18, 0xa7, 0xba, 0xd0, 0x44, 0x6f, 0x33, 0x31, 0x00, 0xf8, 0xf6, 0x12, 0xe3, 0xc5, 0xc7, 0xb5, 0x91, 0x9c, 0x91, 0xb5, 0x75, 0x18, 0x18, 0x8a, 0xab, 0xed, 0x24, 0x11, 0x2e, 0xce, 0x5a, 0x0f, 0x94, 0x5f, 0x2e, 0xca, 0xd3, 0x80, 0xea, 0xe5, 0x34, 0x96, 0x67, 0x8b, 0x6a, 0x26, 0x5e, 0xc8, 0x9d, 0x2c, 0x5e, 0x6c, 0xa2, 0x0c, 0xbf, 0xf0}, + }, + { /* 45P*/ + addYX: fp.Elt{0xb3, 0xbf, 0xa3, 0x85, 0xee, 0xf6, 0x58, 0x02, 0x78, 0xc4, 0x30, 0xd6, 0x57, 0x59, 0x8c, 0x88, 0x08, 0x7c, 0xbc, 0xbe, 0x0a, 0x74, 0xa9, 0xde, 0x69, 0xe7, 0x41, 0xd8, 0xbf, 0x66, 0x8d, 0x3d, 0x28, 0x00, 0x8c, 0x47, 0x65, 0x34, 0xfe, 0x86, 0x9e, 0x6a, 0xf2, 0x41, 0x6a, 0x94, 0xc4, 0x88, 0x75, 0x23, 0x0d, 0x52, 0x69, 0xee, 0x07, 0x89}, + subYX: fp.Elt{0x22, 0x3c, 0xa1, 0x70, 0x58, 0x97, 0x93, 0xbe, 0x59, 0xa8, 0x0b, 0x8a, 0x46, 0x2a, 0x38, 0x1e, 0x08, 0x6b, 0x61, 0x9f, 0xf2, 0x4a, 0x8b, 0x80, 0x68, 0x6e, 0xc8, 0x92, 0x60, 0xf3, 0xc9, 0x89, 0xb2, 0x6d, 0x63, 0xb0, 0xeb, 0x83, 0x15, 0x63, 0x0e, 0x64, 0xbb, 0xb8, 0xfe, 0xb4, 0x81, 0x90, 0x01, 0x28, 0x10, 0xb9, 0x74, 0x6e, 0xde, 0xa4}, + dt2: fp.Elt{0x1a, 0x23, 0x45, 0xa8, 0x6f, 0x4e, 0xa7, 0x4a, 0x0c, 0xeb, 0xb0, 0x43, 0xf9, 0xef, 0x99, 0x60, 0x5b, 0xdb, 0x66, 0xc0, 0x86, 0x71, 0x43, 0xb1, 0x22, 0x7b, 0x1c, 0xe7, 0x8d, 0x09, 0x1d, 0x83, 0x76, 0x9c, 0xd3, 0x5a, 0xdd, 0x42, 0xd9, 0x2f, 0x2d, 0xba, 0x7a, 0xc2, 0xd9, 0x6b, 0xd4, 0x7a, 0xf1, 0xd5, 0x5f, 0x6b, 0x85, 0xbf, 0x0b, 0xf1}, + }, + { /* 47P*/ + addYX: fp.Elt{0xb2, 0x83, 0xfa, 0x1f, 0xd2, 0xce, 0xb6, 0xf2, 0x2d, 0xea, 0x1b, 0xe5, 0x29, 0xa5, 0x72, 0xf9, 0x25, 0x48, 0x4e, 0xf2, 0x50, 0x1b, 0x39, 0xda, 0x34, 0xc5, 0x16, 0x13, 0xb4, 0x0c, 0xa1, 0x00, 0x79, 0x7a, 0xf5, 0x8b, 0xf3, 0x70, 0x14, 0xb6, 0xfc, 0x9a, 0x47, 0x68, 0x1e, 0x42, 0x70, 0x64, 0x2a, 0x84, 0x3e, 0x3d, 0x20, 0x58, 0xf9, 0x6a}, + subYX: fp.Elt{0xd9, 0xee, 0xc0, 0xc4, 0xf5, 0xc2, 0x86, 0xaf, 0x45, 0xd2, 0xd2, 0x87, 0x1b, 0x64, 0xd5, 0xe0, 0x8c, 0x44, 0x00, 0x4f, 0x43, 0x89, 0x04, 0x48, 0x4a, 0x0b, 0xca, 0x94, 0x06, 0x2f, 0x23, 0x5b, 0x6c, 0x8d, 0x44, 0x66, 0x53, 0xf5, 0x5a, 0x20, 0x72, 0x28, 0x58, 0x84, 0xcc, 0x73, 0x22, 0x5e, 0xd1, 0x0b, 0x56, 0x5e, 0x6a, 0xa3, 0x11, 0x91}, + dt2: fp.Elt{0x6e, 0x9f, 0x88, 0xa8, 0x68, 0x2f, 0x12, 0x37, 0x88, 0xfc, 0x92, 0x8f, 0x24, 0xeb, 0x5b, 0x2a, 0x2a, 0xd0, 0x14, 0x40, 0x4c, 0xa9, 0xa4, 0x03, 0x0c, 0x45, 0x48, 0x13, 0xe8, 0xa6, 0x37, 0xab, 0xc0, 0x06, 0x38, 0x6c, 0x96, 0x73, 0x40, 0x6c, 0xc6, 0xea, 0x56, 0xc6, 0xe9, 0x1a, 0x69, 0xeb, 0x7a, 0xd1, 0x33, 0x69, 0x58, 0x2b, 0xea, 0x2f}, + }, + { /* 49P*/ + addYX: fp.Elt{0x58, 0xa8, 0x05, 0x41, 0x00, 0x9d, 0xaa, 0xd9, 0x98, 0xcf, 0xb9, 0x41, 0xb5, 0x4a, 0x8d, 0xe2, 0xe7, 0xc0, 0x72, 0xef, 0xc8, 0x28, 0x6b, 0x68, 0x9d, 0xc9, 0xdf, 0x05, 0x8b, 0xd0, 0x04, 0x74, 0x79, 0x45, 0x52, 0x05, 0xa3, 0x6e, 0x35, 0x3a, 0xe3, 0xef, 0xb2, 0xdc, 0x08, 0x6f, 0x4e, 0x76, 0x85, 0x67, 0xba, 0x23, 0x8f, 0xdd, 0xaf, 0x09}, + subYX: fp.Elt{0xb4, 0x38, 0xc8, 0xff, 0x4f, 0x65, 0x2a, 0x7e, 0xad, 0xb1, 0xc6, 0xb9, 0x3d, 0xd6, 0xf7, 0x14, 0xcf, 0xf6, 0x98, 0x75, 0xbb, 0x47, 0x83, 0x90, 0xe7, 0xe1, 0xf6, 0x14, 0x99, 0x7e, 0xfa, 0xe4, 0x77, 0x24, 0xe3, 0xe7, 0xf0, 0x1e, 0xdb, 0x27, 0x4e, 0x16, 0x04, 0xf2, 0x08, 0x52, 0xfc, 0xec, 0x55, 0xdb, 0x2e, 0x67, 0xe1, 0x94, 0x32, 0x89}, + dt2: fp.Elt{0x00, 0xad, 0x03, 0x35, 0x1a, 0xb1, 0x88, 0xf0, 0xc9, 0x11, 0xe4, 0x12, 0x52, 0x61, 0xfd, 0x8a, 0x1b, 0x6a, 0x0a, 0x4c, 0x42, 0x46, 0x22, 0x0e, 0xa5, 0xf9, 0xe2, 0x50, 0xf2, 0xb2, 0x1f, 0x20, 0x78, 0x10, 0xf6, 0xbf, 0x7f, 0x0c, 0x9c, 0xad, 0x40, 0x8b, 0x82, 0xd4, 0xba, 0x69, 0x09, 0xac, 0x4b, 0x6d, 0xc4, 0x49, 0x17, 0x81, 0x57, 0x3b}, + }, + { /* 51P*/ + addYX: fp.Elt{0x0d, 0xfe, 0xb4, 0x35, 0x11, 0xbd, 0x1d, 0x6b, 0xc2, 0xc5, 0x3b, 0xd2, 0x23, 0x2c, 0x72, 0xe3, 0x48, 0xb1, 0x48, 0x73, 0xfb, 0xa3, 0x21, 0x6e, 0xc0, 0x09, 0x69, 0xac, 0xe1, 0x60, 0xbc, 0x24, 0x03, 0x99, 0x63, 0x0a, 0x00, 0xf0, 0x75, 0xf6, 0x92, 0xc5, 0xd6, 0xdb, 0x51, 0xd4, 0x7d, 0xe6, 0xf4, 0x11, 0x79, 0xd7, 0xc3, 0xaf, 0x48, 0xd0}, + subYX: fp.Elt{0xf4, 0x4f, 0xaf, 0x31, 0xe3, 0x10, 0x89, 0x95, 0xf0, 0x8a, 0xf6, 0x31, 0x9f, 0x48, 0x02, 0xba, 0x42, 0x2b, 0x3c, 0x22, 0x8b, 0xcc, 0x12, 0x98, 0x6e, 0x7a, 0x64, 0x3a, 0xc4, 0xca, 0x32, 0x2a, 0x72, 0xf8, 0x2c, 0xcf, 0x78, 0x5e, 0x7a, 0x75, 0x6e, 0x72, 0x46, 0x48, 0x62, 0x28, 0xac, 0x58, 0x1a, 0xc6, 0x59, 0x88, 0x2a, 0x44, 0x9e, 0x83}, + dt2: fp.Elt{0xb3, 0xde, 0x36, 0xfd, 0xeb, 0x1b, 0xd4, 0x24, 0x1b, 0x08, 0x8c, 0xfe, 0xa9, 0x41, 0xa1, 0x64, 0xf2, 0x6d, 0xdb, 0xf9, 0x94, 0xae, 0x86, 0x71, 0xab, 0x10, 0xbf, 0xa3, 0xb2, 0xa0, 0xdf, 0x10, 0x8c, 0x74, 0xce, 0xb3, 0xfc, 0xdb, 0xba, 0x15, 0xf6, 0x91, 0x7a, 0x9c, 0x36, 0x1e, 0x45, 0x07, 0x3c, 0xec, 0x1a, 0x61, 0x26, 0x93, 0xe3, 0x50}, + }, + { /* 53P*/ + addYX: fp.Elt{0xc5, 0x50, 0xc5, 0x83, 0xb0, 0xbd, 0xd9, 0xf6, 0x6d, 0x15, 0x5e, 0xc1, 0x1a, 0x33, 0xa0, 0xce, 0x13, 0x70, 0x3b, 0xe1, 0x31, 0xc6, 0xc4, 0x02, 0xec, 0x8c, 0xd5, 0x9c, 0x97, 0xd3, 0x12, 0xc4, 0xa2, 0xf9, 0xd5, 0xfb, 0x22, 0x69, 0x94, 0x09, 0x2f, 0x59, 0xce, 0xdb, 0xf2, 0xf2, 0x00, 0xe0, 0xa9, 0x08, 0x44, 0x2e, 0x8b, 0x6b, 0xf5, 0xb3}, + subYX: fp.Elt{0x90, 0xdd, 0xec, 0xa2, 0x65, 0xb7, 0x61, 0xbc, 0xaa, 0x70, 0xa2, 0x15, 0xd8, 0xb0, 0xf8, 0x8e, 0x23, 0x3d, 0x9f, 0x46, 0xa3, 0x29, 0x20, 0xd1, 0xa1, 0x15, 0x81, 0xc6, 0xb6, 0xde, 0xbe, 0x60, 0x63, 0x24, 0xac, 0x15, 0xfb, 0xeb, 0xd3, 0xea, 0x57, 0x13, 0x86, 0x38, 0x1e, 0x22, 0xf4, 0x8c, 0x5d, 0xaf, 0x1b, 0x27, 0x21, 0x4f, 0xa3, 0x63}, + dt2: fp.Elt{0x07, 0x15, 0x87, 0xc4, 0xfd, 0xa1, 0x97, 0x7a, 0x07, 0x1f, 0x56, 0xcc, 0xe3, 0x6a, 0x01, 0x90, 0xce, 0xf9, 0xfa, 0x50, 0xb2, 0xe0, 0x87, 0x8b, 0x6c, 0x63, 0x6c, 0xf6, 0x2a, 0x09, 0xef, 0xef, 0xd2, 0x31, 0x40, 0x25, 0xf6, 0x84, 0xcb, 0xe0, 0xc4, 0x23, 0xc1, 0xcb, 0xe2, 0x02, 0x83, 0x2d, 0xed, 0x74, 0x74, 0x8b, 0xf8, 0x7c, 0x81, 0x18}, + }, + { /* 55P*/ + addYX: fp.Elt{0x9e, 0xe5, 0x59, 0x95, 0x63, 0x2e, 0xac, 0x8b, 0x03, 0x3c, 0xc1, 0x8e, 0xe1, 0x5b, 0x56, 0x3c, 0x16, 0x41, 0xe4, 0xc2, 0x60, 0x0c, 0x6d, 0x65, 0x9f, 0xfc, 0x27, 0x68, 0x43, 0x44, 0x05, 0x12, 0x6c, 0xda, 0x04, 0xef, 0xcf, 0xcf, 0xdc, 0x0a, 0x1a, 0x7f, 0x12, 0xd3, 0xeb, 0x02, 0xb6, 0x04, 0xca, 0xd6, 0xcb, 0xf0, 0x22, 0xba, 0x35, 0x6d}, + subYX: fp.Elt{0x09, 0x6d, 0xf9, 0x64, 0x4c, 0xe6, 0x41, 0xff, 0x01, 0x4d, 0xce, 0x1e, 0xfa, 0x38, 0xa2, 0x25, 0x62, 0xff, 0x03, 0x39, 0x18, 0x91, 0xbb, 0x9d, 0xce, 0x02, 0xf0, 0xf1, 0x3c, 0x55, 0x18, 0xa9, 0xab, 0x4d, 0xd2, 0x35, 0xfd, 0x8d, 0xa9, 0xb2, 0xad, 0xb7, 0x06, 0x6e, 0xc6, 0x69, 0x49, 0xd6, 0x98, 0x98, 0x0b, 0x22, 0x81, 0x6b, 0xbd, 0xa0}, + dt2: fp.Elt{0x22, 0xf4, 0x85, 0x5d, 0x2b, 0xf1, 0x55, 0xa5, 0xd6, 0x27, 0x86, 0x57, 0x12, 0x1f, 0x16, 0x0a, 0x5a, 0x9b, 0xf2, 0x38, 0xb6, 0x28, 0xd8, 0x99, 0x0c, 0x89, 0x1d, 0x7f, 0xca, 0x21, 0x17, 0x1a, 0x0b, 0x02, 0x5f, 0x77, 0x2f, 0x73, 0x30, 0x7c, 0xc8, 0xd7, 0x2b, 0xcc, 0xe7, 0xf3, 0x21, 0xac, 0x53, 0xa7, 0x11, 0x5d, 0xd8, 0x1d, 0x9b, 0xf5}, + }, + { /* 57P*/ + addYX: fp.Elt{0x94, 0x63, 0x5d, 0xef, 0xfd, 0x6d, 0x25, 0x4e, 0x6d, 0x29, 0x03, 0xed, 0x24, 0x28, 0x27, 0x57, 0x47, 0x3e, 0x6a, 0x1a, 0xfe, 0x37, 0xee, 0x5f, 0x83, 0x29, 0x14, 0xfd, 0x78, 0x25, 0x8a, 0xe1, 0x02, 0x38, 0xd8, 0xca, 0x65, 0x55, 0x40, 0x7d, 0x48, 0x2c, 0x7c, 0x7e, 0x60, 0xb6, 0x0c, 0x6d, 0xf7, 0xe8, 0xb3, 0x62, 0x53, 0xd6, 0x9c, 0x2b}, + subYX: fp.Elt{0x47, 0x25, 0x70, 0x62, 0xf5, 0x65, 0x93, 0x62, 0x08, 0xac, 0x59, 0x66, 0xdb, 0x08, 0xd9, 0x1a, 0x19, 0xaf, 0xf4, 0xef, 0x02, 0xa2, 0x78, 0xa9, 0x55, 0x1c, 0xfa, 0x08, 0x11, 0xcb, 0xa3, 0x71, 0x74, 0xb1, 0x62, 0xe7, 0xc7, 0xf3, 0x5a, 0xb5, 0x8b, 0xd4, 0xf6, 0x10, 0x57, 0x79, 0x72, 0x2f, 0x13, 0x86, 0x7b, 0x44, 0x5f, 0x48, 0xfd, 0x88}, + dt2: fp.Elt{0x10, 0x02, 0xcd, 0x05, 0x9a, 0xc3, 0x32, 0x6d, 0x10, 0x3a, 0x74, 0xba, 0x06, 0xc4, 0x3b, 0x34, 0xbc, 0x36, 0xed, 0xa3, 0xba, 0x9a, 0xdb, 0x6d, 0xd4, 0x69, 0x99, 0x97, 0xd0, 0xe4, 0xdd, 0xf5, 0xd4, 0x7c, 0xd3, 0x4e, 0xab, 0xd1, 0x3b, 0xbb, 0xe9, 0xc7, 0x6a, 0x94, 0x25, 0x61, 0xf0, 0x06, 0xc5, 0x12, 0xa8, 0x86, 0xe5, 0x35, 0x46, 0xeb}, + }, + { /* 59P*/ + addYX: fp.Elt{0x9e, 0x95, 0x11, 0xc6, 0xc7, 0xe8, 0xee, 0x5a, 0x26, 0xa0, 0x72, 0x72, 0x59, 0x91, 0x59, 0x16, 0x49, 0x99, 0x7e, 0xbb, 0xd7, 0x15, 0xb4, 0xf2, 0x40, 0xf9, 0x5a, 0x4d, 0xc8, 0xa0, 0xe2, 0x34, 0x7b, 0x34, 0xf3, 0x99, 0xbf, 0xa9, 0xf3, 0x79, 0xc1, 0x1a, 0x0c, 0xf4, 0x86, 0x74, 0x4e, 0xcb, 0xbc, 0x90, 0xad, 0xb6, 0x51, 0x6d, 0xaa, 0x33}, + subYX: fp.Elt{0x9f, 0xd1, 0xc5, 0xa2, 0x6c, 0x24, 0x88, 0x15, 0x71, 0x68, 0xf6, 0x07, 0x45, 0x02, 0xc4, 0x73, 0x7e, 0x75, 0x87, 0xca, 0x7c, 0xf0, 0x92, 0x00, 0x75, 0xd6, 0x5a, 0xdd, 0xe0, 0x64, 0x16, 0x9d, 0x62, 0x80, 0x33, 0x9f, 0xf4, 0x8e, 0x1a, 0x15, 0x1c, 0xd3, 0x0f, 0x4d, 0x4f, 0x62, 0x2d, 0xd7, 0xa5, 0x77, 0xe3, 0xea, 0xf0, 0xfb, 0x1a, 0xdb}, + dt2: fp.Elt{0x6a, 0xa2, 0xb1, 0xaa, 0xfb, 0x5a, 0x32, 0x4e, 0xff, 0x47, 0x06, 0xd5, 0x9a, 0x4f, 0xce, 0x83, 0x5b, 0x82, 0x34, 0x3e, 0x47, 0xb8, 0xf8, 0xe9, 0x7c, 0x67, 0x69, 0x8d, 0x9c, 0xb7, 0xde, 0x57, 0xf4, 0x88, 0x41, 0x56, 0x0c, 0x87, 0x1e, 0xc9, 0x2f, 0x54, 0xbf, 0x5c, 0x68, 0x2c, 0xd9, 0xc4, 0xef, 0x53, 0x73, 0x1e, 0xa6, 0x38, 0x02, 0x10}, + }, + { /* 61P*/ + addYX: fp.Elt{0x08, 0x80, 0x4a, 0xc9, 0xb7, 0xa8, 0x88, 0xd9, 0xfc, 0x6a, 0xc0, 0x3e, 0xc2, 0x33, 0x4d, 0x2b, 0x2a, 0xa3, 0x6d, 0x72, 0x3e, 0xdc, 0x34, 0x68, 0x08, 0xbf, 0x27, 0xef, 0xf4, 0xff, 0xe2, 0x0c, 0x31, 0x0c, 0xa2, 0x0a, 0x1f, 0x65, 0xc1, 0x4c, 0x61, 0xd3, 0x1b, 0xbc, 0x25, 0xb1, 0xd0, 0xd4, 0x89, 0xb2, 0x53, 0xfb, 0x43, 0xa5, 0xaf, 0x04}, + subYX: fp.Elt{0xe3, 0xe1, 0x37, 0xad, 0x58, 0xa9, 0x55, 0x81, 0xee, 0x64, 0x21, 0xb9, 0xf5, 0x4c, 0x35, 0xea, 0x4a, 0xd3, 0x26, 0xaa, 0x90, 0xd4, 0x60, 0x46, 0x09, 0x4b, 0x4a, 0x62, 0xf9, 0xcd, 0xe1, 0xee, 0xbb, 0xc2, 0x09, 0x0b, 0xb0, 0x96, 0x8e, 0x43, 0x77, 0xaf, 0x25, 0x20, 0x5e, 0x47, 0xe4, 0x1d, 0x50, 0x69, 0x74, 0x08, 0xd7, 0xb9, 0x90, 0x13}, + dt2: fp.Elt{0x51, 0x91, 0x95, 0x64, 0x03, 0x16, 0xfd, 0x6e, 0x26, 0x94, 0x6b, 0x61, 0xe7, 0xd9, 0xe0, 0x4a, 0x6d, 0x7c, 0xfa, 0xc0, 0xe2, 0x43, 0x23, 0x53, 0x70, 0xf5, 0x6f, 0x73, 0x8b, 0x81, 0xb0, 0x0c, 0xee, 0x2e, 0x46, 0xf2, 0x8d, 0xa6, 0xfb, 0xb5, 0x1c, 0x33, 0xbf, 0x90, 0x59, 0xc9, 0x7c, 0xb8, 0x6f, 0xad, 0x75, 0x02, 0x90, 0x8e, 0x59, 0x75}, + }, + { /* 63P*/ + addYX: fp.Elt{0x36, 0x4d, 0x77, 0x04, 0xb8, 0x7d, 0x4a, 0xd1, 0xc5, 0xbb, 0x7b, 0x50, 0x5f, 0x8d, 0x9d, 0x62, 0x0f, 0x66, 0x71, 0xec, 0x87, 0xc5, 0x80, 0x82, 0xc8, 0xf4, 0x6a, 0x94, 0x92, 0x5b, 0xb0, 0x16, 0x9b, 0xb2, 0xc9, 0x6f, 0x2b, 0x2d, 0xee, 0x95, 0x73, 0x2e, 0xc2, 0x1b, 0xc5, 0x55, 0x36, 0x86, 0x24, 0xf8, 0x20, 0x05, 0x0d, 0x93, 0xd7, 0x76}, + subYX: fp.Elt{0x7f, 0x01, 0xeb, 0x2e, 0x48, 0x4d, 0x1d, 0xf1, 0x06, 0x7e, 0x7c, 0x2a, 0x43, 0xbf, 0x28, 0xac, 0xe9, 0x58, 0x13, 0xc8, 0xbf, 0x8e, 0xc0, 0xef, 0xe8, 0x4f, 0x46, 0x8a, 0xe7, 0xc0, 0xf6, 0x0f, 0x0a, 0x03, 0x48, 0x91, 0x55, 0x39, 0x2a, 0xe3, 0xdc, 0xf6, 0x22, 0x9d, 0x4d, 0x71, 0x55, 0x68, 0x25, 0x6e, 0x95, 0x52, 0xee, 0x4c, 0xd9, 0x01}, + dt2: fp.Elt{0xac, 0x33, 0x3f, 0x7c, 0x27, 0x35, 0x15, 0x91, 0x33, 0x8d, 0xf9, 0xc4, 0xf4, 0xf3, 0x90, 0x09, 0x75, 0x69, 0x62, 0x9f, 0x61, 0x35, 0x83, 0x92, 0x04, 0xef, 0x96, 0x38, 0x80, 0x9e, 0x88, 0xb3, 0x67, 0x95, 0xbe, 0x79, 0x3c, 0x35, 0xd8, 0xdc, 0xb2, 0x3e, 0x2d, 0xe6, 0x46, 0xbe, 0x81, 0xf3, 0x32, 0x0e, 0x37, 0x23, 0x75, 0x2a, 0x3d, 0xa0}, + }, +} diff --git a/src/circl/ecc/goldilocks/twist_basemult.go b/src/circl/ecc/goldilocks/twist_basemult.go new file mode 100644 index 00000000000..4a21a8b065c --- /dev/null +++ b/src/circl/ecc/goldilocks/twist_basemult.go @@ -0,0 +1,62 @@ +package goldilocks + +import ( + "crypto/subtle" + + mlsb "circl/math/mlsbset" +) + +const ( + // MLSBRecoding parameters + fxT = 448 + fxV = 2 + fxW = 3 + fx2w1 = 1 << (uint(fxW) - 1) +) + +// ScalarBaseMult returns kG where G is the generator point. +func (e twistCurve) ScalarBaseMult(k *Scalar) *twistPoint { + m, err := mlsb.New(fxT, fxV, fxW) + if err != nil { + panic(err) + } + if m.IsExtended() { + panic("not extended") + } + + var isZero int + if k.IsZero() { + isZero = 1 + } + subtle.ConstantTimeCopy(isZero, k[:], order[:]) + + minusK := *k + isEven := 1 - int(k[0]&0x1) + minusK.Neg() + subtle.ConstantTimeCopy(isEven, k[:], minusK[:]) + c, err := m.Encode(k[:]) + if err != nil { + panic(err) + } + + gP := c.Exp(groupMLSB{}) + P := gP.(*twistPoint) + P.cneg(uint(isEven)) + return P +} + +type groupMLSB struct{} + +func (e groupMLSB) ExtendedEltP() mlsb.EltP { return nil } +func (e groupMLSB) Sqr(x mlsb.EltG) { x.(*twistPoint).Double() } +func (e groupMLSB) Mul(x mlsb.EltG, y mlsb.EltP) { x.(*twistPoint).mixAddZ1(y.(*preTwistPointAffine)) } +func (e groupMLSB) Identity() mlsb.EltG { return twistCurve{}.Identity() } +func (e groupMLSB) NewEltP() mlsb.EltP { return &preTwistPointAffine{} } +func (e groupMLSB) Lookup(a mlsb.EltP, v uint, s, u int32) { + Tabj := &tabFixMult[v] + P := a.(*preTwistPointAffine) + for k := range Tabj { + P.cmov(&Tabj[k], uint(subtle.ConstantTimeEq(int32(k), u))) + } + P.cneg(int(s >> 31)) +} diff --git a/src/circl/ecc/p384/LICENSE b/src/circl/ecc/p384/LICENSE new file mode 100644 index 00000000000..4e5596db89d --- /dev/null +++ b/src/circl/ecc/p384/LICENSE @@ -0,0 +1,26 @@ +Copyright (c) 2018, Brendan McMillion. All rights reserved. + +Redistribution and use in source and binary forms, with or without modification, +are permitted provided that the following conditions are met: + +1. Redistributions of source code must retain the above copyright notice, this +list of conditions and the following disclaimer. + +2. Redistributions in binary form must reproduce the above copyright notice, +this list of conditions and the following disclaimer in the documentation and/or +other materials provided with the distribution. + +3. Neither the name of the copyright holder nor the names of its contributors +may be used to endorse or promote products derived from this software without +specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND +ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED +WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE +DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR +ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES +(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON +ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/src/circl/ecc/p384/arith.go b/src/circl/ecc/p384/arith.go new file mode 100644 index 00000000000..7b06bc2365d --- /dev/null +++ b/src/circl/ecc/p384/arith.go @@ -0,0 +1,148 @@ +// +build !noasm,arm64 !noasm,amd64 + +package p384 + +import ( + "math/big" + + "circl/internal/conv" +) + +const sizeFp = 48 + +type fp384 [sizeFp]byte + +func (e fp384) BigInt() *big.Int { return conv.BytesLe2BigInt(e[:]) } +func (e fp384) String() string { return conv.BytesLe2Hex(e[:]) } + +func (e *fp384) SetBigInt(b *big.Int) { + if b.BitLen() > 384 || b.Sign() < 0 { + b = new(big.Int).Mod(b, p.BigInt()) + } + conv.BigInt2BytesLe(e[:], b) +} + +func montEncode(c, a *fp384) { fp384Mul(c, a, &r2) } +func montDecode(c, a *fp384) { fp384Mul(c, a, &fp384{1}) } +func fp384Sqr(c, a *fp384) { fp384Mul(c, a, a) } + +func fp384Inv(z, x *fp384) { + t0, t1, t2, t3, t4 := &fp384{}, &fp384{}, &fp384{}, &fp384{}, &fp384{} + /* alpha_1 */ + fp384Sqr(t4, x) + /* alpha_2 */ + fp384Mul(t4, t4, x) + /* alpha_3 */ + fp384Sqr(t0, t4) + fp384Mul(t0, t0, x) + /* alpha_6 */ + fp384Sqr(t1, t0) + fp384Sqr(t1, t1) + fp384Sqr(t1, t1) + fp384Mul(t1, t1, t0) + /* alpha_12 */ + fp384Sqr(t2, t1) + for i := 0; i < 5; i++ { + fp384Sqr(t2, t2) + } + fp384Mul(t2, t2, t1) + /* alpha_15 */ + for i := 0; i < 3; i++ { + fp384Sqr(t2, t2) + } + fp384Mul(t2, t2, t0) + /* alpha_30 */ + fp384Sqr(t1, t2) + for i := 0; i < 14; i++ { + fp384Sqr(t1, t1) + } + fp384Mul(t1, t1, t2) + /* alpha_60 */ + fp384Sqr(t3, t1) + for i := 0; i < 29; i++ { + fp384Sqr(t3, t3) + } + fp384Mul(t3, t3, t1) + /* T_3 = alpha_30^(2^2) */ + fp384Sqr(t1, t1) + fp384Sqr(t1, t1) + /* alpha_32 */ + *t0 = *t1 + fp384Mul(t0, t0, t4) + /* T_3 = a^(2^32-3) = (alpha_30)^(2^2)*alpha_1 */ + fp384Mul(t1, t1, x) + /* alpha_120 */ + fp384Sqr(t4, t3) + for i := 0; i < 59; i++ { + fp384Sqr(t4, t4) + } + fp384Mul(t4, t4, t3) + /* alpha_240 */ + fp384Sqr(t3, t4) + for i := 0; i < 119; i++ { + fp384Sqr(t3, t3) + } + fp384Mul(t3, t3, t4) + /* alpha_255 */ + for i := 0; i < 15; i++ { + fp384Sqr(t3, t3) + } + fp384Mul(t3, t3, t2) + /* T_5 = a^(2^288-2^32-1) = (alpha_255)^(2^33)*alpha_32 */ + for i := 0; i < 33; i++ { + fp384Sqr(t3, t3) + } + fp384Mul(t3, t3, t0) + /* T_1 = a^(2^384-2^128-2^96+2^32-3) = (T_1)^(2^96)*T_3 */ + fp384Sqr(t4, t3) + for i := 0; i < 95; i++ { + fp384Sqr(t4, t4) + } + fp384Mul(z, t4, t1) +} + +//go:noescape +func fp384Cmov(x, y *fp384, b int) + +//go:noescape +func fp384Neg(c, a *fp384) + +//go:noescape +func fp384Add(c, a, b *fp384) + +//go:noescape +func fp384Sub(c, a, b *fp384) + +//go:noescape +func fp384Mul(c, a, b *fp384) + +var ( + // p is the order of the base field, represented as little-endian 64-bit words. + p = fp384{ + 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + } + // pp satisfies r*rp - p*pp = 1 where rp and pp are both integers. + pp = fp384{ //nolint + 0x01, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xfb, 0xff, 0xff, 0xff, + 0xfa, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff, 0x02, 0x00, 0x00, 0x00, + 0x0c, 0x00, 0x00, 0x00, 0x14, 0x00, 0x00, 0x00, 0x14, 0x00, 0x00, 0x00, + } + // r2 is R^2 where R = 2^384 mod p. + r2 = fp384{ + 0x01, 0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, + 0x00, 0x00, 0x00, 0x00, 0x02, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + } + // bb is the Montgomery encoding of the curve parameter B. + bb = fp384{ + 0xcc, 0x2d, 0x41, 0x9d, 0x71, 0x88, 0x11, 0x08, 0xec, 0x32, 0x4c, 0x7a, + 0xd8, 0xad, 0x29, 0xf7, 0x2e, 0x02, 0x20, 0x19, 0x9b, 0x20, 0xf2, 0x77, + 0xe2, 0x8a, 0x93, 0x94, 0xee, 0x4b, 0x37, 0xe3, 0x94, 0x20, 0x02, 0x1f, + 0xf4, 0x21, 0x2b, 0xb6, 0xf9, 0xbf, 0x4f, 0x60, 0x4b, 0x11, 0x08, 0xcd, + } +) diff --git a/src/circl/ecc/p384/arith_amd64.go b/src/circl/ecc/p384/arith_amd64.go new file mode 100644 index 00000000000..95dd1524467 --- /dev/null +++ b/src/circl/ecc/p384/arith_amd64.go @@ -0,0 +1,7 @@ +// +build amd64,!noasm + +package p384 + +import "internal/cpu" + +var hasBMI2 = cpu.X86.HasBMI2 //nolint diff --git a/src/circl/ecc/p384/arith_amd64.s b/src/circl/ecc/p384/arith_amd64.s new file mode 100644 index 00000000000..7866bca4abe --- /dev/null +++ b/src/circl/ecc/p384/arith_amd64.s @@ -0,0 +1,745 @@ +// +build amd64,!noasm + +#include "textflag.h" + +#define storeBlock(a0,a1,a2,a3,a4,a5, r) \ + MOVQ a0, 0+r \ + MOVQ a1, 8+r \ + MOVQ a2, 16+r \ + MOVQ a3, 24+r \ + MOVQ a4, 32+r \ + MOVQ a5, 40+r + +#define loadBlock(r, a0,a1,a2,a3,a4,a5) \ + MOVQ 0+r, a0 \ + MOVQ 8+r, a1 \ + MOVQ 16+r, a2 \ + MOVQ 24+r, a3 \ + MOVQ 32+r, a4 \ + MOVQ 40+r, a5 + +#define fp384Carry(a0,a1,a2,a3,a4,a5,a6, b0,b1,b2,b3,b4,b5,b6) \ + \ // b = a-p + MOVQ a0, b0 \ + MOVQ a1, b1 \ + MOVQ a2, b2 \ + MOVQ a3, b3 \ + MOVQ a4, b4 \ + MOVQ a5, b5 \ + MOVQ a6, b6 \ + \ + SUBQ ·p+0(SB), b0 \ + SBBQ ·p+8(SB), b1 \ + SBBQ ·p+16(SB), b2 \ + SBBQ ·p+24(SB), b3 \ + SBBQ ·p+32(SB), b4 \ + SBBQ ·p+40(SB), b5 \ + SBBQ $0, b6 \ + \ + \ // if b is negative then return a + \ // else return b + CMOVQCC b0, a0 \ + CMOVQCC b1, a1 \ + CMOVQCC b2, a2 \ + CMOVQCC b3, a3 \ + CMOVQCC b4, a4 \ + CMOVQCC b5, a5 + +#define mul(a0,a1,a2,a3,a4,a5, rb, stack) \ + \ // a0 + MOVQ a0, AX \ + MULQ 0+rb \ + MOVQ AX, R8 \ + MOVQ DX, R9 \ + MOVQ a0, AX \ + MULQ 8+rb \ + ADDQ AX, R9 \ + ADCQ $0, DX \ + MOVQ DX, R10 \ + MOVQ a0, AX \ + MULQ 16+rb \ + ADDQ AX, R10 \ + ADCQ $0, DX \ + MOVQ DX, R11 \ + MOVQ a0, AX \ + MULQ 24+rb \ + ADDQ AX, R11 \ + ADCQ $0, DX \ + MOVQ DX, R12 \ + MOVQ a0, AX \ + MULQ 32+rb \ + ADDQ AX, R12 \ + ADCQ $0, DX \ + MOVQ DX, R13 \ + MOVQ a0, AX \ + MULQ 40+rb \ + ADDQ AX, R13 \ + ADCQ $0, DX \ + MOVQ DX, R14 \ + \ + storeBlock(R8,R9,R10,R11,R12,R13, 0+stack) \ + MOVQ R14, 48+stack \ + \ + \ // a1 + MOVQ a1, AX \ + MULQ 0+rb \ + MOVQ AX, R8 \ + MOVQ DX, R9 \ + MOVQ a1, AX \ + MULQ 8+rb \ + ADDQ AX, R9 \ + ADCQ $0, DX \ + MOVQ DX, R10 \ + MOVQ a1, AX \ + MULQ 16+rb \ + ADDQ AX, R10 \ + ADCQ $0, DX \ + MOVQ DX, R11 \ + MOVQ a1, AX \ + MULQ 24+rb \ + ADDQ AX, R11 \ + ADCQ $0, DX \ + MOVQ DX, R12 \ + MOVQ a1, AX \ + MULQ 32+rb \ + ADDQ AX, R12 \ + ADCQ $0, DX \ + MOVQ DX, R13 \ + MOVQ a1, AX \ + MULQ 40+rb \ + ADDQ AX, R13 \ + ADCQ $0, DX \ + MOVQ DX, R14 \ + \ + ADDQ 8+stack, R8 \ + ADCQ 16+stack, R9 \ + ADCQ 24+stack, R10 \ + ADCQ 32+stack, R11 \ + ADCQ 40+stack, R12 \ + ADCQ 48+stack, R13 \ + ADCQ $0, R14 \ + storeBlock(R8,R9,R10,R11,R12,R13, 8+stack) \ + MOVQ R14, 56+stack \ + \ + \ // a2 + MOVQ a2, AX \ + MULQ 0+rb \ + MOVQ AX, R8 \ + MOVQ DX, R9 \ + MOVQ a2, AX \ + MULQ 8+rb \ + ADDQ AX, R9 \ + ADCQ $0, DX \ + MOVQ DX, R10 \ + MOVQ a2, AX \ + MULQ 16+rb \ + ADDQ AX, R10 \ + ADCQ $0, DX \ + MOVQ DX, R11 \ + MOVQ a2, AX \ + MULQ 24+rb \ + ADDQ AX, R11 \ + ADCQ $0, DX \ + MOVQ DX, R12 \ + MOVQ a2, AX \ + MULQ 32+rb \ + ADDQ AX, R12 \ + ADCQ $0, DX \ + MOVQ DX, R13 \ + MOVQ a2, AX \ + MULQ 40+rb \ + ADDQ AX, R13 \ + ADCQ $0, DX \ + MOVQ DX, R14 \ + \ + ADDQ 16+stack, R8 \ + ADCQ 24+stack, R9 \ + ADCQ 32+stack, R10 \ + ADCQ 40+stack, R11 \ + ADCQ 48+stack, R12 \ + ADCQ 56+stack, R13 \ + ADCQ $0, R14 \ + storeBlock(R8,R9,R10,R11,R12,R13, 16+stack) \ + MOVQ R14, 64+stack \ + \ + \ // a3 + MOVQ a3, AX \ + MULQ 0+rb \ + MOVQ AX, R8 \ + MOVQ DX, R9 \ + MOVQ a3, AX \ + MULQ 8+rb \ + ADDQ AX, R9 \ + ADCQ $0, DX \ + MOVQ DX, R10 \ + MOVQ a3, AX \ + MULQ 16+rb \ + ADDQ AX, R10 \ + ADCQ $0, DX \ + MOVQ DX, R11 \ + MOVQ a3, AX \ + MULQ 24+rb \ + ADDQ AX, R11 \ + ADCQ $0, DX \ + MOVQ DX, R12 \ + MOVQ a3, AX \ + MULQ 32+rb \ + ADDQ AX, R12 \ + ADCQ $0, DX \ + MOVQ DX, R13 \ + MOVQ a3, AX \ + MULQ 40+rb \ + ADDQ AX, R13 \ + ADCQ $0, DX \ + MOVQ DX, R14 \ + \ + ADDQ 24+stack, R8 \ + ADCQ 32+stack, R9 \ + ADCQ 40+stack, R10 \ + ADCQ 48+stack, R11 \ + ADCQ 56+stack, R12 \ + ADCQ 64+stack, R13 \ + ADCQ $0, R14 \ + storeBlock(R8,R9,R10,R11,R12,R13, 24+stack) \ + MOVQ R14, 72+stack \ + \ + \ // a4 + MOVQ a4, AX \ + MULQ 0+rb \ + MOVQ AX, R8 \ + MOVQ DX, R9 \ + MOVQ a4, AX \ + MULQ 8+rb \ + ADDQ AX, R9 \ + ADCQ $0, DX \ + MOVQ DX, R10 \ + MOVQ a4, AX \ + MULQ 16+rb \ + ADDQ AX, R10 \ + ADCQ $0, DX \ + MOVQ DX, R11 \ + MOVQ a4, AX \ + MULQ 24+rb \ + ADDQ AX, R11 \ + ADCQ $0, DX \ + MOVQ DX, R12 \ + MOVQ a4, AX \ + MULQ 32+rb \ + ADDQ AX, R12 \ + ADCQ $0, DX \ + MOVQ DX, R13 \ + MOVQ a4, AX \ + MULQ 40+rb \ + ADDQ AX, R13 \ + ADCQ $0, DX \ + MOVQ DX, R14 \ + \ + ADDQ 32+stack, R8 \ + ADCQ 40+stack, R9 \ + ADCQ 48+stack, R10 \ + ADCQ 56+stack, R11 \ + ADCQ 64+stack, R12 \ + ADCQ 72+stack, R13 \ + ADCQ $0, R14 \ + storeBlock(R8,R9,R10,R11,R12,R13, 32+stack) \ + MOVQ R14, 80+stack \ + \ + \ // a5 + MOVQ a5, AX \ + MULQ 0+rb \ + MOVQ AX, R8 \ + MOVQ DX, R9 \ + MOVQ a5, AX \ + MULQ 8+rb \ + ADDQ AX, R9 \ + ADCQ $0, DX \ + MOVQ DX, R10 \ + MOVQ a5, AX \ + MULQ 16+rb \ + ADDQ AX, R10 \ + ADCQ $0, DX \ + MOVQ DX, R11 \ + MOVQ a5, AX \ + MULQ 24+rb \ + ADDQ AX, R11 \ + ADCQ $0, DX \ + MOVQ DX, R12 \ + MOVQ a5, AX \ + MULQ 32+rb \ + ADDQ AX, R12 \ + ADCQ $0, DX \ + MOVQ DX, R13 \ + MOVQ a5, AX \ + MULQ 40+rb \ + ADDQ AX, R13 \ + ADCQ $0, DX \ + MOVQ DX, R14 \ + \ + ADDQ 40+stack, R8 \ + ADCQ 48+stack, R9 \ + ADCQ 56+stack, R10 \ + ADCQ 64+stack, R11 \ + ADCQ 72+stack, R12 \ + ADCQ 80+stack, R13 \ + ADCQ $0, R14 \ + storeBlock(R8,R9,R10,R11,R12,R13, 40+stack) \ + MOVQ R14, 88+stack + +#define fp384Reduce(stack) \ + \ // m = (T * P') mod R, store m in R8:R9:R10:R11:R12:R13 + MOVQ ·pp+0(SB), AX \ + MULQ 0+stack \ + MOVQ AX, R8 \ + MOVQ DX, R9 \ + MOVQ ·pp+0(SB), AX \ + MULQ 8+stack \ + ADDQ AX, R9 \ + ADCQ $0, DX \ + MOVQ DX, R10 \ + MOVQ ·pp+0(SB), AX \ + MULQ 16+stack \ + ADDQ AX, R10 \ + ADCQ $0, DX \ + MOVQ DX, R11 \ + MOVQ ·pp+0(SB), AX \ + MULQ 24+stack \ + ADDQ AX, R11 \ + ADCQ $0, DX \ + MOVQ DX, R12 \ + MOVQ ·pp+0(SB), AX \ + MULQ 32+stack \ + ADDQ AX, R12 \ + ADCQ $0, DX \ + MOVQ DX, R13 \ + MOVQ ·pp+0(SB), AX \ + MULQ 40+stack \ + ADDQ AX, R13 \ + \ + ADDQ 0+stack, R9 \ + ADCQ 8+stack, R10 \ + ADCQ 16+stack, R11 \ + ADCQ 24+stack, R12 \ + ADCQ 32+stack, R13 \ + \ + MOVQ ·pp+16(SB), AX \ + MULQ 0+stack \ + MOVQ AX, R14 \ + MOVQ DX, R15 \ + MOVQ ·pp+16(SB), AX \ + MULQ 8+stack \ + ADDQ AX, R15 \ + ADCQ $0, DX \ + MOVQ DX, BX \ + MOVQ ·pp+16(SB), AX \ + MULQ 16+stack \ + ADDQ AX, BX \ + ADCQ $0, DX \ + MOVQ DX, CX \ + MOVQ ·pp+16(SB), AX \ + MULQ 24+stack \ + ADDQ AX, CX \ + \ + ADDQ R14, R10 \ + ADCQ R15, R11 \ + ADCQ BX, R12 \ + ADCQ CX, R13 \ + \ + MOVQ ·pp+24(SB), AX \ + MULQ 0+stack \ + MOVQ AX, R14 \ + MOVQ DX, R15 \ + MOVQ ·pp+24(SB), AX \ + MULQ 8+stack \ + ADDQ AX, R15 \ + ADCQ $0, DX \ + MOVQ DX, BX \ + MOVQ ·pp+24(SB), AX \ + MULQ 16+stack \ + ADDQ AX, BX \ + \ + ADDQ R14, R11 \ + ADCQ R15, R12 \ + ADCQ BX, R13 \ + \ + MOVQ ·pp+32(SB), AX \ + MULQ 0+stack \ + MOVQ AX, R14 \ + MOVQ DX, R15 \ + MOVQ ·pp+32(SB), AX \ + MULQ 8+stack \ + ADDQ AX, R15 \ + \ + ADDQ R14, R12 \ + ADCQ R15, R13 \ + \ + MOVQ ·pp+40(SB), AX \ + MULQ 0+stack \ + ADDQ AX, R13 \ + \ + storeBlock(R8,R9,R10,R11,R12,R13, 96+stack) \ + \ + \ // m * P + mul(·p+0(SB),·p+8(SB),·p+16(SB),·p+24(SB),·p+32(SB),·p+40(SB), 96+stack, 144+stack) \ + \ + \ // Add the 768-bit intermediate to m*N + MOVQ $0, DI \ + loadBlock(144+stack, R8,R9,R10,R11,R12,R13) \ + loadBlock(192+stack, R14,R15,AX,BX,CX,DX) \ + \ + ADDQ 0+stack, R8 \ + ADCQ 8+stack, R9 \ + ADCQ 16+stack, R10 \ + ADCQ 24+stack, R11 \ + ADCQ 32+stack, R12 \ + ADCQ 40+stack, R13 \ + ADCQ 48+stack, R14 \ + ADCQ 56+stack, R15 \ + ADCQ 64+stack, AX \ + ADCQ 72+stack, BX \ + ADCQ 80+stack, CX \ + ADCQ 88+stack, DX \ + ADCQ $0, DI \ + \ + fp384Carry(R14,R15,AX,BX,CX,DX,DI, R8,R9,R10,R11,R12,R13,SI) + +#define mulBMI2(a0,a1,a2,a3,a4,a5, rb, stack) \ + MOVQ a0, DX \ + MULXQ 0+rb, R8, R9 \ + MULXQ 8+rb, AX, R10 \ + ADDQ AX, R9 \ + MULXQ 16+rb, AX, R11 \ + ADCQ AX, R10 \ + MULXQ 24+rb, AX, R12 \ + ADCQ AX, R11 \ + MULXQ 32+rb, AX, R13 \ + ADCQ AX, R12 \ + MULXQ 40+rb, AX, R14 \ + ADCQ AX, R13 \ + ADCQ $0, R14 \ + \ + MOVQ R8, 0+stack \ + MOVQ $0, R15 \ + MOVQ $0, R8 \ + \ + MOVQ a1, DX \ + MULXQ 0+rb, AX, BX \ + ADDQ AX, R9 \ + ADCQ BX, R10 \ + MULXQ 16+rb, AX, BX \ + ADCQ AX, R11 \ + ADCQ BX, R12 \ + MULXQ 32+rb, AX, BX \ + ADCQ AX, R13 \ + ADCQ BX, R14 \ + ADCQ $0, R15 \ + MULXQ 8+rb, AX, BX \ + ADDQ AX, R10 \ + ADCQ BX, R11 \ + MULXQ 24+rb, AX, BX \ + ADCQ AX, R12 \ + ADCQ BX, R13 \ + MULXQ 40+rb, AX, BX \ + ADCQ AX, R14 \ + ADCQ BX, R15 \ + ADCQ $0, R8 \ + \ + MOVQ R9, 8+stack \ + MOVQ $0, R9 \ + \ + MOVQ a2, DX \ + MULXQ 0+rb, AX, BX \ + ADDQ AX, R10 \ + ADCQ BX, R11 \ + MULXQ 16+rb, AX, BX \ + ADCQ AX, R12 \ + ADCQ BX, R13 \ + MULXQ 32+rb, AX, BX \ + ADCQ AX, R14 \ + ADCQ BX, R15 \ + ADCQ $0, R8 \ + MULXQ 8+rb, AX, BX \ + ADDQ AX, R11 \ + ADCQ BX, R12 \ + MULXQ 24+rb, AX, BX \ + ADCQ AX, R13 \ + ADCQ BX, R14 \ + MULXQ 40+rb, AX, BX \ + ADCQ AX, R15 \ + ADCQ BX, R8 \ + ADCQ $0, R9 \ + \ + MOVQ R10, 16+stack \ + MOVQ $0, R10 \ + \ + MOVQ a3, DX \ + MULXQ 0+rb, AX, BX \ + ADDQ AX, R11 \ + ADCQ BX, R12 \ + MULXQ 16+rb, AX, BX \ + ADCQ AX, R13 \ + ADCQ BX, R14 \ + MULXQ 32+rb, AX, BX \ + ADCQ AX, R15 \ + ADCQ BX, R8 \ + ADCQ $0, R9 \ + MULXQ 8+rb, AX, BX \ + ADDQ AX, R12 \ + ADCQ BX, R13 \ + MULXQ 24+rb, AX, BX \ + ADCQ AX, R14 \ + ADCQ BX, R15 \ + MULXQ 40+rb, AX, BX \ + ADCQ AX, R8 \ + ADCQ BX, R9 \ + ADCQ $0, R10 \ + \ + MOVQ R11, 24+stack \ + MOVQ $0, R11 \ + \ + MOVQ a4, DX \ + MULXQ 0+rb, AX, BX \ + ADDQ AX, R12 \ + ADCQ BX, R13 \ + MULXQ 16+rb, AX, BX \ + ADCQ AX, R14 \ + ADCQ BX, R15 \ + MULXQ 32+rb, AX, BX \ + ADCQ AX, R8 \ + ADCQ BX, R9 \ + ADCQ $0, R10 \ + MULXQ 8+rb, AX, BX \ + ADDQ AX, R13 \ + ADCQ BX, R14 \ + MULXQ 24+rb, AX, BX \ + ADCQ AX, R15 \ + ADCQ BX, R8 \ + MULXQ 40+rb, AX, BX \ + ADCQ AX, R9 \ + ADCQ BX, R10 \ + ADCQ $0, R11 \ + \ + MOVQ R12, 32+stack \ + \ + MOVQ a5, DX \ + MULXQ 0+rb, AX, BX \ + ADDQ AX, R13 \ + ADCQ BX, R14 \ + MULXQ 16+rb, AX, BX \ + ADCQ AX, R15 \ + ADCQ BX, R8 \ + MULXQ 32+rb, AX, BX \ + ADCQ AX, R9 \ + ADCQ BX, R10 \ + ADCQ $0, R11 \ + MULXQ 8+rb, AX, BX \ + ADDQ AX, R14 \ + ADCQ BX, R15 \ + MULXQ 24+rb, AX, BX \ + ADCQ AX, R8 \ + ADCQ BX, R9 \ + MULXQ 40+rb, AX, BX \ + ADCQ AX, R10 \ + ADCQ BX, R11 \ + \ + MOVQ R13, 40+stack + +#define fp384ReduceBMI2(stack) \ + \ // m = (T * P') mod R, store m in R8:R9:R10:R11:R12:R13 + MOVQ ·pp+0(SB), DX \ + MULXQ 0+stack, R8, R9 \ + MULXQ 8+stack, AX, R10 \ + ADDQ AX, R9 \ + MULXQ 16+stack, AX, R11 \ + ADCQ AX, R10 \ + MULXQ 24+stack, AX, R12 \ + ADCQ AX, R11 \ + MULXQ 32+stack, AX, R13 \ + ADCQ AX, R12 \ + MULXQ 40+stack, AX, BX \ + ADCQ AX, R13 \ + \ + ADDQ 0+stack, R9 \ + ADCQ 8+stack, R10 \ + ADCQ 16+stack, R11 \ + ADCQ 24+stack, R12 \ + ADCQ 32+stack, R13 \ + \ + MOVQ ·pp+16(SB), DX \ + MULXQ 0+stack, AX, BX \ + ADDQ AX, R10 \ + ADCQ BX, R11 \ + MULXQ 16+stack, AX, BX \ + ADCQ AX, R12 \ + ADCQ BX, R13 \ + MULXQ 8+stack, AX, BX \ + ADDQ AX, R11 \ + ADCQ BX, R12 \ + MULXQ 24+stack, AX, BX \ + ADCQ AX, R13 \ + \ + MOVQ ·pp+24(SB), DX \ + MULXQ 0+stack, AX, BX \ + ADDQ AX, R11 \ + ADCQ BX, R12 \ + MULXQ 16+stack, AX, BX \ + ADCQ AX, R13 \ + MULXQ 8+stack, AX, BX \ + ADDQ AX, R12 \ + ADCQ BX, R13 \ + \ + MOVQ ·pp+32(SB), DX \ + MULXQ 0+stack, AX, BX \ + ADDQ AX, R12 \ + ADCQ BX, R13 \ + MULXQ 8+stack, AX, BX \ + ADDQ AX, R13 \ + \ + MOVQ ·pp+40(SB), DX \ + MULXQ 0+stack, AX, BX \ + ADDQ AX, R13 \ + \ + storeBlock(R8,R9,R10,R11,R12,R13, 96+stack) \ + \ + \ // m * P + mulBMI2(·p+0(SB),·p+8(SB),·p+16(SB),·p+24(SB),·p+32(SB),·p+40(SB), 96+stack, 144+stack) \ + \ + \ // Add the 768-bit intermediate to m*N + MOVQ $0, AX \ + loadBlock(144+stack, R12,R13,BX,CX,DX,DI) \ + \ + ADDQ 0+stack, R12 \ + ADCQ 8+stack, R13 \ + ADCQ 16+stack, BX \ + ADCQ 24+stack, CX \ + ADCQ 32+stack, DX \ + ADCQ 40+stack, DI \ + ADCQ 48+stack, R14 \ + ADCQ 56+stack, R15 \ + ADCQ 64+stack, R8 \ + ADCQ 72+stack, R9 \ + ADCQ 80+stack, R10 \ + ADCQ 88+stack, R11 \ + ADCQ $0, AX \ + \ + fp384Carry(R14,R15,R8,R9,R10,R11,AX, R12,R13,BX,CX,DX,DI,SI) + +TEXT ·fp384Neg(SB), NOSPLIT, $0-16 + MOVQ ·p+0(SB), R8 + MOVQ ·p+8(SB), R9 + MOVQ ·p+16(SB), R10 + MOVQ ·p+24(SB), R11 + MOVQ ·p+32(SB), R12 + MOVQ ·p+40(SB), R13 + + MOVQ a+8(FP), DI + SUBQ 0(DI), R8 + SBBQ 8(DI), R9 + SBBQ 16(DI), R10 + SBBQ 24(DI), R11 + SBBQ 32(DI), R12 + SBBQ 40(DI), R13 + + MOVQ $0, R14 + fp384Carry(R8,R9,R10,R11,R12,R13,R14, R15,AX,BX,CX,DX,DI,SI) + + MOVQ c+0(FP), DI + storeBlock(R8,R9,R10,R11,R12,R13, 0(DI)) + RET + +TEXT ·fp384Add(SB), NOSPLIT, $0-24 + MOVQ a+8(FP), DI + MOVQ b+16(FP), SI + + loadBlock(0(DI), R8,R9,R10,R11,R12,R13) + MOVQ $0, R14 + + ADDQ 0(SI), R8 + ADCQ 8(SI), R9 + ADCQ 16(SI), R10 + ADCQ 24(SI), R11 + ADCQ 32(SI), R12 + ADCQ 40(SI), R13 + ADCQ $0, R14 + + fp384Carry(R8,R9,R10,R11,R12,R13,R14, R15,AX,BX,CX,DX,DI,SI) + + MOVQ c+0(FP), DI + storeBlock(R8,R9,R10,R11,R12,R13, 0(DI)) + RET + +TEXT ·fp384Sub(SB), NOSPLIT, $0-24 + MOVQ ·p+0(SB), R8 + MOVQ ·p+8(SB), R9 + MOVQ ·p+16(SB), R10 + MOVQ ·p+24(SB), R11 + MOVQ ·p+32(SB), R12 + MOVQ ·p+40(SB), R13 + + MOVQ b+16(FP), DI + SUBQ 0(DI), R8 + SBBQ 8(DI), R9 + SBBQ 16(DI), R10 + SBBQ 24(DI), R11 + SBBQ 32(DI), R12 + SBBQ 40(DI), R13 + + MOVQ $0, R14 + MOVQ a+8(FP), DI + ADDQ 0(DI), R8 + ADCQ 8(DI), R9 + ADCQ 16(DI), R10 + ADCQ 24(DI), R11 + ADCQ 32(DI), R12 + ADCQ 40(DI), R13 + ADCQ $0, R14 + + fp384Carry(R8,R9,R10,R11,R12,R13,R14, R15,AX,BX,CX,DX,DI,SI) + + MOVQ c+0(FP), DI + storeBlock(R8,R9,R10,R11,R12,R13, 0(DI)) + RET + +TEXT ·fp384Mul(SB), NOSPLIT, $240-24 + MOVQ a+8(FP), DI + MOVQ b+16(FP), SI + + // Jump to a slightly different implementation if MULX isn't supported. + CMPB ·hasBMI2(SB), $0 + JE nobmi2Mul + + // T = a * b + mulBMI2(0(DI),8(DI),16(DI),24(DI),32(DI),40(DI), 0(SI), 0(SP)) + storeBlock(R14,R15,R8,R9,R10,R11, 48(SP)) + + // Reduce T. + fp384ReduceBMI2(0(SP)) + + MOVQ c+0(FP), DI + storeBlock(R14,R15,R8,R9,R10,R11, 0(DI)) + JMP end + +nobmi2Mul: + // T = a * b + mul(0(DI),8(DI),16(DI),24(DI),32(DI),40(DI), 0(SI), 0(SP)) + + // Reduce T. + fp384Reduce(0(SP)) + + MOVQ c+0(FP), DI + storeBlock(R14,R15,AX,BX,CX,DX, 0(DI)) + +end: + RET + +TEXT ·fp384Cmov(SB), NOSPLIT, $0 + MOVQ x+0(FP), DI + MOVQ y+8(FP), SI + MOVQ b+16(FP), BX + TESTQ BX, BX + MOVQ 0(DI), AX; MOVQ 0(SI), DX; CMOVQNE DX, AX; MOVQ AX, 0(DI); + MOVQ 8(DI), AX; MOVQ 8(SI), DX; CMOVQNE DX, AX; MOVQ AX, 8(DI); + MOVQ 16(DI), AX; MOVQ 16(SI), DX; CMOVQNE DX, AX; MOVQ AX, 16(DI); + MOVQ 24(DI), AX; MOVQ 24(SI), DX; CMOVQNE DX, AX; MOVQ AX, 24(DI); + MOVQ 32(DI), AX; MOVQ 32(SI), DX; CMOVQNE DX, AX; MOVQ AX, 32(DI); + MOVQ 40(DI), AX; MOVQ 40(SI), DX; CMOVQNE DX, AX; MOVQ AX, 40(DI); + RET diff --git a/src/circl/ecc/p384/arith_arm64.s b/src/circl/ecc/p384/arith_arm64.s new file mode 100644 index 00000000000..ec93991d426 --- /dev/null +++ b/src/circl/ecc/p384/arith_arm64.s @@ -0,0 +1,511 @@ +// +build arm64,!noasm + +#include "textflag.h" + +TEXT ·fp384Cmov(SB), NOSPLIT, $0 + MOVD x+0(FP), R0 + MOVD y+8(FP), R1 + MOVW b+16(FP), R2 + CMP $0, R2 + LDP 0(R0), (R3, R5) + LDP 0(R1), (R4, R6) + CSEL NE,R4,R3,R7 + CSEL NE,R6,R5,R8 + STP (R7, R8), 0(R0) + LDP 16(R0), (R3, R5) + LDP 16(R1), (R4, R6) + CSEL NE,R4,R3,R7 + CSEL NE,R6,R5,R8 + STP (R7, R8), 16(R0) + LDP 32(R0), (R3, R5) + LDP 32(R1), (R4, R6) + CSEL NE,R4,R3,R7 + CSEL NE,R6,R5,R8 + STP (R7, R8), 32(R0) + RET + +// Compute c = -a mod p +TEXT ·fp384Neg(SB), NOSPLIT, $0-16 + MOVD c+0(FP), R0 + MOVD a+8(FP), R1 + + // Load p in R2-R7, a in R8-R13 + // Compute p-a in R8-R13 + LDP ·p+0(SB), (R2, R3) + LDP 0(R1), (R8, R9) + SUBS R8, R2, R8 + SBCS R9, R3, R9 + LDP ·p+16(SB), (R4, R5) + LDP 16(R1), (R10, R11) + SBCS R10, R4, R10 + SBCS R11, R5, R11 + LDP ·p+32(SB), (R6, R7) + LDP 32(R1), (R12, R13) + SBCS R12, R6, R12 + SBC R13, R7, R13 + + // Compute (p-a)-p in R2-R7 + SUBS R2, R8, R2 + SBCS R3, R9, R3 + SBCS R4, R10, R4 + SBCS R5, R11, R5 + SBCS R6, R12, R6 + SBCS R7, R13, R7 + + // If (p-a)-p < 0 (nearly always), return p-a + // Only return (p-a)-p for a = 0 + // Store result in c + CSEL CC, R8, R2, R2 + CSEL CC, R9, R3, R3 + STP (R2, R3), 0(R0) + CSEL CC, R10, R4, R4 + CSEL CC, R11, R5, R5 + STP (R4, R5), 16(R0) + CSEL CC, R12, R6, R6 + CSEL CC, R13, R7, R7 + STP (R6, R7), 32(R0) + + RET + +// Compute c = a+b mod p +TEXT ·fp384Add(SB), NOSPLIT, $0-24 + MOVD c+0(FP), R0 + MOVD a+8(FP), R1 + MOVD b+16(FP), R2 + + // Load a in R3-R8, b in R9-R14 + // Compute a+b in R3-R9 + LDP 0(R1), (R3, R4) + LDP 0(R2), (R9, R10) + ADDS R9, R3 + ADCS R10, R4 + LDP 16(R1), (R5, R6) + LDP 16(R2), (R11, R12) + ADCS R11, R5 + ADCS R12, R6 + LDP 32(R1), (R7, R8) + LDP 32(R2), (R13, R14) + ADCS R13, R7 + ADCS R14, R8 + ADC ZR, ZR, R9 + + // Load p in R10-R15 + LDP ·p+ 0(SB), (R10, R11) + LDP ·p+16(SB), (R12, R13) + LDP ·p+32(SB), (R14, R15) + + // Compute a+b-p in R10-R16 + SUBS R10, R3, R10 + SBCS R11, R4, R11 + SBCS R12, R5, R12 + SBCS R13, R6, R13 + SBCS R14, R7, R14 + SBCS R15, R8, R15 + SBCS ZR, R9, R16 + + // If a+b-p is negative, return a+b + // Store result in c + CSEL CC, R3, R10, R3 + CSEL CC, R4, R11, R4 + STP (R3, R4), 0(R0) + CSEL CC, R5, R12, R5 + CSEL CC, R6, R13, R6 + STP (R5, R6), 16(R0) + CSEL CC, R7, R14, R7 + CSEL CC, R8, R15, R8 + STP (R7, R8), 32(R0) + + RET + +// Compute c = a-b mod p +TEXT ·fp384Sub(SB), NOSPLIT, $0-24 + MOVD c+0(FP), R0 + MOVD a+8(FP), R1 + MOVD b+16(FP), R2 + + // Load a in R3-R8, b in R9-R14 + // Compute a-b in R3-R9 + LDP 0(R1), (R3, R4) + LDP 0(R2), (R9, R10) + SUBS R9, R3 + SBCS R10, R4 + LDP 16(R1), (R5, R6) + LDP 16(R2), (R11, R12) + SBCS R11, R5 + SBCS R12, R6 + LDP 32(R1), (R7, R8) + LDP 32(R2), (R13, R14) + SBCS R13, R7 + SBCS R14, R8 + SBC ZR, ZR, R9 + + // Load p in R10-R15 + // If a-b < 0, (a-b)+p to R3-R8 + // Store result in c + LDP ·p+ 0(SB), (R10, R11) + AND R9, R10 + LDP ·p+16(SB), (R12, R13) + AND R9, R11 + AND R9, R12 + LDP ·p+32(SB), (R14, R15) + AND R9, R13 + AND R9, R14 + AND R9, R15 + + ADDS R10, R3 + ADCS R11, R4 + STP (R3, R4), 0(R0) + ADCS R12, R5 + ADCS R13, R6 + STP (R5, R6), 16(R0) + ADCS R14, R7 + ADC R15, R8 + STP (R7, R8), 32(R0) + + RET + +// Expects that A0*B0 is already in C0(low),C3(high) and A0*B1 in C1(low),C2(high) +// C0 is not actually touched +// Result of (A0-A2) * (B0-B2) will be in C0-C5 +// Inputs remain intact +#define mul192x192comba(A0,A1,A2, B0,B1,B2, C0,C1,C2,C3,C4,C5, S0,S1,S2,S3) \ + MUL A1, B0, S2 \ + UMULH A1, B0, S3 \ + \ + ADDS C3, C1 \ + ADCS ZR, C2 \ + ADC ZR, ZR, C3 \ + \ + MUL A0, B2, S0 \ + UMULH A0, B2, S1 \ + \ + ADDS S2, C1 \ + ADCS S3, C2 \ + ADC ZR, C3 \ + \ + MUL A1, B1, S2 \ + UMULH A1, B1, S3 \ + \ + ADDS S0, C2 \ + ADCS S1, C3 \ + ADC ZR, ZR, C4 \ + \ + MUL A2, B0, S0 \ + UMULH A2, B0, S1 \ + \ + ADDS S2, C2 \ + ADCS S3, C3 \ + ADC ZR, C4 \ + \ + MUL A1, B2, S2 \ + UMULH A1, B2, S3 \ + \ + ADDS S0, C2 \ + ADCS S1, C3 \ + ADC ZR, C4 \ + \ + MUL A2, B1, S0 \ + UMULH A2, B1, S1 \ + \ + ADDS S2, C3 \ + ADCS S3, C4 \ + ADC ZR, ZR, C5 \ + \ + MUL A2, B2, S2 \ + UMULH A2, B2, S3 \ + \ + ADDS S0, C3 \ + ADCS S1, C4 \ + ADC ZR, C5 \ + \ + ADDS S2, C4 \ + ADC S3, C5 + + +// Assumes that there are at least 96 bytes left on the stack +// Expects that X and Y point to input +// X and Y get overwritten, Z0 will be in Y +#define mul384x384karatsuba(X,Y, Z1,Z2,Z3,Z4,Z5,Z6,Z7,Z8,Z9,Z10,Z11, T0,T1,T2,T3,T4,T5,T6,T7,T8,T9,T10,T11,T12) \ + /* Load a in Z1-Z6, b in T12,Z7-Z11 */ \ + LDP 0(X), ( Z1, Z2) \ + LDP 0(Y), (T12, Z7) \ + MUL Z1, Z7, T1 \ + UMULH Z1, T12, T3 \ + LDP 16(X), ( Z3, Z4) \ + LDP 16(Y), ( Z8, Z9) \ + MUL Z1, T12, T0 \ + UMULH Z1, Z7, T2 \ + LDP 32(X), ( Z5, Z6) \ + LDP 32(Y), (Z10, Z11) \ + \ + /* Compute aL*bL in T0-T5 */ \ + mul192x192comba(Z1,Z2,Z3, T12,Z7,Z8, T0,T1,T2,T3,T4,T5, T6,T7,T8,T9) \ + \ + /* Compute aH*bH in T6-T11, destroys aL and bL */ \ + MUL Z4, Z10, T7 \ + MUL Z4, Z9, T6 \ + UMULH Z4, Z9, T9 \ + UMULH Z4, Z10, T8 \ + mul192x192comba(Z4,Z5,Z6, Z9,Z10,Z11, T6,T7,T8,T9,T10,T11, Z1,Z2,T12,Z7) \ + \ + /* Compute aL*bL + aH*bH in Z1-Z6,T12, destroys aH */ \ + ADDS T0, T6, Z1 \ + ADCS T1, T7, Z2 \ + ADCS T2, T8, Z3 \ + ADCS T3, T9, Z4 \ + ADCS T4, T10, Z5 \ + ADCS T5, T11, Z6 \ + ADC ZR, ZR, T12 \ + \ + /* Add to T0-T11 and store on stack */ \ + STP ( T0, T1), -16(RSP) \ + ADDS Z1, T3 \ + STP ( T2, T3), -32(RSP) \ + ADCS Z2, T4 \ + ADCS Z3, T5 \ + STP ( T4, T5), -48(RSP) \ + ADCS Z4, T6 \ + ADCS Z5, T7 \ + STP ( T6, T7), -64(RSP) \ + ADCS Z6, T8 \ + ADC ZR, T12 \ + STP ( T8, T9), -80(RSP) \ + STP (T10, T11), -96(RSP) \ + \ + /* Load a to Z1-Z6 */ \ + LDP 0(X), (Z1, Z2) \ + LDP 16(X), (Z3, Z4) \ + LDP 32(X), (Z5, Z6) \ + \ + /* Compute |aL-aH| to Z1-Z3, keep borrow in X */ \ + SUBS Z4, Z1 \ + SBCS Z5, Z2 \ + SBCS Z6, Z3 \ + SBC ZR, ZR, X \ + NEGS Z1, Z4 \ + NGCS Z2, Z5 \ + NGC Z3, Z6 \ + ADDS $1, X \ + \ + /* Load b to Z7-Z11,T0 */ \ + LDP 0(Y), ( Z7, Z8) \ + LDP 16(Y), ( Z9, Z10) \ + LDP 32(Y), (Z11, T0) \ + \ + CSEL EQ, Z4, Z1, Z1 \ + CSEL EQ, Z5, Z2 ,Z2 \ + CSEL EQ, Z6, Z3, Z3 \ + \ + /* Compute |bH-bL| to Z7-Z9, keep borrow in Y */ \ + SUBS Z7, Z10 \ + SBCS Z8, Z11 \ + SBCS Z9, T0 \ + SBC ZR, ZR, Y \ + NEGS Z10, Z7 \ + NGCS Z11, Z8 \ + NGC T0, Z9 \ + ADDS $1, Y \ + CSEL EQ, Z7, Z10, Z7 \ + CSEL EQ, Z8, Z11, Z8 \ + CSEL EQ, Z9, T0, Z9 \ + \ + /* Combine borrows */ \ + EOR Y, X \ + \ + /* Compute |aL-aH|*|bH-bL| to Z10,Z11,T0-T3 */ \ + MUL Z1, Z8, Z11 \ + MUL Z1, Z7, Z10 \ + UMULH Z1, Z8, T0 \ + UMULH Z1, Z7, T1 \ + mul192x192comba(Z1,Z2,Z3, Z7,Z8,Z9, Z10,Z11,T0,T1,T2,T3, T4,T5,T6,T7) \ + \ + /* The result has to be negated if exactly one of the operands was negative */ \ + NEGS Z10, Y \ + NGCS Z11, Z1 \ + NGCS T0, Z2 \ + NGCS T1, Z3 \ + NGCS T2, Z4 \ + NGCS T3, Z5 \ + NGC ZR, T4 \ + \ + AND T4, X \ + CMP $1, X \ + CSEL EQ, Y, Z10, Z10 \ + CSEL EQ, Z1, Z11, Z11 \ + CSEL EQ, Z2, T0, T0 \ + CSEL EQ, Z3, T1, T1 \ + CSEL EQ, Z4, T2, T2 \ + CSEL EQ, Z5, T3, T3 \ + \ + /* Add that to the middle part */ \ + LDP -16(RSP), ( Y, Z1) \ + LDP -32(RSP), ( Z2, Z3) \ + LDP -48(RSP), ( Z4, Z5) \ + ADDS Z10, Z3 \ + ADCS Z11, Z4 \ + LDP -64(RSP), ( Z6, Z7) \ + ADCS T0, Z5 \ + ADCS T1, Z6 \ + LDP -80(RSP), ( Z8, Z9) \ + ADCS T2, Z7 \ + ADCS T3, Z8 \ + LDP -96(RSP), (Z10, Z11) \ + ADCS T12, Z9 \ + ADCS ZR, Z10 \ + ADC ZR, Z11 \ + SUBS X, Z9 \ + SBCS ZR, Z10 \ + SBC ZR, Z11 + +// Compute c = a*b*R^-1 mod p +TEXT ·fp384Mul(SB), NOSPLIT, $200-24 + MOVD c+0(FP), R0 + MOVD a+8(FP), R1 + MOVD b+16(FP), R2 + + // Compute a*b in R2-R13 + mul384x384karatsuba(R1, R2, R3,R4,R5,R6,R7,R8,R9,R10,R11,R12,R13, R14,R15,R16,R17,R19,R20,R21,R22,R23,R24,R25,R26,R27) + + // Store a*b on the stack + STP ( R2, R3), -112(RSP) + STP ( R4, R5), -128(RSP) + STP ( R6, R7), -144(RSP) + STP ( R8, R9), -160(RSP) + STP (R10, R11), -176(RSP) + STP (R12, R13), -192(RSP) + + // Compute m = a*b*pp mod 2^384 in R19-R24 + // Store it temporarily in c + MOVD ·pp+0(SB), R14 + MUL R14, R2, R19 + UMULH R14, R2, R20 + + MUL R14, R3, R16 + UMULH R14, R3, R21 + ADDS R16, R20 + ADC ZR, R21 + + MUL R14, R4, R16 + UMULH R14, R4, R22 + ADDS R16, R21 + ADC ZR, R22 + + MUL R14, R5, R16 + UMULH R14, R5, R23 + ADDS R16, R22 + ADC ZR, R23 + + MUL R14, R6, R16 + UMULH R14, R6, R24 + ADDS R16, R23 + ADC ZR, R24 + + MADD R14, R24, R7, R24 + + // ·pp+8(SB) = 1, so we can just add + ADDS R2, R20 + STP (R19, R20), 0(R0) + ADCS R3, R21 + ADCS R4, R22 + ADCS R5, R23 + ADC R6, R24 + + LDP ·pp+16(SB), (R14, R15) + MUL R14, R2, R8 + UMULH R14, R2, R9 + + MUL R14, R3, R16 + UMULH R14, R3, R10 + ADDS R16, R9 + ADC ZR, R10 + + MUL R14, R4, R16 + UMULH R14, R4, R11 + ADDS R16, R10 + ADC ZR, R11 + + MUL R14, R5, R16 + ADD R16, R11 + + ADDS R8, R21 + ADCS R9, R22 + ADCS R10, R23 + ADC R11, R24 + + MUL R15, R2, R8 + UMULH R15, R2, R9 + + MUL R15, R3, R16 + UMULH R15, R3, R10 + ADDS R16, R9 + ADC ZR, R10 + + MADD R15, R10, R4, R10 + + ADDS R8, R22 + STP (R21, R22), 16(R0) + ADCS R9, R23 + ADC R10, R24 + + LDP ·pp+32(SB), (R14, R15) + MUL R14, R2, R8 + UMULH R14, R2, R9 + + MADD R14, R9, R3, R9 + + ADDS R8, R23 + ADC R9, R24 + + MADD R15, R24, R2, R24 + STP (R23, R24), 32(R0) + + // Compute m*p in R1-R12 + MOVD $·p(SB), R1 + mul384x384karatsuba(R0, R1, R2,R3,R4,R5,R6,R7,R8,R9,R10,R11,R12, R13,R14,R15,R16,R17,R19,R20,R21,R22,R23,R24,R25,R26) + + // Add a*b to m*p in R1-R12,R26 + LDP -112(RSP), (R13, R14) + ADDS R13, R1 + LDP -128(RSP), (R15, R16) + ADCS R14, R2 + ADCS R15, R3 + LDP -144(RSP), (R17, R19) + ADCS R16, R4 + ADCS R17, R5 + LDP -160(RSP), (R20, R21) + ADCS R19, R6 + ADCS R20, R7 + LDP -176(RSP), (R22, R23) + ADCS R21, R8 + ADCS R22, R9 + LDP -192(RSP), (R24, R25) + ADCS R23, R10 + ADCS R24, R11 + ADCS R25, R12 + ADC ZR, ZR, R26 + + // Reduce the top half mod p + LDP ·p+ 0(SB), (R13, R14) + SUBS R13, R7, R13 + LDP ·p+16(SB), (R15, R16) + SBCS R14, R8, R14 + SBCS R15, R9, R15 + LDP ·p+32(SB), (R17, R19) + SBCS R16, R10, R16 + SBCS R17, R11, R17 + SBCS R19, R12, R19 + SBCS ZR, R26 + + // Store result in c + MOVD c+0(FP), R0 + CSEL CC, R7, R13, R7 + CSEL CC, R8, R14, R8 + STP ( R7, R8), 0(R0) + CSEL CC, R9, R15, R9 + CSEL CC, R10, R16, R10 + STP ( R9, R10), 16(R0) + CSEL CC, R11, R17, R11 + CSEL CC, R12, R19, R12 + STP (R11, R12), 32(R0) + + RET diff --git a/src/circl/ecc/p384/arith_test.go b/src/circl/ecc/p384/arith_test.go new file mode 100644 index 00000000000..ced843a7870 --- /dev/null +++ b/src/circl/ecc/p384/arith_test.go @@ -0,0 +1,237 @@ +// +build !noasm,arm64 !noasm,amd64 + +package p384 + +import ( + "crypto/elliptic" + "crypto/rand" + "math/big" + "testing" + + "circl/internal/test" +) + +func TestFpCmov(t *testing.T) { + var x, y, z fp384 + for _, b := range []int{-2, -1, 1, 2} { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + z = x + fp384Cmov(&z, &y, b) + got := z + want := y + if got != want { + test.ReportError(t, got, want, b, x, y) + } + } + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + z = x + fp384Cmov(&z, &y, 0) + got := z + want := x + if got != want { + test.ReportError(t, got, want, 0, x, y) + } +} + +func TestFpNegZero(t *testing.T) { + zero, x := &fp384{}, &fp384{} + fp384Neg(x, zero) + got := x.BigInt() + want := zero.BigInt() + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } +} + +func TestFpSetBigInt(t *testing.T) { + P := elliptic.P384().Params().P + + neg := big.NewInt(-0xFF) // negative + zero := big.NewInt(0) // zero + one := big.NewInt(1) // one + two96 := new(big.Int).Lsh(one, 96) // 2^96 + two384 := new(big.Int).Lsh(one, 384) // 2^384 + two384two96 := new(big.Int).Sub(two384, two96) // 2^384-2^96 + two768 := new(big.Int).Lsh(one, 768) // 2^768 + + for id, b := range []*big.Int{ + neg, zero, one, two96, two384, two384two96, two768} { + var x fp384 + x.SetBigInt(b) + got := x.BigInt() + if b.BitLen() > 384 || b.Sign() < 0 { + b.Mod(b, P) + } + want := b + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, id) + } + } +} + +func TestMulZero(t *testing.T) { + x, zero := &fp384{}, &fp384{} + _, _ = rand.Read(x[:]) + + fp384Mul(x, x, zero) + got := x.BigInt() + want := zero.BigInt() + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } +} + +func TestFp(t *testing.T) { + P := elliptic.P384().Params().P + x, y, z := &fp384{}, &fp384{}, &fp384{} + testTimes := 1 << 12 + var bigR, bigR2, bigRinv big.Int + one := big.NewInt(1) + bigR.Lsh(one, 384).Mod(&bigR, P) + bigR2.Lsh(one, 2*384).Mod(&bigR2, P) + bigRinv.ModInverse(&bigR, P) + + t.Run("Encode", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(x[:]) + bigX := x.BigInt() + // fp384 + montEncode(z, x) + got := z.BigInt() + // big.Int + want := bigX.Mul(bigX, &bigR).Mod(bigX, P) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } + }) + t.Run("Decode", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(x[:]) + bigX := x.BigInt() + // fp384 + montDecode(z, x) + got := z.BigInt() + // big.Int + want := bigX.Mul(bigX, new(big.Int).ModInverse(&bigR, P)).Mod(bigX, P) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } + }) + t.Run("Neg", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(x[:]) + bigX := x.BigInt() + // fp384 + fp384Neg(z, x) + got := z.BigInt() + // big.Int + want := bigX.Neg(bigX).Mod(bigX, P) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } + }) + t.Run("Add", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + bigX := x.BigInt() + bigY := y.BigInt() + // fp384 + fp384Add(z, x, y) + got := z.BigInt() + // big.Int + want := bigX.Add(bigX, bigY) + want = want.Mod(want, P) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y) + } + } + }) + t.Run("Sub", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + bigX := x.BigInt() + bigY := y.BigInt() + // fp384 + fp384Sub(z, x, y) + got := z.BigInt() + // big.Int + want := bigX.Sub(bigX, bigY) + want = want.Mod(want, P) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y) + } + } + }) + t.Run("Mul", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + bigX := x.BigInt() + bigY := y.BigInt() + // fp384 + fp384Mul(z, x, y) + got := z.BigInt() + // big.Int + want := bigX.Mul(bigX, bigY).Mul(bigX, &bigRinv).Mod(bigX, P) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y) + } + } + }) + t.Run("Inv", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(x[:]) + bigX := x.BigInt() + // fp384 + fp384Inv(z, x) + got := z.BigInt() + // big.Int + want := bigX.ModInverse(bigX, P).Mul(bigX, &bigR2).Mod(bigX, P) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } + }) +} + +func BenchmarkFp(b *testing.B) { + x, y, z := &fp384{}, &fp384{}, &fp384{} + + b.Run("Add", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fp384Add(z, x, y) + } + }) + + b.Run("Sub", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fp384Sub(z, x, y) + } + }) + + b.Run("Mul", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fp384Mul(z, x, y) + } + }) + + b.Run("Sqr", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fp384Sqr(z, x) + } + }) + + b.Run("Inv", func(b *testing.B) { + for i := 0; i < b.N; i++ { + fp384Inv(z, x) + } + }) +} diff --git a/src/circl/ecc/p384/doc.go b/src/circl/ecc/p384/doc.go new file mode 100644 index 00000000000..05a813a2b69 --- /dev/null +++ b/src/circl/ecc/p384/doc.go @@ -0,0 +1,11 @@ +// Package p384 provides optimized elliptic curve operations on the P-384 curve. +// +// These are some improvements over crypto/elliptic package: +// - Around 10x faster in amd64 architecture. +// - Reduced number of memory allocations. +// - Native support for arm64 architecture. +// - ScalarMult is performed using a constant-time algorithm. +// - ScalarBaseMult fallbacks into ScalarMult. +// - A new method included for double-point multiplication. +// +package p384 diff --git a/src/circl/ecc/p384/opt_test.go b/src/circl/ecc/p384/opt_test.go new file mode 100644 index 00000000000..463e830b74f --- /dev/null +++ b/src/circl/ecc/p384/opt_test.go @@ -0,0 +1,78 @@ +// +build !noasm,arm64 !noasm,amd64 + +package p384 + +import ( + "crypto/elliptic" + "math/big" + "testing" + + "circl/internal/test" +) + +func TestInternals(t *testing.T) { + t.Run("absolute", func(t *testing.T) { + cases := []int32{-2, -1, 0, 1, 2} + expected := []int32{2, 1, 0, 1, 2} + for i := range cases { + got := absolute(cases[i]) + want := expected[i] + if got != want { + test.ReportError(t, got, want, cases[i]) + } + } + }) + + t.Run("toOdd", func(t *testing.T) { + var c curve + k := []byte{0xF0} + oddK, _ := c.toOdd(k) + got := len(oddK) + want := 48 + if got != want { + test.ReportError(t, got, want) + } + + oddK[sizeFp-1] = 0x0 + smallOddK, _ := c.toOdd(oddK) + got = len(smallOddK) + want = 48 + if got != want { + test.ReportError(t, got, want) + } + }) + + t.Run("special k", func(t *testing.T) { + cases := []struct { // known cases that require complete addition + w uint + k int + }{ + {w: 2, k: 2}, + {w: 5, k: 6}, + {w: 6, k: 38}, + {w: 7, k: 102}, + {w: 9, k: 230}, + {w: 12, k: 742}, + {w: 14, k: 4838}, + {w: 17, k: 21222}, + {w: 19, k: 152294}, + } + + var c curve + + StdCurve := elliptic.P384() + params := StdCurve.Params() + for _, caseI := range cases { + k := big.NewInt(int64(caseI.k)).Bytes() + gotX, gotY := c.scalarMultOmega(params.Gx, params.Gy, k, caseI.w) + wantX, wantY := StdCurve.ScalarMult(params.Gx, params.Gy, k) + + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, caseI) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY, caseI) + } + } + }) +} diff --git a/src/circl/ecc/p384/p384.go b/src/circl/ecc/p384/p384.go new file mode 100644 index 00000000000..75005d08df9 --- /dev/null +++ b/src/circl/ecc/p384/p384.go @@ -0,0 +1,28 @@ +package p384 + +import ( + "crypto/elliptic" + "math/big" +) + +// Curve is used to provide the extended functionality and performance of +// elliptic.Curve interface. +type Curve interface { + elliptic.Curve + // IsAtInfinity returns True is the point is the identity point. + IsAtInfinity(X, Y *big.Int) bool + // CombinedMult calculates P=mG+nQ, where G is the generator and + // Q=(Qx,Qy). The scalars m and n are positive integers in big-endian form. + // Runs in non-constant time to be used in signature verification. + CombinedMult(Qx, Qy *big.Int, m, n []byte) (Px, Py *big.Int) +} + +// Params returns the parameters for the curve. Note: The value returned by +// this function fallbacks to the stdlib implementation of elliptic curve +// operations. Use this method to only recover elliptic curve parameters. +func (c curve) Params() *elliptic.CurveParams { return elliptic.P384().Params() } + +// IsAtInfinity returns True is the point is the identity point. +func (c curve) IsAtInfinity(x, y *big.Int) bool { + return x.Sign() == 0 && y.Sign() == 0 +} diff --git a/src/circl/ecc/p384/p384_generic.go b/src/circl/ecc/p384/p384_generic.go new file mode 100644 index 00000000000..3acc38550ec --- /dev/null +++ b/src/circl/ecc/p384/p384_generic.go @@ -0,0 +1,20 @@ +// +build noasm !amd64,!arm64 + +package p384 + +import ( + "crypto/elliptic" + "math/big" +) + +type curve struct{ elliptic.Curve } + +func P384() Curve { return curve{elliptic.P384()} } + +// CombinedMult calculates P=mG+nQ, where G is the generator and Q=(x,y,z). +// The scalars m and n are integers in big-endian form. Non-constant time. +func (c curve) CombinedMult(xQ, yQ *big.Int, m, n []byte) (xP, yP *big.Int) { + x1, y1 := c.ScalarBaseMult(m) + x2, y2 := c.ScalarMult(xQ, yQ, n) + return c.Add(x1, y1, x2, y2) +} diff --git a/src/circl/ecc/p384/p384_test.go b/src/circl/ecc/p384/p384_test.go new file mode 100644 index 00000000000..a174fd6b4e7 --- /dev/null +++ b/src/circl/ecc/p384/p384_test.go @@ -0,0 +1,257 @@ +package p384_test + +import ( + "crypto/elliptic" + "crypto/rand" + "fmt" + "testing" + + "circl/ecc/p384" + "circl/internal/test" +) + +func TestIsOnCurveTrue(t *testing.T) { + CirclCurve := p384.P384() + k := make([]byte, 384/8) + for i := 0; i < 128; i++ { + _, _ = rand.Read(k) + x, y := elliptic.P384().ScalarBaseMult(k) + + got := CirclCurve.IsOnCurve(x, y) + want := true + if got != want { + test.ReportError(t, got, want, k) + } + + x = x.Neg(x) + got = CirclCurve.IsOnCurve(x, y) + want = false + if got != want { + test.ReportError(t, got, want, k) + } + } +} + +func TestAffine(t *testing.T) { + const testTimes = 1 << 7 + CirclCurve := p384.P384() + StdCurve := elliptic.P384() + params := StdCurve.Params() + + t.Run("Addition", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + K1, _ := rand.Int(rand.Reader, params.N) + K2, _ := rand.Int(rand.Reader, params.N) + X1, Y1 := StdCurve.ScalarBaseMult(K1.Bytes()) + X2, Y2 := StdCurve.ScalarBaseMult(K2.Bytes()) + wantX, wantY := StdCurve.Add(X1, Y1, X2, Y2) + gotX, gotY := CirclCurve.Add(X1, Y1, X2, Y2) + + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, K1, K2) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY) + } + } + }) + + t.Run("Double", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + k, _ := rand.Int(rand.Reader, params.N) + x, y := StdCurve.ScalarBaseMult(k.Bytes()) + wantX, wantY := StdCurve.Double(x, y) + + gotX, gotY := CirclCurve.Double(x, y) + + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, k) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY) + } + } + }) +} + +func TestScalarBaseMult(t *testing.T) { + const testTimes = 1 << 6 + CirclCurve := p384.P384() + StdCurve := elliptic.P384() + + t.Run("0P", func(t *testing.T) { + k := make([]byte, 500) + for i := 0; i < len(k); i += 20 { + gotX, gotY := CirclCurve.ScalarBaseMult(k[:i]) + wantX, wantY := StdCurve.ScalarBaseMult(k[:i]) + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, k[:i]) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY) + } + } + }) + + t.Run("kP", func(t *testing.T) { + k := make([]byte, 48) + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(k) + gotX, gotY := CirclCurve.ScalarBaseMult(k) + wantX, wantY := StdCurve.ScalarBaseMult(k) + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, k) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY) + } + } + }) + + t.Run("kSmall", func(t *testing.T) { + k := make([]byte, 16) + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(k) + gotX, gotY := CirclCurve.ScalarBaseMult(k) + wantX, wantY := StdCurve.ScalarBaseMult(k) + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, k) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY) + } + } + }) + + t.Run("kLarge", func(t *testing.T) { + k := make([]byte, 384) + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(k) + gotX, gotY := CirclCurve.ScalarBaseMult(k) + wantX, wantY := StdCurve.ScalarBaseMult(k) + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, k) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY) + } + } + }) +} + +func TestScalarMult(t *testing.T) { + const testTimes = 1 << 6 + CirclCurve := p384.P384() + StdCurve := elliptic.P384() + params := StdCurve.Params() + + t.Run("k=0", func(t *testing.T) { + k := []byte{0x0} + gotX, gotY := CirclCurve.ScalarMult(params.Gx, params.Gy, k) + got := CirclCurve.IsAtInfinity(gotX, gotY) + want := true + if got != want { + test.ReportError(t, got, want) + } + }) + + t.Run("random k", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + k, _ := rand.Int(rand.Reader, params.N) + gotX, gotY := CirclCurve.ScalarMult(params.Gx, params.Gy, k.Bytes()) + wantX, wantY := StdCurve.ScalarMult(params.Gx, params.Gy, k.Bytes()) + + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, k) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY) + } + } + }) + + t.Run("wrong P", func(t *testing.T) { + for i := 0; i < testTimes; i++ { + k, _ := rand.Int(rand.Reader, params.N) + x, _ := rand.Int(rand.Reader, params.P) + y, _ := rand.Int(rand.Reader, params.P) + + got := CirclCurve.IsOnCurve(CirclCurve.ScalarMult(x, y, k.Bytes())) + want := StdCurve.IsOnCurve(StdCurve.ScalarMult(x, y, k.Bytes())) + + if got != want { + test.ReportError(t, got, want, k, x, y) + } + } + }) +} + +func TestCombinedMult(t *testing.T) { + const testTimes = 1 << 7 + CirclCurve := p384.P384() + StdCurve := elliptic.P384() + params := StdCurve.Params() + + for i := 0; i < testTimes; i++ { + K, _ := rand.Int(rand.Reader, params.N) + X, Y := StdCurve.ScalarBaseMult(K.Bytes()) + + K1, _ := rand.Int(rand.Reader, params.N) + K2, _ := rand.Int(rand.Reader, params.N) + x1, y1 := StdCurve.ScalarBaseMult(K1.Bytes()) + x2, y2 := StdCurve.ScalarMult(X, Y, K2.Bytes()) + wantX, wantY := StdCurve.Add(x1, y1, x2, y2) + + gotX, gotY := CirclCurve.CombinedMult(X, Y, K1.Bytes(), K2.Bytes()) + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, K, K1, K2) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY) + } + } +} + +func BenchmarkScalarMult(b *testing.B) { + curve := p384.P384() + params := curve.Params() + + K, _ := rand.Int(rand.Reader, params.N) + M, _ := rand.Int(rand.Reader, params.N) + N, _ := rand.Int(rand.Reader, params.N) + k := K.Bytes() + m := M.Bytes() + n := N.Bytes() + + b.Run("kG", func(b *testing.B) { + for i := 0; i < b.N; i++ { + curve.ScalarBaseMult(k) + } + }) + b.Run("kP", func(b *testing.B) { + for i := 0; i < b.N; i++ { + curve.ScalarMult(params.Gx, params.Gy, k) + } + }) + b.Run("kG+lP", func(b *testing.B) { + for i := 0; i < b.N; i++ { + _, _ = curve.CombinedMult(params.Gx, params.Gy, m, n) + } + }) +} + +func Example_p384() { + // import "circl/ecc/p384" + // import "crypto/elliptic" + circl := p384.P384() + stdlib := elliptic.P384() + + params := circl.Params() + K, _ := rand.Int(rand.Reader, params.N) + k := K.Bytes() + + x1, y1 := circl.ScalarBaseMult(k) + x2, y2 := stdlib.ScalarBaseMult(k) + fmt.Printf("%v, %v", x1.Cmp(x2) == 0, y1.Cmp(y2) == 0) + // Output: true, true +} diff --git a/src/circl/ecc/p384/p384opt.go b/src/circl/ecc/p384/p384opt.go new file mode 100644 index 00000000000..9849b7c540e --- /dev/null +++ b/src/circl/ecc/p384/p384opt.go @@ -0,0 +1,187 @@ +// +build !noasm,arm64 !noasm,amd64 + +package p384 + +import ( + "crypto/subtle" + "math/big" + + "circl/math" +) + +type curve struct{} + +// P384 returns a Curve which implements P-384 (see FIPS 186-3, section D.2.4). +func P384() Curve { return curve{} } + +// IsOnCurve reports whether the given (x,y) lies on the curve. +func (c curve) IsOnCurve(x, y *big.Int) bool { + x1, y1 := &fp384{}, &fp384{} + x1.SetBigInt(x) + y1.SetBigInt(y) + montEncode(x1, x1) + montEncode(y1, y1) + + y2, x3 := &fp384{}, &fp384{} + fp384Sqr(y2, y1) + fp384Sqr(x3, x1) + fp384Mul(x3, x3, x1) + + threeX := &fp384{} + fp384Add(threeX, x1, x1) + fp384Add(threeX, threeX, x1) + + fp384Sub(x3, x3, threeX) + fp384Add(x3, x3, &bb) + + return *y2 == *x3 +} + +// Add returns the sum of (x1,y1) and (x2,y2). +func (c curve) Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int) { + P := newAffinePoint(x1, y1).toJacobian() + P.mixadd(P, newAffinePoint(x2, y2)) + return P.toAffine().toInt() +} + +// Double returns 2*(x,y). +func (c curve) Double(x1, y1 *big.Int) (x, y *big.Int) { + P := newAffinePoint(x1, y1).toJacobian() + P.double() + return P.toAffine().toInt() +} + +// reduceScalar shorten a scalar modulo the order of the curve. +func (c curve) reduceScalar(k []byte) []byte { + const max = sizeFp + if len(k) > max { + bigK := new(big.Int).SetBytes(k) + bigK.Mod(bigK, c.Params().N) + k = bigK.Bytes() + } + if len(k) < max { + k = append(make([]byte, max-len(k)), k...) + } + return k +} + +// toOdd performs k = (-k mod N) if k is even. +func (c curve) toOdd(k []byte) ([]byte, int) { + var X, Y big.Int + X.SetBytes(k) + Y.Neg(&X).Mod(&Y, c.Params().N) + isEven := 1 - int(X.Bit(0)) + x := X.Bytes() + y := Y.Bytes() + + if len(x) < len(y) { + x = append(make([]byte, len(y)-len(x)), x...) + } else if len(x) > len(y) { + y = append(make([]byte, len(x)-len(y)), y...) + } + subtle.ConstantTimeCopy(isEven, x, y) + return x, isEven +} + +// ScalarMult returns (Qx,Qy)=k*(Px,Py) where k is a number in big-endian form. +func (c curve) ScalarMult(x1, y1 *big.Int, k []byte) (x, y *big.Int) { + return c.scalarMultOmega(x1, y1, k, 5) +} + +func (c curve) scalarMultOmega(x1, y1 *big.Int, k []byte, omega uint) (x, y *big.Int) { + k = c.reduceScalar(k) + oddK, isEvenK := c.toOdd(k) + + var scalar big.Int + scalar.SetBytes(oddK) + if scalar.Sign() == 0 { + return new(big.Int), new(big.Int) + } + const bitsN = uint(384) + L := math.SignedDigit(&scalar, omega, bitsN) + + var R jacobianPoint + Q := zeroPoint().toJacobian() + TabP := newAffinePoint(x1, y1).oddMultiples(omega) + for i := len(L) - 1; i > 0; i-- { + for j := uint(0); j < omega-1; j++ { + Q.double() + } + idx := absolute(L[i]) >> 1 + for j := range TabP { + R.cmov(&TabP[j], subtle.ConstantTimeEq(int32(j), idx)) + } + R.cneg(int(L[i]>>31) & 1) + Q.add(Q, &R) + } + // Calculate the last iteration using complete addition formula. + for j := uint(0); j < omega-1; j++ { + Q.double() + } + idx := absolute(L[0]) >> 1 + for j := range TabP { + R.cmov(&TabP[j], subtle.ConstantTimeEq(int32(j), idx)) + } + R.cneg(int(L[0]>>31) & 1) + QQ := Q.toProjective() + QQ.completeAdd(QQ, R.toProjective()) + QQ.cneg(isEvenK) + return QQ.toAffine().toInt() +} + +// ScalarBaseMult returns k*G, where G is the base point of the group +// and k is an integer in big-endian form. +func (c curve) ScalarBaseMult(k []byte) (x, y *big.Int) { + params := c.Params() + return c.ScalarMult(params.Gx, params.Gy, k) +} + +// CombinedMult calculates P=mG+nQ, where G is the generator and Q=(x,y,z). +// The scalars m and n are integers in big-endian form. Non-constant time. +func (c curve) CombinedMult(xQ, yQ *big.Int, m, n []byte) (xP, yP *big.Int) { + const nOmega = uint(5) + var k big.Int + k.SetBytes(m) + nafM := math.OmegaNAF(&k, baseOmega) + k.SetBytes(n) + nafN := math.OmegaNAF(&k, nOmega) + + if len(nafM) > len(nafN) { + nafN = append(nafN, make([]int32, len(nafM)-len(nafN))...) + } else if len(nafM) < len(nafN) { + nafM = append(nafM, make([]int32, len(nafN)-len(nafM))...) + } + + TabQ := newAffinePoint(xQ, yQ).oddMultiples(nOmega) + var jR jacobianPoint + var aR affinePoint + P := zeroPoint().toJacobian() + for i := len(nafN) - 1; i >= 0; i-- { + P.double() + // Generator point + if nafM[i] != 0 { + idxM := absolute(nafM[i]) >> 1 + aR = baseOddMultiples[idxM] + if nafM[i] < 0 { + aR.neg() + } + P.mixadd(P, &aR) + } + // Input point + if nafN[i] != 0 { + idxN := absolute(nafN[i]) >> 1 + jR = TabQ[idxN] + if nafN[i] < 0 { + jR.neg() + } + P.add(P, &jR) + } + } + return P.toAffine().toInt() +} + +// absolute returns always a positive value. +func absolute(x int32) int32 { + mask := x >> 31 + return (x + mask) ^ mask +} diff --git a/src/circl/ecc/p384/point.go b/src/circl/ecc/p384/point.go new file mode 100644 index 00000000000..dca9c618b5c --- /dev/null +++ b/src/circl/ecc/p384/point.go @@ -0,0 +1,357 @@ +// +build !noasm,arm64 !noasm,amd64 + +package p384 + +import ( + "fmt" + "math/big" +) + +// affinePoint represents an affine point of the curve. The point at +// infinity is (0,0) leveraging that it is not an affine point. +type affinePoint struct{ x, y fp384 } + +func newAffinePoint(x, y *big.Int) *affinePoint { + var P affinePoint + P.x.SetBigInt(x) + P.y.SetBigInt(y) + montEncode(&P.x, &P.x) + montEncode(&P.y, &P.y) + return &P +} + +func zeroPoint() *affinePoint { return &affinePoint{} } + +func (ap affinePoint) String() string { + if ap.isZero() { + return "inf" + } + return fmt.Sprintf("x: %v\ny: %v", ap.x, ap.y) +} + +func (ap *affinePoint) isZero() bool { + zero := fp384{} + return ap.x == zero && ap.y == zero +} + +func (ap *affinePoint) neg() { fp384Neg(&ap.y, &ap.y) } + +func (ap *affinePoint) toInt() (x, y *big.Int) { + var x1, y1 fp384 + montDecode(&x1, &ap.x) + montDecode(&y1, &ap.y) + return x1.BigInt(), y1.BigInt() +} + +func (ap *affinePoint) toJacobian() *jacobianPoint { + var P jacobianPoint + if ap.isZero() { + montEncode(&P.x, &fp384{1}) + montEncode(&P.y, &fp384{1}) + } else { + P.x = ap.x + P.y = ap.y + montEncode(&P.z, &fp384{1}) + } + return &P +} + +func (ap *affinePoint) toProjective() *projectivePoint { + var P projectivePoint + if ap.isZero() { + montEncode(&P.y, &fp384{1}) + } else { + P.x = ap.x + P.y = ap.y + montEncode(&P.z, &fp384{1}) + } + return &P +} + +// OddMultiples calculates the points iP for i={1,3,5,7,..., 2^(n-1)-1} +// Ensure that 1 < n < 31, otherwise it returns an empty slice. +func (ap affinePoint) oddMultiples(n uint) []jacobianPoint { + var t []jacobianPoint + if n > 1 && n < 31 { + P := ap.toJacobian() + s := int32(1) << (n - 1) + t = make([]jacobianPoint, s) + t[0] = *P + _2P := *P + _2P.double() + for i := int32(1); i < s; i++ { + t[i].add(&t[i-1], &_2P) + } + } + return t +} + +// p2Point is a point in P^2 +type p2Point struct{ x, y, z fp384 } + +func (P *p2Point) String() string { + return fmt.Sprintf("x: %v\ny: %v\nz: %v", P.x, P.y, P.z) +} + +func (P *p2Point) neg() { fp384Neg(&P.y, &P.y) } + +// condNeg if P is negated if b=1. +func (P *p2Point) cneg(b int) { + var mY fp384 + fp384Neg(&mY, &P.y) + fp384Cmov(&P.y, &mY, b) +} + +// cmov sets P to Q if b=1. +func (P *p2Point) cmov(Q *p2Point, b int) { + fp384Cmov(&P.x, &Q.x, b) + fp384Cmov(&P.y, &Q.y, b) + fp384Cmov(&P.z, &Q.z, b) +} + +func (P *p2Point) toInt() (x, y, z *big.Int) { + var x1, y1, z1 fp384 + montDecode(&x1, &P.x) + montDecode(&y1, &P.y) + montDecode(&z1, &P.z) + return x1.BigInt(), y1.BigInt(), z1.BigInt() +} + +// jacobianPoint represents a point in Jacobian coordinates. The point at +// infinity is any point (x,y,0) such that x and y are different from 0. +type jacobianPoint struct{ p2Point } + +func (P *jacobianPoint) isZero() bool { + zero := fp384{} + return P.x != zero && P.y != zero && P.z == zero +} + +func (P *jacobianPoint) toAffine() *affinePoint { + var aP affinePoint + z, z2 := &fp384{}, &fp384{} + fp384Inv(z, &P.z) + fp384Sqr(z2, z) + fp384Mul(&aP.x, &P.x, z2) + fp384Mul(&aP.y, &P.y, z) + fp384Mul(&aP.y, &aP.y, z2) + return &aP +} + +func (P *jacobianPoint) cmov(Q *jacobianPoint, b int) { P.p2Point.cmov(&Q.p2Point, b) } + +// add calculates P=Q+R such that Q and R are different than the identity point, +// and Q!==R. This function cannot be used for doublings. +func (P *jacobianPoint) add(Q, R *jacobianPoint) { + if Q.isZero() { + *P = *R + return + } else if R.isZero() { + *P = *Q + return + } + + // Cohen-Miyagi-Ono (1998) + // https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2 + X1, Y1, Z1 := &Q.x, &Q.y, &Q.z + X2, Y2, Z2 := &R.x, &R.y, &R.z + Z1Z1, Z2Z2, U1, U2 := &fp384{}, &fp384{}, &fp384{}, &fp384{} + H, HH, HHH, RR := &fp384{}, &fp384{}, &fp384{}, &fp384{} + V, t4, t5, t6, t7, t8 := &fp384{}, &fp384{}, &fp384{}, &fp384{}, &fp384{}, &fp384{} + t0, t1, t2, t3, S1, S2 := &fp384{}, &fp384{}, &fp384{}, &fp384{}, &fp384{}, &fp384{} + fp384Sqr(Z1Z1, Z1) // Z1Z1 = Z1 ^ 2 + fp384Sqr(Z2Z2, Z2) // Z2Z2 = Z2 ^ 2 + fp384Mul(U1, X1, Z2Z2) // U1 = X1 * Z2Z2 + fp384Mul(U2, X2, Z1Z1) // U2 = X2 * Z1Z1 + fp384Mul(t0, Z2, Z2Z2) // t0 = Z2 * Z2Z2 + fp384Mul(S1, Y1, t0) // S1 = Y1 * t0 + fp384Mul(t1, Z1, Z1Z1) // t1 = Z1 * Z1Z1 + fp384Mul(S2, Y2, t1) // S2 = Y2 * t1 + fp384Sub(H, U2, U1) // H = U2 - U1 + fp384Sqr(HH, H) // HH = H ^ 2 + fp384Mul(HHH, H, HH) // HHH = H * HH + fp384Sub(RR, S2, S1) // r = S2 - S1 + fp384Mul(V, U1, HH) // V = U1 * HH + fp384Sqr(t2, RR) // t2 = r ^ 2 + fp384Add(t3, V, V) // t3 = V + V + fp384Sub(t4, t2, HHH) // t4 = t2 - HHH + fp384Sub(&P.x, t4, t3) // X3 = t4 - t3 + fp384Sub(t5, V, &P.x) // t5 = V - X3 + fp384Mul(t6, S1, HHH) // t6 = S1 * HHH + fp384Mul(t7, RR, t5) // t7 = r * t5 + fp384Sub(&P.y, t7, t6) // Y3 = t7 - t6 + fp384Mul(t8, Z2, H) // t8 = Z2 * H + fp384Mul(&P.z, Z1, t8) // Z3 = Z1 * t8 +} + +// mixadd calculates P=Q+R such that P and Q different than the identity point, +// and Q not in {P,-P, O}. +func (P *jacobianPoint) mixadd(Q *jacobianPoint, R *affinePoint) { + if Q.isZero() { + *P = *R.toJacobian() + return + } else if R.isZero() { + *P = *Q + return + } + + z1z1, u2 := &fp384{}, &fp384{} + fp384Sqr(z1z1, &Q.z) + fp384Mul(u2, &R.x, z1z1) + + s2 := &fp384{} + fp384Mul(s2, &R.y, &Q.z) + fp384Mul(s2, s2, z1z1) + if Q.x == *u2 { + if Q.y != *s2 { + *P = *(zeroPoint().toJacobian()) + return + } + *P = *Q + P.double() + return + } + + h, r := &fp384{}, &fp384{} + fp384Sub(h, u2, &Q.x) + fp384Mul(&P.z, h, &Q.z) + fp384Sub(r, s2, &Q.y) + + h2, h3 := &fp384{}, &fp384{} + fp384Sqr(h2, h) + fp384Mul(h3, h2, h) + h3y1 := &fp384{} + fp384Mul(h3y1, h3, &Q.y) + + h2x1 := &fp384{} + fp384Mul(h2x1, h2, &Q.x) + + fp384Sqr(&P.x, r) + fp384Sub(&P.x, &P.x, h3) + fp384Sub(&P.x, &P.x, h2x1) + fp384Sub(&P.x, &P.x, h2x1) + + fp384Sub(&P.y, h2x1, &P.x) + fp384Mul(&P.y, &P.y, r) + fp384Sub(&P.y, &P.y, h3y1) +} + +func (P *jacobianPoint) double() { + delta, gamma, alpha, alpha2 := &fp384{}, &fp384{}, &fp384{}, &fp384{} + fp384Sqr(delta, &P.z) + fp384Sqr(gamma, &P.y) + fp384Sub(alpha, &P.x, delta) + fp384Add(alpha2, &P.x, delta) + fp384Mul(alpha, alpha, alpha2) + *alpha2 = *alpha + fp384Add(alpha, alpha, alpha) + fp384Add(alpha, alpha, alpha2) + + beta := &fp384{} + fp384Mul(beta, &P.x, gamma) + + beta8 := &fp384{} + fp384Sqr(&P.x, alpha) + fp384Add(beta8, beta, beta) + fp384Add(beta8, beta8, beta8) + fp384Add(beta8, beta8, beta8) + fp384Sub(&P.x, &P.x, beta8) + + fp384Add(&P.z, &P.y, &P.z) + fp384Sqr(&P.z, &P.z) + fp384Sub(&P.z, &P.z, gamma) + fp384Sub(&P.z, &P.z, delta) + + fp384Add(beta, beta, beta) + fp384Add(beta, beta, beta) + fp384Sub(beta, beta, &P.x) + + fp384Mul(&P.y, alpha, beta) + + fp384Sqr(gamma, gamma) + fp384Add(gamma, gamma, gamma) + fp384Add(gamma, gamma, gamma) + fp384Add(gamma, gamma, gamma) + fp384Sub(&P.y, &P.y, gamma) +} + +func (P *jacobianPoint) toProjective() *projectivePoint { + var hP projectivePoint + hP.y = P.y + fp384Mul(&hP.x, &P.x, &P.z) + fp384Sqr(&hP.z, &P.z) + fp384Mul(&hP.z, &hP.z, &P.z) + return &hP +} + +// projectivePoint represents a point in projective homogeneous coordinates. +// The point at infinity is (0,y,0) such that y is different from 0. +type projectivePoint struct{ p2Point } + +func (P *projectivePoint) isZero() bool { + zero := fp384{} + return P.x == zero && P.y != zero && P.z == zero +} + +func (P *projectivePoint) toAffine() *affinePoint { + var aP affinePoint + z := &fp384{} + fp384Inv(z, &P.z) + fp384Mul(&aP.x, &P.x, z) + fp384Mul(&aP.y, &P.y, z) + return &aP +} + +// add calculates P=Q+R using complete addition formula for prime groups. +func (P *projectivePoint) completeAdd(Q, R *projectivePoint) { + // Reference: + // "Complete addition formulas for prime order elliptic curves" by + // Costello-Renes-Batina. [Alg.4] (eprint.iacr.org/2015/1060). + X1, Y1, Z1 := &Q.x, &Q.y, &Q.z + X2, Y2, Z2 := &R.x, &R.y, &R.z + X3, Y3, Z3 := &fp384{}, &fp384{}, &fp384{} + t0, t1, t2, t3, t4 := &fp384{}, &fp384{}, &fp384{}, &fp384{}, &fp384{} + fp384Mul(t0, X1, X2) // 1. t0 ← X1 · X2 + fp384Mul(t1, Y1, Y2) // 2. t1 ← Y1 · Y2 + fp384Mul(t2, Z1, Z2) // 3. t2 ← Z1 · Z2 + fp384Add(t3, X1, Y1) // 4. t3 ← X1 + Y1 + fp384Add(t4, X2, Y2) // 5. t4 ← X2 + Y2 + fp384Mul(t3, t3, t4) // 6. t3 ← t3 · t4 + fp384Add(t4, t0, t1) // 7. t4 ← t0 + t1 + fp384Sub(t3, t3, t4) // 8. t3 ← t3 − t4 + fp384Add(t4, Y1, Z1) // 9. t4 ← Y1 + Z1 + fp384Add(X3, Y2, Z2) // 10. X3 ← Y2 + Z2 + fp384Mul(t4, t4, X3) // 11. t4 ← t4 · X3 + fp384Add(X3, t1, t2) // 12. X3 ← t1 + t2 + fp384Sub(t4, t4, X3) // 13. t4 ← t4 − X3 + fp384Add(X3, X1, Z1) // 14. X3 ← X1 + Z1 + fp384Add(Y3, X2, Z2) // 15. Y3 ← X2 + Z2 + fp384Mul(X3, X3, Y3) // 16. X3 ← X3 · Y3 + fp384Add(Y3, t0, t2) // 17. Y3 ← t0 + t2 + fp384Sub(Y3, X3, Y3) // 18. Y3 ← X3 − Y3 + fp384Mul(Z3, &bb, t2) // 19. Z3 ← b · t2 + fp384Sub(X3, Y3, Z3) // 20. X3 ← Y3 − Z3 + fp384Add(Z3, X3, X3) // 21. Z3 ← X3 + X3 + fp384Add(X3, X3, Z3) // 22. X3 ← X3 + Z3 + fp384Sub(Z3, t1, X3) // 23. Z3 ← t1 − X3 + fp384Add(X3, t1, X3) // 24. X3 ← t1 + X3 + fp384Mul(Y3, &bb, Y3) // 25. Y3 ← b · Y3 + fp384Add(t1, t2, t2) // 26. t1 ← t2 + t2 + fp384Add(t2, t1, t2) // 27. t2 ← t1 + t2 + fp384Sub(Y3, Y3, t2) // 28. Y3 ← Y3 − t2 + fp384Sub(Y3, Y3, t0) // 29. Y3 ← Y3 − t0 + fp384Add(t1, Y3, Y3) // 30. t1 ← Y3 + Y3 + fp384Add(Y3, t1, Y3) // 31. Y3 ← t1 + Y3 + fp384Add(t1, t0, t0) // 32. t1 ← t0 + t0 + fp384Add(t0, t1, t0) // 33. t0 ← t1 + t0 + fp384Sub(t0, t0, t2) // 34. t0 ← t0 − t2 + fp384Mul(t1, t4, Y3) // 35. t1 ← t4 · Y3 + fp384Mul(t2, t0, Y3) // 36. t2 ← t0 · Y3 + fp384Mul(Y3, X3, Z3) // 37. Y3 ← X3 · Z3 + fp384Add(Y3, Y3, t2) // 38. Y3 ← Y3 + t2 + fp384Mul(X3, t3, X3) // 39. X3 ← t3 · X3 + fp384Sub(X3, X3, t1) // 40. X3 ← X3 − t1 + fp384Mul(Z3, t4, Z3) // 41. Z3 ← t4 · Z3 + fp384Mul(t1, t3, t0) // 42. t1 ← t3 · t0 + fp384Add(Z3, Z3, t1) // 43. Z3 ← Z3 + t1 + P.x, P.y, P.z = *X3, *Y3, *Z3 +} diff --git a/src/circl/ecc/p384/point_test.go b/src/circl/ecc/p384/point_test.go new file mode 100644 index 00000000000..d2cc0e2cd5f --- /dev/null +++ b/src/circl/ecc/p384/point_test.go @@ -0,0 +1,415 @@ +// +build !noasm,arm64 !noasm,amd64 + +package p384 + +import ( + "crypto/elliptic" + "crypto/rand" + "encoding/binary" + "testing" + + "circl/internal/test" +) + +func randomAffine() *affinePoint { + params := elliptic.P384().Params() + k, _ := rand.Int(rand.Reader, params.N) + return newAffinePoint(params.ScalarBaseMult(k.Bytes())) +} + +func randomJacobian() *jacobianPoint { + params := elliptic.P384().Params() + P := randomAffine().toJacobian() + z, _ := rand.Int(rand.Reader, params.P) + var l fp384 + l.SetBigInt(z) + fp384Mul(&P.z, &P.z, &l) // z = z * l^1 + fp384Mul(&P.y, &P.y, &l) + fp384Sqr(&l, &l) + fp384Mul(&P.x, &P.x, &l) // x = x * l^2 + fp384Mul(&P.y, &P.y, &l) // y = y * l^3 + return P +} + +func randomProjective() *projectivePoint { + return randomJacobian().toProjective() +} + +func TestPointDouble(t *testing.T) { + t.Run("2∞=∞", func(t *testing.T) { + Z := zeroPoint().toJacobian() + Z.double() + got := Z.isZero() + want := true + if got != want { + test.ReportError(t, got, want) + } + }) + + t.Run("2P=P+P", func(t *testing.T) { + StdCurve := elliptic.P384() + for i := 0; i < 128; i++ { + P := randomJacobian() + + x1, y1 := P.toAffine().toInt() + wantX, wantY := StdCurve.Double(x1, y1) + + P.double() + gotX, gotY := P.toAffine().toInt() + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, P) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY) + } + } + }) +} + +func TestPointAdd(t *testing.T) { + StdCurve := elliptic.P384() + Q, R := &jacobianPoint{}, &jacobianPoint{} + Z := zeroPoint().toJacobian() + P := randomJacobian() + + t.Run("∞+∞=∞", func(t *testing.T) { + R.add(Z, Z) + got := R.isZero() + want := true + if got != want { + test.ReportError(t, got, want) + } + }) + + t.Run("∞+P=P", func(t *testing.T) { + R.add(Z, P) + gotX, gotY := R.toAffine().toInt() + wantX, wantY := P.toAffine().toInt() + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, P) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY, P) + } + }) + + t.Run("P+∞=P", func(t *testing.T) { + R.add(P, Z) + gotX, gotY := R.toAffine().toInt() + wantX, wantY := P.toAffine().toInt() + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, P) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY, P) + } + }) + + t.Run("P+(-P)=∞", func(t *testing.T) { + *Q = *P + Q.neg() + R.add(P, Q) + got := R.isZero() + want := true + if got != want { + test.ReportError(t, got, want, P) + } + }) + + t.Run("P+P=2P", func(t *testing.T) { + // This verifies that add function cannot be used for doublings. + for i := 0; i < 128; i++ { + P = randomJacobian() + + R.add(P, P) + gotX, gotY := R.toAffine().toInt() + wantX, wantY := zeroPoint().toInt() + + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, P) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY, P) + } + } + }) + + t.Run("P+Q=R", func(t *testing.T) { + for i := 0; i < 128; i++ { + P = randomJacobian() + Q = randomJacobian() + + x1, y1 := P.toAffine().toInt() + x2, y2 := Q.toAffine().toInt() + wantX, wantY := StdCurve.Add(x1, y1, x2, y2) + + R.add(P, Q) + gotX, gotY := R.toAffine().toInt() + + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, P, Q) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY, P, Q) + } + } + }) +} + +func TestPointCompleteAdd(t *testing.T) { + StdCurve := elliptic.P384() + Q, R := &projectivePoint{}, &projectivePoint{} + Z := zeroPoint().toProjective() + P := randomProjective() + + t.Run("∞+∞=∞", func(t *testing.T) { + R.completeAdd(Z, Z) + got := R.isZero() + want := true + if got != want { + test.ReportError(t, got, want) + } + }) + + t.Run("∞+P=P", func(t *testing.T) { + R.completeAdd(Z, P) + gotX, gotY := R.toAffine().toInt() + wantX, wantY := P.toAffine().toInt() + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, P) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY, P) + } + }) + + t.Run("P+∞=P", func(t *testing.T) { + R.completeAdd(P, Z) + gotX, gotY := R.toAffine().toInt() + wantX, wantY := P.toAffine().toInt() + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, P) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY, P) + } + }) + + t.Run("P+(-P)=∞", func(t *testing.T) { + *Q = *P + Q.cneg(1) + R.completeAdd(P, Q) + got := R.isZero() + want := true + if got != want { + test.ReportError(t, got, want, P) + } + }) + + t.Run("P+P=2P", func(t *testing.T) { + // This verifies that completeAdd can be used for doublings. + for i := 0; i < 128; i++ { + P := randomJacobian() + PP := P.toProjective() + + R.completeAdd(PP, PP) + P.double() + + gotX, gotY := R.toAffine().toInt() + wantX, wantY := P.toAffine().toInt() + + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, P) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY, P) + } + } + }) + + t.Run("P+Q=R", func(t *testing.T) { + for i := 0; i < 128; i++ { + P := randomProjective() + Q := randomProjective() + + x1, y1 := P.toAffine().toInt() + x2, y2 := Q.toAffine().toInt() + wantX, wantY := StdCurve.Add(x1, y1, x2, y2) + + R.completeAdd(P, Q) + gotX, gotY := R.toAffine().toInt() + + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, P, Q) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY, P, Q) + } + } + }) +} + +func TestPointMixAdd(t *testing.T) { + StdCurve := elliptic.P384() + aZ := zeroPoint() + jZ := zeroPoint().toJacobian() + R := &jacobianPoint{} + aQ := &affinePoint{} + aP := randomAffine() + jP := randomJacobian() + + t.Run("∞+∞=∞", func(t *testing.T) { + R.mixadd(jZ, aZ) + got := R.isZero() + want := true + if got != want { + test.ReportError(t, got, want) + } + }) + + t.Run("∞+P=P", func(t *testing.T) { + R.mixadd(jZ, aP) + gotX, gotY := R.toAffine().toInt() + wantX, wantY := aP.toInt() + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, aP) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY) + } + }) + + t.Run("P+∞=P", func(t *testing.T) { + R.mixadd(jP, aZ) + gotX, gotY, gotZ := R.toInt() + wantX, wantY, wantZ := jP.toInt() + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, jP) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY) + } + if gotZ.Cmp(wantZ) != 0 { + test.ReportError(t, gotZ, wantZ) + } + }) + + t.Run("P+(-P)=∞", func(t *testing.T) { + aQ = jP.toAffine() + aQ.neg() + R.mixadd(jP, aQ) + got := R.isZero() + want := true + if got != want { + test.ReportError(t, got, want, jP) + } + }) + + t.Run("P+P=2P", func(t *testing.T) { + for i := 0; i < 128; i++ { + aQ := randomAffine() + jQ := aQ.toJacobian() + + x, y := aQ.toInt() + wantX, wantY := StdCurve.Double(x, y) + + R.mixadd(jQ, aQ) + gotX, gotY := R.toAffine().toInt() + + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, aQ) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY) + } + } + }) + + t.Run("P+Q=R", func(t *testing.T) { + for i := 0; i < 128; i++ { + aP = randomAffine() + jP = randomJacobian() + + x1, y1 := jP.toAffine().toInt() + x2, y2 := aP.toInt() + wantX, wantY := StdCurve.Add(x1, y1, x2, y2) + + R.mixadd(jP, aP) + gotX, gotY := R.toAffine().toInt() + + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, jP, aP) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY) + } + } + }) +} + +func TestOddMultiples(t *testing.T) { + t.Run("invalidOmega", func(t *testing.T) { + for w := uint(0); w < 2; w++ { + P := randomAffine() + PP := P.oddMultiples(w) + got := len(PP) + want := 0 + if got != want { + test.ReportError(t, got, want, w) + } + } + }) + + t.Run("validOmega", func(t *testing.T) { + StdCurve := elliptic.P384() + var jOdd [4]byte + for i := 0; i < 32; i++ { + P := randomAffine() + X, Y := P.toInt() + for w := uint(2); w < 10; w++ { + PP := P.oddMultiples(w) + for j, jP := range PP { + binary.BigEndian.PutUint32(jOdd[:], uint32(2*j+1)) + wantX, wantY := StdCurve.ScalarMult(X, Y, jOdd[:]) + gotX, gotY := jP.toAffine().toInt() + if gotX.Cmp(wantX) != 0 { + test.ReportError(t, gotX, wantX, w, j) + } + if gotY.Cmp(wantY) != 0 { + test.ReportError(t, gotY, wantY) + } + } + } + } + }) +} + +func BenchmarkPoint(b *testing.B) { + P := randomJacobian() + Q := randomJacobian() + R := randomJacobian() + QQ := randomProjective() + RR := randomProjective() + aR := randomAffine() + + b.Run("addition", func(b *testing.B) { + for i := 0; i < b.N; i++ { + R.add(P, Q) + } + }) + b.Run("fullAddition", func(b *testing.B) { + for i := 0; i < b.N; i++ { + RR.completeAdd(RR, QQ) + } + }) + b.Run("mixadd", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.mixadd(P, aR) + } + }) + b.Run("double", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.double() + } + }) +} diff --git a/src/circl/ecc/p384/tableBase.go b/src/circl/ecc/p384/tableBase.go new file mode 100644 index 00000000000..f59b1406563 --- /dev/null +++ b/src/circl/ecc/p384/tableBase.go @@ -0,0 +1,330 @@ +// +build !noasm,arm64 !noasm,amd64 + +package p384 + +const baseOmega = uint(7) + +// baseOddMultiples has [2*i+1] * G at position i. +// Each coordinate has been multiplied by R=2^384 +var baseOddMultiples = [1 << (baseOmega - 1)]affinePoint{ + // 1P + { + x: fp384{0x28, 0xb5, 0xc0, 0x49, 0x66, 0x75, 0xd0, 0x3d, 0x38, 0xce, 0xd6, 0xa0, 0xe2, 0x78, 0xe3, 0x20, 0x6e, 0x4d, 0x1b, 0x54, 0xfc, 0x3a, 0x9c, 0x87, 0xff, 0xe, 0xa3, 0x59, 0x84, 0x86, 0x54, 0x64, 0x2b, 0xde, 0x4e, 0x61, 0x23, 0xf7, 0x2f, 0x81, 0x13, 0x15, 0x9e, 0x29, 0xc2, 0xad, 0x3a, 0x4d}, + y: fp384{0xfe, 0xa4, 0x3, 0x4b, 0xad, 0x3d, 0x4, 0x23, 0xac, 0xa9, 0xb4, 0x7b, 0xbf, 0xa8, 0xbf, 0xa1, 0x50, 0xb0, 0x83, 0x2e, 0x56, 0xe7, 0xad, 0x8b, 0xd9, 0xff, 0xf4, 0x68, 0x19, 0x52, 0xc3, 0xc6, 0x40, 0xa8, 0x69, 0x39, 0x26, 0x2, 0x80, 0xdd, 0xe9, 0xc5, 0x15, 0x5a, 0xc2, 0xab, 0x78, 0x2b}, + }, + // 3P + { + x: fp384{0x73, 0x40, 0xdc, 0xc1, 0xe6, 0xdb, 0xe4, 0x5, 0x9c, 0x77, 0x4f, 0xf0, 0xff, 0xa9, 0x4e, 0xc5, 0xf0, 0xcc, 0x70, 0xa1, 0xe9, 0x34, 0x20, 0x6b, 0x3e, 0x6c, 0x1c, 0xd5, 0x32, 0xd7, 0x48, 0x3a, 0x70, 0xa4, 0x3a, 0x26, 0x2d, 0x7e, 0x6f, 0xe3, 0xac, 0xc3, 0xc1, 0xe7, 0x68, 0xfe, 0x83, 0xd2}, + y: fp384{0x57, 0xe1, 0x4e, 0xc0, 0x21, 0x48, 0x28, 0x7e, 0x6d, 0xe3, 0xe0, 0x7a, 0xa7, 0x89, 0xd7, 0x92, 0x46, 0x74, 0xf6, 0x4e, 0xc0, 0x63, 0x26, 0x13, 0xb4, 0xd0, 0xe1, 0xd2, 0x5a, 0x2d, 0x1, 0x68, 0x39, 0xb3, 0x2, 0x51, 0xb1, 0x68, 0xdb, 0xf6, 0xaf, 0x92, 0x32, 0x98, 0xfc, 0x65, 0x54, 0x46}, + }, + // 5P + { + x: fp384{0xdf, 0xf0, 0xf1, 0x68, 0xba, 0x5e, 0x59, 0xbb, 0x66, 0x34, 0x87, 0xcc, 0xcb, 0xc0, 0x85, 0xc1, 0x3b, 0x70, 0x3c, 0x29, 0xb5, 0xb1, 0x1e, 0x7f, 0xe6, 0x5, 0xcc, 0xaa, 0xf5, 0x2c, 0xdb, 0x60, 0xc6, 0xe4, 0xe8, 0xe2, 0x87, 0xb9, 0x76, 0xc6, 0xfb, 0x8f, 0x17, 0x1d, 0xb1, 0x26, 0xbb, 0xe1}, + y: fp384{0x21, 0xfa, 0x73, 0x70, 0xa0, 0x4b, 0x69, 0x2b, 0x66, 0x45, 0xf3, 0x72, 0x2e, 0x6e, 0xc1, 0x22, 0x99, 0x5b, 0xc3, 0x1, 0x31, 0x1b, 0xb6, 0x80, 0x11, 0x4, 0x2c, 0x98, 0xaf, 0x7f, 0x23, 0x4b, 0x6d, 0x23, 0xde, 0x24, 0x40, 0x94, 0xc5, 0xe6, 0xa3, 0xe4, 0x9, 0xe2, 0xd6, 0xc9, 0xb1, 0x4d}, + }, + // 7P + { + x: fp384{0x2b, 0x22, 0x69, 0x7d, 0xd1, 0xb9, 0x13, 0xdf, 0xb1, 0x74, 0x47, 0x87, 0x5f, 0x41, 0xe6, 0x4c, 0x95, 0xaa, 0x1f, 0x21, 0xf8, 0xdc, 0x1e, 0x73, 0xed, 0x53, 0x97, 0x65, 0xd1, 0x15, 0x42, 0x5f, 0x55, 0xdf, 0xb2, 0x9d, 0x58, 0xdb, 0x93, 0xf8, 0x5b, 0x2, 0x89, 0x1c, 0x81, 0x9f, 0x2c, 0x93}, + y: fp384{0x1e, 0xa6, 0x6, 0x77, 0x20, 0xb2, 0x96, 0x9, 0x79, 0x1c, 0x64, 0xa8, 0xd5, 0x49, 0x53, 0x13, 0x44, 0x8, 0x13, 0x50, 0x6f, 0xd7, 0xaa, 0x65, 0x80, 0xf7, 0xff, 0x1, 0x4, 0x7c, 0xf3, 0xf, 0x6, 0x7, 0x3b, 0x69, 0x8e, 0x23, 0x7f, 0xf5, 0x3e, 0x9b, 0x6c, 0xaf, 0xb6, 0x16, 0xa, 0xd9}, + }, + // 9P + { + x: fp384{0x2f, 0xb9, 0x53, 0x23, 0xe, 0x20, 0x5d, 0x2f, 0xf9, 0xe4, 0xd7, 0x3f, 0x29, 0x87, 0x5d, 0xe3, 0x5d, 0x74, 0x6d, 0xa9, 0x33, 0x48, 0x9, 0x26, 0x3f, 0xff, 0xbf, 0x3c, 0xc1, 0x1d, 0x35, 0xdc, 0x6a, 0x4d, 0xd5, 0xda, 0xc6, 0x64, 0xd4, 0x26, 0x6a, 0x6c, 0x63, 0x53, 0x1d, 0x1d, 0xab, 0x5c}, + y: fp384{0xb0, 0xc0, 0x8e, 0xb1, 0x72, 0x30, 0x81, 0xf2, 0x2f, 0xaa, 0x42, 0xd7, 0x70, 0xe2, 0x77, 0x37, 0xc2, 0xa7, 0x3c, 0x3, 0xc7, 0x61, 0xf0, 0x27, 0xd8, 0xd0, 0xea, 0x68, 0xcc, 0xac, 0xec, 0xa6, 0x54, 0xa7, 0x69, 0xee, 0xf4, 0x29, 0x94, 0x7d, 0xc6, 0xf5, 0xe8, 0x31, 0x34, 0x63, 0x70, 0xe7}, + }, + // 11P + { + x: fp384{0x7d, 0x8c, 0x8b, 0xb6, 0x19, 0x8b, 0x70, 0xc7, 0xba, 0x7a, 0x37, 0x44, 0x7c, 0x7, 0x32, 0x45, 0x4f, 0xd6, 0xda, 0x6c, 0x70, 0x67, 0xcc, 0xd, 0x2, 0x66, 0x7b, 0x14, 0x56, 0xbf, 0xb8, 0x1, 0x79, 0x1d, 0x56, 0xf0, 0x85, 0x98, 0xd8, 0xf8, 0x37, 0xc4, 0xa9, 0x7b, 0xfc, 0xe9, 0x19, 0x9c}, + y: fp384{0x25, 0xba, 0xc4, 0xbd, 0x46, 0xb1, 0x4e, 0x76, 0x83, 0x4b, 0x14, 0xac, 0x6b, 0xe4, 0x4f, 0x60, 0x80, 0xe7, 0x77, 0x8a, 0x29, 0x13, 0xe8, 0x3c, 0x2e, 0x68, 0x9e, 0xfe, 0x36, 0xf, 0x7, 0x2e, 0x7a, 0x28, 0x53, 0x3a, 0xc, 0x1d, 0x82, 0x41, 0x18, 0xf9, 0x33, 0x35, 0x9f, 0x2f, 0xa6, 0x9a}, + }, + // 13P + { + x: fp384{0xfb, 0xbd, 0xcc, 0x75, 0x7e, 0xeb, 0x7a, 0x9b, 0x95, 0x9a, 0x74, 0xf6, 0xc5, 0x28, 0x5e, 0xb2, 0xae, 0xd4, 0xb7, 0x33, 0x46, 0x8e, 0x7a, 0x8a, 0x56, 0xbd, 0xc1, 0xd9, 0xa8, 0x3, 0x52, 0xdb, 0x97, 0xdf, 0x22, 0xed, 0x65, 0x72, 0x65, 0xd2, 0x94, 0x3c, 0xf2, 0x8c, 0xe1, 0x56, 0x1c, 0xb5}, + y: fp384{0x2d, 0x81, 0x3d, 0x6c, 0x59, 0x94, 0xd3, 0xf4, 0xc2, 0xe0, 0xca, 0x87, 0x1a, 0x8f, 0xe8, 0xd8, 0xe3, 0xf, 0x4d, 0xcf, 0x48, 0x2a, 0x9a, 0x78, 0x60, 0x8d, 0xc3, 0xfe, 0x2d, 0xac, 0xfe, 0xb7, 0xc3, 0xe, 0x49, 0x3b, 0x1c, 0xbd, 0xfd, 0x81, 0xe1, 0x79, 0x69, 0xcc, 0xb7, 0xad, 0x17, 0x46}, + }, + // 15P + { + x: fp384{0xa9, 0xf4, 0x9, 0x47, 0x88, 0xd8, 0x6a, 0x44, 0xd8, 0xab, 0x3d, 0xec, 0xe2, 0x10, 0x72, 0x2b, 0x34, 0x7b, 0xe0, 0x50, 0x95, 0xf1, 0xcc, 0x83, 0x75, 0x30, 0x9b, 0x78, 0x17, 0x9, 0x50, 0x59, 0x93, 0x59, 0x8, 0xeb, 0xd4, 0x1f, 0xc0, 0xf, 0x6b, 0x2, 0x3, 0x49, 0x6f, 0xd2, 0x62, 0xfb}, + y: fp384{0xbb, 0x89, 0xe9, 0x6f, 0x9d, 0xcc, 0x9, 0x23, 0x86, 0xd5, 0x4b, 0x14, 0xbd, 0x9c, 0x60, 0x61, 0xc, 0x61, 0x6, 0xde, 0xa0, 0xd3, 0x23, 0x4b, 0x70, 0xf4, 0x98, 0xd8, 0x66, 0x28, 0xdc, 0xdd, 0x97, 0x57, 0xc, 0x40, 0x41, 0xfc, 0x33, 0x87, 0x16, 0x27, 0xbc, 0xd0, 0xfe, 0xc6, 0x68, 0x5a}, + }, + // 17P + { + x: fp384{0xd0, 0x3c, 0x4a, 0x4b, 0x30, 0xe1, 0x3, 0x89, 0x3e, 0xf4, 0xf1, 0x8f, 0x4c, 0xea, 0xa4, 0x3e, 0xd, 0xa1, 0x55, 0xf6, 0x2a, 0x3f, 0xfc, 0xe6, 0xfc, 0xfe, 0x4f, 0x52, 0x7d, 0x73, 0xe3, 0x7b, 0x5e, 0x45, 0x30, 0x53, 0x55, 0x28, 0x69, 0x9f, 0x70, 0xce, 0x75, 0xe4, 0x6e, 0x16, 0x4f, 0x52}, + y: fp384{0x55, 0xf0, 0x12, 0x6c, 0xcd, 0x69, 0xcc, 0x3f, 0xda, 0xc0, 0xb9, 0xd5, 0xff, 0xb6, 0x23, 0x4e, 0x83, 0xf1, 0x6b, 0x33, 0x93, 0x69, 0xce, 0x49, 0x4a, 0x50, 0x54, 0x4a, 0x85, 0x6d, 0x7d, 0xf8, 0x7a, 0x67, 0xc2, 0xb3, 0xf1, 0x5d, 0xeb, 0x25, 0xc9, 0x64, 0xb1, 0x55, 0x6f, 0x98, 0x37, 0xac}, + }, + // 19P + { + x: fp384{0x8, 0x4c, 0xa8, 0xba, 0x4a, 0xed, 0xa2, 0x82, 0x12, 0xc9, 0xa8, 0x41, 0x5f, 0xcc, 0xc4, 0x22, 0x5e, 0xad, 0x4a, 0x15, 0x3b, 0x9c, 0x10, 0xca, 0x8e, 0x53, 0x38, 0xfc, 0x98, 0x12, 0x89, 0x23, 0xae, 0x2, 0x98, 0x53, 0x9c, 0x63, 0xb6, 0xb3, 0x6, 0xd7, 0x90, 0x3, 0x45, 0x1f, 0xf, 0xfa}, + y: fp384{0xd0, 0x21, 0xdc, 0xb0, 0x5d, 0x8e, 0xb7, 0x46, 0xac, 0x2e, 0xda, 0xc3, 0x3c, 0x2d, 0xc7, 0xa8, 0x43, 0xf6, 0xf2, 0x6f, 0x78, 0xb3, 0x70, 0x91, 0xc3, 0x30, 0x7f, 0xb6, 0x9b, 0x79, 0x5a, 0x3f, 0x72, 0xb6, 0x64, 0x82, 0x77, 0xdc, 0xd1, 0x15, 0x64, 0x77, 0x57, 0xe9, 0x23, 0x7b, 0xd4, 0xa1}, + }, + // 21P + { + x: fp384{0x2f, 0xce, 0x22, 0x4, 0x51, 0x5e, 0x26, 0x8, 0x21, 0x9e, 0x2f, 0xdd, 0x96, 0xd4, 0xe0, 0x88, 0x5d, 0xf7, 0x77, 0x61, 0xa0, 0x8a, 0x12, 0x30, 0x69, 0xbe, 0x9e, 0xbd, 0x62, 0xab, 0x59, 0x2e, 0x37, 0xe5, 0xf0, 0x5d, 0x6c, 0xf, 0x1a, 0x1b, 0xb5, 0x12, 0xc0, 0xda, 0x26, 0xc6, 0x16, 0xab}, + y: fp384{0xe7, 0x5d, 0x8c, 0x0, 0x4b, 0x21, 0x14, 0x80, 0xea, 0x7b, 0xf1, 0x38, 0x9e, 0xa, 0x74, 0xaa, 0x98, 0x90, 0x14, 0x8a, 0x49, 0xbb, 0x2e, 0x26, 0x59, 0xcd, 0x27, 0x85, 0x1e, 0x11, 0x54, 0xb4, 0x17, 0x58, 0xea, 0xac, 0x5a, 0xd1, 0x6a, 0x26, 0xba, 0xcc, 0x53, 0x13, 0x41, 0x4f, 0x82, 0x21}, + }, + // 23P + { + x: fp384{0x3b, 0x68, 0xe3, 0x12, 0x4d, 0xe7, 0xb4, 0xd1, 0xf6, 0x8e, 0x9b, 0x56, 0xb, 0xd2, 0xe, 0x99, 0x18, 0xa, 0x9c, 0x42, 0x25, 0xdd, 0xd3, 0xb9, 0x83, 0x17, 0x35, 0x2a, 0xab, 0xb8, 0x75, 0x1c, 0xf0, 0x32, 0x54, 0x90, 0x2b, 0xca, 0xe4, 0x61, 0x24, 0xf2, 0xa8, 0xee, 0x69, 0x6a, 0x82, 0x80}, + y: fp384{0xad, 0xab, 0x52, 0xec, 0x6b, 0x3a, 0xc3, 0x7f, 0x13, 0x48, 0x5e, 0xa6, 0xf0, 0xa3, 0xcc, 0xb, 0xbe, 0xce, 0x27, 0xa5, 0x32, 0xa1, 0xd8, 0x7a, 0x7e, 0x2c, 0xf2, 0xea, 0x50, 0x89, 0x13, 0xf0, 0xc1, 0x18, 0x67, 0x56, 0x37, 0x24, 0x2d, 0x28, 0x59, 0x25, 0x21, 0xe2, 0xd, 0xcb, 0xfc, 0x9d}, + }, + // 25P + { + x: fp384{0x83, 0x3b, 0xce, 0x58, 0x27, 0x72, 0x93, 0x1e, 0x36, 0xfb, 0xb3, 0x3c, 0xfa, 0xd, 0x28, 0xbb, 0x4a, 0x17, 0xbe, 0xe2, 0xd2, 0xf3, 0xd0, 0x57, 0x1e, 0xbe, 0x8a, 0x20, 0x99, 0x1b, 0xd5, 0x9b, 0x24, 0x80, 0x24, 0xde, 0x50, 0xab, 0x9, 0x38, 0x31, 0x73, 0xbb, 0xa5, 0x2c, 0x6e, 0x9c, 0xc2}, + y: fp384{0x5, 0x4f, 0x12, 0x61, 0x2e, 0xfd, 0x44, 0x99, 0x91, 0xe3, 0x9, 0x90, 0x4e, 0xbc, 0xcc, 0x83, 0xcc, 0xa3, 0x24, 0x94, 0x5, 0x8f, 0x62, 0x1, 0x44, 0x43, 0x8e, 0xea, 0x1d, 0xf5, 0xa2, 0xd6, 0x6e, 0xc9, 0xeb, 0x4c, 0x3d, 0x1a, 0x3e, 0xda, 0xdc, 0x9, 0x78, 0xe9, 0x42, 0xfb, 0xe6, 0x1f}, + }, + // 27P + { + x: fp384{0xe4, 0x66, 0x7d, 0x46, 0xd2, 0x82, 0x44, 0xa0, 0x1d, 0x29, 0x78, 0x4d, 0x93, 0x12, 0x19, 0xcf, 0xf9, 0x96, 0x23, 0x48, 0x68, 0x41, 0xd, 0x8e, 0xd0, 0x14, 0x8f, 0xd1, 0xd5, 0xe2, 0x28, 0x72, 0xfe, 0x58, 0x6a, 0x9c, 0x50, 0x8d, 0x7e, 0x2f, 0xec, 0x5a, 0x3e, 0x37, 0xe, 0x78, 0xca, 0xe8}, + y: fp384{0xf8, 0xe9, 0x68, 0x1b, 0xd6, 0xd1, 0xaa, 0x42, 0xf4, 0xf8, 0xe2, 0x69, 0xf5, 0xd7, 0xa6, 0x58, 0xea, 0x1b, 0xda, 0x31, 0xfe, 0xad, 0x79, 0xd7, 0x85, 0x5a, 0xc8, 0x38, 0x6, 0x54, 0x26, 0x7d, 0xdf, 0x3c, 0x4d, 0xd4, 0x95, 0x71, 0xe6, 0x67, 0xd7, 0x4e, 0x13, 0xc5, 0xb, 0xa, 0x82, 0x17}, + }, + // 29P + { + x: fp384{0x70, 0x14, 0x2, 0xd3, 0xc5, 0x6a, 0x9d, 0x1, 0xd6, 0x43, 0x4, 0x78, 0x66, 0x6b, 0x84, 0x25, 0x47, 0x76, 0xc9, 0x55, 0xed, 0x15, 0x3c, 0xce, 0xf, 0xeb, 0x3f, 0xe, 0x49, 0x2d, 0xc2, 0x3d, 0xe4, 0x26, 0xdf, 0xa7, 0xcb, 0xb7, 0x65, 0x20, 0x1f, 0xea, 0x7c, 0x18, 0xe8, 0xa, 0xb0, 0xc8}, + y: fp384{0xd3, 0xde, 0x5d, 0x86, 0xa0, 0x84, 0x52, 0x1a, 0xe2, 0x3d, 0xc8, 0x20, 0x49, 0x16, 0x3c, 0x29, 0xb3, 0x51, 0xe8, 0xcc, 0x26, 0x8d, 0x17, 0xab, 0xfb, 0x5, 0x45, 0x40, 0xb, 0xb1, 0x6d, 0x8e, 0x33, 0x20, 0xc8, 0x90, 0x71, 0x7e, 0xf5, 0xf6, 0x6c, 0xf1, 0x77, 0x59, 0x1, 0x1c, 0x2a, 0x1d}, + }, + // 31P + { + x: fp384{0xa4, 0x6, 0x89, 0x7c, 0x31, 0x89, 0x9c, 0xa3, 0xe6, 0x1e, 0x82, 0x9e, 0xdd, 0xec, 0xe7, 0xb6, 0xe6, 0x4f, 0xdf, 0xf0, 0x40, 0x83, 0xcf, 0x2e, 0x65, 0x49, 0xc1, 0x53, 0xc9, 0x7d, 0x2f, 0xd4, 0x85, 0x82, 0xba, 0xe3, 0xa3, 0x51, 0xfb, 0x1a, 0xd1, 0x5, 0x33, 0xa, 0x4, 0xc4, 0x7, 0x6c}, + y: fp384{0xda, 0xc1, 0x7f, 0x12, 0x88, 0x32, 0xb8, 0xda, 0x8, 0x4b, 0x4c, 0x37, 0x9b, 0x69, 0xa, 0xbc, 0xdd, 0x20, 0xeb, 0x42, 0xab, 0x9b, 0x2a, 0x40, 0x1c, 0x7a, 0x5a, 0x4, 0x4f, 0x46, 0xdd, 0xd7, 0xc4, 0xec, 0xbe, 0x36, 0x6d, 0xd, 0x3d, 0x5b, 0x9d, 0xa1, 0x98, 0x63, 0x75, 0x3e, 0x5a, 0x47}, + }, + // 33P + { + x: fp384{0x63, 0xba, 0xb3, 0x2f, 0x38, 0x3a, 0x33, 0x61, 0x86, 0x3c, 0x94, 0x5b, 0x9d, 0xd, 0x33, 0xdf, 0xaf, 0xf3, 0x5e, 0x95, 0xee, 0xc7, 0xc7, 0xbb, 0xfb, 0x9e, 0xf0, 0x60, 0xc1, 0x1f, 0x63, 0xda, 0x0, 0xc4, 0xd5, 0x41, 0x26, 0x62, 0xaf, 0x68, 0x9d, 0x3e, 0x83, 0x6c, 0xa4, 0x97, 0x9e, 0xcc}, + y: fp384{0x76, 0x5e, 0x62, 0x3a, 0x8e, 0x3e, 0xd7, 0x7f, 0x5e, 0xe5, 0x9, 0xc2, 0x24, 0x61, 0xbf, 0x13, 0x91, 0xb, 0xb9, 0x48, 0xea, 0x7c, 0x46, 0x8, 0xba, 0xa, 0x6f, 0xbb, 0xb9, 0x6e, 0x41, 0x8a, 0x72, 0x10, 0xc3, 0xb8, 0xa1, 0x93, 0xcc, 0x6f, 0xd7, 0xda, 0x57, 0x90, 0x61, 0x2b, 0xfd, 0xa7}, + }, + // 35P + { + x: fp384{0x9b, 0xec, 0x20, 0x37, 0x43, 0xb5, 0xa5, 0x58, 0xb4, 0x2f, 0x7c, 0x2d, 0xd5, 0x0, 0x38, 0xbb, 0xa, 0xbd, 0xe6, 0xdd, 0x20, 0x86, 0x50, 0x4a, 0xfd, 0x83, 0x25, 0xa0, 0x73, 0x62, 0xf1, 0x65, 0x23, 0x85, 0xc7, 0x4f, 0xe3, 0xd8, 0x2b, 0x83, 0xc6, 0x7b, 0x41, 0xe9, 0x75, 0x9f, 0x14, 0xd6}, + y: fp384{0x2a, 0xb5, 0xee, 0x3d, 0xe9, 0x26, 0xb0, 0xfe, 0x56, 0x9, 0x5e, 0xa5, 0x88, 0x80, 0xe1, 0xc, 0xa2, 0x92, 0x80, 0x98, 0x98, 0x89, 0x1, 0x50, 0xee, 0x5e, 0xf3, 0x28, 0xab, 0x9f, 0xf1, 0x22, 0x5c, 0xd3, 0xcc, 0x52, 0x7f, 0x87, 0x8a, 0xac, 0x26, 0x3f, 0xe2, 0x30, 0xd8, 0x8a, 0x3a, 0xb1}, + }, + // 37P + { + x: fp384{0xa3, 0x61, 0x4f, 0xe4, 0x7d, 0xd5, 0x2, 0x2, 0xf2, 0xe, 0x63, 0xb5, 0x4b, 0x70, 0x27, 0x40, 0x5d, 0x4a, 0xb5, 0xf5, 0xdf, 0xe2, 0x29, 0xa1, 0x86, 0x2b, 0x48, 0x97, 0x75, 0xa, 0xb6, 0xac, 0x14, 0x71, 0xf2, 0x7e, 0xe8, 0xed, 0x61, 0x92, 0xb5, 0x58, 0xfc, 0xde, 0xf3, 0x28, 0xba, 0x1e}, + y: fp384{0x9e, 0x58, 0xe5, 0x8b, 0xc9, 0xc0, 0x91, 0x6c, 0xee, 0x4b, 0x59, 0x14, 0xd5, 0x43, 0x16, 0x2f, 0x34, 0xa0, 0x2c, 0x5d, 0x43, 0x12, 0xa9, 0x2e, 0x1f, 0x7d, 0x4, 0x94, 0xa8, 0x49, 0x6, 0xb5, 0x37, 0xa3, 0x8c, 0x63, 0xb5, 0xcb, 0x4f, 0x28, 0x85, 0xbf, 0x85, 0xfe, 0xb7, 0x7, 0xe, 0xfa}, + }, + // 39P + { + x: fp384{0x42, 0xe, 0x6e, 0x50, 0x80, 0x4f, 0x89, 0x7d, 0x46, 0x2c, 0x3d, 0x8e, 0x4a, 0x24, 0x84, 0xd9, 0x6f, 0x0, 0x7f, 0x2b, 0x64, 0xdf, 0x7e, 0x6d, 0x30, 0x62, 0x9b, 0xde, 0x6d, 0xcd, 0xa1, 0x36, 0x65, 0x6, 0x6c, 0xb7, 0x40, 0x50, 0x98, 0xc9, 0xc2, 0x1f, 0x9b, 0xb8, 0xd6, 0xf4, 0x7d, 0x58}, + y: fp384{0x7a, 0xae, 0x71, 0x6a, 0x47, 0x38, 0x6, 0x4c, 0x47, 0x47, 0x29, 0xe8, 0xb3, 0xa, 0x2b, 0x7b, 0xb8, 0x53, 0x31, 0xb5, 0x3a, 0x55, 0x5c, 0x34, 0xe2, 0x9f, 0x6d, 0x43, 0x53, 0xe4, 0x46, 0xb6, 0x40, 0x3, 0xd6, 0x1c, 0x5f, 0x35, 0x95, 0x1a, 0xfb, 0x68, 0x49, 0x7, 0x28, 0xc1, 0x7b, 0x2d}, + }, + // 41P + { + x: fp384{0x4c, 0xd1, 0xa6, 0xbc, 0x87, 0x8e, 0x14, 0xad, 0x1e, 0x20, 0x6a, 0x45, 0x4d, 0xd2, 0xdf, 0x41, 0xf3, 0x68, 0xd, 0xa8, 0x33, 0x29, 0xa8, 0x73, 0x35, 0xa0, 0x2c, 0x85, 0x8d, 0x6c, 0x74, 0x89, 0xae, 0x71, 0xfd, 0x95, 0x88, 0x77, 0xbc, 0xe3, 0x5d, 0x24, 0x92, 0xda, 0x2c, 0xcd, 0x64, 0x87}, + y: fp384{0xe2, 0x23, 0xeb, 0x82, 0x47, 0x2c, 0xfe, 0xa2, 0x6e, 0x9d, 0x3c, 0xf, 0xe0, 0x62, 0xc7, 0x5a, 0x31, 0x6f, 0x64, 0x21, 0xe1, 0xc, 0x86, 0x57, 0x9a, 0x58, 0x9f, 0x4f, 0xc3, 0xd6, 0xc9, 0xbd, 0x2e, 0x27, 0x93, 0xd1, 0xc7, 0x52, 0x99, 0x67, 0xc5, 0xf1, 0x18, 0xeb, 0x2e, 0x70, 0xea, 0x82}, + }, + // 43P + { + x: fp384{0x44, 0x6d, 0x84, 0x0, 0x55, 0x93, 0xfa, 0x37, 0x8c, 0xbc, 0x78, 0x5, 0xc5, 0x2f, 0x11, 0x9, 0x3d, 0x94, 0xc4, 0x39, 0xb2, 0xf5, 0xd9, 0xda, 0x86, 0xbd, 0x6d, 0x41, 0xf0, 0xf5, 0x14, 0x73, 0x56, 0xfb, 0xfe, 0x1, 0xa9, 0x95, 0xf0, 0x5c, 0x93, 0xb3, 0xda, 0x22, 0xad, 0x8b, 0x17, 0x35}, + y: fp384{0xa7, 0xf1, 0xba, 0x36, 0x1b, 0xfc, 0x79, 0xcf, 0x98, 0x54, 0x9e, 0x74, 0x2d, 0xe4, 0x7e, 0x1b, 0xbb, 0x14, 0xe3, 0xed, 0xa9, 0x8a, 0xe7, 0xbc, 0xdf, 0x28, 0x6, 0xbd, 0xf6, 0xe0, 0xf8, 0xaa, 0x48, 0xf9, 0xcb, 0x15, 0x94, 0xb0, 0x74, 0xa9, 0x78, 0x2b, 0x63, 0xc9, 0x63, 0x1f, 0x3f, 0x8f}, + }, + // 45P + { + x: fp384{0x5b, 0xda, 0xdd, 0x4f, 0x56, 0x11, 0xc4, 0xd4, 0x12, 0x91, 0xad, 0x73, 0xc6, 0x65, 0xaf, 0xd4, 0x59, 0x8f, 0xeb, 0x39, 0xbb, 0xe0, 0xe8, 0xff, 0x13, 0xcf, 0x6f, 0x8d, 0xe, 0xc, 0x4, 0xb0, 0x99, 0xb5, 0x2b, 0x1f, 0xc6, 0xc0, 0xe1, 0x99, 0x5, 0x34, 0xac, 0xb2, 0x58, 0xc8, 0x94, 0x9c}, + y: fp384{0x5d, 0xd8, 0xee, 0x6e, 0xd7, 0x78, 0x88, 0x8f, 0x3f, 0xca, 0xfc, 0x51, 0x43, 0xf5, 0xb2, 0x62, 0x18, 0x69, 0xb5, 0xe5, 0xa9, 0x44, 0x3b, 0xeb, 0x93, 0x4e, 0x23, 0xb7, 0x76, 0x66, 0xf9, 0x16, 0x9e, 0xf1, 0x2a, 0xbd, 0x22, 0x77, 0x47, 0x17, 0x85, 0xa4, 0x83, 0xdb, 0x79, 0x29, 0xeb, 0x42}, + }, + // 47P + { + x: fp384{0xca, 0x68, 0xc6, 0xf0, 0x7d, 0x8f, 0x88, 0x6f, 0x6c, 0xc6, 0xd, 0x5f, 0x78, 0x88, 0xc7, 0x65, 0xa0, 0x7, 0x5b, 0x5f, 0x12, 0x85, 0xb1, 0xbf, 0xd0, 0xac, 0x78, 0xd8, 0xf7, 0xbf, 0xa, 0x78, 0x50, 0xf9, 0xc, 0x57, 0xb1, 0x21, 0x4f, 0x50, 0x71, 0x33, 0x23, 0xda, 0xc5, 0x37, 0x5b, 0xea}, + y: fp384{0xd1, 0x7e, 0x43, 0x22, 0xbd, 0xe8, 0x7a, 0x48, 0xb7, 0xf9, 0x9c, 0x24, 0x58, 0x17, 0x70, 0x9c, 0xff, 0x34, 0xfb, 0x98, 0xa8, 0x62, 0x65, 0xf8, 0x91, 0xfc, 0xe0, 0x65, 0xa2, 0xa1, 0xee, 0xdf, 0x23, 0xfc, 0x20, 0x2e, 0x91, 0x6, 0xf0, 0xee, 0x8b, 0x2a, 0xa7, 0xdf, 0xc7, 0xfe, 0x9d, 0xac}, + }, + // 49P + { + x: fp384{0xc6, 0x36, 0x71, 0x69, 0xef, 0x3a, 0x5c, 0xfa, 0xb8, 0x6f, 0xea, 0xa5, 0x63, 0xaf, 0xa5, 0x8e, 0xa4, 0x65, 0xe3, 0x42, 0x65, 0x15, 0x69, 0xa6, 0x86, 0x33, 0x6e, 0x5b, 0x11, 0x6c, 0xc5, 0x47, 0x56, 0x3f, 0xa0, 0xce, 0x2b, 0x83, 0x97, 0x11, 0x9e, 0xea, 0xe4, 0x50, 0xb2, 0xb, 0x47, 0xb}, + y: fp384{0x12, 0x57, 0xb2, 0x13, 0x43, 0xc7, 0x13, 0x31, 0x48, 0x7d, 0x49, 0xd2, 0x4e, 0x17, 0x6c, 0x8d, 0xe8, 0xeb, 0xc9, 0x49, 0xee, 0x86, 0x44, 0xfc, 0xd3, 0xbd, 0x82, 0x7f, 0xd5, 0xed, 0x87, 0x24, 0x2f, 0xbe, 0x57, 0x5b, 0x41, 0x64, 0x1e, 0x77, 0xdb, 0x2b, 0x8b, 0xe2, 0x18, 0xc5, 0x1c, 0x2d}, + }, + // 51P + { + x: fp384{0x8d, 0xac, 0x70, 0x20, 0xc7, 0xca, 0x4c, 0x2c, 0xb8, 0x22, 0x4a, 0xec, 0xca, 0xc0, 0x47, 0x19, 0xd9, 0x78, 0x5a, 0x8c, 0x59, 0xfb, 0xe0, 0xa5, 0xe7, 0x4d, 0xa8, 0x41, 0xd2, 0xe8, 0x4a, 0x46, 0x27, 0xbc, 0xaa, 0xda, 0xe9, 0x16, 0xba, 0x3d, 0x3c, 0xcb, 0x35, 0x4f, 0x50, 0x4a, 0x63, 0x16}, + y: fp384{0x4f, 0xc8, 0x6e, 0xb1, 0xf9, 0x8b, 0xc1, 0xad, 0x35, 0xdd, 0x59, 0x73, 0x7e, 0x6, 0x4d, 0x32, 0xf0, 0x43, 0x5, 0x57, 0xc3, 0xc0, 0xea, 0xda, 0x36, 0x7d, 0x88, 0x3c, 0x0, 0x40, 0x22, 0xb, 0xd, 0x1a, 0x3f, 0x37, 0xe2, 0x89, 0x94, 0xc6, 0x97, 0xd, 0xaa, 0xcb, 0x7d, 0x4, 0x8b, 0x51}, + }, + // 53P + { + x: fp384{0xef, 0x49, 0xde, 0xfb, 0xc6, 0xdd, 0x1b, 0x3b, 0xcc, 0x15, 0x9, 0x8a, 0x26, 0x7c, 0xed, 0xda, 0xa2, 0x22, 0x4, 0xf, 0x61, 0x10, 0x1, 0xb, 0x16, 0x4b, 0xc5, 0xa7, 0x74, 0x5c, 0x48, 0xcf, 0xe2, 0xaa, 0xc3, 0x15, 0xe6, 0xc4, 0x2e, 0x64, 0xea, 0x83, 0xf3, 0xe0, 0x10, 0x8f, 0xba, 0xa8}, + y: fp384{0x1, 0x85, 0x61, 0x95, 0xb4, 0x54, 0x20, 0x2a, 0x8b, 0xfa, 0x9e, 0x8, 0x42, 0x64, 0xec, 0xeb, 0x3e, 0xa8, 0x2f, 0x4e, 0x9a, 0xa1, 0x86, 0x57, 0x63, 0x99, 0x6, 0x39, 0xd1, 0x1a, 0xc7, 0xd2, 0xe2, 0x65, 0x17, 0x48, 0x9a, 0x3d, 0xc9, 0xad, 0x85, 0x94, 0xcc, 0x7e, 0xeb, 0xe3, 0xf2, 0xed}, + }, + // 55P + { + x: fp384{0x67, 0x33, 0x9f, 0x6, 0x60, 0x5f, 0xab, 0xbc, 0x3c, 0xec, 0x18, 0x17, 0xbc, 0x22, 0x66, 0xfd, 0xd6, 0x42, 0xa1, 0xe3, 0x67, 0x78, 0xfb, 0xa4, 0xb3, 0xae, 0x5f, 0x8, 0xbf, 0xd8, 0x78, 0x60, 0x4f, 0x55, 0xf4, 0x60, 0xda, 0xbf, 0x5c, 0xfa, 0x8, 0xd4, 0xc, 0x69, 0xd1, 0xd5, 0xfc, 0xb3}, + y: fp384{0x84, 0x78, 0x1f, 0x28, 0x7d, 0xee, 0xbd, 0x4e, 0xa7, 0x63, 0xa, 0x18, 0xaa, 0x23, 0xaf, 0x82, 0x61, 0x9f, 0x7, 0x3d, 0x7c, 0x10, 0xe3, 0x8d, 0xf8, 0x34, 0x23, 0xbe, 0xcb, 0xb5, 0xc6, 0x17, 0x6, 0xfa, 0xd0, 0x97, 0x39, 0xe7, 0x91, 0x6a, 0xd4, 0xee, 0xce, 0x14, 0x73, 0x25, 0x60, 0x74}, + }, + // 57P + { + x: fp384{0x5c, 0x86, 0x7f, 0xf9, 0x1c, 0xa6, 0x4b, 0xb1, 0xd, 0x8b, 0x4b, 0x69, 0xc1, 0xe4, 0xba, 0x73, 0x62, 0xbf, 0x4b, 0xac, 0xdf, 0x67, 0x49, 0xa1, 0xe0, 0x46, 0xf4, 0x9b, 0x50, 0xd1, 0x9d, 0x1e, 0xef, 0xce, 0x99, 0x1c, 0xeb, 0xf3, 0x52, 0xc0, 0x89, 0xc1, 0x78, 0x7a, 0xa0, 0x7f, 0x4d, 0x81}, + y: fp384{0x5d, 0xb0, 0x74, 0xab, 0x83, 0xa4, 0x1, 0xa1, 0x65, 0x7b, 0x73, 0xa1, 0x58, 0xc2, 0x88, 0x77, 0x3c, 0xa1, 0x9, 0xe8, 0xb7, 0xba, 0x60, 0xd, 0x5b, 0x1d, 0xc8, 0x73, 0xc4, 0x7b, 0x42, 0x8f, 0xfc, 0xc1, 0x52, 0x29, 0x55, 0x30, 0xe1, 0xd2, 0x63, 0xdf, 0x26, 0x4b, 0x9a, 0x3b, 0x82, 0xa}, + }, + // 59P + { + x: fp384{0xc9, 0x64, 0xbf, 0x27, 0xe2, 0x7c, 0x46, 0xaf, 0x4c, 0x97, 0x29, 0xf9, 0x97, 0x68, 0xca, 0xdf, 0x38, 0x27, 0x32, 0x5c, 0x59, 0x3b, 0x47, 0x64, 0x15, 0xe3, 0xd0, 0x1e, 0xcf, 0x17, 0xa9, 0x96, 0xb9, 0x4d, 0xe6, 0xd, 0x5b, 0x43, 0x3, 0x37, 0x46, 0xb6, 0x67, 0x92, 0x67, 0x39, 0xa0, 0x9b}, + y: fp384{0xbe, 0x2f, 0x52, 0x3a, 0xae, 0x2a, 0xc, 0xdf, 0xf0, 0xef, 0x35, 0xb3, 0x41, 0xb7, 0xbd, 0x41, 0x3, 0x97, 0x5, 0x7b, 0xdd, 0x2e, 0xcf, 0xac, 0xce, 0x3c, 0x46, 0x28, 0x30, 0x4b, 0xb3, 0x6f, 0x19, 0xca, 0xe3, 0xd9, 0xb, 0xba, 0xd9, 0x96, 0xc1, 0x55, 0x46, 0x50, 0x12, 0x6f, 0x33, 0xff}, + }, + // 61P + { + x: fp384{0xe0, 0xa6, 0x60, 0xfc, 0xd3, 0x1f, 0xda, 0x48, 0xe8, 0x41, 0x22, 0x22, 0x34, 0x5a, 0xfb, 0x54, 0x80, 0xe0, 0x2a, 0x77, 0x4f, 0xe3, 0x35, 0x60, 0xd0, 0x82, 0x29, 0x33, 0xf2, 0x7f, 0xf7, 0x5f, 0xfd, 0x51, 0xfe, 0x0, 0x73, 0x46, 0x66, 0x23, 0x6, 0xa0, 0x6b, 0xef, 0x49, 0xa0, 0x3e, 0xc9}, + y: fp384{0x66, 0x12, 0x38, 0x7d, 0x17, 0xf1, 0x40, 0x66, 0xac, 0xf4, 0xe9, 0x6a, 0xcd, 0x32, 0x4d, 0x39, 0xeb, 0x3, 0xd3, 0x70, 0x53, 0x88, 0xa7, 0xe6, 0x67, 0x57, 0x27, 0xe5, 0xff, 0x19, 0xda, 0xd, 0x23, 0x6d, 0x46, 0x1, 0x72, 0xc7, 0xa6, 0xb0, 0x29, 0x98, 0xc6, 0x1f, 0x45, 0x11, 0xcc, 0xc4}, + }, + // 63P + { + x: fp384{0xc0, 0x89, 0xed, 0xaa, 0xd7, 0xe6, 0xc0, 0xc5, 0x96, 0x18, 0x9a, 0x14, 0xd6, 0xea, 0xe8, 0x6c, 0x8f, 0x9f, 0x94, 0x8c, 0x45, 0xf7, 0x50, 0x7a, 0xaa, 0x71, 0x2b, 0x6e, 0xf7, 0x35, 0x7e, 0xcd, 0x7a, 0x9f, 0x4, 0x9a, 0x51, 0x9e, 0x15, 0xf6, 0x1e, 0x2d, 0xe5, 0xf1, 0xb0, 0xf0, 0x9b, 0x1c}, + y: fp384{0x80, 0x2c, 0x20, 0x18, 0xf5, 0xc1, 0xb6, 0x3b, 0x1a, 0x7b, 0xcd, 0x1e, 0x62, 0x5f, 0x3a, 0x8d, 0x19, 0x7f, 0xd1, 0x88, 0xe8, 0x34, 0xb0, 0x3b, 0x8d, 0x4, 0xd4, 0x97, 0x49, 0xbd, 0x89, 0xdc, 0x22, 0xdf, 0x35, 0x37, 0x8e, 0x7b, 0xaf, 0xf5, 0xe8, 0x89, 0xa6, 0xa0, 0x12, 0x37, 0xbb, 0x52}, + }, + // 65P + { + x: fp384{0x79, 0x96, 0x9b, 0x83, 0x54, 0x94, 0x46, 0x8e, 0x9f, 0x27, 0x1d, 0xd, 0x3b, 0xa4, 0xcd, 0xbe, 0x80, 0x3c, 0xb6, 0xed, 0x15, 0xdc, 0x9e, 0xcf, 0x2, 0xf0, 0xd5, 0xbd, 0x8a, 0xec, 0x97, 0x45, 0x53, 0x22, 0xb, 0x65, 0xb2, 0x50, 0x3, 0x8b, 0x6f, 0x26, 0xd4, 0x5f, 0x6a, 0x3a, 0x4c, 0xb8}, + y: fp384{0xf9, 0x79, 0xfc, 0x30, 0x3d, 0xd8, 0x16, 0xe, 0xd3, 0x95, 0xd9, 0x3a, 0x83, 0x87, 0xa4, 0xb6, 0x66, 0xc2, 0x2b, 0xde, 0x2c, 0x4b, 0x78, 0xab, 0xdd, 0x66, 0x9d, 0x88, 0x6d, 0x3d, 0x76, 0x19, 0x87, 0xf0, 0xf9, 0xc8, 0x24, 0x6c, 0x86, 0xa2, 0xc9, 0xb1, 0x5b, 0xa5, 0x28, 0x25, 0x6f, 0xea}, + }, + // 67P + { + x: fp384{0xca, 0x72, 0x17, 0x8b, 0xbc, 0x5c, 0xfc, 0x6e, 0x68, 0x4f, 0x63, 0xb, 0x3b, 0xdd, 0xc7, 0xea, 0x85, 0x61, 0x5d, 0xa5, 0xda, 0x5e, 0xd7, 0x65, 0xf7, 0xd8, 0xf3, 0x6e, 0x7e, 0x63, 0x6e, 0x55, 0x25, 0x9d, 0x90, 0x90, 0x4d, 0x3e, 0xaf, 0xf9, 0x5a, 0x3, 0x53, 0xe1, 0x48, 0xca, 0x62, 0xe4}, + y: fp384{0xd1, 0x9e, 0x10, 0xa, 0x7b, 0x3b, 0x76, 0x52, 0x6, 0x5d, 0x78, 0x42, 0xa6, 0xb1, 0x4a, 0x10, 0xbc, 0xe4, 0x59, 0x3f, 0xed, 0x35, 0x7e, 0x1a, 0x3, 0xc0, 0xeb, 0xc6, 0x46, 0xb7, 0x90, 0x59, 0xf9, 0xc5, 0x62, 0x13, 0xf0, 0x6b, 0x6a, 0x9, 0x94, 0x49, 0x79, 0xac, 0x8a, 0xcb, 0x22, 0x83}, + }, + // 69P + { + x: fp384{0x52, 0x27, 0xc, 0x67, 0x74, 0xdf, 0xd3, 0xf8, 0x28, 0x5e, 0x11, 0xa1, 0x59, 0x28, 0xcb, 0x5c, 0x1b, 0x98, 0x19, 0xf, 0xaa, 0xc8, 0x66, 0xcc, 0x65, 0xfd, 0xab, 0x25, 0xb1, 0xc8, 0xbc, 0xd4, 0xca, 0x3c, 0xdd, 0x4f, 0x16, 0xee, 0x86, 0x2c, 0xf4, 0x35, 0xf7, 0xa3, 0x78, 0x5d, 0xd6, 0x59}, + y: fp384{0xce, 0x55, 0xc, 0x7c, 0x28, 0xde, 0x5a, 0x3, 0x4d, 0x99, 0xd3, 0x45, 0x62, 0x9d, 0x76, 0x57, 0xa4, 0x23, 0xd4, 0x2b, 0x89, 0xe4, 0x3a, 0xd1, 0xbc, 0x66, 0xed, 0x82, 0x48, 0xee, 0xce, 0xa, 0x32, 0x7a, 0x16, 0x73, 0x8b, 0x9e, 0x2c, 0x6f, 0x7a, 0xbd, 0x1d, 0x27, 0x0, 0x1, 0xcd, 0xfb}, + }, + // 71P + { + x: fp384{0xb1, 0xfc, 0xfe, 0xef, 0x45, 0xce, 0x2e, 0xc4, 0x41, 0x14, 0xb1, 0xab, 0xb3, 0x31, 0x57, 0xbf, 0x92, 0xa, 0x8d, 0xe5, 0xcf, 0x15, 0xba, 0x93, 0x54, 0xac, 0x8, 0x35, 0x14, 0xde, 0xbb, 0x27, 0xda, 0x5d, 0x25, 0xfe, 0x38, 0x37, 0x12, 0x2b, 0x70, 0xcd, 0x7e, 0x53, 0x5a, 0xaa, 0x4f, 0xb}, + y: fp384{0xc6, 0x83, 0xec, 0xdd, 0x84, 0xd0, 0x44, 0x6a, 0x3d, 0x52, 0x1, 0x8, 0x4d, 0x3c, 0x79, 0x86, 0x19, 0xe3, 0xb3, 0x25, 0x50, 0x28, 0x4f, 0x15, 0x3a, 0x37, 0x64, 0xce, 0xf1, 0xda, 0x44, 0x21, 0x66, 0x95, 0x13, 0x7, 0xee, 0x24, 0xb9, 0xbd, 0x1c, 0xd0, 0x2a, 0x73, 0x28, 0xea, 0xa7, 0xf9}, + }, + // 73P + { + x: fp384{0x2, 0xa7, 0x51, 0xd8, 0x32, 0x5c, 0x38, 0x43, 0x3b, 0x96, 0xe8, 0x1d, 0xb1, 0xa9, 0xc2, 0xa9, 0x24, 0x9b, 0x8b, 0xdf, 0xb, 0x23, 0x8d, 0x5b, 0xc2, 0x31, 0x37, 0x2d, 0x25, 0xa9, 0x29, 0x90, 0xd2, 0xa7, 0xca, 0xe8, 0x4d, 0xb0, 0x8d, 0xb0, 0x3c, 0x67, 0xf4, 0x2b, 0xe7, 0x83, 0x9d, 0xb8}, + y: fp384{0x24, 0x44, 0xf2, 0xe1, 0xbf, 0x39, 0xfd, 0xa8, 0x16, 0xd6, 0xe8, 0xe1, 0xd6, 0xb6, 0x89, 0x9f, 0x6e, 0x21, 0x1d, 0x4f, 0x7b, 0xc8, 0x9f, 0xaf, 0x59, 0x5a, 0x26, 0x92, 0x3, 0x1e, 0xe2, 0x4, 0x73, 0x63, 0xb8, 0x87, 0x3, 0x74, 0x15, 0xb, 0x62, 0xa1, 0x98, 0x7c, 0x3b, 0xaf, 0x65, 0x6f}, + }, + // 75P + { + x: fp384{0xde, 0x3, 0x73, 0x86, 0x14, 0x40, 0x5d, 0x6b, 0xef, 0xb7, 0xa, 0x42, 0xa, 0xc4, 0xcb, 0xc8, 0x96, 0x9a, 0x54, 0x91, 0x89, 0xcf, 0x28, 0x5b, 0x66, 0x8f, 0x2f, 0x39, 0xb4, 0x31, 0x46, 0x5d, 0xc8, 0xb5, 0x67, 0xf3, 0x3d, 0xe2, 0x7e, 0x4a, 0x15, 0x7a, 0xca, 0xe6, 0xf, 0xae, 0xe0, 0xa1}, + y: fp384{0x7c, 0xa2, 0x9f, 0x13, 0xe1, 0x5e, 0x65, 0x2a, 0x1, 0xb9, 0xfa, 0x50, 0xc4, 0xc2, 0x31, 0xa5, 0x71, 0xed, 0xa, 0x43, 0x69, 0xab, 0x62, 0x67, 0x1d, 0x2e, 0x40, 0xf0, 0xe3, 0x39, 0xe2, 0x64, 0x45, 0xe4, 0x7f, 0x95, 0x42, 0x0, 0x87, 0xd7, 0x62, 0x65, 0x7d, 0x41, 0x62, 0xd8, 0x42, 0xfd}, + }, + // 77P + { + x: fp384{0x3f, 0x1a, 0x50, 0x2a, 0xc1, 0x34, 0x21, 0x9f, 0xa7, 0x93, 0x47, 0x33, 0x40, 0x9b, 0x4a, 0x11, 0x25, 0x61, 0x2a, 0x21, 0xc0, 0xb6, 0xcc, 0x27, 0xa3, 0x78, 0xce, 0x98, 0xb9, 0x30, 0xa9, 0xc, 0x27, 0x26, 0xa1, 0x28, 0xb, 0x6, 0x2e, 0x74, 0x16, 0x98, 0x5c, 0xfa, 0x7, 0x36, 0xd2, 0x63}, + y: fp384{0xdc, 0x91, 0x1f, 0xec, 0xa4, 0xcb, 0x4d, 0x77, 0x23, 0x1d, 0x4d, 0xf3, 0x2e, 0x7e, 0xcd, 0x34, 0x3d, 0x3c, 0xfd, 0x49, 0xe, 0x85, 0x0, 0x15, 0xb2, 0xcf, 0xc9, 0x30, 0x0, 0x95, 0x3, 0xdd, 0xa6, 0x41, 0x29, 0x57, 0xe5, 0xc3, 0x61, 0xce, 0x2e, 0xfd, 0x2c, 0x30, 0x75, 0x10, 0x4b, 0xd4}, + }, + // 79P + { + x: fp384{0x24, 0xc2, 0xa6, 0xe9, 0xd4, 0xd9, 0x11, 0xca, 0x85, 0x45, 0xb7, 0xc3, 0x48, 0xc2, 0xda, 0x2c, 0x71, 0x55, 0xca, 0x4, 0xa2, 0x1, 0x89, 0xe5, 0xf0, 0x1, 0x5d, 0xd1, 0x2d, 0x31, 0x1c, 0x49, 0x7c, 0xcb, 0x69, 0x70, 0x8a, 0x81, 0xcc, 0xb3, 0xda, 0x12, 0x39, 0xd5, 0xa5, 0x45, 0xb2, 0x23}, + y: fp384{0x63, 0xb1, 0xb0, 0xa6, 0x8b, 0x83, 0xf7, 0x30, 0x52, 0x55, 0x77, 0x32, 0x3e, 0xeb, 0x52, 0xa0, 0xc1, 0x5e, 0xb9, 0xee, 0xe9, 0x43, 0x32, 0x40, 0xb3, 0x2e, 0x63, 0x8, 0x1b, 0x30, 0x7b, 0x61, 0xf9, 0x81, 0x2, 0xf3, 0xc9, 0x66, 0x1c, 0x94, 0x55, 0xb2, 0x7a, 0x1d, 0xf8, 0x28, 0x97, 0x4b}, + }, + // 81P + { + x: fp384{0x82, 0xf6, 0x6, 0xdb, 0xcb, 0xd3, 0xbd, 0x3c, 0x85, 0x87, 0xc0, 0x86, 0x3e, 0x47, 0x45, 0xde, 0xfb, 0x1b, 0x7b, 0xe0, 0x60, 0x35, 0xcb, 0xd8, 0xaf, 0x38, 0xf1, 0xea, 0x8f, 0x11, 0xc3, 0xf2, 0xaf, 0x6f, 0x43, 0x9f, 0x85, 0x8a, 0x23, 0x11, 0x4f, 0x34, 0xdf, 0x7c, 0xe3, 0xc2, 0x84, 0x9}, + y: fp384{0x4f, 0x58, 0x82, 0xc3, 0x17, 0x3c, 0x8, 0xe1, 0x40, 0xa2, 0x6f, 0x73, 0xd4, 0x14, 0x9a, 0x95, 0x7d, 0x63, 0xf2, 0x18, 0xf0, 0xd2, 0xad, 0x56, 0x8d, 0x27, 0xdd, 0xe5, 0x5e, 0x7a, 0x4, 0x1, 0xa7, 0x6, 0x27, 0xae, 0x63, 0x8d, 0xe3, 0x5d, 0x7e, 0xb8, 0x45, 0x97, 0x60, 0xb7, 0xd7, 0x9d}, + }, + // 83P + { + x: fp384{0x71, 0x40, 0xe9, 0x44, 0xbf, 0xf0, 0x61, 0x8e, 0xb4, 0x5e, 0xf0, 0xd2, 0x7e, 0x84, 0xcf, 0x44, 0xeb, 0x94, 0x66, 0x4a, 0xd, 0xaa, 0x87, 0x84, 0xb5, 0xaa, 0xa4, 0xc7, 0xa1, 0x8c, 0xb8, 0xee, 0x26, 0x89, 0xa, 0x52, 0x3, 0xaa, 0x5b, 0xc2, 0x5, 0x78, 0x3d, 0xc0, 0x6a, 0xb1, 0x75, 0xa0}, + y: fp384{0xc3, 0x70, 0xd9, 0x13, 0x8a, 0xa4, 0x57, 0xc3, 0x3e, 0x64, 0x9, 0x60, 0x70, 0x13, 0x3c, 0x4e, 0x29, 0x4, 0xe6, 0x49, 0x57, 0xa9, 0x21, 0xcf, 0xda, 0xbc, 0x51, 0x22, 0xba, 0x62, 0xa2, 0xa, 0xe4, 0x78, 0x3c, 0x56, 0xd0, 0x7c, 0x2a, 0xb7, 0xf9, 0x1c, 0xce, 0x69, 0xda, 0xfe, 0x3d, 0x77}, + }, + // 85P + { + x: fp384{0x2d, 0x76, 0x6, 0x9b, 0xdf, 0x2c, 0x5d, 0x93, 0x5a, 0x25, 0x7, 0x82, 0xb8, 0xbb, 0x48, 0x21, 0xd8, 0x53, 0x31, 0x5, 0xdd, 0xca, 0xbd, 0x7b, 0x57, 0x6a, 0x25, 0x73, 0xff, 0xaa, 0x53, 0xd9, 0x1, 0x6f, 0x4e, 0x11, 0xe1, 0x8f, 0xa0, 0xb0, 0x4d, 0x4d, 0xe6, 0x46, 0x54, 0x2, 0x35, 0xc8}, + y: fp384{0x57, 0xc1, 0xdb, 0x0, 0xd8, 0xba, 0xcf, 0xe7, 0x69, 0xe9, 0xfb, 0x71, 0x2, 0xae, 0x2a, 0x39, 0x14, 0xe3, 0xeb, 0xb, 0x2a, 0xa7, 0x22, 0x74, 0xf2, 0x52, 0xaf, 0x2c, 0xd2, 0x55, 0xd4, 0xc3, 0x95, 0x51, 0x89, 0xe2, 0x9f, 0x83, 0x31, 0xa2, 0x13, 0xf2, 0x93, 0xc9, 0x92, 0x8d, 0x21, 0x6c}, + }, + // 87P + { + x: fp384{0x2e, 0x37, 0xa0, 0x4a, 0x2e, 0xa0, 0x11, 0x4f, 0x75, 0x77, 0x96, 0x10, 0x30, 0x47, 0x42, 0x59, 0x95, 0x91, 0x80, 0x8b, 0xba, 0xc1, 0xe, 0xdf, 0xf1, 0x3a, 0x3c, 0x9a, 0x8d, 0x92, 0xa, 0xf3, 0x2e, 0x6b, 0x7b, 0x38, 0x20, 0x3, 0x84, 0xc4, 0x22, 0xbb, 0x0, 0xa5, 0x17, 0x34, 0x1b, 0x1c}, + y: fp384{0xf2, 0x66, 0x32, 0xbf, 0xc7, 0xe6, 0xe, 0x69, 0x81, 0x96, 0x90, 0xa7, 0x74, 0x6d, 0x24, 0x18, 0x8f, 0xa8, 0x84, 0xf9, 0x54, 0x24, 0xdf, 0xde, 0x9, 0x9f, 0x55, 0xe7, 0x75, 0x41, 0x94, 0x31, 0xb7, 0x4d, 0x7b, 0xe, 0x88, 0x81, 0xac, 0xbd, 0x68, 0xfe, 0x96, 0xe9, 0xae, 0x6f, 0x4, 0x9f}, + }, + // 89P + { + x: fp384{0xac, 0xd4, 0x71, 0x2d, 0x4b, 0x9, 0x62, 0xc, 0xe0, 0x63, 0xf1, 0x4b, 0xdc, 0x9f, 0xa4, 0x18, 0x1f, 0x72, 0x96, 0x0, 0xb, 0xf3, 0x3d, 0x46, 0x7b, 0x5b, 0xe5, 0xc8, 0x4a, 0x64, 0xd3, 0x67, 0xb6, 0xe2, 0xe0, 0x19, 0x9d, 0xd2, 0x3d, 0xd6, 0x61, 0x73, 0x4b, 0x16, 0xde, 0x5, 0xd1, 0xd0}, + y: fp384{0x8e, 0x18, 0x17, 0x2, 0x4e, 0x5c, 0x86, 0xe5, 0x7e, 0xcf, 0x93, 0x20, 0x1b, 0xb7, 0x61, 0x78, 0x3c, 0x25, 0xaa, 0x2d, 0x51, 0xf0, 0xcc, 0x65, 0xc0, 0xe4, 0x4d, 0xb, 0x9, 0x1, 0x77, 0x14, 0xd9, 0x62, 0xb9, 0x40, 0x35, 0x24, 0x28, 0x1d, 0xf3, 0x37, 0xdf, 0xb8, 0x39, 0xe9, 0xc7, 0x1}, + }, + // 91P + { + x: fp384{0x58, 0x8, 0xba, 0x9c, 0x9c, 0x40, 0xea, 0x5d, 0x63, 0x3f, 0xae, 0x14, 0x1b, 0x42, 0xc2, 0x35, 0x8a, 0x61, 0xc2, 0xbb, 0x34, 0xe5, 0xf6, 0xa4, 0x5f, 0x4f, 0xd7, 0x42, 0x7d, 0x97, 0x4b, 0xb0, 0xb7, 0x3e, 0xdc, 0x59, 0x27, 0x38, 0xe7, 0xe7, 0xb0, 0x23, 0xf2, 0x8b, 0x34, 0x52, 0xf, 0xeb}, + y: fp384{0x58, 0x51, 0xc7, 0xf, 0x67, 0x51, 0x1c, 0x99, 0x6d, 0x2c, 0xde, 0x3f, 0x1a, 0x81, 0x12, 0xd0, 0x3d, 0x34, 0x36, 0x92, 0x31, 0xb3, 0xd0, 0x9, 0xa0, 0xcb, 0xa2, 0x63, 0xc8, 0xe0, 0x78, 0xcb, 0x78, 0x84, 0xb8, 0x9a, 0xbd, 0xb3, 0x9, 0xb, 0xe2, 0xc6, 0x16, 0xf1, 0x3, 0xc7, 0xca, 0x47}, + }, + // 93P + { + x: fp384{0xaf, 0x80, 0x2d, 0xe3, 0x71, 0x4d, 0xd1, 0xeb, 0x5e, 0x67, 0x80, 0x53, 0x4f, 0xc2, 0x1c, 0x1b, 0xcd, 0x42, 0x61, 0xb1, 0x64, 0x47, 0x63, 0x1c, 0xe, 0xb0, 0xfd, 0x7c, 0xde, 0x45, 0x35, 0x7a, 0x54, 0x51, 0xd1, 0xcf, 0x89, 0x16, 0xf9, 0x2d, 0xd7, 0xa2, 0xa, 0x43, 0xb3, 0x55, 0x33, 0x81}, + y: fp384{0x7e, 0xca, 0xf2, 0x85, 0xc9, 0xe2, 0xdc, 0x16, 0x79, 0xbb, 0x3a, 0xe0, 0xf7, 0x3, 0xe3, 0xd9, 0x98, 0x66, 0xb0, 0x3c, 0x10, 0xa8, 0x7c, 0xfe, 0xcb, 0xd, 0x67, 0x71, 0x5b, 0x42, 0x2a, 0x57, 0xe5, 0x68, 0xa2, 0x90, 0x54, 0x39, 0x1b, 0xc7, 0x9, 0x9d, 0xbf, 0x66, 0x8f, 0xf3, 0x71, 0xc0}, + }, + // 95P + { + x: fp384{0x91, 0x3c, 0xbc, 0xd, 0x63, 0xf2, 0xc0, 0xf, 0xb1, 0xcb, 0xc0, 0x9b, 0x16, 0xca, 0x74, 0x9f, 0x77, 0x89, 0xf9, 0xe, 0x9d, 0x7b, 0x60, 0x4a, 0x79, 0x2b, 0x7d, 0xa2, 0xef, 0xb, 0xe9, 0xb, 0xe1, 0x23, 0x7f, 0xad, 0xb5, 0xb, 0x7b, 0x25, 0xe4, 0xd1, 0xea, 0x2f, 0xe5, 0x2f, 0xf4, 0xb8}, + y: fp384{0x92, 0xb5, 0x93, 0x5f, 0x31, 0xe4, 0x78, 0xde, 0x7d, 0x61, 0x79, 0xfd, 0xeb, 0xe7, 0x5f, 0x50, 0xfb, 0xf9, 0x99, 0xdd, 0x14, 0x3f, 0xcc, 0x45, 0x91, 0xb5, 0xc7, 0x3b, 0xe8, 0x64, 0xf, 0x8c, 0xf9, 0x93, 0xab, 0x55, 0xed, 0x4d, 0x36, 0x65, 0x6e, 0x28, 0xdf, 0x42, 0xa5, 0x4b, 0x6d, 0xbb}, + }, + // 97P + { + x: fp384{0xe2, 0x54, 0x5c, 0x7f, 0x5d, 0x3, 0xd2, 0x7c, 0x2c, 0x49, 0x49, 0x4a, 0x0, 0xdb, 0xf0, 0xc1, 0x98, 0x8f, 0x27, 0x65, 0x30, 0x3e, 0x27, 0x8f, 0x9d, 0x9d, 0xef, 0x6f, 0xd1, 0x1e, 0x24, 0x10, 0x16, 0x96, 0x6, 0xac, 0x1b, 0xe5, 0xb1, 0x87, 0x7f, 0x80, 0xd, 0x17, 0xcd, 0x1a, 0x8, 0x8c}, + y: fp384{0x98, 0xb5, 0x73, 0x1c, 0xea, 0x51, 0x50, 0x0, 0xf4, 0x5b, 0x86, 0xd6, 0x12, 0x55, 0xeb, 0xe4, 0xd3, 0x5d, 0xe0, 0x30, 0xf4, 0x4e, 0xd2, 0xd7, 0x9e, 0xa3, 0x89, 0x78, 0xed, 0xe4, 0x47, 0xcb, 0x64, 0x69, 0xf5, 0xc4, 0x91, 0x24, 0x3e, 0x4c, 0x6, 0x30, 0xf0, 0xc4, 0x8e, 0xb7, 0xc6, 0x83}, + }, + // 99P + { + x: fp384{0xa1, 0x84, 0x5f, 0xb0, 0xa9, 0x35, 0x38, 0x6e, 0x4e, 0x17, 0xaa, 0x41, 0xf, 0x9e, 0x4f, 0xbb, 0x69, 0xa4, 0x8b, 0x70, 0x7c, 0x17, 0x41, 0x1b, 0xbd, 0xf8, 0xc8, 0x79, 0xb4, 0xe6, 0xb2, 0xb9, 0xbd, 0xd6, 0xd9, 0x82, 0x9, 0xae, 0x9c, 0xd4, 0x3a, 0x22, 0x28, 0xbb, 0x0, 0x5f, 0x8c, 0x64}, + y: fp384{0xa5, 0xc4, 0x8c, 0x5d, 0x76, 0x85, 0xf4, 0x4, 0x8d, 0xa3, 0xa0, 0x81, 0xdd, 0x96, 0x30, 0xfe, 0xe1, 0x47, 0x82, 0x70, 0x8f, 0x13, 0x75, 0x66, 0x8, 0xea, 0xa0, 0xd1, 0xd8, 0x59, 0xf7, 0xd6, 0x98, 0xd, 0x19, 0x76, 0xb1, 0x93, 0x74, 0x1f, 0xbd, 0x63, 0x2d, 0x32, 0x8b, 0x69, 0xe1, 0x3}, + }, + // 101P + { + x: fp384{0xac, 0xde, 0x8a, 0x9b, 0xf6, 0xc6, 0x66, 0x8e, 0x70, 0x6d, 0xc6, 0x50, 0xfe, 0xf5, 0x39, 0xb5, 0x1a, 0xfb, 0xcc, 0x2e, 0x2c, 0xcd, 0xdd, 0x73, 0xfc, 0x5c, 0x8b, 0x8b, 0xad, 0x1f, 0x3b, 0xd7, 0x10, 0x87, 0xa1, 0x47, 0x35, 0x94, 0xdd, 0x9c, 0xdb, 0x14, 0xc8, 0x7b, 0xbf, 0x92, 0x23, 0x7e}, + y: fp384{0xe8, 0x74, 0x8f, 0x6c, 0xc0, 0x93, 0x41, 0x91, 0x4d, 0xc0, 0x67, 0x1d, 0x21, 0xdc, 0xed, 0xff, 0x93, 0x86, 0xd6, 0xa, 0x85, 0x41, 0xef, 0x1f, 0x54, 0x80, 0x3e, 0xf5, 0x9a, 0x1d, 0x3e, 0xa7, 0x4, 0xc1, 0xe, 0x42, 0x6f, 0x65, 0x9b, 0x90, 0xde, 0xe1, 0x2, 0x17, 0x36, 0x2d, 0x87, 0x73}, + }, + // 103P + { + x: fp384{0x5f, 0x5d, 0x35, 0x21, 0xaa, 0xab, 0x4c, 0xd2, 0xbd, 0x2, 0xd4, 0xaf, 0xe, 0xb1, 0xcb, 0xdd, 0xe1, 0x1d, 0xc2, 0x29, 0x43, 0xd1, 0xf0, 0xd3, 0xfc, 0x84, 0x3d, 0xf2, 0x94, 0x5a, 0xd9, 0x1a, 0xd, 0x53, 0xda, 0xe3, 0x2, 0x79, 0x3a, 0x11, 0x48, 0x10, 0x67, 0x64, 0x8e, 0xa8, 0xd, 0x59}, + y: fp384{0xda, 0xf0, 0x5b, 0x92, 0x82, 0x82, 0xa5, 0xf4, 0xb, 0x6e, 0x2e, 0xe6, 0xe7, 0xe4, 0x52, 0x1a, 0xfd, 0x4d, 0x6f, 0xd8, 0x4e, 0xbb, 0xeb, 0x97, 0xc3, 0xd1, 0xfa, 0x58, 0xc3, 0xd1, 0x1b, 0x60, 0x52, 0x5, 0xe4, 0x2d, 0xa6, 0xd5, 0xe2, 0xd6, 0xed, 0xdb, 0x73, 0x72, 0x37, 0x71, 0x9e, 0xc}, + }, + // 105P + { + x: fp384{0x45, 0x28, 0x80, 0xe5, 0x85, 0x19, 0xe9, 0xe6, 0xbc, 0x1, 0xe2, 0xa6, 0xae, 0xd6, 0x67, 0xc3, 0xbe, 0x23, 0x2c, 0xdd, 0xe5, 0x30, 0x7f, 0x7, 0xe3, 0x75, 0x50, 0x27, 0x9c, 0xf3, 0x2e, 0x86, 0x42, 0x65, 0x80, 0x1a, 0x44, 0x75, 0x2c, 0x2, 0x9c, 0xd0, 0xeb, 0x99, 0x3a, 0x3e, 0xab, 0xd0}, + y: fp384{0xb8, 0x28, 0x90, 0xd9, 0x60, 0xef, 0x67, 0x7d, 0x6b, 0x13, 0xad, 0xa9, 0x4f, 0x36, 0xcf, 0xa5, 0x8c, 0xff, 0x1f, 0xa9, 0xa9, 0x23, 0x2c, 0x37, 0x60, 0x25, 0x20, 0x47, 0x95, 0x7a, 0xd5, 0xd3, 0x23, 0x19, 0x2f, 0x15, 0x45, 0xf1, 0xba, 0xce, 0xa5, 0x73, 0x89, 0x6d, 0x2c, 0xe7, 0x3a, 0xcc}, + }, + // 107P + { + x: fp384{0x23, 0x3f, 0x36, 0xf4, 0xe1, 0xe8, 0x18, 0xd7, 0x90, 0x14, 0x76, 0x4f, 0x20, 0x1e, 0xc2, 0x73, 0x46, 0x5d, 0x7, 0xa0, 0x25, 0xec, 0xc6, 0x27, 0xd0, 0x40, 0x3f, 0x75, 0x56, 0xf4, 0xd4, 0xcc, 0x22, 0x16, 0xa9, 0x60, 0x49, 0x4c, 0x99, 0x50, 0x48, 0xb, 0x74, 0x3f, 0x79, 0x4d, 0x96, 0x77}, + y: fp384{0x2, 0xed, 0x47, 0xf6, 0xe2, 0x55, 0xc9, 0xf4, 0x79, 0x3d, 0x19, 0xe4, 0x9a, 0xc7, 0x4f, 0x84, 0x9f, 0x3f, 0x7f, 0xa2, 0xd1, 0x74, 0x83, 0x48, 0x63, 0x94, 0x65, 0xb8, 0x45, 0xad, 0xd6, 0x95, 0x39, 0x8e, 0x43, 0xc7, 0x78, 0x9f, 0xd9, 0xe1, 0xf2, 0xed, 0xfc, 0x2a, 0x17, 0xa7, 0x82, 0x51}, + }, + // 109P + { + x: fp384{0xfa, 0xb1, 0xde, 0xb2, 0x27, 0x2e, 0xfc, 0xe, 0x4b, 0x18, 0xc1, 0x3c, 0x83, 0x35, 0x7d, 0x9c, 0xc8, 0xbd, 0xdc, 0xa8, 0xf8, 0xc5, 0x41, 0x58, 0xbb, 0x3a, 0xd9, 0xf0, 0x8a, 0xa5, 0x11, 0xa9, 0x87, 0xf8, 0xcf, 0xb9, 0x33, 0x8c, 0xd1, 0x3c, 0x3, 0x24, 0x3f, 0xf1, 0xbb, 0x27, 0x3c, 0x6e}, + y: fp384{0xe6, 0x3a, 0x53, 0xea, 0x12, 0x17, 0x39, 0x5b, 0x5, 0x4c, 0x29, 0x54, 0xb, 0xd9, 0xcd, 0x35, 0xf4, 0xda, 0x60, 0xf5, 0xb4, 0x7f, 0xb5, 0x2d, 0x1d, 0x41, 0xa1, 0xf5, 0xca, 0x33, 0xad, 0x75, 0x68, 0x75, 0x7c, 0x7f, 0x4e, 0x9a, 0xe1, 0x87, 0x5, 0x77, 0x8c, 0x19, 0x56, 0x6c, 0xc4, 0xf4}, + }, + // 111P + { + x: fp384{0xb8, 0x74, 0xbe, 0x5, 0x48, 0xb7, 0xb3, 0x8d, 0xab, 0x5f, 0x76, 0x0, 0x50, 0x80, 0xe0, 0x8, 0xd9, 0x7f, 0x44, 0x50, 0xb, 0x72, 0x44, 0x67, 0x3, 0xbe, 0x27, 0xc7, 0x12, 0x20, 0x55, 0x27, 0x7f, 0x66, 0x2, 0x8b, 0x51, 0x7b, 0x90, 0xc3, 0x14, 0xef, 0xbd, 0xb9, 0xbc, 0xaa, 0x58, 0xa1}, + y: fp384{0x6f, 0xc5, 0x9c, 0xf4, 0x3, 0xfa, 0xdd, 0xaa, 0x96, 0xfb, 0x5, 0xe3, 0xe4, 0xbe, 0x95, 0x10, 0x19, 0x26, 0xc3, 0x93, 0xbc, 0x54, 0xff, 0xa2, 0x85, 0x26, 0xeb, 0x4a, 0xf9, 0xe1, 0xf8, 0xcc, 0xfe, 0xd9, 0x0, 0x23, 0xb8, 0x47, 0x4b, 0xc6, 0xa9, 0x9d, 0x27, 0x8, 0x68, 0x77, 0xca, 0x9}, + }, + // 113P + { + x: fp384{0x12, 0xda, 0xb, 0x9b, 0xb7, 0x86, 0x5b, 0xf8, 0x72, 0x35, 0xe3, 0xbb, 0xd1, 0x16, 0xc6, 0xd2, 0x7f, 0xd2, 0x2b, 0x85, 0xef, 0x15, 0x22, 0xe7, 0xc5, 0x7f, 0x9b, 0x13, 0x9, 0x5b, 0x81, 0xe9, 0xc2, 0xa0, 0x7f, 0x8d, 0x4, 0xdb, 0x5b, 0x4a, 0x86, 0xa9, 0x86, 0xff, 0x17, 0xcd, 0x9f, 0x86}, + y: fp384{0xbe, 0xf6, 0xda, 0x91, 0x17, 0x52, 0x78, 0x32, 0x4, 0x4d, 0x66, 0xd6, 0xf1, 0x7, 0xc0, 0xb9, 0x29, 0x20, 0xb1, 0xe7, 0x2a, 0x72, 0x98, 0x69, 0x67, 0xbb, 0x31, 0xfc, 0xd9, 0xde, 0x7f, 0xbf, 0x57, 0x77, 0xb8, 0x31, 0x7c, 0xd1, 0xe, 0x3d, 0x4b, 0x94, 0xf7, 0x55, 0xf2, 0x3d, 0xb, 0xa1}, + }, + // 115P + { + x: fp384{0x56, 0x8f, 0x49, 0x34, 0x3b, 0x67, 0x4e, 0xaa, 0x6d, 0x45, 0x43, 0xa0, 0xb3, 0xf7, 0x20, 0x91, 0x26, 0x88, 0xa4, 0x26, 0xf3, 0x68, 0xe8, 0x33, 0xfd, 0x6b, 0x40, 0x32, 0xf4, 0xcc, 0x7a, 0xa9, 0x46, 0x7, 0xc5, 0x23, 0x41, 0x2a, 0x44, 0x84, 0x2d, 0x98, 0x50, 0x73, 0x65, 0x69, 0x4c, 0x27}, + y: fp384{0xaa, 0x9e, 0xdc, 0x95, 0xfb, 0xb7, 0x6, 0x31, 0x41, 0xe2, 0x7a, 0xec, 0xb1, 0x1d, 0xbf, 0x3e, 0x86, 0x5b, 0x8a, 0x84, 0xb8, 0x39, 0xdc, 0x0, 0xc6, 0x2e, 0x31, 0xf6, 0x3a, 0x34, 0x9a, 0xdf, 0x3, 0x1f, 0x12, 0xcf, 0x32, 0x9e, 0x2, 0x75, 0xdb, 0x11, 0x5a, 0xcf, 0xf6, 0xbd, 0xc5, 0xc0}, + }, + // 117P + { + x: fp384{0x9a, 0x55, 0x23, 0x7, 0xa8, 0xe7, 0xcc, 0xfd, 0x70, 0xd0, 0x29, 0xa2, 0xe, 0xb3, 0x32, 0x95, 0x61, 0x79, 0x85, 0xfe, 0x94, 0x52, 0x3e, 0x61, 0x8d, 0x73, 0xea, 0x9a, 0x9a, 0x74, 0x9e, 0xad, 0x53, 0xba, 0xac, 0x23, 0xae, 0x6b, 0x7a, 0x51, 0x8b, 0x56, 0x23, 0x78, 0xcd, 0x74, 0x67, 0xf2}, + y: fp384{0x4d, 0x11, 0x53, 0xae, 0xa1, 0x67, 0x7, 0x94, 0x7b, 0x5, 0x8c, 0xeb, 0x4b, 0x3a, 0xcb, 0xc6, 0x0, 0xf6, 0xae, 0x6, 0x5f, 0xc0, 0x99, 0x6d, 0x81, 0x84, 0x79, 0xb2, 0x8d, 0x9b, 0x72, 0xa6, 0x5b, 0x58, 0xf1, 0xbf, 0x82, 0x65, 0x54, 0x7a, 0x73, 0x97, 0xb0, 0x82, 0xb0, 0x9a, 0x50, 0x70}, + }, + // 119P + { + x: fp384{0xd1, 0xd8, 0x29, 0x73, 0xac, 0x95, 0x25, 0x73, 0xc4, 0xbc, 0x73, 0xab, 0x8d, 0x7, 0xf9, 0x59, 0xde, 0x9d, 0xcf, 0x21, 0xb4, 0xe7, 0x55, 0xcd, 0x27, 0xab, 0x5f, 0x87, 0xa1, 0xb, 0x63, 0xa4, 0xcd, 0xf4, 0x9c, 0xec, 0xb8, 0x7f, 0x16, 0x13, 0x77, 0x5, 0x8b, 0x99, 0x57, 0x5c, 0xfc, 0xd2}, + y: fp384{0x6f, 0x1b, 0xf5, 0x5f, 0xc1, 0x60, 0x13, 0x76, 0xeb, 0x9c, 0xcf, 0x6, 0xf2, 0x96, 0xdb, 0xb2, 0x46, 0x8f, 0xdc, 0x99, 0x48, 0xa6, 0x77, 0xd6, 0xe5, 0xb7, 0x9, 0x91, 0xbc, 0xca, 0x9e, 0xeb, 0xa3, 0xb7, 0x21, 0x92, 0xac, 0xb1, 0x1b, 0x9a, 0xcd, 0xa5, 0x40, 0x8a, 0x28, 0x36, 0x65, 0xb1}, + }, + // 121P + { + x: fp384{0x8d, 0xfa, 0x9d, 0x18, 0x40, 0xba, 0x98, 0x51, 0x1e, 0xab, 0x96, 0xa8, 0xe3, 0x16, 0x9a, 0x8c, 0xe4, 0x44, 0x67, 0xba, 0xd6, 0xd5, 0x33, 0x6c, 0x8a, 0x77, 0x72, 0x77, 0xd4, 0xfb, 0x9a, 0xc2, 0xe0, 0xf7, 0x29, 0x93, 0x95, 0x3c, 0xdf, 0x65, 0x81, 0xdb, 0x91, 0x38, 0x1e, 0x3f, 0xcd, 0x79}, + y: fp384{0x9b, 0x1, 0x84, 0xd7, 0xb, 0x8f, 0xaa, 0xca, 0x62, 0x8e, 0x2, 0xe9, 0x6b, 0x4f, 0x40, 0xf5, 0x85, 0x89, 0x4d, 0xae, 0x54, 0x7a, 0x50, 0x95, 0x1b, 0xf2, 0x16, 0xb7, 0xa8, 0x39, 0x1d, 0x9c, 0x7e, 0x5b, 0x26, 0xf8, 0xf9, 0xd, 0x3d, 0x47, 0x16, 0x9, 0x4d, 0xc6, 0xa1, 0xed, 0xae, 0x11}, + }, + // 123P + { + x: fp384{0x80, 0xb, 0x4c, 0xc, 0x48, 0x98, 0x11, 0x15, 0xfe, 0x18, 0x10, 0x2a, 0x4a, 0x7d, 0xb0, 0x46, 0x7b, 0x90, 0x80, 0xea, 0xeb, 0xc3, 0xa9, 0x14, 0x5, 0x44, 0x95, 0x42, 0xee, 0x5, 0x3d, 0x4b, 0xd2, 0x18, 0x4, 0x55, 0x78, 0xfd, 0xd6, 0xd4, 0xa6, 0x82, 0xdc, 0x21, 0x63, 0x4f, 0x4a, 0x8e}, + y: fp384{0xd9, 0xb9, 0x78, 0xa1, 0xf7, 0xd7, 0xe4, 0x1b, 0x9f, 0x8c, 0x78, 0x70, 0x4, 0xba, 0xc6, 0x83, 0xe8, 0xf7, 0x30, 0x9f, 0x3e, 0xaf, 0x82, 0x5a, 0x7b, 0x44, 0x8f, 0x49, 0xf, 0xab, 0x86, 0x8a, 0x33, 0xcf, 0x5c, 0xc2, 0xec, 0xbc, 0xba, 0x3, 0xdd, 0x8a, 0x79, 0x1a, 0xed, 0x62, 0xc4, 0x74}, + }, + // 125P + { + x: fp384{0xbb, 0x44, 0xfb, 0x3c, 0xbc, 0xb8, 0x12, 0x96, 0xda, 0x6a, 0x9d, 0x71, 0x77, 0x56, 0xf2, 0x70, 0xe2, 0x14, 0xf6, 0x46, 0xaa, 0x65, 0xea, 0x50, 0x6d, 0x35, 0x50, 0x34, 0xcf, 0xa8, 0x36, 0x94, 0xac, 0x3, 0x67, 0x3, 0xad, 0xeb, 0xd6, 0x7a, 0xae, 0x48, 0xcf, 0x45, 0xb2, 0xda, 0xb2, 0x3}, + y: fp384{0x1e, 0x6, 0x17, 0x41, 0x2a, 0x3d, 0x95, 0x21, 0xa4, 0x55, 0x4f, 0xed, 0x30, 0xb7, 0x3f, 0xdf, 0x8e, 0xab, 0x19, 0xe1, 0x41, 0x36, 0xf5, 0xec, 0xaa, 0x87, 0x91, 0x21, 0xbc, 0x41, 0x1f, 0x55, 0x2, 0x58, 0x9, 0xb0, 0x4b, 0xa7, 0xd5, 0x7c, 0xcb, 0x5c, 0xf3, 0x72, 0xf5, 0xbf, 0x33, 0x89}, + }, + // 127P + { + x: fp384{0xec, 0x1, 0xa1, 0xec, 0x46, 0x32, 0x75, 0xf7, 0xaf, 0x4, 0x96, 0x56, 0x4c, 0xfa, 0xac, 0x2a, 0x79, 0x62, 0x2c, 0x52, 0x34, 0x8f, 0xf2, 0xee, 0xf, 0x1e, 0x23, 0x74, 0x38, 0xe6, 0xfd, 0x96, 0x9d, 0xf0, 0xe0, 0xd6, 0x1b, 0xb1, 0x2b, 0xa9, 0xb4, 0x5d, 0x39, 0xf, 0x74, 0x4e, 0xe3, 0xbb}, + y: fp384{0xf9, 0x3c, 0x94, 0xbf, 0xdd, 0x59, 0x6e, 0xaa, 0xaa, 0xd5, 0x8a, 0x1, 0xbe, 0xbd, 0x98, 0x56, 0x19, 0xc5, 0x67, 0xa4, 0x44, 0x2a, 0xd2, 0x88, 0xe, 0xb, 0x18, 0xad, 0x39, 0xe3, 0x29, 0x9e, 0x94, 0x2f, 0x7b, 0x36, 0x2e, 0x83, 0xd6, 0xf3, 0x69, 0x80, 0x94, 0xe3, 0x61, 0x2a, 0xe9, 0xc7}, + }, +} diff --git a/src/circl/group/group.go b/src/circl/group/group.go new file mode 100644 index 00000000000..390a8e1bce5 --- /dev/null +++ b/src/circl/group/group.go @@ -0,0 +1,64 @@ +// Package group provides prime-order groups based on elliptic curves. +package group + +import ( + "crypto/elliptic" + "encoding" + "errors" + "io" + + "circl/ecc/p384" +) + +var ( + // P256 is the group generated by P-256 elliptic curve. + P256 Group = wG{elliptic.P256()} + // P384 is the group generated by P-384 elliptic curve. + P384 Group = wG{p384.P384()} + // P521 is the group generated by P-521 elliptic curve. + P521 Group = wG{elliptic.P521()} +) + +// Group represents a prime-order group based on elliptic curves. +type Group interface { + NewElement() Element + NewScalar() Scalar + Identity() Element + Generator() Element + Order() Scalar + RandomElement(io.Reader) Element + RandomScalar(io.Reader) Scalar + HashToElement(data, dst []byte) Element + HashToScalar(data, dst []byte) Scalar +} + +// Element represents an abstract element of a prime-order group. +type Element interface { + IsIdentity() bool + IsEqual(Element) bool + Add(Element, Element) Element + Dbl(Element) Element + Neg(Element) Element + Mul(Element, Scalar) Element + MulGen(Scalar) Element + encoding.BinaryMarshaler + encoding.BinaryUnmarshaler + MarshalBinaryCompress() ([]byte, error) +} + +// Scalar represents an integer scalar. +type Scalar interface { + IsEqual(Scalar) bool + Add(Scalar, Scalar) Scalar + Sub(Scalar, Scalar) Scalar + Mul(Scalar, Scalar) Scalar + Neg(Scalar) Scalar + Inv(Scalar) Scalar + encoding.BinaryMarshaler + encoding.BinaryUnmarshaler +} + +var ( + ErrType = errors.New("type mismatch") + ErrUnmarshal = errors.New("error unmarshaling") +) diff --git a/src/circl/group/group_test.go b/src/circl/group/group_test.go new file mode 100644 index 00000000000..a18ef71bbb6 --- /dev/null +++ b/src/circl/group/group_test.go @@ -0,0 +1,262 @@ +package group_test + +import ( + "bytes" + "crypto/rand" + "fmt" + "testing" + + "circl/group" + "circl/internal/test" +) + +func TestGroup(t *testing.T) { + const testTimes = 1 << 7 + for _, g := range []group.Group{ + group.P256, + group.P384, + group.P521, + } { + g := g + n := g.(fmt.Stringer).String() + t.Run(n+"/Add", func(tt *testing.T) { testAdd(tt, testTimes, g) }) + t.Run(n+"/Neg", func(tt *testing.T) { testNeg(tt, testTimes, g) }) + t.Run(n+"/Mul", func(tt *testing.T) { testMul(tt, testTimes, g) }) + t.Run(n+"/MulGen", func(tt *testing.T) { testMulGen(tt, testTimes, g) }) + t.Run(n+"/Order", func(tt *testing.T) { testOrder(tt, testTimes, g) }) + t.Run(n+"/Marshal", func(tt *testing.T) { testMarshal(tt, testTimes, g) }) + t.Run(n+"/Scalar", func(tt *testing.T) { testScalar(tt, testTimes, g) }) + } +} + +func testAdd(t *testing.T, testTimes int, g group.Group) { + Q := g.NewElement() + for i := 0; i < testTimes; i++ { + P := g.RandomElement(rand.Reader) + + got := Q.Dbl(P).Dbl(Q).Dbl(Q).Dbl(Q) // Q = 16P + + R := g.Identity() + for j := 0; j < 16; j++ { + R.Add(R, P) + } + want := R // R = 16P = P+P...+P + if !got.IsEqual(want) { + test.ReportError(t, got, want, P) + } + } +} + +func testNeg(t *testing.T, testTimes int, g group.Group) { + Q := g.NewElement() + for i := 0; i < testTimes; i++ { + P := g.RandomElement(rand.Reader) + Q.Neg(P) + Q.Add(Q, P) + got := Q.IsIdentity() + want := true + if got != want { + test.ReportError(t, got, want, P) + } + } +} + +func testMul(t *testing.T, testTimes int, g group.Group) { + Q := g.NewElement() + kInv := g.NewScalar() + for i := 0; i < testTimes; i++ { + P := g.RandomElement(rand.Reader) + k := g.RandomScalar(rand.Reader) + kInv.Inv(k) + + Q.Mul(P, k) + Q.Mul(Q, kInv) + + got := P + want := Q + if !got.IsEqual(want) { + test.ReportError(t, got, want, P, k) + } + } +} + +func testMulGen(t *testing.T, testTimes int, g group.Group) { + G := g.Generator() + P := g.NewElement() + Q := g.NewElement() + for i := 0; i < testTimes; i++ { + k := g.RandomScalar(rand.Reader) + + P.Mul(G, k) + Q.MulGen(k) + + got := P + want := Q + if !got.IsEqual(want) { + test.ReportError(t, got, want, P, k) + } + } +} + +func testOrder(t *testing.T, testTimes int, g group.Group) { + Q := g.NewElement() + order := g.Order() + for i := 0; i < testTimes; i++ { + P := g.RandomElement(rand.Reader) + + Q.Mul(P, order) + got := Q.IsIdentity() + want := true + if got != want { + test.ReportError(t, got, want, P) + } + } +} + +func isZero(b []byte) bool { + for i := 0; i < len(b); i++ { + if b[i] != 0x00 { + return false + } + } + return true +} + +func testMarshal(t *testing.T, testTimes int, g group.Group) { + I := g.Identity() + got, _ := I.MarshalBinary() + if !isZero(got) { + test.ReportError(t, got, "Non-zero identity") + } + got, _ = I.MarshalBinaryCompress() + if !isZero(got) { + test.ReportError(t, got, "Non-zero identity") + } + II := g.NewElement() + err := II.UnmarshalBinary(got) + if err != nil || !I.IsEqual(II) { + test.ReportError(t, I, II) + } + + got1 := g.NewElement() + got2 := g.NewElement() + for i := 0; i < testTimes; i++ { + x := g.RandomElement(rand.Reader) + enc1, _ := x.MarshalBinary() + enc2, _ := x.MarshalBinaryCompress() + + err1 := got1.UnmarshalBinary(enc1) + err2 := got2.UnmarshalBinary(enc2) + if err1 != nil || !x.IsEqual(got1) { + test.ReportError(t, got1, x) + } + if err2 != nil || !x.IsEqual(got2) { + test.ReportError(t, got2, x) + } + } +} + +func testScalar(t *testing.T, testTimes int, g group.Group) { + c := g.NewScalar() + d := g.NewScalar() + e := g.NewScalar() + f := g.NewScalar() + for i := 0; i < testTimes; i++ { + a := g.RandomScalar(rand.Reader) + b := g.RandomScalar(rand.Reader) + c.Add(a, b) + d.Sub(a, b) + e.Mul(c, d) + + c.Mul(a, a) + d.Mul(b, b) + d.Neg(d) + f.Add(c, d) + enc1, err1 := e.MarshalBinary() + enc2, err2 := f.MarshalBinary() + if err1 != nil || err2 != nil || !bytes.Equal(enc1, enc2) { + test.ReportError(t, enc1, enc2, a, b) + } + } +} + +func BenchmarkElement(b *testing.B) { + for _, g := range []group.Group{ + group.P256, + group.P384, + group.P521, + } { + x := g.RandomElement(rand.Reader) + y := g.RandomElement(rand.Reader) + n := g.RandomScalar(rand.Reader) + name := g.(fmt.Stringer).String() + b.Run(name+"/Add", func(b *testing.B) { + for i := 0; i < b.N; i++ { + x.Add(x, y) + } + }) + b.Run(name+"/Dbl", func(b *testing.B) { + for i := 0; i < b.N; i++ { + x.Dbl(x) + } + }) + b.Run(name+"/Mul", func(b *testing.B) { + for i := 0; i < b.N; i++ { + y.Mul(x, n) + } + }) + b.Run(name+"/MulGen", func(b *testing.B) { + for i := 0; i < b.N; i++ { + x.MulGen(n) + } + }) + } +} + +func BenchmarkScalar(b *testing.B) { + for _, g := range []group.Group{ + group.P256, + group.P384, + group.P521, + } { + x := g.RandomScalar(rand.Reader) + y := g.RandomScalar(rand.Reader) + name := g.(fmt.Stringer).String() + b.Run(name+"/Add", func(b *testing.B) { + for i := 0; i < b.N; i++ { + x.Add(x, y) + } + }) + b.Run(name+"/Mul", func(b *testing.B) { + for i := 0; i < b.N; i++ { + x.Mul(x, y) + } + }) + b.Run(name+"/Inv", func(b *testing.B) { + for i := 0; i < b.N; i++ { + y.Inv(x) + } + }) + } +} + +func BenchmarkHash(b *testing.B) { + for _, g := range []group.Group{ + group.P256, + group.P384, + group.P521, + } { + g := g + name := g.(fmt.Stringer).String() + b.Run(name+"/HashToElement", func(b *testing.B) { + for i := 0; i < b.N; i++ { + g.HashToElement(nil, nil) + } + }) + b.Run(name+"/HashToScalar", func(b *testing.B) { + for i := 0; i < b.N; i++ { + g.HashToScalar(nil, nil) + } + }) + } +} diff --git a/src/circl/group/hash.go b/src/circl/group/hash.go new file mode 100644 index 00000000000..e439771553f --- /dev/null +++ b/src/circl/group/hash.go @@ -0,0 +1,90 @@ +package group + +import ( + "crypto" + "math/big" +) + +// FieldHasher allows to hash byte strings producing one or more field elements. +type FieldHasher interface { + // HashToField generates a set of elements {u1,..., uN} = Hash(b). + HashToField(u []big.Int, b []byte) +} + +type expanderXMD struct { + h crypto.Hash + p *big.Int + L uint + dst []byte +} + +// NewExpanderMD returns a hash function based on a Merkle-Damgård hash function. +func NewExpanderMD(h crypto.Hash, p *big.Int, L uint, dst []byte) FieldHasher { + const maxDSTLength = 255 + var dstPrime []byte + if l := len(dst); l > maxDSTLength { + H := h.New() + _, _ = H.Write([]byte("H2C-OVERSIZE-DST-")) + _, _ = H.Write(dst) + dstPrime = H.Sum(nil) + } else { + dstPrime = make([]byte, l, l+1) + copy(dstPrime, dst) + } + dstPrime = append(dstPrime, byte(len(dstPrime))) + return expanderXMD{h, p, L, dstPrime} +} + +func (e expanderXMD) HashToField(u []big.Int, b []byte) { + count := uint(len(u)) + bytes := e.expand(b, count*e.L) + for i := range u { + j := uint(i) * e.L + u[i].Mod(u[i].SetBytes(bytes[j:j+e.L]), e.p) + } +} + +func (e expanderXMD) expand(msg []byte, n uint) []byte { + H := e.h.New() + bLen := uint(H.Size()) + ell := (n + (bLen - 1)) / bLen + if ell > 255 { + panic("too big") + } + + zPad := make([]byte, H.BlockSize()) + libStr := []byte{0, 0} + libStr[0] = byte((n >> 8) & 0xFF) + libStr[1] = byte(n & 0xFF) + + H.Reset() + _, _ = H.Write(zPad) + _, _ = H.Write(msg) + _, _ = H.Write(libStr) + _, _ = H.Write([]byte{0}) + _, _ = H.Write(e.dst) + b0 := H.Sum(nil) + + H.Reset() + _, _ = H.Write(b0) + _, _ = H.Write([]byte{1}) + _, _ = H.Write(e.dst) + bi := H.Sum(nil) + pseudo := append([]byte{}, bi...) + for i := uint(2); i <= ell; i++ { + H.Reset() + _, _ = H.Write(xor(bi, b0)) + _, _ = H.Write([]byte{byte(i)}) + _, _ = H.Write(e.dst) + bi = H.Sum(nil) + pseudo = append(pseudo, bi...) + } + return pseudo[0:n] +} + +func xor(x, y []byte) []byte { + for i := range x { + x[i] ^= y[i] + } + return x +} diff --git a/src/circl/group/short.go b/src/circl/group/short.go new file mode 100644 index 00000000000..00060ba081c --- /dev/null +++ b/src/circl/group/short.go @@ -0,0 +1,335 @@ +package group + +import ( + "crypto" + "crypto/elliptic" + _ "crypto/sha256" // to link libraries + _ "crypto/sha512" // to link libraries + "crypto/subtle" + "fmt" + "io" + "math/big" +) + +type wG struct { + elliptic.Curve +} + +func (g wG) String() string { return g.Params().Name } +func (g wG) NewElement() Element { return g.Identity() } +func (g wG) NewScalar() Scalar { return &wScl{g, nil} } +func (g wG) Identity() Element { return &wElt{g, new(big.Int), new(big.Int)} } +func (g wG) Generator() Element { return &wElt{g, g.Params().Gx, g.Params().Gy} } +func (g wG) Order() Scalar { s := &wScl{g, nil}; s.fromBig(g.Params().N); return s } +func (g wG) RandomElement(rd io.Reader) Element { + b := make([]byte, (g.Params().BitSize+7)/8) + _, _ = io.ReadFull(rd, b) + return g.HashToElement(b, nil) +} +func (g wG) RandomScalar(rd io.Reader) Scalar { + b := make([]byte, (g.Params().BitSize+7)/8) + _, _ = io.ReadFull(rd, b) + return g.HashToScalar(b, nil) +} +func (g wG) getHasher(dst []byte) wHash { + var Z, C2 big.Int + var h crypto.Hash + var L uint + switch g.Params().BitSize { + case 256: + Z.SetInt64(-10) + C2.SetString("0x78bc71a02d89ec07214623f6d0f955072c7cc05604a5a6e23ffbf67115fa5301", 0) + h = crypto.SHA256 + L = 48 + case 384: + Z.SetInt64(-12) + C2.SetString("0x19877cc1041b7555743c0ae2e3a3e61fb2aaa2e0e87ea557a563d8b598a0940d0a697a9e0b9e92cfaa314f583c9d066", 0) + h = crypto.SHA512 + L = 72 + case 521: + Z.SetInt64(-4) + C2.SetInt64(8) + h = crypto.SHA512 + L = 98 + default: + panic("curve not supported") + } + return wHash{ + sswu3mod4{g, &Z, &C2}, + NewExpanderMD(h, g.Params().P, L, dst), + NewExpanderMD(h, g.Params().N, L, dst), + } +} +func (g wG) cvtElt(e Element) *wElt { + ee, ok := e.(*wElt) + if !ok || g.Params().BitSize != ee.Params().BitSize { + panic(ErrType) + } + return ee +} +func (g wG) cvtScl(s Scalar) *wScl { + ss, ok := s.(*wScl) + if !ok || g.Params().BitSize != ss.Params().BitSize { + panic(ErrType) + } + return ss +} + +type wElt struct { + wG + x, y *big.Int +} + +func (e *wElt) String() string { return fmt.Sprintf("x: 0x%v\ny: 0x%v", e.x.Text(16), e.y.Text(16)) } +func (e *wElt) IsIdentity() bool { return e.x.Sign() == 0 && e.y.Sign() == 0 } +func (e *wElt) IsEqual(o Element) bool { + oo := e.cvtElt(o) + return e.x.Cmp(oo.x) == 0 && e.y.Cmp(oo.y) == 0 +} +func (e *wElt) Add(a, b Element) Element { + aa, bb := e.cvtElt(a), e.cvtElt(b) + e.x, e.y = e.Curve.Add(aa.x, aa.y, bb.x, bb.y) + return e +} +func (e *wElt) Dbl(a Element) Element { + aa := e.cvtElt(a) + e.x, e.y = e.Curve.Double(aa.x, aa.y) + return e +} +func (e *wElt) Neg(a Element) Element { + aa := e.cvtElt(a) + e.x.Set(aa.x) + e.y.Neg(aa.y) + return e +} +func (e *wElt) Mul(a Element, s Scalar) Element { + aa, ss := e.cvtElt(a), e.cvtScl(s) + e.x, e.y = e.ScalarMult(aa.x, aa.y, ss.k) + return e +} +func (e *wElt) MulGen(s Scalar) Element { + ss := e.cvtScl(s) + e.x, e.y = e.ScalarBaseMult(ss.k) + return e +} +func (e *wElt) MarshalBinary() ([]byte, error) { + if e.IsIdentity() { + return []byte{0x0}, nil + } + return elliptic.Marshal(e.wG, e.x, e.y), nil +} +func (e *wElt) MarshalBinaryCompress() ([]byte, error) { + if e.IsIdentity() { + return []byte{0x0}, nil + } + l := (e.Params().BitSize + 7) / 8 + data := make([]byte, 1+l) + bytes := e.x.Bytes() + copy(data[1+l-len(bytes):], bytes) + data[0] = 0x02 | byte(e.y.Bit(0)) + return data, nil +} +func (e *wElt) UnmarshalBinary(b []byte) error { + byteLen := (e.Params().BitSize + 7) / 8 + l := len(b) + switch { + case l == 1 && b[0] == 0x00: // point at infinity + e.x.SetInt64(0) + e.y.SetInt64(0) + case l == 1+byteLen && (b[0] == 0x02 || b[0] == 0x03): // compressed + p := e.wG.Params().P + x := new(big.Int).SetBytes(b[1:]) + y := new(big.Int) + y.Mul(x, x) // x^2 + y.Mul(y, x) // x^3 + y.Sub(y, x) // x^3-x + y.Sub(y, x) // x^3-2x + y.Sub(y, x) // x^3-3x + y.Add(y, e.wG.Params().B) // x^3-3x+b + y.Mod(y, p) // + qr := y.ModSqrt(y, p) // sqrt(x^3-3x+b) + if qr == nil { + return ErrUnmarshal + } + if byte(y.Bit(0)) != (b[0] & 1) { + y.Neg(y).Mod(y, p) + } + e.x, e.y = x, y + case l == 1+2*byteLen && b[0] == 0x04: // uncompressed + x, y := elliptic.Unmarshal(e.wG, b) + if x == nil { + return ErrUnmarshal + } + e.x, e.y = x, y + default: + return ErrUnmarshal + } + return nil +} + +type wScl struct { + wG + k []byte +} + +func (s *wScl) String() string { return fmt.Sprintf("0x%x", s.k) } +func (s *wScl) IsEqual(a Scalar) bool { + aa := s.cvtScl(a) + return subtle.ConstantTimeCompare(s.k, aa.k) == 1 +} +func (s *wScl) fromBig(b *big.Int) { + _ = s.UnmarshalBinary(b.Bytes()) +} +func (s *wScl) Add(a, b Scalar) Scalar { + aa, bb := s.cvtScl(a), s.cvtScl(b) + r := new(big.Int) + r.SetBytes(aa.k).Add(r, new(big.Int).SetBytes(bb.k)).Mod(r, s.Params().N) + s.fromBig(r) + return s +} +func (s *wScl) Sub(a, b Scalar) Scalar { + aa, bb := s.cvtScl(a), s.cvtScl(b) + r := new(big.Int) + r.SetBytes(aa.k).Sub(r, new(big.Int).SetBytes(bb.k)).Mod(r, s.Params().N) + s.fromBig(r) + return s +} +func (s *wScl) Mul(a, b Scalar) Scalar { + aa, bb := s.cvtScl(a), s.cvtScl(b) + r := new(big.Int) + r.SetBytes(aa.k).Mul(r, new(big.Int).SetBytes(bb.k)).Mod(r, s.Params().N) + s.fromBig(r) + return s +} +func (s *wScl) Neg(a Scalar) Scalar { + aa := s.cvtScl(a) + r := new(big.Int) + r.SetBytes(aa.k).Neg(r).Mod(r, s.Params().N) + s.fromBig(r) + return s +} +func (s *wScl) Inv(a Scalar) Scalar { + aa := s.cvtScl(a) + r := new(big.Int) + r.SetBytes(aa.k).ModInverse(r, s.Params().N) + s.fromBig(r) + return s +} +func (s *wScl) MarshalBinary() (data []byte, err error) { + data = make([]byte, (s.Params().BitSize+7)/8) + copy(data, s.k) + return data, nil +} +func (s *wScl) UnmarshalBinary(b []byte) error { + l := (s.Params().BitSize + 7) / 8 + s.k = make([]byte, l) + copy(s.k[l-len(b):l], b) + return nil +} + +type wHash struct { + sswu3mod4 + elt FieldHasher + scl FieldHasher +} + +func (g wG) HashToElement(b, dst []byte) Element { + var u [2]big.Int + h := g.getHasher(dst) + h.elt.HashToField(u[:], b) + Q0 := h.Map(&u[0]) + Q1 := h.Map(&u[1]) + return Q0.Add(Q0, Q1) +} + +func (g wG) HashToScalar(b, dst []byte) Scalar { + var u [1]big.Int + h := g.getHasher(dst) + h.scl.HashToField(u[:], b) + s := g.NewScalar().(*wScl) + s.fromBig(&u[0]) + return s +} + +type sswu3mod4 struct { + wG + Z *big.Int + C2 *big.Int // c2 = sqrt(-Z^3) +} + +func (s sswu3mod4) Map(u *big.Int) Element { + tv1 := new(big.Int) + tv2 := new(big.Int) + tv3 := new(big.Int) + tv4 := new(big.Int) + xn := new(big.Int) + xd := new(big.Int) + x1n := new(big.Int) + x2n := new(big.Int) + gx1 := new(big.Int) + gxd := new(big.Int) + y1 := new(big.Int) + y2 := new(big.Int) + x := new(big.Int) + y := new(big.Int) + + A := big.NewInt(-3) + B := s.Params().B + p := s.Params().P + c1 := new(big.Int) + c1.Sub(p, big.NewInt(3)).Rsh(c1, 2) // 1. c1 = (q - 3) / 4 + + add := func(c, a, b *big.Int) { c.Add(a, b).Mod(c, p) } + mul := func(c, a, b *big.Int) { c.Mul(a, b).Mod(c, p) } + sqr := func(c, a *big.Int) { c.Mul(a, a).Mod(c, p) } + exp := func(c, a, b *big.Int) { c.Exp(a, b, p) } + sgn := func(a *big.Int) uint { a.Mod(a, p); return a.Bit(0) } + cmv := func(c, a, b *big.Int, k bool) { + if k { + c.Set(b) + } else { + c.Set(a) + } + } + + sqr(tv1, u) // 1. tv1 = u^2 + mul(tv3, s.Z, tv1) // 2. tv3 = Z * tv1 + sqr(tv2, tv3) // 3. tv2 = tv3^2 + add(xd, tv2, tv3) // 4. xd = tv2 + tv3 + add(x1n, xd, big.NewInt(1)) // 5. x1n = xd + 1 + mul(x1n, x1n, B) // 6. x1n = x1n * B + tv4.Neg(A) // + mul(xd, tv4, xd) // 7. xd = -A * xd + e1 := xd.Sign() == 0 // 8. e1 = xd == 0 + mul(tv4, s.Z, A) // + cmv(xd, xd, tv4, e1) // 9. xd = CMOV(xd, Z * A, e1) + sqr(tv2, xd) // 10. tv2 = xd^2 + mul(gxd, tv2, xd) // 11. gxd = tv2 * xd + mul(tv2, A, tv2) // 12. tv2 = A * tv2 + sqr(gx1, x1n) // 13. gx1 = x1n^2 + add(gx1, gx1, tv2) // 14. gx1 = gx1 + tv2 + mul(gx1, gx1, x1n) // 15. gx1 = gx1 * x1n + mul(tv2, B, gxd) // 16. tv2 = B * gxd + add(gx1, gx1, tv2) // 17. gx1 = gx1 + tv2 + sqr(tv4, gxd) // 18. tv4 = gxd^2 + mul(tv2, gx1, gxd) // 19. tv2 = gx1 * gxd + mul(tv4, tv4, tv2) // 20. tv4 = tv4 * tv2 + exp(y1, tv4, c1) // 21. y1 = tv4^c1 + mul(y1, y1, tv2) // 22. y1 = y1 * tv2 + mul(x2n, tv3, x1n) // 23. x2n = tv3 * x1n + mul(y2, y1, s.C2) // 24. y2 = y1 * c2 + mul(y2, y2, tv1) // 25. y2 = y2 * tv1 + mul(y2, y2, u) // 26. y2 = y2 * u + sqr(tv2, y1) // 27. tv2 = y1^2 + mul(tv2, tv2, gxd) // 28. tv2 = tv2 * gxd + e2 := tv2.Cmp(gx1) == 0 // 29. e2 = tv2 == gx1 + cmv(xn, x2n, x1n, e2) // 30. xn = CMOV(x2n, x1n, e2) + cmv(y, y2, y1, e2) // 31. y = CMOV(y2, y1, e2) + e3 := sgn(u) == sgn(y) // 32. e3 = sgn0(u) == sgn0(y) + tv1.Neg(y) // + cmv(y, tv1, y, e3) // 33. y = CMOV(-y, y, e3) + tv1.ModInverse(xd, p) // + mul(x, xn, tv1) // 34. return (xn, xd, y, 1) + y.Mod(y, p) + return &wElt{s.wG, x, y} +} diff --git a/src/circl/hpke/aead.go b/src/circl/hpke/aead.go new file mode 100644 index 00000000000..72264c44cce --- /dev/null +++ b/src/circl/hpke/aead.go @@ -0,0 +1,98 @@ +package hpke + +import ( + "crypto/cipher" + "fmt" +) + +type encdecContext struct { + // Serialized parameters + suite Suite + exporterSecret []byte + key []byte + baseNonce []byte + sequenceNumber []byte + + // Operational parameters + cipher.AEAD + nonce []byte +} + +type sealContext struct{ *encdecContext } +type openContext struct{ *encdecContext } + +// Export takes a context string exporterContext and a desired length (in +// bytes), and produces a secret derived from the internal exporter secret +// using the corresponding KDF Expand function. It panics if length is +// greater than 255*N bytes, where N is the size (in bytes) of the KDF's +// output. +func (c *encdecContext) Export(exporterContext []byte, length uint) []byte { + maxLength := uint(255 * c.suite.kdfID.ExtractSize()) + if length > maxLength { + panic(fmt.Errorf("output length must be lesser than %v bytes", maxLength)) + } + return c.suite.labeledExpand(c.exporterSecret, []byte("sec"), + exporterContext, uint16(length)) +} + +func (c *encdecContext) Suite() Suite { + return c.suite +} + +func (c *encdecContext) calcNonce() []byte { + for i := range c.baseNonce { + c.nonce[i] = c.baseNonce[i] ^ c.sequenceNumber[i] + } + return c.nonce +} + +func (c *encdecContext) increment() error { + // tests whether the sequence number is all-ones, which prevents an + // overflow after the increment. + allOnes := byte(0xFF) + for i := range c.sequenceNumber { + allOnes &= c.sequenceNumber[i] + } + if allOnes == byte(0xFF) { + return errAEADSeqOverflows + } + + // performs an increment by 1 and verifies whether the sequence overflows. + carry := uint(1) + for i := len(c.sequenceNumber) - 1; i >= 0; i-- { + sum := uint(c.sequenceNumber[i]) + carry + carry = sum >> 8 + c.sequenceNumber[i] = byte(sum & 0xFF) + } + if carry != 0 { + return errAEADSeqOverflows + } + return nil +} + +func (c *sealContext) Seal(pt, aad []byte) ([]byte, error) { + ct := c.AEAD.Seal(nil, c.calcNonce(), pt, aad) + err := c.increment() + if err != nil { + for i := range ct { + ct[i] = 0 + } + return nil, err + } + return ct, nil +} + +func (c *openContext) Open(ct, aad []byte) ([]byte, error) { + pt, err := c.AEAD.Open(nil, c.calcNonce(), ct, aad) + if err != nil { + return nil, err + } + err = c.increment() + if err != nil { + for i := range pt { + pt[i] = 0 + } + return nil, err + } + return pt, nil +} diff --git a/src/circl/hpke/aead_test.go b/src/circl/hpke/aead_test.go new file mode 100644 index 00000000000..3fe1bfa4c5f --- /dev/null +++ b/src/circl/hpke/aead_test.go @@ -0,0 +1,182 @@ +package hpke + +import ( + "bytes" + "crypto/rand" + "fmt" + "testing" + + "circl/internal/test" +) + +func TestAeadExporter(t *testing.T) { + suite := Suite{kdfID: KDF_HKDF_SHA256, aeadID: AEAD_AES128GCM} + exporter := &encdecContext{suite: suite} + maxLength := uint(255 * suite.kdfID.ExtractSize()) + + err := test.CheckPanic(func() { + exporter.Export([]byte("exporter"), maxLength+1) + }) + test.CheckNoErr(t, err, "exporter max size") +} + +func setupAeadTest() (*sealContext, *openContext, error) { + suite := Suite{aeadID: AEAD_AES128GCM} + key := make([]byte, suite.aeadID.KeySize()) + if n, err := rand.Read(key); err != nil { + return nil, nil, err + } else if n != len(key) { + return nil, nil, fmt.Errorf("unexpected key size: got %d; want %d", n, len(key)) + } + + aead, err := suite.aeadID.New(key) + if err != nil { + return nil, nil, err + } + + Nn := aead.NonceSize() + baseNonce := make([]byte, Nn) + if n, err := rand.Read(baseNonce); err != nil { + return nil, nil, err + } else if n != len(baseNonce) { + return nil, nil, fmt.Errorf("unexpected base nonce size: got %d; want %d", n, len(baseNonce)) + } + + sealer := &sealContext{&encdecContext{ + suite, nil, nil, baseNonce, make([]byte, Nn), aead, make([]byte, Nn)}, + } + opener := &openContext{&encdecContext{ + suite, nil, nil, baseNonce, make([]byte, Nn), aead, make([]byte, Nn)}, + } + return sealer, opener, nil +} + +func TestAeadNonceUpdate(t *testing.T) { + sealer, opener, err := setupAeadTest() + test.CheckNoErr(t, err, "setup failed") + + pt := []byte("plaintext") + aad := []byte("aad") + + numAttempts := 2 + var prevCt []byte + for i := 0; i < numAttempts; i++ { + ct, err := sealer.Seal(pt, aad) + if err != nil { + t.Fatalf("encryption failed: %s", err) + } + + if prevCt != nil && bytes.Equal(ct, prevCt) { + t.Error("ciphertext matches the previous (nonce not updated)") + } + + _, err = opener.Open(ct, aad) + if err != nil { + t.Errorf("decryption failed: %s", err) + } + + prevCt = ct + } +} + +func TestOpenPhaseMismatch(t *testing.T) { + sealer, opener, err := setupAeadTest() + test.CheckNoErr(t, err, "setup failed") + + pt := []byte("plaintext") + aad := []byte("aad") + + ct, err := sealer.Seal(pt, aad) + if err != nil { + t.Fatalf("encryption failed: %s", err) + } + + recovered, err := opener.Open(ct, aad) + if err != nil { + t.Fatalf("decryption failed: %s", err) + } + + if !bytes.Equal(pt, recovered) { + t.Fatal("Plaintext mismatch") + } + + _, err = opener.Open(ct, aad) + if err == nil { + t.Fatal("decryption succeeded when it should have failed") + } +} + +func TestSealPhaseMismatch(t *testing.T) { + sealer, opener, err := setupAeadTest() + test.CheckNoErr(t, err, "setup failed") + + pt := []byte("plaintext") + aad := []byte("aad") + + _, err = sealer.Seal(pt, aad) + if err != nil { + t.Fatalf("encryption failed: %s", err) + } + + ct, err := sealer.Seal(pt, aad) + if err != nil { + t.Fatalf("encryption failed: %s", err) + } + + _, err = opener.Open(ct, aad) + if err == nil { + t.Fatal("decryption succeeded when it should have failed") + } +} + +func TestAeadSeqOverflow(t *testing.T) { + sealer, opener, err := setupAeadTest() + test.CheckNoErr(t, err, "setup failed") + + Nn := len(sealer.baseNonce) + pt := []byte("plaintext") + aad := []byte("aad") + + // Sets sequence number to 256 before its max value = 0xFF...FF. + for i := 0; i < Nn; i++ { + sealer.sequenceNumber[i] = 0xFF + opener.sequenceNumber[i] = 0xFF + } + sealer.sequenceNumber[Nn-1] = 0x00 + opener.sequenceNumber[Nn-1] = 0x00 + + numAttempts := 260 + wantCorrect := 2 * 255 + wantIncorrect := 2*numAttempts - wantCorrect + gotCorrect := 0 + gotIncorrect := 0 + + for i := 0; i < numAttempts; i++ { + ct, err := sealer.Seal(pt, aad) + switch true { + case ct != nil && err == nil: + gotCorrect++ + case ct == nil && err != nil: + gotIncorrect++ + default: + t.FailNow() + } + + pt2, err := opener.Open(ct, aad) + switch true { + case pt2 != nil && err == nil: + gotCorrect++ + case pt2 == nil && err != nil: + gotIncorrect++ + default: + t.FailNow() + } + } + + if gotCorrect != wantCorrect { + test.ReportError(t, gotCorrect, wantCorrect) + } + if gotIncorrect != wantIncorrect { + test.ReportError(t, gotIncorrect, wantIncorrect) + } +} diff --git a/src/circl/hpke/algs.go b/src/circl/hpke/algs.go new file mode 100644 index 00000000000..1e106ede781 --- /dev/null +++ b/src/circl/hpke/algs.go @@ -0,0 +1,263 @@ +package hpke + +import ( + "crypto" + "crypto/aes" + "crypto/cipher" + "crypto/elliptic" + "fmt" + "hash" + "io" + + "circl/dh/x25519" + "circl/dh/x448" + "circl/ecc/p384" + "circl/kem" + "golang.org/x/crypto/chacha20poly1305" + "golang.org/x/crypto/hkdf" +) + +type KEM uint16 + +//nolint:golint,stylecheck +const ( + // KEM_P256_HKDF_SHA256 is a KEM using P256 curve and HKDF with SHA-256. + KEM_P256_HKDF_SHA256 KEM = 0x10 + // KEM_P384_HKDF_SHA384 is a KEM using P384 curve and HKDF with SHA-384. + KEM_P384_HKDF_SHA384 KEM = 0x11 + // KEM_P521_HKDF_SHA512 is a KEM using P521 curve and HKDF with SHA-512. + KEM_P521_HKDF_SHA512 KEM = 0x12 + // KEM_X25519_HKDF_SHA256 is a KEM using X25519 Diffie-Hellman function + // and HKDF with SHA-256. + KEM_X25519_HKDF_SHA256 KEM = 0x20 + // KEM_X448_HKDF_SHA512 is a KEM using X448 Diffie-Hellman function and + // HKDF with SHA-512. + KEM_X448_HKDF_SHA512 KEM = 0x21 +) + +// IsValid returns true if the KEM identifier is supported by the HPKE package. +func (k KEM) IsValid() bool { + switch k { + case KEM_P256_HKDF_SHA256, + KEM_P384_HKDF_SHA384, + KEM_P521_HKDF_SHA512, + KEM_X25519_HKDF_SHA256, + KEM_X448_HKDF_SHA512: + return true + default: + return false + } +} + +// Scheme returns an instance of a KEM that supports authentication. Panics if +// the KEM identifier is invalid. +func (k KEM) Scheme() kem.AuthScheme { + switch k { + case KEM_P256_HKDF_SHA256: + return dhkemp256hkdfsha256 + case KEM_P384_HKDF_SHA384: + return dhkemp384hkdfsha384 + case KEM_P521_HKDF_SHA512: + return dhkemp521hkdfsha512 + case KEM_X25519_HKDF_SHA256: + return dhkemx25519hkdfsha256 + case KEM_X448_HKDF_SHA512: + return dhkemx448hkdfsha512 + default: + panic(errInvalidKEM) + } +} + +func (k KEM) validatePublicKey(pk kem.PublicKey) bool { + switch k { + case KEM_P256_HKDF_SHA256, KEM_P384_HKDF_SHA384, KEM_P521_HKDF_SHA512: + pub, ok := pk.(*shortKEMPubKey) + return ok && k == pub.scheme.id && pub.Validate() + case KEM_X25519_HKDF_SHA256, KEM_X448_HKDF_SHA512: + pub, ok := pk.(*xKEMPubKey) + return ok && k == pub.scheme.id && pub.Validate() + default: + panic(errInvalidKEM) + } +} + +func (k KEM) validatePrivateKey(sk kem.PrivateKey) bool { + switch k { + case KEM_P256_HKDF_SHA256, KEM_P384_HKDF_SHA384, KEM_P521_HKDF_SHA512: + priv, ok := sk.(*shortKEMPrivKey) + return ok && k == priv.scheme.id && priv.Validate() + case KEM_X25519_HKDF_SHA256, KEM_X448_HKDF_SHA512: + priv, ok := sk.(*xKEMPrivKey) + return ok && k == priv.scheme.id && priv.Validate() + default: + panic(errInvalidKEM) + } +} + +type KDF uint16 + +//nolint:golint,stylecheck +const ( + // KDF_HKDF_SHA256 is a KDF using HKDF with SHA-256. + KDF_HKDF_SHA256 KDF = 0x01 + // KDF_HKDF_SHA384 is a KDF using HKDF with SHA-384. + KDF_HKDF_SHA384 KDF = 0x02 + // KDF_HKDF_SHA512 is a KDF using HKDF with SHA-512. + KDF_HKDF_SHA512 KDF = 0x03 +) + +func (k KDF) IsValid() bool { + switch k { + case KDF_HKDF_SHA256, + KDF_HKDF_SHA384, + KDF_HKDF_SHA512: + return true + default: + return false + } +} + +// ExtractSize returns the size (in bytes) of the pseudorandom key produced +// by KDF.Extract. +func (k KDF) ExtractSize() int { + switch k { + case KDF_HKDF_SHA256: + return crypto.SHA256.Size() + case KDF_HKDF_SHA384: + return crypto.SHA384.Size() + case KDF_HKDF_SHA512: + return crypto.SHA512.Size() + default: + panic(errInvalidKDF) + } +} + +// Extract derives a pseudorandom key from a high-entropy, secret input and a +// salt. The size of the output is determined by KDF.ExtractSize. +func (k KDF) Extract(secret, salt []byte) (pseudorandomKey []byte) { + return hkdf.Extract(k.hash(), secret, salt) +} + +// Expand derives a variable length pseudorandom string from a pseudorandom key +// and an information string. Panics if the pseudorandom key is less +// than N bytes, or if the output length is greater than 255*N bytes, +// where N is the size returned by KDF.Extract function. +func (k KDF) Expand(pseudorandomKey, info []byte, outputLen uint) []byte { + extractSize := k.ExtractSize() + if len(pseudorandomKey) < extractSize { + panic(fmt.Errorf("pseudorandom key must be %v bytes", extractSize)) + } + maxLength := uint(255 * extractSize) + if outputLen > maxLength { + panic(fmt.Errorf("output length must be less than %v bytes", maxLength)) + } + output := make([]byte, outputLen) + rd := hkdf.Expand(k.hash(), pseudorandomKey[:extractSize], info) + _, err := io.ReadFull(rd, output) + if err != nil { + panic(err) + } + return output +} + +func (k KDF) hash() func() hash.Hash { + switch k { + case KDF_HKDF_SHA256: + return crypto.SHA256.New + case KDF_HKDF_SHA384: + return crypto.SHA384.New + case KDF_HKDF_SHA512: + return crypto.SHA512.New + default: + panic(errInvalidKDF) + } +} + +type AEAD uint16 + +//nolint:golint,stylecheck +const ( + // AEAD_AES128GCM is AES-128 block cipher in Galois Counter Mode (GCM). + AEAD_AES128GCM AEAD = 0x01 + // AEAD_AES256GCM is AES-256 block cipher in Galois Counter Mode (GCM). + AEAD_AES256GCM AEAD = 0x02 + // AEAD_ChaCha20Poly1305 is ChaCha20 stream cipher and Poly1305 MAC. + AEAD_ChaCha20Poly1305 AEAD = 0x03 +) + +// New instantiates an AEAD cipher from the identifier, returns an error if the +// identifier is not known. +func (a AEAD) New(key []byte) (cipher.AEAD, error) { + switch a { + case AEAD_AES128GCM, AEAD_AES256GCM: + block, err := aes.NewCipher(key) + if err != nil { + return nil, err + } + return cipher.NewGCM(block) + case AEAD_ChaCha20Poly1305: + return chacha20poly1305.New(key) + default: + panic(errInvalidAEAD) + } +} + +func (a AEAD) IsValid() bool { + switch a { + case AEAD_AES128GCM, + AEAD_AES256GCM, + AEAD_ChaCha20Poly1305: + return true + default: + return false + } +} + +// KeySize returns the size in bytes of the keys used by AEAD cipher. +func (a AEAD) KeySize() uint { + switch a { + case AEAD_AES128GCM: + return 16 + case AEAD_AES256GCM: + return 32 + case AEAD_ChaCha20Poly1305: + return chacha20poly1305.KeySize + default: + panic(errInvalidAEAD) + } +} + +var dhkemp256hkdfsha256, dhkemp384hkdfsha384, dhkemp521hkdfsha512 shortKEM +var dhkemx25519hkdfsha256, dhkemx448hkdfsha512 xKEM + +func init() { + dhkemp256hkdfsha256.Curve = elliptic.P256() + dhkemp256hkdfsha256.kemBase.id = KEM_P256_HKDF_SHA256 + dhkemp256hkdfsha256.kemBase.name = "HPKE_KEM_P256_HKDF_SHA256" + dhkemp256hkdfsha256.kemBase.Hash = crypto.SHA256 + dhkemp256hkdfsha256.kemBase.dhKEM = dhkemp256hkdfsha256 + + dhkemp384hkdfsha384.Curve = p384.P384() + dhkemp384hkdfsha384.kemBase.id = KEM_P384_HKDF_SHA384 + dhkemp384hkdfsha384.kemBase.name = "HPKE_KEM_P384_HKDF_SHA384" + dhkemp384hkdfsha384.kemBase.Hash = crypto.SHA384 + dhkemp384hkdfsha384.kemBase.dhKEM = dhkemp384hkdfsha384 + + dhkemp521hkdfsha512.Curve = elliptic.P521() + dhkemp521hkdfsha512.kemBase.id = KEM_P521_HKDF_SHA512 + dhkemp521hkdfsha512.kemBase.name = "HPKE_KEM_P521_HKDF_SHA512" + dhkemp521hkdfsha512.kemBase.Hash = crypto.SHA512 + dhkemp521hkdfsha512.kemBase.dhKEM = dhkemp521hkdfsha512 + + dhkemx25519hkdfsha256.size = x25519.Size + dhkemx25519hkdfsha256.kemBase.id = KEM_X25519_HKDF_SHA256 + dhkemx25519hkdfsha256.kemBase.name = "HPKE_KEM_X25519_HKDF_SHA256" + dhkemx25519hkdfsha256.kemBase.Hash = crypto.SHA256 + dhkemx25519hkdfsha256.kemBase.dhKEM = dhkemx25519hkdfsha256 + + dhkemx448hkdfsha512.size = x448.Size + dhkemx448hkdfsha512.kemBase.id = KEM_X448_HKDF_SHA512 + dhkemx448hkdfsha512.kemBase.name = "HPKE_KEM_X448_HKDF_SHA512" + dhkemx448hkdfsha512.kemBase.Hash = crypto.SHA512 + dhkemx448hkdfsha512.kemBase.dhKEM = dhkemx448hkdfsha512 +} diff --git a/src/circl/hpke/hpke.go b/src/circl/hpke/hpke.go new file mode 100644 index 00000000000..8c347156f7f --- /dev/null +++ b/src/circl/hpke/hpke.go @@ -0,0 +1,294 @@ +// Package hpke implements the Hybrid Public Key Encryption (HPKE) standard +// specified by draft-irtf-cfrg-hpke-07. +// +// HPKE works for any combination of a public-key encapsulation mechanism +// (KEM), a key derivation function (KDF), and an authenticated encryption +// scheme with additional data (AEAD). +// +// Specification in +// https://datatracker.ietf.org/doc/draft-irtf-cfrg-hpke +// +// BUG(cjpatton): This package does not implement the "Export-Only" mode of the +// HPKE context. In particular, it does not recognize the AEAD codepoint +// reserved for this purpose (0xFFFF). +package hpke + +import ( + "crypto/rand" + "encoding" + "errors" + "io" + + "circl/kem" +) + +const versionLabel = "HPKE-v1" + +// Context defines the capabilities of an HPKE context. +type Context interface { + encoding.BinaryMarshaler + // Export takes a context string exporterContext and a desired length (in + // bytes), and produces a secret derived from the internal exporter secret + // using the corresponding KDF Expand function. It panics if length is + // greater than 255*N bytes, where N is the size (in bytes) of the KDF's + // output. + Export(exporterContext []byte, length uint) []byte + // Suite returns the cipher suite corresponding to this context. + Suite() Suite +} + +// Sealer encrypts a plaintext using an AEAD encryption. +type Sealer interface { + Context + // Seal takes a plaintext and associated data to produce a ciphertext. + // The nonce is handled by the Sealer and incremented after each call. + Seal(pt, aad []byte) (ct []byte, err error) +} + +// Opener decrypts a ciphertext using an AEAD encryption. +type Opener interface { + Context + // Open takes a ciphertext and associated data to recover, if successful, + // the plaintext. The nonce is handled by the Opener and incremented after + // each call. + Open(ct, aad []byte) (pt []byte, err error) +} + +// modeID represents an HPKE variant. +type modeID = uint8 + +const ( + // modeBase to enable encryption to the holder of a given KEM private key. + modeBase modeID = 0x00 + // modePSK extends the base mode by allowing the Receiver to authenticate + // that the sender possessed a given pre-shared key (PSK). + modePSK modeID = 0x01 + // modeAuth extends the base mode by allowing the Receiver to authenticate + // that the sender possessed a given KEM private key. + modeAuth modeID = 0x02 + // modeAuthPSK provides a combination of the PSK and Auth modes. + modeAuthPSK modeID = 0x03 +) + +// Suite is an HPKE cipher suite consisting of a KEM, KDF, and AEAD algorithm. +type Suite struct { + kemID KEM + kdfID KDF + aeadID AEAD +} + +// NewSuite builds a Suite from a specified set of algorithms. Panics +// if an algorithm identifier is not valid. +func NewSuite(kemID KEM, kdfID KDF, aeadID AEAD) Suite { + s := Suite{kemID, kdfID, aeadID} + if !s.isValid() { + panic(errInvalidHPKESuite) + } + return s +} + +type state struct { + Suite + modeID modeID + skS kem.PrivateKey + pkS kem.PublicKey + psk []byte + pskID []byte + info []byte +} + +// Sender performs hybrid public-key encryption. +type Sender struct { + state + pkR kem.PublicKey +} + +// NewSender creates a Sender with knowledge of the receiver's public-key. +func (suite Suite) NewSender(pkR kem.PublicKey, info []byte) (*Sender, error) { + if !suite.kemID.validatePublicKey(pkR) { + return nil, errInvalidKEMPublicKey + } + + return &Sender{ + state: state{Suite: suite, info: info}, + pkR: pkR, + }, nil +} + +// Setup generates a new HPKE context used for Base Mode encryption. +// Returns the Sealer and corresponding encapsulated key. +func (s *Sender) Setup(rnd io.Reader) (enc []byte, seal Sealer, err error) { + s.modeID = modeBase + return s.allSetup(rnd) +} + +// SetupAuth generates a new HPKE context used for Auth Mode encryption. +// Returns the Sealer and corresponding encapsulated key. +func (s *Sender) SetupAuth(rnd io.Reader, skS kem.PrivateKey) ( + enc []byte, seal Sealer, err error, +) { + if !s.kemID.validatePrivateKey(skS) { + return nil, nil, errInvalidKEMPrivateKey + } + + s.modeID = modeAuth + s.state.skS = skS + return s.allSetup(rnd) +} + +// SetupPSK generates a new HPKE context used for PSK Mode encryption. +// Returns the Sealer and corresponding encapsulated key. +func (s *Sender) SetupPSK(rnd io.Reader, psk, pskID []byte) ( + enc []byte, seal Sealer, err error, +) { + s.modeID = modePSK + s.state.psk = psk + s.state.pskID = pskID + return s.allSetup(rnd) +} + +// SetupAuthPSK generates a new HPKE context used for Auth-PSK Mode encryption. +// Returns the Sealer and corresponding encapsulated key. +func (s *Sender) SetupAuthPSK(rnd io.Reader, skS kem.PrivateKey, psk, pskID []byte) ( + enc []byte, seal Sealer, err error, +) { + if !s.kemID.validatePrivateKey(skS) { + return nil, nil, errInvalidKEMPrivateKey + } + + s.modeID = modeAuthPSK + s.state.skS = skS + s.state.psk = psk + s.state.pskID = pskID + return s.allSetup(rnd) +} + +// Receiver performs hybrid public-key decryption. +type Receiver struct { + state + skR kem.PrivateKey + enc []byte +} + +// NewReceiver creates a Receiver with knowledge of a private key. +func (suite Suite) NewReceiver(skR kem.PrivateKey, info []byte) ( + *Receiver, error, +) { + if !suite.kemID.validatePrivateKey(skR) { + return nil, errInvalidKEMPrivateKey + } + + return &Receiver{state: state{Suite: suite, info: info}, skR: skR}, nil +} + +// Setup generates a new HPKE context used for Base Mode encryption. +// Setup takes an encapsulated key and returns an Opener. +func (r *Receiver) Setup(enc []byte) (Opener, error) { + r.modeID = modeBase + r.enc = enc + return r.allSetup() +} + +// SetupAuth generates a new HPKE context used for Auth Mode encryption. +// SetupAuth takes an encapsulated key and a public key, and returns an Opener. +func (r *Receiver) SetupAuth(enc []byte, pkS kem.PublicKey) (Opener, error) { + if !r.kemID.validatePublicKey(pkS) { + return nil, errInvalidKEMPublicKey + } + + r.modeID = modeAuth + r.enc = enc + r.state.pkS = pkS + return r.allSetup() +} + +// SetupPSK generates a new HPKE context used for PSK Mode encryption. +// SetupPSK takes an encapsulated key, and a pre-shared key; and returns an +// Opener. +func (r *Receiver) SetupPSK(enc, psk, pskID []byte) (Opener, error) { + r.modeID = modePSK + r.enc = enc + r.state.psk = psk + r.state.pskID = pskID + return r.allSetup() +} + +// SetupAuthPSK generates a new HPKE context used for Auth-PSK Mode encryption. +// SetupAuthPSK takes an encapsulated key, a public key, and a pre-shared key; +// and returns an Opener. +func (r *Receiver) SetupAuthPSK(enc, psk, pskID []byte, pkS kem.PublicKey) ( + Opener, error) { + if !r.kemID.validatePublicKey(pkS) { + return nil, errInvalidKEMPublicKey + } + + r.modeID = modeAuthPSK + r.enc = enc + r.state.psk = psk + r.state.pskID = pskID + r.state.pkS = pkS + return r.allSetup() +} + +func (s *Sender) allSetup(rnd io.Reader) ([]byte, Sealer, error) { + scheme := s.kemID.Scheme() + + if rnd == nil { + rnd = rand.Reader + } + seed := make([]byte, scheme.SeedSize()) + _, err := io.ReadFull(rnd, seed) + if err != nil { + return nil, nil, err + } + + var enc, ss []byte + switch s.modeID { + case modeBase, modePSK: + enc, ss, err = scheme.EncapsulateDeterministically(s.pkR, seed) + case modeAuth, modeAuthPSK: + enc, ss, err = scheme.AuthEncapsulateDeterministically(s.pkR, s.skS, seed) + } + if err != nil { + return nil, nil, err + } + + ctx, err := s.keySchedule(ss, s.info, s.psk, s.pskID) + if err != nil { + return nil, nil, err + } + + return enc, &sealContext{ctx}, nil +} + +func (r *Receiver) allSetup() (Opener, error) { + var err error + var ss []byte + scheme := r.kemID.Scheme() + switch r.modeID { + case modeBase, modePSK: + ss, err = scheme.Decapsulate(r.skR, r.enc) + case modeAuth, modeAuthPSK: + ss, err = scheme.AuthDecapsulate(r.skR, r.enc, r.pkS) + } + if err != nil { + return nil, err + } + + ctx, err := r.keySchedule(ss, r.info, r.psk, r.pskID) + if err != nil { + return nil, err + } + return &openContext{ctx}, nil +} + +var ( + errInvalidHPKESuite = errors.New("hpke: invalid HPKE suite") + errInvalidKDF = errors.New("hpke: invalid KDF identifier") + errInvalidKEM = errors.New("hpke: invalid KEM identifier") + errInvalidAEAD = errors.New("hpke: invalid AEAD identifier") + errInvalidKEMPublicKey = errors.New("hpke: invalid KEM public key") + errInvalidKEMPrivateKey = errors.New("hpke: invalid KEM private key") + errInvalidKEMSharedSecret = errors.New("hpke: invalid KEM shared secret") + errAEADSeqOverflows = errors.New("hpke: AEAD sequence number overflows") +) diff --git a/src/circl/hpke/hpke_test.go b/src/circl/hpke/hpke_test.go new file mode 100644 index 00000000000..7723588d510 --- /dev/null +++ b/src/circl/hpke/hpke_test.go @@ -0,0 +1,63 @@ +package hpke_test + +import ( + "bytes" + "crypto/rand" + "fmt" + + "circl/hpke" +) + +func Example() { + // import "circl/hpke" + // import "crypto/rand" + + // HPKE suite is a domain parameter. + kemID := hpke.KEM_P384_HKDF_SHA384 + kdfID := hpke.KDF_HKDF_SHA384 + aeadID := hpke.AEAD_AES256GCM + suite := hpke.NewSuite(kemID, kdfID, aeadID) + info := []byte("public info string, known to both Alice and Bob") + + // Bob prepares to receive messages and announces his public key. + publicBob, privateBob, err := kemID.Scheme().GenerateKeyPair() + if err != nil { + panic(err) + } + Bob, err := suite.NewReceiver(privateBob, info) + if err != nil { + panic(err) + } + + // Alice gets Bob's public key. + Alice, err := suite.NewSender(publicBob, info) + if err != nil { + panic(err) + } + enc, sealer, err := Alice.Setup(rand.Reader) + if err != nil { + panic(err) + } + + // Alice encrypts some plaintext and sends the ciphertext to Bob. + ptAlice := []byte("text encrypted to Bob's public key") + aad := []byte("additional public data") + ct, err := sealer.Seal(ptAlice, aad) + if err != nil { + panic(err) + } + + // Bob decrypts the ciphertext. + opener, err := Bob.Setup(enc) + if err != nil { + panic(err) + } + ptBob, err := opener.Open(ct, aad) + if err != nil { + panic(err) + } + + // Plaintext was sent successfully. + fmt.Println(bytes.Equal(ptAlice, ptBob)) + // Output: true +} diff --git a/src/circl/hpke/kembase.go b/src/circl/hpke/kembase.go new file mode 100644 index 00000000000..7dc4c629e26 --- /dev/null +++ b/src/circl/hpke/kembase.go @@ -0,0 +1,238 @@ +package hpke + +import ( + "crypto" + "crypto/rand" + _ "crypto/sha256" // linking sha256 packages. + _ "crypto/sha512" // linking sha512 packages. + "encoding/binary" + "io" + + "circl/kem" + "golang.org/x/crypto/hkdf" +) + +type dhKEM interface { + sizeDH() int + calcDH(dh []byte, sk kem.PrivateKey, pk kem.PublicKey) error + SeedSize() int + DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) + UnmarshalBinaryPrivateKey(data []byte) (kem.PrivateKey, error) + UnmarshalBinaryPublicKey(data []byte) (kem.PublicKey, error) +} + +type kemBase struct { + id KEM + name string + crypto.Hash + dhKEM +} + +func (k kemBase) Name() string { return k.name } +func (k kemBase) SharedKeySize() int { return k.Hash.Size() } + +func (k kemBase) getSuiteID() (sid [5]byte) { + sid[0], sid[1], sid[2] = 'K', 'E', 'M' + binary.BigEndian.PutUint16(sid[3:5], uint16(k.id)) + return +} + +func (k kemBase) extractExpand(dh, kemCtx []byte) []byte { + eaePkr := k.labeledExtract(nil, []byte("eae_prk"), dh) + return k.labeledExpand( + eaePkr, + []byte("shared_secret"), + kemCtx, + uint16(k.Size()), + ) +} + +func (k kemBase) labeledExtract(salt, label, info []byte) []byte { + suiteID := k.getSuiteID() + labeledIKM := append(append(append(append( + make([]byte, 0, len(versionLabel)+len(suiteID)+len(label)+len(info)), + versionLabel...), + suiteID[:]...), + label...), + info...) + return hkdf.Extract(k.New, labeledIKM, salt) +} + +func (k kemBase) labeledExpand(prk, label, info []byte, l uint16) []byte { + suiteID := k.getSuiteID() + labeledInfo := make( + []byte, + 2, + 2+len(versionLabel)+len(suiteID)+len(label)+len(info), + ) + binary.BigEndian.PutUint16(labeledInfo[0:2], l) + labeledInfo = append(append(append(append(labeledInfo, + versionLabel...), + suiteID[:]...), + label...), + info...) + b := make([]byte, l) + rd := hkdf.Expand(k.New, prk, labeledInfo) + if _, err := io.ReadFull(rd, b); err != nil { + panic(err) + } + return b +} + +func (k kemBase) AuthEncapsulate(pkr kem.PublicKey, sks kem.PrivateKey) ( + ct []byte, ss []byte, err error, +) { + seed := make([]byte, k.SeedSize()) + _, err = io.ReadFull(rand.Reader, seed) + if err != nil { + return nil, nil, err + } + + return k.authEncap(pkr, sks, seed) +} + +func (k kemBase) Encapsulate(pkr kem.PublicKey) ( + ct []byte, ss []byte, err error, +) { + seed := make([]byte, k.SeedSize()) + _, err = io.ReadFull(rand.Reader, seed) + if err != nil { + return nil, nil, err + } + + return k.encap(pkr, seed) +} + +func (k kemBase) AuthEncapsulateDeterministically( + pkr kem.PublicKey, sks kem.PrivateKey, seed []byte, +) (ct, ss []byte, err error) { + return k.authEncap(pkr, sks, seed) +} + +func (k kemBase) EncapsulateDeterministically(pkr kem.PublicKey, seed []byte) ( + ct, ss []byte, err error) { + return k.encap(pkr, seed) +} + +func (k kemBase) encap( + pkR kem.PublicKey, + seed []byte, +) (ct []byte, ss []byte, err error) { + dh := make([]byte, k.sizeDH()) + enc, kemCtx, err := k.coreEncap(dh, pkR, seed) + if err != nil { + return nil, nil, err + } + ss = k.extractExpand(dh, kemCtx) + return enc, ss, nil +} + +func (k kemBase) authEncap( + pkR kem.PublicKey, + skS kem.PrivateKey, + seed []byte, +) (ct []byte, ss []byte, err error) { + dhLen := k.sizeDH() + dh := make([]byte, 2*dhLen) + enc, kemCtx, err := k.coreEncap(dh[:dhLen], pkR, seed) + if err != nil { + return nil, nil, err + } + + err = k.calcDH(dh[dhLen:], skS, pkR) + if err != nil { + return nil, nil, err + } + + pkS := skS.Public() + pkSm, err := pkS.MarshalBinary() + if err != nil { + return nil, nil, err + } + kemCtx = append(kemCtx, pkSm...) + + ss = k.extractExpand(dh, kemCtx) + return enc, ss, nil +} + +func (k kemBase) coreEncap( + dh []byte, + pkR kem.PublicKey, + seed []byte, +) (enc []byte, kemCtx []byte, err error) { + pkE, skE := k.DeriveKeyPair(seed) + err = k.calcDH(dh, skE, pkR) + if err != nil { + return nil, nil, err + } + + enc, err = pkE.MarshalBinary() + if err != nil { + return nil, nil, err + } + pkRm, err := pkR.MarshalBinary() + if err != nil { + return nil, nil, err + } + kemCtx = append(append([]byte{}, enc...), pkRm...) + + return enc, kemCtx, nil +} + +func (k kemBase) Decapsulate(skr kem.PrivateKey, ct []byte) ([]byte, error) { + dh := make([]byte, k.sizeDH()) + kemCtx, err := k.coreDecap(dh, skr, ct) + if err != nil { + return nil, err + } + return k.extractExpand(dh, kemCtx), nil +} + +func (k kemBase) AuthDecapsulate( + skR kem.PrivateKey, + ct []byte, + pkS kem.PublicKey, +) ([]byte, error) { + dhLen := k.sizeDH() + dh := make([]byte, 2*dhLen) + kemCtx, err := k.coreDecap(dh[:dhLen], skR, ct) + if err != nil { + return nil, err + } + + err = k.calcDH(dh[dhLen:], skR, pkS) + if err != nil { + return nil, err + } + + pkSm, err := pkS.MarshalBinary() + if err != nil { + return nil, err + } + kemCtx = append(kemCtx, pkSm...) + return k.extractExpand(dh, kemCtx), nil +} + +func (k kemBase) coreDecap( + dh []byte, + skR kem.PrivateKey, + ct []byte, +) ([]byte, error) { + pkE, err := k.UnmarshalBinaryPublicKey(ct) + if err != nil { + return nil, err + } + + err = k.calcDH(dh, skR, pkE) + if err != nil { + return nil, err + } + + pkR := skR.Public() + pkRm, err := pkR.MarshalBinary() + if err != nil { + return nil, err + } + + return append(append([]byte{}, ct...), pkRm...), nil +} diff --git a/src/circl/hpke/marshal.go b/src/circl/hpke/marshal.go new file mode 100644 index 00000000000..c6e851ad601 --- /dev/null +++ b/src/circl/hpke/marshal.go @@ -0,0 +1,151 @@ +package hpke + +import ( + "errors" + + "golang.org/x/crypto/cryptobyte" +) + +// marshal serializes an HPKE context. +func (c *encdecContext) marshal() ([]byte, error) { + var b cryptobyte.Builder + b.AddUint16(uint16(c.suite.kemID)) + b.AddUint16(uint16(c.suite.kdfID)) + b.AddUint16(uint16(c.suite.aeadID)) + b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(c.exporterSecret) + }) + b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(c.key) + }) + b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(c.baseNonce) + }) + b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(c.sequenceNumber) + }) + return b.Bytes() +} + +// unmarshalContext parses an HPKE context. +func unmarshalContext(raw []byte) (*encdecContext, error) { + var ( + err error + t cryptobyte.String + ) + + c := new(encdecContext) + s := cryptobyte.String(raw) + if !s.ReadUint16((*uint16)(&c.suite.kemID)) || + !s.ReadUint16((*uint16)(&c.suite.kdfID)) || + !s.ReadUint16((*uint16)(&c.suite.aeadID)) || + !s.ReadUint8LengthPrefixed(&t) || + !t.ReadBytes(&c.exporterSecret, len(t)) || + !s.ReadUint8LengthPrefixed(&t) || + !t.ReadBytes(&c.key, len(t)) || + !s.ReadUint8LengthPrefixed(&t) || + !t.ReadBytes(&c.baseNonce, len(t)) || + !s.ReadUint8LengthPrefixed(&t) || + !t.ReadBytes(&c.sequenceNumber, len(t)) { + return nil, errors.New("failed to parse context") + } + + if !c.suite.isValid() { + return nil, errInvalidHPKESuite + } + + Nh := c.suite.kdfID.ExtractSize() + if len(c.exporterSecret) != Nh { + return nil, errors.New("invalid exporter secret length") + } + + Nk := int(c.suite.aeadID.KeySize()) + if len(c.key) != Nk { + return nil, errors.New("invalid key length") + } + + c.AEAD, err = c.suite.aeadID.New(c.key) + if err != nil { + return nil, err + } + + Nn := c.AEAD.NonceSize() + if len(c.baseNonce) != Nn { + return nil, errors.New("invalid base nonce length") + } + if len(c.sequenceNumber) != Nn { + return nil, errors.New("invalid sequence number length") + } + c.nonce = make([]byte, Nn) + + return c, nil +} + +// MarshalBinary serializes an HPKE sealer according to the format specified +// below. (Expressed in TLS syntax.) Note that this format is not defined by +// the HPKE standard. +// +// enum { sealer(0), opener(1) } HpkeRole; +// +// struct { +// HpkeKemId kem_id; // draft-irtf-cfrg-hpke-07 +// HpkeKdfId kdf_id; // draft-irtf-cfrg-hpke-07 +// HpkeAeadId aead_id; // draft-irtf-cfrg-hpke-07 +// opaque exporter_secret<0..255>; +// opaque key<0..255>; +// opaque base_nonce<0..255>; +// opaque seq<0..255>; +// } HpkeContext; +// +// struct { +// HpkeRole role = 0; // sealer +// HpkeContext context; +// } HpkeSealer; +func (c *sealContext) MarshalBinary() ([]byte, error) { + rawContext, err := c.encdecContext.marshal() + if err != nil { + return nil, err + } + return append([]byte{0}, rawContext...), nil +} + +// UnmarshalSealer parses an HPKE sealer. +func UnmarshalSealer(raw []byte) (Sealer, error) { + if raw[0] != 0 { + return nil, errors.New("incorrect role") + } + context, err := unmarshalContext(raw[1:]) + if err != nil { + return nil, err + } + return &sealContext{context}, nil +} + +// MarshalBinary serializes an HPKE opener according to the format specified +// below. (Expressed in TLS syntax.) Note that this format is not defined by the +// HPKE standard. +// +// struct { +// HpkeRole role = 1; // opener +// HpkeContext context; +// } HpkeOpener; +func (c *openContext) MarshalBinary() ([]byte, error) { + rawContext, err := c.encdecContext.marshal() + if err != nil { + return nil, err + } + return append([]byte{1}, rawContext...), nil +} + +// UnmarshalOpener parses a serialized HPKE opener and returns the corresponding +// Opener. +func UnmarshalOpener(raw []byte) (Opener, error) { + if raw[0] != 1 { + return nil, errors.New("incorrect role") + } + context, err := unmarshalContext(raw[1:]) + if err != nil { + return nil, err + } + return &openContext{context}, nil +} diff --git a/src/circl/hpke/marshal_test.go b/src/circl/hpke/marshal_test.go new file mode 100644 index 00000000000..a11f6b83e30 --- /dev/null +++ b/src/circl/hpke/marshal_test.go @@ -0,0 +1,84 @@ +package hpke + +import ( + "bytes" + "crypto/rand" + "testing" +) + +func contextEqual(a, b *encdecContext) bool { + an := make([]byte, a.NonceSize()) + bn := make([]byte, b.NonceSize()) + ac := a.AEAD.Seal(nil, an, nil, nil) + bc := b.AEAD.Seal(nil, bn, nil, nil) + return a.suite == b.suite && + bytes.Equal(a.exporterSecret, b.exporterSecret) && + bytes.Equal(a.key, b.key) && + bytes.Equal(a.baseNonce, b.baseNonce) && + bytes.Equal(a.sequenceNumber, b.sequenceNumber) && + bytes.Equal(ac, bc) && + len(a.nonce) == len(b.nonce) && + len(a.nonce) == len(a.baseNonce) +} + +func TestContextSerialization(t *testing.T) { + s := NewSuite(KEM_P384_HKDF_SHA384, KDF_HKDF_SHA384, AEAD_AES256GCM) + info := []byte("some info string") + + pk, sk, err := s.kemID.Scheme().GenerateKeyPair() + if err != nil { + t.Fatal(err) + } + receiver, err := s.NewReceiver(sk, info) + if err != nil { + t.Fatal(err) + } + sender, err := s.NewSender(pk, info) + if err != nil { + t.Fatal(err) + } + enc, sealer, err := sender.Setup(rand.Reader) + if err != nil { + t.Fatal(err) + } + opener, err := receiver.Setup(enc) + if err != nil { + t.Fatal(err) + } + + rawSealer, err := sealer.MarshalBinary() + if err != nil { + t.Fatal(err) + } + parsedSealer, err := UnmarshalSealer(rawSealer) + if err != nil { + t.Fatal(err) + } + if !contextEqual( + sealer.(*sealContext).encdecContext, + parsedSealer.(*sealContext).encdecContext) { + t.Error("parsed sealer does not match original") + } + _, err = UnmarshalOpener(rawSealer) + if err == nil { + t.Error("parsing a sealer as an opener succeeded; want failure") + } + + rawOpener, err := opener.MarshalBinary() + if err != nil { + t.Fatal(err) + } + parsedOpener, err := UnmarshalOpener(rawOpener) + if err != nil { + t.Fatal(err) + } + if !contextEqual( + opener.(*openContext).encdecContext, + parsedOpener.(*openContext).encdecContext) { + t.Error("parsed opener does not match original") + } + _, err = UnmarshalSealer(rawOpener) + if err == nil { + t.Error("parsing an opener as a sealer succeeded; want failure") + } +} diff --git a/src/circl/hpke/shortkem.go b/src/circl/hpke/shortkem.go new file mode 100644 index 00000000000..b29135dedf1 --- /dev/null +++ b/src/circl/hpke/shortkem.go @@ -0,0 +1,158 @@ +package hpke + +import ( + "crypto/elliptic" + "crypto/rand" + _ "crypto/sha256" // linking sha256 packages. + _ "crypto/sha512" // linking sha512 packages. + "crypto/subtle" + "fmt" + "math/big" + + "circl/kem" +) + +type shortKEM struct { + kemBase + elliptic.Curve +} + +func (s shortKEM) PrivateKeySize() int { return s.byteSize() } +func (s shortKEM) SeedSize() int { return s.byteSize() } +func (s shortKEM) CiphertextSize() int { return 1 + 2*s.byteSize() } +func (s shortKEM) PublicKeySize() int { return 1 + 2*s.byteSize() } +func (s shortKEM) EncapsulationSeedSize() int { return s.byteSize() } + +func (s shortKEM) byteSize() int { return (s.Params().BitSize + 7) / 8 } + +func (s shortKEM) sizeDH() int { return s.byteSize() } +func (s shortKEM) calcDH(dh []byte, sk kem.PrivateKey, pk kem.PublicKey) error { + PK := pk.(*shortKEMPubKey) + SK := sk.(*shortKEMPrivKey) + l := len(dh) + x, _ := s.ScalarMult(PK.x, PK.y, SK.priv) // only x-coordinate is used. + if x.Sign() == 0 { + return errInvalidKEMSharedSecret + } + b := x.Bytes() + copy(dh[l-len(b):l], b) + return nil +} + +// Deterministicallly derives a keypair from a seed. If you're unsure, +// you're better off using GenerateKey(). +// +// Panics if seed is not of length SeedSize(). +func (s shortKEM) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + // Implementation based on + // https://www.ietf.org/archive/id/draft-irtf-cfrg-hpke-07.html#name-derivekeypair + if len(seed) != s.SeedSize() { + panic(kem.ErrSeedSize) + } + + var bitmask = byte(0xFF) + if s.Params().BitSize == 521 { + bitmask = 0x01 + } + + dkpPrk := s.labeledExtract(nil, []byte("dkp_prk"), seed) + var bytes []byte + ctr := 0 + for skBig := new(big.Int); skBig.Sign() == 0 || skBig.Cmp(s.Params().N) >= 0; ctr++ { + if ctr > 255 { + panic("derive key error") + } + bytes = s.labeledExpand( + dkpPrk, + []byte("candidate"), + []byte{byte(ctr)}, + uint16(s.byteSize()), + ) + bytes[0] &= bitmask + skBig.SetBytes(bytes) + } + l := s.PrivateKeySize() + sk := &shortKEMPrivKey{s, make([]byte, l), nil} + copy(sk.priv[l-len(bytes):], bytes) + return sk.Public(), sk +} +func (s shortKEM) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + sk, x, y, err := elliptic.GenerateKey(s, rand.Reader) + pub := &shortKEMPubKey{s, x, y} + return pub, &shortKEMPrivKey{s, sk, pub}, err +} + +func (s shortKEM) UnmarshalBinaryPrivateKey(data []byte) ( + kem.PrivateKey, error) { + l := s.PrivateKeySize() + if len(data) < l { + return nil, errInvalidKEMPrivateKey + } + sk := &shortKEMPrivKey{s, make([]byte, l), nil} + copy(sk.priv[l-len(data):l], data[:l]) + return sk, nil +} +func (s shortKEM) UnmarshalBinaryPublicKey(data []byte) (kem.PublicKey, error) { + x, y := elliptic.Unmarshal(s, data) + if x == nil { + return nil, errInvalidKEMPublicKey + } + return &shortKEMPubKey{s, x, y}, nil +} + +type shortKEMPubKey struct { + scheme shortKEM + x, y *big.Int +} + +func (k *shortKEMPubKey) String() string { + return fmt.Sprintf("x: %v\ny: %v", k.x.Text(16), k.y.Text(16)) +} +func (k *shortKEMPubKey) Scheme() kem.Scheme { return k.scheme } +func (k *shortKEMPubKey) MarshalBinary() ([]byte, error) { + return elliptic.Marshal(k.scheme, k.x, k.y), nil +} +func (k *shortKEMPubKey) Equal(pk kem.PublicKey) bool { + k1, ok := pk.(*shortKEMPubKey) + return ok && + k.scheme.Params().Name == k1.scheme.Params().Name && + k.x.Cmp(k1.x) == 0 && + k.y.Cmp(k1.y) == 0 +} +func (k *shortKEMPubKey) Validate() bool { + p := k.scheme.Params().P + notAtInfinity := k.x.Sign() > 0 && k.y.Sign() > 0 + lessThanP := k.x.Cmp(p) < 0 && k.y.Cmp(p) < 0 + onCurve := k.scheme.IsOnCurve(k.x, k.y) + return notAtInfinity && lessThanP && onCurve +} + +type shortKEMPrivKey struct { + scheme shortKEM + priv []byte + pub *shortKEMPubKey +} + +func (k *shortKEMPrivKey) String() string { return fmt.Sprintf("%x", k.priv) } +func (k *shortKEMPrivKey) Scheme() kem.Scheme { return k.scheme } +func (k *shortKEMPrivKey) MarshalBinary() ([]byte, error) { + return append(make([]byte, 0, k.scheme.PrivateKeySize()), k.priv...), nil +} +func (k *shortKEMPrivKey) Equal(pk kem.PrivateKey) bool { + k1, ok := pk.(*shortKEMPrivKey) + return ok && + k.scheme.Params().Name == k1.scheme.Params().Name && + subtle.ConstantTimeCompare(k.priv, k1.priv) == 1 +} +func (k *shortKEMPrivKey) Public() kem.PublicKey { + if k.pub == nil { + x, y := k.scheme.ScalarBaseMult(k.priv) + k.pub = &shortKEMPubKey{k.scheme, x, y} + } + return k.pub +} +func (k *shortKEMPrivKey) Validate() bool { + n := new(big.Int).SetBytes(k.priv) + order := k.scheme.Curve.Params().N + return len(k.priv) == k.scheme.PrivateKeySize() && n.Cmp(order) < 0 +} diff --git a/src/circl/hpke/testdata/vectors_v08_779d028.json b/src/circl/hpke/testdata/vectors_v08_779d028.json new file mode 100644 index 00000000000..450dca4f560 --- /dev/null +++ b/src/circl/hpke/testdata/vectors_v08_779d028.json @@ -0,0 +1 @@ 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\ No newline at end of file diff --git a/src/circl/hpke/util.go b/src/circl/hpke/util.go new file mode 100644 index 00000000000..53290aedc4f --- /dev/null +++ b/src/circl/hpke/util.go @@ -0,0 +1,118 @@ +package hpke + +import ( + "encoding/binary" + "errors" + "fmt" +) + +func (st state) keySchedule(ss, info, psk, pskID []byte) (*encdecContext, error) { + if err := st.verifyPSKInputs(psk, pskID); err != nil { + return nil, err + } + + pskIDHash := st.labeledExtract(nil, []byte("psk_id_hash"), pskID) + infoHash := st.labeledExtract(nil, []byte("info_hash"), info) + keySchCtx := append(append( + []byte{st.modeID}, + pskIDHash...), + infoHash...) + + secret := st.labeledExtract(ss, []byte("secret"), psk) + + Nk := uint16(st.aeadID.KeySize()) + key := st.labeledExpand(secret, []byte("key"), keySchCtx, Nk) + + aead, err := st.aeadID.New(key) + if err != nil { + return nil, err + } + + Nn := uint16(aead.NonceSize()) + baseNonce := st.labeledExpand(secret, []byte("base_nonce"), keySchCtx, Nn) + exporterSecret := st.labeledExpand( + secret, + []byte("exp"), + keySchCtx, + uint16(st.kdfID.ExtractSize()), + ) + + return &encdecContext{ + st.Suite, + exporterSecret, + key, + baseNonce, + make([]byte, Nn), + aead, + make([]byte, Nn), + }, nil +} + +func (st state) verifyPSKInputs(psk, pskID []byte) error { + gotPSK := psk != nil + gotPSKID := pskID != nil + if gotPSK != gotPSKID { + return errors.New("inconsistent PSK inputs") + } + switch st.modeID { + case modeBase | modeAuth: + if gotPSK { + return errors.New("PSK input provided when not needed") + } + case modePSK | modeAuthPSK: + if !gotPSK { + return errors.New("missing required PSK input") + } + } + return nil +} + +// Params returns the codepoints for the algorithms comprising the suite. +func (suite Suite) Params() (KEM, KDF, AEAD) { + return suite.kemID, suite.kdfID, suite.aeadID +} + +func (suite Suite) String() string { + return fmt.Sprintf( + "kem_id: %v kdf_id: %v aead_id: %v", + suite.kemID, suite.kdfID, suite.aeadID, + ) +} + +func (suite Suite) getSuiteID() (id [10]byte) { + id[0], id[1], id[2], id[3] = 'H', 'P', 'K', 'E' + binary.BigEndian.PutUint16(id[4:6], uint16(suite.kemID)) + binary.BigEndian.PutUint16(id[6:8], uint16(suite.kdfID)) + binary.BigEndian.PutUint16(id[8:10], uint16(suite.aeadID)) + return +} + +func (suite Suite) isValid() bool { + return suite.kemID.IsValid() && + suite.kdfID.IsValid() && + suite.aeadID.IsValid() +} + +func (suite Suite) labeledExtract(salt, label, ikm []byte) []byte { + suiteID := suite.getSuiteID() + labeledIKM := append(append(append(append( + make([]byte, 0, len(versionLabel)+len(suiteID)+len(label)+len(ikm)), + versionLabel...), + suiteID[:]...), + label...), + ikm...) + return suite.kdfID.Extract(labeledIKM, salt) +} + +func (suite Suite) labeledExpand(prk, label, info []byte, l uint16) []byte { + suiteID := suite.getSuiteID() + labeledInfo := make([]byte, + 2, 2+len(versionLabel)+len(suiteID)+len(label)+len(info)) + binary.BigEndian.PutUint16(labeledInfo[0:2], l) + labeledInfo = append(append(append(append(labeledInfo, + versionLabel...), + suiteID[:]...), + label...), + info...) + return suite.kdfID.Expand(prk, labeledInfo, uint(l)) +} diff --git a/src/circl/hpke/vectors_test.go b/src/circl/hpke/vectors_test.go new file mode 100644 index 00000000000..b1240b7c056 --- /dev/null +++ b/src/circl/hpke/vectors_test.go @@ -0,0 +1,235 @@ +package hpke + +import ( + "bytes" + "encoding/hex" + "encoding/json" + "fmt" + "io/ioutil" + "os" + "testing" + + "circl/internal/test" + "circl/kem" +) + +func TestVectors(t *testing.T) { + // Test vectors from + // https://github.com/cfrg/draft-irtf-cfrg-hpke/blob/master/test-vectors.json + vectors := readFile(t, "testdata/vectors_v08_779d028.json") + for i, v := range vectors { + t.Run(fmt.Sprintf("v%v", i), v.verify) + } +} + +func (v *vector) verify(t *testing.T) { + m := v.ModeID + kem, kdf, aead := KEM(v.KemID), KDF(v.KdfID), AEAD(v.AeadID) + if !kem.IsValid() { + t.Skipf("Skipping test with unknown KEM: %x", kem) + } + if !kdf.IsValid() { + t.Skipf("Skipping test with unknown KDF: %x", kdf) + } + if !aead.IsValid() { + t.Skipf("Skipping test with unknown AEAD: %x", aead) + } + s := NewSuite(kem, kdf, aead) + + sender, recv := v.getActors(t, kem.Scheme(), s) + sealer, opener := v.setup(t, kem.Scheme(), sender, recv, m, s) + + v.checkAead(t, (sealer.(*sealContext)).encdecContext, m) + v.checkAead(t, (opener.(*openContext)).encdecContext, m) + v.checkEncryptions(t, sealer, opener, m) + v.checkExports(t, sealer, m) + v.checkExports(t, opener, m) +} + +func (v *vector) getActors(t *testing.T, dhkem kem.Scheme, s Suite) ( + *Sender, *Receiver) { + h := s.String() + "\n" + + pkR, err := dhkem.UnmarshalBinaryPublicKey(hexB(t, v.PkRm)) + test.CheckNoErr(t, err, h+"bad public key") + + skR, err := dhkem.UnmarshalBinaryPrivateKey(hexB(t, v.SkRm)) + test.CheckNoErr(t, err, h+"bad private key") + + info := hexB(t, v.Info) + sender, err := s.NewSender(pkR, info) + test.CheckNoErr(t, err, h+"err sender") + + recv, err := s.NewReceiver(skR, info) + test.CheckNoErr(t, err, h+"err receiver") + + return sender, recv +} + +func (v *vector) setup(t *testing.T, k kem.Scheme, + se *Sender, re *Receiver, + m modeID, s Suite, +) (sealer Sealer, opener Opener) { + seed := hexB(t, v.IkmE) + rd := bytes.NewReader(seed) + + var enc []byte + var skS kem.PrivateKey + var pkS kem.PublicKey + var errS, errR, errPK, errSK error + + switch v.ModeID { + case modeBase: + enc, sealer, errS = se.Setup(rd) + if errS == nil { + opener, errR = re.Setup(enc) + } + + case modePSK: + psk, pskid := hexB(t, v.Psk), hexB(t, v.PskID) + enc, sealer, errS = se.SetupPSK(rd, psk, pskid) + if errS == nil { + opener, errR = re.SetupPSK(enc, psk, pskid) + } + + case modeAuth: + skS, errSK = k.UnmarshalBinaryPrivateKey(hexB(t, v.SkSm)) + if errSK == nil { + pkS, errPK = k.UnmarshalBinaryPublicKey(hexB(t, v.PkSm)) + if errPK == nil { + enc, sealer, errS = se.SetupAuth(rd, skS) + if errS == nil { + opener, errR = re.SetupAuth(enc, pkS) + } + } + } + + case modeAuthPSK: + psk, pskid := hexB(t, v.Psk), hexB(t, v.PskID) + skS, errSK = k.UnmarshalBinaryPrivateKey(hexB(t, v.SkSm)) + if errSK == nil { + pkS, errPK = k.UnmarshalBinaryPublicKey(hexB(t, v.PkSm)) + if errPK == nil { + enc, sealer, errS = se.SetupAuthPSK(rd, skS, psk, pskid) + if errS == nil { + opener, errR = re.SetupAuthPSK(enc, psk, pskid, pkS) + } + } + } + } + + h := fmt.Sprintf("mode: %v %v\n", m, s) + test.CheckNoErr(t, errS, h+"error on sender setup") + test.CheckNoErr(t, errR, h+"error on receiver setup") + test.CheckNoErr(t, errSK, h+"bad private key") + test.CheckNoErr(t, errPK, h+"bad public key") + + return sealer, opener +} + +func (v *vector) checkAead(t *testing.T, e *encdecContext, m modeID) { + got := e.baseNonce + want := hexB(t, v.BaseNonce) + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, m, e.Suite()) + } + + got = e.exporterSecret + want = hexB(t, v.ExporterSecret) + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, m, e.Suite()) + } +} + +func (v *vector) checkEncryptions( + t *testing.T, + se Sealer, + op Opener, + m modeID, +) { + for j, encv := range v.Encryptions { + pt := hexB(t, encv.Plaintext) + aad := hexB(t, encv.Aad) + + ct, err := se.Seal(pt, aad) + test.CheckNoErr(t, err, "error on sealing") + + got, err := op.Open(ct, aad) + test.CheckNoErr(t, err, "error on opening") + + want := pt + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, m, se.Suite(), j) + } + } +} + +func (v *vector) checkExports(t *testing.T, context Context, m modeID) { + for j, expv := range v.Exports { + ctx := hexB(t, expv.ExportContext) + want := hexB(t, expv.ExportValue) + + got := context.Export(ctx, uint(expv.ExportLength)) + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, m, context.Suite(), j) + } + } +} + +func hexB(t *testing.T, x string) []byte { + t.Helper() + z, err := hex.DecodeString(x) + test.CheckNoErr(t, err, "") + return z +} + +func readFile(t *testing.T, fileName string) []vector { + jsonFile, err := os.Open(fileName) + if err != nil { + t.Fatalf("File %v can not be opened. Error: %v", fileName, err) + } + defer jsonFile.Close() + input, _ := ioutil.ReadAll(jsonFile) + var vectors []vector + err = json.Unmarshal(input, &vectors) + if err != nil { + t.Fatalf("File %v can not be loaded. Error: %v", fileName, err) + } + return vectors +} + +type vector struct { + ModeID uint8 `json:"mode"` + KemID uint16 `json:"kem_id"` + KdfID uint16 `json:"kdf_id"` + AeadID uint16 `json:"aead_id"` + Info string `json:"info"` + IkmR string `json:"ikmR"` + IkmE string `json:"ikmE"` + SkRm string `json:"skRm"` + SkEm string `json:"skEm"` + SkSm string `json:"skSm"` + Psk string `json:"psk"` + PskID string `json:"psk_id"` + PkSm string `json:"pkSm"` + PkRm string `json:"pkRm"` + PkEm string `json:"pkEm"` + Enc string `json:"enc"` + SharedSecret string `json:"shared_secret"` + KeyScheduleContext string `json:"key_schedule_context"` + Secret string `json:"secret"` + Key string `json:"key"` + BaseNonce string `json:"base_nonce"` + ExporterSecret string `json:"exporter_secret"` + Encryptions []struct { + Aad string `json:"aad"` + Ciphertext string `json:"ciphertext"` + Nonce string `json:"nonce"` + Plaintext string `json:"plaintext"` + } `json:"encryptions"` + Exports []struct { + ExportContext string `json:"exportContext"` + ExportLength int `json:"exportLength"` + ExportValue string `json:"exportValue"` + } `json:"exports"` +} diff --git a/src/circl/hpke/xkem.go b/src/circl/hpke/xkem.go new file mode 100644 index 00000000000..136c2c534c2 --- /dev/null +++ b/src/circl/hpke/xkem.go @@ -0,0 +1,154 @@ +package hpke + +import ( + "bytes" + "crypto/rand" + _ "crypto/sha256" // linking sha256 packages. + _ "crypto/sha512" // linking sha512 packages. + "crypto/subtle" + "fmt" + "io" + + "circl/dh/x25519" + "circl/dh/x448" + "circl/kem" +) + +type xKEM struct { + kemBase + size int +} + +func (x xKEM) PrivateKeySize() int { return x.size } +func (x xKEM) SeedSize() int { return x.size } +func (x xKEM) CiphertextSize() int { return x.size } +func (x xKEM) PublicKeySize() int { return x.size } +func (x xKEM) EncapsulationSeedSize() int { return x.size } + +func (x xKEM) sizeDH() int { return x.size } +func (x xKEM) calcDH(dh []byte, sk kem.PrivateKey, pk kem.PublicKey) error { + PK := pk.(*xKEMPubKey) + SK := sk.(*xKEMPrivKey) + switch x.size { + case x25519.Size: + var ss, sKey, pKey x25519.Key + copy(sKey[:], SK.priv) + copy(pKey[:], PK.pub) + if !x25519.Shared(&ss, &sKey, &pKey) { + return errInvalidKEMSharedSecret + } + copy(dh, ss[:]) + case x448.Size: + var ss, sKey, pKey x448.Key + copy(sKey[:], SK.priv) + copy(pKey[:], PK.pub) + if !x448.Shared(&ss, &sKey, &pKey) { + return errInvalidKEMSharedSecret + } + copy(dh, ss[:]) + } + return nil +} + +// Deterministicallly derives a keypair from a seed. If you're unsure, +// you're better off using GenerateKey(). +// +// Panics if seed is not of length SeedSize(). +func (x xKEM) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + // Implementation based on + // https://www.ietf.org/archive/id/draft-irtf-cfrg-hpke-07.html#name-derivekeypair + if len(seed) != x.SeedSize() { + panic(kem.ErrSeedSize) + } + sk := &xKEMPrivKey{scheme: x, priv: make([]byte, x.size)} + dkpPrk := x.labeledExtract(nil, []byte("dkp_prk"), seed) + bytes := x.labeledExpand( + dkpPrk, + []byte("sk"), + nil, + uint16(x.PrivateKeySize()), + ) + copy(sk.priv, bytes) + return sk.Public(), sk +} +func (x xKEM) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + sk := &xKEMPrivKey{scheme: x, priv: make([]byte, x.PrivateKeySize())} + _, err := io.ReadFull(rand.Reader, sk.priv) + if err != nil { + return nil, nil, err + } + return sk.Public(), sk, nil +} +func (x xKEM) UnmarshalBinaryPrivateKey(data []byte) (kem.PrivateKey, error) { + l := x.PrivateKeySize() + if len(data) < l { + return nil, errInvalidKEMPrivateKey + } + sk := &xKEMPrivKey{x, make([]byte, l), nil} + copy(sk.priv, data[:l]) + return sk, nil +} +func (x xKEM) UnmarshalBinaryPublicKey(data []byte) (kem.PublicKey, error) { + l := x.PublicKeySize() + if len(data) < l { + return nil, errInvalidKEMPublicKey + } + pk := &xKEMPubKey{x, make([]byte, l)} + copy(pk.pub, data[:l]) + return pk, nil +} + +type xKEMPubKey struct { + scheme xKEM + pub []byte +} + +func (k *xKEMPubKey) String() string { return fmt.Sprintf("%x", k.pub) } +func (k *xKEMPubKey) Scheme() kem.Scheme { return k.scheme } +func (k *xKEMPubKey) MarshalBinary() ([]byte, error) { + return append(make([]byte, 0, k.scheme.PublicKeySize()), k.pub...), nil +} +func (k *xKEMPubKey) Equal(pk kem.PublicKey) bool { + k1, ok := pk.(*xKEMPubKey) + return ok && + k.scheme.id == k1.scheme.id && + bytes.Equal(k.pub, k1.pub) +} +func (k *xKEMPubKey) Validate() bool { return len(k.pub) == k.scheme.PublicKeySize() } + +type xKEMPrivKey struct { + scheme xKEM + priv []byte + pub *xKEMPubKey +} + +func (k *xKEMPrivKey) String() string { return fmt.Sprintf("%x", k.priv) } +func (k *xKEMPrivKey) Scheme() kem.Scheme { return k.scheme } +func (k *xKEMPrivKey) MarshalBinary() ([]byte, error) { + return append(make([]byte, 0, k.scheme.PrivateKeySize()), k.priv...), nil +} +func (k *xKEMPrivKey) Equal(pk kem.PrivateKey) bool { + k1, ok := pk.(*xKEMPrivKey) + return ok && + k.scheme.id == k1.scheme.id && + subtle.ConstantTimeCompare(k.priv, k1.priv) == 1 +} +func (k *xKEMPrivKey) Public() kem.PublicKey { + if k.pub == nil { + k.pub = &xKEMPubKey{scheme: k.scheme, pub: make([]byte, k.scheme.size)} + switch k.scheme.size { + case x25519.Size: + var sk, pk x25519.Key + copy(sk[:], k.priv) + x25519.KeyGen(&pk, &sk) + copy(k.pub.pub, pk[:]) + case x448.Size: + var sk, pk x448.Key + copy(sk[:], k.priv) + x448.KeyGen(&pk, &sk) + copy(k.pub.pub, pk[:]) + } + } + return k.pub +} +func (k *xKEMPrivKey) Validate() bool { return len(k.priv) == k.scheme.PrivateKeySize() } diff --git a/src/circl/internal/conv/conv.go b/src/circl/internal/conv/conv.go new file mode 100644 index 00000000000..9ee8f5e6d2e --- /dev/null +++ b/src/circl/internal/conv/conv.go @@ -0,0 +1,89 @@ +package conv + +import ( + "fmt" + "math/big" + "strings" +) + +// BytesLe2Hex returns an hexadecimal string of a number stored in a +// little-endian order slice x. +func BytesLe2Hex(x []byte) string { + b := &strings.Builder{} + b.Grow(2*len(x) + 2) + fmt.Fprint(b, "0x") + if len(x) == 0 { + fmt.Fprint(b, "00") + } + for i := len(x) - 1; i >= 0; i-- { + fmt.Fprintf(b, "%02x", x[i]) + } + return b.String() +} + +// BytesLe2BigInt converts a little-endian slice x into a big-endian +// math/big.Int. +func BytesLe2BigInt(x []byte) *big.Int { + n := len(x) + b := new(big.Int) + if len(x) > 0 { + y := make([]byte, n) + for i := 0; i < n; i++ { + y[n-1-i] = x[i] + } + b.SetBytes(y) + } + return b +} + +// BigInt2BytesLe stores a positive big.Int number x into a little-endian slice z. +// The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros). +// If x does not fit in the slice or is negative, z is not modified. +func BigInt2BytesLe(z []byte, x *big.Int) { + xLen := (x.BitLen() + 7) >> 3 + zLen := len(z) + if zLen >= xLen && x.Sign() >= 0 { + y := x.Bytes() + for i := 0; i < xLen; i++ { + z[i] = y[xLen-1-i] + } + for i := xLen; i < zLen; i++ { + z[i] = 0 + } + } +} + +// Uint64Le2BigInt converts a little-endian slice x into a big number. +func Uint64Le2BigInt(x []uint64) *big.Int { + n := len(x) + b := new(big.Int) + var bi big.Int + for i := n - 1; i >= 0; i-- { + bi.SetUint64(x[i]) + b.Lsh(b, 64) + b.Add(b, &bi) + } + return b +} + +// BigInt2Uint64Le stores a positive big.Int number x into a little-endian slice z. +// The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros). +// If x does not fit in the slice or is negative, z is not modified. +func BigInt2Uint64Le(z []uint64, x *big.Int) { + xLen := (x.BitLen() + 63) >> 6 // number of 64-bit words + zLen := len(z) + if zLen >= xLen && x.Sign() > 0 { + var y, yi big.Int + y.Set(x) + two64 := big.NewInt(1) + two64.Lsh(two64, 64).Sub(two64, big.NewInt(1)) + for i := 0; i < xLen; i++ { + yi.And(&y, two64) + z[i] = yi.Uint64() + y.Rsh(&y, 64) + } + } + for i := xLen; i < zLen; i++ { + z[i] = 0 + } +} diff --git a/src/circl/internal/nist/drbg.go b/src/circl/internal/nist/drbg.go new file mode 100644 index 00000000000..e541ec46170 --- /dev/null +++ b/src/circl/internal/nist/drbg.go @@ -0,0 +1,64 @@ +// Package nist implements helpers to generate NIST's Known Answer Tests (KATs). +package nist + +import ( + "crypto/aes" +) + +// See NIST's PQCgenKAT.c. +type DRBG struct { + key [32]byte + v [16]byte +} + +func (g *DRBG) incV() { + for j := 15; j >= 0; j-- { + if g.v[j] == 255 { + g.v[j] = 0 + } else { + g.v[j]++ + break + } + } +} + +// AES256_CTR_DRBG_Update(pd, &g.key, &g.v). +func (g *DRBG) update(pd *[48]byte) { + var buf [48]byte + b, _ := aes.NewCipher(g.key[:]) + for i := 0; i < 3; i++ { + g.incV() + b.Encrypt(buf[i*16:(i+1)*16], g.v[:]) + } + if pd != nil { + for i := 0; i < 48; i++ { + buf[i] ^= pd[i] + } + } + copy(g.key[:], buf[:32]) + copy(g.v[:], buf[32:]) +} + +// randombyte_init(seed, NULL, 256). +func NewDRBG(seed *[48]byte) (g DRBG) { + g.update(seed) + return +} + +// randombytes. +func (g *DRBG) Fill(x []byte) { + var block [16]byte + + b, _ := aes.NewCipher(g.key[:]) + for len(x) > 0 { + g.incV() + b.Encrypt(block[:], g.v[:]) + if len(x) < 16 { + copy(x[:], block[:len(x)]) + break + } + copy(x[:], block[:]) + x = x[16:] + } + g.update(nil) +} diff --git a/src/circl/internal/sha3/doc.go b/src/circl/internal/sha3/doc.go new file mode 100644 index 00000000000..c06a330ff96 --- /dev/null +++ b/src/circl/internal/sha3/doc.go @@ -0,0 +1,66 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package sha3 implements the SHA-3 fixed-output-length hash functions and +// the SHAKE variable-output-length hash functions defined by FIPS-202. +// +// Both types of hash function use the "sponge" construction and the Keccak +// permutation. For a detailed specification see http://keccak.noekeon.org/ +// +// +// Guidance +// +// If you aren't sure what function you need, use SHAKE256 with at least 64 +// bytes of output. The SHAKE instances are faster than the SHA3 instances; +// the latter have to allocate memory to conform to the hash.Hash interface. +// +// If you need a secret-key MAC (message authentication code), prepend the +// secret key to the input, hash with SHAKE256 and read at least 32 bytes of +// output. +// +// +// Security strengths +// +// The SHA3-x (x equals 224, 256, 384, or 512) functions have a security +// strength against preimage attacks of x bits. Since they only produce "x" +// bits of output, their collision-resistance is only "x/2" bits. +// +// The SHAKE-256 and -128 functions have a generic security strength of 256 and +// 128 bits against all attacks, provided that at least 2x bits of their output +// is used. Requesting more than 64 or 32 bytes of output, respectively, does +// not increase the collision-resistance of the SHAKE functions. +// +// +// The sponge construction +// +// A sponge builds a pseudo-random function from a public pseudo-random +// permutation, by applying the permutation to a state of "rate + capacity" +// bytes, but hiding "capacity" of the bytes. +// +// A sponge starts out with a zero state. To hash an input using a sponge, up +// to "rate" bytes of the input are XORed into the sponge's state. The sponge +// is then "full" and the permutation is applied to "empty" it. This process is +// repeated until all the input has been "absorbed". The input is then padded. +// The digest is "squeezed" from the sponge in the same way, except that output +// is copied out instead of input being XORed in. +// +// A sponge is parameterized by its generic security strength, which is equal +// to half its capacity; capacity + rate is equal to the permutation's width. +// Since the KeccakF-1600 permutation is 1600 bits (200 bytes) wide, this means +// that the security strength of a sponge instance is equal to (1600 - bitrate) / 2. +// +// +// Recommendations +// +// The SHAKE functions are recommended for most new uses. They can produce +// output of arbitrary length. SHAKE256, with an output length of at least +// 64 bytes, provides 256-bit security against all attacks. The Keccak team +// recommends it for most applications upgrading from SHA2-512. (NIST chose a +// much stronger, but much slower, sponge instance for SHA3-512.) +// +// The SHA-3 functions are "drop-in" replacements for the SHA-2 functions. +// They produce output of the same length, with the same security strengths +// against all attacks. This means, in particular, that SHA3-256 only has +// 128-bit collision resistance, because its output length is 32 bytes. +package sha3 diff --git a/src/circl/internal/sha3/hashes.go b/src/circl/internal/sha3/hashes.go new file mode 100644 index 00000000000..7d2365a76ed --- /dev/null +++ b/src/circl/internal/sha3/hashes.go @@ -0,0 +1,69 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// This file provides functions for creating instances of the SHA-3 +// and SHAKE hash functions, as well as utility functions for hashing +// bytes. + +// New224 creates a new SHA3-224 hash. +// Its generic security strength is 224 bits against preimage attacks, +// and 112 bits against collision attacks. +func New224() State { + return State{rate: 144, outputLen: 28, dsbyte: 0x06} +} + +// New256 creates a new SHA3-256 hash. +// Its generic security strength is 256 bits against preimage attacks, +// and 128 bits against collision attacks. +func New256() State { + return State{rate: 136, outputLen: 32, dsbyte: 0x06} +} + +// New384 creates a new SHA3-384 hash. +// Its generic security strength is 384 bits against preimage attacks, +// and 192 bits against collision attacks. +func New384() State { + return State{rate: 104, outputLen: 48, dsbyte: 0x06} +} + +// New512 creates a new SHA3-512 hash. +// Its generic security strength is 512 bits against preimage attacks, +// and 256 bits against collision attacks. +func New512() State { + return State{rate: 72, outputLen: 64, dsbyte: 0x06} +} + +// Sum224 returns the SHA3-224 digest of the data. +func Sum224(data []byte) (digest [28]byte) { + h := New224() + _, _ = h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum256 returns the SHA3-256 digest of the data. +func Sum256(data []byte) (digest [32]byte) { + h := New256() + _, _ = h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum384 returns the SHA3-384 digest of the data. +func Sum384(data []byte) (digest [48]byte) { + h := New384() + _, _ = h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum512 returns the SHA3-512 digest of the data. +func Sum512(data []byte) (digest [64]byte) { + h := New512() + _, _ = h.Write(data) + h.Sum(digest[:0]) + return +} diff --git a/src/circl/internal/sha3/keccakf.go b/src/circl/internal/sha3/keccakf.go new file mode 100644 index 00000000000..3c5d278fdee --- /dev/null +++ b/src/circl/internal/sha3/keccakf.go @@ -0,0 +1,384 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build !amd64 appengine gccgo + +package sha3 + +// KeccakF1600 applies the Keccak permutation to a 1600b-wide +// state represented as a slice of 25 uint64s. +func KeccakF1600(a *[25]uint64) { + // Implementation translated from Keccak-inplace.c + // in the keccak reference code. + var t, bc0, bc1, bc2, bc3, bc4, d0, d1, d2, d3, d4 uint64 + + for i := 0; i < 24; i += 4 { + // Combines the 5 steps in each round into 2 steps. + // Unrolls 4 rounds per loop and spreads some steps across rounds. + + // Round 1 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[6] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[12] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[18] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[24] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i] + a[6] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[16] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[22] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[3] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[10] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[1] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[7] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[19] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[20] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[11] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[23] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[4] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[5] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[2] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[8] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[14] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[15] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + // Round 2 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[16] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[7] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[23] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[14] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i+1] + a[16] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[11] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[2] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[18] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[20] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[6] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[22] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[4] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[15] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[1] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[8] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[24] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[10] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[12] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[3] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[19] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[5] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + // Round 3 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[11] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[22] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[8] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[19] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i+2] + a[11] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[1] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[12] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[23] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[15] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[16] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[2] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[24] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[5] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[6] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[3] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[14] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[20] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[7] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[18] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[4] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[10] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + // Round 4 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[1] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[2] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[3] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[4] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ RC[i+3] + a[1] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[6] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[7] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[8] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[5] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[11] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[12] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[14] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[10] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[16] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[18] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[19] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[15] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[22] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[23] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[24] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[20] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + } +} diff --git a/src/circl/internal/sha3/keccakf_amd64.go b/src/circl/internal/sha3/keccakf_amd64.go new file mode 100644 index 00000000000..107d04a8a10 --- /dev/null +++ b/src/circl/internal/sha3/keccakf_amd64.go @@ -0,0 +1,13 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build amd64,!appengine,!gccgo + +package sha3 + +// This function is implemented in keccakf_amd64.s. + +//go:noescape + +func KeccakF1600(state *[25]uint64) diff --git a/src/circl/internal/sha3/keccakf_amd64.s b/src/circl/internal/sha3/keccakf_amd64.s new file mode 100644 index 00000000000..8589363a435 --- /dev/null +++ b/src/circl/internal/sha3/keccakf_amd64.s @@ -0,0 +1,390 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build amd64,!appengine,!gccgo + +// This code was translated into a form compatible with 6a from the public +// domain sources at https://github.com/gvanas/KeccakCodePackage + +// Offsets in state +#define _ba (0*8) +#define _be (1*8) +#define _bi (2*8) +#define _bo (3*8) +#define _bu (4*8) +#define _ga (5*8) +#define _ge (6*8) +#define _gi (7*8) +#define _go (8*8) +#define _gu (9*8) +#define _ka (10*8) +#define _ke (11*8) +#define _ki (12*8) +#define _ko (13*8) +#define _ku (14*8) +#define _ma (15*8) +#define _me (16*8) +#define _mi (17*8) +#define _mo (18*8) +#define _mu (19*8) +#define _sa (20*8) +#define _se (21*8) +#define _si (22*8) +#define _so (23*8) +#define _su (24*8) + +// Temporary registers +#define rT1 AX + +// Round vars +#define rpState DI +#define rpStack SP + +#define rDa BX +#define rDe CX +#define rDi DX +#define rDo R8 +#define rDu R9 + +#define rBa R10 +#define rBe R11 +#define rBi R12 +#define rBo R13 +#define rBu R14 + +#define rCa SI +#define rCe BP +#define rCi rBi +#define rCo rBo +#define rCu R15 + +#define MOVQ_RBI_RCE MOVQ rBi, rCe +#define XORQ_RT1_RCA XORQ rT1, rCa +#define XORQ_RT1_RCE XORQ rT1, rCe +#define XORQ_RBA_RCU XORQ rBa, rCu +#define XORQ_RBE_RCU XORQ rBe, rCu +#define XORQ_RDU_RCU XORQ rDu, rCu +#define XORQ_RDA_RCA XORQ rDa, rCa +#define XORQ_RDE_RCE XORQ rDe, rCe + +#define mKeccakRound(iState, oState, rc, B_RBI_RCE, G_RT1_RCA, G_RT1_RCE, G_RBA_RCU, K_RT1_RCA, K_RT1_RCE, K_RBA_RCU, M_RT1_RCA, M_RT1_RCE, M_RBE_RCU, S_RDU_RCU, S_RDA_RCA, S_RDE_RCE) \ + /* Prepare round */ \ + MOVQ rCe, rDa; \ + ROLQ $1, rDa; \ + \ + MOVQ _bi(iState), rCi; \ + XORQ _gi(iState), rDi; \ + XORQ rCu, rDa; \ + XORQ _ki(iState), rCi; \ + XORQ _mi(iState), rDi; \ + XORQ rDi, rCi; \ + \ + MOVQ rCi, rDe; \ + ROLQ $1, rDe; \ + \ + MOVQ _bo(iState), rCo; \ + XORQ _go(iState), rDo; \ + XORQ rCa, rDe; \ + XORQ _ko(iState), rCo; \ + XORQ _mo(iState), rDo; \ + XORQ rDo, rCo; \ + \ + MOVQ rCo, rDi; \ + ROLQ $1, rDi; \ + \ + MOVQ rCu, rDo; \ + XORQ rCe, rDi; \ + ROLQ $1, rDo; \ + \ + MOVQ rCa, rDu; \ + XORQ rCi, rDo; \ + ROLQ $1, rDu; \ + \ + /* Result b */ \ + MOVQ _ba(iState), rBa; \ + MOVQ _ge(iState), rBe; \ + XORQ rCo, rDu; \ + MOVQ _ki(iState), rBi; \ + MOVQ _mo(iState), rBo; \ + MOVQ _su(iState), rBu; \ + XORQ rDe, rBe; \ + ROLQ $44, rBe; \ + XORQ rDi, rBi; \ + XORQ rDa, rBa; \ + ROLQ $43, rBi; \ + \ + MOVQ rBe, rCa; \ + MOVQ rc, rT1; \ + ORQ rBi, rCa; \ + XORQ rBa, rT1; \ + XORQ rT1, rCa; \ + MOVQ rCa, _ba(oState); \ + \ + XORQ rDu, rBu; \ + ROLQ $14, rBu; \ + MOVQ rBa, rCu; \ + ANDQ rBe, rCu; \ + XORQ rBu, rCu; \ + MOVQ rCu, _bu(oState); \ + \ + XORQ rDo, rBo; \ + ROLQ $21, rBo; \ + MOVQ rBo, rT1; \ + ANDQ rBu, rT1; \ + XORQ rBi, rT1; \ + MOVQ rT1, _bi(oState); \ + \ + NOTQ rBi; \ + ORQ rBa, rBu; \ + ORQ rBo, rBi; \ + XORQ rBo, rBu; \ + XORQ rBe, rBi; \ + MOVQ rBu, _bo(oState); \ + MOVQ rBi, _be(oState); \ + B_RBI_RCE; \ + \ + /* Result g */ \ + MOVQ _gu(iState), rBe; \ + XORQ rDu, rBe; \ + MOVQ _ka(iState), rBi; \ + ROLQ $20, rBe; \ + XORQ rDa, rBi; \ + ROLQ $3, rBi; \ + MOVQ _bo(iState), rBa; \ + MOVQ rBe, rT1; \ + ORQ rBi, rT1; \ + XORQ rDo, rBa; \ + MOVQ _me(iState), rBo; \ + MOVQ _si(iState), rBu; \ + ROLQ $28, rBa; \ + XORQ rBa, rT1; \ + MOVQ rT1, _ga(oState); \ + G_RT1_RCA; \ + \ + XORQ rDe, rBo; \ + ROLQ $45, rBo; \ + MOVQ rBi, rT1; \ + ANDQ rBo, rT1; \ + XORQ rBe, rT1; \ + MOVQ rT1, _ge(oState); \ + G_RT1_RCE; \ + \ + XORQ rDi, rBu; \ + ROLQ $61, rBu; \ + MOVQ rBu, rT1; \ + ORQ rBa, rT1; \ + XORQ rBo, rT1; \ + MOVQ rT1, _go(oState); \ + \ + ANDQ rBe, rBa; \ + XORQ rBu, rBa; \ + MOVQ rBa, _gu(oState); \ + NOTQ rBu; \ + G_RBA_RCU; \ + \ + ORQ rBu, rBo; \ + XORQ rBi, rBo; \ + MOVQ rBo, _gi(oState); \ + \ + /* Result k */ \ + MOVQ _be(iState), rBa; \ + MOVQ _gi(iState), rBe; \ + MOVQ _ko(iState), rBi; \ + MOVQ _mu(iState), rBo; \ + MOVQ _sa(iState), rBu; \ + XORQ rDi, rBe; \ + ROLQ $6, rBe; \ + XORQ rDo, rBi; \ + ROLQ $25, rBi; \ + MOVQ rBe, rT1; \ + ORQ rBi, rT1; \ + XORQ rDe, rBa; \ + ROLQ $1, rBa; \ + XORQ rBa, rT1; \ + MOVQ rT1, _ka(oState); \ + K_RT1_RCA; \ + \ + XORQ rDu, rBo; \ + ROLQ $8, rBo; \ + MOVQ rBi, rT1; \ + ANDQ rBo, rT1; \ + XORQ rBe, rT1; \ + MOVQ rT1, _ke(oState); \ + K_RT1_RCE; \ + \ + XORQ rDa, rBu; \ + ROLQ $18, rBu; \ + NOTQ rBo; \ + MOVQ rBo, rT1; \ + ANDQ rBu, rT1; \ + XORQ rBi, rT1; \ + MOVQ rT1, _ki(oState); \ + \ + MOVQ rBu, rT1; \ + ORQ rBa, rT1; \ + XORQ rBo, rT1; \ + MOVQ rT1, _ko(oState); \ + \ + ANDQ rBe, rBa; \ + XORQ rBu, rBa; \ + MOVQ rBa, _ku(oState); \ + K_RBA_RCU; \ + \ + /* Result m */ \ + MOVQ _ga(iState), rBe; \ + XORQ rDa, rBe; \ + MOVQ _ke(iState), rBi; \ + ROLQ $36, rBe; \ + XORQ rDe, rBi; \ + MOVQ _bu(iState), rBa; \ + ROLQ $10, rBi; \ + MOVQ rBe, rT1; \ + MOVQ _mi(iState), rBo; \ + ANDQ rBi, rT1; \ + XORQ rDu, rBa; \ + MOVQ _so(iState), rBu; \ + ROLQ $27, rBa; \ + XORQ rBa, rT1; \ + MOVQ rT1, _ma(oState); \ + M_RT1_RCA; \ + \ + XORQ rDi, rBo; \ + ROLQ $15, rBo; \ + MOVQ rBi, rT1; \ + ORQ rBo, rT1; \ + XORQ rBe, rT1; \ + MOVQ rT1, _me(oState); \ + M_RT1_RCE; \ + \ + XORQ rDo, rBu; \ + ROLQ $56, rBu; \ + NOTQ rBo; \ + MOVQ rBo, rT1; \ + ORQ rBu, rT1; \ + XORQ rBi, rT1; \ + MOVQ rT1, _mi(oState); \ + \ + ORQ rBa, rBe; \ + XORQ rBu, rBe; \ + MOVQ rBe, _mu(oState); \ + \ + ANDQ rBa, rBu; \ + XORQ rBo, rBu; \ + MOVQ rBu, _mo(oState); \ + M_RBE_RCU; \ + \ + /* Result s */ \ + MOVQ _bi(iState), rBa; \ + MOVQ _go(iState), rBe; \ + MOVQ _ku(iState), rBi; \ + XORQ rDi, rBa; \ + MOVQ _ma(iState), rBo; \ + ROLQ $62, rBa; \ + XORQ rDo, rBe; \ + MOVQ _se(iState), rBu; \ + ROLQ $55, rBe; \ + \ + XORQ rDu, rBi; \ + MOVQ rBa, rDu; \ + XORQ rDe, rBu; \ + ROLQ $2, rBu; \ + ANDQ rBe, rDu; \ + XORQ rBu, rDu; \ + MOVQ rDu, _su(oState); \ + \ + ROLQ $39, rBi; \ + S_RDU_RCU; \ + NOTQ rBe; \ + XORQ rDa, rBo; \ + MOVQ rBe, rDa; \ + ANDQ rBi, rDa; \ + XORQ rBa, rDa; \ + MOVQ rDa, _sa(oState); \ + S_RDA_RCA; \ + \ + ROLQ $41, rBo; \ + MOVQ rBi, rDe; \ + ORQ rBo, rDe; \ + XORQ rBe, rDe; \ + MOVQ rDe, _se(oState); \ + S_RDE_RCE; \ + \ + MOVQ rBo, rDi; \ + MOVQ rBu, rDo; \ + ANDQ rBu, rDi; \ + ORQ rBa, rDo; \ + XORQ rBi, rDi; \ + XORQ rBo, rDo; \ + MOVQ rDi, _si(oState); \ + MOVQ rDo, _so(oState) \ + +// func KeccakF1600(state *[25]uint64) +TEXT ·KeccakF1600(SB), 0, $200-8 + MOVQ state+0(FP), rpState + + // Convert the user state into an internal state + NOTQ _be(rpState) + NOTQ _bi(rpState) + NOTQ _go(rpState) + NOTQ _ki(rpState) + NOTQ _mi(rpState) + NOTQ _sa(rpState) + + // Execute the KeccakF permutation + MOVQ _ba(rpState), rCa + MOVQ _be(rpState), rCe + MOVQ _bu(rpState), rCu + + XORQ _ga(rpState), rCa + XORQ _ge(rpState), rCe + XORQ _gu(rpState), rCu + + XORQ _ka(rpState), rCa + XORQ _ke(rpState), rCe + XORQ _ku(rpState), rCu + + XORQ _ma(rpState), rCa + XORQ _me(rpState), rCe + XORQ _mu(rpState), rCu + + XORQ _sa(rpState), rCa + XORQ _se(rpState), rCe + MOVQ _si(rpState), rDi + MOVQ _so(rpState), rDo + XORQ _su(rpState), rCu + + mKeccakRound(rpState, rpStack, $0x0000000000000001, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x0000000000008082, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x800000000000808a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000080008000, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000000000808b, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x0000000080000001, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000080008081, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000008009, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000000000008a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x0000000000000088, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x0000000080008009, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x000000008000000a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000008000808b, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x800000000000008b, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000000008089, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000008003, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000000008002, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000000080, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000000000800a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x800000008000000a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000080008081, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000008080, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x0000000080000001, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000080008008, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP) + + // Revert the internal state to the user state + NOTQ _be(rpState) + NOTQ _bi(rpState) + NOTQ _go(rpState) + NOTQ _ki(rpState) + NOTQ _mi(rpState) + NOTQ _sa(rpState) + + RET diff --git a/src/circl/internal/sha3/rc.go b/src/circl/internal/sha3/rc.go new file mode 100644 index 00000000000..6a3df42f305 --- /dev/null +++ b/src/circl/internal/sha3/rc.go @@ -0,0 +1,29 @@ +package sha3 + +// RC stores the round constants for use in the ι step. +var RC = [24]uint64{ + 0x0000000000000001, + 0x0000000000008082, + 0x800000000000808A, + 0x8000000080008000, + 0x000000000000808B, + 0x0000000080000001, + 0x8000000080008081, + 0x8000000000008009, + 0x000000000000008A, + 0x0000000000000088, + 0x0000000080008009, + 0x000000008000000A, + 0x000000008000808B, + 0x800000000000008B, + 0x8000000000008089, + 0x8000000000008003, + 0x8000000000008002, + 0x8000000000000080, + 0x000000000000800A, + 0x800000008000000A, + 0x8000000080008081, + 0x8000000000008080, + 0x0000000080000001, + 0x8000000080008008, +} diff --git a/src/circl/internal/sha3/sha3.go b/src/circl/internal/sha3/sha3.go new file mode 100644 index 00000000000..e688054370b --- /dev/null +++ b/src/circl/internal/sha3/sha3.go @@ -0,0 +1,193 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// spongeDirection indicates the direction bytes are flowing through the sponge. +type spongeDirection int + +const ( + // spongeAbsorbing indicates that the sponge is absorbing input. + spongeAbsorbing spongeDirection = iota + // spongeSqueezing indicates that the sponge is being squeezed. + spongeSqueezing +) + +const ( + // maxRate is the maximum size of the internal buffer. SHAKE-256 + // currently needs the largest buffer. + maxRate = 168 +) + +type State struct { + // Generic sponge components. + a [25]uint64 // main state of the hash + buf []byte // points into storage + rate int // the number of bytes of state to use + + // dsbyte contains the "domain separation" bits and the first bit of + // the padding. Sections 6.1 and 6.2 of [1] separate the outputs of the + // SHA-3 and SHAKE functions by appending bitstrings to the message. + // Using a little-endian bit-ordering convention, these are "01" for SHA-3 + // and "1111" for SHAKE, or 00000010b and 00001111b, respectively. Then the + // padding rule from section 5.1 is applied to pad the message to a multiple + // of the rate, which involves adding a "1" bit, zero or more "0" bits, and + // a final "1" bit. We merge the first "1" bit from the padding into dsbyte, + // giving 00000110b (0x06) and 00011111b (0x1f). + // [1] http://csrc.nist.gov/publications/drafts/fips-202/fips_202_draft.pdf + // "Draft FIPS 202: SHA-3 Standard: Permutation-Based Hash and + // Extendable-Output Functions (May 2014)" + dsbyte byte + + storage storageBuf + + // Specific to SHA-3 and SHAKE. + outputLen int // the default output size in bytes + state spongeDirection // whether the sponge is absorbing or squeezing +} + +// BlockSize returns the rate of sponge underlying this hash function. +func (d *State) BlockSize() int { return d.rate } + +// Size returns the output size of the hash function in bytes. +func (d *State) Size() int { return d.outputLen } + +// Reset clears the internal state by zeroing the sponge state and +// the byte buffer, and setting Sponge.state to absorbing. +func (d *State) Reset() { + // Zero the permutation's state. + for i := range d.a { + d.a[i] = 0 + } + d.state = spongeAbsorbing + d.buf = d.storage.asBytes()[:0] +} + +func (d *State) clone() *State { + ret := *d + if ret.state == spongeAbsorbing { + ret.buf = ret.storage.asBytes()[:len(ret.buf)] + } else { + ret.buf = ret.storage.asBytes()[d.rate-cap(d.buf) : d.rate] + } + + return &ret +} + +// permute applies the KeccakF-1600 permutation. It handles +// any input-output buffering. +func (d *State) permute() { + switch d.state { + case spongeAbsorbing: + // If we're absorbing, we need to xor the input into the state + // before applying the permutation. + xorIn(d, d.buf) + d.buf = d.storage.asBytes()[:0] + KeccakF1600(&d.a) + case spongeSqueezing: + // If we're squeezing, we need to apply the permutation before + // copying more output. + KeccakF1600(&d.a) + d.buf = d.storage.asBytes()[:d.rate] + copyOut(d, d.buf) + } +} + +// pads appends the domain separation bits in dsbyte, applies +// the multi-bitrate 10..1 padding rule, and permutes the state. +func (d *State) padAndPermute(dsbyte byte) { + if d.buf == nil { + d.buf = d.storage.asBytes()[:0] + } + // Pad with this instance's domain-separator bits. We know that there's + // at least one byte of space in d.buf because, if it were full, + // permute would have been called to empty it. dsbyte also contains the + // first one bit for the padding. See the comment in the state struct. + d.buf = append(d.buf, dsbyte) + zerosStart := len(d.buf) + d.buf = d.storage.asBytes()[:d.rate] + for i := zerosStart; i < d.rate; i++ { + d.buf[i] = 0 + } + // This adds the final one bit for the padding. Because of the way that + // bits are numbered from the LSB upwards, the final bit is the MSB of + // the last byte. + d.buf[d.rate-1] ^= 0x80 + // Apply the permutation + d.permute() + d.state = spongeSqueezing + d.buf = d.storage.asBytes()[:d.rate] + copyOut(d, d.buf) +} + +// Write absorbs more data into the hash's state. It produces an error +// if more data is written to the ShakeHash after writing +func (d *State) Write(p []byte) (written int, err error) { + if d.state != spongeAbsorbing { + panic("sha3: write to sponge after read") + } + if d.buf == nil { + d.buf = d.storage.asBytes()[:0] + } + written = len(p) + + for len(p) > 0 { + if len(d.buf) == 0 && len(p) >= d.rate { + // The fast path; absorb a full "rate" bytes of input and apply the permutation. + xorIn(d, p[:d.rate]) + p = p[d.rate:] + KeccakF1600(&d.a) + } else { + // The slow path; buffer the input until we can fill the sponge, and then xor it in. + todo := d.rate - len(d.buf) + if todo > len(p) { + todo = len(p) + } + d.buf = append(d.buf, p[:todo]...) + p = p[todo:] + + // If the sponge is full, apply the permutation. + if len(d.buf) == d.rate { + d.permute() + } + } + } + + return written, nil +} + +// Read squeezes an arbitrary number of bytes from the sponge. +func (d *State) Read(out []byte) (n int, err error) { + // If we're still absorbing, pad and apply the permutation. + if d.state == spongeAbsorbing { + d.padAndPermute(d.dsbyte) + } + + n = len(out) + + // Now, do the squeezing. + for len(out) > 0 { + n := copy(out, d.buf) + d.buf = d.buf[n:] + out = out[n:] + + // Apply the permutation if we've squeezed the sponge dry. + if len(d.buf) == 0 { + d.permute() + } + } + + return +} + +// Sum applies padding to the hash state and then squeezes out the desired +// number of output bytes. +func (d *State) Sum(in []byte) []byte { + // Make a copy of the original hash so that caller can keep writing + // and summing. + dup := d.clone() + hash := make([]byte, dup.outputLen) + _, _ = dup.Read(hash) + return append(in, hash...) +} diff --git a/src/circl/internal/sha3/sha3_s390x.s b/src/circl/internal/sha3/sha3_s390x.s new file mode 100644 index 00000000000..8a4458f63f9 --- /dev/null +++ b/src/circl/internal/sha3/sha3_s390x.s @@ -0,0 +1,33 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build !gccgo,!appengine + +#include "textflag.h" + +// func kimd(function code, chain *[200]byte, src []byte) +TEXT ·kimd(SB), NOFRAME|NOSPLIT, $0-40 + MOVD function+0(FP), R0 + MOVD chain+8(FP), R1 + LMG src+16(FP), R2, R3 // R2=base, R3=len + +continue: + WORD $0xB93E0002 // KIMD --, R2 + BVS continue // continue if interrupted + MOVD $0, R0 // reset R0 for pre-go1.8 compilers + RET + +// func klmd(function code, chain *[200]byte, dst, src []byte) +TEXT ·klmd(SB), NOFRAME|NOSPLIT, $0-64 + // TODO: SHAKE support + MOVD function+0(FP), R0 + MOVD chain+8(FP), R1 + LMG dst+16(FP), R2, R3 // R2=base, R3=len + LMG src+40(FP), R4, R5 // R4=base, R5=len + +continue: + WORD $0xB93F0024 // KLMD R2, R4 + BVS continue // continue if interrupted + MOVD $0, R0 // reset R0 for pre-go1.8 compilers + RET diff --git a/src/circl/internal/sha3/sha3_test.go b/src/circl/internal/sha3/sha3_test.go new file mode 100644 index 00000000000..b2a4d4b58aa --- /dev/null +++ b/src/circl/internal/sha3/sha3_test.go @@ -0,0 +1,269 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// Tests include all the ShortMsgKATs provided by the Keccak team at +// https://github.com/gvanas/KeccakCodePackage +// +// They only include the zero-bit case of the bitwise testvectors +// published by NIST in the draft of FIPS-202. + +import ( + "bytes" + "compress/flate" + "encoding/hex" + "encoding/json" + "fmt" + "math/rand" + "os" + "strings" + "testing" +) + +const ( + katFilename = "testdata/keccakKats.json.deflate" +) + +// testDigests contains functions returning hash.Hash instances +// with output-length equal to the KAT length for SHA-3, Keccak +// and SHAKE instances. +var testDigests = map[string]func() State{ + "SHA3-224": New224, + "SHA3-256": New256, + "SHA3-384": New384, + "SHA3-512": New512, +} + +// structs used to marshal JSON test-cases. +type KeccakKats struct { + Kats map[string][]struct { + Digest string `json:"digest"` + Length int64 `json:"length"` + Message string `json:"message"` + + // Defined only for cSHAKE + N string `json:"N"` + S string `json:"S"` + } +} + +// nolint:unparam +func testUnalignedAndGeneric(t *testing.T, testf func(impl string)) { + xorInOrig, copyOutOrig := xorIn, copyOut + xorIn, copyOut = xorInGeneric, copyOutGeneric + testf("generic") + if xorImplementationUnaligned != "generic" { + xorIn, copyOut = xorInUnaligned, copyOutUnaligned + testf("unaligned") + } + xorIn, copyOut = xorInOrig, copyOutOrig +} + +// TestKeccakKats tests the SHA-3 and Shake implementations against all the +// ShortMsgKATs from https://github.com/gvanas/KeccakCodePackage +// (The testvectors are stored in keccakKats.json.deflate due to their length.) +func TestKeccakKats(t *testing.T) { + testUnalignedAndGeneric(t, func(impl string) { + // Read the KATs. + deflated, err := os.Open(katFilename) + if err != nil { + t.Errorf("error opening %s: %s", katFilename, err) + } + file := flate.NewReader(deflated) + dec := json.NewDecoder(file) + var katSet KeccakKats + err = dec.Decode(&katSet) + if err != nil { + t.Errorf("error decoding KATs: %s", err) + } + + for algo, function := range testDigests { + d := function() + for _, kat := range katSet.Kats[algo] { + d.Reset() + in, err := hex.DecodeString(kat.Message) + if err != nil { + t.Errorf("error decoding KAT: %s", err) + } + _, _ = d.Write(in[:kat.Length/8]) + got := strings.ToUpper(hex.EncodeToString(d.Sum(nil))) + if got != kat.Digest { + t.Errorf("function=%s, implementation=%s, length=%d\nmessage:\n %s\ngot:\n %s\nwanted:\n %s", + algo, impl, kat.Length, kat.Message, got, kat.Digest) + t.Logf("wanted %+v", kat) + t.FailNow() + } + continue + } + } + }) +} + +// TestUnalignedWrite tests that writing data in an arbitrary pattern with +// small input buffers. +func TestUnalignedWrite(t *testing.T) { + testUnalignedAndGeneric(t, func(impl string) { + buf := sequentialBytes(0x10000) + for alg, df := range testDigests { + d := df() + d.Reset() + _, _ = d.Write(buf) + want := d.Sum(nil) + d.Reset() + for i := 0; i < len(buf); { + // Cycle through offsets which make a 137 byte sequence. + // Because 137 is prime this sequence should exercise all corner cases. + offsets := [17]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1} + for _, j := range offsets { + if v := len(buf) - i; v < j { + j = v + } + _, _ = d.Write(buf[i : i+j]) + i += j + } + } + got := d.Sum(nil) + if !bytes.Equal(got, want) { + t.Errorf("Unaligned writes, implementation=%s, alg=%s\ngot %q, want %q", impl, alg, got, want) + } + } + }) +} + +// TestAppend checks that appending works when reallocation is necessary. +func TestAppend(t *testing.T) { + testUnalignedAndGeneric(t, func(impl string) { + d := New224() + + for capacity := 2; capacity <= 66; capacity += 64 { + // The first time around the loop, Sum will have to reallocate. + // The second time, it will not. + buf := make([]byte, 2, capacity) + d.Reset() + _, _ = d.Write([]byte{0xcc}) + buf = d.Sum(buf) + expected := "0000DF70ADC49B2E76EEE3A6931B93FA41841C3AF2CDF5B32A18B5478C39" + if got := strings.ToUpper(hex.EncodeToString(buf)); got != expected { + t.Errorf("got %s, want %s", got, expected) + } + } + }) +} + +// TestAppendNoRealloc tests that appending works when no reallocation is necessary. +func TestAppendNoRealloc(t *testing.T) { + testUnalignedAndGeneric(t, func(impl string) { + buf := make([]byte, 1, 200) + d := New224() + _, _ = d.Write([]byte{0xcc}) + buf = d.Sum(buf) + expected := "00DF70ADC49B2E76EEE3A6931B93FA41841C3AF2CDF5B32A18B5478C39" + if got := strings.ToUpper(hex.EncodeToString(buf)); got != expected { + t.Errorf("%s: got %s, want %s", impl, got, expected) + } + }) +} + +// sequentialBytes produces a buffer of size consecutive bytes 0x00, 0x01, ..., used for testing. +// +// The alignment of each slice is intentionally randomized to detect alignment +// issues in the implementation. See https://golang.org/issue/37644. +// Ideally, the compiler should fuzz the alignment itself. +// (See https://golang.org/issue/35128.) +func sequentialBytes(size int) []byte { + alignmentOffset := rand.Intn(8) // nolint:gosec + result := make([]byte, size+alignmentOffset)[alignmentOffset:] + for i := range result { + result[i] = byte(i) + } + return result +} + +// BenchmarkPermutationFunction measures the speed of the permutation function +// with no input data. +func BenchmarkPermutationFunction(b *testing.B) { + b.SetBytes(int64(200)) + var lanes [25]uint64 + for i := 0; i < b.N; i++ { + KeccakF1600(&lanes) + } +} + +// benchmarkHash tests the speed to hash num buffers of buflen each. +func benchmarkHash(b *testing.B, h State, size, num int) { + b.StopTimer() + h.Reset() + data := sequentialBytes(size) + b.SetBytes(int64(size * num)) + b.StartTimer() + + var state []byte + for i := 0; i < b.N; i++ { + for j := 0; j < num; j++ { + _, _ = h.Write(data) + } + state = h.Sum(state[:0]) + } + b.StopTimer() + h.Reset() +} + +// benchmarkShake is specialized to the Shake instances, which don't +// require a copy on reading output. +func benchmarkShake(b *testing.B, h State, size, num int) { + b.StopTimer() + h.Reset() + data := sequentialBytes(size) + d := make([]byte, 32) + + b.SetBytes(int64(size * num)) + b.StartTimer() + + for i := 0; i < b.N; i++ { + h.Reset() + for j := 0; j < num; j++ { + _, _ = h.Write(data) + } + _, _ = h.Read(d) + } +} + +func BenchmarkSha3_512_MTU(b *testing.B) { benchmarkHash(b, New512(), 1350, 1) } +func BenchmarkSha3_384_MTU(b *testing.B) { benchmarkHash(b, New384(), 1350, 1) } +func BenchmarkSha3_256_MTU(b *testing.B) { benchmarkHash(b, New256(), 1350, 1) } +func BenchmarkSha3_224_MTU(b *testing.B) { benchmarkHash(b, New224(), 1350, 1) } + +func BenchmarkShake128_MTU(b *testing.B) { benchmarkShake(b, NewShake128(), 1350, 1) } +func BenchmarkShake256_MTU(b *testing.B) { benchmarkShake(b, NewShake256(), 1350, 1) } +func BenchmarkShake256_16x(b *testing.B) { benchmarkShake(b, NewShake256(), 16, 1024) } +func BenchmarkShake256_1MiB(b *testing.B) { benchmarkShake(b, NewShake256(), 1024, 1024) } + +func BenchmarkSha3_512_1MiB(b *testing.B) { benchmarkHash(b, New512(), 1024, 1024) } + +func Example_sum() { + buf := []byte("some data to hash") + // A hash needs to be 64 bytes long to have 256-bit collision resistance. + h := make([]byte, 64) + // Compute a 64-byte hash of buf and put it in h. + ShakeSum256(h, buf) + fmt.Printf("%x\n", h) + // Output: 0f65fe41fc353e52c55667bb9e2b27bfcc8476f2c413e9437d272ee3194a4e3146d05ec04a25d16b8f577c19b82d16b1424c3e022e783d2b4da98de3658d363d +} + +func Example_mac() { + k := []byte("this is a secret key; you should generate a strong random key that's at least 32 bytes long") + buf := []byte("and this is some data to authenticate") + // A MAC with 32 bytes of output has 256-bit security strength -- if you use at least a 32-byte-long key. + h := make([]byte, 32) + d := NewShake256() + // Write the key into the hash. + _, _ = d.Write(k) + // Now write the data. + _, _ = d.Write(buf) + // Read 32 bytes of output from the hash into h. + _, _ = d.Read(h) + fmt.Printf("%x\n", h) + // Output: 78de2974bd2711d5549ffd32b753ef0f5fa80a0db2556db60f0987eb8a9218ff +} diff --git a/src/circl/internal/sha3/shake.go b/src/circl/internal/sha3/shake.go new file mode 100644 index 00000000000..b92c5b7d785 --- /dev/null +++ b/src/circl/internal/sha3/shake.go @@ -0,0 +1,79 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// This file defines the ShakeHash interface, and provides +// functions for creating SHAKE and cSHAKE instances, as well as utility +// functions for hashing bytes to arbitrary-length output. +// +// +// SHAKE implementation is based on FIPS PUB 202 [1] +// cSHAKE implementations is based on NIST SP 800-185 [2] +// +// [1] https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf +// [2] https://doi.org/10.6028/NIST.SP.800-185 + +import ( + "io" +) + +// ShakeHash defines the interface to hash functions that +// support arbitrary-length output. +type ShakeHash interface { + // Write absorbs more data into the hash's state. It panics if input is + // written to it after output has been read from it. + io.Writer + + // Read reads more output from the hash; reading affects the hash's + // state. (ShakeHash.Read is thus very different from Hash.Sum) + // It never returns an error. + io.Reader + + // Clone returns a copy of the ShakeHash in its current state. + Clone() ShakeHash + + // Reset resets the ShakeHash to its initial state. + Reset() +} + +// Consts for configuring initial SHA-3 state +const ( + dsbyteShake = 0x1f + rate128 = 168 + rate256 = 136 +) + +// Clone returns copy of SHAKE context within its current state. +func (d *State) Clone() ShakeHash { + return d.clone() +} + +// NewShake128 creates a new SHAKE128 variable-output-length ShakeHash. +// Its generic security strength is 128 bits against all attacks if at +// least 32 bytes of its output are used. +func NewShake128() State { + return State{rate: rate128, dsbyte: dsbyteShake} +} + +// NewShake256 creates a new SHAKE256 variable-output-length ShakeHash. +// Its generic security strength is 256 bits against all attacks if +// at least 64 bytes of its output are used. +func NewShake256() State { + return State{rate: rate256, dsbyte: dsbyteShake} +} + +// ShakeSum128 writes an arbitrary-length digest of data into hash. +func ShakeSum128(hash, data []byte) { + h := NewShake128() + _, _ = h.Write(data) + _, _ = h.Read(hash) +} + +// ShakeSum256 writes an arbitrary-length digest of data into hash. +func ShakeSum256(hash, data []byte) { + h := NewShake256() + _, _ = h.Write(data) + _, _ = h.Read(hash) +} diff --git a/src/circl/internal/sha3/testdata/keccakKats.json.deflate b/src/circl/internal/sha3/testdata/keccakKats.json.deflate new file mode 100644 index 00000000000..7a94c2f8bce Binary files /dev/null and b/src/circl/internal/sha3/testdata/keccakKats.json.deflate differ diff --git a/src/circl/internal/sha3/xor.go b/src/circl/internal/sha3/xor.go new file mode 100644 index 00000000000..079b650141c --- /dev/null +++ b/src/circl/internal/sha3/xor.go @@ -0,0 +1,23 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build !amd64,!386,!ppc64le appengine + +package sha3 + +// A storageBuf is an aligned array of maxRate bytes. +type storageBuf [maxRate]byte + +func (b *storageBuf) asBytes() *[maxRate]byte { + return (*[maxRate]byte)(b) +} + +var ( + xorIn = xorInGeneric + copyOut = copyOutGeneric + xorInUnaligned = xorInGeneric + copyOutUnaligned = copyOutGeneric +) + +const xorImplementationUnaligned = "generic" diff --git a/src/circl/internal/sha3/xor_generic.go b/src/circl/internal/sha3/xor_generic.go new file mode 100644 index 00000000000..8dec02d58cf --- /dev/null +++ b/src/circl/internal/sha3/xor_generic.go @@ -0,0 +1,28 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +import "encoding/binary" + +// xorInGeneric xors the bytes in buf into the state; it +// makes no non-portable assumptions about memory layout +// or alignment. +func xorInGeneric(d *State, buf []byte) { + n := len(buf) / 8 + + for i := 0; i < n; i++ { + a := binary.LittleEndian.Uint64(buf) + d.a[i] ^= a + buf = buf[8:] + } +} + +// copyOutGeneric copies ulint64s to a byte buffer. +func copyOutGeneric(d *State, b []byte) { + for i := 0; len(b) >= 8; i++ { + binary.LittleEndian.PutUint64(b, d.a[i]) + b = b[8:] + } +} diff --git a/src/circl/internal/sha3/xor_unaligned.go b/src/circl/internal/sha3/xor_unaligned.go new file mode 100644 index 00000000000..03affc304cd --- /dev/null +++ b/src/circl/internal/sha3/xor_unaligned.go @@ -0,0 +1,67 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build amd64 386 ppc64le +// +build !appengine + +package sha3 + +import "unsafe" + +// A storageBuf is an aligned array of maxRate bytes. +type storageBuf [maxRate / 8]uint64 + +func (b *storageBuf) asBytes() *[maxRate]byte { + return (*[maxRate]byte)(unsafe.Pointer(b)) +} + +// xorInUnaligned uses unaligned reads and writes to update d.a to contain d.a +// XOR buf. +func xorInUnaligned(d *State, buf []byte) { + n := len(buf) + bw := (*[maxRate / 8]uint64)(unsafe.Pointer(&buf[0]))[: n/8 : n/8] + if n >= 72 { + d.a[0] ^= bw[0] + d.a[1] ^= bw[1] + d.a[2] ^= bw[2] + d.a[3] ^= bw[3] + d.a[4] ^= bw[4] + d.a[5] ^= bw[5] + d.a[6] ^= bw[6] + d.a[7] ^= bw[7] + d.a[8] ^= bw[8] + } + if n >= 104 { + d.a[9] ^= bw[9] + d.a[10] ^= bw[10] + d.a[11] ^= bw[11] + d.a[12] ^= bw[12] + } + if n >= 136 { + d.a[13] ^= bw[13] + d.a[14] ^= bw[14] + d.a[15] ^= bw[15] + d.a[16] ^= bw[16] + } + if n >= 144 { + d.a[17] ^= bw[17] + } + if n >= 168 { + d.a[18] ^= bw[18] + d.a[19] ^= bw[19] + d.a[20] ^= bw[20] + } +} + +func copyOutUnaligned(d *State, buf []byte) { + ab := (*[maxRate]uint8)(unsafe.Pointer(&d.a[0])) + copy(buf, ab[:]) +} + +var ( + xorIn = xorInUnaligned + copyOut = copyOutUnaligned +) + +const xorImplementationUnaligned = "unaligned" diff --git a/src/circl/internal/test/test.go b/src/circl/internal/test/test.go new file mode 100644 index 00000000000..d256ee29a0c --- /dev/null +++ b/src/circl/internal/test/test.go @@ -0,0 +1,60 @@ +package test + +import ( + "errors" + "fmt" + "strings" + "testing" +) + +// ReportError reports an error if got is different from want. +func ReportError(t *testing.T, got, want interface{}, inputs ...interface{}) { + b := &strings.Builder{} + fmt.Fprint(b, "\n") + for i, in := range inputs { + fmt.Fprintf(b, "in[%v]: %v\n", i, in) + } + fmt.Fprintf(b, "got: %v\nwant: %v", got, want) + t.Helper() + t.Fatalf(b.String()) +} + +// CheckOk fails the test if result == false. +func CheckOk(result bool, msg string, t testing.TB) { + t.Helper() + + if !result { + t.Fatal(msg) + } +} + +// checkErr fails on error condition. mustFail indicates whether err is expected +// to be nil or not. +func checkErr(t testing.TB, err error, mustFail bool, msg string) { + t.Helper() + if err != nil && !mustFail { + t.Fatalf("msg: %v\nerr: %v", msg, err) + } + + if err == nil && mustFail { + t.Fatalf("msg: %v\nerr: %v", msg, err) + } +} + +// CheckNoErr fails if err !=nil. Print msg as an error message. +func CheckNoErr(t testing.TB, err error, msg string) { t.Helper(); checkErr(t, err, false, msg) } + +// CheckIsErr fails if err ==nil. Print msg as an error message. +func CheckIsErr(t testing.TB, err error, msg string) { t.Helper(); checkErr(t, err, true, msg) } + +// CheckPanic returns true if call to function 'f' caused panic. +func CheckPanic(f func()) error { + var hasPanicked = errors.New("no panic detected") + defer func() { + if r := recover(); r != nil { + hasPanicked = nil + } + }() + f() + return hasPanicked +} diff --git a/src/circl/kem/hybrid/hybrid.go b/src/circl/kem/hybrid/hybrid.go new file mode 100644 index 00000000000..3bcb7b25efe --- /dev/null +++ b/src/circl/kem/hybrid/hybrid.go @@ -0,0 +1,312 @@ +// Package hybrid defines several hybrid classical/quantum KEMs. +// +// KEMs are combined by simple concatenation of shared secrets, cipher texts, +// public keys, etc, see +// +// https://datatracker.ietf.org/doc/draft-ietf-tls-hybrid-design/ +// https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-56Cr2.pdf +// +// Note that this is only fine if the shared secret is used in its entirety +// in a next step, such as being hashed or used as key. +// +// For deriving a KEM keypair deterministically and encapsulating +// deterministically, we expand a single seed to both using SHAKE256, +// so that a non-uniform seed (such as a shared secret generated by a hybrid +// KEM where one of the KEMs is weak) doesn't impact just one of the KEMs. +package hybrid + +import ( + "errors" + + "circl/kem" + + "circl/hpke" + "circl/kem/kyber/kyber1024" + "circl/kem/kyber/kyber512" + "circl/kem/kyber/kyber768" + + "circl/internal/sha3" +) + +var ErrUninitialized = errors.New("public or private key not initialized") + +// Returns the hybrid KEM of Kyber512 and X25519. +func Kyber512X25519() kem.Scheme { return kyber512X } + +// Returns the hybrid KEM of Kyber768 and X448. +func Kyber768X448() kem.Scheme { return kyber768X } + +// Returns the hybrid KEM of Kyber1024 and X448. +func Kyber1024X448() kem.Scheme { return kyber1024X } + +var kyber512X kem.Scheme = &scheme{ + "Kyber512-X25519", + kyber512.Scheme(), + hpke.KEM_X25519_HKDF_SHA256.Scheme(), +} +var kyber768X kem.Scheme = &scheme{ + "Kyber768-X448", + kyber768.Scheme(), + hpke.KEM_X448_HKDF_SHA512.Scheme(), +} +var kyber1024X kem.Scheme = &scheme{ + "Kyber1024-X448", + kyber1024.Scheme(), + hpke.KEM_X448_HKDF_SHA512.Scheme(), +} + +// Public key of a hybrid KEM. +type publicKey struct { + scheme *scheme + first kem.PublicKey + second kem.PublicKey +} + +// Private key of a hybrid KEM. +type privateKey struct { + scheme *scheme + first kem.PrivateKey + second kem.PrivateKey +} + +// Scheme for a hybrid KEM. +type scheme struct { + name string + first kem.Scheme + second kem.Scheme +} + +func (sch *scheme) Name() string { return sch.name } +func (sch *scheme) PublicKeySize() int { + return sch.first.PublicKeySize() + sch.second.PublicKeySize() +} +func (sch *scheme) PrivateKeySize() int { + return sch.first.PrivateKeySize() + sch.second.PrivateKeySize() +} +func (sch *scheme) SeedSize() int { + first := sch.first.SeedSize() + second := sch.second.SeedSize() + ret := second + if first > second { + ret = first + } + if ret > 32 { + panic("SeedSize too big for SHAKE256") + } + return ret +} +func (sch *scheme) SharedKeySize() int { + return sch.first.SharedKeySize() + sch.second.SharedKeySize() +} +func (sch *scheme) CiphertextSize() int { + return sch.first.CiphertextSize() + sch.second.CiphertextSize() +} +func (sch *scheme) EncapsulationSeedSize() int { + first := sch.first.EncapsulationSeedSize() + second := sch.second.EncapsulationSeedSize() + ret := second + if first > second { + ret = first + } + if ret > 32 { + panic("EncapsulationSeedSize too big for SHAKE256") + } + return ret +} + +func (sk *privateKey) Scheme() kem.Scheme { return sk.scheme } +func (pk *publicKey) Scheme() kem.Scheme { return pk.scheme } + +func (sk *privateKey) MarshalBinary() ([]byte, error) { + if sk.first == nil || sk.second == nil { + return nil, ErrUninitialized + } + first, err := sk.first.MarshalBinary() + if err != nil { + return nil, err + } + second, err := sk.second.MarshalBinary() + if err != nil { + return nil, err + } + return append(first, second...), nil +} + +func (sk *privateKey) Equal(other kem.PrivateKey) bool { + oth, ok := other.(*privateKey) + if !ok { + return false + } + if sk.first == nil && sk.second == nil && oth.first == nil && oth.second == nil { + return true + } + if sk.first == nil || sk.second == nil || oth.first == nil || oth.second == nil { + return false + } + return sk.first.Equal(oth.first) && sk.second.Equal(oth.second) +} + +func (sk *privateKey) Public() kem.PublicKey { + return &publicKey{sk.scheme, sk.first.Public(), sk.second.Public()} +} + +func (pk *publicKey) Equal(other kem.PublicKey) bool { + oth, ok := other.(*publicKey) + if !ok { + return false + } + if pk.first == nil && pk.second == nil && oth.first == nil && oth.second == nil { + return true + } + if pk.first == nil || pk.second == nil || oth.first == nil || oth.second == nil { + return false + } + return pk.first.Equal(oth.first) && pk.second.Equal(oth.second) +} + +func (pk *publicKey) MarshalBinary() ([]byte, error) { + if pk.first == nil || pk.second == nil { + return nil, ErrUninitialized + } + first, err := pk.first.MarshalBinary() + if err != nil { + return nil, err + } + second, err := pk.second.MarshalBinary() + if err != nil { + return nil, err + } + return append(first, second...), nil +} + +func (sch *scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + pk1, sk1, err := sch.first.GenerateKeyPair() + if err != nil { + return nil, nil, err + } + pk2, sk2, err := sch.second.GenerateKeyPair() + if err != nil { + return nil, nil, err + } + + return &publicKey{sch, pk1, pk2}, &privateKey{sch, sk1, sk2}, nil +} + +func (sch *scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + if len(seed) != sch.SeedSize() { + panic(kem.ErrSeedSize) + } + h := sha3.NewShake256() + _, _ = h.Write(seed) + first := make([]byte, sch.first.SeedSize()) + second := make([]byte, sch.second.SeedSize()) + _, _ = h.Read(first) + _, _ = h.Read(second) + + pk1, sk1 := sch.first.DeriveKeyPair(first) + pk2, sk2 := sch.second.DeriveKeyPair(second) + + return &publicKey{sch, pk1, pk2}, &privateKey{sch, sk1, sk2} +} + +func (sch *scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { + pub, ok := pk.(*publicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + + ct1, ss1, err := sch.first.Encapsulate(pub.first) + if err != nil { + return nil, nil, err + } + + ct2, ss2, err := sch.second.Encapsulate(pub.second) + if err != nil { + return nil, nil, err + } + + return append(ct1, ct2...), append(ss1, ss2...), nil +} + +func (sch *scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) ( + ct, ss []byte, err error) { + if len(seed) != sch.EncapsulationSeedSize() { + return nil, nil, kem.ErrSeedSize + } + + h := sha3.NewShake256() + _, _ = h.Write(seed) + first := make([]byte, sch.first.EncapsulationSeedSize()) + second := make([]byte, sch.second.EncapsulationSeedSize()) + _, _ = h.Read(first) + _, _ = h.Read(second) + + pub, ok := pk.(*publicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + + ct1, ss1, err := sch.first.EncapsulateDeterministically(pub.first, first) + if err != nil { + return nil, nil, err + } + ct2, ss2, err := sch.second.EncapsulateDeterministically(pub.second, second) + if err != nil { + return nil, nil, err + } + return append(ct1, ct2...), append(ss1, ss2...), nil +} + +func (sch *scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { + if len(ct) != sch.CiphertextSize() { + return nil, kem.ErrCiphertextSize + } + + priv, ok := sk.(*privateKey) + if !ok { + return nil, kem.ErrTypeMismatch + } + + firstSize := sch.first.CiphertextSize() + ss1, err := sch.first.Decapsulate(priv.first, ct[:firstSize]) + if err != nil { + return nil, err + } + ss2, err := sch.second.Decapsulate(priv.second, ct[firstSize:]) + if err != nil { + return nil, err + } + return append(ss1, ss2...), nil +} + +func (sch *scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { + if len(buf) != sch.PublicKeySize() { + return nil, kem.ErrPubKeySize + } + firstSize := sch.first.PublicKeySize() + pk1, err := sch.first.UnmarshalBinaryPublicKey(buf[:firstSize]) + if err != nil { + return nil, err + } + pk2, err := sch.second.UnmarshalBinaryPublicKey(buf[firstSize:]) + if err != nil { + return nil, err + } + return &publicKey{sch, pk1, pk2}, nil +} + +func (sch *scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { + if len(buf) != sch.PrivateKeySize() { + return nil, kem.ErrPrivKeySize + } + firstSize := sch.first.PrivateKeySize() + sk1, err := sch.first.UnmarshalBinaryPrivateKey(buf[:firstSize]) + if err != nil { + return nil, err + } + sk2, err := sch.second.UnmarshalBinaryPrivateKey(buf[firstSize:]) + if err != nil { + return nil, err + } + return &privateKey{sch, sk1, sk2}, nil +} diff --git a/src/circl/kem/kem.go b/src/circl/kem/kem.go new file mode 100644 index 00000000000..9f6c6d3eeed --- /dev/null +++ b/src/circl/kem/kem.go @@ -0,0 +1,118 @@ +// Package kem provides a unified interface for KEM schemes. +// +// A register of schemes is available in the package +// +// circl/kem/schemes +package kem + +import ( + "encoding" + "errors" +) + +// A KEM public key +type PublicKey interface { + // Returns the scheme for this public key + Scheme() Scheme + + encoding.BinaryMarshaler + Equal(PublicKey) bool +} + +// A KEM private key +type PrivateKey interface { + // Returns the scheme for this private key + Scheme() Scheme + + encoding.BinaryMarshaler + Equal(PrivateKey) bool + Public() PublicKey +} + +// A Scheme represents a specific instance of a KEM. +type Scheme interface { + // Name of the scheme + Name() string + + // GenerateKeyPair creates a new key pair. + GenerateKeyPair() (PublicKey, PrivateKey, error) + + // Encapsulate generates a shared key ss for the public key and + // encapsulates it into a ciphertext ct. + Encapsulate(pk PublicKey) (ct, ss []byte, err error) + + // Returns the shared key encapsulated in ciphertext ct for the + // private key sk. + Decapsulate(sk PrivateKey, ct []byte) ([]byte, error) + + // Unmarshals a PublicKey from the provided buffer. + UnmarshalBinaryPublicKey([]byte) (PublicKey, error) + + // Unmarshals a PrivateKey from the provided buffer. + UnmarshalBinaryPrivateKey([]byte) (PrivateKey, error) + + // Size of encapsulated keys. + CiphertextSize() int + + // Size of established shared keys. + SharedKeySize() int + + // Size of packed private keys. + PrivateKeySize() int + + // Size of packed public keys. + PublicKeySize() int + + // DeriveKeyPair deterministicallly derives a pair of keys from a seed. + // Panics if the length of seed is not equal to the value returned by + // SeedSize. + DeriveKeyPair(seed []byte) (PublicKey, PrivateKey) + + // Size of seed used in DeriveKey + SeedSize() int + + // EncapsulateDeterministically generates a shared key ss for the public + // key deterministically from the given seed and encapsulates it into + // a ciphertext ct. If unsure, you're better off using Encapsulate(). + EncapsulateDeterministically(pk PublicKey, seed []byte) ( + ct, ss []byte, err error) + + // Size of seed used in EncapsulateDeterministically(). + EncapsulationSeedSize() int +} + +// AuthScheme represents a KEM that supports authenticated key encapsulation. +type AuthScheme interface { + Scheme + AuthEncapsulate(pkr PublicKey, sks PrivateKey) (ct, ss []byte, err error) + AuthEncapsulateDeterministically(pkr PublicKey, sks PrivateKey, seed []byte) (ct, ss []byte, err error) + AuthDecapsulate(skr PrivateKey, ct []byte, pks PublicKey) ([]byte, error) +} + +var ( + // ErrTypeMismatch is the error used if types of, for instance, private + // and public keys don't match + ErrTypeMismatch = errors.New("types mismatch") + + // ErrSeedSize is the error used if the provided seed is of the wrong + // size. + ErrSeedSize = errors.New("wrong seed size") + + // ErrPubKeySize is the error used if the provided public key is of + // the wrong size. + ErrPubKeySize = errors.New("wrong size for public key") + + // ErrCiphertextSize is the error used if the provided ciphertext + // is of the wrong size. + ErrCiphertextSize = errors.New("wrong size for ciphertext") + + // ErrPrivKeySize is the error used if the provided private key is of + // the wrong size. + ErrPrivKeySize = errors.New("wrong size for private key") + + // ErrPubKey is the error used if the provided public key is invalid. + ErrPubKey = errors.New("invalid public key") + + // ErrCipherText is the error used if the provided ciphertext is invalid. + ErrCipherText = errors.New("invalid ciphertext") +) diff --git a/src/circl/kem/kyber/doc.go b/src/circl/kem/kyber/doc.go new file mode 100644 index 00000000000..6cc828f2b10 --- /dev/null +++ b/src/circl/kem/kyber/doc.go @@ -0,0 +1,11 @@ +//go:generate go run gen.go + +// Package kyber implements the CRYSTALS-Kyber.CCAKEM IND-CCA2 secure +// key encapsulation mechanism (KEM) as submitted to round 3 of the NIST PQC +// competition and described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +// +// The related public key encryption scheme CRYSTALS-Kyber.CPAPKE can be +// found in the package circl/pke/kyber. +package kyber diff --git a/src/circl/kem/kyber/gen.go b/src/circl/kem/kyber/gen.go new file mode 100644 index 00000000000..a844b813547 --- /dev/null +++ b/src/circl/kem/kyber/gen.go @@ -0,0 +1,59 @@ +// +build ignore + +// Autogenerates wrappers from templates to prevent too much duplicated code +// between the code for different modes. +package main + +import ( + "bytes" + "io/ioutil" + "strings" + "text/template" +) + +type Instance struct { + Name string +} + +func (m Instance) Pkg() string { + return strings.ToLower(m.Name) +} + +var ( + Instances = []Instance{ + {Name: "Kyber512"}, + {Name: "Kyber768"}, + {Name: "Kyber1024"}, + } + TemplateWarning = "// Code generated from" +) + +func main() { + generatePackageFiles() +} + +// Generates instance/kyber.go from templates/pkg.templ.go +func generatePackageFiles() { + tl, err := template.ParseFiles("templates/pkg.templ.go") + if err != nil { + panic(err) + } + + for _, mode := range Instances { + buf := new(bytes.Buffer) + err := tl.Execute(buf, mode) + if err != nil { + panic(err) + } + + res := string(buf.Bytes()) + offset := strings.Index(res, TemplateWarning) + if offset == -1 { + panic("Missing template warning in pkg.templ.go") + } + err = ioutil.WriteFile(mode.Pkg()+"/kyber.go", []byte(res[offset:]), 0644) + if err != nil { + panic(err) + } + } +} diff --git a/src/circl/kem/kyber/kat_test.go b/src/circl/kem/kyber/kat_test.go new file mode 100644 index 00000000000..710be078e93 --- /dev/null +++ b/src/circl/kem/kyber/kat_test.go @@ -0,0 +1,78 @@ +package kyber + +// Code to generate the NIST "PQCsignKAT" test vectors. +// See PQCsignKAT_sign.c and randombytes.c in the reference implementation. + +import ( + "bytes" + "crypto/sha256" + "fmt" + "testing" + + "circl/internal/nist" + "circl/kem/schemes" +) + +func TestPQCgenKATKem(t *testing.T) { + kats := []struct { + name string + want string + }{ + // Computed from reference implementation + {"Kyber1024", "89248f2f33f7f4f7051729111f3049c409a933ec904aedadf035f30fa5646cd5"}, + {"Kyber768", "a1e122cad3c24bc51622e4c242d8b8acbcd3f618fee4220400605ca8f9ea02c2"}, + {"Kyber512", "e9c2bd37133fcb40772f81559f14b1f58dccd1c816701be9ba6214d43baf4547"}, + } + for _, kat := range kats { + kat := kat + t.Run(kat.name, func(t *testing.T) { + testPQCgenKATKem(t, kat.name, kat.want) + }) + } +} + +func testPQCgenKATKem(t *testing.T, name, expected string) { + scheme := schemes.ByName(name) + if scheme == nil { + t.Fatal() + } + + var seed [48]byte + kseed := make([]byte, scheme.SeedSize()) + eseed := make([]byte, scheme.EncapsulationSeedSize()) + for i := 0; i < 48; i++ { + seed[i] = byte(i) + } + f := sha256.New() + g := nist.NewDRBG(&seed) + fmt.Fprintf(f, "# %s\n\n", name) + for i := 0; i < 100; i++ { + g.Fill(seed[:]) + fmt.Fprintf(f, "count = %d\n", i) + fmt.Fprintf(f, "seed = %X\n", seed) + g2 := nist.NewDRBG(&seed) + + // This is not equivalent to g2.Fill(kseed[:]). As the reference + // implementation calls randombytes twice generating the keypair, + // we have to do that as well. + g2.Fill(kseed[:32]) + g2.Fill(kseed[32:]) + + g2.Fill(eseed) + pk, sk := scheme.DeriveKeyPair(kseed) + ppk, _ := pk.MarshalBinary() + psk, _ := sk.MarshalBinary() + ct, ss, _ := scheme.EncapsulateDeterministically(pk, eseed) + ss2, _ := scheme.Decapsulate(sk, ct) + if !bytes.Equal(ss, ss2) { + t.Fatal() + } + fmt.Fprintf(f, "pk = %X\n", ppk) + fmt.Fprintf(f, "sk = %X\n", psk) + fmt.Fprintf(f, "ct = %X\n", ct) + fmt.Fprintf(f, "ss = %X\n\n", ss) + } + if fmt.Sprintf("%x", f.Sum(nil)) != expected { + t.Fatal() + } +} diff --git a/src/circl/kem/kyber/kyber1024/kyber.go b/src/circl/kem/kyber/kyber1024/kyber.go new file mode 100644 index 00000000000..4cdc5cca240 --- /dev/null +++ b/src/circl/kem/kyber/kyber1024/kyber.go @@ -0,0 +1,402 @@ +// Code generated from pkg.templ.go. DO NOT EDIT. + +// Package kyber1024 implements the IND-CCA2 secure key encapsulation mechanism +// Kyber1024.CCAKEM as submitted to round 3 of the NIST PQC competition and +// described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +package kyber1024 + +import ( + "circl/internal/sha3" + "circl/kem" + cpapke "circl/pke/kyber/kyber1024" + + "bytes" + cryptoRand "crypto/rand" + "crypto/subtle" + "io" +) + +const ( + // Size of seed for NewKeyFromSeed + KeySeedSize = cpapke.KeySeedSize + 32 + + // Size of seed for EncapsulateTo. + EncapsulationSeedSize = 32 + + // Size of the established shared key. + SharedKeySize = 32 + + // Size of the encapsulated shared key. + CiphertextSize = cpapke.CiphertextSize + + // Size of a packed public key. + PublicKeySize = cpapke.PublicKeySize + + // Size of a packed private key. + PrivateKeySize = cpapke.PrivateKeySize + cpapke.PublicKeySize + 64 +) + +// Type of a Kyber1024.CCAKEM public key +type PublicKey struct { + pk *cpapke.PublicKey + + hpk [32]byte // H(pk) +} + +// Type of a Kyber1024.CCAKEM private key +type PrivateKey struct { + sk *cpapke.PrivateKey + pk *cpapke.PublicKey + hpk [32]byte // H(pk) + z [32]byte +} + +// NewKeyFromSeed derives a public/private keypair deterministically +// from the given seed. +// +// Panics if seed is not of length KeySeedSize. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + var sk PrivateKey + var pk PublicKey + + if len(seed) != KeySeedSize { + panic("seed must be of length KeySeedSize") + } + + pk.pk, sk.sk = cpapke.NewKeyFromSeed(seed[:cpapke.KeySeedSize]) + sk.pk = pk.pk + copy(sk.z[:], seed[cpapke.KeySeedSize:]) + + // Compute H(pk) + var ppk [cpapke.PublicKeySize]byte + sk.pk.Pack(ppk[:]) + h := sha3.New256() + h.Write(ppk[:]) + h.Sum(sk.hpk[:0]) + copy(pk.hpk[:], sk.hpk[:]) + + return &pk, &sk +} + +// GenerateKeyPair generates public and private keys using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKeyPair(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [KeySeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(seed[:]) + return pk, sk, nil +} + +// EncapsulateTo generates a shared key and ciphertext that contains it +// for the public key using randomness from seed and writes the shared key +// to ss and ciphertext to ct. +// +// Panics if ss, ct or seed are not of length SharedKeySize, CiphertextSize +// and EncapsulationSeedSize respectively. +// +// seed may be nil, in which case crypto/rand.Reader is used to generate one. +func (pk *PublicKey) EncapsulateTo(ct, ss []byte, seed []byte) { + if seed == nil { + seed := make([]byte, EncapsulationSeedSize) + cryptoRand.Read(seed[:]) + } else { + if len(seed) != EncapsulationSeedSize { + panic("seed must be of length EncapsulationSeedSize") + } + } + + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + + if len(ss) != SharedKeySize { + panic("ss must be of length SharedKeySize") + } + + // m = H(seed) + var m [32]byte + h := sha3.New256() + h.Write(seed[:]) + h.Sum(m[:0]) + + // (K', r) = G(m ‖ H(pk)) + var kr [64]byte + g := sha3.New512() + g.Write(m[:]) + g.Write(pk.hpk[:]) + g.Sum(kr[:0]) + + // c = Kyber.CPAPKE.Enc(pk, m, r) + pk.pk.EncryptTo(ct, kr[32:], m[:]) + + // Compute H(c) and put in second slot of kr, which will be (K', H(c)). + h.Reset() + h.Write(ct[:CiphertextSize]) + h.Sum(kr[32:32]) + + // K = KDF(K' ‖ H(c)) + kdf := sha3.NewShake256() + kdf.Write(kr[:]) + kdf.Read(ss[:SharedKeySize]) +} + +// DecapsulateTo computes the shared key which is encapsulated in ct +// for the private key. +// +// Panics if ct or ss are not of length CiphertextSize and SharedKeySize +// respectively. +func (sk *PrivateKey) DecapsulateTo(ss, ct []byte) { + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + + if len(ss) != SharedKeySize { + panic("ss must be of length SharedKeySize") + } + + // m' = Kyber.CPAPKE.Dec(sk, ct) + var m2 [32]byte + sk.sk.DecryptTo(m2[:], ct) + + // (K'', r') = G(m' ‖ H(pk)) + var kr2 [64]byte + g := sha3.New512() + g.Write(m2[:]) + g.Write(sk.hpk[:]) + g.Sum(kr2[:0]) + + // c' = Kyber.CPAPKE.Enc(pk, m', r') + var ct2 [CiphertextSize]byte + sk.pk.EncryptTo(ct2[:], kr2[32:], m2[:]) + + // Compute H(c) and put in second slot of kr2, which will be (K'', H(c)). + h := sha3.New256() + h.Write(ct[:CiphertextSize]) + h.Sum(kr2[32:32]) + + // Replace K'' by z in the first slot of kr2 if c ≠ c'. + subtle.ConstantTimeCopy( + 1-subtle.ConstantTimeCompare(ct, ct2[:]), + kr2[:32], + sk.z[:], + ) + + // K = KDF(K''/z, H(c)) + kdf := sha3.NewShake256() + kdf.Write(kr2[:]) + kdf.Read(ss[:SharedKeySize]) +} + +// Packs sk to buf. +// +// Panics if buf is not of size PrivateKeySize. +func (sk *PrivateKey) Pack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of length PrivateKeySize") + } + + sk.sk.Pack(buf[:cpapke.PrivateKeySize]) + buf = buf[cpapke.PrivateKeySize:] + sk.pk.Pack(buf[:cpapke.PublicKeySize]) + buf = buf[cpapke.PublicKeySize:] + copy(buf, sk.hpk[:]) + buf = buf[32:] + copy(buf, sk.z[:]) +} + +// Unpacks sk from buf. +// +// Panics if buf is not of size PrivateKeySize. +func (sk *PrivateKey) Unpack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of length PrivateKeySize") + } + + sk.sk = new(cpapke.PrivateKey) + sk.sk.Unpack(buf[:cpapke.PrivateKeySize]) + buf = buf[cpapke.PrivateKeySize:] + sk.pk = new(cpapke.PublicKey) + sk.pk.Unpack(buf[:cpapke.PublicKeySize]) + buf = buf[cpapke.PublicKeySize:] + copy(sk.hpk[:], buf[:32]) + copy(sk.z[:], buf[32:]) +} + +// Packs pk to buf. +// +// Panics if buf is not of size PublicKeySize. +func (pk *PublicKey) Pack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of length PublicKeySize") + } + + pk.pk.Pack(buf) +} + +// Unpacks pk from buf. +// +// Panics if buf is not of size PublicKeySize. +func (pk *PublicKey) Unpack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of length PublicKeySize") + } + + pk.pk = new(cpapke.PublicKey) + pk.pk.Unpack(buf) + + // Compute cached H(pk) + h := sha3.New256() + h.Write(buf) + h.Sum(pk.hpk[:0]) +} + +// Boilerplate down below for the KEM scheme API. + +type scheme struct{} + +var sch kem.Scheme = &scheme{} + +// Scheme returns a KEM interface. +func Scheme() kem.Scheme { return sch } + +func (*scheme) Name() string { return "Kyber1024" } +func (*scheme) PublicKeySize() int { return PublicKeySize } +func (*scheme) PrivateKeySize() int { return PrivateKeySize } +func (*scheme) SeedSize() int { return KeySeedSize } +func (*scheme) SharedKeySize() int { return SharedKeySize } +func (*scheme) CiphertextSize() int { return CiphertextSize } +func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } + +func (sk *PrivateKey) Scheme() kem.Scheme { return sch } +func (pk *PublicKey) Scheme() kem.Scheme { return sch } + +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + var ret [PrivateKeySize]byte + sk.Pack(ret[:]) + return ret[:], nil +} + +func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { + oth, ok := other.(*PrivateKey) + if !ok { + return false + } + if sk.pk == nil && oth.pk == nil { + return true + } + if sk.pk == nil || oth.pk == nil { + return false + } + if !bytes.Equal(sk.hpk[:], oth.hpk[:]) || + !bytes.Equal(sk.z[:], oth.z[:]) { + return false + } + return sk.sk.Equal(oth.sk) +} + +func (pk *PublicKey) Equal(other kem.PublicKey) bool { + oth, ok := other.(*PublicKey) + if !ok { + return false + } + if pk.pk == nil && oth.pk == nil { + return true + } + if pk.pk == nil || oth.pk == nil { + return false + } + return bytes.Equal(pk.hpk[:], oth.hpk[:]) +} + +func (sk *PrivateKey) Public() kem.PublicKey { + pk := new(PublicKey) + pk.pk = sk.pk + copy(pk.hpk[:], sk.hpk[:]) + return pk +} + +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + var ret [PublicKeySize]byte + pk.Pack(ret[:]) + return ret[:], nil +} + +func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + return GenerateKeyPair(cryptoRand.Reader) +} + +func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + if len(seed) != KeySeedSize { + panic(kem.ErrSeedSize) + } + return NewKeyFromSeed(seed[:]) +} + +func (*scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { + ct = make([]byte, CiphertextSize) + ss = make([]byte, SharedKeySize) + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + pub.EncapsulateTo(ct, ss, nil) + return +} + +func (*scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) ( + ct, ss []byte, err error) { + if len(seed) != EncapsulationSeedSize { + return nil, nil, kem.ErrSeedSize + } + + ct = make([]byte, CiphertextSize) + ss = make([]byte, SharedKeySize) + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + pub.EncapsulateTo(ct, ss, seed) + return +} + +func (*scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { + if len(ct) != CiphertextSize { + return nil, kem.ErrCiphertextSize + } + + priv, ok := sk.(*PrivateKey) + if !ok { + return nil, kem.ErrTypeMismatch + } + ss := make([]byte, SharedKeySize) + priv.DecapsulateTo(ss, ct) + return ss, nil +} + +func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { + if len(buf) != PublicKeySize { + return nil, kem.ErrPubKeySize + } + var ret PublicKey + ret.Unpack(buf) + return &ret, nil +} + +func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { + if len(buf) != PrivateKeySize { + return nil, kem.ErrPrivKeySize + } + var ret PrivateKey + ret.Unpack(buf) + return &ret, nil +} diff --git a/src/circl/kem/kyber/kyber512/kyber.go b/src/circl/kem/kyber/kyber512/kyber.go new file mode 100644 index 00000000000..45b0fc9d057 --- /dev/null +++ b/src/circl/kem/kyber/kyber512/kyber.go @@ -0,0 +1,402 @@ +// Code generated from pkg.templ.go. DO NOT EDIT. + +// Package kyber512 implements the IND-CCA2 secure key encapsulation mechanism +// Kyber512.CCAKEM as submitted to round 3 of the NIST PQC competition and +// described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +package kyber512 + +import ( + "circl/internal/sha3" + "circl/kem" + cpapke "circl/pke/kyber/kyber512" + + "bytes" + cryptoRand "crypto/rand" + "crypto/subtle" + "io" +) + +const ( + // Size of seed for NewKeyFromSeed + KeySeedSize = cpapke.KeySeedSize + 32 + + // Size of seed for EncapsulateTo. + EncapsulationSeedSize = 32 + + // Size of the established shared key. + SharedKeySize = 32 + + // Size of the encapsulated shared key. + CiphertextSize = cpapke.CiphertextSize + + // Size of a packed public key. + PublicKeySize = cpapke.PublicKeySize + + // Size of a packed private key. + PrivateKeySize = cpapke.PrivateKeySize + cpapke.PublicKeySize + 64 +) + +// Type of a Kyber512.CCAKEM public key +type PublicKey struct { + pk *cpapke.PublicKey + + hpk [32]byte // H(pk) +} + +// Type of a Kyber512.CCAKEM private key +type PrivateKey struct { + sk *cpapke.PrivateKey + pk *cpapke.PublicKey + hpk [32]byte // H(pk) + z [32]byte +} + +// NewKeyFromSeed derives a public/private keypair deterministically +// from the given seed. +// +// Panics if seed is not of length KeySeedSize. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + var sk PrivateKey + var pk PublicKey + + if len(seed) != KeySeedSize { + panic("seed must be of length KeySeedSize") + } + + pk.pk, sk.sk = cpapke.NewKeyFromSeed(seed[:cpapke.KeySeedSize]) + sk.pk = pk.pk + copy(sk.z[:], seed[cpapke.KeySeedSize:]) + + // Compute H(pk) + var ppk [cpapke.PublicKeySize]byte + sk.pk.Pack(ppk[:]) + h := sha3.New256() + h.Write(ppk[:]) + h.Sum(sk.hpk[:0]) + copy(pk.hpk[:], sk.hpk[:]) + + return &pk, &sk +} + +// GenerateKeyPair generates public and private keys using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKeyPair(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [KeySeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(seed[:]) + return pk, sk, nil +} + +// EncapsulateTo generates a shared key and ciphertext that contains it +// for the public key using randomness from seed and writes the shared key +// to ss and ciphertext to ct. +// +// Panics if ss, ct or seed are not of length SharedKeySize, CiphertextSize +// and EncapsulationSeedSize respectively. +// +// seed may be nil, in which case crypto/rand.Reader is used to generate one. +func (pk *PublicKey) EncapsulateTo(ct, ss []byte, seed []byte) { + if seed == nil { + seed := make([]byte, EncapsulationSeedSize) + cryptoRand.Read(seed[:]) + } else { + if len(seed) != EncapsulationSeedSize { + panic("seed must be of length EncapsulationSeedSize") + } + } + + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + + if len(ss) != SharedKeySize { + panic("ss must be of length SharedKeySize") + } + + // m = H(seed) + var m [32]byte + h := sha3.New256() + h.Write(seed[:]) + h.Sum(m[:0]) + + // (K', r) = G(m ‖ H(pk)) + var kr [64]byte + g := sha3.New512() + g.Write(m[:]) + g.Write(pk.hpk[:]) + g.Sum(kr[:0]) + + // c = Kyber.CPAPKE.Enc(pk, m, r) + pk.pk.EncryptTo(ct, kr[32:], m[:]) + + // Compute H(c) and put in second slot of kr, which will be (K', H(c)). + h.Reset() + h.Write(ct[:CiphertextSize]) + h.Sum(kr[32:32]) + + // K = KDF(K' ‖ H(c)) + kdf := sha3.NewShake256() + kdf.Write(kr[:]) + kdf.Read(ss[:SharedKeySize]) +} + +// DecapsulateTo computes the shared key which is encapsulated in ct +// for the private key. +// +// Panics if ct or ss are not of length CiphertextSize and SharedKeySize +// respectively. +func (sk *PrivateKey) DecapsulateTo(ss, ct []byte) { + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + + if len(ss) != SharedKeySize { + panic("ss must be of length SharedKeySize") + } + + // m' = Kyber.CPAPKE.Dec(sk, ct) + var m2 [32]byte + sk.sk.DecryptTo(m2[:], ct) + + // (K'', r') = G(m' ‖ H(pk)) + var kr2 [64]byte + g := sha3.New512() + g.Write(m2[:]) + g.Write(sk.hpk[:]) + g.Sum(kr2[:0]) + + // c' = Kyber.CPAPKE.Enc(pk, m', r') + var ct2 [CiphertextSize]byte + sk.pk.EncryptTo(ct2[:], kr2[32:], m2[:]) + + // Compute H(c) and put in second slot of kr2, which will be (K'', H(c)). + h := sha3.New256() + h.Write(ct[:CiphertextSize]) + h.Sum(kr2[32:32]) + + // Replace K'' by z in the first slot of kr2 if c ≠ c'. + subtle.ConstantTimeCopy( + 1-subtle.ConstantTimeCompare(ct, ct2[:]), + kr2[:32], + sk.z[:], + ) + + // K = KDF(K''/z, H(c)) + kdf := sha3.NewShake256() + kdf.Write(kr2[:]) + kdf.Read(ss[:SharedKeySize]) +} + +// Packs sk to buf. +// +// Panics if buf is not of size PrivateKeySize. +func (sk *PrivateKey) Pack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of length PrivateKeySize") + } + + sk.sk.Pack(buf[:cpapke.PrivateKeySize]) + buf = buf[cpapke.PrivateKeySize:] + sk.pk.Pack(buf[:cpapke.PublicKeySize]) + buf = buf[cpapke.PublicKeySize:] + copy(buf, sk.hpk[:]) + buf = buf[32:] + copy(buf, sk.z[:]) +} + +// Unpacks sk from buf. +// +// Panics if buf is not of size PrivateKeySize. +func (sk *PrivateKey) Unpack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of length PrivateKeySize") + } + + sk.sk = new(cpapke.PrivateKey) + sk.sk.Unpack(buf[:cpapke.PrivateKeySize]) + buf = buf[cpapke.PrivateKeySize:] + sk.pk = new(cpapke.PublicKey) + sk.pk.Unpack(buf[:cpapke.PublicKeySize]) + buf = buf[cpapke.PublicKeySize:] + copy(sk.hpk[:], buf[:32]) + copy(sk.z[:], buf[32:]) +} + +// Packs pk to buf. +// +// Panics if buf is not of size PublicKeySize. +func (pk *PublicKey) Pack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of length PublicKeySize") + } + + pk.pk.Pack(buf) +} + +// Unpacks pk from buf. +// +// Panics if buf is not of size PublicKeySize. +func (pk *PublicKey) Unpack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of length PublicKeySize") + } + + pk.pk = new(cpapke.PublicKey) + pk.pk.Unpack(buf) + + // Compute cached H(pk) + h := sha3.New256() + h.Write(buf) + h.Sum(pk.hpk[:0]) +} + +// Boilerplate down below for the KEM scheme API. + +type scheme struct{} + +var sch kem.Scheme = &scheme{} + +// Scheme returns a KEM interface. +func Scheme() kem.Scheme { return sch } + +func (*scheme) Name() string { return "Kyber512" } +func (*scheme) PublicKeySize() int { return PublicKeySize } +func (*scheme) PrivateKeySize() int { return PrivateKeySize } +func (*scheme) SeedSize() int { return KeySeedSize } +func (*scheme) SharedKeySize() int { return SharedKeySize } +func (*scheme) CiphertextSize() int { return CiphertextSize } +func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } + +func (sk *PrivateKey) Scheme() kem.Scheme { return sch } +func (pk *PublicKey) Scheme() kem.Scheme { return sch } + +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + var ret [PrivateKeySize]byte + sk.Pack(ret[:]) + return ret[:], nil +} + +func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { + oth, ok := other.(*PrivateKey) + if !ok { + return false + } + if sk.pk == nil && oth.pk == nil { + return true + } + if sk.pk == nil || oth.pk == nil { + return false + } + if !bytes.Equal(sk.hpk[:], oth.hpk[:]) || + !bytes.Equal(sk.z[:], oth.z[:]) { + return false + } + return sk.sk.Equal(oth.sk) +} + +func (pk *PublicKey) Equal(other kem.PublicKey) bool { + oth, ok := other.(*PublicKey) + if !ok { + return false + } + if pk.pk == nil && oth.pk == nil { + return true + } + if pk.pk == nil || oth.pk == nil { + return false + } + return bytes.Equal(pk.hpk[:], oth.hpk[:]) +} + +func (sk *PrivateKey) Public() kem.PublicKey { + pk := new(PublicKey) + pk.pk = sk.pk + copy(pk.hpk[:], sk.hpk[:]) + return pk +} + +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + var ret [PublicKeySize]byte + pk.Pack(ret[:]) + return ret[:], nil +} + +func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + return GenerateKeyPair(cryptoRand.Reader) +} + +func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + if len(seed) != KeySeedSize { + panic(kem.ErrSeedSize) + } + return NewKeyFromSeed(seed[:]) +} + +func (*scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { + ct = make([]byte, CiphertextSize) + ss = make([]byte, SharedKeySize) + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + pub.EncapsulateTo(ct, ss, nil) + return +} + +func (*scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) ( + ct, ss []byte, err error) { + if len(seed) != EncapsulationSeedSize { + return nil, nil, kem.ErrSeedSize + } + + ct = make([]byte, CiphertextSize) + ss = make([]byte, SharedKeySize) + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + pub.EncapsulateTo(ct, ss, seed) + return +} + +func (*scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { + if len(ct) != CiphertextSize { + return nil, kem.ErrCiphertextSize + } + + priv, ok := sk.(*PrivateKey) + if !ok { + return nil, kem.ErrTypeMismatch + } + ss := make([]byte, SharedKeySize) + priv.DecapsulateTo(ss, ct) + return ss, nil +} + +func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { + if len(buf) != PublicKeySize { + return nil, kem.ErrPubKeySize + } + var ret PublicKey + ret.Unpack(buf) + return &ret, nil +} + +func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { + if len(buf) != PrivateKeySize { + return nil, kem.ErrPrivKeySize + } + var ret PrivateKey + ret.Unpack(buf) + return &ret, nil +} diff --git a/src/circl/kem/kyber/kyber768/kyber.go b/src/circl/kem/kyber/kyber768/kyber.go new file mode 100644 index 00000000000..70232c6b52b --- /dev/null +++ b/src/circl/kem/kyber/kyber768/kyber.go @@ -0,0 +1,402 @@ +// Code generated from pkg.templ.go. DO NOT EDIT. + +// Package kyber768 implements the IND-CCA2 secure key encapsulation mechanism +// Kyber768.CCAKEM as submitted to round 3 of the NIST PQC competition and +// described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +package kyber768 + +import ( + "circl/internal/sha3" + "circl/kem" + cpapke "circl/pke/kyber/kyber768" + + "bytes" + cryptoRand "crypto/rand" + "crypto/subtle" + "io" +) + +const ( + // Size of seed for NewKeyFromSeed + KeySeedSize = cpapke.KeySeedSize + 32 + + // Size of seed for EncapsulateTo. + EncapsulationSeedSize = 32 + + // Size of the established shared key. + SharedKeySize = 32 + + // Size of the encapsulated shared key. + CiphertextSize = cpapke.CiphertextSize + + // Size of a packed public key. + PublicKeySize = cpapke.PublicKeySize + + // Size of a packed private key. + PrivateKeySize = cpapke.PrivateKeySize + cpapke.PublicKeySize + 64 +) + +// Type of a Kyber768.CCAKEM public key +type PublicKey struct { + pk *cpapke.PublicKey + + hpk [32]byte // H(pk) +} + +// Type of a Kyber768.CCAKEM private key +type PrivateKey struct { + sk *cpapke.PrivateKey + pk *cpapke.PublicKey + hpk [32]byte // H(pk) + z [32]byte +} + +// NewKeyFromSeed derives a public/private keypair deterministically +// from the given seed. +// +// Panics if seed is not of length KeySeedSize. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + var sk PrivateKey + var pk PublicKey + + if len(seed) != KeySeedSize { + panic("seed must be of length KeySeedSize") + } + + pk.pk, sk.sk = cpapke.NewKeyFromSeed(seed[:cpapke.KeySeedSize]) + sk.pk = pk.pk + copy(sk.z[:], seed[cpapke.KeySeedSize:]) + + // Compute H(pk) + var ppk [cpapke.PublicKeySize]byte + sk.pk.Pack(ppk[:]) + h := sha3.New256() + h.Write(ppk[:]) + h.Sum(sk.hpk[:0]) + copy(pk.hpk[:], sk.hpk[:]) + + return &pk, &sk +} + +// GenerateKeyPair generates public and private keys using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKeyPair(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [KeySeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(seed[:]) + return pk, sk, nil +} + +// EncapsulateTo generates a shared key and ciphertext that contains it +// for the public key using randomness from seed and writes the shared key +// to ss and ciphertext to ct. +// +// Panics if ss, ct or seed are not of length SharedKeySize, CiphertextSize +// and EncapsulationSeedSize respectively. +// +// seed may be nil, in which case crypto/rand.Reader is used to generate one. +func (pk *PublicKey) EncapsulateTo(ct, ss []byte, seed []byte) { + if seed == nil { + seed := make([]byte, EncapsulationSeedSize) + cryptoRand.Read(seed[:]) + } else { + if len(seed) != EncapsulationSeedSize { + panic("seed must be of length EncapsulationSeedSize") + } + } + + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + + if len(ss) != SharedKeySize { + panic("ss must be of length SharedKeySize") + } + + // m = H(seed) + var m [32]byte + h := sha3.New256() + h.Write(seed[:]) + h.Sum(m[:0]) + + // (K', r) = G(m ‖ H(pk)) + var kr [64]byte + g := sha3.New512() + g.Write(m[:]) + g.Write(pk.hpk[:]) + g.Sum(kr[:0]) + + // c = Kyber.CPAPKE.Enc(pk, m, r) + pk.pk.EncryptTo(ct, kr[32:], m[:]) + + // Compute H(c) and put in second slot of kr, which will be (K', H(c)). + h.Reset() + h.Write(ct[:CiphertextSize]) + h.Sum(kr[32:32]) + + // K = KDF(K' ‖ H(c)) + kdf := sha3.NewShake256() + kdf.Write(kr[:]) + kdf.Read(ss[:SharedKeySize]) +} + +// DecapsulateTo computes the shared key which is encapsulated in ct +// for the private key. +// +// Panics if ct or ss are not of length CiphertextSize and SharedKeySize +// respectively. +func (sk *PrivateKey) DecapsulateTo(ss, ct []byte) { + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + + if len(ss) != SharedKeySize { + panic("ss must be of length SharedKeySize") + } + + // m' = Kyber.CPAPKE.Dec(sk, ct) + var m2 [32]byte + sk.sk.DecryptTo(m2[:], ct) + + // (K'', r') = G(m' ‖ H(pk)) + var kr2 [64]byte + g := sha3.New512() + g.Write(m2[:]) + g.Write(sk.hpk[:]) + g.Sum(kr2[:0]) + + // c' = Kyber.CPAPKE.Enc(pk, m', r') + var ct2 [CiphertextSize]byte + sk.pk.EncryptTo(ct2[:], kr2[32:], m2[:]) + + // Compute H(c) and put in second slot of kr2, which will be (K'', H(c)). + h := sha3.New256() + h.Write(ct[:CiphertextSize]) + h.Sum(kr2[32:32]) + + // Replace K'' by z in the first slot of kr2 if c ≠ c'. + subtle.ConstantTimeCopy( + 1-subtle.ConstantTimeCompare(ct, ct2[:]), + kr2[:32], + sk.z[:], + ) + + // K = KDF(K''/z, H(c)) + kdf := sha3.NewShake256() + kdf.Write(kr2[:]) + kdf.Read(ss[:SharedKeySize]) +} + +// Packs sk to buf. +// +// Panics if buf is not of size PrivateKeySize. +func (sk *PrivateKey) Pack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of length PrivateKeySize") + } + + sk.sk.Pack(buf[:cpapke.PrivateKeySize]) + buf = buf[cpapke.PrivateKeySize:] + sk.pk.Pack(buf[:cpapke.PublicKeySize]) + buf = buf[cpapke.PublicKeySize:] + copy(buf, sk.hpk[:]) + buf = buf[32:] + copy(buf, sk.z[:]) +} + +// Unpacks sk from buf. +// +// Panics if buf is not of size PrivateKeySize. +func (sk *PrivateKey) Unpack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of length PrivateKeySize") + } + + sk.sk = new(cpapke.PrivateKey) + sk.sk.Unpack(buf[:cpapke.PrivateKeySize]) + buf = buf[cpapke.PrivateKeySize:] + sk.pk = new(cpapke.PublicKey) + sk.pk.Unpack(buf[:cpapke.PublicKeySize]) + buf = buf[cpapke.PublicKeySize:] + copy(sk.hpk[:], buf[:32]) + copy(sk.z[:], buf[32:]) +} + +// Packs pk to buf. +// +// Panics if buf is not of size PublicKeySize. +func (pk *PublicKey) Pack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of length PublicKeySize") + } + + pk.pk.Pack(buf) +} + +// Unpacks pk from buf. +// +// Panics if buf is not of size PublicKeySize. +func (pk *PublicKey) Unpack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of length PublicKeySize") + } + + pk.pk = new(cpapke.PublicKey) + pk.pk.Unpack(buf) + + // Compute cached H(pk) + h := sha3.New256() + h.Write(buf) + h.Sum(pk.hpk[:0]) +} + +// Boilerplate down below for the KEM scheme API. + +type scheme struct{} + +var sch kem.Scheme = &scheme{} + +// Scheme returns a KEM interface. +func Scheme() kem.Scheme { return sch } + +func (*scheme) Name() string { return "Kyber768" } +func (*scheme) PublicKeySize() int { return PublicKeySize } +func (*scheme) PrivateKeySize() int { return PrivateKeySize } +func (*scheme) SeedSize() int { return KeySeedSize } +func (*scheme) SharedKeySize() int { return SharedKeySize } +func (*scheme) CiphertextSize() int { return CiphertextSize } +func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } + +func (sk *PrivateKey) Scheme() kem.Scheme { return sch } +func (pk *PublicKey) Scheme() kem.Scheme { return sch } + +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + var ret [PrivateKeySize]byte + sk.Pack(ret[:]) + return ret[:], nil +} + +func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { + oth, ok := other.(*PrivateKey) + if !ok { + return false + } + if sk.pk == nil && oth.pk == nil { + return true + } + if sk.pk == nil || oth.pk == nil { + return false + } + if !bytes.Equal(sk.hpk[:], oth.hpk[:]) || + !bytes.Equal(sk.z[:], oth.z[:]) { + return false + } + return sk.sk.Equal(oth.sk) +} + +func (pk *PublicKey) Equal(other kem.PublicKey) bool { + oth, ok := other.(*PublicKey) + if !ok { + return false + } + if pk.pk == nil && oth.pk == nil { + return true + } + if pk.pk == nil || oth.pk == nil { + return false + } + return bytes.Equal(pk.hpk[:], oth.hpk[:]) +} + +func (sk *PrivateKey) Public() kem.PublicKey { + pk := new(PublicKey) + pk.pk = sk.pk + copy(pk.hpk[:], sk.hpk[:]) + return pk +} + +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + var ret [PublicKeySize]byte + pk.Pack(ret[:]) + return ret[:], nil +} + +func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + return GenerateKeyPair(cryptoRand.Reader) +} + +func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + if len(seed) != KeySeedSize { + panic(kem.ErrSeedSize) + } + return NewKeyFromSeed(seed[:]) +} + +func (*scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { + ct = make([]byte, CiphertextSize) + ss = make([]byte, SharedKeySize) + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + pub.EncapsulateTo(ct, ss, nil) + return +} + +func (*scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) ( + ct, ss []byte, err error) { + if len(seed) != EncapsulationSeedSize { + return nil, nil, kem.ErrSeedSize + } + + ct = make([]byte, CiphertextSize) + ss = make([]byte, SharedKeySize) + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + pub.EncapsulateTo(ct, ss, seed) + return +} + +func (*scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { + if len(ct) != CiphertextSize { + return nil, kem.ErrCiphertextSize + } + + priv, ok := sk.(*PrivateKey) + if !ok { + return nil, kem.ErrTypeMismatch + } + ss := make([]byte, SharedKeySize) + priv.DecapsulateTo(ss, ct) + return ss, nil +} + +func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { + if len(buf) != PublicKeySize { + return nil, kem.ErrPubKeySize + } + var ret PublicKey + ret.Unpack(buf) + return &ret, nil +} + +func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { + if len(buf) != PrivateKeySize { + return nil, kem.ErrPrivKeySize + } + var ret PrivateKey + ret.Unpack(buf) + return &ret, nil +} diff --git a/src/circl/kem/kyber/templates/pkg.templ.go b/src/circl/kem/kyber/templates/pkg.templ.go new file mode 100644 index 00000000000..3d6edd32a99 --- /dev/null +++ b/src/circl/kem/kyber/templates/pkg.templ.go @@ -0,0 +1,406 @@ +// +build ignore +// The previous line (and this one up to the warning below) is removed by the +// template generator. + +// Code generated from pkg.templ.go. DO NOT EDIT. + +// Package {{.Pkg}} implements the IND-CCA2 secure key encapsulation mechanism +// {{.Name}}.CCAKEM as submitted to round 3 of the NIST PQC competition and +// described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +package {{.Pkg}} + +import ( + "circl/internal/sha3" + "circl/kem" + cpapke "circl/pke/kyber/{{.Pkg}}" + + "bytes" + cryptoRand "crypto/rand" + "crypto/subtle" + "io" +) + +const ( + // Size of seed for NewKeyFromSeed + KeySeedSize = cpapke.KeySeedSize + 32 + + // Size of seed for EncapsulateTo. + EncapsulationSeedSize = 32 + + // Size of the established shared key. + SharedKeySize = 32 + + // Size of the encapsulated shared key. + CiphertextSize = cpapke.CiphertextSize + + // Size of a packed public key. + PublicKeySize = cpapke.PublicKeySize + + // Size of a packed private key. + PrivateKeySize = cpapke.PrivateKeySize + cpapke.PublicKeySize + 64 +) + +// Type of a {{.Name}}.CCAKEM public key +type PublicKey struct { + pk *cpapke.PublicKey + + hpk [32]byte // H(pk) +} + +// Type of a {{.Name}}.CCAKEM private key +type PrivateKey struct { + sk *cpapke.PrivateKey + pk *cpapke.PublicKey + hpk [32]byte // H(pk) + z [32]byte +} + +// NewKeyFromSeed derives a public/private keypair deterministically +// from the given seed. +// +// Panics if seed is not of length KeySeedSize. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + var sk PrivateKey + var pk PublicKey + + if len(seed) != KeySeedSize { + panic("seed must be of length KeySeedSize") + } + + pk.pk, sk.sk = cpapke.NewKeyFromSeed(seed[:cpapke.KeySeedSize]) + sk.pk = pk.pk + copy(sk.z[:], seed[cpapke.KeySeedSize:]) + + // Compute H(pk) + var ppk [cpapke.PublicKeySize]byte + sk.pk.Pack(ppk[:]) + h := sha3.New256() + h.Write(ppk[:]) + h.Sum(sk.hpk[:0]) + copy(pk.hpk[:], sk.hpk[:]) + + return &pk, &sk +} + +// GenerateKeyPair generates public and private keys using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKeyPair(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [KeySeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(seed[:]) + return pk, sk, nil +} + +// EncapsulateTo generates a shared key and ciphertext that contains it +// for the public key using randomness from seed and writes the shared key +// to ss and ciphertext to ct. +// +// Panics if ss, ct or seed are not of length SharedKeySize, CiphertextSize +// and EncapsulationSeedSize respectively. +// +// seed may be nil, in which case crypto/rand.Reader is used to generate one. +func (pk *PublicKey) EncapsulateTo(ct, ss []byte, seed []byte) { + if seed == nil { + seed := make([]byte, EncapsulationSeedSize) + cryptoRand.Read(seed[:]) + } else { + if len(seed) != EncapsulationSeedSize { + panic("seed must be of length EncapsulationSeedSize") + } + } + + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + + if len(ss) != SharedKeySize { + panic("ss must be of length SharedKeySize") + } + + // m = H(seed) + var m [32]byte + h := sha3.New256() + h.Write(seed[:]) + h.Sum(m[:0]) + + // (K', r) = G(m ‖ H(pk)) + var kr [64]byte + g := sha3.New512() + g.Write(m[:]) + g.Write(pk.hpk[:]) + g.Sum(kr[:0]) + + // c = Kyber.CPAPKE.Enc(pk, m, r) + pk.pk.EncryptTo(ct, kr[32:], m[:]) + + // Compute H(c) and put in second slot of kr, which will be (K', H(c)). + h.Reset() + h.Write(ct[:CiphertextSize]) + h.Sum(kr[32:32]) + + // K = KDF(K' ‖ H(c)) + kdf := sha3.NewShake256() + kdf.Write(kr[:]) + kdf.Read(ss[:SharedKeySize]) +} + +// DecapsulateTo computes the shared key which is encapsulated in ct +// for the private key. +// +// Panics if ct or ss are not of length CiphertextSize and SharedKeySize +// respectively. +func (sk *PrivateKey) DecapsulateTo(ss, ct []byte) { + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + + if len(ss) != SharedKeySize { + panic("ss must be of length SharedKeySize") + } + + // m' = Kyber.CPAPKE.Dec(sk, ct) + var m2 [32]byte + sk.sk.DecryptTo(m2[:], ct) + + // (K'', r') = G(m' ‖ H(pk)) + var kr2 [64]byte + g := sha3.New512() + g.Write(m2[:]) + g.Write(sk.hpk[:]) + g.Sum(kr2[:0]) + + // c' = Kyber.CPAPKE.Enc(pk, m', r') + var ct2 [CiphertextSize]byte + sk.pk.EncryptTo(ct2[:], kr2[32:], m2[:]) + + // Compute H(c) and put in second slot of kr2, which will be (K'', H(c)). + h := sha3.New256() + h.Write(ct[:CiphertextSize]) + h.Sum(kr2[32:32]) + + // Replace K'' by z in the first slot of kr2 if c ≠ c'. + subtle.ConstantTimeCopy( + 1-subtle.ConstantTimeCompare(ct, ct2[:]), + kr2[:32], + sk.z[:], + ) + + // K = KDF(K''/z, H(c)) + kdf := sha3.NewShake256() + kdf.Write(kr2[:]) + kdf.Read(ss[:SharedKeySize]) +} + +// Packs sk to buf. +// +// Panics if buf is not of size PrivateKeySize. +func (sk *PrivateKey) Pack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of length PrivateKeySize") + } + + sk.sk.Pack(buf[:cpapke.PrivateKeySize]) + buf = buf[cpapke.PrivateKeySize:] + sk.pk.Pack(buf[:cpapke.PublicKeySize]) + buf = buf[cpapke.PublicKeySize:] + copy(buf, sk.hpk[:]) + buf = buf[32:] + copy(buf, sk.z[:]) +} + +// Unpacks sk from buf. +// +// Panics if buf is not of size PrivateKeySize. +func (sk *PrivateKey) Unpack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of length PrivateKeySize") + } + + sk.sk = new(cpapke.PrivateKey) + sk.sk.Unpack(buf[:cpapke.PrivateKeySize]) + buf = buf[cpapke.PrivateKeySize:] + sk.pk = new(cpapke.PublicKey) + sk.pk.Unpack(buf[:cpapke.PublicKeySize]) + buf = buf[cpapke.PublicKeySize:] + copy(sk.hpk[:], buf[:32]) + copy(sk.z[:], buf[32:]) +} + +// Packs pk to buf. +// +// Panics if buf is not of size PublicKeySize. +func (pk *PublicKey) Pack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of length PublicKeySize") + } + + pk.pk.Pack(buf) +} + +// Unpacks pk from buf. +// +// Panics if buf is not of size PublicKeySize. +func (pk *PublicKey) Unpack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of length PublicKeySize") + } + + pk.pk = new(cpapke.PublicKey) + pk.pk.Unpack(buf) + + // Compute cached H(pk) + h := sha3.New256() + h.Write(buf) + h.Sum(pk.hpk[:0]) +} + +// Boilerplate down below for the KEM scheme API. + +type scheme struct{} + +var sch kem.Scheme = &scheme{} + +// Scheme returns a KEM interface. +func Scheme() kem.Scheme { return sch } + +func (*scheme) Name() string { return "{{ .Name }}" } +func (*scheme) PublicKeySize() int { return PublicKeySize } +func (*scheme) PrivateKeySize() int { return PrivateKeySize } +func (*scheme) SeedSize() int { return KeySeedSize } +func (*scheme) SharedKeySize() int { return SharedKeySize } +func (*scheme) CiphertextSize() int { return CiphertextSize } +func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } + +func (sk *PrivateKey) Scheme() kem.Scheme { return sch } +func (pk *PublicKey) Scheme() kem.Scheme { return sch } + +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + var ret [PrivateKeySize]byte + sk.Pack(ret[:]) + return ret[:], nil +} + +func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { + oth, ok := other.(*PrivateKey) + if !ok { + return false + } + if sk.pk == nil && oth.pk == nil { + return true + } + if sk.pk == nil || oth.pk == nil { + return false + } + if !bytes.Equal(sk.hpk[:], oth.hpk[:]) || + !bytes.Equal(sk.z[:], oth.z[:]) { + return false + } + return sk.sk.Equal(oth.sk) +} + +func (pk *PublicKey) Equal(other kem.PublicKey) bool { + oth, ok := other.(*PublicKey) + if !ok { + return false + } + if pk.pk == nil && oth.pk == nil { + return true + } + if pk.pk == nil || oth.pk == nil { + return false + } + return bytes.Equal(pk.hpk[:], oth.hpk[:]) +} + +func (sk *PrivateKey) Public() kem.PublicKey { + pk := new(PublicKey) + pk.pk = sk.pk + copy(pk.hpk[:], sk.hpk[:]) + return pk +} + +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + var ret [PublicKeySize]byte + pk.Pack(ret[:]) + return ret[:], nil +} + +func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + return GenerateKeyPair(cryptoRand.Reader) +} + +func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + if len(seed) != KeySeedSize { + panic(kem.ErrSeedSize) + } + return NewKeyFromSeed(seed[:]) +} + +func (*scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) { + ct = make([]byte, CiphertextSize) + ss = make([]byte, SharedKeySize) + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + pub.EncapsulateTo(ct, ss, nil) + return +} + +func (*scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) ( + ct, ss []byte, err error) { + if len(seed) != EncapsulationSeedSize { + return nil, nil, kem.ErrSeedSize + } + + ct = make([]byte, CiphertextSize) + ss = make([]byte, SharedKeySize) + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + pub.EncapsulateTo(ct, ss, seed) + return +} + +func (*scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { + if len(ct) != CiphertextSize { + return nil, kem.ErrCiphertextSize + } + + priv, ok := sk.(*PrivateKey) + if !ok { + return nil, kem.ErrTypeMismatch + } + ss := make([]byte, SharedKeySize) + priv.DecapsulateTo(ss, ct) + return ss, nil +} + +func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { + if len(buf) != PublicKeySize { + return nil, kem.ErrPubKeySize + } + var ret PublicKey + ret.Unpack(buf) + return &ret, nil +} + +func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { + if len(buf) != PrivateKeySize { + return nil, kem.ErrPrivKeySize + } + var ret PrivateKey + ret.Unpack(buf) + return &ret, nil +} diff --git a/src/circl/kem/schemes/schemes.go b/src/circl/kem/schemes/schemes.go new file mode 100644 index 00000000000..50d9228556f --- /dev/null +++ b/src/circl/kem/schemes/schemes.go @@ -0,0 +1,63 @@ +// Package schemes contains a register of KEM schemes. +// +// Schemes Implemented +// +// Based on standard elliptic curves: +// HPKE_KEM_P256_HKDF_SHA256, HPKE_KEM_P384_HKDF_SHA384, HPKE_KEM_P521_HKDF_SHA512 +// Based on standard Diffie-Hellman functions: +// HPKE_KEM_X25519_HKDF_SHA256, HPKE_KEM_X448_HKDF_SHA512 +// Post-quantum kems: +// Kyber512, Kyber768, Kyber1024 +// SIKEp434, SIKEp503, SIKEp751 +package schemes + +import ( + "strings" + + "circl/hpke" + "circl/kem" + "circl/kem/hybrid" + "circl/kem/kyber/kyber1024" + "circl/kem/kyber/kyber512" + "circl/kem/kyber/kyber768" + "circl/kem/sike/sikep434" + "circl/kem/sike/sikep503" + "circl/kem/sike/sikep751" +) + +var allSchemes = [...]kem.Scheme{ + hpke.KEM_P256_HKDF_SHA256.Scheme(), + hpke.KEM_P384_HKDF_SHA384.Scheme(), + hpke.KEM_P521_HKDF_SHA512.Scheme(), + hpke.KEM_X25519_HKDF_SHA256.Scheme(), + hpke.KEM_X448_HKDF_SHA512.Scheme(), + kyber512.Scheme(), + kyber768.Scheme(), + kyber1024.Scheme(), + sikep434.Scheme(), + sikep503.Scheme(), + sikep751.Scheme(), + hybrid.Kyber512X25519(), + hybrid.Kyber768X448(), + hybrid.Kyber1024X448(), +} + +var allSchemeNames map[string]kem.Scheme + +func init() { + allSchemeNames = make(map[string]kem.Scheme) + for _, scheme := range allSchemes { + allSchemeNames[strings.ToLower(scheme.Name())] = scheme + } +} + +// ByName returns the scheme with the given name and nil if it is not +// supported. +// +// Names are case insensitive. +func ByName(name string) kem.Scheme { + return allSchemeNames[strings.ToLower(name)] +} + +// All returns all KEM schemes supported. +func All() []kem.Scheme { a := allSchemes; return a[:] } diff --git a/src/circl/kem/schemes/schemes_test.go b/src/circl/kem/schemes/schemes_test.go new file mode 100644 index 00000000000..8530c95bb68 --- /dev/null +++ b/src/circl/kem/schemes/schemes_test.go @@ -0,0 +1,149 @@ +package schemes_test + +import ( + "bytes" + "fmt" + "testing" + + "circl/kem/schemes" +) + +func TestCaseSensitivity(t *testing.T) { + if schemes.ByName("kyber512") != schemes.ByName("Kyber512") { + t.Fatal() + } +} + +func BenchmarkGenerateKeyPair(b *testing.B) { + allSchemes := schemes.All() + for _, scheme := range allSchemes { + scheme := scheme + b.Run(scheme.Name(), func(b *testing.B) { + for i := 0; i < b.N; i++ { + _, _, _ = scheme.GenerateKeyPair() + } + }) + } +} + +func BenchmarkEncapsulate(b *testing.B) { + allSchemes := schemes.All() + for _, scheme := range allSchemes { + scheme := scheme + pk, _, _ := scheme.GenerateKeyPair() + b.Run(scheme.Name(), func(b *testing.B) { + for i := 0; i < b.N; i++ { + _, _, _ = scheme.Encapsulate(pk) + } + }) + } +} + +func BenchmarkDecapsulate(b *testing.B) { + allSchemes := schemes.All() + for _, scheme := range allSchemes { + scheme := scheme + pk, sk, _ := scheme.GenerateKeyPair() + ct, _, _ := scheme.Encapsulate(pk) + b.Run(scheme.Name(), func(b *testing.B) { + for i := 0; i < b.N; i++ { + _, _ = scheme.Decapsulate(sk, ct) + } + }) + } +} + +func TestApi(t *testing.T) { + allSchemes := schemes.All() + for _, scheme := range allSchemes { + scheme := scheme + t.Run(scheme.Name(), func(t *testing.T) { + if scheme == nil { + t.Fatal() + } + + pk, sk, err := scheme.GenerateKeyPair() + if err != nil { + t.Fatal() + } + + packedPk, err := pk.MarshalBinary() + if err != nil { + t.Fatal() + } + + if len(packedPk) != scheme.PublicKeySize() { + t.Fatal() + } + + packedSk, err := sk.MarshalBinary() + if err != nil { + t.Fatal() + } + + if len(packedSk) != scheme.PrivateKeySize() { + t.Fatal() + } + + pk2, err := scheme.UnmarshalBinaryPublicKey(packedPk) + if err != nil { + t.Fatal() + } + + sk2, err := scheme.UnmarshalBinaryPrivateKey(packedSk) + if err != nil { + t.Fatal() + } + + if !sk.Equal(sk2) { + t.Fatal() + } + + if !pk.Equal(pk2) { + t.Fatal() + } + + ct, ss, err := scheme.Encapsulate(pk2) + if err != nil { + t.Fatal(err) + } + if len(ct) != scheme.CiphertextSize() { + t.Fatal() + } + if len(ss) != scheme.SharedKeySize() { + t.Fatal() + } + + ss2, err := scheme.Decapsulate(sk2, ct) + if err != nil { + t.Fatal(err) + } + if !bytes.Equal(ss, ss2) { + t.Fatal() + } + }) + } +} + +func Example_schemes() { + // import "circl/kem/schemes" + + for _, sch := range schemes.All() { + fmt.Println(sch.Name()) + } + // Output: + // HPKE_KEM_P256_HKDF_SHA256 + // HPKE_KEM_P384_HKDF_SHA384 + // HPKE_KEM_P521_HKDF_SHA512 + // HPKE_KEM_X25519_HKDF_SHA256 + // HPKE_KEM_X448_HKDF_SHA512 + // Kyber512 + // Kyber768 + // Kyber1024 + // SIKEp434 + // SIKEp503 + // SIKEp751 + // Kyber512-X25519 + // Kyber768-X448 + // Kyber1024-X448 +} diff --git a/src/circl/kem/sike/doc.go b/src/circl/kem/sike/doc.go new file mode 100644 index 00000000000..a2cb5e34bff --- /dev/null +++ b/src/circl/kem/sike/doc.go @@ -0,0 +1,4 @@ +//go:generate go run gen.go + +// Package sike contains the SIKE key encapsulation mechanism. +package sike diff --git a/src/circl/kem/sike/gen.go b/src/circl/kem/sike/gen.go new file mode 100644 index 00000000000..149ce43e388 --- /dev/null +++ b/src/circl/kem/sike/gen.go @@ -0,0 +1,68 @@ +// +build ignore + +// Autogenerates wrappers from templates to prevent too much duplicated code +// between the code for different modes. +package main + +import ( + "bytes" + "fmt" + "io/ioutil" + "strings" + "text/template" +) + +type Instance struct { + Bits int +} + +func (m Instance) Pkg() string { + return strings.ToLower(m.Name()) +} + +func (m Instance) Name() string { + return fmt.Sprintf("SIKEp%d", m.Bits) +} + +func (m Instance) Field() string { + return fmt.Sprintf("Fp%d", m.Bits) +} + +var ( + Instances = []Instance{ + {Bits: 434}, + {Bits: 503}, + {Bits: 751}, + } + TemplateWarning = "// Code generated from" +) + +func main() { + generatePackageFiles() +} + +// Generates instance/sike.go from templates/pkg.templ.go +func generatePackageFiles() { + tl, err := template.ParseFiles("templates/pkg.templ.go") + if err != nil { + panic(err) + } + + for _, mode := range Instances { + buf := new(bytes.Buffer) + err := tl.Execute(buf, mode) + if err != nil { + panic(err) + } + + res := string(buf.Bytes()) + offset := strings.Index(res, TemplateWarning) + if offset == -1 { + panic("Missing template warning in pkg.templ.go") + } + err = ioutil.WriteFile(mode.Pkg()+"/sike.go", []byte(res[offset:]), 0644) + if err != nil { + panic(err) + } + } +} diff --git a/src/circl/kem/sike/sikep434/sike.go b/src/circl/kem/sike/sikep434/sike.go new file mode 100644 index 00000000000..c97ac8d29fe --- /dev/null +++ b/src/circl/kem/sike/sikep434/sike.go @@ -0,0 +1,196 @@ +// Code generated from pkg.templ.go. DO NOT EDIT. + +// Package sikep434 implements the key encapsulation mechanism SIKEp434. +package sikep434 + +import ( + "circl/dh/sidh" + "circl/internal/sha3" + "circl/kem" + + "bytes" + cryptoRand "crypto/rand" + "crypto/subtle" + "io" +) + +type PrivateKey struct { + sk *sidh.PrivateKey + pk *sidh.PublicKey +} + +type PublicKey sidh.PublicKey + +const ( + SeedSize = 32 + EncapsulationSeedSize = 32 +) + +type scheme struct{} + +var sch kem.Scheme = &scheme{} + +// Scheme returns a KEM interface. +func Scheme() kem.Scheme { return sch } + +var params *sidh.KEM + +func (*scheme) Name() string { return "SIKEp434" } +func (*scheme) PublicKeySize() int { return params.PublicKeySize() } +func (*scheme) PrivateKeySize() int { return params.PrivateKeySize() } +func (*scheme) SeedSize() int { return SeedSize } +func (*scheme) SharedKeySize() int { return params.SharedSecretSize() } +func (*scheme) CiphertextSize() int { return params.CiphertextSize() } +func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } + +func (sk *PrivateKey) Scheme() kem.Scheme { return sch } +func (pk *PublicKey) Scheme() kem.Scheme { return sch } + +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + ret := make([]byte, sk.sk.Size()) + sk.sk.Export(ret) + return ret, nil +} + +func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { + oth, ok := other.(*PrivateKey) + if !ok { + return false + } + a, _ := sk.MarshalBinary() + b, _ := oth.MarshalBinary() + return subtle.ConstantTimeCompare(a, b) == 1 +} + +func (sk *PrivateKey) Public() kem.PublicKey { + if sk.pk == nil { + sk.pk = sidh.NewPublicKey(sidh.Fp434, sidh.KeyVariantSike) + sk.sk.GeneratePublicKey(sk.pk) + } + return (*PublicKey)(sk.pk) +} + +func (pk *PublicKey) Equal(other kem.PublicKey) bool { + oth, ok := other.(*PublicKey) + if !ok { + return false + } + a, _ := pk.MarshalBinary() + b, _ := oth.MarshalBinary() + return bytes.Equal(a, b) +} + +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + cpk := (*sidh.PublicKey)(pk) + ret := make([]byte, cpk.Size()) + cpk.Export(ret) + return ret, nil +} + +func GenerateKeyPair(rand io.Reader) (kem.PublicKey, kem.PrivateKey, error) { + sk := sidh.NewPrivateKey(sidh.Fp434, sidh.KeyVariantSike) + + if err := sk.Generate(rand); err != nil { + return nil, nil, err + } + priv := &PrivateKey{sk: sk} + + return priv.Public(), priv, nil +} + +func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + return GenerateKeyPair(cryptoRand.Reader) +} + +func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + if len(seed) != SeedSize { + panic(kem.ErrSeedSize) + } + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + pk, sk, err := GenerateKeyPair(&h) + + if err != nil { + panic(err) + } + + return pk, sk +} + +func (sch *scheme) Encapsulate(pk kem.PublicKey) (ct []byte, ss []byte, err error) { + var seed [EncapsulationSeedSize]byte + cryptoRand.Read(seed[:]) + return sch.EncapsulateDeterministically(pk, seed[:]) +} + +func (sch *scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) (ct []byte, ss []byte, err error) { + if len(seed) != EncapsulationSeedSize { + return nil, nil, kem.ErrSeedSize + } + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + + ct = make([]byte, sch.CiphertextSize()) + ss = make([]byte, sch.SharedKeySize()) + + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + ctx := sidh.NewSike434(&h) + + if err := ctx.Encapsulate(ct, ss, (*sidh.PublicKey)(pub)); err != nil { + return nil, nil, err + } + return ct, ss, nil +} + +func (sch *scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { + if len(ct) != sch.CiphertextSize() { + return nil, kem.ErrCiphertextSize + } + + priv, ok := sk.(*PrivateKey) + if !ok { + return nil, kem.ErrTypeMismatch + } + + sikePub := sidh.NewPublicKey(sidh.Fp434, sidh.KeyVariantSike) + priv.sk.GeneratePublicKey(sikePub) + + ss := make([]byte, sch.SharedKeySize()) + + ctx := sidh.NewSike434(nil) + if err := ctx.Decapsulate(ss, priv.sk, sikePub, ct); err != nil { + return nil, err + } + + return ss, nil +} + +func (sch *scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { + if len(buf) != sch.PublicKeySize() { + return nil, kem.ErrPubKeySize + } + pk := sidh.NewPublicKey(sidh.Fp434, sidh.KeyVariantSike) + if err := pk.Import(buf); err != nil { + return nil, err + } + return (*PublicKey)(pk), nil +} + +func (sch *scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { + if len(buf) != sch.PrivateKeySize() { + return nil, kem.ErrPrivKeySize + } + sk := sidh.NewPrivateKey(sidh.Fp434, sidh.KeyVariantSike) + if err := sk.Import(buf); err != nil { + return nil, err + } + return &PrivateKey{sk: sk}, nil +} + +func init() { + params = sidh.NewSike434(nil) +} diff --git a/src/circl/kem/sike/sikep503/sike.go b/src/circl/kem/sike/sikep503/sike.go new file mode 100644 index 00000000000..3bd699273ef --- /dev/null +++ b/src/circl/kem/sike/sikep503/sike.go @@ -0,0 +1,196 @@ +// Code generated from pkg.templ.go. DO NOT EDIT. + +// Package sikep503 implements the key encapsulation mechanism SIKEp503. +package sikep503 + +import ( + "circl/dh/sidh" + "circl/internal/sha3" + "circl/kem" + + "bytes" + cryptoRand "crypto/rand" + "crypto/subtle" + "io" +) + +type PrivateKey struct { + sk *sidh.PrivateKey + pk *sidh.PublicKey +} + +type PublicKey sidh.PublicKey + +const ( + SeedSize = 32 + EncapsulationSeedSize = 32 +) + +type scheme struct{} + +var sch kem.Scheme = &scheme{} + +// Scheme returns a KEM interface. +func Scheme() kem.Scheme { return sch } + +var params *sidh.KEM + +func (*scheme) Name() string { return "SIKEp503" } +func (*scheme) PublicKeySize() int { return params.PublicKeySize() } +func (*scheme) PrivateKeySize() int { return params.PrivateKeySize() } +func (*scheme) SeedSize() int { return SeedSize } +func (*scheme) SharedKeySize() int { return params.SharedSecretSize() } +func (*scheme) CiphertextSize() int { return params.CiphertextSize() } +func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } + +func (sk *PrivateKey) Scheme() kem.Scheme { return sch } +func (pk *PublicKey) Scheme() kem.Scheme { return sch } + +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + ret := make([]byte, sk.sk.Size()) + sk.sk.Export(ret) + return ret, nil +} + +func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { + oth, ok := other.(*PrivateKey) + if !ok { + return false + } + a, _ := sk.MarshalBinary() + b, _ := oth.MarshalBinary() + return subtle.ConstantTimeCompare(a, b) == 1 +} + +func (sk *PrivateKey) Public() kem.PublicKey { + if sk.pk == nil { + sk.pk = sidh.NewPublicKey(sidh.Fp503, sidh.KeyVariantSike) + sk.sk.GeneratePublicKey(sk.pk) + } + return (*PublicKey)(sk.pk) +} + +func (pk *PublicKey) Equal(other kem.PublicKey) bool { + oth, ok := other.(*PublicKey) + if !ok { + return false + } + a, _ := pk.MarshalBinary() + b, _ := oth.MarshalBinary() + return bytes.Equal(a, b) +} + +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + cpk := (*sidh.PublicKey)(pk) + ret := make([]byte, cpk.Size()) + cpk.Export(ret) + return ret, nil +} + +func GenerateKeyPair(rand io.Reader) (kem.PublicKey, kem.PrivateKey, error) { + sk := sidh.NewPrivateKey(sidh.Fp503, sidh.KeyVariantSike) + + if err := sk.Generate(rand); err != nil { + return nil, nil, err + } + priv := &PrivateKey{sk: sk} + + return priv.Public(), priv, nil +} + +func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + return GenerateKeyPair(cryptoRand.Reader) +} + +func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + if len(seed) != SeedSize { + panic(kem.ErrSeedSize) + } + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + pk, sk, err := GenerateKeyPair(&h) + + if err != nil { + panic(err) + } + + return pk, sk +} + +func (sch *scheme) Encapsulate(pk kem.PublicKey) (ct []byte, ss []byte, err error) { + var seed [EncapsulationSeedSize]byte + cryptoRand.Read(seed[:]) + return sch.EncapsulateDeterministically(pk, seed[:]) +} + +func (sch *scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) (ct []byte, ss []byte, err error) { + if len(seed) != EncapsulationSeedSize { + return nil, nil, kem.ErrSeedSize + } + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + + ct = make([]byte, sch.CiphertextSize()) + ss = make([]byte, sch.SharedKeySize()) + + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + ctx := sidh.NewSike503(&h) + + if err := ctx.Encapsulate(ct, ss, (*sidh.PublicKey)(pub)); err != nil { + return nil, nil, err + } + return ct, ss, nil +} + +func (sch *scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { + if len(ct) != sch.CiphertextSize() { + return nil, kem.ErrCiphertextSize + } + + priv, ok := sk.(*PrivateKey) + if !ok { + return nil, kem.ErrTypeMismatch + } + + sikePub := sidh.NewPublicKey(sidh.Fp503, sidh.KeyVariantSike) + priv.sk.GeneratePublicKey(sikePub) + + ss := make([]byte, sch.SharedKeySize()) + + ctx := sidh.NewSike503(nil) + if err := ctx.Decapsulate(ss, priv.sk, sikePub, ct); err != nil { + return nil, err + } + + return ss, nil +} + +func (sch *scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { + if len(buf) != sch.PublicKeySize() { + return nil, kem.ErrPubKeySize + } + pk := sidh.NewPublicKey(sidh.Fp503, sidh.KeyVariantSike) + if err := pk.Import(buf); err != nil { + return nil, err + } + return (*PublicKey)(pk), nil +} + +func (sch *scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { + if len(buf) != sch.PrivateKeySize() { + return nil, kem.ErrPrivKeySize + } + sk := sidh.NewPrivateKey(sidh.Fp503, sidh.KeyVariantSike) + if err := sk.Import(buf); err != nil { + return nil, err + } + return &PrivateKey{sk: sk}, nil +} + +func init() { + params = sidh.NewSike503(nil) +} diff --git a/src/circl/kem/sike/sikep751/sike.go b/src/circl/kem/sike/sikep751/sike.go new file mode 100644 index 00000000000..2ed61eb324f --- /dev/null +++ b/src/circl/kem/sike/sikep751/sike.go @@ -0,0 +1,196 @@ +// Code generated from pkg.templ.go. DO NOT EDIT. + +// Package sikep751 implements the key encapsulation mechanism SIKEp751. +package sikep751 + +import ( + "circl/dh/sidh" + "circl/internal/sha3" + "circl/kem" + + "bytes" + cryptoRand "crypto/rand" + "crypto/subtle" + "io" +) + +type PrivateKey struct { + sk *sidh.PrivateKey + pk *sidh.PublicKey +} + +type PublicKey sidh.PublicKey + +const ( + SeedSize = 32 + EncapsulationSeedSize = 32 +) + +type scheme struct{} + +var sch kem.Scheme = &scheme{} + +// Scheme returns a KEM interface. +func Scheme() kem.Scheme { return sch } + +var params *sidh.KEM + +func (*scheme) Name() string { return "SIKEp751" } +func (*scheme) PublicKeySize() int { return params.PublicKeySize() } +func (*scheme) PrivateKeySize() int { return params.PrivateKeySize() } +func (*scheme) SeedSize() int { return SeedSize } +func (*scheme) SharedKeySize() int { return params.SharedSecretSize() } +func (*scheme) CiphertextSize() int { return params.CiphertextSize() } +func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } + +func (sk *PrivateKey) Scheme() kem.Scheme { return sch } +func (pk *PublicKey) Scheme() kem.Scheme { return sch } + +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + ret := make([]byte, sk.sk.Size()) + sk.sk.Export(ret) + return ret, nil +} + +func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { + oth, ok := other.(*PrivateKey) + if !ok { + return false + } + a, _ := sk.MarshalBinary() + b, _ := oth.MarshalBinary() + return subtle.ConstantTimeCompare(a, b) == 1 +} + +func (sk *PrivateKey) Public() kem.PublicKey { + if sk.pk == nil { + sk.pk = sidh.NewPublicKey(sidh.Fp751, sidh.KeyVariantSike) + sk.sk.GeneratePublicKey(sk.pk) + } + return (*PublicKey)(sk.pk) +} + +func (pk *PublicKey) Equal(other kem.PublicKey) bool { + oth, ok := other.(*PublicKey) + if !ok { + return false + } + a, _ := pk.MarshalBinary() + b, _ := oth.MarshalBinary() + return bytes.Equal(a, b) +} + +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + cpk := (*sidh.PublicKey)(pk) + ret := make([]byte, cpk.Size()) + cpk.Export(ret) + return ret, nil +} + +func GenerateKeyPair(rand io.Reader) (kem.PublicKey, kem.PrivateKey, error) { + sk := sidh.NewPrivateKey(sidh.Fp751, sidh.KeyVariantSike) + + if err := sk.Generate(rand); err != nil { + return nil, nil, err + } + priv := &PrivateKey{sk: sk} + + return priv.Public(), priv, nil +} + +func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + return GenerateKeyPair(cryptoRand.Reader) +} + +func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + if len(seed) != SeedSize { + panic(kem.ErrSeedSize) + } + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + pk, sk, err := GenerateKeyPair(&h) + + if err != nil { + panic(err) + } + + return pk, sk +} + +func (sch *scheme) Encapsulate(pk kem.PublicKey) (ct []byte, ss []byte, err error) { + var seed [EncapsulationSeedSize]byte + cryptoRand.Read(seed[:]) + return sch.EncapsulateDeterministically(pk, seed[:]) +} + +func (sch *scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) (ct []byte, ss []byte, err error) { + if len(seed) != EncapsulationSeedSize { + return nil, nil, kem.ErrSeedSize + } + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + + ct = make([]byte, sch.CiphertextSize()) + ss = make([]byte, sch.SharedKeySize()) + + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + ctx := sidh.NewSike751(&h) + + if err := ctx.Encapsulate(ct, ss, (*sidh.PublicKey)(pub)); err != nil { + return nil, nil, err + } + return ct, ss, nil +} + +func (sch *scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { + if len(ct) != sch.CiphertextSize() { + return nil, kem.ErrCiphertextSize + } + + priv, ok := sk.(*PrivateKey) + if !ok { + return nil, kem.ErrTypeMismatch + } + + sikePub := sidh.NewPublicKey(sidh.Fp751, sidh.KeyVariantSike) + priv.sk.GeneratePublicKey(sikePub) + + ss := make([]byte, sch.SharedKeySize()) + + ctx := sidh.NewSike751(nil) + if err := ctx.Decapsulate(ss, priv.sk, sikePub, ct); err != nil { + return nil, err + } + + return ss, nil +} + +func (sch *scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { + if len(buf) != sch.PublicKeySize() { + return nil, kem.ErrPubKeySize + } + pk := sidh.NewPublicKey(sidh.Fp751, sidh.KeyVariantSike) + if err := pk.Import(buf); err != nil { + return nil, err + } + return (*PublicKey)(pk), nil +} + +func (sch *scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { + if len(buf) != sch.PrivateKeySize() { + return nil, kem.ErrPrivKeySize + } + sk := sidh.NewPrivateKey(sidh.Fp751, sidh.KeyVariantSike) + if err := sk.Import(buf); err != nil { + return nil, err + } + return &PrivateKey{sk: sk}, nil +} + +func init() { + params = sidh.NewSike751(nil) +} diff --git a/src/circl/kem/sike/templates/pkg.templ.go b/src/circl/kem/sike/templates/pkg.templ.go new file mode 100644 index 00000000000..948cf013ca7 --- /dev/null +++ b/src/circl/kem/sike/templates/pkg.templ.go @@ -0,0 +1,200 @@ +// +build ignore +// The previous line (and this one up to the warning below) is removed by the +// template generator. + +// Code generated from pkg.templ.go. DO NOT EDIT. + +// Package {{.Pkg}} implements the key encapsulation mechanism {{.Name}}. +package {{.Pkg}} + +import ( + "circl/dh/sidh" + "circl/internal/sha3" + "circl/kem" + + "bytes" + cryptoRand "crypto/rand" + "crypto/subtle" + "io" +) + +type PrivateKey struct { + sk *sidh.PrivateKey + pk *sidh.PublicKey +} + +type PublicKey sidh.PublicKey + +const ( + SeedSize = 32 + EncapsulationSeedSize = 32 +) + +type scheme struct{} + +var sch kem.Scheme = &scheme{} + +// Scheme returns a KEM interface. +func Scheme() kem.Scheme { return sch } + +var params *sidh.KEM + +func (*scheme) Name() string { return "{{.Name}}" } +func (*scheme) PublicKeySize() int { return params.PublicKeySize() } +func (*scheme) PrivateKeySize() int { return params.PrivateKeySize() } +func (*scheme) SeedSize() int { return SeedSize } +func (*scheme) SharedKeySize() int { return params.SharedSecretSize() } +func (*scheme) CiphertextSize() int { return params.CiphertextSize() } +func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize } + +func (sk *PrivateKey) Scheme() kem.Scheme { return sch } +func (pk *PublicKey) Scheme() kem.Scheme { return sch } + +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + ret := make([]byte, sk.sk.Size()) + sk.sk.Export(ret) + return ret, nil +} + +func (sk *PrivateKey) Equal(other kem.PrivateKey) bool { + oth, ok := other.(*PrivateKey) + if !ok { + return false + } + a, _ := sk.MarshalBinary() + b, _ := oth.MarshalBinary() + return subtle.ConstantTimeCompare(a, b) == 1 +} + +func (sk *PrivateKey) Public() kem.PublicKey { + if sk.pk == nil { + sk.pk = sidh.NewPublicKey(sidh.{{.Field}}, sidh.KeyVariantSike) + sk.sk.GeneratePublicKey(sk.pk) + } + return (*PublicKey)(sk.pk) +} + +func (pk *PublicKey) Equal(other kem.PublicKey) bool { + oth, ok := other.(*PublicKey) + if !ok { + return false + } + a, _ := pk.MarshalBinary() + b, _ := oth.MarshalBinary() + return bytes.Equal(a, b) +} + +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + cpk := (*sidh.PublicKey)(pk) + ret := make([]byte, cpk.Size()) + cpk.Export(ret) + return ret, nil +} + +func GenerateKeyPair(rand io.Reader) (kem.PublicKey, kem.PrivateKey, error) { + sk := sidh.NewPrivateKey(sidh.{{.Field}}, sidh.KeyVariantSike) + + if err := sk.Generate(rand); err != nil { + return nil, nil, err + } + priv := &PrivateKey{sk: sk} + + return priv.Public(), priv, nil +} + +func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) { + return GenerateKeyPair(cryptoRand.Reader) +} + +func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) { + if len(seed) != SeedSize { + panic(kem.ErrSeedSize) + } + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + pk, sk, err := GenerateKeyPair(&h) + + if err != nil { + panic(err) + } + + return pk, sk +} + +func (sch *scheme) Encapsulate(pk kem.PublicKey) (ct []byte, ss []byte, err error) { + var seed [EncapsulationSeedSize]byte + cryptoRand.Read(seed[:]) + return sch.EncapsulateDeterministically(pk, seed[:]) +} + +func (sch *scheme) EncapsulateDeterministically(pk kem.PublicKey, seed []byte) (ct []byte, ss []byte, err error) { + if len(seed) != EncapsulationSeedSize { + return nil, nil, kem.ErrSeedSize + } + + pub, ok := pk.(*PublicKey) + if !ok { + return nil, nil, kem.ErrTypeMismatch + } + + ct = make([]byte, sch.CiphertextSize()) + ss = make([]byte, sch.SharedKeySize()) + + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + ctx := sidh.NewSike{{.Bits}}(&h) + + if err := ctx.Encapsulate(ct, ss, (*sidh.PublicKey)(pub)); err != nil { + return nil, nil, err + } + return ct, ss, nil +} + +func (sch *scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) { + if len(ct) != sch.CiphertextSize() { + return nil, kem.ErrCiphertextSize + } + + priv, ok := sk.(*PrivateKey) + if !ok { + return nil, kem.ErrTypeMismatch + } + + sikePub := sidh.NewPublicKey(sidh.{{.Field}}, sidh.KeyVariantSike) + priv.sk.GeneratePublicKey(sikePub) + + ss := make([]byte, sch.SharedKeySize()) + + ctx := sidh.NewSike{{.Bits}}(nil) + if err := ctx.Decapsulate(ss, priv.sk, sikePub, ct); err != nil { + return nil, err + } + + return ss, nil +} + +func (sch *scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) { + if len(buf) != sch.PublicKeySize() { + return nil, kem.ErrPubKeySize + } + pk := sidh.NewPublicKey(sidh.{{.Field}}, sidh.KeyVariantSike) + if err := pk.Import(buf); err != nil { + return nil, err + } + return (*PublicKey)(pk), nil +} + +func (sch *scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) { + if len(buf) != sch.PrivateKeySize() { + return nil, kem.ErrPrivKeySize + } + sk := sidh.NewPrivateKey(sidh.{{.Field}}, sidh.KeyVariantSike) + if err := sk.Import(buf); err != nil { + return nil, err + } + return &PrivateKey{sk: sk}, nil +} + +func init() { + params = sidh.NewSike{{.Bits}}(nil) +} diff --git a/src/circl/math/fp25519/fp.go b/src/circl/math/fp25519/fp.go new file mode 100644 index 00000000000..c0880e13cf3 --- /dev/null +++ b/src/circl/math/fp25519/fp.go @@ -0,0 +1,205 @@ +// Package fp25519 provides prime field arithmetic over GF(2^255-19). +package fp25519 + +import ( + "errors" + + "circl/internal/conv" +) + +// Size in bytes of an element. +const Size = 32 + +// Elt is a prime field element. +type Elt [Size]byte + +func (e Elt) String() string { return conv.BytesLe2Hex(e[:]) } + +// p is the prime modulus 2^255-19. +var p = Elt{ + 0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, +} + +// P returns the prime modulus 2^255-19. +func P() Elt { return p } + +// ToBytes stores in b the little-endian byte representation of x. +func ToBytes(b []byte, x *Elt) error { + if len(b) != Size { + return errors.New("wrong size") + } + Modp(x) + copy(b, x[:]) + return nil +} + +// IsZero returns true if x is equal to 0. +func IsZero(x *Elt) bool { Modp(x); return *x == Elt{} } + +// SetOne assigns x=1. +func SetOne(x *Elt) { *x = Elt{}; x[0] = 1 } + +// Neg calculates z = -x. +func Neg(z, x *Elt) { Sub(z, &p, x) } + +// InvSqrt calculates z = sqrt(x/y) iff x/y is a quadratic-residue, which is +// indicated by returning isQR = true. Otherwise, when x/y is a quadratic +// non-residue, z will have an undetermined value and isQR = false. +func InvSqrt(z, x, y *Elt) (isQR bool) { + sqrtMinusOne := &Elt{ + 0xb0, 0xa0, 0x0e, 0x4a, 0x27, 0x1b, 0xee, 0xc4, + 0x78, 0xe4, 0x2f, 0xad, 0x06, 0x18, 0x43, 0x2f, + 0xa7, 0xd7, 0xfb, 0x3d, 0x99, 0x00, 0x4d, 0x2b, + 0x0b, 0xdf, 0xc1, 0x4f, 0x80, 0x24, 0x83, 0x2b, + } + t0, t1, t2, t3 := &Elt{}, &Elt{}, &Elt{}, &Elt{} + + Mul(t0, x, y) // t0 = u*v + Sqr(t1, y) // t1 = v^2 + Mul(t2, t0, t1) // t2 = u*v^3 + Sqr(t0, t1) // t0 = v^4 + Mul(t1, t0, t2) // t1 = u*v^7 + + var Tab [4]*Elt + Tab[0] = &Elt{} + Tab[1] = &Elt{} + Tab[2] = t3 + Tab[3] = t1 + + *Tab[0] = *t1 + Sqr(Tab[0], Tab[0]) + Sqr(Tab[1], Tab[0]) + Sqr(Tab[1], Tab[1]) + Mul(Tab[1], Tab[1], Tab[3]) + Mul(Tab[0], Tab[0], Tab[1]) + Sqr(Tab[0], Tab[0]) + Mul(Tab[0], Tab[0], Tab[1]) + Sqr(Tab[1], Tab[0]) + for i := 0; i < 4; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[0]) + Sqr(Tab[2], Tab[1]) + for i := 0; i < 4; i++ { + Sqr(Tab[2], Tab[2]) + } + Mul(Tab[2], Tab[2], Tab[0]) + Sqr(Tab[1], Tab[2]) + for i := 0; i < 14; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[2]) + Sqr(Tab[2], Tab[1]) + for i := 0; i < 29; i++ { + Sqr(Tab[2], Tab[2]) + } + Mul(Tab[2], Tab[2], Tab[1]) + Sqr(Tab[1], Tab[2]) + for i := 0; i < 59; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[2]) + for i := 0; i < 5; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[0]) + Sqr(Tab[2], Tab[1]) + for i := 0; i < 124; i++ { + Sqr(Tab[2], Tab[2]) + } + Mul(Tab[2], Tab[2], Tab[1]) + Sqr(Tab[2], Tab[2]) + Sqr(Tab[2], Tab[2]) + Mul(Tab[2], Tab[2], Tab[3]) + + Mul(z, t3, t2) // z = xy^(p+3)/8 = xy^3*(xy^7)^(p-5)/8 + // Checking whether y z^2 == x + Sqr(t0, z) // t0 = z^2 + Mul(t0, t0, y) // t0 = yz^2 + Sub(t1, t0, x) // t1 = t0-u + Add(t2, t0, x) // t2 = t0+u + if IsZero(t1) { + return true + } else if IsZero(t2) { + Mul(z, z, sqrtMinusOne) // z = z*sqrt(-1) + return true + } else { + return false + } +} + +// Inv calculates z = 1/x mod p. +func Inv(z, x *Elt) { + x0, x1, x2 := &Elt{}, &Elt{}, &Elt{} + Sqr(x1, x) + Sqr(x0, x1) + Sqr(x0, x0) + Mul(x0, x0, x) + Mul(z, x0, x1) + Sqr(x1, z) + Mul(x0, x0, x1) + Sqr(x1, x0) + for i := 0; i < 4; i++ { + Sqr(x1, x1) + } + Mul(x0, x0, x1) + Sqr(x1, x0) + for i := 0; i < 9; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, x0) + Sqr(x2, x1) + for i := 0; i < 19; i++ { + Sqr(x2, x2) + } + Mul(x2, x2, x1) + for i := 0; i < 10; i++ { + Sqr(x2, x2) + } + Mul(x2, x2, x0) + Sqr(x0, x2) + for i := 0; i < 49; i++ { + Sqr(x0, x0) + } + Mul(x0, x0, x2) + Sqr(x1, x0) + for i := 0; i < 99; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, x0) + for i := 0; i < 50; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, x2) + for i := 0; i < 5; i++ { + Sqr(x1, x1) + } + Mul(z, z, x1) +} + +// Cmov assigns y to x if n is 1. +func Cmov(x, y *Elt, n uint) { cmov(x, y, n) } + +// Cswap interchanges x and y if n is 1. +func Cswap(x, y *Elt, n uint) { cswap(x, y, n) } + +// Add calculates z = x+y mod p. +func Add(z, x, y *Elt) { add(z, x, y) } + +// Sub calculates z = x-y mod p. +func Sub(z, x, y *Elt) { sub(z, x, y) } + +// AddSub calculates (x,y) = (x+y mod p, x-y mod p). +func AddSub(x, y *Elt) { addsub(x, y) } + +// Mul calculates z = x*y mod p. +func Mul(z, x, y *Elt) { mul(z, x, y) } + +// Sqr calculates z = x^2 mod p. +func Sqr(z, x *Elt) { sqr(z, x) } + +// Modp ensures that z is between [0,p-1]. +func Modp(z *Elt) { modp(z) } diff --git a/src/circl/math/fp25519/fp_amd64.go b/src/circl/math/fp25519/fp_amd64.go new file mode 100644 index 00000000000..cc2a1f4ac7b --- /dev/null +++ b/src/circl/math/fp25519/fp_amd64.go @@ -0,0 +1,44 @@ +// +build amd64,!purego + +package fp25519 + +import ( + "internal/cpu" +) + +var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX + +var _ = hasBmi2Adx + +func cmov(x, y *Elt, n uint) { cmovAmd64(x, y, n) } +func cswap(x, y *Elt, n uint) { cswapAmd64(x, y, n) } +func add(z, x, y *Elt) { addAmd64(z, x, y) } +func sub(z, x, y *Elt) { subAmd64(z, x, y) } +func addsub(x, y *Elt) { addsubAmd64(x, y) } +func mul(z, x, y *Elt) { mulAmd64(z, x, y) } +func sqr(z, x *Elt) { sqrAmd64(z, x) } +func modp(z *Elt) { modpAmd64(z) } + +//go:noescape +func cmovAmd64(x, y *Elt, n uint) + +//go:noescape +func cswapAmd64(x, y *Elt, n uint) + +//go:noescape +func addAmd64(z, x, y *Elt) + +//go:noescape +func subAmd64(z, x, y *Elt) + +//go:noescape +func addsubAmd64(x, y *Elt) + +//go:noescape +func mulAmd64(z, x, y *Elt) + +//go:noescape +func sqrAmd64(z, x *Elt) + +//go:noescape +func modpAmd64(z *Elt) diff --git a/src/circl/math/fp25519/fp_amd64.h b/src/circl/math/fp25519/fp_amd64.h new file mode 100644 index 00000000000..7b25f16e416 --- /dev/null +++ b/src/circl/math/fp25519/fp_amd64.h @@ -0,0 +1,350 @@ +// This code was imported from https://github.com/armfazh/rfc7748_precomputed + +// CHECK_BMI2ADX triggers bmi2adx if supported, +// otherwise it fallbacks to legacy code. +#define CHECK_BMI2ADX(label, legacy, bmi2adx) \ + CMPB ·hasBmi2Adx(SB), $0 \ + JE label \ + bmi2adx \ + RET \ + label: \ + legacy \ + RET + +// cselect is a conditional move +// if b=1: it copies y into x; +// if b=0: x remains with the same value; +// if b<> 0,1: undefined. +// Uses: AX, DX, FLAGS +// Instr: x86_64, cmov +#define cselect(x,y,b) \ + TESTQ b, b \ + MOVQ 0+x, AX; MOVQ 0+y, DX; CMOVQNE DX, AX; MOVQ AX, 0+x; \ + MOVQ 8+x, AX; MOVQ 8+y, DX; CMOVQNE DX, AX; MOVQ AX, 8+x; \ + MOVQ 16+x, AX; MOVQ 16+y, DX; CMOVQNE DX, AX; MOVQ AX, 16+x; \ + MOVQ 24+x, AX; MOVQ 24+y, DX; CMOVQNE DX, AX; MOVQ AX, 24+x; + +// cswap is a conditional swap +// if b=1: x,y <- y,x; +// if b=0: x,y remain with the same values; +// if b<> 0,1: undefined. +// Uses: AX, DX, R8, FLAGS +// Instr: x86_64, cmov +#define cswap(x,y,b) \ + TESTQ b, b \ + MOVQ 0+x, AX; MOVQ AX, R8; MOVQ 0+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 0+x; MOVQ DX, 0+y; \ + MOVQ 8+x, AX; MOVQ AX, R8; MOVQ 8+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 8+x; MOVQ DX, 8+y; \ + MOVQ 16+x, AX; MOVQ AX, R8; MOVQ 16+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 16+x; MOVQ DX, 16+y; \ + MOVQ 24+x, AX; MOVQ AX, R8; MOVQ 24+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 24+x; MOVQ DX, 24+y; + +// additionLeg adds x and y and stores in z +// Uses: AX, DX, R8-R11, FLAGS +// Instr: x86_64, cmov +#define additionLeg(z,x,y) \ + MOVL $38, AX; \ + MOVL $0, DX; \ + MOVQ 0+x, R8; ADDQ 0+y, R8; \ + MOVQ 8+x, R9; ADCQ 8+y, R9; \ + MOVQ 16+x, R10; ADCQ 16+y, R10; \ + MOVQ 24+x, R11; ADCQ 24+y, R11; \ + CMOVQCS AX, DX; \ + ADDQ DX, R8; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ $0, R11; MOVQ R11, 24+z; \ + MOVL $0, DX; \ + CMOVQCS AX, DX; \ + ADDQ DX, R8; MOVQ R8, 0+z; + +// additionAdx adds x and y and stores in z +// Uses: AX, DX, R8-R11, FLAGS +// Instr: x86_64, cmov, adx +#define additionAdx(z,x,y) \ + MOVL $38, AX; \ + XORL DX, DX; \ + MOVQ 0+x, R8; ADCXQ 0+y, R8; \ + MOVQ 8+x, R9; ADCXQ 8+y, R9; \ + MOVQ 16+x, R10; ADCXQ 16+y, R10; \ + MOVQ 24+x, R11; ADCXQ 24+y, R11; \ + CMOVQCS AX, DX ; \ + XORL AX, AX; \ + ADCXQ DX, R8; \ + ADCXQ AX, R9; MOVQ R9, 8+z; \ + ADCXQ AX, R10; MOVQ R10, 16+z; \ + ADCXQ AX, R11; MOVQ R11, 24+z; \ + MOVL $38, DX; \ + CMOVQCS DX, AX; \ + ADDQ AX, R8; MOVQ R8, 0+z; + +// subtraction subtracts y from x and stores in z +// Uses: AX, DX, R8-R11, FLAGS +// Instr: x86_64, cmov +#define subtraction(z,x,y) \ + MOVL $38, AX; \ + MOVQ 0+x, R8; SUBQ 0+y, R8; \ + MOVQ 8+x, R9; SBBQ 8+y, R9; \ + MOVQ 16+x, R10; SBBQ 16+y, R10; \ + MOVQ 24+x, R11; SBBQ 24+y, R11; \ + MOVL $0, DX; \ + CMOVQCS AX, DX; \ + SUBQ DX, R8; \ + SBBQ $0, R9; MOVQ R9, 8+z; \ + SBBQ $0, R10; MOVQ R10, 16+z; \ + SBBQ $0, R11; MOVQ R11, 24+z; \ + MOVL $0, DX; \ + CMOVQCS AX, DX; \ + SUBQ DX, R8; MOVQ R8, 0+z; + +// integerMulAdx multiplies x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64, bmi2, adx +#define integerMulAdx(z,x,y) \ + MOVQ 0+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R8; MOVQ AX, 0+z; \ + MULXQ 8+x, AX, R9; ADCXQ AX, R8; \ + MULXQ 16+x, AX, R10; ADCXQ AX, R9; \ + MULXQ 24+x, AX, R11; ADCXQ AX, R10; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R11; \ + MOVQ 8+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R12; ADCXQ R8, AX; MOVQ AX, 8+z; \ + MULXQ 8+x, AX, R13; ADCXQ R9, R12; ADOXQ AX, R12; \ + MULXQ 16+x, AX, R14; ADCXQ R10, R13; ADOXQ AX, R13; \ + MULXQ 24+x, AX, R15; ADCXQ R11, R14; ADOXQ AX, R14; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R15; ADOXQ AX, R15; \ + MOVQ 16+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R8; ADCXQ R12, AX; MOVQ AX, 16+z; \ + MULXQ 8+x, AX, R9; ADCXQ R13, R8; ADOXQ AX, R8; \ + MULXQ 16+x, AX, R10; ADCXQ R14, R9; ADOXQ AX, R9; \ + MULXQ 24+x, AX, R11; ADCXQ R15, R10; ADOXQ AX, R10; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R11; ADOXQ AX, R11; \ + MOVQ 24+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R12; ADCXQ R8, AX; MOVQ AX, 24+z; \ + MULXQ 8+x, AX, R13; ADCXQ R9, R12; ADOXQ AX, R12; MOVQ R12, 32+z; \ + MULXQ 16+x, AX, R14; ADCXQ R10, R13; ADOXQ AX, R13; MOVQ R13, 40+z; \ + MULXQ 24+x, AX, R15; ADCXQ R11, R14; ADOXQ AX, R14; MOVQ R14, 48+z; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R15; ADOXQ AX, R15; MOVQ R15, 56+z; + +// integerMulLeg multiplies x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64 +#define integerMulLeg(z,x,y) \ + MOVQ 0+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, 0+z; MOVQ DX, R15; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R13, R15; \ + ADCQ R14, R10; MOVQ R10, 16+z; \ + ADCQ AX, R11; MOVQ R11, 24+z; \ + ADCQ $0, DX; MOVQ DX, 32+z; \ + MOVQ 8+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R12, R15; MOVQ R15, 8+z; \ + ADCQ R13, R9; \ + ADCQ R14, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + ADCQ 16+z, R9; MOVQ R9, R15; \ + ADCQ 24+z, R10; MOVQ R10, 24+z; \ + ADCQ 32+z, R11; MOVQ R11, 32+z; \ + ADCQ $0, DX; MOVQ DX, 40+z; \ + MOVQ 16+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R12, R15; MOVQ R15, 16+z; \ + ADCQ R13, R9; \ + ADCQ R14, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + ADCQ 24+z, R9; MOVQ R9, R15; \ + ADCQ 32+z, R10; MOVQ R10, 32+z; \ + ADCQ 40+z, R11; MOVQ R11, 40+z; \ + ADCQ $0, DX; MOVQ DX, 48+z; \ + MOVQ 24+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R12, R15; MOVQ R15, 24+z; \ + ADCQ R13, R9; \ + ADCQ R14, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + ADCQ 32+z, R9; MOVQ R9, 32+z; \ + ADCQ 40+z, R10; MOVQ R10, 40+z; \ + ADCQ 48+z, R11; MOVQ R11, 48+z; \ + ADCQ $0, DX; MOVQ DX, 56+z; + +// integerSqrLeg squares x and stores in z +// Uses: AX, CX, DX, R8-R15, FLAGS +// Instr: x86_64 +#define integerSqrLeg(z,x) \ + MOVQ 0+x, R8; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R9; MOVQ DX, R10; /* A[0]*A[1] */ \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; /* A[0]*A[2] */ \ + MOVQ 24+x, AX; MULQ R8; MOVQ AX, R15; MOVQ DX, R12; /* A[0]*A[3] */ \ + MOVQ 24+x, R8; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, CX; MOVQ DX, R13; /* A[3]*A[1] */ \ + MOVQ 16+x, AX; MULQ R8; /* A[3]*A[2] */ \ + \ + ADDQ R14, R10;\ + ADCQ R15, R11; MOVL $0, R15;\ + ADCQ CX, R12;\ + ADCQ AX, R13;\ + ADCQ $0, DX; MOVQ DX, R14;\ + MOVQ 8+x, AX; MULQ 16+x;\ + \ + ADDQ AX, R11;\ + ADCQ DX, R12;\ + ADCQ $0, R13;\ + ADCQ $0, R14;\ + ADCQ $0, R15;\ + \ + SHLQ $1, R14, R15; MOVQ R15, 56+z;\ + SHLQ $1, R13, R14; MOVQ R14, 48+z;\ + SHLQ $1, R12, R13; MOVQ R13, 40+z;\ + SHLQ $1, R11, R12; MOVQ R12, 32+z;\ + SHLQ $1, R10, R11; MOVQ R11, 24+z;\ + SHLQ $1, R9, R10; MOVQ R10, 16+z;\ + SHLQ $1, R9; MOVQ R9, 8+z;\ + \ + MOVQ 0+x,AX; MULQ AX; MOVQ AX, 0+z; MOVQ DX, R9;\ + MOVQ 8+x,AX; MULQ AX; MOVQ AX, R10; MOVQ DX, R11;\ + MOVQ 16+x,AX; MULQ AX; MOVQ AX, R12; MOVQ DX, R13;\ + MOVQ 24+x,AX; MULQ AX; MOVQ AX, R14; MOVQ DX, R15;\ + \ + ADDQ 8+z, R9; MOVQ R9, 8+z;\ + ADCQ 16+z, R10; MOVQ R10, 16+z;\ + ADCQ 24+z, R11; MOVQ R11, 24+z;\ + ADCQ 32+z, R12; MOVQ R12, 32+z;\ + ADCQ 40+z, R13; MOVQ R13, 40+z;\ + ADCQ 48+z, R14; MOVQ R14, 48+z;\ + ADCQ 56+z, R15; MOVQ R15, 56+z; + +// integerSqrAdx squares x and stores in z +// Uses: AX, CX, DX, R8-R15, FLAGS +// Instr: x86_64, bmi2, adx +#define integerSqrAdx(z,x) \ + MOVQ 0+x, DX; /* A[0] */ \ + MULXQ 8+x, R8, R14; /* A[1]*A[0] */ XORL R15, R15; \ + MULXQ 16+x, R9, R10; /* A[2]*A[0] */ ADCXQ R14, R9; \ + MULXQ 24+x, AX, CX; /* A[3]*A[0] */ ADCXQ AX, R10; \ + MOVQ 24+x, DX; /* A[3] */ \ + MULXQ 8+x, R11, R12; /* A[1]*A[3] */ ADCXQ CX, R11; \ + MULXQ 16+x, AX, R13; /* A[2]*A[3] */ ADCXQ AX, R12; \ + MOVQ 8+x, DX; /* A[1] */ ADCXQ R15, R13; \ + MULXQ 16+x, AX, CX; /* A[2]*A[1] */ MOVL $0, R14; \ + ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADCXQ R15, R14; \ + XORL R15, R15; \ + ADOXQ AX, R10; ADCXQ R8, R8; \ + ADOXQ CX, R11; ADCXQ R9, R9; \ + ADOXQ R15, R12; ADCXQ R10, R10; \ + ADOXQ R15, R13; ADCXQ R11, R11; \ + ADOXQ R15, R14; ADCXQ R12, R12; \ + ;;;;;;;;;;;;;;; ADCXQ R13, R13; \ + ;;;;;;;;;;;;;;; ADCXQ R14, R14; \ + MOVQ 0+x, DX; MULXQ DX, AX, CX; /* A[0]^2 */ \ + ;;;;;;;;;;;;;;; MOVQ AX, 0+z; \ + ADDQ CX, R8; MOVQ R8, 8+z; \ + MOVQ 8+x, DX; MULXQ DX, AX, CX; /* A[1]^2 */ \ + ADCQ AX, R9; MOVQ R9, 16+z; \ + ADCQ CX, R10; MOVQ R10, 24+z; \ + MOVQ 16+x, DX; MULXQ DX, AX, CX; /* A[2]^2 */ \ + ADCQ AX, R11; MOVQ R11, 32+z; \ + ADCQ CX, R12; MOVQ R12, 40+z; \ + MOVQ 24+x, DX; MULXQ DX, AX, CX; /* A[3]^2 */ \ + ADCQ AX, R13; MOVQ R13, 48+z; \ + ADCQ CX, R14; MOVQ R14, 56+z; + +// reduceFromDouble finds z congruent to x modulo p such that 0> 63) + // PUT BIT 255 IN CARRY FLAG AND CLEAR + x3 &^= 1 << 63 + + x0, c0 := bits.Add64(x0, cx, 0) + x1, c1 := bits.Add64(x1, 0, c0) + x2, c2 := bits.Add64(x2, 0, c1) + x3, _ = bits.Add64(x3, 0, c2) + + // TEST FOR BIT 255 AGAIN; ONLY TRIGGERED ON OVERFLOW MODULO 2^255-19 + // cx = C[255] ? 0 : 19 + cx = uint64(19) &^ (-(x3 >> 63)) + // CLEAR BIT 255 + x3 &^= 1 << 63 + + x0, c0 = bits.Sub64(x0, cx, 0) + x1, c1 = bits.Sub64(x1, 0, c0) + x2, c2 = bits.Sub64(x2, 0, c1) + x3, _ = bits.Sub64(x3, 0, c2) + + binary.LittleEndian.PutUint64(x[0*8:1*8], x0) + binary.LittleEndian.PutUint64(x[1*8:2*8], x1) + binary.LittleEndian.PutUint64(x[2*8:3*8], x2) + binary.LittleEndian.PutUint64(x[3*8:4*8], x3) +} + +func red64(z *Elt, x0, x1, x2, x3, x4, x5, x6, x7 uint64) { + h0, l0 := bits.Mul64(x4, 38) + h1, l1 := bits.Mul64(x5, 38) + h2, l2 := bits.Mul64(x6, 38) + h3, l3 := bits.Mul64(x7, 38) + + l1, c0 := bits.Add64(h0, l1, 0) + l2, c1 := bits.Add64(h1, l2, c0) + l3, c2 := bits.Add64(h2, l3, c1) + l4, _ := bits.Add64(h3, 0, c2) + + l0, c0 = bits.Add64(l0, x0, 0) + l1, c1 = bits.Add64(l1, x1, c0) + l2, c2 = bits.Add64(l2, x2, c1) + l3, c3 := bits.Add64(l3, x3, c2) + l4, _ = bits.Add64(l4, 0, c3) + + _, l4 = bits.Mul64(l4, 38) + l0, c0 = bits.Add64(l0, l4, 0) + z1, c1 := bits.Add64(l1, 0, c0) + z2, c2 := bits.Add64(l2, 0, c1) + z3, c3 := bits.Add64(l3, 0, c2) + z0, _ := bits.Add64(l0, (-c3)&38, 0) + + binary.LittleEndian.PutUint64(z[0*8:1*8], z0) + binary.LittleEndian.PutUint64(z[1*8:2*8], z1) + binary.LittleEndian.PutUint64(z[2*8:3*8], z2) + binary.LittleEndian.PutUint64(z[3*8:4*8], z3) +} diff --git a/src/circl/math/fp25519/fp_noasm.go b/src/circl/math/fp25519/fp_noasm.go new file mode 100644 index 00000000000..08a07b6671f --- /dev/null +++ b/src/circl/math/fp25519/fp_noasm.go @@ -0,0 +1,12 @@ +// +build !amd64 purego + +package fp25519 + +func cmov(x, y *Elt, n uint) { cmovGeneric(x, y, n) } +func cswap(x, y *Elt, n uint) { cswapGeneric(x, y, n) } +func add(z, x, y *Elt) { addGeneric(z, x, y) } +func sub(z, x, y *Elt) { subGeneric(z, x, y) } +func addsub(x, y *Elt) { addsubGeneric(x, y) } +func mul(z, x, y *Elt) { mulGeneric(z, x, y) } +func sqr(z, x *Elt) { sqrGeneric(z, x) } +func modp(z *Elt) { modpGeneric(z) } diff --git a/src/circl/math/fp25519/fp_test.go b/src/circl/math/fp25519/fp_test.go new file mode 100644 index 00000000000..072d6d52157 --- /dev/null +++ b/src/circl/math/fp25519/fp_test.go @@ -0,0 +1,426 @@ +package fp25519 + +import ( + "crypto/rand" + "errors" + "fmt" + "math/big" + "testing" + + "circl/internal/conv" + "circl/internal/test" +) + +type tcmov func(x, y *Elt, n uint) +type tcswap func(x, y *Elt, n uint) +type tadd func(z, x, y *Elt) +type tsub func(z, x, y *Elt) +type taddsub func(x, y *Elt) +type tmul func(z, x, y *Elt) +type tsqr func(z, x *Elt) +type tmodp func(z *Elt) + +func testCmov(t *testing.T, f tcmov) { + const numTests = 1 << 9 + var x, y Elt + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + b := uint(y[0] & 0x1) + want := conv.BytesLe2BigInt(x[:]) + if b != 0 { + want = conv.BytesLe2BigInt(y[:]) + } + + f(&x, &y, b) + got := conv.BytesLe2BigInt(x[:]) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y, b) + } + } +} + +func testCswap(t *testing.T, f tcswap) { + const numTests = 1 << 9 + var x, y Elt + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + b := uint(y[0] & 0x1) + want0 := conv.BytesLe2BigInt(x[:]) + want1 := conv.BytesLe2BigInt(y[:]) + if b != 0 { + want0 = conv.BytesLe2BigInt(y[:]) + want1 = conv.BytesLe2BigInt(x[:]) + } + + f(&x, &y, b) + got0 := conv.BytesLe2BigInt(x[:]) + got1 := conv.BytesLe2BigInt(y[:]) + + if got0.Cmp(want0) != 0 { + test.ReportError(t, got0, want0, x, y, b) + } + if got1.Cmp(want1) != 0 { + test.ReportError(t, got1, want1, x, y, b) + } + } +} + +func testAdd(t *testing.T, f tadd) { + const numTests = 1 << 9 + var x, y, z Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + f(&z, &x, &y) + Modp(&z) + got := conv.BytesLe2BigInt(z[:]) + + xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) + want := xx.Add(xx, yy).Mod(xx, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y) + } + } +} + +func testSub(t *testing.T, f tsub) { + const numTests = 1 << 9 + var x, y, z Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + f(&z, &x, &y) + Modp(&z) + got := conv.BytesLe2BigInt(z[:]) + + xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) + want := xx.Sub(xx, yy).Mod(xx, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y) + } + } +} + +func testAddSub(t *testing.T, f taddsub) { + const numTests = 1 << 9 + var x, y Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + want0, want1 := big.NewInt(0), big.NewInt(0) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) + want0.Add(xx, yy).Mod(want0, p) + want1.Sub(xx, yy).Mod(want1, p) + + f(&x, &y) + Modp(&x) + Modp(&y) + got0 := conv.BytesLe2BigInt(x[:]) + got1 := conv.BytesLe2BigInt(y[:]) + + if got0.Cmp(want0) != 0 { + test.ReportError(t, got0, want0, x, y) + } + if got1.Cmp(want1) != 0 { + test.ReportError(t, got1, want1, x, y) + } + } +} + +func testMul(t *testing.T, f tmul) { + const numTests = 1 << 9 + var x, y, z Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + f(&z, &x, &y) + Modp(&z) + got := conv.BytesLe2BigInt(z[:]) + + xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) + want := xx.Mul(xx, yy).Mod(xx, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y) + } + } +} + +func testSqr(t *testing.T, f tsqr) { + const numTests = 1 << 9 + var x, z Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + f(&z, &x) + Modp(&z) + got := conv.BytesLe2BigInt(z[:]) + + xx := conv.BytesLe2BigInt(x[:]) + want := xx.Mul(xx, xx).Mod(xx, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } +} + +func testModp(t *testing.T, f tmodp) { + const numTests = 1 << 9 + var x Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + two256 := big.NewInt(1) + two256.Lsh(two256, 256) + want := new(big.Int) + for i := 0; i < numTests; i++ { + bigX, _ := rand.Int(rand.Reader, two256) + bigX.Add(bigX, p).Mod(bigX, two256) + conv.BigInt2BytesLe(x[:], bigX) + + f(&x) + got := conv.BytesLe2BigInt(x[:]) + + want.Mod(bigX, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, bigX) + } + } +} + +func TestIsZero(t *testing.T) { + var x Elt + got := IsZero(&x) + want := true + if got != want { + test.ReportError(t, got, want, x) + } + + SetOne(&x) + got = IsZero(&x) + want = false + if got != want { + test.ReportError(t, got, want, x) + } + + x = P() + got = IsZero(&x) + want = true + if got != want { + test.ReportError(t, got, want, x) + } + + x = Elt{ // 2P + 0xda, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + } + got = IsZero(&x) + want = true + if got != want { + test.ReportError(t, got, want, x) + } +} + +func TestToBytes(t *testing.T) { + const numTests = 1 << 9 + var x Elt + var got, want [Size]byte + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + err := ToBytes(got[:], &x) + conv.BigInt2BytesLe(want[:], conv.BytesLe2BigInt(x[:])) + if got != want || err != nil { + test.ReportError(t, got, want, x) + } + } + + { + var small [Size + 1]byte + got := ToBytes(small[:], &x) + want := errors.New("wrong size") + if got.Error() != want.Error() { + test.ReportError(t, got, want) + } + } +} + +func TestString(t *testing.T) { + const numTests = 1 << 9 + var x Elt + var bigX big.Int + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + got, _ := bigX.SetString(fmt.Sprint(x), 0) + want := conv.BytesLe2BigInt(x[:]) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } +} + +func TestNeg(t *testing.T) { + const numTests = 1 << 9 + var x, z Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + Neg(&z, &x) + Modp(&z) + got := conv.BytesLe2BigInt(z[:]) + + bigX := conv.BytesLe2BigInt(x[:]) + want := bigX.Neg(bigX).Mod(bigX, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, bigX) + } + } +} + +func TestInv(t *testing.T) { + const numTests = 1 << 9 + var x, z Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + Inv(&z, &x) + Modp(&z) + got := conv.BytesLe2BigInt(z[:]) + + xx := conv.BytesLe2BigInt(x[:]) + want := xx.ModInverse(xx, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } +} + +func TestInvSqrt(t *testing.T) { + const numTests = 1 << 9 + var x, y, z Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + exp := big.NewInt(3) + exp.Add(p, exp).Rsh(exp, 3) + var frac, root, sqRoot big.Int + var wantQR bool + var want *big.Int + sqrtMinusOne, _ := new(big.Int).SetString("2b8324804fc1df0b2b4d00993dfbd7a72f431806ad2fe478c4ee1b274a0ea0b0", 16) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + + gotQR := InvSqrt(&z, &x, &y) + Modp(&z) + got := conv.BytesLe2BigInt(z[:]) + + xx := conv.BytesLe2BigInt(x[:]) + yy := conv.BytesLe2BigInt(y[:]) + frac.ModInverse(yy, p).Mul(&frac, xx).Mod(&frac, p) + root.Exp(&frac, exp, p) + sqRoot.Mul(&root, &root).Mod(&sqRoot, p) + + if sqRoot.Cmp(&frac) == 0 { + want = &root + wantQR = true + } else { + frac.Neg(&frac).Mod(&frac, p) + if sqRoot.Cmp(&frac) == 0 { + want = root.Mul(&root, sqrtMinusOne).Mod(&root, p) + wantQR = true + } else { + want = big.NewInt(0) + wantQR = false + } + } + + if wantQR { + if gotQR != wantQR || got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y) + } + } else { + if gotQR != wantQR { + test.ReportError(t, gotQR, wantQR, x, y) + } + } + } +} + +func TestGeneric(t *testing.T) { + t.Run("Cmov", func(t *testing.T) { testCmov(t, cmovGeneric) }) + t.Run("Cswap", func(t *testing.T) { testCswap(t, cswapGeneric) }) + t.Run("Add", func(t *testing.T) { testAdd(t, addGeneric) }) + t.Run("Sub", func(t *testing.T) { testSub(t, subGeneric) }) + t.Run("AddSub", func(t *testing.T) { testAddSub(t, addsubGeneric) }) + t.Run("Mul", func(t *testing.T) { testMul(t, mulGeneric) }) + t.Run("Sqr", func(t *testing.T) { testSqr(t, sqrGeneric) }) + t.Run("Modp", func(t *testing.T) { testModp(t, modpGeneric) }) +} + +func TestNative(t *testing.T) { + t.Run("Cmov", func(t *testing.T) { testCmov(t, Cmov) }) + t.Run("Cswap", func(t *testing.T) { testCswap(t, Cswap) }) + t.Run("Add", func(t *testing.T) { testAdd(t, Add) }) + t.Run("Sub", func(t *testing.T) { testSub(t, Sub) }) + t.Run("AddSub", func(t *testing.T) { testAddSub(t, AddSub) }) + t.Run("Mul", func(t *testing.T) { testMul(t, Mul) }) + t.Run("Sqr", func(t *testing.T) { testSqr(t, Sqr) }) + t.Run("Modp", func(t *testing.T) { testModp(t, Modp) }) +} +func BenchmarkFp(b *testing.B) { + var x, y, z Elt + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + _, _ = rand.Read(z[:]) + b.Run("Add", func(b *testing.B) { + for i := 0; i < b.N; i++ { + Add(&x, &y, &z) + } + }) + b.Run("Sub", func(b *testing.B) { + for i := 0; i < b.N; i++ { + Sub(&x, &y, &z) + } + }) + b.Run("Mul", func(b *testing.B) { + for i := 0; i < b.N; i++ { + Mul(&x, &y, &z) + } + }) + b.Run("Sqr", func(b *testing.B) { + for i := 0; i < b.N; i++ { + Sqr(&x, &y) + } + }) + b.Run("Inv", func(b *testing.B) { + for i := 0; i < b.N; i++ { + Inv(&x, &y) + } + }) + b.Run("InvSqrt", func(b *testing.B) { + for i := 0; i < b.N; i++ { + InvSqrt(&z, &x, &y) + } + }) +} diff --git a/src/circl/math/fp448/edgecases_test.go b/src/circl/math/fp448/edgecases_test.go new file mode 100644 index 00000000000..8c6f9d69501 --- /dev/null +++ b/src/circl/math/fp448/edgecases_test.go @@ -0,0 +1,101 @@ +package fp448 + +import ( + "encoding/binary" + "math/big" + "testing" + + "circl/internal/conv" + "circl/internal/test" +) + +func TestEdgeCases(t *testing.T) { + t.Run("red64", func(t *testing.T) { ecRed64(t) }) +} + +func ecRed64(t *testing.T) { + var cases = [][2 * Size]byte{ + { + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + }, + { + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + }, + { + 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x45, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + }, + } + two448 := big.NewInt(1) + two448.Lsh(two448, 448) // 2^448 + mask448 := big.NewInt(1) + mask448.Sub(two448, mask448) // 2^448-1 + two224plus1 := big.NewInt(1) + two224plus1.Lsh(two224plus1, 224) + two224plus1.Add(two224plus1, big.NewInt(1)) // 2^224+1 + + var got, want Elt + var lo, hi [7]uint64 + for _, c := range cases { + cLo := c[0*Size:] + cHi := c[1*Size:] + for i := range lo { + lo[i] = binary.LittleEndian.Uint64(cLo[i*8 : (i+1)*8]) + hi[i] = binary.LittleEndian.Uint64(cHi[i*8 : (i+1)*8]) + } + red64(&got, &lo, &hi) + + tt := conv.BytesLe2BigInt(c[:2*Size]) + + var loBig, hiBig big.Int + for tt.Cmp(two448) >= 0 { + loBig.And(tt, mask448) + hiBig.Rsh(tt, 448) + tt.Mul(&hiBig, two224plus1) + tt.Add(tt, &loBig) + } + conv.BigInt2BytesLe(want[:], tt) + + if got != want { + test.ReportError(t, got, want, conv.BytesLe2BigInt(c[:2*Size])) + } + } +} diff --git a/src/circl/math/fp448/fp.go b/src/circl/math/fp448/fp.go new file mode 100644 index 00000000000..c444f3edf4a --- /dev/null +++ b/src/circl/math/fp448/fp.go @@ -0,0 +1,164 @@ +// Package fp448 provides prime field arithmetic over GF(2^448-2^224-1). +package fp448 + +import ( + "errors" + + "circl/internal/conv" +) + +// Size in bytes of an element. +const Size = 56 + +// Elt is a prime field element. +type Elt [Size]byte + +func (e Elt) String() string { return conv.BytesLe2Hex(e[:]) } + +// p is the prime modulus 2^448-2^224-1. +var p = Elt{ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, +} + +// P returns the prime modulus 2^448-2^224-1. +func P() Elt { return p } + +// ToBytes stores in b the little-endian byte representation of x. +func ToBytes(b []byte, x *Elt) error { + if len(b) != Size { + return errors.New("wrong size") + } + Modp(x) + copy(b, x[:]) + return nil +} + +// IsZero returns true if x is equal to 0. +func IsZero(x *Elt) bool { Modp(x); return *x == Elt{} } + +// IsOne returns true if x is equal to 1. +func IsOne(x *Elt) bool { Modp(x); return *x == Elt{1} } + +// SetOne assigns x=1. +func SetOne(x *Elt) { *x = Elt{1} } + +// One returns the 1 element. +func One() (x Elt) { x = Elt{1}; return } + +// Neg calculates z = -x. +func Neg(z, x *Elt) { Sub(z, &p, x) } + +// Modp ensures that z is between [0,p-1]. +func Modp(z *Elt) { Sub(z, z, &p) } + +// InvSqrt calculates z = sqrt(x/y) iff x/y is a quadratic-residue. If so, +// isQR = true; otherwise, isQR = false, since x/y is a quadratic non-residue, +// and z = sqrt(-x/y). +func InvSqrt(z, x, y *Elt) (isQR bool) { + // First note that x^(2(k+1)) = x^(p-1)/2 * x = legendre(x) * x + // so that's x if x is a quadratic residue and -x otherwise. + // Next, y^(6k+3) = y^(4k+2) * y^(2k+1) = y^(p-1) * y^((p-1)/2) = legendre(y). + // So the z we compute satisfies z^2 y = x^(2(k+1)) y^(6k+3) = legendre(x)*legendre(y). + // Thus if x and y are quadratic residues, then z is indeed sqrt(x/y). + t0, t1 := &Elt{}, &Elt{} + Mul(t0, x, y) // x*y + Sqr(t1, y) // y^2 + Mul(t1, t0, t1) // x*y^3 + powPminus3div4(z, t1) // (x*y^3)^k + Mul(z, z, t0) // z = x*y*(x*y^3)^k = x^(k+1) * y^(3k+1) + + // Check if x/y is a quadratic residue + Sqr(t0, z) // z^2 + Mul(t0, t0, y) // y*z^2 + Sub(t0, t0, x) // y*z^2-x + return IsZero(t0) +} + +// Inv calculates z = 1/x mod p. +func Inv(z, x *Elt) { + // Calculates z = x^(4k+1) = x^(p-3+1) = x^(p-2) = x^-1, where k = (p-3)/4. + t := &Elt{} + powPminus3div4(t, x) // t = x^k + Sqr(t, t) // t = x^2k + Sqr(t, t) // t = x^4k + Mul(z, t, x) // z = x^(4k+1) +} + +// powPminus3div4 calculates z = x^k mod p, where k = (p-3)/4. +func powPminus3div4(z, x *Elt) { + x0, x1 := &Elt{}, &Elt{} + Sqr(z, x) + Mul(z, z, x) + Sqr(x0, z) + Mul(x0, x0, x) + Sqr(z, x0) + Sqr(z, z) + Sqr(z, z) + Mul(z, z, x0) + Sqr(x1, z) + for i := 0; i < 5; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, z) + Sqr(z, x1) + for i := 0; i < 11; i++ { + Sqr(z, z) + } + Mul(z, z, x1) + Sqr(z, z) + Sqr(z, z) + Sqr(z, z) + Mul(z, z, x0) + Sqr(x1, z) + for i := 0; i < 26; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, z) + Sqr(z, x1) + for i := 0; i < 53; i++ { + Sqr(z, z) + } + Mul(z, z, x1) + Sqr(z, z) + Sqr(z, z) + Sqr(z, z) + Mul(z, z, x0) + Sqr(x1, z) + for i := 0; i < 110; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, z) + Sqr(z, x1) + Mul(z, z, x) + for i := 0; i < 223; i++ { + Sqr(z, z) + } + Mul(z, z, x1) +} + +// Cmov assigns y to x if n is 1. +func Cmov(x, y *Elt, n uint) { cmov(x, y, n) } + +// Cswap interchanges x and y if n is 1. +func Cswap(x, y *Elt, n uint) { cswap(x, y, n) } + +// Add calculates z = x+y mod p. +func Add(z, x, y *Elt) { add(z, x, y) } + +// Sub calculates z = x-y mod p. +func Sub(z, x, y *Elt) { sub(z, x, y) } + +// AddSub calculates (x,y) = (x+y mod p, x-y mod p). +func AddSub(x, y *Elt) { addsub(x, y) } + +// Mul calculates z = x*y mod p. +func Mul(z, x, y *Elt) { mul(z, x, y) } + +// Sqr calculates z = x^2 mod p. +func Sqr(z, x *Elt) { sqr(z, x) } diff --git a/src/circl/math/fp448/fp_amd64.go b/src/circl/math/fp448/fp_amd64.go new file mode 100644 index 00000000000..0e59b313ee9 --- /dev/null +++ b/src/circl/math/fp448/fp_amd64.go @@ -0,0 +1,42 @@ +// +build amd64,!purego + +package fp448 + +import ( + "internal/cpu" +) + +var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX + +var _ = hasBmi2Adx + +func cmov(x, y *Elt, n uint) { cmovAmd64(x, y, n) } +func cswap(x, y *Elt, n uint) { cswapAmd64(x, y, n) } +func add(z, x, y *Elt) { addAmd64(z, x, y) } +func sub(z, x, y *Elt) { subAmd64(z, x, y) } +func addsub(x, y *Elt) { addsubAmd64(x, y) } +func mul(z, x, y *Elt) { mulAmd64(z, x, y) } +func sqr(z, x *Elt) { sqrAmd64(z, x) } + +/* Functions defined in fp_amd64.s */ + +//go:noescape +func cmovAmd64(x, y *Elt, n uint) + +//go:noescape +func cswapAmd64(x, y *Elt, n uint) + +//go:noescape +func addAmd64(z, x, y *Elt) + +//go:noescape +func subAmd64(z, x, y *Elt) + +//go:noescape +func addsubAmd64(x, y *Elt) + +//go:noescape +func mulAmd64(z, x, y *Elt) + +//go:noescape +func sqrAmd64(z, x *Elt) diff --git a/src/circl/math/fp448/fp_amd64.h b/src/circl/math/fp448/fp_amd64.h new file mode 100644 index 00000000000..0b7dea174b9 --- /dev/null +++ b/src/circl/math/fp448/fp_amd64.h @@ -0,0 +1,590 @@ +// This code was imported from https://github.com/armfazh/rfc7748_precomputed + +// CHECK_BMI2ADX triggers bmi2adx if supported, +// otherwise it fallbacks to legacy code. +#define CHECK_BMI2ADX(label, legacy, bmi2adx) \ + CMPB ·hasBmi2Adx(SB), $0 \ + JE label \ + bmi2adx \ + RET \ + label: \ + legacy \ + RET + +// cselect is a conditional move +// if b=1: it copies y into x; +// if b=0: x remains with the same value; +// if b<> 0,1: undefined. +// Uses: AX, DX, FLAGS +// Instr: x86_64, cmov +#define cselect(x,y,b) \ + TESTQ b, b \ + MOVQ 0+x, AX; MOVQ 0+y, DX; CMOVQNE DX, AX; MOVQ AX, 0+x; \ + MOVQ 8+x, AX; MOVQ 8+y, DX; CMOVQNE DX, AX; MOVQ AX, 8+x; \ + MOVQ 16+x, AX; MOVQ 16+y, DX; CMOVQNE DX, AX; MOVQ AX, 16+x; \ + MOVQ 24+x, AX; MOVQ 24+y, DX; CMOVQNE DX, AX; MOVQ AX, 24+x; \ + MOVQ 32+x, AX; MOVQ 32+y, DX; CMOVQNE DX, AX; MOVQ AX, 32+x; \ + MOVQ 40+x, AX; MOVQ 40+y, DX; CMOVQNE DX, AX; MOVQ AX, 40+x; \ + MOVQ 48+x, AX; MOVQ 48+y, DX; CMOVQNE DX, AX; MOVQ AX, 48+x; + +// cswap is a conditional swap +// if b=1: x,y <- y,x; +// if b=0: x,y remain with the same values; +// if b<> 0,1: undefined. +// Uses: AX, DX, R8, FLAGS +// Instr: x86_64, cmov +#define cswap(x,y,b) \ + TESTQ b, b \ + MOVQ 0+x, AX; MOVQ AX, R8; MOVQ 0+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 0+x; MOVQ DX, 0+y; \ + MOVQ 8+x, AX; MOVQ AX, R8; MOVQ 8+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 8+x; MOVQ DX, 8+y; \ + MOVQ 16+x, AX; MOVQ AX, R8; MOVQ 16+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 16+x; MOVQ DX, 16+y; \ + MOVQ 24+x, AX; MOVQ AX, R8; MOVQ 24+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 24+x; MOVQ DX, 24+y; \ + MOVQ 32+x, AX; MOVQ AX, R8; MOVQ 32+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 32+x; MOVQ DX, 32+y; \ + MOVQ 40+x, AX; MOVQ AX, R8; MOVQ 40+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 40+x; MOVQ DX, 40+y; \ + MOVQ 48+x, AX; MOVQ AX, R8; MOVQ 48+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 48+x; MOVQ DX, 48+y; + +// additionLeg adds x and y and stores in z +// Uses: AX, DX, R8-R14, FLAGS +// Instr: x86_64 +#define additionLeg(z,x,y) \ + MOVQ 0+x, R8; ADDQ 0+y, R8; \ + MOVQ 8+x, R9; ADCQ 8+y, R9; \ + MOVQ 16+x, R10; ADCQ 16+y, R10; \ + MOVQ 24+x, R11; ADCQ 24+y, R11; \ + MOVQ 32+x, R12; ADCQ 32+y, R12; \ + MOVQ 40+x, R13; ADCQ 40+y, R13; \ + MOVQ 48+x, R14; ADCQ 48+y, R14; \ + MOVQ $0, AX; ADCQ $0, AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + ADDQ AX, R8; MOVQ $0, AX; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ DX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + ADCQ $0, AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + ADDQ AX, R8; MOVQ R8, 0+z; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ DX, R11; MOVQ R11, 24+z; \ + ADCQ $0, R12; MOVQ R12, 32+z; \ + ADCQ $0, R13; MOVQ R13, 40+z; \ + ADCQ $0, R14; MOVQ R14, 48+z; + + +// additionAdx adds x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64, adx +#define additionAdx(z,x,y) \ + MOVL $32, R15; \ + XORL DX, DX; \ + MOVQ 0+x, R8; ADCXQ 0+y, R8; \ + MOVQ 8+x, R9; ADCXQ 8+y, R9; \ + MOVQ 16+x, R10; ADCXQ 16+y, R10; \ + MOVQ 24+x, R11; ADCXQ 24+y, R11; \ + MOVQ 32+x, R12; ADCXQ 32+y, R12; \ + MOVQ 40+x, R13; ADCXQ 40+y, R13; \ + MOVQ 48+x, R14; ADCXQ 48+y, R14; \ + ;;;;;;;;;;;;;;; ADCXQ DX, DX; \ + XORL AX, AX; \ + ADCXQ DX, R8; SHLXQ R15, DX, DX; \ + ADCXQ AX, R9; \ + ADCXQ AX, R10; \ + ADCXQ DX, R11; \ + ADCXQ AX, R12; \ + ADCXQ AX, R13; \ + ADCXQ AX, R14; \ + ADCXQ AX, AX; \ + XORL DX, DX; \ + ADCXQ AX, R8; MOVQ R8, 0+z; SHLXQ R15, AX, AX; \ + ADCXQ DX, R9; MOVQ R9, 8+z; \ + ADCXQ DX, R10; MOVQ R10, 16+z; \ + ADCXQ AX, R11; MOVQ R11, 24+z; \ + ADCXQ DX, R12; MOVQ R12, 32+z; \ + ADCXQ DX, R13; MOVQ R13, 40+z; \ + ADCXQ DX, R14; MOVQ R14, 48+z; + +// subtraction subtracts y from x and stores in z +// Uses: AX, DX, R8-R14, FLAGS +// Instr: x86_64 +#define subtraction(z,x,y) \ + MOVQ 0+x, R8; SUBQ 0+y, R8; \ + MOVQ 8+x, R9; SBBQ 8+y, R9; \ + MOVQ 16+x, R10; SBBQ 16+y, R10; \ + MOVQ 24+x, R11; SBBQ 24+y, R11; \ + MOVQ 32+x, R12; SBBQ 32+y, R12; \ + MOVQ 40+x, R13; SBBQ 40+y, R13; \ + MOVQ 48+x, R14; SBBQ 48+y, R14; \ + MOVQ $0, AX; SETCS AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + SUBQ AX, R8; MOVQ $0, AX; \ + SBBQ $0, R9; \ + SBBQ $0, R10; \ + SBBQ DX, R11; \ + SBBQ $0, R12; \ + SBBQ $0, R13; \ + SBBQ $0, R14; \ + SETCS AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + SUBQ AX, R8; MOVQ R8, 0+z; \ + SBBQ $0, R9; MOVQ R9, 8+z; \ + SBBQ $0, R10; MOVQ R10, 16+z; \ + SBBQ DX, R11; MOVQ R11, 24+z; \ + SBBQ $0, R12; MOVQ R12, 32+z; \ + SBBQ $0, R13; MOVQ R13, 40+z; \ + SBBQ $0, R14; MOVQ R14, 48+z; + +// maddBmi2Adx multiplies x and y and accumulates in z +// Uses: AX, DX, R15, FLAGS +// Instr: x86_64, bmi2, adx +#define maddBmi2Adx(z,x,y,i,r0,r1,r2,r3,r4,r5,r6) \ + MOVQ i+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R8; ADOXQ AX, r0; ADCXQ R8, r1; MOVQ r0,i+z; \ + MULXQ 8+x, AX, r0; ADOXQ AX, r1; ADCXQ r0, r2; MOVQ $0, R8; \ + MULXQ 16+x, AX, r0; ADOXQ AX, r2; ADCXQ r0, r3; \ + MULXQ 24+x, AX, r0; ADOXQ AX, r3; ADCXQ r0, r4; \ + MULXQ 32+x, AX, r0; ADOXQ AX, r4; ADCXQ r0, r5; \ + MULXQ 40+x, AX, r0; ADOXQ AX, r5; ADCXQ r0, r6; \ + MULXQ 48+x, AX, r0; ADOXQ AX, r6; ADCXQ R8, r0; \ + ;;;;;;;;;;;;;;;;;;; ADOXQ R8, r0; + +// integerMulAdx multiplies x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64, bmi2, adx +#define integerMulAdx(z,x,y) \ + MOVQ 0+y, DX; XORL AX, AX; MOVQ $0, R8; \ + MULXQ 0+x, AX, R9; MOVQ AX, 0+z; \ + MULXQ 8+x, AX, R10; ADCXQ AX, R9; \ + MULXQ 16+x, AX, R11; ADCXQ AX, R10; \ + MULXQ 24+x, AX, R12; ADCXQ AX, R11; \ + MULXQ 32+x, AX, R13; ADCXQ AX, R12; \ + MULXQ 40+x, AX, R14; ADCXQ AX, R13; \ + MULXQ 48+x, AX, R15; ADCXQ AX, R14; \ + ;;;;;;;;;;;;;;;;;;;; ADCXQ R8, R15; \ + maddBmi2Adx(z,x,y, 8, R9,R10,R11,R12,R13,R14,R15) \ + maddBmi2Adx(z,x,y,16,R10,R11,R12,R13,R14,R15, R9) \ + maddBmi2Adx(z,x,y,24,R11,R12,R13,R14,R15, R9,R10) \ + maddBmi2Adx(z,x,y,32,R12,R13,R14,R15, R9,R10,R11) \ + maddBmi2Adx(z,x,y,40,R13,R14,R15, R9,R10,R11,R12) \ + maddBmi2Adx(z,x,y,48,R14,R15, R9,R10,R11,R12,R13) \ + MOVQ R15, 56+z; \ + MOVQ R9, 64+z; \ + MOVQ R10, 72+z; \ + MOVQ R11, 80+z; \ + MOVQ R12, 88+z; \ + MOVQ R13, 96+z; \ + MOVQ R14, 104+z; + +// maddLegacy multiplies x and y and accumulates in z +// Uses: AX, DX, R15, FLAGS +// Instr: x86_64 +#define maddLegacy(z,x,y,i) \ + MOVQ i+y, R15; \ + MOVQ 0+x, AX; MULQ R15; MOVQ AX, R8; ;;;;;;;;;;;; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R15; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R15; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R15; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; \ + MOVQ 32+x, AX; MULQ R15; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; \ + MOVQ 40+x, AX; MULQ R15; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX, R14; \ + MOVQ 48+x, AX; MULQ R15; ADDQ AX, R14; ADCQ $0, DX; \ + ADDQ 0+i+z, R8; MOVQ R8, 0+i+z; \ + ADCQ 8+i+z, R9; MOVQ R9, 8+i+z; \ + ADCQ 16+i+z, R10; MOVQ R10, 16+i+z; \ + ADCQ 24+i+z, R11; MOVQ R11, 24+i+z; \ + ADCQ 32+i+z, R12; MOVQ R12, 32+i+z; \ + ADCQ 40+i+z, R13; MOVQ R13, 40+i+z; \ + ADCQ 48+i+z, R14; MOVQ R14, 48+i+z; \ + ADCQ $0, DX; MOVQ DX, 56+i+z; + +// integerMulLeg multiplies x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64 +#define integerMulLeg(z,x,y) \ + MOVQ 0+y, R15; \ + MOVQ 0+x, AX; MULQ R15; MOVQ AX, 0+z; ;;;;;;;;;;;; MOVQ DX, R8; \ + MOVQ 8+x, AX; MULQ R15; ADDQ AX, R8; ADCQ $0, DX; MOVQ DX, R9; MOVQ R8, 8+z; \ + MOVQ 16+x, AX; MULQ R15; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; MOVQ R9, 16+z; \ + MOVQ 24+x, AX; MULQ R15; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; MOVQ R10, 24+z; \ + MOVQ 32+x, AX; MULQ R15; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; MOVQ R11, 32+z; \ + MOVQ 40+x, AX; MULQ R15; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; MOVQ R12, 40+z; \ + MOVQ 48+x, AX; MULQ R15; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX,56+z; MOVQ R13, 48+z; \ + maddLegacy(z,x,y, 8) \ + maddLegacy(z,x,y,16) \ + maddLegacy(z,x,y,24) \ + maddLegacy(z,x,y,32) \ + maddLegacy(z,x,y,40) \ + maddLegacy(z,x,y,48) + +// integerSqrLeg squares x and stores in z +// Uses: AX, CX, DX, R8-R15, FLAGS +// Instr: x86_64 +#define integerSqrLeg(z,x) \ + XORL R15, R15; \ + MOVQ 0+x, CX; \ + MOVQ CX, AX; MULQ CX; MOVQ AX, 0+z; MOVQ DX, R8; \ + ADDQ CX, CX; ADCQ $0, R15; \ + MOVQ 8+x, AX; MULQ CX; ADDQ AX, R8; ADCQ $0, DX; MOVQ DX, R9; MOVQ R8, 8+z; \ + MOVQ 16+x, AX; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; \ + MOVQ 24+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; \ + MOVQ 32+x, AX; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX, R14; \ + \ + MOVQ 8+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; MOVQ R9,16+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 8+x, AX; ADDQ AX, DX; ADCQ $0, R11; MOVQ DX, R8; \ + ADDQ 8+x, CX; ADCQ $0, R15; \ + MOVQ 16+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; ADDQ R8, R10; ADCQ $0, DX; MOVQ DX, R8; MOVQ R10, 24+z; \ + MOVQ 24+x, AX; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; ADDQ R8, R11; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 32+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; ADDQ R8, R12; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; ADDQ R8, R13; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R14; ADCQ $0, DX; ADDQ R8, R14; ADCQ $0, DX; MOVQ DX, R9; \ + \ + MOVQ 16+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; MOVQ R11, 32+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 16+x,AX; ADDQ AX, DX; ADCQ $0, R13; MOVQ DX, R8; \ + ADDQ 16+x, CX; ADCQ $0, R15; \ + MOVQ 24+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; ADDQ R8, R12; ADCQ $0, DX; MOVQ DX, R8; MOVQ R12, 40+z; \ + MOVQ 32+x, AX; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; ADDQ R8, R13; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R14; ADCQ $0, DX; ADDQ R8, R14; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; ADDQ R8, R9; ADCQ $0, DX; MOVQ DX,R10; \ + \ + MOVQ 24+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; MOVQ R13, 48+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 24+x,AX; ADDQ AX, DX; ADCQ $0, R9; MOVQ DX, R8; \ + ADDQ 24+x, CX; ADCQ $0, R15; \ + MOVQ 32+x, AX; MULQ CX; ADDQ AX, R14; ADCQ $0, DX; ADDQ R8, R14; ADCQ $0, DX; MOVQ DX, R8; MOVQ R14, 56+z; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; ADDQ R8, R9; ADCQ $0, DX; MOVQ DX, R8; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; ADDQ R8, R10; ADCQ $0, DX; MOVQ DX,R11; \ + \ + MOVQ 32+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R9; ADCQ $0, DX; MOVQ R9, 64+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 32+x,AX; ADDQ AX, DX; ADCQ $0, R11; MOVQ DX, R8; \ + ADDQ 32+x, CX; ADCQ $0, R15; \ + MOVQ 40+x, AX; MULQ CX; ADDQ AX, R10; ADCQ $0, DX; ADDQ R8, R10; ADCQ $0, DX; MOVQ DX, R8; MOVQ R10, 72+z; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; ADDQ R8, R11; ADCQ $0, DX; MOVQ DX,R12; \ + \ + XORL R13, R13; \ + XORL R14, R14; \ + MOVQ 40+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R11; ADCQ $0, DX; MOVQ R11, 80+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 40+x,AX; ADDQ AX, DX; ADCQ $0, R13; MOVQ DX, R8; \ + ADDQ 40+x, CX; ADCQ $0, R15; \ + MOVQ 48+x, AX; MULQ CX; ADDQ AX, R12; ADCQ $0, DX; ADDQ R8, R12; ADCQ $0, DX; MOVQ DX, R8; MOVQ R12, 88+z; \ + ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADDQ R8, R13; ADCQ $0,R14; \ + \ + XORL R9, R9; \ + MOVQ 48+x, CX; \ + MOVQ CX, AX; ADDQ R15, CX; MOVQ $0, R15; ADCQ $0, R15; \ + ;;;;;;;;;;;;;; MULQ CX; ADDQ AX, R13; ADCQ $0, DX; MOVQ R13, 96+z; \ + MOVQ R15, AX; NEGQ AX; ANDQ 48+x,AX; ADDQ AX, DX; ADCQ $0, R9; MOVQ DX, R8; \ + ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADDQ R8,R14; ADCQ $0, R9; MOVQ R14, 104+z; + + +// integerSqrAdx squares x and stores in z +// Uses: AX, CX, DX, R8-R15, FLAGS +// Instr: x86_64, bmi2, adx +#define integerSqrAdx(z,x) \ + XORL R15, R15; \ + MOVQ 0+x, DX; \ + ;;;;;;;;;;;;;; MULXQ DX, AX, R8; MOVQ AX, 0+z; \ + ADDQ DX, DX; ADCQ $0, R15; CLC; \ + MULXQ 8+x, AX, R9; ADCXQ AX, R8; MOVQ R8, 8+z; \ + MULXQ 16+x, AX, R10; ADCXQ AX, R9; MOVQ $0, R8;\ + MULXQ 24+x, AX, R11; ADCXQ AX, R10; \ + MULXQ 32+x, AX, R12; ADCXQ AX, R11; \ + MULXQ 40+x, AX, R13; ADCXQ AX, R12; \ + MULXQ 48+x, AX, R14; ADCXQ AX, R13; \ + ;;;;;;;;;;;;;;;;;;;; ADCXQ R8, R14; \ + \ + MOVQ 8+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 8+x, R8; \ + ADDQ AX, R9; MOVQ R9, 16+z; \ + ADCQ CX, R8; \ + ADCQ $0, R11; \ + ADDQ 8+x, DX; \ + ADCQ $0, R15; \ + XORL R9, R9; ;;;;;;;;;;;;;;;;;;;;; ADOXQ R8, R10; \ + MULXQ 16+x, AX, CX; ADCXQ AX, R10; ADOXQ CX, R11; MOVQ R10, 24+z; \ + MULXQ 24+x, AX, CX; ADCXQ AX, R11; ADOXQ CX, R12; MOVQ $0, R10; \ + MULXQ 32+x, AX, CX; ADCXQ AX, R12; ADOXQ CX, R13; \ + MULXQ 40+x, AX, CX; ADCXQ AX, R13; ADOXQ CX, R14; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R14; ADOXQ CX, R9; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R10, R9; \ + \ + MOVQ 16+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 16+x, R8; \ + ADDQ AX, R11; MOVQ R11, 32+z; \ + ADCQ CX, R8; \ + ADCQ $0, R13; \ + ADDQ 16+x, DX; \ + ADCQ $0, R15; \ + XORL R11, R11; ;;;;;;;;;;;;;;;;;;; ADOXQ R8, R12; \ + MULXQ 24+x, AX, CX; ADCXQ AX, R12; ADOXQ CX, R13; MOVQ R12, 40+z; \ + MULXQ 32+x, AX, CX; ADCXQ AX, R13; ADOXQ CX, R14; MOVQ $0, R12; \ + MULXQ 40+x, AX, CX; ADCXQ AX, R14; ADOXQ CX, R9; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R9; ADOXQ CX, R10; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R11,R10; \ + \ + MOVQ 24+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 24+x, R8; \ + ADDQ AX, R13; MOVQ R13, 48+z; \ + ADCQ CX, R8; \ + ADCQ $0, R9; \ + ADDQ 24+x, DX; \ + ADCQ $0, R15; \ + XORL R13, R13; ;;;;;;;;;;;;;;;;;;; ADOXQ R8, R14; \ + MULXQ 32+x, AX, CX; ADCXQ AX, R14; ADOXQ CX, R9; MOVQ R14, 56+z; \ + MULXQ 40+x, AX, CX; ADCXQ AX, R9; ADOXQ CX, R10; MOVQ $0, R14; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R10; ADOXQ CX, R11; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R12,R11; \ + \ + MOVQ 32+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 32+x, R8; \ + ADDQ AX, R9; MOVQ R9, 64+z; \ + ADCQ CX, R8; \ + ADCQ $0, R11; \ + ADDQ 32+x, DX; \ + ADCQ $0, R15; \ + XORL R9, R9; ;;;;;;;;;;;;;;;;;;;;; ADOXQ R8, R10; \ + MULXQ 40+x, AX, CX; ADCXQ AX, R10; ADOXQ CX, R11; MOVQ R10, 72+z; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R11; ADOXQ CX, R12; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R13,R12; \ + \ + MOVQ 40+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 40+x, R8; \ + ADDQ AX, R11; MOVQ R11, 80+z; \ + ADCQ CX, R8; \ + ADCQ $0, R13; \ + ADDQ 40+x, DX; \ + ADCQ $0, R15; \ + XORL R11, R11; ;;;;;;;;;;;;;;;;;;; ADOXQ R8, R12; \ + MULXQ 48+x, AX, CX; ADCXQ AX, R12; ADOXQ CX, R13; MOVQ R12, 88+z; \ + ;;;;;;;;;;;;;;;;;;; ADCXQ R14,R13; \ + \ + MOVQ 48+x, DX; \ + MOVQ DX, AX; ADDQ R15, DX; MOVQ $0, R15; ADCQ $0, R15; \ + MULXQ AX, AX, CX; \ + MOVQ R15, R8; NEGQ R8; ANDQ 48+x, R8; \ + XORL R10, R10; ;;;;;;;;;;;;;; ADOXQ CX, R14; \ + ;;;;;;;;;;;;;; ADCXQ AX, R13; ;;;;;;;;;;;;;; MOVQ R13, 96+z; \ + ;;;;;;;;;;;;;; ADCXQ R8, R14; MOVQ R14, 104+z; + +// reduceFromDoubleLeg finds a z=x modulo p such that z<2^448 and stores in z +// Uses: AX, R8-R15, FLAGS +// Instr: x86_64 +#define reduceFromDoubleLeg(z,x) \ + /* ( ,2C13,2C12,2C11,2C10|C10,C9,C8, C7) + (C6,...,C0) */ \ + /* (r14, r13, r12, r11, r10,r9,r8,r15) */ \ + MOVQ 80+x,AX; MOVQ AX,R10; \ + MOVQ $0xFFFFFFFF00000000, R8; \ + ANDQ R8,R10; \ + \ + MOVQ $0,R14; \ + MOVQ 104+x,R13; SHLQ $1,R13,R14; \ + MOVQ 96+x,R12; SHLQ $1,R12,R13; \ + MOVQ 88+x,R11; SHLQ $1,R11,R12; \ + MOVQ 72+x, R9; SHLQ $1,R10,R11; \ + MOVQ 64+x, R8; SHLQ $1,R10; \ + MOVQ $0xFFFFFFFF,R15; ANDQ R15,AX; ORQ AX,R10; \ + MOVQ 56+x,R15; \ + \ + ADDQ 0+x,R15; MOVQ R15, 0+z; MOVQ 56+x,R15; \ + ADCQ 8+x, R8; MOVQ R8, 8+z; MOVQ 64+x, R8; \ + ADCQ 16+x, R9; MOVQ R9,16+z; MOVQ 72+x, R9; \ + ADCQ 24+x,R10; MOVQ R10,24+z; MOVQ 80+x,R10; \ + ADCQ 32+x,R11; MOVQ R11,32+z; MOVQ 88+x,R11; \ + ADCQ 40+x,R12; MOVQ R12,40+z; MOVQ 96+x,R12; \ + ADCQ 48+x,R13; MOVQ R13,48+z; MOVQ 104+x,R13; \ + ADCQ $0,R14; \ + /* (c10c9,c9c8,c8c7,c7c13,c13c12,c12c11,c11c10) + (c6,...,c0) */ \ + /* ( r9, r8, r15, r13, r12, r11, r10) */ \ + MOVQ R10, AX; \ + SHRQ $32,R11,R10; \ + SHRQ $32,R12,R11; \ + SHRQ $32,R13,R12; \ + SHRQ $32,R15,R13; \ + SHRQ $32, R8,R15; \ + SHRQ $32, R9, R8; \ + SHRQ $32, AX, R9; \ + \ + ADDQ 0+z,R10; \ + ADCQ 8+z,R11; \ + ADCQ 16+z,R12; \ + ADCQ 24+z,R13; \ + ADCQ 32+z,R15; \ + ADCQ 40+z, R8; \ + ADCQ 48+z, R9; \ + ADCQ $0,R14; \ + /* ( c7) + (c6,...,c0) */ \ + /* (r14) */ \ + MOVQ R14, AX; SHLQ $32, AX; \ + ADDQ R14,R10; MOVQ $0,R14; \ + ADCQ $0,R11; \ + ADCQ $0,R12; \ + ADCQ AX,R13; \ + ADCQ $0,R15; \ + ADCQ $0, R8; \ + ADCQ $0, R9; \ + ADCQ $0,R14; \ + /* ( c7) + (c6,...,c0) */ \ + /* (r14) */ \ + MOVQ R14, AX; SHLQ $32,AX; \ + ADDQ R14,R10; MOVQ R10, 0+z; \ + ADCQ $0,R11; MOVQ R11, 8+z; \ + ADCQ $0,R12; MOVQ R12,16+z; \ + ADCQ AX,R13; MOVQ R13,24+z; \ + ADCQ $0,R15; MOVQ R15,32+z; \ + ADCQ $0, R8; MOVQ R8,40+z; \ + ADCQ $0, R9; MOVQ R9,48+z; + +// reduceFromDoubleAdx finds a z=x modulo p such that z<2^448 and stores in z +// Uses: AX, R8-R15, FLAGS +// Instr: x86_64, adx +#define reduceFromDoubleAdx(z,x) \ + /* ( ,2C13,2C12,2C11,2C10|C10,C9,C8, C7) + (C6,...,C0) */ \ + /* (r14, r13, r12, r11, r10,r9,r8,r15) */ \ + MOVQ 80+x,AX; MOVQ AX,R10; \ + MOVQ $0xFFFFFFFF00000000, R8; \ + ANDQ R8,R10; \ + \ + MOVQ $0,R14; \ + MOVQ 104+x,R13; SHLQ $1,R13,R14; \ + MOVQ 96+x,R12; SHLQ $1,R12,R13; \ + MOVQ 88+x,R11; SHLQ $1,R11,R12; \ + MOVQ 72+x, R9; SHLQ $1,R10,R11; \ + MOVQ 64+x, R8; SHLQ $1,R10; \ + MOVQ $0xFFFFFFFF,R15; ANDQ R15,AX; ORQ AX,R10; \ + MOVQ 56+x,R15; \ + \ + XORL AX,AX; \ + ADCXQ 0+x,R15; MOVQ R15, 0+z; MOVQ 56+x,R15; \ + ADCXQ 8+x, R8; MOVQ R8, 8+z; MOVQ 64+x, R8; \ + ADCXQ 16+x, R9; MOVQ R9,16+z; MOVQ 72+x, R9; \ + ADCXQ 24+x,R10; MOVQ R10,24+z; MOVQ 80+x,R10; \ + ADCXQ 32+x,R11; MOVQ R11,32+z; MOVQ 88+x,R11; \ + ADCXQ 40+x,R12; MOVQ R12,40+z; MOVQ 96+x,R12; \ + ADCXQ 48+x,R13; MOVQ R13,48+z; MOVQ 104+x,R13; \ + ADCXQ AX,R14; \ + /* (c10c9,c9c8,c8c7,c7c13,c13c12,c12c11,c11c10) + (c6,...,c0) */ \ + /* ( r9, r8, r15, r13, r12, r11, r10) */ \ + MOVQ R10, AX; \ + SHRQ $32,R11,R10; \ + SHRQ $32,R12,R11; \ + SHRQ $32,R13,R12; \ + SHRQ $32,R15,R13; \ + SHRQ $32, R8,R15; \ + SHRQ $32, R9, R8; \ + SHRQ $32, AX, R9; \ + \ + XORL AX,AX; \ + ADCXQ 0+z,R10; \ + ADCXQ 8+z,R11; \ + ADCXQ 16+z,R12; \ + ADCXQ 24+z,R13; \ + ADCXQ 32+z,R15; \ + ADCXQ 40+z, R8; \ + ADCXQ 48+z, R9; \ + ADCXQ AX,R14; \ + /* ( c7) + (c6,...,c0) */ \ + /* (r14) */ \ + MOVQ R14, AX; SHLQ $32, AX; \ + CLC; \ + ADCXQ R14,R10; MOVQ $0,R14; \ + ADCXQ R14,R11; \ + ADCXQ R14,R12; \ + ADCXQ AX,R13; \ + ADCXQ R14,R15; \ + ADCXQ R14, R8; \ + ADCXQ R14, R9; \ + ADCXQ R14,R14; \ + /* ( c7) + (c6,...,c0) */ \ + /* (r14) */ \ + MOVQ R14, AX; SHLQ $32, AX; \ + CLC; \ + ADCXQ R14,R10; MOVQ R10, 0+z; MOVQ $0,R14; \ + ADCXQ R14,R11; MOVQ R11, 8+z; \ + ADCXQ R14,R12; MOVQ R12,16+z; \ + ADCXQ AX,R13; MOVQ R13,24+z; \ + ADCXQ R14,R15; MOVQ R15,32+z; \ + ADCXQ R14, R8; MOVQ R8,40+z; \ + ADCXQ R14, R9; MOVQ R9,48+z; + +// addSub calculates two operations: x,y = x+y,x-y +// Uses: AX, DX, R8-R15, FLAGS +#define addSub(x,y) \ + MOVQ 0+x, R8; ADDQ 0+y, R8; \ + MOVQ 8+x, R9; ADCQ 8+y, R9; \ + MOVQ 16+x, R10; ADCQ 16+y, R10; \ + MOVQ 24+x, R11; ADCQ 24+y, R11; \ + MOVQ 32+x, R12; ADCQ 32+y, R12; \ + MOVQ 40+x, R13; ADCQ 40+y, R13; \ + MOVQ 48+x, R14; ADCQ 48+y, R14; \ + MOVQ $0, AX; ADCQ $0, AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + ADDQ AX, R8; MOVQ $0, AX; \ + ADCQ $0, R9; \ + ADCQ $0, R10; \ + ADCQ DX, R11; \ + ADCQ $0, R12; \ + ADCQ $0, R13; \ + ADCQ $0, R14; \ + ADCQ $0, AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + ADDQ AX, R8; MOVQ 0+x,AX; MOVQ R8, 0+x; MOVQ AX, R8; \ + ADCQ $0, R9; MOVQ 8+x,AX; MOVQ R9, 8+x; MOVQ AX, R9; \ + ADCQ $0, R10; MOVQ 16+x,AX; MOVQ R10, 16+x; MOVQ AX, R10; \ + ADCQ DX, R11; MOVQ 24+x,AX; MOVQ R11, 24+x; MOVQ AX, R11; \ + ADCQ $0, R12; MOVQ 32+x,AX; MOVQ R12, 32+x; MOVQ AX, R12; \ + ADCQ $0, R13; MOVQ 40+x,AX; MOVQ R13, 40+x; MOVQ AX, R13; \ + ADCQ $0, R14; MOVQ 48+x,AX; MOVQ R14, 48+x; MOVQ AX, R14; \ + SUBQ 0+y, R8; \ + SBBQ 8+y, R9; \ + SBBQ 16+y, R10; \ + SBBQ 24+y, R11; \ + SBBQ 32+y, R12; \ + SBBQ 40+y, R13; \ + SBBQ 48+y, R14; \ + MOVQ $0, AX; SETCS AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + SUBQ AX, R8; MOVQ $0, AX; \ + SBBQ $0, R9; \ + SBBQ $0, R10; \ + SBBQ DX, R11; \ + SBBQ $0, R12; \ + SBBQ $0, R13; \ + SBBQ $0, R14; \ + SETCS AX; \ + MOVQ AX, DX; \ + SHLQ $32, DX; \ + SUBQ AX, R8; MOVQ R8, 0+y; \ + SBBQ $0, R9; MOVQ R9, 8+y; \ + SBBQ $0, R10; MOVQ R10, 16+y; \ + SBBQ DX, R11; MOVQ R11, 24+y; \ + SBBQ $0, R12; MOVQ R12, 32+y; \ + SBBQ $0, R13; MOVQ R13, 40+y; \ + SBBQ $0, R14; MOVQ R14, 48+y; diff --git a/src/circl/math/fp448/fp_amd64.s b/src/circl/math/fp448/fp_amd64.s new file mode 100644 index 00000000000..435addf5e6c --- /dev/null +++ b/src/circl/math/fp448/fp_amd64.s @@ -0,0 +1,74 @@ +// +build amd64 + +#include "textflag.h" +#include "fp_amd64.h" + +// func cmovAmd64(x, y *Elt, n uint) +TEXT ·cmovAmd64(SB),NOSPLIT,$0-24 + MOVQ x+0(FP), DI + MOVQ y+8(FP), SI + MOVQ n+16(FP), BX + cselect(0(DI),0(SI),BX) + RET + +// func cswapAmd64(x, y *Elt, n uint) +TEXT ·cswapAmd64(SB),NOSPLIT,$0-24 + MOVQ x+0(FP), DI + MOVQ y+8(FP), SI + MOVQ n+16(FP), BX + cswap(0(DI),0(SI),BX) + RET + +// func subAmd64(z, x, y *Elt) +TEXT ·subAmd64(SB),NOSPLIT,$0-24 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + MOVQ y+16(FP), BX + subtraction(0(DI),0(SI),0(BX)) + RET + +// func addsubAmd64(x, y *Elt) +TEXT ·addsubAmd64(SB),NOSPLIT,$0-16 + MOVQ x+0(FP), DI + MOVQ y+8(FP), SI + addSub(0(DI),0(SI)) + RET + +#define addLegacy \ + additionLeg(0(DI),0(SI),0(BX)) +#define addBmi2Adx \ + additionAdx(0(DI),0(SI),0(BX)) + +#define mulLegacy \ + integerMulLeg(0(SP),0(SI),0(BX)) \ + reduceFromDoubleLeg(0(DI),0(SP)) +#define mulBmi2Adx \ + integerMulAdx(0(SP),0(SI),0(BX)) \ + reduceFromDoubleAdx(0(DI),0(SP)) + +#define sqrLegacy \ + integerSqrLeg(0(SP),0(SI)) \ + reduceFromDoubleLeg(0(DI),0(SP)) +#define sqrBmi2Adx \ + integerSqrAdx(0(SP),0(SI)) \ + reduceFromDoubleAdx(0(DI),0(SP)) + +// func addAmd64(z, x, y *Elt) +TEXT ·addAmd64(SB),NOSPLIT,$0-24 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + MOVQ y+16(FP), BX + CHECK_BMI2ADX(LADD, addLegacy, addBmi2Adx) + +// func mulAmd64(z, x, y *Elt) +TEXT ·mulAmd64(SB),NOSPLIT,$112-24 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + MOVQ y+16(FP), BX + CHECK_BMI2ADX(LMUL, mulLegacy, mulBmi2Adx) + +// func sqrAmd64(z, x *Elt) +TEXT ·sqrAmd64(SB),NOSPLIT,$112-16 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + CHECK_BMI2ADX(LSQR, sqrLegacy, sqrBmi2Adx) diff --git a/src/circl/math/fp448/fp_generic.go b/src/circl/math/fp448/fp_generic.go new file mode 100644 index 00000000000..47a0b63205f --- /dev/null +++ b/src/circl/math/fp448/fp_generic.go @@ -0,0 +1,339 @@ +package fp448 + +import ( + "encoding/binary" + "math/bits" +) + +func cmovGeneric(x, y *Elt, n uint) { + m := -uint64(n & 0x1) + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + x0 = (x0 &^ m) | (y0 & m) + x1 = (x1 &^ m) | (y1 & m) + x2 = (x2 &^ m) | (y2 & m) + x3 = (x3 &^ m) | (y3 & m) + x4 = (x4 &^ m) | (y4 & m) + x5 = (x5 &^ m) | (y5 & m) + x6 = (x6 &^ m) | (y6 & m) + + binary.LittleEndian.PutUint64(x[0*8:1*8], x0) + binary.LittleEndian.PutUint64(x[1*8:2*8], x1) + binary.LittleEndian.PutUint64(x[2*8:3*8], x2) + binary.LittleEndian.PutUint64(x[3*8:4*8], x3) + binary.LittleEndian.PutUint64(x[4*8:5*8], x4) + binary.LittleEndian.PutUint64(x[5*8:6*8], x5) + binary.LittleEndian.PutUint64(x[6*8:7*8], x6) +} + +func cswapGeneric(x, y *Elt, n uint) { + m := -uint64(n & 0x1) + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + t0 := m & (x0 ^ y0) + t1 := m & (x1 ^ y1) + t2 := m & (x2 ^ y2) + t3 := m & (x3 ^ y3) + t4 := m & (x4 ^ y4) + t5 := m & (x5 ^ y5) + t6 := m & (x6 ^ y6) + x0 ^= t0 + x1 ^= t1 + x2 ^= t2 + x3 ^= t3 + x4 ^= t4 + x5 ^= t5 + x6 ^= t6 + y0 ^= t0 + y1 ^= t1 + y2 ^= t2 + y3 ^= t3 + y4 ^= t4 + y5 ^= t5 + y6 ^= t6 + + binary.LittleEndian.PutUint64(x[0*8:1*8], x0) + binary.LittleEndian.PutUint64(x[1*8:2*8], x1) + binary.LittleEndian.PutUint64(x[2*8:3*8], x2) + binary.LittleEndian.PutUint64(x[3*8:4*8], x3) + binary.LittleEndian.PutUint64(x[4*8:5*8], x4) + binary.LittleEndian.PutUint64(x[5*8:6*8], x5) + binary.LittleEndian.PutUint64(x[6*8:7*8], x6) + + binary.LittleEndian.PutUint64(y[0*8:1*8], y0) + binary.LittleEndian.PutUint64(y[1*8:2*8], y1) + binary.LittleEndian.PutUint64(y[2*8:3*8], y2) + binary.LittleEndian.PutUint64(y[3*8:4*8], y3) + binary.LittleEndian.PutUint64(y[4*8:5*8], y4) + binary.LittleEndian.PutUint64(y[5*8:6*8], y5) + binary.LittleEndian.PutUint64(y[6*8:7*8], y6) +} + +func addGeneric(z, x, y *Elt) { + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + z0, c0 := bits.Add64(x0, y0, 0) + z1, c1 := bits.Add64(x1, y1, c0) + z2, c2 := bits.Add64(x2, y2, c1) + z3, c3 := bits.Add64(x3, y3, c2) + z4, c4 := bits.Add64(x4, y4, c3) + z5, c5 := bits.Add64(x5, y5, c4) + z6, z7 := bits.Add64(x6, y6, c5) + + z0, c0 = bits.Add64(z0, z7, 0) + z1, c1 = bits.Add64(z1, 0, c0) + z2, c2 = bits.Add64(z2, 0, c1) + z3, c3 = bits.Add64(z3, z7<<32, c2) + z4, c4 = bits.Add64(z4, 0, c3) + z5, c5 = bits.Add64(z5, 0, c4) + z6, z7 = bits.Add64(z6, 0, c5) + + z0, c0 = bits.Add64(z0, z7, 0) + z1, c1 = bits.Add64(z1, 0, c0) + z2, c2 = bits.Add64(z2, 0, c1) + z3, c3 = bits.Add64(z3, z7<<32, c2) + z4, c4 = bits.Add64(z4, 0, c3) + z5, c5 = bits.Add64(z5, 0, c4) + z6, _ = bits.Add64(z6, 0, c5) + + binary.LittleEndian.PutUint64(z[0*8:1*8], z0) + binary.LittleEndian.PutUint64(z[1*8:2*8], z1) + binary.LittleEndian.PutUint64(z[2*8:3*8], z2) + binary.LittleEndian.PutUint64(z[3*8:4*8], z3) + binary.LittleEndian.PutUint64(z[4*8:5*8], z4) + binary.LittleEndian.PutUint64(z[5*8:6*8], z5) + binary.LittleEndian.PutUint64(z[6*8:7*8], z6) +} + +func subGeneric(z, x, y *Elt) { + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + z0, c0 := bits.Sub64(x0, y0, 0) + z1, c1 := bits.Sub64(x1, y1, c0) + z2, c2 := bits.Sub64(x2, y2, c1) + z3, c3 := bits.Sub64(x3, y3, c2) + z4, c4 := bits.Sub64(x4, y4, c3) + z5, c5 := bits.Sub64(x5, y5, c4) + z6, z7 := bits.Sub64(x6, y6, c5) + + z0, c0 = bits.Sub64(z0, z7, 0) + z1, c1 = bits.Sub64(z1, 0, c0) + z2, c2 = bits.Sub64(z2, 0, c1) + z3, c3 = bits.Sub64(z3, z7<<32, c2) + z4, c4 = bits.Sub64(z4, 0, c3) + z5, c5 = bits.Sub64(z5, 0, c4) + z6, z7 = bits.Sub64(z6, 0, c5) + + z0, c0 = bits.Sub64(z0, z7, 0) + z1, c1 = bits.Sub64(z1, 0, c0) + z2, c2 = bits.Sub64(z2, 0, c1) + z3, c3 = bits.Sub64(z3, z7<<32, c2) + z4, c4 = bits.Sub64(z4, 0, c3) + z5, c5 = bits.Sub64(z5, 0, c4) + z6, _ = bits.Sub64(z6, 0, c5) + + binary.LittleEndian.PutUint64(z[0*8:1*8], z0) + binary.LittleEndian.PutUint64(z[1*8:2*8], z1) + binary.LittleEndian.PutUint64(z[2*8:3*8], z2) + binary.LittleEndian.PutUint64(z[3*8:4*8], z3) + binary.LittleEndian.PutUint64(z[4*8:5*8], z4) + binary.LittleEndian.PutUint64(z[5*8:6*8], z5) + binary.LittleEndian.PutUint64(z[6*8:7*8], z6) +} + +func addsubGeneric(x, y *Elt) { + z := &Elt{} + addGeneric(z, x, y) + subGeneric(y, x, y) + *x = *z +} + +func mulGeneric(z, x, y *Elt) { + x0 := binary.LittleEndian.Uint64(x[0*8 : 1*8]) + x1 := binary.LittleEndian.Uint64(x[1*8 : 2*8]) + x2 := binary.LittleEndian.Uint64(x[2*8 : 3*8]) + x3 := binary.LittleEndian.Uint64(x[3*8 : 4*8]) + x4 := binary.LittleEndian.Uint64(x[4*8 : 5*8]) + x5 := binary.LittleEndian.Uint64(x[5*8 : 6*8]) + x6 := binary.LittleEndian.Uint64(x[6*8 : 7*8]) + + y0 := binary.LittleEndian.Uint64(y[0*8 : 1*8]) + y1 := binary.LittleEndian.Uint64(y[1*8 : 2*8]) + y2 := binary.LittleEndian.Uint64(y[2*8 : 3*8]) + y3 := binary.LittleEndian.Uint64(y[3*8 : 4*8]) + y4 := binary.LittleEndian.Uint64(y[4*8 : 5*8]) + y5 := binary.LittleEndian.Uint64(y[5*8 : 6*8]) + y6 := binary.LittleEndian.Uint64(y[6*8 : 7*8]) + + yy := [7]uint64{y0, y1, y2, y3, y4, y5, y6} + zz := [7]uint64{} + + yi := yy[0] + h0, l0 := bits.Mul64(x0, yi) + h1, l1 := bits.Mul64(x1, yi) + h2, l2 := bits.Mul64(x2, yi) + h3, l3 := bits.Mul64(x3, yi) + h4, l4 := bits.Mul64(x4, yi) + h5, l5 := bits.Mul64(x5, yi) + h6, l6 := bits.Mul64(x6, yi) + + zz[0] = l0 + a0, c0 := bits.Add64(h0, l1, 0) + a1, c1 := bits.Add64(h1, l2, c0) + a2, c2 := bits.Add64(h2, l3, c1) + a3, c3 := bits.Add64(h3, l4, c2) + a4, c4 := bits.Add64(h4, l5, c3) + a5, c5 := bits.Add64(h5, l6, c4) + a6, _ := bits.Add64(h6, 0, c5) + + for i := 1; i < 7; i++ { + yi = yy[i] + h0, l0 = bits.Mul64(x0, yi) + h1, l1 = bits.Mul64(x1, yi) + h2, l2 = bits.Mul64(x2, yi) + h3, l3 = bits.Mul64(x3, yi) + h4, l4 = bits.Mul64(x4, yi) + h5, l5 = bits.Mul64(x5, yi) + h6, l6 = bits.Mul64(x6, yi) + + zz[i], c0 = bits.Add64(a0, l0, 0) + a0, c1 = bits.Add64(a1, l1, c0) + a1, c2 = bits.Add64(a2, l2, c1) + a2, c3 = bits.Add64(a3, l3, c2) + a3, c4 = bits.Add64(a4, l4, c3) + a4, c5 = bits.Add64(a5, l5, c4) + a5, a6 = bits.Add64(a6, l6, c5) + + a0, c0 = bits.Add64(a0, h0, 0) + a1, c1 = bits.Add64(a1, h1, c0) + a2, c2 = bits.Add64(a2, h2, c1) + a3, c3 = bits.Add64(a3, h3, c2) + a4, c4 = bits.Add64(a4, h4, c3) + a5, c5 = bits.Add64(a5, h5, c4) + a6, _ = bits.Add64(a6, h6, c5) + } + red64(z, &zz, &[7]uint64{a0, a1, a2, a3, a4, a5, a6}) +} + +func sqrGeneric(z, x *Elt) { mulGeneric(z, x, x) } + +func red64(z *Elt, l, h *[7]uint64) { + /* (2C13, 2C12, 2C11, 2C10|C10, C9, C8, C7) + (C6,...,C0) */ + h0 := h[0] + h1 := h[1] + h2 := h[2] + h3 := ((h[3] & (0xFFFFFFFF << 32)) << 1) | (h[3] & 0xFFFFFFFF) + h4 := (h[3] >> 63) | (h[4] << 1) + h5 := (h[4] >> 63) | (h[5] << 1) + h6 := (h[5] >> 63) | (h[6] << 1) + h7 := (h[6] >> 63) + + l0, c0 := bits.Add64(h0, l[0], 0) + l1, c1 := bits.Add64(h1, l[1], c0) + l2, c2 := bits.Add64(h2, l[2], c1) + l3, c3 := bits.Add64(h3, l[3], c2) + l4, c4 := bits.Add64(h4, l[4], c3) + l5, c5 := bits.Add64(h5, l[5], c4) + l6, c6 := bits.Add64(h6, l[6], c5) + l7, _ := bits.Add64(h7, 0, c6) + + /* (C10C9, C9C8,C8C7,C7C13,C13C12,C12C11,C11C10) + (C6,...,C0) */ + h0 = (h[3] >> 32) | (h[4] << 32) + h1 = (h[4] >> 32) | (h[5] << 32) + h2 = (h[5] >> 32) | (h[6] << 32) + h3 = (h[6] >> 32) | (h[0] << 32) + h4 = (h[0] >> 32) | (h[1] << 32) + h5 = (h[1] >> 32) | (h[2] << 32) + h6 = (h[2] >> 32) | (h[3] << 32) + + l0, c0 = bits.Add64(l0, h0, 0) + l1, c1 = bits.Add64(l1, h1, c0) + l2, c2 = bits.Add64(l2, h2, c1) + l3, c3 = bits.Add64(l3, h3, c2) + l4, c4 = bits.Add64(l4, h4, c3) + l5, c5 = bits.Add64(l5, h5, c4) + l6, c6 = bits.Add64(l6, h6, c5) + l7, _ = bits.Add64(l7, 0, c6) + + /* (C7) + (C6,...,C0) */ + l0, c0 = bits.Add64(l0, l7, 0) + l1, c1 = bits.Add64(l1, 0, c0) + l2, c2 = bits.Add64(l2, 0, c1) + l3, c3 = bits.Add64(l3, l7<<32, c2) + l4, c4 = bits.Add64(l4, 0, c3) + l5, c5 = bits.Add64(l5, 0, c4) + l6, l7 = bits.Add64(l6, 0, c5) + + /* (C7) + (C6,...,C0) */ + l0, c0 = bits.Add64(l0, l7, 0) + l1, c1 = bits.Add64(l1, 0, c0) + l2, c2 = bits.Add64(l2, 0, c1) + l3, c3 = bits.Add64(l3, l7<<32, c2) + l4, c4 = bits.Add64(l4, 0, c3) + l5, c5 = bits.Add64(l5, 0, c4) + l6, _ = bits.Add64(l6, 0, c5) + + binary.LittleEndian.PutUint64(z[0*8:1*8], l0) + binary.LittleEndian.PutUint64(z[1*8:2*8], l1) + binary.LittleEndian.PutUint64(z[2*8:3*8], l2) + binary.LittleEndian.PutUint64(z[3*8:4*8], l3) + binary.LittleEndian.PutUint64(z[4*8:5*8], l4) + binary.LittleEndian.PutUint64(z[5*8:6*8], l5) + binary.LittleEndian.PutUint64(z[6*8:7*8], l6) +} diff --git a/src/circl/math/fp448/fp_noasm.go b/src/circl/math/fp448/fp_noasm.go new file mode 100644 index 00000000000..efde50a665c --- /dev/null +++ b/src/circl/math/fp448/fp_noasm.go @@ -0,0 +1,11 @@ +// +build !amd64 purego + +package fp448 + +func cmov(x, y *Elt, n uint) { cmovGeneric(x, y, n) } +func cswap(x, y *Elt, n uint) { cswapGeneric(x, y, n) } +func add(z, x, y *Elt) { addGeneric(z, x, y) } +func sub(z, x, y *Elt) { subGeneric(z, x, y) } +func addsub(x, y *Elt) { addsubGeneric(x, y) } +func mul(z, x, y *Elt) { mulGeneric(z, x, y) } +func sqr(z, x *Elt) { sqrGeneric(z, x) } diff --git a/src/circl/math/fp448/fp_test.go b/src/circl/math/fp448/fp_test.go new file mode 100644 index 00000000000..e0fd3693f57 --- /dev/null +++ b/src/circl/math/fp448/fp_test.go @@ -0,0 +1,393 @@ +package fp448 + +import ( + "crypto/rand" + "fmt" + "math/big" + "testing" + + "circl/internal/conv" + "circl/internal/test" +) + +func testCmov(t *testing.T, f func(x, y *Elt, n uint)) { + const numTests = 1 << 9 + var x, y Elt + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + b := uint(y[0] & 0x1) + want := conv.BytesLe2BigInt(x[:]) + if b != 0 { + want = conv.BytesLe2BigInt(y[:]) + } + + f(&x, &y, b) + got := conv.BytesLe2BigInt(x[:]) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y, b) + } + } +} + +func testCswap(t *testing.T, f func(x, y *Elt, n uint)) { + const numTests = 1 << 9 + var x, y Elt + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + b := uint(y[0] & 0x1) + want0 := conv.BytesLe2BigInt(x[:]) + want1 := conv.BytesLe2BigInt(y[:]) + if b != 0 { + want0 = conv.BytesLe2BigInt(y[:]) + want1 = conv.BytesLe2BigInt(x[:]) + } + + f(&x, &y, b) + got0 := conv.BytesLe2BigInt(x[:]) + got1 := conv.BytesLe2BigInt(y[:]) + + if got0.Cmp(want0) != 0 { + test.ReportError(t, got0, want0, x, y, b) + } + if got1.Cmp(want1) != 0 { + test.ReportError(t, got1, want1, x, y, b) + } + } +} + +func testAdd(t *testing.T, f func(z, x, y *Elt)) { + const numTests = 1 << 9 + var x, y, z Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + f(&z, &x, &y) + Modp(&z) + got := conv.BytesLe2BigInt(z[:]) + + xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) + want := xx.Add(xx, yy).Mod(xx, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y) + } + } +} + +func testSub(t *testing.T, f func(z, x, y *Elt)) { + const numTests = 1 << 9 + var x, y, z Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + f(&z, &x, &y) + Modp(&z) + got := conv.BytesLe2BigInt(z[:]) + + xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) + want := xx.Sub(xx, yy).Mod(xx, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y) + } + } +} + +func testAddSub(t *testing.T, f func(x, y *Elt)) { + const numTests = 1 << 9 + var x, y Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + want0, want1 := big.NewInt(0), big.NewInt(0) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) + want0.Add(xx, yy).Mod(want0, p) + want1.Sub(xx, yy).Mod(want1, p) + + f(&x, &y) + Modp(&x) + Modp(&y) + got0 := conv.BytesLe2BigInt(x[:]) + got1 := conv.BytesLe2BigInt(y[:]) + + if got0.Cmp(want0) != 0 { + test.ReportError(t, got0, want0, x, y) + } + if got1.Cmp(want1) != 0 { + test.ReportError(t, got1, want1, x, y) + } + } +} + +func testMul(t *testing.T, f func(z, x, y *Elt)) { + const numTests = 1 << 9 + var x, y, z Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + f(&z, &x, &y) + Modp(&z) + got := conv.BytesLe2BigInt(z[:]) + + xx, yy := conv.BytesLe2BigInt(x[:]), conv.BytesLe2BigInt(y[:]) + want := xx.Mul(xx, yy).Mod(xx, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y) + } + } +} + +func testSqr(t *testing.T, f func(z, x *Elt)) { + const numTests = 1 << 9 + var x, z Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + f(&z, &x) + Modp(&z) + got := conv.BytesLe2BigInt(z[:]) + + xx := conv.BytesLe2BigInt(x[:]) + want := xx.Mul(xx, xx).Mod(xx, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } +} + +func TestModp(t *testing.T) { + const numTests = 1 << 9 + var x Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + two256 := big.NewInt(1) + two256.Lsh(two256, 256) + want := new(big.Int) + for i := 0; i < numTests; i++ { + bigX, _ := rand.Int(rand.Reader, two256) + bigX.Add(bigX, p).Mod(bigX, two256) + conv.BigInt2BytesLe(x[:], bigX) + + Modp(&x) + got := conv.BytesLe2BigInt(x[:]) + + want.Mod(bigX, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, bigX) + } + } +} + +func TestIsZero(t *testing.T) { + var x Elt + got := IsZero(&x) + want := true + if got != want { + test.ReportError(t, got, want, x) + } + + SetOne(&x) + got = IsZero(&x) + want = false + if got != want { + test.ReportError(t, got, want, x) + } + + x = P() + got = IsZero(&x) + want = true + if got != want { + test.ReportError(t, got, want, x) + } +} + +func TestToBytes(t *testing.T) { + const numTests = 1 << 9 + var x Elt + var got, want [Size]byte + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + err := ToBytes(got[:], &x) + conv.BigInt2BytesLe(want[:], conv.BytesLe2BigInt(x[:])) + + if err != nil || got != want { + test.ReportError(t, got, want, x) + } + } + var largeSlice [Size + 1]byte + err := ToBytes(largeSlice[:], &x) + if err == nil { + test.ReportError(t, got, want, largeSlice) + } +} + +func TestString(t *testing.T) { + const numTests = 1 << 9 + var x Elt + var bigX big.Int + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + got, _ := bigX.SetString(fmt.Sprint(x), 0) + want := conv.BytesLe2BigInt(x[:]) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } +} + +func TestNeg(t *testing.T) { + const numTests = 1 << 9 + var x, z Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + Neg(&z, &x) + Modp(&z) + got := conv.BytesLe2BigInt(z[:]) + + bigX := conv.BytesLe2BigInt(x[:]) + want := bigX.Neg(bigX).Mod(bigX, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, bigX) + } + } +} + +func TestInv(t *testing.T) { + const numTests = 1 << 9 + var x, z Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + Inv(&z, &x) + Modp(&z) + got := conv.BytesLe2BigInt(z[:]) + + xx := conv.BytesLe2BigInt(x[:]) + want := xx.ModInverse(xx, p) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } +} + +func TestInvSqrt(t *testing.T) { + const numTests = 1 << 9 + var x, y, z Elt + prime := P() + p := conv.BytesLe2BigInt(prime[:]) + exp := big.NewInt(1) + exp.Add(p, exp).Rsh(exp, 2) + var frac, root, sqRoot big.Int + var wantQR bool + var want *big.Int + for i := 0; i < numTests; i++ { + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + + gotQR := InvSqrt(&z, &x, &y) + Modp(&z) + got := conv.BytesLe2BigInt(z[:]) + + xx := conv.BytesLe2BigInt(x[:]) + yy := conv.BytesLe2BigInt(y[:]) + frac.ModInverse(yy, p).Mul(&frac, xx).Mod(&frac, p) + root.Exp(&frac, exp, p) + sqRoot.Mul(&root, &root).Mod(&sqRoot, p) + + if sqRoot.Cmp(&frac) == 0 { + want = &root + wantQR = true + } else { + want = big.NewInt(0) + wantQR = false + } + + if wantQR { + if gotQR != wantQR || got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, y) + } + } else { + if gotQR != wantQR { + test.ReportError(t, gotQR, wantQR, x, y) + } + } + } +} + +func TestGeneric(t *testing.T) { + t.Run("Cmov", func(t *testing.T) { testCmov(t, cmovGeneric) }) + t.Run("Cswap", func(t *testing.T) { testCswap(t, cswapGeneric) }) + t.Run("Add", func(t *testing.T) { testAdd(t, addGeneric) }) + t.Run("Sub", func(t *testing.T) { testSub(t, subGeneric) }) + t.Run("AddSub", func(t *testing.T) { testAddSub(t, addsubGeneric) }) + t.Run("Mul", func(t *testing.T) { testMul(t, mulGeneric) }) + t.Run("Sqr", func(t *testing.T) { testSqr(t, sqrGeneric) }) +} + +func TestNative(t *testing.T) { + t.Run("Cmov", func(t *testing.T) { testCmov(t, Cmov) }) + t.Run("Cswap", func(t *testing.T) { testCswap(t, Cswap) }) + t.Run("Add", func(t *testing.T) { testAdd(t, Add) }) + t.Run("Sub", func(t *testing.T) { testSub(t, Sub) }) + t.Run("AddSub", func(t *testing.T) { testAddSub(t, AddSub) }) + t.Run("Mul", func(t *testing.T) { testMul(t, Mul) }) + t.Run("Sqr", func(t *testing.T) { testSqr(t, Sqr) }) +} + +func BenchmarkFp(b *testing.B) { + var x, y, z Elt + _, _ = rand.Read(x[:]) + _, _ = rand.Read(y[:]) + _, _ = rand.Read(z[:]) + b.Run("Add", func(b *testing.B) { + for i := 0; i < b.N; i++ { + Add(&x, &y, &z) + } + }) + b.Run("Sub", func(b *testing.B) { + for i := 0; i < b.N; i++ { + Sub(&x, &y, &z) + } + }) + b.Run("Mul", func(b *testing.B) { + for i := 0; i < b.N; i++ { + Mul(&x, &y, &z) + } + }) + b.Run("Sqr", func(b *testing.B) { + for i := 0; i < b.N; i++ { + Sqr(&x, &y) + } + }) + b.Run("Inv", func(b *testing.B) { + for i := 0; i < b.N; i++ { + Inv(&x, &y) + } + }) + b.Run("InvSqrt", func(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = InvSqrt(&z, &x, &y) + } + }) +} diff --git a/src/circl/math/fp448/fuzzer.go b/src/circl/math/fp448/fuzzer.go new file mode 100644 index 00000000000..0ff6e788d47 --- /dev/null +++ b/src/circl/math/fp448/fuzzer.go @@ -0,0 +1,73 @@ +// +build gofuzz + +// How to run the fuzzer: +// $ go get -u github.com/dvyukov/go-fuzz/go-fuzz +// $ go get -u github.com/dvyukov/go-fuzz/go-fuzz-build +// $ go-fuzz-build -libfuzzer -func FuzzReduction -o lib.a +// $ clang -fsanitize=fuzzer lib.a -o fu.exe +// $ ./fu.exe +package fp448 + +import ( + "encoding/binary" + "fmt" + "math/big" + + "circl/internal/conv" +) + +// FuzzReduction is a fuzzer target for red64 function, which reduces t +// (112 bits) to a number t' (56 bits) congruent modulo p448. +func FuzzReduction(data []byte) int { + if len(data) != 2*Size { + return -1 + } + var got, want Elt + var lo, hi [7]uint64 + a := data[:Size] + b := data[Size:] + lo[0] = binary.LittleEndian.Uint64(a[0*8 : 1*8]) + lo[1] = binary.LittleEndian.Uint64(a[1*8 : 2*8]) + lo[2] = binary.LittleEndian.Uint64(a[2*8 : 3*8]) + lo[3] = binary.LittleEndian.Uint64(a[3*8 : 4*8]) + lo[4] = binary.LittleEndian.Uint64(a[4*8 : 5*8]) + lo[5] = binary.LittleEndian.Uint64(a[5*8 : 6*8]) + lo[6] = binary.LittleEndian.Uint64(a[6*8 : 7*8]) + + hi[0] = binary.LittleEndian.Uint64(b[0*8 : 1*8]) + hi[1] = binary.LittleEndian.Uint64(b[1*8 : 2*8]) + hi[2] = binary.LittleEndian.Uint64(b[2*8 : 3*8]) + hi[3] = binary.LittleEndian.Uint64(b[3*8 : 4*8]) + hi[4] = binary.LittleEndian.Uint64(b[4*8 : 5*8]) + hi[5] = binary.LittleEndian.Uint64(b[5*8 : 6*8]) + hi[6] = binary.LittleEndian.Uint64(b[6*8 : 7*8]) + + red64(&got, &lo, &hi) + + t := conv.BytesLe2BigInt(data[:2*Size]) + + two448 := big.NewInt(1) + two448.Lsh(two448, 448) // 2^448 + mask448 := big.NewInt(1) + mask448.Sub(two448, mask448) // 2^448-1 + two224plus1 := big.NewInt(1) + two224plus1.Lsh(two224plus1, 224) + two224plus1.Add(two224plus1, big.NewInt(1)) // 2^224+1 + + var loBig, hiBig big.Int + for t.Cmp(two448) >= 0 { + loBig.And(t, mask448) + hiBig.Rsh(t, 448) + t.Mul(&hiBig, two224plus1) + t.Add(t, &loBig) + } + conv.BigInt2BytesLe(want[:], t) + + if got != want { + fmt.Printf("in: %v\n", conv.BytesLe2BigInt(data[:2*Size])) + fmt.Printf("got: %v\n", got) + fmt.Printf("want: %v\n", want) + panic("error found") + } + return 1 +} diff --git a/src/circl/math/mlsbset/mlsbset.go b/src/circl/math/mlsbset/mlsbset.go new file mode 100644 index 00000000000..8af4f4b8c9f --- /dev/null +++ b/src/circl/math/mlsbset/mlsbset.go @@ -0,0 +1,122 @@ +// Package mlsbset provides a constant-time exponentiation method with precomputation. +// +// References: "Efficient and secure algorithms for GLV-based scalar +// multiplication and their implementation on GLV–GLS curves" by (Faz-Hernandez et al.) +// - https://doi.org/10.1007/s13389-014-0085-7 +// - https://eprint.iacr.org/2013/158 +package mlsbset + +import ( + "errors" + "fmt" + "math/big" + + "circl/internal/conv" +) + +// EltG is a group element. +type EltG interface{} + +// EltP is a precomputed group element. +type EltP interface{} + +// Group defines the operations required by MLSBSet exponentiation method. +type Group interface { + Identity() EltG // Returns the identity of the group. + Sqr(x EltG) // Calculates x = x^2. + Mul(x EltG, y EltP) // Calculates x = x*y. + NewEltP() EltP // Returns an arbitrary precomputed element. + ExtendedEltP() EltP // Returns the precomputed element x^(2^(w*d)). + Lookup(a EltP, v uint, s, u int32) // Sets a = s*T[v][u]. +} + +// Params contains the parameters of the encoding. +type Params struct { + T uint // T is the maximum size (in bits) of exponents. + V uint // V is the number of tables. + W uint // W is the window size. + E uint // E is the number of digits per table. + D uint // D is the number of digits in total. + L uint // L is the length of the code. +} + +// Encoder allows to convert integers into valid powers. +type Encoder struct{ p Params } + +// New produces an encoder of the MLSBSet algorithm. +func New(t, v, w uint) (Encoder, error) { + if !(t > 1 && v >= 1 && w >= 2) { + return Encoder{}, errors.New("t>1, v>=1, w>=2") + } + e := (t + w*v - 1) / (w * v) + d := e * v + l := d * w + return Encoder{Params{t, v, w, e, d, l}}, nil +} + +// Encode converts an odd integer k into a valid power for exponentiation. +func (m Encoder) Encode(k []byte) (*Power, error) { + if len(k) == 0 { + return nil, errors.New("empty slice") + } + if !(len(k) <= int(m.p.L+7)>>3) { + return nil, errors.New("k too big") + } + if k[0]%2 == 0 { + return nil, errors.New("k must be odd") + } + ap := int((m.p.L+7)/8) - len(k) + k = append(k, make([]byte, ap)...) + s := m.signs(k) + b := make([]int32, m.p.L-m.p.D) + c := conv.BytesLe2BigInt(k) + c.Rsh(c, m.p.D) + var bi big.Int + for i := m.p.D; i < m.p.L; i++ { + c0 := int32(c.Bit(0)) + b[i-m.p.D] = s[i%m.p.D] * c0 + bi.SetInt64(int64(b[i-m.p.D] >> 1)) + c.Rsh(c, 1) + c.Sub(c, &bi) + } + carry := int(c.Int64()) + return &Power{m, s, b, carry}, nil +} + +// signs calculates the set of signs. +func (m Encoder) signs(k []byte) []int32 { + s := make([]int32, m.p.D) + s[m.p.D-1] = 1 + for i := uint(1); i < m.p.D; i++ { + ki := int32((k[i>>3] >> (i & 0x7)) & 0x1) + s[i-1] = 2*ki - 1 + } + return s +} + +// GetParams returns the complementary parameters of the encoding. +func (m Encoder) GetParams() Params { return m.p } + +// tableSize returns the size of each table. +func (m Encoder) tableSize() uint { return 1 << (m.p.W - 1) } + +// Elts returns the total number of elements that must be precomputed. +func (m Encoder) Elts() uint { return m.p.V * m.tableSize() } + +// IsExtended returns true if the element x^(2^(wd)) must be calculated. +func (m Encoder) IsExtended() bool { q := m.p.T / (m.p.V * m.p.W); return m.p.T == q*m.p.V*m.p.W } + +// Ops returns the number of squares and multiplications executed during an exponentiation. +func (m Encoder) Ops() (S uint, M uint) { + S = m.p.E + M = m.p.E * m.p.V + if m.IsExtended() { + M++ + } + return +} + +func (m Encoder) String() string { + return fmt.Sprintf("T: %v W: %v V: %v e: %v d: %v l: %v wv|t: %v", + m.p.T, m.p.W, m.p.V, m.p.E, m.p.D, m.p.L, m.IsExtended()) +} diff --git a/src/circl/math/mlsbset/mlsbset_test.go b/src/circl/math/mlsbset/mlsbset_test.go new file mode 100644 index 00000000000..39c7be2dddf --- /dev/null +++ b/src/circl/math/mlsbset/mlsbset_test.go @@ -0,0 +1,151 @@ +package mlsbset_test + +import ( + "crypto/rand" + "errors" + "math/big" + "testing" + + "circl/internal/conv" + "circl/internal/test" + "circl/math/mlsbset" +) + +func TestExp(t *testing.T) { + T := uint(126) + for v := uint(1); v <= 5; v++ { + for w := uint(2); w <= 5; w++ { + m, err := mlsbset.New(T, v, w) + if err != nil { + test.ReportError(t, err, nil) + } + testExp(t, m) + } + } +} + +func testExp(t *testing.T, m mlsbset.Encoder) { + const testTimes = 1 << 8 + params := m.GetParams() + TBytes := (params.T + 7) / 8 + topBits := (byte(1) << (params.T % 8)) - 1 + k := make([]byte, TBytes) + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(k) + k[0] |= 1 + k[TBytes-1] &= topBits + + c, err := m.Encode(k) + if err != nil { + test.ReportError(t, err, nil) + } + + g := zzAdd{m.GetParams()} + a := c.Exp(g) + + got := a.(*big.Int) + want := conv.BytesLe2BigInt(k) + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, m) + } + } +} + +type zzAdd struct{ set mlsbset.Params } + +func (zzAdd) Identity() mlsbset.EltG { return big.NewInt(0) } +func (zzAdd) NewEltP() mlsbset.EltP { return new(big.Int) } +func (zzAdd) Sqr(x mlsbset.EltG) { + a := x.(*big.Int) + a.Add(a, a) +} +func (zzAdd) Mul(x mlsbset.EltG, y mlsbset.EltP) { + a := x.(*big.Int) + b := y.(*big.Int) + a.Add(a, b) +} +func (z zzAdd) ExtendedEltP() mlsbset.EltP { + a := big.NewInt(1) + a.Lsh(a, z.set.W*z.set.D) + return a +} +func (z zzAdd) Lookup(x mlsbset.EltP, idTable uint, sgnElt int32, idElt int32) { + a := x.(*big.Int) + a.SetInt64(1) + a.Lsh(a, z.set.E*idTable) // 2^(e*v) + sum := big.NewInt(0) + for i := int(z.set.W - 2); i >= 0; i-- { + ui := big.NewInt(int64((idElt >> uint(i)) & 0x1)) + sum.Add(sum, ui) + sum.Lsh(sum, z.set.D) + } + sum.Add(sum, big.NewInt(1)) + a.Mul(a, sum) + if sgnElt == -1 { + a.Neg(a) + } +} + +func TestEncodeErr(t *testing.T) { + t.Run("mArgs", func(t *testing.T) { + _, got := mlsbset.New(0, 0, 0) + want := errors.New("t>1, v>=1, w>=2") + if got.Error() != want.Error() { + test.ReportError(t, got, want) + } + }) + t.Run("kOdd", func(t *testing.T) { + m, _ := mlsbset.New(16, 2, 2) + k := make([]byte, 2) + _, got := m.Encode(k) + want := errors.New("k must be odd") + if got.Error() != want.Error() { + test.ReportError(t, got, want) + } + }) + t.Run("kBig", func(t *testing.T) { + m, _ := mlsbset.New(16, 2, 2) + k := make([]byte, 4) + _, got := m.Encode(k) + want := errors.New("k too big") + if got.Error() != want.Error() { + test.ReportError(t, got, want) + } + }) + t.Run("kEmpty", func(t *testing.T) { + m, _ := mlsbset.New(16, 2, 2) + k := []byte{} + _, got := m.Encode(k) + want := errors.New("empty slice") + if got.Error() != want.Error() { + test.ReportError(t, got, want) + } + }) +} + +func BenchmarkEncode(b *testing.B) { + t, v, w := uint(256), uint(2), uint(3) + m, _ := mlsbset.New(t, v, w) + params := m.GetParams() + TBytes := (params.T + 7) / 8 + topBits := (byte(1) << (params.T % 8)) - 1 + + k := make([]byte, TBytes) + _, _ = rand.Read(k) + k[0] |= 1 + k[TBytes-1] &= topBits + + c, _ := m.Encode(k) + g := zzAdd{params} + + b.Run("Encode", func(b *testing.B) { + for i := 0; i < b.N; i++ { + _, _ = m.Encode(k) + } + }) + b.Run("Exp", func(b *testing.B) { + for i := 0; i < b.N; i++ { + c.Exp(g) + } + }) +} diff --git a/src/circl/math/mlsbset/power.go b/src/circl/math/mlsbset/power.go new file mode 100644 index 00000000000..3f214c3046a --- /dev/null +++ b/src/circl/math/mlsbset/power.go @@ -0,0 +1,64 @@ +package mlsbset + +import "fmt" + +// Power is a valid exponent produced by the MLSBSet encoding algorithm. +type Power struct { + set Encoder // parameters of code. + s []int32 // set of signs. + b []int32 // set of digits. + c int // carry is {0,1}. +} + +// Exp is calculates x^k, where x is a predetermined element of a group G. +func (p *Power) Exp(G Group) EltG { + a, b := G.Identity(), G.NewEltP() + for e := int(p.set.p.E - 1); e >= 0; e-- { + G.Sqr(a) + for v := uint(0); v < p.set.p.V; v++ { + sgnElt, idElt := p.Digit(v, uint(e)) + G.Lookup(b, v, sgnElt, idElt) + G.Mul(a, b) + } + } + if p.set.IsExtended() && p.c == 1 { + G.Mul(a, G.ExtendedEltP()) + } + return a +} + +// Digit returns the (v,e)-th digit and its sign. +func (p *Power) Digit(v, e uint) (sgn, dig int32) { + sgn = p.bit(0, v, e) + dig = 0 + for i := p.set.p.W - 1; i > 0; i-- { + dig = 2*dig + p.bit(i, v, e) + } + mask := dig >> 31 + dig = (dig + mask) ^ mask + return sgn, dig +} + +// bit returns the (w,v,e)-th bit of the code. +func (p *Power) bit(w, v, e uint) int32 { + if !(w < p.set.p.W && + v < p.set.p.V && + e < p.set.p.E) { + panic(fmt.Errorf("indexes outside (%v,%v,%v)", w, v, e)) + } + if w == 0 { + return p.s[p.set.p.E*v+e] + } + return p.b[p.set.p.D*(w-1)+p.set.p.E*v+e] +} + +func (p *Power) String() string { + dig := "" + for j := uint(0); j < p.set.p.V; j++ { + for i := uint(0); i < p.set.p.E; i++ { + s, d := p.Digit(j, i) + dig += fmt.Sprintf("(%2v,%2v) = %+2v %+2v\n", j, i, s, d) + } + } + return fmt.Sprintf("len: %v\ncarry: %v\ndigits:\n%v", len(p.b)+len(p.s), p.c, dig) +} diff --git a/src/circl/math/wnaf.go b/src/circl/math/wnaf.go new file mode 100644 index 00000000000..df7a9c9bacb --- /dev/null +++ b/src/circl/math/wnaf.go @@ -0,0 +1,84 @@ +// Package math provides some utility functions for big integers. +package math + +import "math/big" + +// SignedDigit obtains the signed-digit recoding of n and returns a list L of +// digits such that n = sum( L[i]*2^(i*(w-1)) ), and each L[i] is an odd number +// in the set {±1, ±3, ..., ±2^(w-1)-1}. The third parameter ensures that the +// output has ceil(l/(w-1)) digits. +// +// Restrictions: +// - n is odd and n > 0. +// - 1 < w < 32. +// - l >= bit length of n. +// +// References: +// - Alg.6 in "Exponent Recoding and Regular Exponentiation Algorithms" +// by Joye-Tunstall. http://doi.org/10.1007/978-3-642-02384-2_21 +// - Alg.6 in "Selecting Elliptic Curves for Cryptography: An Efficiency and +// Security Analysis" by Bos et al. http://doi.org/10.1007/s13389-015-0097-y +func SignedDigit(n *big.Int, w, l uint) []int32 { + if n.Sign() <= 0 || n.Bit(0) == 0 { + panic("n must be non-zero, odd, and positive") + } + if w <= 1 || w >= 32 { + panic("Verify that 1 < w < 32") + } + if uint(n.BitLen()) > l { + panic("n is too big to fit in l digits") + } + lenN := (l + (w - 1) - 1) / (w - 1) // ceil(l/(w-1)) + L := make([]int32, lenN+1) + var k, v big.Int + k.Set(n) + + var i uint + for i = 0; i < lenN; i++ { + words := k.Bits() + value := int32(words[0] & ((1 << w) - 1)) + value -= int32(1) << (w - 1) + L[i] = value + v.SetInt64(int64(value)) + k.Sub(&k, &v) + k.Rsh(&k, w-1) + } + L[i] = int32(k.Int64()) + return L +} + +// OmegaNAF obtains the window-w Non-Adjacent Form of a positive number n and +// 1 < w < 32. The returned slice L holds n = sum( L[i]*2^i ). +// +// Reference: +// - Alg.9 "Efficient arithmetic on Koblitz curves" by Solinas. +// http://doi.org/10.1023/A:1008306223194 +func OmegaNAF(n *big.Int, w uint) (L []int32) { + if n.Sign() < 0 { + panic("n must be positive") + } + if w <= 1 || w >= 32 { + panic("Verify that 1 < w < 32") + } + + L = make([]int32, n.BitLen()+1) + var k, v big.Int + k.Set(n) + + i := 0 + for ; k.Sign() > 0; i++ { + value := int32(0) + if k.Bit(0) == 1 { + words := k.Bits() + value = int32(words[0] & ((1 << w) - 1)) + if value >= (int32(1) << (w - 1)) { + value -= int32(1) << w + } + v.SetInt64(int64(value)) + k.Sub(&k, &v) + } + L[i] = value + k.Rsh(&k, 1) + } + return L[:i] +} diff --git a/src/circl/math/wnaf_test.go b/src/circl/math/wnaf_test.go new file mode 100644 index 00000000000..17c2a911cae --- /dev/null +++ b/src/circl/math/wnaf_test.go @@ -0,0 +1,92 @@ +package math + +import ( + "crypto/rand" + "fmt" + "math/big" + "testing" + + "circl/internal/test" +) + +func TestOmegaNAF(t *testing.T) { + testTimes := 1 << 7 + var max big.Int + max.SetInt64(1) + max.Lsh(&max, 128) + + for w := uint(2); w < 10; w++ { + for j := 0; j < testTimes; j++ { + x, _ := rand.Int(rand.Reader, &max) + L := OmegaNAF(x, w) + + var y big.Int + for i := len(L) - 1; i >= 0; i-- { + y.Add(&y, &y).Add(&y, big.NewInt(int64(L[i]))) + } + want := x + got := &y + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, w) + } + } + } +} + +func TestOmegaNAFRegular(t *testing.T) { + testTimes := 1 << 7 + Two128 := big.NewInt(1) + Two128.Lsh(Two128, 128) + + for w := uint(2); w < 10; w++ { + for j := 0; j < testTimes; j++ { + x, _ := rand.Int(rand.Reader, Two128) + x.SetBit(x, 0, uint(1)) // odd-numbers + L := SignedDigit(x, w, 128) + + var y big.Int + for i := len(L) - 1; i >= 0; i-- { + y.Lsh(&y, w-1) + y.Add(&y, big.NewInt(int64(L[i]))) + } + want := x + got := &y + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x, w) + } + } + } +} + +func BenchmarkOmegaNAF(b *testing.B) { + Two128 := big.NewInt(1) + Two128.Lsh(Two128, 128) + + for w := uint(2); w < 6; w++ { + w := w // pin variable + b.Run(fmt.Sprintf("%v", w), func(b *testing.B) { + x, _ := rand.Int(rand.Reader, Two128) + b.ResetTimer() + for i := 0; i < b.N; i++ { + _ = OmegaNAF(x, w) + } + }) + } +} + +func BenchmarkOmegaNAFRegular(b *testing.B) { + Two128 := big.NewInt(1) + Two128.Lsh(Two128, 128) + + for w := uint(2); w < 6; w++ { + w := w // pin variable + b.Run(fmt.Sprintf("%v", w), func(b *testing.B) { + x, _ := rand.Int(rand.Reader, Two128) + x.SetBit(x, 0, uint(1)) // odd-numbers + b.ResetTimer() + for i := 0; i < b.N; i++ { + _ = SignedDigit(x, w, 128) + } + }) + } +} diff --git a/src/circl/oprf/client.go b/src/circl/oprf/client.go new file mode 100644 index 00000000000..4b81e40b745 --- /dev/null +++ b/src/circl/oprf/client.go @@ -0,0 +1,188 @@ +package oprf + +import ( + "crypto/rand" + "errors" + + "circl/group" +) + +// Client is a representation of a OPRF client during protocol execution. +type Client struct { + suite + pkS *PublicKey +} + +// ClientRequest is a structure to encapsulate the output of a Request call. +type ClientRequest struct { + inputs [][]byte + blinds []Blind + elements []group.Element +} + +// BlindedElements returns the serialized blinded elements produced for the client request. +func (r ClientRequest) BlindedElements() [][]byte { + var err error + serializedBlinds := make([][]byte, len(r.elements)) + for i := range r.elements { + serializedBlinds[i], err = r.elements[i].MarshalBinaryCompress() + if err != nil { + return nil + } + } + return serializedBlinds +} + +// NewClient creates a client in base mode. +func NewClient(id SuiteID) (*Client, error) { + suite, err := suiteFromID(id, BaseMode) + if err != nil { + return nil, err + } + return &Client{*suite, nil}, nil +} + +// NewVerifiableClient creates a client in verifiable mode. A server's public +// key must be provided. +func NewVerifiableClient(id SuiteID, pkS *PublicKey) (*Client, error) { + suite, err := suiteFromID(id, VerifiableMode) + if err != nil { + return nil, err + } + if pkS == nil { + return nil, errors.New("no public key was provided") + } else if id != pkS.s { // Verifies key corresponds to SuiteID. + return nil, errors.New("key doesn't match with suite") + } + return &Client{*suite, pkS}, nil +} + +// Request generates a request for server passing an array of inputs to be +// evaluated by server. +func (c *Client) Request(inputs [][]byte) (*ClientRequest, error) { + if len(inputs) == 0 { + return nil, errors.New("few inputs") + } + + blinds := make([]Blind, len(inputs)) + for i := range inputs { + blinds[i] = c.suite.Group.RandomScalar(rand.Reader) + } + + return c.blind(inputs, blinds) +} + +func (c *Client) blind(inputs [][]byte, blinds []Blind) (*ClientRequest, error) { + blindedElements := make([]group.Element, len(inputs)) + for i := range inputs { + p := c.suite.Group.HashToElement(inputs[i], c.suite.getDST(hashToGroupDST)) + blindedElements[i] = c.suite.Group.NewElement() + blindedElements[i].Mul(p, blinds[i]) + } + return &ClientRequest{inputs, blinds, blindedElements}, nil +} + +// Finalize computes the signed token from the server Evaluation and returns +// the output of the OPRF protocol. The function uses server's public key +// to verify the proof in verifiable mode. +func (c *Client) Finalize(r *ClientRequest, e *Evaluation) ([][]byte, error) { + l := len(r.blinds) + if len(r.elements) != l || len(e.Elements) != l { + return nil, errors.New("mismatch number of elements") + } + + var err error + evals := make([]group.Element, len(e.Elements)) + for i := range e.Elements { + evals[i] = c.suite.Group.NewElement() + err = evals[i].UnmarshalBinary(e.Elements[i]) + if err != nil { + return nil, err + } + } + + if c.Mode == VerifiableMode { + if !c.verifyProof(r.elements, evals, *e.Proof) { + return nil, errors.New("invalid proof") + } + } + + unblindedElements, err := c.unblind(evals, r.blinds) + if err != nil { + return nil, err + } + outputs := make([][]byte, l) + for i := 0; i < l; i++ { + outputs[i] = c.finalizeHash(r.inputs[i], unblindedElements[i]) + } + return outputs, nil +} + +func (c *Client) verifyProof(blinds []group.Element, elements []group.Element, proof Proof) bool { + pkSm, err := c.pkS.Serialize() + if err != nil { + return false + } + + M, Z, err := c.computeComposites(nil, c.pkS.e, blinds, elements) + if err != nil { + return false + } + + a0, err := M.MarshalBinaryCompress() + if err != nil { + return false + } + a1, err := Z.MarshalBinaryCompress() + if err != nil { + return false + } + + sG := c.suite.Group.NewElement() + ss := c.suite.Group.NewScalar() + err = ss.UnmarshalBinary(proof.S) + if err != nil { + return false + } + sG.MulGen(ss) + + cP := c.suite.Group.NewElement() + cc := c.suite.Group.NewScalar() + err = cc.UnmarshalBinary(proof.C) + if err != nil { + return false + } + cP.Mul(c.pkS.e, cc) + sG.Add(sG, cP) + a2, err := sG.MarshalBinaryCompress() + if err != nil { + return false + } + + sM := c.suite.Group.NewElement() + sM.Mul(M, ss) + cZ := c.suite.Group.NewElement() + cZ.Mul(Z, cc) + sM.Add(sM, cZ) + a3, err := sM.MarshalBinaryCompress() + if err != nil { + return false + } + + gotC := c.doChallenge([5][]byte{pkSm, a0, a1, a2, a3}) + return gotC.IsEqual(cc) +} + +func (c *Client) unblind(e []group.Element, blinds []Blind) ([][]byte, error) { + var err error + unblindedElements := make([][]byte, len(e)) + invBlind := c.Group.NewScalar() + for i := range e { + invBlind.Inv(blinds[i]) + unblindedElements[i], err = c.scalarMult(e[i], invBlind) + if err != nil { + return nil, err + } + } + return unblindedElements, nil +} diff --git a/src/circl/oprf/keys.go b/src/circl/oprf/keys.go new file mode 100644 index 00000000000..db93d7903e1 --- /dev/null +++ b/src/circl/oprf/keys.go @@ -0,0 +1,62 @@ +package oprf + +import ( + "circl/group" +) + +type PrivateKey struct { + s SuiteID + k group.Scalar +} +type PublicKey struct { + s SuiteID + e group.Element +} + +func (k *PrivateKey) Serialize() ([]byte, error) { return k.k.MarshalBinary() } +func (k *PublicKey) Serialize() ([]byte, error) { return k.e.MarshalBinaryCompress() } + +func (k *PrivateKey) Deserialize(id SuiteID, data []byte) error { + suite, err := suiteFromID(id, BaseMode) + if err != nil { + return err + } + k.s = id + k.k = suite.Group.NewScalar() + return k.k.UnmarshalBinary(data) +} + +func (k *PublicKey) Deserialize(id SuiteID, data []byte) error { + suite, err := suiteFromID(id, BaseMode) + if err != nil { + return err + } + k.s = id + k.e = suite.Group.NewElement() + return k.e.UnmarshalBinary(data) +} + +func (k *PrivateKey) Public() *PublicKey { + suite, _ := suiteFromID(k.s, BaseMode) + publicKey := suite.Group.NewElement() + publicKey.MulGen(k.k) + return &PublicKey{k.s, publicKey} +} + +// GenerateKey generates a pair of keys in accordance with the suite. +func GenerateKey(id SuiteID) (*PrivateKey, error) { + suite, err := suiteFromID(id, BaseMode) + if err != nil { + return nil, err + } + return suite.generateKey(), nil +} + +// DeriveKey derives a pair of keys given a seed and in accordance with the suite. +func DeriveKey(id SuiteID, seed []byte) (*PrivateKey, error) { + suite, err := suiteFromID(id, BaseMode) + if err != nil { + return nil, err + } + return suite.deriveKey(seed), nil +} diff --git a/src/circl/oprf/oprf.go b/src/circl/oprf/oprf.go new file mode 100644 index 00000000000..5268616b1fe --- /dev/null +++ b/src/circl/oprf/oprf.go @@ -0,0 +1,243 @@ +// Package oprf provides an Oblivious Pseudo-Random Function protocol. +// +// An Oblivious Pseudorandom Function (OPRFs) is a two-party protocol for +// computing the output of a PRF. One party (the server) holds the PRF secret +// key, and the other (the client) holds the PRF input. +// +// Obliviousness: Ensures that the server does not learn anything +// about the client's input during the Evaluation step. +// +// Verifiability: Allows the client to verify that the server used +// a committed secret key during Evaluation step. +// +// OPRF is defined on draft-irtf-cfrg-voprf: https://datatracker.ietf.org/doc/draft-irtf-cfrg-voprf +// +package oprf + +import ( + "crypto" + "crypto/rand" + "encoding/binary" + "errors" + "io" + + "circl/group" +) + +const ( + version = "VOPRF06-" + seedDST = "Seed-" + challengeDST = "Challenge-" + finalizeDST = "Finalize-" + compositeDST = "Composite-" + hashToGroupDST = "HashToGroup-" + hashToScalarDST = "HashToScalar-" +) + +// SuiteID identifies supported suites. +type SuiteID = uint16 + +const ( + // OPRFP256 represents the OPRF with P-256 and SHA-256. + OPRFP256 SuiteID = 0x0003 + // OPRFP384 represents the OPRF with P-384 and SHA-512. + OPRFP384 SuiteID = 0x0004 + // OPRFP521 represents the OPRF with P-521 and SHA-512. + OPRFP521 SuiteID = 0x0005 +) + +// Mode specifies properties of the OPRF protocol. +type Mode = uint8 + +const ( + // BaseMode provides obliviousness. + BaseMode Mode = 0x00 + // VerifiableMode provides obliviousness and verifiability. + VerifiableMode Mode = 0x01 +) + +// ErrUnsupportedSuite is thrown when requesting a non-supported suite. +var ErrUnsupportedSuite = errors.New("non-supported suite") + +type Blind group.Scalar +type SerializedElement = []byte +type Blinded = []byte + +type Proof struct { + C, S []byte +} + +type Evaluation struct { + Elements []SerializedElement + Proof *Proof +} + +type suite struct { + SuiteID + Mode + group.Group + crypto.Hash +} + +func suiteFromID(id SuiteID, m Mode) (*suite, error) { + if !(m == BaseMode || m == VerifiableMode) { + return nil, ErrUnsupportedSuite + } + switch id { + case OPRFP256: + return &suite{id, m, group.P256, crypto.SHA256}, nil + case OPRFP384: + return &suite{id, m, group.P384, crypto.SHA512}, nil + case OPRFP521: + return &suite{id, m, group.P521, crypto.SHA512}, nil + default: + return nil, ErrUnsupportedSuite + } +} + +func (s *suite) GetMode() Mode { return s.Mode } +func (s *suite) getDST(name string) []byte { + return append(append(append([]byte{}, + []byte(version)...), + []byte(name)...), + []byte{s.Mode, 0, byte(s.SuiteID)}...) +} + +func (s *suite) generateKey() *PrivateKey { + privateKey := s.Group.RandomScalar(rand.Reader) + return &PrivateKey{s.SuiteID, privateKey} +} + +func (s *suite) deriveKey(seed []byte) *PrivateKey { + privateKey := s.Group.HashToScalar(seed, nil) + return &PrivateKey{s.SuiteID, privateKey} +} + +func (s *suite) scalarMult(e group.Element, k group.Scalar) ([]byte, error) { + t := s.Group.NewElement() + t.Mul(e, k) + return t.MarshalBinaryCompress() +} + +func (s *suite) finalizeHash(input, element []byte) []byte { + h := s.New() + + lenBuf := []byte{0, 0} + + binary.BigEndian.PutUint16(lenBuf, uint16(len(input))) + mustWrite(h, lenBuf) + mustWrite(h, input) + + binary.BigEndian.PutUint16(lenBuf, uint16(len(element))) + mustWrite(h, lenBuf) + mustWrite(h, element) + + dst := s.getDST(finalizeDST) + binary.BigEndian.PutUint16(lenBuf, uint16(len(dst))) + mustWrite(h, lenBuf) + mustWrite(h, dst) + + return h.Sum(nil) +} + +func mustWrite(h io.Writer, bytes []byte) { + bytesLen, err := h.Write(bytes) + if err != nil { + panic(err) + } + if len(bytes) != bytesLen { + panic("failed to write") + } +} + +func (s *suite) computeComposites( + k group.Scalar, + B group.Element, + Cs []group.Element, + Ds []group.Element, +) (group.Element, group.Element, error) { + Bm, err := B.MarshalBinaryCompress() + if err != nil { + return nil, nil, err + } + + lenBuf := []byte{0, 0} + H := s.New() + + binary.BigEndian.PutUint16(lenBuf, uint16(len(Bm))) + mustWrite(H, lenBuf) + mustWrite(H, Bm) + + dst := s.getDST(seedDST) + binary.BigEndian.PutUint16(lenBuf, uint16(len(dst))) + mustWrite(H, lenBuf) + mustWrite(H, dst) + + seed := H.Sum(nil) + + M := s.Group.Identity() + Z := s.Group.Identity() + h2sDST := s.getDST(hashToScalarDST) + for i := range Cs { + h2Input := []byte{} + + Ci, err := Cs[i].MarshalBinaryCompress() + if err != nil { + return nil, nil, err + } + + Di, err := Ds[i].MarshalBinaryCompress() + if err != nil { + return nil, nil, err + } + + binary.BigEndian.PutUint16(lenBuf, uint16(len(seed))) + h2Input = append(append(h2Input, lenBuf...), seed...) + + binary.BigEndian.PutUint16(lenBuf, uint16(i)) + h2Input = append(h2Input, lenBuf...) + + binary.BigEndian.PutUint16(lenBuf, uint16(len(Ci))) + h2Input = append(append(h2Input, lenBuf...), Ci...) + + binary.BigEndian.PutUint16(lenBuf, uint16(len(Di))) + h2Input = append(append(h2Input, lenBuf...), Di...) + + dst := s.getDST(compositeDST) + binary.BigEndian.PutUint16(lenBuf, uint16(len(dst))) + h2Input = append(append(h2Input, lenBuf...), dst...) + + di := s.Group.HashToScalar(h2Input, h2sDST) + Mi := s.Group.NewElement() + Mi.Mul(Cs[i], di) + M.Add(M, Mi) + + if k == nil { + Zi := s.Group.NewElement() + Zi.Mul(Ds[i], di) + Z.Add(Z, Zi) + } + } + + if k != nil { + Z.Mul(M, k) + } + + return M, Z, nil +} + +func (s *suite) doChallenge(a [5][]byte) group.Scalar { + h2Input := []byte{} + lenBuf := []byte{0, 0} + + for i := range a { + binary.BigEndian.PutUint16(lenBuf, uint16(len(a[i]))) + h2Input = append(append(h2Input, lenBuf...), a[i]...) + } + + dst := s.getDST(challengeDST) + binary.BigEndian.PutUint16(lenBuf, uint16(len(dst))) + h2Input = append(append(h2Input, lenBuf...), dst...) + + return s.Group.HashToScalar(h2Input, s.getDST(hashToScalarDST)) +} diff --git a/src/circl/oprf/oprf_test.go b/src/circl/oprf/oprf_test.go new file mode 100644 index 00000000000..7a006d7a687 --- /dev/null +++ b/src/circl/oprf/oprf_test.go @@ -0,0 +1,127 @@ +package oprf_test + +import ( + "bytes" + "fmt" + "testing" + + "circl/internal/test" + "circl/oprf" +) + +func TestOPRF(t *testing.T) { + for _, suite := range []oprf.SuiteID{ + oprf.OPRFP256, + oprf.OPRFP384, + oprf.OPRFP521, + } { + for _, mode := range []oprf.Mode{ + oprf.BaseMode, + oprf.VerifiableMode, + } { + suite, mode := suite, mode + name := fmt.Sprintf("Suite%v/Mode%v", suite, mode) + t.Run("API/"+name, func(tt *testing.T) { testAPI(tt, suite, mode) }) + t.Run("Serde/"+name, func(tt *testing.T) { testSerialization(tt, suite, mode) }) + } + } +} + +func testSerialization(t *testing.T, suite oprf.SuiteID, mode oprf.Mode) { + privateKey, err := oprf.GenerateKey(suite) + test.CheckNoErr(t, err, "invalid key generation") + + var server *oprf.Server + if mode == oprf.BaseMode { + server, err = oprf.NewServer(suite, privateKey) + } else if mode == oprf.VerifiableMode { + server, err = oprf.NewVerifiableServer(suite, privateKey) + } + test.CheckNoErr(t, err, "invalid setup of server") + + input := []byte("hello world") + outputA, err := server.FullEvaluate(input) + test.CheckNoErr(t, err, "wrong full evaluate") + + encoded, err := privateKey.Serialize() + test.CheckNoErr(t, err, "wrong serialize") + + recoveredPrivateKey := new(oprf.PrivateKey) + err = recoveredPrivateKey.Deserialize(suite, encoded) + test.CheckNoErr(t, err, "wrong deserialize") + + var recoveredServer *oprf.Server + if mode == oprf.BaseMode { + recoveredServer, err = oprf.NewServer(suite, recoveredPrivateKey) + } else if mode == oprf.VerifiableMode { + recoveredServer, err = oprf.NewVerifiableServer(suite, recoveredPrivateKey) + } + test.CheckNoErr(t, err, "invalid setup of server with key") + + outputB, err := recoveredServer.FullEvaluate(input) + test.CheckNoErr(t, err, "invalid full evaluate") + + got := outputA + want := outputB + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, suite, mode) + } +} + +func testAPI(t *testing.T, suite oprf.SuiteID, mode oprf.Mode) { + var err error + var server *oprf.Server + if mode == oprf.BaseMode { + server, err = oprf.NewServer(suite, nil) + } else if mode == oprf.VerifiableMode { + server, err = oprf.NewVerifiableServer(suite, nil) + } + test.CheckNoErr(t, err, "invalid setup of server") + + var client *oprf.Client + if mode == oprf.BaseMode { + client, err = oprf.NewClient(suite) + } else if mode == oprf.VerifiableMode { + pkS := server.GetPublicKey() + client, err = oprf.NewVerifiableClient(suite, pkS) + } + test.CheckNoErr(t, err, "invalid setup of client") + + inputs := [][]byte{{0x00}, {0xFF}} + cr, err := client.Request(inputs) + if err != nil { + t.Fatal("invalid blinding of client: " + err.Error()) + } + + eval, err := server.Evaluate(cr.BlindedElements()) + if err != nil { + t.Fatal("invalid evaluation of server: " + err.Error()) + } + if eval == nil { + t.Fatal("invalid evaluation of server: no evaluation") + } + + clientOutputs, err := client.Finalize(cr, eval) + if err != nil { + t.Fatal("invalid unblinding of client: " + err.Error()) + } + + if clientOutputs == nil { + t.Fatal("invalid finalizing of client: no final byte array.") + } + + for i := range inputs { + valid := server.VerifyFinalize(inputs[i], clientOutputs[i]) + if !valid { + t.Fatal("Invalid verification from the server") + } + + serverOutput, err := server.FullEvaluate(inputs[i]) + if err != nil { + t.Fatal("FullEvaluate failed", err) + } + if !bytes.Equal(serverOutput, clientOutputs[i]) { + t.Fatalf("Client and server OPRF output mismatch, got client output %x, expected server output %x", serverOutput, clientOutputs[i]) + } + } +} diff --git a/src/circl/oprf/server.go b/src/circl/oprf/server.go new file mode 100644 index 00000000000..f566f8e920c --- /dev/null +++ b/src/circl/oprf/server.go @@ -0,0 +1,163 @@ +package oprf + +import ( + "crypto/rand" + "crypto/subtle" + "errors" + + "circl/group" +) + +// Server is a representation of a OPRF server during protocol execution. +type Server struct { + suite + privateKey PrivateKey +} + +// NewServer creates a Server in base mode, and generates a key if no skS is +// provided. +func NewServer(id SuiteID, skS *PrivateKey) (*Server, error) { + return newServer(id, BaseMode, skS) +} + +// NewVerifiableServer creates a Server in verifiable mode, and generates a +// key if no skS is provided. +func NewVerifiableServer(id SuiteID, skS *PrivateKey) (*Server, error) { + return newServer(id, VerifiableMode, skS) +} + +func newServer(id SuiteID, m Mode, skS *PrivateKey) (*Server, error) { + suite, err := suiteFromID(id, m) + if err != nil { + return nil, err + } + if skS == nil { + skS = suite.generateKey() + } else if id != skS.s { // Verifies key corresponds to SuiteID. + return nil, errors.New("key doesn't match with suite") + } + + return &Server{*suite, *skS}, nil +} + +// GetPublicKey returns the public key corresponding to the server. +func (s *Server) GetPublicKey() *PublicKey { return s.privateKey.Public() } + +// Evaluate evaluates a set of blinded inputs from the client. +func (s *Server) Evaluate(blindedElements []Blinded) (*Evaluation, error) { + rr := s.suite.Group.RandomScalar(rand.Reader) + return s.evaluateWithProofScalar(blindedElements, rr) +} + +// Evaluate evaluates a set of blinded inputs from the client using a fixed +// random scalar for proof generation +func (s *Server) evaluateWithProofScalar(blindedElements []Blinded, proofScalar group.Scalar) (*Evaluation, error) { + l := len(blindedElements) + if l == 0 { + return nil, errors.New("no elements to evaluate") + } + + var err error + input := make([]group.Element, l) + eval := make([]group.Element, l) + out := make([]SerializedElement, l) + + for i := range blindedElements { + input[i] = s.suite.NewElement() + err = input[i].UnmarshalBinary(blindedElements[i]) + if err != nil { + return nil, err + } + + eval[i] = s.Group.NewElement() + eval[i].Mul(input[i], s.privateKey.k) + + e, err := eval[i].MarshalBinaryCompress() + if err != nil { + return nil, err + } + out[i] = e + } + + var proof *Proof + if s.Mode == VerifiableMode { + proof, err = s.generateProofWithRandomScalar(s.privateKey.k, s.Generator(), s.privateKey.Public().e, input, eval, proofScalar) + if err != nil { + return nil, err + } + } + + return &Evaluation{out, proof}, nil +} + +// FullEvaluate performs a full OPRF protocol at server-side. +func (s *Server) FullEvaluate(input []byte) ([]byte, error) { + p := s.Group.HashToElement(input, s.getDST(hashToGroupDST)) + + ser, err := s.scalarMult(p, s.privateKey.k) + if err != nil { + return nil, err + } + + return s.finalizeHash(input, ser), nil +} + +// VerifyFinalize performs a full OPRF protocol and returns true if the output +// matches the expected output. +func (s *Server) VerifyFinalize(input, expectedOutput []byte) bool { + gotOutput, err := s.FullEvaluate(input) + if err != nil { + return false + } + return subtle.ConstantTimeCompare(gotOutput, expectedOutput) == 1 +} + +func (s *Server) generateProofWithRandomScalar(k group.Scalar, A, B group.Element, Cs []group.Element, Ds []group.Element, rr group.Scalar) (*Proof, error) { + M, Z, err := s.computeComposites(k, B, Cs, Ds) + if err != nil { + return nil, err + } + + Bm, err := B.MarshalBinaryCompress() + if err != nil { + return nil, err + } + + a0, err := M.MarshalBinaryCompress() + if err != nil { + return nil, err + } + a1, err := Z.MarshalBinaryCompress() + if err != nil { + return nil, err + } + + a2e := s.Group.NewElement() + a2e.Mul(A, rr) + a2, err := a2e.MarshalBinaryCompress() + if err != nil { + return nil, err + } + + a3e := s.Group.NewElement() + a3e.Mul(M, rr) + a3, err := a3e.MarshalBinaryCompress() + if err != nil { + return nil, err + } + + cc := s.doChallenge([5][]byte{Bm, a0, a1, a2, a3}) + ss := s.suite.Group.NewScalar() + ss.Mul(cc, s.privateKey.k) + ss.Sub(rr, ss) + + serC, err := cc.MarshalBinary() + if err != nil { + return nil, err + } + serS, err := ss.MarshalBinary() + if err != nil { + return nil, err + } + return &Proof{serC, serS}, nil +} diff --git a/src/circl/oprf/testdata/allVectors_v06.json b/src/circl/oprf/testdata/allVectors_v06.json new file mode 100644 index 00000000000..3026b03e72b --- /dev/null +++ b/src/circl/oprf/testdata/allVectors_v06.json @@ -0,0 +1,392 @@ +[ + { + "groupDST": "564f50524630362d48617368546f47726f75702d000001", + "hash": "SHA512", + "mode": 0, + "seed": "a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3a3", + "skSm": "031806835f6808c8ac3808672e25a7802d94346bb33b52d712331f34faa64d08", + "suiteID": 1, + "suiteName": "OPRF(ristretto255, SHA-512)", + "vectors": [ + { + "Batch": 1, + "Blind": "c604c785ada70d77a5256ae21767de8c3304115237d262134f5e46e512cf8e03", + "BlindedElement": "3c7f2d901c0d4f245503a186086fbdf5d8b4408432b25c5163e8b5a19c258348", + "EvaluationElement": "1a34dc32aa2a725530c9d4d32485427889e8e97f4e9d353d19096ed3d83dd93e", + "Input": "00", + "Output": "6b6e7c7820a781f6d2b01d54df03afcf3c3a6769fca4ea9afbde6a0003417cb13feaa6362979c8d48541b675584cc0d15ace06488c37681fc75b13e2fa94c2f1" + 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"ac58e69b069115d6045a579c15f6d8acb7b79c9f2e282a04418614acdf47c188458bedd62df32723824ec36290b0f3d58a5b6449617c9d9f6c62bbcdedf2a0bc" + }, + { + "Batch": 1, + "Blind": "009055c99bf9591cb0eab2a72d044c05ca2cc2ef9b609a38546f74b6d688f70cf205f782fa11a0d61b2f5a8a2a1143368327f3077c68a1545e9aafbba6a90dc0d40a", + "BlindedElement": "0201dfa5dc7ea17f0cf60caa26d2a488e7af296268834b35eaff497488a211670008a74ed649b20379ab63a3ff8f2dd718f5418cb30ec317e68b5c8014a577b19710a3", + "EvaluationElement": "0201f9e9ced6cc6884d09a13a9003879db318f9ca4d21c7847ada8ff07d5f6c6282bb798742dab33eee83aa918d7bf1b95411744af8f9ed012488a7c7a937948782955", + "EvaluationProof": { + "c": "00c3dfb0f1ceeb63efde4099ada3df76b39f5f6870ea128e0b7a537119e3018f474149385b3890a06d4efa2c5e4a1c4d52f44bd77931c698fb739b93f85f10663107", + "r": "00b5dfc19eb96faba6382ec845097904db87240b9dd47b1e487ec625f11a7ba2cc3de74c5078a81806f74dd65065273c5bd886c7f87ff8c5f39f90320718eff747e3", + "s": "007bf680d9bf9fc615d4ef572e1848b7706b576022613eae3ddc98569c9c45312c3b6ed5c2dad5b369473c4cb03d0cba4f03f1e6194a3dc5539b11064a50cb36c5a6" + }, + "Input": "5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a", + "Output": "1718de160ae4b4d52cd6e16a31b12b194f73d575dffdd5775247790ee850c3f308aeb7a5c25e5ab591d6cd41666d26e39c91d879272cddccee4a359a95e82f54" + }, + { + "Batch": 2, + "Blind": "01c6cf092d80c7cf2cb55388d899515238094c800bdd9c65f71780ba85f5ae9b4703e17e559ca3ccd1944f9a70536c175f11a827452672b60d4e9f89eba281046e29,00cba1ba1a337759061965a423d9d3d6e1e1006dc8984ad28a4c93ecfc36fc2171046b3c4284855cfa2434ed98db9e68a597db2c14728fade716a6a82d600444b26e", + "BlindedElement": "0300be204aba0367d902f293aa8bda66a136f7e3962dfafab88ba04aacf62a4e63993060704cd1714cf7af4e16ea0a1c91ff7506a65b40253f6ae019b7a6160d50c814,0200082b5f723e4a635902e5bbf27fea807792399af5ac8d276bc6aa62bc1685cb6bdb2ff1c92979d4413da3627df180d709ddd03597fc8f095c6826fd97e8adbceca9", + "EvaluationElement": "02000c06fac6eb3c7f72ae831fd7040c51ff6c4d4d0861d7c79a29147103cb74be98f117ff896d9aa649a3ce62faddc7cdeee3b22c0ffa6bde7c86b6bb70b130fd75f3,0200ffacea2081f3e2325b9006fcde2e5ad027d1999192b136a79a5d01abf499f4c361b0284bf4c7ff4b58b36bd51c572dfae9560d6a74244fab80208685e98ad3ed2f", + "EvaluationProof": { + "c": "01b332952114e5872163edd501ca381a502deb8009ebe578a8675f3ac65e2fb48e70c76a7d0476a72af12caf5716fbea3ab66fb3cdc3c30c5ac382964f8a202f377c", + "r": "00d47b0d4ca4c64825ba085de242042b84d9ebe3b2e9de07678ff96713dfe16f40f2c662a56ed2db95e1e7bf2dea02bd1fa76e953a630772f68b53baade9962d1646", + "s": "009e8332567d0ec42ced34b0129688c4d80caa43fefb081f36ddf062fcc82dd31ee819b07e70b52e6ad65c419d3f96b3d492191913ff9615371a4b715091e7f1baea" + }, + "Input": "00,5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a", + "Output": "ac58e69b069115d6045a579c15f6d8acb7b79c9f2e282a04418614acdf47c188458bedd62df32723824ec36290b0f3d58a5b6449617c9d9f6c62bbcdedf2a0bc,1718de160ae4b4d52cd6e16a31b12b194f73d575dffdd5775247790ee850c3f308aeb7a5c25e5ab591d6cd41666d26e39c91d879272cddccee4a359a95e82f54" + } + ] + } +] diff --git a/src/circl/oprf/vectors_test.go b/src/circl/oprf/vectors_test.go new file mode 100644 index 00000000000..600e5fd8e4e --- /dev/null +++ b/src/circl/oprf/vectors_test.go @@ -0,0 +1,204 @@ +package oprf + +import ( + "bytes" + "encoding/hex" + "encoding/json" + "fmt" + "io/ioutil" + "os" + "strings" + "testing" + + "circl/group" + "circl/internal/test" +) + +type vector struct { + ID uint16 `json:"suiteID"` + Name string `json:"suiteName"` + Mode uint8 `json:"mode"` + Hash string `json:"hash"` + PkSm string `json:"pkSm"` + SkSm string `json:"skSm"` + Seed string `json:"seed"` + GroupDST string `json:"groupDST"` + Vectors []struct { + Batch int `json:"Batch"` + Blind string `json:"Blind"` + BlindedElement string `json:"BlindedElement"` + EvaluationElement string `json:"EvaluationElement"` + EvaluationProof struct { + R string `json:"r"` + C string `json:"c"` + S string `json:"s"` + } `json:"EvaluationProof"` + Input string `json:"Input"` + Output string `json:"Output"` + } `json:"vectors"` +} + +func toBytes(t *testing.T, s, errMsg string) []byte { + bytes, err := hex.DecodeString(s) + test.CheckNoErr(t, err, "decoding "+errMsg) + return bytes +} + +func toListBytes(t *testing.T, s, errMsg string) [][]byte { + strs := strings.Split(s, ",") + out := make([][]byte, len(strs)) + for i := range strs { + out[i] = toBytes(t, strs[i], errMsg) + } + return out +} + +func toScalar(t *testing.T, g group.Group, s, errMsg string) group.Scalar { + r := g.NewScalar() + rBytes := toBytes(t, s, errMsg) + err := r.UnmarshalBinary(rBytes) + test.CheckNoErr(t, err, errMsg) + return r +} + +func readFile(t *testing.T, fileName string) []vector { + jsonFile, err := os.Open(fileName) + if err != nil { + t.Fatalf("File %v can not be opened. Error: %v", fileName, err) + } + defer jsonFile.Close() + input, _ := ioutil.ReadAll(jsonFile) + + var v []vector + err = json.Unmarshal(input, &v) + if err != nil { + t.Fatalf("File %v can not be loaded. Error: %v", fileName, err) + } + return v +} + +func (v *vector) SetUpParties(t *testing.T) (s *Server, c *Client) { + seed := toBytes(t, v.Seed, "seed for keys") + privateKey, err := DeriveKey(v.ID, seed) + test.CheckNoErr(t, err, "deriving key") + + got, err := privateKey.Serialize() + test.CheckNoErr(t, err, "serlalizing key") + want := toBytes(t, v.SkSm, "private key") + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, v.Name, v.Mode) + } + + if v.Mode == BaseMode { + s, err = NewServer(v.ID, privateKey) + } else if v.Mode == VerifiableMode { + s, err = NewVerifiableServer(v.ID, privateKey) + } + test.CheckNoErr(t, err, "invalid setup of server") + + if v.Mode == BaseMode { + c, err = NewClient(v.ID) + } else if v.Mode == VerifiableMode { + pkSm := toBytes(t, v.PkSm, "public key") + publicKey := new(PublicKey) + err = publicKey.Deserialize(v.ID, pkSm) + test.CheckNoErr(t, err, "invalid public key") + c, err = NewVerifiableClient(v.ID, publicKey) + } + test.CheckNoErr(t, err, "invalid setup of client") + + return s, c +} + +func (v *vector) compareLists(t *testing.T, got, want [][]byte) { + for i := range got { + if !bytes.Equal(got[i], want[i]) { + test.ReportError(t, got[i], want[i], v.Name, v.Mode, i) + } + } +} + +func (v *vector) compareStrings(t *testing.T, got, want string) { + if got != want { + test.ReportError(t, got, want, v.Name, v.Mode) + } +} + +func (v *vector) test(t *testing.T) { + server, client := v.SetUpParties(t) + + var publicKey *PublicKey + if v.Mode == VerifiableMode { + pkSm := toBytes(t, v.PkSm, "public key") + publicKey = new(PublicKey) + err := publicKey.Deserialize(v.ID, pkSm) + test.CheckNoErr(t, err, "invalid public key") + } + + for i, vi := range v.Vectors { + inputs := toListBytes(t, vi.Input, "input") + blindsBytes := toListBytes(t, vi.Blind, "blind") + + blinds := make([]Blind, len(blindsBytes)) + for j := range blindsBytes { + blinds[j] = client.suite.Group.NewScalar() + err := blinds[j].UnmarshalBinary(blindsBytes[j]) + test.CheckNoErr(t, err, "invalid blind") + } + + clientReq, err := client.blind(inputs, blinds) + test.CheckNoErr(t, err, "invalid client request") + v.compareLists(t, + clientReq.BlindedElements(), + toListBytes(t, vi.BlindedElement, "blindedElement"), + ) + + rr := toScalar(t, client.suite.Group, vi.EvaluationProof.R, "invalid proof random scalar") + + eval, err := server.evaluateWithProofScalar(clientReq.BlindedElements(), rr) + test.CheckNoErr(t, err, "invalid evaluation") + v.compareLists(t, + eval.Elements, + toListBytes(t, vi.EvaluationElement, "evaluation"), + ) + + if v.Mode == VerifiableMode { + v.compareStrings(t, hex.EncodeToString(eval.Proof.C), vi.EvaluationProof.C) + v.compareStrings(t, hex.EncodeToString(eval.Proof.S), vi.EvaluationProof.S) + } + + outputs, err := client.Finalize(clientReq, eval) + test.CheckNoErr(t, err, "invalid finalize") + expectedOutputs := toListBytes(t, vi.Output, "output") + v.compareLists(t, + outputs, + expectedOutputs, + ) + + for j := range inputs { + output, err := server.FullEvaluate(inputs[j]) + test.CheckNoErr(t, err, "invalid full evaluate") + got := output + want := expectedOutputs[j] + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, v.Name, v.Mode, i, j) + } + + test.CheckOk(server.VerifyFinalize(inputs[j], output), "verify finalize", t) + } + } +} + +func TestVectors(t *testing.T) { + // Test vectors from https://datatracker.ietf.org/doc/draft-irtf-cfrg-voprf + v := readFile(t, "testdata/allVectors_v06.json") + + for i := range v { + id := v[i].ID + if !(id == OPRFP256 || id == OPRFP384 || id == OPRFP521) { + t.Logf(v[i].Name + " not supported yet") + continue + } + t.Run(fmt.Sprintf("Suite%v/Mode%v", id, v[i].Mode), v[i].test) + } +} diff --git a/src/circl/pke/doc.go b/src/circl/pke/doc.go new file mode 100644 index 00000000000..e79425c875c --- /dev/null +++ b/src/circl/pke/doc.go @@ -0,0 +1,2 @@ +// Package pke provides a variety of public key encryption mechanisms. +package pke diff --git a/src/circl/pke/kyber/gen.go b/src/circl/pke/kyber/gen.go new file mode 100644 index 00000000000..0b079f89103 --- /dev/null +++ b/src/circl/pke/kyber/gen.go @@ -0,0 +1,201 @@ +// +build ignore + +// Autogenerates wrappers from templates to prevent too much duplicated code +// between the code for different modes. +package main + +import ( + "bytes" + "fmt" + "io/ioutil" + "os" + "path" + "strings" + "text/template" +) + +type Instance struct { + Name string + K int + Eta1 int + CiphertextSize int + DU int + DV int +} + +func (m Instance) Pkg() string { + return strings.ToLower(m.Name) +} +func (m Instance) Impl() string { + return "impl" + m.Name +} + +var ( + Instances = []Instance{ + { + Name: "Kyber512", + Eta1: 3, + K: 2, + CiphertextSize: 768, + DU: 10, + DV: 4, + }, + { + Name: "Kyber768", + Eta1: 2, + K: 3, + CiphertextSize: 1088, + DU: 10, + DV: 4, + }, + { + Name: "Kyber1024", + Eta1: 2, + K: 4, + CiphertextSize: 1568, + DU: 11, + DV: 5, + }, + } + TemplateWarning = "// Code generated from" +) + +func main() { + generatePackageFiles() + generateParamsFiles() + generateSourceFiles() +} + +// Generates instance/internal/params.go from templates/params.templ.go +func generateParamsFiles() { + tl, err := template.ParseFiles("templates/params.templ.go") + if err != nil { + panic(err) + } + + for _, mode := range Instances { + buf := new(bytes.Buffer) + err := tl.Execute(buf, mode) + if err != nil { + panic(err) + } + + res := string(buf.Bytes()) + offset := strings.Index(res, TemplateWarning) + if offset == -1 { + panic("Missing template warning in params.templ.go") + } + err = ioutil.WriteFile(mode.Pkg()+"/internal/params.go", + []byte(res[offset:]), 0644) + if err != nil { + panic(err) + } + } +} + +// Generates instance/kyber.go from templates/pkg.templ.go +func generatePackageFiles() { + tl, err := template.ParseFiles("templates/pkg.templ.go") + if err != nil { + panic(err) + } + + for _, mode := range Instances { + buf := new(bytes.Buffer) + err := tl.Execute(buf, mode) + if err != nil { + panic(err) + } + + res := string(buf.Bytes()) + offset := strings.Index(res, TemplateWarning) + if offset == -1 { + panic("Missing template warning in pkg.templ.go") + } + err = ioutil.WriteFile(mode.Pkg()+"/kyber.go", []byte(res[offset:]), 0644) + if err != nil { + panic(err) + } + } +} + +// Copies kyber512 source files to other modes +func generateSourceFiles() { + files := make(map[string][]byte) + + // Ignore mode specific files. + ignored := func(x string) bool { + return x == "params.go" || x == "params_test.go" + } + + fs, err := ioutil.ReadDir("kyber512/internal") + if err != nil { + panic(err) + } + + // Read files + for _, f := range fs { + name := f.Name() + if ignored(name) { + continue + } + files[name], err = ioutil.ReadFile(path.Join("kyber512/internal", name)) + if err != nil { + panic(err) + } + } + + // Go over modes + for _, mode := range Instances { + if mode.Name == "Kyber512" { + continue + } + + fs, err = ioutil.ReadDir(path.Join(mode.Pkg(), "internal")) + for _, f := range fs { + name := f.Name() + fn := path.Join(mode.Pkg(), "internal", name) + if ignored(name) { + continue + } + _, ok := files[name] + if !ok { + fmt.Printf("Removing superfluous file: %s\n", fn) + err = os.Remove(fn) + if err != nil { + panic(err) + } + } + if f.Mode().IsDir() { + panic(fmt.Sprintf("%s: is a directory", fn)) + } + if f.Mode()&os.ModeSymlink != 0 { + fmt.Printf("Removing symlink: %s\n", fn) + err = os.Remove(fn) + if err != nil { + panic(err) + } + } + } + for name, expected := range files { + fn := path.Join(mode.Pkg(), "internal", name) + expected = []byte(fmt.Sprintf( + "%s kyber512/internal/%s by gen.go\n\n%s", + TemplateWarning, + name, + string(expected), + )) + got, err := ioutil.ReadFile(fn) + if err == nil { + if bytes.Equal(got, expected) { + continue + } + } + fmt.Printf("Updating %s\n", fn) + err = ioutil.WriteFile(fn, expected, 0644) + if err != nil { + panic(err) + } + } + } +} diff --git a/src/circl/pke/kyber/internal/common/amd64.go b/src/circl/pke/kyber/internal/common/amd64.go new file mode 100644 index 00000000000..84b738016e1 --- /dev/null +++ b/src/circl/pke/kyber/internal/common/amd64.go @@ -0,0 +1,301 @@ +// +build amd64 + +package common + +import ( + "internal/cpu" +) + +// ZetasAVX2 contains all ζ used in NTT (like the Zetas array), but also +// the values int16(zeta * 62209) for each zeta, which is used in +// Montgomery reduction. There is some duplication and reordering as +// compared to Zetas to make it more covenient for use with AVX2. +var ZetasAVX2 = [...]int16{ + // level 1: int16(Zetas[1]*62209) and Zetas[1] + 31499, 2571, + + // level 2 + // + // int16(Zetas[2]*62209), Zetas[2], int16(Zetas[3]*62209), Zetas[3] + 14746, 2970, 788, 1812, + + // level 3, like level 2. + 13525, 1493, -12402, 1422, 28191, 287, -16694, 202, + + 0, 0, // padding + + // layer 4. offset: 1*16 + // + // The precomputed multiplication and zetas are grouped by 16 at a + // time as used in the set of butterflies, etc. + -20906, -20906, -20906, -20906, -20906, -20906, -20906, -20906, + 27758, 27758, 27758, 27758, 27758, 27758, 27758, 27758, + 3158, 3158, 3158, 3158, 3158, 3158, 3158, 3158, + 622, 622, 622, 622, 622, 622, 622, 622, + -3799, -3799, -3799, -3799, -3799, -3799, -3799, -3799, + -15690, -15690, -15690, -15690, -15690, -15690, -15690, -15690, + 1577, 1577, 1577, 1577, 1577, 1577, 1577, 1577, + 182, 182, 182, 182, 182, 182, 182, 182, + 10690, 10690, 10690, 10690, 10690, 10690, 10690, 10690, + 1359, 1359, 1359, 1359, 1359, 1359, 1359, 1359, + 962, 962, 962, 962, 962, 962, 962, 962, + 2127, 2127, 2127, 2127, 2127, 2127, 2127, 2127, + -11201, -11201, -11201, -11201, -11201, -11201, -11201, -11201, + 31164, 31164, 31164, 31164, 31164, 31164, 31164, 31164, + 1855, 1855, 1855, 1855, 1855, 1855, 1855, 1855, + 1468, 1468, 1468, 1468, 1468, 1468, 1468, 1468, + + // layer 5. offset: 9*16 + -5827, -5827, -5827, -5827, 17364, 17364, 17364, 17364, + -26360, -26360, -26360, -26360, -29057, -29057, -29057, -29057, + 573, 573, 573, 573, 2004, 2004, 2004, 2004, + 264, 264, 264, 264, 383, 383, 383, 383, + 5572, 5572, 5572, 5572, -1102, -1102, -1102, -1102, + 21439, 21439, 21439, 21439, -26241, -26241, -26241, -26241, + 2500, 2500, 2500, 2500, 1458, 1458, 1458, 1458, + 1727, 1727, 1727, 1727, 3199, 3199, 3199, 3199, + -28072, -28072, -28072, -28072, 24313, 24313, 24313, 24313, + -10532, -10532, -10532, -10532, 8800, 8800, 8800, 8800, + 2648, 2648, 2648, 2648, 1017, 1017, 1017, 1017, + 732, 732, 732, 732, 608, 608, 608, 608, + 18427, 18427, 18427, 18427, 8859, 8859, 8859, 8859, + 26676, 26676, 26676, 26676, -16162, -16162, -16162, -16162, + 1787, 1787, 1787, 1787, 411, 411, 411, 411, + 3124, 3124, 3124, 3124, 1758, 1758, 1758, 1758, + + // layer 6. offset: 17*16 + -5689, -5689, -6516, -6516, 1497, 1497, 30967, 30967, + -23564, -23564, 20179, 20179, 20711, 20711, 25081, 25081, + 1223, 1223, 652, 652, 2777, 2777, 1015, 1015, + 2036, 2036, 1491, 1491, 3047, 3047, 1785, 1785, + -12796, -12796, 26617, 26617, 16065, 16065, -12441, -12441, + 9135, 9135, -649, -649, -25986, -25986, 27837, 27837, + 516, 516, 3321, 3321, 3009, 3009, 2663, 2663, + 1711, 1711, 2167, 2167, 126, 126, 1469, 1469, + 19884, 19884, -28249, -28249, -15886, -15886, -8898, -8898, + -28309, -28309, 9076, 9076, -30198, -30198, 18250, 18250, + 2476, 2476, 3239, 3239, 3058, 3058, 830, 830, + 107, 107, 1908, 1908, 3082, 3082, 2378, 2378, + 13427, 13427, 14017, 14017, -29155, -29155, -12756, -12756, + 16832, 16832, 4312, 4312, -24155, -24155, -17914, -17914, + 2931, 2931, 961, 961, 1821, 1821, 2604, 2604, + 448, 448, 2264, 2264, 677, 677, 2054, 2054, + + // layer 7. offset: 25*16 + -334, 11182, -11477, 13387, -32226, -14233, 20494, -21655, + -27738, 13131, 945, -4586, -14882, 23093, 6182, 5493, + 2226, 430, 555, 843, 2078, 871, 1550, 105, + 422, 587, 177, 3094, 3038, 2869, 1574, 1653, + 32011, -32502, 10631, 30318, 29176, -18741, -28761, 12639, + -18485, 20100, 17561, 18525, -14430, 19529, -5275, -12618, + 3083, 778, 1159, 3182, 2552, 1483, 2727, 1119, + 1739, 644, 2457, 349, 418, 329, 3173, 3254, + -31183, 20297, 25435, 2146, -7382, 15356, 24392, -32384, + -20926, -6279, 10946, -14902, 24215, -11044, 16990, 14470, + 817, 1097, 603, 610, 1322, 2044, 1864, 384, + 2114, 3193, 1218, 1994, 2455, 220, 2142, 1670, + 10336, -21497, -7933, -20198, -22501, 23211, 10907, -17442, + 31637, -23859, 28644, -20257, 23998, 7757, -17422, 23132, + 2144, 1799, 2051, 794, 1819, 2475, 2459, 478, + 3221, 3021, 996, 991, 958, 1869, 1522, 1628, + + // layer 1 inverse + 23132, -17422, 7757, 23998, -20257, 28644, -23859, 31637, + -17442, 10907, 23211, -22501, -20198, -7933, -21497, 10336, + 1628, 1522, 1869, 958, 991, 996, 3021, 3221, + 478, 2459, 2475, 1819, 794, 2051, 1799, 2144, + 14470, 16990, -11044, 24215, -14902, 10946, -6279, -20926, + -32384, 24392, 15356, -7382, 2146, 25435, 20297, -31183, + 1670, 2142, 220, 2455, 1994, 1218, 3193, 2114, + 384, 1864, 2044, 1322, 610, 603, 1097, 817, + -12618, -5275, 19529, -14430, 18525, 17561, 20100, -18485, + 12639, -28761, -18741, 29176, 30318, 10631, -32502, 32011, + 3254, 3173, 329, 418, 349, 2457, 644, 1739, + 1119, 2727, 1483, 2552, 3182, 1159, 778, 3083, + 5493, 6182, 23093, -14882, -4586, 945, 13131, -27738, + -21655, 20494, -14233, -32226, 13387, -11477, 11182, -334, + 1653, 1574, 2869, 3038, 3094, 177, 587, 422, + 105, 1550, 871, 2078, 843, 555, 430, 2226, + + // layer 2 inverse + -17914, -17914, -24155, -24155, 4312, 4312, 16832, 16832, + -12756, -12756, -29155, -29155, 14017, 14017, 13427, 13427, + 2054, 2054, 677, 677, 2264, 2264, 448, 448, + 2604, 2604, 1821, 1821, 961, 961, 2931, 2931, + 18250, 18250, -30198, -30198, 9076, 9076, -28309, -28309, + -8898, -8898, -15886, -15886, -28249, -28249, 19884, 19884, + 2378, 2378, 3082, 3082, 1908, 1908, 107, 107, + 830, 830, 3058, 3058, 3239, 3239, 2476, 2476, + 27837, 27837, -25986, -25986, -649, -649, 9135, 9135, + -12441, -12441, 16065, 16065, 26617, 26617, -12796, -12796, + 1469, 1469, 126, 126, 2167, 2167, 1711, 1711, + 2663, 2663, 3009, 3009, 3321, 3321, 516, 516, + 25081, 25081, 20711, 20711, 20179, 20179, -23564, -23564, + 30967, 30967, 1497, 1497, -6516, -6516, -5689, -5689, + 1785, 1785, 3047, 3047, 1491, 1491, 2036, 2036, + 1015, 1015, 2777, 2777, 652, 652, 1223, 1223, + + // layer 3 inverse + -16162, -16162, -16162, -16162, 26676, 26676, 26676, 26676, + 8859, 8859, 8859, 8859, 18427, 18427, 18427, 18427, + 1758, 1758, 1758, 1758, 3124, 3124, 3124, 3124, + 411, 411, 411, 411, 1787, 1787, 1787, 1787, + 8800, 8800, 8800, 8800, -10532, -10532, -10532, -10532, + 24313, 24313, 24313, 24313, -28072, -28072, -28072, -28072, + 608, 608, 608, 608, 732, 732, 732, 732, + 1017, 1017, 1017, 1017, 2648, 2648, 2648, 2648, + -26241, -26241, -26241, -26241, 21439, 21439, 21439, 21439, + -1102, -1102, -1102, -1102, 5572, 5572, 5572, 5572, + 3199, 3199, 3199, 3199, 1727, 1727, 1727, 1727, + 1458, 1458, 1458, 1458, 2500, 2500, 2500, 2500, + -29057, -29057, -29057, -29057, -26360, -26360, -26360, -26360, + 17364, 17364, 17364, 17364, -5827, -5827, -5827, -5827, + 383, 383, 383, 383, 264, 264, 264, 264, + 2004, 2004, 2004, 2004, 573, 573, 573, 573, + + // layer 4 inverse + 31164, 31164, 31164, 31164, 31164, 31164, 31164, 31164, + -11201, -11201, -11201, -11201, -11201, -11201, -11201, -11201, + 1468, 1468, 1468, 1468, 1468, 1468, 1468, 1468, + 1855, 1855, 1855, 1855, 1855, 1855, 1855, 1855, + 1359, 1359, 1359, 1359, 1359, 1359, 1359, 1359, + 10690, 10690, 10690, 10690, 10690, 10690, 10690, 10690, + 2127, 2127, 2127, 2127, 2127, 2127, 2127, 2127, + 962, 962, 962, 962, 962, 962, 962, 962, + -15690, -15690, -15690, -15690, -15690, -15690, -15690, -15690, + -3799, -3799, -3799, -3799, -3799, -3799, -3799, -3799, + 182, 182, 182, 182, 182, 182, 182, 182, + 1577, 1577, 1577, 1577, 1577, 1577, 1577, 1577, + 27758, 27758, 27758, 27758, 27758, 27758, 27758, 27758, + -20906, -20906, -20906, -20906, -20906, -20906, -20906, -20906, + 622, 622, 622, 622, 622, 622, 622, 622, + 3158, 3158, 3158, 3158, 3158, 3158, 3158, 3158, + + // layer 5 inverse + -16694, 202, 28191, 287, -12402, 1422, 13525, 1493, + + // layer 6 inverse + 788, 1812, 14746, 2970, + + // layer 7 inverse + 31499, 2571, +} + +// Sets p to a + b. Does not normalize coefficients. +func (p *Poly) Add(a, b *Poly) { + if cpu.X86.HasAVX2 { + addAVX2( + (*[N]int16)(p), + (*[N]int16)(a), + (*[N]int16)(b), + ) + } else { + p.addGeneric(a, b) + } +} + +// Sets p to a - b. Does not normalize coefficients. +func (p *Poly) Sub(a, b *Poly) { + if cpu.X86.HasAVX2 { + subAVX2( + (*[N]int16)(p), + (*[N]int16)(a), + (*[N]int16)(b), + ) + } else { + p.subGeneric(a, b) + } +} + +// Executes an in-place forward "NTT" on p. +// +// Assumes the coefficients are in absolute value ≤q. The resulting +// coefficients are in absolute value ≤7q. If the input is in Montgomery +// form, then the result is in Montgomery form and so (by linearity of the NTT) +// if the input is in regular form, then the result is also in regular form. +// The order of coefficients will be "tangled". These can be put back into +// their proper order by calling Detangle(). +func (p *Poly) NTT() { + if cpu.X86.HasAVX2 { + nttAVX2((*[N]int16)(p)) + } else { + p.nttGeneric() + } +} + +// Executes an in-place inverse "NTT" on p and multiply by the Montgomery +// factor R. +// +// Requires coefficients to be in "tangled" order, see Tangle(). +// Assumes the coefficients are in absolute value ≤q. The resulting +// coefficients are in absolute value ≤q. If the input is in Montgomery +// form, then the result is in Montgomery form and so (by linearity) +// if the input is in regular form, then the result is also in regular form. +func (p *Poly) InvNTT() { + if cpu.X86.HasAVX2 { + invNttAVX2((*[N]int16)(p)) + } else { + p.invNTTGeneric() + } +} + +// Sets p to the "pointwise" multiplication of a and b. +// +// That is: InvNTT(p) = InvNTT(a) * InvNTT(b). Assumes a and b are in +// Montgomery form. Products between coefficients of a and b must be strictly +// bounded in absolute value by 2¹⁵q. p will be in Montgomery form and +// bounded in absolute value by 2q. +// +// Requires a and b to be in "tangled" order, see Tangle(). p will be in +// tangled order as well. +func (p *Poly) MulHat(a, b *Poly) { + if cpu.X86.HasAVX2 { + mulHatAVX2( + (*[N]int16)(p), + (*[N]int16)(a), + (*[N]int16)(b), + ) + } else { + p.mulHatGeneric(a, b) + } +} + +// Puts p into the right form to be used with (among others) InvNTT(). +func (p *Poly) Tangle() { + if cpu.X86.HasAVX2 { + tangleAVX2((*[N]int16)(p)) + } + + // When AVX2 is not available, we use the standard order. +} + +// Puts p back into standard form. +func (p *Poly) Detangle() { + if cpu.X86.HasAVX2 { + detangleAVX2((*[N]int16)(p)) + } + + // When AVX2 is not available, we use the standard order. +} + +// Almost normalizes coefficients. +// +// Ensures each coefficient is in {0, …, q}. +func (p *Poly) BarrettReduce() { + if cpu.X86.HasAVX2 { + barrettReduceAVX2((*[N]int16)(p)) + } else { + p.barrettReduceGeneric() + } +} + +// Normalizes coefficients. +// +// Ensures each coefficient is in {0, …, q-1}. +func (p *Poly) Normalize() { + if cpu.X86.HasAVX2 { + normalizeAVX2((*[N]int16)(p)) + } else { + p.normalizeGeneric() + } +} diff --git a/src/circl/pke/kyber/internal/common/amd64.s b/src/circl/pke/kyber/internal/common/amd64.s new file mode 100644 index 00000000000..d8205465e17 --- /dev/null +++ b/src/circl/pke/kyber/internal/common/amd64.s @@ -0,0 +1,2354 @@ +// Code generated by command: go run src.go -out ../amd64.s -stubs ../stubs_amd64.go -pkg common. DO NOT EDIT. + +// +build amd64 + +#include "textflag.h" + +// func addAVX2(p *[256]int16, a *[256]int16, b *[256]int16) +// Requires: AVX, AVX2 +TEXT ·addAVX2(SB), NOSPLIT, $0-24 + MOVQ p+0(FP), AX + MOVQ a+8(FP), CX + MOVQ b+16(FP), DX + VMOVDQU (CX), Y0 + VMOVDQU 32(CX), Y2 + VMOVDQU 64(CX), Y4 + VMOVDQU 96(CX), Y6 + VMOVDQU 128(CX), Y8 + VMOVDQU 160(CX), Y10 + VMOVDQU 192(CX), Y12 + VMOVDQU 224(CX), Y14 + VMOVDQU (DX), Y1 + VMOVDQU 32(DX), Y3 + VMOVDQU 64(DX), Y5 + VMOVDQU 96(DX), Y7 + VMOVDQU 128(DX), Y9 + VMOVDQU 160(DX), Y11 + VMOVDQU 192(DX), Y13 + VMOVDQU 224(DX), Y15 + VPADDW Y0, Y1, Y1 + VPADDW Y2, Y3, Y3 + VPADDW Y4, Y5, Y5 + VPADDW Y6, Y7, Y7 + VPADDW Y8, Y9, Y9 + VPADDW Y10, Y11, Y11 + VPADDW Y12, Y13, Y13 + VPADDW Y14, Y15, Y15 + VMOVDQU Y1, (AX) + VMOVDQU Y3, 32(AX) + VMOVDQU Y5, 64(AX) + VMOVDQU Y7, 96(AX) + VMOVDQU Y9, 128(AX) + VMOVDQU Y11, 160(AX) + VMOVDQU Y13, 192(AX) + VMOVDQU Y15, 224(AX) + VMOVDQU 256(CX), Y0 + VMOVDQU 288(CX), Y2 + VMOVDQU 320(CX), Y4 + VMOVDQU 352(CX), Y6 + VMOVDQU 384(CX), Y8 + VMOVDQU 416(CX), Y10 + VMOVDQU 448(CX), Y12 + VMOVDQU 480(CX), Y14 + VMOVDQU 256(DX), Y1 + VMOVDQU 288(DX), Y3 + VMOVDQU 320(DX), Y5 + VMOVDQU 352(DX), Y7 + VMOVDQU 384(DX), Y9 + VMOVDQU 416(DX), Y11 + VMOVDQU 448(DX), Y13 + VMOVDQU 480(DX), Y15 + VPADDW Y0, Y1, Y1 + VPADDW Y2, Y3, Y3 + VPADDW Y4, Y5, Y5 + VPADDW Y6, Y7, Y7 + VPADDW Y8, Y9, Y9 + VPADDW Y10, Y11, Y11 + VPADDW Y12, Y13, Y13 + VPADDW Y14, Y15, Y15 + VMOVDQU Y1, 256(AX) + VMOVDQU Y3, 288(AX) + VMOVDQU Y5, 320(AX) + VMOVDQU Y7, 352(AX) + VMOVDQU Y9, 384(AX) + VMOVDQU Y11, 416(AX) + VMOVDQU Y13, 448(AX) + VMOVDQU Y15, 480(AX) + RET + +// func subAVX2(p *[256]int16, a *[256]int16, b *[256]int16) +// Requires: AVX, AVX2 +TEXT ·subAVX2(SB), NOSPLIT, $0-24 + MOVQ p+0(FP), AX + MOVQ a+8(FP), CX + MOVQ b+16(FP), DX + VMOVDQU (CX), Y0 + VMOVDQU 32(CX), Y2 + VMOVDQU 64(CX), Y4 + VMOVDQU 96(CX), Y6 + VMOVDQU 128(CX), Y8 + VMOVDQU 160(CX), Y10 + VMOVDQU 192(CX), Y12 + VMOVDQU 224(CX), Y14 + VMOVDQU (DX), Y1 + VMOVDQU 32(DX), Y3 + VMOVDQU 64(DX), Y5 + VMOVDQU 96(DX), Y7 + VMOVDQU 128(DX), Y9 + VMOVDQU 160(DX), Y11 + VMOVDQU 192(DX), Y13 + VMOVDQU 224(DX), Y15 + VPSUBW Y1, Y0, Y1 + VPSUBW Y3, Y2, Y3 + VPSUBW Y5, Y4, Y5 + VPSUBW Y7, Y6, Y7 + VPSUBW Y9, Y8, Y9 + VPSUBW Y11, Y10, Y11 + VPSUBW Y13, Y12, Y13 + VPSUBW Y15, Y14, Y15 + VMOVDQU Y1, (AX) + VMOVDQU Y3, 32(AX) + VMOVDQU Y5, 64(AX) + VMOVDQU Y7, 96(AX) + VMOVDQU Y9, 128(AX) + VMOVDQU Y11, 160(AX) + VMOVDQU Y13, 192(AX) + VMOVDQU Y15, 224(AX) + VMOVDQU 256(CX), Y0 + VMOVDQU 288(CX), Y2 + VMOVDQU 320(CX), Y4 + VMOVDQU 352(CX), Y6 + VMOVDQU 384(CX), Y8 + VMOVDQU 416(CX), Y10 + VMOVDQU 448(CX), Y12 + VMOVDQU 480(CX), Y14 + VMOVDQU 256(DX), Y1 + VMOVDQU 288(DX), Y3 + VMOVDQU 320(DX), Y5 + VMOVDQU 352(DX), Y7 + VMOVDQU 384(DX), Y9 + VMOVDQU 416(DX), Y11 + VMOVDQU 448(DX), Y13 + VMOVDQU 480(DX), Y15 + VPSUBW Y1, Y0, Y1 + VPSUBW Y3, Y2, Y3 + VPSUBW Y5, Y4, Y5 + VPSUBW Y7, Y6, Y7 + VPSUBW Y9, Y8, Y9 + VPSUBW Y11, Y10, Y11 + VPSUBW Y13, Y12, Y13 + VPSUBW Y15, Y14, Y15 + VMOVDQU Y1, 256(AX) + VMOVDQU Y3, 288(AX) + VMOVDQU Y5, 320(AX) + VMOVDQU Y7, 352(AX) + VMOVDQU Y9, 384(AX) + VMOVDQU Y11, 416(AX) + VMOVDQU Y13, 448(AX) + VMOVDQU Y15, 480(AX) + RET + +// func nttAVX2(p *[256]int16) +// Requires: AVX, AVX2 +TEXT ·nttAVX2(SB), NOSPLIT, $0-8 + MOVQ p+0(FP), AX + LEAQ ·ZetasAVX2+0(SB), CX + MOVL $0x00000d01, DX + VMOVD DX, X0 + VPBROADCASTW X0, Y15 + VPBROADCASTW (CX), Y0 + VPBROADCASTW 2(CX), Y1 + VMOVDQU (AX), Y7 + VMOVDQU 32(AX), Y8 + VMOVDQU 64(AX), Y9 + VMOVDQU 96(AX), Y10 + VMOVDQU 256(AX), Y11 + VMOVDQU 288(AX), Y12 + VMOVDQU 320(AX), Y13 + VMOVDQU 352(AX), Y14 + VPMULLW Y11, Y0, Y2 + VPMULLW Y12, Y0, Y3 + VPMULLW Y13, Y0, Y4 + VPMULLW Y14, Y0, Y5 + VPMULHW Y11, Y1, Y11 + VPMULHW Y12, Y1, Y12 + VPMULHW Y13, Y1, Y13 + VPMULHW Y14, Y1, Y14 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y11, Y2 + VPSUBW Y3, Y12, Y3 + VPSUBW Y4, Y13, Y4 + VPSUBW Y5, Y14, Y5 + VPSUBW Y2, Y7, Y11 + VPSUBW Y3, Y8, Y12 + VPSUBW Y4, Y9, Y13 + VPSUBW Y5, Y10, Y14 + VPADDW Y2, Y7, Y7 + VPADDW Y3, Y8, Y8 + VPADDW Y4, Y9, Y9 + VPADDW Y5, Y10, Y10 + VMOVDQU Y7, (AX) + VMOVDQU Y8, 32(AX) + VMOVDQU Y9, 64(AX) + VMOVDQU Y10, 96(AX) + VMOVDQU Y11, 256(AX) + VMOVDQU Y12, 288(AX) + VMOVDQU Y13, 320(AX) + VMOVDQU Y14, 352(AX) + VMOVDQU 128(AX), Y7 + VMOVDQU 160(AX), Y8 + VMOVDQU 192(AX), Y9 + VMOVDQU 224(AX), Y10 + VMOVDQU 384(AX), Y11 + VMOVDQU 416(AX), Y12 + VMOVDQU 448(AX), Y13 + VMOVDQU 480(AX), Y14 + VPMULLW Y11, Y0, Y2 + VPMULLW Y12, Y0, Y3 + VPMULLW Y13, Y0, Y4 + VPMULLW Y14, Y0, Y5 + VPMULHW Y11, Y1, Y11 + VPMULHW Y12, Y1, Y12 + VPMULHW Y13, Y1, Y13 + VPMULHW Y14, Y1, Y14 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y11, Y2 + VPSUBW Y3, Y12, Y3 + VPSUBW Y4, Y13, Y4 + VPSUBW Y5, Y14, Y5 + VPSUBW Y2, Y7, Y11 + VPSUBW Y3, Y8, Y12 + VPSUBW Y4, Y9, Y13 + VPSUBW Y5, Y10, Y14 + VPADDW Y2, Y7, Y7 + VPADDW Y3, Y8, Y8 + VPADDW Y4, Y9, Y9 + VPADDW Y5, Y10, Y10 + VMOVDQU Y7, 128(AX) + VMOVDQU Y8, 160(AX) + VMOVDQU Y9, 192(AX) + VMOVDQU Y10, 224(AX) + VMOVDQU Y11, 384(AX) + VMOVDQU Y12, 416(AX) + VMOVDQU Y13, 448(AX) + VMOVDQU Y14, 480(AX) + VPBROADCASTW 4(CX), Y0 + VPBROADCASTW 6(CX), Y1 + VMOVDQU (AX), Y7 + VMOVDQU 32(AX), Y8 + VMOVDQU 64(AX), Y9 + VMOVDQU 96(AX), Y10 + VMOVDQU 128(AX), Y11 + VMOVDQU 160(AX), Y12 + VMOVDQU 192(AX), Y13 + VMOVDQU 224(AX), Y14 + VPMULLW Y11, Y0, Y2 + VPMULLW Y12, Y0, Y3 + VPMULLW Y13, Y0, Y4 + VPMULLW Y14, Y0, Y5 + VPMULHW Y11, Y1, Y11 + VPMULHW Y12, Y1, Y12 + VPMULHW Y13, Y1, Y13 + VPMULHW Y14, Y1, Y14 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y11, Y2 + VPSUBW Y3, Y12, Y3 + VPSUBW Y4, Y13, Y4 + VPSUBW Y5, Y14, Y5 + VPSUBW Y2, Y7, Y11 + VPSUBW Y3, Y8, Y12 + VPSUBW Y4, Y9, Y13 + VPSUBW Y5, Y10, Y14 + VPADDW Y2, Y7, Y7 + VPADDW Y3, Y8, Y8 + VPADDW Y4, Y9, Y9 + VPADDW Y5, Y10, Y10 + VPBROADCASTW 12(CX), Y0 + VPBROADCASTW 14(CX), Y1 + VPBROADCASTW 16(CX), Y2 + VPBROADCASTW 18(CX), Y3 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y13, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y13, Y3, Y13 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y9, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y13, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y9 + VPSUBW Y5, Y8, Y10 + VPSUBW Y6, Y11, Y13 + VPSUBW Y0, Y12, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y8, Y8 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y12, Y12 + VMOVDQU 32(CX), Y0 + VMOVDQU 64(CX), Y1 + VMOVDQU 96(CX), Y2 + VMOVDQU 128(CX), Y3 + VPERM2I128 $0x20, Y9, Y7, Y4 + VPERM2I128 $0x31, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VPERM2I128 $0x20, Y10, Y8, Y4 + VPERM2I128 $0x31, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VPERM2I128 $0x20, Y13, Y11, Y4 + VPERM2I128 $0x31, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VPERM2I128 $0x20, Y14, Y12, Y4 + VPERM2I128 $0x31, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPMULLW Y8, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y12, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y8, Y1, Y8 + VPMULHW Y10, Y1, Y10 + VPMULHW Y12, Y3, Y12 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y8, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y12, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y8 + VPSUBW Y5, Y9, Y10 + VPSUBW Y6, Y11, Y12 + VPSUBW Y0, Y13, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y9, Y9 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y13, Y13 + VMOVDQU 288(CX), Y0 + VMOVDQU 320(CX), Y1 + VMOVDQU 352(CX), Y2 + VMOVDQU 384(CX), Y3 + VPUNPCKLQDQ Y8, Y7, Y4 + VPUNPCKHQDQ Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPUNPCKLQDQ Y10, Y9, Y4 + VPUNPCKHQDQ Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPUNPCKLQDQ Y12, Y11, Y4 + VPUNPCKHQDQ Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPUNPCKLQDQ Y14, Y13, Y4 + VPUNPCKHQDQ Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y13, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y13, Y3, Y13 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y9, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y13, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y9 + VPSUBW Y5, Y8, Y10 + VPSUBW Y6, Y11, Y13 + VPSUBW Y0, Y12, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y8, Y8 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y12, Y12 + VMOVDQU 544(CX), Y0 + VMOVDQU 576(CX), Y1 + VMOVDQU 608(CX), Y2 + VMOVDQU 640(CX), Y3 + VMOVSLDUP Y9, Y4 + VPBLENDD $0xaa, Y4, Y7, Y4 + VPSRLQ $0x20, Y7, Y7 + VPBLENDD $0xaa, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VMOVSLDUP Y10, Y4 + VPBLENDD $0xaa, Y4, Y8, Y4 + VPSRLQ $0x20, Y8, Y8 + VPBLENDD $0xaa, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VMOVSLDUP Y13, Y4 + VPBLENDD $0xaa, Y4, Y11, Y4 + VPSRLQ $0x20, Y11, Y11 + VPBLENDD $0xaa, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VMOVSLDUP Y14, Y4 + VPBLENDD $0xaa, Y4, Y12, Y4 + VPSRLQ $0x20, Y12, Y12 + VPBLENDD $0xaa, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPMULLW Y8, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y12, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y8, Y1, Y8 + VPMULHW Y10, Y1, Y10 + VPMULHW Y12, Y3, Y12 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y8, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y12, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y8 + VPSUBW Y5, Y9, Y10 + VPSUBW Y6, Y11, Y12 + VPSUBW Y0, Y13, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y9, Y9 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y13, Y13 + VMOVDQU 800(CX), Y0 + VMOVDQU 832(CX), Y1 + VMOVDQU 864(CX), Y2 + VMOVDQU 896(CX), Y3 + VPSLLD $0x10, Y8, Y4 + VPBLENDW $0xaa, Y4, Y7, Y4 + VPSRLD $0x10, Y7, Y7 + VPBLENDW $0xaa, Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPSLLD $0x10, Y10, Y4 + VPBLENDW $0xaa, Y4, Y9, Y4 + VPSRLD $0x10, Y9, Y9 + VPBLENDW $0xaa, Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPSLLD $0x10, Y12, Y4 + VPBLENDW $0xaa, Y4, Y11, Y4 + VPSRLD $0x10, Y11, Y11 + VPBLENDW $0xaa, Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPSLLD $0x10, Y14, Y4 + VPBLENDW $0xaa, Y4, Y13, Y4 + VPSRLD $0x10, Y13, Y13 + VPBLENDW $0xaa, Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y13, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y13, Y3, Y13 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y9, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y13, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y9 + VPSUBW Y5, Y8, Y10 + VPSUBW Y6, Y11, Y13 + VPSUBW Y0, Y12, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y8, Y8 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y12, Y12 + VMOVDQU Y7, (AX) + VMOVDQU Y8, 32(AX) + VMOVDQU Y9, 64(AX) + VMOVDQU Y10, 96(AX) + VMOVDQU Y11, 128(AX) + VMOVDQU Y12, 160(AX) + VMOVDQU Y13, 192(AX) + VMOVDQU Y14, 224(AX) + VPBROADCASTW 8(CX), Y0 + VPBROADCASTW 10(CX), Y1 + VMOVDQU 256(AX), Y7 + VMOVDQU 288(AX), Y8 + VMOVDQU 320(AX), Y9 + VMOVDQU 352(AX), Y10 + VMOVDQU 384(AX), Y11 + VMOVDQU 416(AX), Y12 + VMOVDQU 448(AX), Y13 + VMOVDQU 480(AX), Y14 + VPMULLW Y11, Y0, Y2 + VPMULLW Y12, Y0, Y3 + VPMULLW Y13, Y0, Y4 + VPMULLW Y14, Y0, Y5 + VPMULHW Y11, Y1, Y11 + VPMULHW Y12, Y1, Y12 + VPMULHW Y13, Y1, Y13 + VPMULHW Y14, Y1, Y14 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y11, Y2 + VPSUBW Y3, Y12, Y3 + VPSUBW Y4, Y13, Y4 + VPSUBW Y5, Y14, Y5 + VPSUBW Y2, Y7, Y11 + VPSUBW Y3, Y8, Y12 + VPSUBW Y4, Y9, Y13 + VPSUBW Y5, Y10, Y14 + VPADDW Y2, Y7, Y7 + VPADDW Y3, Y8, Y8 + VPADDW Y4, Y9, Y9 + VPADDW Y5, Y10, Y10 + VPBROADCASTW 20(CX), Y0 + VPBROADCASTW 22(CX), Y1 + VPBROADCASTW 24(CX), Y2 + VPBROADCASTW 26(CX), Y3 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y13, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y13, Y3, Y13 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y9, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y13, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y9 + VPSUBW Y5, Y8, Y10 + VPSUBW Y6, Y11, Y13 + VPSUBW Y0, Y12, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y8, Y8 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y12, Y12 + VMOVDQU 160(CX), Y0 + VMOVDQU 192(CX), Y1 + VMOVDQU 224(CX), Y2 + VMOVDQU 256(CX), Y3 + VPERM2I128 $0x20, Y9, Y7, Y4 + VPERM2I128 $0x31, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VPERM2I128 $0x20, Y10, Y8, Y4 + VPERM2I128 $0x31, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VPERM2I128 $0x20, Y13, Y11, Y4 + VPERM2I128 $0x31, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VPERM2I128 $0x20, Y14, Y12, Y4 + VPERM2I128 $0x31, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPMULLW Y8, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y12, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y8, Y1, Y8 + VPMULHW Y10, Y1, Y10 + VPMULHW Y12, Y3, Y12 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y8, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y12, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y8 + VPSUBW Y5, Y9, Y10 + VPSUBW Y6, Y11, Y12 + VPSUBW Y0, Y13, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y9, Y9 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y13, Y13 + VMOVDQU 416(CX), Y0 + VMOVDQU 448(CX), Y1 + VMOVDQU 480(CX), Y2 + VMOVDQU 512(CX), Y3 + VPUNPCKLQDQ Y8, Y7, Y4 + VPUNPCKHQDQ Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPUNPCKLQDQ Y10, Y9, Y4 + VPUNPCKHQDQ Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPUNPCKLQDQ Y12, Y11, Y4 + VPUNPCKHQDQ Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPUNPCKLQDQ Y14, Y13, Y4 + VPUNPCKHQDQ Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y13, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y13, Y3, Y13 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y9, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y13, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y9 + VPSUBW Y5, Y8, Y10 + VPSUBW Y6, Y11, Y13 + VPSUBW Y0, Y12, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y8, Y8 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y12, Y12 + VMOVDQU 672(CX), Y0 + VMOVDQU 704(CX), Y1 + VMOVDQU 736(CX), Y2 + VMOVDQU 768(CX), Y3 + VMOVSLDUP Y9, Y4 + VPBLENDD $0xaa, Y4, Y7, Y4 + VPSRLQ $0x20, Y7, Y7 + VPBLENDD $0xaa, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VMOVSLDUP Y10, Y4 + VPBLENDD $0xaa, Y4, Y8, Y4 + VPSRLQ $0x20, Y8, Y8 + VPBLENDD $0xaa, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VMOVSLDUP Y13, Y4 + VPBLENDD $0xaa, Y4, Y11, Y4 + VPSRLQ $0x20, Y11, Y11 + VPBLENDD $0xaa, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VMOVSLDUP Y14, Y4 + VPBLENDD $0xaa, Y4, Y12, Y4 + VPSRLQ $0x20, Y12, Y12 + VPBLENDD $0xaa, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPMULLW Y8, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y12, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y8, Y1, Y8 + VPMULHW Y10, Y1, Y10 + VPMULHW Y12, Y3, Y12 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y8, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y12, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y8 + VPSUBW Y5, Y9, Y10 + VPSUBW Y6, Y11, Y12 + VPSUBW Y0, Y13, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y9, Y9 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y13, Y13 + VMOVDQU 928(CX), Y0 + VMOVDQU 960(CX), Y1 + VMOVDQU 992(CX), Y2 + VMOVDQU 1024(CX), Y3 + VPSLLD $0x10, Y8, Y4 + VPBLENDW $0xaa, Y4, Y7, Y4 + VPSRLD $0x10, Y7, Y7 + VPBLENDW $0xaa, Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPSLLD $0x10, Y10, Y4 + VPBLENDW $0xaa, Y4, Y9, Y4 + VPSRLD $0x10, Y9, Y9 + VPBLENDW $0xaa, Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPSLLD $0x10, Y12, Y4 + VPBLENDW $0xaa, Y4, Y11, Y4 + VPSRLD $0x10, Y11, Y11 + VPBLENDW $0xaa, Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPSLLD $0x10, Y14, Y4 + VPBLENDW $0xaa, Y4, Y13, Y4 + VPSRLD $0x10, Y13, Y13 + VPBLENDW $0xaa, Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULLW Y13, Y2, Y6 + VPMULLW Y14, Y2, Y0 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y13, Y3, Y13 + VPMULHW Y14, Y3, Y14 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPMULHW Y6, Y15, Y6 + VPMULHW Y0, Y15, Y0 + VPSUBW Y4, Y9, Y4 + VPSUBW Y5, Y10, Y5 + VPSUBW Y6, Y13, Y6 + VPSUBW Y0, Y14, Y0 + VPSUBW Y4, Y7, Y9 + VPSUBW Y5, Y8, Y10 + VPSUBW Y6, Y11, Y13 + VPSUBW Y0, Y12, Y14 + VPADDW Y4, Y7, Y7 + VPADDW Y5, Y8, Y8 + VPADDW Y6, Y11, Y11 + VPADDW Y0, Y12, Y12 + VMOVDQU Y7, 256(AX) + VMOVDQU Y8, 288(AX) + VMOVDQU Y9, 320(AX) + VMOVDQU Y10, 352(AX) + VMOVDQU Y11, 384(AX) + VMOVDQU Y12, 416(AX) + VMOVDQU Y13, 448(AX) + VMOVDQU Y14, 480(AX) + RET + +// func invNttAVX2(p *[256]int16) +// Requires: AVX, AVX2 +TEXT ·invNttAVX2(SB), NOSPLIT, $0-8 + MOVQ p+0(FP), AX + LEAQ ·ZetasAVX2+0(SB), CX + MOVL $0x00000d01, DX + VMOVD DX, X0 + VPBROADCASTW X0, Y15 + VMOVDQU (AX), Y7 + VMOVDQU 32(AX), Y8 + VMOVDQU 64(AX), Y9 + VMOVDQU 96(AX), Y10 + VMOVDQU 128(AX), Y11 + VMOVDQU 160(AX), Y12 + VMOVDQU 192(AX), Y13 + VMOVDQU 224(AX), Y14 + VMOVDQU 1056(CX), Y0 + VMOVDQU 1088(CX), Y1 + VMOVDQU 1120(CX), Y2 + VMOVDQU 1152(CX), Y3 + VPSUBW Y7, Y9, Y4 + VPSUBW Y8, Y10, Y5 + VPSUBW Y11, Y13, Y6 + VPADDW Y7, Y9, Y7 + VPADDW Y8, Y10, Y8 + VPADDW Y11, Y13, Y11 + VPMULLW Y4, Y0, Y9 + VPMULLW Y5, Y0, Y10 + VPSUBW Y12, Y14, Y0 + VPMULLW Y6, Y2, Y13 + VPADDW Y12, Y14, Y12 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y9, Y4, Y9 + VPSUBW Y10, Y5, Y10 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y0, Y14 + VMOVDQU 1312(CX), Y0 + VMOVDQU 1344(CX), Y1 + VMOVDQU 1376(CX), Y2 + VMOVDQU 1408(CX), Y3 + VPSLLD $0x10, Y8, Y4 + VPBLENDW $0xaa, Y4, Y7, Y4 + VPSRLD $0x10, Y7, Y7 + VPBLENDW $0xaa, Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPSLLD $0x10, Y10, Y4 + VPBLENDW $0xaa, Y4, Y9, Y4 + VPSRLD $0x10, Y9, Y9 + VPBLENDW $0xaa, Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPSLLD $0x10, Y12, Y4 + VPBLENDW $0xaa, Y4, Y11, Y4 + VPSRLD $0x10, Y11, Y11 + VPBLENDW $0xaa, Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPSLLD $0x10, Y14, Y4 + VPBLENDW $0xaa, Y4, Y13, Y4 + VPSRLD $0x10, Y13, Y13 + VPBLENDW $0xaa, Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPSUBW Y7, Y8, Y4 + VPSUBW Y9, Y10, Y5 + VPSUBW Y11, Y12, Y6 + VPADDW Y7, Y8, Y7 + VPADDW Y9, Y10, Y9 + VPADDW Y11, Y12, Y11 + VPMULLW Y4, Y0, Y8 + VPMULLW Y5, Y0, Y10 + VPSUBW Y13, Y14, Y0 + VPMULLW Y6, Y2, Y12 + VPADDW Y13, Y14, Y13 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y8, Y15, Y8 + VPMULHW Y10, Y15, Y10 + VPMULHW Y12, Y15, Y12 + VPMULHW Y14, Y15, Y14 + VPSUBW Y8, Y4, Y8 + VPSUBW Y10, Y5, Y10 + VPSUBW Y12, Y6, Y12 + VPSUBW Y14, Y0, Y14 + VMOVDQU 1568(CX), Y0 + VMOVDQU 1600(CX), Y1 + VMOVDQU 1632(CX), Y2 + VMOVDQU 1664(CX), Y3 + VMOVSLDUP Y9, Y4 + VPBLENDD $0xaa, Y4, Y7, Y4 + VPSRLQ $0x20, Y7, Y7 + VPBLENDD $0xaa, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VMOVSLDUP Y10, Y4 + VPBLENDD $0xaa, Y4, Y8, Y4 + VPSRLQ $0x20, Y8, Y8 + VPBLENDD $0xaa, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VMOVSLDUP Y13, Y4 + VPBLENDD $0xaa, Y4, Y11, Y4 + VPSRLQ $0x20, Y11, Y11 + VPBLENDD $0xaa, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VMOVSLDUP Y14, Y4 + VPBLENDD $0xaa, Y4, Y12, Y4 + VPSRLQ $0x20, Y12, Y12 + VPBLENDD $0xaa, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPSUBW Y7, Y9, Y4 + VPSUBW Y8, Y10, Y5 + VPSUBW Y11, Y13, Y6 + VPADDW Y7, Y9, Y7 + VPADDW Y8, Y10, Y8 + VPADDW Y11, Y13, Y11 + VPMULLW Y4, Y0, Y9 + VPMULLW Y5, Y0, Y10 + VPSUBW Y12, Y14, Y0 + VPMULLW Y6, Y2, Y13 + VPADDW Y12, Y14, Y12 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y9, Y4, Y9 + VPSUBW Y10, Y5, Y10 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y0, Y14 + MOVL $0x00004ebf, DX + VMOVD DX, X0 + VPBROADCASTW X0, Y4 + VPMULHW Y4, Y7, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y7, Y7 + VPMULHW Y4, Y11, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y11, Y11 + VMOVDQU 1824(CX), Y0 + VMOVDQU 1856(CX), Y1 + VMOVDQU 1888(CX), Y2 + VMOVDQU 1920(CX), Y3 + VPUNPCKLQDQ Y8, Y7, Y4 + VPUNPCKHQDQ Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPUNPCKLQDQ Y10, Y9, Y4 + VPUNPCKHQDQ Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPUNPCKLQDQ Y12, Y11, Y4 + VPUNPCKHQDQ Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPUNPCKLQDQ Y14, Y13, Y4 + VPUNPCKHQDQ Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPSUBW Y7, Y8, Y4 + VPSUBW Y9, Y10, Y5 + VPSUBW Y11, Y12, Y6 + VPADDW Y7, Y8, Y7 + VPADDW Y9, Y10, Y9 + VPADDW Y11, Y12, Y11 + VPMULLW Y4, Y0, Y8 + VPMULLW Y5, Y0, Y10 + VPSUBW Y13, Y14, Y0 + VPMULLW Y6, Y2, Y12 + VPADDW Y13, Y14, Y13 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y8, Y15, Y8 + VPMULHW Y10, Y15, Y10 + VPMULHW Y12, Y15, Y12 + VPMULHW Y14, Y15, Y14 + VPSUBW Y8, Y4, Y8 + VPSUBW Y10, Y5, Y10 + VPSUBW Y12, Y6, Y12 + VPSUBW Y14, Y0, Y14 + VPBROADCASTW 2080(CX), Y0 + VPBROADCASTW 2082(CX), Y1 + VPBROADCASTW 2084(CX), Y2 + VPBROADCASTW 2086(CX), Y3 + VPERM2I128 $0x20, Y9, Y7, Y4 + VPERM2I128 $0x31, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VPERM2I128 $0x20, Y10, Y8, Y4 + VPERM2I128 $0x31, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VPERM2I128 $0x20, Y13, Y11, Y4 + VPERM2I128 $0x31, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VPERM2I128 $0x20, Y14, Y12, Y4 + VPERM2I128 $0x31, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPSUBW Y7, Y9, Y4 + VPSUBW Y8, Y10, Y5 + VPSUBW Y11, Y13, Y6 + VPADDW Y7, Y9, Y7 + VPADDW Y8, Y10, Y8 + VPADDW Y11, Y13, Y11 + VPMULLW Y4, Y0, Y9 + VPMULLW Y5, Y0, Y10 + VPSUBW Y12, Y14, Y0 + VPMULLW Y6, Y2, Y13 + VPADDW Y12, Y14, Y12 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y9, Y4, Y9 + VPSUBW Y10, Y5, Y10 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y0, Y14 + MOVL $0x00004ebf, DX + VMOVD DX, X0 + VPBROADCASTW X0, Y4 + VPMULHW Y4, Y7, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y7, Y7 + VPMULHW Y4, Y11, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y11, Y11 + VPBROADCASTW 2096(CX), Y0 + VPBROADCASTW 2098(CX), Y1 + VPSUBW Y7, Y11, Y4 + VPSUBW Y8, Y12, Y5 + VPSUBW Y9, Y13, Y6 + VPADDW Y7, Y11, Y7 + VPADDW Y8, Y12, Y8 + VPADDW Y9, Y13, Y9 + VPMULLW Y4, Y0, Y11 + VPMULLW Y5, Y0, Y12 + VPSUBW Y10, Y14, Y2 + VPMULLW Y6, Y0, Y13 + VPADDW Y10, Y14, Y10 + VPMULLW Y2, Y0, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y1, Y6 + VPMULHW Y2, Y1, Y2 + VPMULHW Y11, Y15, Y11 + VPMULHW Y12, Y15, Y12 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y11, Y4, Y11 + VPSUBW Y12, Y5, Y12 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y2, Y14 + VMOVDQU Y7, (AX) + VMOVDQU Y8, 32(AX) + VMOVDQU Y9, 64(AX) + VMOVDQU Y10, 96(AX) + VMOVDQU Y11, 128(AX) + VMOVDQU Y12, 160(AX) + VMOVDQU Y13, 192(AX) + VMOVDQU Y14, 224(AX) + VMOVDQU 256(AX), Y7 + VMOVDQU 288(AX), Y8 + VMOVDQU 320(AX), Y9 + VMOVDQU 352(AX), Y10 + VMOVDQU 384(AX), Y11 + VMOVDQU 416(AX), Y12 + VMOVDQU 448(AX), Y13 + VMOVDQU 480(AX), Y14 + VMOVDQU 1184(CX), Y0 + VMOVDQU 1216(CX), Y1 + VMOVDQU 1248(CX), Y2 + VMOVDQU 1280(CX), Y3 + VPSUBW Y7, Y9, Y4 + VPSUBW Y8, Y10, Y5 + VPSUBW Y11, Y13, Y6 + VPADDW Y7, Y9, Y7 + VPADDW Y8, Y10, Y8 + VPADDW Y11, Y13, Y11 + VPMULLW Y4, Y0, Y9 + VPMULLW Y5, Y0, Y10 + VPSUBW Y12, Y14, Y0 + VPMULLW Y6, Y2, Y13 + VPADDW Y12, Y14, Y12 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y9, Y4, Y9 + VPSUBW Y10, Y5, Y10 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y0, Y14 + VMOVDQU 1440(CX), Y0 + VMOVDQU 1472(CX), Y1 + VMOVDQU 1504(CX), Y2 + VMOVDQU 1536(CX), Y3 + VPSLLD $0x10, Y8, Y4 + VPBLENDW $0xaa, Y4, Y7, Y4 + VPSRLD $0x10, Y7, Y7 + VPBLENDW $0xaa, Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPSLLD $0x10, Y10, Y4 + VPBLENDW $0xaa, Y4, Y9, Y4 + VPSRLD $0x10, Y9, Y9 + VPBLENDW $0xaa, Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPSLLD $0x10, Y12, Y4 + VPBLENDW $0xaa, Y4, Y11, Y4 + VPSRLD $0x10, Y11, Y11 + VPBLENDW $0xaa, Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPSLLD $0x10, Y14, Y4 + VPBLENDW $0xaa, Y4, Y13, Y4 + VPSRLD $0x10, Y13, Y13 + VPBLENDW $0xaa, Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPSUBW Y7, Y8, Y4 + VPSUBW Y9, Y10, Y5 + VPSUBW Y11, Y12, Y6 + VPADDW Y7, Y8, Y7 + VPADDW Y9, Y10, Y9 + VPADDW Y11, Y12, Y11 + VPMULLW Y4, Y0, Y8 + VPMULLW Y5, Y0, Y10 + VPSUBW Y13, Y14, Y0 + VPMULLW Y6, Y2, Y12 + VPADDW Y13, Y14, Y13 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y8, Y15, Y8 + VPMULHW Y10, Y15, Y10 + VPMULHW Y12, Y15, Y12 + VPMULHW Y14, Y15, Y14 + VPSUBW Y8, Y4, Y8 + VPSUBW Y10, Y5, Y10 + VPSUBW Y12, Y6, Y12 + VPSUBW Y14, Y0, Y14 + VMOVDQU 1696(CX), Y0 + VMOVDQU 1728(CX), Y1 + VMOVDQU 1760(CX), Y2 + VMOVDQU 1792(CX), Y3 + VMOVSLDUP Y9, Y4 + VPBLENDD $0xaa, Y4, Y7, Y4 + VPSRLQ $0x20, Y7, Y7 + VPBLENDD $0xaa, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VMOVSLDUP Y10, Y4 + VPBLENDD $0xaa, Y4, Y8, Y4 + VPSRLQ $0x20, Y8, Y8 + VPBLENDD $0xaa, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VMOVSLDUP Y13, Y4 + VPBLENDD $0xaa, Y4, Y11, Y4 + VPSRLQ $0x20, Y11, Y11 + VPBLENDD $0xaa, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VMOVSLDUP Y14, Y4 + VPBLENDD $0xaa, Y4, Y12, Y4 + VPSRLQ $0x20, Y12, Y12 + VPBLENDD $0xaa, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPSUBW Y7, Y9, Y4 + VPSUBW Y8, Y10, Y5 + VPSUBW Y11, Y13, Y6 + VPADDW Y7, Y9, Y7 + VPADDW Y8, Y10, Y8 + VPADDW Y11, Y13, Y11 + VPMULLW Y4, Y0, Y9 + VPMULLW Y5, Y0, Y10 + VPSUBW Y12, Y14, Y0 + VPMULLW Y6, Y2, Y13 + VPADDW Y12, Y14, Y12 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y9, Y4, Y9 + VPSUBW Y10, Y5, Y10 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y0, Y14 + MOVL $0x00004ebf, DX + VMOVD DX, X0 + VPBROADCASTW X0, Y4 + VPMULHW Y4, Y7, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y7, Y7 + VPMULHW Y4, Y11, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y11, Y11 + VMOVDQU 1952(CX), Y0 + VMOVDQU 1984(CX), Y1 + VMOVDQU 2016(CX), Y2 + VMOVDQU 2048(CX), Y3 + VPUNPCKLQDQ Y8, Y7, Y4 + VPUNPCKHQDQ Y8, Y7, Y8 + VMOVDQA Y4, Y7 + VPUNPCKLQDQ Y10, Y9, Y4 + VPUNPCKHQDQ Y10, Y9, Y10 + VMOVDQA Y4, Y9 + VPUNPCKLQDQ Y12, Y11, Y4 + VPUNPCKHQDQ Y12, Y11, Y12 + VMOVDQA Y4, Y11 + VPUNPCKLQDQ Y14, Y13, Y4 + VPUNPCKHQDQ Y14, Y13, Y14 + VMOVDQA Y4, Y13 + VPSUBW Y7, Y8, Y4 + VPSUBW Y9, Y10, Y5 + VPSUBW Y11, Y12, Y6 + VPADDW Y7, Y8, Y7 + VPADDW Y9, Y10, Y9 + VPADDW Y11, Y12, Y11 + VPMULLW Y4, Y0, Y8 + VPMULLW Y5, Y0, Y10 + VPSUBW Y13, Y14, Y0 + VPMULLW Y6, Y2, Y12 + VPADDW Y13, Y14, Y13 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y8, Y15, Y8 + VPMULHW Y10, Y15, Y10 + VPMULHW Y12, Y15, Y12 + VPMULHW Y14, Y15, Y14 + VPSUBW Y8, Y4, Y8 + VPSUBW Y10, Y5, Y10 + VPSUBW Y12, Y6, Y12 + VPSUBW Y14, Y0, Y14 + VPBROADCASTW 2088(CX), Y0 + VPBROADCASTW 2090(CX), Y1 + VPBROADCASTW 2092(CX), Y2 + VPBROADCASTW 2094(CX), Y3 + VPERM2I128 $0x20, Y9, Y7, Y4 + VPERM2I128 $0x31, Y9, Y7, Y9 + VMOVDQA Y4, Y7 + VPERM2I128 $0x20, Y10, Y8, Y4 + VPERM2I128 $0x31, Y10, Y8, Y10 + VMOVDQA Y4, Y8 + VPERM2I128 $0x20, Y13, Y11, Y4 + VPERM2I128 $0x31, Y13, Y11, Y13 + VMOVDQA Y4, Y11 + VPERM2I128 $0x20, Y14, Y12, Y4 + VPERM2I128 $0x31, Y14, Y12, Y14 + VMOVDQA Y4, Y12 + VPSUBW Y7, Y9, Y4 + VPSUBW Y8, Y10, Y5 + VPSUBW Y11, Y13, Y6 + VPADDW Y7, Y9, Y7 + VPADDW Y8, Y10, Y8 + VPADDW Y11, Y13, Y11 + VPMULLW Y4, Y0, Y9 + VPMULLW Y5, Y0, Y10 + VPSUBW Y12, Y14, Y0 + VPMULLW Y6, Y2, Y13 + VPADDW Y12, Y14, Y12 + VPMULLW Y0, Y2, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y3, Y6 + VPMULHW Y0, Y3, Y0 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y9, Y4, Y9 + VPSUBW Y10, Y5, Y10 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y0, Y14 + MOVL $0x00004ebf, DX + VMOVD DX, X0 + VPBROADCASTW X0, Y4 + VPMULHW Y4, Y7, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y7, Y7 + VPMULHW Y4, Y11, Y5 + VPSRAW $0x0a, Y5, Y5 + VPMULLW Y15, Y5, Y5 + VPSUBW Y5, Y11, Y11 + VPBROADCASTW 2100(CX), Y0 + VPBROADCASTW 2102(CX), Y1 + VPSUBW Y7, Y11, Y4 + VPSUBW Y8, Y12, Y5 + VPSUBW Y9, Y13, Y6 + VPADDW Y7, Y11, Y7 + VPADDW Y8, Y12, Y8 + VPADDW Y9, Y13, Y9 + VPMULLW Y4, Y0, Y11 + VPMULLW Y5, Y0, Y12 + VPSUBW Y10, Y14, Y2 + VPMULLW Y6, Y0, Y13 + VPADDW Y10, Y14, Y10 + VPMULLW Y2, Y0, Y14 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y6, Y1, Y6 + VPMULHW Y2, Y1, Y2 + VPMULHW Y11, Y15, Y11 + VPMULHW Y12, Y15, Y12 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y11, Y4, Y11 + VPSUBW Y12, Y5, Y12 + VPSUBW Y13, Y6, Y13 + VPSUBW Y14, Y2, Y14 + VMOVDQU Y7, 256(AX) + VMOVDQU Y8, 288(AX) + VMOVDQU Y9, 320(AX) + VMOVDQU Y10, 352(AX) + VMOVDQU Y11, 384(AX) + VMOVDQU Y12, 416(AX) + VMOVDQU Y13, 448(AX) + VMOVDQU Y14, 480(AX) + VPBROADCASTW 2104(CX), Y0 + VPBROADCASTW 2106(CX), Y1 + VMOVDQU (AX), Y7 + VMOVDQU 32(AX), Y8 + VMOVDQU 64(AX), Y9 + VMOVDQU 96(AX), Y10 + VMOVDQU 256(AX), Y11 + VMOVDQU 288(AX), Y12 + VMOVDQU 320(AX), Y13 + VMOVDQU 352(AX), Y14 + VPSUBW Y7, Y11, Y2 + VPSUBW Y8, Y12, Y3 + VPSUBW Y9, Y13, Y4 + VPADDW Y7, Y11, Y7 + VPADDW Y8, Y12, Y8 + VPADDW Y9, Y13, Y9 + VPMULLW Y2, Y0, Y11 + VPMULLW Y3, Y0, Y12 + VPSUBW Y10, Y14, Y5 + VPMULLW Y4, Y0, Y13 + VPADDW Y10, Y14, Y10 + VPMULLW Y5, Y0, Y14 + VPMULHW Y2, Y1, Y2 + VPMULHW Y3, Y1, Y3 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y11, Y15, Y11 + VPMULHW Y12, Y15, Y12 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y11, Y2, Y11 + VPSUBW Y12, Y3, Y12 + VPSUBW Y13, Y4, Y13 + VPSUBW Y14, Y5, Y14 + MOVL $0xffffd8a1, DX + VMOVD DX, X0 + VPBROADCASTW X0, Y0 + MOVL $0x000005a1, DX + VMOVD DX, X1 + VPBROADCASTW X1, Y1 + VPMULLW Y7, Y0, Y2 + VPMULLW Y8, Y0, Y3 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULHW Y7, Y1, Y7 + VPMULHW Y8, Y1, Y8 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y7, Y7 + VPSUBW Y3, Y8, Y8 + VPSUBW Y4, Y9, Y9 + VPSUBW Y5, Y10, Y10 + VPMULLW Y11, Y0, Y2 + VPMULLW Y12, Y0, Y3 + VPMULLW Y13, Y0, Y4 + VPMULLW Y14, Y0, Y5 + VPMULHW Y11, Y1, Y11 + VPMULHW Y12, Y1, Y12 + VPMULHW Y13, Y1, Y13 + VPMULHW Y14, Y1, Y14 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y11, Y11 + VPSUBW Y3, Y12, Y12 + VPSUBW Y4, Y13, Y13 + VPSUBW Y5, Y14, Y14 + VMOVDQU Y7, (AX) + VMOVDQU Y8, 32(AX) + VMOVDQU Y9, 64(AX) + VMOVDQU Y10, 96(AX) + VMOVDQU Y11, 256(AX) + VMOVDQU Y12, 288(AX) + VMOVDQU Y13, 320(AX) + VMOVDQU Y14, 352(AX) + VPBROADCASTW 2104(CX), Y0 + VPBROADCASTW 2106(CX), Y1 + VMOVDQU 128(AX), Y7 + VMOVDQU 160(AX), Y8 + VMOVDQU 192(AX), Y9 + VMOVDQU 224(AX), Y10 + VMOVDQU 384(AX), Y11 + VMOVDQU 416(AX), Y12 + VMOVDQU 448(AX), Y13 + VMOVDQU 480(AX), Y14 + VPSUBW Y7, Y11, Y2 + VPSUBW Y8, Y12, Y3 + VPSUBW Y9, Y13, Y4 + VPADDW Y7, Y11, Y7 + VPADDW Y8, Y12, Y8 + VPADDW Y9, Y13, Y9 + VPMULLW Y2, Y0, Y11 + VPMULLW Y3, Y0, Y12 + VPSUBW Y10, Y14, Y5 + VPMULLW Y4, Y0, Y13 + VPADDW Y10, Y14, Y10 + VPMULLW Y5, Y0, Y14 + VPMULHW Y2, Y1, Y2 + VPMULHW Y3, Y1, Y3 + VPMULHW Y4, Y1, Y4 + VPMULHW Y5, Y1, Y5 + VPMULHW Y11, Y15, Y11 + VPMULHW Y12, Y15, Y12 + VPMULHW Y13, Y15, Y13 + VPMULHW Y14, Y15, Y14 + VPSUBW Y11, Y2, Y11 + VPSUBW Y12, Y3, Y12 + VPSUBW Y13, Y4, Y13 + VPSUBW Y14, Y5, Y14 + MOVL $0xffffd8a1, CX + VMOVD CX, X0 + VPBROADCASTW X0, Y0 + MOVL $0x000005a1, CX + VMOVD CX, X1 + VPBROADCASTW X1, Y1 + VPMULLW Y7, Y0, Y2 + VPMULLW Y8, Y0, Y3 + VPMULLW Y9, Y0, Y4 + VPMULLW Y10, Y0, Y5 + VPMULHW Y7, Y1, Y7 + VPMULHW Y8, Y1, Y8 + VPMULHW Y9, Y1, Y9 + VPMULHW Y10, Y1, Y10 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y7, Y7 + VPSUBW Y3, Y8, Y8 + VPSUBW Y4, Y9, Y9 + VPSUBW Y5, Y10, Y10 + VPMULLW Y11, Y0, Y2 + VPMULLW Y12, Y0, Y3 + VPMULLW Y13, Y0, Y4 + VPMULLW Y14, Y0, Y5 + VPMULHW Y11, Y1, Y11 + VPMULHW Y12, Y1, Y12 + VPMULHW Y13, Y1, Y13 + VPMULHW Y14, Y1, Y14 + VPMULHW Y2, Y15, Y2 + VPMULHW Y3, Y15, Y3 + VPMULHW Y4, Y15, Y4 + VPMULHW Y5, Y15, Y5 + VPSUBW Y2, Y11, Y11 + VPSUBW Y3, Y12, Y12 + VPSUBW Y4, Y13, Y13 + VPSUBW Y5, Y14, Y14 + VMOVDQU Y7, 128(AX) + VMOVDQU Y8, 160(AX) + VMOVDQU Y9, 192(AX) + VMOVDQU Y10, 224(AX) + VMOVDQU Y11, 384(AX) + VMOVDQU Y12, 416(AX) + VMOVDQU Y13, 448(AX) + VMOVDQU Y14, 480(AX) + RET + +// func mulHatAVX2(p *[256]int16, a *[256]int16, b *[256]int16) +// Requires: AVX, AVX2 +TEXT ·mulHatAVX2(SB), NOSPLIT, $8-24 + MOVQ p+0(FP), AX + MOVQ a+8(FP), CX + MOVQ b+16(FP), DX + LEAQ ·ZetasAVX2+0(SB), BX + MOVL $0xfffff301, BP + VMOVD BP, X0 + VPBROADCASTW X0, Y14 + MOVL $0x00000d01, BP + VMOVD BP, X0 + VPBROADCASTW X0, Y15 + VMOVDQU (CX), Y0 + VMOVDQU 32(CX), Y1 + VMOVDQU 64(CX), Y2 + VMOVDQU 96(CX), Y3 + VMOVDQU (DX), Y4 + VMOVDQU 32(DX), Y5 + VMOVDQU 64(DX), Y6 + VMOVDQU 96(DX), Y7 + VPMULLW Y1, Y5, Y8 + VPMULLW Y0, Y4, Y9 + VPMULLW Y0, Y5, Y10 + VPMULLW Y1, Y4, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y1, Y5, Y12 + VPMULHW Y0, Y4, Y13 + VPMULHW Y0, Y5, Y0 + VPMULHW Y1, Y4, Y1 + VMOVDQA Y12, Y4 + VMOVDQA Y13, Y5 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y4, Y4 + VPSUBW Y9, Y5, Y5 + VPSUBW Y10, Y0, Y0 + VPSUBW Y11, Y1, Y1 + VMOVDQU 800(BX), Y12 + VMOVDQU 832(BX), Y13 + VPMULLW Y4, Y12, Y8 + VPMULHW Y4, Y13, Y4 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y4, Y4 + VPADDW Y4, Y5, Y4 + VPADDW Y0, Y1, Y5 + VPMULLW Y3, Y7, Y8 + VPMULLW Y2, Y6, Y9 + VPMULLW Y2, Y7, Y10 + VPMULLW Y3, Y6, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y3, Y7, Y12 + VPMULHW Y2, Y6, Y13 + VPMULHW Y2, Y7, Y2 + VPMULHW Y3, Y6, Y3 + VMOVDQA Y12, Y6 + VMOVDQA Y13, Y7 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y6, Y6 + VPSUBW Y9, Y7, Y7 + VPSUBW Y10, Y2, Y2 + VPSUBW Y11, Y3, Y3 + VMOVDQU 800(BX), Y12 + VMOVDQU 832(BX), Y13 + VPMULLW Y6, Y12, Y8 + VPMULHW Y6, Y13, Y6 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y6, Y6 + VPSUBW Y6, Y7, Y6 + VPADDW Y2, Y3, Y7 + VMOVDQU Y4, (AX) + VMOVDQU Y5, 32(AX) + VMOVDQU Y6, 64(AX) + VMOVDQU Y7, 96(AX) + VMOVDQU 128(CX), Y0 + VMOVDQU 160(CX), Y1 + VMOVDQU 192(CX), Y2 + VMOVDQU 224(CX), Y3 + VMOVDQU 128(DX), Y4 + VMOVDQU 160(DX), Y5 + VMOVDQU 192(DX), Y6 + VMOVDQU 224(DX), Y7 + VPMULLW Y1, Y5, Y8 + VPMULLW Y0, Y4, Y9 + VPMULLW Y0, Y5, Y10 + VPMULLW Y1, Y4, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y1, Y5, Y12 + VPMULHW Y0, Y4, Y13 + VPMULHW Y0, Y5, Y0 + VPMULHW Y1, Y4, Y1 + VMOVDQA Y12, Y4 + VMOVDQA Y13, Y5 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y4, Y4 + VPSUBW Y9, Y5, Y5 + VPSUBW Y10, Y0, Y0 + VPSUBW Y11, Y1, Y1 + VMOVDQU 864(BX), Y12 + VMOVDQU 896(BX), Y13 + VPMULLW Y4, Y12, Y8 + VPMULHW Y4, Y13, Y4 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y4, Y4 + VPADDW Y4, Y5, Y4 + VPADDW Y0, Y1, Y5 + VPMULLW Y3, Y7, Y8 + VPMULLW Y2, Y6, Y9 + VPMULLW Y2, Y7, Y10 + VPMULLW Y3, Y6, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y3, Y7, Y12 + VPMULHW Y2, Y6, Y13 + VPMULHW Y2, Y7, Y2 + VPMULHW Y3, Y6, Y3 + VMOVDQA Y12, Y6 + VMOVDQA Y13, Y7 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y6, Y6 + VPSUBW Y9, Y7, Y7 + VPSUBW Y10, Y2, Y2 + VPSUBW Y11, Y3, Y3 + VMOVDQU 864(BX), Y12 + VMOVDQU 896(BX), Y13 + VPMULLW Y6, Y12, Y8 + VPMULHW Y6, Y13, Y6 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y6, Y6 + VPSUBW Y6, Y7, Y6 + VPADDW Y2, Y3, Y7 + VMOVDQU Y4, 128(AX) + VMOVDQU Y5, 160(AX) + VMOVDQU Y6, 192(AX) + VMOVDQU Y7, 224(AX) + VMOVDQU 256(CX), Y0 + VMOVDQU 288(CX), Y1 + VMOVDQU 320(CX), Y2 + VMOVDQU 352(CX), Y3 + VMOVDQU 256(DX), Y4 + VMOVDQU 288(DX), Y5 + VMOVDQU 320(DX), Y6 + VMOVDQU 352(DX), Y7 + VPMULLW Y1, Y5, Y8 + VPMULLW Y0, Y4, Y9 + VPMULLW Y0, Y5, Y10 + VPMULLW Y1, Y4, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y1, Y5, Y12 + VPMULHW Y0, Y4, Y13 + VPMULHW Y0, Y5, Y0 + VPMULHW Y1, Y4, Y1 + VMOVDQA Y12, Y4 + VMOVDQA Y13, Y5 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y4, Y4 + VPSUBW Y9, Y5, Y5 + VPSUBW Y10, Y0, Y0 + VPSUBW Y11, Y1, Y1 + VMOVDQU 928(BX), Y12 + VMOVDQU 960(BX), Y13 + VPMULLW Y4, Y12, Y8 + VPMULHW Y4, Y13, Y4 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y4, Y4 + VPADDW Y4, Y5, Y4 + VPADDW Y0, Y1, Y5 + VPMULLW Y3, Y7, Y8 + VPMULLW Y2, Y6, Y9 + VPMULLW Y2, Y7, Y10 + VPMULLW Y3, Y6, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y3, Y7, Y12 + VPMULHW Y2, Y6, Y13 + VPMULHW Y2, Y7, Y2 + VPMULHW Y3, Y6, Y3 + VMOVDQA Y12, Y6 + VMOVDQA Y13, Y7 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y6, Y6 + VPSUBW Y9, Y7, Y7 + VPSUBW Y10, Y2, Y2 + VPSUBW Y11, Y3, Y3 + VMOVDQU 928(BX), Y12 + VMOVDQU 960(BX), Y13 + VPMULLW Y6, Y12, Y8 + VPMULHW Y6, Y13, Y6 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y6, Y6 + VPSUBW Y6, Y7, Y6 + VPADDW Y2, Y3, Y7 + VMOVDQU Y4, 256(AX) + VMOVDQU Y5, 288(AX) + VMOVDQU Y6, 320(AX) + VMOVDQU Y7, 352(AX) + VMOVDQU 384(CX), Y0 + VMOVDQU 416(CX), Y1 + VMOVDQU 448(CX), Y2 + VMOVDQU 480(CX), Y3 + VMOVDQU 384(DX), Y4 + VMOVDQU 416(DX), Y5 + VMOVDQU 448(DX), Y6 + VMOVDQU 480(DX), Y7 + VPMULLW Y1, Y5, Y8 + VPMULLW Y0, Y4, Y9 + VPMULLW Y0, Y5, Y10 + VPMULLW Y1, Y4, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y1, Y5, Y12 + VPMULHW Y0, Y4, Y13 + VPMULHW Y0, Y5, Y0 + VPMULHW Y1, Y4, Y1 + VMOVDQA Y12, Y4 + VMOVDQA Y13, Y5 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y4, Y4 + VPSUBW Y9, Y5, Y5 + VPSUBW Y10, Y0, Y0 + VPSUBW Y11, Y1, Y1 + VMOVDQU 992(BX), Y12 + VMOVDQU 1024(BX), Y13 + VPMULLW Y4, Y12, Y8 + VPMULHW Y4, Y13, Y4 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y4, Y4 + VPADDW Y4, Y5, Y4 + VPADDW Y0, Y1, Y5 + VPMULLW Y3, Y7, Y8 + VPMULLW Y2, Y6, Y9 + VPMULLW Y2, Y7, Y10 + VPMULLW Y3, Y6, Y11 + VPMULLW Y8, Y14, Y8 + VPMULLW Y9, Y14, Y9 + VPMULLW Y10, Y14, Y10 + VPMULLW Y11, Y14, Y11 + VPMULHW Y3, Y7, Y12 + VPMULHW Y2, Y6, Y13 + VPMULHW Y2, Y7, Y2 + VPMULHW Y3, Y6, Y3 + VMOVDQA Y12, Y6 + VMOVDQA Y13, Y7 + VPMULHW Y8, Y15, Y8 + VPMULHW Y9, Y15, Y9 + VPMULHW Y10, Y15, Y10 + VPMULHW Y11, Y15, Y11 + VPSUBW Y8, Y6, Y6 + VPSUBW Y9, Y7, Y7 + VPSUBW Y10, Y2, Y2 + VPSUBW Y11, Y3, Y3 + VMOVDQU 992(BX), Y12 + VMOVDQU 1024(BX), Y13 + VPMULLW Y6, Y12, Y8 + VPMULHW Y6, Y13, Y6 + VPMULHW Y8, Y15, Y8 + VPSUBW Y8, Y6, Y6 + VPSUBW Y6, Y7, Y6 + VPADDW Y2, Y3, Y7 + VMOVDQU Y4, 384(AX) + VMOVDQU Y5, 416(AX) + VMOVDQU Y6, 448(AX) + VMOVDQU Y7, 480(AX) + RET + +// func detangleAVX2(p *[256]int16) +// Requires: AVX, AVX2 +TEXT ·detangleAVX2(SB), NOSPLIT, $0-8 + MOVQ p+0(FP), AX + VMOVDQU (AX), Y0 + VMOVDQU 32(AX), Y1 + VMOVDQU 64(AX), Y2 + VMOVDQU 96(AX), Y3 + VMOVDQU 128(AX), Y4 + VMOVDQU 160(AX), Y5 + VMOVDQU 192(AX), Y6 + VMOVDQU 224(AX), Y7 + VPSLLD $0x10, Y1, Y8 + VPBLENDW $0xaa, Y8, Y0, Y8 + VPSRLD $0x10, Y0, Y0 + VPBLENDW $0xaa, Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPSLLD $0x10, Y3, Y8 + VPBLENDW $0xaa, Y8, Y2, Y8 + VPSRLD $0x10, Y2, Y2 + VPBLENDW $0xaa, Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPSLLD $0x10, Y5, Y8 + VPBLENDW $0xaa, Y8, Y4, Y8 + VPSRLD $0x10, Y4, Y4 + VPBLENDW $0xaa, Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPSLLD $0x10, Y7, Y8 + VPBLENDW $0xaa, Y8, Y6, Y8 + VPSRLD $0x10, Y6, Y6 + VPBLENDW $0xaa, Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VMOVSLDUP Y2, Y8 + VPBLENDD $0xaa, Y8, Y0, Y8 + VPSRLQ $0x20, Y0, Y0 + VPBLENDD $0xaa, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VMOVSLDUP Y3, Y8 + VPBLENDD $0xaa, Y8, Y1, Y8 + VPSRLQ $0x20, Y1, Y1 + VPBLENDD $0xaa, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VMOVSLDUP Y6, Y8 + VPBLENDD $0xaa, Y8, Y4, Y8 + VPSRLQ $0x20, Y4, Y4 + VPBLENDD $0xaa, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VMOVSLDUP Y7, Y8 + VPBLENDD $0xaa, Y8, Y5, Y8 + VPSRLQ $0x20, Y5, Y5 + VPBLENDD $0xaa, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VPUNPCKLQDQ Y1, Y0, Y8 + VPUNPCKHQDQ Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPUNPCKLQDQ Y3, Y2, Y8 + VPUNPCKHQDQ Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPUNPCKLQDQ Y5, Y4, Y8 + VPUNPCKHQDQ Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPUNPCKLQDQ Y7, Y6, Y8 + VPUNPCKHQDQ Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VPERM2I128 $0x20, Y2, Y0, Y8 + VPERM2I128 $0x31, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VPERM2I128 $0x20, Y3, Y1, Y8 + VPERM2I128 $0x31, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VPERM2I128 $0x20, Y6, Y4, Y8 + VPERM2I128 $0x31, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VPERM2I128 $0x20, Y7, Y5, Y8 + VPERM2I128 $0x31, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VMOVDQU Y0, (AX) + VMOVDQU Y1, 32(AX) + VMOVDQU Y2, 64(AX) + VMOVDQU Y3, 96(AX) + VMOVDQU Y4, 128(AX) + VMOVDQU Y5, 160(AX) + VMOVDQU Y6, 192(AX) + VMOVDQU Y7, 224(AX) + VMOVDQU 256(AX), Y0 + VMOVDQU 288(AX), Y1 + VMOVDQU 320(AX), Y2 + VMOVDQU 352(AX), Y3 + VMOVDQU 384(AX), Y4 + VMOVDQU 416(AX), Y5 + VMOVDQU 448(AX), Y6 + VMOVDQU 480(AX), Y7 + VPSLLD $0x10, Y1, Y8 + VPBLENDW $0xaa, Y8, Y0, Y8 + VPSRLD $0x10, Y0, Y0 + VPBLENDW $0xaa, Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPSLLD $0x10, Y3, Y8 + VPBLENDW $0xaa, Y8, Y2, Y8 + VPSRLD $0x10, Y2, Y2 + VPBLENDW $0xaa, Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPSLLD $0x10, Y5, Y8 + VPBLENDW $0xaa, Y8, Y4, Y8 + VPSRLD $0x10, Y4, Y4 + VPBLENDW $0xaa, Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPSLLD $0x10, Y7, Y8 + VPBLENDW $0xaa, Y8, Y6, Y8 + VPSRLD $0x10, Y6, Y6 + VPBLENDW $0xaa, Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VMOVSLDUP Y2, Y8 + VPBLENDD $0xaa, Y8, Y0, Y8 + VPSRLQ $0x20, Y0, Y0 + VPBLENDD $0xaa, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VMOVSLDUP Y3, Y8 + VPBLENDD $0xaa, Y8, Y1, Y8 + VPSRLQ $0x20, Y1, Y1 + VPBLENDD $0xaa, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VMOVSLDUP Y6, Y8 + VPBLENDD $0xaa, Y8, Y4, Y8 + VPSRLQ $0x20, Y4, Y4 + VPBLENDD $0xaa, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VMOVSLDUP Y7, Y8 + VPBLENDD $0xaa, Y8, Y5, Y8 + VPSRLQ $0x20, Y5, Y5 + VPBLENDD $0xaa, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VPUNPCKLQDQ Y1, Y0, Y8 + VPUNPCKHQDQ Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPUNPCKLQDQ Y3, Y2, Y8 + VPUNPCKHQDQ Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPUNPCKLQDQ Y5, Y4, Y8 + VPUNPCKHQDQ Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPUNPCKLQDQ Y7, Y6, Y8 + VPUNPCKHQDQ Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VPERM2I128 $0x20, Y2, Y0, Y8 + VPERM2I128 $0x31, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VPERM2I128 $0x20, Y3, Y1, Y8 + VPERM2I128 $0x31, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VPERM2I128 $0x20, Y6, Y4, Y8 + VPERM2I128 $0x31, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VPERM2I128 $0x20, Y7, Y5, Y8 + VPERM2I128 $0x31, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VMOVDQU Y0, 256(AX) + VMOVDQU Y1, 288(AX) + VMOVDQU Y2, 320(AX) + VMOVDQU Y3, 352(AX) + VMOVDQU Y4, 384(AX) + VMOVDQU Y5, 416(AX) + VMOVDQU Y6, 448(AX) + VMOVDQU Y7, 480(AX) + RET + +// func tangleAVX2(p *[256]int16) +// Requires: AVX, AVX2 +TEXT ·tangleAVX2(SB), NOSPLIT, $0-8 + MOVQ p+0(FP), AX + VMOVDQU (AX), Y0 + VMOVDQU 32(AX), Y1 + VMOVDQU 64(AX), Y2 + VMOVDQU 96(AX), Y3 + VMOVDQU 128(AX), Y4 + VMOVDQU 160(AX), Y5 + VMOVDQU 192(AX), Y6 + VMOVDQU 224(AX), Y7 + VPERM2I128 $0x20, Y2, Y0, Y8 + VPERM2I128 $0x31, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VPERM2I128 $0x20, Y3, Y1, Y8 + VPERM2I128 $0x31, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VPERM2I128 $0x20, Y6, Y4, Y8 + VPERM2I128 $0x31, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VPERM2I128 $0x20, Y7, Y5, Y8 + VPERM2I128 $0x31, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VPUNPCKLQDQ Y1, Y0, Y8 + VPUNPCKHQDQ Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPUNPCKLQDQ Y3, Y2, Y8 + VPUNPCKHQDQ Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPUNPCKLQDQ Y5, Y4, Y8 + VPUNPCKHQDQ Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPUNPCKLQDQ Y7, Y6, Y8 + VPUNPCKHQDQ Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VMOVSLDUP Y2, Y8 + VPBLENDD $0xaa, Y8, Y0, Y8 + VPSRLQ $0x20, Y0, Y0 + VPBLENDD $0xaa, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VMOVSLDUP Y3, Y8 + VPBLENDD $0xaa, Y8, Y1, Y8 + VPSRLQ $0x20, Y1, Y1 + VPBLENDD $0xaa, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VMOVSLDUP Y6, Y8 + VPBLENDD $0xaa, Y8, Y4, Y8 + VPSRLQ $0x20, Y4, Y4 + VPBLENDD $0xaa, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VMOVSLDUP Y7, Y8 + VPBLENDD $0xaa, Y8, Y5, Y8 + VPSRLQ $0x20, Y5, Y5 + VPBLENDD $0xaa, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VPSLLD $0x10, Y1, Y8 + VPBLENDW $0xaa, Y8, Y0, Y8 + VPSRLD $0x10, Y0, Y0 + VPBLENDW $0xaa, Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPSLLD $0x10, Y3, Y8 + VPBLENDW $0xaa, Y8, Y2, Y8 + VPSRLD $0x10, Y2, Y2 + VPBLENDW $0xaa, Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPSLLD $0x10, Y5, Y8 + VPBLENDW $0xaa, Y8, Y4, Y8 + VPSRLD $0x10, Y4, Y4 + VPBLENDW $0xaa, Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPSLLD $0x10, Y7, Y8 + VPBLENDW $0xaa, Y8, Y6, Y8 + VPSRLD $0x10, Y6, Y6 + VPBLENDW $0xaa, Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VMOVDQU Y0, (AX) + VMOVDQU Y1, 32(AX) + VMOVDQU Y2, 64(AX) + VMOVDQU Y3, 96(AX) + VMOVDQU Y4, 128(AX) + VMOVDQU Y5, 160(AX) + VMOVDQU Y6, 192(AX) + VMOVDQU Y7, 224(AX) + VMOVDQU 256(AX), Y0 + VMOVDQU 288(AX), Y1 + VMOVDQU 320(AX), Y2 + VMOVDQU 352(AX), Y3 + VMOVDQU 384(AX), Y4 + VMOVDQU 416(AX), Y5 + VMOVDQU 448(AX), Y6 + VMOVDQU 480(AX), Y7 + VPERM2I128 $0x20, Y2, Y0, Y8 + VPERM2I128 $0x31, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VPERM2I128 $0x20, Y3, Y1, Y8 + VPERM2I128 $0x31, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VPERM2I128 $0x20, Y6, Y4, Y8 + VPERM2I128 $0x31, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VPERM2I128 $0x20, Y7, Y5, Y8 + VPERM2I128 $0x31, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VPUNPCKLQDQ Y1, Y0, Y8 + VPUNPCKHQDQ Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPUNPCKLQDQ Y3, Y2, Y8 + VPUNPCKHQDQ Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPUNPCKLQDQ Y5, Y4, Y8 + VPUNPCKHQDQ Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPUNPCKLQDQ Y7, Y6, Y8 + VPUNPCKHQDQ Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VMOVSLDUP Y2, Y8 + VPBLENDD $0xaa, Y8, Y0, Y8 + VPSRLQ $0x20, Y0, Y0 + VPBLENDD $0xaa, Y2, Y0, Y2 + VMOVDQA Y8, Y0 + VMOVSLDUP Y3, Y8 + VPBLENDD $0xaa, Y8, Y1, Y8 + VPSRLQ $0x20, Y1, Y1 + VPBLENDD $0xaa, Y3, Y1, Y3 + VMOVDQA Y8, Y1 + VMOVSLDUP Y6, Y8 + VPBLENDD $0xaa, Y8, Y4, Y8 + VPSRLQ $0x20, Y4, Y4 + VPBLENDD $0xaa, Y6, Y4, Y6 + VMOVDQA Y8, Y4 + VMOVSLDUP Y7, Y8 + VPBLENDD $0xaa, Y8, Y5, Y8 + VPSRLQ $0x20, Y5, Y5 + VPBLENDD $0xaa, Y7, Y5, Y7 + VMOVDQA Y8, Y5 + VPSLLD $0x10, Y1, Y8 + VPBLENDW $0xaa, Y8, Y0, Y8 + VPSRLD $0x10, Y0, Y0 + VPBLENDW $0xaa, Y1, Y0, Y1 + VMOVDQA Y8, Y0 + VPSLLD $0x10, Y3, Y8 + VPBLENDW $0xaa, Y8, Y2, Y8 + VPSRLD $0x10, Y2, Y2 + VPBLENDW $0xaa, Y3, Y2, Y3 + VMOVDQA Y8, Y2 + VPSLLD $0x10, Y5, Y8 + VPBLENDW $0xaa, Y8, Y4, Y8 + VPSRLD $0x10, Y4, Y4 + VPBLENDW $0xaa, Y5, Y4, Y5 + VMOVDQA Y8, Y4 + VPSLLD $0x10, Y7, Y8 + VPBLENDW $0xaa, Y8, Y6, Y8 + VPSRLD $0x10, Y6, Y6 + VPBLENDW $0xaa, Y7, Y6, Y7 + VMOVDQA Y8, Y6 + VMOVDQU Y0, 256(AX) + VMOVDQU Y1, 288(AX) + VMOVDQU Y2, 320(AX) + VMOVDQU Y3, 352(AX) + VMOVDQU Y4, 384(AX) + VMOVDQU Y5, 416(AX) + VMOVDQU Y6, 448(AX) + VMOVDQU Y7, 480(AX) + RET + +// func barrettReduceAVX2(p *[256]int16) +// Requires: AVX, AVX2 +TEXT ·barrettReduceAVX2(SB), NOSPLIT, $0-8 + MOVQ p+0(FP), AX + MOVL $0x00000d01, CX + VMOVD CX, X0 + VPBROADCASTW X0, Y9 + MOVL $0x00004ebf, CX + VMOVD CX, X0 + VPBROADCASTW X0, Y8 + VMOVDQU (AX), Y0 + VMOVDQU 32(AX), Y1 + VMOVDQU 64(AX), Y2 + VMOVDQU 96(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VMOVDQU Y0, (AX) + VMOVDQU Y1, 32(AX) + VMOVDQU Y2, 64(AX) + VMOVDQU Y3, 96(AX) + VMOVDQU 128(AX), Y0 + VMOVDQU 160(AX), Y1 + VMOVDQU 192(AX), Y2 + VMOVDQU 224(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VMOVDQU Y0, 128(AX) + VMOVDQU Y1, 160(AX) + VMOVDQU Y2, 192(AX) + VMOVDQU Y3, 224(AX) + VMOVDQU 256(AX), Y0 + VMOVDQU 288(AX), Y1 + VMOVDQU 320(AX), Y2 + VMOVDQU 352(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VMOVDQU Y0, 256(AX) + VMOVDQU Y1, 288(AX) + VMOVDQU Y2, 320(AX) + VMOVDQU Y3, 352(AX) + VMOVDQU 384(AX), Y0 + VMOVDQU 416(AX), Y1 + VMOVDQU 448(AX), Y2 + VMOVDQU 480(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VMOVDQU Y0, 384(AX) + VMOVDQU Y1, 416(AX) + VMOVDQU Y2, 448(AX) + VMOVDQU Y3, 480(AX) + RET + +// func normalizeAVX2(p *[256]int16) +// Requires: AVX, AVX2 +TEXT ·normalizeAVX2(SB), NOSPLIT, $0-8 + MOVQ p+0(FP), AX + MOVL $0x00000d01, CX + VMOVD CX, X0 + VPBROADCASTW X0, Y9 + MOVL $0x00004ebf, CX + VMOVD CX, X0 + VPBROADCASTW X0, Y8 + VMOVDQU (AX), Y0 + VMOVDQU 32(AX), Y1 + VMOVDQU 64(AX), Y2 + VMOVDQU 96(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VPSUBW Y9, Y0, Y0 + VPSUBW Y9, Y1, Y1 + VPSUBW Y9, Y2, Y2 + VPSUBW Y9, Y3, Y3 + VPSRAW $0x0f, Y0, Y4 + VPSRAW $0x0f, Y1, Y5 + VPSRAW $0x0f, Y2, Y6 + VPSRAW $0x0f, Y3, Y7 + VPAND Y4, Y9, Y4 + VPAND Y5, Y9, Y5 + VPAND Y6, Y9, Y6 + VPAND Y7, Y9, Y7 + VPADDW Y0, Y4, Y0 + VPADDW Y1, Y5, Y1 + VPADDW Y2, Y6, Y2 + VPADDW Y3, Y7, Y3 + VMOVDQU Y0, (AX) + VMOVDQU Y1, 32(AX) + VMOVDQU Y2, 64(AX) + VMOVDQU Y3, 96(AX) + VMOVDQU 128(AX), Y0 + VMOVDQU 160(AX), Y1 + VMOVDQU 192(AX), Y2 + VMOVDQU 224(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VPSUBW Y9, Y0, Y0 + VPSUBW Y9, Y1, Y1 + VPSUBW Y9, Y2, Y2 + VPSUBW Y9, Y3, Y3 + VPSRAW $0x0f, Y0, Y4 + VPSRAW $0x0f, Y1, Y5 + VPSRAW $0x0f, Y2, Y6 + VPSRAW $0x0f, Y3, Y7 + VPAND Y4, Y9, Y4 + VPAND Y5, Y9, Y5 + VPAND Y6, Y9, Y6 + VPAND Y7, Y9, Y7 + VPADDW Y0, Y4, Y0 + VPADDW Y1, Y5, Y1 + VPADDW Y2, Y6, Y2 + VPADDW Y3, Y7, Y3 + VMOVDQU Y0, 128(AX) + VMOVDQU Y1, 160(AX) + VMOVDQU Y2, 192(AX) + VMOVDQU Y3, 224(AX) + VMOVDQU 256(AX), Y0 + VMOVDQU 288(AX), Y1 + VMOVDQU 320(AX), Y2 + VMOVDQU 352(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VPSUBW Y9, Y0, Y0 + VPSUBW Y9, Y1, Y1 + VPSUBW Y9, Y2, Y2 + VPSUBW Y9, Y3, Y3 + VPSRAW $0x0f, Y0, Y4 + VPSRAW $0x0f, Y1, Y5 + VPSRAW $0x0f, Y2, Y6 + VPSRAW $0x0f, Y3, Y7 + VPAND Y4, Y9, Y4 + VPAND Y5, Y9, Y5 + VPAND Y6, Y9, Y6 + VPAND Y7, Y9, Y7 + VPADDW Y0, Y4, Y0 + VPADDW Y1, Y5, Y1 + VPADDW Y2, Y6, Y2 + VPADDW Y3, Y7, Y3 + VMOVDQU Y0, 256(AX) + VMOVDQU Y1, 288(AX) + VMOVDQU Y2, 320(AX) + VMOVDQU Y3, 352(AX) + VMOVDQU 384(AX), Y0 + VMOVDQU 416(AX), Y1 + VMOVDQU 448(AX), Y2 + VMOVDQU 480(AX), Y3 + VPMULHW Y8, Y0, Y4 + VPMULHW Y8, Y1, Y5 + VPMULHW Y8, Y2, Y6 + VPMULHW Y8, Y3, Y7 + VPSRAW $0x0a, Y4, Y4 + VPSRAW $0x0a, Y5, Y5 + VPSRAW $0x0a, Y6, Y6 + VPSRAW $0x0a, Y7, Y7 + VPMULLW Y9, Y4, Y4 + VPMULLW Y9, Y5, Y5 + VPMULLW Y9, Y6, Y6 + VPMULLW Y9, Y7, Y7 + VPSUBW Y4, Y0, Y0 + VPSUBW Y5, Y1, Y1 + VPSUBW Y6, Y2, Y2 + VPSUBW Y7, Y3, Y3 + VPSUBW Y9, Y0, Y0 + VPSUBW Y9, Y1, Y1 + VPSUBW Y9, Y2, Y2 + VPSUBW Y9, Y3, Y3 + VPSRAW $0x0f, Y0, Y4 + VPSRAW $0x0f, Y1, Y5 + VPSRAW $0x0f, Y2, Y6 + VPSRAW $0x0f, Y3, Y7 + VPAND Y4, Y9, Y4 + VPAND Y5, Y9, Y5 + VPAND Y6, Y9, Y6 + VPAND Y7, Y9, Y7 + VPADDW Y0, Y4, Y0 + VPADDW Y1, Y5, Y1 + VPADDW Y2, Y6, Y2 + VPADDW Y3, Y7, Y3 + VMOVDQU Y0, 384(AX) + VMOVDQU Y1, 416(AX) + VMOVDQU Y2, 448(AX) + VMOVDQU Y3, 480(AX) + RET diff --git a/src/circl/pke/kyber/internal/common/field.go b/src/circl/pke/kyber/internal/common/field.go new file mode 100644 index 00000000000..33744dff73f --- /dev/null +++ b/src/circl/pke/kyber/internal/common/field.go @@ -0,0 +1,74 @@ +package common + +// Given -2¹⁵ q ≤ x < 2¹⁵ q, returns -q < y < q with x 2⁻¹⁶ = y (mod q). +func montReduce(x int32) int16 { + // This is Montgomery reduction with R=2¹⁶. + // + // Note gcd(2¹⁶, q) = 1 as q is prime. Write q' := 62209 = q⁻¹ mod R. + // First we compute + // + // m := ((x mod R) q') mod R + // = x q' mod R + // = int16(x q') + // = int16(int32(x) * int32(q')) + // + // Note that x q' might be as big as 2³² and could overflow the int32 + // multiplication in the last line. However for any int32s a and b, + // we have int32(int64(a)*int64(b)) = int32(a*b) and so the result is ok. + m := int16(x * 62209) + + // Note that x - m q is divisable by R; indeed modulo R we have + // + // x - m q ≡ x - x q' q ≡ x - x q⁻¹ q ≡ x - x = 0. + // + // We return y := (x - m q) / R. Note that y is indeed correct as + // modulo q we have + // + // y ≡ x R⁻¹ - m q R⁻¹ = x R⁻¹ + // + // and as both 2¹⁵ q ≤ m q, x < 2¹⁵ q, we have + // 2¹⁶ q ≤ x - m q < 2¹⁶ and so q ≤ (x - m q) / R < q as desired. + return int16(uint32(x-int32(m)*int32(Q)) >> 16) +} + +// Given any x, returns x R mod q where R=2¹⁶. +func toMont(x int16) int16 { + // Note |1353 x| ≤ 1353 2¹⁵ ≤ 13318 q ≤ 2¹⁵ q and so we're within + // the bounds of montReduce. + return montReduce(int32(x) * 1353) // 1353 = R² mod q. +} + +// Given any x, compute 0 ≤ y ≤ q with x = y (mod q). +// +// Beware: we might have barrettReduce(x) = q ≠ 0 for some x. In fact, +// this happens if and only if x = -nq for some positive integer n. +func barrettReduce(x int16) int16 { + // This is standard Barrett reduction. + // + // For any x we have x mod q = x - ⌊x/q⌋ q. We will use 20159/2²⁶ as + // an approximation of 1/q. Note that 0 ≤ 20159/2²⁶ - 1/q ≤ 0.135/2²⁶ + // and so | x 20156/2²⁶ - x/q | ≤ 2⁻¹⁰ for |x| ≤ 2¹⁶. For all x + // not a multiple of q, the number x/q is further than 1/q from any integer + // and so ⌊x 20156/2²⁶⌋ = ⌊x/q⌋. If x is a multiple of q and x is positive, + // then x 20156/2²⁶ is larger than x/q so ⌊x 20156/2²⁶⌋ = ⌊x/q⌋ as well. + // Finally, if x is negative multiple of q, then ⌊x 20156/2²⁶⌋ = ⌊x/q⌋-1. + // Thus + // [ q if x=-nq for pos. integer n + // x - ⌊x 20156/2²⁶⌋ q = [ + // [ x mod q otherwise + // + // To compute actually compute this, note that + // + // ⌊x 20156/2²⁶⌋ = (20159 x) >> 26. + return x - int16((int32(x)*20159)>>26)*Q +} + +// Returns x if x < q and x - q otherwise. Assumes x ≥ -29439. +func csubq(x int16) int16 { + x -= Q // no overflow due to assumption x ≥ -29439. + // If x is positive, then x >> 15 = 0. If x is negative, + // then uint16(x >> 15) = 2¹⁶-1. So this will add back in q + // if x was smaller than q. + x += (x >> 15) & Q + return x +} diff --git a/src/circl/pke/kyber/internal/common/field_test.go b/src/circl/pke/kyber/internal/common/field_test.go new file mode 100644 index 00000000000..db2e4ebd105 --- /dev/null +++ b/src/circl/pke/kyber/internal/common/field_test.go @@ -0,0 +1,86 @@ +package common + +import ( + "flag" + mathRand "math/rand" + "testing" +) + +var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests") + +func modQ32(x int32) int16 { + y := int16(x % int32(Q)) + if y < 0 { + y += Q + } + return y +} + +func TestBarrettReduceFull(t *testing.T) { + if !*runVeryLongTest { + t.SkipNow() + } + for x := -1 << 15; x <= 1<<15; x++ { + y1 := barrettReduce(int16(x)) + y2 := int16(x) % Q + if y2 < 0 { + y2 += Q + } + if x < 0 && int16(-x)%Q == 0 { + y1 -= Q + } + if y1 != y2 { + t.Fatalf("%d %d %d", x, y1, y2) + } + } +} + +func TestMontReduce(t *testing.T) { + for i := 0; i < 1000; i++ { + x := mathRand.Int31n(int32(Q)*(1<<16)) - int32(Q)*(1<<15) + y := montReduce(x) + if modQ32(x) != modQ32(int32(y)*(1<<16)) { + t.Fatalf("%d", x) + } + } +} + +func TestToMontFull(t *testing.T) { + if !*runVeryLongTest { + t.SkipNow() + } + for x := -(1 << 15); x < 1<<15; x++ { + y := toMont(int16(x)) + if modQ32(int32(y)) != modQ32(int32(x*2285)) { + t.Fatalf("%d", x) + } + } +} + +func TestMontReduceFull(t *testing.T) { + if !*runVeryLongTest { + t.SkipNow() + } + for x := -int32(Q) * (1 << 15); x <= int32(Q)*(1<<15); x++ { + y := montReduce(x) + if modQ32(x) != modQ32(int32(y)*(1<<16)) { + t.Fatalf("%d", x) + } + } +} + +func TestCSubQFull(t *testing.T) { + if !*runVeryLongTest { + t.SkipNow() + } + for x := -29439; x < 1<<15; x++ { + y1 := csubq(int16(x)) + y2 := x + if int16(x) >= Q { + y2 -= int(Q) + } + if y1 != int16(y2) { + t.Fatalf("%d", x) + } + } +} diff --git a/src/circl/pke/kyber/internal/common/generic.go b/src/circl/pke/kyber/internal/common/generic.go new file mode 100644 index 00000000000..a9c85f59822 --- /dev/null +++ b/src/circl/pke/kyber/internal/common/generic.go @@ -0,0 +1,76 @@ +// +build !amd64 + +package common + +// Sets p to a + b. Does not normalize coefficients. +func (p *Poly) Add(a, b *Poly) { + p.addGeneric(a, b) +} + +// Sets p to a - b. Does not normalize coefficients. +func (p *Poly) Sub(a, b *Poly) { + p.subGeneric(a, b) +} + +// Executes an in-place forward "NTT" on p. +// +// Assumes the coefficients are in absolute value ≤q. The resulting +// coefficients are in absolute value ≤7q. If the input is in Montgomery +// form, then the result is in Montgomery form and so (by linearity of the NTT) +// if the input is in regular form, then the result is also in regular form. +// The order of coefficients will be "tangled". These can be put back into +// their proper order by calling Detangle(). +func (p *Poly) NTT() { + p.nttGeneric() +} + +// Executes an in-place inverse "NTT" on p and multiply by the Montgomery +// factor R. +// +// Requires coefficients to be in "tangled" order, see Tangle(). +// Assumes the coefficients are in absolute value ≤q. The resulting +// coefficients are in absolute value ≤q. If the input is in Montgomery +// form, then the result is in Montgomery form and so (by linearity) +// if the input is in regular form, then the result is also in regular form. +func (p *Poly) InvNTT() { + p.invNTTGeneric() +} + +// Sets p to the "pointwise" multiplication of a and b. +// +// That is: InvNTT(p) = InvNTT(a) * InvNTT(b). Assumes a and b are in +// Montgomery form. Products between coefficients of a and b must be strictly +// bounded in absolute value by 2¹⁵q. p will be in Montgomery form and +// bounded in absolute value by 2q. +// +// Requires a and b to be in "tangled" order, see Tangle(). p will be in +// tangled order as well. +func (p *Poly) MulHat(a, b *Poly) { + p.mulHatGeneric(a, b) +} + +// Puts p into the right form to be used with (among others) InvNTT(). +func (p *Poly) Tangle() { + // In the generic implementation there is no advantage to using a + // different order, so we use the standard order everywhere. +} + +// Puts p back into standard form. +func (p *Poly) Detangle() { + // In the generic implementation there is no advantage to using a + // different order, so we use the standard order everywhere. +} + +// Almost normalizes coefficients. +// +// Ensures each coefficient is in {0, …, q}. +func (p *Poly) BarrettReduce() { + p.barrettReduceGeneric() +} + +// Normalizes coefficients. +// +// Ensures each coefficient is in {0, …, q-1}. +func (p *Poly) Normalize() { + p.normalizeGeneric() +} diff --git a/src/circl/pke/kyber/internal/common/ntt.go b/src/circl/pke/kyber/internal/common/ntt.go new file mode 100644 index 00000000000..b6c1f7405fd --- /dev/null +++ b/src/circl/pke/kyber/internal/common/ntt.go @@ -0,0 +1,193 @@ +package common + +// Zetas lists precomputed powers of the primitive root of unity in +// Montgomery representation used for the NTT: +// +// Zetas[i] = ζᵇʳᵛ⁽ⁱ⁾ R mod q +// +// where ζ = 17, brv(i) is the bitreversal of a 7-bit number and R=2¹⁶ mod q. +// +// The following Python code generates the Zetas arrays: +// +// q = 13*2**8 + 1; zeta = 17 +// R = 2**16 % q # Montgomery const. +// def brv(x): return int(''.join(reversed(bin(x)[2:].zfill(7))),2) +// print([(pow(zeta, brv(i), q)*R)%q for i in range(128)]) +var Zetas = [128]int16{ + 2285, 2571, 2970, 1812, 1493, 1422, 287, 202, 3158, 622, 1577, 182, + 962, 2127, 1855, 1468, 573, 2004, 264, 383, 2500, 1458, 1727, 3199, + 2648, 1017, 732, 608, 1787, 411, 3124, 1758, 1223, 652, 2777, 1015, + 2036, 1491, 3047, 1785, 516, 3321, 3009, 2663, 1711, 2167, 126, + 1469, 2476, 3239, 3058, 830, 107, 1908, 3082, 2378, 2931, 961, 1821, + 2604, 448, 2264, 677, 2054, 2226, 430, 555, 843, 2078, 871, 1550, + 105, 422, 587, 177, 3094, 3038, 2869, 1574, 1653, 3083, 778, 1159, + 3182, 2552, 1483, 2727, 1119, 1739, 644, 2457, 349, 418, 329, 3173, + 3254, 817, 1097, 603, 610, 1322, 2044, 1864, 384, 2114, 3193, 1218, + 1994, 2455, 220, 2142, 1670, 2144, 1799, 2051, 794, 1819, 2475, + 2459, 478, 3221, 3021, 996, 991, 958, 1869, 1522, 1628, +} + +// InvNTTReductions keeps track of which coefficients to apply Barrett +// reduction to in Poly.InvNTT(). +// +// Generated in a lazily: once a butterfly is computed which is about to +// overflow the int16, the largest coefficient is reduced. If that is +// not enough, the other coefficient is reduced as well. +// +// This is actually optimal, as proven in https://eprint.iacr.org/2020/1377.pdf +var InvNTTReductions = [...]int{ + -1, // after layer 1 + -1, // after layer 2 + 16, 17, 48, 49, 80, 81, 112, 113, 144, 145, 176, 177, 208, 209, 240, + 241, -1, // after layer 3 + 0, 1, 32, 33, 34, 35, 64, 65, 96, 97, 98, 99, 128, 129, 160, 161, 162, 163, + 192, 193, 224, 225, 226, 227, -1, // after layer 4 + 2, 3, 66, 67, 68, 69, 70, 71, 130, 131, 194, 195, 196, 197, 198, + 199, -1, // after layer 5 + 4, 5, 6, 7, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, + 143, -1, // after layer 6 + -1, // after layer 7 +} + +// Executes an in-place forward "NTT" on p. +// +// Assumes the coefficients are in absolute value ≤q. The resulting +// coefficients are in absolute value ≤7q. If the input is in Montgomery +// form, then the result is in Montgomery form and so (by linearity of the NTT) +// if the input is in regular form, then the result is also in regular form. +// The order of coefficients will be "tangled". These can be put back into +// their proper order by calling Detangle(). +func (p *Poly) nttGeneric() { + // Note that ℤ_q does not have a primitive 512ᵗʰ root of unity (as 512 + // does not divide into q) and so we cannot do a regular NTT. ℤ_q + // does have a primitive 256ᵗʰ root of unity, the smallest of which + // is ζ := 17. + // + // Recall that our base ring R := ℤ_q[x] / (x²⁵⁶ + 1). The polynomial + // x²⁵⁶+1 will not split completely (as its roots would be 512ᵗʰ roots + // of unity.) However, it does split almost (using ζ¹²⁸ = -1): + // + // x²⁵⁶ + 1 = (x²)¹²⁸ - ζ¹²⁸ + // = ((x²)⁶⁴ - ζ⁶⁴)((x²)⁶⁴ + ζ⁶⁴) + // = ((x²)³² - ζ³²)((x²)³² + ζ³²)((x²)³² - ζ⁹⁶)((x²)³² + ζ⁹⁶) + // ⋮ + // = (x² - ζ)(x² + ζ)(x² - ζ⁶⁵)(x² + ζ⁶⁵) … (x² + ζ¹²⁷) + // + // Note that the powers of ζ that appear (from th second line down) are + // in binary + // + // 010000 110000 + // 001000 101000 011000 111000 + // 000100 100100 010100 110100 001100 101100 011100 111100 + // … + // + // That is: brv(2), brv(3), brv(4), …, where brv(x) denotes the 7-bit + // bitreversal of x. These powers of ζ are given by the Zetas array. + // + // The polynomials x² ± ζⁱ are irreducible and coprime, hence by + // the Chinese Remainder Theorem we know + // + // ℤ_q[x]/(x²⁵⁶+1) → ℤ_q[x]/(x²-ζ) x … x ℤ_q[x]/(x²+ζ¹²⁷) + // + // given by a ↦ ( a mod x²-z, …, a mod x²+z¹²⁷ ) + // is an isomorphism, which is the "NTT". It can be efficiently computed by + // + // + // a ↦ ( a mod (x²)⁶⁴ - ζ⁶⁴, a mod (x²)⁶⁴ + ζ⁶⁴ ) + // ↦ ( a mod (x²)³² - ζ³², a mod (x²)³² + ζ³², + // a mod (x²)⁹⁶ - ζ⁹⁶, a mod (x²)⁹⁶ + ζ⁹⁶ ) + // + // et cetera + // + // If N was 8 then this can be pictured in the following diagram: + // + // https://cnx.org/resources/17ee4dfe517a6adda05377b25a00bf6e6c93c334/File0026.png + // + // Each cross is a Cooley-Tukey butterfly: it's the map + // + // (a, b) ↦ (a + ζ, a - ζ) + // + // for the appropriate power ζ for that column and row group. + + k := 0 // Index into Zetas + + // l runs effectively over the columns in the diagram above; it is half the + // height of a row group, i.e. the number of butterflies in each row group. + // In the diagram above it would be 4, 2, 1. + for l := N / 2; l > 1; l >>= 1 { + // On the nᵗʰ iteration of the l-loop, the absolute value of the + // coefficients are bounded by nq. + + // offset effectively loops over the row groups in this column; it is + // the first row in the row group. + for offset := 0; offset < N-l; offset += 2 * l { + k++ + zeta := int32(Zetas[k]) + + // j loops over each butterfly in the row group. + for j := offset; j < offset+l; j++ { + t := montReduce(zeta * int32(p[j+l])) + p[j+l] = p[j] - t + p[j] += t + } + } + } +} + +// Executes an in-place inverse "NTT" on p and multiply by the Montgomery +// factor R. +// +// Requires coefficients to be in "tangled" order, see Tangle(). +// Assumes the coefficients are in absolute value ≤q. The resulting +// coefficients are in absolute value ≤q. If the input is in Montgomery +// form, then the result is in Montgomery form and so (by linearity) +// if the input is in regular form, then the result is also in regular form. +func (p *Poly) invNTTGeneric() { + k := 127 // Index into Zetas + r := -1 // Index into InvNTTReductions. + + // We basically do the oppposite of NTT, but postpone dividing by 2 in the + // inverse of the Cooley-Tukey butterfly and accumulate that into a big + // division by 2⁷ at the end. See the comments in the NTT() function. + + for l := 2; l < N; l <<= 1 { + for offset := 0; offset < N-l; offset += 2 * l { + // As we're inverting, we need powers of ζ⁻¹ (instead of ζ). + // To be precise, we need ζᵇʳᵛ⁽ᵏ⁾⁻¹²⁸. However, as ζ⁻¹²⁸ = -1, + // we can use the existing Zetas table instead of + // keeping a separate InvZetas table as in Dilithium. + + minZeta := int32(Zetas[k]) + k-- + + for j := offset; j < offset+l; j++ { + // Gentleman-Sande butterfly: (a, b) ↦ (a + b, ζ(a-b)) + t := p[j+l] - p[j] + p[j] += p[j+l] + p[j+l] = montReduce(minZeta * int32(t)) + + // Note that if we had |a| < αq and |b| < βq before the + // butterfly, then now we have |a| < (α+β)q and |b| < q. + } + } + + // We let the InvNTTReductions instruct us which coefficients to + // Barrett reduce. See TestInvNTTReductions, which tests whether + // there is an overflow. + for { + r++ + i := InvNTTReductions[r] + if i < 0 { + break + } + p[i] = barrettReduce(p[i]) + } + } + + for j := 0; j < N; j++ { + // Note 1441 = (128)⁻¹ R². The coefficients are bounded by 9q, so + // as 1441 * 9 ≈ 2¹⁴ < 2¹⁵, we're within the required bounds + // for montReduce(). + p[j] = montReduce(1441 * int32(p[j])) + } +} diff --git a/src/circl/pke/kyber/internal/common/ntt_test.go b/src/circl/pke/kyber/internal/common/ntt_test.go new file mode 100644 index 00000000000..10ad08dbf56 --- /dev/null +++ b/src/circl/pke/kyber/internal/common/ntt_test.go @@ -0,0 +1,142 @@ +package common + +import ( + mathRand "math/rand" + "testing" +) + +func BenchmarkNTT(b *testing.B) { + var a Poly + for i := 0; i < b.N; i++ { + a.NTT() + } +} + +func BenchmarkNTTGeneric(b *testing.B) { + var a Poly + for i := 0; i < b.N; i++ { + a.nttGeneric() + } +} + +func BenchmarkInvNTT(b *testing.B) { + var a Poly + for i := 0; i < b.N; i++ { + a.InvNTT() + } +} + +func BenchmarkInvNTTGeneric(b *testing.B) { + var a Poly + for i := 0; i < b.N; i++ { + a.invNTTGeneric() + } +} + +func (p *Poly) Rand() { + for i := 0; i < N; i++ { + p[i] = int16(mathRand.Intn(int(Q))) + } +} + +func (p *Poly) RandAbsLeQ() { + for i := 0; i < N; i++ { + p[i] = int16(mathRand.Intn(int(2*Q))) - Q + } +} + +func TestNTTAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var p, q1, q2 Poly + p.RandAbsLeQ() + q1 = p + q2 = p + q1.NTT() + q1.Detangle() + q2.nttGeneric() + if q1 != q2 { + t.Fatalf("NTT(%v) = \n%v \n!= %v", p, q2, q1) + } + } +} + +func TestInvNTTAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var p, q1, q2 Poly + p.RandAbsLeQ() + q1 = p + q2 = p + q1.Tangle() + q1.InvNTT() + q2.invNTTGeneric() + + q1.Normalize() + q2.Normalize() + + if q1 != q2 { + t.Fatalf("InvNTT(%v) = \n%v \n!= %v", p, q2, q1) + } + } +} + +func TestNTT(t *testing.T) { + for k := 0; k < 1000; k++ { + var p, q Poly + p.RandAbsLeQ() + q = p + q.Normalize() + p.NTT() + for i := 0; i < N; i++ { + if p[i] > 7*Q || 7*Q < p[i] { + t.Fatal() + } + } + p.Normalize() + p.InvNTT() + for i := 0; i < N; i++ { + if p[i] > Q || p[i] < -Q { + t.Fatal() + } + } + p.Normalize() + for i := 0; i < N; i++ { + if int32(p[i]) != (int32(q[i])*(1<<16))%int32(Q) { + t.Fatal() + } + } + } +} + +func TestInvNTTReductions(t *testing.T) { + // Simulates bounds on coefficients in InvNTT. + + xs := [256]int{} + for i := 0; i < 256; i++ { + xs[i] = 1 + } + + r := -1 + for layer := 1; layer < 8; layer++ { + w := 1 << uint(layer) + i := 0 + for i+w < 256 { + xs[i] = xs[i] + xs[i+w] + if xs[i] > 9 { + t.Fatal() + } + xs[i+w] = 1 + i++ + if i%w == 0 { + i += w + } + } + for { + r++ + i := InvNTTReductions[r] + if i < 0 { + break + } + xs[i] = 1 + } + } +} diff --git a/src/circl/pke/kyber/internal/common/params.go b/src/circl/pke/kyber/internal/common/params.go new file mode 100644 index 00000000000..8e2bc85e1ec --- /dev/null +++ b/src/circl/pke/kyber/internal/common/params.go @@ -0,0 +1,22 @@ +package common + +import ( + "circl/pke/kyber/internal/common/params" +) + +const ( + // Q is the parameter q ≡ 3329 = 2¹¹ + 2¹⁰ + 2⁸ + 1. + Q = params.Q + + // N is the parameter N: the length of the polynomials + N = params.N + + // PolySize is the size of a packed polynomial. + PolySize = params.PolySize + + // PlaintextSize is the size of the plaintext + PlaintextSize = params.PlaintextSize + + // Eta2 is the parameter η₂ + Eta2 = params.Eta2 +) diff --git a/src/circl/pke/kyber/internal/common/params/params.go b/src/circl/pke/kyber/internal/common/params/params.go new file mode 100644 index 00000000000..f7fe31ab521 --- /dev/null +++ b/src/circl/pke/kyber/internal/common/params/params.go @@ -0,0 +1,21 @@ +package params + +// We put these parameters in a separate package so that the Go code, +// such as asm/src.go, that generates assembler can import it. + +const ( + // Q is the parameter q ≡ 3329 = 2¹¹ + 2¹⁰ + 2⁸ + 1. + Q int16 = 3329 + + // N is the parameter N: the length of the polynomials + N int = 256 + + // PolySize is the size of a packed polynomial. + PolySize int = 384 + + // PlaintextSize is the size of the plaintext + PlaintextSize = 32 + + // Eta2 is the parameter η₂ + Eta2 = 2 +) diff --git a/src/circl/pke/kyber/internal/common/poly.go b/src/circl/pke/kyber/internal/common/poly.go new file mode 100644 index 00000000000..f6842152bbd --- /dev/null +++ b/src/circl/pke/kyber/internal/common/poly.go @@ -0,0 +1,324 @@ +package common + +// An element of our base ring R which are polynomials over ℤ_q +// modulo the equation Xᴺ = -1, where q=3329 and N=256. +// +// This type is also used to store NTT-transformed polynomials, +// see Poly.NTT(). +// +// Coefficients aren't always reduced. See Normalize(). +type Poly [N]int16 + +// Sets p to a + b. Does not normalize coefficients. +func (p *Poly) addGeneric(a, b *Poly) { + for i := 0; i < N; i++ { + p[i] = a[i] + b[i] + } +} + +// Sets p to a - b. Does not normalize coefficients. +func (p *Poly) subGeneric(a, b *Poly) { + for i := 0; i < N; i++ { + p[i] = a[i] - b[i] + } +} + +// Almost normalizes coefficients. +// +// Ensures each coefficient is in {0, …, q}. +func (p *Poly) barrettReduceGeneric() { + for i := 0; i < N; i++ { + p[i] = barrettReduce(p[i]) + } +} + +// Normalizes coefficients. +// +// Ensures each coefficient is in {0, …, q-1}. +func (p *Poly) normalizeGeneric() { + for i := 0; i < N; i++ { + p[i] = csubq(barrettReduce(p[i])) + } +} + +// Multiplies p in-place by the Montgomery factor 2¹⁶. +// +// Coefficients of p can be artbitray. Resulting coefficients are bounded +// in absolute value by q. +func (p *Poly) ToMont() { + for i := 0; i < N; i++ { + p[i] = toMont(p[i]) + } +} + +// Sets p to the "pointwise" multiplication of a and b. +// +// That is: InvNTT(p) = InvNTT(a) * InvNTT(b). Assumes a and b are in +// Montgomery form. Products between coefficients of a and b must be strictly +// bounded in absolute value by 2¹⁵q. p will be in Montgomery form and +// bounded in absolute value by 2q. +// +// Requires a and b to be in "tangled" order, see Tangle(). p will be in +// tangled order as well. +func (p *Poly) mulHatGeneric(a, b *Poly) { + // Recall from the discussion in NTT(), that a transformed polynomial is + // an element of ℤ_q[x]/(x²-ζ) x … x ℤ_q[x]/(x²+ζ¹²⁷); + // that is: 128 degree-one polynomials instead of simply 256 elements + // from ℤ_q as in the regular NTT. So instead of pointwise multiplication, + // we multiply the 128 pairs of degree-one polynomials modulo the + // right equation: + // + // (a₁ + a₂x)(b₁ + b₂x) = a₁b₁ + a₂b₂ζ' + (a₁b₂ + a₂b₁)x, + // + // where ζ' is the appropriate power of ζ. + + k := 64 + for i := 0; i < N; i += 4 { + zeta := int32(Zetas[k]) + k++ + + p0 := montReduce(int32(a[i+1]) * int32(b[i+1])) + p0 = montReduce(int32(p0) * zeta) + p0 += montReduce(int32(a[i]) * int32(b[i])) + + p1 := montReduce(int32(a[i]) * int32(b[i+1])) + p1 += montReduce(int32(a[i+1]) * int32(b[i])) + + p[i] = p0 + p[i+1] = p1 + + p2 := montReduce(int32(a[i+3]) * int32(b[i+3])) + p2 = -montReduce(int32(p2) * zeta) + p2 += montReduce(int32(a[i+2]) * int32(b[i+2])) + + p3 := montReduce(int32(a[i+2]) * int32(b[i+3])) + p3 += montReduce(int32(a[i+3]) * int32(b[i+2])) + + p[i+2] = p2 + p[i+3] = p3 + } +} + +// Packs p into buf. buf should be of length PolySize. +// +// Assumes p is normalized (and not just Barrett reduced) and "tangled", +// see Tangle(). +func (p *Poly) Pack(buf []byte) { + q := *p + q.Detangle() + for i := 0; i < 128; i++ { + t0 := q[2*i] + t1 := q[2*i+1] + buf[3*i] = byte(t0) + buf[3*i+1] = byte(t0>>8) | byte(t1<<4) + buf[3*i+2] = byte(t1 >> 4) + } +} + +// Unpacks p from buf. +// +// buf should be of length PolySize. p will be "tangled", see Detangle(). +// +// p will not be normalized; instead 0 ≤ p[i] < 4096. +func (p *Poly) Unpack(buf []byte) { + for i := 0; i < 128; i++ { + p[2*i] = int16(buf[3*i]) | ((int16(buf[3*i+1]) << 8) & 0xfff) + p[2*i+1] = int16(buf[3*i+1]>>4) | (int16(buf[3*i+2]) << 4) + } + p.Tangle() +} + +// Set p to Decompress_q(m, 1). +// +// p will be normalized. m has to be of PlaintextSize. +func (p *Poly) DecompressMessage(m []byte) { + // Decompress_q(x, 1) = ⌈xq/2⌋ = ⌊xq/2+½⌋ = (xq+1) >> 1 and so + // Decompress_q(0, 1) = 0 and Decompress_q(1, 1) = (q+1)/2. + for i := 0; i < 32; i++ { + for j := 0; j < 8; j++ { + bit := (m[i] >> uint(j)) & 1 + + // Set coefficient to either 0 or (q+1)/2 depending on the bit. + p[8*i+j] = -int16(bit) & ((Q + 1) / 2) + } + } +} + +// Writes Compress_q(p, 1) to m. +// +// Assumes p is normalized. m has to be of length at least PlaintextSize. +func (p *Poly) CompressMessageTo(m []byte) { + // Compress_q(x, 1) is 1 on {833, …, 2496} and zero elsewhere. + for i := 0; i < 32; i++ { + m[i] = 0 + for j := 0; j < 8; j++ { + x := 1664 - p[8*i+j] + // With the previous substitution, we want to return 1 if + // and only if x is in {831, …, -832}. + x = (x >> 15) ^ x + // Note (x >> 15)ˣ if x≥0 and -x-1 otherwise. Thus now we want + // to return 1 iff x ≤ 831, ie. x - 832 < 0. + x -= 832 + m[i] |= ((byte(x >> 15)) & 1) << uint(j) + } + } +} + +// Set p to Decompress_q(m, 1). +// +// Assumes d is in {3, 4, 5, 10, 11}. p will be normalized. +func (p *Poly) Decompress(m []byte, d int) { + // Decompress_q(x, d) = ⌈(q/2ᵈ)x⌋ + // = ⌊(q/2ᵈ)x+½⌋ + // = ⌊(qx + 2ᵈ⁻¹)/2ᵈ⌋ + // = (qx + (1<<(d-1))) >> d + switch d { + case 4: + for i := 0; i < N/2; i++ { + p[2*i] = int16(((1 << 3) + + uint32(m[i]&15)*uint32(Q)) >> 4) + p[2*i+1] = int16(((1 << 3) + + uint32(m[i]>>4)*uint32(Q)) >> 4) + } + case 5: + var t [8]uint16 + idx := 0 + for i := 0; i < N/8; i++ { + t[0] = uint16(m[idx]) + t[1] = (uint16(m[idx]) >> 5) | (uint16(m[idx+1] << 3)) + t[2] = uint16(m[idx+1]) >> 2 + t[3] = (uint16(m[idx+1]) >> 7) | (uint16(m[idx+2] << 1)) + t[4] = (uint16(m[idx+2]) >> 4) | (uint16(m[idx+3] << 4)) + t[5] = uint16(m[idx+3]) >> 1 + t[6] = (uint16(m[idx+3]) >> 6) | (uint16(m[idx+4] << 2)) + t[7] = uint16(m[idx+4]) >> 3 + + for j := 0; j < 8; j++ { + p[8*i+j] = int16(((1 << 4) + + uint32(t[j]&((1<<5)-1))*uint32(Q)) >> 5) + } + + idx += 5 + } + + case 10: + var t [4]uint16 + idx := 0 + for i := 0; i < N/4; i++ { + t[0] = uint16(m[idx]) | (uint16(m[idx+1]) << 8) + t[1] = (uint16(m[idx+1]) >> 2) | (uint16(m[idx+2]) << 6) + t[2] = (uint16(m[idx+2]) >> 4) | (uint16(m[idx+3]) << 4) + t[3] = (uint16(m[idx+3]) >> 6) | (uint16(m[idx+4]) << 2) + + for j := 0; j < 4; j++ { + p[4*i+j] = int16(((1 << 9) + + uint32(t[j]&((1<<10)-1))*uint32(Q)) >> 10) + } + + idx += 5 + } + case 11: + var t [8]uint16 + idx := 0 + for i := 0; i < N/8; i++ { + t[0] = uint16(m[idx]) | (uint16(m[idx+1]) << 8) + t[1] = (uint16(m[idx+1]) >> 3) | (uint16(m[idx+2]) << 5) + t[2] = (uint16(m[idx+2]) >> 6) | (uint16(m[idx+3]) << 2) | (uint16(m[idx+4]) << 10) + t[3] = (uint16(m[idx+4]) >> 1) | (uint16(m[idx+5]) << 7) + t[4] = (uint16(m[idx+5]) >> 4) | (uint16(m[idx+6]) << 4) + t[5] = (uint16(m[idx+6]) >> 7) | (uint16(m[idx+7]) << 1) | (uint16(m[idx+8]) << 9) + t[6] = (uint16(m[idx+8]) >> 2) | (uint16(m[idx+9]) << 6) + t[7] = (uint16(m[idx+9]) >> 5) | (uint16(m[idx+10]) << 3) + + for j := 0; j < 8; j++ { + p[8*i+j] = int16(((1 << 10) + + uint32(t[j]&((1<<11)-1))*uint32(Q)) >> 11) + } + + idx += 11 + } + default: + panic("unsupported d") + } +} + +// Writes Compress_q(p, d) to m. +// +// Assumes p is normalized and d is in {3, 4, 5, 10, 11}. +func (p *Poly) CompressTo(m []byte, d int) { + // Compress_q(x, d) = ⌈(2ᵈ/q)x⌋ mod⁺ 2ᵈ + // = ⌊(2ᵈ/q)x+½⌋ mod⁺ 2ᵈ + // = ⌊((x << d) + q/2) / q⌋ mod⁺ 2ᵈ + // = DIV((x << d) + q/2, q) & ((1<>3) | byte(t[2]<<2) | byte(t[3]<<7) + m[idx+2] = byte(t[3]>>1) | byte(t[4]<<4) + m[idx+3] = byte(t[4]>>4) | byte(t[5]<<1) | byte(t[6]<<6) + m[idx+4] = byte(t[6]>>2) | byte(t[7]<<3) + idx += 5 + } + + case 10: + var t [4]uint16 + idx := 0 + for i := 0; i < N/4; i++ { + for j := 0; j < 4; j++ { + t[j] = uint16(((uint32(p[4*i+j])<<10)+uint32(Q)/2)/ + uint32(Q)) & ((1 << 10) - 1) + } + m[idx] = byte(t[0]) + m[idx+1] = byte(t[0]>>8) | byte(t[1]<<2) + m[idx+2] = byte(t[1]>>6) | byte(t[2]<<4) + m[idx+3] = byte(t[2]>>4) | byte(t[3]<<6) + m[idx+4] = byte(t[3] >> 2) + idx += 5 + } + case 11: + var t [8]uint16 + idx := 0 + for i := 0; i < N/8; i++ { + for j := 0; j < 8; j++ { + t[j] = uint16(((uint32(p[8*i+j])<<11)+uint32(Q)/2)/ + uint32(Q)) & ((1 << 11) - 1) + } + m[idx] = byte(t[0]) + m[idx+1] = byte(t[0]>>8) | byte(t[1]<<3) + m[idx+2] = byte(t[1]>>5) | byte(t[2]<<6) + m[idx+3] = byte(t[2] >> 2) + m[idx+4] = byte(t[2]>>10) | byte(t[3]<<1) + m[idx+5] = byte(t[3]>>7) | byte(t[4]<<4) + m[idx+6] = byte(t[4]>>4) | byte(t[5]<<7) + m[idx+7] = byte(t[5] >> 1) + m[idx+8] = byte(t[5]>>9) | byte(t[6]<<2) + m[idx+9] = byte(t[6]>>6) | byte(t[7]<<5) + m[idx+10] = byte(t[7] >> 3) + idx += 11 + } + default: + panic("unsupported d") + } +} diff --git a/src/circl/pke/kyber/internal/common/poly_test.go b/src/circl/pke/kyber/internal/common/poly_test.go new file mode 100644 index 00000000000..3bc56f96496 --- /dev/null +++ b/src/circl/pke/kyber/internal/common/poly_test.go @@ -0,0 +1,269 @@ +package common + +import ( + cryptoRand "crypto/rand" + "fmt" + mathRand "math/rand" + "testing" +) + +func (p *Poly) RandAbsLe9Q() { + for i := 0; i < N; i++ { + p[i] = int16(mathRand.Intn(18*int(Q) - 9*int(Q))) + } +} + +// Returns x mod^± q +func sModQ(x int16) int16 { + x = x % Q + if x >= (Q-1)/2 { + x = x - Q + } + return x +} + +func TestDecompressMessage(t *testing.T) { + var m, m2 [PlaintextSize]byte + var p Poly + for i := 0; i < 1000; i++ { + _, _ = cryptoRand.Read(m[:]) + p.DecompressMessage(m[:]) + p.CompressMessageTo(m2[:]) + if m != m2 { + t.Fatal() + } + } +} + +func TestCompress(t *testing.T) { + for _, d := range []int{4, 5, 10, 11} { + d := d + t.Run(fmt.Sprintf("d=%d", d), func(t *testing.T) { + var p, q Poly + bound := (Q + (1 << uint(d))) >> uint(d+1) + buf := make([]byte, (N*d-1)/8+1) + for i := 0; i < 1000; i++ { + p.Rand() + p.CompressTo(buf, d) + q.Decompress(buf, d) + for j := 0; j < N; j++ { + diff := sModQ(p[j] - q[j]) + if diff < 0 { + diff = -diff + } + if diff > bound { + t.Logf("%v\n", buf) + t.Fatalf("|%d - %d mod^± q| = %d > %d, j=%d", + p[i], q[j], diff, bound, j) + } + } + } + }) + } +} + +func TestCompressMessage(t *testing.T) { + var p Poly + var m [32]byte + ok := true + for i := 0; i < int(Q); i++ { + p[0] = int16(i) + p.CompressMessageTo(m[:]) + want := byte(0) + if i >= 833 && i < 2497 { + want = 1 + } + if m[0] != want { + ok = false + t.Logf("%d %d %d", i, want, m[0]) + } + } + if !ok { + t.Fatal() + } +} + +func TestMulHat(t *testing.T) { + for k := 0; k < 1000; k++ { + var a, b, p, ah, bh, ph Poly + a.RandAbsLeQ() + b.RandAbsLeQ() + b[0] = 1 + + ah = a + bh = b + ah.NTT() + bh.NTT() + ph.MulHat(&ah, &bh) + ph.BarrettReduce() + ph.InvNTT() + + for i := 0; i < N; i++ { + for j := 0; j < N; j++ { + v := montReduce(int32(a[i]) * int32(b[j])) + k := i + j + if k >= N { + // Recall xᴺ = -1. + k -= N + v = -v + } + p[k] = barrettReduce(v + p[k]) + } + } + + for i := 0; i < N; i++ { + p[i] = int16((int32(p[i]) * ((1 << 16) % int32(Q))) % int32(Q)) + } + + p.Normalize() + ph.Normalize() + a.Normalize() + b.Normalize() + + if p != ph { + t.Fatalf("%v\n%v\n%v\n%v", a, b, p, ph) + } + } +} + +func TestAddAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var p1, p2, a, b Poly + a.RandAbsLeQ() + b.RandAbsLeQ() + p1.Add(&a, &b) + p2.addGeneric(&a, &b) + if p1 != p2 { + t.Fatalf("Add(%v, %v) = \n%v \n!= %v", a, b, p1, p2) + } + } +} + +func BenchmarkAdd(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.Add(&p, &p) + } +} + +func BenchmarkAddGeneric(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.addGeneric(&p, &p) + } +} + +func TestSubAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var p1, p2, a, b Poly + a.RandAbsLeQ() + b.RandAbsLeQ() + p1.Sub(&a, &b) + p2.subGeneric(&a, &b) + if p1 != p2 { + t.Fatalf("Sub(%v, %v) = \n%v \n!= %v", a, b, p1, p2) + } + } +} + +func BenchmarkSub(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.Sub(&p, &p) + } +} + +func BenchmarkSubGeneric(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.subGeneric(&p, &p) + } +} + +func TestMulHatAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var p1, p2, a, b Poly + a.RandAbsLeQ() + b.RandAbsLeQ() + a2 := a + b2 := b + a2.Tangle() + b2.Tangle() + p1.MulHat(&a2, &b2) + p1.Detangle() + p2.mulHatGeneric(&a, &b) + if p1 != p2 { + t.Fatalf("MulHat(%v, %v) = \n%v \n!= %v", a, b, p1, p2) + } + } +} + +func BenchmarkMulHat(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.MulHat(&p, &p) + } +} + +func BenchmarkMulHatGeneric(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.mulHatGeneric(&p, &p) + } +} + +func BenchmarkBarrettReduce(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.BarrettReduce() + } +} + +func BenchmarkBarrettReduceGeneric(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.barrettReduceGeneric() + } +} + +func TestBarrettReduceAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var p1, p2, a Poly + a.RandAbsLe9Q() + p1 = a + p2 = a + p1.BarrettReduce() + p2.barrettReduceGeneric() + if p1 != p2 { + t.Fatalf("BarrettReduce(%v) = \n%v \n!= %v", a, p1, p2) + } + } +} + +func BenchmarkNormalize(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.Normalize() + } +} + +func BenchmarkNormalizeGeneric(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.barrettReduceGeneric() + } +} + +func TestNormalizeAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var p1, p2, a Poly + a.RandAbsLe9Q() + p1 = a + p2 = a + p1.Normalize() + p2.normalizeGeneric() + if p1 != p2 { + t.Fatalf("Normalize(%v) = \n%v \n!= %v", a, p1, p2) + } + } +} diff --git a/src/circl/pke/kyber/internal/common/sample.go b/src/circl/pke/kyber/internal/common/sample.go new file mode 100644 index 00000000000..97eb282dcf2 --- /dev/null +++ b/src/circl/pke/kyber/internal/common/sample.go @@ -0,0 +1,236 @@ +package common + +import ( + "circl/internal/sha3" + "circl/simd/keccakf1600" + + "encoding/binary" +) + +// DeriveX4Available indicates whether the system supports the quick fourway +// sampling variants like PolyDeriveUniformX4. +var DeriveX4Available = keccakf1600.IsEnabledX4() + +// Samples p from a centered binomial distribution with given η. +// +// Essentially CBD_η(PRF(seed, nonce)) from the specification. +func (p *Poly) DeriveNoise(seed []byte, nonce uint8, eta int) { + switch eta { + case 2: + p.DeriveNoise2(seed, nonce) + case 3: + p.DeriveNoise3(seed, nonce) + default: + panic("unsupported eta") + } +} + +// Sample p from a centered binomial distribution with n=6 and p=½ - that is: +// coefficients are in {-3, -2, -1, 0, 1, 2, 3} with probabilities {1/64, 3/32, +// 15/64, 5/16, 16/64, 3/32, 1/64}. +func (p *Poly) DeriveNoise3(seed []byte, nonce uint8) { + keySuffix := [1]byte{nonce} + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Write(keySuffix[:]) + + // The distribution at hand is exactly the same as that + // of (a₁ + a₂ + a₃) - (b₁ + b₂+b₃) where a_i,b_i~U(1). Thus we need + // 6 bits per coefficients, thus 192 bytes of input entropy. + + // We add two extra zero bytes in the buffer to be able to read 8 bytes + // at the same time (while using only 6.) + var buf [192 + 2]byte + _, _ = h.Read(buf[:192]) + + for i := 0; i < 32; i++ { + // t is interpreted as a₁ + 2a₂ + 4a₃ + 8b₁ + 16b₂ + …. + t := binary.LittleEndian.Uint64(buf[6*i:]) + + d := t & 0x249249249249 // a₁ + 8b₁ + … + d += (t >> 1) & 0x249249249249 // a₁ + a₂ + 8(b₁ + b₂) + … + d += (t >> 2) & 0x249249249249 // a₁ + a₂ + a₃ + 4(b₁ + b₂ + b₃) + … + + for j := 0; j < 8; j++ { + a := int16(d) & 0x7 // a₁ + a₂ + a₃ + d >>= 3 + b := int16(d) & 0x7 // b₁ + b₂ + b₃ + d >>= 3 + p[8*i+j] = a - b + } + } +} + +// Sample p from a centered binomial distribution with n=4 and p=½ - that is: +// coefficients are in {-2, -1, 0, 1, 2} with probabilities {1/16, 1/4, +// 3/8, 1/4, 1/16}. +func (p *Poly) DeriveNoise2(seed []byte, nonce uint8) { + keySuffix := [1]byte{nonce} + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Write(keySuffix[:]) + + // The distribution at hand is exactly the same as that + // of (a + a') - (b + b') where a,a',b,b'~U(1). Thus we need 4 bits per + // coefficients, thus 128 bytes of input entropy. + + var buf [128]byte + _, _ = h.Read(buf[:]) + + for i := 0; i < 16; i++ { + // t is interpreted as a + 2a' + 4b + 8b' + …. + t := binary.LittleEndian.Uint64(buf[8*i:]) + + d := t & 0x5555555555555555 // a + 4b + … + d += (t >> 1) & 0x5555555555555555 // a+a' + 4(b + b') + … + + for j := 0; j < 16; j++ { + a := int16(d) & 0x3 + d >>= 2 + b := int16(d) & 0x3 + d >>= 2 + p[16*i+j] = a - b + } + } +} + +// For each i, sample ps[i] uniformly from the given seed for coordinates +// xs[i] and ys[i]. ps[i] may be nil and is ignored in that case. +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformX4(ps [4]*Poly, seed *[32]byte, xs, ys [4]uint8) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 4; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the coordinates, the SHAKE128 domain separator (0b1111), the + // start of the padding (0b…001) and the end of the padding 0b100…. + // Recall that the rate of SHAKE128 is 168; ie. 21 uint64s. + for j := 0; j < 4; j++ { + state[4*4+j] = uint64(xs[j]) | (uint64(ys[j]) << 8) | (0x1f << 16) + state[20*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = N // mark nil polynomials as completed + } + } + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each of + // the four SHAKE128 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == N { + continue + } + for i := 0; i < 7; i++ { + var t [16]uint16 + + v1 := state[i*3*4+j] + v2 := state[(i*3+1)*4+j] + v3 := state[(i*3+2)*4+j] + + t[0] = uint16(v1) & 0xfff + t[1] = uint16(v1>>12) & 0xfff + t[2] = uint16(v1>>24) & 0xfff + t[3] = uint16(v1>>36) & 0xfff + t[4] = uint16(v1>>48) & 0xfff + t[5] = uint16((v1>>60)|(v2<<4)) & 0xfff + + t[6] = uint16(v2>>8) & 0xfff + t[7] = uint16(v2>>20) & 0xfff + t[8] = uint16(v2>>32) & 0xfff + t[9] = uint16(v2>>44) & 0xfff + t[10] = uint16((v2>>56)|(v3<<8)) & 0xfff + + t[11] = uint16(v3>>4) & 0xfff + t[12] = uint16(v3>>16) & 0xfff + t[13] = uint16(v3>>28) & 0xfff + t[14] = uint16(v3>>40) & 0xfff + t[15] = uint16(v3>>52) & 0xfff + + for k := 0; k < 16; k++ { + if t[k] < uint16(Q) { + ps[j][idx[j]] = int16(t[k]) + idx[j]++ + if idx[j] == N { + continue PolyLoop + } + } + } + } + + done = false + } + } + + for i := 0; i < 4; i++ { + if ps[i] != nil { + ps[i].Tangle() + } + } +} + +// Sample p uniformly from the given seed and x and y coordinates. +// +// Coefficients are reduced and will be in "tangled" order. See Tangle(). +func (p *Poly) DeriveUniform(seed *[32]byte, x, y uint8) { + var seedSuffix [2]byte + var buf [168]byte // rate of SHAKE-128 + + seedSuffix[0] = x + seedSuffix[1] = y + + h := sha3.NewShake128() + _, _ = h.Write(seed[:]) + _, _ = h.Write(seedSuffix[:]) + + i := 0 + for { + _, _ = h.Read(buf[:]) + + for j := 0; j < 168; j += 3 { + t1 := (uint16(buf[j]) | (uint16(buf[j+1]) << 8)) & 0xfff + t2 := (uint16(buf[j+1]>>4) | (uint16(buf[j+2]) << 4)) & 0xfff + + if t1 < uint16(Q) { + p[i] = int16(t1) + i++ + + if i == N { + break + } + } + + if t2 < uint16(Q) { + p[i] = int16(t2) + i++ + + if i == N { + break + } + } + } + + if i == N { + break + } + } + + p.Tangle() +} diff --git a/src/circl/pke/kyber/internal/common/sample_test.go b/src/circl/pke/kyber/internal/common/sample_test.go new file mode 100644 index 00000000000..50f351974b6 --- /dev/null +++ b/src/circl/pke/kyber/internal/common/sample_test.go @@ -0,0 +1,191 @@ +package common + +import ( + "testing" +) + +func BenchmarkDeriveNoise2(b *testing.B) { + var p Poly + var seed [32]byte + for i := 0; i < b.N; i++ { + p.DeriveNoise2(seed[:], 37) + } +} + +func BenchmarkDeriveNoise3(b *testing.B) { + var p Poly + var seed [32]byte + for i := 0; i < b.N; i++ { + p.DeriveNoise3(seed[:], 37) + } +} + +func TestPolyDeriveNoise3Ref(t *testing.T) { + var p Poly + + want := Poly{ + 0, 0, 1, -1, 0, 2, 0, -1, -1, 3, 0, 1, -2, -2, 0, 1, -2, + 1, 0, -2, 3, 0, 0, 0, 1, 3, 1, 1, 2, 1, -1, -1, -1, 0, 1, + 0, 1, 0, 2, 0, 1, -2, 0, -1, -1, -2, 1, -1, -1, 2, -1, 1, + 1, 2, -3, -1, -1, 0, 0, 0, 0, 1, -1, -2, -2, 0, -2, 0, 0, + 0, 1, 0, -1, -1, 1, -2, 2, 0, 0, 2, -2, 0, 1, 0, 1, 1, 1, + 0, 1, -2, -1, -2, -1, 1, 0, 0, 0, 0, 0, 1, 0, -1, -1, 0, + -1, 1, 0, 1, 0, -1, -1, 0, -2, 2, 0, -2, 1, -1, 0, 1, -1, + -1, 2, 1, 0, 0, -2, -1, 2, 0, 0, 0, -1, -1, 3, 1, 0, 1, 0, + 1, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0, -1, -1, -1, 0, 1, 3, 1, + 0, 1, 0, 1, -1, -1, -1, -1, 0, 0, -2, -1, -1, 2, 0, 1, 0, + 1, 0, 2, -2, 0, 1, 1, -3, -1, -2, -1, 0, 1, 0, 1, -2, 2, + 2, 1, 1, 0, -1, 0, -1, -1, 1, 0, -1, 2, 1, -1, 1, 2, -2, + 1, 2, 0, 1, 2, 1, 0, 0, 2, 1, 2, 1, 0, 2, 1, 0, 0, -1, -1, + 1, -1, 0, 1, -1, 2, 2, 0, 0, -1, 1, 1, 1, 1, 0, 0, -2, 0, + -1, 1, 2, 0, 0, 1, 1, -1, 1, 0, 1, + } + + var seed [32]byte + + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + + p.DeriveNoise3(seed[:], 37) + + if p != want { + t.Fatal() + } +} + +func TestPolyDeriveNoise2Ref(t *testing.T) { + var p Poly + + want := Poly{ + 1, 0, 1, -1, -1, -2, -1, -1, 2, 0, -1, 0, 0, -1, + 1, 1, -1, 1, 0, 2, -2, 0, 1, 2, 0, 0, -1, 1, 0, -1, + 1, -1, 1, 2, 1, 1, 0, -1, 1, -1, -2, -1, 1, -1, -1, + -1, 2, -1, -1, 0, 0, 1, 1, -1, 1, 1, 1, 1, -1, -2, + 0, 1, 0, 0, 2, 1, -1, 2, 0, 0, 1, 1, 0, -1, 0, 0, + -1, -1, 2, 0, 1, -1, 2, -1, -1, -1, -1, 0, -2, 0, + 2, 1, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, -1, -1, 0, + -1, 0, 0, -2, 1, 1, 0, 1, 0, 1, 0, 1, 1, -1, 2, 0, + 1, -1, 1, 2, 0, 0, 0, 0, -1, -1, -1, 0, 1, 0, -1, + 2, 0, 0, 1, 1, 1, 0, 1, -1, 1, 2, 1, 0, 2, -1, 1, + -1, -2, -1, -2, -1, 1, 0, -2, -2, -1, 1, 0, 0, 0, + 0, 1, 0, 0, 0, 2, 2, 0, 1, 0, -1, -1, 0, 2, 0, 0, + -2, 1, 0, 2, 1, -1, -2, 0, 0, -1, 1, 1, 0, 0, 2, + 0, 1, 1, -2, 1, -2, 1, 1, 0, 2, 0, -1, 0, -1, 0, + 1, 2, 0, 1, 0, -2, 1, -2, -2, 1, -1, 0, -1, 1, 1, + 0, 0, 0, 1, 0, -1, 1, 1, 0, 0, 0, 0, 1, 0, 1, -1, + 0, 1, -1, -1, 2, 0, 0, 1, -1, 0, 1, -1, 0, + } + + var seed [32]byte + + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + + p.DeriveNoise2(seed[:], 37) + + if p != want { + t.Fatal() + } +} + +func TestPolyDeriveUniformRef(t *testing.T) { + var p Poly + + // Generated by reference implementation. + want := Poly{ + 797, 993, 161, 6, 2608, 2385, 2096, 2661, 1676, 247, 2440, + 342, 634, 194, 1570, 2848, 986, 684, 3148, 3208, 2018, 351, + 2288, 612, 1394, 170, 1521, 3119, 58, 596, 2093, 1549, 409, + 2156, 1934, 1730, 1324, 388, 446, 418, 1719, 2202, 1812, + 98, 1019, 2369, 214, 2699, 28, 1523, 2824, 273, 402, 2899, + 246, 210, 1288, 863, 2708, 177, 3076, 349, 44, 949, 854, + 1371, 957, 292, 2502, 1617, 1501, 254, 7, 1761, 2581, 2206, + 2655, 1211, 629, 1274, 2358, 816, 2766, 2115, 2985, 1006, + 2433, 856, 2596, 3192, 1, 1378, 2345, 707, 1891, 1669, 536, + 1221, 710, 2511, 120, 1176, 322, 1897, 2309, 595, 2950, + 1171, 801, 1848, 695, 2912, 1396, 1931, 1775, 2904, 893, + 2507, 1810, 2873, 253, 1529, 1047, 2615, 1687, 831, 1414, + 965, 3169, 1887, 753, 3246, 1937, 115, 2953, 586, 545, 1621, + 1667, 3187, 1654, 1988, 1857, 512, 1239, 1219, 898, 3106, + 391, 1331, 2228, 3169, 586, 2412, 845, 768, 156, 662, 478, + 1693, 2632, 573, 2434, 1671, 173, 969, 364, 1663, 2701, + 2169, 813, 1000, 1471, 720, 2431, 2530, 3161, 733, 1691, + 527, 2634, 335, 26, 2377, 1707, 767, 3020, 950, 502, 426, + 1138, 3208, 2607, 2389, 44, 1358, 1392, 2334, 875, 2097, + 173, 1697, 2578, 942, 1817, 974, 1165, 2853, 1958, 2973, + 3282, 271, 1236, 1677, 2230, 673, 1554, 96, 242, 1729, 2518, + 1884, 2272, 71, 1382, 924, 1807, 1610, 456, 1148, 2479, + 2152, 238, 2208, 2329, 713, 1175, 1196, 757, 1078, 3190, + 3169, 708, 3117, 154, 1751, 3225, 1364, 154, 23, 2842, 1105, + 1419, 79, 5, 2013, + } + + var seed [32]byte + + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + + p.DeriveUniform(&seed, 1, 0) + p.Detangle() + p.Normalize() + + if p != want { + t.Fatalf("%v\n%v", p, want) + } +} + +func BenchmarkPolyDeriveUniform(b *testing.B) { + var p Poly + var seed [32]byte + for i := 0; i < b.N; i++ { + p.DeriveUniform(&seed, 0, 0) + } +} + +func BenchmarkPolyDeriveUniformX4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + + var p [4]Poly + var seed [32]byte + for i := 0; i < b.N; i++ { + PolyDeriveUniformX4( + [4]*Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, + [4]uint8{0, 1, 2, 3}, + [4]uint8{4, 5, 6, 7}, + ) + } +} + +func TestPolyDeriveUniformX4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + + var p2 Poly + var p [4]Poly + var seed [32]byte + + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformX4( + [4]*Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, + [4]uint8{0, 1, 2, 3}, + [4]uint8{4, 5, 6, 7}, + ) + + for i := 0; i < 4; i++ { + p2.DeriveUniform(&seed, uint8(i), uint8(i+4)) + if p2 != p[i] { + t.Fatalf("%d\n%v\n%v", i, p2, p[i]) + } + } +} diff --git a/src/circl/pke/kyber/internal/common/stubs_amd64.go b/src/circl/pke/kyber/internal/common/stubs_amd64.go new file mode 100644 index 00000000000..0dfec393063 --- /dev/null +++ b/src/circl/pke/kyber/internal/common/stubs_amd64.go @@ -0,0 +1,32 @@ +// Code generated by command: go run src.go -out ../amd64.s -stubs ../stubs_amd64.go -pkg common. DO NOT EDIT. + +// +build amd64 + +package common + +//go:noescape +func addAVX2(p *[256]int16, a *[256]int16, b *[256]int16) + +//go:noescape +func subAVX2(p *[256]int16, a *[256]int16, b *[256]int16) + +//go:noescape +func nttAVX2(p *[256]int16) + +//go:noescape +func invNttAVX2(p *[256]int16) + +//go:noescape +func mulHatAVX2(p *[256]int16, a *[256]int16, b *[256]int16) + +//go:noescape +func detangleAVX2(p *[256]int16) + +//go:noescape +func tangleAVX2(p *[256]int16) + +//go:noescape +func barrettReduceAVX2(p *[256]int16) + +//go:noescape +func normalizeAVX2(p *[256]int16) diff --git a/src/circl/pke/kyber/kyber.go b/src/circl/pke/kyber/kyber.go new file mode 100644 index 00000000000..fb4d88a2b4d --- /dev/null +++ b/src/circl/pke/kyber/kyber.go @@ -0,0 +1,10 @@ +//go:generate go run gen.go + +// Package kyber implements the CRYSTALS-Kyber.CPAPKE public key encrpyption +// as submitted to round 3 of the NIST PQC competition and described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +// +// The related key encapsulation mechanism (KEM) CRYSTALS-Kyber.CCAKEM can +// be found in the package circl/kem/kyber. +package kyber diff --git a/src/circl/pke/kyber/kyber1024/internal/cpapke.go b/src/circl/pke/kyber/kyber1024/internal/cpapke.go new file mode 100644 index 00000000000..89642b17de4 --- /dev/null +++ b/src/circl/pke/kyber/kyber1024/internal/cpapke.go @@ -0,0 +1,177 @@ +// Code generated from kyber512/internal/cpapke.go by gen.go + +package internal + +import ( + "circl/internal/sha3" + "circl/pke/kyber/internal/common" +) + +// A Kyber.CPAPKE private key. +type PrivateKey struct { + sh Vec // NTT(s), normalized +} + +// A Kyber.CPAPKE public key. +type PublicKey struct { + rho [32]byte // ρ, the seed for the matrix A + th Vec // NTT(t), normalized + + // cached values + aT Mat // the matrix Aᵀ +} + +// Packs the private key to buf. +func (sk *PrivateKey) Pack(buf []byte) { + sk.sh.Pack(buf) +} + +// Unpacks the private key from buf. +func (sk *PrivateKey) Unpack(buf []byte) { + sk.sh.Unpack(buf) + sk.sh.Normalize() +} + +// Packs the public key to buf. +func (pk *PublicKey) Pack(buf []byte) { + pk.th.Pack(buf) + copy(buf[K*common.PolySize:], pk.rho[:]) +} + +// Unpacks the public key from buf. +func (pk *PublicKey) Unpack(buf []byte) { + pk.th.Unpack(buf) + pk.th.Normalize() + copy(pk.rho[:], buf[K*common.PolySize:]) + pk.aT.Derive(&pk.rho, true) +} + +// Derives a new Kyber.CPAPKE keypair from the given seed. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + var pk PublicKey + var sk PrivateKey + + var expandedSeed [64]byte + + // XXX use internal sha3 implementation + h := sha3.New512() + _, _ = h.Write(seed) + + // This writes hash into expandedSeed. Yes, this is idiomatic Go. + h.Sum(expandedSeed[:0]) + + copy(pk.rho[:], expandedSeed[:32]) + sigma := expandedSeed[32:] // σ, the noise seed + + pk.aT.Derive(&pk.rho, false) // Expand ρ to matrix A; we'll transpose later + + var eh Vec + sk.sh.DeriveNoise(sigma, 0, Eta1) // Sample secret vector s + sk.sh.NTT() + sk.sh.Normalize() + + eh.DeriveNoise(sigma, K, Eta1) // Sample blind e + eh.NTT() + + // Next, we compute t = A s + e. + for i := 0; i < K; i++ { + // Note that coefficients of s are bounded by q and those of A + // are bounded by 4.5q and so their product is bounded by 2¹⁵q + // as required for multiplication. + PolyDotHat(&pk.th[i], &pk.aT[i], &sk.sh) + + // A and s were not in Montgomery form, so the Montgomery + // multiplications in the inner product added a factor R⁻¹ which + // we'll cancel out now. This will also ensure the coefficients of + // t are bounded in absolute value by q. + pk.th[i].ToMont() + } + + pk.th.Add(&pk.th, &eh) // bounded by 8q. + pk.th.Normalize() + pk.aT.Transpose() + + return &pk, &sk +} + +// Decrypts ciphertext ct meant for private key sk to plaintext pt. +func (sk *PrivateKey) DecryptTo(pt, ct []byte) { + var u Vec + var v, m common.Poly + + u.Decompress(ct, DU) + v.Decompress(ct[K*compressedPolySize(DU):], DV) + + // Compute m = v - + u.NTT() + PolyDotHat(&m, &sk.sh, &u) + m.BarrettReduce() + m.InvNTT() + m.Sub(&v, &m) + m.Normalize() + + // Compress polynomial m to original message + m.CompressMessageTo(pt) +} + +// Encrypts message pt for the public key to ciphertext ct using randomness +// from seed. +// +// seed has to be of length SeedSize, pt of PlaintextSize and ct of +// CiphertextSize. +func (pk *PublicKey) EncryptTo(ct, seed, pt []byte) { + var rh, e1, u Vec + var e2, v, m common.Poly + + // Sample r, e₁ and e₂ from B_η + rh.DeriveNoise(seed, 0, Eta1) + rh.NTT() + rh.BarrettReduce() + + e1.DeriveNoise(seed, K, common.Eta2) + e2.DeriveNoise(seed, 2*K, common.Eta2) + + // Next we compute u = Aᵀ r + e₁. First Aᵀ. + for i := 0; i < K; i++ { + // Note that coefficients of r are bounded by q and those of Aᵀ + // are bounded by 4.5q and so their product is bounded by 2¹⁵q + // as required for multiplication. + PolyDotHat(&u[i], &pk.aT[i], &rh) + } + + u.BarrettReduce() + + // Aᵀ and r were not in Montgomery form, so the Montgomery + // multiplications in the inner product added a factor R⁻¹ which + // the InvNTT cancels out. + u.InvNTT() + + u.Add(&u, &e1) // u = Aᵀ r + e₁ + + // Next compute v = + e₂ + Decompress_q(m, 1). + PolyDotHat(&v, &pk.th, &rh) + v.BarrettReduce() + v.InvNTT() + + m.DecompressMessage(pt) + v.Add(&v, &m) + v.Add(&v, &e2) // v = + e₂ + Decompress_q(m, 1) + + // Pack ciphertext + u.Normalize() + v.Normalize() + + u.CompressTo(ct, DU) + v.CompressTo(ct[K*compressedPolySize(DU):], DV) +} + +// Returns whether sk equals other. +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + ret := int16(0) + for i := 0; i < K; i++ { + for j := 0; j < common.N; j++ { + ret |= sk.sh[i][j] ^ other.sh[i][j] + } + } + return ret == 0 +} diff --git a/src/circl/pke/kyber/kyber1024/internal/cpapke_test.go b/src/circl/pke/kyber/kyber1024/internal/cpapke_test.go new file mode 100644 index 00000000000..2d5552397c1 --- /dev/null +++ b/src/circl/pke/kyber/kyber1024/internal/cpapke_test.go @@ -0,0 +1,38 @@ +// Code generated from kyber512/internal/cpapke_test.go by gen.go + +package internal + +import ( + "crypto/rand" + "testing" +) + +func TestEncryptThenDecrypt(t *testing.T) { + var seed [32]byte + var coin [SeedSize]byte + + for i := 0; i < 32; i++ { + seed[i] = byte(i) + coin[i] = byte(i) + } + + for i := 0; i < 100; i++ { + seed[0] = byte(i) + pk, sk := NewKeyFromSeed(seed[:]) + + for j := 0; j < 100; j++ { + var msg, msg2 [PlaintextSize]byte + var ct [CiphertextSize]byte + + _, _ = rand.Read(msg[:]) + _, _ = rand.Read(coin[:]) + + pk.EncryptTo(ct[:], coin[:], msg[:]) + sk.DecryptTo(msg2[:], ct[:]) + + if msg != msg2 { + t.Fatalf("%v %v %v", ct, msg, msg2) + } + } + } +} diff --git a/src/circl/pke/kyber/kyber1024/internal/mat.go b/src/circl/pke/kyber/kyber1024/internal/mat.go new file mode 100644 index 00000000000..cc1decfd58e --- /dev/null +++ b/src/circl/pke/kyber/kyber1024/internal/mat.go @@ -0,0 +1,85 @@ +// Code generated from kyber512/internal/mat.go by gen.go + +package internal + +import ( + "circl/pke/kyber/internal/common" +) + +// A k by k matrix of polynomials. +type Mat [K]Vec + +// Expands the given seed to the corresponding matrix A or its transpose Aᵀ. +func (m *Mat) Derive(seed *[32]byte, transpose bool) { + if !common.DeriveX4Available { + if transpose { + for i := 0; i < K; i++ { + for j := 0; j < K; j++ { + m[i][j].DeriveUniform(seed, uint8(i), uint8(j)) + } + } + } else { + for i := 0; i < K; i++ { + for j := 0; j < K; j++ { + m[i][j].DeriveUniform(seed, uint8(j), uint8(i)) + } + } + } + return + } + + var ps [4]*common.Poly + var xs [4]uint8 + var ys [4]uint8 + x := uint8(0) + y := uint8(0) + + for x != K { + idx := 0 + for ; idx < 4; idx++ { + ps[idx] = &m[x][y] + + if transpose { + xs[idx] = x + ys[idx] = y + } else { + xs[idx] = y + ys[idx] = x + } + + y++ + if y == K { + x++ + y = 0 + + if x == K { + if idx == 0 { + // If there is just one left, then a plain DeriveUniform + // is quicker than the X4 variant. + ps[0].DeriveUniform(seed, xs[0], ys[0]) + return + } + + for idx++; idx < 4; idx++ { + ps[idx] = nil + } + + break + } + } + } + + common.PolyDeriveUniformX4(ps, seed, xs, ys) + } +} + +// Tranposes A in place. +func (m *Mat) Transpose() { + for i := 0; i < K-1; i++ { + for j := i + 1; j < K; j++ { + t := m[i][j] + m[i][j] = m[j][i] + m[j][i] = t + } + } +} diff --git a/src/circl/pke/kyber/kyber1024/internal/params.go b/src/circl/pke/kyber/kyber1024/internal/params.go new file mode 100644 index 00000000000..1664adf1e98 --- /dev/null +++ b/src/circl/pke/kyber/kyber1024/internal/params.go @@ -0,0 +1,21 @@ +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +import ( + "circl/pke/kyber/internal/common" +) + +const ( + K = 4 + Eta1 = 2 + DU = 11 + DV = 5 + PublicKeySize = 32 + K*common.PolySize + + PrivateKeySize = K * common.PolySize + + PlaintextSize = common.PlaintextSize + SeedSize = 32 + CiphertextSize = 1568 +) diff --git a/src/circl/pke/kyber/kyber1024/internal/vec.go b/src/circl/pke/kyber/kyber1024/internal/vec.go new file mode 100644 index 00000000000..3af1c8fed49 --- /dev/null +++ b/src/circl/pke/kyber/kyber1024/internal/vec.go @@ -0,0 +1,125 @@ +// Code generated from kyber512/internal/vec.go by gen.go + +package internal + +import ( + "circl/pke/kyber/internal/common" +) + +// A vector of K polynomials +type Vec [K]common.Poly + +// Samples v[i] from a centered binomial distribution with given η, +// seed and nonce+i. +// +// Essentially CBD_η(PRF(seed, nonce+i)) from the specification. +func (v *Vec) DeriveNoise(seed []byte, nonce uint8, eta int) { + for i := 0; i < K; i++ { + v[i].DeriveNoise(seed, nonce+uint8(i), eta) + } +} + +// Sets p to the inner product of a and b using "pointwise" multiplication. +// +// See MulHat() and NTT() for a description of the multiplication. +// Assumes a and b are in Montgomery form. p will be in Montgomery form, +// and its coefficients will be bounded in absolute value by 2kq. +// If a and b are not in Montgomery form, then the action is the same +// as "pointwise" multiplication followed by multiplying by R⁻¹, the inverse +// of the Montgomery factor. +func PolyDotHat(p *common.Poly, a, b *Vec) { + var t common.Poly + *p = common.Poly{} // set p to zero + for i := 0; i < K; i++ { + t.MulHat(&a[i], &b[i]) + p.Add(&t, p) + } +} + +// Almost normalizes coefficients in-place. +// +// Ensures each coefficient is in {0, …, q}. +func (v *Vec) BarrettReduce() { + for i := 0; i < K; i++ { + v[i].BarrettReduce() + } +} + +// Normalizes coefficients in-place. +// +// Ensures each coefficient is in {0, …, q-1}. +func (v *Vec) Normalize() { + for i := 0; i < K; i++ { + v[i].Normalize() + } +} + +// Applies in-place inverse NTT(). See Poly.InvNTT() for assumptions. +func (v *Vec) InvNTT() { + for i := 0; i < K; i++ { + v[i].InvNTT() + } +} + +// Applies in-place forward NTT(). See Poly.NTT() for assumptions. +func (v *Vec) NTT() { + for i := 0; i < K; i++ { + v[i].NTT() + } +} + +// Sets v to a + b. +func (v *Vec) Add(a, b *Vec) { + for i := 0; i < K; i++ { + v[i].Add(&a[i], &b[i]) + } +} + +// Packs v into buf, which must be of length K*PolySize. +func (v *Vec) Pack(buf []byte) { + for i := 0; i < K; i++ { + v[i].Pack(buf[common.PolySize*i:]) + } +} + +// Unpacks v from buf which must be of length K*PolySize. +func (v *Vec) Unpack(buf []byte) { + for i := 0; i < K; i++ { + v[i].Unpack(buf[common.PolySize*i:]) + } +} + +// Writes Compress_q(v, d) to m. +// +// Assumes v is normalized and d is in {3, 4, 5, 10, 11}. +func (v *Vec) CompressTo(m []byte, d int) { + size := compressedPolySize(d) + for i := 0; i < K; i++ { + v[i].CompressTo(m[size*i:], d) + } +} + +// Set v to Decompress_q(m, 1). +// +// Assumes d is in {3, 4, 5, 10, 11}. v will be normalized. +func (v *Vec) Decompress(m []byte, d int) { + size := compressedPolySize(d) + for i := 0; i < K; i++ { + v[i].Decompress(m[size*i:], d) + } +} + +// ⌈(256 d)/8⌉ +func compressedPolySize(d int) int { + switch d { + case 4: + return 128 + case 5: + return 160 + case 10: + return 320 + case 11: + return 352 + } + panic("unsupported d") +} diff --git a/src/circl/pke/kyber/kyber1024/kyber.go b/src/circl/pke/kyber/kyber1024/kyber.go new file mode 100644 index 00000000000..a3585bc0665 --- /dev/null +++ b/src/circl/pke/kyber/kyber1024/kyber.go @@ -0,0 +1,145 @@ +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// kyber1024 implements the IND-CPA-secure Public Key Encryption +// scheme Kyber1024.CPAPKE as submitted to round 3 of the NIST PQC competition +// and described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +package kyber1024 + +import ( + cryptoRand "crypto/rand" + "io" + + "circl/pke/kyber/kyber1024/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + KeySeedSize = internal.SeedSize + + // Size of seed for EncryptTo + EncryptionSeedSize = internal.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a ciphertext + CiphertextSize = internal.CiphertextSize + + // Size of a plaintext + PlaintextSize = internal.PlaintextSize +) + +// PublicKey is the type of Kyber1024.CPAPKE public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of Kyber1024.CPAPKE private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [KeySeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := internal.NewKeyFromSeed(seed[:]) + return (*PublicKey)(pk), (*PrivateKey)(sk), nil +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +// +// Panics if seed is not of length KeySeedSize. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + if len(seed) != KeySeedSize { + panic("seed must be of length KeySeedSize") + } + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// EncryptTo encrypts message pt for the public key and writes the ciphertext +// to ct using randomness from seed. +// +// This function panics if the lengths of pt, seed and ct are not +// PlaintextSize, EncryptionSeedSize and CiphertextSize respectively. +func (pk *PublicKey) EncryptTo(ct []byte, pt []byte, seed []byte) { + if len(pt) != PlaintextSize { + panic("pt must be of length PlaintextSize") + } + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + if len(seed) != EncryptionSeedSize { + panic("seed must be of length EncryptionSeedSize") + } + (*internal.PublicKey)(pk).EncryptTo(ct, pt, seed) +} + +// DecryptTo decrypts message ct for the private key and writes the +// plaintext to pt. +// +// This function panics if the lengths of ct and pt are not +// CiphertextSize and PlaintextSize respectively. +func (sk *PrivateKey) DecryptTo(pt []byte, ct []byte) { + if len(pt) != PlaintextSize { + panic("pt must be of length PlaintextSize") + } + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + (*internal.PrivateKey)(sk).DecryptTo(pt, ct) +} + +// Packs pk into the given buffer. +// +// Panics if buf is not of length PublicKeySize. +func (pk *PublicKey) Pack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of size PublicKeySize") + } + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs sk into the given buffer. +// +// Panics if buf is not of length PrivateKeySize. +func (sk *PrivateKey) Pack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of size PrivateKeySize") + } + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Unpacks pk from the given buffer. +// +// Panics if buf is not of length PublicKeySize. +func (pk *PublicKey) Unpack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of size PublicKeySize") + } + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Unpacks sk from the given buffer. +// +// Panics if buf is not of length PrivateKeySize. +func (sk *PrivateKey) Unpack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of size PrivateKeySize") + } + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Returns whether the two private keys are equal. +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(other)) +} diff --git a/src/circl/pke/kyber/kyber512/internal/cpapke.go b/src/circl/pke/kyber/kyber512/internal/cpapke.go new file mode 100644 index 00000000000..1efffddbc52 --- /dev/null +++ b/src/circl/pke/kyber/kyber512/internal/cpapke.go @@ -0,0 +1,175 @@ +package internal + +import ( + "circl/internal/sha3" + "circl/pke/kyber/internal/common" +) + +// A Kyber.CPAPKE private key. +type PrivateKey struct { + sh Vec // NTT(s), normalized +} + +// A Kyber.CPAPKE public key. +type PublicKey struct { + rho [32]byte // ρ, the seed for the matrix A + th Vec // NTT(t), normalized + + // cached values + aT Mat // the matrix Aᵀ +} + +// Packs the private key to buf. +func (sk *PrivateKey) Pack(buf []byte) { + sk.sh.Pack(buf) +} + +// Unpacks the private key from buf. +func (sk *PrivateKey) Unpack(buf []byte) { + sk.sh.Unpack(buf) + sk.sh.Normalize() +} + +// Packs the public key to buf. +func (pk *PublicKey) Pack(buf []byte) { + pk.th.Pack(buf) + copy(buf[K*common.PolySize:], pk.rho[:]) +} + +// Unpacks the public key from buf. +func (pk *PublicKey) Unpack(buf []byte) { + pk.th.Unpack(buf) + pk.th.Normalize() + copy(pk.rho[:], buf[K*common.PolySize:]) + pk.aT.Derive(&pk.rho, true) +} + +// Derives a new Kyber.CPAPKE keypair from the given seed. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + var pk PublicKey + var sk PrivateKey + + var expandedSeed [64]byte + + // XXX use internal sha3 implementation + h := sha3.New512() + _, _ = h.Write(seed) + + // This writes hash into expandedSeed. Yes, this is idiomatic Go. + h.Sum(expandedSeed[:0]) + + copy(pk.rho[:], expandedSeed[:32]) + sigma := expandedSeed[32:] // σ, the noise seed + + pk.aT.Derive(&pk.rho, false) // Expand ρ to matrix A; we'll transpose later + + var eh Vec + sk.sh.DeriveNoise(sigma, 0, Eta1) // Sample secret vector s + sk.sh.NTT() + sk.sh.Normalize() + + eh.DeriveNoise(sigma, K, Eta1) // Sample blind e + eh.NTT() + + // Next, we compute t = A s + e. + for i := 0; i < K; i++ { + // Note that coefficients of s are bounded by q and those of A + // are bounded by 4.5q and so their product is bounded by 2¹⁵q + // as required for multiplication. + PolyDotHat(&pk.th[i], &pk.aT[i], &sk.sh) + + // A and s were not in Montgomery form, so the Montgomery + // multiplications in the inner product added a factor R⁻¹ which + // we'll cancel out now. This will also ensure the coefficients of + // t are bounded in absolute value by q. + pk.th[i].ToMont() + } + + pk.th.Add(&pk.th, &eh) // bounded by 8q. + pk.th.Normalize() + pk.aT.Transpose() + + return &pk, &sk +} + +// Decrypts ciphertext ct meant for private key sk to plaintext pt. +func (sk *PrivateKey) DecryptTo(pt, ct []byte) { + var u Vec + var v, m common.Poly + + u.Decompress(ct, DU) + v.Decompress(ct[K*compressedPolySize(DU):], DV) + + // Compute m = v - + u.NTT() + PolyDotHat(&m, &sk.sh, &u) + m.BarrettReduce() + m.InvNTT() + m.Sub(&v, &m) + m.Normalize() + + // Compress polynomial m to original message + m.CompressMessageTo(pt) +} + +// Encrypts message pt for the public key to ciphertext ct using randomness +// from seed. +// +// seed has to be of length SeedSize, pt of PlaintextSize and ct of +// CiphertextSize. +func (pk *PublicKey) EncryptTo(ct, seed, pt []byte) { + var rh, e1, u Vec + var e2, v, m common.Poly + + // Sample r, e₁ and e₂ from B_η + rh.DeriveNoise(seed, 0, Eta1) + rh.NTT() + rh.BarrettReduce() + + e1.DeriveNoise(seed, K, common.Eta2) + e2.DeriveNoise(seed, 2*K, common.Eta2) + + // Next we compute u = Aᵀ r + e₁. First Aᵀ. + for i := 0; i < K; i++ { + // Note that coefficients of r are bounded by q and those of Aᵀ + // are bounded by 4.5q and so their product is bounded by 2¹⁵q + // as required for multiplication. + PolyDotHat(&u[i], &pk.aT[i], &rh) + } + + u.BarrettReduce() + + // Aᵀ and r were not in Montgomery form, so the Montgomery + // multiplications in the inner product added a factor R⁻¹ which + // the InvNTT cancels out. + u.InvNTT() + + u.Add(&u, &e1) // u = Aᵀ r + e₁ + + // Next compute v = + e₂ + Decompress_q(m, 1). + PolyDotHat(&v, &pk.th, &rh) + v.BarrettReduce() + v.InvNTT() + + m.DecompressMessage(pt) + v.Add(&v, &m) + v.Add(&v, &e2) // v = + e₂ + Decompress_q(m, 1) + + // Pack ciphertext + u.Normalize() + v.Normalize() + + u.CompressTo(ct, DU) + v.CompressTo(ct[K*compressedPolySize(DU):], DV) +} + +// Returns whether sk equals other. +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + ret := int16(0) + for i := 0; i < K; i++ { + for j := 0; j < common.N; j++ { + ret |= sk.sh[i][j] ^ other.sh[i][j] + } + } + return ret == 0 +} diff --git a/src/circl/pke/kyber/kyber512/internal/cpapke_test.go b/src/circl/pke/kyber/kyber512/internal/cpapke_test.go new file mode 100644 index 00000000000..98d573b5db2 --- /dev/null +++ b/src/circl/pke/kyber/kyber512/internal/cpapke_test.go @@ -0,0 +1,36 @@ +package internal + +import ( + "crypto/rand" + "testing" +) + +func TestEncryptThenDecrypt(t *testing.T) { + var seed [32]byte + var coin [SeedSize]byte + + for i := 0; i < 32; i++ { + seed[i] = byte(i) + coin[i] = byte(i) + } + + for i := 0; i < 100; i++ { + seed[0] = byte(i) + pk, sk := NewKeyFromSeed(seed[:]) + + for j := 0; j < 100; j++ { + var msg, msg2 [PlaintextSize]byte + var ct [CiphertextSize]byte + + _, _ = rand.Read(msg[:]) + _, _ = rand.Read(coin[:]) + + pk.EncryptTo(ct[:], coin[:], msg[:]) + sk.DecryptTo(msg2[:], ct[:]) + + if msg != msg2 { + t.Fatalf("%v %v %v", ct, msg, msg2) + } + } + } +} diff --git a/src/circl/pke/kyber/kyber512/internal/mat.go b/src/circl/pke/kyber/kyber512/internal/mat.go new file mode 100644 index 00000000000..7f6727f14f1 --- /dev/null +++ b/src/circl/pke/kyber/kyber512/internal/mat.go @@ -0,0 +1,83 @@ +package internal + +import ( + "circl/pke/kyber/internal/common" +) + +// A k by k matrix of polynomials. +type Mat [K]Vec + +// Expands the given seed to the corresponding matrix A or its transpose Aᵀ. +func (m *Mat) Derive(seed *[32]byte, transpose bool) { + if !common.DeriveX4Available { + if transpose { + for i := 0; i < K; i++ { + for j := 0; j < K; j++ { + m[i][j].DeriveUniform(seed, uint8(i), uint8(j)) + } + } + } else { + for i := 0; i < K; i++ { + for j := 0; j < K; j++ { + m[i][j].DeriveUniform(seed, uint8(j), uint8(i)) + } + } + } + return + } + + var ps [4]*common.Poly + var xs [4]uint8 + var ys [4]uint8 + x := uint8(0) + y := uint8(0) + + for x != K { + idx := 0 + for ; idx < 4; idx++ { + ps[idx] = &m[x][y] + + if transpose { + xs[idx] = x + ys[idx] = y + } else { + xs[idx] = y + ys[idx] = x + } + + y++ + if y == K { + x++ + y = 0 + + if x == K { + if idx == 0 { + // If there is just one left, then a plain DeriveUniform + // is quicker than the X4 variant. + ps[0].DeriveUniform(seed, xs[0], ys[0]) + return + } + + for idx++; idx < 4; idx++ { + ps[idx] = nil + } + + break + } + } + } + + common.PolyDeriveUniformX4(ps, seed, xs, ys) + } +} + +// Tranposes A in place. +func (m *Mat) Transpose() { + for i := 0; i < K-1; i++ { + for j := i + 1; j < K; j++ { + t := m[i][j] + m[i][j] = m[j][i] + m[j][i] = t + } + } +} diff --git a/src/circl/pke/kyber/kyber512/internal/params.go b/src/circl/pke/kyber/kyber512/internal/params.go new file mode 100644 index 00000000000..b82e1380fb0 --- /dev/null +++ b/src/circl/pke/kyber/kyber512/internal/params.go @@ -0,0 +1,21 @@ +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +import ( + "circl/pke/kyber/internal/common" +) + +const ( + K = 2 + Eta1 = 3 + DU = 10 + DV = 4 + PublicKeySize = 32 + K*common.PolySize + + PrivateKeySize = K * common.PolySize + + PlaintextSize = common.PlaintextSize + SeedSize = 32 + CiphertextSize = 768 +) diff --git a/src/circl/pke/kyber/kyber512/internal/vec.go b/src/circl/pke/kyber/kyber512/internal/vec.go new file mode 100644 index 00000000000..21a0604a333 --- /dev/null +++ b/src/circl/pke/kyber/kyber512/internal/vec.go @@ -0,0 +1,123 @@ +package internal + +import ( + "circl/pke/kyber/internal/common" +) + +// A vector of K polynomials +type Vec [K]common.Poly + +// Samples v[i] from a centered binomial distribution with given η, +// seed and nonce+i. +// +// Essentially CBD_η(PRF(seed, nonce+i)) from the specification. +func (v *Vec) DeriveNoise(seed []byte, nonce uint8, eta int) { + for i := 0; i < K; i++ { + v[i].DeriveNoise(seed, nonce+uint8(i), eta) + } +} + +// Sets p to the inner product of a and b using "pointwise" multiplication. +// +// See MulHat() and NTT() for a description of the multiplication. +// Assumes a and b are in Montgomery form. p will be in Montgomery form, +// and its coefficients will be bounded in absolute value by 2kq. +// If a and b are not in Montgomery form, then the action is the same +// as "pointwise" multiplication followed by multiplying by R⁻¹, the inverse +// of the Montgomery factor. +func PolyDotHat(p *common.Poly, a, b *Vec) { + var t common.Poly + *p = common.Poly{} // set p to zero + for i := 0; i < K; i++ { + t.MulHat(&a[i], &b[i]) + p.Add(&t, p) + } +} + +// Almost normalizes coefficients in-place. +// +// Ensures each coefficient is in {0, …, q}. +func (v *Vec) BarrettReduce() { + for i := 0; i < K; i++ { + v[i].BarrettReduce() + } +} + +// Normalizes coefficients in-place. +// +// Ensures each coefficient is in {0, …, q-1}. +func (v *Vec) Normalize() { + for i := 0; i < K; i++ { + v[i].Normalize() + } +} + +// Applies in-place inverse NTT(). See Poly.InvNTT() for assumptions. +func (v *Vec) InvNTT() { + for i := 0; i < K; i++ { + v[i].InvNTT() + } +} + +// Applies in-place forward NTT(). See Poly.NTT() for assumptions. +func (v *Vec) NTT() { + for i := 0; i < K; i++ { + v[i].NTT() + } +} + +// Sets v to a + b. +func (v *Vec) Add(a, b *Vec) { + for i := 0; i < K; i++ { + v[i].Add(&a[i], &b[i]) + } +} + +// Packs v into buf, which must be of length K*PolySize. +func (v *Vec) Pack(buf []byte) { + for i := 0; i < K; i++ { + v[i].Pack(buf[common.PolySize*i:]) + } +} + +// Unpacks v from buf which must be of length K*PolySize. +func (v *Vec) Unpack(buf []byte) { + for i := 0; i < K; i++ { + v[i].Unpack(buf[common.PolySize*i:]) + } +} + +// Writes Compress_q(v, d) to m. +// +// Assumes v is normalized and d is in {3, 4, 5, 10, 11}. +func (v *Vec) CompressTo(m []byte, d int) { + size := compressedPolySize(d) + for i := 0; i < K; i++ { + v[i].CompressTo(m[size*i:], d) + } +} + +// Set v to Decompress_q(m, 1). +// +// Assumes d is in {3, 4, 5, 10, 11}. v will be normalized. +func (v *Vec) Decompress(m []byte, d int) { + size := compressedPolySize(d) + for i := 0; i < K; i++ { + v[i].Decompress(m[size*i:], d) + } +} + +// ⌈(256 d)/8⌉ +func compressedPolySize(d int) int { + switch d { + case 4: + return 128 + case 5: + return 160 + case 10: + return 320 + case 11: + return 352 + } + panic("unsupported d") +} diff --git a/src/circl/pke/kyber/kyber512/kyber.go b/src/circl/pke/kyber/kyber512/kyber.go new file mode 100644 index 00000000000..b62a0333484 --- /dev/null +++ b/src/circl/pke/kyber/kyber512/kyber.go @@ -0,0 +1,145 @@ +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// kyber512 implements the IND-CPA-secure Public Key Encryption +// scheme Kyber512.CPAPKE as submitted to round 3 of the NIST PQC competition +// and described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +package kyber512 + +import ( + cryptoRand "crypto/rand" + "io" + + "circl/pke/kyber/kyber512/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + KeySeedSize = internal.SeedSize + + // Size of seed for EncryptTo + EncryptionSeedSize = internal.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a ciphertext + CiphertextSize = internal.CiphertextSize + + // Size of a plaintext + PlaintextSize = internal.PlaintextSize +) + +// PublicKey is the type of Kyber512.CPAPKE public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of Kyber512.CPAPKE private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [KeySeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := internal.NewKeyFromSeed(seed[:]) + return (*PublicKey)(pk), (*PrivateKey)(sk), nil +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +// +// Panics if seed is not of length KeySeedSize. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + if len(seed) != KeySeedSize { + panic("seed must be of length KeySeedSize") + } + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// EncryptTo encrypts message pt for the public key and writes the ciphertext +// to ct using randomness from seed. +// +// This function panics if the lengths of pt, seed and ct are not +// PlaintextSize, EncryptionSeedSize and CiphertextSize respectively. +func (pk *PublicKey) EncryptTo(ct []byte, pt []byte, seed []byte) { + if len(pt) != PlaintextSize { + panic("pt must be of length PlaintextSize") + } + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + if len(seed) != EncryptionSeedSize { + panic("seed must be of length EncryptionSeedSize") + } + (*internal.PublicKey)(pk).EncryptTo(ct, pt, seed) +} + +// DecryptTo decrypts message ct for the private key and writes the +// plaintext to pt. +// +// This function panics if the lengths of ct and pt are not +// CiphertextSize and PlaintextSize respectively. +func (sk *PrivateKey) DecryptTo(pt []byte, ct []byte) { + if len(pt) != PlaintextSize { + panic("pt must be of length PlaintextSize") + } + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + (*internal.PrivateKey)(sk).DecryptTo(pt, ct) +} + +// Packs pk into the given buffer. +// +// Panics if buf is not of length PublicKeySize. +func (pk *PublicKey) Pack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of size PublicKeySize") + } + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs sk into the given buffer. +// +// Panics if buf is not of length PrivateKeySize. +func (sk *PrivateKey) Pack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of size PrivateKeySize") + } + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Unpacks pk from the given buffer. +// +// Panics if buf is not of length PublicKeySize. +func (pk *PublicKey) Unpack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of size PublicKeySize") + } + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Unpacks sk from the given buffer. +// +// Panics if buf is not of length PrivateKeySize. +func (sk *PrivateKey) Unpack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of size PrivateKeySize") + } + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Returns whether the two private keys are equal. +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(other)) +} diff --git a/src/circl/pke/kyber/kyber768/internal/cpapke.go b/src/circl/pke/kyber/kyber768/internal/cpapke.go new file mode 100644 index 00000000000..89642b17de4 --- /dev/null +++ b/src/circl/pke/kyber/kyber768/internal/cpapke.go @@ -0,0 +1,177 @@ +// Code generated from kyber512/internal/cpapke.go by gen.go + +package internal + +import ( + "circl/internal/sha3" + "circl/pke/kyber/internal/common" +) + +// A Kyber.CPAPKE private key. +type PrivateKey struct { + sh Vec // NTT(s), normalized +} + +// A Kyber.CPAPKE public key. +type PublicKey struct { + rho [32]byte // ρ, the seed for the matrix A + th Vec // NTT(t), normalized + + // cached values + aT Mat // the matrix Aᵀ +} + +// Packs the private key to buf. +func (sk *PrivateKey) Pack(buf []byte) { + sk.sh.Pack(buf) +} + +// Unpacks the private key from buf. +func (sk *PrivateKey) Unpack(buf []byte) { + sk.sh.Unpack(buf) + sk.sh.Normalize() +} + +// Packs the public key to buf. +func (pk *PublicKey) Pack(buf []byte) { + pk.th.Pack(buf) + copy(buf[K*common.PolySize:], pk.rho[:]) +} + +// Unpacks the public key from buf. +func (pk *PublicKey) Unpack(buf []byte) { + pk.th.Unpack(buf) + pk.th.Normalize() + copy(pk.rho[:], buf[K*common.PolySize:]) + pk.aT.Derive(&pk.rho, true) +} + +// Derives a new Kyber.CPAPKE keypair from the given seed. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + var pk PublicKey + var sk PrivateKey + + var expandedSeed [64]byte + + // XXX use internal sha3 implementation + h := sha3.New512() + _, _ = h.Write(seed) + + // This writes hash into expandedSeed. Yes, this is idiomatic Go. + h.Sum(expandedSeed[:0]) + + copy(pk.rho[:], expandedSeed[:32]) + sigma := expandedSeed[32:] // σ, the noise seed + + pk.aT.Derive(&pk.rho, false) // Expand ρ to matrix A; we'll transpose later + + var eh Vec + sk.sh.DeriveNoise(sigma, 0, Eta1) // Sample secret vector s + sk.sh.NTT() + sk.sh.Normalize() + + eh.DeriveNoise(sigma, K, Eta1) // Sample blind e + eh.NTT() + + // Next, we compute t = A s + e. + for i := 0; i < K; i++ { + // Note that coefficients of s are bounded by q and those of A + // are bounded by 4.5q and so their product is bounded by 2¹⁵q + // as required for multiplication. + PolyDotHat(&pk.th[i], &pk.aT[i], &sk.sh) + + // A and s were not in Montgomery form, so the Montgomery + // multiplications in the inner product added a factor R⁻¹ which + // we'll cancel out now. This will also ensure the coefficients of + // t are bounded in absolute value by q. + pk.th[i].ToMont() + } + + pk.th.Add(&pk.th, &eh) // bounded by 8q. + pk.th.Normalize() + pk.aT.Transpose() + + return &pk, &sk +} + +// Decrypts ciphertext ct meant for private key sk to plaintext pt. +func (sk *PrivateKey) DecryptTo(pt, ct []byte) { + var u Vec + var v, m common.Poly + + u.Decompress(ct, DU) + v.Decompress(ct[K*compressedPolySize(DU):], DV) + + // Compute m = v - + u.NTT() + PolyDotHat(&m, &sk.sh, &u) + m.BarrettReduce() + m.InvNTT() + m.Sub(&v, &m) + m.Normalize() + + // Compress polynomial m to original message + m.CompressMessageTo(pt) +} + +// Encrypts message pt for the public key to ciphertext ct using randomness +// from seed. +// +// seed has to be of length SeedSize, pt of PlaintextSize and ct of +// CiphertextSize. +func (pk *PublicKey) EncryptTo(ct, seed, pt []byte) { + var rh, e1, u Vec + var e2, v, m common.Poly + + // Sample r, e₁ and e₂ from B_η + rh.DeriveNoise(seed, 0, Eta1) + rh.NTT() + rh.BarrettReduce() + + e1.DeriveNoise(seed, K, common.Eta2) + e2.DeriveNoise(seed, 2*K, common.Eta2) + + // Next we compute u = Aᵀ r + e₁. First Aᵀ. + for i := 0; i < K; i++ { + // Note that coefficients of r are bounded by q and those of Aᵀ + // are bounded by 4.5q and so their product is bounded by 2¹⁵q + // as required for multiplication. + PolyDotHat(&u[i], &pk.aT[i], &rh) + } + + u.BarrettReduce() + + // Aᵀ and r were not in Montgomery form, so the Montgomery + // multiplications in the inner product added a factor R⁻¹ which + // the InvNTT cancels out. + u.InvNTT() + + u.Add(&u, &e1) // u = Aᵀ r + e₁ + + // Next compute v = + e₂ + Decompress_q(m, 1). + PolyDotHat(&v, &pk.th, &rh) + v.BarrettReduce() + v.InvNTT() + + m.DecompressMessage(pt) + v.Add(&v, &m) + v.Add(&v, &e2) // v = + e₂ + Decompress_q(m, 1) + + // Pack ciphertext + u.Normalize() + v.Normalize() + + u.CompressTo(ct, DU) + v.CompressTo(ct[K*compressedPolySize(DU):], DV) +} + +// Returns whether sk equals other. +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + ret := int16(0) + for i := 0; i < K; i++ { + for j := 0; j < common.N; j++ { + ret |= sk.sh[i][j] ^ other.sh[i][j] + } + } + return ret == 0 +} diff --git a/src/circl/pke/kyber/kyber768/internal/cpapke_test.go b/src/circl/pke/kyber/kyber768/internal/cpapke_test.go new file mode 100644 index 00000000000..2d5552397c1 --- /dev/null +++ b/src/circl/pke/kyber/kyber768/internal/cpapke_test.go @@ -0,0 +1,38 @@ +// Code generated from kyber512/internal/cpapke_test.go by gen.go + +package internal + +import ( + "crypto/rand" + "testing" +) + +func TestEncryptThenDecrypt(t *testing.T) { + var seed [32]byte + var coin [SeedSize]byte + + for i := 0; i < 32; i++ { + seed[i] = byte(i) + coin[i] = byte(i) + } + + for i := 0; i < 100; i++ { + seed[0] = byte(i) + pk, sk := NewKeyFromSeed(seed[:]) + + for j := 0; j < 100; j++ { + var msg, msg2 [PlaintextSize]byte + var ct [CiphertextSize]byte + + _, _ = rand.Read(msg[:]) + _, _ = rand.Read(coin[:]) + + pk.EncryptTo(ct[:], coin[:], msg[:]) + sk.DecryptTo(msg2[:], ct[:]) + + if msg != msg2 { + t.Fatalf("%v %v %v", ct, msg, msg2) + } + } + } +} diff --git a/src/circl/pke/kyber/kyber768/internal/mat.go b/src/circl/pke/kyber/kyber768/internal/mat.go new file mode 100644 index 00000000000..cc1decfd58e --- /dev/null +++ b/src/circl/pke/kyber/kyber768/internal/mat.go @@ -0,0 +1,85 @@ +// Code generated from kyber512/internal/mat.go by gen.go + +package internal + +import ( + "circl/pke/kyber/internal/common" +) + +// A k by k matrix of polynomials. +type Mat [K]Vec + +// Expands the given seed to the corresponding matrix A or its transpose Aᵀ. +func (m *Mat) Derive(seed *[32]byte, transpose bool) { + if !common.DeriveX4Available { + if transpose { + for i := 0; i < K; i++ { + for j := 0; j < K; j++ { + m[i][j].DeriveUniform(seed, uint8(i), uint8(j)) + } + } + } else { + for i := 0; i < K; i++ { + for j := 0; j < K; j++ { + m[i][j].DeriveUniform(seed, uint8(j), uint8(i)) + } + } + } + return + } + + var ps [4]*common.Poly + var xs [4]uint8 + var ys [4]uint8 + x := uint8(0) + y := uint8(0) + + for x != K { + idx := 0 + for ; idx < 4; idx++ { + ps[idx] = &m[x][y] + + if transpose { + xs[idx] = x + ys[idx] = y + } else { + xs[idx] = y + ys[idx] = x + } + + y++ + if y == K { + x++ + y = 0 + + if x == K { + if idx == 0 { + // If there is just one left, then a plain DeriveUniform + // is quicker than the X4 variant. + ps[0].DeriveUniform(seed, xs[0], ys[0]) + return + } + + for idx++; idx < 4; idx++ { + ps[idx] = nil + } + + break + } + } + } + + common.PolyDeriveUniformX4(ps, seed, xs, ys) + } +} + +// Tranposes A in place. +func (m *Mat) Transpose() { + for i := 0; i < K-1; i++ { + for j := i + 1; j < K; j++ { + t := m[i][j] + m[i][j] = m[j][i] + m[j][i] = t + } + } +} diff --git a/src/circl/pke/kyber/kyber768/internal/params.go b/src/circl/pke/kyber/kyber768/internal/params.go new file mode 100644 index 00000000000..07e39fd9fd3 --- /dev/null +++ b/src/circl/pke/kyber/kyber768/internal/params.go @@ -0,0 +1,21 @@ +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +import ( + "circl/pke/kyber/internal/common" +) + +const ( + K = 3 + Eta1 = 2 + DU = 10 + DV = 4 + PublicKeySize = 32 + K*common.PolySize + + PrivateKeySize = K * common.PolySize + + PlaintextSize = common.PlaintextSize + SeedSize = 32 + CiphertextSize = 1088 +) diff --git a/src/circl/pke/kyber/kyber768/internal/vec.go b/src/circl/pke/kyber/kyber768/internal/vec.go new file mode 100644 index 00000000000..3af1c8fed49 --- /dev/null +++ b/src/circl/pke/kyber/kyber768/internal/vec.go @@ -0,0 +1,125 @@ +// Code generated from kyber512/internal/vec.go by gen.go + +package internal + +import ( + "circl/pke/kyber/internal/common" +) + +// A vector of K polynomials +type Vec [K]common.Poly + +// Samples v[i] from a centered binomial distribution with given η, +// seed and nonce+i. +// +// Essentially CBD_η(PRF(seed, nonce+i)) from the specification. +func (v *Vec) DeriveNoise(seed []byte, nonce uint8, eta int) { + for i := 0; i < K; i++ { + v[i].DeriveNoise(seed, nonce+uint8(i), eta) + } +} + +// Sets p to the inner product of a and b using "pointwise" multiplication. +// +// See MulHat() and NTT() for a description of the multiplication. +// Assumes a and b are in Montgomery form. p will be in Montgomery form, +// and its coefficients will be bounded in absolute value by 2kq. +// If a and b are not in Montgomery form, then the action is the same +// as "pointwise" multiplication followed by multiplying by R⁻¹, the inverse +// of the Montgomery factor. +func PolyDotHat(p *common.Poly, a, b *Vec) { + var t common.Poly + *p = common.Poly{} // set p to zero + for i := 0; i < K; i++ { + t.MulHat(&a[i], &b[i]) + p.Add(&t, p) + } +} + +// Almost normalizes coefficients in-place. +// +// Ensures each coefficient is in {0, …, q}. +func (v *Vec) BarrettReduce() { + for i := 0; i < K; i++ { + v[i].BarrettReduce() + } +} + +// Normalizes coefficients in-place. +// +// Ensures each coefficient is in {0, …, q-1}. +func (v *Vec) Normalize() { + for i := 0; i < K; i++ { + v[i].Normalize() + } +} + +// Applies in-place inverse NTT(). See Poly.InvNTT() for assumptions. +func (v *Vec) InvNTT() { + for i := 0; i < K; i++ { + v[i].InvNTT() + } +} + +// Applies in-place forward NTT(). See Poly.NTT() for assumptions. +func (v *Vec) NTT() { + for i := 0; i < K; i++ { + v[i].NTT() + } +} + +// Sets v to a + b. +func (v *Vec) Add(a, b *Vec) { + for i := 0; i < K; i++ { + v[i].Add(&a[i], &b[i]) + } +} + +// Packs v into buf, which must be of length K*PolySize. +func (v *Vec) Pack(buf []byte) { + for i := 0; i < K; i++ { + v[i].Pack(buf[common.PolySize*i:]) + } +} + +// Unpacks v from buf which must be of length K*PolySize. +func (v *Vec) Unpack(buf []byte) { + for i := 0; i < K; i++ { + v[i].Unpack(buf[common.PolySize*i:]) + } +} + +// Writes Compress_q(v, d) to m. +// +// Assumes v is normalized and d is in {3, 4, 5, 10, 11}. +func (v *Vec) CompressTo(m []byte, d int) { + size := compressedPolySize(d) + for i := 0; i < K; i++ { + v[i].CompressTo(m[size*i:], d) + } +} + +// Set v to Decompress_q(m, 1). +// +// Assumes d is in {3, 4, 5, 10, 11}. v will be normalized. +func (v *Vec) Decompress(m []byte, d int) { + size := compressedPolySize(d) + for i := 0; i < K; i++ { + v[i].Decompress(m[size*i:], d) + } +} + +// ⌈(256 d)/8⌉ +func compressedPolySize(d int) int { + switch d { + case 4: + return 128 + case 5: + return 160 + case 10: + return 320 + case 11: + return 352 + } + panic("unsupported d") +} diff --git a/src/circl/pke/kyber/kyber768/kyber.go b/src/circl/pke/kyber/kyber768/kyber.go new file mode 100644 index 00000000000..5284c754efc --- /dev/null +++ b/src/circl/pke/kyber/kyber768/kyber.go @@ -0,0 +1,145 @@ +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// kyber768 implements the IND-CPA-secure Public Key Encryption +// scheme Kyber768.CPAPKE as submitted to round 3 of the NIST PQC competition +// and described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +package kyber768 + +import ( + cryptoRand "crypto/rand" + "io" + + "circl/pke/kyber/kyber768/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + KeySeedSize = internal.SeedSize + + // Size of seed for EncryptTo + EncryptionSeedSize = internal.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a ciphertext + CiphertextSize = internal.CiphertextSize + + // Size of a plaintext + PlaintextSize = internal.PlaintextSize +) + +// PublicKey is the type of Kyber768.CPAPKE public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of Kyber768.CPAPKE private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [KeySeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := internal.NewKeyFromSeed(seed[:]) + return (*PublicKey)(pk), (*PrivateKey)(sk), nil +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +// +// Panics if seed is not of length KeySeedSize. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + if len(seed) != KeySeedSize { + panic("seed must be of length KeySeedSize") + } + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// EncryptTo encrypts message pt for the public key and writes the ciphertext +// to ct using randomness from seed. +// +// This function panics if the lengths of pt, seed and ct are not +// PlaintextSize, EncryptionSeedSize and CiphertextSize respectively. +func (pk *PublicKey) EncryptTo(ct []byte, pt []byte, seed []byte) { + if len(pt) != PlaintextSize { + panic("pt must be of length PlaintextSize") + } + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + if len(seed) != EncryptionSeedSize { + panic("seed must be of length EncryptionSeedSize") + } + (*internal.PublicKey)(pk).EncryptTo(ct, pt, seed) +} + +// DecryptTo decrypts message ct for the private key and writes the +// plaintext to pt. +// +// This function panics if the lengths of ct and pt are not +// CiphertextSize and PlaintextSize respectively. +func (sk *PrivateKey) DecryptTo(pt []byte, ct []byte) { + if len(pt) != PlaintextSize { + panic("pt must be of length PlaintextSize") + } + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + (*internal.PrivateKey)(sk).DecryptTo(pt, ct) +} + +// Packs pk into the given buffer. +// +// Panics if buf is not of length PublicKeySize. +func (pk *PublicKey) Pack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of size PublicKeySize") + } + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs sk into the given buffer. +// +// Panics if buf is not of length PrivateKeySize. +func (sk *PrivateKey) Pack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of size PrivateKeySize") + } + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Unpacks pk from the given buffer. +// +// Panics if buf is not of length PublicKeySize. +func (pk *PublicKey) Unpack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of size PublicKeySize") + } + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Unpacks sk from the given buffer. +// +// Panics if buf is not of length PrivateKeySize. +func (sk *PrivateKey) Unpack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of size PrivateKeySize") + } + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Returns whether the two private keys are equal. +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(other)) +} diff --git a/src/circl/pke/kyber/templates/params.templ.go b/src/circl/pke/kyber/templates/params.templ.go new file mode 100644 index 00000000000..dc280ad9f60 --- /dev/null +++ b/src/circl/pke/kyber/templates/params.templ.go @@ -0,0 +1,25 @@ +// +build ignore +// The previous line (and this one up to the warning below) is removed by the +// template generator. + +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +import ( + "circl/pke/kyber/internal/common" +) + +const ( + K = {{ .K }} + Eta1 = {{ .Eta1 }} + DU = {{ .DU }} + DV = {{ .DV }} + PublicKeySize = 32 + K*common.PolySize + + PrivateKeySize = K * common.PolySize + + PlaintextSize = common.PlaintextSize + SeedSize = 32 + CiphertextSize = {{ .CiphertextSize }} +) diff --git a/src/circl/pke/kyber/templates/pkg.templ.go b/src/circl/pke/kyber/templates/pkg.templ.go new file mode 100644 index 00000000000..33d11cf3f4e --- /dev/null +++ b/src/circl/pke/kyber/templates/pkg.templ.go @@ -0,0 +1,149 @@ +// +build ignore +// The previous line (and this one up to the warning below) is removed by the +// template generator. + +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// {{ .Pkg }} implements the IND-CPA-secure Public Key Encryption +// scheme {{ .Name }}.CPAPKE as submitted to round 3 of the NIST PQC competition +// and described in +// +// https://pq-crystals.org/kyber/data/kyber-specification-round3.pdf +package {{ .Pkg }} + +import ( + cryptoRand "crypto/rand" + "io" + + "circl/pke/kyber/{{ .Pkg }}/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + KeySeedSize = internal.SeedSize + + // Size of seed for EncryptTo + EncryptionSeedSize = internal.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a ciphertext + CiphertextSize = internal.CiphertextSize + + // Size of a plaintext + PlaintextSize = internal.PlaintextSize +) + +// PublicKey is the type of {{ .Name }}.CPAPKE public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of {{ .Name }}.CPAPKE private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [KeySeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := internal.NewKeyFromSeed(seed[:]) + return (*PublicKey)(pk), (*PrivateKey)(sk), nil +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +// +// Panics if seed is not of length KeySeedSize. +func NewKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) { + if len(seed) != KeySeedSize { + panic("seed must be of length KeySeedSize") + } + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// EncryptTo encrypts message pt for the public key and writes the ciphertext +// to ct using randomness from seed. +// +// This function panics if the lengths of pt, seed and ct are not +// PlaintextSize, EncryptionSeedSize and CiphertextSize respectively. +func (pk *PublicKey) EncryptTo(ct []byte, pt []byte, seed []byte) { + if len(pt) != PlaintextSize { + panic("pt must be of length PlaintextSize") + } + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + if len(seed) != EncryptionSeedSize { + panic("seed must be of length EncryptionSeedSize") + } + (*internal.PublicKey)(pk).EncryptTo(ct, pt, seed) +} + +// DecryptTo decrypts message ct for the private key and writes the +// plaintext to pt. +// +// This function panics if the lengths of ct and pt are not +// CiphertextSize and PlaintextSize respectively. +func (sk *PrivateKey) DecryptTo(pt []byte, ct []byte) { + if len(pt) != PlaintextSize { + panic("pt must be of length PlaintextSize") + } + if len(ct) != CiphertextSize { + panic("ct must be of length CiphertextSize") + } + (*internal.PrivateKey)(sk).DecryptTo(pt, ct) +} + +// Packs pk into the given buffer. +// +// Panics if buf is not of length PublicKeySize. +func (pk *PublicKey) Pack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of size PublicKeySize") + } + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs sk into the given buffer. +// +// Panics if buf is not of length PrivateKeySize. +func (sk *PrivateKey) Pack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of size PrivateKeySize") + } + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Unpacks pk from the given buffer. +// +// Panics if buf is not of length PublicKeySize. +func (pk *PublicKey) Unpack(buf []byte) { + if len(buf) != PublicKeySize { + panic("buf must be of size PublicKeySize") + } + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Unpacks sk from the given buffer. +// +// Panics if buf is not of length PrivateKeySize. +func (sk *PrivateKey) Unpack(buf []byte) { + if len(buf) != PrivateKeySize { + panic("buf must be of size PrivateKeySize") + } + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Returns whether the two private keys are equal. +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(other)) +} diff --git a/src/circl/pki/pki.go b/src/circl/pki/pki.go new file mode 100644 index 00000000000..b6a49e69ad2 --- /dev/null +++ b/src/circl/pki/pki.go @@ -0,0 +1,180 @@ +package pki + +import ( + "crypto/x509/pkix" + "encoding/asn1" + "encoding/pem" + "errors" + "strings" + + "circl/sign" + "circl/sign/schemes" +) + +var allSchemesByOID map[string]sign.Scheme +var allSchemesByTLS map[uint]sign.Scheme + +type pkixPrivKey struct { + Version int + Algorithm pkix.AlgorithmIdentifier + PrivateKey []byte +} + +func init() { + allSchemesByOID = make(map[string]sign.Scheme) + allSchemesByTLS = make(map[uint]sign.Scheme) + for _, scheme := range schemes.All() { + if cert, ok := scheme.(CertificateScheme); ok { + allSchemesByOID[cert.Oid().String()] = scheme + } + if tlsScheme, ok := scheme.(TLSScheme); ok { + allSchemesByTLS[tlsScheme.TLSIdentifier()] = scheme + } + } +} + +func SchemeByOid(oid asn1.ObjectIdentifier) sign.Scheme { return allSchemesByOID[oid.String()] } + +func SchemeByTLSID(id uint) sign.Scheme { return allSchemesByTLS[id] } + +// Additional methods when the signature scheme is supported in X509. +type CertificateScheme interface { + // Return the appropriate OIDs for this instance. It is implicitly + // assumed that the encoding is simple: e.g. uses the same OID for + // signature and public key like Ed25519. + Oid() asn1.ObjectIdentifier +} + +// Additional methods when the signature scheme is supported in TLS. +type TLSScheme interface { + TLSIdentifier() uint +} + +func UnmarshalPEMPublicKey(data []byte) (sign.PublicKey, error) { + block, rest := pem.Decode(data) + if len(rest) != 0 { + return nil, errors.New("trailing data") + } + if !strings.HasSuffix(block.Type, "PUBLIC KEY") { + return nil, errors.New("pem block type is not public key") + } + + return UnmarshalPKIXPublicKey(block.Bytes) +} + +func UnmarshalPKIXPublicKey(data []byte) (sign.PublicKey, error) { + var pkix struct { + Raw asn1.RawContent + Algorithm pkix.AlgorithmIdentifier + PublicKey asn1.BitString + } + if rest, err := asn1.Unmarshal(data, &pkix); err != nil { + return nil, err + } else if len(rest) != 0 { + return nil, errors.New("trailing data") + } + scheme := SchemeByOid(pkix.Algorithm.Algorithm) + if scheme == nil { + return nil, errors.New("unsupported public key algorithm") + } + return scheme.UnmarshalBinaryPublicKey(pkix.PublicKey.RightAlign()) +} + +func UnmarshalPEMPrivateKey(data []byte) (sign.PrivateKey, error) { + block, rest := pem.Decode(data) + if len(rest) != 0 { + return nil, errors.New("trailing") + } + if !strings.HasSuffix(block.Type, "PRIVATE KEY") { + return nil, errors.New("pem block type is not private key") + } + + return UnmarshalPKIXPrivateKey(block.Bytes) +} + +func UnmarshalPKIXPrivateKey(data []byte) (sign.PrivateKey, error) { + var pkix pkixPrivKey + if rest, err := asn1.Unmarshal(data, &pkix); err != nil { + return nil, err + } else if len(rest) != 0 { + return nil, errors.New("trailing data") + } + scheme := SchemeByOid(pkix.Algorithm.Algorithm) + if scheme == nil { + return nil, errors.New("unsupported public key algorithm") + } + var sk []byte + if rest, err := asn1.Unmarshal(pkix.PrivateKey, &sk); err != nil { + return nil, err + } else if len(rest) > 0 { + return nil, errors.New("trailing data") + } + return scheme.UnmarshalBinaryPrivateKey(sk) +} + +func MarshalPEMPublicKey(pk sign.PublicKey) ([]byte, error) { + data, err := MarshalPKIXPublicKey(pk) + if err != nil { + return nil, err + } + str := pem.EncodeToMemory(&pem.Block{ + Type: "PUBLIC KEY", + Bytes: data, + }) + return str, nil +} + +func MarshalPKIXPublicKey(pk sign.PublicKey) ([]byte, error) { + data, err := pk.MarshalBinary() + if err != nil { + return nil, err + } + + scheme := pk.Scheme() + return asn1.Marshal(struct { + pkix.AlgorithmIdentifier + asn1.BitString + }{ + pkix.AlgorithmIdentifier{ + Algorithm: scheme.(CertificateScheme).Oid(), + }, + asn1.BitString{ + Bytes: data, + BitLength: len(data) * 8, + }, + }) +} + +func MarshalPEMPrivateKey(sk sign.PrivateKey) ([]byte, error) { + data, err := MarshalPKIXPrivateKey(sk) + if err != nil { + return nil, err + } + str := pem.EncodeToMemory(&pem.Block{ + Type: sk.Scheme().Name() + " PRIVATE KEY", + Bytes: data, + }, + ) + return str, nil +} + +func MarshalPKIXPrivateKey(sk sign.PrivateKey) ([]byte, error) { + data, err := sk.MarshalBinary() + if err != nil { + return nil, err + } + + data, err = asn1.Marshal(data) + if err != nil { + return nil, err + } + + scheme := sk.Scheme() + return asn1.Marshal(pkixPrivKey{ + 0, + pkix.AlgorithmIdentifier{ + Algorithm: scheme.(CertificateScheme).Oid(), + }, + data, + }) +} diff --git a/src/circl/pki/pki_test.go b/src/circl/pki/pki_test.go new file mode 100644 index 00000000000..208544ce3e8 --- /dev/null +++ b/src/circl/pki/pki_test.go @@ -0,0 +1,56 @@ +package pki_test + +import ( + "testing" + + "circl/pki" + "circl/sign/schemes" +) + +func TestPEM(t *testing.T) { + for _, scheme := range schemes.All() { + scheme := scheme + t.Run(scheme.Name(), func(t *testing.T) { + if scheme == nil { + t.Fatal() + } + + _, ok := scheme.(pki.CertificateScheme) + if !ok { + return + } + + pk, sk, err := scheme.GenerateKey() + if err != nil { + t.Fatal(err) + } + + packedPk, err := pki.MarshalPEMPublicKey(pk) + if err != nil { + t.Fatal(err) + } + + pk2, err := pki.UnmarshalPEMPublicKey(packedPk) + if err != nil { + t.Fatal(err) + } + if !pk.Equal(pk2) { + t.Fatal() + } + + packedSk, err := pki.MarshalPEMPrivateKey(sk) + if err != nil { + t.Fatal(err) + } + + sk2, err := pki.UnmarshalPEMPrivateKey(packedSk) + if err != nil { + t.Fatal(err) + } + + if !sk.Equal(sk2) { + t.Fatal() + } + }) + } +} diff --git a/src/circl/sign/dilithium/dilithium.go b/src/circl/sign/dilithium/dilithium.go new file mode 100644 index 00000000000..211b54f244f --- /dev/null +++ b/src/circl/sign/dilithium/dilithium.go @@ -0,0 +1,118 @@ +//go:generate go run gen.go + +// dilithium implements the CRYSTALS-Dilithium signature schemes +// as submitted to round2 of the NIST PQC competition and described in +// +// https://pq-crystals.org/dilithium/data/dilithium-specification-round2.pdf +// +// Each of the eight different modes of Dilithium is implemented by a +// subpackage. For instance, Dilithium III (the recommended mode) +// can be found in +// +// circl/sign/dilithium/mode3 +// +// If your choice for mode is fixed compile-time, use the subpackages. +// This package provides a convenient wrapper around all of the subpackages +// so one can be chosen at runtime. +// +// The authors of Dilithium recommend to combine it with a "pre-quantum" +// signature scheme. The packages +// +// circl/sign/eddilithium3 +// circl/sign/eddilithium4 +// +// implement such hybrids of Dilithium3 with Ed25519 respectively and +// Dilithium4 with Ed448. These packages are a drop in replacements for the +// mode subpackages of this package. +package dilithium + +import ( + "crypto" + "io" +) + +// PublicKey is a Dilithium public key. +// +// The structure contains values precomputed during unpacking/key generation +// and is therefore significantly larger than a packed public key. +type PublicKey interface { + // Packs public key + Bytes() []byte +} + +// PrivateKey is a Dilithium public key. +// +// The structure contains values precomputed during unpacking/key generation +// and is therefore significantly larger than a packed private key. +type PrivateKey interface { + // Packs private key + Bytes() []byte + + crypto.Signer +} + +// Mode is a certain configuration of the Dilithium signature scheme. +type Mode interface { + // GenerateKey generates a public/private key pair using entropy from rand. + // If rand is nil, crypto/rand.Reader will be used. + GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) + + // NewKeyFromSeed derives a public/private key pair using the given seed. + // Panics if len(seed) != SeedSize() + NewKeyFromSeed(seed []byte) (PublicKey, PrivateKey) + + // NewKeyFromExpandedSeed derives a public/private key pair using the + // given expanded seed. + // + // Use NewKeyFromSeed instead of this function. This function is only exposed + // to generate the NIST KAT test vectors. + NewKeyFromExpandedSeed(seed *[96]byte) (PublicKey, PrivateKey) + + // Sign signs the given message and returns the signature. + // It will panic if sk has not been generated for this mode. + Sign(sk PrivateKey, msg []byte) []byte + + // Verify checks whether the given signature by pk on msg is valid. + // It will panic if pk is of the wrong mode. + Verify(pk PublicKey, msg []byte, signature []byte) bool + + // Unpacks a public key. Panics if the buffer is not of PublicKeySize() + // length. Precomputes values to speed up subsequent calls to Verify. + PublicKeyFromBytes([]byte) PublicKey + + // Unpacks a private key. Panics if the buffer is not + // of PrivateKeySize() length. Precomputes values to speed up subsequent + // calls to Sign(To). + PrivateKeyFromBytes([]byte) PrivateKey + + // SeedSize returns the size of the seed for NewKeyFromSeed + SeedSize() int + + // PublicKeySize returns the size of a packed PublicKey + PublicKeySize() int + + // PrivateKeySize returns the size of a packed PrivateKey + PrivateKeySize() int + + // SignatureSize returns the size of a signature + SignatureSize() int + + // Name returns the name of this mode + Name() string +} + +var modes = make(map[string]Mode) + +// ModeNames returns the list of supported modes. +func ModeNames() []string { + names := []string{} + for name := range modes { + names = append(names, name) + } + return names +} + +// ModeByName returns the mode with the given name or nil when not supported. +func ModeByName(name string) Mode { + return modes[name] +} diff --git a/src/circl/sign/dilithium/dilithium_test.go b/src/circl/sign/dilithium/dilithium_test.go new file mode 100644 index 00000000000..c6ae319cdf6 --- /dev/null +++ b/src/circl/sign/dilithium/dilithium_test.go @@ -0,0 +1,56 @@ +package dilithium + +import ( + "encoding/hex" + "testing" + + "circl/internal/sha3" +) + +func hexHash(in []byte) string { + var ret [16]byte + h := sha3.NewShake256() + _, _ = h.Write(in[:]) + _, _ = h.Read(ret[:]) + return hex.EncodeToString(ret[:]) +} + +func testNewKeyFromSeed(t *testing.T, name, esk, epk string) { + mode := ModeByName(name) + if mode == nil { + t.Fatal() + } + var seed [96]byte + h := sha3.NewShake128() + _, _ = h.Write(make([]byte, mode.SeedSize())) + _, _ = h.Read(seed[:]) + pk, sk := mode.NewKeyFromExpandedSeed(&seed) + pkh := hexHash(pk.Bytes()) + skh := hexHash(sk.Bytes()) + if pkh != epk { + t.Fatalf("%s expected pk %s, got %s", name, epk, pkh) + } + if skh != esk { + t.Fatalf("%s expected pk %s, got %s", name, esk, skh) + } +} + +func TestNewKeyFromSeed(t *testing.T) { + // Test vectors generated from reference implementation + testNewKeyFromSeed(t, "Dilithium1", + "af470e12a57d00c04c4a2b5998f41c71", "83616951b98312a97ea10e12b7b69675") + testNewKeyFromSeed(t, "Dilithium2", + "48dec3d688330dfc68f9bf4277fb92e1", "38e7339d00e64348cb2f965ecf9ee38b") + testNewKeyFromSeed(t, "Dilithium3", + "a44fcf1f43d124865c63cbf381a3b7eb", "b725d31fb709664f8587e2fb6a60fe80") + testNewKeyFromSeed(t, "Dilithium4", + "e054319bbabd2e156c56e8ee923c2a8e", "e7997fc71a6796056d4633a40769c495") + testNewKeyFromSeed(t, "Dilithium1-AES", + "be55853ce1d2c1113fc96f1295928789", "7782ac146d9e636221329cfe64647112") + testNewKeyFromSeed(t, "Dilithium2-AES", + "2abfd0d294ce1b2bab5b860482c4bbc1", "23c4e9516662394e88e559cf2874d7a4") + testNewKeyFromSeed(t, "Dilithium3-AES", + "ba72ed309182aa509e595013b3ad9089", "887baaf3a98d0aa6b95c8c1a6867e609") + testNewKeyFromSeed(t, "Dilithium4-AES", + "7c1c8b5df63fd096901da43c00fa71e8", "f7f850c1d8ff82c868ab2f188ac624b3") +} diff --git a/src/circl/sign/dilithium/example_test.go b/src/circl/sign/dilithium/example_test.go new file mode 100644 index 00000000000..1c370fb7771 --- /dev/null +++ b/src/circl/sign/dilithium/example_test.go @@ -0,0 +1,56 @@ +package dilithium_test + +import ( + "fmt" + "sort" + + "circl/sign/dilithium" +) + +func Example() { + // Check supported modes + modes := dilithium.ModeNames() + sort.Strings(modes) + fmt.Printf("Supported modes: %v\n", modes) + + // Pick Dilithium mode III. + mode := dilithium.ModeByName("Dilithium3") + if mode == nil { + panic("Mode3 not supported") + } + + // Alternatively one could simply write + // + // mode := dilithium.Mode3 + + // Generates a keypair. + pk, sk, err := mode.GenerateKey(nil) + if err != nil { + panic(err) + } + // (Alternatively one can derive a keypair from a seed, + // see mode.NewKeyFromSeed().) + + // Packs public and private key + packedSk := sk.Bytes() + packedPk := pk.Bytes() + + // Load it again + sk2 := mode.PrivateKeyFromBytes(packedSk) + pk2 := mode.PublicKeyFromBytes(packedPk) + + // Creates a signature on our message with the generated private key. + msg := []byte("Some message") + signature := mode.Sign(sk2, msg) + + // Checks whether a signature is correct + if !mode.Verify(pk2, msg, signature) { + panic("incorrect signature") + } + + fmt.Printf("O.K.") + + // Output: + // Supported modes: [Dilithium1 Dilithium1-AES Dilithium2 Dilithium2-AES Dilithium3 Dilithium3-AES Dilithium4 Dilithium4-AES] + // O.K. +} diff --git a/src/circl/sign/dilithium/internal/common/aes.go b/src/circl/sign/dilithium/internal/common/aes.go new file mode 100644 index 00000000000..91602d7a6f6 --- /dev/null +++ b/src/circl/sign/dilithium/internal/common/aes.go @@ -0,0 +1,46 @@ +package common + +import ( + "crypto/aes" + "crypto/cipher" + "encoding/binary" +) + +// AES CTR stream used as a replacement for SHAKE in Dilithium[1234]-AES. +type AesStream struct { + c cipher.Block + counter uint64 + nonce uint16 +} + +// Create a new AesStream as a replacement of SHAKE128. (Note that +// not all occurrences of SHAKE are replaced by AES in the AES-variants). +func NewAesStream128(key *[32]byte, nonce uint16) AesStream { + c, _ := aes.NewCipher(key[:]) + return AesStream{c: c, nonce: nonce} +} + +// Create a new AesStream as a replacement of SHAKE256. (Note that +// not all occurrences of SHAKE are replaced by AES in the AES-variants.) +// +// Yes, in an AES mode, Dilithium throws away the last 16 bytes of a seed ... +// See the remark at the end of the caption of Figure 4 in the Round 2 spec. +func NewAesStream256(key *[48]byte, nonce uint16) AesStream { + c, _ := aes.NewCipher(key[:32]) + return AesStream{c: c, nonce: nonce} +} + +// Squeeze some more blocks from the AES CTR stream into buf. +// +// Assumes length of buf is a multiple of 16. +func (s *AesStream) SqueezeInto(buf []byte) { + var tmp [16]byte + binary.LittleEndian.PutUint16(tmp[:], s.nonce) + + for len(buf) != 0 { + binary.BigEndian.PutUint64(tmp[8:], s.counter) + s.counter++ + s.c.Encrypt(buf, tmp[:]) + buf = buf[16:] + } +} diff --git a/src/circl/sign/dilithium/internal/common/amd64.go b/src/circl/sign/dilithium/internal/common/amd64.go new file mode 100644 index 00000000000..fea6551a828 --- /dev/null +++ b/src/circl/sign/dilithium/internal/common/amd64.go @@ -0,0 +1,183 @@ +// +build amd64 + +package common + +import ( + "internal/cpu" +) + +// Execute an in-place forward NTT on as. +// +// Assumes the coefficients are in Montgomery representation and bounded +// by 2*Q. The resulting coefficients are again in Montgomery representation, +// but are only bounded bt 18*Q. +func (p *Poly) NTT() { + if cpu.X86.HasAVX2 { + nttAVX2( + (*[N]uint32)(p), + ) + } else { + p.nttGeneric() + } +} + +// Execute an in-place inverse NTT and multiply by Montgomery factor R +// +// Assumes the coefficients are in Montgomery representation and bounded +// by 2*Q. The resulting coefficients are again in Montgomery representation +// and bounded by 2*Q. +func (p *Poly) InvNTT() { + if cpu.X86.HasAVX2 { + invNttAVX2( + (*[N]uint32)(p), + ) + } else { + p.invNttGeneric() + } +} + +// Sets p to the polynomial whose coefficients are the pointwise multiplication +// of those of a and b. The coefficients of p are bounded by 2q. +// +// Assumes a and b are in Montgomery form and that the pointwise product +// of each coefficient is below 2³² q. +func (p *Poly) MulHat(a, b *Poly) { + if cpu.X86.HasAVX2 { + mulHatAVX2( + (*[N]uint32)(p), + (*[N]uint32)(a), + (*[N]uint32)(b), + ) + } else { + p.mulHatGeneric(a, b) + } +} + +// Sets p to a + b. Does not normalize polynomials. +func (p *Poly) Add(a, b *Poly) { + if cpu.X86.HasAVX2 { + addAVX2( + (*[N]uint32)(p), + (*[N]uint32)(a), + (*[N]uint32)(b), + ) + } else { + p.addGeneric(a, b) + } +} + +// Sets p to a - b. +// +// Warning: assumes coefficients of b are less than 2q. +// Sets p to a + b. Does not normalize polynomials. +func (p *Poly) Sub(a, b *Poly) { + if cpu.X86.HasAVX2 { + subAVX2( + (*[N]uint32)(p), + (*[N]uint32)(a), + (*[N]uint32)(b), + ) + } else { + p.subGeneric(a, b) + } +} + +// Writes p whose coefficients are in [0, 16) to buf, which must be of +// length N/2. +func (p *Poly) PackLe16(buf []byte) { + if cpu.X86.HasAVX2 { + if len(buf) < PolyLe16Size { + panic("buf too small") + } + packLe16AVX2( + (*[N]uint32)(p), + &buf[0], + ) + } else { + p.packLe16Generic(buf) + } +} + +// Reduces each of the coefficients to <2q. +func (p *Poly) ReduceLe2Q() { + if cpu.X86.HasAVX2 { + reduceLe2QAVX2((*[N]uint32)(p)) + } else { + p.reduceLe2QGeneric() + } +} + +// Reduce each of the coefficients to > 23 + x2 := x & 0x7FFFFF // 2²³-1 + return x2 + (x1 << 13) - x1 +} + +// Returns x mod q. +func modQ(x uint32) uint32 { + return le2qModQ(reduceLe2Q(x)) +} + +// For x R ≤ q 2³², find y ≤ 2q with y = x mod q. +func montReduceLe2Q(x uint64) uint32 { + // Qinv = 4236238847 = -(q⁻¹) mod 2³² + m := (x * Qinv) & 0xffffffff + return uint32((x + m*uint64(Q)) >> 32) +} + +// Returns x mod q for 0 ≤ x < 2q. +func le2qModQ(x uint32) uint32 { + x -= Q + mask := uint32(int32(x) >> 31) // mask is 2³²-1 if x was neg.; 0 otherwise + return x + (mask & Q) +} + +// Splits 0 ≤ a < Q into a0 and a1 with a = a1*2ᴰ + a0 +// and -2ᴰ⁻¹ < a0 < 2ᴰ⁻¹. Returns a0 + Q and a1. +func power2round(a uint32) (a0plusQ, a1 uint32) { + // We effectively compute a0 = a mod± 2ᵈ + // and a1 = (a - a0) / 2ᵈ. + a0 := a & ((1 << D) - 1) // a mod 2ᵈ + + // a0 is one of 0, 1, ..., 2ᵈ⁻¹-1, 2ᵈ⁻¹, 2ᵈ⁻¹+1, ..., 2ᵈ-1 + a0 -= (1 << (D - 1)) + 1 + // now a0 is -2ᵈ⁻¹-1, -2ᵈ⁻¹, ..., -2, -1, 0, ..., 2ᵈ⁻¹-2 + // Next, we add 2ᴰ to those a0 that are negative (seen as int32). + a0 += uint32(int32(a0)>>31) & (1 << D) + // now a0 is 2ᵈ⁻¹-1, 2ᵈ⁻¹, ..., 2ᵈ-2, 2ᵈ-1, 0, ..., 2ᵈ⁻¹-2 + a0 -= (1 << (D - 1)) - 1 + // now a0 id 0, 1, 2, ..., 2ᵈ⁻¹-1, 2ᵈ⁻¹-1, -2ᵈ⁻¹-1, ... + // which is what we want. + a0plusQ = Q + a0 + a1 = (a - a0) >> D + return +} + +// Splits 0 ≤ a < Q into a0 and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2, +// except for when we would have a1 = (Q-1)/α = 16 in which case a1=0 is taken +// and -α/2 ≤ a₀ < 0. Returns a₀ + Q. Note 0 ≤ a₁ ≤ 15. +// Note α = 2*γ₂ = γ₁ with the chosen parameters of Dilithium. +func decompose(a uint32) (a0plusQ, a1 uint32) { + // Finds 0 ≤ t < 1.5α with t = a mod α. (Recall α=2¹⁹ - 2⁹.) + t := int32(a & 0x7ffff) + t += (int32(a) >> 19) << 9 + + // If 0 ≤ t < α, then the following computes a mod± α with the same + // argument as in power2round(). If α ≤ t < 1.5α, then the following + // subtracts α, which thus also computes a mod± α. + t -= Alpha/2 + 1 + t += (t >> 31) & Alpha + t -= Alpha/2 - 1 + + a1 = a - uint32(t) + + // We want to divide α out of a₁ (to get the proper value of a1). + // As our values are relatively small and α=2¹⁹-2⁹, we can simply + // divide by 2¹⁹ and add one. There is one corner case we have to deal + // with: if a₁=0 then 0/α=0≠1=0/2¹⁹+1, so we need to get rid of the +1. + u := ((a1 - 1) >> 31) & 1 // u=1 if a₁=0 + a1 = (a1 >> 19) + 1 + a1 -= u // correct for the case a₁=0 + + a0plusQ = Q + uint32(t) + + // Now deal with the corner case of the definition, if a₁=(Q-1)/α, + // then we use a₁=0. Note (Q-1)/α=2⁴. + a0plusQ -= a1 >> 4 // to compensate, we only have to move the -1. + a1 &= 15 // set a₀=0 if a₁=16 + return +} + +// Assume 0 ≤ r, f < Q with ‖f‖_∞ ≤ α/2. Decompose r as r = r1*α + r0 as +// computed by decompose(). Write r' := r - f (mod Q). Now, decompose +// r'=r-f again as r' = r'1*α + r'0 using decompose(). As f is small, we +// have r'1 = r1 + h, where h ∈ {-1, 0, 1}. makeHint() computes |h| +// given z0 := r0 - f (mod Q) and r1. With |h|, which is called the hint, +// we can reconstruct r1 using only r' = r - f, which is done by useHint(). +// To wit: +// +// useHint( r - f, makeHint( r0 - f, r1 ) ) = r1. +// +// Assumes 0 ≤ z0 < Q. +func makeHint(z0, r1 uint32) uint32 { + // If -α/2 < r0 - f ≤ α/2, then r1*α + r0 - f is a valid decomposition of r' + // with the restrictions of decompose() and so r'1 = r1. So the hint + // should be 0. This is covered by the first two inequalities. + // There is one other case: if r0 - f = -α/2, then r1*α + r0 - f is also + // a valid decomposition if r1 = 0. In the other cases a one is carried + // and the hint should be 1. + if z0 <= Gamma2 || z0 > Q-Gamma2 || (z0 == Q-Gamma2 && r1 == 0) { + return 0 + } + return 1 +} + +// Uses the hint created by makeHint() to reconstruct r1 from r'=r-f; see +// documentation of makeHint() for context. +// Assumes 0 ≤ r' < Q. +func useHint(rp uint32, hint uint32) uint32 { + rp0plusQ, rp1 := decompose(rp) + if hint == 0 { + return rp1 + } + if rp0plusQ > Q { + return (rp1 + 1) & 15 + } + return (rp1 - 1) & 15 +} diff --git a/src/circl/sign/dilithium/internal/common/field_test.go b/src/circl/sign/dilithium/internal/common/field_test.go new file mode 100644 index 00000000000..3be7f6abca4 --- /dev/null +++ b/src/circl/sign/dilithium/internal/common/field_test.go @@ -0,0 +1,106 @@ +package common + +import ( + "flag" + "math/rand" + "testing" +) + +var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests") + +func TestModQ(t *testing.T) { + for i := 0; i < 1000; i++ { + x := rand.Uint32() + y := modQ(x) + if y > Q { + t.Fatalf("modQ(%d) > Q", x) + } + if y != x%Q { + t.Fatalf("modQ(%d) != %d (mod Q)", x, x) + } + } +} + +func TestReduceLe2Q(t *testing.T) { + for i := 0; i < 1000; i++ { + x := rand.Uint32() + y := reduceLe2Q(x) + if y > 2*Q { + t.Fatalf("reduce_le2q(%d) > 2Q", x) + } + if y%Q != x%Q { + t.Fatalf("reduce_le2q(%d) != %d (mod Q)", x, x) + } + } +} + +func TestPower2Round(t *testing.T) { + for a := uint32(0); a < Q; a++ { + a0PlusQ, a1 := power2round(a) + a0 := int32(a0PlusQ) - int32(Q) + if int32(a) != a0+int32((1<= a0) || (a0 > 1<<(D-1)) { + t.Fatalf("power2round(%v): a0 out of bounds", a) + } + if a1 > (1 << (23 - 14)) { // 23 ~ 2log Q. + t.Fatalf("power2round(%v): a1 out of bounds", a) + } + } +} + +func TestDecompose(t *testing.T) { + for a := uint32(0); a < Q; a++ { + a0PlusQ, a1 := decompose(a) + a0 := int32(a0PlusQ) - int32(Q) + recombined := a0 + int32(Alpha*a1) + if a1 == 0 && recombined < 0 { + recombined += Q + if -(Alpha/2) > a0 || a0 >= 0 { + t.Fatalf("decompose(%v): a0 out of bounds", a) + } + } else { + if (-(Alpha / 2) >= a0) || (a0 > Alpha/2) { + t.Fatalf("decompose(%v): a0 out of bounds", a) + } + } + if int32(a) != recombined { + t.Fatalf("decompose(%v) doesn't recombine %v %v", a, a0, a1) + } + } +} + +func TestMakeHint(t *testing.T) { + if !*runVeryLongTest { + t.SkipNow() + } + for w := uint32(0); w < Q; w++ { + w0, w1 := decompose(w) + for fn := uint32(0); fn <= Gamma2; fn++ { + fsign := false + for { + var f uint32 + if fsign { + if fn == 0 { + break + } + f = Q - fn + } else { + f = fn + } + + hint := makeHint(reduceLe2Q(w0+Q-f), w1) + w1p := useHint(reduceLe2Q(w+Q-f), hint) + if w1p != w1 { + t.Fatal() + } + + if fsign { + break + } + fsign = true + } + } + } +} diff --git a/src/circl/sign/dilithium/internal/common/generic.go b/src/circl/sign/dilithium/internal/common/generic.go new file mode 100644 index 00000000000..8dd555d354c --- /dev/null +++ b/src/circl/sign/dilithium/internal/common/generic.go @@ -0,0 +1,95 @@ +// +build !amd64 + +package common + +// Execute an in-place forward NTT on as. +// +// Assumes the coefficients are in Montgomery representation and bounded +// by 2*Q. The resulting coefficients are again in Montgomery representation, +// but are only bounded bt 18*Q. +func (p *Poly) NTT() { + p.nttGeneric() +} + +// Execute an in-place inverse NTT and multiply by Montgomery factor R +// +// Assumes the coefficients are in Montgomery representation and bounded +// by 2*Q. The resulting coefficients are again in Montgomery representation +// and bounded by 2*Q. +func (p *Poly) InvNTT() { + p.invNttGeneric() +} + +// Sets p to the polynomial whose coefficients are the pointwise multiplication +// of those of a and b. The coefficients of p are bounded by 2q. +// +// Assumes a and b are in Montgomery form and that the pointwise product +// of each coefficient is below 2³² q. +func (p *Poly) MulHat(a, b *Poly) { + p.mulHatGeneric(a, b) +} + +// Sets p to a + b. Does not normalize polynomials. +func (p *Poly) Add(a, b *Poly) { + p.addGeneric(a, b) +} + +// Sets p to a - b. +// +// Warning: assumes coefficients of b are less than 2q. +// Sets p to a + b. Does not normalize polynomials. +func (p *Poly) Sub(a, b *Poly) { + p.subGeneric(a, b) +} + +// Writes p whose coefficients are in [0, 16) to buf, which must be of +// length N/2. +func (p *Poly) PackLe16(buf []byte) { + p.packLe16Generic(buf) +} + +// Reduces each of the coefficients to <2q. +func (p *Poly) ReduceLe2Q() { + p.reduceLe2QGeneric() +} + +// Reduce each of the coefficients to 0; l >>= 1 { + // On the n-th iteration of the l-loop, the coefficients start off + // bounded by n*2*Q. + // + // offset effectively loops over the row groups in this column; it + // is the first row in the row group. + for offset := uint(0); offset < N-l; offset += 2 * l { + k++ + zeta := uint64(Zetas[k]) + + // j loops over each butterfly in the row group. + for j := offset; j < offset+l; j++ { + t := montReduceLe2Q(zeta * uint64(p[j+l])) + p[j+l] = p[j] + (2*Q - t) // Cooley--Tukey butterfly + p[j] += t + } + } + } +} + +// Execute an in-place inverse NTT and multiply by Montgomery factor R +// +// Assumes the coefficients are in Montgomery representation and bounded +// by 2*Q. The resulting coefficients are again in Montgomery representation +// and bounded by 2*Q. +func (p *Poly) invNttGeneric() { + k := 0 // Index into InvZetas + + // We basically do the opposite of NTT, but postpone dividing by 2 in the + // inverse of the Cooley--Tukey butterfly and accumulate that to a big + // division by 2⁸ at the end. See comments in the NTT() function. + + for l := uint(1); l < N; l <<= 1 { + // On the n-th iteration of the l-loop, the coefficients start off + // bounded by 2ⁿ⁻¹*2*Q, so by 256*Q on the last. + for offset := uint(0); offset < N-l; offset += 2 * l { + zeta := uint64(InvZetas[k]) + k++ + for j := offset; j < offset+l; j++ { + t := p[j] // Gentleman--Sande butterfly + p[j] = t + p[j+l] + t += 256*Q - p[j+l] + p[j+l] = montReduceLe2Q(zeta * uint64(t)) + } + } + } + + for j := uint(0); j < N; j++ { + // ROver256 = 41978 = (256)⁻¹ R² + p[j] = montReduceLe2Q(ROver256 * uint64(p[j])) + } +} diff --git a/src/circl/sign/dilithium/internal/common/ntt_test.go b/src/circl/sign/dilithium/internal/common/ntt_test.go new file mode 100644 index 00000000000..3081dc09288 --- /dev/null +++ b/src/circl/sign/dilithium/internal/common/ntt_test.go @@ -0,0 +1,82 @@ +package common + +import ( + "math/rand" + "testing" +) + +func (p *Poly) RandLe2Q() { + for i := uint(0); i < N; i++ { + p[i] = uint32(rand.Intn(int(2 * Q))) + } +} + +func TestNTTAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var p Poly + p.RandLe2Q() + q1 := p + q2 := p + q1.NTT() + q2.nttGeneric() + if q1 != q2 { + t.Fatalf("NTT(%v) = %v != %v", p, q1, q2) + } + } +} + +func TestNTT(t *testing.T) { + for k := 0; k < 1000; k++ { + var p, q Poly + p.RandLe2Q() + q = p + q.Normalize() + p.NTT() + for i := uint(0); i < N; i++ { + if p[i] > 18*Q { + t.Fatalf("NTT(%v)[%d] = %d > 18*Q", q, i, p[i]) + } + } + p.ReduceLe2Q() + p.InvNTT() + for i := uint(0); i < N; i++ { + if p[i] > 2*Q { + t.Fatalf("InvNTT(%v)[%d] > 2*Q", q, i) + } + } + p.Normalize() + for i := uint(0); i < N; i++ { + if p[i] != uint32((uint64(q[i])*uint64(1<<32))%Q) { + t.Fatalf("%v != %v", p, q) + } + } + } +} + +func BenchmarkNTTGeneric(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.nttGeneric() + } +} + +func BenchmarkInvNTTGeneric(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.invNttGeneric() + } +} + +func BenchmarkNTT(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.NTT() + } +} + +func BenchmarkInvNTT(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.InvNTT() + } +} diff --git a/src/circl/sign/dilithium/internal/common/pack.go b/src/circl/sign/dilithium/internal/common/pack.go new file mode 100644 index 00000000000..eb9bdca8a1d --- /dev/null +++ b/src/circl/sign/dilithium/internal/common/pack.go @@ -0,0 +1,242 @@ +package common + +import ( + "encoding/binary" +) + +// Sets p to the polynomial whose coefficients are less than 512 encoded +// into buf (which must be of size PolyT1Size). +// +// p will be normalized. +func (p *Poly) UnpackT1(buf []byte) { + j := 0 + for i := 0; i < PolyT1Size; i += 9 { + p[j] = (uint32(buf[i]) | (uint32(buf[i+1]) << 8)) & 0x1ff + p[j+1] = (uint32(buf[i+1]>>1) | (uint32(buf[i+2]) << 7)) & 0x1ff + p[j+2] = (uint32(buf[i+2]>>2) | (uint32(buf[i+3]) << 6)) & 0x1ff + p[j+3] = (uint32(buf[i+3]>>3) | (uint32(buf[i+4]) << 5)) & 0x1ff + p[j+4] = (uint32(buf[i+4]>>4) | (uint32(buf[i+5]) << 4)) & 0x1ff + p[j+5] = (uint32(buf[i+5]>>5) | (uint32(buf[i+6]) << 3)) & 0x1ff + p[j+6] = (uint32(buf[i+6]>>6) | (uint32(buf[i+7]) << 2)) & 0x1ff + p[j+7] = (uint32(buf[i+7]>>7) | (uint32(buf[i+8]) << 1)) & 0x1ff + j += 8 + } +} + +// Writes p whose coefficients are in (-2ᵈ⁻¹, 2ᵈ⁻¹] into buf which +// has to be of length at least PolyT0Size. +// +// Assumes that the coefficients are not normalized, but lie in the +// range (q-2ᵈ⁻¹, q+2ᵈ⁻¹]. +func (p *Poly) PackT0(buf []byte) { + j := 0 + for i := 0; i < PolyT0Size; i += 7 { + p0 := Q + (1 << (D - 1)) - p[j] + p1 := Q + (1 << (D - 1)) - p[j+1] + p2 := Q + (1 << (D - 1)) - p[j+2] + p3 := Q + (1 << (D - 1)) - p[j+3] + + buf[i] = byte(p0) + buf[i+1] = byte(p0>>8) | byte(p1<<6) + buf[i+2] = byte(p1 >> 2) + buf[i+3] = byte(p1>>10) | byte(p2<<4) + buf[i+4] = byte(p2 >> 4) + buf[i+5] = byte(p2>>12) | byte(p3<<2) + buf[i+6] = byte(p3 >> 6) + j += 4 + } +} + +// Sets p to the polynomial packed into buf by PackT0. +// +// The coefficients of p will not be normalized, but will lie +// in (-2ᵈ⁻¹, 2ᵈ⁻¹]. +func (p *Poly) UnpackT0(buf []byte) { + j := 0 + for i := 0; i < PolyT0Size; i += 7 { + p[j] = Q + (1 << (D - 1)) - ((uint32(buf[i]) | + (uint32(buf[i+1]) << 8)) & 0x3fff) + p[j+1] = Q + (1 << (D - 1)) - (((uint32(buf[i+1]) >> 6) | + (uint32(buf[i+2]) << 2) | + (uint32(buf[i+3]) << 10)) & 0x3fff) + p[j+2] = Q + (1 << (D - 1)) - (((uint32(buf[i+3]) >> 4) | + (uint32(buf[i+4]) << 4) | + (uint32(buf[i+5]) << 12)) & 0x3fff) + p[j+3] = Q + (1 << (D - 1)) - ((uint32(buf[i+5]) >> 2) | + (uint32(buf[i+6]) << 6)) + j += 4 + } +} + +// Writes p whose coefficients are less than 512 into buf, which must be +// of size at least PolyT1Size . +// +// Assumes coefficients of p are normalized. +func (p *Poly) PackT1(buf []byte) { + j := 0 + for i := 0; i < PolyT1Size; i += 9 { + buf[i] = byte(p[j]) + buf[i+1] = byte(p[j]>>8) | byte(p[j+1]<<1) + buf[i+2] = byte(p[j+1]>>7) | byte(p[j+2]<<2) + buf[i+3] = byte(p[j+2]>>6) | byte(p[j+3]<<3) + buf[i+4] = byte(p[j+3]>>5) | byte(p[j+4]<<4) + buf[i+5] = byte(p[j+4]>>4) | byte(p[j+5]<<5) + buf[i+6] = byte(p[j+5]>>3) | byte(p[j+6]<<6) + buf[i+7] = byte(p[j+6]>>2) | byte(p[j+7]<<7) + buf[i+8] = byte(p[j+7] >> 1) + j += 8 + } +} + +// Writes p whose coefficients are in norm less than γ₁ into buf +// which has to be of length PolyLeGamma1Size. +// +// Assumes p is normalized. +func (p *Poly) PackLeGamma1(buf []byte) { + j := 0 + for i := 0; i < PolyLeGamma1Size; i += 5 { + // Coefficients are in [0, γ₁) ∪ (Q-γ₁, Q) + p0 := Gamma1 - 1 - p[j] // ... in [0, γ₁) ∪ [γ₁-1-Q, 2(γ₁-1)-Q] + p0 += uint32(int32(p0)>>31) & Q // ... in [0, 2(γ₁-1)] + p1 := Gamma1 - 1 - p[j+1] + p1 += uint32(int32(p1)>>31) & Q + + buf[i] = byte(p0) + buf[i+1] = byte(p0 >> 8) + buf[i+2] = byte(p0>>16) | byte(p1<<4) + buf[i+3] = byte(p1 >> 4) + buf[i+4] = byte(p1 >> 12) + j += 2 + } +} + +// Sets p to the polynomial packed into buf by PackLeGamma1. +// +// p will be normalized. +// +// Beware, for arbitrary buf the coefficients of p might exceed γ₁. +func (p *Poly) UnpackLeGamma1(buf []byte) { + j := 0 + for i := 0; i < PolyLeGamma1Size; i += 40 { + a0 := binary.LittleEndian.Uint64(buf[i:]) + a1 := binary.LittleEndian.Uint64(buf[i+8:]) + a2 := binary.LittleEndian.Uint64(buf[i+16:]) + a3 := binary.LittleEndian.Uint64(buf[i+24:]) + a4 := binary.LittleEndian.Uint64(buf[i+32:]) + + p0 := Gamma1 - 1 - uint32(a0&0xfffff) + p1 := Gamma1 - 1 - uint32((a0>>20)&0xfffff) + p2 := Gamma1 - 1 - uint32((a0>>40)&0xfffff) + p3 := Gamma1 - 1 - uint32(((a0>>60)|(a1<<4))&0xfffff) + p4 := Gamma1 - 1 - uint32((a1>>16)&0xfffff) + p5 := Gamma1 - 1 - uint32((a1>>36)&0xfffff) + p6 := Gamma1 - 1 - uint32(((a1>>56)|(a2<<8))&0xfffff) + p7 := Gamma1 - 1 - uint32((a2>>12)&0xfffff) + p8 := Gamma1 - 1 - uint32((a2>>32)&0xfffff) + p9 := Gamma1 - 1 - uint32(((a2>>52)|(a3<<12))&0xfffff) + p10 := Gamma1 - 1 - uint32((a3>>8)&0xfffff) + p11 := Gamma1 - 1 - uint32((a3>>28)&0xfffff) + p12 := Gamma1 - 1 - uint32(((a3>>48)|(a4<<16))&0xfffff) + p13 := Gamma1 - 1 - uint32((a4>>4)&0xfffff) + p14 := Gamma1 - 1 - uint32((a4>>24)&0xfffff) + p15 := Gamma1 - 1 - uint32((a4>>44)&0xfffff) + + p0 += uint32(int32(p0)>>31) & Q + p1 += uint32(int32(p1)>>31) & Q + p2 += uint32(int32(p2)>>31) & Q + p3 += uint32(int32(p3)>>31) & Q + p4 += uint32(int32(p4)>>31) & Q + p5 += uint32(int32(p5)>>31) & Q + p6 += uint32(int32(p6)>>31) & Q + p7 += uint32(int32(p7)>>31) & Q + p8 += uint32(int32(p8)>>31) & Q + p9 += uint32(int32(p9)>>31) & Q + p10 += uint32(int32(p10)>>31) & Q + p11 += uint32(int32(p11)>>31) & Q + p12 += uint32(int32(p12)>>31) & Q + p13 += uint32(int32(p13)>>31) & Q + p14 += uint32(int32(p14)>>31) & Q + p15 += uint32(int32(p15)>>31) & Q + + p[j] = p0 + p[j+1] = p1 + p[j+2] = p2 + p[j+3] = p3 + p[j+4] = p4 + p[j+5] = p5 + p[j+6] = p6 + p[j+7] = p7 + p[j+8] = p8 + p[j+9] = p9 + p[j+10] = p10 + p[j+11] = p11 + p[j+12] = p12 + p[j+13] = p13 + p[j+14] = p14 + p[j+15] = p15 + + j += 16 + } +} + +// Writes p whose coefficients are in [0, 16) to buf, which must be of +// length N/2. +func (p *Poly) packLe16Generic(buf []byte) { + j := 0 + for i := 0; i < PolyLe16Size; i++ { + buf[i] = byte(p[j]) | byte(p[j+1]<<4) + j += 2 + } +} + +// Writes p with 60 non-zero coefficients {-1,1} to buf, which must have +// length 40. +func (p *Poly) PackB60(buf []byte) { + // We start with a mask of the non-zero positions of p (which is 32 bytes) + // and then append 60 packed bits, where a one indicates a negative + // coefficients. + var signs uint64 + mask := uint64(1) + for i := 0; i < 32; i++ { + buf[i] = 0 + for j := 0; j < 8; j++ { + if p[8*i+j] != 0 { + buf[i] |= 1 << uint(j) + if p[8*i+j] == Q-1 { + signs |= mask + } + mask <<= 1 + } + } + } + for i := uint64(0); i < 8; i++ { + buf[i+32] = uint8(signs >> (8 * i)) + } +} + +// UnpackB60 sets p to the polynomial packed into buf with Poly.PackB60(). +// +// Returns whether unpacking was successful. +func (p *Poly) UnpackB60(buf []byte) bool { + *p = Poly{} // zero p + signs := (uint64(buf[32]) | (uint64(buf[33]) << 8) | + (uint64(buf[34]) << 16) | (uint64(buf[35]) << 24) | + (uint64(buf[36]) << 32) | (uint64(buf[37]) << 40) | + (uint64(buf[38]) << 48) | (uint64(buf[39]) << 56)) + if signs>>60 != 0 { + return false // ensure unused bits are zero for strong unforgeability + } + + for i := 0; i < 32; i++ { + for j := 0; j < 8; j++ { + if (buf[i]>>uint(j))&1 == 1 { + p[8*i+j] = 1 + // Note 1 ^ (1 | (Q-1)) = Q-1 and (-1)&x = x + p[8*i+j] ^= uint32(-(signs & 1)) & (1 | (Q - 1)) + signs >>= 1 + } + } + } + + return true +} diff --git a/src/circl/sign/dilithium/internal/common/pack_test.go b/src/circl/sign/dilithium/internal/common/pack_test.go new file mode 100644 index 00000000000..561d41ec2bb --- /dev/null +++ b/src/circl/sign/dilithium/internal/common/pack_test.go @@ -0,0 +1,45 @@ +package common + +import ( + "math/rand" + "testing" +) + +func TestPackLe16AgainstGeneric(t *testing.T) { + var p Poly + var buf1, buf2 [PolyLe16Size]byte + for j := 0; j < 1000; j++ { + for i := 0; i < 256; i++ { + p[i] = uint32(rand.Intn(16)) + } + p.PackLe16(buf1[:]) + p.packLe16Generic(buf2[:]) + if buf1 != buf2 { + t.Fatal() + } + } +} + +func BenchmarkPackLe16(b *testing.B) { + var p Poly + var buf [PolyLe16Size]byte + for i := 0; i < b.N; i++ { + p.PackLe16(buf[:]) + } +} + +func BenchmarkPackLe16Generic(b *testing.B) { + var p Poly + var buf [PolyLe16Size]byte + for i := 0; i < b.N; i++ { + p.packLe16Generic(buf[:]) + } +} + +func BenchmarkUnpackLeGamma1(b *testing.B) { + var p Poly + var buf [PolyLeGamma1Size]byte + for i := 0; i < b.N; i++ { + p.UnpackLeGamma1(buf[:]) + } +} diff --git a/src/circl/sign/dilithium/internal/common/params.go b/src/circl/sign/dilithium/internal/common/params.go new file mode 100644 index 00000000000..24589161dd7 --- /dev/null +++ b/src/circl/sign/dilithium/internal/common/params.go @@ -0,0 +1,22 @@ +package common + +import ( + "circl/sign/dilithium/internal/common/params" +) + +const ( + SeedSize = params.SeedSize + N = params.N + Q = params.Q + QBits = params.QBits + Qinv = params.Qinv + ROver256 = params.ROver256 + D = params.D + Gamma1 = params.Gamma1 + Gamma2 = params.Gamma2 + Alpha = params.Alpha + PolyT1Size = params.PolyT1Size + PolyT0Size = params.PolyT0Size + PolyLeGamma1Size = params.PolyLeGamma1Size + PolyLe16Size = params.PolyLe16Size +) diff --git a/src/circl/sign/dilithium/internal/common/params/params.go b/src/circl/sign/dilithium/internal/common/params/params.go new file mode 100644 index 00000000000..1c1219ade67 --- /dev/null +++ b/src/circl/sign/dilithium/internal/common/params/params.go @@ -0,0 +1,31 @@ +package params + +// We put these parameters in a separate package so that the Go code, +// such as ntt_amd64_src.go, that generates assembler can import it. + +const ( + SeedSize = 32 + N = 256 + Q = 8380417 // 2²³ - 2¹³ + 1 + QBits = 23 + Qinv = 4236238847 // = -(q^-1) mod 2³² + ROver256 = 41978 // = (256)⁻¹ R², where R = q mod 2³² + D = 14 + Gamma1 = (Q - 1) / 16 + Gamma2 = Gamma1 / 2 // = Alpha/2 + Alpha = 2 * Gamma2 // = Gamma1 + + // Size of T1 packed. (Note that the formula is not valid in general, + // but it is for the parameters used in the modes of Dilithium.) + PolyT1Size = (N * (QBits - D)) / 8 + + // Size of T0 packed. (Note that the formula is not valid in general, + // but it is for the parameters used in the modes of Dilithium.) + PolyT0Size = (N * D) / 8 + + // Size of a packed polynomial of norm <γ₁. + PolyLeGamma1Size = (N * (QBits - 3)) / 8 + + // Size of a packed polynomial whose coefficients are in [0,16). + PolyLe16Size = N / 2 +) diff --git a/src/circl/sign/dilithium/internal/common/poly.go b/src/circl/sign/dilithium/internal/common/poly.go new file mode 100644 index 00000000000..eae4e5c3aa6 --- /dev/null +++ b/src/circl/sign/dilithium/internal/common/poly.go @@ -0,0 +1,148 @@ +package common + +// An element of our base ring R which are polynomials over Z_q modulo +// the equation Xᴺ = -1, where q=2²³ - 2¹³ + 1 and N=256. +// +// Coefficients aren't always reduced. See Normalize(). +type Poly [N]uint32 + +// Reduces each of the coefficients to <2q. +func (p *Poly) reduceLe2QGeneric() { + for i := uint(0); i < N; i++ { + p[i] = reduceLe2Q(p[i]) + } +} + +// Reduce each of the coefficients to > 31) + // Sets x to {0, 1, ..., (Q-1)/2, (Q-1)/2, ..., 1} + x = int32((Q-1)/2) - x + if uint32(x) >= bound { + return true + } + } + return false +} + +// Splits each of the coefficients using decompose. +// +// Requires p to be normalized. +func (p *Poly) decomposeGeneric(p0PlusQ, p1 *Poly) { + for i := 0; i < N; i++ { + p0PlusQ[i], p1[i] = decompose(p[i]) + } +} + +// Splits p into p1 and p0 such that [i]p1 * 2ᴰ + [i]p0 = [i]p +// with -2ᴰ⁻¹ < [i]p0 ≤ 2ᴰ⁻¹. Returns p0 + Q and p1. +// +// Requires the coefficients of p to be normalized. +func (p *Poly) Power2Round(p0PlusQ, p1 *Poly) { + for i := 0; i < N; i++ { + p0PlusQ[i], p1[i] = power2round(p[i]) + } +} + +// Sets p to the hint polynomial for p0 the modified low bits and p1 +// the unmodified high bits --- see makeHint(). +// +// Returns the number of ones in the hint polynomial. +func (p *Poly) makeHintGeneric(p0, p1 *Poly) (pop uint32) { + for i := 0; i < N; i++ { + h := makeHint(p0[i], p1[i]) + pop += h + p[i] = h + } + return +} + +// Computes corrections to the high bits of the polynomial q according +// to the hints in h and sets p to the corrected high bits. Returns p. +func (p *Poly) UseHint(q, hint *Poly) *Poly { + var q0PlusQ Poly + + // See useHint() and makeHint() for an explanation. We reimplement it + // here so that we can call Poly.Decompose(), which might be way faster + // than calling decompose() in a loop (for instance when having AVX2.) + + q.Decompose(&q0PlusQ, p) + + for i := 0; i < N; i++ { + if hint[i] == 0 { + continue + } + if q0PlusQ[i] > Q { + p[i] = (p[i] + 1) & 15 + } else { + p[i] = (p[i] - 1) & 15 + } + } + + return p +} + +// Sets p to the polynomial whose coefficients are the pointwise multiplication +// of those of a and b. The coefficients of p are bounded by 2q. +// +// Assumes a and b are in Montgomery form and that the pointwise product +// of each coefficient is below 2³² q. +func (p *Poly) mulHatGeneric(a, b *Poly) { + for i := 0; i < N; i++ { + p[i] = montReduceLe2Q(uint64(a[i]) * uint64(b[i])) + } +} + +// Sets p to 2ᵈ q without reducing. +// +// So it requires the coefficients of p to be less than 2³²⁻ᴰ. +func (p *Poly) mulBy2toDGeneric(q *Poly) { + for i := 0; i < N; i++ { + p[i] = q[i] << D + } +} diff --git a/src/circl/sign/dilithium/internal/common/poly_test.go b/src/circl/sign/dilithium/internal/common/poly_test.go new file mode 100644 index 00000000000..350de0c2a51 --- /dev/null +++ b/src/circl/sign/dilithium/internal/common/poly_test.go @@ -0,0 +1,298 @@ +package common + +import ( + "math/rand" + "testing" +) + +func TestExceeds(t *testing.T) { + for i := 0; i < N; i++ { + var p Poly + for v := 0; v < 10; v++ { + p[i] = uint32(v) + if p.Exceeds(uint32(10)) { + t.Fatal() + } + p[i] = Q - uint32(v) + if p.Exceeds(uint32(10)) { + t.Fatal() + } + } + for v := 10; v < 20; v++ { + p[i] = uint32(v) + if !p.Exceeds(uint32(10)) { + t.Fatal() + } + p[i] = Q - uint32(v) + if !p.Exceeds(uint32(10)) { + t.Fatal() + } + } + } +} + +func TestMakeHintAgainstGeneric(t *testing.T) { + var p0, p1, h1, h2 Poly + for i := 0; i < 255; i++ { + if i&3 == 1 { + p0[i] = Gamma2 / 2 + } else if i&3 == 2 { + p0[i] = Q - Gamma2/2 + } else if i&3 == 0 { + p0[i] = Q - Gamma2 + } else { + p0[i] = 2 * Gamma2 + } + + if (i>>2)&1 == 1 { + p1[i] = 1234 + } else { + p1[i] = 0 + } + } + + pop1 := h1.makeHintGeneric(&p0, &p1) + pop2 := h2.MakeHint(&p0, &p1) + if h1 != h2 { + t.Fatal() + } + if pop1 != pop2 { + t.Fatal() + } +} + +func TestComposeAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var p, a0, b0, a1, b1 Poly + p.RandLe2Q() + p.Normalize() + p.Decompose(&a0, &a1) + p.decomposeGeneric(&b0, &b1) + if a0 != b0 && a1 != b1 { + t.Fatal() + } + } +} + +func TestSubAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var p1, p2, a, b Poly + a.RandLe2Q() + b.RandLe2Q() + p1.Sub(&a, &b) + p2.subGeneric(&a, &b) + if p1 != p2 { + t.Fatalf("Sub(%v, %v) =\n%v\n!= %v", a, b, p1, p2) + } + } +} + +func TestAddAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var p1, p2, a, b Poly + a.RandLe2Q() + b.RandLe2Q() + p1.Add(&a, &b) + p2.addGeneric(&a, &b) + if p1 != p2 { + t.Fatalf("Add(%v, %v) =\n%v\n!= %v", a, b, p1, p2) + } + } +} + +func TestMulHatAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var p1, p2, a, b Poly + a.RandLe2Q() + b.RandLe2Q() + p1.MulHat(&a, &b) + p2.mulHatGeneric(&a, &b) + if p1 != p2 { + t.Fatalf("MulHat(%v, %v) =\n%v\n!= %v", a, b, p1, p2) + } + } +} + +func TestReduceLe2QAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var a Poly + for j := 0; j < N; j++ { + a[j] = rand.Uint32() + } + p1 := a + p2 := a + p1.reduceLe2QGeneric() + p2.ReduceLe2Q() + if p1 != p2 { + t.Fatalf("%v !=\n%v", p1, p2) + } + } +} + +func TestNormalizeAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var a Poly + for j := 0; j < N; j++ { + a[j] = rand.Uint32() + } + p1 := a + p2 := a + p1.normalizeGeneric() + p2.Normalize() + if p1 != p2 { + t.Fatalf("%v !=\n%v", p1, p2) + } + } +} + +func TestMulBy2ToDAgainstGeneric(t *testing.T) { + for k := 0; k < 1000; k++ { + var p1, p2, q Poly + q.RandLe2Q() + p1.mulBy2toDGeneric(&q) + p2.MulBy2toD(&q) + if p1 != p2 { + t.Fatalf("MulBy2ToD(%v) =\n%v\n!= %v", q, p1, p2) + } + } +} + +func BenchmarkNormalizeGeneric(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.normalizeGeneric() + } +} + +func BenchmarkMulHatGeneric(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.mulHatGeneric(&p, &p) + } +} + +func BenchmarkAddGeneric(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.addGeneric(&p, &p) + } +} + +func BenchmarkSubGeneric(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.subGeneric(&p, &p) + } +} + +func BenchmarkReduceLe2QGeneric(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.reduceLe2QGeneric() + } +} + +func BenchmarkNormalizeAssumingLe2QGeneric(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.normalizeAssumingLe2QGeneric() + } +} + +func BenchmarkExceedsGeneric(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.exceedsGeneric(uint32(10)) + } +} + +func BenchmarkDecomposeGeneric(b *testing.B) { + var p, p0, p1 Poly + for i := 0; i < b.N; i++ { + p.decomposeGeneric(&p0, &p1) + } +} + +func BenchmarkMakeHintGeneric(b *testing.B) { + var p, p0, p1 Poly + for i := 0; i < b.N; i++ { + p.makeHintGeneric(&p0, &p1) + } +} + +func BenchmarkMulBy2toDGeneric(b *testing.B) { + var p, q Poly + for i := 0; i < b.N; i++ { + p.mulBy2toDGeneric(&q) + } +} + +func BenchmarkMulHat(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.MulHat(&p, &p) + } +} + +func BenchmarkAdd(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.Add(&p, &p) + } +} + +func BenchmarkSub(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.Sub(&p, &p) + } +} + +func BenchmarkReduceLe2Q(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.ReduceLe2Q() + } +} + +func BenchmarkNormalize(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.Normalize() + } +} + +func BenchmarkNormalizeAssumingLe2Q(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.NormalizeAssumingLe2Q() + } +} + +func BenchmarkExceeds(b *testing.B) { + var p Poly + for i := 0; i < b.N; i++ { + p.Exceeds(uint32(10)) + } +} + +func BenchmarkDecompose(b *testing.B) { + var p, p0, p1 Poly + for i := 0; i < b.N; i++ { + p.Decompose(&p0, &p1) + } +} + +func BenchmarkMakeHint(b *testing.B) { + var p, p0, p1 Poly + for i := 0; i < b.N; i++ { + p.MakeHint(&p0, &p1) + } +} + +func BenchmarkMulBy2toD(b *testing.B) { + var p, q Poly + for i := 0; i < b.N; i++ { + p.MulBy2toD(&q) + } +} diff --git a/src/circl/sign/dilithium/internal/common/stubs_amd64.go b/src/circl/sign/dilithium/internal/common/stubs_amd64.go new file mode 100644 index 00000000000..a731af9421b --- /dev/null +++ b/src/circl/sign/dilithium/internal/common/stubs_amd64.go @@ -0,0 +1,41 @@ +// Code generated by command: go run src.go -out ../amd64.s -stubs ../stubs_amd64.go -pkg common. DO NOT EDIT. + +// +build amd64 + +package common + +//go:noescape +func nttAVX2(p *[256]uint32) + +//go:noescape +func invNttAVX2(p *[256]uint32) + +//go:noescape +func mulHatAVX2(p *[256]uint32, a *[256]uint32, b *[256]uint32) + +//go:noescape +func addAVX2(p *[256]uint32, a *[256]uint32, b *[256]uint32) + +//go:noescape +func subAVX2(p *[256]uint32, a *[256]uint32, b *[256]uint32) + +//go:noescape +func packLe16AVX2(p *[256]uint32, buf *byte) + +//go:noescape +func reduceLe2QAVX2(p *[256]uint32) + +//go:noescape +func le2qModQAVX2(p *[256]uint32) + +//go:noescape +func exceedsAVX2(p *[256]uint32, bound uint32) uint8 + +//go:noescape +func decomposeAVX2(p *[256]uint32, p0PlusQ *[256]uint32, p1 *[256]uint32) + +//go:noescape +func makeHintAVX2(p *[256]uint32, p0 *[256]uint32, p1 *[256]uint32) uint32 + +//go:noescape +func mulBy2toDAVX2(p *[256]uint32, q *[256]uint32) diff --git a/src/circl/sign/dilithium/kat_test.go b/src/circl/sign/dilithium/kat_test.go new file mode 100644 index 00000000000..97d516b6d4c --- /dev/null +++ b/src/circl/sign/dilithium/kat_test.go @@ -0,0 +1,60 @@ +package dilithium + +// Code to generate the NIST "PQCsignKAT" test vectors. +// See PQCsignKAT_sign.c and randombytes.c in the reference implementation. + +import ( + "crypto/sha256" + "fmt" + "testing" + + "circl/internal/nist" +) + +func TestPQCgenKATSign(t *testing.T) { + // From SHA256SUMS in the reference implementation. + testPQCgenKATSign(t, "Dilithium1", "dd83f8584fded0398547827edff081969335c32069f3e4a9dbd865fd5c2ecd2b") + testPQCgenKATSign(t, "Dilithium2", "532f4a7a416bba96b607395a6d07fc0eaab1f1f968e49758d2a97c718de832e7") + testPQCgenKATSign(t, "Dilithium3", "37a16744627f2566180a547d022f03a36d22c50080303027179751070e626c72") + testPQCgenKATSign(t, "Dilithium4", "4c2e6d7c8675e9345e3ab7036a4e9fb786549d242462ba9b68f58db94e84147a") + testPQCgenKATSign(t, "Dilithium1-AES", "68fabe91565c9a664d2461c7510ac32419eadfac0566dc3e9141d276bb98e11a") + testPQCgenKATSign(t, "Dilithium2-AES", "08865a608edcdb5723769c583b37c17c9ff8cae578f1d88df7e173ed06dd23fa") + testPQCgenKATSign(t, "Dilithium3-AES", "f3c5fcceafa9fb2462721f272791a26c9a123b3a07fad7e07dfec232085fdd7f") + testPQCgenKATSign(t, "Dilithium4-AES", "8de4e2ac2032f714263aa0d045275ec62b6f192f8828cfe82b63ec0b0b32deb6") +} + +func testPQCgenKATSign(t *testing.T, name, expected string) { + mode := ModeByName(name) + if mode == nil { + t.Fatal() + } + + var seed [48]byte + var eseed [96]byte + for i := 0; i < 48; i++ { + seed[i] = byte(i) + } + f := sha256.New() + g := nist.NewDRBG(&seed) + fmt.Fprintf(f, "# %s\n\n", name) + for i := 0; i < 100; i++ { + mlen := 33 * (i + 1) + g.Fill(seed[:]) + msg := make([]byte, mlen) + g.Fill(msg[:]) + fmt.Fprintf(f, "count = %d\n", i) + fmt.Fprintf(f, "seed = %X\n", seed) + fmt.Fprintf(f, "mlen = %d\n", mlen) + fmt.Fprintf(f, "msg = %X\n", msg) + g2 := nist.NewDRBG(&seed) + g2.Fill(eseed[:]) + pk, sk := mode.NewKeyFromExpandedSeed(&eseed) + fmt.Fprintf(f, "pk = %X\n", pk.Bytes()) + fmt.Fprintf(f, "sk = %X\n", sk.Bytes()) + fmt.Fprintf(f, "smlen = %d\n", mlen+mode.SignatureSize()) + fmt.Fprintf(f, "sm = %X%X\n\n", mode.Sign(sk, msg[:]), msg) + } + if fmt.Sprintf("%x", f.Sum(nil)) != expected { + t.Fatal() + } +} diff --git a/src/circl/sign/dilithium/mode1.go b/src/circl/sign/dilithium/mode1.go new file mode 100644 index 00000000000..89ee1a620e7 --- /dev/null +++ b/src/circl/sign/dilithium/mode1.go @@ -0,0 +1,95 @@ +// Code generated from mode.templ.go. DO NOT EDIT. + +package dilithium + +import ( + "fmt" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode1" +) + +// implMode1 implements the mode.Mode interface for Dilithium1. +type implMode1 struct{} + +// Mode1 is Dilithium in mode "Dilithium1". +var Mode1 Mode = &implMode1{} + +func (m *implMode1) GenerateKey(rand io.Reader) ( + PublicKey, PrivateKey, error) { + return mode1.GenerateKey(rand) +} + +func (m *implMode1) NewKeyFromExpandedSeed(seed *[96]byte) (PublicKey, + PrivateKey) { + return mode1.NewKeyFromExpandedSeed(seed) +} + +func (m *implMode1) NewKeyFromSeed(seed []byte) (PublicKey, + PrivateKey) { + if len(seed) != common.SeedSize { + panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) + } + seedBuf := [common.SeedSize]byte{} + copy(seedBuf[:], seed) + return mode1.NewKeyFromSeed(&seedBuf) +} + +func (m *implMode1) Sign(sk PrivateKey, msg []byte) []byte { + isk := sk.(*mode1.PrivateKey) + ret := [mode1.SignatureSize]byte{} + mode1.SignTo(isk, msg, ret[:]) + return ret[:] +} + +func (m *implMode1) Verify(pk PublicKey, msg []byte, signature []byte) bool { + ipk := pk.(*mode1.PublicKey) + return mode1.Verify(ipk, msg, signature) +} + +func (m *implMode1) PublicKeyFromBytes(data []byte) PublicKey { + var ret mode1.PublicKey + if len(data) != mode1.PublicKeySize { + panic("packed public key must be of mode1.PublicKeySize bytes") + } + var buf [mode1.PublicKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode1) PrivateKeyFromBytes(data []byte) PrivateKey { + var ret mode1.PrivateKey + if len(data) != mode1.PrivateKeySize { + panic("packed public key must be of mode1.PrivateKeySize bytes") + } + var buf [mode1.PrivateKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode1) SeedSize() int { + return common.SeedSize +} + +func (m *implMode1) PublicKeySize() int { + return mode1.PublicKeySize +} + +func (m *implMode1) PrivateKeySize() int { + return mode1.PrivateKeySize +} + +func (m *implMode1) SignatureSize() int { + return mode1.SignatureSize +} + +func (m *implMode1) Name() string { + return "Dilithium1" +} + +func init() { + modes["Dilithium1"] = Mode1 +} diff --git a/src/circl/sign/dilithium/mode1/dilithium.go b/src/circl/sign/dilithium/mode1/dilithium.go new file mode 100644 index 00000000000..193fe67ccce --- /dev/null +++ b/src/circl/sign/dilithium/mode1/dilithium.go @@ -0,0 +1,191 @@ +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// mode1 implements the CRYSTALS-Dilithium signature scheme Dilithium1 +// as submitted to round2 of the NIST PQC competition and described in +// +// https://pq-crystals.org/dilithium/data/dilithium-specification-round2.pdf +package mode1 + +import ( + "crypto" + "errors" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode1/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + SeedSize = common.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a signature + SignatureSize = internal.SignatureSize +) + +// PublicKey is the type of Dilithium1 public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of Dilithium1 private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + pk, sk, err := internal.GenerateKey(rand) + return (*PublicKey)(pk), (*PrivateKey)(sk), err +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromExpandedSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// SignTo signs the given message and writes the signature into signature. +// It will panic if signature is not of length at least SignatureSize. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + internal.SignTo( + (*internal.PrivateKey)(sk), + msg, + signature, + ) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + return internal.Verify( + (*internal.PublicKey)(pk), + msg, + signature, + ) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Packs the public key. +func (pk *PublicKey) Bytes() []byte { + var buf [PublicKeySize]byte + pk.Pack(&buf) + return buf[:] +} + +// Packs the private key. +func (sk *PrivateKey) Bytes() []byte { + var buf [PrivateKeySize]byte + sk.Pack(&buf) + return buf[:] +} + +// Packs the public key. +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + return pk.Bytes(), nil +} + +// Packs the private key. +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + return sk.Bytes(), nil +} + +// Unpacks the public key from data. +func (pk *PublicKey) UnmarshalBinary(data []byte) error { + if len(data) != PublicKeySize { + return errors.New("packed public key must be of mode1.PublicKeySize bytes") + } + var buf [PublicKeySize]byte + copy(buf[:], data) + pk.Unpack(&buf) + return nil +} + +// Unpacks the private key from data. +func (sk *PrivateKey) UnmarshalBinary(data []byte) error { + if len(data) != PrivateKeySize { + return errors.New("packed private key must be of mode1.PrivateKeySize bytes") + } + var buf [PrivateKeySize]byte + copy(buf[:], data) + sk.Unpack(&buf) + return nil +} + +// Sign signs the given message. +// +// opts.HashFunc() must return zero, which can be achieved by passing +// crypto.Hash(0) for opts. rand is ignored. Will only return an error +// if opts.HashFunc() is non-zero. +// +// This function is used to make PrivateKey implement the crypto.Signer +// interface. The package-level SignTo function might be more convenient +// to use. +func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( + signature []byte, err error) { + var sig [SignatureSize]byte + + if opts.HashFunc() != crypto.Hash(0) { + return nil, errors.New("dilithium: cannot sign hashed message") + } + + SignTo(sk, msg, sig[:]) + return sig[:], nil +} + +// Computes the public key corresponding to this private key. +// +// Returns a *PublicKey. The type crypto.PublicKey is used to make +// PrivateKey implement the crypto.Signer interface. +func (sk *PrivateKey) Public() crypto.PublicKey { + return (*PublicKey)((*internal.PrivateKey)(sk).Public()) +} + +// Equal returns whether the two private keys equal. +func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { + castOther, ok := other.(*PrivateKey) + if !ok { + return false + } + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) +} + +// Equal returns whether the two public keys equal. +func (pk *PublicKey) Equal(other crypto.PublicKey) bool { + castOther, ok := other.(*PublicKey) + if !ok { + return false + } + return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) +} diff --git a/src/circl/sign/dilithium/mode1/internal/dilithium.go b/src/circl/sign/dilithium/mode1/internal/dilithium.go new file mode 100644 index 00000000000..fb0eaaf1963 --- /dev/null +++ b/src/circl/sign/dilithium/mode1/internal/dilithium.go @@ -0,0 +1,446 @@ +// Code generated from mode3/internal/dilithium.go by gen.go + +package internal + +import ( + cryptoRand "crypto/rand" + "crypto/subtle" + "io" + + "circl/internal/sha3" + "circl/sign/dilithium/internal/common" +) + +const ( + // Size of a packed polynomial of norm ≤η. + // (Note that the formula is not valid in general.) + PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8 +) + +// PublicKey is the type of Dilithium public keys. +type PublicKey struct { + rho [32]byte + t1 VecK + + // Cached values + t1p [common.PolyT1Size * K]byte + A *Mat + tr *[48]byte +} + +// PrivateKey is the type of Dilithium private keys. +type PrivateKey struct { + rho [32]byte + key [32]byte + s1 VecL + s2 VecK + t0 VecK + tr [48]byte + + // Cached values + A Mat // ExpandA(ρ) + s1h VecL // NTT(s₁) + s2h VecK // NTT(s₂) + t0h VecK // NTT(t₀) +} + +type unpackedSignature struct { + z VecL + hint VecK + c common.Poly +} + +// Packs the signature into buf. +func (sig *unpackedSignature) Pack(buf []byte) { + sig.z.PackLeGamma1(buf[:]) + sig.hint.PackHint(buf[L*common.PolyLeGamma1Size:]) + sig.c.PackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) +} + +// Sets sig to the signature encoded in the buffer. +// +// Returns whether buf contains a properly packed signature. +func (sig *unpackedSignature) Unpack(buf []byte) bool { + if len(buf) < SignatureSize { + return false + } + sig.z.UnpackLeGamma1(buf[:]) + if sig.z.Exceeds(common.Gamma1 - Beta) { + return false + } + if !sig.hint.UnpackHint(buf[L*common.PolyLeGamma1Size:]) { + return false + } + sig.c.UnpackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) + return true +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + copy(buf[:32], pk.rho[:]) + copy(buf[32:], pk.t1p[:]) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + copy(pk.rho[:], buf[:32]) + copy(pk.t1p[:], buf[32:]) + + pk.t1.UnpackT1(pk.t1p[:]) + pk.A = new(Mat) + pk.A.Derive(&pk.rho) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + pk.tr = new([48]byte) + h := sha3.NewShake256() + _, _ = h.Write(buf[:]) + _, _ = h.Read(pk.tr[:]) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + copy(buf[:32], sk.rho[:]) + copy(buf[32:64], sk.key[:]) + copy(buf[64:112], sk.tr[:]) + offset := 112 + sk.s1.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.PackT0(buf[offset:]) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + copy(sk.rho[:], buf[:32]) + copy(sk.key[:], buf[32:64]) + copy(sk.tr[:], buf[64:112]) + offset := 112 + sk.s1.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.UnpackT0(buf[offset:]) + + // Cached values + sk.A.Derive(&sk.rho) + sk.t0h = sk.t0 + sk.t0h.NTT() + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() +} + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [32]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(&seed) + return pk, sk, nil +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + var pk PublicKey + var sk PrivateKey + var sSeed [32]byte + + copy(pk.rho[:], seed[:32]) + copy(sSeed[:], seed[32:64]) + copy(sk.key[:], seed[64:]) + copy(sk.rho[:], pk.rho[:]) + + sk.A.Derive(&pk.rho) + + for i := uint16(0); i < L; i++ { + PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i) + } + + for i := uint16(0); i < K; i++ { + PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L) + } + + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() + + sk.computeT0andT1(&sk.t0, &pk.t1) + + sk.t0h = sk.t0 + sk.t0h.NTT() + + // Complete public key far enough to be packed + pk.t1.PackT1(pk.t1p[:]) + pk.A = &sk.A + + // Finish private key + var packedPk [PublicKeySize]byte + pk.Pack(&packedPk) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + h := sha3.NewShake256() + _, _ = h.Write(packedPk[:]) + _, _ = h.Read(sk.tr[:]) + + // Finish cache of public key + pk.tr = &sk.tr + + return &pk, &sk +} + +// Computes t0 and t1 from sk.s1h, sk.s2 and sk.A. +func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) { + var t VecK + + // Set t to A s₁ + s₂ + for i := 0; i < K; i++ { + PolyDotHat(&t[i], &sk.A[i], &sk.s1h) + t[i].ReduceLe2Q() + t[i].InvNTT() + } + t.Add(&t, &sk.s2) + t.Normalize() + + // Compute t₀, t₁ = Power2Round(t) + t.Power2Round(t0, t1) +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) { + var buf [96]byte + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Read(buf[:]) + return NewKeyFromExpandedSeed(&buf) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + var sig unpackedSignature + var mu [48]byte + var zh VecL + var Az, Az2dct1, w1 VecK + var ch, cp common.Poly + + // Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β + // and ensured that there at most ω ones in pk.hint. + if !sig.Unpack(signature) { + return false + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(pk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // Compute Az + zh = sig.z + zh.NTT() + + for i := 0; i < K; i++ { + PolyDotHat(&Az[i], &pk.A[i], &zh) + } + + // Next, we compute Az - 2ᵈ·c·t₁. + // Note that the coefficients of t₁ are bounded by 256 = 2⁹, + // so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q, + // which is small enough for NTT(). + Az2dct1.MulBy2toD(&pk.t1) + Az2dct1.NTT() + ch = sig.c + ch.NTT() + for i := 0; i < K; i++ { + Az2dct1[i].MulHat(&Az2dct1[i], &ch) + } + Az2dct1.Sub(&Az, &Az2dct1) + Az2dct1.ReduceLe2Q() + Az2dct1.InvNTT() + Az2dct1.NormalizeAssumingLe2Q() + + // UseHint(pk.hint, Az - 2ᵈ·c·t₁) + // = UseHint(pk.hint, w - c·s₂ + c·t₀) + // = UseHint(pk.hint, r + c·t₀) + // = r₁ = w₁. + w1.UseHint(&Az2dct1, &sig.hint) + + // c' = H(μ, w₁) + PolyDeriveUniformB60(&cp, &mu, &w1) + return sig.c == cp +} + +// SignTo signs the given message and writes the signature into signature. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + var mu, rhop [48]byte + var y, yh VecL + var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK + var ch common.Poly + var yNonce uint16 + var sig unpackedSignature + + if len(signature) < SignatureSize { + panic("Signature does not fit in that byteslice") + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(sk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // ρ' = CRH(μ ‖ key) + h.Reset() + _, _ = h.Write(sk.key[:]) + _, _ = h.Write(mu[:]) + _, _ = h.Read(rhop[:]) + + // Main rejection loop + attempt := 0 + for { + attempt++ + if attempt >= 576 { + // Depending on the mode, one try has a chance between 1/7 and 1/4 + // of succeeding. Thus it is safe to say that 576 iterations + // are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸. + panic("This should only happen 1 in 2^{128}: something is wrong.") + } + + // y = ExpandMask(ρ', key) + VecLDeriveUniformLeGamma1(&y, &rhop, yNonce) + yNonce += uint16(L) + + // Set w to A y + yh = y + yh.NTT() + for i := 0; i < K; i++ { + PolyDotHat(&w[i], &sk.A[i], &yh) + w[i].ReduceLe2Q() + w[i].InvNTT() + } + + // Decompose w into w₀ and w₁ + w.NormalizeAssumingLe2Q() + w.Decompose(&w0, &w1) + + // c = H(μ, w₁) + PolyDeriveUniformB60(&sig.c, &mu, &w1) + ch = sig.c + ch.NTT() + + // Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β. + // + // By Lemma 3 of the specification this is equivalent to checking that + // both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition + // w - c·s₂ = r₁ α + r₀ as computed by decompose(). + // See also §4.1 of the specification. + for i := 0; i < K; i++ { + w0mcs2[i].MulHat(&ch, &sk.s2h[i]) + w0mcs2[i].InvNTT() + } + w0mcs2.Sub(&w0, &w0mcs2) + w0mcs2.Normalize() + + if w0mcs2.Exceeds(common.Gamma2 - Beta) { + continue + } + + // z = y + c·s₁ + for i := 0; i < L; i++ { + sig.z[i].MulHat(&ch, &sk.s1h[i]) + sig.z[i].InvNTT() + } + sig.z.Add(&sig.z, &y) + sig.z.Normalize() + + // Ensure ‖z‖_∞ < γ₁ - β + if sig.z.Exceeds(common.Gamma1 - Beta) { + continue + } + + // Compute c·t₀ + for i := 0; i < K; i++ { + ct0[i].MulHat(&ch, &sk.t0h[i]) + ct0[i].InvNTT() + } + ct0.NormalizeAssumingLe2Q() + + // Ensure ‖c·t₀‖_∞ < γ₂. + if ct0.Exceeds(common.Gamma2) { + continue + } + + // Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0. + // Note that we're not using makeHint() in the obvious way as we + // do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂. Instead we note + // that our makeHint() is actually the same as a makeHint for a + // different decomposition: + // + // Earlier we ensured indirectly with a check that r₁ = w₁ where + // r = w - c·s₂. Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂. + // Thus MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁) + // and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁). + // As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct. + w0mcs2pct0.Add(&w0mcs2, &ct0) + w0mcs2pct0.NormalizeAssumingLe2Q() + hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1) + if hintPop > Omega { + continue + } + + break + } + + sig.Pack(signature[:]) +} + +// Computes the public key corresponding to this private key. +func (sk *PrivateKey) Public() *PublicKey { + var t0 VecK + pk := &PublicKey{ + rho: sk.rho, + A: &sk.A, + tr: &sk.tr, + } + sk.computeT0andT1(&t0, &pk.t1) + pk.t1.PackT1(pk.t1p[:]) + return pk +} + +// Equal returns whether the two public keys are equal +func (pk *PublicKey) Equal(other *PublicKey) bool { + return pk.rho == other.rho && pk.t1 == other.t1 +} + +// Equal returns whether the two private keys are equal +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) & + subtle.ConstantTimeCompare(sk.key[:], other.key[:]) & + subtle.ConstantTimeCompare(sk.tr[:], other.tr[:])) + + acc := uint32(0) + for i := 0; i < L; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s1[i][j] ^ other.s1[i][j] + } + } + for i := 0; i < K; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s2[i][j] ^ other.s2[i][j] + acc |= sk.t0[i][j] ^ other.t0[i][j] + } + } + return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1 +} diff --git a/src/circl/sign/dilithium/mode1/internal/dilithium_test.go b/src/circl/sign/dilithium/mode1/internal/dilithium_test.go new file mode 100644 index 00000000000..42ce6dbe5d1 --- /dev/null +++ b/src/circl/sign/dilithium/mode1/internal/dilithium_test.go @@ -0,0 +1,131 @@ +// Code generated from mode3/internal/dilithium_test.go by gen.go + +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Checks whether p is normalized. Only used in tests. +func PolyNormalized(p *common.Poly) bool { + p2 := *p + p2.Normalize() + return p2 == *p +} + +func BenchmarkSkUnpack(b *testing.B) { + var buf [PrivateKeySize]byte + var sk PrivateKey + for i := 0; i < b.N; i++ { + sk.Unpack(&buf) + } +} + +func BenchmarkPkUnpack(b *testing.B) { + var buf [PublicKeySize]byte + var pk PublicKey + for i := 0; i < b.N; i++ { + pk.Unpack(&buf) + } +} + +func BenchmarkVerify(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of verification (as in the reference + // implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + pk, sk := NewKeyFromSeed(&seed) + SignTo(sk, msg[:], sig[:]) + b.ResetTimer() + for i := 0; i < b.N; i++ { + // We should generate a new signature for every verify attempt, + // as this influences the time a little bit. This difference, however, + // is small and generating a new signature in between creates a lot + // pressure on the allocator which makes an accurate measurement hard. + Verify(pk, msg[:], sig[:]) + } +} + +func BenchmarkSign(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of signing (as in the reference implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + _, sk := NewKeyFromSeed(&seed) + b.ResetTimer() + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(msg[:], uint64(i)) + SignTo(sk, msg[:], sig[:]) + } +} + +func BenchmarkGenerateKey(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + NewKeyFromSeed(&seed) + } +} + +func BenchmarkPublicFromPrivate(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + b.StopTimer() + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + _, sk := NewKeyFromSeed(&seed) + b.StartTimer() + sk.Public() + } +} + +func TestSignThenVerifyAndPkSkPacking(t *testing.T) { + var seed [common.SeedSize]byte + var sig [SignatureSize]byte + var msg [8]byte + var pkb [PublicKeySize]byte + var skb [PrivateKeySize]byte + var pk2 PublicKey + var sk2 PrivateKey + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + if !sk.Equal(sk) { + t.Fatal() + } + for j := uint64(0); j < 10; j++ { + binary.LittleEndian.PutUint64(msg[:], j) + SignTo(sk, msg[:], sig[:]) + if !Verify(pk, msg[:], sig[:]) { + t.Fatal() + } + } + pk.Pack(&pkb) + pk2.Unpack(&pkb) + if !pk.Equal(&pk2) { + t.Fatal() + } + sk.Pack(&skb) + sk2.Unpack(&skb) + if !sk.Equal(&sk2) { + t.Fatal() + } + } +} + +func TestPublicFromPrivate(t *testing.T) { + var seed [common.SeedSize]byte + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + pk2 := sk.Public() + if !pk.Equal(pk2) { + t.Fatal() + } + } +} diff --git a/src/circl/sign/dilithium/mode1/internal/mat.go b/src/circl/sign/dilithium/mode1/internal/mat.go new file mode 100644 index 00000000000..a2411b0566d --- /dev/null +++ b/src/circl/sign/dilithium/mode1/internal/mat.go @@ -0,0 +1,59 @@ +// Code generated from mode3/internal/mat.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A k by l matrix of polynomials. +type Mat [K]VecL + +// Expands the given seed to a complete matrix. +// +// This function is called ExpandA in the specification. +func (m *Mat) Derive(seed *[32]byte) { + if !DeriveX4Available { + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + PolyDeriveUniform(&m[i][j], seed, (i<<8)+j) + } + } + return + } + + idx := 0 + var nonces [4]uint16 + var ps [4]*common.Poly + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + nonces[idx] = (i << 8) + j + ps[idx] = &m[i][j] + idx++ + if idx == 4 { + idx = 0 + PolyDeriveUniformX4(ps, seed, nonces) + } + } + } + if idx != 0 { + for i := idx; i < 4; i++ { + ps[i] = nil + } + PolyDeriveUniformX4(ps, seed, nonces) + } +} + +// Set p to the inner product of a and b using pointwise multiplication. +// +// Assumes a and b are in Montgomery form and their coefficients are +// pairwise sufficiently small to multiply, see Poly.MulHat(). Resulting +// coefficients are bounded by 2Lq. +func PolyDotHat(p *common.Poly, a, b *VecL) { + var t common.Poly + *p = common.Poly{} // zero p + for i := 0; i < L; i++ { + t.MulHat(&a[i], &b[i]) + p.Add(&t, p) + } +} diff --git a/src/circl/sign/dilithium/mode1/internal/pack.go b/src/circl/sign/dilithium/mode1/internal/pack.go new file mode 100644 index 00000000000..ecf3971cd20 --- /dev/null +++ b/src/circl/sign/dilithium/mode1/internal/pack.go @@ -0,0 +1,141 @@ +// Code generated from mode3/internal/pack.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// Writes p with norm less than or equal η into buf, which must be of +// size PolyLeqEtaSize. +// +// Assumes coefficients of p are not normalized, but in [q-η,q+η]. +func PolyPackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + buf[i] = (byte(common.Q+Eta-p[j]) | + byte(common.Q+Eta-p[j+1])<<4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + buf[i] = (byte(common.Q+Eta-p[j]) | + (byte(common.Q+Eta-p[j+1]) << 3) | + (byte(common.Q+Eta-p[j+2]) << 6)) + buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) | + (byte(common.Q+Eta-p[j+3]) << 1) | + (byte(common.Q+Eta-p[j+4]) << 4) | + (byte(common.Q+Eta-p[j+5]) << 7)) + buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) | + (byte(common.Q+Eta-p[j+6]) << 2) | + (byte(common.Q+Eta-p[j+7]) << 5)) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Sets p to the polynomial of norm less than or equal η encoded in the +// given buffer of size PolyLeqEtaSize. +// +// Output coefficients of p are not normalized, but in [q-η,q+η] provided +// buf was created using PackLeqEta. +// +// Beware, for arbitrary buf the coefficients of p might en up in +// the interval [q-2^b,q+2^b] where b is the least b with η≤2^b. +func PolyUnpackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + p[j] = common.Q + Eta - uint32(buf[i]&15) + p[j+1] = common.Q + Eta - uint32(buf[i]>>4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + p[j] = common.Q + Eta - uint32(buf[i]&7) + p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7) + p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7)) + p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7) + p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7) + p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7)) + p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7) + p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Writes v with coefficients in {0, 1} of which at most ω non-zero +// to buf, which must have length ω+k. +func (v *VecK) PackHint(buf []byte) { + // The packed hint starts with the indices of the non-zero coefficients + // For instance: + // + // (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹) + // + // Yields + // + // 56, 100, 255, 2, 23, 1 + // + // Then we pad with zeroes until we have a list of ω items: + // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0 + // + // Then we finish with a list of the switch-over-indices in this + // list between polynomials, so: + // + // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6 + + off := uint8(0) + for i := 0; i < K; i++ { + for j := uint16(0); j < common.N; j++ { + if v[i][j] != 0 { + buf[off] = uint8(j) + off++ + } + } + buf[Omega+i] = off + } + for ; off < Omega; off++ { + buf[off] = 0 + } +} + +// Sets v to the vector encoded using VecK.PackHint() +// +// Returns whether unpacking was successful. +func (v *VecK) UnpackHint(buf []byte) bool { + // A priori, there would be several reasonable ways to encode the same + // hint vector. We take care to only allow only one encoding, to ensure + // "strong unforgeability". + // + // See PackHint() source for description of the encoding. + *v = VecK{} // zero v + prevSOP := uint8(0) // previous switch-over-point + for i := 0; i < K; i++ { + SOP := buf[Omega+i] + if SOP < prevSOP || SOP > Omega { + return false // ensures switch-over-points are increasing + } + for j := prevSOP; j < SOP; j++ { + if j > prevSOP && buf[j] <= buf[j-1] { + return false // ensures indices are increasing (within a poly) + } + v[i][buf[j]] = 1 + } + prevSOP = SOP + } + for j := prevSOP; j < Omega; j++ { + if buf[j] != 0 { + return false // ensures padding indices are zero + } + } + + return true +} diff --git a/src/circl/sign/dilithium/mode1/internal/pack_test.go b/src/circl/sign/dilithium/mode1/internal/pack_test.go new file mode 100644 index 00000000000..35bea5b6db3 --- /dev/null +++ b/src/circl/sign/dilithium/mode1/internal/pack_test.go @@ -0,0 +1,85 @@ +// Code generated from mode3/internal/pack_test.go by gen.go + +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestPolyPackLeqEta(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [PolyLeqEtaSize]byte + + for i := uint16(0); i < 100; i++ { + // Note that DeriveUniformLeqEta sets p to the right kind of + // unnormalized vector. + PolyDeriveUniformLeqEta(&p1, &seed, i) + for j := 0; j < PolyLeqEtaSize; j++ { + if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta { + t.Fatalf("DerveUniformLeqEta out of bounds") + } + } + PolyPackLeqEta(&p1, buf[:]) + PolyUnpackLeqEta(&p2, buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT1(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p1, &seed, i) + p1.Normalize() + for j := 0; j < common.N; j++ { + p1[j] &= 0x1ff + } + p1.PackT1(buf[:]) + p2.UnpackT1(buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT0(t *testing.T) { + var p, p0, p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT0Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p, &seed, i) + p.Normalize() + p.Power2Round(&p0, &p1) + + p0.PackT0(buf[:]) + p2.UnpackT0(buf[:]) + if p0 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackLeGamma1(t *testing.T) { + var p0, p1 common.Poly + var seed [48]byte + var buf [common.PolyLeGamma1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniformLeGamma1(&p0, &seed, i) + p0.Normalize() + + p0.PackLeGamma1(buf[:]) + p1.UnpackLeGamma1(buf[:]) + if p0 != p1 { + t.Fatalf("%v != %v", p0, p1) + } + } +} diff --git a/src/circl/sign/dilithium/mode1/internal/params.go b/src/circl/sign/dilithium/mode1/internal/params.go new file mode 100644 index 00000000000..28e49b4dc39 --- /dev/null +++ b/src/circl/sign/dilithium/mode1/internal/params.go @@ -0,0 +1,17 @@ +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +const ( + Name = "Dilithium1" + UseAES = false + PublicKeySize = 896 + PrivateKeySize = 2096 + SignatureSize = 1387 + K = 3 + L = 2 + Eta = 7 + DoubleEtaBits = 4 + Beta = 375 + Omega = 64 +) diff --git a/src/circl/sign/dilithium/mode1/internal/params_test.go b/src/circl/sign/dilithium/mode1/internal/params_test.go new file mode 100644 index 00000000000..65b2af1e26f --- /dev/null +++ b/src/circl/sign/dilithium/mode1/internal/params_test.go @@ -0,0 +1,51 @@ +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Tests specific to the current mode + +func TestVectorDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + p2 := common.Poly{ + 3, 0, 2, 3, 8380412, 8380414, 2, 2, 8380415, 8380416, + 8380416, 1, 7, 8380411, 4, 7, 2, 8380414, 8380412, 0, 3, + 8380413, 4, 8380410, 8380414, 8380410, 8380413, 8380412, + 8380410, 8380410, 7, 3, 8380412, 3, 8380411, 8380414, 7, + 8380415, 1, 8380416, 7, 8380414, 2, 4, 7, 8380416, 4, 5, + 5, 2, 1, 8380411, 7, 3, 4, 8380416, 8380415, 2, 2, 8380410, + 7, 5, 0, 8380411, 8380416, 7, 8380412, 5, 8380411, 5, 4, + 1, 4, 2, 8380414, 8380416, 3, 4, 8380414, 8380410, 8380414, + 7, 8380415, 8380412, 8380411, 6, 8380415, 8380410, 8380413, + 0, 8380416, 8380412, 8380411, 6, 8380415, 8380410, 8380410, + 8380413, 7, 8380415, 3, 1, 0, 8380414, 4, 8380410, 8380412, + 5, 6, 0, 1, 8380410, 8380413, 8380410, 6, 8380411, 0, + 8380415, 3, 8380411, 2, 3, 6, 8380410, 8380410, 0, 0, 6, + 8380414, 0, 6, 8380411, 8380412, 8380412, 5, 7, 2, 8380413, + 8380410, 0, 0, 4, 0, 5, 8380416, 1, 5, 7, 7, 8380410, 2, + 0, 8380412, 6, 5, 4, 8380411, 0, 0, 7, 8380414, 8380416, + 8380410, 4, 0, 8380411, 8380410, 8380413, 8380414, 3, + 8380413, 8380414, 8380415, 7, 8380411, 8380414, 8380410, + 5, 6, 8380410, 6, 8380415, 4, 0, 0, 8380416, 8380415, + 8380415, 8380415, 4, 8380410, 8380411, 8380415, 8380412, + 6, 1, 4, 1, 2, 8380411, 0, 8380416, 4, 8380414, 8380416, + 6, 5, 1, 3, 8380414, 4, 8380414, 8380414, 3, 2, 2, 8380413, + 2, 8380412, 0, 8380416, 8380415, 8380414, 0, 3, 8380413, + 3, 8380410, 7, 8380410, 8380414, 8380412, 1, 4, 2, 8380415, + 2, 8380410, 8380410, 8380410, 4, 8380413, 4, 4, 0, 3, + 8380410, 5, 8380413, 8380414, 8380415, 4, 1, 8380410, 7, + 8380413, + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeqEta(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} diff --git a/src/circl/sign/dilithium/mode1/internal/sample.go b/src/circl/sign/dilithium/mode1/internal/sample.go new file mode 100644 index 00000000000..8d01e8ef776 --- /dev/null +++ b/src/circl/sign/dilithium/mode1/internal/sample.go @@ -0,0 +1,563 @@ +// Code generated from mode3/internal/sample.go by gen.go + +package internal + +import ( + "circl/internal/sha3" + "circl/simd/keccakf1600" + + "circl/sign/dilithium/internal/common" + + "encoding/binary" +) + +// DeriveX4Available indicates whether the system supports the quick fourway +// sampling variants like PolyDeriveUniformX4. +var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES + +// For each i, sample ps[i] uniformly with coefficients of norm less than γ₁ +// using the the given seed and nonces[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformLeGamma1X4(ps [4]*common.Poly, seed *[48]byte, + nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE256 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE256 is 136 --- i.e. 17 uint64s. + for j := 0; j < 4; j++ { + state[6*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[16*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + // Each try requires 15 bits. 15 does not divide into 64, nor in 136, + // so we will have to carry some bits from a previous uint64 to the next. + var carry [4]uint32 + + // Shift is the amount of bits in the carry. + var shift [4]uint + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 17 uint64s of each + // of the four SHAKE256 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := 0; i < 17; i++ { + var t [4]uint32 + tCount := 3 + + // Get the next three or four 20 bit numbers. + qw := state[i*4+j] + qwl := (qw << shift[j]) | uint64(carry[j]) + t[0] = uint32(qwl & 0xfffff) + t[1] = uint32((qwl >> 20) & 0xfffff) + t[2] = uint32((qwl >> 40) & 0xfffff) + + if shift[j] == 16 { + t[3] = uint32(qw >> 44) + shift[j] = 0 + carry[j] = 0 + tCount = 4 + } else { + shift[j] += 4 + carry[j] = uint32(qw >> (64 - shift[j])) + } + + // Check if they're coefficients. + for k := 0; k < tCount; k++ { + if t[k] <= 2*common.Gamma1-2 { + ps[j][idx[j]] = common.Q + common.Gamma1 - 1 - t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + + done = false + } + } +} + +// For each i, sample ps[i] uniformly from the given seed and nonces[i]. +// ps[i] may be nil and is ignored in that case. +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 4; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE128 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s. + for j := 0; j < 4; j++ { + state[4*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[20*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each + // of the four SHAKE128 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + for i := 0; i < 7; i++ { + var t [8]uint32 + t[0] = uint32(state[i*3*4+j] & 0x7fffff) + t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff) + t[2] = uint32((state[i*3*4+j] >> 48) | + ((state[(i*3+1)*4+j] & 0x7f) << 16)) + t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff) + t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff) + t[5] = uint32((state[(i*3+1)*4+j] >> 56) | + ((state[(i*3+2)*4+j] & 0x7fff) << 8)) + t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff) + t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff) + + for k := 0; k < 8; k++ { + if t[k] < common.Q { + ps[j][idx[j]] = t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + done = false + } + } +} + +// Sample p uniformly from the given seed and nonce. +// +// p will be normalized. +func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) { + var i, length int + var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks + + if UseAES { + length = 12 * 16 + } else { + length = 168 + } + + sample := func() { + // Note that 3 divides into 168 and 12*16, so we use up buf completely. + for j := 0; j < length && i < common.N; j += 3 { + t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0x7fffff + + // We use rejection sampling + if t < common.Q { + p[i] = t + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample p uniformly with coefficients of norm less than or equal η, +// using the given seed and nonce. +// +// p will not be normalized, but will have coefficients in [q-η,q+η]. +func PolyDeriveUniformLeqEta(p *common.Poly, seed *[32]byte, nonce uint16) { + // Assumes 2 < η < 8. + var i, length int + var buf [11 * 16]byte // fits 168B SHAKE-128 rate and 11 16B AES blocks + + if UseAES { + length = 11 * 16 + } else { + length = 168 + } + + sample := func() { + // We use rejection sampling + for j := 0; j < length && i < common.N; j++ { + var t1, t2 uint32 + if Eta <= 3 { // branch is eliminated by compiler + t1 = uint32(buf[j]) & 7 + t2 = uint32(buf[j]) >> 5 + } else { + t1 = uint32(buf[j]) & 15 + t2 = uint32(buf[j]) >> 4 + } + if t1 <= 2*Eta { + p[i] = common.Q + Eta - t1 + i++ + } + if t2 <= 2*Eta && i < common.N { + p[i] = common.Q + Eta - t2 + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + + // 168 is SHAKE-128 rate + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample v[i] uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce+i +// +// v[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func VecLDeriveUniformLeGamma1(v *VecL, seed *[48]byte, nonce uint16) { + if !DeriveX4Available { + for i := 0; i < L; i++ { + PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i)) + } + return + } + + var ps [4]*common.Poly + nonces := [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3} + for i := 0; i < L && i < 4; i++ { + ps[i] = &v[i] + } + + // PolyDeriveUniformLeGamma1X4 is slower than, but not twice as slow as, + // PolyDeriveUniformLeGamma. + PolyDeriveUniformLeGamma1X4(ps, seed, nonces) + if L == 5 { + PolyDeriveUniformLeGamma1(&v[L-1], seed, nonce+4) + } else if L > 5 || L < 2 { + panic("VecLDeriveUniformLeGamma1 does not support that L") + } +} + +// Sample p uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce. +// +// p will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[48]byte, nonce uint16) { + // Assumes γ₁ is less than 2²⁰. + var length, i int + + // Fits 10 16B AES blocks, which aligns nicely as we take 5 bytes at + // a time. The SHAKE-256 rate, however, is 136. As 136 is 1 modulo 5, + // we are left with 1 byte after the first block, which we include in the + // next block. So we need 4 bytes leeway in our buffer. The total 160 + // fits easily in 160. + var buf [160]byte + + sample := func() { + // We use rejection sampling + for j := 0; j < length-4 && i < common.N; j += 5 { + t1 := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0xfffff + t2 := ((uint32(buf[j+2]) >> 4) | (uint32(buf[j+3]) << 4) | + (uint32(buf[j+4]) << 12)) + + if t1 <= 2*common.Gamma1-2 { + p[i] = common.Q + common.Gamma1 - 1 - t1 + i++ + } + if t2 <= 2*common.Gamma1-2 && i < common.N { + p[i] = common.Q + common.Gamma1 - 1 - t2 + i++ + } + } + } + if UseAES { + length = 160 + h := common.NewAesStream256(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:]) + sample() + } + } else { + length = 136 + var iv [48 + 2]byte // 48 byte seed + uint16 nonce + bufOffset := 0 // where to put the next block + + h := sha3.NewShake256() + copy(iv[:48], seed[:]) + iv[48] = uint8(nonce) + iv[49] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[bufOffset : bufOffset+136]) + sample() + + bufOffset++ + if bufOffset == 5 { + bufOffset = 0 + } + + // Move remaining bytes at the end to the start. + for j := 0; j < bufOffset; j++ { + buf[j] = buf[135+j] + } + } + } +} + +// For each i, sample ps[i] uniformly with 60 non-zero coefficients in {q-1,1} +// using the the given seed and w1[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will be normalized. +// +// Can only be called when DeriveX4Available is true. +// +// This function is currently not used (yet). +func PolyDeriveUniformB60X4(ps [4]*common.Poly, seed *[48]byte, + w1 [4]*VecK) { + // Pack the w1s + var w1Packed [4][common.PolyLe16Size * K]byte + for j := 0; j < 4; j++ { + if ps[j] != nil { + w1[j].PackLe16(w1Packed[j][:]) + } + } + + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the start of the packed w₁s + offset := 0 // offset into w1Packed[j] + for i := 6; i < 17; i++ { + for j := 0; j < 4; j++ { + state[i*4+j] = binary.LittleEndian.Uint64(w1Packed[j][offset : offset+8]) + } + offset += 8 + } + + offset -= 8 + + // Absorb the remainder of the packed w₁s. +PermuteLoop: + for { + perm.Permute() + + for i := 0; i < 17; i++ { + offset += 8 + if offset == len(w1Packed[0]) { + // SHAKE256 domain separator and padding + for j := 0; j < 4; j++ { + state[i*4+j] ^= 0x1f + state[16*4+j] ^= 0x80 << 56 + } + perm.Permute() + + break PermuteLoop + } + + for j := 0; j < 4; j++ { + state[i*4+j] ^= binary.LittleEndian.Uint64( + w1Packed[j][offset : offset+8]) + } + } + } + + var signs [4]uint64 + var idx [4]uint16 // indices into ps + + for j := 0; j < 4; j++ { + if ps[j] != nil { + signs[j] = state[j] + *ps[j] = common.Poly{} // zero ps[j] + idx[j] = common.N - 60 + } else { + idx[j] = common.N // mark as completed + } + } + + stateOffset := 1 + for { + done := true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := stateOffset; i < 17; i++ { + var bs [8]byte + binary.LittleEndian.PutUint64(bs[:], state[4*i+j]) + for k := 0; k < 8; k++ { + b := uint16(bs[k]) + + if b > idx[j] { + continue + } + + ps[j][idx[j]] = ps[j][b] + ps[j][b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1))) + signs[j] >>= 1 + + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + + done = false + } + + if done { + break + } + + perm.Permute() + stateOffset = 0 + } +} + +// Samples p uniformly with 60 non-zero coefficients in {q-1,1}. +// +// The polynomial p will be normalized. +func PolyDeriveUniformB60(p *common.Poly, seed *[48]byte, w1 *VecK) { + var w1Packed [common.PolyLe16Size * K]byte + var buf [136]byte // SHAKE-256 rate is 136 + + w1.PackLe16(w1Packed[:]) + + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Write(w1Packed[:]) + _, _ = h.Read(buf[:]) + + // Essentially we generate a sequence of 60 ones or minus ones, + // prepend 196 zeroes and shuffle the concatenation using the + // usual algorithm (Fisher--Yates.) + signs := binary.LittleEndian.Uint64(buf[:]) + bufOff := 8 // offset into buf + + *p = common.Poly{} // zero p + for i := uint16(common.N - 60); i < common.N; i++ { + var b uint16 + + // Find location of where to move the new coefficient to using + // rejection sampling. + for { + if bufOff >= 136 { + _, _ = h.Read(buf[:]) + bufOff = 0 + } + + b = uint16(buf[bufOff]) + bufOff++ + + if b <= i { + break + } + } + + p[i] = p[b] + p[b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1))) + signs >>= 1 + } +} diff --git a/src/circl/sign/dilithium/mode1/internal/sample_test.go b/src/circl/sign/dilithium/mode1/internal/sample_test.go new file mode 100644 index 00000000000..f4f0a51c1c9 --- /dev/null +++ b/src/circl/sign/dilithium/mode1/internal/sample_test.go @@ -0,0 +1,407 @@ +// Code generated from mode3/internal/sample_test.go by gen.go + +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestVectorDeriveUniform(t *testing.T) { + var p, p2 common.Poly + var seed [32]byte + if UseAES { + p2 = common.Poly{ + 6724291, 310295, 6949524, 4464039, 1482136, 2522903, + 7025059, 3006320, 7286364, 7516512, 3361305, 1955529, + 4765954, 1725325, 6933066, 4299100, 6625173, 4272792, + 583034, 4971409, 2259140, 7715362, 3975394, 2341624, + 5481174, 8150082, 365246, 5491939, 1083120, 7517301, + 3104783, 2475292, 184149, 6425226, 4591622, 5964030, + 4729604, 5471092, 1828227, 1082044, 2516245, 1692580, + 3274844, 5443294, 7256740, 4989638, 3191250, 7479519, + 5124211, 5603858, 1230692, 2513454, 2828034, 4254312, + 1512596, 5245430, 5517392, 2814840, 932545, 6826733, + 3511094, 4075348, 3233981, 7268882, 2913733, 4870249, + 4123492, 8124406, 4016949, 5478752, 2750895, 603525, + 5724798, 3985430, 3483012, 6434230, 3136996, 8297976, + 4107616, 7307748, 6962904, 7544473, 1193110, 3448595, + 4814773, 5607932, 8221314, 1054046, 1541208, 1866050, + 8227412, 2925778, 5293953, 2065416, 4972769, 3616283, + 7990594, 1105530, 7121836, 1170740, 7417431, 633146, + 253820, 7235019, 3539504, 6807707, 451390, 5481526, + 2859902, 1063061, 4579730, 7126652, 7033767, 4294814, + 1414604, 7620048, 1953268, 8304556, 1156814, 1182881, + 5311519, 3057534, 5277666, 682843, 2070398, 2874278, + 4859533, 6376664, 6694074, 1590242, 2620706, 8331066, + 5643845, 5037538, 2891516, 7004879, 3754327, 5031296, + 5463118, 2420870, 8116529, 5517696, 7435129, 3873963, + 710407, 713806, 175647, 4274571, 2655021, 7319503, + 3027243, 7129679, 4213435, 2429323, 4643873, 4568526, + 649664, 1720514, 6497260, 2683517, 7672754, 7105190, + 3148405, 5898369, 5667677, 8050874, 1587139, 7315260, + 4337416, 2202680, 2338714, 557467, 6752058, 2469794, + 485071, 1617604, 3590498, 2151466, 2005823, 7727956, + 7776292, 6783433, 6787146, 1732833, 3596857, 7436284, + 4483349, 4970142, 4472608, 6478342, 1236215, 5695744, + 2280717, 2889355, 3233946, 5187812, 978685, 5177364, + 2922353, 4824807, 5302883, 6739803, 8092453, 5883903, + 816553, 6041174, 8317591, 1459178, 5332455, 1835058, + 1368601, 2820950, 3479224, 2589540, 7992934, 3421045, + 4657128, 8292902, 4153567, 3553988, 7830320, 6722913, + 2555309, 4149801, 8328975, 1560545, 7757473, 3106458, + 4310856, 7135453, 3481032, 652626, 1841361, 8126828, + 6250018, 300536, 7380070, 8174419, 1418793, 6208185, + 3906256, 6679016, 1605701, 3561489, 5819724, 5746996, + 8044214, 7087187, 7102330, 4962927, 4253983, 7108567, + 4119736, 6584065, 441634, 6941656, + } + } else { + p2 = common.Poly{ + 2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052, + 3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357, + 6066350, 8126097, 1179080, 4787182, 6552182, 6713644, + 1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938, + 1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431, + 1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545, + 7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071, + 105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855, + 5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453, + 5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453, + 3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874, + 5614778, 2248550, 1756499, 8280764, 8263880, 7600081, + 5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562, + 7483939, 4938664, 6863397, 5126354, 5218129, 6236086, + 4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737, + 1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595, + 6830029, 1548850, 6593138, 6849097, 1518037, 2859442, + 7772265, 7325153, 3281191, 7856131, 4995056, 4684325, + 1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778, + 7973479, 3171829, 5624626, 3540123, 7150120, 8313283, + 3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342, + 7501562, 5826142, 2709813, 8245473, 2369045, 2782257, + 5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983, + 5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375, + 267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500, + 2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008, + 8258986, 2183134, 2302072, 4674924, 4306056, 7465311, + 6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700, + 2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533, + 255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625, + 6997719, 6260212, 6186962, 6636650, 7836834, 7998017, + 2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598, + 4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947, + 6195178, 5552390, 6804584, 6305468, 5731980, 6095195, + 3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054, + 4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780, + 3740517, 5224226, 3547288, 2083124, 4699398, 3654239, + 5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706, + 4352830, + } + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniform(&p, &seed, 30000) + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniform(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniform(&p, &seed, uint16(i)) + if !PolyNormalized(&p) { + t.Fatal() + } + } +} + +func TestDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeqEta(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-Eta || p[j] > common.Q+Eta { + t.Fatal() + } + } + } +} + +func TestDeriveUniformLeGamma1(t *testing.T) { + var p common.Poly + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-common.Gamma1 || p[j] > common.Q+common.Gamma1 { + t.Fatal() + } + } + } +} + +func TestVectorDeriveUniformLeGamma1(t *testing.T) { + var p, p2 common.Poly + var seed [48]byte + if UseAES { + p2 = common.Poly{ + 90940, 8133770, 8210940, 8218464, 8362467, 431142, 98024, + 320453, 7892373, 144162, 495313, 7910122, 308198, 8024421, + 8313699, 8323445, 8242093, 7946588, 418979, 427179, 353562, + 20972, 455962, 213062, 361787, 8141790, 8321931, 7885366, + 88645, 181202, 8094142, 8303121, 8059515, 7919812, 191865, + 7910073, 7896561, 8096830, 7899355, 8338900, 72693, 236799, + 8183042, 347570, 8153528, 8364233, 8077851, 8312277, 104682, + 8037310, 8356199, 7994081, 240369, 70229, 8108858, 8175836, + 466639, 50909, 339919, 8029663, 341659, 154398, 64345, + 97101, 212245, 8285367, 521225, 325882, 296235, 8110929, + 8015814, 7953234, 158409, 329908, 8331330, 449258, 167701, + 8197796, 8228247, 7940020, 1985, 304704, 475316, 8037482, + 8250449, 304557, 8216567, 432266, 213295, 8162216, 381001, + 7995314, 7988689, 128534, 245586, 67041, 8232744, 398441, + 223116, 443612, 149856, 222852, 158723, 54746, 171906, + 163070, 353915, 8263276, 8016812, 8229081, 31827, 489715, + 450171, 8069106, 53220, 7932381, 7955335, 8197363, 201044, + 8306733, 446376, 8211025, 7889271, 8070595, 495514, 8158685, + 7524, 7973394, 247673, 4293, 184924, 457334, 138349, 8123964, + 284179, 8255307, 8068216, 8291492, 243759, 8060601, 20962, + 8058389, 420953, 8305974, 455136, 8218139, 7121, 147703, + 7951253, 394376, 8127066, 365861, 8062390, 8138732, 366555, + 8280514, 221, 395861, 7968769, 7977119, 8098083, 343056, + 8190769, 223361, 163270, 203059, 109219, 8228600, 8127695, + 321016, 295979, 8201961, 49891, 8335504, 8190386, 8190984, + 8278654, 336364, 7878013, 7922436, 7974101, 8075534, 8200852, + 8333820, 415982, 8089662, 149553, 7946740, 474102, 7937116, + 8026845, 356056, 191053, 86928, 8218644, 8375040, 8029184, + 8025675, 8193350, 295360, 7905768, 487174, 8362961, 386108, + 282213, 8373318, 50167, 8238992, 7911505, 493459, 8335164, + 8079327, 250697, 263154, 221028, 40778, 87515, 8372585, + 504728, 7980935, 8307600, 298972, 427523, 93352, 89915, + 391490, 80320, 7975008, 336136, 7949815, 8048682, 8332244, + 8204778, 8177783, 7910684, 7925292, 518641, 59663, 53608, + 222225, 463772, 8022091, 8173722, 8291385, 472741, 8105898, + 7943299, 267137, 7957660, 371874, 409084, 203750, 477334, + 83412, 111278, 120444, + } + } else { + p2 = common.Poly{ + 338083, 7978692, 8044913, 373628, 427855, 79725, 91018, + 349821, 501552, 7955127, 8316400, 290708, 216142, 8199666, + 8040144, 109426, 8177916, 8200218, 8125680, 358131, 160961, + 497383, 25361, 156297, 8033745, 7897189, 48397, 498732, + 464556, 7862704, 8308667, 236080, 91240, 8328377, 326190, + 509979, 8313264, 8106493, 8210965, 8328036, 172602, 8108765, + 8192963, 8361660, 8026473, 7932022, 322006, 8305874, 8254440, + 7866474, 373371, 8023413, 8221878, 486124, 36080, 8324512, + 8042056, 7984472, 8048111, 7910387, 8205382, 8259636, 188609, + 8316587, 59306, 119803, 8067108, 8155455, 8153450, 7983908, + 8222256, 21521, 114297, 8069037, 151621, 8014482, 8052856, + 376107, 8004652, 175001, 8079461, 8351123, 8021484, 144547, + 7908116, 8278100, 8136941, 142399, 8026843, 8081852, 124334, + 242796, 266768, 7919478, 7954016, 28927, 8329064, 514031, + 423911, 27907, 8142788, 8078298, 273978, 382723, 8148646, + 186476, 8030712, 8067268, 356250, 145817, 60045, 122764, + 56856, 8225416, 136437, 199652, 8343127, 8109765, 7936848, + 446966, 8351681, 288663, 409663, 512988, 8350788, 8191864, + 8366223, 281267, 7921696, 8213978, 442484, 67457, 8030602, + 238514, 230458, 8301866, 8359700, 150320, 143893, 461735, + 225443, 8027502, 151113, 365244, 7911438, 82498, 405398, + 8207009, 8108255, 367485, 514660, 8294055, 8168958, 127725, + 402955, 8051625, 7859029, 7980052, 321819, 7949587, 125778, + 8287078, 131972, 499609, 256795, 8180323, 8269393, 5878, + 8145473, 8238676, 383855, 415547, 424071, 241989, 8165743, + 8207329, 149608, 8315331, 7901850, 8114275, 360650, 516061, + 255090, 8277977, 270877, 8125200, 479248, 7991711, 8028595, + 73426, 8215429, 208217, 153872, 429336, 229856, 461204, + 236682, 7930158, 8298847, 228327, 8009399, 8111520, 345025, + 386495, 93454, 8336429, 8161305, 7980811, 286795, 162808, + 224476, 7972825, 85118, 287488, 8029791, 119071, 371, 518524, + 473496, 451205, 127000, 19233, 211519, 2442, 7950959, 481888, + 8041598, 8281176, 437202, 7912610, 8080153, 8237500, 7926828, + 8009421, 204880, 62495, 8192310, 8314388, 98616, 182368, + 323894, 59901, 481049, 8139275, 7872144, 254106, 376257, + 93339, 301342, 366536, 438920, 84773, 461471, 8125755, + 7930085, 405116, + } + } + for i := 0; i < 48; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeGamma1(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniformB60(t *testing.T) { + var p common.Poly + var w1 VecK + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformB60(&p, &seed, &w1) + nonzero := 0 + for j := 0; j < common.N; j++ { + if p[j] != 0 { + if p[j] != 1 && p[j] != common.Q-1 { + t.Fatal() + } + nonzero++ + } + } + if nonzero != 60 { + t.Fatal() + } + } +} + +func TestDeriveUniformX4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [32]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, + nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniform(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatal() + } + } +} + +func TestDeriveUniformB60X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + var w1s [4]VecK + for j := 0; j < 4; j++ { + for k := 0; k < K; k++ { + for i := 0; i < common.N; i++ { + w1s[j][k][i] = uint32(j+k*4+i*4*K) & 15 + } + } + } + PolyDeriveUniformB60X4( + [4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, + [4]*VecK{&w1s[0], &w1s[1], &w1s[2], &w1s[3]}, + ) + for j := 0; j < 4; j++ { + PolyDeriveUniformB60(&p, &seed, &w1s[j]) + if ps[j] != p { + t.Fatalf("%v %v", ps[j], p) + } + } +} + +func TestDeriveUniformLeGamma1X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatalf("%d\n%v\n%v", i, p, ps[i]) + } + } +} + +func BenchmarkPolyDeriveUniformB60(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60(&p, &seed, &w1) + } +} + +func BenchmarkPolyDeriveUniformB60X4(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60X4( + [4]*common.Poly{&p, &p, &p, &p}, + &seed, + [4]*VecK{&w1, &w1, &w1, &w1}, + ) + } +} + +func BenchmarkPolyDeriveUniform(b *testing.B) { + var seed [32]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniform(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformX4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [32]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) { + var seed [48]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1X4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [48]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} diff --git a/src/circl/sign/dilithium/mode1/internal/vec.go b/src/circl/sign/dilithium/mode1/internal/vec.go new file mode 100644 index 00000000000..a20a8b0224e --- /dev/null +++ b/src/circl/sign/dilithium/mode1/internal/vec.go @@ -0,0 +1,281 @@ +// Code generated from mode3/internal/vec.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A vector of L polynomials. +type VecL [L]common.Poly + +// A vector of K polynomials. +type VecK [K]common.Poly + +// Normalize the polynomials in this vector. +func (v *VecL) Normalize() { + for i := 0; i < L; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecL) NormalizeAssumingLe2Q() { + for i := 0; i < L; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecL) Add(w, u *VecL) { + for i := 0; i < L; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecL) NTT() { + for i := 0; i < L; i++ { + v[i].NTT() + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecL) Exceeds(bound uint32) bool { + for i := 0; i < L; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Decompose(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecL) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeqEta(). +func (v *VecL) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sequentially packs each polynomial using Poly.PackLeGamma1(). +func (v *VecL) PackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].PackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeGamma1(). +func (v *VecL) UnpackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].UnpackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Normalize the polynomials in this vector. +func (v *VecK) Normalize() { + for i := 0; i < K; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecK) NormalizeAssumingLe2Q() { + for i := 0; i < K; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecK) Add(w, u *VecK) { + for i := 0; i < K; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecK) Exceeds(bound uint32) bool { + for i := 0; i < K; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Decompose(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sets v to the hint vector for v0 the modified low bits and v1 +// the unmodified high bits --- see makeHint(). +// +// Returns the number of ones in the hint vector. +func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) { + for i := 0; i < K; i++ { + pop += v[i].MakeHint(&v0[i], &v1[i]) + } + return +} + +// Computes corrections to the high bits of the polynomials in the vector +// w using the hints in h and sets v to the corrected high bits. Returns v. +// See useHint(). +func (v *VecK) UseHint(q, hint *VecK) *VecK { + for i := 0; i < K; i++ { + v[i].UseHint(&q[i], &hint[i]) + } + return v +} + +// Sequentially packs each polynomial using Poly.PackT1(). +func (v *VecK) PackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sets v to the vector packed into buf by PackT1(). +func (v *VecK) UnpackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sequentially packs each polynomial using Poly.PackT0(). +func (v *VecK) PackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sets v to the vector packed into buf by PackT0(). +func (v *VecK) UnpackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecK) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecK.PackLeqEta(). +func (v *VecK) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecK) NTT() { + for i := 0; i < K; i++ { + v[i].NTT() + } +} + +// Sequentially packs each polynomial using Poly.PackLe16(). +func (v *VecK) PackLe16(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackLe16(buf[offset:]) + offset += common.PolyLe16Size + } +} + +// Sets v to a - b. +// +// Warning: assumes coefficients of the polynomials of b are less than 2q. +func (v *VecK) Sub(a, b *VecK) { + for i := 0; i < K; i++ { + v[i].Sub(&a[i], &b[i]) + } +} + +// Sets v to 2ᵈ w without reducing. +func (v *VecK) MulBy2toD(w *VecK) { + for i := 0; i < K; i++ { + v[i].MulBy2toD(&w[i]) + } +} + +// Applies InvNTT componentwise. See Poly.InvNTT() for details. +func (v *VecK) InvNTT() { + for i := 0; i < K; i++ { + v[i].InvNTT() + } +} + +// Applies Poly.ReduceLe2Q() componentwise. +func (v *VecK) ReduceLe2Q() { + for i := 0; i < K; i++ { + v[i].ReduceLe2Q() + } +} diff --git a/src/circl/sign/dilithium/mode1aes.go b/src/circl/sign/dilithium/mode1aes.go new file mode 100644 index 00000000000..5af1f7c0e4b --- /dev/null +++ b/src/circl/sign/dilithium/mode1aes.go @@ -0,0 +1,95 @@ +// Code generated from mode.templ.go. DO NOT EDIT. + +package dilithium + +import ( + "fmt" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode1aes" +) + +// implMode1AES implements the mode.Mode interface for Dilithium1-AES. +type implMode1AES struct{} + +// Mode1AES is Dilithium in mode "Dilithium1-AES". +var Mode1AES Mode = &implMode1AES{} + +func (m *implMode1AES) GenerateKey(rand io.Reader) ( + PublicKey, PrivateKey, error) { + return mode1aes.GenerateKey(rand) +} + +func (m *implMode1AES) NewKeyFromExpandedSeed(seed *[96]byte) (PublicKey, + PrivateKey) { + return mode1aes.NewKeyFromExpandedSeed(seed) +} + +func (m *implMode1AES) NewKeyFromSeed(seed []byte) (PublicKey, + PrivateKey) { + if len(seed) != common.SeedSize { + panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) + } + seedBuf := [common.SeedSize]byte{} + copy(seedBuf[:], seed) + return mode1aes.NewKeyFromSeed(&seedBuf) +} + +func (m *implMode1AES) Sign(sk PrivateKey, msg []byte) []byte { + isk := sk.(*mode1aes.PrivateKey) + ret := [mode1aes.SignatureSize]byte{} + mode1aes.SignTo(isk, msg, ret[:]) + return ret[:] +} + +func (m *implMode1AES) Verify(pk PublicKey, msg []byte, signature []byte) bool { + ipk := pk.(*mode1aes.PublicKey) + return mode1aes.Verify(ipk, msg, signature) +} + +func (m *implMode1AES) PublicKeyFromBytes(data []byte) PublicKey { + var ret mode1aes.PublicKey + if len(data) != mode1aes.PublicKeySize { + panic("packed public key must be of mode1aes.PublicKeySize bytes") + } + var buf [mode1aes.PublicKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode1AES) PrivateKeyFromBytes(data []byte) PrivateKey { + var ret mode1aes.PrivateKey + if len(data) != mode1aes.PrivateKeySize { + panic("packed public key must be of mode1aes.PrivateKeySize bytes") + } + var buf [mode1aes.PrivateKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode1AES) SeedSize() int { + return common.SeedSize +} + +func (m *implMode1AES) PublicKeySize() int { + return mode1aes.PublicKeySize +} + +func (m *implMode1AES) PrivateKeySize() int { + return mode1aes.PrivateKeySize +} + +func (m *implMode1AES) SignatureSize() int { + return mode1aes.SignatureSize +} + +func (m *implMode1AES) Name() string { + return "Dilithium1-AES" +} + +func init() { + modes["Dilithium1-AES"] = Mode1AES +} diff --git a/src/circl/sign/dilithium/mode1aes/dilithium.go b/src/circl/sign/dilithium/mode1aes/dilithium.go new file mode 100644 index 00000000000..08d3565e16b --- /dev/null +++ b/src/circl/sign/dilithium/mode1aes/dilithium.go @@ -0,0 +1,191 @@ +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// mode1aes implements the CRYSTALS-Dilithium signature scheme Dilithium1-AES +// as submitted to round2 of the NIST PQC competition and described in +// +// https://pq-crystals.org/dilithium/data/dilithium-specification-round2.pdf +package mode1aes + +import ( + "crypto" + "errors" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode1aes/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + SeedSize = common.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a signature + SignatureSize = internal.SignatureSize +) + +// PublicKey is the type of Dilithium1-AES public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of Dilithium1-AES private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + pk, sk, err := internal.GenerateKey(rand) + return (*PublicKey)(pk), (*PrivateKey)(sk), err +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromExpandedSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// SignTo signs the given message and writes the signature into signature. +// It will panic if signature is not of length at least SignatureSize. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + internal.SignTo( + (*internal.PrivateKey)(sk), + msg, + signature, + ) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + return internal.Verify( + (*internal.PublicKey)(pk), + msg, + signature, + ) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Packs the public key. +func (pk *PublicKey) Bytes() []byte { + var buf [PublicKeySize]byte + pk.Pack(&buf) + return buf[:] +} + +// Packs the private key. +func (sk *PrivateKey) Bytes() []byte { + var buf [PrivateKeySize]byte + sk.Pack(&buf) + return buf[:] +} + +// Packs the public key. +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + return pk.Bytes(), nil +} + +// Packs the private key. +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + return sk.Bytes(), nil +} + +// Unpacks the public key from data. +func (pk *PublicKey) UnmarshalBinary(data []byte) error { + if len(data) != PublicKeySize { + return errors.New("packed public key must be of mode1aes.PublicKeySize bytes") + } + var buf [PublicKeySize]byte + copy(buf[:], data) + pk.Unpack(&buf) + return nil +} + +// Unpacks the private key from data. +func (sk *PrivateKey) UnmarshalBinary(data []byte) error { + if len(data) != PrivateKeySize { + return errors.New("packed private key must be of mode1aes.PrivateKeySize bytes") + } + var buf [PrivateKeySize]byte + copy(buf[:], data) + sk.Unpack(&buf) + return nil +} + +// Sign signs the given message. +// +// opts.HashFunc() must return zero, which can be achieved by passing +// crypto.Hash(0) for opts. rand is ignored. Will only return an error +// if opts.HashFunc() is non-zero. +// +// This function is used to make PrivateKey implement the crypto.Signer +// interface. The package-level SignTo function might be more convenient +// to use. +func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( + signature []byte, err error) { + var sig [SignatureSize]byte + + if opts.HashFunc() != crypto.Hash(0) { + return nil, errors.New("dilithium: cannot sign hashed message") + } + + SignTo(sk, msg, sig[:]) + return sig[:], nil +} + +// Computes the public key corresponding to this private key. +// +// Returns a *PublicKey. The type crypto.PublicKey is used to make +// PrivateKey implement the crypto.Signer interface. +func (sk *PrivateKey) Public() crypto.PublicKey { + return (*PublicKey)((*internal.PrivateKey)(sk).Public()) +} + +// Equal returns whether the two private keys equal. +func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { + castOther, ok := other.(*PrivateKey) + if !ok { + return false + } + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) +} + +// Equal returns whether the two public keys equal. +func (pk *PublicKey) Equal(other crypto.PublicKey) bool { + castOther, ok := other.(*PublicKey) + if !ok { + return false + } + return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) +} diff --git a/src/circl/sign/dilithium/mode1aes/internal/dilithium.go b/src/circl/sign/dilithium/mode1aes/internal/dilithium.go new file mode 100644 index 00000000000..fb0eaaf1963 --- /dev/null +++ b/src/circl/sign/dilithium/mode1aes/internal/dilithium.go @@ -0,0 +1,446 @@ +// Code generated from mode3/internal/dilithium.go by gen.go + +package internal + +import ( + cryptoRand "crypto/rand" + "crypto/subtle" + "io" + + "circl/internal/sha3" + "circl/sign/dilithium/internal/common" +) + +const ( + // Size of a packed polynomial of norm ≤η. + // (Note that the formula is not valid in general.) + PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8 +) + +// PublicKey is the type of Dilithium public keys. +type PublicKey struct { + rho [32]byte + t1 VecK + + // Cached values + t1p [common.PolyT1Size * K]byte + A *Mat + tr *[48]byte +} + +// PrivateKey is the type of Dilithium private keys. +type PrivateKey struct { + rho [32]byte + key [32]byte + s1 VecL + s2 VecK + t0 VecK + tr [48]byte + + // Cached values + A Mat // ExpandA(ρ) + s1h VecL // NTT(s₁) + s2h VecK // NTT(s₂) + t0h VecK // NTT(t₀) +} + +type unpackedSignature struct { + z VecL + hint VecK + c common.Poly +} + +// Packs the signature into buf. +func (sig *unpackedSignature) Pack(buf []byte) { + sig.z.PackLeGamma1(buf[:]) + sig.hint.PackHint(buf[L*common.PolyLeGamma1Size:]) + sig.c.PackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) +} + +// Sets sig to the signature encoded in the buffer. +// +// Returns whether buf contains a properly packed signature. +func (sig *unpackedSignature) Unpack(buf []byte) bool { + if len(buf) < SignatureSize { + return false + } + sig.z.UnpackLeGamma1(buf[:]) + if sig.z.Exceeds(common.Gamma1 - Beta) { + return false + } + if !sig.hint.UnpackHint(buf[L*common.PolyLeGamma1Size:]) { + return false + } + sig.c.UnpackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) + return true +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + copy(buf[:32], pk.rho[:]) + copy(buf[32:], pk.t1p[:]) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + copy(pk.rho[:], buf[:32]) + copy(pk.t1p[:], buf[32:]) + + pk.t1.UnpackT1(pk.t1p[:]) + pk.A = new(Mat) + pk.A.Derive(&pk.rho) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + pk.tr = new([48]byte) + h := sha3.NewShake256() + _, _ = h.Write(buf[:]) + _, _ = h.Read(pk.tr[:]) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + copy(buf[:32], sk.rho[:]) + copy(buf[32:64], sk.key[:]) + copy(buf[64:112], sk.tr[:]) + offset := 112 + sk.s1.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.PackT0(buf[offset:]) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + copy(sk.rho[:], buf[:32]) + copy(sk.key[:], buf[32:64]) + copy(sk.tr[:], buf[64:112]) + offset := 112 + sk.s1.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.UnpackT0(buf[offset:]) + + // Cached values + sk.A.Derive(&sk.rho) + sk.t0h = sk.t0 + sk.t0h.NTT() + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() +} + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [32]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(&seed) + return pk, sk, nil +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + var pk PublicKey + var sk PrivateKey + var sSeed [32]byte + + copy(pk.rho[:], seed[:32]) + copy(sSeed[:], seed[32:64]) + copy(sk.key[:], seed[64:]) + copy(sk.rho[:], pk.rho[:]) + + sk.A.Derive(&pk.rho) + + for i := uint16(0); i < L; i++ { + PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i) + } + + for i := uint16(0); i < K; i++ { + PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L) + } + + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() + + sk.computeT0andT1(&sk.t0, &pk.t1) + + sk.t0h = sk.t0 + sk.t0h.NTT() + + // Complete public key far enough to be packed + pk.t1.PackT1(pk.t1p[:]) + pk.A = &sk.A + + // Finish private key + var packedPk [PublicKeySize]byte + pk.Pack(&packedPk) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + h := sha3.NewShake256() + _, _ = h.Write(packedPk[:]) + _, _ = h.Read(sk.tr[:]) + + // Finish cache of public key + pk.tr = &sk.tr + + return &pk, &sk +} + +// Computes t0 and t1 from sk.s1h, sk.s2 and sk.A. +func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) { + var t VecK + + // Set t to A s₁ + s₂ + for i := 0; i < K; i++ { + PolyDotHat(&t[i], &sk.A[i], &sk.s1h) + t[i].ReduceLe2Q() + t[i].InvNTT() + } + t.Add(&t, &sk.s2) + t.Normalize() + + // Compute t₀, t₁ = Power2Round(t) + t.Power2Round(t0, t1) +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) { + var buf [96]byte + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Read(buf[:]) + return NewKeyFromExpandedSeed(&buf) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + var sig unpackedSignature + var mu [48]byte + var zh VecL + var Az, Az2dct1, w1 VecK + var ch, cp common.Poly + + // Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β + // and ensured that there at most ω ones in pk.hint. + if !sig.Unpack(signature) { + return false + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(pk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // Compute Az + zh = sig.z + zh.NTT() + + for i := 0; i < K; i++ { + PolyDotHat(&Az[i], &pk.A[i], &zh) + } + + // Next, we compute Az - 2ᵈ·c·t₁. + // Note that the coefficients of t₁ are bounded by 256 = 2⁹, + // so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q, + // which is small enough for NTT(). + Az2dct1.MulBy2toD(&pk.t1) + Az2dct1.NTT() + ch = sig.c + ch.NTT() + for i := 0; i < K; i++ { + Az2dct1[i].MulHat(&Az2dct1[i], &ch) + } + Az2dct1.Sub(&Az, &Az2dct1) + Az2dct1.ReduceLe2Q() + Az2dct1.InvNTT() + Az2dct1.NormalizeAssumingLe2Q() + + // UseHint(pk.hint, Az - 2ᵈ·c·t₁) + // = UseHint(pk.hint, w - c·s₂ + c·t₀) + // = UseHint(pk.hint, r + c·t₀) + // = r₁ = w₁. + w1.UseHint(&Az2dct1, &sig.hint) + + // c' = H(μ, w₁) + PolyDeriveUniformB60(&cp, &mu, &w1) + return sig.c == cp +} + +// SignTo signs the given message and writes the signature into signature. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + var mu, rhop [48]byte + var y, yh VecL + var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK + var ch common.Poly + var yNonce uint16 + var sig unpackedSignature + + if len(signature) < SignatureSize { + panic("Signature does not fit in that byteslice") + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(sk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // ρ' = CRH(μ ‖ key) + h.Reset() + _, _ = h.Write(sk.key[:]) + _, _ = h.Write(mu[:]) + _, _ = h.Read(rhop[:]) + + // Main rejection loop + attempt := 0 + for { + attempt++ + if attempt >= 576 { + // Depending on the mode, one try has a chance between 1/7 and 1/4 + // of succeeding. Thus it is safe to say that 576 iterations + // are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸. + panic("This should only happen 1 in 2^{128}: something is wrong.") + } + + // y = ExpandMask(ρ', key) + VecLDeriveUniformLeGamma1(&y, &rhop, yNonce) + yNonce += uint16(L) + + // Set w to A y + yh = y + yh.NTT() + for i := 0; i < K; i++ { + PolyDotHat(&w[i], &sk.A[i], &yh) + w[i].ReduceLe2Q() + w[i].InvNTT() + } + + // Decompose w into w₀ and w₁ + w.NormalizeAssumingLe2Q() + w.Decompose(&w0, &w1) + + // c = H(μ, w₁) + PolyDeriveUniformB60(&sig.c, &mu, &w1) + ch = sig.c + ch.NTT() + + // Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β. + // + // By Lemma 3 of the specification this is equivalent to checking that + // both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition + // w - c·s₂ = r₁ α + r₀ as computed by decompose(). + // See also §4.1 of the specification. + for i := 0; i < K; i++ { + w0mcs2[i].MulHat(&ch, &sk.s2h[i]) + w0mcs2[i].InvNTT() + } + w0mcs2.Sub(&w0, &w0mcs2) + w0mcs2.Normalize() + + if w0mcs2.Exceeds(common.Gamma2 - Beta) { + continue + } + + // z = y + c·s₁ + for i := 0; i < L; i++ { + sig.z[i].MulHat(&ch, &sk.s1h[i]) + sig.z[i].InvNTT() + } + sig.z.Add(&sig.z, &y) + sig.z.Normalize() + + // Ensure ‖z‖_∞ < γ₁ - β + if sig.z.Exceeds(common.Gamma1 - Beta) { + continue + } + + // Compute c·t₀ + for i := 0; i < K; i++ { + ct0[i].MulHat(&ch, &sk.t0h[i]) + ct0[i].InvNTT() + } + ct0.NormalizeAssumingLe2Q() + + // Ensure ‖c·t₀‖_∞ < γ₂. + if ct0.Exceeds(common.Gamma2) { + continue + } + + // Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0. + // Note that we're not using makeHint() in the obvious way as we + // do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂. Instead we note + // that our makeHint() is actually the same as a makeHint for a + // different decomposition: + // + // Earlier we ensured indirectly with a check that r₁ = w₁ where + // r = w - c·s₂. Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂. + // Thus MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁) + // and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁). + // As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct. + w0mcs2pct0.Add(&w0mcs2, &ct0) + w0mcs2pct0.NormalizeAssumingLe2Q() + hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1) + if hintPop > Omega { + continue + } + + break + } + + sig.Pack(signature[:]) +} + +// Computes the public key corresponding to this private key. +func (sk *PrivateKey) Public() *PublicKey { + var t0 VecK + pk := &PublicKey{ + rho: sk.rho, + A: &sk.A, + tr: &sk.tr, + } + sk.computeT0andT1(&t0, &pk.t1) + pk.t1.PackT1(pk.t1p[:]) + return pk +} + +// Equal returns whether the two public keys are equal +func (pk *PublicKey) Equal(other *PublicKey) bool { + return pk.rho == other.rho && pk.t1 == other.t1 +} + +// Equal returns whether the two private keys are equal +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) & + subtle.ConstantTimeCompare(sk.key[:], other.key[:]) & + subtle.ConstantTimeCompare(sk.tr[:], other.tr[:])) + + acc := uint32(0) + for i := 0; i < L; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s1[i][j] ^ other.s1[i][j] + } + } + for i := 0; i < K; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s2[i][j] ^ other.s2[i][j] + acc |= sk.t0[i][j] ^ other.t0[i][j] + } + } + return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1 +} diff --git a/src/circl/sign/dilithium/mode1aes/internal/dilithium_test.go b/src/circl/sign/dilithium/mode1aes/internal/dilithium_test.go new file mode 100644 index 00000000000..42ce6dbe5d1 --- /dev/null +++ b/src/circl/sign/dilithium/mode1aes/internal/dilithium_test.go @@ -0,0 +1,131 @@ +// Code generated from mode3/internal/dilithium_test.go by gen.go + +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Checks whether p is normalized. Only used in tests. +func PolyNormalized(p *common.Poly) bool { + p2 := *p + p2.Normalize() + return p2 == *p +} + +func BenchmarkSkUnpack(b *testing.B) { + var buf [PrivateKeySize]byte + var sk PrivateKey + for i := 0; i < b.N; i++ { + sk.Unpack(&buf) + } +} + +func BenchmarkPkUnpack(b *testing.B) { + var buf [PublicKeySize]byte + var pk PublicKey + for i := 0; i < b.N; i++ { + pk.Unpack(&buf) + } +} + +func BenchmarkVerify(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of verification (as in the reference + // implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + pk, sk := NewKeyFromSeed(&seed) + SignTo(sk, msg[:], sig[:]) + b.ResetTimer() + for i := 0; i < b.N; i++ { + // We should generate a new signature for every verify attempt, + // as this influences the time a little bit. This difference, however, + // is small and generating a new signature in between creates a lot + // pressure on the allocator which makes an accurate measurement hard. + Verify(pk, msg[:], sig[:]) + } +} + +func BenchmarkSign(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of signing (as in the reference implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + _, sk := NewKeyFromSeed(&seed) + b.ResetTimer() + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(msg[:], uint64(i)) + SignTo(sk, msg[:], sig[:]) + } +} + +func BenchmarkGenerateKey(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + NewKeyFromSeed(&seed) + } +} + +func BenchmarkPublicFromPrivate(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + b.StopTimer() + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + _, sk := NewKeyFromSeed(&seed) + b.StartTimer() + sk.Public() + } +} + +func TestSignThenVerifyAndPkSkPacking(t *testing.T) { + var seed [common.SeedSize]byte + var sig [SignatureSize]byte + var msg [8]byte + var pkb [PublicKeySize]byte + var skb [PrivateKeySize]byte + var pk2 PublicKey + var sk2 PrivateKey + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + if !sk.Equal(sk) { + t.Fatal() + } + for j := uint64(0); j < 10; j++ { + binary.LittleEndian.PutUint64(msg[:], j) + SignTo(sk, msg[:], sig[:]) + if !Verify(pk, msg[:], sig[:]) { + t.Fatal() + } + } + pk.Pack(&pkb) + pk2.Unpack(&pkb) + if !pk.Equal(&pk2) { + t.Fatal() + } + sk.Pack(&skb) + sk2.Unpack(&skb) + if !sk.Equal(&sk2) { + t.Fatal() + } + } +} + +func TestPublicFromPrivate(t *testing.T) { + var seed [common.SeedSize]byte + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + pk2 := sk.Public() + if !pk.Equal(pk2) { + t.Fatal() + } + } +} diff --git a/src/circl/sign/dilithium/mode1aes/internal/mat.go b/src/circl/sign/dilithium/mode1aes/internal/mat.go new file mode 100644 index 00000000000..a2411b0566d --- /dev/null +++ b/src/circl/sign/dilithium/mode1aes/internal/mat.go @@ -0,0 +1,59 @@ +// Code generated from mode3/internal/mat.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A k by l matrix of polynomials. +type Mat [K]VecL + +// Expands the given seed to a complete matrix. +// +// This function is called ExpandA in the specification. +func (m *Mat) Derive(seed *[32]byte) { + if !DeriveX4Available { + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + PolyDeriveUniform(&m[i][j], seed, (i<<8)+j) + } + } + return + } + + idx := 0 + var nonces [4]uint16 + var ps [4]*common.Poly + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + nonces[idx] = (i << 8) + j + ps[idx] = &m[i][j] + idx++ + if idx == 4 { + idx = 0 + PolyDeriveUniformX4(ps, seed, nonces) + } + } + } + if idx != 0 { + for i := idx; i < 4; i++ { + ps[i] = nil + } + PolyDeriveUniformX4(ps, seed, nonces) + } +} + +// Set p to the inner product of a and b using pointwise multiplication. +// +// Assumes a and b are in Montgomery form and their coefficients are +// pairwise sufficiently small to multiply, see Poly.MulHat(). Resulting +// coefficients are bounded by 2Lq. +func PolyDotHat(p *common.Poly, a, b *VecL) { + var t common.Poly + *p = common.Poly{} // zero p + for i := 0; i < L; i++ { + t.MulHat(&a[i], &b[i]) + p.Add(&t, p) + } +} diff --git a/src/circl/sign/dilithium/mode1aes/internal/pack.go b/src/circl/sign/dilithium/mode1aes/internal/pack.go new file mode 100644 index 00000000000..ecf3971cd20 --- /dev/null +++ b/src/circl/sign/dilithium/mode1aes/internal/pack.go @@ -0,0 +1,141 @@ +// Code generated from mode3/internal/pack.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// Writes p with norm less than or equal η into buf, which must be of +// size PolyLeqEtaSize. +// +// Assumes coefficients of p are not normalized, but in [q-η,q+η]. +func PolyPackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + buf[i] = (byte(common.Q+Eta-p[j]) | + byte(common.Q+Eta-p[j+1])<<4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + buf[i] = (byte(common.Q+Eta-p[j]) | + (byte(common.Q+Eta-p[j+1]) << 3) | + (byte(common.Q+Eta-p[j+2]) << 6)) + buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) | + (byte(common.Q+Eta-p[j+3]) << 1) | + (byte(common.Q+Eta-p[j+4]) << 4) | + (byte(common.Q+Eta-p[j+5]) << 7)) + buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) | + (byte(common.Q+Eta-p[j+6]) << 2) | + (byte(common.Q+Eta-p[j+7]) << 5)) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Sets p to the polynomial of norm less than or equal η encoded in the +// given buffer of size PolyLeqEtaSize. +// +// Output coefficients of p are not normalized, but in [q-η,q+η] provided +// buf was created using PackLeqEta. +// +// Beware, for arbitrary buf the coefficients of p might en up in +// the interval [q-2^b,q+2^b] where b is the least b with η≤2^b. +func PolyUnpackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + p[j] = common.Q + Eta - uint32(buf[i]&15) + p[j+1] = common.Q + Eta - uint32(buf[i]>>4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + p[j] = common.Q + Eta - uint32(buf[i]&7) + p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7) + p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7)) + p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7) + p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7) + p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7)) + p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7) + p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Writes v with coefficients in {0, 1} of which at most ω non-zero +// to buf, which must have length ω+k. +func (v *VecK) PackHint(buf []byte) { + // The packed hint starts with the indices of the non-zero coefficients + // For instance: + // + // (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹) + // + // Yields + // + // 56, 100, 255, 2, 23, 1 + // + // Then we pad with zeroes until we have a list of ω items: + // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0 + // + // Then we finish with a list of the switch-over-indices in this + // list between polynomials, so: + // + // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6 + + off := uint8(0) + for i := 0; i < K; i++ { + for j := uint16(0); j < common.N; j++ { + if v[i][j] != 0 { + buf[off] = uint8(j) + off++ + } + } + buf[Omega+i] = off + } + for ; off < Omega; off++ { + buf[off] = 0 + } +} + +// Sets v to the vector encoded using VecK.PackHint() +// +// Returns whether unpacking was successful. +func (v *VecK) UnpackHint(buf []byte) bool { + // A priori, there would be several reasonable ways to encode the same + // hint vector. We take care to only allow only one encoding, to ensure + // "strong unforgeability". + // + // See PackHint() source for description of the encoding. + *v = VecK{} // zero v + prevSOP := uint8(0) // previous switch-over-point + for i := 0; i < K; i++ { + SOP := buf[Omega+i] + if SOP < prevSOP || SOP > Omega { + return false // ensures switch-over-points are increasing + } + for j := prevSOP; j < SOP; j++ { + if j > prevSOP && buf[j] <= buf[j-1] { + return false // ensures indices are increasing (within a poly) + } + v[i][buf[j]] = 1 + } + prevSOP = SOP + } + for j := prevSOP; j < Omega; j++ { + if buf[j] != 0 { + return false // ensures padding indices are zero + } + } + + return true +} diff --git a/src/circl/sign/dilithium/mode1aes/internal/pack_test.go b/src/circl/sign/dilithium/mode1aes/internal/pack_test.go new file mode 100644 index 00000000000..35bea5b6db3 --- /dev/null +++ b/src/circl/sign/dilithium/mode1aes/internal/pack_test.go @@ -0,0 +1,85 @@ +// Code generated from mode3/internal/pack_test.go by gen.go + +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestPolyPackLeqEta(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [PolyLeqEtaSize]byte + + for i := uint16(0); i < 100; i++ { + // Note that DeriveUniformLeqEta sets p to the right kind of + // unnormalized vector. + PolyDeriveUniformLeqEta(&p1, &seed, i) + for j := 0; j < PolyLeqEtaSize; j++ { + if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta { + t.Fatalf("DerveUniformLeqEta out of bounds") + } + } + PolyPackLeqEta(&p1, buf[:]) + PolyUnpackLeqEta(&p2, buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT1(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p1, &seed, i) + p1.Normalize() + for j := 0; j < common.N; j++ { + p1[j] &= 0x1ff + } + p1.PackT1(buf[:]) + p2.UnpackT1(buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT0(t *testing.T) { + var p, p0, p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT0Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p, &seed, i) + p.Normalize() + p.Power2Round(&p0, &p1) + + p0.PackT0(buf[:]) + p2.UnpackT0(buf[:]) + if p0 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackLeGamma1(t *testing.T) { + var p0, p1 common.Poly + var seed [48]byte + var buf [common.PolyLeGamma1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniformLeGamma1(&p0, &seed, i) + p0.Normalize() + + p0.PackLeGamma1(buf[:]) + p1.UnpackLeGamma1(buf[:]) + if p0 != p1 { + t.Fatalf("%v != %v", p0, p1) + } + } +} diff --git a/src/circl/sign/dilithium/mode1aes/internal/params.go b/src/circl/sign/dilithium/mode1aes/internal/params.go new file mode 100644 index 00000000000..d97f6b84464 --- /dev/null +++ b/src/circl/sign/dilithium/mode1aes/internal/params.go @@ -0,0 +1,17 @@ +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +const ( + Name = "Dilithium1-AES" + UseAES = true + PublicKeySize = 896 + PrivateKeySize = 2096 + SignatureSize = 1387 + K = 3 + L = 2 + Eta = 7 + DoubleEtaBits = 4 + Beta = 375 + Omega = 64 +) diff --git a/src/circl/sign/dilithium/mode1aes/internal/params_test.go b/src/circl/sign/dilithium/mode1aes/internal/params_test.go new file mode 100644 index 00000000000..cb64178d507 --- /dev/null +++ b/src/circl/sign/dilithium/mode1aes/internal/params_test.go @@ -0,0 +1,48 @@ +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Tests specific to the current mode + +func TestVectorDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + p2 := common.Poly{ + 4, 8380412, 8380414, 8380415, 1, 1, 0, 6, 8380412, 8380413, 3, + 7, 3, 8380415, 8380414, 7, 8380414, 1, 0, 8380414, 8380411, 6, + 3, 3, 8380416, 8380415, 8380411, 8380415, 1, 6, 0, 6, 0, 1, + 8380414, 4, 8380414, 6, 4, 8380413, 1, 7, 0, 8380411, 8380411, + 8380414, 8380412, 2, 8380410, 5, 1, 7, 1, 6, 8380413, 5, 8380415, + 6, 8380414, 3, 4, 8380413, 8380415, 8380412, 1, 8380411, 8380411, + 8380415, 5, 7, 8380415, 8380413, 8380416, 8380412, 8380411, + 8380416, 4, 2, 8380414, 6, 8380414, 3, 8380414, 8380412, 8380415, + 8380410, 8380412, 2, 8380415, 8380415, 6, 3, 2, 8380415, 0, 6, + 2, 8380410, 8380416, 8380415, 5, 4, 6, 8380412, 8380414, 0, 2, + 8380410, 8380416, 7, 6, 8380415, 8380413, 8380411, 8380413, 3, + 3, 8380412, 8380416, 0, 5, 5, 5, 5, 8380414, 8380413, 2, 0, 5, + 8380410, 8380416, 8380414, 8380412, 8380413, 8380416, 8380414, + 8380413, 4, 8380414, 1, 8380411, 5, 8380414, 4, 2, 5, 3, 8380412, + 2, 8380412, 8380410, 8380413, 5, 8380415, 2, 8380416, 4, 8380410, + 8380412, 8380412, 4, 2, 7, 1, 8380416, 7, 6, 2, 0, 3, 8380413, + 5, 7, 7, 1, 5, 8380412, 6, 2, 8380412, 2, 5, 2, 2, 8380412, 5, + 7, 8380414, 8380416, 8380414, 7, 5, 8380410, 1, 7, 7, 6, 1, 3, + 8380410, 7, 7, 8380413, 8380411, 3, 7, 8380413, 5, 8380416, 3, + 3, 0, 8380413, 0, 4, 8380411, 4, 8380416, 2, 8380410, 8380413, + 8380415, 8380412, 8380413, 5, 8380416, 7, 8380415, 2, 6, 2, 1, + 1, 5, 3, 8380414, 4, 8380411, 8380415, 8380415, 8380412, 2, + 8380416, 6, 4, 8380410, 8380411, 8380410, 7, 4, 2, 3, 8380414, + 8380414, 8380413, 8380410, + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeqEta(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} diff --git a/src/circl/sign/dilithium/mode1aes/internal/sample.go b/src/circl/sign/dilithium/mode1aes/internal/sample.go new file mode 100644 index 00000000000..8d01e8ef776 --- /dev/null +++ b/src/circl/sign/dilithium/mode1aes/internal/sample.go @@ -0,0 +1,563 @@ +// Code generated from mode3/internal/sample.go by gen.go + +package internal + +import ( + "circl/internal/sha3" + "circl/simd/keccakf1600" + + "circl/sign/dilithium/internal/common" + + "encoding/binary" +) + +// DeriveX4Available indicates whether the system supports the quick fourway +// sampling variants like PolyDeriveUniformX4. +var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES + +// For each i, sample ps[i] uniformly with coefficients of norm less than γ₁ +// using the the given seed and nonces[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformLeGamma1X4(ps [4]*common.Poly, seed *[48]byte, + nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE256 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE256 is 136 --- i.e. 17 uint64s. + for j := 0; j < 4; j++ { + state[6*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[16*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + // Each try requires 15 bits. 15 does not divide into 64, nor in 136, + // so we will have to carry some bits from a previous uint64 to the next. + var carry [4]uint32 + + // Shift is the amount of bits in the carry. + var shift [4]uint + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 17 uint64s of each + // of the four SHAKE256 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := 0; i < 17; i++ { + var t [4]uint32 + tCount := 3 + + // Get the next three or four 20 bit numbers. + qw := state[i*4+j] + qwl := (qw << shift[j]) | uint64(carry[j]) + t[0] = uint32(qwl & 0xfffff) + t[1] = uint32((qwl >> 20) & 0xfffff) + t[2] = uint32((qwl >> 40) & 0xfffff) + + if shift[j] == 16 { + t[3] = uint32(qw >> 44) + shift[j] = 0 + carry[j] = 0 + tCount = 4 + } else { + shift[j] += 4 + carry[j] = uint32(qw >> (64 - shift[j])) + } + + // Check if they're coefficients. + for k := 0; k < tCount; k++ { + if t[k] <= 2*common.Gamma1-2 { + ps[j][idx[j]] = common.Q + common.Gamma1 - 1 - t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + + done = false + } + } +} + +// For each i, sample ps[i] uniformly from the given seed and nonces[i]. +// ps[i] may be nil and is ignored in that case. +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 4; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE128 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s. + for j := 0; j < 4; j++ { + state[4*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[20*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each + // of the four SHAKE128 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + for i := 0; i < 7; i++ { + var t [8]uint32 + t[0] = uint32(state[i*3*4+j] & 0x7fffff) + t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff) + t[2] = uint32((state[i*3*4+j] >> 48) | + ((state[(i*3+1)*4+j] & 0x7f) << 16)) + t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff) + t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff) + t[5] = uint32((state[(i*3+1)*4+j] >> 56) | + ((state[(i*3+2)*4+j] & 0x7fff) << 8)) + t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff) + t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff) + + for k := 0; k < 8; k++ { + if t[k] < common.Q { + ps[j][idx[j]] = t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + done = false + } + } +} + +// Sample p uniformly from the given seed and nonce. +// +// p will be normalized. +func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) { + var i, length int + var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks + + if UseAES { + length = 12 * 16 + } else { + length = 168 + } + + sample := func() { + // Note that 3 divides into 168 and 12*16, so we use up buf completely. + for j := 0; j < length && i < common.N; j += 3 { + t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0x7fffff + + // We use rejection sampling + if t < common.Q { + p[i] = t + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample p uniformly with coefficients of norm less than or equal η, +// using the given seed and nonce. +// +// p will not be normalized, but will have coefficients in [q-η,q+η]. +func PolyDeriveUniformLeqEta(p *common.Poly, seed *[32]byte, nonce uint16) { + // Assumes 2 < η < 8. + var i, length int + var buf [11 * 16]byte // fits 168B SHAKE-128 rate and 11 16B AES blocks + + if UseAES { + length = 11 * 16 + } else { + length = 168 + } + + sample := func() { + // We use rejection sampling + for j := 0; j < length && i < common.N; j++ { + var t1, t2 uint32 + if Eta <= 3 { // branch is eliminated by compiler + t1 = uint32(buf[j]) & 7 + t2 = uint32(buf[j]) >> 5 + } else { + t1 = uint32(buf[j]) & 15 + t2 = uint32(buf[j]) >> 4 + } + if t1 <= 2*Eta { + p[i] = common.Q + Eta - t1 + i++ + } + if t2 <= 2*Eta && i < common.N { + p[i] = common.Q + Eta - t2 + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + + // 168 is SHAKE-128 rate + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample v[i] uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce+i +// +// v[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func VecLDeriveUniformLeGamma1(v *VecL, seed *[48]byte, nonce uint16) { + if !DeriveX4Available { + for i := 0; i < L; i++ { + PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i)) + } + return + } + + var ps [4]*common.Poly + nonces := [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3} + for i := 0; i < L && i < 4; i++ { + ps[i] = &v[i] + } + + // PolyDeriveUniformLeGamma1X4 is slower than, but not twice as slow as, + // PolyDeriveUniformLeGamma. + PolyDeriveUniformLeGamma1X4(ps, seed, nonces) + if L == 5 { + PolyDeriveUniformLeGamma1(&v[L-1], seed, nonce+4) + } else if L > 5 || L < 2 { + panic("VecLDeriveUniformLeGamma1 does not support that L") + } +} + +// Sample p uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce. +// +// p will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[48]byte, nonce uint16) { + // Assumes γ₁ is less than 2²⁰. + var length, i int + + // Fits 10 16B AES blocks, which aligns nicely as we take 5 bytes at + // a time. The SHAKE-256 rate, however, is 136. As 136 is 1 modulo 5, + // we are left with 1 byte after the first block, which we include in the + // next block. So we need 4 bytes leeway in our buffer. The total 160 + // fits easily in 160. + var buf [160]byte + + sample := func() { + // We use rejection sampling + for j := 0; j < length-4 && i < common.N; j += 5 { + t1 := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0xfffff + t2 := ((uint32(buf[j+2]) >> 4) | (uint32(buf[j+3]) << 4) | + (uint32(buf[j+4]) << 12)) + + if t1 <= 2*common.Gamma1-2 { + p[i] = common.Q + common.Gamma1 - 1 - t1 + i++ + } + if t2 <= 2*common.Gamma1-2 && i < common.N { + p[i] = common.Q + common.Gamma1 - 1 - t2 + i++ + } + } + } + if UseAES { + length = 160 + h := common.NewAesStream256(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:]) + sample() + } + } else { + length = 136 + var iv [48 + 2]byte // 48 byte seed + uint16 nonce + bufOffset := 0 // where to put the next block + + h := sha3.NewShake256() + copy(iv[:48], seed[:]) + iv[48] = uint8(nonce) + iv[49] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[bufOffset : bufOffset+136]) + sample() + + bufOffset++ + if bufOffset == 5 { + bufOffset = 0 + } + + // Move remaining bytes at the end to the start. + for j := 0; j < bufOffset; j++ { + buf[j] = buf[135+j] + } + } + } +} + +// For each i, sample ps[i] uniformly with 60 non-zero coefficients in {q-1,1} +// using the the given seed and w1[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will be normalized. +// +// Can only be called when DeriveX4Available is true. +// +// This function is currently not used (yet). +func PolyDeriveUniformB60X4(ps [4]*common.Poly, seed *[48]byte, + w1 [4]*VecK) { + // Pack the w1s + var w1Packed [4][common.PolyLe16Size * K]byte + for j := 0; j < 4; j++ { + if ps[j] != nil { + w1[j].PackLe16(w1Packed[j][:]) + } + } + + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the start of the packed w₁s + offset := 0 // offset into w1Packed[j] + for i := 6; i < 17; i++ { + for j := 0; j < 4; j++ { + state[i*4+j] = binary.LittleEndian.Uint64(w1Packed[j][offset : offset+8]) + } + offset += 8 + } + + offset -= 8 + + // Absorb the remainder of the packed w₁s. +PermuteLoop: + for { + perm.Permute() + + for i := 0; i < 17; i++ { + offset += 8 + if offset == len(w1Packed[0]) { + // SHAKE256 domain separator and padding + for j := 0; j < 4; j++ { + state[i*4+j] ^= 0x1f + state[16*4+j] ^= 0x80 << 56 + } + perm.Permute() + + break PermuteLoop + } + + for j := 0; j < 4; j++ { + state[i*4+j] ^= binary.LittleEndian.Uint64( + w1Packed[j][offset : offset+8]) + } + } + } + + var signs [4]uint64 + var idx [4]uint16 // indices into ps + + for j := 0; j < 4; j++ { + if ps[j] != nil { + signs[j] = state[j] + *ps[j] = common.Poly{} // zero ps[j] + idx[j] = common.N - 60 + } else { + idx[j] = common.N // mark as completed + } + } + + stateOffset := 1 + for { + done := true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := stateOffset; i < 17; i++ { + var bs [8]byte + binary.LittleEndian.PutUint64(bs[:], state[4*i+j]) + for k := 0; k < 8; k++ { + b := uint16(bs[k]) + + if b > idx[j] { + continue + } + + ps[j][idx[j]] = ps[j][b] + ps[j][b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1))) + signs[j] >>= 1 + + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + + done = false + } + + if done { + break + } + + perm.Permute() + stateOffset = 0 + } +} + +// Samples p uniformly with 60 non-zero coefficients in {q-1,1}. +// +// The polynomial p will be normalized. +func PolyDeriveUniformB60(p *common.Poly, seed *[48]byte, w1 *VecK) { + var w1Packed [common.PolyLe16Size * K]byte + var buf [136]byte // SHAKE-256 rate is 136 + + w1.PackLe16(w1Packed[:]) + + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Write(w1Packed[:]) + _, _ = h.Read(buf[:]) + + // Essentially we generate a sequence of 60 ones or minus ones, + // prepend 196 zeroes and shuffle the concatenation using the + // usual algorithm (Fisher--Yates.) + signs := binary.LittleEndian.Uint64(buf[:]) + bufOff := 8 // offset into buf + + *p = common.Poly{} // zero p + for i := uint16(common.N - 60); i < common.N; i++ { + var b uint16 + + // Find location of where to move the new coefficient to using + // rejection sampling. + for { + if bufOff >= 136 { + _, _ = h.Read(buf[:]) + bufOff = 0 + } + + b = uint16(buf[bufOff]) + bufOff++ + + if b <= i { + break + } + } + + p[i] = p[b] + p[b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1))) + signs >>= 1 + } +} diff --git a/src/circl/sign/dilithium/mode1aes/internal/sample_test.go b/src/circl/sign/dilithium/mode1aes/internal/sample_test.go new file mode 100644 index 00000000000..f4f0a51c1c9 --- /dev/null +++ b/src/circl/sign/dilithium/mode1aes/internal/sample_test.go @@ -0,0 +1,407 @@ +// Code generated from mode3/internal/sample_test.go by gen.go + +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestVectorDeriveUniform(t *testing.T) { + var p, p2 common.Poly + var seed [32]byte + if UseAES { + p2 = common.Poly{ + 6724291, 310295, 6949524, 4464039, 1482136, 2522903, + 7025059, 3006320, 7286364, 7516512, 3361305, 1955529, + 4765954, 1725325, 6933066, 4299100, 6625173, 4272792, + 583034, 4971409, 2259140, 7715362, 3975394, 2341624, + 5481174, 8150082, 365246, 5491939, 1083120, 7517301, + 3104783, 2475292, 184149, 6425226, 4591622, 5964030, + 4729604, 5471092, 1828227, 1082044, 2516245, 1692580, + 3274844, 5443294, 7256740, 4989638, 3191250, 7479519, + 5124211, 5603858, 1230692, 2513454, 2828034, 4254312, + 1512596, 5245430, 5517392, 2814840, 932545, 6826733, + 3511094, 4075348, 3233981, 7268882, 2913733, 4870249, + 4123492, 8124406, 4016949, 5478752, 2750895, 603525, + 5724798, 3985430, 3483012, 6434230, 3136996, 8297976, + 4107616, 7307748, 6962904, 7544473, 1193110, 3448595, + 4814773, 5607932, 8221314, 1054046, 1541208, 1866050, + 8227412, 2925778, 5293953, 2065416, 4972769, 3616283, + 7990594, 1105530, 7121836, 1170740, 7417431, 633146, + 253820, 7235019, 3539504, 6807707, 451390, 5481526, + 2859902, 1063061, 4579730, 7126652, 7033767, 4294814, + 1414604, 7620048, 1953268, 8304556, 1156814, 1182881, + 5311519, 3057534, 5277666, 682843, 2070398, 2874278, + 4859533, 6376664, 6694074, 1590242, 2620706, 8331066, + 5643845, 5037538, 2891516, 7004879, 3754327, 5031296, + 5463118, 2420870, 8116529, 5517696, 7435129, 3873963, + 710407, 713806, 175647, 4274571, 2655021, 7319503, + 3027243, 7129679, 4213435, 2429323, 4643873, 4568526, + 649664, 1720514, 6497260, 2683517, 7672754, 7105190, + 3148405, 5898369, 5667677, 8050874, 1587139, 7315260, + 4337416, 2202680, 2338714, 557467, 6752058, 2469794, + 485071, 1617604, 3590498, 2151466, 2005823, 7727956, + 7776292, 6783433, 6787146, 1732833, 3596857, 7436284, + 4483349, 4970142, 4472608, 6478342, 1236215, 5695744, + 2280717, 2889355, 3233946, 5187812, 978685, 5177364, + 2922353, 4824807, 5302883, 6739803, 8092453, 5883903, + 816553, 6041174, 8317591, 1459178, 5332455, 1835058, + 1368601, 2820950, 3479224, 2589540, 7992934, 3421045, + 4657128, 8292902, 4153567, 3553988, 7830320, 6722913, + 2555309, 4149801, 8328975, 1560545, 7757473, 3106458, + 4310856, 7135453, 3481032, 652626, 1841361, 8126828, + 6250018, 300536, 7380070, 8174419, 1418793, 6208185, + 3906256, 6679016, 1605701, 3561489, 5819724, 5746996, + 8044214, 7087187, 7102330, 4962927, 4253983, 7108567, + 4119736, 6584065, 441634, 6941656, + } + } else { + p2 = common.Poly{ + 2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052, + 3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357, + 6066350, 8126097, 1179080, 4787182, 6552182, 6713644, + 1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938, + 1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431, + 1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545, + 7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071, + 105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855, + 5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453, + 5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453, + 3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874, + 5614778, 2248550, 1756499, 8280764, 8263880, 7600081, + 5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562, + 7483939, 4938664, 6863397, 5126354, 5218129, 6236086, + 4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737, + 1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595, + 6830029, 1548850, 6593138, 6849097, 1518037, 2859442, + 7772265, 7325153, 3281191, 7856131, 4995056, 4684325, + 1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778, + 7973479, 3171829, 5624626, 3540123, 7150120, 8313283, + 3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342, + 7501562, 5826142, 2709813, 8245473, 2369045, 2782257, + 5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983, + 5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375, + 267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500, + 2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008, + 8258986, 2183134, 2302072, 4674924, 4306056, 7465311, + 6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700, + 2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533, + 255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625, + 6997719, 6260212, 6186962, 6636650, 7836834, 7998017, + 2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598, + 4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947, + 6195178, 5552390, 6804584, 6305468, 5731980, 6095195, + 3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054, + 4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780, + 3740517, 5224226, 3547288, 2083124, 4699398, 3654239, + 5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706, + 4352830, + } + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniform(&p, &seed, 30000) + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniform(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniform(&p, &seed, uint16(i)) + if !PolyNormalized(&p) { + t.Fatal() + } + } +} + +func TestDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeqEta(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-Eta || p[j] > common.Q+Eta { + t.Fatal() + } + } + } +} + +func TestDeriveUniformLeGamma1(t *testing.T) { + var p common.Poly + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-common.Gamma1 || p[j] > common.Q+common.Gamma1 { + t.Fatal() + } + } + } +} + +func TestVectorDeriveUniformLeGamma1(t *testing.T) { + var p, p2 common.Poly + var seed [48]byte + if UseAES { + p2 = common.Poly{ + 90940, 8133770, 8210940, 8218464, 8362467, 431142, 98024, + 320453, 7892373, 144162, 495313, 7910122, 308198, 8024421, + 8313699, 8323445, 8242093, 7946588, 418979, 427179, 353562, + 20972, 455962, 213062, 361787, 8141790, 8321931, 7885366, + 88645, 181202, 8094142, 8303121, 8059515, 7919812, 191865, + 7910073, 7896561, 8096830, 7899355, 8338900, 72693, 236799, + 8183042, 347570, 8153528, 8364233, 8077851, 8312277, 104682, + 8037310, 8356199, 7994081, 240369, 70229, 8108858, 8175836, + 466639, 50909, 339919, 8029663, 341659, 154398, 64345, + 97101, 212245, 8285367, 521225, 325882, 296235, 8110929, + 8015814, 7953234, 158409, 329908, 8331330, 449258, 167701, + 8197796, 8228247, 7940020, 1985, 304704, 475316, 8037482, + 8250449, 304557, 8216567, 432266, 213295, 8162216, 381001, + 7995314, 7988689, 128534, 245586, 67041, 8232744, 398441, + 223116, 443612, 149856, 222852, 158723, 54746, 171906, + 163070, 353915, 8263276, 8016812, 8229081, 31827, 489715, + 450171, 8069106, 53220, 7932381, 7955335, 8197363, 201044, + 8306733, 446376, 8211025, 7889271, 8070595, 495514, 8158685, + 7524, 7973394, 247673, 4293, 184924, 457334, 138349, 8123964, + 284179, 8255307, 8068216, 8291492, 243759, 8060601, 20962, + 8058389, 420953, 8305974, 455136, 8218139, 7121, 147703, + 7951253, 394376, 8127066, 365861, 8062390, 8138732, 366555, + 8280514, 221, 395861, 7968769, 7977119, 8098083, 343056, + 8190769, 223361, 163270, 203059, 109219, 8228600, 8127695, + 321016, 295979, 8201961, 49891, 8335504, 8190386, 8190984, + 8278654, 336364, 7878013, 7922436, 7974101, 8075534, 8200852, + 8333820, 415982, 8089662, 149553, 7946740, 474102, 7937116, + 8026845, 356056, 191053, 86928, 8218644, 8375040, 8029184, + 8025675, 8193350, 295360, 7905768, 487174, 8362961, 386108, + 282213, 8373318, 50167, 8238992, 7911505, 493459, 8335164, + 8079327, 250697, 263154, 221028, 40778, 87515, 8372585, + 504728, 7980935, 8307600, 298972, 427523, 93352, 89915, + 391490, 80320, 7975008, 336136, 7949815, 8048682, 8332244, + 8204778, 8177783, 7910684, 7925292, 518641, 59663, 53608, + 222225, 463772, 8022091, 8173722, 8291385, 472741, 8105898, + 7943299, 267137, 7957660, 371874, 409084, 203750, 477334, + 83412, 111278, 120444, + } + } else { + p2 = common.Poly{ + 338083, 7978692, 8044913, 373628, 427855, 79725, 91018, + 349821, 501552, 7955127, 8316400, 290708, 216142, 8199666, + 8040144, 109426, 8177916, 8200218, 8125680, 358131, 160961, + 497383, 25361, 156297, 8033745, 7897189, 48397, 498732, + 464556, 7862704, 8308667, 236080, 91240, 8328377, 326190, + 509979, 8313264, 8106493, 8210965, 8328036, 172602, 8108765, + 8192963, 8361660, 8026473, 7932022, 322006, 8305874, 8254440, + 7866474, 373371, 8023413, 8221878, 486124, 36080, 8324512, + 8042056, 7984472, 8048111, 7910387, 8205382, 8259636, 188609, + 8316587, 59306, 119803, 8067108, 8155455, 8153450, 7983908, + 8222256, 21521, 114297, 8069037, 151621, 8014482, 8052856, + 376107, 8004652, 175001, 8079461, 8351123, 8021484, 144547, + 7908116, 8278100, 8136941, 142399, 8026843, 8081852, 124334, + 242796, 266768, 7919478, 7954016, 28927, 8329064, 514031, + 423911, 27907, 8142788, 8078298, 273978, 382723, 8148646, + 186476, 8030712, 8067268, 356250, 145817, 60045, 122764, + 56856, 8225416, 136437, 199652, 8343127, 8109765, 7936848, + 446966, 8351681, 288663, 409663, 512988, 8350788, 8191864, + 8366223, 281267, 7921696, 8213978, 442484, 67457, 8030602, + 238514, 230458, 8301866, 8359700, 150320, 143893, 461735, + 225443, 8027502, 151113, 365244, 7911438, 82498, 405398, + 8207009, 8108255, 367485, 514660, 8294055, 8168958, 127725, + 402955, 8051625, 7859029, 7980052, 321819, 7949587, 125778, + 8287078, 131972, 499609, 256795, 8180323, 8269393, 5878, + 8145473, 8238676, 383855, 415547, 424071, 241989, 8165743, + 8207329, 149608, 8315331, 7901850, 8114275, 360650, 516061, + 255090, 8277977, 270877, 8125200, 479248, 7991711, 8028595, + 73426, 8215429, 208217, 153872, 429336, 229856, 461204, + 236682, 7930158, 8298847, 228327, 8009399, 8111520, 345025, + 386495, 93454, 8336429, 8161305, 7980811, 286795, 162808, + 224476, 7972825, 85118, 287488, 8029791, 119071, 371, 518524, + 473496, 451205, 127000, 19233, 211519, 2442, 7950959, 481888, + 8041598, 8281176, 437202, 7912610, 8080153, 8237500, 7926828, + 8009421, 204880, 62495, 8192310, 8314388, 98616, 182368, + 323894, 59901, 481049, 8139275, 7872144, 254106, 376257, + 93339, 301342, 366536, 438920, 84773, 461471, 8125755, + 7930085, 405116, + } + } + for i := 0; i < 48; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeGamma1(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniformB60(t *testing.T) { + var p common.Poly + var w1 VecK + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformB60(&p, &seed, &w1) + nonzero := 0 + for j := 0; j < common.N; j++ { + if p[j] != 0 { + if p[j] != 1 && p[j] != common.Q-1 { + t.Fatal() + } + nonzero++ + } + } + if nonzero != 60 { + t.Fatal() + } + } +} + +func TestDeriveUniformX4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [32]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, + nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniform(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatal() + } + } +} + +func TestDeriveUniformB60X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + var w1s [4]VecK + for j := 0; j < 4; j++ { + for k := 0; k < K; k++ { + for i := 0; i < common.N; i++ { + w1s[j][k][i] = uint32(j+k*4+i*4*K) & 15 + } + } + } + PolyDeriveUniformB60X4( + [4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, + [4]*VecK{&w1s[0], &w1s[1], &w1s[2], &w1s[3]}, + ) + for j := 0; j < 4; j++ { + PolyDeriveUniformB60(&p, &seed, &w1s[j]) + if ps[j] != p { + t.Fatalf("%v %v", ps[j], p) + } + } +} + +func TestDeriveUniformLeGamma1X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatalf("%d\n%v\n%v", i, p, ps[i]) + } + } +} + +func BenchmarkPolyDeriveUniformB60(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60(&p, &seed, &w1) + } +} + +func BenchmarkPolyDeriveUniformB60X4(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60X4( + [4]*common.Poly{&p, &p, &p, &p}, + &seed, + [4]*VecK{&w1, &w1, &w1, &w1}, + ) + } +} + +func BenchmarkPolyDeriveUniform(b *testing.B) { + var seed [32]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniform(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformX4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [32]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) { + var seed [48]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1X4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [48]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} diff --git a/src/circl/sign/dilithium/mode1aes/internal/vec.go b/src/circl/sign/dilithium/mode1aes/internal/vec.go new file mode 100644 index 00000000000..a20a8b0224e --- /dev/null +++ b/src/circl/sign/dilithium/mode1aes/internal/vec.go @@ -0,0 +1,281 @@ +// Code generated from mode3/internal/vec.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A vector of L polynomials. +type VecL [L]common.Poly + +// A vector of K polynomials. +type VecK [K]common.Poly + +// Normalize the polynomials in this vector. +func (v *VecL) Normalize() { + for i := 0; i < L; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecL) NormalizeAssumingLe2Q() { + for i := 0; i < L; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecL) Add(w, u *VecL) { + for i := 0; i < L; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecL) NTT() { + for i := 0; i < L; i++ { + v[i].NTT() + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecL) Exceeds(bound uint32) bool { + for i := 0; i < L; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Decompose(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecL) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeqEta(). +func (v *VecL) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sequentially packs each polynomial using Poly.PackLeGamma1(). +func (v *VecL) PackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].PackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeGamma1(). +func (v *VecL) UnpackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].UnpackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Normalize the polynomials in this vector. +func (v *VecK) Normalize() { + for i := 0; i < K; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecK) NormalizeAssumingLe2Q() { + for i := 0; i < K; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecK) Add(w, u *VecK) { + for i := 0; i < K; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecK) Exceeds(bound uint32) bool { + for i := 0; i < K; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Decompose(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sets v to the hint vector for v0 the modified low bits and v1 +// the unmodified high bits --- see makeHint(). +// +// Returns the number of ones in the hint vector. +func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) { + for i := 0; i < K; i++ { + pop += v[i].MakeHint(&v0[i], &v1[i]) + } + return +} + +// Computes corrections to the high bits of the polynomials in the vector +// w using the hints in h and sets v to the corrected high bits. Returns v. +// See useHint(). +func (v *VecK) UseHint(q, hint *VecK) *VecK { + for i := 0; i < K; i++ { + v[i].UseHint(&q[i], &hint[i]) + } + return v +} + +// Sequentially packs each polynomial using Poly.PackT1(). +func (v *VecK) PackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sets v to the vector packed into buf by PackT1(). +func (v *VecK) UnpackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sequentially packs each polynomial using Poly.PackT0(). +func (v *VecK) PackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sets v to the vector packed into buf by PackT0(). +func (v *VecK) UnpackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecK) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecK.PackLeqEta(). +func (v *VecK) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecK) NTT() { + for i := 0; i < K; i++ { + v[i].NTT() + } +} + +// Sequentially packs each polynomial using Poly.PackLe16(). +func (v *VecK) PackLe16(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackLe16(buf[offset:]) + offset += common.PolyLe16Size + } +} + +// Sets v to a - b. +// +// Warning: assumes coefficients of the polynomials of b are less than 2q. +func (v *VecK) Sub(a, b *VecK) { + for i := 0; i < K; i++ { + v[i].Sub(&a[i], &b[i]) + } +} + +// Sets v to 2ᵈ w without reducing. +func (v *VecK) MulBy2toD(w *VecK) { + for i := 0; i < K; i++ { + v[i].MulBy2toD(&w[i]) + } +} + +// Applies InvNTT componentwise. See Poly.InvNTT() for details. +func (v *VecK) InvNTT() { + for i := 0; i < K; i++ { + v[i].InvNTT() + } +} + +// Applies Poly.ReduceLe2Q() componentwise. +func (v *VecK) ReduceLe2Q() { + for i := 0; i < K; i++ { + v[i].ReduceLe2Q() + } +} diff --git a/src/circl/sign/dilithium/mode2.go b/src/circl/sign/dilithium/mode2.go new file mode 100644 index 00000000000..a2d7c895c6e --- /dev/null +++ b/src/circl/sign/dilithium/mode2.go @@ -0,0 +1,95 @@ +// Code generated from mode.templ.go. DO NOT EDIT. + +package dilithium + +import ( + "fmt" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode2" +) + +// implMode2 implements the mode.Mode interface for Dilithium2. +type implMode2 struct{} + +// Mode2 is Dilithium in mode "Dilithium2". +var Mode2 Mode = &implMode2{} + +func (m *implMode2) GenerateKey(rand io.Reader) ( + PublicKey, PrivateKey, error) { + return mode2.GenerateKey(rand) +} + +func (m *implMode2) NewKeyFromExpandedSeed(seed *[96]byte) (PublicKey, + PrivateKey) { + return mode2.NewKeyFromExpandedSeed(seed) +} + +func (m *implMode2) NewKeyFromSeed(seed []byte) (PublicKey, + PrivateKey) { + if len(seed) != common.SeedSize { + panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) + } + seedBuf := [common.SeedSize]byte{} + copy(seedBuf[:], seed) + return mode2.NewKeyFromSeed(&seedBuf) +} + +func (m *implMode2) Sign(sk PrivateKey, msg []byte) []byte { + isk := sk.(*mode2.PrivateKey) + ret := [mode2.SignatureSize]byte{} + mode2.SignTo(isk, msg, ret[:]) + return ret[:] +} + +func (m *implMode2) Verify(pk PublicKey, msg []byte, signature []byte) bool { + ipk := pk.(*mode2.PublicKey) + return mode2.Verify(ipk, msg, signature) +} + +func (m *implMode2) PublicKeyFromBytes(data []byte) PublicKey { + var ret mode2.PublicKey + if len(data) != mode2.PublicKeySize { + panic("packed public key must be of mode2.PublicKeySize bytes") + } + var buf [mode2.PublicKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode2) PrivateKeyFromBytes(data []byte) PrivateKey { + var ret mode2.PrivateKey + if len(data) != mode2.PrivateKeySize { + panic("packed public key must be of mode2.PrivateKeySize bytes") + } + var buf [mode2.PrivateKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode2) SeedSize() int { + return common.SeedSize +} + +func (m *implMode2) PublicKeySize() int { + return mode2.PublicKeySize +} + +func (m *implMode2) PrivateKeySize() int { + return mode2.PrivateKeySize +} + +func (m *implMode2) SignatureSize() int { + return mode2.SignatureSize +} + +func (m *implMode2) Name() string { + return "Dilithium2" +} + +func init() { + modes["Dilithium2"] = Mode2 +} diff --git a/src/circl/sign/dilithium/mode2/dilithium.go b/src/circl/sign/dilithium/mode2/dilithium.go new file mode 100644 index 00000000000..d1fa999ab6a --- /dev/null +++ b/src/circl/sign/dilithium/mode2/dilithium.go @@ -0,0 +1,191 @@ +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// mode2 implements the CRYSTALS-Dilithium signature scheme Dilithium2 +// as submitted to round2 of the NIST PQC competition and described in +// +// https://pq-crystals.org/dilithium/data/dilithium-specification-round2.pdf +package mode2 + +import ( + "crypto" + "errors" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode2/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + SeedSize = common.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a signature + SignatureSize = internal.SignatureSize +) + +// PublicKey is the type of Dilithium2 public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of Dilithium2 private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + pk, sk, err := internal.GenerateKey(rand) + return (*PublicKey)(pk), (*PrivateKey)(sk), err +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromExpandedSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// SignTo signs the given message and writes the signature into signature. +// It will panic if signature is not of length at least SignatureSize. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + internal.SignTo( + (*internal.PrivateKey)(sk), + msg, + signature, + ) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + return internal.Verify( + (*internal.PublicKey)(pk), + msg, + signature, + ) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Packs the public key. +func (pk *PublicKey) Bytes() []byte { + var buf [PublicKeySize]byte + pk.Pack(&buf) + return buf[:] +} + +// Packs the private key. +func (sk *PrivateKey) Bytes() []byte { + var buf [PrivateKeySize]byte + sk.Pack(&buf) + return buf[:] +} + +// Packs the public key. +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + return pk.Bytes(), nil +} + +// Packs the private key. +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + return sk.Bytes(), nil +} + +// Unpacks the public key from data. +func (pk *PublicKey) UnmarshalBinary(data []byte) error { + if len(data) != PublicKeySize { + return errors.New("packed public key must be of mode2.PublicKeySize bytes") + } + var buf [PublicKeySize]byte + copy(buf[:], data) + pk.Unpack(&buf) + return nil +} + +// Unpacks the private key from data. +func (sk *PrivateKey) UnmarshalBinary(data []byte) error { + if len(data) != PrivateKeySize { + return errors.New("packed private key must be of mode2.PrivateKeySize bytes") + } + var buf [PrivateKeySize]byte + copy(buf[:], data) + sk.Unpack(&buf) + return nil +} + +// Sign signs the given message. +// +// opts.HashFunc() must return zero, which can be achieved by passing +// crypto.Hash(0) for opts. rand is ignored. Will only return an error +// if opts.HashFunc() is non-zero. +// +// This function is used to make PrivateKey implement the crypto.Signer +// interface. The package-level SignTo function might be more convenient +// to use. +func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( + signature []byte, err error) { + var sig [SignatureSize]byte + + if opts.HashFunc() != crypto.Hash(0) { + return nil, errors.New("dilithium: cannot sign hashed message") + } + + SignTo(sk, msg, sig[:]) + return sig[:], nil +} + +// Computes the public key corresponding to this private key. +// +// Returns a *PublicKey. The type crypto.PublicKey is used to make +// PrivateKey implement the crypto.Signer interface. +func (sk *PrivateKey) Public() crypto.PublicKey { + return (*PublicKey)((*internal.PrivateKey)(sk).Public()) +} + +// Equal returns whether the two private keys equal. +func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { + castOther, ok := other.(*PrivateKey) + if !ok { + return false + } + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) +} + +// Equal returns whether the two public keys equal. +func (pk *PublicKey) Equal(other crypto.PublicKey) bool { + castOther, ok := other.(*PublicKey) + if !ok { + return false + } + return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) +} diff --git a/src/circl/sign/dilithium/mode2/internal/dilithium.go b/src/circl/sign/dilithium/mode2/internal/dilithium.go new file mode 100644 index 00000000000..fb0eaaf1963 --- /dev/null +++ b/src/circl/sign/dilithium/mode2/internal/dilithium.go @@ -0,0 +1,446 @@ +// Code generated from mode3/internal/dilithium.go by gen.go + +package internal + +import ( + cryptoRand "crypto/rand" + "crypto/subtle" + "io" + + "circl/internal/sha3" + "circl/sign/dilithium/internal/common" +) + +const ( + // Size of a packed polynomial of norm ≤η. + // (Note that the formula is not valid in general.) + PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8 +) + +// PublicKey is the type of Dilithium public keys. +type PublicKey struct { + rho [32]byte + t1 VecK + + // Cached values + t1p [common.PolyT1Size * K]byte + A *Mat + tr *[48]byte +} + +// PrivateKey is the type of Dilithium private keys. +type PrivateKey struct { + rho [32]byte + key [32]byte + s1 VecL + s2 VecK + t0 VecK + tr [48]byte + + // Cached values + A Mat // ExpandA(ρ) + s1h VecL // NTT(s₁) + s2h VecK // NTT(s₂) + t0h VecK // NTT(t₀) +} + +type unpackedSignature struct { + z VecL + hint VecK + c common.Poly +} + +// Packs the signature into buf. +func (sig *unpackedSignature) Pack(buf []byte) { + sig.z.PackLeGamma1(buf[:]) + sig.hint.PackHint(buf[L*common.PolyLeGamma1Size:]) + sig.c.PackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) +} + +// Sets sig to the signature encoded in the buffer. +// +// Returns whether buf contains a properly packed signature. +func (sig *unpackedSignature) Unpack(buf []byte) bool { + if len(buf) < SignatureSize { + return false + } + sig.z.UnpackLeGamma1(buf[:]) + if sig.z.Exceeds(common.Gamma1 - Beta) { + return false + } + if !sig.hint.UnpackHint(buf[L*common.PolyLeGamma1Size:]) { + return false + } + sig.c.UnpackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) + return true +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + copy(buf[:32], pk.rho[:]) + copy(buf[32:], pk.t1p[:]) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + copy(pk.rho[:], buf[:32]) + copy(pk.t1p[:], buf[32:]) + + pk.t1.UnpackT1(pk.t1p[:]) + pk.A = new(Mat) + pk.A.Derive(&pk.rho) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + pk.tr = new([48]byte) + h := sha3.NewShake256() + _, _ = h.Write(buf[:]) + _, _ = h.Read(pk.tr[:]) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + copy(buf[:32], sk.rho[:]) + copy(buf[32:64], sk.key[:]) + copy(buf[64:112], sk.tr[:]) + offset := 112 + sk.s1.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.PackT0(buf[offset:]) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + copy(sk.rho[:], buf[:32]) + copy(sk.key[:], buf[32:64]) + copy(sk.tr[:], buf[64:112]) + offset := 112 + sk.s1.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.UnpackT0(buf[offset:]) + + // Cached values + sk.A.Derive(&sk.rho) + sk.t0h = sk.t0 + sk.t0h.NTT() + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() +} + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [32]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(&seed) + return pk, sk, nil +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + var pk PublicKey + var sk PrivateKey + var sSeed [32]byte + + copy(pk.rho[:], seed[:32]) + copy(sSeed[:], seed[32:64]) + copy(sk.key[:], seed[64:]) + copy(sk.rho[:], pk.rho[:]) + + sk.A.Derive(&pk.rho) + + for i := uint16(0); i < L; i++ { + PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i) + } + + for i := uint16(0); i < K; i++ { + PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L) + } + + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() + + sk.computeT0andT1(&sk.t0, &pk.t1) + + sk.t0h = sk.t0 + sk.t0h.NTT() + + // Complete public key far enough to be packed + pk.t1.PackT1(pk.t1p[:]) + pk.A = &sk.A + + // Finish private key + var packedPk [PublicKeySize]byte + pk.Pack(&packedPk) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + h := sha3.NewShake256() + _, _ = h.Write(packedPk[:]) + _, _ = h.Read(sk.tr[:]) + + // Finish cache of public key + pk.tr = &sk.tr + + return &pk, &sk +} + +// Computes t0 and t1 from sk.s1h, sk.s2 and sk.A. +func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) { + var t VecK + + // Set t to A s₁ + s₂ + for i := 0; i < K; i++ { + PolyDotHat(&t[i], &sk.A[i], &sk.s1h) + t[i].ReduceLe2Q() + t[i].InvNTT() + } + t.Add(&t, &sk.s2) + t.Normalize() + + // Compute t₀, t₁ = Power2Round(t) + t.Power2Round(t0, t1) +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) { + var buf [96]byte + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Read(buf[:]) + return NewKeyFromExpandedSeed(&buf) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + var sig unpackedSignature + var mu [48]byte + var zh VecL + var Az, Az2dct1, w1 VecK + var ch, cp common.Poly + + // Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β + // and ensured that there at most ω ones in pk.hint. + if !sig.Unpack(signature) { + return false + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(pk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // Compute Az + zh = sig.z + zh.NTT() + + for i := 0; i < K; i++ { + PolyDotHat(&Az[i], &pk.A[i], &zh) + } + + // Next, we compute Az - 2ᵈ·c·t₁. + // Note that the coefficients of t₁ are bounded by 256 = 2⁹, + // so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q, + // which is small enough for NTT(). + Az2dct1.MulBy2toD(&pk.t1) + Az2dct1.NTT() + ch = sig.c + ch.NTT() + for i := 0; i < K; i++ { + Az2dct1[i].MulHat(&Az2dct1[i], &ch) + } + Az2dct1.Sub(&Az, &Az2dct1) + Az2dct1.ReduceLe2Q() + Az2dct1.InvNTT() + Az2dct1.NormalizeAssumingLe2Q() + + // UseHint(pk.hint, Az - 2ᵈ·c·t₁) + // = UseHint(pk.hint, w - c·s₂ + c·t₀) + // = UseHint(pk.hint, r + c·t₀) + // = r₁ = w₁. + w1.UseHint(&Az2dct1, &sig.hint) + + // c' = H(μ, w₁) + PolyDeriveUniformB60(&cp, &mu, &w1) + return sig.c == cp +} + +// SignTo signs the given message and writes the signature into signature. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + var mu, rhop [48]byte + var y, yh VecL + var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK + var ch common.Poly + var yNonce uint16 + var sig unpackedSignature + + if len(signature) < SignatureSize { + panic("Signature does not fit in that byteslice") + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(sk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // ρ' = CRH(μ ‖ key) + h.Reset() + _, _ = h.Write(sk.key[:]) + _, _ = h.Write(mu[:]) + _, _ = h.Read(rhop[:]) + + // Main rejection loop + attempt := 0 + for { + attempt++ + if attempt >= 576 { + // Depending on the mode, one try has a chance between 1/7 and 1/4 + // of succeeding. Thus it is safe to say that 576 iterations + // are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸. + panic("This should only happen 1 in 2^{128}: something is wrong.") + } + + // y = ExpandMask(ρ', key) + VecLDeriveUniformLeGamma1(&y, &rhop, yNonce) + yNonce += uint16(L) + + // Set w to A y + yh = y + yh.NTT() + for i := 0; i < K; i++ { + PolyDotHat(&w[i], &sk.A[i], &yh) + w[i].ReduceLe2Q() + w[i].InvNTT() + } + + // Decompose w into w₀ and w₁ + w.NormalizeAssumingLe2Q() + w.Decompose(&w0, &w1) + + // c = H(μ, w₁) + PolyDeriveUniformB60(&sig.c, &mu, &w1) + ch = sig.c + ch.NTT() + + // Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β. + // + // By Lemma 3 of the specification this is equivalent to checking that + // both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition + // w - c·s₂ = r₁ α + r₀ as computed by decompose(). + // See also §4.1 of the specification. + for i := 0; i < K; i++ { + w0mcs2[i].MulHat(&ch, &sk.s2h[i]) + w0mcs2[i].InvNTT() + } + w0mcs2.Sub(&w0, &w0mcs2) + w0mcs2.Normalize() + + if w0mcs2.Exceeds(common.Gamma2 - Beta) { + continue + } + + // z = y + c·s₁ + for i := 0; i < L; i++ { + sig.z[i].MulHat(&ch, &sk.s1h[i]) + sig.z[i].InvNTT() + } + sig.z.Add(&sig.z, &y) + sig.z.Normalize() + + // Ensure ‖z‖_∞ < γ₁ - β + if sig.z.Exceeds(common.Gamma1 - Beta) { + continue + } + + // Compute c·t₀ + for i := 0; i < K; i++ { + ct0[i].MulHat(&ch, &sk.t0h[i]) + ct0[i].InvNTT() + } + ct0.NormalizeAssumingLe2Q() + + // Ensure ‖c·t₀‖_∞ < γ₂. + if ct0.Exceeds(common.Gamma2) { + continue + } + + // Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0. + // Note that we're not using makeHint() in the obvious way as we + // do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂. Instead we note + // that our makeHint() is actually the same as a makeHint for a + // different decomposition: + // + // Earlier we ensured indirectly with a check that r₁ = w₁ where + // r = w - c·s₂. Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂. + // Thus MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁) + // and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁). + // As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct. + w0mcs2pct0.Add(&w0mcs2, &ct0) + w0mcs2pct0.NormalizeAssumingLe2Q() + hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1) + if hintPop > Omega { + continue + } + + break + } + + sig.Pack(signature[:]) +} + +// Computes the public key corresponding to this private key. +func (sk *PrivateKey) Public() *PublicKey { + var t0 VecK + pk := &PublicKey{ + rho: sk.rho, + A: &sk.A, + tr: &sk.tr, + } + sk.computeT0andT1(&t0, &pk.t1) + pk.t1.PackT1(pk.t1p[:]) + return pk +} + +// Equal returns whether the two public keys are equal +func (pk *PublicKey) Equal(other *PublicKey) bool { + return pk.rho == other.rho && pk.t1 == other.t1 +} + +// Equal returns whether the two private keys are equal +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) & + subtle.ConstantTimeCompare(sk.key[:], other.key[:]) & + subtle.ConstantTimeCompare(sk.tr[:], other.tr[:])) + + acc := uint32(0) + for i := 0; i < L; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s1[i][j] ^ other.s1[i][j] + } + } + for i := 0; i < K; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s2[i][j] ^ other.s2[i][j] + acc |= sk.t0[i][j] ^ other.t0[i][j] + } + } + return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1 +} diff --git a/src/circl/sign/dilithium/mode2/internal/dilithium_test.go b/src/circl/sign/dilithium/mode2/internal/dilithium_test.go new file mode 100644 index 00000000000..42ce6dbe5d1 --- /dev/null +++ b/src/circl/sign/dilithium/mode2/internal/dilithium_test.go @@ -0,0 +1,131 @@ +// Code generated from mode3/internal/dilithium_test.go by gen.go + +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Checks whether p is normalized. Only used in tests. +func PolyNormalized(p *common.Poly) bool { + p2 := *p + p2.Normalize() + return p2 == *p +} + +func BenchmarkSkUnpack(b *testing.B) { + var buf [PrivateKeySize]byte + var sk PrivateKey + for i := 0; i < b.N; i++ { + sk.Unpack(&buf) + } +} + +func BenchmarkPkUnpack(b *testing.B) { + var buf [PublicKeySize]byte + var pk PublicKey + for i := 0; i < b.N; i++ { + pk.Unpack(&buf) + } +} + +func BenchmarkVerify(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of verification (as in the reference + // implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + pk, sk := NewKeyFromSeed(&seed) + SignTo(sk, msg[:], sig[:]) + b.ResetTimer() + for i := 0; i < b.N; i++ { + // We should generate a new signature for every verify attempt, + // as this influences the time a little bit. This difference, however, + // is small and generating a new signature in between creates a lot + // pressure on the allocator which makes an accurate measurement hard. + Verify(pk, msg[:], sig[:]) + } +} + +func BenchmarkSign(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of signing (as in the reference implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + _, sk := NewKeyFromSeed(&seed) + b.ResetTimer() + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(msg[:], uint64(i)) + SignTo(sk, msg[:], sig[:]) + } +} + +func BenchmarkGenerateKey(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + NewKeyFromSeed(&seed) + } +} + +func BenchmarkPublicFromPrivate(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + b.StopTimer() + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + _, sk := NewKeyFromSeed(&seed) + b.StartTimer() + sk.Public() + } +} + +func TestSignThenVerifyAndPkSkPacking(t *testing.T) { + var seed [common.SeedSize]byte + var sig [SignatureSize]byte + var msg [8]byte + var pkb [PublicKeySize]byte + var skb [PrivateKeySize]byte + var pk2 PublicKey + var sk2 PrivateKey + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + if !sk.Equal(sk) { + t.Fatal() + } + for j := uint64(0); j < 10; j++ { + binary.LittleEndian.PutUint64(msg[:], j) + SignTo(sk, msg[:], sig[:]) + if !Verify(pk, msg[:], sig[:]) { + t.Fatal() + } + } + pk.Pack(&pkb) + pk2.Unpack(&pkb) + if !pk.Equal(&pk2) { + t.Fatal() + } + sk.Pack(&skb) + sk2.Unpack(&skb) + if !sk.Equal(&sk2) { + t.Fatal() + } + } +} + +func TestPublicFromPrivate(t *testing.T) { + var seed [common.SeedSize]byte + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + pk2 := sk.Public() + if !pk.Equal(pk2) { + t.Fatal() + } + } +} diff --git a/src/circl/sign/dilithium/mode2/internal/mat.go b/src/circl/sign/dilithium/mode2/internal/mat.go new file mode 100644 index 00000000000..a2411b0566d --- /dev/null +++ b/src/circl/sign/dilithium/mode2/internal/mat.go @@ -0,0 +1,59 @@ +// Code generated from mode3/internal/mat.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A k by l matrix of polynomials. +type Mat [K]VecL + +// Expands the given seed to a complete matrix. +// +// This function is called ExpandA in the specification. +func (m *Mat) Derive(seed *[32]byte) { + if !DeriveX4Available { + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + PolyDeriveUniform(&m[i][j], seed, (i<<8)+j) + } + } + return + } + + idx := 0 + var nonces [4]uint16 + var ps [4]*common.Poly + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + nonces[idx] = (i << 8) + j + ps[idx] = &m[i][j] + idx++ + if idx == 4 { + idx = 0 + PolyDeriveUniformX4(ps, seed, nonces) + } + } + } + if idx != 0 { + for i := idx; i < 4; i++ { + ps[i] = nil + } + PolyDeriveUniformX4(ps, seed, nonces) + } +} + +// Set p to the inner product of a and b using pointwise multiplication. +// +// Assumes a and b are in Montgomery form and their coefficients are +// pairwise sufficiently small to multiply, see Poly.MulHat(). Resulting +// coefficients are bounded by 2Lq. +func PolyDotHat(p *common.Poly, a, b *VecL) { + var t common.Poly + *p = common.Poly{} // zero p + for i := 0; i < L; i++ { + t.MulHat(&a[i], &b[i]) + p.Add(&t, p) + } +} diff --git a/src/circl/sign/dilithium/mode2/internal/pack.go b/src/circl/sign/dilithium/mode2/internal/pack.go new file mode 100644 index 00000000000..ecf3971cd20 --- /dev/null +++ b/src/circl/sign/dilithium/mode2/internal/pack.go @@ -0,0 +1,141 @@ +// Code generated from mode3/internal/pack.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// Writes p with norm less than or equal η into buf, which must be of +// size PolyLeqEtaSize. +// +// Assumes coefficients of p are not normalized, but in [q-η,q+η]. +func PolyPackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + buf[i] = (byte(common.Q+Eta-p[j]) | + byte(common.Q+Eta-p[j+1])<<4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + buf[i] = (byte(common.Q+Eta-p[j]) | + (byte(common.Q+Eta-p[j+1]) << 3) | + (byte(common.Q+Eta-p[j+2]) << 6)) + buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) | + (byte(common.Q+Eta-p[j+3]) << 1) | + (byte(common.Q+Eta-p[j+4]) << 4) | + (byte(common.Q+Eta-p[j+5]) << 7)) + buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) | + (byte(common.Q+Eta-p[j+6]) << 2) | + (byte(common.Q+Eta-p[j+7]) << 5)) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Sets p to the polynomial of norm less than or equal η encoded in the +// given buffer of size PolyLeqEtaSize. +// +// Output coefficients of p are not normalized, but in [q-η,q+η] provided +// buf was created using PackLeqEta. +// +// Beware, for arbitrary buf the coefficients of p might en up in +// the interval [q-2^b,q+2^b] where b is the least b with η≤2^b. +func PolyUnpackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + p[j] = common.Q + Eta - uint32(buf[i]&15) + p[j+1] = common.Q + Eta - uint32(buf[i]>>4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + p[j] = common.Q + Eta - uint32(buf[i]&7) + p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7) + p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7)) + p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7) + p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7) + p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7)) + p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7) + p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Writes v with coefficients in {0, 1} of which at most ω non-zero +// to buf, which must have length ω+k. +func (v *VecK) PackHint(buf []byte) { + // The packed hint starts with the indices of the non-zero coefficients + // For instance: + // + // (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹) + // + // Yields + // + // 56, 100, 255, 2, 23, 1 + // + // Then we pad with zeroes until we have a list of ω items: + // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0 + // + // Then we finish with a list of the switch-over-indices in this + // list between polynomials, so: + // + // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6 + + off := uint8(0) + for i := 0; i < K; i++ { + for j := uint16(0); j < common.N; j++ { + if v[i][j] != 0 { + buf[off] = uint8(j) + off++ + } + } + buf[Omega+i] = off + } + for ; off < Omega; off++ { + buf[off] = 0 + } +} + +// Sets v to the vector encoded using VecK.PackHint() +// +// Returns whether unpacking was successful. +func (v *VecK) UnpackHint(buf []byte) bool { + // A priori, there would be several reasonable ways to encode the same + // hint vector. We take care to only allow only one encoding, to ensure + // "strong unforgeability". + // + // See PackHint() source for description of the encoding. + *v = VecK{} // zero v + prevSOP := uint8(0) // previous switch-over-point + for i := 0; i < K; i++ { + SOP := buf[Omega+i] + if SOP < prevSOP || SOP > Omega { + return false // ensures switch-over-points are increasing + } + for j := prevSOP; j < SOP; j++ { + if j > prevSOP && buf[j] <= buf[j-1] { + return false // ensures indices are increasing (within a poly) + } + v[i][buf[j]] = 1 + } + prevSOP = SOP + } + for j := prevSOP; j < Omega; j++ { + if buf[j] != 0 { + return false // ensures padding indices are zero + } + } + + return true +} diff --git a/src/circl/sign/dilithium/mode2/internal/pack_test.go b/src/circl/sign/dilithium/mode2/internal/pack_test.go new file mode 100644 index 00000000000..35bea5b6db3 --- /dev/null +++ b/src/circl/sign/dilithium/mode2/internal/pack_test.go @@ -0,0 +1,85 @@ +// Code generated from mode3/internal/pack_test.go by gen.go + +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestPolyPackLeqEta(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [PolyLeqEtaSize]byte + + for i := uint16(0); i < 100; i++ { + // Note that DeriveUniformLeqEta sets p to the right kind of + // unnormalized vector. + PolyDeriveUniformLeqEta(&p1, &seed, i) + for j := 0; j < PolyLeqEtaSize; j++ { + if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta { + t.Fatalf("DerveUniformLeqEta out of bounds") + } + } + PolyPackLeqEta(&p1, buf[:]) + PolyUnpackLeqEta(&p2, buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT1(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p1, &seed, i) + p1.Normalize() + for j := 0; j < common.N; j++ { + p1[j] &= 0x1ff + } + p1.PackT1(buf[:]) + p2.UnpackT1(buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT0(t *testing.T) { + var p, p0, p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT0Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p, &seed, i) + p.Normalize() + p.Power2Round(&p0, &p1) + + p0.PackT0(buf[:]) + p2.UnpackT0(buf[:]) + if p0 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackLeGamma1(t *testing.T) { + var p0, p1 common.Poly + var seed [48]byte + var buf [common.PolyLeGamma1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniformLeGamma1(&p0, &seed, i) + p0.Normalize() + + p0.PackLeGamma1(buf[:]) + p1.UnpackLeGamma1(buf[:]) + if p0 != p1 { + t.Fatalf("%v != %v", p0, p1) + } + } +} diff --git a/src/circl/sign/dilithium/mode2/internal/params.go b/src/circl/sign/dilithium/mode2/internal/params.go new file mode 100644 index 00000000000..9ae9df1f832 --- /dev/null +++ b/src/circl/sign/dilithium/mode2/internal/params.go @@ -0,0 +1,17 @@ +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +const ( + Name = "Dilithium2" + UseAES = false + PublicKeySize = 1184 + PrivateKeySize = 2800 + SignatureSize = 2044 + K = 4 + L = 3 + Eta = 6 + DoubleEtaBits = 4 + Beta = 325 + Omega = 80 +) diff --git a/src/circl/sign/dilithium/mode2/internal/params_test.go b/src/circl/sign/dilithium/mode2/internal/params_test.go new file mode 100644 index 00000000000..5021f8c9f1e --- /dev/null +++ b/src/circl/sign/dilithium/mode2/internal/params_test.go @@ -0,0 +1,51 @@ +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Tests specific to the current mode + +func TestVectorDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + p2 := common.Poly{ + 2, 8380416, 1, 2, 8380411, 8380413, 1, 1, 8380414, 8380415, + 8380415, 0, 6, 3, 6, 1, 8380413, 8380411, 8380416, 2, + 8380412, 3, 8380413, 8380412, 8380411, 6, 2, 8380411, 2, + 8380413, 6, 8380414, 0, 8380415, 6, 8380413, 1, 3, 6, + 8380415, 3, 4, 4, 1, 0, 6, 2, 3, 8380415, 8380414, 1, 1, + 6, 4, 8380416, 8380415, 6, 8380411, 4, 4, 3, 0, 3, 1, + 8380413, 8380415, 2, 3, 8380413, 8380413, 6, 8380414, + 8380411, 5, 8380414, 8380412, 8380416, 8380415, 8380411, + 5, 8380414, 8380412, 6, 8380414, 2, 0, 8380416, 8380413, + 3, 8380411, 4, 5, 8380416, 0, 8380412, 5, 8380416, 8380414, + 2, 1, 2, 5, 8380416, 8380416, 5, 8380413, 8380416, 5, + 8380411, 8380411, 4, 6, 1, 8380412, 8380416, 8380416, 3, + 8380416, 4, 8380415, 0, 4, 6, 6, 1, 8380416, 8380411, 5, + 4, 3, 8380416, 8380416, 6, 8380413, 8380415, 3, 8380416, + 8380412, 8380413, 2, 8380412, 8380413, 8380414, 6, 8380413, + 4, 5, 5, 8380414, 3, 8380416, 8380416, 8380415, 8380414, + 8380414, 8380414, 3, 8380414, 8380411, 5, 0, 3, 0, 1, + 8380416, 8380415, 3, 8380413, 8380415, 5, 4, 0, 2, 8380413, + 3, 8380413, 8380413, 2, 1, 1, 8380412, 1, 8380411, 8380416, + 8380415, 8380414, 8380413, 8380416, 2, 8380412, 2, 6, + 8380413, 8380411, 0, 3, 1, 8380414, 1, 3, 8380412, 3, 3, + 8380416, 2, 4, 8380412, 8380413, 8380414, 3, 0, 6, 8380412, + 8380415, 8380416, 5, 5, 0, 6, 8380415, 8380413, 8380414, + 5, 6, 3, 6, 3, 5, 5, 8380415, 6, 4, 8380416, 3, 2, 6, + 8380414, 2, 8380415, 6, 8380412, 8380413, 8380415, 1, 2, + 0, 8380411, 6, 8380413, 6, 8380414, 8380416, 8380415, + 8380414, 1, 8380412, + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeqEta(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} diff --git a/src/circl/sign/dilithium/mode2/internal/sample.go b/src/circl/sign/dilithium/mode2/internal/sample.go new file mode 100644 index 00000000000..8d01e8ef776 --- /dev/null +++ b/src/circl/sign/dilithium/mode2/internal/sample.go @@ -0,0 +1,563 @@ +// Code generated from mode3/internal/sample.go by gen.go + +package internal + +import ( + "circl/internal/sha3" + "circl/simd/keccakf1600" + + "circl/sign/dilithium/internal/common" + + "encoding/binary" +) + +// DeriveX4Available indicates whether the system supports the quick fourway +// sampling variants like PolyDeriveUniformX4. +var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES + +// For each i, sample ps[i] uniformly with coefficients of norm less than γ₁ +// using the the given seed and nonces[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformLeGamma1X4(ps [4]*common.Poly, seed *[48]byte, + nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE256 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE256 is 136 --- i.e. 17 uint64s. + for j := 0; j < 4; j++ { + state[6*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[16*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + // Each try requires 15 bits. 15 does not divide into 64, nor in 136, + // so we will have to carry some bits from a previous uint64 to the next. + var carry [4]uint32 + + // Shift is the amount of bits in the carry. + var shift [4]uint + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 17 uint64s of each + // of the four SHAKE256 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := 0; i < 17; i++ { + var t [4]uint32 + tCount := 3 + + // Get the next three or four 20 bit numbers. + qw := state[i*4+j] + qwl := (qw << shift[j]) | uint64(carry[j]) + t[0] = uint32(qwl & 0xfffff) + t[1] = uint32((qwl >> 20) & 0xfffff) + t[2] = uint32((qwl >> 40) & 0xfffff) + + if shift[j] == 16 { + t[3] = uint32(qw >> 44) + shift[j] = 0 + carry[j] = 0 + tCount = 4 + } else { + shift[j] += 4 + carry[j] = uint32(qw >> (64 - shift[j])) + } + + // Check if they're coefficients. + for k := 0; k < tCount; k++ { + if t[k] <= 2*common.Gamma1-2 { + ps[j][idx[j]] = common.Q + common.Gamma1 - 1 - t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + + done = false + } + } +} + +// For each i, sample ps[i] uniformly from the given seed and nonces[i]. +// ps[i] may be nil and is ignored in that case. +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 4; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE128 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s. + for j := 0; j < 4; j++ { + state[4*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[20*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each + // of the four SHAKE128 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + for i := 0; i < 7; i++ { + var t [8]uint32 + t[0] = uint32(state[i*3*4+j] & 0x7fffff) + t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff) + t[2] = uint32((state[i*3*4+j] >> 48) | + ((state[(i*3+1)*4+j] & 0x7f) << 16)) + t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff) + t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff) + t[5] = uint32((state[(i*3+1)*4+j] >> 56) | + ((state[(i*3+2)*4+j] & 0x7fff) << 8)) + t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff) + t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff) + + for k := 0; k < 8; k++ { + if t[k] < common.Q { + ps[j][idx[j]] = t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + done = false + } + } +} + +// Sample p uniformly from the given seed and nonce. +// +// p will be normalized. +func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) { + var i, length int + var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks + + if UseAES { + length = 12 * 16 + } else { + length = 168 + } + + sample := func() { + // Note that 3 divides into 168 and 12*16, so we use up buf completely. + for j := 0; j < length && i < common.N; j += 3 { + t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0x7fffff + + // We use rejection sampling + if t < common.Q { + p[i] = t + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample p uniformly with coefficients of norm less than or equal η, +// using the given seed and nonce. +// +// p will not be normalized, but will have coefficients in [q-η,q+η]. +func PolyDeriveUniformLeqEta(p *common.Poly, seed *[32]byte, nonce uint16) { + // Assumes 2 < η < 8. + var i, length int + var buf [11 * 16]byte // fits 168B SHAKE-128 rate and 11 16B AES blocks + + if UseAES { + length = 11 * 16 + } else { + length = 168 + } + + sample := func() { + // We use rejection sampling + for j := 0; j < length && i < common.N; j++ { + var t1, t2 uint32 + if Eta <= 3 { // branch is eliminated by compiler + t1 = uint32(buf[j]) & 7 + t2 = uint32(buf[j]) >> 5 + } else { + t1 = uint32(buf[j]) & 15 + t2 = uint32(buf[j]) >> 4 + } + if t1 <= 2*Eta { + p[i] = common.Q + Eta - t1 + i++ + } + if t2 <= 2*Eta && i < common.N { + p[i] = common.Q + Eta - t2 + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + + // 168 is SHAKE-128 rate + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample v[i] uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce+i +// +// v[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func VecLDeriveUniformLeGamma1(v *VecL, seed *[48]byte, nonce uint16) { + if !DeriveX4Available { + for i := 0; i < L; i++ { + PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i)) + } + return + } + + var ps [4]*common.Poly + nonces := [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3} + for i := 0; i < L && i < 4; i++ { + ps[i] = &v[i] + } + + // PolyDeriveUniformLeGamma1X4 is slower than, but not twice as slow as, + // PolyDeriveUniformLeGamma. + PolyDeriveUniformLeGamma1X4(ps, seed, nonces) + if L == 5 { + PolyDeriveUniformLeGamma1(&v[L-1], seed, nonce+4) + } else if L > 5 || L < 2 { + panic("VecLDeriveUniformLeGamma1 does not support that L") + } +} + +// Sample p uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce. +// +// p will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[48]byte, nonce uint16) { + // Assumes γ₁ is less than 2²⁰. + var length, i int + + // Fits 10 16B AES blocks, which aligns nicely as we take 5 bytes at + // a time. The SHAKE-256 rate, however, is 136. As 136 is 1 modulo 5, + // we are left with 1 byte after the first block, which we include in the + // next block. So we need 4 bytes leeway in our buffer. The total 160 + // fits easily in 160. + var buf [160]byte + + sample := func() { + // We use rejection sampling + for j := 0; j < length-4 && i < common.N; j += 5 { + t1 := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0xfffff + t2 := ((uint32(buf[j+2]) >> 4) | (uint32(buf[j+3]) << 4) | + (uint32(buf[j+4]) << 12)) + + if t1 <= 2*common.Gamma1-2 { + p[i] = common.Q + common.Gamma1 - 1 - t1 + i++ + } + if t2 <= 2*common.Gamma1-2 && i < common.N { + p[i] = common.Q + common.Gamma1 - 1 - t2 + i++ + } + } + } + if UseAES { + length = 160 + h := common.NewAesStream256(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:]) + sample() + } + } else { + length = 136 + var iv [48 + 2]byte // 48 byte seed + uint16 nonce + bufOffset := 0 // where to put the next block + + h := sha3.NewShake256() + copy(iv[:48], seed[:]) + iv[48] = uint8(nonce) + iv[49] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[bufOffset : bufOffset+136]) + sample() + + bufOffset++ + if bufOffset == 5 { + bufOffset = 0 + } + + // Move remaining bytes at the end to the start. + for j := 0; j < bufOffset; j++ { + buf[j] = buf[135+j] + } + } + } +} + +// For each i, sample ps[i] uniformly with 60 non-zero coefficients in {q-1,1} +// using the the given seed and w1[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will be normalized. +// +// Can only be called when DeriveX4Available is true. +// +// This function is currently not used (yet). +func PolyDeriveUniformB60X4(ps [4]*common.Poly, seed *[48]byte, + w1 [4]*VecK) { + // Pack the w1s + var w1Packed [4][common.PolyLe16Size * K]byte + for j := 0; j < 4; j++ { + if ps[j] != nil { + w1[j].PackLe16(w1Packed[j][:]) + } + } + + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the start of the packed w₁s + offset := 0 // offset into w1Packed[j] + for i := 6; i < 17; i++ { + for j := 0; j < 4; j++ { + state[i*4+j] = binary.LittleEndian.Uint64(w1Packed[j][offset : offset+8]) + } + offset += 8 + } + + offset -= 8 + + // Absorb the remainder of the packed w₁s. +PermuteLoop: + for { + perm.Permute() + + for i := 0; i < 17; i++ { + offset += 8 + if offset == len(w1Packed[0]) { + // SHAKE256 domain separator and padding + for j := 0; j < 4; j++ { + state[i*4+j] ^= 0x1f + state[16*4+j] ^= 0x80 << 56 + } + perm.Permute() + + break PermuteLoop + } + + for j := 0; j < 4; j++ { + state[i*4+j] ^= binary.LittleEndian.Uint64( + w1Packed[j][offset : offset+8]) + } + } + } + + var signs [4]uint64 + var idx [4]uint16 // indices into ps + + for j := 0; j < 4; j++ { + if ps[j] != nil { + signs[j] = state[j] + *ps[j] = common.Poly{} // zero ps[j] + idx[j] = common.N - 60 + } else { + idx[j] = common.N // mark as completed + } + } + + stateOffset := 1 + for { + done := true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := stateOffset; i < 17; i++ { + var bs [8]byte + binary.LittleEndian.PutUint64(bs[:], state[4*i+j]) + for k := 0; k < 8; k++ { + b := uint16(bs[k]) + + if b > idx[j] { + continue + } + + ps[j][idx[j]] = ps[j][b] + ps[j][b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1))) + signs[j] >>= 1 + + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + + done = false + } + + if done { + break + } + + perm.Permute() + stateOffset = 0 + } +} + +// Samples p uniformly with 60 non-zero coefficients in {q-1,1}. +// +// The polynomial p will be normalized. +func PolyDeriveUniformB60(p *common.Poly, seed *[48]byte, w1 *VecK) { + var w1Packed [common.PolyLe16Size * K]byte + var buf [136]byte // SHAKE-256 rate is 136 + + w1.PackLe16(w1Packed[:]) + + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Write(w1Packed[:]) + _, _ = h.Read(buf[:]) + + // Essentially we generate a sequence of 60 ones or minus ones, + // prepend 196 zeroes and shuffle the concatenation using the + // usual algorithm (Fisher--Yates.) + signs := binary.LittleEndian.Uint64(buf[:]) + bufOff := 8 // offset into buf + + *p = common.Poly{} // zero p + for i := uint16(common.N - 60); i < common.N; i++ { + var b uint16 + + // Find location of where to move the new coefficient to using + // rejection sampling. + for { + if bufOff >= 136 { + _, _ = h.Read(buf[:]) + bufOff = 0 + } + + b = uint16(buf[bufOff]) + bufOff++ + + if b <= i { + break + } + } + + p[i] = p[b] + p[b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1))) + signs >>= 1 + } +} diff --git a/src/circl/sign/dilithium/mode2/internal/sample_test.go b/src/circl/sign/dilithium/mode2/internal/sample_test.go new file mode 100644 index 00000000000..f4f0a51c1c9 --- /dev/null +++ b/src/circl/sign/dilithium/mode2/internal/sample_test.go @@ -0,0 +1,407 @@ +// Code generated from mode3/internal/sample_test.go by gen.go + +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestVectorDeriveUniform(t *testing.T) { + var p, p2 common.Poly + var seed [32]byte + if UseAES { + p2 = common.Poly{ + 6724291, 310295, 6949524, 4464039, 1482136, 2522903, + 7025059, 3006320, 7286364, 7516512, 3361305, 1955529, + 4765954, 1725325, 6933066, 4299100, 6625173, 4272792, + 583034, 4971409, 2259140, 7715362, 3975394, 2341624, + 5481174, 8150082, 365246, 5491939, 1083120, 7517301, + 3104783, 2475292, 184149, 6425226, 4591622, 5964030, + 4729604, 5471092, 1828227, 1082044, 2516245, 1692580, + 3274844, 5443294, 7256740, 4989638, 3191250, 7479519, + 5124211, 5603858, 1230692, 2513454, 2828034, 4254312, + 1512596, 5245430, 5517392, 2814840, 932545, 6826733, + 3511094, 4075348, 3233981, 7268882, 2913733, 4870249, + 4123492, 8124406, 4016949, 5478752, 2750895, 603525, + 5724798, 3985430, 3483012, 6434230, 3136996, 8297976, + 4107616, 7307748, 6962904, 7544473, 1193110, 3448595, + 4814773, 5607932, 8221314, 1054046, 1541208, 1866050, + 8227412, 2925778, 5293953, 2065416, 4972769, 3616283, + 7990594, 1105530, 7121836, 1170740, 7417431, 633146, + 253820, 7235019, 3539504, 6807707, 451390, 5481526, + 2859902, 1063061, 4579730, 7126652, 7033767, 4294814, + 1414604, 7620048, 1953268, 8304556, 1156814, 1182881, + 5311519, 3057534, 5277666, 682843, 2070398, 2874278, + 4859533, 6376664, 6694074, 1590242, 2620706, 8331066, + 5643845, 5037538, 2891516, 7004879, 3754327, 5031296, + 5463118, 2420870, 8116529, 5517696, 7435129, 3873963, + 710407, 713806, 175647, 4274571, 2655021, 7319503, + 3027243, 7129679, 4213435, 2429323, 4643873, 4568526, + 649664, 1720514, 6497260, 2683517, 7672754, 7105190, + 3148405, 5898369, 5667677, 8050874, 1587139, 7315260, + 4337416, 2202680, 2338714, 557467, 6752058, 2469794, + 485071, 1617604, 3590498, 2151466, 2005823, 7727956, + 7776292, 6783433, 6787146, 1732833, 3596857, 7436284, + 4483349, 4970142, 4472608, 6478342, 1236215, 5695744, + 2280717, 2889355, 3233946, 5187812, 978685, 5177364, + 2922353, 4824807, 5302883, 6739803, 8092453, 5883903, + 816553, 6041174, 8317591, 1459178, 5332455, 1835058, + 1368601, 2820950, 3479224, 2589540, 7992934, 3421045, + 4657128, 8292902, 4153567, 3553988, 7830320, 6722913, + 2555309, 4149801, 8328975, 1560545, 7757473, 3106458, + 4310856, 7135453, 3481032, 652626, 1841361, 8126828, + 6250018, 300536, 7380070, 8174419, 1418793, 6208185, + 3906256, 6679016, 1605701, 3561489, 5819724, 5746996, + 8044214, 7087187, 7102330, 4962927, 4253983, 7108567, + 4119736, 6584065, 441634, 6941656, + } + } else { + p2 = common.Poly{ + 2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052, + 3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357, + 6066350, 8126097, 1179080, 4787182, 6552182, 6713644, + 1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938, + 1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431, + 1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545, + 7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071, + 105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855, + 5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453, + 5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453, + 3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874, + 5614778, 2248550, 1756499, 8280764, 8263880, 7600081, + 5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562, + 7483939, 4938664, 6863397, 5126354, 5218129, 6236086, + 4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737, + 1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595, + 6830029, 1548850, 6593138, 6849097, 1518037, 2859442, + 7772265, 7325153, 3281191, 7856131, 4995056, 4684325, + 1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778, + 7973479, 3171829, 5624626, 3540123, 7150120, 8313283, + 3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342, + 7501562, 5826142, 2709813, 8245473, 2369045, 2782257, + 5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983, + 5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375, + 267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500, + 2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008, + 8258986, 2183134, 2302072, 4674924, 4306056, 7465311, + 6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700, + 2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533, + 255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625, + 6997719, 6260212, 6186962, 6636650, 7836834, 7998017, + 2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598, + 4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947, + 6195178, 5552390, 6804584, 6305468, 5731980, 6095195, + 3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054, + 4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780, + 3740517, 5224226, 3547288, 2083124, 4699398, 3654239, + 5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706, + 4352830, + } + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniform(&p, &seed, 30000) + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniform(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniform(&p, &seed, uint16(i)) + if !PolyNormalized(&p) { + t.Fatal() + } + } +} + +func TestDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeqEta(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-Eta || p[j] > common.Q+Eta { + t.Fatal() + } + } + } +} + +func TestDeriveUniformLeGamma1(t *testing.T) { + var p common.Poly + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-common.Gamma1 || p[j] > common.Q+common.Gamma1 { + t.Fatal() + } + } + } +} + +func TestVectorDeriveUniformLeGamma1(t *testing.T) { + var p, p2 common.Poly + var seed [48]byte + if UseAES { + p2 = common.Poly{ + 90940, 8133770, 8210940, 8218464, 8362467, 431142, 98024, + 320453, 7892373, 144162, 495313, 7910122, 308198, 8024421, + 8313699, 8323445, 8242093, 7946588, 418979, 427179, 353562, + 20972, 455962, 213062, 361787, 8141790, 8321931, 7885366, + 88645, 181202, 8094142, 8303121, 8059515, 7919812, 191865, + 7910073, 7896561, 8096830, 7899355, 8338900, 72693, 236799, + 8183042, 347570, 8153528, 8364233, 8077851, 8312277, 104682, + 8037310, 8356199, 7994081, 240369, 70229, 8108858, 8175836, + 466639, 50909, 339919, 8029663, 341659, 154398, 64345, + 97101, 212245, 8285367, 521225, 325882, 296235, 8110929, + 8015814, 7953234, 158409, 329908, 8331330, 449258, 167701, + 8197796, 8228247, 7940020, 1985, 304704, 475316, 8037482, + 8250449, 304557, 8216567, 432266, 213295, 8162216, 381001, + 7995314, 7988689, 128534, 245586, 67041, 8232744, 398441, + 223116, 443612, 149856, 222852, 158723, 54746, 171906, + 163070, 353915, 8263276, 8016812, 8229081, 31827, 489715, + 450171, 8069106, 53220, 7932381, 7955335, 8197363, 201044, + 8306733, 446376, 8211025, 7889271, 8070595, 495514, 8158685, + 7524, 7973394, 247673, 4293, 184924, 457334, 138349, 8123964, + 284179, 8255307, 8068216, 8291492, 243759, 8060601, 20962, + 8058389, 420953, 8305974, 455136, 8218139, 7121, 147703, + 7951253, 394376, 8127066, 365861, 8062390, 8138732, 366555, + 8280514, 221, 395861, 7968769, 7977119, 8098083, 343056, + 8190769, 223361, 163270, 203059, 109219, 8228600, 8127695, + 321016, 295979, 8201961, 49891, 8335504, 8190386, 8190984, + 8278654, 336364, 7878013, 7922436, 7974101, 8075534, 8200852, + 8333820, 415982, 8089662, 149553, 7946740, 474102, 7937116, + 8026845, 356056, 191053, 86928, 8218644, 8375040, 8029184, + 8025675, 8193350, 295360, 7905768, 487174, 8362961, 386108, + 282213, 8373318, 50167, 8238992, 7911505, 493459, 8335164, + 8079327, 250697, 263154, 221028, 40778, 87515, 8372585, + 504728, 7980935, 8307600, 298972, 427523, 93352, 89915, + 391490, 80320, 7975008, 336136, 7949815, 8048682, 8332244, + 8204778, 8177783, 7910684, 7925292, 518641, 59663, 53608, + 222225, 463772, 8022091, 8173722, 8291385, 472741, 8105898, + 7943299, 267137, 7957660, 371874, 409084, 203750, 477334, + 83412, 111278, 120444, + } + } else { + p2 = common.Poly{ + 338083, 7978692, 8044913, 373628, 427855, 79725, 91018, + 349821, 501552, 7955127, 8316400, 290708, 216142, 8199666, + 8040144, 109426, 8177916, 8200218, 8125680, 358131, 160961, + 497383, 25361, 156297, 8033745, 7897189, 48397, 498732, + 464556, 7862704, 8308667, 236080, 91240, 8328377, 326190, + 509979, 8313264, 8106493, 8210965, 8328036, 172602, 8108765, + 8192963, 8361660, 8026473, 7932022, 322006, 8305874, 8254440, + 7866474, 373371, 8023413, 8221878, 486124, 36080, 8324512, + 8042056, 7984472, 8048111, 7910387, 8205382, 8259636, 188609, + 8316587, 59306, 119803, 8067108, 8155455, 8153450, 7983908, + 8222256, 21521, 114297, 8069037, 151621, 8014482, 8052856, + 376107, 8004652, 175001, 8079461, 8351123, 8021484, 144547, + 7908116, 8278100, 8136941, 142399, 8026843, 8081852, 124334, + 242796, 266768, 7919478, 7954016, 28927, 8329064, 514031, + 423911, 27907, 8142788, 8078298, 273978, 382723, 8148646, + 186476, 8030712, 8067268, 356250, 145817, 60045, 122764, + 56856, 8225416, 136437, 199652, 8343127, 8109765, 7936848, + 446966, 8351681, 288663, 409663, 512988, 8350788, 8191864, + 8366223, 281267, 7921696, 8213978, 442484, 67457, 8030602, + 238514, 230458, 8301866, 8359700, 150320, 143893, 461735, + 225443, 8027502, 151113, 365244, 7911438, 82498, 405398, + 8207009, 8108255, 367485, 514660, 8294055, 8168958, 127725, + 402955, 8051625, 7859029, 7980052, 321819, 7949587, 125778, + 8287078, 131972, 499609, 256795, 8180323, 8269393, 5878, + 8145473, 8238676, 383855, 415547, 424071, 241989, 8165743, + 8207329, 149608, 8315331, 7901850, 8114275, 360650, 516061, + 255090, 8277977, 270877, 8125200, 479248, 7991711, 8028595, + 73426, 8215429, 208217, 153872, 429336, 229856, 461204, + 236682, 7930158, 8298847, 228327, 8009399, 8111520, 345025, + 386495, 93454, 8336429, 8161305, 7980811, 286795, 162808, + 224476, 7972825, 85118, 287488, 8029791, 119071, 371, 518524, + 473496, 451205, 127000, 19233, 211519, 2442, 7950959, 481888, + 8041598, 8281176, 437202, 7912610, 8080153, 8237500, 7926828, + 8009421, 204880, 62495, 8192310, 8314388, 98616, 182368, + 323894, 59901, 481049, 8139275, 7872144, 254106, 376257, + 93339, 301342, 366536, 438920, 84773, 461471, 8125755, + 7930085, 405116, + } + } + for i := 0; i < 48; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeGamma1(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniformB60(t *testing.T) { + var p common.Poly + var w1 VecK + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformB60(&p, &seed, &w1) + nonzero := 0 + for j := 0; j < common.N; j++ { + if p[j] != 0 { + if p[j] != 1 && p[j] != common.Q-1 { + t.Fatal() + } + nonzero++ + } + } + if nonzero != 60 { + t.Fatal() + } + } +} + +func TestDeriveUniformX4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [32]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, + nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniform(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatal() + } + } +} + +func TestDeriveUniformB60X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + var w1s [4]VecK + for j := 0; j < 4; j++ { + for k := 0; k < K; k++ { + for i := 0; i < common.N; i++ { + w1s[j][k][i] = uint32(j+k*4+i*4*K) & 15 + } + } + } + PolyDeriveUniformB60X4( + [4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, + [4]*VecK{&w1s[0], &w1s[1], &w1s[2], &w1s[3]}, + ) + for j := 0; j < 4; j++ { + PolyDeriveUniformB60(&p, &seed, &w1s[j]) + if ps[j] != p { + t.Fatalf("%v %v", ps[j], p) + } + } +} + +func TestDeriveUniformLeGamma1X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatalf("%d\n%v\n%v", i, p, ps[i]) + } + } +} + +func BenchmarkPolyDeriveUniformB60(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60(&p, &seed, &w1) + } +} + +func BenchmarkPolyDeriveUniformB60X4(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60X4( + [4]*common.Poly{&p, &p, &p, &p}, + &seed, + [4]*VecK{&w1, &w1, &w1, &w1}, + ) + } +} + +func BenchmarkPolyDeriveUniform(b *testing.B) { + var seed [32]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniform(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformX4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [32]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) { + var seed [48]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1X4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [48]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} diff --git a/src/circl/sign/dilithium/mode2/internal/vec.go b/src/circl/sign/dilithium/mode2/internal/vec.go new file mode 100644 index 00000000000..a20a8b0224e --- /dev/null +++ b/src/circl/sign/dilithium/mode2/internal/vec.go @@ -0,0 +1,281 @@ +// Code generated from mode3/internal/vec.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A vector of L polynomials. +type VecL [L]common.Poly + +// A vector of K polynomials. +type VecK [K]common.Poly + +// Normalize the polynomials in this vector. +func (v *VecL) Normalize() { + for i := 0; i < L; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecL) NormalizeAssumingLe2Q() { + for i := 0; i < L; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecL) Add(w, u *VecL) { + for i := 0; i < L; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecL) NTT() { + for i := 0; i < L; i++ { + v[i].NTT() + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecL) Exceeds(bound uint32) bool { + for i := 0; i < L; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Decompose(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecL) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeqEta(). +func (v *VecL) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sequentially packs each polynomial using Poly.PackLeGamma1(). +func (v *VecL) PackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].PackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeGamma1(). +func (v *VecL) UnpackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].UnpackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Normalize the polynomials in this vector. +func (v *VecK) Normalize() { + for i := 0; i < K; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecK) NormalizeAssumingLe2Q() { + for i := 0; i < K; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecK) Add(w, u *VecK) { + for i := 0; i < K; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecK) Exceeds(bound uint32) bool { + for i := 0; i < K; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Decompose(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sets v to the hint vector for v0 the modified low bits and v1 +// the unmodified high bits --- see makeHint(). +// +// Returns the number of ones in the hint vector. +func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) { + for i := 0; i < K; i++ { + pop += v[i].MakeHint(&v0[i], &v1[i]) + } + return +} + +// Computes corrections to the high bits of the polynomials in the vector +// w using the hints in h and sets v to the corrected high bits. Returns v. +// See useHint(). +func (v *VecK) UseHint(q, hint *VecK) *VecK { + for i := 0; i < K; i++ { + v[i].UseHint(&q[i], &hint[i]) + } + return v +} + +// Sequentially packs each polynomial using Poly.PackT1(). +func (v *VecK) PackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sets v to the vector packed into buf by PackT1(). +func (v *VecK) UnpackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sequentially packs each polynomial using Poly.PackT0(). +func (v *VecK) PackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sets v to the vector packed into buf by PackT0(). +func (v *VecK) UnpackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecK) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecK.PackLeqEta(). +func (v *VecK) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecK) NTT() { + for i := 0; i < K; i++ { + v[i].NTT() + } +} + +// Sequentially packs each polynomial using Poly.PackLe16(). +func (v *VecK) PackLe16(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackLe16(buf[offset:]) + offset += common.PolyLe16Size + } +} + +// Sets v to a - b. +// +// Warning: assumes coefficients of the polynomials of b are less than 2q. +func (v *VecK) Sub(a, b *VecK) { + for i := 0; i < K; i++ { + v[i].Sub(&a[i], &b[i]) + } +} + +// Sets v to 2ᵈ w without reducing. +func (v *VecK) MulBy2toD(w *VecK) { + for i := 0; i < K; i++ { + v[i].MulBy2toD(&w[i]) + } +} + +// Applies InvNTT componentwise. See Poly.InvNTT() for details. +func (v *VecK) InvNTT() { + for i := 0; i < K; i++ { + v[i].InvNTT() + } +} + +// Applies Poly.ReduceLe2Q() componentwise. +func (v *VecK) ReduceLe2Q() { + for i := 0; i < K; i++ { + v[i].ReduceLe2Q() + } +} diff --git a/src/circl/sign/dilithium/mode2aes.go b/src/circl/sign/dilithium/mode2aes.go new file mode 100644 index 00000000000..32566691932 --- /dev/null +++ b/src/circl/sign/dilithium/mode2aes.go @@ -0,0 +1,95 @@ +// Code generated from mode.templ.go. DO NOT EDIT. + +package dilithium + +import ( + "fmt" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode2aes" +) + +// implMode2AES implements the mode.Mode interface for Dilithium2-AES. +type implMode2AES struct{} + +// Mode2AES is Dilithium in mode "Dilithium2-AES". +var Mode2AES Mode = &implMode2AES{} + +func (m *implMode2AES) GenerateKey(rand io.Reader) ( + PublicKey, PrivateKey, error) { + return mode2aes.GenerateKey(rand) +} + +func (m *implMode2AES) NewKeyFromExpandedSeed(seed *[96]byte) (PublicKey, + PrivateKey) { + return mode2aes.NewKeyFromExpandedSeed(seed) +} + +func (m *implMode2AES) NewKeyFromSeed(seed []byte) (PublicKey, + PrivateKey) { + if len(seed) != common.SeedSize { + panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) + } + seedBuf := [common.SeedSize]byte{} + copy(seedBuf[:], seed) + return mode2aes.NewKeyFromSeed(&seedBuf) +} + +func (m *implMode2AES) Sign(sk PrivateKey, msg []byte) []byte { + isk := sk.(*mode2aes.PrivateKey) + ret := [mode2aes.SignatureSize]byte{} + mode2aes.SignTo(isk, msg, ret[:]) + return ret[:] +} + +func (m *implMode2AES) Verify(pk PublicKey, msg []byte, signature []byte) bool { + ipk := pk.(*mode2aes.PublicKey) + return mode2aes.Verify(ipk, msg, signature) +} + +func (m *implMode2AES) PublicKeyFromBytes(data []byte) PublicKey { + var ret mode2aes.PublicKey + if len(data) != mode2aes.PublicKeySize { + panic("packed public key must be of mode2aes.PublicKeySize bytes") + } + var buf [mode2aes.PublicKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode2AES) PrivateKeyFromBytes(data []byte) PrivateKey { + var ret mode2aes.PrivateKey + if len(data) != mode2aes.PrivateKeySize { + panic("packed public key must be of mode2aes.PrivateKeySize bytes") + } + var buf [mode2aes.PrivateKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode2AES) SeedSize() int { + return common.SeedSize +} + +func (m *implMode2AES) PublicKeySize() int { + return mode2aes.PublicKeySize +} + +func (m *implMode2AES) PrivateKeySize() int { + return mode2aes.PrivateKeySize +} + +func (m *implMode2AES) SignatureSize() int { + return mode2aes.SignatureSize +} + +func (m *implMode2AES) Name() string { + return "Dilithium2-AES" +} + +func init() { + modes["Dilithium2-AES"] = Mode2AES +} diff --git a/src/circl/sign/dilithium/mode2aes/dilithium.go b/src/circl/sign/dilithium/mode2aes/dilithium.go new file mode 100644 index 00000000000..aaf3d4f987c --- /dev/null +++ b/src/circl/sign/dilithium/mode2aes/dilithium.go @@ -0,0 +1,191 @@ +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// mode2aes implements the CRYSTALS-Dilithium signature scheme Dilithium2-AES +// as submitted to round2 of the NIST PQC competition and described in +// +// https://pq-crystals.org/dilithium/data/dilithium-specification-round2.pdf +package mode2aes + +import ( + "crypto" + "errors" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode2aes/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + SeedSize = common.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a signature + SignatureSize = internal.SignatureSize +) + +// PublicKey is the type of Dilithium2-AES public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of Dilithium2-AES private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + pk, sk, err := internal.GenerateKey(rand) + return (*PublicKey)(pk), (*PrivateKey)(sk), err +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromExpandedSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// SignTo signs the given message and writes the signature into signature. +// It will panic if signature is not of length at least SignatureSize. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + internal.SignTo( + (*internal.PrivateKey)(sk), + msg, + signature, + ) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + return internal.Verify( + (*internal.PublicKey)(pk), + msg, + signature, + ) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Packs the public key. +func (pk *PublicKey) Bytes() []byte { + var buf [PublicKeySize]byte + pk.Pack(&buf) + return buf[:] +} + +// Packs the private key. +func (sk *PrivateKey) Bytes() []byte { + var buf [PrivateKeySize]byte + sk.Pack(&buf) + return buf[:] +} + +// Packs the public key. +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + return pk.Bytes(), nil +} + +// Packs the private key. +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + return sk.Bytes(), nil +} + +// Unpacks the public key from data. +func (pk *PublicKey) UnmarshalBinary(data []byte) error { + if len(data) != PublicKeySize { + return errors.New("packed public key must be of mode2aes.PublicKeySize bytes") + } + var buf [PublicKeySize]byte + copy(buf[:], data) + pk.Unpack(&buf) + return nil +} + +// Unpacks the private key from data. +func (sk *PrivateKey) UnmarshalBinary(data []byte) error { + if len(data) != PrivateKeySize { + return errors.New("packed private key must be of mode2aes.PrivateKeySize bytes") + } + var buf [PrivateKeySize]byte + copy(buf[:], data) + sk.Unpack(&buf) + return nil +} + +// Sign signs the given message. +// +// opts.HashFunc() must return zero, which can be achieved by passing +// crypto.Hash(0) for opts. rand is ignored. Will only return an error +// if opts.HashFunc() is non-zero. +// +// This function is used to make PrivateKey implement the crypto.Signer +// interface. The package-level SignTo function might be more convenient +// to use. +func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( + signature []byte, err error) { + var sig [SignatureSize]byte + + if opts.HashFunc() != crypto.Hash(0) { + return nil, errors.New("dilithium: cannot sign hashed message") + } + + SignTo(sk, msg, sig[:]) + return sig[:], nil +} + +// Computes the public key corresponding to this private key. +// +// Returns a *PublicKey. The type crypto.PublicKey is used to make +// PrivateKey implement the crypto.Signer interface. +func (sk *PrivateKey) Public() crypto.PublicKey { + return (*PublicKey)((*internal.PrivateKey)(sk).Public()) +} + +// Equal returns whether the two private keys equal. +func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { + castOther, ok := other.(*PrivateKey) + if !ok { + return false + } + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) +} + +// Equal returns whether the two public keys equal. +func (pk *PublicKey) Equal(other crypto.PublicKey) bool { + castOther, ok := other.(*PublicKey) + if !ok { + return false + } + return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) +} diff --git a/src/circl/sign/dilithium/mode2aes/internal/dilithium.go b/src/circl/sign/dilithium/mode2aes/internal/dilithium.go new file mode 100644 index 00000000000..fb0eaaf1963 --- /dev/null +++ b/src/circl/sign/dilithium/mode2aes/internal/dilithium.go @@ -0,0 +1,446 @@ +// Code generated from mode3/internal/dilithium.go by gen.go + +package internal + +import ( + cryptoRand "crypto/rand" + "crypto/subtle" + "io" + + "circl/internal/sha3" + "circl/sign/dilithium/internal/common" +) + +const ( + // Size of a packed polynomial of norm ≤η. + // (Note that the formula is not valid in general.) + PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8 +) + +// PublicKey is the type of Dilithium public keys. +type PublicKey struct { + rho [32]byte + t1 VecK + + // Cached values + t1p [common.PolyT1Size * K]byte + A *Mat + tr *[48]byte +} + +// PrivateKey is the type of Dilithium private keys. +type PrivateKey struct { + rho [32]byte + key [32]byte + s1 VecL + s2 VecK + t0 VecK + tr [48]byte + + // Cached values + A Mat // ExpandA(ρ) + s1h VecL // NTT(s₁) + s2h VecK // NTT(s₂) + t0h VecK // NTT(t₀) +} + +type unpackedSignature struct { + z VecL + hint VecK + c common.Poly +} + +// Packs the signature into buf. +func (sig *unpackedSignature) Pack(buf []byte) { + sig.z.PackLeGamma1(buf[:]) + sig.hint.PackHint(buf[L*common.PolyLeGamma1Size:]) + sig.c.PackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) +} + +// Sets sig to the signature encoded in the buffer. +// +// Returns whether buf contains a properly packed signature. +func (sig *unpackedSignature) Unpack(buf []byte) bool { + if len(buf) < SignatureSize { + return false + } + sig.z.UnpackLeGamma1(buf[:]) + if sig.z.Exceeds(common.Gamma1 - Beta) { + return false + } + if !sig.hint.UnpackHint(buf[L*common.PolyLeGamma1Size:]) { + return false + } + sig.c.UnpackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) + return true +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + copy(buf[:32], pk.rho[:]) + copy(buf[32:], pk.t1p[:]) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + copy(pk.rho[:], buf[:32]) + copy(pk.t1p[:], buf[32:]) + + pk.t1.UnpackT1(pk.t1p[:]) + pk.A = new(Mat) + pk.A.Derive(&pk.rho) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + pk.tr = new([48]byte) + h := sha3.NewShake256() + _, _ = h.Write(buf[:]) + _, _ = h.Read(pk.tr[:]) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + copy(buf[:32], sk.rho[:]) + copy(buf[32:64], sk.key[:]) + copy(buf[64:112], sk.tr[:]) + offset := 112 + sk.s1.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.PackT0(buf[offset:]) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + copy(sk.rho[:], buf[:32]) + copy(sk.key[:], buf[32:64]) + copy(sk.tr[:], buf[64:112]) + offset := 112 + sk.s1.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.UnpackT0(buf[offset:]) + + // Cached values + sk.A.Derive(&sk.rho) + sk.t0h = sk.t0 + sk.t0h.NTT() + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() +} + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [32]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(&seed) + return pk, sk, nil +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + var pk PublicKey + var sk PrivateKey + var sSeed [32]byte + + copy(pk.rho[:], seed[:32]) + copy(sSeed[:], seed[32:64]) + copy(sk.key[:], seed[64:]) + copy(sk.rho[:], pk.rho[:]) + + sk.A.Derive(&pk.rho) + + for i := uint16(0); i < L; i++ { + PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i) + } + + for i := uint16(0); i < K; i++ { + PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L) + } + + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() + + sk.computeT0andT1(&sk.t0, &pk.t1) + + sk.t0h = sk.t0 + sk.t0h.NTT() + + // Complete public key far enough to be packed + pk.t1.PackT1(pk.t1p[:]) + pk.A = &sk.A + + // Finish private key + var packedPk [PublicKeySize]byte + pk.Pack(&packedPk) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + h := sha3.NewShake256() + _, _ = h.Write(packedPk[:]) + _, _ = h.Read(sk.tr[:]) + + // Finish cache of public key + pk.tr = &sk.tr + + return &pk, &sk +} + +// Computes t0 and t1 from sk.s1h, sk.s2 and sk.A. +func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) { + var t VecK + + // Set t to A s₁ + s₂ + for i := 0; i < K; i++ { + PolyDotHat(&t[i], &sk.A[i], &sk.s1h) + t[i].ReduceLe2Q() + t[i].InvNTT() + } + t.Add(&t, &sk.s2) + t.Normalize() + + // Compute t₀, t₁ = Power2Round(t) + t.Power2Round(t0, t1) +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) { + var buf [96]byte + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Read(buf[:]) + return NewKeyFromExpandedSeed(&buf) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + var sig unpackedSignature + var mu [48]byte + var zh VecL + var Az, Az2dct1, w1 VecK + var ch, cp common.Poly + + // Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β + // and ensured that there at most ω ones in pk.hint. + if !sig.Unpack(signature) { + return false + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(pk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // Compute Az + zh = sig.z + zh.NTT() + + for i := 0; i < K; i++ { + PolyDotHat(&Az[i], &pk.A[i], &zh) + } + + // Next, we compute Az - 2ᵈ·c·t₁. + // Note that the coefficients of t₁ are bounded by 256 = 2⁹, + // so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q, + // which is small enough for NTT(). + Az2dct1.MulBy2toD(&pk.t1) + Az2dct1.NTT() + ch = sig.c + ch.NTT() + for i := 0; i < K; i++ { + Az2dct1[i].MulHat(&Az2dct1[i], &ch) + } + Az2dct1.Sub(&Az, &Az2dct1) + Az2dct1.ReduceLe2Q() + Az2dct1.InvNTT() + Az2dct1.NormalizeAssumingLe2Q() + + // UseHint(pk.hint, Az - 2ᵈ·c·t₁) + // = UseHint(pk.hint, w - c·s₂ + c·t₀) + // = UseHint(pk.hint, r + c·t₀) + // = r₁ = w₁. + w1.UseHint(&Az2dct1, &sig.hint) + + // c' = H(μ, w₁) + PolyDeriveUniformB60(&cp, &mu, &w1) + return sig.c == cp +} + +// SignTo signs the given message and writes the signature into signature. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + var mu, rhop [48]byte + var y, yh VecL + var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK + var ch common.Poly + var yNonce uint16 + var sig unpackedSignature + + if len(signature) < SignatureSize { + panic("Signature does not fit in that byteslice") + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(sk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // ρ' = CRH(μ ‖ key) + h.Reset() + _, _ = h.Write(sk.key[:]) + _, _ = h.Write(mu[:]) + _, _ = h.Read(rhop[:]) + + // Main rejection loop + attempt := 0 + for { + attempt++ + if attempt >= 576 { + // Depending on the mode, one try has a chance between 1/7 and 1/4 + // of succeeding. Thus it is safe to say that 576 iterations + // are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸. + panic("This should only happen 1 in 2^{128}: something is wrong.") + } + + // y = ExpandMask(ρ', key) + VecLDeriveUniformLeGamma1(&y, &rhop, yNonce) + yNonce += uint16(L) + + // Set w to A y + yh = y + yh.NTT() + for i := 0; i < K; i++ { + PolyDotHat(&w[i], &sk.A[i], &yh) + w[i].ReduceLe2Q() + w[i].InvNTT() + } + + // Decompose w into w₀ and w₁ + w.NormalizeAssumingLe2Q() + w.Decompose(&w0, &w1) + + // c = H(μ, w₁) + PolyDeriveUniformB60(&sig.c, &mu, &w1) + ch = sig.c + ch.NTT() + + // Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β. + // + // By Lemma 3 of the specification this is equivalent to checking that + // both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition + // w - c·s₂ = r₁ α + r₀ as computed by decompose(). + // See also §4.1 of the specification. + for i := 0; i < K; i++ { + w0mcs2[i].MulHat(&ch, &sk.s2h[i]) + w0mcs2[i].InvNTT() + } + w0mcs2.Sub(&w0, &w0mcs2) + w0mcs2.Normalize() + + if w0mcs2.Exceeds(common.Gamma2 - Beta) { + continue + } + + // z = y + c·s₁ + for i := 0; i < L; i++ { + sig.z[i].MulHat(&ch, &sk.s1h[i]) + sig.z[i].InvNTT() + } + sig.z.Add(&sig.z, &y) + sig.z.Normalize() + + // Ensure ‖z‖_∞ < γ₁ - β + if sig.z.Exceeds(common.Gamma1 - Beta) { + continue + } + + // Compute c·t₀ + for i := 0; i < K; i++ { + ct0[i].MulHat(&ch, &sk.t0h[i]) + ct0[i].InvNTT() + } + ct0.NormalizeAssumingLe2Q() + + // Ensure ‖c·t₀‖_∞ < γ₂. + if ct0.Exceeds(common.Gamma2) { + continue + } + + // Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0. + // Note that we're not using makeHint() in the obvious way as we + // do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂. Instead we note + // that our makeHint() is actually the same as a makeHint for a + // different decomposition: + // + // Earlier we ensured indirectly with a check that r₁ = w₁ where + // r = w - c·s₂. Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂. + // Thus MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁) + // and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁). + // As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct. + w0mcs2pct0.Add(&w0mcs2, &ct0) + w0mcs2pct0.NormalizeAssumingLe2Q() + hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1) + if hintPop > Omega { + continue + } + + break + } + + sig.Pack(signature[:]) +} + +// Computes the public key corresponding to this private key. +func (sk *PrivateKey) Public() *PublicKey { + var t0 VecK + pk := &PublicKey{ + rho: sk.rho, + A: &sk.A, + tr: &sk.tr, + } + sk.computeT0andT1(&t0, &pk.t1) + pk.t1.PackT1(pk.t1p[:]) + return pk +} + +// Equal returns whether the two public keys are equal +func (pk *PublicKey) Equal(other *PublicKey) bool { + return pk.rho == other.rho && pk.t1 == other.t1 +} + +// Equal returns whether the two private keys are equal +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) & + subtle.ConstantTimeCompare(sk.key[:], other.key[:]) & + subtle.ConstantTimeCompare(sk.tr[:], other.tr[:])) + + acc := uint32(0) + for i := 0; i < L; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s1[i][j] ^ other.s1[i][j] + } + } + for i := 0; i < K; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s2[i][j] ^ other.s2[i][j] + acc |= sk.t0[i][j] ^ other.t0[i][j] + } + } + return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1 +} diff --git a/src/circl/sign/dilithium/mode2aes/internal/dilithium_test.go b/src/circl/sign/dilithium/mode2aes/internal/dilithium_test.go new file mode 100644 index 00000000000..42ce6dbe5d1 --- /dev/null +++ b/src/circl/sign/dilithium/mode2aes/internal/dilithium_test.go @@ -0,0 +1,131 @@ +// Code generated from mode3/internal/dilithium_test.go by gen.go + +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Checks whether p is normalized. Only used in tests. +func PolyNormalized(p *common.Poly) bool { + p2 := *p + p2.Normalize() + return p2 == *p +} + +func BenchmarkSkUnpack(b *testing.B) { + var buf [PrivateKeySize]byte + var sk PrivateKey + for i := 0; i < b.N; i++ { + sk.Unpack(&buf) + } +} + +func BenchmarkPkUnpack(b *testing.B) { + var buf [PublicKeySize]byte + var pk PublicKey + for i := 0; i < b.N; i++ { + pk.Unpack(&buf) + } +} + +func BenchmarkVerify(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of verification (as in the reference + // implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + pk, sk := NewKeyFromSeed(&seed) + SignTo(sk, msg[:], sig[:]) + b.ResetTimer() + for i := 0; i < b.N; i++ { + // We should generate a new signature for every verify attempt, + // as this influences the time a little bit. This difference, however, + // is small and generating a new signature in between creates a lot + // pressure on the allocator which makes an accurate measurement hard. + Verify(pk, msg[:], sig[:]) + } +} + +func BenchmarkSign(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of signing (as in the reference implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + _, sk := NewKeyFromSeed(&seed) + b.ResetTimer() + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(msg[:], uint64(i)) + SignTo(sk, msg[:], sig[:]) + } +} + +func BenchmarkGenerateKey(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + NewKeyFromSeed(&seed) + } +} + +func BenchmarkPublicFromPrivate(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + b.StopTimer() + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + _, sk := NewKeyFromSeed(&seed) + b.StartTimer() + sk.Public() + } +} + +func TestSignThenVerifyAndPkSkPacking(t *testing.T) { + var seed [common.SeedSize]byte + var sig [SignatureSize]byte + var msg [8]byte + var pkb [PublicKeySize]byte + var skb [PrivateKeySize]byte + var pk2 PublicKey + var sk2 PrivateKey + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + if !sk.Equal(sk) { + t.Fatal() + } + for j := uint64(0); j < 10; j++ { + binary.LittleEndian.PutUint64(msg[:], j) + SignTo(sk, msg[:], sig[:]) + if !Verify(pk, msg[:], sig[:]) { + t.Fatal() + } + } + pk.Pack(&pkb) + pk2.Unpack(&pkb) + if !pk.Equal(&pk2) { + t.Fatal() + } + sk.Pack(&skb) + sk2.Unpack(&skb) + if !sk.Equal(&sk2) { + t.Fatal() + } + } +} + +func TestPublicFromPrivate(t *testing.T) { + var seed [common.SeedSize]byte + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + pk2 := sk.Public() + if !pk.Equal(pk2) { + t.Fatal() + } + } +} diff --git a/src/circl/sign/dilithium/mode2aes/internal/mat.go b/src/circl/sign/dilithium/mode2aes/internal/mat.go new file mode 100644 index 00000000000..a2411b0566d --- /dev/null +++ b/src/circl/sign/dilithium/mode2aes/internal/mat.go @@ -0,0 +1,59 @@ +// Code generated from mode3/internal/mat.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A k by l matrix of polynomials. +type Mat [K]VecL + +// Expands the given seed to a complete matrix. +// +// This function is called ExpandA in the specification. +func (m *Mat) Derive(seed *[32]byte) { + if !DeriveX4Available { + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + PolyDeriveUniform(&m[i][j], seed, (i<<8)+j) + } + } + return + } + + idx := 0 + var nonces [4]uint16 + var ps [4]*common.Poly + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + nonces[idx] = (i << 8) + j + ps[idx] = &m[i][j] + idx++ + if idx == 4 { + idx = 0 + PolyDeriveUniformX4(ps, seed, nonces) + } + } + } + if idx != 0 { + for i := idx; i < 4; i++ { + ps[i] = nil + } + PolyDeriveUniformX4(ps, seed, nonces) + } +} + +// Set p to the inner product of a and b using pointwise multiplication. +// +// Assumes a and b are in Montgomery form and their coefficients are +// pairwise sufficiently small to multiply, see Poly.MulHat(). Resulting +// coefficients are bounded by 2Lq. +func PolyDotHat(p *common.Poly, a, b *VecL) { + var t common.Poly + *p = common.Poly{} // zero p + for i := 0; i < L; i++ { + t.MulHat(&a[i], &b[i]) + p.Add(&t, p) + } +} diff --git a/src/circl/sign/dilithium/mode2aes/internal/pack.go b/src/circl/sign/dilithium/mode2aes/internal/pack.go new file mode 100644 index 00000000000..ecf3971cd20 --- /dev/null +++ b/src/circl/sign/dilithium/mode2aes/internal/pack.go @@ -0,0 +1,141 @@ +// Code generated from mode3/internal/pack.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// Writes p with norm less than or equal η into buf, which must be of +// size PolyLeqEtaSize. +// +// Assumes coefficients of p are not normalized, but in [q-η,q+η]. +func PolyPackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + buf[i] = (byte(common.Q+Eta-p[j]) | + byte(common.Q+Eta-p[j+1])<<4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + buf[i] = (byte(common.Q+Eta-p[j]) | + (byte(common.Q+Eta-p[j+1]) << 3) | + (byte(common.Q+Eta-p[j+2]) << 6)) + buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) | + (byte(common.Q+Eta-p[j+3]) << 1) | + (byte(common.Q+Eta-p[j+4]) << 4) | + (byte(common.Q+Eta-p[j+5]) << 7)) + buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) | + (byte(common.Q+Eta-p[j+6]) << 2) | + (byte(common.Q+Eta-p[j+7]) << 5)) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Sets p to the polynomial of norm less than or equal η encoded in the +// given buffer of size PolyLeqEtaSize. +// +// Output coefficients of p are not normalized, but in [q-η,q+η] provided +// buf was created using PackLeqEta. +// +// Beware, for arbitrary buf the coefficients of p might en up in +// the interval [q-2^b,q+2^b] where b is the least b with η≤2^b. +func PolyUnpackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + p[j] = common.Q + Eta - uint32(buf[i]&15) + p[j+1] = common.Q + Eta - uint32(buf[i]>>4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + p[j] = common.Q + Eta - uint32(buf[i]&7) + p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7) + p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7)) + p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7) + p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7) + p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7)) + p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7) + p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Writes v with coefficients in {0, 1} of which at most ω non-zero +// to buf, which must have length ω+k. +func (v *VecK) PackHint(buf []byte) { + // The packed hint starts with the indices of the non-zero coefficients + // For instance: + // + // (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹) + // + // Yields + // + // 56, 100, 255, 2, 23, 1 + // + // Then we pad with zeroes until we have a list of ω items: + // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0 + // + // Then we finish with a list of the switch-over-indices in this + // list between polynomials, so: + // + // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6 + + off := uint8(0) + for i := 0; i < K; i++ { + for j := uint16(0); j < common.N; j++ { + if v[i][j] != 0 { + buf[off] = uint8(j) + off++ + } + } + buf[Omega+i] = off + } + for ; off < Omega; off++ { + buf[off] = 0 + } +} + +// Sets v to the vector encoded using VecK.PackHint() +// +// Returns whether unpacking was successful. +func (v *VecK) UnpackHint(buf []byte) bool { + // A priori, there would be several reasonable ways to encode the same + // hint vector. We take care to only allow only one encoding, to ensure + // "strong unforgeability". + // + // See PackHint() source for description of the encoding. + *v = VecK{} // zero v + prevSOP := uint8(0) // previous switch-over-point + for i := 0; i < K; i++ { + SOP := buf[Omega+i] + if SOP < prevSOP || SOP > Omega { + return false // ensures switch-over-points are increasing + } + for j := prevSOP; j < SOP; j++ { + if j > prevSOP && buf[j] <= buf[j-1] { + return false // ensures indices are increasing (within a poly) + } + v[i][buf[j]] = 1 + } + prevSOP = SOP + } + for j := prevSOP; j < Omega; j++ { + if buf[j] != 0 { + return false // ensures padding indices are zero + } + } + + return true +} diff --git a/src/circl/sign/dilithium/mode2aes/internal/pack_test.go b/src/circl/sign/dilithium/mode2aes/internal/pack_test.go new file mode 100644 index 00000000000..35bea5b6db3 --- /dev/null +++ b/src/circl/sign/dilithium/mode2aes/internal/pack_test.go @@ -0,0 +1,85 @@ +// Code generated from mode3/internal/pack_test.go by gen.go + +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestPolyPackLeqEta(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [PolyLeqEtaSize]byte + + for i := uint16(0); i < 100; i++ { + // Note that DeriveUniformLeqEta sets p to the right kind of + // unnormalized vector. + PolyDeriveUniformLeqEta(&p1, &seed, i) + for j := 0; j < PolyLeqEtaSize; j++ { + if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta { + t.Fatalf("DerveUniformLeqEta out of bounds") + } + } + PolyPackLeqEta(&p1, buf[:]) + PolyUnpackLeqEta(&p2, buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT1(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p1, &seed, i) + p1.Normalize() + for j := 0; j < common.N; j++ { + p1[j] &= 0x1ff + } + p1.PackT1(buf[:]) + p2.UnpackT1(buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT0(t *testing.T) { + var p, p0, p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT0Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p, &seed, i) + p.Normalize() + p.Power2Round(&p0, &p1) + + p0.PackT0(buf[:]) + p2.UnpackT0(buf[:]) + if p0 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackLeGamma1(t *testing.T) { + var p0, p1 common.Poly + var seed [48]byte + var buf [common.PolyLeGamma1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniformLeGamma1(&p0, &seed, i) + p0.Normalize() + + p0.PackLeGamma1(buf[:]) + p1.UnpackLeGamma1(buf[:]) + if p0 != p1 { + t.Fatalf("%v != %v", p0, p1) + } + } +} diff --git a/src/circl/sign/dilithium/mode2aes/internal/params.go b/src/circl/sign/dilithium/mode2aes/internal/params.go new file mode 100644 index 00000000000..10859166ef1 --- /dev/null +++ b/src/circl/sign/dilithium/mode2aes/internal/params.go @@ -0,0 +1,17 @@ +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +const ( + Name = "Dilithium2-AES" + UseAES = true + PublicKeySize = 1184 + PrivateKeySize = 2800 + SignatureSize = 2044 + K = 4 + L = 3 + Eta = 6 + DoubleEtaBits = 4 + Beta = 325 + Omega = 80 +) diff --git a/src/circl/sign/dilithium/mode2aes/internal/params_test.go b/src/circl/sign/dilithium/mode2aes/internal/params_test.go new file mode 100644 index 00000000000..6a0eab37707 --- /dev/null +++ b/src/circl/sign/dilithium/mode2aes/internal/params_test.go @@ -0,0 +1,47 @@ +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Tests specific to the current mode + +func TestVectorDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + p2 := common.Poly{ + 3, 8380411, 8380413, 8380414, 0, 0, 8380416, 5, 8380411, 8380412, + 2, 6, 2, 8380414, 8380413, 6, 8380413, 0, 8380416, 8380413, 5, + 2, 2, 8380415, 8380414, 8380414, 0, 5, 8380416, 5, 8380416, 0, + 8380413, 3, 8380413, 5, 3, 8380412, 0, 6, 8380416, 8380413, + 8380411, 1, 4, 0, 6, 0, 5, 8380412, 4, 8380414, 5, 8380413, 2, + 3, 8380412, 8380414, 8380411, 0, 8380414, 4, 6, 8380414, 8380412, + 8380415, 8380411, 8380415, 3, 1, 8380413, 5, 8380413, 2, 8380413, + 8380411, 8380414, 8380411, 1, 8380414, 8380414, 5, 2, 1, 8380414, + 8380416, 5, 1, 8380415, 8380414, 4, 3, 5, 8380411, 8380413, + 8380416, 1, 8380415, 6, 5, 8380414, 8380412, 8380412, 2, 2, + 8380411, 8380415, 8380416, 4, 4, 4, 4, 8380413, 8380412, 1, + 8380416, 4, 8380415, 8380413, 8380411, 8380412, 8380415, 8380413, + 8380412, 3, 8380413, 0, 4, 8380413, 3, 1, 4, 2, 8380411, 1, + 8380411, 8380412, 4, 8380414, 1, 8380415, 3, 8380411, 8380411, + 3, 1, 6, 0, 8380415, 6, 5, 1, 8380416, 2, 8380412, 4, 6, 6, 0, + 4, 8380411, 5, 1, 8380411, 1, 4, 1, 1, 8380411, 4, 6, 8380413, + 8380415, 8380413, 6, 4, 0, 6, 6, 5, 0, 2, 6, 6, 8380412, 2, 6, + 8380412, 4, 8380415, 2, 2, 8380416, 8380412, 8380416, 3, 3, + 8380415, 1, 8380412, 8380414, 8380411, 8380412, 4, 8380415, 6, + 8380414, 1, 5, 1, 0, 0, 4, 2, 8380413, 3, 8380414, 8380414, + 8380411, 1, 8380415, 5, 3, 6, 3, 1, 2, 8380413, 8380413, 8380412, + 0, 0, 8380411, 4, 4, 8380411, 2, 4, 5, 8380412, 6, 3, 6, 4, 4, + 8380416, 3, 8380416, 6, 3, 8380411, 4, 5, 4, 8380415, 1, + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeqEta(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} diff --git a/src/circl/sign/dilithium/mode2aes/internal/sample.go b/src/circl/sign/dilithium/mode2aes/internal/sample.go new file mode 100644 index 00000000000..8d01e8ef776 --- /dev/null +++ b/src/circl/sign/dilithium/mode2aes/internal/sample.go @@ -0,0 +1,563 @@ +// Code generated from mode3/internal/sample.go by gen.go + +package internal + +import ( + "circl/internal/sha3" + "circl/simd/keccakf1600" + + "circl/sign/dilithium/internal/common" + + "encoding/binary" +) + +// DeriveX4Available indicates whether the system supports the quick fourway +// sampling variants like PolyDeriveUniformX4. +var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES + +// For each i, sample ps[i] uniformly with coefficients of norm less than γ₁ +// using the the given seed and nonces[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformLeGamma1X4(ps [4]*common.Poly, seed *[48]byte, + nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE256 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE256 is 136 --- i.e. 17 uint64s. + for j := 0; j < 4; j++ { + state[6*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[16*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + // Each try requires 15 bits. 15 does not divide into 64, nor in 136, + // so we will have to carry some bits from a previous uint64 to the next. + var carry [4]uint32 + + // Shift is the amount of bits in the carry. + var shift [4]uint + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 17 uint64s of each + // of the four SHAKE256 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := 0; i < 17; i++ { + var t [4]uint32 + tCount := 3 + + // Get the next three or four 20 bit numbers. + qw := state[i*4+j] + qwl := (qw << shift[j]) | uint64(carry[j]) + t[0] = uint32(qwl & 0xfffff) + t[1] = uint32((qwl >> 20) & 0xfffff) + t[2] = uint32((qwl >> 40) & 0xfffff) + + if shift[j] == 16 { + t[3] = uint32(qw >> 44) + shift[j] = 0 + carry[j] = 0 + tCount = 4 + } else { + shift[j] += 4 + carry[j] = uint32(qw >> (64 - shift[j])) + } + + // Check if they're coefficients. + for k := 0; k < tCount; k++ { + if t[k] <= 2*common.Gamma1-2 { + ps[j][idx[j]] = common.Q + common.Gamma1 - 1 - t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + + done = false + } + } +} + +// For each i, sample ps[i] uniformly from the given seed and nonces[i]. +// ps[i] may be nil and is ignored in that case. +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 4; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE128 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s. + for j := 0; j < 4; j++ { + state[4*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[20*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each + // of the four SHAKE128 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + for i := 0; i < 7; i++ { + var t [8]uint32 + t[0] = uint32(state[i*3*4+j] & 0x7fffff) + t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff) + t[2] = uint32((state[i*3*4+j] >> 48) | + ((state[(i*3+1)*4+j] & 0x7f) << 16)) + t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff) + t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff) + t[5] = uint32((state[(i*3+1)*4+j] >> 56) | + ((state[(i*3+2)*4+j] & 0x7fff) << 8)) + t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff) + t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff) + + for k := 0; k < 8; k++ { + if t[k] < common.Q { + ps[j][idx[j]] = t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + done = false + } + } +} + +// Sample p uniformly from the given seed and nonce. +// +// p will be normalized. +func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) { + var i, length int + var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks + + if UseAES { + length = 12 * 16 + } else { + length = 168 + } + + sample := func() { + // Note that 3 divides into 168 and 12*16, so we use up buf completely. + for j := 0; j < length && i < common.N; j += 3 { + t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0x7fffff + + // We use rejection sampling + if t < common.Q { + p[i] = t + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample p uniformly with coefficients of norm less than or equal η, +// using the given seed and nonce. +// +// p will not be normalized, but will have coefficients in [q-η,q+η]. +func PolyDeriveUniformLeqEta(p *common.Poly, seed *[32]byte, nonce uint16) { + // Assumes 2 < η < 8. + var i, length int + var buf [11 * 16]byte // fits 168B SHAKE-128 rate and 11 16B AES blocks + + if UseAES { + length = 11 * 16 + } else { + length = 168 + } + + sample := func() { + // We use rejection sampling + for j := 0; j < length && i < common.N; j++ { + var t1, t2 uint32 + if Eta <= 3 { // branch is eliminated by compiler + t1 = uint32(buf[j]) & 7 + t2 = uint32(buf[j]) >> 5 + } else { + t1 = uint32(buf[j]) & 15 + t2 = uint32(buf[j]) >> 4 + } + if t1 <= 2*Eta { + p[i] = common.Q + Eta - t1 + i++ + } + if t2 <= 2*Eta && i < common.N { + p[i] = common.Q + Eta - t2 + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + + // 168 is SHAKE-128 rate + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample v[i] uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce+i +// +// v[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func VecLDeriveUniformLeGamma1(v *VecL, seed *[48]byte, nonce uint16) { + if !DeriveX4Available { + for i := 0; i < L; i++ { + PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i)) + } + return + } + + var ps [4]*common.Poly + nonces := [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3} + for i := 0; i < L && i < 4; i++ { + ps[i] = &v[i] + } + + // PolyDeriveUniformLeGamma1X4 is slower than, but not twice as slow as, + // PolyDeriveUniformLeGamma. + PolyDeriveUniformLeGamma1X4(ps, seed, nonces) + if L == 5 { + PolyDeriveUniformLeGamma1(&v[L-1], seed, nonce+4) + } else if L > 5 || L < 2 { + panic("VecLDeriveUniformLeGamma1 does not support that L") + } +} + +// Sample p uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce. +// +// p will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[48]byte, nonce uint16) { + // Assumes γ₁ is less than 2²⁰. + var length, i int + + // Fits 10 16B AES blocks, which aligns nicely as we take 5 bytes at + // a time. The SHAKE-256 rate, however, is 136. As 136 is 1 modulo 5, + // we are left with 1 byte after the first block, which we include in the + // next block. So we need 4 bytes leeway in our buffer. The total 160 + // fits easily in 160. + var buf [160]byte + + sample := func() { + // We use rejection sampling + for j := 0; j < length-4 && i < common.N; j += 5 { + t1 := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0xfffff + t2 := ((uint32(buf[j+2]) >> 4) | (uint32(buf[j+3]) << 4) | + (uint32(buf[j+4]) << 12)) + + if t1 <= 2*common.Gamma1-2 { + p[i] = common.Q + common.Gamma1 - 1 - t1 + i++ + } + if t2 <= 2*common.Gamma1-2 && i < common.N { + p[i] = common.Q + common.Gamma1 - 1 - t2 + i++ + } + } + } + if UseAES { + length = 160 + h := common.NewAesStream256(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:]) + sample() + } + } else { + length = 136 + var iv [48 + 2]byte // 48 byte seed + uint16 nonce + bufOffset := 0 // where to put the next block + + h := sha3.NewShake256() + copy(iv[:48], seed[:]) + iv[48] = uint8(nonce) + iv[49] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[bufOffset : bufOffset+136]) + sample() + + bufOffset++ + if bufOffset == 5 { + bufOffset = 0 + } + + // Move remaining bytes at the end to the start. + for j := 0; j < bufOffset; j++ { + buf[j] = buf[135+j] + } + } + } +} + +// For each i, sample ps[i] uniformly with 60 non-zero coefficients in {q-1,1} +// using the the given seed and w1[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will be normalized. +// +// Can only be called when DeriveX4Available is true. +// +// This function is currently not used (yet). +func PolyDeriveUniformB60X4(ps [4]*common.Poly, seed *[48]byte, + w1 [4]*VecK) { + // Pack the w1s + var w1Packed [4][common.PolyLe16Size * K]byte + for j := 0; j < 4; j++ { + if ps[j] != nil { + w1[j].PackLe16(w1Packed[j][:]) + } + } + + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the start of the packed w₁s + offset := 0 // offset into w1Packed[j] + for i := 6; i < 17; i++ { + for j := 0; j < 4; j++ { + state[i*4+j] = binary.LittleEndian.Uint64(w1Packed[j][offset : offset+8]) + } + offset += 8 + } + + offset -= 8 + + // Absorb the remainder of the packed w₁s. +PermuteLoop: + for { + perm.Permute() + + for i := 0; i < 17; i++ { + offset += 8 + if offset == len(w1Packed[0]) { + // SHAKE256 domain separator and padding + for j := 0; j < 4; j++ { + state[i*4+j] ^= 0x1f + state[16*4+j] ^= 0x80 << 56 + } + perm.Permute() + + break PermuteLoop + } + + for j := 0; j < 4; j++ { + state[i*4+j] ^= binary.LittleEndian.Uint64( + w1Packed[j][offset : offset+8]) + } + } + } + + var signs [4]uint64 + var idx [4]uint16 // indices into ps + + for j := 0; j < 4; j++ { + if ps[j] != nil { + signs[j] = state[j] + *ps[j] = common.Poly{} // zero ps[j] + idx[j] = common.N - 60 + } else { + idx[j] = common.N // mark as completed + } + } + + stateOffset := 1 + for { + done := true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := stateOffset; i < 17; i++ { + var bs [8]byte + binary.LittleEndian.PutUint64(bs[:], state[4*i+j]) + for k := 0; k < 8; k++ { + b := uint16(bs[k]) + + if b > idx[j] { + continue + } + + ps[j][idx[j]] = ps[j][b] + ps[j][b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1))) + signs[j] >>= 1 + + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + + done = false + } + + if done { + break + } + + perm.Permute() + stateOffset = 0 + } +} + +// Samples p uniformly with 60 non-zero coefficients in {q-1,1}. +// +// The polynomial p will be normalized. +func PolyDeriveUniformB60(p *common.Poly, seed *[48]byte, w1 *VecK) { + var w1Packed [common.PolyLe16Size * K]byte + var buf [136]byte // SHAKE-256 rate is 136 + + w1.PackLe16(w1Packed[:]) + + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Write(w1Packed[:]) + _, _ = h.Read(buf[:]) + + // Essentially we generate a sequence of 60 ones or minus ones, + // prepend 196 zeroes and shuffle the concatenation using the + // usual algorithm (Fisher--Yates.) + signs := binary.LittleEndian.Uint64(buf[:]) + bufOff := 8 // offset into buf + + *p = common.Poly{} // zero p + for i := uint16(common.N - 60); i < common.N; i++ { + var b uint16 + + // Find location of where to move the new coefficient to using + // rejection sampling. + for { + if bufOff >= 136 { + _, _ = h.Read(buf[:]) + bufOff = 0 + } + + b = uint16(buf[bufOff]) + bufOff++ + + if b <= i { + break + } + } + + p[i] = p[b] + p[b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1))) + signs >>= 1 + } +} diff --git a/src/circl/sign/dilithium/mode2aes/internal/sample_test.go b/src/circl/sign/dilithium/mode2aes/internal/sample_test.go new file mode 100644 index 00000000000..f4f0a51c1c9 --- /dev/null +++ b/src/circl/sign/dilithium/mode2aes/internal/sample_test.go @@ -0,0 +1,407 @@ +// Code generated from mode3/internal/sample_test.go by gen.go + +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestVectorDeriveUniform(t *testing.T) { + var p, p2 common.Poly + var seed [32]byte + if UseAES { + p2 = common.Poly{ + 6724291, 310295, 6949524, 4464039, 1482136, 2522903, + 7025059, 3006320, 7286364, 7516512, 3361305, 1955529, + 4765954, 1725325, 6933066, 4299100, 6625173, 4272792, + 583034, 4971409, 2259140, 7715362, 3975394, 2341624, + 5481174, 8150082, 365246, 5491939, 1083120, 7517301, + 3104783, 2475292, 184149, 6425226, 4591622, 5964030, + 4729604, 5471092, 1828227, 1082044, 2516245, 1692580, + 3274844, 5443294, 7256740, 4989638, 3191250, 7479519, + 5124211, 5603858, 1230692, 2513454, 2828034, 4254312, + 1512596, 5245430, 5517392, 2814840, 932545, 6826733, + 3511094, 4075348, 3233981, 7268882, 2913733, 4870249, + 4123492, 8124406, 4016949, 5478752, 2750895, 603525, + 5724798, 3985430, 3483012, 6434230, 3136996, 8297976, + 4107616, 7307748, 6962904, 7544473, 1193110, 3448595, + 4814773, 5607932, 8221314, 1054046, 1541208, 1866050, + 8227412, 2925778, 5293953, 2065416, 4972769, 3616283, + 7990594, 1105530, 7121836, 1170740, 7417431, 633146, + 253820, 7235019, 3539504, 6807707, 451390, 5481526, + 2859902, 1063061, 4579730, 7126652, 7033767, 4294814, + 1414604, 7620048, 1953268, 8304556, 1156814, 1182881, + 5311519, 3057534, 5277666, 682843, 2070398, 2874278, + 4859533, 6376664, 6694074, 1590242, 2620706, 8331066, + 5643845, 5037538, 2891516, 7004879, 3754327, 5031296, + 5463118, 2420870, 8116529, 5517696, 7435129, 3873963, + 710407, 713806, 175647, 4274571, 2655021, 7319503, + 3027243, 7129679, 4213435, 2429323, 4643873, 4568526, + 649664, 1720514, 6497260, 2683517, 7672754, 7105190, + 3148405, 5898369, 5667677, 8050874, 1587139, 7315260, + 4337416, 2202680, 2338714, 557467, 6752058, 2469794, + 485071, 1617604, 3590498, 2151466, 2005823, 7727956, + 7776292, 6783433, 6787146, 1732833, 3596857, 7436284, + 4483349, 4970142, 4472608, 6478342, 1236215, 5695744, + 2280717, 2889355, 3233946, 5187812, 978685, 5177364, + 2922353, 4824807, 5302883, 6739803, 8092453, 5883903, + 816553, 6041174, 8317591, 1459178, 5332455, 1835058, + 1368601, 2820950, 3479224, 2589540, 7992934, 3421045, + 4657128, 8292902, 4153567, 3553988, 7830320, 6722913, + 2555309, 4149801, 8328975, 1560545, 7757473, 3106458, + 4310856, 7135453, 3481032, 652626, 1841361, 8126828, + 6250018, 300536, 7380070, 8174419, 1418793, 6208185, + 3906256, 6679016, 1605701, 3561489, 5819724, 5746996, + 8044214, 7087187, 7102330, 4962927, 4253983, 7108567, + 4119736, 6584065, 441634, 6941656, + } + } else { + p2 = common.Poly{ + 2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052, + 3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357, + 6066350, 8126097, 1179080, 4787182, 6552182, 6713644, + 1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938, + 1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431, + 1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545, + 7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071, + 105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855, + 5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453, + 5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453, + 3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874, + 5614778, 2248550, 1756499, 8280764, 8263880, 7600081, + 5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562, + 7483939, 4938664, 6863397, 5126354, 5218129, 6236086, + 4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737, + 1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595, + 6830029, 1548850, 6593138, 6849097, 1518037, 2859442, + 7772265, 7325153, 3281191, 7856131, 4995056, 4684325, + 1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778, + 7973479, 3171829, 5624626, 3540123, 7150120, 8313283, + 3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342, + 7501562, 5826142, 2709813, 8245473, 2369045, 2782257, + 5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983, + 5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375, + 267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500, + 2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008, + 8258986, 2183134, 2302072, 4674924, 4306056, 7465311, + 6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700, + 2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533, + 255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625, + 6997719, 6260212, 6186962, 6636650, 7836834, 7998017, + 2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598, + 4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947, + 6195178, 5552390, 6804584, 6305468, 5731980, 6095195, + 3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054, + 4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780, + 3740517, 5224226, 3547288, 2083124, 4699398, 3654239, + 5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706, + 4352830, + } + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniform(&p, &seed, 30000) + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniform(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniform(&p, &seed, uint16(i)) + if !PolyNormalized(&p) { + t.Fatal() + } + } +} + +func TestDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeqEta(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-Eta || p[j] > common.Q+Eta { + t.Fatal() + } + } + } +} + +func TestDeriveUniformLeGamma1(t *testing.T) { + var p common.Poly + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-common.Gamma1 || p[j] > common.Q+common.Gamma1 { + t.Fatal() + } + } + } +} + +func TestVectorDeriveUniformLeGamma1(t *testing.T) { + var p, p2 common.Poly + var seed [48]byte + if UseAES { + p2 = common.Poly{ + 90940, 8133770, 8210940, 8218464, 8362467, 431142, 98024, + 320453, 7892373, 144162, 495313, 7910122, 308198, 8024421, + 8313699, 8323445, 8242093, 7946588, 418979, 427179, 353562, + 20972, 455962, 213062, 361787, 8141790, 8321931, 7885366, + 88645, 181202, 8094142, 8303121, 8059515, 7919812, 191865, + 7910073, 7896561, 8096830, 7899355, 8338900, 72693, 236799, + 8183042, 347570, 8153528, 8364233, 8077851, 8312277, 104682, + 8037310, 8356199, 7994081, 240369, 70229, 8108858, 8175836, + 466639, 50909, 339919, 8029663, 341659, 154398, 64345, + 97101, 212245, 8285367, 521225, 325882, 296235, 8110929, + 8015814, 7953234, 158409, 329908, 8331330, 449258, 167701, + 8197796, 8228247, 7940020, 1985, 304704, 475316, 8037482, + 8250449, 304557, 8216567, 432266, 213295, 8162216, 381001, + 7995314, 7988689, 128534, 245586, 67041, 8232744, 398441, + 223116, 443612, 149856, 222852, 158723, 54746, 171906, + 163070, 353915, 8263276, 8016812, 8229081, 31827, 489715, + 450171, 8069106, 53220, 7932381, 7955335, 8197363, 201044, + 8306733, 446376, 8211025, 7889271, 8070595, 495514, 8158685, + 7524, 7973394, 247673, 4293, 184924, 457334, 138349, 8123964, + 284179, 8255307, 8068216, 8291492, 243759, 8060601, 20962, + 8058389, 420953, 8305974, 455136, 8218139, 7121, 147703, + 7951253, 394376, 8127066, 365861, 8062390, 8138732, 366555, + 8280514, 221, 395861, 7968769, 7977119, 8098083, 343056, + 8190769, 223361, 163270, 203059, 109219, 8228600, 8127695, + 321016, 295979, 8201961, 49891, 8335504, 8190386, 8190984, + 8278654, 336364, 7878013, 7922436, 7974101, 8075534, 8200852, + 8333820, 415982, 8089662, 149553, 7946740, 474102, 7937116, + 8026845, 356056, 191053, 86928, 8218644, 8375040, 8029184, + 8025675, 8193350, 295360, 7905768, 487174, 8362961, 386108, + 282213, 8373318, 50167, 8238992, 7911505, 493459, 8335164, + 8079327, 250697, 263154, 221028, 40778, 87515, 8372585, + 504728, 7980935, 8307600, 298972, 427523, 93352, 89915, + 391490, 80320, 7975008, 336136, 7949815, 8048682, 8332244, + 8204778, 8177783, 7910684, 7925292, 518641, 59663, 53608, + 222225, 463772, 8022091, 8173722, 8291385, 472741, 8105898, + 7943299, 267137, 7957660, 371874, 409084, 203750, 477334, + 83412, 111278, 120444, + } + } else { + p2 = common.Poly{ + 338083, 7978692, 8044913, 373628, 427855, 79725, 91018, + 349821, 501552, 7955127, 8316400, 290708, 216142, 8199666, + 8040144, 109426, 8177916, 8200218, 8125680, 358131, 160961, + 497383, 25361, 156297, 8033745, 7897189, 48397, 498732, + 464556, 7862704, 8308667, 236080, 91240, 8328377, 326190, + 509979, 8313264, 8106493, 8210965, 8328036, 172602, 8108765, + 8192963, 8361660, 8026473, 7932022, 322006, 8305874, 8254440, + 7866474, 373371, 8023413, 8221878, 486124, 36080, 8324512, + 8042056, 7984472, 8048111, 7910387, 8205382, 8259636, 188609, + 8316587, 59306, 119803, 8067108, 8155455, 8153450, 7983908, + 8222256, 21521, 114297, 8069037, 151621, 8014482, 8052856, + 376107, 8004652, 175001, 8079461, 8351123, 8021484, 144547, + 7908116, 8278100, 8136941, 142399, 8026843, 8081852, 124334, + 242796, 266768, 7919478, 7954016, 28927, 8329064, 514031, + 423911, 27907, 8142788, 8078298, 273978, 382723, 8148646, + 186476, 8030712, 8067268, 356250, 145817, 60045, 122764, + 56856, 8225416, 136437, 199652, 8343127, 8109765, 7936848, + 446966, 8351681, 288663, 409663, 512988, 8350788, 8191864, + 8366223, 281267, 7921696, 8213978, 442484, 67457, 8030602, + 238514, 230458, 8301866, 8359700, 150320, 143893, 461735, + 225443, 8027502, 151113, 365244, 7911438, 82498, 405398, + 8207009, 8108255, 367485, 514660, 8294055, 8168958, 127725, + 402955, 8051625, 7859029, 7980052, 321819, 7949587, 125778, + 8287078, 131972, 499609, 256795, 8180323, 8269393, 5878, + 8145473, 8238676, 383855, 415547, 424071, 241989, 8165743, + 8207329, 149608, 8315331, 7901850, 8114275, 360650, 516061, + 255090, 8277977, 270877, 8125200, 479248, 7991711, 8028595, + 73426, 8215429, 208217, 153872, 429336, 229856, 461204, + 236682, 7930158, 8298847, 228327, 8009399, 8111520, 345025, + 386495, 93454, 8336429, 8161305, 7980811, 286795, 162808, + 224476, 7972825, 85118, 287488, 8029791, 119071, 371, 518524, + 473496, 451205, 127000, 19233, 211519, 2442, 7950959, 481888, + 8041598, 8281176, 437202, 7912610, 8080153, 8237500, 7926828, + 8009421, 204880, 62495, 8192310, 8314388, 98616, 182368, + 323894, 59901, 481049, 8139275, 7872144, 254106, 376257, + 93339, 301342, 366536, 438920, 84773, 461471, 8125755, + 7930085, 405116, + } + } + for i := 0; i < 48; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeGamma1(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniformB60(t *testing.T) { + var p common.Poly + var w1 VecK + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformB60(&p, &seed, &w1) + nonzero := 0 + for j := 0; j < common.N; j++ { + if p[j] != 0 { + if p[j] != 1 && p[j] != common.Q-1 { + t.Fatal() + } + nonzero++ + } + } + if nonzero != 60 { + t.Fatal() + } + } +} + +func TestDeriveUniformX4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [32]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, + nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniform(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatal() + } + } +} + +func TestDeriveUniformB60X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + var w1s [4]VecK + for j := 0; j < 4; j++ { + for k := 0; k < K; k++ { + for i := 0; i < common.N; i++ { + w1s[j][k][i] = uint32(j+k*4+i*4*K) & 15 + } + } + } + PolyDeriveUniformB60X4( + [4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, + [4]*VecK{&w1s[0], &w1s[1], &w1s[2], &w1s[3]}, + ) + for j := 0; j < 4; j++ { + PolyDeriveUniformB60(&p, &seed, &w1s[j]) + if ps[j] != p { + t.Fatalf("%v %v", ps[j], p) + } + } +} + +func TestDeriveUniformLeGamma1X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatalf("%d\n%v\n%v", i, p, ps[i]) + } + } +} + +func BenchmarkPolyDeriveUniformB60(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60(&p, &seed, &w1) + } +} + +func BenchmarkPolyDeriveUniformB60X4(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60X4( + [4]*common.Poly{&p, &p, &p, &p}, + &seed, + [4]*VecK{&w1, &w1, &w1, &w1}, + ) + } +} + +func BenchmarkPolyDeriveUniform(b *testing.B) { + var seed [32]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniform(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformX4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [32]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) { + var seed [48]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1X4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [48]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} diff --git a/src/circl/sign/dilithium/mode2aes/internal/vec.go b/src/circl/sign/dilithium/mode2aes/internal/vec.go new file mode 100644 index 00000000000..a20a8b0224e --- /dev/null +++ b/src/circl/sign/dilithium/mode2aes/internal/vec.go @@ -0,0 +1,281 @@ +// Code generated from mode3/internal/vec.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A vector of L polynomials. +type VecL [L]common.Poly + +// A vector of K polynomials. +type VecK [K]common.Poly + +// Normalize the polynomials in this vector. +func (v *VecL) Normalize() { + for i := 0; i < L; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecL) NormalizeAssumingLe2Q() { + for i := 0; i < L; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecL) Add(w, u *VecL) { + for i := 0; i < L; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecL) NTT() { + for i := 0; i < L; i++ { + v[i].NTT() + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecL) Exceeds(bound uint32) bool { + for i := 0; i < L; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Decompose(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecL) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeqEta(). +func (v *VecL) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sequentially packs each polynomial using Poly.PackLeGamma1(). +func (v *VecL) PackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].PackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeGamma1(). +func (v *VecL) UnpackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].UnpackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Normalize the polynomials in this vector. +func (v *VecK) Normalize() { + for i := 0; i < K; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecK) NormalizeAssumingLe2Q() { + for i := 0; i < K; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecK) Add(w, u *VecK) { + for i := 0; i < K; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecK) Exceeds(bound uint32) bool { + for i := 0; i < K; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Decompose(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sets v to the hint vector for v0 the modified low bits and v1 +// the unmodified high bits --- see makeHint(). +// +// Returns the number of ones in the hint vector. +func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) { + for i := 0; i < K; i++ { + pop += v[i].MakeHint(&v0[i], &v1[i]) + } + return +} + +// Computes corrections to the high bits of the polynomials in the vector +// w using the hints in h and sets v to the corrected high bits. Returns v. +// See useHint(). +func (v *VecK) UseHint(q, hint *VecK) *VecK { + for i := 0; i < K; i++ { + v[i].UseHint(&q[i], &hint[i]) + } + return v +} + +// Sequentially packs each polynomial using Poly.PackT1(). +func (v *VecK) PackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sets v to the vector packed into buf by PackT1(). +func (v *VecK) UnpackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sequentially packs each polynomial using Poly.PackT0(). +func (v *VecK) PackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sets v to the vector packed into buf by PackT0(). +func (v *VecK) UnpackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecK) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecK.PackLeqEta(). +func (v *VecK) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecK) NTT() { + for i := 0; i < K; i++ { + v[i].NTT() + } +} + +// Sequentially packs each polynomial using Poly.PackLe16(). +func (v *VecK) PackLe16(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackLe16(buf[offset:]) + offset += common.PolyLe16Size + } +} + +// Sets v to a - b. +// +// Warning: assumes coefficients of the polynomials of b are less than 2q. +func (v *VecK) Sub(a, b *VecK) { + for i := 0; i < K; i++ { + v[i].Sub(&a[i], &b[i]) + } +} + +// Sets v to 2ᵈ w without reducing. +func (v *VecK) MulBy2toD(w *VecK) { + for i := 0; i < K; i++ { + v[i].MulBy2toD(&w[i]) + } +} + +// Applies InvNTT componentwise. See Poly.InvNTT() for details. +func (v *VecK) InvNTT() { + for i := 0; i < K; i++ { + v[i].InvNTT() + } +} + +// Applies Poly.ReduceLe2Q() componentwise. +func (v *VecK) ReduceLe2Q() { + for i := 0; i < K; i++ { + v[i].ReduceLe2Q() + } +} diff --git a/src/circl/sign/dilithium/mode3.go b/src/circl/sign/dilithium/mode3.go new file mode 100644 index 00000000000..1c2eefdee99 --- /dev/null +++ b/src/circl/sign/dilithium/mode3.go @@ -0,0 +1,95 @@ +// Code generated from mode.templ.go. DO NOT EDIT. + +package dilithium + +import ( + "fmt" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode3" +) + +// implMode3 implements the mode.Mode interface for Dilithium3. +type implMode3 struct{} + +// Mode3 is Dilithium in mode "Dilithium3". +var Mode3 Mode = &implMode3{} + +func (m *implMode3) GenerateKey(rand io.Reader) ( + PublicKey, PrivateKey, error) { + return mode3.GenerateKey(rand) +} + +func (m *implMode3) NewKeyFromExpandedSeed(seed *[96]byte) (PublicKey, + PrivateKey) { + return mode3.NewKeyFromExpandedSeed(seed) +} + +func (m *implMode3) NewKeyFromSeed(seed []byte) (PublicKey, + PrivateKey) { + if len(seed) != common.SeedSize { + panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) + } + seedBuf := [common.SeedSize]byte{} + copy(seedBuf[:], seed) + return mode3.NewKeyFromSeed(&seedBuf) +} + +func (m *implMode3) Sign(sk PrivateKey, msg []byte) []byte { + isk := sk.(*mode3.PrivateKey) + ret := [mode3.SignatureSize]byte{} + mode3.SignTo(isk, msg, ret[:]) + return ret[:] +} + +func (m *implMode3) Verify(pk PublicKey, msg []byte, signature []byte) bool { + ipk := pk.(*mode3.PublicKey) + return mode3.Verify(ipk, msg, signature) +} + +func (m *implMode3) PublicKeyFromBytes(data []byte) PublicKey { + var ret mode3.PublicKey + if len(data) != mode3.PublicKeySize { + panic("packed public key must be of mode3.PublicKeySize bytes") + } + var buf [mode3.PublicKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode3) PrivateKeyFromBytes(data []byte) PrivateKey { + var ret mode3.PrivateKey + if len(data) != mode3.PrivateKeySize { + panic("packed public key must be of mode3.PrivateKeySize bytes") + } + var buf [mode3.PrivateKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode3) SeedSize() int { + return common.SeedSize +} + +func (m *implMode3) PublicKeySize() int { + return mode3.PublicKeySize +} + +func (m *implMode3) PrivateKeySize() int { + return mode3.PrivateKeySize +} + +func (m *implMode3) SignatureSize() int { + return mode3.SignatureSize +} + +func (m *implMode3) Name() string { + return "Dilithium3" +} + +func init() { + modes["Dilithium3"] = Mode3 +} diff --git a/src/circl/sign/dilithium/mode3/dilithium.go b/src/circl/sign/dilithium/mode3/dilithium.go new file mode 100644 index 00000000000..bcadea2f8d2 --- /dev/null +++ b/src/circl/sign/dilithium/mode3/dilithium.go @@ -0,0 +1,191 @@ +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// mode3 implements the CRYSTALS-Dilithium signature scheme Dilithium3 +// as submitted to round2 of the NIST PQC competition and described in +// +// https://pq-crystals.org/dilithium/data/dilithium-specification-round2.pdf +package mode3 + +import ( + "crypto" + "errors" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode3/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + SeedSize = common.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a signature + SignatureSize = internal.SignatureSize +) + +// PublicKey is the type of Dilithium3 public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of Dilithium3 private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + pk, sk, err := internal.GenerateKey(rand) + return (*PublicKey)(pk), (*PrivateKey)(sk), err +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromExpandedSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// SignTo signs the given message and writes the signature into signature. +// It will panic if signature is not of length at least SignatureSize. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + internal.SignTo( + (*internal.PrivateKey)(sk), + msg, + signature, + ) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + return internal.Verify( + (*internal.PublicKey)(pk), + msg, + signature, + ) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Packs the public key. +func (pk *PublicKey) Bytes() []byte { + var buf [PublicKeySize]byte + pk.Pack(&buf) + return buf[:] +} + +// Packs the private key. +func (sk *PrivateKey) Bytes() []byte { + var buf [PrivateKeySize]byte + sk.Pack(&buf) + return buf[:] +} + +// Packs the public key. +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + return pk.Bytes(), nil +} + +// Packs the private key. +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + return sk.Bytes(), nil +} + +// Unpacks the public key from data. +func (pk *PublicKey) UnmarshalBinary(data []byte) error { + if len(data) != PublicKeySize { + return errors.New("packed public key must be of mode3.PublicKeySize bytes") + } + var buf [PublicKeySize]byte + copy(buf[:], data) + pk.Unpack(&buf) + return nil +} + +// Unpacks the private key from data. +func (sk *PrivateKey) UnmarshalBinary(data []byte) error { + if len(data) != PrivateKeySize { + return errors.New("packed private key must be of mode3.PrivateKeySize bytes") + } + var buf [PrivateKeySize]byte + copy(buf[:], data) + sk.Unpack(&buf) + return nil +} + +// Sign signs the given message. +// +// opts.HashFunc() must return zero, which can be achieved by passing +// crypto.Hash(0) for opts. rand is ignored. Will only return an error +// if opts.HashFunc() is non-zero. +// +// This function is used to make PrivateKey implement the crypto.Signer +// interface. The package-level SignTo function might be more convenient +// to use. +func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( + signature []byte, err error) { + var sig [SignatureSize]byte + + if opts.HashFunc() != crypto.Hash(0) { + return nil, errors.New("dilithium: cannot sign hashed message") + } + + SignTo(sk, msg, sig[:]) + return sig[:], nil +} + +// Computes the public key corresponding to this private key. +// +// Returns a *PublicKey. The type crypto.PublicKey is used to make +// PrivateKey implement the crypto.Signer interface. +func (sk *PrivateKey) Public() crypto.PublicKey { + return (*PublicKey)((*internal.PrivateKey)(sk).Public()) +} + +// Equal returns whether the two private keys equal. +func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { + castOther, ok := other.(*PrivateKey) + if !ok { + return false + } + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) +} + +// Equal returns whether the two public keys equal. +func (pk *PublicKey) Equal(other crypto.PublicKey) bool { + castOther, ok := other.(*PublicKey) + if !ok { + return false + } + return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) +} diff --git a/src/circl/sign/dilithium/mode3/internal/dilithium.go b/src/circl/sign/dilithium/mode3/internal/dilithium.go new file mode 100644 index 00000000000..3c16cdbe69d --- /dev/null +++ b/src/circl/sign/dilithium/mode3/internal/dilithium.go @@ -0,0 +1,444 @@ +package internal + +import ( + cryptoRand "crypto/rand" + "crypto/subtle" + "io" + + "circl/internal/sha3" + "circl/sign/dilithium/internal/common" +) + +const ( + // Size of a packed polynomial of norm ≤η. + // (Note that the formula is not valid in general.) + PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8 +) + +// PublicKey is the type of Dilithium public keys. +type PublicKey struct { + rho [32]byte + t1 VecK + + // Cached values + t1p [common.PolyT1Size * K]byte + A *Mat + tr *[48]byte +} + +// PrivateKey is the type of Dilithium private keys. +type PrivateKey struct { + rho [32]byte + key [32]byte + s1 VecL + s2 VecK + t0 VecK + tr [48]byte + + // Cached values + A Mat // ExpandA(ρ) + s1h VecL // NTT(s₁) + s2h VecK // NTT(s₂) + t0h VecK // NTT(t₀) +} + +type unpackedSignature struct { + z VecL + hint VecK + c common.Poly +} + +// Packs the signature into buf. +func (sig *unpackedSignature) Pack(buf []byte) { + sig.z.PackLeGamma1(buf[:]) + sig.hint.PackHint(buf[L*common.PolyLeGamma1Size:]) + sig.c.PackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) +} + +// Sets sig to the signature encoded in the buffer. +// +// Returns whether buf contains a properly packed signature. +func (sig *unpackedSignature) Unpack(buf []byte) bool { + if len(buf) < SignatureSize { + return false + } + sig.z.UnpackLeGamma1(buf[:]) + if sig.z.Exceeds(common.Gamma1 - Beta) { + return false + } + if !sig.hint.UnpackHint(buf[L*common.PolyLeGamma1Size:]) { + return false + } + sig.c.UnpackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) + return true +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + copy(buf[:32], pk.rho[:]) + copy(buf[32:], pk.t1p[:]) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + copy(pk.rho[:], buf[:32]) + copy(pk.t1p[:], buf[32:]) + + pk.t1.UnpackT1(pk.t1p[:]) + pk.A = new(Mat) + pk.A.Derive(&pk.rho) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + pk.tr = new([48]byte) + h := sha3.NewShake256() + _, _ = h.Write(buf[:]) + _, _ = h.Read(pk.tr[:]) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + copy(buf[:32], sk.rho[:]) + copy(buf[32:64], sk.key[:]) + copy(buf[64:112], sk.tr[:]) + offset := 112 + sk.s1.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.PackT0(buf[offset:]) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + copy(sk.rho[:], buf[:32]) + copy(sk.key[:], buf[32:64]) + copy(sk.tr[:], buf[64:112]) + offset := 112 + sk.s1.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.UnpackT0(buf[offset:]) + + // Cached values + sk.A.Derive(&sk.rho) + sk.t0h = sk.t0 + sk.t0h.NTT() + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() +} + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [32]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(&seed) + return pk, sk, nil +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + var pk PublicKey + var sk PrivateKey + var sSeed [32]byte + + copy(pk.rho[:], seed[:32]) + copy(sSeed[:], seed[32:64]) + copy(sk.key[:], seed[64:]) + copy(sk.rho[:], pk.rho[:]) + + sk.A.Derive(&pk.rho) + + for i := uint16(0); i < L; i++ { + PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i) + } + + for i := uint16(0); i < K; i++ { + PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L) + } + + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() + + sk.computeT0andT1(&sk.t0, &pk.t1) + + sk.t0h = sk.t0 + sk.t0h.NTT() + + // Complete public key far enough to be packed + pk.t1.PackT1(pk.t1p[:]) + pk.A = &sk.A + + // Finish private key + var packedPk [PublicKeySize]byte + pk.Pack(&packedPk) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + h := sha3.NewShake256() + _, _ = h.Write(packedPk[:]) + _, _ = h.Read(sk.tr[:]) + + // Finish cache of public key + pk.tr = &sk.tr + + return &pk, &sk +} + +// Computes t0 and t1 from sk.s1h, sk.s2 and sk.A. +func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) { + var t VecK + + // Set t to A s₁ + s₂ + for i := 0; i < K; i++ { + PolyDotHat(&t[i], &sk.A[i], &sk.s1h) + t[i].ReduceLe2Q() + t[i].InvNTT() + } + t.Add(&t, &sk.s2) + t.Normalize() + + // Compute t₀, t₁ = Power2Round(t) + t.Power2Round(t0, t1) +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) { + var buf [96]byte + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Read(buf[:]) + return NewKeyFromExpandedSeed(&buf) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + var sig unpackedSignature + var mu [48]byte + var zh VecL + var Az, Az2dct1, w1 VecK + var ch, cp common.Poly + + // Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β + // and ensured that there at most ω ones in pk.hint. + if !sig.Unpack(signature) { + return false + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(pk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // Compute Az + zh = sig.z + zh.NTT() + + for i := 0; i < K; i++ { + PolyDotHat(&Az[i], &pk.A[i], &zh) + } + + // Next, we compute Az - 2ᵈ·c·t₁. + // Note that the coefficients of t₁ are bounded by 256 = 2⁹, + // so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q, + // which is small enough for NTT(). + Az2dct1.MulBy2toD(&pk.t1) + Az2dct1.NTT() + ch = sig.c + ch.NTT() + for i := 0; i < K; i++ { + Az2dct1[i].MulHat(&Az2dct1[i], &ch) + } + Az2dct1.Sub(&Az, &Az2dct1) + Az2dct1.ReduceLe2Q() + Az2dct1.InvNTT() + Az2dct1.NormalizeAssumingLe2Q() + + // UseHint(pk.hint, Az - 2ᵈ·c·t₁) + // = UseHint(pk.hint, w - c·s₂ + c·t₀) + // = UseHint(pk.hint, r + c·t₀) + // = r₁ = w₁. + w1.UseHint(&Az2dct1, &sig.hint) + + // c' = H(μ, w₁) + PolyDeriveUniformB60(&cp, &mu, &w1) + return sig.c == cp +} + +// SignTo signs the given message and writes the signature into signature. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + var mu, rhop [48]byte + var y, yh VecL + var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK + var ch common.Poly + var yNonce uint16 + var sig unpackedSignature + + if len(signature) < SignatureSize { + panic("Signature does not fit in that byteslice") + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(sk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // ρ' = CRH(μ ‖ key) + h.Reset() + _, _ = h.Write(sk.key[:]) + _, _ = h.Write(mu[:]) + _, _ = h.Read(rhop[:]) + + // Main rejection loop + attempt := 0 + for { + attempt++ + if attempt >= 576 { + // Depending on the mode, one try has a chance between 1/7 and 1/4 + // of succeeding. Thus it is safe to say that 576 iterations + // are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸. + panic("This should only happen 1 in 2^{128}: something is wrong.") + } + + // y = ExpandMask(ρ', key) + VecLDeriveUniformLeGamma1(&y, &rhop, yNonce) + yNonce += uint16(L) + + // Set w to A y + yh = y + yh.NTT() + for i := 0; i < K; i++ { + PolyDotHat(&w[i], &sk.A[i], &yh) + w[i].ReduceLe2Q() + w[i].InvNTT() + } + + // Decompose w into w₀ and w₁ + w.NormalizeAssumingLe2Q() + w.Decompose(&w0, &w1) + + // c = H(μ, w₁) + PolyDeriveUniformB60(&sig.c, &mu, &w1) + ch = sig.c + ch.NTT() + + // Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β. + // + // By Lemma 3 of the specification this is equivalent to checking that + // both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition + // w - c·s₂ = r₁ α + r₀ as computed by decompose(). + // See also §4.1 of the specification. + for i := 0; i < K; i++ { + w0mcs2[i].MulHat(&ch, &sk.s2h[i]) + w0mcs2[i].InvNTT() + } + w0mcs2.Sub(&w0, &w0mcs2) + w0mcs2.Normalize() + + if w0mcs2.Exceeds(common.Gamma2 - Beta) { + continue + } + + // z = y + c·s₁ + for i := 0; i < L; i++ { + sig.z[i].MulHat(&ch, &sk.s1h[i]) + sig.z[i].InvNTT() + } + sig.z.Add(&sig.z, &y) + sig.z.Normalize() + + // Ensure ‖z‖_∞ < γ₁ - β + if sig.z.Exceeds(common.Gamma1 - Beta) { + continue + } + + // Compute c·t₀ + for i := 0; i < K; i++ { + ct0[i].MulHat(&ch, &sk.t0h[i]) + ct0[i].InvNTT() + } + ct0.NormalizeAssumingLe2Q() + + // Ensure ‖c·t₀‖_∞ < γ₂. + if ct0.Exceeds(common.Gamma2) { + continue + } + + // Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0. + // Note that we're not using makeHint() in the obvious way as we + // do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂. Instead we note + // that our makeHint() is actually the same as a makeHint for a + // different decomposition: + // + // Earlier we ensured indirectly with a check that r₁ = w₁ where + // r = w - c·s₂. Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂. + // Thus MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁) + // and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁). + // As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct. + w0mcs2pct0.Add(&w0mcs2, &ct0) + w0mcs2pct0.NormalizeAssumingLe2Q() + hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1) + if hintPop > Omega { + continue + } + + break + } + + sig.Pack(signature[:]) +} + +// Computes the public key corresponding to this private key. +func (sk *PrivateKey) Public() *PublicKey { + var t0 VecK + pk := &PublicKey{ + rho: sk.rho, + A: &sk.A, + tr: &sk.tr, + } + sk.computeT0andT1(&t0, &pk.t1) + pk.t1.PackT1(pk.t1p[:]) + return pk +} + +// Equal returns whether the two public keys are equal +func (pk *PublicKey) Equal(other *PublicKey) bool { + return pk.rho == other.rho && pk.t1 == other.t1 +} + +// Equal returns whether the two private keys are equal +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) & + subtle.ConstantTimeCompare(sk.key[:], other.key[:]) & + subtle.ConstantTimeCompare(sk.tr[:], other.tr[:])) + + acc := uint32(0) + for i := 0; i < L; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s1[i][j] ^ other.s1[i][j] + } + } + for i := 0; i < K; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s2[i][j] ^ other.s2[i][j] + acc |= sk.t0[i][j] ^ other.t0[i][j] + } + } + return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1 +} diff --git a/src/circl/sign/dilithium/mode3/internal/dilithium_test.go b/src/circl/sign/dilithium/mode3/internal/dilithium_test.go new file mode 100644 index 00000000000..52bf78d8c04 --- /dev/null +++ b/src/circl/sign/dilithium/mode3/internal/dilithium_test.go @@ -0,0 +1,129 @@ +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Checks whether p is normalized. Only used in tests. +func PolyNormalized(p *common.Poly) bool { + p2 := *p + p2.Normalize() + return p2 == *p +} + +func BenchmarkSkUnpack(b *testing.B) { + var buf [PrivateKeySize]byte + var sk PrivateKey + for i := 0; i < b.N; i++ { + sk.Unpack(&buf) + } +} + +func BenchmarkPkUnpack(b *testing.B) { + var buf [PublicKeySize]byte + var pk PublicKey + for i := 0; i < b.N; i++ { + pk.Unpack(&buf) + } +} + +func BenchmarkVerify(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of verification (as in the reference + // implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + pk, sk := NewKeyFromSeed(&seed) + SignTo(sk, msg[:], sig[:]) + b.ResetTimer() + for i := 0; i < b.N; i++ { + // We should generate a new signature for every verify attempt, + // as this influences the time a little bit. This difference, however, + // is small and generating a new signature in between creates a lot + // pressure on the allocator which makes an accurate measurement hard. + Verify(pk, msg[:], sig[:]) + } +} + +func BenchmarkSign(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of signing (as in the reference implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + _, sk := NewKeyFromSeed(&seed) + b.ResetTimer() + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(msg[:], uint64(i)) + SignTo(sk, msg[:], sig[:]) + } +} + +func BenchmarkGenerateKey(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + NewKeyFromSeed(&seed) + } +} + +func BenchmarkPublicFromPrivate(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + b.StopTimer() + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + _, sk := NewKeyFromSeed(&seed) + b.StartTimer() + sk.Public() + } +} + +func TestSignThenVerifyAndPkSkPacking(t *testing.T) { + var seed [common.SeedSize]byte + var sig [SignatureSize]byte + var msg [8]byte + var pkb [PublicKeySize]byte + var skb [PrivateKeySize]byte + var pk2 PublicKey + var sk2 PrivateKey + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + if !sk.Equal(sk) { + t.Fatal() + } + for j := uint64(0); j < 10; j++ { + binary.LittleEndian.PutUint64(msg[:], j) + SignTo(sk, msg[:], sig[:]) + if !Verify(pk, msg[:], sig[:]) { + t.Fatal() + } + } + pk.Pack(&pkb) + pk2.Unpack(&pkb) + if !pk.Equal(&pk2) { + t.Fatal() + } + sk.Pack(&skb) + sk2.Unpack(&skb) + if !sk.Equal(&sk2) { + t.Fatal() + } + } +} + +func TestPublicFromPrivate(t *testing.T) { + var seed [common.SeedSize]byte + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + pk2 := sk.Public() + if !pk.Equal(pk2) { + t.Fatal() + } + } +} diff --git a/src/circl/sign/dilithium/mode3/internal/mat.go b/src/circl/sign/dilithium/mode3/internal/mat.go new file mode 100644 index 00000000000..aa839097fab --- /dev/null +++ b/src/circl/sign/dilithium/mode3/internal/mat.go @@ -0,0 +1,57 @@ +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A k by l matrix of polynomials. +type Mat [K]VecL + +// Expands the given seed to a complete matrix. +// +// This function is called ExpandA in the specification. +func (m *Mat) Derive(seed *[32]byte) { + if !DeriveX4Available { + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + PolyDeriveUniform(&m[i][j], seed, (i<<8)+j) + } + } + return + } + + idx := 0 + var nonces [4]uint16 + var ps [4]*common.Poly + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + nonces[idx] = (i << 8) + j + ps[idx] = &m[i][j] + idx++ + if idx == 4 { + idx = 0 + PolyDeriveUniformX4(ps, seed, nonces) + } + } + } + if idx != 0 { + for i := idx; i < 4; i++ { + ps[i] = nil + } + PolyDeriveUniformX4(ps, seed, nonces) + } +} + +// Set p to the inner product of a and b using pointwise multiplication. +// +// Assumes a and b are in Montgomery form and their coefficients are +// pairwise sufficiently small to multiply, see Poly.MulHat(). Resulting +// coefficients are bounded by 2Lq. +func PolyDotHat(p *common.Poly, a, b *VecL) { + var t common.Poly + *p = common.Poly{} // zero p + for i := 0; i < L; i++ { + t.MulHat(&a[i], &b[i]) + p.Add(&t, p) + } +} diff --git a/src/circl/sign/dilithium/mode3/internal/pack.go b/src/circl/sign/dilithium/mode3/internal/pack.go new file mode 100644 index 00000000000..827717f25ad --- /dev/null +++ b/src/circl/sign/dilithium/mode3/internal/pack.go @@ -0,0 +1,139 @@ +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// Writes p with norm less than or equal η into buf, which must be of +// size PolyLeqEtaSize. +// +// Assumes coefficients of p are not normalized, but in [q-η,q+η]. +func PolyPackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + buf[i] = (byte(common.Q+Eta-p[j]) | + byte(common.Q+Eta-p[j+1])<<4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + buf[i] = (byte(common.Q+Eta-p[j]) | + (byte(common.Q+Eta-p[j+1]) << 3) | + (byte(common.Q+Eta-p[j+2]) << 6)) + buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) | + (byte(common.Q+Eta-p[j+3]) << 1) | + (byte(common.Q+Eta-p[j+4]) << 4) | + (byte(common.Q+Eta-p[j+5]) << 7)) + buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) | + (byte(common.Q+Eta-p[j+6]) << 2) | + (byte(common.Q+Eta-p[j+7]) << 5)) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Sets p to the polynomial of norm less than or equal η encoded in the +// given buffer of size PolyLeqEtaSize. +// +// Output coefficients of p are not normalized, but in [q-η,q+η] provided +// buf was created using PackLeqEta. +// +// Beware, for arbitrary buf the coefficients of p might en up in +// the interval [q-2^b,q+2^b] where b is the least b with η≤2^b. +func PolyUnpackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + p[j] = common.Q + Eta - uint32(buf[i]&15) + p[j+1] = common.Q + Eta - uint32(buf[i]>>4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + p[j] = common.Q + Eta - uint32(buf[i]&7) + p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7) + p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7)) + p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7) + p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7) + p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7)) + p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7) + p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Writes v with coefficients in {0, 1} of which at most ω non-zero +// to buf, which must have length ω+k. +func (v *VecK) PackHint(buf []byte) { + // The packed hint starts with the indices of the non-zero coefficients + // For instance: + // + // (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹) + // + // Yields + // + // 56, 100, 255, 2, 23, 1 + // + // Then we pad with zeroes until we have a list of ω items: + // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0 + // + // Then we finish with a list of the switch-over-indices in this + // list between polynomials, so: + // + // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6 + + off := uint8(0) + for i := 0; i < K; i++ { + for j := uint16(0); j < common.N; j++ { + if v[i][j] != 0 { + buf[off] = uint8(j) + off++ + } + } + buf[Omega+i] = off + } + for ; off < Omega; off++ { + buf[off] = 0 + } +} + +// Sets v to the vector encoded using VecK.PackHint() +// +// Returns whether unpacking was successful. +func (v *VecK) UnpackHint(buf []byte) bool { + // A priori, there would be several reasonable ways to encode the same + // hint vector. We take care to only allow only one encoding, to ensure + // "strong unforgeability". + // + // See PackHint() source for description of the encoding. + *v = VecK{} // zero v + prevSOP := uint8(0) // previous switch-over-point + for i := 0; i < K; i++ { + SOP := buf[Omega+i] + if SOP < prevSOP || SOP > Omega { + return false // ensures switch-over-points are increasing + } + for j := prevSOP; j < SOP; j++ { + if j > prevSOP && buf[j] <= buf[j-1] { + return false // ensures indices are increasing (within a poly) + } + v[i][buf[j]] = 1 + } + prevSOP = SOP + } + for j := prevSOP; j < Omega; j++ { + if buf[j] != 0 { + return false // ensures padding indices are zero + } + } + + return true +} diff --git a/src/circl/sign/dilithium/mode3/internal/pack_test.go b/src/circl/sign/dilithium/mode3/internal/pack_test.go new file mode 100644 index 00000000000..f7565b79a23 --- /dev/null +++ b/src/circl/sign/dilithium/mode3/internal/pack_test.go @@ -0,0 +1,83 @@ +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestPolyPackLeqEta(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [PolyLeqEtaSize]byte + + for i := uint16(0); i < 100; i++ { + // Note that DeriveUniformLeqEta sets p to the right kind of + // unnormalized vector. + PolyDeriveUniformLeqEta(&p1, &seed, i) + for j := 0; j < PolyLeqEtaSize; j++ { + if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta { + t.Fatalf("DerveUniformLeqEta out of bounds") + } + } + PolyPackLeqEta(&p1, buf[:]) + PolyUnpackLeqEta(&p2, buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT1(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p1, &seed, i) + p1.Normalize() + for j := 0; j < common.N; j++ { + p1[j] &= 0x1ff + } + p1.PackT1(buf[:]) + p2.UnpackT1(buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT0(t *testing.T) { + var p, p0, p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT0Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p, &seed, i) + p.Normalize() + p.Power2Round(&p0, &p1) + + p0.PackT0(buf[:]) + p2.UnpackT0(buf[:]) + if p0 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackLeGamma1(t *testing.T) { + var p0, p1 common.Poly + var seed [48]byte + var buf [common.PolyLeGamma1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniformLeGamma1(&p0, &seed, i) + p0.Normalize() + + p0.PackLeGamma1(buf[:]) + p1.UnpackLeGamma1(buf[:]) + if p0 != p1 { + t.Fatalf("%v != %v", p0, p1) + } + } +} diff --git a/src/circl/sign/dilithium/mode3/internal/params.go b/src/circl/sign/dilithium/mode3/internal/params.go new file mode 100644 index 00000000000..8de4e19aab6 --- /dev/null +++ b/src/circl/sign/dilithium/mode3/internal/params.go @@ -0,0 +1,17 @@ +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +const ( + Name = "Dilithium3" + UseAES = false + PublicKeySize = 1472 + PrivateKeySize = 3504 + SignatureSize = 2701 + K = 5 + L = 4 + Eta = 5 + DoubleEtaBits = 4 + Beta = 275 + Omega = 96 +) diff --git a/src/circl/sign/dilithium/mode3/internal/params_test.go b/src/circl/sign/dilithium/mode3/internal/params_test.go new file mode 100644 index 00000000000..4a6cf34dbcf --- /dev/null +++ b/src/circl/sign/dilithium/mode3/internal/params_test.go @@ -0,0 +1,50 @@ +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Tests specific to the current mode + +func TestVectorDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + p2 := common.Poly{ + 1, 8380415, 0, 1, 8380412, 0, 0, 8380413, 8380414, 8380414, + 8380416, 5, 2, 5, 0, 8380412, 8380415, 1, 2, 8380412, 5, + 1, 1, 8380412, 5, 8380413, 8380416, 8380414, 5, 8380412, + 0, 2, 5, 8380414, 2, 3, 3, 0, 8380416, 5, 1, 2, 8380414, + 8380413, 0, 0, 5, 3, 8380415, 8380414, 5, 3, 3, 2, 8380416, + 2, 0, 8380412, 8380414, 1, 2, 8380412, 8380412, 5, 8380413, + 4, 8380413, 8380415, 8380414, 4, 8380413, 5, 8380413, 1, + 8380416, 8380415, 8380412, 2, 3, 4, 8380415, 8380416, 4, + 8380415, 8380413, 1, 0, 1, 4, 8380415, 8380415, 4, 8380412, + 8380415, 4, 3, 5, 0, 8380415, 8380415, 2, 8380415, 3, + 8380414, 8380416, 3, 5, 5, 0, 8380415, 4, 3, 2, 8380415, + 8380415, 5, 8380412, 8380414, 2, 8380415, 8380412, 1, + 8380412, 8380413, 5, 8380412, 3, 4, 4, 8380413, 2, 8380415, + 8380415, 8380414, 8380413, 8380413, 8380413, 2, 8380413, + 4, 8380416, 2, 8380416, 0, 8380415, 8380414, 2, 8380412, + 8380414, 4, 3, 8380416, 1, 8380412, 2, 8380412, 8380412, + 1, 0, 0, 0, 8380415, 8380414, 8380413, 8380412, 8380415, + 1, 1, 5, 8380412, 8380416, 2, 0, 8380413, 0, 2, 2, 2, + 8380415, 1, 3, 8380412, 8380413, 2, 8380416, 5, 8380414, + 8380415, 4, 4, 8380416, 5, 8380414, 8380412, 8380413, 4, + 5, 2, 5, 2, 4, 4, 8380414, 5, 3, 8380415, 2, 1, 5, 8380413, + 1, 8380414, 5, 8380412, 8380414, 0, 1, 8380416, 5, 8380412, + 5, 8380413, 8380415, 8380414, 8380413, 0, 5, 1, 8380412, + 8380415, 8380412, 8380416, 5, 2, 0, 3, 0, 4, 0, 8380416, + 0, 8380413, 2, 0, 8380416, 8380416, 8380412, 3, 8380412, + 1, 2, 8380414, 3, 4, 3, 0, + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeqEta(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} diff --git a/src/circl/sign/dilithium/mode3/internal/sample.go b/src/circl/sign/dilithium/mode3/internal/sample.go new file mode 100644 index 00000000000..c19a01c7b99 --- /dev/null +++ b/src/circl/sign/dilithium/mode3/internal/sample.go @@ -0,0 +1,561 @@ +package internal + +import ( + "circl/internal/sha3" + "circl/simd/keccakf1600" + + "circl/sign/dilithium/internal/common" + + "encoding/binary" +) + +// DeriveX4Available indicates whether the system supports the quick fourway +// sampling variants like PolyDeriveUniformX4. +var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES + +// For each i, sample ps[i] uniformly with coefficients of norm less than γ₁ +// using the the given seed and nonces[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformLeGamma1X4(ps [4]*common.Poly, seed *[48]byte, + nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE256 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE256 is 136 --- i.e. 17 uint64s. + for j := 0; j < 4; j++ { + state[6*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[16*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + // Each try requires 15 bits. 15 does not divide into 64, nor in 136, + // so we will have to carry some bits from a previous uint64 to the next. + var carry [4]uint32 + + // Shift is the amount of bits in the carry. + var shift [4]uint + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 17 uint64s of each + // of the four SHAKE256 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := 0; i < 17; i++ { + var t [4]uint32 + tCount := 3 + + // Get the next three or four 20 bit numbers. + qw := state[i*4+j] + qwl := (qw << shift[j]) | uint64(carry[j]) + t[0] = uint32(qwl & 0xfffff) + t[1] = uint32((qwl >> 20) & 0xfffff) + t[2] = uint32((qwl >> 40) & 0xfffff) + + if shift[j] == 16 { + t[3] = uint32(qw >> 44) + shift[j] = 0 + carry[j] = 0 + tCount = 4 + } else { + shift[j] += 4 + carry[j] = uint32(qw >> (64 - shift[j])) + } + + // Check if they're coefficients. + for k := 0; k < tCount; k++ { + if t[k] <= 2*common.Gamma1-2 { + ps[j][idx[j]] = common.Q + common.Gamma1 - 1 - t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + + done = false + } + } +} + +// For each i, sample ps[i] uniformly from the given seed and nonces[i]. +// ps[i] may be nil and is ignored in that case. +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 4; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE128 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s. + for j := 0; j < 4; j++ { + state[4*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[20*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each + // of the four SHAKE128 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + for i := 0; i < 7; i++ { + var t [8]uint32 + t[0] = uint32(state[i*3*4+j] & 0x7fffff) + t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff) + t[2] = uint32((state[i*3*4+j] >> 48) | + ((state[(i*3+1)*4+j] & 0x7f) << 16)) + t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff) + t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff) + t[5] = uint32((state[(i*3+1)*4+j] >> 56) | + ((state[(i*3+2)*4+j] & 0x7fff) << 8)) + t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff) + t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff) + + for k := 0; k < 8; k++ { + if t[k] < common.Q { + ps[j][idx[j]] = t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + done = false + } + } +} + +// Sample p uniformly from the given seed and nonce. +// +// p will be normalized. +func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) { + var i, length int + var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks + + if UseAES { + length = 12 * 16 + } else { + length = 168 + } + + sample := func() { + // Note that 3 divides into 168 and 12*16, so we use up buf completely. + for j := 0; j < length && i < common.N; j += 3 { + t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0x7fffff + + // We use rejection sampling + if t < common.Q { + p[i] = t + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample p uniformly with coefficients of norm less than or equal η, +// using the given seed and nonce. +// +// p will not be normalized, but will have coefficients in [q-η,q+η]. +func PolyDeriveUniformLeqEta(p *common.Poly, seed *[32]byte, nonce uint16) { + // Assumes 2 < η < 8. + var i, length int + var buf [11 * 16]byte // fits 168B SHAKE-128 rate and 11 16B AES blocks + + if UseAES { + length = 11 * 16 + } else { + length = 168 + } + + sample := func() { + // We use rejection sampling + for j := 0; j < length && i < common.N; j++ { + var t1, t2 uint32 + if Eta <= 3 { // branch is eliminated by compiler + t1 = uint32(buf[j]) & 7 + t2 = uint32(buf[j]) >> 5 + } else { + t1 = uint32(buf[j]) & 15 + t2 = uint32(buf[j]) >> 4 + } + if t1 <= 2*Eta { + p[i] = common.Q + Eta - t1 + i++ + } + if t2 <= 2*Eta && i < common.N { + p[i] = common.Q + Eta - t2 + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + + // 168 is SHAKE-128 rate + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample v[i] uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce+i +// +// v[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func VecLDeriveUniformLeGamma1(v *VecL, seed *[48]byte, nonce uint16) { + if !DeriveX4Available { + for i := 0; i < L; i++ { + PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i)) + } + return + } + + var ps [4]*common.Poly + nonces := [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3} + for i := 0; i < L && i < 4; i++ { + ps[i] = &v[i] + } + + // PolyDeriveUniformLeGamma1X4 is slower than, but not twice as slow as, + // PolyDeriveUniformLeGamma. + PolyDeriveUniformLeGamma1X4(ps, seed, nonces) + if L == 5 { + PolyDeriveUniformLeGamma1(&v[L-1], seed, nonce+4) + } else if L > 5 || L < 2 { + panic("VecLDeriveUniformLeGamma1 does not support that L") + } +} + +// Sample p uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce. +// +// p will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[48]byte, nonce uint16) { + // Assumes γ₁ is less than 2²⁰. + var length, i int + + // Fits 10 16B AES blocks, which aligns nicely as we take 5 bytes at + // a time. The SHAKE-256 rate, however, is 136. As 136 is 1 modulo 5, + // we are left with 1 byte after the first block, which we include in the + // next block. So we need 4 bytes leeway in our buffer. The total 160 + // fits easily in 160. + var buf [160]byte + + sample := func() { + // We use rejection sampling + for j := 0; j < length-4 && i < common.N; j += 5 { + t1 := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0xfffff + t2 := ((uint32(buf[j+2]) >> 4) | (uint32(buf[j+3]) << 4) | + (uint32(buf[j+4]) << 12)) + + if t1 <= 2*common.Gamma1-2 { + p[i] = common.Q + common.Gamma1 - 1 - t1 + i++ + } + if t2 <= 2*common.Gamma1-2 && i < common.N { + p[i] = common.Q + common.Gamma1 - 1 - t2 + i++ + } + } + } + if UseAES { + length = 160 + h := common.NewAesStream256(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:]) + sample() + } + } else { + length = 136 + var iv [48 + 2]byte // 48 byte seed + uint16 nonce + bufOffset := 0 // where to put the next block + + h := sha3.NewShake256() + copy(iv[:48], seed[:]) + iv[48] = uint8(nonce) + iv[49] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[bufOffset : bufOffset+136]) + sample() + + bufOffset++ + if bufOffset == 5 { + bufOffset = 0 + } + + // Move remaining bytes at the end to the start. + for j := 0; j < bufOffset; j++ { + buf[j] = buf[135+j] + } + } + } +} + +// For each i, sample ps[i] uniformly with 60 non-zero coefficients in {q-1,1} +// using the the given seed and w1[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will be normalized. +// +// Can only be called when DeriveX4Available is true. +// +// This function is currently not used (yet). +func PolyDeriveUniformB60X4(ps [4]*common.Poly, seed *[48]byte, + w1 [4]*VecK) { + // Pack the w1s + var w1Packed [4][common.PolyLe16Size * K]byte + for j := 0; j < 4; j++ { + if ps[j] != nil { + w1[j].PackLe16(w1Packed[j][:]) + } + } + + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the start of the packed w₁s + offset := 0 // offset into w1Packed[j] + for i := 6; i < 17; i++ { + for j := 0; j < 4; j++ { + state[i*4+j] = binary.LittleEndian.Uint64(w1Packed[j][offset : offset+8]) + } + offset += 8 + } + + offset -= 8 + + // Absorb the remainder of the packed w₁s. +PermuteLoop: + for { + perm.Permute() + + for i := 0; i < 17; i++ { + offset += 8 + if offset == len(w1Packed[0]) { + // SHAKE256 domain separator and padding + for j := 0; j < 4; j++ { + state[i*4+j] ^= 0x1f + state[16*4+j] ^= 0x80 << 56 + } + perm.Permute() + + break PermuteLoop + } + + for j := 0; j < 4; j++ { + state[i*4+j] ^= binary.LittleEndian.Uint64( + w1Packed[j][offset : offset+8]) + } + } + } + + var signs [4]uint64 + var idx [4]uint16 // indices into ps + + for j := 0; j < 4; j++ { + if ps[j] != nil { + signs[j] = state[j] + *ps[j] = common.Poly{} // zero ps[j] + idx[j] = common.N - 60 + } else { + idx[j] = common.N // mark as completed + } + } + + stateOffset := 1 + for { + done := true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := stateOffset; i < 17; i++ { + var bs [8]byte + binary.LittleEndian.PutUint64(bs[:], state[4*i+j]) + for k := 0; k < 8; k++ { + b := uint16(bs[k]) + + if b > idx[j] { + continue + } + + ps[j][idx[j]] = ps[j][b] + ps[j][b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1))) + signs[j] >>= 1 + + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + + done = false + } + + if done { + break + } + + perm.Permute() + stateOffset = 0 + } +} + +// Samples p uniformly with 60 non-zero coefficients in {q-1,1}. +// +// The polynomial p will be normalized. +func PolyDeriveUniformB60(p *common.Poly, seed *[48]byte, w1 *VecK) { + var w1Packed [common.PolyLe16Size * K]byte + var buf [136]byte // SHAKE-256 rate is 136 + + w1.PackLe16(w1Packed[:]) + + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Write(w1Packed[:]) + _, _ = h.Read(buf[:]) + + // Essentially we generate a sequence of 60 ones or minus ones, + // prepend 196 zeroes and shuffle the concatenation using the + // usual algorithm (Fisher--Yates.) + signs := binary.LittleEndian.Uint64(buf[:]) + bufOff := 8 // offset into buf + + *p = common.Poly{} // zero p + for i := uint16(common.N - 60); i < common.N; i++ { + var b uint16 + + // Find location of where to move the new coefficient to using + // rejection sampling. + for { + if bufOff >= 136 { + _, _ = h.Read(buf[:]) + bufOff = 0 + } + + b = uint16(buf[bufOff]) + bufOff++ + + if b <= i { + break + } + } + + p[i] = p[b] + p[b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1))) + signs >>= 1 + } +} diff --git a/src/circl/sign/dilithium/mode3/internal/sample_test.go b/src/circl/sign/dilithium/mode3/internal/sample_test.go new file mode 100644 index 00000000000..1e54642c785 --- /dev/null +++ b/src/circl/sign/dilithium/mode3/internal/sample_test.go @@ -0,0 +1,405 @@ +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestVectorDeriveUniform(t *testing.T) { + var p, p2 common.Poly + var seed [32]byte + if UseAES { + p2 = common.Poly{ + 6724291, 310295, 6949524, 4464039, 1482136, 2522903, + 7025059, 3006320, 7286364, 7516512, 3361305, 1955529, + 4765954, 1725325, 6933066, 4299100, 6625173, 4272792, + 583034, 4971409, 2259140, 7715362, 3975394, 2341624, + 5481174, 8150082, 365246, 5491939, 1083120, 7517301, + 3104783, 2475292, 184149, 6425226, 4591622, 5964030, + 4729604, 5471092, 1828227, 1082044, 2516245, 1692580, + 3274844, 5443294, 7256740, 4989638, 3191250, 7479519, + 5124211, 5603858, 1230692, 2513454, 2828034, 4254312, + 1512596, 5245430, 5517392, 2814840, 932545, 6826733, + 3511094, 4075348, 3233981, 7268882, 2913733, 4870249, + 4123492, 8124406, 4016949, 5478752, 2750895, 603525, + 5724798, 3985430, 3483012, 6434230, 3136996, 8297976, + 4107616, 7307748, 6962904, 7544473, 1193110, 3448595, + 4814773, 5607932, 8221314, 1054046, 1541208, 1866050, + 8227412, 2925778, 5293953, 2065416, 4972769, 3616283, + 7990594, 1105530, 7121836, 1170740, 7417431, 633146, + 253820, 7235019, 3539504, 6807707, 451390, 5481526, + 2859902, 1063061, 4579730, 7126652, 7033767, 4294814, + 1414604, 7620048, 1953268, 8304556, 1156814, 1182881, + 5311519, 3057534, 5277666, 682843, 2070398, 2874278, + 4859533, 6376664, 6694074, 1590242, 2620706, 8331066, + 5643845, 5037538, 2891516, 7004879, 3754327, 5031296, + 5463118, 2420870, 8116529, 5517696, 7435129, 3873963, + 710407, 713806, 175647, 4274571, 2655021, 7319503, + 3027243, 7129679, 4213435, 2429323, 4643873, 4568526, + 649664, 1720514, 6497260, 2683517, 7672754, 7105190, + 3148405, 5898369, 5667677, 8050874, 1587139, 7315260, + 4337416, 2202680, 2338714, 557467, 6752058, 2469794, + 485071, 1617604, 3590498, 2151466, 2005823, 7727956, + 7776292, 6783433, 6787146, 1732833, 3596857, 7436284, + 4483349, 4970142, 4472608, 6478342, 1236215, 5695744, + 2280717, 2889355, 3233946, 5187812, 978685, 5177364, + 2922353, 4824807, 5302883, 6739803, 8092453, 5883903, + 816553, 6041174, 8317591, 1459178, 5332455, 1835058, + 1368601, 2820950, 3479224, 2589540, 7992934, 3421045, + 4657128, 8292902, 4153567, 3553988, 7830320, 6722913, + 2555309, 4149801, 8328975, 1560545, 7757473, 3106458, + 4310856, 7135453, 3481032, 652626, 1841361, 8126828, + 6250018, 300536, 7380070, 8174419, 1418793, 6208185, + 3906256, 6679016, 1605701, 3561489, 5819724, 5746996, + 8044214, 7087187, 7102330, 4962927, 4253983, 7108567, + 4119736, 6584065, 441634, 6941656, + } + } else { + p2 = common.Poly{ + 2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052, + 3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357, + 6066350, 8126097, 1179080, 4787182, 6552182, 6713644, + 1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938, + 1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431, + 1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545, + 7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071, + 105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855, + 5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453, + 5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453, + 3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874, + 5614778, 2248550, 1756499, 8280764, 8263880, 7600081, + 5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562, + 7483939, 4938664, 6863397, 5126354, 5218129, 6236086, + 4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737, + 1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595, + 6830029, 1548850, 6593138, 6849097, 1518037, 2859442, + 7772265, 7325153, 3281191, 7856131, 4995056, 4684325, + 1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778, + 7973479, 3171829, 5624626, 3540123, 7150120, 8313283, + 3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342, + 7501562, 5826142, 2709813, 8245473, 2369045, 2782257, + 5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983, + 5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375, + 267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500, + 2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008, + 8258986, 2183134, 2302072, 4674924, 4306056, 7465311, + 6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700, + 2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533, + 255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625, + 6997719, 6260212, 6186962, 6636650, 7836834, 7998017, + 2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598, + 4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947, + 6195178, 5552390, 6804584, 6305468, 5731980, 6095195, + 3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054, + 4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780, + 3740517, 5224226, 3547288, 2083124, 4699398, 3654239, + 5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706, + 4352830, + } + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniform(&p, &seed, 30000) + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniform(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniform(&p, &seed, uint16(i)) + if !PolyNormalized(&p) { + t.Fatal() + } + } +} + +func TestDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeqEta(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-Eta || p[j] > common.Q+Eta { + t.Fatal() + } + } + } +} + +func TestDeriveUniformLeGamma1(t *testing.T) { + var p common.Poly + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-common.Gamma1 || p[j] > common.Q+common.Gamma1 { + t.Fatal() + } + } + } +} + +func TestVectorDeriveUniformLeGamma1(t *testing.T) { + var p, p2 common.Poly + var seed [48]byte + if UseAES { + p2 = common.Poly{ + 90940, 8133770, 8210940, 8218464, 8362467, 431142, 98024, + 320453, 7892373, 144162, 495313, 7910122, 308198, 8024421, + 8313699, 8323445, 8242093, 7946588, 418979, 427179, 353562, + 20972, 455962, 213062, 361787, 8141790, 8321931, 7885366, + 88645, 181202, 8094142, 8303121, 8059515, 7919812, 191865, + 7910073, 7896561, 8096830, 7899355, 8338900, 72693, 236799, + 8183042, 347570, 8153528, 8364233, 8077851, 8312277, 104682, + 8037310, 8356199, 7994081, 240369, 70229, 8108858, 8175836, + 466639, 50909, 339919, 8029663, 341659, 154398, 64345, + 97101, 212245, 8285367, 521225, 325882, 296235, 8110929, + 8015814, 7953234, 158409, 329908, 8331330, 449258, 167701, + 8197796, 8228247, 7940020, 1985, 304704, 475316, 8037482, + 8250449, 304557, 8216567, 432266, 213295, 8162216, 381001, + 7995314, 7988689, 128534, 245586, 67041, 8232744, 398441, + 223116, 443612, 149856, 222852, 158723, 54746, 171906, + 163070, 353915, 8263276, 8016812, 8229081, 31827, 489715, + 450171, 8069106, 53220, 7932381, 7955335, 8197363, 201044, + 8306733, 446376, 8211025, 7889271, 8070595, 495514, 8158685, + 7524, 7973394, 247673, 4293, 184924, 457334, 138349, 8123964, + 284179, 8255307, 8068216, 8291492, 243759, 8060601, 20962, + 8058389, 420953, 8305974, 455136, 8218139, 7121, 147703, + 7951253, 394376, 8127066, 365861, 8062390, 8138732, 366555, + 8280514, 221, 395861, 7968769, 7977119, 8098083, 343056, + 8190769, 223361, 163270, 203059, 109219, 8228600, 8127695, + 321016, 295979, 8201961, 49891, 8335504, 8190386, 8190984, + 8278654, 336364, 7878013, 7922436, 7974101, 8075534, 8200852, + 8333820, 415982, 8089662, 149553, 7946740, 474102, 7937116, + 8026845, 356056, 191053, 86928, 8218644, 8375040, 8029184, + 8025675, 8193350, 295360, 7905768, 487174, 8362961, 386108, + 282213, 8373318, 50167, 8238992, 7911505, 493459, 8335164, + 8079327, 250697, 263154, 221028, 40778, 87515, 8372585, + 504728, 7980935, 8307600, 298972, 427523, 93352, 89915, + 391490, 80320, 7975008, 336136, 7949815, 8048682, 8332244, + 8204778, 8177783, 7910684, 7925292, 518641, 59663, 53608, + 222225, 463772, 8022091, 8173722, 8291385, 472741, 8105898, + 7943299, 267137, 7957660, 371874, 409084, 203750, 477334, + 83412, 111278, 120444, + } + } else { + p2 = common.Poly{ + 338083, 7978692, 8044913, 373628, 427855, 79725, 91018, + 349821, 501552, 7955127, 8316400, 290708, 216142, 8199666, + 8040144, 109426, 8177916, 8200218, 8125680, 358131, 160961, + 497383, 25361, 156297, 8033745, 7897189, 48397, 498732, + 464556, 7862704, 8308667, 236080, 91240, 8328377, 326190, + 509979, 8313264, 8106493, 8210965, 8328036, 172602, 8108765, + 8192963, 8361660, 8026473, 7932022, 322006, 8305874, 8254440, + 7866474, 373371, 8023413, 8221878, 486124, 36080, 8324512, + 8042056, 7984472, 8048111, 7910387, 8205382, 8259636, 188609, + 8316587, 59306, 119803, 8067108, 8155455, 8153450, 7983908, + 8222256, 21521, 114297, 8069037, 151621, 8014482, 8052856, + 376107, 8004652, 175001, 8079461, 8351123, 8021484, 144547, + 7908116, 8278100, 8136941, 142399, 8026843, 8081852, 124334, + 242796, 266768, 7919478, 7954016, 28927, 8329064, 514031, + 423911, 27907, 8142788, 8078298, 273978, 382723, 8148646, + 186476, 8030712, 8067268, 356250, 145817, 60045, 122764, + 56856, 8225416, 136437, 199652, 8343127, 8109765, 7936848, + 446966, 8351681, 288663, 409663, 512988, 8350788, 8191864, + 8366223, 281267, 7921696, 8213978, 442484, 67457, 8030602, + 238514, 230458, 8301866, 8359700, 150320, 143893, 461735, + 225443, 8027502, 151113, 365244, 7911438, 82498, 405398, + 8207009, 8108255, 367485, 514660, 8294055, 8168958, 127725, + 402955, 8051625, 7859029, 7980052, 321819, 7949587, 125778, + 8287078, 131972, 499609, 256795, 8180323, 8269393, 5878, + 8145473, 8238676, 383855, 415547, 424071, 241989, 8165743, + 8207329, 149608, 8315331, 7901850, 8114275, 360650, 516061, + 255090, 8277977, 270877, 8125200, 479248, 7991711, 8028595, + 73426, 8215429, 208217, 153872, 429336, 229856, 461204, + 236682, 7930158, 8298847, 228327, 8009399, 8111520, 345025, + 386495, 93454, 8336429, 8161305, 7980811, 286795, 162808, + 224476, 7972825, 85118, 287488, 8029791, 119071, 371, 518524, + 473496, 451205, 127000, 19233, 211519, 2442, 7950959, 481888, + 8041598, 8281176, 437202, 7912610, 8080153, 8237500, 7926828, + 8009421, 204880, 62495, 8192310, 8314388, 98616, 182368, + 323894, 59901, 481049, 8139275, 7872144, 254106, 376257, + 93339, 301342, 366536, 438920, 84773, 461471, 8125755, + 7930085, 405116, + } + } + for i := 0; i < 48; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeGamma1(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniformB60(t *testing.T) { + var p common.Poly + var w1 VecK + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformB60(&p, &seed, &w1) + nonzero := 0 + for j := 0; j < common.N; j++ { + if p[j] != 0 { + if p[j] != 1 && p[j] != common.Q-1 { + t.Fatal() + } + nonzero++ + } + } + if nonzero != 60 { + t.Fatal() + } + } +} + +func TestDeriveUniformX4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [32]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, + nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniform(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatal() + } + } +} + +func TestDeriveUniformB60X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + var w1s [4]VecK + for j := 0; j < 4; j++ { + for k := 0; k < K; k++ { + for i := 0; i < common.N; i++ { + w1s[j][k][i] = uint32(j+k*4+i*4*K) & 15 + } + } + } + PolyDeriveUniformB60X4( + [4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, + [4]*VecK{&w1s[0], &w1s[1], &w1s[2], &w1s[3]}, + ) + for j := 0; j < 4; j++ { + PolyDeriveUniformB60(&p, &seed, &w1s[j]) + if ps[j] != p { + t.Fatalf("%v %v", ps[j], p) + } + } +} + +func TestDeriveUniformLeGamma1X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatalf("%d\n%v\n%v", i, p, ps[i]) + } + } +} + +func BenchmarkPolyDeriveUniformB60(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60(&p, &seed, &w1) + } +} + +func BenchmarkPolyDeriveUniformB60X4(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60X4( + [4]*common.Poly{&p, &p, &p, &p}, + &seed, + [4]*VecK{&w1, &w1, &w1, &w1}, + ) + } +} + +func BenchmarkPolyDeriveUniform(b *testing.B) { + var seed [32]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniform(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformX4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [32]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) { + var seed [48]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1X4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [48]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} diff --git a/src/circl/sign/dilithium/mode3/internal/vec.go b/src/circl/sign/dilithium/mode3/internal/vec.go new file mode 100644 index 00000000000..177792c2754 --- /dev/null +++ b/src/circl/sign/dilithium/mode3/internal/vec.go @@ -0,0 +1,279 @@ +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A vector of L polynomials. +type VecL [L]common.Poly + +// A vector of K polynomials. +type VecK [K]common.Poly + +// Normalize the polynomials in this vector. +func (v *VecL) Normalize() { + for i := 0; i < L; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecL) NormalizeAssumingLe2Q() { + for i := 0; i < L; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecL) Add(w, u *VecL) { + for i := 0; i < L; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecL) NTT() { + for i := 0; i < L; i++ { + v[i].NTT() + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecL) Exceeds(bound uint32) bool { + for i := 0; i < L; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Decompose(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecL) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeqEta(). +func (v *VecL) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sequentially packs each polynomial using Poly.PackLeGamma1(). +func (v *VecL) PackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].PackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeGamma1(). +func (v *VecL) UnpackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].UnpackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Normalize the polynomials in this vector. +func (v *VecK) Normalize() { + for i := 0; i < K; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecK) NormalizeAssumingLe2Q() { + for i := 0; i < K; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecK) Add(w, u *VecK) { + for i := 0; i < K; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecK) Exceeds(bound uint32) bool { + for i := 0; i < K; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Decompose(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sets v to the hint vector for v0 the modified low bits and v1 +// the unmodified high bits --- see makeHint(). +// +// Returns the number of ones in the hint vector. +func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) { + for i := 0; i < K; i++ { + pop += v[i].MakeHint(&v0[i], &v1[i]) + } + return +} + +// Computes corrections to the high bits of the polynomials in the vector +// w using the hints in h and sets v to the corrected high bits. Returns v. +// See useHint(). +func (v *VecK) UseHint(q, hint *VecK) *VecK { + for i := 0; i < K; i++ { + v[i].UseHint(&q[i], &hint[i]) + } + return v +} + +// Sequentially packs each polynomial using Poly.PackT1(). +func (v *VecK) PackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sets v to the vector packed into buf by PackT1(). +func (v *VecK) UnpackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sequentially packs each polynomial using Poly.PackT0(). +func (v *VecK) PackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sets v to the vector packed into buf by PackT0(). +func (v *VecK) UnpackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecK) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecK.PackLeqEta(). +func (v *VecK) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecK) NTT() { + for i := 0; i < K; i++ { + v[i].NTT() + } +} + +// Sequentially packs each polynomial using Poly.PackLe16(). +func (v *VecK) PackLe16(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackLe16(buf[offset:]) + offset += common.PolyLe16Size + } +} + +// Sets v to a - b. +// +// Warning: assumes coefficients of the polynomials of b are less than 2q. +func (v *VecK) Sub(a, b *VecK) { + for i := 0; i < K; i++ { + v[i].Sub(&a[i], &b[i]) + } +} + +// Sets v to 2ᵈ w without reducing. +func (v *VecK) MulBy2toD(w *VecK) { + for i := 0; i < K; i++ { + v[i].MulBy2toD(&w[i]) + } +} + +// Applies InvNTT componentwise. See Poly.InvNTT() for details. +func (v *VecK) InvNTT() { + for i := 0; i < K; i++ { + v[i].InvNTT() + } +} + +// Applies Poly.ReduceLe2Q() componentwise. +func (v *VecK) ReduceLe2Q() { + for i := 0; i < K; i++ { + v[i].ReduceLe2Q() + } +} diff --git a/src/circl/sign/dilithium/mode3aes.go b/src/circl/sign/dilithium/mode3aes.go new file mode 100644 index 00000000000..54049edbb3a --- /dev/null +++ b/src/circl/sign/dilithium/mode3aes.go @@ -0,0 +1,95 @@ +// Code generated from mode.templ.go. DO NOT EDIT. + +package dilithium + +import ( + "fmt" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode3aes" +) + +// implMode3AES implements the mode.Mode interface for Dilithium3-AES. +type implMode3AES struct{} + +// Mode3AES is Dilithium in mode "Dilithium3-AES". +var Mode3AES Mode = &implMode3AES{} + +func (m *implMode3AES) GenerateKey(rand io.Reader) ( + PublicKey, PrivateKey, error) { + return mode3aes.GenerateKey(rand) +} + +func (m *implMode3AES) NewKeyFromExpandedSeed(seed *[96]byte) (PublicKey, + PrivateKey) { + return mode3aes.NewKeyFromExpandedSeed(seed) +} + +func (m *implMode3AES) NewKeyFromSeed(seed []byte) (PublicKey, + PrivateKey) { + if len(seed) != common.SeedSize { + panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) + } + seedBuf := [common.SeedSize]byte{} + copy(seedBuf[:], seed) + return mode3aes.NewKeyFromSeed(&seedBuf) +} + +func (m *implMode3AES) Sign(sk PrivateKey, msg []byte) []byte { + isk := sk.(*mode3aes.PrivateKey) + ret := [mode3aes.SignatureSize]byte{} + mode3aes.SignTo(isk, msg, ret[:]) + return ret[:] +} + +func (m *implMode3AES) Verify(pk PublicKey, msg []byte, signature []byte) bool { + ipk := pk.(*mode3aes.PublicKey) + return mode3aes.Verify(ipk, msg, signature) +} + +func (m *implMode3AES) PublicKeyFromBytes(data []byte) PublicKey { + var ret mode3aes.PublicKey + if len(data) != mode3aes.PublicKeySize { + panic("packed public key must be of mode3aes.PublicKeySize bytes") + } + var buf [mode3aes.PublicKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode3AES) PrivateKeyFromBytes(data []byte) PrivateKey { + var ret mode3aes.PrivateKey + if len(data) != mode3aes.PrivateKeySize { + panic("packed public key must be of mode3aes.PrivateKeySize bytes") + } + var buf [mode3aes.PrivateKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode3AES) SeedSize() int { + return common.SeedSize +} + +func (m *implMode3AES) PublicKeySize() int { + return mode3aes.PublicKeySize +} + +func (m *implMode3AES) PrivateKeySize() int { + return mode3aes.PrivateKeySize +} + +func (m *implMode3AES) SignatureSize() int { + return mode3aes.SignatureSize +} + +func (m *implMode3AES) Name() string { + return "Dilithium3-AES" +} + +func init() { + modes["Dilithium3-AES"] = Mode3AES +} diff --git a/src/circl/sign/dilithium/mode3aes/dilithium.go b/src/circl/sign/dilithium/mode3aes/dilithium.go new file mode 100644 index 00000000000..a2a3b03359d --- /dev/null +++ b/src/circl/sign/dilithium/mode3aes/dilithium.go @@ -0,0 +1,191 @@ +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// mode3aes implements the CRYSTALS-Dilithium signature scheme Dilithium3-AES +// as submitted to round2 of the NIST PQC competition and described in +// +// https://pq-crystals.org/dilithium/data/dilithium-specification-round2.pdf +package mode3aes + +import ( + "crypto" + "errors" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode3aes/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + SeedSize = common.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a signature + SignatureSize = internal.SignatureSize +) + +// PublicKey is the type of Dilithium3-AES public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of Dilithium3-AES private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + pk, sk, err := internal.GenerateKey(rand) + return (*PublicKey)(pk), (*PrivateKey)(sk), err +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromExpandedSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// SignTo signs the given message and writes the signature into signature. +// It will panic if signature is not of length at least SignatureSize. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + internal.SignTo( + (*internal.PrivateKey)(sk), + msg, + signature, + ) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + return internal.Verify( + (*internal.PublicKey)(pk), + msg, + signature, + ) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Packs the public key. +func (pk *PublicKey) Bytes() []byte { + var buf [PublicKeySize]byte + pk.Pack(&buf) + return buf[:] +} + +// Packs the private key. +func (sk *PrivateKey) Bytes() []byte { + var buf [PrivateKeySize]byte + sk.Pack(&buf) + return buf[:] +} + +// Packs the public key. +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + return pk.Bytes(), nil +} + +// Packs the private key. +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + return sk.Bytes(), nil +} + +// Unpacks the public key from data. +func (pk *PublicKey) UnmarshalBinary(data []byte) error { + if len(data) != PublicKeySize { + return errors.New("packed public key must be of mode3aes.PublicKeySize bytes") + } + var buf [PublicKeySize]byte + copy(buf[:], data) + pk.Unpack(&buf) + return nil +} + +// Unpacks the private key from data. +func (sk *PrivateKey) UnmarshalBinary(data []byte) error { + if len(data) != PrivateKeySize { + return errors.New("packed private key must be of mode3aes.PrivateKeySize bytes") + } + var buf [PrivateKeySize]byte + copy(buf[:], data) + sk.Unpack(&buf) + return nil +} + +// Sign signs the given message. +// +// opts.HashFunc() must return zero, which can be achieved by passing +// crypto.Hash(0) for opts. rand is ignored. Will only return an error +// if opts.HashFunc() is non-zero. +// +// This function is used to make PrivateKey implement the crypto.Signer +// interface. The package-level SignTo function might be more convenient +// to use. +func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( + signature []byte, err error) { + var sig [SignatureSize]byte + + if opts.HashFunc() != crypto.Hash(0) { + return nil, errors.New("dilithium: cannot sign hashed message") + } + + SignTo(sk, msg, sig[:]) + return sig[:], nil +} + +// Computes the public key corresponding to this private key. +// +// Returns a *PublicKey. The type crypto.PublicKey is used to make +// PrivateKey implement the crypto.Signer interface. +func (sk *PrivateKey) Public() crypto.PublicKey { + return (*PublicKey)((*internal.PrivateKey)(sk).Public()) +} + +// Equal returns whether the two private keys equal. +func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { + castOther, ok := other.(*PrivateKey) + if !ok { + return false + } + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) +} + +// Equal returns whether the two public keys equal. +func (pk *PublicKey) Equal(other crypto.PublicKey) bool { + castOther, ok := other.(*PublicKey) + if !ok { + return false + } + return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) +} diff --git a/src/circl/sign/dilithium/mode3aes/internal/dilithium.go b/src/circl/sign/dilithium/mode3aes/internal/dilithium.go new file mode 100644 index 00000000000..fb0eaaf1963 --- /dev/null +++ b/src/circl/sign/dilithium/mode3aes/internal/dilithium.go @@ -0,0 +1,446 @@ +// Code generated from mode3/internal/dilithium.go by gen.go + +package internal + +import ( + cryptoRand "crypto/rand" + "crypto/subtle" + "io" + + "circl/internal/sha3" + "circl/sign/dilithium/internal/common" +) + +const ( + // Size of a packed polynomial of norm ≤η. + // (Note that the formula is not valid in general.) + PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8 +) + +// PublicKey is the type of Dilithium public keys. +type PublicKey struct { + rho [32]byte + t1 VecK + + // Cached values + t1p [common.PolyT1Size * K]byte + A *Mat + tr *[48]byte +} + +// PrivateKey is the type of Dilithium private keys. +type PrivateKey struct { + rho [32]byte + key [32]byte + s1 VecL + s2 VecK + t0 VecK + tr [48]byte + + // Cached values + A Mat // ExpandA(ρ) + s1h VecL // NTT(s₁) + s2h VecK // NTT(s₂) + t0h VecK // NTT(t₀) +} + +type unpackedSignature struct { + z VecL + hint VecK + c common.Poly +} + +// Packs the signature into buf. +func (sig *unpackedSignature) Pack(buf []byte) { + sig.z.PackLeGamma1(buf[:]) + sig.hint.PackHint(buf[L*common.PolyLeGamma1Size:]) + sig.c.PackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) +} + +// Sets sig to the signature encoded in the buffer. +// +// Returns whether buf contains a properly packed signature. +func (sig *unpackedSignature) Unpack(buf []byte) bool { + if len(buf) < SignatureSize { + return false + } + sig.z.UnpackLeGamma1(buf[:]) + if sig.z.Exceeds(common.Gamma1 - Beta) { + return false + } + if !sig.hint.UnpackHint(buf[L*common.PolyLeGamma1Size:]) { + return false + } + sig.c.UnpackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) + return true +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + copy(buf[:32], pk.rho[:]) + copy(buf[32:], pk.t1p[:]) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + copy(pk.rho[:], buf[:32]) + copy(pk.t1p[:], buf[32:]) + + pk.t1.UnpackT1(pk.t1p[:]) + pk.A = new(Mat) + pk.A.Derive(&pk.rho) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + pk.tr = new([48]byte) + h := sha3.NewShake256() + _, _ = h.Write(buf[:]) + _, _ = h.Read(pk.tr[:]) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + copy(buf[:32], sk.rho[:]) + copy(buf[32:64], sk.key[:]) + copy(buf[64:112], sk.tr[:]) + offset := 112 + sk.s1.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.PackT0(buf[offset:]) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + copy(sk.rho[:], buf[:32]) + copy(sk.key[:], buf[32:64]) + copy(sk.tr[:], buf[64:112]) + offset := 112 + sk.s1.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.UnpackT0(buf[offset:]) + + // Cached values + sk.A.Derive(&sk.rho) + sk.t0h = sk.t0 + sk.t0h.NTT() + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() +} + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [32]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(&seed) + return pk, sk, nil +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + var pk PublicKey + var sk PrivateKey + var sSeed [32]byte + + copy(pk.rho[:], seed[:32]) + copy(sSeed[:], seed[32:64]) + copy(sk.key[:], seed[64:]) + copy(sk.rho[:], pk.rho[:]) + + sk.A.Derive(&pk.rho) + + for i := uint16(0); i < L; i++ { + PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i) + } + + for i := uint16(0); i < K; i++ { + PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L) + } + + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() + + sk.computeT0andT1(&sk.t0, &pk.t1) + + sk.t0h = sk.t0 + sk.t0h.NTT() + + // Complete public key far enough to be packed + pk.t1.PackT1(pk.t1p[:]) + pk.A = &sk.A + + // Finish private key + var packedPk [PublicKeySize]byte + pk.Pack(&packedPk) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + h := sha3.NewShake256() + _, _ = h.Write(packedPk[:]) + _, _ = h.Read(sk.tr[:]) + + // Finish cache of public key + pk.tr = &sk.tr + + return &pk, &sk +} + +// Computes t0 and t1 from sk.s1h, sk.s2 and sk.A. +func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) { + var t VecK + + // Set t to A s₁ + s₂ + for i := 0; i < K; i++ { + PolyDotHat(&t[i], &sk.A[i], &sk.s1h) + t[i].ReduceLe2Q() + t[i].InvNTT() + } + t.Add(&t, &sk.s2) + t.Normalize() + + // Compute t₀, t₁ = Power2Round(t) + t.Power2Round(t0, t1) +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) { + var buf [96]byte + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Read(buf[:]) + return NewKeyFromExpandedSeed(&buf) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + var sig unpackedSignature + var mu [48]byte + var zh VecL + var Az, Az2dct1, w1 VecK + var ch, cp common.Poly + + // Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β + // and ensured that there at most ω ones in pk.hint. + if !sig.Unpack(signature) { + return false + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(pk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // Compute Az + zh = sig.z + zh.NTT() + + for i := 0; i < K; i++ { + PolyDotHat(&Az[i], &pk.A[i], &zh) + } + + // Next, we compute Az - 2ᵈ·c·t₁. + // Note that the coefficients of t₁ are bounded by 256 = 2⁹, + // so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q, + // which is small enough for NTT(). + Az2dct1.MulBy2toD(&pk.t1) + Az2dct1.NTT() + ch = sig.c + ch.NTT() + for i := 0; i < K; i++ { + Az2dct1[i].MulHat(&Az2dct1[i], &ch) + } + Az2dct1.Sub(&Az, &Az2dct1) + Az2dct1.ReduceLe2Q() + Az2dct1.InvNTT() + Az2dct1.NormalizeAssumingLe2Q() + + // UseHint(pk.hint, Az - 2ᵈ·c·t₁) + // = UseHint(pk.hint, w - c·s₂ + c·t₀) + // = UseHint(pk.hint, r + c·t₀) + // = r₁ = w₁. + w1.UseHint(&Az2dct1, &sig.hint) + + // c' = H(μ, w₁) + PolyDeriveUniformB60(&cp, &mu, &w1) + return sig.c == cp +} + +// SignTo signs the given message and writes the signature into signature. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + var mu, rhop [48]byte + var y, yh VecL + var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK + var ch common.Poly + var yNonce uint16 + var sig unpackedSignature + + if len(signature) < SignatureSize { + panic("Signature does not fit in that byteslice") + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(sk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // ρ' = CRH(μ ‖ key) + h.Reset() + _, _ = h.Write(sk.key[:]) + _, _ = h.Write(mu[:]) + _, _ = h.Read(rhop[:]) + + // Main rejection loop + attempt := 0 + for { + attempt++ + if attempt >= 576 { + // Depending on the mode, one try has a chance between 1/7 and 1/4 + // of succeeding. Thus it is safe to say that 576 iterations + // are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸. + panic("This should only happen 1 in 2^{128}: something is wrong.") + } + + // y = ExpandMask(ρ', key) + VecLDeriveUniformLeGamma1(&y, &rhop, yNonce) + yNonce += uint16(L) + + // Set w to A y + yh = y + yh.NTT() + for i := 0; i < K; i++ { + PolyDotHat(&w[i], &sk.A[i], &yh) + w[i].ReduceLe2Q() + w[i].InvNTT() + } + + // Decompose w into w₀ and w₁ + w.NormalizeAssumingLe2Q() + w.Decompose(&w0, &w1) + + // c = H(μ, w₁) + PolyDeriveUniformB60(&sig.c, &mu, &w1) + ch = sig.c + ch.NTT() + + // Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β. + // + // By Lemma 3 of the specification this is equivalent to checking that + // both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition + // w - c·s₂ = r₁ α + r₀ as computed by decompose(). + // See also §4.1 of the specification. + for i := 0; i < K; i++ { + w0mcs2[i].MulHat(&ch, &sk.s2h[i]) + w0mcs2[i].InvNTT() + } + w0mcs2.Sub(&w0, &w0mcs2) + w0mcs2.Normalize() + + if w0mcs2.Exceeds(common.Gamma2 - Beta) { + continue + } + + // z = y + c·s₁ + for i := 0; i < L; i++ { + sig.z[i].MulHat(&ch, &sk.s1h[i]) + sig.z[i].InvNTT() + } + sig.z.Add(&sig.z, &y) + sig.z.Normalize() + + // Ensure ‖z‖_∞ < γ₁ - β + if sig.z.Exceeds(common.Gamma1 - Beta) { + continue + } + + // Compute c·t₀ + for i := 0; i < K; i++ { + ct0[i].MulHat(&ch, &sk.t0h[i]) + ct0[i].InvNTT() + } + ct0.NormalizeAssumingLe2Q() + + // Ensure ‖c·t₀‖_∞ < γ₂. + if ct0.Exceeds(common.Gamma2) { + continue + } + + // Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0. + // Note that we're not using makeHint() in the obvious way as we + // do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂. Instead we note + // that our makeHint() is actually the same as a makeHint for a + // different decomposition: + // + // Earlier we ensured indirectly with a check that r₁ = w₁ where + // r = w - c·s₂. Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂. + // Thus MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁) + // and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁). + // As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct. + w0mcs2pct0.Add(&w0mcs2, &ct0) + w0mcs2pct0.NormalizeAssumingLe2Q() + hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1) + if hintPop > Omega { + continue + } + + break + } + + sig.Pack(signature[:]) +} + +// Computes the public key corresponding to this private key. +func (sk *PrivateKey) Public() *PublicKey { + var t0 VecK + pk := &PublicKey{ + rho: sk.rho, + A: &sk.A, + tr: &sk.tr, + } + sk.computeT0andT1(&t0, &pk.t1) + pk.t1.PackT1(pk.t1p[:]) + return pk +} + +// Equal returns whether the two public keys are equal +func (pk *PublicKey) Equal(other *PublicKey) bool { + return pk.rho == other.rho && pk.t1 == other.t1 +} + +// Equal returns whether the two private keys are equal +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) & + subtle.ConstantTimeCompare(sk.key[:], other.key[:]) & + subtle.ConstantTimeCompare(sk.tr[:], other.tr[:])) + + acc := uint32(0) + for i := 0; i < L; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s1[i][j] ^ other.s1[i][j] + } + } + for i := 0; i < K; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s2[i][j] ^ other.s2[i][j] + acc |= sk.t0[i][j] ^ other.t0[i][j] + } + } + return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1 +} diff --git a/src/circl/sign/dilithium/mode3aes/internal/dilithium_test.go b/src/circl/sign/dilithium/mode3aes/internal/dilithium_test.go new file mode 100644 index 00000000000..42ce6dbe5d1 --- /dev/null +++ b/src/circl/sign/dilithium/mode3aes/internal/dilithium_test.go @@ -0,0 +1,131 @@ +// Code generated from mode3/internal/dilithium_test.go by gen.go + +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Checks whether p is normalized. Only used in tests. +func PolyNormalized(p *common.Poly) bool { + p2 := *p + p2.Normalize() + return p2 == *p +} + +func BenchmarkSkUnpack(b *testing.B) { + var buf [PrivateKeySize]byte + var sk PrivateKey + for i := 0; i < b.N; i++ { + sk.Unpack(&buf) + } +} + +func BenchmarkPkUnpack(b *testing.B) { + var buf [PublicKeySize]byte + var pk PublicKey + for i := 0; i < b.N; i++ { + pk.Unpack(&buf) + } +} + +func BenchmarkVerify(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of verification (as in the reference + // implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + pk, sk := NewKeyFromSeed(&seed) + SignTo(sk, msg[:], sig[:]) + b.ResetTimer() + for i := 0; i < b.N; i++ { + // We should generate a new signature for every verify attempt, + // as this influences the time a little bit. This difference, however, + // is small and generating a new signature in between creates a lot + // pressure on the allocator which makes an accurate measurement hard. + Verify(pk, msg[:], sig[:]) + } +} + +func BenchmarkSign(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of signing (as in the reference implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + _, sk := NewKeyFromSeed(&seed) + b.ResetTimer() + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(msg[:], uint64(i)) + SignTo(sk, msg[:], sig[:]) + } +} + +func BenchmarkGenerateKey(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + NewKeyFromSeed(&seed) + } +} + +func BenchmarkPublicFromPrivate(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + b.StopTimer() + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + _, sk := NewKeyFromSeed(&seed) + b.StartTimer() + sk.Public() + } +} + +func TestSignThenVerifyAndPkSkPacking(t *testing.T) { + var seed [common.SeedSize]byte + var sig [SignatureSize]byte + var msg [8]byte + var pkb [PublicKeySize]byte + var skb [PrivateKeySize]byte + var pk2 PublicKey + var sk2 PrivateKey + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + if !sk.Equal(sk) { + t.Fatal() + } + for j := uint64(0); j < 10; j++ { + binary.LittleEndian.PutUint64(msg[:], j) + SignTo(sk, msg[:], sig[:]) + if !Verify(pk, msg[:], sig[:]) { + t.Fatal() + } + } + pk.Pack(&pkb) + pk2.Unpack(&pkb) + if !pk.Equal(&pk2) { + t.Fatal() + } + sk.Pack(&skb) + sk2.Unpack(&skb) + if !sk.Equal(&sk2) { + t.Fatal() + } + } +} + +func TestPublicFromPrivate(t *testing.T) { + var seed [common.SeedSize]byte + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + pk2 := sk.Public() + if !pk.Equal(pk2) { + t.Fatal() + } + } +} diff --git a/src/circl/sign/dilithium/mode3aes/internal/mat.go b/src/circl/sign/dilithium/mode3aes/internal/mat.go new file mode 100644 index 00000000000..a2411b0566d --- /dev/null +++ b/src/circl/sign/dilithium/mode3aes/internal/mat.go @@ -0,0 +1,59 @@ +// Code generated from mode3/internal/mat.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A k by l matrix of polynomials. +type Mat [K]VecL + +// Expands the given seed to a complete matrix. +// +// This function is called ExpandA in the specification. +func (m *Mat) Derive(seed *[32]byte) { + if !DeriveX4Available { + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + PolyDeriveUniform(&m[i][j], seed, (i<<8)+j) + } + } + return + } + + idx := 0 + var nonces [4]uint16 + var ps [4]*common.Poly + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + nonces[idx] = (i << 8) + j + ps[idx] = &m[i][j] + idx++ + if idx == 4 { + idx = 0 + PolyDeriveUniformX4(ps, seed, nonces) + } + } + } + if idx != 0 { + for i := idx; i < 4; i++ { + ps[i] = nil + } + PolyDeriveUniformX4(ps, seed, nonces) + } +} + +// Set p to the inner product of a and b using pointwise multiplication. +// +// Assumes a and b are in Montgomery form and their coefficients are +// pairwise sufficiently small to multiply, see Poly.MulHat(). Resulting +// coefficients are bounded by 2Lq. +func PolyDotHat(p *common.Poly, a, b *VecL) { + var t common.Poly + *p = common.Poly{} // zero p + for i := 0; i < L; i++ { + t.MulHat(&a[i], &b[i]) + p.Add(&t, p) + } +} diff --git a/src/circl/sign/dilithium/mode3aes/internal/pack.go b/src/circl/sign/dilithium/mode3aes/internal/pack.go new file mode 100644 index 00000000000..ecf3971cd20 --- /dev/null +++ b/src/circl/sign/dilithium/mode3aes/internal/pack.go @@ -0,0 +1,141 @@ +// Code generated from mode3/internal/pack.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// Writes p with norm less than or equal η into buf, which must be of +// size PolyLeqEtaSize. +// +// Assumes coefficients of p are not normalized, but in [q-η,q+η]. +func PolyPackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + buf[i] = (byte(common.Q+Eta-p[j]) | + byte(common.Q+Eta-p[j+1])<<4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + buf[i] = (byte(common.Q+Eta-p[j]) | + (byte(common.Q+Eta-p[j+1]) << 3) | + (byte(common.Q+Eta-p[j+2]) << 6)) + buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) | + (byte(common.Q+Eta-p[j+3]) << 1) | + (byte(common.Q+Eta-p[j+4]) << 4) | + (byte(common.Q+Eta-p[j+5]) << 7)) + buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) | + (byte(common.Q+Eta-p[j+6]) << 2) | + (byte(common.Q+Eta-p[j+7]) << 5)) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Sets p to the polynomial of norm less than or equal η encoded in the +// given buffer of size PolyLeqEtaSize. +// +// Output coefficients of p are not normalized, but in [q-η,q+η] provided +// buf was created using PackLeqEta. +// +// Beware, for arbitrary buf the coefficients of p might en up in +// the interval [q-2^b,q+2^b] where b is the least b with η≤2^b. +func PolyUnpackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + p[j] = common.Q + Eta - uint32(buf[i]&15) + p[j+1] = common.Q + Eta - uint32(buf[i]>>4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + p[j] = common.Q + Eta - uint32(buf[i]&7) + p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7) + p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7)) + p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7) + p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7) + p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7)) + p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7) + p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Writes v with coefficients in {0, 1} of which at most ω non-zero +// to buf, which must have length ω+k. +func (v *VecK) PackHint(buf []byte) { + // The packed hint starts with the indices of the non-zero coefficients + // For instance: + // + // (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹) + // + // Yields + // + // 56, 100, 255, 2, 23, 1 + // + // Then we pad with zeroes until we have a list of ω items: + // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0 + // + // Then we finish with a list of the switch-over-indices in this + // list between polynomials, so: + // + // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6 + + off := uint8(0) + for i := 0; i < K; i++ { + for j := uint16(0); j < common.N; j++ { + if v[i][j] != 0 { + buf[off] = uint8(j) + off++ + } + } + buf[Omega+i] = off + } + for ; off < Omega; off++ { + buf[off] = 0 + } +} + +// Sets v to the vector encoded using VecK.PackHint() +// +// Returns whether unpacking was successful. +func (v *VecK) UnpackHint(buf []byte) bool { + // A priori, there would be several reasonable ways to encode the same + // hint vector. We take care to only allow only one encoding, to ensure + // "strong unforgeability". + // + // See PackHint() source for description of the encoding. + *v = VecK{} // zero v + prevSOP := uint8(0) // previous switch-over-point + for i := 0; i < K; i++ { + SOP := buf[Omega+i] + if SOP < prevSOP || SOP > Omega { + return false // ensures switch-over-points are increasing + } + for j := prevSOP; j < SOP; j++ { + if j > prevSOP && buf[j] <= buf[j-1] { + return false // ensures indices are increasing (within a poly) + } + v[i][buf[j]] = 1 + } + prevSOP = SOP + } + for j := prevSOP; j < Omega; j++ { + if buf[j] != 0 { + return false // ensures padding indices are zero + } + } + + return true +} diff --git a/src/circl/sign/dilithium/mode3aes/internal/pack_test.go b/src/circl/sign/dilithium/mode3aes/internal/pack_test.go new file mode 100644 index 00000000000..35bea5b6db3 --- /dev/null +++ b/src/circl/sign/dilithium/mode3aes/internal/pack_test.go @@ -0,0 +1,85 @@ +// Code generated from mode3/internal/pack_test.go by gen.go + +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestPolyPackLeqEta(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [PolyLeqEtaSize]byte + + for i := uint16(0); i < 100; i++ { + // Note that DeriveUniformLeqEta sets p to the right kind of + // unnormalized vector. + PolyDeriveUniformLeqEta(&p1, &seed, i) + for j := 0; j < PolyLeqEtaSize; j++ { + if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta { + t.Fatalf("DerveUniformLeqEta out of bounds") + } + } + PolyPackLeqEta(&p1, buf[:]) + PolyUnpackLeqEta(&p2, buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT1(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p1, &seed, i) + p1.Normalize() + for j := 0; j < common.N; j++ { + p1[j] &= 0x1ff + } + p1.PackT1(buf[:]) + p2.UnpackT1(buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT0(t *testing.T) { + var p, p0, p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT0Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p, &seed, i) + p.Normalize() + p.Power2Round(&p0, &p1) + + p0.PackT0(buf[:]) + p2.UnpackT0(buf[:]) + if p0 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackLeGamma1(t *testing.T) { + var p0, p1 common.Poly + var seed [48]byte + var buf [common.PolyLeGamma1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniformLeGamma1(&p0, &seed, i) + p0.Normalize() + + p0.PackLeGamma1(buf[:]) + p1.UnpackLeGamma1(buf[:]) + if p0 != p1 { + t.Fatalf("%v != %v", p0, p1) + } + } +} diff --git a/src/circl/sign/dilithium/mode3aes/internal/params.go b/src/circl/sign/dilithium/mode3aes/internal/params.go new file mode 100644 index 00000000000..286d1f97e8c --- /dev/null +++ b/src/circl/sign/dilithium/mode3aes/internal/params.go @@ -0,0 +1,17 @@ +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +const ( + Name = "Dilithium3-AES" + UseAES = true + PublicKeySize = 1472 + PrivateKeySize = 3504 + SignatureSize = 2701 + K = 5 + L = 4 + Eta = 5 + DoubleEtaBits = 4 + Beta = 275 + Omega = 96 +) diff --git a/src/circl/sign/dilithium/mode3aes/internal/params_test.go b/src/circl/sign/dilithium/mode3aes/internal/params_test.go new file mode 100644 index 00000000000..6d5dfcee7cf --- /dev/null +++ b/src/circl/sign/dilithium/mode3aes/internal/params_test.go @@ -0,0 +1,49 @@ +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Tests specific to the current mode + +func TestVectorDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + p2 := common.Poly{ + 2, 8380412, 8380413, 8380416, 8380416, 8380415, 4, 1, 5, + 1, 8380413, 8380412, 5, 8380412, 8380416, 8380415, 8380412, + 4, 1, 1, 8380414, 8380413, 8380413, 8380416, 4, 8380415, + 4, 8380415, 8380416, 8380412, 2, 8380412, 4, 2, 8380416, + 5, 8380415, 8380412, 0, 3, 8380416, 5, 8380416, 4, 3, + 8380413, 4, 8380412, 1, 2, 8380413, 8380416, 8380413, 3, + 5, 8380413, 8380414, 8380414, 2, 0, 8380412, 4, 8380412, + 1, 8380412, 8380413, 0, 8380413, 8380413, 4, 1, 0, 8380413, + 8380415, 4, 0, 8380414, 8380413, 3, 2, 4, 8380412, 8380415, + 0, 8380414, 5, 4, 8380413, 1, 1, 8380414, 8380415, 3, 3, + 3, 3, 8380412, 0, 8380415, 3, 8380414, 8380412, 8380414, + 8380412, 2, 8380412, 8380416, 3, 8380412, 2, 0, 3, 1, 0, + 3, 8380413, 0, 8380414, 2, 2, 0, 5, 8380416, 8380414, 5, + 4, 0, 8380415, 1, 3, 5, 5, 8380416, 3, 4, 0, 0, 3, 0, 0, + 3, 5, 8380412, 8380414, 8380412, 5, 3, 8380416, 5, 5, 4, + 8380416, 1, 5, 5, 1, 5, 3, 8380414, 1, 1, 8380415, 8380415, + 2, 2, 8380414, 0, 8380413, 3, 8380414, 5, 8380413, 0, 4, + 0, 8380416, 8380416, 3, 1, 8380412, 2, 8380413, 8380413, + 0, 8380414, 4, 2, 5, 2, 0, 1, 8380412, 8380412, 8380416, + 8380416, 3, 3, 1, 3, 4, 5, 2, 5, 3, 3, 8380415, 2, 8380415, + 5, 2, 3, 4, 3, 8380414, 0, 1, 8380416, 8380415, 3, 4, 3, + 8380412, 0, 8380416, 8380412, 3, 5, 8380415, 3, 3, 8380414, + 8380416, 8380412, 5, 1, 8380413, 1, 4, 8380415, 8380413, + 8380416, 8380413, 5, 5, 0, 5, 0, 5, 2, 1, 8380414, 8380415, + 2, 8380412, 8380412, 4, + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeqEta(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} diff --git a/src/circl/sign/dilithium/mode3aes/internal/sample.go b/src/circl/sign/dilithium/mode3aes/internal/sample.go new file mode 100644 index 00000000000..8d01e8ef776 --- /dev/null +++ b/src/circl/sign/dilithium/mode3aes/internal/sample.go @@ -0,0 +1,563 @@ +// Code generated from mode3/internal/sample.go by gen.go + +package internal + +import ( + "circl/internal/sha3" + "circl/simd/keccakf1600" + + "circl/sign/dilithium/internal/common" + + "encoding/binary" +) + +// DeriveX4Available indicates whether the system supports the quick fourway +// sampling variants like PolyDeriveUniformX4. +var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES + +// For each i, sample ps[i] uniformly with coefficients of norm less than γ₁ +// using the the given seed and nonces[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformLeGamma1X4(ps [4]*common.Poly, seed *[48]byte, + nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE256 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE256 is 136 --- i.e. 17 uint64s. + for j := 0; j < 4; j++ { + state[6*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[16*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + // Each try requires 15 bits. 15 does not divide into 64, nor in 136, + // so we will have to carry some bits from a previous uint64 to the next. + var carry [4]uint32 + + // Shift is the amount of bits in the carry. + var shift [4]uint + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 17 uint64s of each + // of the four SHAKE256 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := 0; i < 17; i++ { + var t [4]uint32 + tCount := 3 + + // Get the next three or four 20 bit numbers. + qw := state[i*4+j] + qwl := (qw << shift[j]) | uint64(carry[j]) + t[0] = uint32(qwl & 0xfffff) + t[1] = uint32((qwl >> 20) & 0xfffff) + t[2] = uint32((qwl >> 40) & 0xfffff) + + if shift[j] == 16 { + t[3] = uint32(qw >> 44) + shift[j] = 0 + carry[j] = 0 + tCount = 4 + } else { + shift[j] += 4 + carry[j] = uint32(qw >> (64 - shift[j])) + } + + // Check if they're coefficients. + for k := 0; k < tCount; k++ { + if t[k] <= 2*common.Gamma1-2 { + ps[j][idx[j]] = common.Q + common.Gamma1 - 1 - t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + + done = false + } + } +} + +// For each i, sample ps[i] uniformly from the given seed and nonces[i]. +// ps[i] may be nil and is ignored in that case. +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 4; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE128 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s. + for j := 0; j < 4; j++ { + state[4*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[20*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each + // of the four SHAKE128 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + for i := 0; i < 7; i++ { + var t [8]uint32 + t[0] = uint32(state[i*3*4+j] & 0x7fffff) + t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff) + t[2] = uint32((state[i*3*4+j] >> 48) | + ((state[(i*3+1)*4+j] & 0x7f) << 16)) + t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff) + t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff) + t[5] = uint32((state[(i*3+1)*4+j] >> 56) | + ((state[(i*3+2)*4+j] & 0x7fff) << 8)) + t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff) + t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff) + + for k := 0; k < 8; k++ { + if t[k] < common.Q { + ps[j][idx[j]] = t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + done = false + } + } +} + +// Sample p uniformly from the given seed and nonce. +// +// p will be normalized. +func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) { + var i, length int + var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks + + if UseAES { + length = 12 * 16 + } else { + length = 168 + } + + sample := func() { + // Note that 3 divides into 168 and 12*16, so we use up buf completely. + for j := 0; j < length && i < common.N; j += 3 { + t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0x7fffff + + // We use rejection sampling + if t < common.Q { + p[i] = t + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample p uniformly with coefficients of norm less than or equal η, +// using the given seed and nonce. +// +// p will not be normalized, but will have coefficients in [q-η,q+η]. +func PolyDeriveUniformLeqEta(p *common.Poly, seed *[32]byte, nonce uint16) { + // Assumes 2 < η < 8. + var i, length int + var buf [11 * 16]byte // fits 168B SHAKE-128 rate and 11 16B AES blocks + + if UseAES { + length = 11 * 16 + } else { + length = 168 + } + + sample := func() { + // We use rejection sampling + for j := 0; j < length && i < common.N; j++ { + var t1, t2 uint32 + if Eta <= 3 { // branch is eliminated by compiler + t1 = uint32(buf[j]) & 7 + t2 = uint32(buf[j]) >> 5 + } else { + t1 = uint32(buf[j]) & 15 + t2 = uint32(buf[j]) >> 4 + } + if t1 <= 2*Eta { + p[i] = common.Q + Eta - t1 + i++ + } + if t2 <= 2*Eta && i < common.N { + p[i] = common.Q + Eta - t2 + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + + // 168 is SHAKE-128 rate + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample v[i] uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce+i +// +// v[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func VecLDeriveUniformLeGamma1(v *VecL, seed *[48]byte, nonce uint16) { + if !DeriveX4Available { + for i := 0; i < L; i++ { + PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i)) + } + return + } + + var ps [4]*common.Poly + nonces := [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3} + for i := 0; i < L && i < 4; i++ { + ps[i] = &v[i] + } + + // PolyDeriveUniformLeGamma1X4 is slower than, but not twice as slow as, + // PolyDeriveUniformLeGamma. + PolyDeriveUniformLeGamma1X4(ps, seed, nonces) + if L == 5 { + PolyDeriveUniformLeGamma1(&v[L-1], seed, nonce+4) + } else if L > 5 || L < 2 { + panic("VecLDeriveUniformLeGamma1 does not support that L") + } +} + +// Sample p uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce. +// +// p will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[48]byte, nonce uint16) { + // Assumes γ₁ is less than 2²⁰. + var length, i int + + // Fits 10 16B AES blocks, which aligns nicely as we take 5 bytes at + // a time. The SHAKE-256 rate, however, is 136. As 136 is 1 modulo 5, + // we are left with 1 byte after the first block, which we include in the + // next block. So we need 4 bytes leeway in our buffer. The total 160 + // fits easily in 160. + var buf [160]byte + + sample := func() { + // We use rejection sampling + for j := 0; j < length-4 && i < common.N; j += 5 { + t1 := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0xfffff + t2 := ((uint32(buf[j+2]) >> 4) | (uint32(buf[j+3]) << 4) | + (uint32(buf[j+4]) << 12)) + + if t1 <= 2*common.Gamma1-2 { + p[i] = common.Q + common.Gamma1 - 1 - t1 + i++ + } + if t2 <= 2*common.Gamma1-2 && i < common.N { + p[i] = common.Q + common.Gamma1 - 1 - t2 + i++ + } + } + } + if UseAES { + length = 160 + h := common.NewAesStream256(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:]) + sample() + } + } else { + length = 136 + var iv [48 + 2]byte // 48 byte seed + uint16 nonce + bufOffset := 0 // where to put the next block + + h := sha3.NewShake256() + copy(iv[:48], seed[:]) + iv[48] = uint8(nonce) + iv[49] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[bufOffset : bufOffset+136]) + sample() + + bufOffset++ + if bufOffset == 5 { + bufOffset = 0 + } + + // Move remaining bytes at the end to the start. + for j := 0; j < bufOffset; j++ { + buf[j] = buf[135+j] + } + } + } +} + +// For each i, sample ps[i] uniformly with 60 non-zero coefficients in {q-1,1} +// using the the given seed and w1[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will be normalized. +// +// Can only be called when DeriveX4Available is true. +// +// This function is currently not used (yet). +func PolyDeriveUniformB60X4(ps [4]*common.Poly, seed *[48]byte, + w1 [4]*VecK) { + // Pack the w1s + var w1Packed [4][common.PolyLe16Size * K]byte + for j := 0; j < 4; j++ { + if ps[j] != nil { + w1[j].PackLe16(w1Packed[j][:]) + } + } + + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the start of the packed w₁s + offset := 0 // offset into w1Packed[j] + for i := 6; i < 17; i++ { + for j := 0; j < 4; j++ { + state[i*4+j] = binary.LittleEndian.Uint64(w1Packed[j][offset : offset+8]) + } + offset += 8 + } + + offset -= 8 + + // Absorb the remainder of the packed w₁s. +PermuteLoop: + for { + perm.Permute() + + for i := 0; i < 17; i++ { + offset += 8 + if offset == len(w1Packed[0]) { + // SHAKE256 domain separator and padding + for j := 0; j < 4; j++ { + state[i*4+j] ^= 0x1f + state[16*4+j] ^= 0x80 << 56 + } + perm.Permute() + + break PermuteLoop + } + + for j := 0; j < 4; j++ { + state[i*4+j] ^= binary.LittleEndian.Uint64( + w1Packed[j][offset : offset+8]) + } + } + } + + var signs [4]uint64 + var idx [4]uint16 // indices into ps + + for j := 0; j < 4; j++ { + if ps[j] != nil { + signs[j] = state[j] + *ps[j] = common.Poly{} // zero ps[j] + idx[j] = common.N - 60 + } else { + idx[j] = common.N // mark as completed + } + } + + stateOffset := 1 + for { + done := true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := stateOffset; i < 17; i++ { + var bs [8]byte + binary.LittleEndian.PutUint64(bs[:], state[4*i+j]) + for k := 0; k < 8; k++ { + b := uint16(bs[k]) + + if b > idx[j] { + continue + } + + ps[j][idx[j]] = ps[j][b] + ps[j][b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1))) + signs[j] >>= 1 + + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + + done = false + } + + if done { + break + } + + perm.Permute() + stateOffset = 0 + } +} + +// Samples p uniformly with 60 non-zero coefficients in {q-1,1}. +// +// The polynomial p will be normalized. +func PolyDeriveUniformB60(p *common.Poly, seed *[48]byte, w1 *VecK) { + var w1Packed [common.PolyLe16Size * K]byte + var buf [136]byte // SHAKE-256 rate is 136 + + w1.PackLe16(w1Packed[:]) + + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Write(w1Packed[:]) + _, _ = h.Read(buf[:]) + + // Essentially we generate a sequence of 60 ones or minus ones, + // prepend 196 zeroes and shuffle the concatenation using the + // usual algorithm (Fisher--Yates.) + signs := binary.LittleEndian.Uint64(buf[:]) + bufOff := 8 // offset into buf + + *p = common.Poly{} // zero p + for i := uint16(common.N - 60); i < common.N; i++ { + var b uint16 + + // Find location of where to move the new coefficient to using + // rejection sampling. + for { + if bufOff >= 136 { + _, _ = h.Read(buf[:]) + bufOff = 0 + } + + b = uint16(buf[bufOff]) + bufOff++ + + if b <= i { + break + } + } + + p[i] = p[b] + p[b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1))) + signs >>= 1 + } +} diff --git a/src/circl/sign/dilithium/mode3aes/internal/sample_test.go b/src/circl/sign/dilithium/mode3aes/internal/sample_test.go new file mode 100644 index 00000000000..f4f0a51c1c9 --- /dev/null +++ b/src/circl/sign/dilithium/mode3aes/internal/sample_test.go @@ -0,0 +1,407 @@ +// Code generated from mode3/internal/sample_test.go by gen.go + +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestVectorDeriveUniform(t *testing.T) { + var p, p2 common.Poly + var seed [32]byte + if UseAES { + p2 = common.Poly{ + 6724291, 310295, 6949524, 4464039, 1482136, 2522903, + 7025059, 3006320, 7286364, 7516512, 3361305, 1955529, + 4765954, 1725325, 6933066, 4299100, 6625173, 4272792, + 583034, 4971409, 2259140, 7715362, 3975394, 2341624, + 5481174, 8150082, 365246, 5491939, 1083120, 7517301, + 3104783, 2475292, 184149, 6425226, 4591622, 5964030, + 4729604, 5471092, 1828227, 1082044, 2516245, 1692580, + 3274844, 5443294, 7256740, 4989638, 3191250, 7479519, + 5124211, 5603858, 1230692, 2513454, 2828034, 4254312, + 1512596, 5245430, 5517392, 2814840, 932545, 6826733, + 3511094, 4075348, 3233981, 7268882, 2913733, 4870249, + 4123492, 8124406, 4016949, 5478752, 2750895, 603525, + 5724798, 3985430, 3483012, 6434230, 3136996, 8297976, + 4107616, 7307748, 6962904, 7544473, 1193110, 3448595, + 4814773, 5607932, 8221314, 1054046, 1541208, 1866050, + 8227412, 2925778, 5293953, 2065416, 4972769, 3616283, + 7990594, 1105530, 7121836, 1170740, 7417431, 633146, + 253820, 7235019, 3539504, 6807707, 451390, 5481526, + 2859902, 1063061, 4579730, 7126652, 7033767, 4294814, + 1414604, 7620048, 1953268, 8304556, 1156814, 1182881, + 5311519, 3057534, 5277666, 682843, 2070398, 2874278, + 4859533, 6376664, 6694074, 1590242, 2620706, 8331066, + 5643845, 5037538, 2891516, 7004879, 3754327, 5031296, + 5463118, 2420870, 8116529, 5517696, 7435129, 3873963, + 710407, 713806, 175647, 4274571, 2655021, 7319503, + 3027243, 7129679, 4213435, 2429323, 4643873, 4568526, + 649664, 1720514, 6497260, 2683517, 7672754, 7105190, + 3148405, 5898369, 5667677, 8050874, 1587139, 7315260, + 4337416, 2202680, 2338714, 557467, 6752058, 2469794, + 485071, 1617604, 3590498, 2151466, 2005823, 7727956, + 7776292, 6783433, 6787146, 1732833, 3596857, 7436284, + 4483349, 4970142, 4472608, 6478342, 1236215, 5695744, + 2280717, 2889355, 3233946, 5187812, 978685, 5177364, + 2922353, 4824807, 5302883, 6739803, 8092453, 5883903, + 816553, 6041174, 8317591, 1459178, 5332455, 1835058, + 1368601, 2820950, 3479224, 2589540, 7992934, 3421045, + 4657128, 8292902, 4153567, 3553988, 7830320, 6722913, + 2555309, 4149801, 8328975, 1560545, 7757473, 3106458, + 4310856, 7135453, 3481032, 652626, 1841361, 8126828, + 6250018, 300536, 7380070, 8174419, 1418793, 6208185, + 3906256, 6679016, 1605701, 3561489, 5819724, 5746996, + 8044214, 7087187, 7102330, 4962927, 4253983, 7108567, + 4119736, 6584065, 441634, 6941656, + } + } else { + p2 = common.Poly{ + 2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052, + 3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357, + 6066350, 8126097, 1179080, 4787182, 6552182, 6713644, + 1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938, + 1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431, + 1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545, + 7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071, + 105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855, + 5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453, + 5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453, + 3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874, + 5614778, 2248550, 1756499, 8280764, 8263880, 7600081, + 5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562, + 7483939, 4938664, 6863397, 5126354, 5218129, 6236086, + 4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737, + 1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595, + 6830029, 1548850, 6593138, 6849097, 1518037, 2859442, + 7772265, 7325153, 3281191, 7856131, 4995056, 4684325, + 1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778, + 7973479, 3171829, 5624626, 3540123, 7150120, 8313283, + 3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342, + 7501562, 5826142, 2709813, 8245473, 2369045, 2782257, + 5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983, + 5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375, + 267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500, + 2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008, + 8258986, 2183134, 2302072, 4674924, 4306056, 7465311, + 6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700, + 2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533, + 255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625, + 6997719, 6260212, 6186962, 6636650, 7836834, 7998017, + 2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598, + 4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947, + 6195178, 5552390, 6804584, 6305468, 5731980, 6095195, + 3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054, + 4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780, + 3740517, 5224226, 3547288, 2083124, 4699398, 3654239, + 5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706, + 4352830, + } + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniform(&p, &seed, 30000) + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniform(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniform(&p, &seed, uint16(i)) + if !PolyNormalized(&p) { + t.Fatal() + } + } +} + +func TestDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeqEta(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-Eta || p[j] > common.Q+Eta { + t.Fatal() + } + } + } +} + +func TestDeriveUniformLeGamma1(t *testing.T) { + var p common.Poly + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-common.Gamma1 || p[j] > common.Q+common.Gamma1 { + t.Fatal() + } + } + } +} + +func TestVectorDeriveUniformLeGamma1(t *testing.T) { + var p, p2 common.Poly + var seed [48]byte + if UseAES { + p2 = common.Poly{ + 90940, 8133770, 8210940, 8218464, 8362467, 431142, 98024, + 320453, 7892373, 144162, 495313, 7910122, 308198, 8024421, + 8313699, 8323445, 8242093, 7946588, 418979, 427179, 353562, + 20972, 455962, 213062, 361787, 8141790, 8321931, 7885366, + 88645, 181202, 8094142, 8303121, 8059515, 7919812, 191865, + 7910073, 7896561, 8096830, 7899355, 8338900, 72693, 236799, + 8183042, 347570, 8153528, 8364233, 8077851, 8312277, 104682, + 8037310, 8356199, 7994081, 240369, 70229, 8108858, 8175836, + 466639, 50909, 339919, 8029663, 341659, 154398, 64345, + 97101, 212245, 8285367, 521225, 325882, 296235, 8110929, + 8015814, 7953234, 158409, 329908, 8331330, 449258, 167701, + 8197796, 8228247, 7940020, 1985, 304704, 475316, 8037482, + 8250449, 304557, 8216567, 432266, 213295, 8162216, 381001, + 7995314, 7988689, 128534, 245586, 67041, 8232744, 398441, + 223116, 443612, 149856, 222852, 158723, 54746, 171906, + 163070, 353915, 8263276, 8016812, 8229081, 31827, 489715, + 450171, 8069106, 53220, 7932381, 7955335, 8197363, 201044, + 8306733, 446376, 8211025, 7889271, 8070595, 495514, 8158685, + 7524, 7973394, 247673, 4293, 184924, 457334, 138349, 8123964, + 284179, 8255307, 8068216, 8291492, 243759, 8060601, 20962, + 8058389, 420953, 8305974, 455136, 8218139, 7121, 147703, + 7951253, 394376, 8127066, 365861, 8062390, 8138732, 366555, + 8280514, 221, 395861, 7968769, 7977119, 8098083, 343056, + 8190769, 223361, 163270, 203059, 109219, 8228600, 8127695, + 321016, 295979, 8201961, 49891, 8335504, 8190386, 8190984, + 8278654, 336364, 7878013, 7922436, 7974101, 8075534, 8200852, + 8333820, 415982, 8089662, 149553, 7946740, 474102, 7937116, + 8026845, 356056, 191053, 86928, 8218644, 8375040, 8029184, + 8025675, 8193350, 295360, 7905768, 487174, 8362961, 386108, + 282213, 8373318, 50167, 8238992, 7911505, 493459, 8335164, + 8079327, 250697, 263154, 221028, 40778, 87515, 8372585, + 504728, 7980935, 8307600, 298972, 427523, 93352, 89915, + 391490, 80320, 7975008, 336136, 7949815, 8048682, 8332244, + 8204778, 8177783, 7910684, 7925292, 518641, 59663, 53608, + 222225, 463772, 8022091, 8173722, 8291385, 472741, 8105898, + 7943299, 267137, 7957660, 371874, 409084, 203750, 477334, + 83412, 111278, 120444, + } + } else { + p2 = common.Poly{ + 338083, 7978692, 8044913, 373628, 427855, 79725, 91018, + 349821, 501552, 7955127, 8316400, 290708, 216142, 8199666, + 8040144, 109426, 8177916, 8200218, 8125680, 358131, 160961, + 497383, 25361, 156297, 8033745, 7897189, 48397, 498732, + 464556, 7862704, 8308667, 236080, 91240, 8328377, 326190, + 509979, 8313264, 8106493, 8210965, 8328036, 172602, 8108765, + 8192963, 8361660, 8026473, 7932022, 322006, 8305874, 8254440, + 7866474, 373371, 8023413, 8221878, 486124, 36080, 8324512, + 8042056, 7984472, 8048111, 7910387, 8205382, 8259636, 188609, + 8316587, 59306, 119803, 8067108, 8155455, 8153450, 7983908, + 8222256, 21521, 114297, 8069037, 151621, 8014482, 8052856, + 376107, 8004652, 175001, 8079461, 8351123, 8021484, 144547, + 7908116, 8278100, 8136941, 142399, 8026843, 8081852, 124334, + 242796, 266768, 7919478, 7954016, 28927, 8329064, 514031, + 423911, 27907, 8142788, 8078298, 273978, 382723, 8148646, + 186476, 8030712, 8067268, 356250, 145817, 60045, 122764, + 56856, 8225416, 136437, 199652, 8343127, 8109765, 7936848, + 446966, 8351681, 288663, 409663, 512988, 8350788, 8191864, + 8366223, 281267, 7921696, 8213978, 442484, 67457, 8030602, + 238514, 230458, 8301866, 8359700, 150320, 143893, 461735, + 225443, 8027502, 151113, 365244, 7911438, 82498, 405398, + 8207009, 8108255, 367485, 514660, 8294055, 8168958, 127725, + 402955, 8051625, 7859029, 7980052, 321819, 7949587, 125778, + 8287078, 131972, 499609, 256795, 8180323, 8269393, 5878, + 8145473, 8238676, 383855, 415547, 424071, 241989, 8165743, + 8207329, 149608, 8315331, 7901850, 8114275, 360650, 516061, + 255090, 8277977, 270877, 8125200, 479248, 7991711, 8028595, + 73426, 8215429, 208217, 153872, 429336, 229856, 461204, + 236682, 7930158, 8298847, 228327, 8009399, 8111520, 345025, + 386495, 93454, 8336429, 8161305, 7980811, 286795, 162808, + 224476, 7972825, 85118, 287488, 8029791, 119071, 371, 518524, + 473496, 451205, 127000, 19233, 211519, 2442, 7950959, 481888, + 8041598, 8281176, 437202, 7912610, 8080153, 8237500, 7926828, + 8009421, 204880, 62495, 8192310, 8314388, 98616, 182368, + 323894, 59901, 481049, 8139275, 7872144, 254106, 376257, + 93339, 301342, 366536, 438920, 84773, 461471, 8125755, + 7930085, 405116, + } + } + for i := 0; i < 48; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeGamma1(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniformB60(t *testing.T) { + var p common.Poly + var w1 VecK + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformB60(&p, &seed, &w1) + nonzero := 0 + for j := 0; j < common.N; j++ { + if p[j] != 0 { + if p[j] != 1 && p[j] != common.Q-1 { + t.Fatal() + } + nonzero++ + } + } + if nonzero != 60 { + t.Fatal() + } + } +} + +func TestDeriveUniformX4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [32]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, + nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniform(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatal() + } + } +} + +func TestDeriveUniformB60X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + var w1s [4]VecK + for j := 0; j < 4; j++ { + for k := 0; k < K; k++ { + for i := 0; i < common.N; i++ { + w1s[j][k][i] = uint32(j+k*4+i*4*K) & 15 + } + } + } + PolyDeriveUniformB60X4( + [4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, + [4]*VecK{&w1s[0], &w1s[1], &w1s[2], &w1s[3]}, + ) + for j := 0; j < 4; j++ { + PolyDeriveUniformB60(&p, &seed, &w1s[j]) + if ps[j] != p { + t.Fatalf("%v %v", ps[j], p) + } + } +} + +func TestDeriveUniformLeGamma1X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatalf("%d\n%v\n%v", i, p, ps[i]) + } + } +} + +func BenchmarkPolyDeriveUniformB60(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60(&p, &seed, &w1) + } +} + +func BenchmarkPolyDeriveUniformB60X4(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60X4( + [4]*common.Poly{&p, &p, &p, &p}, + &seed, + [4]*VecK{&w1, &w1, &w1, &w1}, + ) + } +} + +func BenchmarkPolyDeriveUniform(b *testing.B) { + var seed [32]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniform(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformX4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [32]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) { + var seed [48]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1X4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [48]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} diff --git a/src/circl/sign/dilithium/mode3aes/internal/vec.go b/src/circl/sign/dilithium/mode3aes/internal/vec.go new file mode 100644 index 00000000000..a20a8b0224e --- /dev/null +++ b/src/circl/sign/dilithium/mode3aes/internal/vec.go @@ -0,0 +1,281 @@ +// Code generated from mode3/internal/vec.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A vector of L polynomials. +type VecL [L]common.Poly + +// A vector of K polynomials. +type VecK [K]common.Poly + +// Normalize the polynomials in this vector. +func (v *VecL) Normalize() { + for i := 0; i < L; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecL) NormalizeAssumingLe2Q() { + for i := 0; i < L; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecL) Add(w, u *VecL) { + for i := 0; i < L; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecL) NTT() { + for i := 0; i < L; i++ { + v[i].NTT() + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecL) Exceeds(bound uint32) bool { + for i := 0; i < L; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Decompose(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecL) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeqEta(). +func (v *VecL) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sequentially packs each polynomial using Poly.PackLeGamma1(). +func (v *VecL) PackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].PackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeGamma1(). +func (v *VecL) UnpackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].UnpackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Normalize the polynomials in this vector. +func (v *VecK) Normalize() { + for i := 0; i < K; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecK) NormalizeAssumingLe2Q() { + for i := 0; i < K; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecK) Add(w, u *VecK) { + for i := 0; i < K; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecK) Exceeds(bound uint32) bool { + for i := 0; i < K; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Decompose(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sets v to the hint vector for v0 the modified low bits and v1 +// the unmodified high bits --- see makeHint(). +// +// Returns the number of ones in the hint vector. +func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) { + for i := 0; i < K; i++ { + pop += v[i].MakeHint(&v0[i], &v1[i]) + } + return +} + +// Computes corrections to the high bits of the polynomials in the vector +// w using the hints in h and sets v to the corrected high bits. Returns v. +// See useHint(). +func (v *VecK) UseHint(q, hint *VecK) *VecK { + for i := 0; i < K; i++ { + v[i].UseHint(&q[i], &hint[i]) + } + return v +} + +// Sequentially packs each polynomial using Poly.PackT1(). +func (v *VecK) PackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sets v to the vector packed into buf by PackT1(). +func (v *VecK) UnpackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sequentially packs each polynomial using Poly.PackT0(). +func (v *VecK) PackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sets v to the vector packed into buf by PackT0(). +func (v *VecK) UnpackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecK) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecK.PackLeqEta(). +func (v *VecK) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecK) NTT() { + for i := 0; i < K; i++ { + v[i].NTT() + } +} + +// Sequentially packs each polynomial using Poly.PackLe16(). +func (v *VecK) PackLe16(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackLe16(buf[offset:]) + offset += common.PolyLe16Size + } +} + +// Sets v to a - b. +// +// Warning: assumes coefficients of the polynomials of b are less than 2q. +func (v *VecK) Sub(a, b *VecK) { + for i := 0; i < K; i++ { + v[i].Sub(&a[i], &b[i]) + } +} + +// Sets v to 2ᵈ w without reducing. +func (v *VecK) MulBy2toD(w *VecK) { + for i := 0; i < K; i++ { + v[i].MulBy2toD(&w[i]) + } +} + +// Applies InvNTT componentwise. See Poly.InvNTT() for details. +func (v *VecK) InvNTT() { + for i := 0; i < K; i++ { + v[i].InvNTT() + } +} + +// Applies Poly.ReduceLe2Q() componentwise. +func (v *VecK) ReduceLe2Q() { + for i := 0; i < K; i++ { + v[i].ReduceLe2Q() + } +} diff --git a/src/circl/sign/dilithium/mode4.go b/src/circl/sign/dilithium/mode4.go new file mode 100644 index 00000000000..f71550011bd --- /dev/null +++ b/src/circl/sign/dilithium/mode4.go @@ -0,0 +1,95 @@ +// Code generated from mode.templ.go. DO NOT EDIT. + +package dilithium + +import ( + "fmt" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode4" +) + +// implMode4 implements the mode.Mode interface for Dilithium4. +type implMode4 struct{} + +// Mode4 is Dilithium in mode "Dilithium4". +var Mode4 Mode = &implMode4{} + +func (m *implMode4) GenerateKey(rand io.Reader) ( + PublicKey, PrivateKey, error) { + return mode4.GenerateKey(rand) +} + +func (m *implMode4) NewKeyFromExpandedSeed(seed *[96]byte) (PublicKey, + PrivateKey) { + return mode4.NewKeyFromExpandedSeed(seed) +} + +func (m *implMode4) NewKeyFromSeed(seed []byte) (PublicKey, + PrivateKey) { + if len(seed) != common.SeedSize { + panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) + } + seedBuf := [common.SeedSize]byte{} + copy(seedBuf[:], seed) + return mode4.NewKeyFromSeed(&seedBuf) +} + +func (m *implMode4) Sign(sk PrivateKey, msg []byte) []byte { + isk := sk.(*mode4.PrivateKey) + ret := [mode4.SignatureSize]byte{} + mode4.SignTo(isk, msg, ret[:]) + return ret[:] +} + +func (m *implMode4) Verify(pk PublicKey, msg []byte, signature []byte) bool { + ipk := pk.(*mode4.PublicKey) + return mode4.Verify(ipk, msg, signature) +} + +func (m *implMode4) PublicKeyFromBytes(data []byte) PublicKey { + var ret mode4.PublicKey + if len(data) != mode4.PublicKeySize { + panic("packed public key must be of mode4.PublicKeySize bytes") + } + var buf [mode4.PublicKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode4) PrivateKeyFromBytes(data []byte) PrivateKey { + var ret mode4.PrivateKey + if len(data) != mode4.PrivateKeySize { + panic("packed public key must be of mode4.PrivateKeySize bytes") + } + var buf [mode4.PrivateKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode4) SeedSize() int { + return common.SeedSize +} + +func (m *implMode4) PublicKeySize() int { + return mode4.PublicKeySize +} + +func (m *implMode4) PrivateKeySize() int { + return mode4.PrivateKeySize +} + +func (m *implMode4) SignatureSize() int { + return mode4.SignatureSize +} + +func (m *implMode4) Name() string { + return "Dilithium4" +} + +func init() { + modes["Dilithium4"] = Mode4 +} diff --git a/src/circl/sign/dilithium/mode4/dilithium.go b/src/circl/sign/dilithium/mode4/dilithium.go new file mode 100644 index 00000000000..b880ad09411 --- /dev/null +++ b/src/circl/sign/dilithium/mode4/dilithium.go @@ -0,0 +1,191 @@ +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// mode4 implements the CRYSTALS-Dilithium signature scheme Dilithium4 +// as submitted to round2 of the NIST PQC competition and described in +// +// https://pq-crystals.org/dilithium/data/dilithium-specification-round2.pdf +package mode4 + +import ( + "crypto" + "errors" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode4/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + SeedSize = common.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a signature + SignatureSize = internal.SignatureSize +) + +// PublicKey is the type of Dilithium4 public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of Dilithium4 private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + pk, sk, err := internal.GenerateKey(rand) + return (*PublicKey)(pk), (*PrivateKey)(sk), err +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromExpandedSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// SignTo signs the given message and writes the signature into signature. +// It will panic if signature is not of length at least SignatureSize. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + internal.SignTo( + (*internal.PrivateKey)(sk), + msg, + signature, + ) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + return internal.Verify( + (*internal.PublicKey)(pk), + msg, + signature, + ) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Packs the public key. +func (pk *PublicKey) Bytes() []byte { + var buf [PublicKeySize]byte + pk.Pack(&buf) + return buf[:] +} + +// Packs the private key. +func (sk *PrivateKey) Bytes() []byte { + var buf [PrivateKeySize]byte + sk.Pack(&buf) + return buf[:] +} + +// Packs the public key. +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + return pk.Bytes(), nil +} + +// Packs the private key. +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + return sk.Bytes(), nil +} + +// Unpacks the public key from data. +func (pk *PublicKey) UnmarshalBinary(data []byte) error { + if len(data) != PublicKeySize { + return errors.New("packed public key must be of mode4.PublicKeySize bytes") + } + var buf [PublicKeySize]byte + copy(buf[:], data) + pk.Unpack(&buf) + return nil +} + +// Unpacks the private key from data. +func (sk *PrivateKey) UnmarshalBinary(data []byte) error { + if len(data) != PrivateKeySize { + return errors.New("packed private key must be of mode4.PrivateKeySize bytes") + } + var buf [PrivateKeySize]byte + copy(buf[:], data) + sk.Unpack(&buf) + return nil +} + +// Sign signs the given message. +// +// opts.HashFunc() must return zero, which can be achieved by passing +// crypto.Hash(0) for opts. rand is ignored. Will only return an error +// if opts.HashFunc() is non-zero. +// +// This function is used to make PrivateKey implement the crypto.Signer +// interface. The package-level SignTo function might be more convenient +// to use. +func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( + signature []byte, err error) { + var sig [SignatureSize]byte + + if opts.HashFunc() != crypto.Hash(0) { + return nil, errors.New("dilithium: cannot sign hashed message") + } + + SignTo(sk, msg, sig[:]) + return sig[:], nil +} + +// Computes the public key corresponding to this private key. +// +// Returns a *PublicKey. The type crypto.PublicKey is used to make +// PrivateKey implement the crypto.Signer interface. +func (sk *PrivateKey) Public() crypto.PublicKey { + return (*PublicKey)((*internal.PrivateKey)(sk).Public()) +} + +// Equal returns whether the two private keys equal. +func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { + castOther, ok := other.(*PrivateKey) + if !ok { + return false + } + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) +} + +// Equal returns whether the two public keys equal. +func (pk *PublicKey) Equal(other crypto.PublicKey) bool { + castOther, ok := other.(*PublicKey) + if !ok { + return false + } + return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) +} diff --git a/src/circl/sign/dilithium/mode4/internal/dilithium.go b/src/circl/sign/dilithium/mode4/internal/dilithium.go new file mode 100644 index 00000000000..fb0eaaf1963 --- /dev/null +++ b/src/circl/sign/dilithium/mode4/internal/dilithium.go @@ -0,0 +1,446 @@ +// Code generated from mode3/internal/dilithium.go by gen.go + +package internal + +import ( + cryptoRand "crypto/rand" + "crypto/subtle" + "io" + + "circl/internal/sha3" + "circl/sign/dilithium/internal/common" +) + +const ( + // Size of a packed polynomial of norm ≤η. + // (Note that the formula is not valid in general.) + PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8 +) + +// PublicKey is the type of Dilithium public keys. +type PublicKey struct { + rho [32]byte + t1 VecK + + // Cached values + t1p [common.PolyT1Size * K]byte + A *Mat + tr *[48]byte +} + +// PrivateKey is the type of Dilithium private keys. +type PrivateKey struct { + rho [32]byte + key [32]byte + s1 VecL + s2 VecK + t0 VecK + tr [48]byte + + // Cached values + A Mat // ExpandA(ρ) + s1h VecL // NTT(s₁) + s2h VecK // NTT(s₂) + t0h VecK // NTT(t₀) +} + +type unpackedSignature struct { + z VecL + hint VecK + c common.Poly +} + +// Packs the signature into buf. +func (sig *unpackedSignature) Pack(buf []byte) { + sig.z.PackLeGamma1(buf[:]) + sig.hint.PackHint(buf[L*common.PolyLeGamma1Size:]) + sig.c.PackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) +} + +// Sets sig to the signature encoded in the buffer. +// +// Returns whether buf contains a properly packed signature. +func (sig *unpackedSignature) Unpack(buf []byte) bool { + if len(buf) < SignatureSize { + return false + } + sig.z.UnpackLeGamma1(buf[:]) + if sig.z.Exceeds(common.Gamma1 - Beta) { + return false + } + if !sig.hint.UnpackHint(buf[L*common.PolyLeGamma1Size:]) { + return false + } + sig.c.UnpackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) + return true +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + copy(buf[:32], pk.rho[:]) + copy(buf[32:], pk.t1p[:]) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + copy(pk.rho[:], buf[:32]) + copy(pk.t1p[:], buf[32:]) + + pk.t1.UnpackT1(pk.t1p[:]) + pk.A = new(Mat) + pk.A.Derive(&pk.rho) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + pk.tr = new([48]byte) + h := sha3.NewShake256() + _, _ = h.Write(buf[:]) + _, _ = h.Read(pk.tr[:]) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + copy(buf[:32], sk.rho[:]) + copy(buf[32:64], sk.key[:]) + copy(buf[64:112], sk.tr[:]) + offset := 112 + sk.s1.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.PackT0(buf[offset:]) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + copy(sk.rho[:], buf[:32]) + copy(sk.key[:], buf[32:64]) + copy(sk.tr[:], buf[64:112]) + offset := 112 + sk.s1.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.UnpackT0(buf[offset:]) + + // Cached values + sk.A.Derive(&sk.rho) + sk.t0h = sk.t0 + sk.t0h.NTT() + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() +} + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [32]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(&seed) + return pk, sk, nil +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + var pk PublicKey + var sk PrivateKey + var sSeed [32]byte + + copy(pk.rho[:], seed[:32]) + copy(sSeed[:], seed[32:64]) + copy(sk.key[:], seed[64:]) + copy(sk.rho[:], pk.rho[:]) + + sk.A.Derive(&pk.rho) + + for i := uint16(0); i < L; i++ { + PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i) + } + + for i := uint16(0); i < K; i++ { + PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L) + } + + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() + + sk.computeT0andT1(&sk.t0, &pk.t1) + + sk.t0h = sk.t0 + sk.t0h.NTT() + + // Complete public key far enough to be packed + pk.t1.PackT1(pk.t1p[:]) + pk.A = &sk.A + + // Finish private key + var packedPk [PublicKeySize]byte + pk.Pack(&packedPk) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + h := sha3.NewShake256() + _, _ = h.Write(packedPk[:]) + _, _ = h.Read(sk.tr[:]) + + // Finish cache of public key + pk.tr = &sk.tr + + return &pk, &sk +} + +// Computes t0 and t1 from sk.s1h, sk.s2 and sk.A. +func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) { + var t VecK + + // Set t to A s₁ + s₂ + for i := 0; i < K; i++ { + PolyDotHat(&t[i], &sk.A[i], &sk.s1h) + t[i].ReduceLe2Q() + t[i].InvNTT() + } + t.Add(&t, &sk.s2) + t.Normalize() + + // Compute t₀, t₁ = Power2Round(t) + t.Power2Round(t0, t1) +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) { + var buf [96]byte + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Read(buf[:]) + return NewKeyFromExpandedSeed(&buf) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + var sig unpackedSignature + var mu [48]byte + var zh VecL + var Az, Az2dct1, w1 VecK + var ch, cp common.Poly + + // Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β + // and ensured that there at most ω ones in pk.hint. + if !sig.Unpack(signature) { + return false + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(pk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // Compute Az + zh = sig.z + zh.NTT() + + for i := 0; i < K; i++ { + PolyDotHat(&Az[i], &pk.A[i], &zh) + } + + // Next, we compute Az - 2ᵈ·c·t₁. + // Note that the coefficients of t₁ are bounded by 256 = 2⁹, + // so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q, + // which is small enough for NTT(). + Az2dct1.MulBy2toD(&pk.t1) + Az2dct1.NTT() + ch = sig.c + ch.NTT() + for i := 0; i < K; i++ { + Az2dct1[i].MulHat(&Az2dct1[i], &ch) + } + Az2dct1.Sub(&Az, &Az2dct1) + Az2dct1.ReduceLe2Q() + Az2dct1.InvNTT() + Az2dct1.NormalizeAssumingLe2Q() + + // UseHint(pk.hint, Az - 2ᵈ·c·t₁) + // = UseHint(pk.hint, w - c·s₂ + c·t₀) + // = UseHint(pk.hint, r + c·t₀) + // = r₁ = w₁. + w1.UseHint(&Az2dct1, &sig.hint) + + // c' = H(μ, w₁) + PolyDeriveUniformB60(&cp, &mu, &w1) + return sig.c == cp +} + +// SignTo signs the given message and writes the signature into signature. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + var mu, rhop [48]byte + var y, yh VecL + var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK + var ch common.Poly + var yNonce uint16 + var sig unpackedSignature + + if len(signature) < SignatureSize { + panic("Signature does not fit in that byteslice") + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(sk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // ρ' = CRH(μ ‖ key) + h.Reset() + _, _ = h.Write(sk.key[:]) + _, _ = h.Write(mu[:]) + _, _ = h.Read(rhop[:]) + + // Main rejection loop + attempt := 0 + for { + attempt++ + if attempt >= 576 { + // Depending on the mode, one try has a chance between 1/7 and 1/4 + // of succeeding. Thus it is safe to say that 576 iterations + // are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸. + panic("This should only happen 1 in 2^{128}: something is wrong.") + } + + // y = ExpandMask(ρ', key) + VecLDeriveUniformLeGamma1(&y, &rhop, yNonce) + yNonce += uint16(L) + + // Set w to A y + yh = y + yh.NTT() + for i := 0; i < K; i++ { + PolyDotHat(&w[i], &sk.A[i], &yh) + w[i].ReduceLe2Q() + w[i].InvNTT() + } + + // Decompose w into w₀ and w₁ + w.NormalizeAssumingLe2Q() + w.Decompose(&w0, &w1) + + // c = H(μ, w₁) + PolyDeriveUniformB60(&sig.c, &mu, &w1) + ch = sig.c + ch.NTT() + + // Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β. + // + // By Lemma 3 of the specification this is equivalent to checking that + // both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition + // w - c·s₂ = r₁ α + r₀ as computed by decompose(). + // See also §4.1 of the specification. + for i := 0; i < K; i++ { + w0mcs2[i].MulHat(&ch, &sk.s2h[i]) + w0mcs2[i].InvNTT() + } + w0mcs2.Sub(&w0, &w0mcs2) + w0mcs2.Normalize() + + if w0mcs2.Exceeds(common.Gamma2 - Beta) { + continue + } + + // z = y + c·s₁ + for i := 0; i < L; i++ { + sig.z[i].MulHat(&ch, &sk.s1h[i]) + sig.z[i].InvNTT() + } + sig.z.Add(&sig.z, &y) + sig.z.Normalize() + + // Ensure ‖z‖_∞ < γ₁ - β + if sig.z.Exceeds(common.Gamma1 - Beta) { + continue + } + + // Compute c·t₀ + for i := 0; i < K; i++ { + ct0[i].MulHat(&ch, &sk.t0h[i]) + ct0[i].InvNTT() + } + ct0.NormalizeAssumingLe2Q() + + // Ensure ‖c·t₀‖_∞ < γ₂. + if ct0.Exceeds(common.Gamma2) { + continue + } + + // Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0. + // Note that we're not using makeHint() in the obvious way as we + // do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂. Instead we note + // that our makeHint() is actually the same as a makeHint for a + // different decomposition: + // + // Earlier we ensured indirectly with a check that r₁ = w₁ where + // r = w - c·s₂. Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂. + // Thus MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁) + // and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁). + // As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct. + w0mcs2pct0.Add(&w0mcs2, &ct0) + w0mcs2pct0.NormalizeAssumingLe2Q() + hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1) + if hintPop > Omega { + continue + } + + break + } + + sig.Pack(signature[:]) +} + +// Computes the public key corresponding to this private key. +func (sk *PrivateKey) Public() *PublicKey { + var t0 VecK + pk := &PublicKey{ + rho: sk.rho, + A: &sk.A, + tr: &sk.tr, + } + sk.computeT0andT1(&t0, &pk.t1) + pk.t1.PackT1(pk.t1p[:]) + return pk +} + +// Equal returns whether the two public keys are equal +func (pk *PublicKey) Equal(other *PublicKey) bool { + return pk.rho == other.rho && pk.t1 == other.t1 +} + +// Equal returns whether the two private keys are equal +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) & + subtle.ConstantTimeCompare(sk.key[:], other.key[:]) & + subtle.ConstantTimeCompare(sk.tr[:], other.tr[:])) + + acc := uint32(0) + for i := 0; i < L; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s1[i][j] ^ other.s1[i][j] + } + } + for i := 0; i < K; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s2[i][j] ^ other.s2[i][j] + acc |= sk.t0[i][j] ^ other.t0[i][j] + } + } + return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1 +} diff --git a/src/circl/sign/dilithium/mode4/internal/dilithium_test.go b/src/circl/sign/dilithium/mode4/internal/dilithium_test.go new file mode 100644 index 00000000000..42ce6dbe5d1 --- /dev/null +++ b/src/circl/sign/dilithium/mode4/internal/dilithium_test.go @@ -0,0 +1,131 @@ +// Code generated from mode3/internal/dilithium_test.go by gen.go + +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Checks whether p is normalized. Only used in tests. +func PolyNormalized(p *common.Poly) bool { + p2 := *p + p2.Normalize() + return p2 == *p +} + +func BenchmarkSkUnpack(b *testing.B) { + var buf [PrivateKeySize]byte + var sk PrivateKey + for i := 0; i < b.N; i++ { + sk.Unpack(&buf) + } +} + +func BenchmarkPkUnpack(b *testing.B) { + var buf [PublicKeySize]byte + var pk PublicKey + for i := 0; i < b.N; i++ { + pk.Unpack(&buf) + } +} + +func BenchmarkVerify(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of verification (as in the reference + // implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + pk, sk := NewKeyFromSeed(&seed) + SignTo(sk, msg[:], sig[:]) + b.ResetTimer() + for i := 0; i < b.N; i++ { + // We should generate a new signature for every verify attempt, + // as this influences the time a little bit. This difference, however, + // is small and generating a new signature in between creates a lot + // pressure on the allocator which makes an accurate measurement hard. + Verify(pk, msg[:], sig[:]) + } +} + +func BenchmarkSign(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of signing (as in the reference implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + _, sk := NewKeyFromSeed(&seed) + b.ResetTimer() + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(msg[:], uint64(i)) + SignTo(sk, msg[:], sig[:]) + } +} + +func BenchmarkGenerateKey(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + NewKeyFromSeed(&seed) + } +} + +func BenchmarkPublicFromPrivate(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + b.StopTimer() + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + _, sk := NewKeyFromSeed(&seed) + b.StartTimer() + sk.Public() + } +} + +func TestSignThenVerifyAndPkSkPacking(t *testing.T) { + var seed [common.SeedSize]byte + var sig [SignatureSize]byte + var msg [8]byte + var pkb [PublicKeySize]byte + var skb [PrivateKeySize]byte + var pk2 PublicKey + var sk2 PrivateKey + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + if !sk.Equal(sk) { + t.Fatal() + } + for j := uint64(0); j < 10; j++ { + binary.LittleEndian.PutUint64(msg[:], j) + SignTo(sk, msg[:], sig[:]) + if !Verify(pk, msg[:], sig[:]) { + t.Fatal() + } + } + pk.Pack(&pkb) + pk2.Unpack(&pkb) + if !pk.Equal(&pk2) { + t.Fatal() + } + sk.Pack(&skb) + sk2.Unpack(&skb) + if !sk.Equal(&sk2) { + t.Fatal() + } + } +} + +func TestPublicFromPrivate(t *testing.T) { + var seed [common.SeedSize]byte + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + pk2 := sk.Public() + if !pk.Equal(pk2) { + t.Fatal() + } + } +} diff --git a/src/circl/sign/dilithium/mode4/internal/mat.go b/src/circl/sign/dilithium/mode4/internal/mat.go new file mode 100644 index 00000000000..a2411b0566d --- /dev/null +++ b/src/circl/sign/dilithium/mode4/internal/mat.go @@ -0,0 +1,59 @@ +// Code generated from mode3/internal/mat.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A k by l matrix of polynomials. +type Mat [K]VecL + +// Expands the given seed to a complete matrix. +// +// This function is called ExpandA in the specification. +func (m *Mat) Derive(seed *[32]byte) { + if !DeriveX4Available { + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + PolyDeriveUniform(&m[i][j], seed, (i<<8)+j) + } + } + return + } + + idx := 0 + var nonces [4]uint16 + var ps [4]*common.Poly + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + nonces[idx] = (i << 8) + j + ps[idx] = &m[i][j] + idx++ + if idx == 4 { + idx = 0 + PolyDeriveUniformX4(ps, seed, nonces) + } + } + } + if idx != 0 { + for i := idx; i < 4; i++ { + ps[i] = nil + } + PolyDeriveUniformX4(ps, seed, nonces) + } +} + +// Set p to the inner product of a and b using pointwise multiplication. +// +// Assumes a and b are in Montgomery form and their coefficients are +// pairwise sufficiently small to multiply, see Poly.MulHat(). Resulting +// coefficients are bounded by 2Lq. +func PolyDotHat(p *common.Poly, a, b *VecL) { + var t common.Poly + *p = common.Poly{} // zero p + for i := 0; i < L; i++ { + t.MulHat(&a[i], &b[i]) + p.Add(&t, p) + } +} diff --git a/src/circl/sign/dilithium/mode4/internal/pack.go b/src/circl/sign/dilithium/mode4/internal/pack.go new file mode 100644 index 00000000000..ecf3971cd20 --- /dev/null +++ b/src/circl/sign/dilithium/mode4/internal/pack.go @@ -0,0 +1,141 @@ +// Code generated from mode3/internal/pack.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// Writes p with norm less than or equal η into buf, which must be of +// size PolyLeqEtaSize. +// +// Assumes coefficients of p are not normalized, but in [q-η,q+η]. +func PolyPackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + buf[i] = (byte(common.Q+Eta-p[j]) | + byte(common.Q+Eta-p[j+1])<<4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + buf[i] = (byte(common.Q+Eta-p[j]) | + (byte(common.Q+Eta-p[j+1]) << 3) | + (byte(common.Q+Eta-p[j+2]) << 6)) + buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) | + (byte(common.Q+Eta-p[j+3]) << 1) | + (byte(common.Q+Eta-p[j+4]) << 4) | + (byte(common.Q+Eta-p[j+5]) << 7)) + buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) | + (byte(common.Q+Eta-p[j+6]) << 2) | + (byte(common.Q+Eta-p[j+7]) << 5)) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Sets p to the polynomial of norm less than or equal η encoded in the +// given buffer of size PolyLeqEtaSize. +// +// Output coefficients of p are not normalized, but in [q-η,q+η] provided +// buf was created using PackLeqEta. +// +// Beware, for arbitrary buf the coefficients of p might en up in +// the interval [q-2^b,q+2^b] where b is the least b with η≤2^b. +func PolyUnpackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + p[j] = common.Q + Eta - uint32(buf[i]&15) + p[j+1] = common.Q + Eta - uint32(buf[i]>>4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + p[j] = common.Q + Eta - uint32(buf[i]&7) + p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7) + p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7)) + p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7) + p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7) + p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7)) + p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7) + p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Writes v with coefficients in {0, 1} of which at most ω non-zero +// to buf, which must have length ω+k. +func (v *VecK) PackHint(buf []byte) { + // The packed hint starts with the indices of the non-zero coefficients + // For instance: + // + // (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹) + // + // Yields + // + // 56, 100, 255, 2, 23, 1 + // + // Then we pad with zeroes until we have a list of ω items: + // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0 + // + // Then we finish with a list of the switch-over-indices in this + // list between polynomials, so: + // + // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6 + + off := uint8(0) + for i := 0; i < K; i++ { + for j := uint16(0); j < common.N; j++ { + if v[i][j] != 0 { + buf[off] = uint8(j) + off++ + } + } + buf[Omega+i] = off + } + for ; off < Omega; off++ { + buf[off] = 0 + } +} + +// Sets v to the vector encoded using VecK.PackHint() +// +// Returns whether unpacking was successful. +func (v *VecK) UnpackHint(buf []byte) bool { + // A priori, there would be several reasonable ways to encode the same + // hint vector. We take care to only allow only one encoding, to ensure + // "strong unforgeability". + // + // See PackHint() source for description of the encoding. + *v = VecK{} // zero v + prevSOP := uint8(0) // previous switch-over-point + for i := 0; i < K; i++ { + SOP := buf[Omega+i] + if SOP < prevSOP || SOP > Omega { + return false // ensures switch-over-points are increasing + } + for j := prevSOP; j < SOP; j++ { + if j > prevSOP && buf[j] <= buf[j-1] { + return false // ensures indices are increasing (within a poly) + } + v[i][buf[j]] = 1 + } + prevSOP = SOP + } + for j := prevSOP; j < Omega; j++ { + if buf[j] != 0 { + return false // ensures padding indices are zero + } + } + + return true +} diff --git a/src/circl/sign/dilithium/mode4/internal/pack_test.go b/src/circl/sign/dilithium/mode4/internal/pack_test.go new file mode 100644 index 00000000000..35bea5b6db3 --- /dev/null +++ b/src/circl/sign/dilithium/mode4/internal/pack_test.go @@ -0,0 +1,85 @@ +// Code generated from mode3/internal/pack_test.go by gen.go + +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestPolyPackLeqEta(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [PolyLeqEtaSize]byte + + for i := uint16(0); i < 100; i++ { + // Note that DeriveUniformLeqEta sets p to the right kind of + // unnormalized vector. + PolyDeriveUniformLeqEta(&p1, &seed, i) + for j := 0; j < PolyLeqEtaSize; j++ { + if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta { + t.Fatalf("DerveUniformLeqEta out of bounds") + } + } + PolyPackLeqEta(&p1, buf[:]) + PolyUnpackLeqEta(&p2, buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT1(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p1, &seed, i) + p1.Normalize() + for j := 0; j < common.N; j++ { + p1[j] &= 0x1ff + } + p1.PackT1(buf[:]) + p2.UnpackT1(buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT0(t *testing.T) { + var p, p0, p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT0Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p, &seed, i) + p.Normalize() + p.Power2Round(&p0, &p1) + + p0.PackT0(buf[:]) + p2.UnpackT0(buf[:]) + if p0 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackLeGamma1(t *testing.T) { + var p0, p1 common.Poly + var seed [48]byte + var buf [common.PolyLeGamma1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniformLeGamma1(&p0, &seed, i) + p0.Normalize() + + p0.PackLeGamma1(buf[:]) + p1.UnpackLeGamma1(buf[:]) + if p0 != p1 { + t.Fatalf("%v != %v", p0, p1) + } + } +} diff --git a/src/circl/sign/dilithium/mode4/internal/params.go b/src/circl/sign/dilithium/mode4/internal/params.go new file mode 100644 index 00000000000..98101670df2 --- /dev/null +++ b/src/circl/sign/dilithium/mode4/internal/params.go @@ -0,0 +1,17 @@ +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +const ( + Name = "Dilithium4" + UseAES = false + PublicKeySize = 1760 + PrivateKeySize = 3856 + SignatureSize = 3366 + K = 6 + L = 5 + Eta = 3 + DoubleEtaBits = 3 + Beta = 175 + Omega = 120 +) diff --git a/src/circl/sign/dilithium/mode4/internal/params_test.go b/src/circl/sign/dilithium/mode4/internal/params_test.go new file mode 100644 index 00000000000..689a56685f0 --- /dev/null +++ b/src/circl/sign/dilithium/mode4/internal/params_test.go @@ -0,0 +1,49 @@ +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Tests specific to the current mode + +func TestVectorDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + p2 := common.Poly{ + 8380416, 0, 8380415, 1, 8380416, 8380415, 1, 8380415, + 8380416, 3, 8380416, 8380414, 3, 8380415, 2, 3, 1, 1, + 8380414, 1, 0, 2, 8380414, 8380415, 8380415, 8380416, + 8380414, 3, 8380416, 8380414, 8380416, 8380414, 1, 3, 2, + 0, 8380416, 3, 8380415, 8380415, 2, 3, 8380416, 0, 2, 1, + 1, 8380414, 8380414, 3, 1, 0, 8380416, 2, 1, 8380415, 3, + 2, 8380414, 3, 3, 8380414, 1, 8380414, 1, 2, 8380414, 2, + 8380415, 8380415, 3, 1, 0, 8380415, 8380414, 8380415, 3, + 8380416, 8380416, 8380414, 2, 8380416, 8380414, 0, 0, 3, + 8380414, 8380415, 2, 8380416, 8380414, 0, 3, 2, 1, 8380414, + 0, 1, 0, 8380416, 2, 2, 0, 8380414, 0, 2, 8380414, 8380416, + 1, 8380415, 1, 8380416, 3, 8380414, 0, 2, 8380415, 3, + 8380415, 8380414, 8380416, 2, 3, 1, 0, 0, 2, 1, 3, 0, 1, + 3, 3, 8380415, 0, 8380416, 3, 1, 2, 8380415, 0, 3, 1, + 8380416, 8380414, 2, 8380414, 8380414, 0, 8380415, 8380416, + 8380415, 1, 8380416, 3, 8380414, 1, 1, 3, 8380414, 3, 2, + 2, 0, 3, 8380416, 2, 8380416, 0, 8380415, 8380416, 8380416, + 3, 8380414, 0, 0, 8380415, 8380414, 8380416, 2, 1, 8380416, + 2, 2, 8380414, 1, 1, 2, 1, 8380415, 8380416, 1, 1, 0, 1, + 8380416, 0, 8380416, 2, 8380415, 1, 0, 1, 8380414, 3, + 8380414, 8380415, 8380416, 0, 0, 1, 2, 8380415, 8380414, + 0, 8380415, 0, 2, 0, 8380416, 1, 8380415, 1, 8380416, 0, + 0, 8380414, 3, 0, 3, 0, 2, 3, 0, 3, 8380416, 8380415, + 8380415, 8380416, 2, 3, 0, 3, 2, 8380415, 3, 2, 8380416, + 8380415, 3, 1, 0, 8380414, 2, 8380416, 3, + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeqEta(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} diff --git a/src/circl/sign/dilithium/mode4/internal/sample.go b/src/circl/sign/dilithium/mode4/internal/sample.go new file mode 100644 index 00000000000..8d01e8ef776 --- /dev/null +++ b/src/circl/sign/dilithium/mode4/internal/sample.go @@ -0,0 +1,563 @@ +// Code generated from mode3/internal/sample.go by gen.go + +package internal + +import ( + "circl/internal/sha3" + "circl/simd/keccakf1600" + + "circl/sign/dilithium/internal/common" + + "encoding/binary" +) + +// DeriveX4Available indicates whether the system supports the quick fourway +// sampling variants like PolyDeriveUniformX4. +var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES + +// For each i, sample ps[i] uniformly with coefficients of norm less than γ₁ +// using the the given seed and nonces[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformLeGamma1X4(ps [4]*common.Poly, seed *[48]byte, + nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE256 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE256 is 136 --- i.e. 17 uint64s. + for j := 0; j < 4; j++ { + state[6*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[16*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + // Each try requires 15 bits. 15 does not divide into 64, nor in 136, + // so we will have to carry some bits from a previous uint64 to the next. + var carry [4]uint32 + + // Shift is the amount of bits in the carry. + var shift [4]uint + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 17 uint64s of each + // of the four SHAKE256 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := 0; i < 17; i++ { + var t [4]uint32 + tCount := 3 + + // Get the next three or four 20 bit numbers. + qw := state[i*4+j] + qwl := (qw << shift[j]) | uint64(carry[j]) + t[0] = uint32(qwl & 0xfffff) + t[1] = uint32((qwl >> 20) & 0xfffff) + t[2] = uint32((qwl >> 40) & 0xfffff) + + if shift[j] == 16 { + t[3] = uint32(qw >> 44) + shift[j] = 0 + carry[j] = 0 + tCount = 4 + } else { + shift[j] += 4 + carry[j] = uint32(qw >> (64 - shift[j])) + } + + // Check if they're coefficients. + for k := 0; k < tCount; k++ { + if t[k] <= 2*common.Gamma1-2 { + ps[j][idx[j]] = common.Q + common.Gamma1 - 1 - t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + + done = false + } + } +} + +// For each i, sample ps[i] uniformly from the given seed and nonces[i]. +// ps[i] may be nil and is ignored in that case. +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 4; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE128 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s. + for j := 0; j < 4; j++ { + state[4*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[20*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each + // of the four SHAKE128 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + for i := 0; i < 7; i++ { + var t [8]uint32 + t[0] = uint32(state[i*3*4+j] & 0x7fffff) + t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff) + t[2] = uint32((state[i*3*4+j] >> 48) | + ((state[(i*3+1)*4+j] & 0x7f) << 16)) + t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff) + t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff) + t[5] = uint32((state[(i*3+1)*4+j] >> 56) | + ((state[(i*3+2)*4+j] & 0x7fff) << 8)) + t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff) + t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff) + + for k := 0; k < 8; k++ { + if t[k] < common.Q { + ps[j][idx[j]] = t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + done = false + } + } +} + +// Sample p uniformly from the given seed and nonce. +// +// p will be normalized. +func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) { + var i, length int + var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks + + if UseAES { + length = 12 * 16 + } else { + length = 168 + } + + sample := func() { + // Note that 3 divides into 168 and 12*16, so we use up buf completely. + for j := 0; j < length && i < common.N; j += 3 { + t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0x7fffff + + // We use rejection sampling + if t < common.Q { + p[i] = t + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample p uniformly with coefficients of norm less than or equal η, +// using the given seed and nonce. +// +// p will not be normalized, but will have coefficients in [q-η,q+η]. +func PolyDeriveUniformLeqEta(p *common.Poly, seed *[32]byte, nonce uint16) { + // Assumes 2 < η < 8. + var i, length int + var buf [11 * 16]byte // fits 168B SHAKE-128 rate and 11 16B AES blocks + + if UseAES { + length = 11 * 16 + } else { + length = 168 + } + + sample := func() { + // We use rejection sampling + for j := 0; j < length && i < common.N; j++ { + var t1, t2 uint32 + if Eta <= 3 { // branch is eliminated by compiler + t1 = uint32(buf[j]) & 7 + t2 = uint32(buf[j]) >> 5 + } else { + t1 = uint32(buf[j]) & 15 + t2 = uint32(buf[j]) >> 4 + } + if t1 <= 2*Eta { + p[i] = common.Q + Eta - t1 + i++ + } + if t2 <= 2*Eta && i < common.N { + p[i] = common.Q + Eta - t2 + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + + // 168 is SHAKE-128 rate + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample v[i] uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce+i +// +// v[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func VecLDeriveUniformLeGamma1(v *VecL, seed *[48]byte, nonce uint16) { + if !DeriveX4Available { + for i := 0; i < L; i++ { + PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i)) + } + return + } + + var ps [4]*common.Poly + nonces := [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3} + for i := 0; i < L && i < 4; i++ { + ps[i] = &v[i] + } + + // PolyDeriveUniformLeGamma1X4 is slower than, but not twice as slow as, + // PolyDeriveUniformLeGamma. + PolyDeriveUniformLeGamma1X4(ps, seed, nonces) + if L == 5 { + PolyDeriveUniformLeGamma1(&v[L-1], seed, nonce+4) + } else if L > 5 || L < 2 { + panic("VecLDeriveUniformLeGamma1 does not support that L") + } +} + +// Sample p uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce. +// +// p will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[48]byte, nonce uint16) { + // Assumes γ₁ is less than 2²⁰. + var length, i int + + // Fits 10 16B AES blocks, which aligns nicely as we take 5 bytes at + // a time. The SHAKE-256 rate, however, is 136. As 136 is 1 modulo 5, + // we are left with 1 byte after the first block, which we include in the + // next block. So we need 4 bytes leeway in our buffer. The total 160 + // fits easily in 160. + var buf [160]byte + + sample := func() { + // We use rejection sampling + for j := 0; j < length-4 && i < common.N; j += 5 { + t1 := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0xfffff + t2 := ((uint32(buf[j+2]) >> 4) | (uint32(buf[j+3]) << 4) | + (uint32(buf[j+4]) << 12)) + + if t1 <= 2*common.Gamma1-2 { + p[i] = common.Q + common.Gamma1 - 1 - t1 + i++ + } + if t2 <= 2*common.Gamma1-2 && i < common.N { + p[i] = common.Q + common.Gamma1 - 1 - t2 + i++ + } + } + } + if UseAES { + length = 160 + h := common.NewAesStream256(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:]) + sample() + } + } else { + length = 136 + var iv [48 + 2]byte // 48 byte seed + uint16 nonce + bufOffset := 0 // where to put the next block + + h := sha3.NewShake256() + copy(iv[:48], seed[:]) + iv[48] = uint8(nonce) + iv[49] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[bufOffset : bufOffset+136]) + sample() + + bufOffset++ + if bufOffset == 5 { + bufOffset = 0 + } + + // Move remaining bytes at the end to the start. + for j := 0; j < bufOffset; j++ { + buf[j] = buf[135+j] + } + } + } +} + +// For each i, sample ps[i] uniformly with 60 non-zero coefficients in {q-1,1} +// using the the given seed and w1[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will be normalized. +// +// Can only be called when DeriveX4Available is true. +// +// This function is currently not used (yet). +func PolyDeriveUniformB60X4(ps [4]*common.Poly, seed *[48]byte, + w1 [4]*VecK) { + // Pack the w1s + var w1Packed [4][common.PolyLe16Size * K]byte + for j := 0; j < 4; j++ { + if ps[j] != nil { + w1[j].PackLe16(w1Packed[j][:]) + } + } + + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the start of the packed w₁s + offset := 0 // offset into w1Packed[j] + for i := 6; i < 17; i++ { + for j := 0; j < 4; j++ { + state[i*4+j] = binary.LittleEndian.Uint64(w1Packed[j][offset : offset+8]) + } + offset += 8 + } + + offset -= 8 + + // Absorb the remainder of the packed w₁s. +PermuteLoop: + for { + perm.Permute() + + for i := 0; i < 17; i++ { + offset += 8 + if offset == len(w1Packed[0]) { + // SHAKE256 domain separator and padding + for j := 0; j < 4; j++ { + state[i*4+j] ^= 0x1f + state[16*4+j] ^= 0x80 << 56 + } + perm.Permute() + + break PermuteLoop + } + + for j := 0; j < 4; j++ { + state[i*4+j] ^= binary.LittleEndian.Uint64( + w1Packed[j][offset : offset+8]) + } + } + } + + var signs [4]uint64 + var idx [4]uint16 // indices into ps + + for j := 0; j < 4; j++ { + if ps[j] != nil { + signs[j] = state[j] + *ps[j] = common.Poly{} // zero ps[j] + idx[j] = common.N - 60 + } else { + idx[j] = common.N // mark as completed + } + } + + stateOffset := 1 + for { + done := true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := stateOffset; i < 17; i++ { + var bs [8]byte + binary.LittleEndian.PutUint64(bs[:], state[4*i+j]) + for k := 0; k < 8; k++ { + b := uint16(bs[k]) + + if b > idx[j] { + continue + } + + ps[j][idx[j]] = ps[j][b] + ps[j][b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1))) + signs[j] >>= 1 + + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + + done = false + } + + if done { + break + } + + perm.Permute() + stateOffset = 0 + } +} + +// Samples p uniformly with 60 non-zero coefficients in {q-1,1}. +// +// The polynomial p will be normalized. +func PolyDeriveUniformB60(p *common.Poly, seed *[48]byte, w1 *VecK) { + var w1Packed [common.PolyLe16Size * K]byte + var buf [136]byte // SHAKE-256 rate is 136 + + w1.PackLe16(w1Packed[:]) + + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Write(w1Packed[:]) + _, _ = h.Read(buf[:]) + + // Essentially we generate a sequence of 60 ones or minus ones, + // prepend 196 zeroes and shuffle the concatenation using the + // usual algorithm (Fisher--Yates.) + signs := binary.LittleEndian.Uint64(buf[:]) + bufOff := 8 // offset into buf + + *p = common.Poly{} // zero p + for i := uint16(common.N - 60); i < common.N; i++ { + var b uint16 + + // Find location of where to move the new coefficient to using + // rejection sampling. + for { + if bufOff >= 136 { + _, _ = h.Read(buf[:]) + bufOff = 0 + } + + b = uint16(buf[bufOff]) + bufOff++ + + if b <= i { + break + } + } + + p[i] = p[b] + p[b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1))) + signs >>= 1 + } +} diff --git a/src/circl/sign/dilithium/mode4/internal/sample_test.go b/src/circl/sign/dilithium/mode4/internal/sample_test.go new file mode 100644 index 00000000000..f4f0a51c1c9 --- /dev/null +++ b/src/circl/sign/dilithium/mode4/internal/sample_test.go @@ -0,0 +1,407 @@ +// Code generated from mode3/internal/sample_test.go by gen.go + +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestVectorDeriveUniform(t *testing.T) { + var p, p2 common.Poly + var seed [32]byte + if UseAES { + p2 = common.Poly{ + 6724291, 310295, 6949524, 4464039, 1482136, 2522903, + 7025059, 3006320, 7286364, 7516512, 3361305, 1955529, + 4765954, 1725325, 6933066, 4299100, 6625173, 4272792, + 583034, 4971409, 2259140, 7715362, 3975394, 2341624, + 5481174, 8150082, 365246, 5491939, 1083120, 7517301, + 3104783, 2475292, 184149, 6425226, 4591622, 5964030, + 4729604, 5471092, 1828227, 1082044, 2516245, 1692580, + 3274844, 5443294, 7256740, 4989638, 3191250, 7479519, + 5124211, 5603858, 1230692, 2513454, 2828034, 4254312, + 1512596, 5245430, 5517392, 2814840, 932545, 6826733, + 3511094, 4075348, 3233981, 7268882, 2913733, 4870249, + 4123492, 8124406, 4016949, 5478752, 2750895, 603525, + 5724798, 3985430, 3483012, 6434230, 3136996, 8297976, + 4107616, 7307748, 6962904, 7544473, 1193110, 3448595, + 4814773, 5607932, 8221314, 1054046, 1541208, 1866050, + 8227412, 2925778, 5293953, 2065416, 4972769, 3616283, + 7990594, 1105530, 7121836, 1170740, 7417431, 633146, + 253820, 7235019, 3539504, 6807707, 451390, 5481526, + 2859902, 1063061, 4579730, 7126652, 7033767, 4294814, + 1414604, 7620048, 1953268, 8304556, 1156814, 1182881, + 5311519, 3057534, 5277666, 682843, 2070398, 2874278, + 4859533, 6376664, 6694074, 1590242, 2620706, 8331066, + 5643845, 5037538, 2891516, 7004879, 3754327, 5031296, + 5463118, 2420870, 8116529, 5517696, 7435129, 3873963, + 710407, 713806, 175647, 4274571, 2655021, 7319503, + 3027243, 7129679, 4213435, 2429323, 4643873, 4568526, + 649664, 1720514, 6497260, 2683517, 7672754, 7105190, + 3148405, 5898369, 5667677, 8050874, 1587139, 7315260, + 4337416, 2202680, 2338714, 557467, 6752058, 2469794, + 485071, 1617604, 3590498, 2151466, 2005823, 7727956, + 7776292, 6783433, 6787146, 1732833, 3596857, 7436284, + 4483349, 4970142, 4472608, 6478342, 1236215, 5695744, + 2280717, 2889355, 3233946, 5187812, 978685, 5177364, + 2922353, 4824807, 5302883, 6739803, 8092453, 5883903, + 816553, 6041174, 8317591, 1459178, 5332455, 1835058, + 1368601, 2820950, 3479224, 2589540, 7992934, 3421045, + 4657128, 8292902, 4153567, 3553988, 7830320, 6722913, + 2555309, 4149801, 8328975, 1560545, 7757473, 3106458, + 4310856, 7135453, 3481032, 652626, 1841361, 8126828, + 6250018, 300536, 7380070, 8174419, 1418793, 6208185, + 3906256, 6679016, 1605701, 3561489, 5819724, 5746996, + 8044214, 7087187, 7102330, 4962927, 4253983, 7108567, + 4119736, 6584065, 441634, 6941656, + } + } else { + p2 = common.Poly{ + 2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052, + 3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357, + 6066350, 8126097, 1179080, 4787182, 6552182, 6713644, + 1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938, + 1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431, + 1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545, + 7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071, + 105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855, + 5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453, + 5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453, + 3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874, + 5614778, 2248550, 1756499, 8280764, 8263880, 7600081, + 5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562, + 7483939, 4938664, 6863397, 5126354, 5218129, 6236086, + 4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737, + 1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595, + 6830029, 1548850, 6593138, 6849097, 1518037, 2859442, + 7772265, 7325153, 3281191, 7856131, 4995056, 4684325, + 1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778, + 7973479, 3171829, 5624626, 3540123, 7150120, 8313283, + 3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342, + 7501562, 5826142, 2709813, 8245473, 2369045, 2782257, + 5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983, + 5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375, + 267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500, + 2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008, + 8258986, 2183134, 2302072, 4674924, 4306056, 7465311, + 6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700, + 2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533, + 255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625, + 6997719, 6260212, 6186962, 6636650, 7836834, 7998017, + 2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598, + 4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947, + 6195178, 5552390, 6804584, 6305468, 5731980, 6095195, + 3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054, + 4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780, + 3740517, 5224226, 3547288, 2083124, 4699398, 3654239, + 5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706, + 4352830, + } + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniform(&p, &seed, 30000) + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniform(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniform(&p, &seed, uint16(i)) + if !PolyNormalized(&p) { + t.Fatal() + } + } +} + +func TestDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeqEta(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-Eta || p[j] > common.Q+Eta { + t.Fatal() + } + } + } +} + +func TestDeriveUniformLeGamma1(t *testing.T) { + var p common.Poly + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-common.Gamma1 || p[j] > common.Q+common.Gamma1 { + t.Fatal() + } + } + } +} + +func TestVectorDeriveUniformLeGamma1(t *testing.T) { + var p, p2 common.Poly + var seed [48]byte + if UseAES { + p2 = common.Poly{ + 90940, 8133770, 8210940, 8218464, 8362467, 431142, 98024, + 320453, 7892373, 144162, 495313, 7910122, 308198, 8024421, + 8313699, 8323445, 8242093, 7946588, 418979, 427179, 353562, + 20972, 455962, 213062, 361787, 8141790, 8321931, 7885366, + 88645, 181202, 8094142, 8303121, 8059515, 7919812, 191865, + 7910073, 7896561, 8096830, 7899355, 8338900, 72693, 236799, + 8183042, 347570, 8153528, 8364233, 8077851, 8312277, 104682, + 8037310, 8356199, 7994081, 240369, 70229, 8108858, 8175836, + 466639, 50909, 339919, 8029663, 341659, 154398, 64345, + 97101, 212245, 8285367, 521225, 325882, 296235, 8110929, + 8015814, 7953234, 158409, 329908, 8331330, 449258, 167701, + 8197796, 8228247, 7940020, 1985, 304704, 475316, 8037482, + 8250449, 304557, 8216567, 432266, 213295, 8162216, 381001, + 7995314, 7988689, 128534, 245586, 67041, 8232744, 398441, + 223116, 443612, 149856, 222852, 158723, 54746, 171906, + 163070, 353915, 8263276, 8016812, 8229081, 31827, 489715, + 450171, 8069106, 53220, 7932381, 7955335, 8197363, 201044, + 8306733, 446376, 8211025, 7889271, 8070595, 495514, 8158685, + 7524, 7973394, 247673, 4293, 184924, 457334, 138349, 8123964, + 284179, 8255307, 8068216, 8291492, 243759, 8060601, 20962, + 8058389, 420953, 8305974, 455136, 8218139, 7121, 147703, + 7951253, 394376, 8127066, 365861, 8062390, 8138732, 366555, + 8280514, 221, 395861, 7968769, 7977119, 8098083, 343056, + 8190769, 223361, 163270, 203059, 109219, 8228600, 8127695, + 321016, 295979, 8201961, 49891, 8335504, 8190386, 8190984, + 8278654, 336364, 7878013, 7922436, 7974101, 8075534, 8200852, + 8333820, 415982, 8089662, 149553, 7946740, 474102, 7937116, + 8026845, 356056, 191053, 86928, 8218644, 8375040, 8029184, + 8025675, 8193350, 295360, 7905768, 487174, 8362961, 386108, + 282213, 8373318, 50167, 8238992, 7911505, 493459, 8335164, + 8079327, 250697, 263154, 221028, 40778, 87515, 8372585, + 504728, 7980935, 8307600, 298972, 427523, 93352, 89915, + 391490, 80320, 7975008, 336136, 7949815, 8048682, 8332244, + 8204778, 8177783, 7910684, 7925292, 518641, 59663, 53608, + 222225, 463772, 8022091, 8173722, 8291385, 472741, 8105898, + 7943299, 267137, 7957660, 371874, 409084, 203750, 477334, + 83412, 111278, 120444, + } + } else { + p2 = common.Poly{ + 338083, 7978692, 8044913, 373628, 427855, 79725, 91018, + 349821, 501552, 7955127, 8316400, 290708, 216142, 8199666, + 8040144, 109426, 8177916, 8200218, 8125680, 358131, 160961, + 497383, 25361, 156297, 8033745, 7897189, 48397, 498732, + 464556, 7862704, 8308667, 236080, 91240, 8328377, 326190, + 509979, 8313264, 8106493, 8210965, 8328036, 172602, 8108765, + 8192963, 8361660, 8026473, 7932022, 322006, 8305874, 8254440, + 7866474, 373371, 8023413, 8221878, 486124, 36080, 8324512, + 8042056, 7984472, 8048111, 7910387, 8205382, 8259636, 188609, + 8316587, 59306, 119803, 8067108, 8155455, 8153450, 7983908, + 8222256, 21521, 114297, 8069037, 151621, 8014482, 8052856, + 376107, 8004652, 175001, 8079461, 8351123, 8021484, 144547, + 7908116, 8278100, 8136941, 142399, 8026843, 8081852, 124334, + 242796, 266768, 7919478, 7954016, 28927, 8329064, 514031, + 423911, 27907, 8142788, 8078298, 273978, 382723, 8148646, + 186476, 8030712, 8067268, 356250, 145817, 60045, 122764, + 56856, 8225416, 136437, 199652, 8343127, 8109765, 7936848, + 446966, 8351681, 288663, 409663, 512988, 8350788, 8191864, + 8366223, 281267, 7921696, 8213978, 442484, 67457, 8030602, + 238514, 230458, 8301866, 8359700, 150320, 143893, 461735, + 225443, 8027502, 151113, 365244, 7911438, 82498, 405398, + 8207009, 8108255, 367485, 514660, 8294055, 8168958, 127725, + 402955, 8051625, 7859029, 7980052, 321819, 7949587, 125778, + 8287078, 131972, 499609, 256795, 8180323, 8269393, 5878, + 8145473, 8238676, 383855, 415547, 424071, 241989, 8165743, + 8207329, 149608, 8315331, 7901850, 8114275, 360650, 516061, + 255090, 8277977, 270877, 8125200, 479248, 7991711, 8028595, + 73426, 8215429, 208217, 153872, 429336, 229856, 461204, + 236682, 7930158, 8298847, 228327, 8009399, 8111520, 345025, + 386495, 93454, 8336429, 8161305, 7980811, 286795, 162808, + 224476, 7972825, 85118, 287488, 8029791, 119071, 371, 518524, + 473496, 451205, 127000, 19233, 211519, 2442, 7950959, 481888, + 8041598, 8281176, 437202, 7912610, 8080153, 8237500, 7926828, + 8009421, 204880, 62495, 8192310, 8314388, 98616, 182368, + 323894, 59901, 481049, 8139275, 7872144, 254106, 376257, + 93339, 301342, 366536, 438920, 84773, 461471, 8125755, + 7930085, 405116, + } + } + for i := 0; i < 48; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeGamma1(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniformB60(t *testing.T) { + var p common.Poly + var w1 VecK + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformB60(&p, &seed, &w1) + nonzero := 0 + for j := 0; j < common.N; j++ { + if p[j] != 0 { + if p[j] != 1 && p[j] != common.Q-1 { + t.Fatal() + } + nonzero++ + } + } + if nonzero != 60 { + t.Fatal() + } + } +} + +func TestDeriveUniformX4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [32]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, + nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniform(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatal() + } + } +} + +func TestDeriveUniformB60X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + var w1s [4]VecK + for j := 0; j < 4; j++ { + for k := 0; k < K; k++ { + for i := 0; i < common.N; i++ { + w1s[j][k][i] = uint32(j+k*4+i*4*K) & 15 + } + } + } + PolyDeriveUniformB60X4( + [4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, + [4]*VecK{&w1s[0], &w1s[1], &w1s[2], &w1s[3]}, + ) + for j := 0; j < 4; j++ { + PolyDeriveUniformB60(&p, &seed, &w1s[j]) + if ps[j] != p { + t.Fatalf("%v %v", ps[j], p) + } + } +} + +func TestDeriveUniformLeGamma1X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatalf("%d\n%v\n%v", i, p, ps[i]) + } + } +} + +func BenchmarkPolyDeriveUniformB60(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60(&p, &seed, &w1) + } +} + +func BenchmarkPolyDeriveUniformB60X4(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60X4( + [4]*common.Poly{&p, &p, &p, &p}, + &seed, + [4]*VecK{&w1, &w1, &w1, &w1}, + ) + } +} + +func BenchmarkPolyDeriveUniform(b *testing.B) { + var seed [32]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniform(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformX4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [32]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) { + var seed [48]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1X4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [48]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} diff --git a/src/circl/sign/dilithium/mode4/internal/vec.go b/src/circl/sign/dilithium/mode4/internal/vec.go new file mode 100644 index 00000000000..a20a8b0224e --- /dev/null +++ b/src/circl/sign/dilithium/mode4/internal/vec.go @@ -0,0 +1,281 @@ +// Code generated from mode3/internal/vec.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A vector of L polynomials. +type VecL [L]common.Poly + +// A vector of K polynomials. +type VecK [K]common.Poly + +// Normalize the polynomials in this vector. +func (v *VecL) Normalize() { + for i := 0; i < L; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecL) NormalizeAssumingLe2Q() { + for i := 0; i < L; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecL) Add(w, u *VecL) { + for i := 0; i < L; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecL) NTT() { + for i := 0; i < L; i++ { + v[i].NTT() + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecL) Exceeds(bound uint32) bool { + for i := 0; i < L; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Decompose(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecL) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeqEta(). +func (v *VecL) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sequentially packs each polynomial using Poly.PackLeGamma1(). +func (v *VecL) PackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].PackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeGamma1(). +func (v *VecL) UnpackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].UnpackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Normalize the polynomials in this vector. +func (v *VecK) Normalize() { + for i := 0; i < K; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecK) NormalizeAssumingLe2Q() { + for i := 0; i < K; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecK) Add(w, u *VecK) { + for i := 0; i < K; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecK) Exceeds(bound uint32) bool { + for i := 0; i < K; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Decompose(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sets v to the hint vector for v0 the modified low bits and v1 +// the unmodified high bits --- see makeHint(). +// +// Returns the number of ones in the hint vector. +func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) { + for i := 0; i < K; i++ { + pop += v[i].MakeHint(&v0[i], &v1[i]) + } + return +} + +// Computes corrections to the high bits of the polynomials in the vector +// w using the hints in h and sets v to the corrected high bits. Returns v. +// See useHint(). +func (v *VecK) UseHint(q, hint *VecK) *VecK { + for i := 0; i < K; i++ { + v[i].UseHint(&q[i], &hint[i]) + } + return v +} + +// Sequentially packs each polynomial using Poly.PackT1(). +func (v *VecK) PackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sets v to the vector packed into buf by PackT1(). +func (v *VecK) UnpackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sequentially packs each polynomial using Poly.PackT0(). +func (v *VecK) PackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sets v to the vector packed into buf by PackT0(). +func (v *VecK) UnpackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecK) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecK.PackLeqEta(). +func (v *VecK) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecK) NTT() { + for i := 0; i < K; i++ { + v[i].NTT() + } +} + +// Sequentially packs each polynomial using Poly.PackLe16(). +func (v *VecK) PackLe16(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackLe16(buf[offset:]) + offset += common.PolyLe16Size + } +} + +// Sets v to a - b. +// +// Warning: assumes coefficients of the polynomials of b are less than 2q. +func (v *VecK) Sub(a, b *VecK) { + for i := 0; i < K; i++ { + v[i].Sub(&a[i], &b[i]) + } +} + +// Sets v to 2ᵈ w without reducing. +func (v *VecK) MulBy2toD(w *VecK) { + for i := 0; i < K; i++ { + v[i].MulBy2toD(&w[i]) + } +} + +// Applies InvNTT componentwise. See Poly.InvNTT() for details. +func (v *VecK) InvNTT() { + for i := 0; i < K; i++ { + v[i].InvNTT() + } +} + +// Applies Poly.ReduceLe2Q() componentwise. +func (v *VecK) ReduceLe2Q() { + for i := 0; i < K; i++ { + v[i].ReduceLe2Q() + } +} diff --git a/src/circl/sign/dilithium/mode4aes.go b/src/circl/sign/dilithium/mode4aes.go new file mode 100644 index 00000000000..0a5ab4e787b --- /dev/null +++ b/src/circl/sign/dilithium/mode4aes.go @@ -0,0 +1,95 @@ +// Code generated from mode.templ.go. DO NOT EDIT. + +package dilithium + +import ( + "fmt" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode4aes" +) + +// implMode4AES implements the mode.Mode interface for Dilithium4-AES. +type implMode4AES struct{} + +// Mode4AES is Dilithium in mode "Dilithium4-AES". +var Mode4AES Mode = &implMode4AES{} + +func (m *implMode4AES) GenerateKey(rand io.Reader) ( + PublicKey, PrivateKey, error) { + return mode4aes.GenerateKey(rand) +} + +func (m *implMode4AES) NewKeyFromExpandedSeed(seed *[96]byte) (PublicKey, + PrivateKey) { + return mode4aes.NewKeyFromExpandedSeed(seed) +} + +func (m *implMode4AES) NewKeyFromSeed(seed []byte) (PublicKey, + PrivateKey) { + if len(seed) != common.SeedSize { + panic(fmt.Sprintf("seed must be of length %d", common.SeedSize)) + } + seedBuf := [common.SeedSize]byte{} + copy(seedBuf[:], seed) + return mode4aes.NewKeyFromSeed(&seedBuf) +} + +func (m *implMode4AES) Sign(sk PrivateKey, msg []byte) []byte { + isk := sk.(*mode4aes.PrivateKey) + ret := [mode4aes.SignatureSize]byte{} + mode4aes.SignTo(isk, msg, ret[:]) + return ret[:] +} + +func (m *implMode4AES) Verify(pk PublicKey, msg []byte, signature []byte) bool { + ipk := pk.(*mode4aes.PublicKey) + return mode4aes.Verify(ipk, msg, signature) +} + +func (m *implMode4AES) PublicKeyFromBytes(data []byte) PublicKey { + var ret mode4aes.PublicKey + if len(data) != mode4aes.PublicKeySize { + panic("packed public key must be of mode4aes.PublicKeySize bytes") + } + var buf [mode4aes.PublicKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode4AES) PrivateKeyFromBytes(data []byte) PrivateKey { + var ret mode4aes.PrivateKey + if len(data) != mode4aes.PrivateKeySize { + panic("packed public key must be of mode4aes.PrivateKeySize bytes") + } + var buf [mode4aes.PrivateKeySize]byte + copy(buf[:], data) + ret.Unpack(&buf) + return &ret +} + +func (m *implMode4AES) SeedSize() int { + return common.SeedSize +} + +func (m *implMode4AES) PublicKeySize() int { + return mode4aes.PublicKeySize +} + +func (m *implMode4AES) PrivateKeySize() int { + return mode4aes.PrivateKeySize +} + +func (m *implMode4AES) SignatureSize() int { + return mode4aes.SignatureSize +} + +func (m *implMode4AES) Name() string { + return "Dilithium4-AES" +} + +func init() { + modes["Dilithium4-AES"] = Mode4AES +} diff --git a/src/circl/sign/dilithium/mode4aes/dilithium.go b/src/circl/sign/dilithium/mode4aes/dilithium.go new file mode 100644 index 00000000000..7f831d38625 --- /dev/null +++ b/src/circl/sign/dilithium/mode4aes/dilithium.go @@ -0,0 +1,191 @@ +// Code generated from modePkg.templ.go. DO NOT EDIT. + +// mode4aes implements the CRYSTALS-Dilithium signature scheme Dilithium4-AES +// as submitted to round2 of the NIST PQC competition and described in +// +// https://pq-crystals.org/dilithium/data/dilithium-specification-round2.pdf +package mode4aes + +import ( + "crypto" + "errors" + "io" + + "circl/sign/dilithium/internal/common" + "circl/sign/dilithium/mode4aes/internal" +) + +const ( + // Size of seed for NewKeyFromSeed + SeedSize = common.SeedSize + + // Size of a packed PublicKey + PublicKeySize = internal.PublicKeySize + + // Size of a packed PrivateKey + PrivateKeySize = internal.PrivateKeySize + + // Size of a signature + SignatureSize = internal.SignatureSize +) + +// PublicKey is the type of Dilithium4-AES public key +type PublicKey internal.PublicKey + +// PrivateKey is the type of Dilithium4-AES private key +type PrivateKey internal.PrivateKey + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + pk, sk, err := internal.GenerateKey(rand) + return (*PublicKey)(pk), (*PrivateKey)(sk), err +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + pk, sk := internal.NewKeyFromExpandedSeed(seed) + return (*PublicKey)(pk), (*PrivateKey)(sk) +} + +// SignTo signs the given message and writes the signature into signature. +// It will panic if signature is not of length at least SignatureSize. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + internal.SignTo( + (*internal.PrivateKey)(sk), + msg, + signature, + ) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + return internal.Verify( + (*internal.PublicKey)(pk), + msg, + signature, + ) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Unpack(buf) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Unpack(buf) +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + (*internal.PublicKey)(pk).Pack(buf) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + (*internal.PrivateKey)(sk).Pack(buf) +} + +// Packs the public key. +func (pk *PublicKey) Bytes() []byte { + var buf [PublicKeySize]byte + pk.Pack(&buf) + return buf[:] +} + +// Packs the private key. +func (sk *PrivateKey) Bytes() []byte { + var buf [PrivateKeySize]byte + sk.Pack(&buf) + return buf[:] +} + +// Packs the public key. +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + return pk.Bytes(), nil +} + +// Packs the private key. +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + return sk.Bytes(), nil +} + +// Unpacks the public key from data. +func (pk *PublicKey) UnmarshalBinary(data []byte) error { + if len(data) != PublicKeySize { + return errors.New("packed public key must be of mode4aes.PublicKeySize bytes") + } + var buf [PublicKeySize]byte + copy(buf[:], data) + pk.Unpack(&buf) + return nil +} + +// Unpacks the private key from data. +func (sk *PrivateKey) UnmarshalBinary(data []byte) error { + if len(data) != PrivateKeySize { + return errors.New("packed private key must be of mode4aes.PrivateKeySize bytes") + } + var buf [PrivateKeySize]byte + copy(buf[:], data) + sk.Unpack(&buf) + return nil +} + +// Sign signs the given message. +// +// opts.HashFunc() must return zero, which can be achieved by passing +// crypto.Hash(0) for opts. rand is ignored. Will only return an error +// if opts.HashFunc() is non-zero. +// +// This function is used to make PrivateKey implement the crypto.Signer +// interface. The package-level SignTo function might be more convenient +// to use. +func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( + signature []byte, err error) { + var sig [SignatureSize]byte + + if opts.HashFunc() != crypto.Hash(0) { + return nil, errors.New("dilithium: cannot sign hashed message") + } + + SignTo(sk, msg, sig[:]) + return sig[:], nil +} + +// Computes the public key corresponding to this private key. +// +// Returns a *PublicKey. The type crypto.PublicKey is used to make +// PrivateKey implement the crypto.Signer interface. +func (sk *PrivateKey) Public() crypto.PublicKey { + return (*PublicKey)((*internal.PrivateKey)(sk).Public()) +} + +// Equal returns whether the two private keys equal. +func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { + castOther, ok := other.(*PrivateKey) + if !ok { + return false + } + return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther)) +} + +// Equal returns whether the two public keys equal. +func (pk *PublicKey) Equal(other crypto.PublicKey) bool { + castOther, ok := other.(*PublicKey) + if !ok { + return false + } + return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther)) +} diff --git a/src/circl/sign/dilithium/mode4aes/internal/dilithium.go b/src/circl/sign/dilithium/mode4aes/internal/dilithium.go new file mode 100644 index 00000000000..fb0eaaf1963 --- /dev/null +++ b/src/circl/sign/dilithium/mode4aes/internal/dilithium.go @@ -0,0 +1,446 @@ +// Code generated from mode3/internal/dilithium.go by gen.go + +package internal + +import ( + cryptoRand "crypto/rand" + "crypto/subtle" + "io" + + "circl/internal/sha3" + "circl/sign/dilithium/internal/common" +) + +const ( + // Size of a packed polynomial of norm ≤η. + // (Note that the formula is not valid in general.) + PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8 +) + +// PublicKey is the type of Dilithium public keys. +type PublicKey struct { + rho [32]byte + t1 VecK + + // Cached values + t1p [common.PolyT1Size * K]byte + A *Mat + tr *[48]byte +} + +// PrivateKey is the type of Dilithium private keys. +type PrivateKey struct { + rho [32]byte + key [32]byte + s1 VecL + s2 VecK + t0 VecK + tr [48]byte + + // Cached values + A Mat // ExpandA(ρ) + s1h VecL // NTT(s₁) + s2h VecK // NTT(s₂) + t0h VecK // NTT(t₀) +} + +type unpackedSignature struct { + z VecL + hint VecK + c common.Poly +} + +// Packs the signature into buf. +func (sig *unpackedSignature) Pack(buf []byte) { + sig.z.PackLeGamma1(buf[:]) + sig.hint.PackHint(buf[L*common.PolyLeGamma1Size:]) + sig.c.PackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) +} + +// Sets sig to the signature encoded in the buffer. +// +// Returns whether buf contains a properly packed signature. +func (sig *unpackedSignature) Unpack(buf []byte) bool { + if len(buf) < SignatureSize { + return false + } + sig.z.UnpackLeGamma1(buf[:]) + if sig.z.Exceeds(common.Gamma1 - Beta) { + return false + } + if !sig.hint.UnpackHint(buf[L*common.PolyLeGamma1Size:]) { + return false + } + sig.c.UnpackB60(buf[L*common.PolyLeGamma1Size+Omega+K:]) + return true +} + +// Packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + copy(buf[:32], pk.rho[:]) + copy(buf[32:], pk.t1p[:]) +} + +// Sets pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + copy(pk.rho[:], buf[:32]) + copy(pk.t1p[:], buf[32:]) + + pk.t1.UnpackT1(pk.t1p[:]) + pk.A = new(Mat) + pk.A.Derive(&pk.rho) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + pk.tr = new([48]byte) + h := sha3.NewShake256() + _, _ = h.Write(buf[:]) + _, _ = h.Read(pk.tr[:]) +} + +// Packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + copy(buf[:32], sk.rho[:]) + copy(buf[32:64], sk.key[:]) + copy(buf[64:112], sk.tr[:]) + offset := 112 + sk.s1.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.PackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.PackT0(buf[offset:]) +} + +// Sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + copy(sk.rho[:], buf[:32]) + copy(sk.key[:], buf[32:64]) + copy(sk.tr[:], buf[64:112]) + offset := 112 + sk.s1.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * L + sk.s2.UnpackLeqEta(buf[offset:]) + offset += PolyLeqEtaSize * K + sk.t0.UnpackT0(buf[offset:]) + + // Cached values + sk.A.Derive(&sk.rho) + sk.t0h = sk.t0 + sk.t0h.NTT() + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() +} + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [32]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + pk, sk := NewKeyFromSeed(&seed) + return pk, sk, nil +} + +// NewKeyFromExpandedSeed derives a public/private key pair using the +// given expanded seed. +// +// Use NewKeyFromSeed instead of this function. This function is only exposed +// to generate the NIST KAT test vectors. +func NewKeyFromExpandedSeed(seed *[96]byte) (*PublicKey, *PrivateKey) { + var pk PublicKey + var sk PrivateKey + var sSeed [32]byte + + copy(pk.rho[:], seed[:32]) + copy(sSeed[:], seed[32:64]) + copy(sk.key[:], seed[64:]) + copy(sk.rho[:], pk.rho[:]) + + sk.A.Derive(&pk.rho) + + for i := uint16(0); i < L; i++ { + PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i) + } + + for i := uint16(0); i < K; i++ { + PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L) + } + + sk.s1h = sk.s1 + sk.s1h.NTT() + sk.s2h = sk.s2 + sk.s2h.NTT() + + sk.computeT0andT1(&sk.t0, &pk.t1) + + sk.t0h = sk.t0 + sk.t0h.NTT() + + // Complete public key far enough to be packed + pk.t1.PackT1(pk.t1p[:]) + pk.A = &sk.A + + // Finish private key + var packedPk [PublicKeySize]byte + pk.Pack(&packedPk) + + // tr = CRH(ρ ‖ t1) = CRH(pk) + h := sha3.NewShake256() + _, _ = h.Write(packedPk[:]) + _, _ = h.Read(sk.tr[:]) + + // Finish cache of public key + pk.tr = &sk.tr + + return &pk, &sk +} + +// Computes t0 and t1 from sk.s1h, sk.s2 and sk.A. +func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) { + var t VecK + + // Set t to A s₁ + s₂ + for i := 0; i < K; i++ { + PolyDotHat(&t[i], &sk.A[i], &sk.s1h) + t[i].ReduceLe2Q() + t[i].InvNTT() + } + t.Add(&t, &sk.s2) + t.Normalize() + + // Compute t₀, t₁ = Power2Round(t) + t.Power2Round(t0, t1) +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) { + var buf [96]byte + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Read(buf[:]) + return NewKeyFromExpandedSeed(&buf) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + var sig unpackedSignature + var mu [48]byte + var zh VecL + var Az, Az2dct1, w1 VecK + var ch, cp common.Poly + + // Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β + // and ensured that there at most ω ones in pk.hint. + if !sig.Unpack(signature) { + return false + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(pk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // Compute Az + zh = sig.z + zh.NTT() + + for i := 0; i < K; i++ { + PolyDotHat(&Az[i], &pk.A[i], &zh) + } + + // Next, we compute Az - 2ᵈ·c·t₁. + // Note that the coefficients of t₁ are bounded by 256 = 2⁹, + // so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q, + // which is small enough for NTT(). + Az2dct1.MulBy2toD(&pk.t1) + Az2dct1.NTT() + ch = sig.c + ch.NTT() + for i := 0; i < K; i++ { + Az2dct1[i].MulHat(&Az2dct1[i], &ch) + } + Az2dct1.Sub(&Az, &Az2dct1) + Az2dct1.ReduceLe2Q() + Az2dct1.InvNTT() + Az2dct1.NormalizeAssumingLe2Q() + + // UseHint(pk.hint, Az - 2ᵈ·c·t₁) + // = UseHint(pk.hint, w - c·s₂ + c·t₀) + // = UseHint(pk.hint, r + c·t₀) + // = r₁ = w₁. + w1.UseHint(&Az2dct1, &sig.hint) + + // c' = H(μ, w₁) + PolyDeriveUniformB60(&cp, &mu, &w1) + return sig.c == cp +} + +// SignTo signs the given message and writes the signature into signature. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + var mu, rhop [48]byte + var y, yh VecL + var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK + var ch common.Poly + var yNonce uint16 + var sig unpackedSignature + + if len(signature) < SignatureSize { + panic("Signature does not fit in that byteslice") + } + + // μ = CRH(tr ‖ msg) + h := sha3.NewShake256() + _, _ = h.Write(sk.tr[:]) + _, _ = h.Write(msg) + _, _ = h.Read(mu[:]) + + // ρ' = CRH(μ ‖ key) + h.Reset() + _, _ = h.Write(sk.key[:]) + _, _ = h.Write(mu[:]) + _, _ = h.Read(rhop[:]) + + // Main rejection loop + attempt := 0 + for { + attempt++ + if attempt >= 576 { + // Depending on the mode, one try has a chance between 1/7 and 1/4 + // of succeeding. Thus it is safe to say that 576 iterations + // are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸. + panic("This should only happen 1 in 2^{128}: something is wrong.") + } + + // y = ExpandMask(ρ', key) + VecLDeriveUniformLeGamma1(&y, &rhop, yNonce) + yNonce += uint16(L) + + // Set w to A y + yh = y + yh.NTT() + for i := 0; i < K; i++ { + PolyDotHat(&w[i], &sk.A[i], &yh) + w[i].ReduceLe2Q() + w[i].InvNTT() + } + + // Decompose w into w₀ and w₁ + w.NormalizeAssumingLe2Q() + w.Decompose(&w0, &w1) + + // c = H(μ, w₁) + PolyDeriveUniformB60(&sig.c, &mu, &w1) + ch = sig.c + ch.NTT() + + // Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β. + // + // By Lemma 3 of the specification this is equivalent to checking that + // both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition + // w - c·s₂ = r₁ α + r₀ as computed by decompose(). + // See also §4.1 of the specification. + for i := 0; i < K; i++ { + w0mcs2[i].MulHat(&ch, &sk.s2h[i]) + w0mcs2[i].InvNTT() + } + w0mcs2.Sub(&w0, &w0mcs2) + w0mcs2.Normalize() + + if w0mcs2.Exceeds(common.Gamma2 - Beta) { + continue + } + + // z = y + c·s₁ + for i := 0; i < L; i++ { + sig.z[i].MulHat(&ch, &sk.s1h[i]) + sig.z[i].InvNTT() + } + sig.z.Add(&sig.z, &y) + sig.z.Normalize() + + // Ensure ‖z‖_∞ < γ₁ - β + if sig.z.Exceeds(common.Gamma1 - Beta) { + continue + } + + // Compute c·t₀ + for i := 0; i < K; i++ { + ct0[i].MulHat(&ch, &sk.t0h[i]) + ct0[i].InvNTT() + } + ct0.NormalizeAssumingLe2Q() + + // Ensure ‖c·t₀‖_∞ < γ₂. + if ct0.Exceeds(common.Gamma2) { + continue + } + + // Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0. + // Note that we're not using makeHint() in the obvious way as we + // do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂. Instead we note + // that our makeHint() is actually the same as a makeHint for a + // different decomposition: + // + // Earlier we ensured indirectly with a check that r₁ = w₁ where + // r = w - c·s₂. Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂. + // Thus MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁) + // and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁). + // As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct. + w0mcs2pct0.Add(&w0mcs2, &ct0) + w0mcs2pct0.NormalizeAssumingLe2Q() + hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1) + if hintPop > Omega { + continue + } + + break + } + + sig.Pack(signature[:]) +} + +// Computes the public key corresponding to this private key. +func (sk *PrivateKey) Public() *PublicKey { + var t0 VecK + pk := &PublicKey{ + rho: sk.rho, + A: &sk.A, + tr: &sk.tr, + } + sk.computeT0andT1(&t0, &pk.t1) + pk.t1.PackT1(pk.t1p[:]) + return pk +} + +// Equal returns whether the two public keys are equal +func (pk *PublicKey) Equal(other *PublicKey) bool { + return pk.rho == other.rho && pk.t1 == other.t1 +} + +// Equal returns whether the two private keys are equal +func (sk *PrivateKey) Equal(other *PrivateKey) bool { + ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) & + subtle.ConstantTimeCompare(sk.key[:], other.key[:]) & + subtle.ConstantTimeCompare(sk.tr[:], other.tr[:])) + + acc := uint32(0) + for i := 0; i < L; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s1[i][j] ^ other.s1[i][j] + } + } + for i := 0; i < K; i++ { + for j := 0; j < common.N; j++ { + acc |= sk.s2[i][j] ^ other.s2[i][j] + acc |= sk.t0[i][j] ^ other.t0[i][j] + } + } + return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1 +} diff --git a/src/circl/sign/dilithium/mode4aes/internal/dilithium_test.go b/src/circl/sign/dilithium/mode4aes/internal/dilithium_test.go new file mode 100644 index 00000000000..42ce6dbe5d1 --- /dev/null +++ b/src/circl/sign/dilithium/mode4aes/internal/dilithium_test.go @@ -0,0 +1,131 @@ +// Code generated from mode3/internal/dilithium_test.go by gen.go + +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Checks whether p is normalized. Only used in tests. +func PolyNormalized(p *common.Poly) bool { + p2 := *p + p2.Normalize() + return p2 == *p +} + +func BenchmarkSkUnpack(b *testing.B) { + var buf [PrivateKeySize]byte + var sk PrivateKey + for i := 0; i < b.N; i++ { + sk.Unpack(&buf) + } +} + +func BenchmarkPkUnpack(b *testing.B) { + var buf [PublicKeySize]byte + var pk PublicKey + for i := 0; i < b.N; i++ { + pk.Unpack(&buf) + } +} + +func BenchmarkVerify(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of verification (as in the reference + // implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + pk, sk := NewKeyFromSeed(&seed) + SignTo(sk, msg[:], sig[:]) + b.ResetTimer() + for i := 0; i < b.N; i++ { + // We should generate a new signature for every verify attempt, + // as this influences the time a little bit. This difference, however, + // is small and generating a new signature in between creates a lot + // pressure on the allocator which makes an accurate measurement hard. + Verify(pk, msg[:], sig[:]) + } +} + +func BenchmarkSign(b *testing.B) { + // Note that the expansion of the matrix A is done at Unpacking/Keygen + // instead of at the moment of signing (as in the reference implementation.) + var seed [32]byte + var msg [8]byte + var sig [SignatureSize]byte + _, sk := NewKeyFromSeed(&seed) + b.ResetTimer() + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(msg[:], uint64(i)) + SignTo(sk, msg[:], sig[:]) + } +} + +func BenchmarkGenerateKey(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + NewKeyFromSeed(&seed) + } +} + +func BenchmarkPublicFromPrivate(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + b.StopTimer() + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + _, sk := NewKeyFromSeed(&seed) + b.StartTimer() + sk.Public() + } +} + +func TestSignThenVerifyAndPkSkPacking(t *testing.T) { + var seed [common.SeedSize]byte + var sig [SignatureSize]byte + var msg [8]byte + var pkb [PublicKeySize]byte + var skb [PrivateKeySize]byte + var pk2 PublicKey + var sk2 PrivateKey + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + if !sk.Equal(sk) { + t.Fatal() + } + for j := uint64(0); j < 10; j++ { + binary.LittleEndian.PutUint64(msg[:], j) + SignTo(sk, msg[:], sig[:]) + if !Verify(pk, msg[:], sig[:]) { + t.Fatal() + } + } + pk.Pack(&pkb) + pk2.Unpack(&pkb) + if !pk.Equal(&pk2) { + t.Fatal() + } + sk.Pack(&skb) + sk2.Unpack(&skb) + if !sk.Equal(&sk2) { + t.Fatal() + } + } +} + +func TestPublicFromPrivate(t *testing.T) { + var seed [common.SeedSize]byte + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := NewKeyFromSeed(&seed) + pk2 := sk.Public() + if !pk.Equal(pk2) { + t.Fatal() + } + } +} diff --git a/src/circl/sign/dilithium/mode4aes/internal/mat.go b/src/circl/sign/dilithium/mode4aes/internal/mat.go new file mode 100644 index 00000000000..a2411b0566d --- /dev/null +++ b/src/circl/sign/dilithium/mode4aes/internal/mat.go @@ -0,0 +1,59 @@ +// Code generated from mode3/internal/mat.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A k by l matrix of polynomials. +type Mat [K]VecL + +// Expands the given seed to a complete matrix. +// +// This function is called ExpandA in the specification. +func (m *Mat) Derive(seed *[32]byte) { + if !DeriveX4Available { + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + PolyDeriveUniform(&m[i][j], seed, (i<<8)+j) + } + } + return + } + + idx := 0 + var nonces [4]uint16 + var ps [4]*common.Poly + for i := uint16(0); i < K; i++ { + for j := uint16(0); j < L; j++ { + nonces[idx] = (i << 8) + j + ps[idx] = &m[i][j] + idx++ + if idx == 4 { + idx = 0 + PolyDeriveUniformX4(ps, seed, nonces) + } + } + } + if idx != 0 { + for i := idx; i < 4; i++ { + ps[i] = nil + } + PolyDeriveUniformX4(ps, seed, nonces) + } +} + +// Set p to the inner product of a and b using pointwise multiplication. +// +// Assumes a and b are in Montgomery form and their coefficients are +// pairwise sufficiently small to multiply, see Poly.MulHat(). Resulting +// coefficients are bounded by 2Lq. +func PolyDotHat(p *common.Poly, a, b *VecL) { + var t common.Poly + *p = common.Poly{} // zero p + for i := 0; i < L; i++ { + t.MulHat(&a[i], &b[i]) + p.Add(&t, p) + } +} diff --git a/src/circl/sign/dilithium/mode4aes/internal/pack.go b/src/circl/sign/dilithium/mode4aes/internal/pack.go new file mode 100644 index 00000000000..ecf3971cd20 --- /dev/null +++ b/src/circl/sign/dilithium/mode4aes/internal/pack.go @@ -0,0 +1,141 @@ +// Code generated from mode3/internal/pack.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// Writes p with norm less than or equal η into buf, which must be of +// size PolyLeqEtaSize. +// +// Assumes coefficients of p are not normalized, but in [q-η,q+η]. +func PolyPackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + buf[i] = (byte(common.Q+Eta-p[j]) | + byte(common.Q+Eta-p[j+1])<<4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + buf[i] = (byte(common.Q+Eta-p[j]) | + (byte(common.Q+Eta-p[j+1]) << 3) | + (byte(common.Q+Eta-p[j+2]) << 6)) + buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) | + (byte(common.Q+Eta-p[j+3]) << 1) | + (byte(common.Q+Eta-p[j+4]) << 4) | + (byte(common.Q+Eta-p[j+5]) << 7)) + buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) | + (byte(common.Q+Eta-p[j+6]) << 2) | + (byte(common.Q+Eta-p[j+7]) << 5)) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Sets p to the polynomial of norm less than or equal η encoded in the +// given buffer of size PolyLeqEtaSize. +// +// Output coefficients of p are not normalized, but in [q-η,q+η] provided +// buf was created using PackLeqEta. +// +// Beware, for arbitrary buf the coefficients of p might en up in +// the interval [q-2^b,q+2^b] where b is the least b with η≤2^b. +func PolyUnpackLeqEta(p *common.Poly, buf []byte) { + if DoubleEtaBits == 4 { // compiler eliminates branch + j := 0 + for i := 0; i < PolyLeqEtaSize; i++ { + p[j] = common.Q + Eta - uint32(buf[i]&15) + p[j+1] = common.Q + Eta - uint32(buf[i]>>4) + j += 2 + } + } else if DoubleEtaBits == 3 { + j := 0 + for i := 0; i < PolyLeqEtaSize; i += 3 { + p[j] = common.Q + Eta - uint32(buf[i]&7) + p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7) + p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7)) + p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7) + p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7) + p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7)) + p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7) + p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7) + j += 8 + } + } else { + panic("eta not supported") + } +} + +// Writes v with coefficients in {0, 1} of which at most ω non-zero +// to buf, which must have length ω+k. +func (v *VecK) PackHint(buf []byte) { + // The packed hint starts with the indices of the non-zero coefficients + // For instance: + // + // (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹) + // + // Yields + // + // 56, 100, 255, 2, 23, 1 + // + // Then we pad with zeroes until we have a list of ω items: + // // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0 + // + // Then we finish with a list of the switch-over-indices in this + // list between polynomials, so: + // + // 56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6 + + off := uint8(0) + for i := 0; i < K; i++ { + for j := uint16(0); j < common.N; j++ { + if v[i][j] != 0 { + buf[off] = uint8(j) + off++ + } + } + buf[Omega+i] = off + } + for ; off < Omega; off++ { + buf[off] = 0 + } +} + +// Sets v to the vector encoded using VecK.PackHint() +// +// Returns whether unpacking was successful. +func (v *VecK) UnpackHint(buf []byte) bool { + // A priori, there would be several reasonable ways to encode the same + // hint vector. We take care to only allow only one encoding, to ensure + // "strong unforgeability". + // + // See PackHint() source for description of the encoding. + *v = VecK{} // zero v + prevSOP := uint8(0) // previous switch-over-point + for i := 0; i < K; i++ { + SOP := buf[Omega+i] + if SOP < prevSOP || SOP > Omega { + return false // ensures switch-over-points are increasing + } + for j := prevSOP; j < SOP; j++ { + if j > prevSOP && buf[j] <= buf[j-1] { + return false // ensures indices are increasing (within a poly) + } + v[i][buf[j]] = 1 + } + prevSOP = SOP + } + for j := prevSOP; j < Omega; j++ { + if buf[j] != 0 { + return false // ensures padding indices are zero + } + } + + return true +} diff --git a/src/circl/sign/dilithium/mode4aes/internal/pack_test.go b/src/circl/sign/dilithium/mode4aes/internal/pack_test.go new file mode 100644 index 00000000000..35bea5b6db3 --- /dev/null +++ b/src/circl/sign/dilithium/mode4aes/internal/pack_test.go @@ -0,0 +1,85 @@ +// Code generated from mode3/internal/pack_test.go by gen.go + +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestPolyPackLeqEta(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [PolyLeqEtaSize]byte + + for i := uint16(0); i < 100; i++ { + // Note that DeriveUniformLeqEta sets p to the right kind of + // unnormalized vector. + PolyDeriveUniformLeqEta(&p1, &seed, i) + for j := 0; j < PolyLeqEtaSize; j++ { + if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta { + t.Fatalf("DerveUniformLeqEta out of bounds") + } + } + PolyPackLeqEta(&p1, buf[:]) + PolyUnpackLeqEta(&p2, buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT1(t *testing.T) { + var p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p1, &seed, i) + p1.Normalize() + for j := 0; j < common.N; j++ { + p1[j] &= 0x1ff + } + p1.PackT1(buf[:]) + p2.UnpackT1(buf[:]) + if p1 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackT0(t *testing.T) { + var p, p0, p1, p2 common.Poly + var seed [32]byte + var buf [common.PolyT0Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniform(&p, &seed, i) + p.Normalize() + p.Power2Round(&p0, &p1) + + p0.PackT0(buf[:]) + p2.UnpackT0(buf[:]) + if p0 != p2 { + t.Fatalf("%v != %v", p1, p2) + } + } +} + +func TestPolyPackLeGamma1(t *testing.T) { + var p0, p1 common.Poly + var seed [48]byte + var buf [common.PolyLeGamma1Size]byte + + for i := uint16(0); i < 100; i++ { + PolyDeriveUniformLeGamma1(&p0, &seed, i) + p0.Normalize() + + p0.PackLeGamma1(buf[:]) + p1.UnpackLeGamma1(buf[:]) + if p0 != p1 { + t.Fatalf("%v != %v", p0, p1) + } + } +} diff --git a/src/circl/sign/dilithium/mode4aes/internal/params.go b/src/circl/sign/dilithium/mode4aes/internal/params.go new file mode 100644 index 00000000000..e0f3b24fafe --- /dev/null +++ b/src/circl/sign/dilithium/mode4aes/internal/params.go @@ -0,0 +1,17 @@ +// Code generated from params.templ.go. DO NOT EDIT. + +package internal + +const ( + Name = "Dilithium4-AES" + UseAES = true + PublicKeySize = 1760 + PrivateKeySize = 3856 + SignatureSize = 3366 + K = 6 + L = 5 + Eta = 3 + DoubleEtaBits = 3 + Beta = 175 + Omega = 120 +) diff --git a/src/circl/sign/dilithium/mode4aes/internal/params_test.go b/src/circl/sign/dilithium/mode4aes/internal/params_test.go new file mode 100644 index 00000000000..0e50e20c729 --- /dev/null +++ b/src/circl/sign/dilithium/mode4aes/internal/params_test.go @@ -0,0 +1,47 @@ +package internal + +import ( + "testing" + + "circl/sign/dilithium/internal/common" +) + +// Tests specific to the current mode + +func TestVectorDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + p2 := common.Poly{ + 0, 8380414, 1, 8380416, 8380414, 0, 3, 8380416, 8380415, 8380416, + 3, 8380416, 8380416, 1, 3, 1, 0, 8380415, 8380415, 3, 8380416, + 1, 3, 8380416, 8380415, 8380416, 8380414, 3, 3, 0, 8380414, + 8380415, 0, 8380415, 2, 2, 0, 0, 3, 0, 8380414, 8380415, 8380415, + 8380416, 1, 8380414, 2, 0, 3, 0, 2, 8380415, 1, 2, 3, 1, 1, 0, + 8380415, 2, 8380414, 8380414, 8380414, 8380415, 8380416, 1, 3, + 2, 8380415, 3, 8380414, 8380415, 8380416, 0, 1, 1, 3, 1, 1, 1, + 8380414, 2, 8380416, 1, 2, 8380416, 2, 1, 8380415, 8380416, 3, + 8380415, 3, 8380416, 1, 2, 2, 8380414, 1, 0, 8380415, 3, 3, 2, + 8380416, 0, 8380414, 0, 1, 8380416, 8380414, 3, 0, 1, 2, 1, 2, + 1, 8380415, 8380415, 0, 1, 3, 8380415, 8380416, 8380415, 3, 1, + 8380415, 0, 8380415, 8380414, 8380414, 1, 8380415, 0, 1, 1, 1, + 8380416, 1, 8380416, 8380414, 8380415, 1, 8380416, 8380415, + 8380416, 0, 8380416, 8380414, 0, 1, 3, 8380414, 8380416, 3, 3, + 8380415, 0, 8380416, 8380415, 1, 3, 3, 0, 2, 8380416, 3, 8380415, + 8380414, 8380415, 2, 8380415, 1, 8380414, 1, 3, 1, 8380416, 1, + 3, 1, 8380414, 3, 3, 3, 8380414, 1, 8380414, 3, 3, 0, 8380414, + 8380416, 3, 0, 2, 3, 1, 8380416, 0, 0, 0, 0, 8380414, 0, 8380416, + 8380415, 0, 8380416, 8380416, 8380415, 1, 8380416, 3, 8380416, + 8380415, 3, 8380415, 0, 8380414, 2, 8380416, 8380415, 0, 8380414, + 2, 8380416, 8380416, 1, 3, 2, 2, 8380414, 8380414, 8380414, 3, + 0, 1, 8380416, 8380415, 1, 8380415, 8380414, 0, 8380414, 8380414, + 1, 2, 8380416, 1, 1, 8380414, 2, 8380415, + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeqEta(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} diff --git a/src/circl/sign/dilithium/mode4aes/internal/sample.go b/src/circl/sign/dilithium/mode4aes/internal/sample.go new file mode 100644 index 00000000000..8d01e8ef776 --- /dev/null +++ b/src/circl/sign/dilithium/mode4aes/internal/sample.go @@ -0,0 +1,563 @@ +// Code generated from mode3/internal/sample.go by gen.go + +package internal + +import ( + "circl/internal/sha3" + "circl/simd/keccakf1600" + + "circl/sign/dilithium/internal/common" + + "encoding/binary" +) + +// DeriveX4Available indicates whether the system supports the quick fourway +// sampling variants like PolyDeriveUniformX4. +var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES + +// For each i, sample ps[i] uniformly with coefficients of norm less than γ₁ +// using the the given seed and nonces[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformLeGamma1X4(ps [4]*common.Poly, seed *[48]byte, + nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE256 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE256 is 136 --- i.e. 17 uint64s. + for j := 0; j < 4; j++ { + state[6*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[16*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + // Each try requires 15 bits. 15 does not divide into 64, nor in 136, + // so we will have to carry some bits from a previous uint64 to the next. + var carry [4]uint32 + + // Shift is the amount of bits in the carry. + var shift [4]uint + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 17 uint64s of each + // of the four SHAKE256 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := 0; i < 17; i++ { + var t [4]uint32 + tCount := 3 + + // Get the next three or four 20 bit numbers. + qw := state[i*4+j] + qwl := (qw << shift[j]) | uint64(carry[j]) + t[0] = uint32(qwl & 0xfffff) + t[1] = uint32((qwl >> 20) & 0xfffff) + t[2] = uint32((qwl >> 40) & 0xfffff) + + if shift[j] == 16 { + t[3] = uint32(qw >> 44) + shift[j] = 0 + carry[j] = 0 + tCount = 4 + } else { + shift[j] += 4 + carry[j] = uint32(qw >> (64 - shift[j])) + } + + // Check if they're coefficients. + for k := 0; k < tCount; k++ { + if t[k] <= 2*common.Gamma1-2 { + ps[j][idx[j]] = common.Q + common.Gamma1 - 1 - t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + + done = false + } + } +} + +// For each i, sample ps[i] uniformly from the given seed and nonces[i]. +// ps[i] may be nil and is ignored in that case. +// +// Can only be called when DeriveX4Available is true. +func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) { + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 4; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the nonces, the SHAKE128 domain separator (0b1111), the + // start of the padding (0b...001) and the end of the padding 0b100... + // Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s. + for j := 0; j < 4; j++ { + state[4*4+j] = uint64(nonces[j]) | (0x1f << 16) + state[20*4+j] = 0x80 << 56 + } + + var idx [4]int // indices into ps + for j := 0; j < 4; j++ { + if ps[j] == nil { + idx[j] = common.N // mark nil polynomial as completed + } + } + + done := false + for !done { + // Applies KeccaK-f[1600] to state to get the next 21 uint64s of each + // of the four SHAKE128 streams. + perm.Permute() + + done = true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + for i := 0; i < 7; i++ { + var t [8]uint32 + t[0] = uint32(state[i*3*4+j] & 0x7fffff) + t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff) + t[2] = uint32((state[i*3*4+j] >> 48) | + ((state[(i*3+1)*4+j] & 0x7f) << 16)) + t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff) + t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff) + t[5] = uint32((state[(i*3+1)*4+j] >> 56) | + ((state[(i*3+2)*4+j] & 0x7fff) << 8)) + t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff) + t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff) + + for k := 0; k < 8; k++ { + if t[k] < common.Q { + ps[j][idx[j]] = t[k] + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + } + done = false + } + } +} + +// Sample p uniformly from the given seed and nonce. +// +// p will be normalized. +func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) { + var i, length int + var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks + + if UseAES { + length = 12 * 16 + } else { + length = 168 + } + + sample := func() { + // Note that 3 divides into 168 and 12*16, so we use up buf completely. + for j := 0; j < length && i < common.N; j += 3 { + t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0x7fffff + + // We use rejection sampling + if t < common.Q { + p[i] = t + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample p uniformly with coefficients of norm less than or equal η, +// using the given seed and nonce. +// +// p will not be normalized, but will have coefficients in [q-η,q+η]. +func PolyDeriveUniformLeqEta(p *common.Poly, seed *[32]byte, nonce uint16) { + // Assumes 2 < η < 8. + var i, length int + var buf [11 * 16]byte // fits 168B SHAKE-128 rate and 11 16B AES blocks + + if UseAES { + length = 11 * 16 + } else { + length = 168 + } + + sample := func() { + // We use rejection sampling + for j := 0; j < length && i < common.N; j++ { + var t1, t2 uint32 + if Eta <= 3 { // branch is eliminated by compiler + t1 = uint32(buf[j]) & 7 + t2 = uint32(buf[j]) >> 5 + } else { + t1 = uint32(buf[j]) & 15 + t2 = uint32(buf[j]) >> 4 + } + if t1 <= 2*Eta { + p[i] = common.Q + Eta - t1 + i++ + } + if t2 <= 2*Eta && i < common.N { + p[i] = common.Q + Eta - t2 + i++ + } + } + } + + if UseAES { + h := common.NewAesStream128(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:length]) + sample() + } + } else { + var iv [32 + 2]byte // 32 byte seed + uint16 nonce + + h := sha3.NewShake128() + copy(iv[:32], seed[:]) + iv[32] = uint8(nonce) + iv[33] = uint8(nonce >> 8) + + // 168 is SHAKE-128 rate + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[:168]) + sample() + } + } +} + +// Sample v[i] uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce+i +// +// v[i] will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func VecLDeriveUniformLeGamma1(v *VecL, seed *[48]byte, nonce uint16) { + if !DeriveX4Available { + for i := 0; i < L; i++ { + PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i)) + } + return + } + + var ps [4]*common.Poly + nonces := [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3} + for i := 0; i < L && i < 4; i++ { + ps[i] = &v[i] + } + + // PolyDeriveUniformLeGamma1X4 is slower than, but not twice as slow as, + // PolyDeriveUniformLeGamma. + PolyDeriveUniformLeGamma1X4(ps, seed, nonces) + if L == 5 { + PolyDeriveUniformLeGamma1(&v[L-1], seed, nonce+4) + } else if L > 5 || L < 2 { + panic("VecLDeriveUniformLeGamma1 does not support that L") + } +} + +// Sample p uniformly with coefficients of norm less than γ₁ using the +// given seed and nonce. +// +// p will not be normalized, but have coefficients in the +// interval (q-γ₁,q+γ₁). +func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[48]byte, nonce uint16) { + // Assumes γ₁ is less than 2²⁰. + var length, i int + + // Fits 10 16B AES blocks, which aligns nicely as we take 5 bytes at + // a time. The SHAKE-256 rate, however, is 136. As 136 is 1 modulo 5, + // we are left with 1 byte after the first block, which we include in the + // next block. So we need 4 bytes leeway in our buffer. The total 160 + // fits easily in 160. + var buf [160]byte + + sample := func() { + // We use rejection sampling + for j := 0; j < length-4 && i < common.N; j += 5 { + t1 := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) | + (uint32(buf[j+2]) << 16)) & 0xfffff + t2 := ((uint32(buf[j+2]) >> 4) | (uint32(buf[j+3]) << 4) | + (uint32(buf[j+4]) << 12)) + + if t1 <= 2*common.Gamma1-2 { + p[i] = common.Q + common.Gamma1 - 1 - t1 + i++ + } + if t2 <= 2*common.Gamma1-2 && i < common.N { + p[i] = common.Q + common.Gamma1 - 1 - t2 + i++ + } + } + } + if UseAES { + length = 160 + h := common.NewAesStream256(seed, nonce) + + for i < common.N { + h.SqueezeInto(buf[:]) + sample() + } + } else { + length = 136 + var iv [48 + 2]byte // 48 byte seed + uint16 nonce + bufOffset := 0 // where to put the next block + + h := sha3.NewShake256() + copy(iv[:48], seed[:]) + iv[48] = uint8(nonce) + iv[49] = uint8(nonce >> 8) + _, _ = h.Write(iv[:]) + + for i < common.N { + _, _ = h.Read(buf[bufOffset : bufOffset+136]) + sample() + + bufOffset++ + if bufOffset == 5 { + bufOffset = 0 + } + + // Move remaining bytes at the end to the start. + for j := 0; j < bufOffset; j++ { + buf[j] = buf[135+j] + } + } + } +} + +// For each i, sample ps[i] uniformly with 60 non-zero coefficients in {q-1,1} +// using the the given seed and w1[i]. ps[i] may be nil and is ignored +// in that case. ps[i] will be normalized. +// +// Can only be called when DeriveX4Available is true. +// +// This function is currently not used (yet). +func PolyDeriveUniformB60X4(ps [4]*common.Poly, seed *[48]byte, + w1 [4]*VecK) { + // Pack the w1s + var w1Packed [4][common.PolyLe16Size * K]byte + for j := 0; j < 4; j++ { + if ps[j] != nil { + w1[j].PackLe16(w1Packed[j][:]) + } + } + + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // Absorb the seed in the four states + for i := 0; i < 6; i++ { + v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)]) + for j := 0; j < 4; j++ { + state[i*4+j] = v + } + } + + // Absorb the start of the packed w₁s + offset := 0 // offset into w1Packed[j] + for i := 6; i < 17; i++ { + for j := 0; j < 4; j++ { + state[i*4+j] = binary.LittleEndian.Uint64(w1Packed[j][offset : offset+8]) + } + offset += 8 + } + + offset -= 8 + + // Absorb the remainder of the packed w₁s. +PermuteLoop: + for { + perm.Permute() + + for i := 0; i < 17; i++ { + offset += 8 + if offset == len(w1Packed[0]) { + // SHAKE256 domain separator and padding + for j := 0; j < 4; j++ { + state[i*4+j] ^= 0x1f + state[16*4+j] ^= 0x80 << 56 + } + perm.Permute() + + break PermuteLoop + } + + for j := 0; j < 4; j++ { + state[i*4+j] ^= binary.LittleEndian.Uint64( + w1Packed[j][offset : offset+8]) + } + } + } + + var signs [4]uint64 + var idx [4]uint16 // indices into ps + + for j := 0; j < 4; j++ { + if ps[j] != nil { + signs[j] = state[j] + *ps[j] = common.Poly{} // zero ps[j] + idx[j] = common.N - 60 + } else { + idx[j] = common.N // mark as completed + } + } + + stateOffset := 1 + for { + done := true + + PolyLoop: + for j := 0; j < 4; j++ { + if idx[j] == common.N { + continue + } + + for i := stateOffset; i < 17; i++ { + var bs [8]byte + binary.LittleEndian.PutUint64(bs[:], state[4*i+j]) + for k := 0; k < 8; k++ { + b := uint16(bs[k]) + + if b > idx[j] { + continue + } + + ps[j][idx[j]] = ps[j][b] + ps[j][b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1))) + signs[j] >>= 1 + + idx[j]++ + if idx[j] == common.N { + continue PolyLoop + } + } + } + + done = false + } + + if done { + break + } + + perm.Permute() + stateOffset = 0 + } +} + +// Samples p uniformly with 60 non-zero coefficients in {q-1,1}. +// +// The polynomial p will be normalized. +func PolyDeriveUniformB60(p *common.Poly, seed *[48]byte, w1 *VecK) { + var w1Packed [common.PolyLe16Size * K]byte + var buf [136]byte // SHAKE-256 rate is 136 + + w1.PackLe16(w1Packed[:]) + + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Write(w1Packed[:]) + _, _ = h.Read(buf[:]) + + // Essentially we generate a sequence of 60 ones or minus ones, + // prepend 196 zeroes and shuffle the concatenation using the + // usual algorithm (Fisher--Yates.) + signs := binary.LittleEndian.Uint64(buf[:]) + bufOff := 8 // offset into buf + + *p = common.Poly{} // zero p + for i := uint16(common.N - 60); i < common.N; i++ { + var b uint16 + + // Find location of where to move the new coefficient to using + // rejection sampling. + for { + if bufOff >= 136 { + _, _ = h.Read(buf[:]) + bufOff = 0 + } + + b = uint16(buf[bufOff]) + bufOff++ + + if b <= i { + break + } + } + + p[i] = p[b] + p[b] = 1 + // Takes least significant bit of signs and uses it for the sign. + // Note 1 ^ (1 | (Q-1)) = Q-1. + p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1))) + signs >>= 1 + } +} diff --git a/src/circl/sign/dilithium/mode4aes/internal/sample_test.go b/src/circl/sign/dilithium/mode4aes/internal/sample_test.go new file mode 100644 index 00000000000..f4f0a51c1c9 --- /dev/null +++ b/src/circl/sign/dilithium/mode4aes/internal/sample_test.go @@ -0,0 +1,407 @@ +// Code generated from mode3/internal/sample_test.go by gen.go + +package internal + +import ( + "encoding/binary" + "testing" + + "circl/sign/dilithium/internal/common" +) + +func TestVectorDeriveUniform(t *testing.T) { + var p, p2 common.Poly + var seed [32]byte + if UseAES { + p2 = common.Poly{ + 6724291, 310295, 6949524, 4464039, 1482136, 2522903, + 7025059, 3006320, 7286364, 7516512, 3361305, 1955529, + 4765954, 1725325, 6933066, 4299100, 6625173, 4272792, + 583034, 4971409, 2259140, 7715362, 3975394, 2341624, + 5481174, 8150082, 365246, 5491939, 1083120, 7517301, + 3104783, 2475292, 184149, 6425226, 4591622, 5964030, + 4729604, 5471092, 1828227, 1082044, 2516245, 1692580, + 3274844, 5443294, 7256740, 4989638, 3191250, 7479519, + 5124211, 5603858, 1230692, 2513454, 2828034, 4254312, + 1512596, 5245430, 5517392, 2814840, 932545, 6826733, + 3511094, 4075348, 3233981, 7268882, 2913733, 4870249, + 4123492, 8124406, 4016949, 5478752, 2750895, 603525, + 5724798, 3985430, 3483012, 6434230, 3136996, 8297976, + 4107616, 7307748, 6962904, 7544473, 1193110, 3448595, + 4814773, 5607932, 8221314, 1054046, 1541208, 1866050, + 8227412, 2925778, 5293953, 2065416, 4972769, 3616283, + 7990594, 1105530, 7121836, 1170740, 7417431, 633146, + 253820, 7235019, 3539504, 6807707, 451390, 5481526, + 2859902, 1063061, 4579730, 7126652, 7033767, 4294814, + 1414604, 7620048, 1953268, 8304556, 1156814, 1182881, + 5311519, 3057534, 5277666, 682843, 2070398, 2874278, + 4859533, 6376664, 6694074, 1590242, 2620706, 8331066, + 5643845, 5037538, 2891516, 7004879, 3754327, 5031296, + 5463118, 2420870, 8116529, 5517696, 7435129, 3873963, + 710407, 713806, 175647, 4274571, 2655021, 7319503, + 3027243, 7129679, 4213435, 2429323, 4643873, 4568526, + 649664, 1720514, 6497260, 2683517, 7672754, 7105190, + 3148405, 5898369, 5667677, 8050874, 1587139, 7315260, + 4337416, 2202680, 2338714, 557467, 6752058, 2469794, + 485071, 1617604, 3590498, 2151466, 2005823, 7727956, + 7776292, 6783433, 6787146, 1732833, 3596857, 7436284, + 4483349, 4970142, 4472608, 6478342, 1236215, 5695744, + 2280717, 2889355, 3233946, 5187812, 978685, 5177364, + 2922353, 4824807, 5302883, 6739803, 8092453, 5883903, + 816553, 6041174, 8317591, 1459178, 5332455, 1835058, + 1368601, 2820950, 3479224, 2589540, 7992934, 3421045, + 4657128, 8292902, 4153567, 3553988, 7830320, 6722913, + 2555309, 4149801, 8328975, 1560545, 7757473, 3106458, + 4310856, 7135453, 3481032, 652626, 1841361, 8126828, + 6250018, 300536, 7380070, 8174419, 1418793, 6208185, + 3906256, 6679016, 1605701, 3561489, 5819724, 5746996, + 8044214, 7087187, 7102330, 4962927, 4253983, 7108567, + 4119736, 6584065, 441634, 6941656, + } + } else { + p2 = common.Poly{ + 2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052, + 3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357, + 6066350, 8126097, 1179080, 4787182, 6552182, 6713644, + 1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938, + 1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431, + 1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545, + 7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071, + 105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855, + 5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453, + 5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453, + 3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874, + 5614778, 2248550, 1756499, 8280764, 8263880, 7600081, + 5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562, + 7483939, 4938664, 6863397, 5126354, 5218129, 6236086, + 4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737, + 1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595, + 6830029, 1548850, 6593138, 6849097, 1518037, 2859442, + 7772265, 7325153, 3281191, 7856131, 4995056, 4684325, + 1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778, + 7973479, 3171829, 5624626, 3540123, 7150120, 8313283, + 3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342, + 7501562, 5826142, 2709813, 8245473, 2369045, 2782257, + 5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983, + 5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375, + 267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500, + 2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008, + 8258986, 2183134, 2302072, 4674924, 4306056, 7465311, + 6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700, + 2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533, + 255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625, + 6997719, 6260212, 6186962, 6636650, 7836834, 7998017, + 2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598, + 4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947, + 6195178, 5552390, 6804584, 6305468, 5731980, 6095195, + 3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054, + 4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780, + 3740517, 5224226, 3547288, 2083124, 4699398, 3654239, + 5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706, + 4352830, + } + } + for i := 0; i < 32; i++ { + seed[i] = byte(i) + } + PolyDeriveUniform(&p, &seed, 30000) + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniform(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniform(&p, &seed, uint16(i)) + if !PolyNormalized(&p) { + t.Fatal() + } + } +} + +func TestDeriveUniformLeqEta(t *testing.T) { + var p common.Poly + var seed [32]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeqEta(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-Eta || p[j] > common.Q+Eta { + t.Fatal() + } + } + } +} + +func TestDeriveUniformLeGamma1(t *testing.T) { + var p common.Poly + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + for j := 0; j < common.N; j++ { + if p[j] < common.Q-common.Gamma1 || p[j] > common.Q+common.Gamma1 { + t.Fatal() + } + } + } +} + +func TestVectorDeriveUniformLeGamma1(t *testing.T) { + var p, p2 common.Poly + var seed [48]byte + if UseAES { + p2 = common.Poly{ + 90940, 8133770, 8210940, 8218464, 8362467, 431142, 98024, + 320453, 7892373, 144162, 495313, 7910122, 308198, 8024421, + 8313699, 8323445, 8242093, 7946588, 418979, 427179, 353562, + 20972, 455962, 213062, 361787, 8141790, 8321931, 7885366, + 88645, 181202, 8094142, 8303121, 8059515, 7919812, 191865, + 7910073, 7896561, 8096830, 7899355, 8338900, 72693, 236799, + 8183042, 347570, 8153528, 8364233, 8077851, 8312277, 104682, + 8037310, 8356199, 7994081, 240369, 70229, 8108858, 8175836, + 466639, 50909, 339919, 8029663, 341659, 154398, 64345, + 97101, 212245, 8285367, 521225, 325882, 296235, 8110929, + 8015814, 7953234, 158409, 329908, 8331330, 449258, 167701, + 8197796, 8228247, 7940020, 1985, 304704, 475316, 8037482, + 8250449, 304557, 8216567, 432266, 213295, 8162216, 381001, + 7995314, 7988689, 128534, 245586, 67041, 8232744, 398441, + 223116, 443612, 149856, 222852, 158723, 54746, 171906, + 163070, 353915, 8263276, 8016812, 8229081, 31827, 489715, + 450171, 8069106, 53220, 7932381, 7955335, 8197363, 201044, + 8306733, 446376, 8211025, 7889271, 8070595, 495514, 8158685, + 7524, 7973394, 247673, 4293, 184924, 457334, 138349, 8123964, + 284179, 8255307, 8068216, 8291492, 243759, 8060601, 20962, + 8058389, 420953, 8305974, 455136, 8218139, 7121, 147703, + 7951253, 394376, 8127066, 365861, 8062390, 8138732, 366555, + 8280514, 221, 395861, 7968769, 7977119, 8098083, 343056, + 8190769, 223361, 163270, 203059, 109219, 8228600, 8127695, + 321016, 295979, 8201961, 49891, 8335504, 8190386, 8190984, + 8278654, 336364, 7878013, 7922436, 7974101, 8075534, 8200852, + 8333820, 415982, 8089662, 149553, 7946740, 474102, 7937116, + 8026845, 356056, 191053, 86928, 8218644, 8375040, 8029184, + 8025675, 8193350, 295360, 7905768, 487174, 8362961, 386108, + 282213, 8373318, 50167, 8238992, 7911505, 493459, 8335164, + 8079327, 250697, 263154, 221028, 40778, 87515, 8372585, + 504728, 7980935, 8307600, 298972, 427523, 93352, 89915, + 391490, 80320, 7975008, 336136, 7949815, 8048682, 8332244, + 8204778, 8177783, 7910684, 7925292, 518641, 59663, 53608, + 222225, 463772, 8022091, 8173722, 8291385, 472741, 8105898, + 7943299, 267137, 7957660, 371874, 409084, 203750, 477334, + 83412, 111278, 120444, + } + } else { + p2 = common.Poly{ + 338083, 7978692, 8044913, 373628, 427855, 79725, 91018, + 349821, 501552, 7955127, 8316400, 290708, 216142, 8199666, + 8040144, 109426, 8177916, 8200218, 8125680, 358131, 160961, + 497383, 25361, 156297, 8033745, 7897189, 48397, 498732, + 464556, 7862704, 8308667, 236080, 91240, 8328377, 326190, + 509979, 8313264, 8106493, 8210965, 8328036, 172602, 8108765, + 8192963, 8361660, 8026473, 7932022, 322006, 8305874, 8254440, + 7866474, 373371, 8023413, 8221878, 486124, 36080, 8324512, + 8042056, 7984472, 8048111, 7910387, 8205382, 8259636, 188609, + 8316587, 59306, 119803, 8067108, 8155455, 8153450, 7983908, + 8222256, 21521, 114297, 8069037, 151621, 8014482, 8052856, + 376107, 8004652, 175001, 8079461, 8351123, 8021484, 144547, + 7908116, 8278100, 8136941, 142399, 8026843, 8081852, 124334, + 242796, 266768, 7919478, 7954016, 28927, 8329064, 514031, + 423911, 27907, 8142788, 8078298, 273978, 382723, 8148646, + 186476, 8030712, 8067268, 356250, 145817, 60045, 122764, + 56856, 8225416, 136437, 199652, 8343127, 8109765, 7936848, + 446966, 8351681, 288663, 409663, 512988, 8350788, 8191864, + 8366223, 281267, 7921696, 8213978, 442484, 67457, 8030602, + 238514, 230458, 8301866, 8359700, 150320, 143893, 461735, + 225443, 8027502, 151113, 365244, 7911438, 82498, 405398, + 8207009, 8108255, 367485, 514660, 8294055, 8168958, 127725, + 402955, 8051625, 7859029, 7980052, 321819, 7949587, 125778, + 8287078, 131972, 499609, 256795, 8180323, 8269393, 5878, + 8145473, 8238676, 383855, 415547, 424071, 241989, 8165743, + 8207329, 149608, 8315331, 7901850, 8114275, 360650, 516061, + 255090, 8277977, 270877, 8125200, 479248, 7991711, 8028595, + 73426, 8215429, 208217, 153872, 429336, 229856, 461204, + 236682, 7930158, 8298847, 228327, 8009399, 8111520, 345025, + 386495, 93454, 8336429, 8161305, 7980811, 286795, 162808, + 224476, 7972825, 85118, 287488, 8029791, 119071, 371, 518524, + 473496, 451205, 127000, 19233, 211519, 2442, 7950959, 481888, + 8041598, 8281176, 437202, 7912610, 8080153, 8237500, 7926828, + 8009421, 204880, 62495, 8192310, 8314388, 98616, 182368, + 323894, 59901, 481049, 8139275, 7872144, 254106, 376257, + 93339, 301342, 366536, 438920, 84773, 461471, 8125755, + 7930085, 405116, + } + } + for i := 0; i < 48; i++ { + seed[i] = byte(i) + } + PolyDeriveUniformLeGamma1(&p, &seed, 30000) + p.Normalize() + if p != p2 { + t.Fatalf("%v != %v", p, p2) + } +} + +func TestDeriveUniformB60(t *testing.T) { + var p common.Poly + var w1 VecK + var seed [48]byte + for i := 0; i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + PolyDeriveUniformB60(&p, &seed, &w1) + nonzero := 0 + for j := 0; j < common.N; j++ { + if p[j] != 0 { + if p[j] != 1 && p[j] != common.Q-1 { + t.Fatal() + } + nonzero++ + } + } + if nonzero != 60 { + t.Fatal() + } + } +} + +func TestDeriveUniformX4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [32]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed, + nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniform(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatal() + } + } +} + +func TestDeriveUniformB60X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + var w1s [4]VecK + for j := 0; j < 4; j++ { + for k := 0; k < K; k++ { + for i := 0; i < common.N; i++ { + w1s[j][k][i] = uint32(j+k*4+i*4*K) & 15 + } + } + } + PolyDeriveUniformB60X4( + [4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, + [4]*VecK{&w1s[0], &w1s[1], &w1s[2], &w1s[3]}, + ) + for j := 0; j < 4; j++ { + PolyDeriveUniformB60(&p, &seed, &w1s[j]) + if ps[j] != p { + t.Fatalf("%v %v", ps[j], p) + } + } +} + +func TestDeriveUniformLeGamma1X4(t *testing.T) { + if !DeriveX4Available { + t.SkipNow() + } + var ps [4]common.Poly + var p common.Poly + var seed [48]byte + nonces := [4]uint16{12345, 54321, 13532, 37377} + + for i := 0; i < len(seed); i++ { + seed[i] = byte(i) + } + + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, + &seed, nonces) + for i := 0; i < 4; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, nonces[i]) + if ps[i] != p { + t.Fatalf("%d\n%v\n%v", i, p, ps[i]) + } + } +} + +func BenchmarkPolyDeriveUniformB60(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60(&p, &seed, &w1) + } +} + +func BenchmarkPolyDeriveUniformB60X4(b *testing.B) { + var seed [48]byte + var p common.Poly + var w1 VecK + for i := 0; i < b.N; i++ { + w1[0][0] = uint32(i) + PolyDeriveUniformB60X4( + [4]*common.Poly{&p, &p, &p, &p}, + &seed, + [4]*VecK{&w1, &w1, &w1, &w1}, + ) + } +} + +func BenchmarkPolyDeriveUniform(b *testing.B) { + var seed [32]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniform(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformX4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [32]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) { + var seed [48]byte + var p common.Poly + for i := 0; i < b.N; i++ { + PolyDeriveUniformLeGamma1(&p, &seed, uint16(i)) + } +} + +func BenchmarkPolyDeriveUniformLeGamma1X4(b *testing.B) { + if !DeriveX4Available { + b.SkipNow() + } + var seed [48]byte + var p [4]common.Poly + for i := 0; i < b.N; i++ { + nonce := uint16(4 * i) + PolyDeriveUniformLeGamma1X4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]}, + &seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3}) + } +} diff --git a/src/circl/sign/dilithium/mode4aes/internal/vec.go b/src/circl/sign/dilithium/mode4aes/internal/vec.go new file mode 100644 index 00000000000..a20a8b0224e --- /dev/null +++ b/src/circl/sign/dilithium/mode4aes/internal/vec.go @@ -0,0 +1,281 @@ +// Code generated from mode3/internal/vec.go by gen.go + +package internal + +import ( + "circl/sign/dilithium/internal/common" +) + +// A vector of L polynomials. +type VecL [L]common.Poly + +// A vector of K polynomials. +type VecK [K]common.Poly + +// Normalize the polynomials in this vector. +func (v *VecL) Normalize() { + for i := 0; i < L; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecL) NormalizeAssumingLe2Q() { + for i := 0; i < L; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecL) Add(w, u *VecL) { + for i := 0; i < L; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecL) NTT() { + for i := 0; i < L; i++ { + v[i].NTT() + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecL) Exceeds(bound uint32) bool { + for i := 0; i < L; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecL) Decompose(v0PlusQ, v1 *VecL) { + for i := 0; i < L; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecL) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeqEta(). +func (v *VecL) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sequentially packs each polynomial using Poly.PackLeGamma1(). +func (v *VecL) PackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].PackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Sets v to the polynomials packed in buf using VecL.PackLeGamma1(). +func (v *VecL) UnpackLeGamma1(buf []byte) { + offset := 0 + for i := 0; i < L; i++ { + v[i].UnpackLeGamma1(buf[offset:]) + offset += common.PolyLeGamma1Size + } +} + +// Normalize the polynomials in this vector. +func (v *VecK) Normalize() { + for i := 0; i < K; i++ { + v[i].Normalize() + } +} + +// Normalize the polynomials in this vector assuming their coefficients +// are already bounded by 2q. +func (v *VecK) NormalizeAssumingLe2Q() { + for i := 0; i < K; i++ { + v[i].NormalizeAssumingLe2Q() + } +} + +// Sets v to w + u. Does not normalize. +func (v *VecK) Add(w, u *VecK) { + for i := 0; i < K; i++ { + v[i].Add(&w[i], &u[i]) + } +} + +// Checks whether any of the coefficients exceeds the given bound in supnorm +// +// Requires the vector to be normalized. +func (v *VecK) Exceeds(bound uint32) bool { + for i := 0; i < K; i++ { + if v[i].Exceeds(bound) { + return true + } + } + return false +} + +// Applies Poly.Power2Round componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Power2Round(&v0PlusQ[i], &v1[i]) + } +} + +// Applies Poly.Decompose componentwise. +// +// Requires the vector to be normalized. +func (v *VecK) Decompose(v0PlusQ, v1 *VecK) { + for i := 0; i < K; i++ { + v[i].Decompose(&v0PlusQ[i], &v1[i]) + } +} + +// Sets v to the hint vector for v0 the modified low bits and v1 +// the unmodified high bits --- see makeHint(). +// +// Returns the number of ones in the hint vector. +func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) { + for i := 0; i < K; i++ { + pop += v[i].MakeHint(&v0[i], &v1[i]) + } + return +} + +// Computes corrections to the high bits of the polynomials in the vector +// w using the hints in h and sets v to the corrected high bits. Returns v. +// See useHint(). +func (v *VecK) UseHint(q, hint *VecK) *VecK { + for i := 0; i < K; i++ { + v[i].UseHint(&q[i], &hint[i]) + } + return v +} + +// Sequentially packs each polynomial using Poly.PackT1(). +func (v *VecK) PackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sets v to the vector packed into buf by PackT1(). +func (v *VecK) UnpackT1(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT1(buf[offset:]) + offset += common.PolyT1Size + } +} + +// Sequentially packs each polynomial using Poly.PackT0(). +func (v *VecK) PackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sets v to the vector packed into buf by PackT0(). +func (v *VecK) UnpackT0(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].UnpackT0(buf[offset:]) + offset += common.PolyT0Size + } +} + +// Sequentially packs each polynomial using Poly.PackLeqEta(). +func (v *VecK) PackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyPackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Sets v to the polynomials packed in buf using VecK.PackLeqEta(). +func (v *VecK) UnpackLeqEta(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + PolyUnpackLeqEta(&v[i], buf[offset:]) + offset += PolyLeqEtaSize + } +} + +// Applies NTT componentwise. See Poly.NTT() for details. +func (v *VecK) NTT() { + for i := 0; i < K; i++ { + v[i].NTT() + } +} + +// Sequentially packs each polynomial using Poly.PackLe16(). +func (v *VecK) PackLe16(buf []byte) { + offset := 0 + for i := 0; i < K; i++ { + v[i].PackLe16(buf[offset:]) + offset += common.PolyLe16Size + } +} + +// Sets v to a - b. +// +// Warning: assumes coefficients of the polynomials of b are less than 2q. +func (v *VecK) Sub(a, b *VecK) { + for i := 0; i < K; i++ { + v[i].Sub(&a[i], &b[i]) + } +} + +// Sets v to 2ᵈ w without reducing. +func (v *VecK) MulBy2toD(w *VecK) { + for i := 0; i < K; i++ { + v[i].MulBy2toD(&w[i]) + } +} + +// Applies InvNTT componentwise. See Poly.InvNTT() for details. +func (v *VecK) InvNTT() { + for i := 0; i < K; i++ { + v[i].InvNTT() + } +} + +// Applies Poly.ReduceLe2Q() componentwise. +func (v *VecK) ReduceLe2Q() { + for i := 0; i < K; i++ { + v[i].ReduceLe2Q() + } +} diff --git a/src/circl/sign/ed25519/ed25519.go b/src/circl/sign/ed25519/ed25519.go new file mode 100644 index 00000000000..caf56e95cb0 --- /dev/null +++ b/src/circl/sign/ed25519/ed25519.go @@ -0,0 +1,452 @@ +// Package ed25519 implements Ed25519 signature scheme as described in RFC-8032. +// +// This package provides optimized implementations of the three signature +// variants and maintaining closer compatiblilty with crypto/ed25519. +// +// | Scheme Name | Sign Function | Verification | Context | +// |-------------|-------------------|---------------|-------------------| +// | Ed25519 | Sign | Verify | None | +// | Ed25519Ph | SignPh | VerifyPh | Yes, can be empty | +// | Ed25519Ctx | SignWithCtx | VerifyWithCtx | Yes, non-empty | +// | All above | (PrivateKey).Sign | VerifyAny | As above | +// +// Specific functions for sign and verify are defined. A generic signing +// function for all schemes is available through the crypto.Signer interface, +// which is implemented by the PrivateKey type. A correspond all-in-one +// verification method is provided by the VerifyAny function. +// +// Signing with Ed25519Ph or Ed25519Ctx requires a context string for domain +// separation. This parameter is passed using a SignerOptions struct defined +// in this package. While Ed25519Ph accepts an empty context, Ed25519Ctx +// enforces non-empty context strings. +// +// Compatibility with crypto.ed25519 +// +// These functions are compatible with the “Ed25519” function defined in +// RFC-8032. However, unlike RFC 8032's formulation, this package's private +// key representation includes a public key suffix to make multiple signing +// operations with the same key more efficient. This package refers to the +// RFC-8032 private key as the “seed”. +// +// References +// +// - RFC-8032: https://rfc-editor.org/rfc/rfc8032.txt +// - Ed25519: https://ed25519.cr.yp.to/ +// - EdDSA: High-speed high-security signatures. https://doi.org/10.1007/s13389-012-0027-1 +package ed25519 + +import ( + "bytes" + "crypto" + cryptoRand "crypto/rand" + "crypto/sha512" + "crypto/subtle" + "errors" + "fmt" + "io" + "strconv" + + "circl/sign" +) + +const ( + // ContextMaxSize is the maximum length (in bytes) allowed for context. + ContextMaxSize = 255 + // PublicKeySize is the size, in bytes, of public keys as used in this package. + PublicKeySize = 32 + // PrivateKeySize is the size, in bytes, of private keys as used in this package. + PrivateKeySize = 64 + // SignatureSize is the size, in bytes, of signatures generated and verified by this package. + SignatureSize = 64 + // SeedSize is the size, in bytes, of private key seeds. These are the private key representations used by RFC 8032. + SeedSize = 32 +) + +const ( + paramB = 256 / 8 // Size of keys in bytes. +) + +// SignerOptions implements crypto.SignerOpts and augments with parameters +// that are specific to the Ed25519 signature schemes. +type SignerOptions struct { + // Hash must be crypto.Hash(0) for Ed25519/Ed25519ctx, or crypto.SHA512 + // for Ed25519ph. + crypto.Hash + + // Context is an optional domain separation string for Ed25519ph and a + // must for Ed25519ctx. Its length must be less or equal than 255 bytes. + Context string + + // Scheme is an identifier for choosing a signature scheme. The zero value + // is ED25519. + Scheme SchemeID +} + +// SchemeID is an identifier for each signature scheme. +type SchemeID uint + +const ( + ED25519 SchemeID = iota + ED25519Ph + ED25519Ctx +) + +// PrivateKey is the type of Ed25519 private keys. It implements crypto.Signer. +type PrivateKey []byte + +// Equal reports whether priv and x have the same value. +func (priv PrivateKey) Equal(x crypto.PrivateKey) bool { + xx, ok := x.(PrivateKey) + return ok && subtle.ConstantTimeCompare(priv, xx) == 1 +} + +// Public returns the PublicKey corresponding to priv. +func (priv PrivateKey) Public() crypto.PublicKey { + publicKey := make(PublicKey, PublicKeySize) + copy(publicKey, priv[SeedSize:]) + return publicKey +} + +// Seed returns the private key seed corresponding to priv. It is provided for +// interoperability with RFC 8032. RFC 8032's private keys correspond to seeds +// in this package. +func (priv PrivateKey) Seed() []byte { + seed := make([]byte, SeedSize) + copy(seed, priv[:SeedSize]) + return seed +} + +func (priv PrivateKey) Scheme() sign.Scheme { return sch } + +func (pub PublicKey) Scheme() sign.Scheme { return sch } + +func (priv PrivateKey) MarshalBinary() (data []byte, err error) { + privateKey := make(PrivateKey, PrivateKeySize) + copy(privateKey, priv) + return privateKey, nil +} + +func (pub PublicKey) MarshalBinary() (data []byte, err error) { + publicKey := make(PublicKey, PublicKeySize) + copy(publicKey, pub) + return publicKey, nil +} + +// Equal reports whether pub and x have the same value. +func (pub PublicKey) Equal(x crypto.PublicKey) bool { + xx, ok := x.(PublicKey) + return ok && bytes.Equal(pub, xx) +} + +// Sign creates a signature of a message with priv key. +// This function is compatible with crypto.ed25519 and also supports the +// three signature variants defined in RFC-8032, namely Ed25519 (or pure +// EdDSA), Ed25519Ph, and Ed25519Ctx. +// The opts.HashFunc() must return zero to specify either Ed25519 or Ed25519Ctx +// variant. This can be achieved by passing crypto.Hash(0) as the value for +// opts. +// The opts.HashFunc() must return SHA512 to specify the Ed25519Ph variant. +// This can be achieved by passing crypto.SHA512 as the value for opts. +// Use a SignerOptions struct (defined in this package) to pass a context +// string for signing. +func (priv PrivateKey) Sign( + rand io.Reader, + message []byte, + opts crypto.SignerOpts) (signature []byte, err error) { + var ctx string + var scheme SchemeID + if o, ok := opts.(SignerOptions); ok { + ctx = o.Context + scheme = o.Scheme + } + + switch true { + case scheme == ED25519 && opts.HashFunc() == crypto.Hash(0): + return Sign(priv, message), nil + case scheme == ED25519Ph && opts.HashFunc() == crypto.SHA512: + return SignPh(priv, message, ctx), nil + case scheme == ED25519Ctx && opts.HashFunc() == crypto.Hash(0) && len(ctx) > 0: + return SignWithCtx(priv, message, ctx), nil + default: + return nil, errors.New("ed25519: bad hash algorithm") + } +} + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) { + if rand == nil { + rand = cryptoRand.Reader + } + + seed := make([]byte, SeedSize) + if _, err := io.ReadFull(rand, seed); err != nil { + return nil, nil, err + } + + privateKey := NewKeyFromSeed(seed) + publicKey := make(PublicKey, PublicKeySize) + copy(publicKey, privateKey[SeedSize:]) + + return publicKey, privateKey, nil +} + +// NewKeyFromSeed calculates a private key from a seed. It will panic if +// len(seed) is not SeedSize. This function is provided for interoperability +// with RFC 8032. RFC 8032's private keys correspond to seeds in this +// package. +func NewKeyFromSeed(seed []byte) PrivateKey { + privateKey := make(PrivateKey, PrivateKeySize) + newKeyFromSeed(privateKey, seed) + return privateKey +} + +func newKeyFromSeed(privateKey, seed []byte) { + if l := len(seed); l != SeedSize { + panic("ed25519: bad seed length: " + strconv.Itoa(l)) + } + var P pointR1 + k := sha512.Sum512(seed) + clamp(k[:]) + reduceModOrder(k[:paramB], false) + P.fixedMult(k[:paramB]) + copy(privateKey[:SeedSize], seed) + _ = P.ToBytes(privateKey[SeedSize:]) +} + +func signAll(signature []byte, privateKey PrivateKey, message, ctx []byte, preHash bool) { + if l := len(privateKey); l != PrivateKeySize { + panic("ed25519: bad private key length: " + strconv.Itoa(l)) + } + + H := sha512.New() + var PHM []byte + + if preHash { + _, _ = H.Write(message) + PHM = H.Sum(nil) + H.Reset() + } else { + PHM = message + } + + // 1. Hash the 32-byte private key using SHA-512. + _, _ = H.Write(privateKey[:SeedSize]) + h := H.Sum(nil) + clamp(h[:]) + prefix, s := h[paramB:], h[:paramB] + + // 2. Compute SHA-512(dom2(F, C) || prefix || PH(M)) + H.Reset() + + writeDom(H, ctx, preHash) + + _, _ = H.Write(prefix) + _, _ = H.Write(PHM) + r := H.Sum(nil) + reduceModOrder(r[:], true) + + // 3. Compute the point [r]B. + var P pointR1 + P.fixedMult(r[:paramB]) + R := (&[paramB]byte{})[:] + if err := P.ToBytes(R); err != nil { + panic(err) + } + + // 4. Compute SHA512(dom2(F, C) || R || A || PH(M)). + H.Reset() + + writeDom(H, ctx, preHash) + + _, _ = H.Write(R) + _, _ = H.Write(privateKey[SeedSize:]) + _, _ = H.Write(PHM) + hRAM := H.Sum(nil) + + reduceModOrder(hRAM[:], true) + + // 5. Compute S = (r + k * s) mod order. + S := (&[paramB]byte{})[:] + calculateS(S, r[:paramB], hRAM[:paramB], s) + + // 6. The signature is the concatenation of R and S. + copy(signature[:paramB], R[:]) + copy(signature[paramB:], S[:]) +} + +// Sign signs the message with privateKey and returns a signature. +// This function supports the signature variant defined in RFC-8032: Ed25519, +// also known as the pure version of EdDSA. +// It will panic if len(privateKey) is not PrivateKeySize. +func Sign(privateKey PrivateKey, message []byte) []byte { + signature := make([]byte, SignatureSize) + signAll(signature, privateKey, message, []byte(""), false) + return signature +} + +// SignPh creates a signature of a message with private key and context. +// This function supports the signature variant defined in RFC-8032: Ed25519ph, +// meaning it internally hashes the message using SHA-512, and optionally +// accepts a context string. +// It will panic if len(privateKey) is not PrivateKeySize. +// Context could be passed to this function, which length should be no more than +// ContextMaxSize=255. It can be empty. +func SignPh(privateKey PrivateKey, message []byte, ctx string) []byte { + if len(ctx) > ContextMaxSize { + panic(fmt.Errorf("ed25519: bad context length: %v", len(ctx))) + } + + signature := make([]byte, SignatureSize) + signAll(signature, privateKey, message, []byte(ctx), true) + return signature +} + +// SignWithCtx creates a signature of a message with private key and context. +// This function supports the signature variant defined in RFC-8032: Ed25519ctx, +// meaning it accepts a non-empty context string. +// It will panic if len(privateKey) is not PrivateKeySize. +// Context must be passed to this function, which length should be no more than +// ContextMaxSize=255 and cannot be empty. +func SignWithCtx(privateKey PrivateKey, message []byte, ctx string) []byte { + if len(ctx) == 0 || len(ctx) > ContextMaxSize { + panic(fmt.Errorf("ed25519: bad context length: %v > %v", len(ctx), ContextMaxSize)) + } + + signature := make([]byte, SignatureSize) + signAll(signature, privateKey, message, []byte(ctx), false) + return signature +} + +func verify(public PublicKey, message, signature, ctx []byte, preHash bool) bool { + if len(public) != PublicKeySize || + len(signature) != SignatureSize || + !isLessThanOrder(signature[paramB:]) { + return false + } + + var P pointR1 + if ok := P.FromBytes(public); !ok { + return false + } + + H := sha512.New() + var PHM []byte + + if preHash { + _, _ = H.Write(message) + PHM = H.Sum(nil) + H.Reset() + } else { + PHM = message + } + + R := signature[:paramB] + + writeDom(H, ctx, preHash) + + _, _ = H.Write(R) + _, _ = H.Write(public) + _, _ = H.Write(PHM) + hRAM := H.Sum(nil) + reduceModOrder(hRAM[:], true) + + var Q pointR1 + encR := (&[paramB]byte{})[:] + P.neg() + Q.doubleMult(&P, signature[paramB:], hRAM[:paramB]) + _ = Q.ToBytes(encR) + return bytes.Equal(R, encR) +} + +// VerifyAny returns true if the signature is valid. Failure cases are invalid +// signature, or when the public key cannot be decoded. +// This function supports all the three signature variants defined in RFC-8032, +// namely Ed25519 (or pure EdDSA), Ed25519Ph, and Ed25519Ctx. +// The opts.HashFunc() must return zero to specify either Ed25519 or Ed25519Ctx +// variant. This can be achieved by passing crypto.Hash(0) as the value for opts. +// The opts.HashFunc() must return SHA512 to specify the Ed25519Ph variant. +// This can be achieved by passing crypto.SHA512 as the value for opts. +// Use a SignerOptions struct to pass a context string for signing. +func VerifyAny(public PublicKey, message, signature []byte, opts crypto.SignerOpts) bool { + var ctx string + var scheme SchemeID + if o, ok := opts.(SignerOptions); ok { + ctx = o.Context + scheme = o.Scheme + } + + switch true { + case scheme == ED25519 && opts.HashFunc() == crypto.Hash(0): + return Verify(public, message, signature) + case scheme == ED25519Ph && opts.HashFunc() == crypto.SHA512: + return VerifyPh(public, message, signature, ctx) + case scheme == ED25519Ctx && opts.HashFunc() == crypto.Hash(0) && len(ctx) > 0: + return VerifyWithCtx(public, message, signature, ctx) + default: + return false + } +} + +// Verify returns true if the signature is valid. Failure cases are invalid +// signature, or when the public key cannot be decoded. +// This function supports the signature variant defined in RFC-8032: Ed25519, +// also known as the pure version of EdDSA. +func Verify(public PublicKey, message, signature []byte) bool { + return verify(public, message, signature, []byte(""), false) +} + +// VerifyPh returns true if the signature is valid. Failure cases are invalid +// signature, or when the public key cannot be decoded. +// This function supports the signature variant defined in RFC-8032: Ed25519ph, +// meaning it internally hashes the message using SHA-512. +// Context could be passed to this function, which length should be no more than +// 255. It can be empty. +func VerifyPh(public PublicKey, message, signature []byte, ctx string) bool { + return verify(public, message, signature, []byte(ctx), true) +} + +// VerifyWithCtx returns true if the signature is valid. Failure cases are invalid +// signature, or when the public key cannot be decoded, or when context is +// not provided. +// This function supports the signature variant defined in RFC-8032: Ed25519ctx, +// meaning it does not handle prehashed messages. Non-empty context string must be +// provided, and must not be more than 255 of length. +func VerifyWithCtx(public PublicKey, message, signature []byte, ctx string) bool { + if len(ctx) == 0 || len(ctx) > ContextMaxSize { + return false + } + + return verify(public, message, signature, []byte(ctx), false) +} + +func clamp(k []byte) { + k[0] &= 248 + k[paramB-1] = (k[paramB-1] & 127) | 64 +} + +// isLessThanOrder returns true if 0 <= x < order. +func isLessThanOrder(x []byte) bool { + i := len(order) - 1 + for i > 0 && x[i] == order[i] { + i-- + } + return x[i] < order[i] +} + +func writeDom(h io.Writer, ctx []byte, preHash bool) { + dom2 := "SigEd25519 no Ed25519 collisions" + + if len(ctx) > 0 { + _, _ = h.Write([]byte(dom2)) + if preHash { + _, _ = h.Write([]byte{byte(0x01), byte(len(ctx))}) + } else { + _, _ = h.Write([]byte{byte(0x00), byte(len(ctx))}) + } + _, _ = h.Write(ctx) + } else if preHash { + _, _ = h.Write([]byte(dom2)) + _, _ = h.Write([]byte{0x01, 0x00}) + } +} diff --git a/src/circl/sign/ed25519/ed25519_test.go b/src/circl/sign/ed25519/ed25519_test.go new file mode 100644 index 00000000000..7c1f523da06 --- /dev/null +++ b/src/circl/sign/ed25519/ed25519_test.go @@ -0,0 +1,103 @@ +package ed25519_test + +import ( + "testing" + + "circl/sign/ed25519" +) + +type zeroReader struct{} + +func (zeroReader) Read(buf []byte) (int, error) { + for i := range buf { + buf[i] = 0 + } + return len(buf), nil +} + +func TestMalleability(t *testing.T) { + // https://tools.ietf.org/html/rfc8032#section-5.1.7 adds an additional test + // that s be in [0, order). This prevents someone from adding a multiple of + // order to s and obtaining a second valid signature for the same message. + msg := []byte{0x54, 0x65, 0x73, 0x74} + sig := []byte{ + 0x7c, 0x38, 0xe0, 0x26, 0xf2, 0x9e, 0x14, 0xaa, 0xbd, 0x05, 0x9a, + 0x0f, 0x2d, 0xb8, 0xb0, 0xcd, 0x78, 0x30, 0x40, 0x60, 0x9a, 0x8b, + 0xe6, 0x84, 0xdb, 0x12, 0xf8, 0x2a, 0x27, 0x77, 0x4a, 0xb0, 0x67, + 0x65, 0x4b, 0xce, 0x38, 0x32, 0xc2, 0xd7, 0x6f, 0x8f, 0x6f, 0x5d, + 0xaf, 0xc0, 0x8d, 0x93, 0x39, 0xd4, 0xee, 0xf6, 0x76, 0x57, 0x33, + 0x36, 0xa5, 0xc5, 0x1e, 0xb6, 0xf9, 0x46, 0xb3, 0x1d, + } + publicKey := []byte{ + 0x7d, 0x4d, 0x0e, 0x7f, 0x61, 0x53, 0xa6, 0x9b, 0x62, 0x42, 0xb5, + 0x22, 0xab, 0xbe, 0xe6, 0x85, 0xfd, 0xa4, 0x42, 0x0f, 0x88, 0x34, + 0xb1, 0x08, 0xc3, 0xbd, 0xae, 0x36, 0x9e, 0xf5, 0x49, 0xfa, + } + + if ed25519.Verify(publicKey, msg, sig) { + t.Fatal("non-canonical signature accepted") + } +} + +func TestPublic(t *testing.T) { + var zero zeroReader + pub, priv, err := ed25519.GenerateKey(zero) + if err != nil { + t.Fatal(err) + } + if !priv.Equal(priv) { + t.FailNow() + } + if !pub.Equal(pub) { + t.FailNow() + } + pub2 := priv.Public() + if !pub.Equal(pub2) { + t.FailNow() + } +} + +func BenchmarkKeyGeneration(b *testing.B) { + var zero zeroReader + for i := 0; i < b.N; i++ { + if _, _, err := ed25519.GenerateKey(zero); err != nil { + b.Fatal(err) + } + } +} + +func BenchmarkNewKeyFromSeed(b *testing.B) { + seed := make([]byte, ed25519.SeedSize) + b.ReportAllocs() + for i := 0; i < b.N; i++ { + _ = ed25519.NewKeyFromSeed(seed) + } +} + +func BenchmarkSigning(b *testing.B) { + var zero zeroReader + _, priv, err := ed25519.GenerateKey(zero) + if err != nil { + b.Fatal(err) + } + message := []byte("Hello, world!") + b.ReportAllocs() + b.ResetTimer() + for i := 0; i < b.N; i++ { + ed25519.Sign(priv, message) + } +} + +func BenchmarkVerification(b *testing.B) { + var zero zeroReader + pub, priv, err := ed25519.GenerateKey(zero) + if err != nil { + b.Fatal(err) + } + message := []byte("Hello, world!") + signature := ed25519.Sign(priv, message) + b.ResetTimer() + for i := 0; i < b.N; i++ { + ed25519.Verify(pub, message, signature) + } +} diff --git a/src/circl/sign/ed25519/extra_test.go b/src/circl/sign/ed25519/extra_test.go new file mode 100644 index 00000000000..c2023e7f072 --- /dev/null +++ b/src/circl/sign/ed25519/extra_test.go @@ -0,0 +1,249 @@ +package ed25519_test + +import ( + "bytes" + "crypto" + "crypto/rand" + "errors" + "fmt" + "testing" + + "circl/internal/test" + "circl/sign/ed25519" +) + +func TestWrongPublicKey(t *testing.T) { + wrongPublicKeys := [...][ed25519.PublicKeySize]byte{ + { // y = p + 0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, + }, + { // y > p + 0xed + 1, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, + }, + { // x^2 = u/v = (y^2-1)/(dy^2+1) is not a quadratic residue + 0x9a, 0x0a, 0xbe, 0xc6, 0x23, 0xcb, 0x5a, 0x23, + 0x4e, 0x49, 0xd8, 0x92, 0xc2, 0x72, 0xd5, 0xa8, + 0x27, 0xff, 0x42, 0x07, 0x7d, 0xe3, 0xf2, 0xb4, + 0x74, 0x75, 0x9d, 0x04, 0x34, 0xed, 0xa6, 0x70, + }, + { // y = 1 and x^2 = u/v = 0, and the sign of X is 1 + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 | 0x80, + }, + { // y = -1 and x^2 = u/v = 0, and the sign of X is 1 + 0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f | 0x80, + }, + } + sig := (&[ed25519.SignatureSize]byte{})[:] + for _, public := range wrongPublicKeys { + got := ed25519.Verify(public[:], []byte(""), sig) + want := false + if got != want { + test.ReportError(t, got, want, public) + } + } +} + +func TestSigner(t *testing.T) { + seed := (&[ed25519.SeedSize]byte{})[:] + _, _ = rand.Read(seed) + key := ed25519.NewKeyFromSeed(seed) + + priv := key.Seed() + if !bytes.Equal(seed, priv) { + got := priv + want := seed + test.ReportError(t, got, want) + } + + for _, o := range []ed25519.SignerOptions{ + {Scheme: ed25519.ED25519, Hash: crypto.Hash(0), Context: ""}, + {Scheme: ed25519.ED25519Ph, Hash: crypto.SHA512, Context: ""}, + {Scheme: ed25519.ED25519Ph, Hash: crypto.SHA512, Context: "non-empty"}, + {Scheme: ed25519.ED25519Ctx, Hash: crypto.Hash(0), Context: "non-empty"}, + } { + testSigner(t, key, o) + } +} + +func testSigner(t *testing.T, signer crypto.Signer, ops ed25519.SignerOptions) { + msg := make([]byte, 64) + _, _ = rand.Read(msg) + + sig, err := signer.Sign(nil, msg, ops) + if err != nil { + got := err + var want error + test.ReportError(t, got, want, ops) + } + + if len(sig) != ed25519.SignatureSize { + got := len(sig) + want := ed25519.SignatureSize + test.ReportError(t, got, want, ops) + } + + pubSigner, ok := signer.Public().(ed25519.PublicKey) + if !ok { + got := ok + want := true + test.ReportError(t, got, want, ops) + } + + got := ed25519.VerifyAny(pubSigner, msg, sig, ops) + want := true + if got != want { + test.ReportError(t, got, want, ops) + } +} + +type badReader struct{} + +func (badReader) Read([]byte) (int, error) { return 0, errors.New("cannot read") } + +func TestErrors(t *testing.T) { + t.Run("badHash", func(t *testing.T) { + var msg [16]byte + ops := crypto.SHA224 + _, priv, _ := ed25519.GenerateKey(nil) + _, got := priv.Sign(nil, msg[:], ops) + want := errors.New("ed25519: bad hash algorithm") + if got.Error() != want.Error() { + test.ReportError(t, got, want) + } + }) + t.Run("badReader", func(t *testing.T) { + _, _, got := ed25519.GenerateKey(badReader{}) + want := errors.New("cannot read") + if got.Error() != want.Error() { + test.ReportError(t, got, want) + } + }) + t.Run("wrongSeedSize", func(t *testing.T) { + var seed [256]byte + var want error + got := test.CheckPanic(func() { ed25519.NewKeyFromSeed(seed[:]) }) + if got != want { + test.ReportError(t, got, want) + } + }) +} + +func BenchmarkEd25519Ph(b *testing.B) { + msg := make([]byte, 128) + _, _ = rand.Read(msg) + + b.Run("Sign", func(b *testing.B) { + _, key, _ := ed25519.GenerateKey(rand.Reader) + ctx := "" + b.ResetTimer() + for i := 0; i < b.N; i++ { + _ = ed25519.SignPh(key, msg, ctx) + } + }) + b.Run("Verify", func(b *testing.B) { + pub, priv, _ := ed25519.GenerateKey(rand.Reader) + ctx := "" + sig := ed25519.SignPh(priv, msg, ctx) + b.ResetTimer() + for i := 0; i < b.N; i++ { + ed25519.VerifyPh(pub, msg, sig, ctx) + } + }) +} + +func BenchmarkEd25519Ctx(b *testing.B) { + ctx := "a context" + msg := make([]byte, 128) + _, _ = rand.Read(msg) + b.Run("Sign", func(b *testing.B) { + _, priv, _ := ed25519.GenerateKey(rand.Reader) + b.ResetTimer() + for i := 0; i < b.N; i++ { + _ = ed25519.SignWithCtx(priv, msg, ctx) + } + }) + b.Run("Verify", func(b *testing.B) { + pub, priv, _ := ed25519.GenerateKey(rand.Reader) + sig := ed25519.SignWithCtx(priv, msg, ctx) + b.ResetTimer() + for i := 0; i < b.N; i++ { + ed25519.VerifyWithCtx(pub, msg, sig, ctx) + } + }) +} + +func Example_ed25519() { + // import "circl/sign/ed25519" + // import "crypto/rand" + + // Generating Alice's key pair + pub, priv, err := ed25519.GenerateKey(rand.Reader) + if err != nil { + panic("error on generating keys") + } + + // Alice signs a message. + message := []byte("A message to be signed") + signature := ed25519.Sign(priv, message) + + // Anyone can verify the signature using Alice's public key. + ok := ed25519.Verify(pub, message, signature) + fmt.Println(ok) + // Output: true +} + +func ExampleSignPh() { + // import "circl/sign/ed25519" + // import "crypto/rand" + + // Generating Alice's key pair + pub, priv, err := ed25519.GenerateKey(rand.Reader) + if err != nil { + panic("error on generating keys") + } + + // Alice signs a message. + message := []byte("A message to be signed") + ctx := "an optional context string" + + signature := ed25519.SignPh(priv, message, ctx) + + // Anyone can verify the signature using Alice's public key. + ok := ed25519.VerifyPh(pub, message, signature, ctx) + fmt.Println(ok) + // Output: true +} + +func ExampleSignWithCtx() { + // import "circl/sign/ed25519" + // import "crypto/rand" + + // Generating Alice's key pair + pub, priv, err := ed25519.GenerateKey(rand.Reader) + if err != nil { + panic("error on generating keys") + } + + // Alice signs a message. + message := []byte("A message to be signed") + ctx := "a non-empty context string" + + signature := ed25519.SignWithCtx(priv, message, ctx) + + // Anyone can verify the signature using Alice's public key. + ok := ed25519.VerifyWithCtx(pub, message, signature, ctx) + fmt.Println(ok) + // Output: true +} diff --git a/src/circl/sign/ed25519/modular.go b/src/circl/sign/ed25519/modular.go new file mode 100644 index 00000000000..10efafdcafb --- /dev/null +++ b/src/circl/sign/ed25519/modular.go @@ -0,0 +1,175 @@ +package ed25519 + +import ( + "encoding/binary" + "math/bits" +) + +var order = [paramB]byte{ + 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, + 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, +} + +// isLessThan returns true if 0 <= x < y, and assumes that slices have the same length. +func isLessThan(x, y []byte) bool { + i := len(x) - 1 + for i > 0 && x[i] == y[i] { + i-- + } + return x[i] < y[i] +} + +// reduceModOrder calculates k = k mod order of the curve. +func reduceModOrder(k []byte, is512Bit bool) { + var X [((2 * paramB) * 8) / 64]uint64 + numWords := len(k) >> 3 + for i := 0; i < numWords; i++ { + X[i] = binary.LittleEndian.Uint64(k[i*8 : (i+1)*8]) + } + red512(&X, is512Bit) + for i := 0; i < numWords; i++ { + binary.LittleEndian.PutUint64(k[i*8:(i+1)*8], X[i]) + } +} + +// red512 calculates x = x mod Order of the curve. +func red512(x *[8]uint64, full bool) { + // Implementation of Algs.(14.47)+(14.52) of Handbook of Applied + // Cryptography, by A. Menezes, P. van Oorschot, and S. Vanstone. + const ( + ell0 = uint64(0x5812631a5cf5d3ed) + ell1 = uint64(0x14def9dea2f79cd6) + ell160 = uint64(0x812631a5cf5d3ed0) + ell161 = uint64(0x4def9dea2f79cd65) + ell162 = uint64(0x0000000000000001) + ) + + var c0, c1, c2, c3 uint64 + r0, r1, r2, r3, r4 := x[0], x[1], x[2], x[3], uint64(0) + + if full { + q0, q1, q2, q3 := x[4], x[5], x[6], x[7] + + for i := 0; i < 3; i++ { + h0, s0 := bits.Mul64(q0, ell160) + h1, s1 := bits.Mul64(q1, ell160) + h2, s2 := bits.Mul64(q2, ell160) + h3, s3 := bits.Mul64(q3, ell160) + + s1, c0 = bits.Add64(h0, s1, 0) + s2, c1 = bits.Add64(h1, s2, c0) + s3, c2 = bits.Add64(h2, s3, c1) + s4, _ := bits.Add64(h3, 0, c2) + + h0, l0 := bits.Mul64(q0, ell161) + h1, l1 := bits.Mul64(q1, ell161) + h2, l2 := bits.Mul64(q2, ell161) + h3, l3 := bits.Mul64(q3, ell161) + + l1, c0 = bits.Add64(h0, l1, 0) + l2, c1 = bits.Add64(h1, l2, c0) + l3, c2 = bits.Add64(h2, l3, c1) + l4, _ := bits.Add64(h3, 0, c2) + + s1, c0 = bits.Add64(s1, l0, 0) + s2, c1 = bits.Add64(s2, l1, c0) + s3, c2 = bits.Add64(s3, l2, c1) + s4, c3 = bits.Add64(s4, l3, c2) + s5, s6 := bits.Add64(l4, 0, c3) + + s2, c0 = bits.Add64(s2, q0, 0) + s3, c1 = bits.Add64(s3, q1, c0) + s4, c2 = bits.Add64(s4, q2, c1) + s5, c3 = bits.Add64(s5, q3, c2) + s6, s7 := bits.Add64(s6, 0, c3) + + q := q0 | q1 | q2 | q3 + m := -((q | -q) >> 63) // if q=0 then m=0...0 else m=1..1 + s0 &= m + s1 &= m + s2 &= m + s3 &= m + q0, q1, q2, q3 = s4, s5, s6, s7 + + if (i+1)%2 == 0 { + r0, c0 = bits.Add64(r0, s0, 0) + r1, c1 = bits.Add64(r1, s1, c0) + r2, c2 = bits.Add64(r2, s2, c1) + r3, c3 = bits.Add64(r3, s3, c2) + r4, _ = bits.Add64(r4, 0, c3) + } else { + r0, c0 = bits.Sub64(r0, s0, 0) + r1, c1 = bits.Sub64(r1, s1, c0) + r2, c2 = bits.Sub64(r2, s2, c1) + r3, c3 = bits.Sub64(r3, s3, c2) + r4, _ = bits.Sub64(r4, 0, c3) + } + } + + m := -(r4 >> 63) + r0, c0 = bits.Add64(r0, m&ell160, 0) + r1, c1 = bits.Add64(r1, m&ell161, c0) + r2, c2 = bits.Add64(r2, m&ell162, c1) + r3, c3 = bits.Add64(r3, 0, c2) + r4, _ = bits.Add64(r4, m&1, c3) + x[4], x[5], x[6], x[7] = 0, 0, 0, 0 + } + + q0 := (r4 << 4) | (r3 >> 60) + r3 &= (uint64(1) << 60) - 1 + + h0, s0 := bits.Mul64(ell0, q0) + h1, s1 := bits.Mul64(ell1, q0) + s1, c0 = bits.Add64(h0, s1, 0) + s2, _ := bits.Add64(h1, 0, c0) + + r0, c0 = bits.Sub64(r0, s0, 0) + r1, c1 = bits.Sub64(r1, s1, c0) + r2, c2 = bits.Sub64(r2, s2, c1) + r3, _ = bits.Sub64(r3, 0, c2) + + x[0], x[1], x[2], x[3] = r0, r1, r2, r3 +} + +// calculateS performs s = r+k*a mod Order of the curve. +func calculateS(s, r, k, a []byte) { + K := [4]uint64{ + binary.LittleEndian.Uint64(k[0*8 : 1*8]), + binary.LittleEndian.Uint64(k[1*8 : 2*8]), + binary.LittleEndian.Uint64(k[2*8 : 3*8]), + binary.LittleEndian.Uint64(k[3*8 : 4*8]), + } + S := [8]uint64{ + binary.LittleEndian.Uint64(r[0*8 : 1*8]), + binary.LittleEndian.Uint64(r[1*8 : 2*8]), + binary.LittleEndian.Uint64(r[2*8 : 3*8]), + binary.LittleEndian.Uint64(r[3*8 : 4*8]), + } + var c3 uint64 + for i := range K { + ai := binary.LittleEndian.Uint64(a[i*8 : (i+1)*8]) + + h0, l0 := bits.Mul64(K[0], ai) + h1, l1 := bits.Mul64(K[1], ai) + h2, l2 := bits.Mul64(K[2], ai) + h3, l3 := bits.Mul64(K[3], ai) + + l1, c0 := bits.Add64(h0, l1, 0) + l2, c1 := bits.Add64(h1, l2, c0) + l3, c2 := bits.Add64(h2, l3, c1) + l4, _ := bits.Add64(h3, 0, c2) + + S[i+0], c0 = bits.Add64(S[i+0], l0, 0) + S[i+1], c1 = bits.Add64(S[i+1], l1, c0) + S[i+2], c2 = bits.Add64(S[i+2], l2, c1) + S[i+3], c3 = bits.Add64(S[i+3], l3, c2) + S[i+4], _ = bits.Add64(S[i+4], l4, c3) + } + red512(&S, true) + binary.LittleEndian.PutUint64(s[0*8:1*8], S[0]) + binary.LittleEndian.PutUint64(s[1*8:2*8], S[1]) + binary.LittleEndian.PutUint64(s[2*8:3*8], S[2]) + binary.LittleEndian.PutUint64(s[3*8:4*8], S[3]) +} diff --git a/src/circl/sign/ed25519/modular_test.go b/src/circl/sign/ed25519/modular_test.go new file mode 100644 index 00000000000..0838b5075b1 --- /dev/null +++ b/src/circl/sign/ed25519/modular_test.go @@ -0,0 +1,91 @@ +package ed25519 + +import ( + "crypto/rand" + "testing" + + "circl/internal/conv" + "circl/internal/test" +) + +func TestCalculateS(t *testing.T) { + const testTimes = 1 << 10 + s := make([]byte, paramB) + k := make([]byte, paramB) + r := make([]byte, paramB) + a := make([]byte, paramB) + orderBig := conv.BytesLe2BigInt(order[:]) + + for i := 0; i < testTimes; i++ { + _, _ = rand.Read(k[:]) + _, _ = rand.Read(r[:]) + _, _ = rand.Read(a[:]) + bigK := conv.BytesLe2BigInt(k[:]) + bigR := conv.BytesLe2BigInt(r[:]) + bigA := conv.BytesLe2BigInt(a[:]) + + calculateS(s, r, k, a) + got := conv.BytesLe2BigInt(s[:]) + + bigK.Mul(bigK, bigA).Add(bigK, bigR) + want := bigK.Mod(bigK, orderBig) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, k, r, a) + } + } +} + +func TestReduction(t *testing.T) { + const testTimes = 1 << 10 + var x, y [paramB * 2]byte + orderBig := conv.BytesLe2BigInt(order[:]) + + for i := 0; i < testTimes; i++ { + for _, j := range []int{paramB, 2 * paramB} { + _, _ = rand.Read(x[:j]) + bigX := conv.BytesLe2BigInt(x[:j]) + copy(y[:j], x[:j]) + + reduceModOrder(y[:j], true) + got := conv.BytesLe2BigInt(y[:]) + + want := bigX.Mod(bigX, orderBig) + + if got.Cmp(want) != 0 { + test.ReportError(t, got, want, x) + } + } + } +} + +func TestRangeOrder(t *testing.T) { + aboveOrder := [...][paramB]byte{ + { // order + 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, + 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, + }, + { // order+1 + 0xed + 1, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, + 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, + }, + { // all-ones + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + }, + } + + for i := range aboveOrder { + got := isLessThanOrder(aboveOrder[i][:]) + want := false + if got != want { + test.ReportError(t, got, want, i, aboveOrder[i]) + } + } +} diff --git a/src/circl/sign/ed25519/mult.go b/src/circl/sign/ed25519/mult.go new file mode 100644 index 00000000000..282cc91ca03 --- /dev/null +++ b/src/circl/sign/ed25519/mult.go @@ -0,0 +1,179 @@ +package ed25519 + +import ( + "crypto/subtle" + "encoding/binary" + "math/bits" + + "circl/internal/conv" + "circl/math" + fp "circl/math/fp25519" +) + +var paramD = fp.Elt{ + 0xa3, 0x78, 0x59, 0x13, 0xca, 0x4d, 0xeb, 0x75, + 0xab, 0xd8, 0x41, 0x41, 0x4d, 0x0a, 0x70, 0x00, + 0x98, 0xe8, 0x79, 0x77, 0x79, 0x40, 0xc7, 0x8c, + 0x73, 0xfe, 0x6f, 0x2b, 0xee, 0x6c, 0x03, 0x52, +} + +// mLSBRecoding parameters. +const ( + fxT = 257 + fxV = 2 + fxW = 3 + fx2w1 = 1 << (uint(fxW) - 1) + numWords64 = (paramB * 8 / 64) +) + +// mLSBRecoding is the odd-only modified LSB-set. +// +// Reference: +// "Efficient and secure algorithms for GLV-based scalar multiplication and +// their implementation on GLV–GLS curves" by (Faz-Hernandez et al.) +// http://doi.org/10.1007/s13389-014-0085-7. +func mLSBRecoding(L []int8, k []byte) { + const ee = (fxT + fxW*fxV - 1) / (fxW * fxV) + const dd = ee * fxV + const ll = dd * fxW + if len(L) == (ll + 1) { + var m [numWords64 + 1]uint64 + for i := 0; i < numWords64; i++ { + m[i] = binary.LittleEndian.Uint64(k[8*i : 8*i+8]) + } + condAddOrderN(&m) + L[dd-1] = 1 + for i := 0; i < dd-1; i++ { + kip1 := (m[(i+1)/64] >> (uint(i+1) % 64)) & 0x1 + L[i] = int8(kip1<<1) - 1 + } + { // right-shift by d + right := uint(dd % 64) + left := uint(64) - right + lim := ((numWords64+1)*64 - dd) / 64 + j := dd / 64 + for i := 0; i < lim; i++ { + m[i] = (m[i+j] >> right) | (m[i+j+1] << left) + } + m[lim] = m[lim+j] >> right + } + for i := dd; i < ll; i++ { + L[i] = L[i%dd] * int8(m[0]&0x1) + div2subY(m[:], int64(L[i]>>1), numWords64) + } + L[ll] = int8(m[0]) + } +} + +// absolute returns always a positive value. +func absolute(x int32) int32 { + mask := x >> 31 + return (x + mask) ^ mask +} + +// condAddOrderN updates x = x+order if x is even, otherwise x remains unchanged. +func condAddOrderN(x *[numWords64 + 1]uint64) { + isOdd := (x[0] & 0x1) - 1 + c := uint64(0) + for i := 0; i < numWords64; i++ { + orderWord := binary.LittleEndian.Uint64(order[8*i : 8*i+8]) + o := isOdd & orderWord + x0, c0 := bits.Add64(x[i], o, c) + x[i] = x0 + c = c0 + } + x[numWords64], _ = bits.Add64(x[numWords64], 0, c) +} + +// div2subY update x = (x/2) - y. +func div2subY(x []uint64, y int64, l int) { + s := uint64(y >> 63) + for i := 0; i < l-1; i++ { + x[i] = (x[i] >> 1) | (x[i+1] << 63) + } + x[l-1] = (x[l-1] >> 1) + + b := uint64(0) + x0, b0 := bits.Sub64(x[0], uint64(y), b) + x[0] = x0 + b = b0 + for i := 1; i < l-1; i++ { + x0, b0 := bits.Sub64(x[i], s, b) + x[i] = x0 + b = b0 + } + x[l-1], _ = bits.Sub64(x[l-1], s, b) +} + +func (P *pointR1) fixedMult(scalar []byte) { + if len(scalar) != paramB { + panic("wrong scalar size") + } + const ee = (fxT + fxW*fxV - 1) / (fxW * fxV) + const dd = ee * fxV + const ll = dd * fxW + + L := make([]int8, ll+1) + mLSBRecoding(L[:], scalar) + S := &pointR3{} + P.SetIdentity() + for ii := ee - 1; ii >= 0; ii-- { + P.double() + for j := 0; j < fxV; j++ { + dig := L[fxW*dd-j*ee+ii-ee] + for i := (fxW-1)*dd - j*ee + ii - ee; i >= (2*dd - j*ee + ii - ee); i = i - dd { + dig = 2*dig + L[i] + } + idx := absolute(int32(dig)) + sig := L[dd-j*ee+ii-ee] + Tabj := &tabSign[fxV-j-1] + for k := 0; k < fx2w1; k++ { + S.cmov(&Tabj[k], subtle.ConstantTimeEq(int32(k), idx)) + } + S.cneg(subtle.ConstantTimeEq(int32(sig), -1)) + P.mixAdd(S) + } + } +} + +const ( + omegaFix = 7 + omegaVar = 5 +) + +// doubleMult returns P=mG+nQ. +func (P *pointR1) doubleMult(Q *pointR1, m, n []byte) { + nafFix := math.OmegaNAF(conv.BytesLe2BigInt(m), omegaFix) + nafVar := math.OmegaNAF(conv.BytesLe2BigInt(n), omegaVar) + + if len(nafFix) > len(nafVar) { + nafVar = append(nafVar, make([]int32, len(nafFix)-len(nafVar))...) + } else if len(nafFix) < len(nafVar) { + nafFix = append(nafFix, make([]int32, len(nafVar)-len(nafFix))...) + } + + var TabQ [1 << (omegaVar - 2)]pointR2 + Q.oddMultiples(TabQ[:]) + P.SetIdentity() + for i := len(nafFix) - 1; i >= 0; i-- { + P.double() + // Generator point + if nafFix[i] != 0 { + idxM := absolute(nafFix[i]) >> 1 + R := tabVerif[idxM] + if nafFix[i] < 0 { + R.neg() + } + P.mixAdd(&R) + } + // Variable input point + if nafVar[i] != 0 { + idxN := absolute(nafVar[i]) >> 1 + S := TabQ[idxN] + if nafVar[i] < 0 { + S.neg() + } + P.add(&S) + } + } +} diff --git a/src/circl/sign/ed25519/point.go b/src/circl/sign/ed25519/point.go new file mode 100644 index 00000000000..18f84d4d968 --- /dev/null +++ b/src/circl/sign/ed25519/point.go @@ -0,0 +1,193 @@ +package ed25519 + +import fp "circl/math/fp25519" + +type pointR1 struct{ x, y, z, ta, tb fp.Elt } +type pointR2 struct { + pointR3 + z2 fp.Elt +} +type pointR3 struct{ addYX, subYX, dt2 fp.Elt } + +func (P *pointR1) neg() { + fp.Neg(&P.x, &P.x) + fp.Neg(&P.ta, &P.ta) +} + +func (P *pointR1) SetIdentity() { + P.x = fp.Elt{} + fp.SetOne(&P.y) + fp.SetOne(&P.z) + P.ta = fp.Elt{} + P.tb = fp.Elt{} +} + +func (P *pointR1) toAffine() { + fp.Inv(&P.z, &P.z) + fp.Mul(&P.x, &P.x, &P.z) + fp.Mul(&P.y, &P.y, &P.z) + fp.Modp(&P.x) + fp.Modp(&P.y) + fp.SetOne(&P.z) + P.ta = P.x + P.tb = P.y +} + +func (P *pointR1) ToBytes(k []byte) error { + P.toAffine() + var x [fp.Size]byte + err := fp.ToBytes(k[:fp.Size], &P.y) + if err != nil { + return err + } + err = fp.ToBytes(x[:], &P.x) + if err != nil { + return err + } + b := x[0] & 1 + k[paramB-1] = k[paramB-1] | (b << 7) + return nil +} + +func (P *pointR1) FromBytes(k []byte) bool { + if len(k) != paramB { + panic("wrong size") + } + signX := k[paramB-1] >> 7 + copy(P.y[:], k[:fp.Size]) + P.y[fp.Size-1] &= 0x7F + p := fp.P() + if !isLessThan(P.y[:], p[:]) { + return false + } + + one, u, v := &fp.Elt{}, &fp.Elt{}, &fp.Elt{} + fp.SetOne(one) + fp.Sqr(u, &P.y) // u = y^2 + fp.Mul(v, u, ¶mD) // v = dy^2 + fp.Sub(u, u, one) // u = y^2-1 + fp.Add(v, v, one) // v = dy^2+1 + isQR := fp.InvSqrt(&P.x, u, v) // x = sqrt(u/v) + if !isQR { + return false + } + fp.Modp(&P.x) // x = x mod p + if fp.IsZero(&P.x) && signX == 1 { + return false + } + if signX != (P.x[0] & 1) { + fp.Neg(&P.x, &P.x) + } + P.ta = P.x + P.tb = P.y + fp.SetOne(&P.z) + return true +} + +// double calculates 2P for curves with A=-1. +func (P *pointR1) double() { + Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb + a, b, c, e, f, g, h := Px, Py, Pz, Pta, Px, Py, Ptb + fp.Add(e, Px, Py) // x+y + fp.Sqr(a, Px) // A = x^2 + fp.Sqr(b, Py) // B = y^2 + fp.Sqr(c, Pz) // z^2 + fp.Add(c, c, c) // C = 2*z^2 + fp.Add(h, a, b) // H = A+B + fp.Sqr(e, e) // (x+y)^2 + fp.Sub(e, e, h) // E = (x+y)^2-A-B + fp.Sub(g, b, a) // G = B-A + fp.Sub(f, c, g) // F = C-G + fp.Mul(Pz, f, g) // Z = F * G + fp.Mul(Px, e, f) // X = E * F + fp.Mul(Py, g, h) // Y = G * H, T = E * H +} + +func (P *pointR1) mixAdd(Q *pointR3) { + fp.Add(&P.z, &P.z, &P.z) // D = 2*z1 + P.coreAddition(Q) +} + +func (P *pointR1) add(Q *pointR2) { + fp.Mul(&P.z, &P.z, &Q.z2) // D = 2*z1*z2 + P.coreAddition(&Q.pointR3) +} + +// coreAddition calculates P=P+Q for curves with A=-1. +func (P *pointR1) coreAddition(Q *pointR3) { + Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb + addYX2, subYX2, dt2 := &Q.addYX, &Q.subYX, &Q.dt2 + a, b, c, d, e, f, g, h := Px, Py, &fp.Elt{}, Pz, Pta, Px, Py, Ptb + fp.Mul(c, Pta, Ptb) // t1 = ta*tb + fp.Sub(h, Py, Px) // y1-x1 + fp.Add(b, Py, Px) // y1+x1 + fp.Mul(a, h, subYX2) // A = (y1-x1)*(y2-x2) + fp.Mul(b, b, addYX2) // B = (y1+x1)*(y2+x2) + fp.Mul(c, c, dt2) // C = 2*D*t1*t2 + fp.Sub(e, b, a) // E = B-A + fp.Add(h, b, a) // H = B+A + fp.Sub(f, d, c) // F = D-C + fp.Add(g, d, c) // G = D+C + fp.Mul(Pz, f, g) // Z = F * G + fp.Mul(Px, e, f) // X = E * F + fp.Mul(Py, g, h) // Y = G * H, T = E * H +} + +func (P *pointR1) oddMultiples(T []pointR2) { + var R pointR2 + n := len(T) + T[0].fromR1(P) + _2P := *P + _2P.double() + R.fromR1(&_2P) + for i := 1; i < n; i++ { + P.add(&R) + T[i].fromR1(P) + } +} + +func (P *pointR1) isEqual(Q *pointR1) bool { + l, r := &fp.Elt{}, &fp.Elt{} + fp.Mul(l, &P.x, &Q.z) + fp.Mul(r, &Q.x, &P.z) + fp.Sub(l, l, r) + b := fp.IsZero(l) + fp.Mul(l, &P.y, &Q.z) + fp.Mul(r, &Q.y, &P.z) + fp.Sub(l, l, r) + b = b && fp.IsZero(l) + fp.Mul(l, &P.ta, &P.tb) + fp.Mul(l, l, &Q.z) + fp.Mul(r, &Q.ta, &Q.tb) + fp.Mul(r, r, &P.z) + fp.Sub(l, l, r) + b = b && fp.IsZero(l) + return b +} + +func (P *pointR3) neg() { + P.addYX, P.subYX = P.subYX, P.addYX + fp.Neg(&P.dt2, &P.dt2) +} + +func (P *pointR2) fromR1(Q *pointR1) { + fp.Add(&P.addYX, &Q.y, &Q.x) + fp.Sub(&P.subYX, &Q.y, &Q.x) + fp.Mul(&P.dt2, &Q.ta, &Q.tb) + fp.Mul(&P.dt2, &P.dt2, ¶mD) + fp.Add(&P.dt2, &P.dt2, &P.dt2) + fp.Add(&P.z2, &Q.z, &Q.z) +} + +func (P *pointR3) cneg(b int) { + t := &fp.Elt{} + fp.Cswap(&P.addYX, &P.subYX, uint(b)) + fp.Neg(t, &P.dt2) + fp.Cmov(&P.dt2, t, uint(b)) +} + +func (P *pointR3) cmov(Q *pointR3, b int) { + fp.Cmov(&P.addYX, &Q.addYX, uint(b)) + fp.Cmov(&P.subYX, &Q.subYX, uint(b)) + fp.Cmov(&P.dt2, &Q.dt2, uint(b)) +} diff --git a/src/circl/sign/ed25519/point_test.go b/src/circl/sign/ed25519/point_test.go new file mode 100644 index 00000000000..b64fa205ada --- /dev/null +++ b/src/circl/sign/ed25519/point_test.go @@ -0,0 +1,114 @@ +package ed25519 + +import ( + "crypto/rand" + "flag" + "testing" + + "circl/internal/test" +) + +func randomPoint(P *pointR1) { + k := make([]byte, paramB) + _, _ = rand.Read(k[:]) + P.fixedMult(k) +} + +func TestPoint(t *testing.T) { + const testTimes = 1 << 10 + + t.Run("add", func(t *testing.T) { + var P pointR1 + var Q pointR1 + var R pointR2 + for i := 0; i < testTimes; i++ { + randomPoint(&P) + _16P := P + R.fromR1(&P) + // 16P = 2^4P + for j := 0; j < 4; j++ { + _16P.double() + } + // 16P = P+P...+P + Q.SetIdentity() + for j := 0; j < 16; j++ { + Q.add(&R) + } + + got := _16P.isEqual(&Q) + want := true + if got != want { + test.ReportError(t, got, want, P) + } + } + }) + + t.Run("fixed", func(t *testing.T) { + var P, Q, R pointR1 + k := make([]byte, paramB) + l := make([]byte, paramB) + for i := 0; i < testTimes; i++ { + randomPoint(&P) + _, _ = rand.Read(k[:]) + + Q.fixedMult(k[:]) + R.doubleMult(&P, k[:], l[:]) + + got := Q.isEqual(&R) + want := true + if got != want { + test.ReportError(t, got, want, P, k) + } + } + }) +} + +var runLongBench = flag.Bool("long", false, "runs longer benchmark") + +func BenchmarkPoint(b *testing.B) { + if !*runLongBench { + b.Log("Skipped one long bench, add -long flag to run longer bench") + b.SkipNow() + } + + k := make([]byte, paramB) + l := make([]byte, paramB) + _, _ = rand.Read(k) + _, _ = rand.Read(l) + + var P pointR1 + var Q pointR2 + var R pointR3 + randomPoint(&P) + Q.fromR1(&P) + b.Run("toAffine", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.toAffine() + } + }) + b.Run("double", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.double() + } + }) + b.Run("mixadd", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.mixAdd(&R) + } + }) + b.Run("add", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.add(&Q) + } + }) + b.Run("fixedMult", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.fixedMult(k) + } + }) + b.Run("doubleMult", func(b *testing.B) { + for i := 0; i < b.N; i++ { + P.doubleMult(&P, k, l) + } + }) +} diff --git a/src/circl/sign/ed25519/pubkey.go b/src/circl/sign/ed25519/pubkey.go new file mode 100644 index 00000000000..ff41805982b --- /dev/null +++ b/src/circl/sign/ed25519/pubkey.go @@ -0,0 +1,8 @@ +// +build go1.13 + +package ed25519 + +import cryptoEd25519 "crypto/ed25519" + +// PublicKey is the type of Ed25519 public keys. +type PublicKey cryptoEd25519.PublicKey diff --git a/src/circl/sign/ed25519/pubkey112.go b/src/circl/sign/ed25519/pubkey112.go new file mode 100644 index 00000000000..46f66113da7 --- /dev/null +++ b/src/circl/sign/ed25519/pubkey112.go @@ -0,0 +1,6 @@ +// +build !go1.13 + +package ed25519 + +// PublicKey is the type of Ed25519 public keys. +type PublicKey []byte diff --git a/src/circl/sign/ed25519/rfc8032_test.go b/src/circl/sign/ed25519/rfc8032_test.go new file mode 100644 index 00000000000..efb2354575d --- /dev/null +++ b/src/circl/sign/ed25519/rfc8032_test.go @@ -0,0 +1,486 @@ +package ed25519_test + +import ( + "archive/zip" + "bufio" + "bytes" + "encoding/hex" + "fmt" + "strings" + "testing" + + "circl/internal/test" + "circl/sign/ed25519" +) + +type rfc8032Vector struct { + private ed25519.PrivateKey + public ed25519.PublicKey + message []byte + signature []byte +} + +func (v *rfc8032Vector) fetch(line string) { + values := strings.Split(line, ":") + if len(values) != 5 { + panic(fmt.Errorf("len: %v %v", len(values), values)) + } + v.private, _ = hex.DecodeString(values[0]) + v.public, _ = hex.DecodeString(values[1]) + v.message, _ = hex.DecodeString(values[2]) + v.signature, _ = hex.DecodeString(values[3]) + v.private = v.private[:ed25519.SeedSize] + v.signature = v.signature[:ed25519.SignatureSize] +} + +func (v *rfc8032Vector) test(t *testing.T, lineNum int) { + key := ed25519.NewKeyFromSeed(v.private) + { + got := key.Public().(ed25519.PublicKey) + want := v.public + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, lineNum, v) + } + + got = ed25519.Sign(key, v.message) + want = v.signature + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, lineNum, v) + } + } + { + got := ed25519.Verify(key.Public().(ed25519.PublicKey), v.message, v.signature) + want := true + if got != want { + test.ReportError(t, got, want, lineNum, v) + } + } +} + +func TestRFC8032(t *testing.T) { + const nameFile = "testdata/sign.input.zip" + zipFile, err := zip.OpenReader(nameFile) + if err != nil { + t.Fatalf("File %v can not be opened. Error: %v", nameFile, err) + } + defer zipFile.Close() + + for _, f := range zipFile.File { + unzipped, err := f.Open() + if err != nil { + t.Fatalf("File %v can not be opened. Error: %v", f.Name, err) + } + defer unzipped.Close() + + fScanner := bufio.NewScanner(unzipped) + var v rfc8032Vector + for i := 1; fScanner.Scan(); i++ { + v.fetch(fScanner.Text()) + v.test(t, i) + } + } +} + +type vector struct { + name string + scheme string + sk []byte + pk []byte + sig []byte + msg []byte + msgLen uint + ph bool + ctx []byte + ctxLen uint +} + +var vectorsEd25519 = [...]vector{ + { + name: "-----TEST 1", + scheme: "Ed25519Pure", + sk: []byte{ + 0x9d, 0x61, 0xb1, 0x9d, 0xef, 0xfd, 0x5a, 0x60, 0xba, 0x84, 0x4a, 0xf4, 0x92, 0xec, 0x2c, 0xc4, + 0x44, 0x49, 0xc5, 0x69, 0x7b, 0x32, 0x69, 0x19, 0x70, 0x3b, 0xac, 0x03, 0x1c, 0xae, 0x7f, 0x60, + }, + pk: []byte{ + 0xd7, 0x5a, 0x98, 0x01, 0x82, 0xb1, 0x0a, 0xb7, 0xd5, 0x4b, 0xfe, 0xd3, 0xc9, 0x64, 0x07, 0x3a, + 0x0e, 0xe1, 0x72, 0xf3, 0xda, 0xa6, 0x23, 0x25, 0xaf, 0x02, 0x1a, 0x68, 0xf7, 0x07, 0x51, 0x1a, + }, + msg: []byte{}, + msgLen: 0, + sig: []byte{ + 0xe5, 0x56, 0x43, 0x00, 0xc3, 0x60, 0xac, 0x72, 0x90, 0x86, 0xe2, 0xcc, 0x80, 0x6e, 0x82, 0x8a, + 0x84, 0x87, 0x7f, 0x1e, 0xb8, 0xe5, 0xd9, 0x74, 0xd8, 0x73, 0xe0, 0x65, 0x22, 0x49, 0x01, 0x55, + 0x5f, 0xb8, 0x82, 0x15, 0x90, 0xa3, 0x3b, 0xac, 0xc6, 0x1e, 0x39, 0x70, 0x1c, 0xf9, 0xb4, 0x6b, + 0xd2, 0x5b, 0xf5, 0xf0, 0x59, 0x5b, 0xbe, 0x24, 0x65, 0x51, 0x41, 0x43, 0x8e, 0x7a, 0x10, 0x0b, + }, + ph: false, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----TEST 2", + scheme: "Ed25519Pure", + sk: []byte{ + 0x4c, 0xcd, 0x08, 0x9b, 0x28, 0xff, 0x96, 0xda, 0x9d, 0xb6, 0xc3, 0x46, 0xec, 0x11, 0x4e, 0x0f, + 0x5b, 0x8a, 0x31, 0x9f, 0x35, 0xab, 0xa6, 0x24, 0xda, 0x8c, 0xf6, 0xed, 0x4f, 0xb8, 0xa6, 0xfb, + }, + pk: []byte{ + 0x3d, 0x40, 0x17, 0xc3, 0xe8, 0x43, 0x89, 0x5a, 0x92, 0xb7, 0x0a, 0xa7, 0x4d, 0x1b, 0x7e, 0xbc, + 0x9c, 0x98, 0x2c, 0xcf, 0x2e, 0xc4, 0x96, 0x8c, 0xc0, 0xcd, 0x55, 0xf1, 0x2a, 0xf4, 0x66, 0x0c, + }, + msg: []byte{ + 0x72, + }, + msgLen: 1, + sig: []byte{ + 0x92, 0xa0, 0x09, 0xa9, 0xf0, 0xd4, 0xca, 0xb8, 0x72, 0x0e, 0x82, 0x0b, 0x5f, 0x64, 0x25, 0x40, + 0xa2, 0xb2, 0x7b, 0x54, 0x16, 0x50, 0x3f, 0x8f, 0xb3, 0x76, 0x22, 0x23, 0xeb, 0xdb, 0x69, 0xda, + 0x08, 0x5a, 0xc1, 0xe4, 0x3e, 0x15, 0x99, 0x6e, 0x45, 0x8f, 0x36, 0x13, 0xd0, 0xf1, 0x1d, 0x8c, + 0x38, 0x7b, 0x2e, 0xae, 0xb4, 0x30, 0x2a, 0xee, 0xb0, 0x0d, 0x29, 0x16, 0x12, 0xbb, 0x0c, 0x00, + }, + ph: false, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----TEST 3", + scheme: "Ed25519Pure", + sk: []byte{ + 0xc5, 0xaa, 0x8d, 0xf4, 0x3f, 0x9f, 0x83, 0x7b, 0xed, 0xb7, 0x44, 0x2f, 0x31, 0xdc, 0xb7, 0xb1, + 0x66, 0xd3, 0x85, 0x35, 0x07, 0x6f, 0x09, 0x4b, 0x85, 0xce, 0x3a, 0x2e, 0x0b, 0x44, 0x58, 0xf7, + }, + pk: []byte{ + 0xfc, 0x51, 0xcd, 0x8e, 0x62, 0x18, 0xa1, 0xa3, 0x8d, 0xa4, 0x7e, 0xd0, 0x02, 0x30, 0xf0, 0x58, + 0x08, 0x16, 0xed, 0x13, 0xba, 0x33, 0x03, 0xac, 0x5d, 0xeb, 0x91, 0x15, 0x48, 0x90, 0x80, 0x25, + }, + msg: []byte{ + 0xaf, 0x82, + }, + msgLen: 2, + sig: []byte{ + 0x62, 0x91, 0xd6, 0x57, 0xde, 0xec, 0x24, 0x02, 0x48, 0x27, 0xe6, 0x9c, 0x3a, 0xbe, 0x01, 0xa3, + 0x0c, 0xe5, 0x48, 0xa2, 0x84, 0x74, 0x3a, 0x44, 0x5e, 0x36, 0x80, 0xd7, 0xdb, 0x5a, 0xc3, 0xac, + 0x18, 0xff, 0x9b, 0x53, 0x8d, 0x16, 0xf2, 0x90, 0xae, 0x67, 0xf7, 0x60, 0x98, 0x4d, 0xc6, 0x59, + 0x4a, 0x7c, 0x15, 0xe9, 0x71, 0x6e, 0xd2, 0x8d, 0xc0, 0x27, 0xbe, 0xce, 0xea, 0x1e, 0xc4, 0x0a, + }, + ph: false, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----TEST 1024", + scheme: "Ed25519Pure", + sk: []byte{ + 0xf5, 0xe5, 0x76, 0x7c, 0xf1, 0x53, 0x31, 0x95, 0x17, 0x63, 0x0f, 0x22, 0x68, 0x76, 0xb8, 0x6c, + 0x81, 0x60, 0xcc, 0x58, 0x3b, 0xc0, 0x13, 0x74, 0x4c, 0x6b, 0xf2, 0x55, 0xf5, 0xcc, 0x0e, 0xe5, + }, + pk: []byte{ + 0x27, 0x81, 0x17, 0xfc, 0x14, 0x4c, 0x72, 0x34, 0x0f, 0x67, 0xd0, 0xf2, 0x31, 0x6e, 0x83, 0x86, + 0xce, 0xff, 0xbf, 0x2b, 0x24, 0x28, 0xc9, 0xc5, 0x1f, 0xef, 0x7c, 0x59, 0x7f, 0x1d, 0x42, 0x6e, + }, + msg: []byte{ + 0x08, 0xb8, 0xb2, 0xb7, 0x33, 0x42, 0x42, 0x43, 0x76, 0x0f, 0xe4, 0x26, 0xa4, 0xb5, 0x49, 0x08, + 0x63, 0x21, 0x10, 0xa6, 0x6c, 0x2f, 0x65, 0x91, 0xea, 0xbd, 0x33, 0x45, 0xe3, 0xe4, 0xeb, 0x98, + 0xfa, 0x6e, 0x26, 0x4b, 0xf0, 0x9e, 0xfe, 0x12, 0xee, 0x50, 0xf8, 0xf5, 0x4e, 0x9f, 0x77, 0xb1, + 0xe3, 0x55, 0xf6, 0xc5, 0x05, 0x44, 0xe2, 0x3f, 0xb1, 0x43, 0x3d, 0xdf, 0x73, 0xbe, 0x84, 0xd8, + 0x79, 0xde, 0x7c, 0x00, 0x46, 0xdc, 0x49, 0x96, 0xd9, 0xe7, 0x73, 0xf4, 0xbc, 0x9e, 0xfe, 0x57, + 0x38, 0x82, 0x9a, 0xdb, 0x26, 0xc8, 0x1b, 0x37, 0xc9, 0x3a, 0x1b, 0x27, 0x0b, 0x20, 0x32, 0x9d, + 0x65, 0x86, 0x75, 0xfc, 0x6e, 0xa5, 0x34, 0xe0, 0x81, 0x0a, 0x44, 0x32, 0x82, 0x6b, 0xf5, 0x8c, + 0x94, 0x1e, 0xfb, 0x65, 0xd5, 0x7a, 0x33, 0x8b, 0xbd, 0x2e, 0x26, 0x64, 0x0f, 0x89, 0xff, 0xbc, + 0x1a, 0x85, 0x8e, 0xfc, 0xb8, 0x55, 0x0e, 0xe3, 0xa5, 0xe1, 0x99, 0x8b, 0xd1, 0x77, 0xe9, 0x3a, + 0x73, 0x63, 0xc3, 0x44, 0xfe, 0x6b, 0x19, 0x9e, 0xe5, 0xd0, 0x2e, 0x82, 0xd5, 0x22, 0xc4, 0xfe, + 0xba, 0x15, 0x45, 0x2f, 0x80, 0x28, 0x8a, 0x82, 0x1a, 0x57, 0x91, 0x16, 0xec, 0x6d, 0xad, 0x2b, + 0x3b, 0x31, 0x0d, 0xa9, 0x03, 0x40, 0x1a, 0xa6, 0x21, 0x00, 0xab, 0x5d, 0x1a, 0x36, 0x55, 0x3e, + 0x06, 0x20, 0x3b, 0x33, 0x89, 0x0c, 0xc9, 0xb8, 0x32, 0xf7, 0x9e, 0xf8, 0x05, 0x60, 0xcc, 0xb9, + 0xa3, 0x9c, 0xe7, 0x67, 0x96, 0x7e, 0xd6, 0x28, 0xc6, 0xad, 0x57, 0x3c, 0xb1, 0x16, 0xdb, 0xef, + 0xef, 0xd7, 0x54, 0x99, 0xda, 0x96, 0xbd, 0x68, 0xa8, 0xa9, 0x7b, 0x92, 0x8a, 0x8b, 0xbc, 0x10, + 0x3b, 0x66, 0x21, 0xfc, 0xde, 0x2b, 0xec, 0xa1, 0x23, 0x1d, 0x20, 0x6b, 0xe6, 0xcd, 0x9e, 0xc7, + 0xaf, 0xf6, 0xf6, 0xc9, 0x4f, 0xcd, 0x72, 0x04, 0xed, 0x34, 0x55, 0xc6, 0x8c, 0x83, 0xf4, 0xa4, + 0x1d, 0xa4, 0xaf, 0x2b, 0x74, 0xef, 0x5c, 0x53, 0xf1, 0xd8, 0xac, 0x70, 0xbd, 0xcb, 0x7e, 0xd1, + 0x85, 0xce, 0x81, 0xbd, 0x84, 0x35, 0x9d, 0x44, 0x25, 0x4d, 0x95, 0x62, 0x9e, 0x98, 0x55, 0xa9, + 0x4a, 0x7c, 0x19, 0x58, 0xd1, 0xf8, 0xad, 0xa5, 0xd0, 0x53, 0x2e, 0xd8, 0xa5, 0xaa, 0x3f, 0xb2, + 0xd1, 0x7b, 0xa7, 0x0e, 0xb6, 0x24, 0x8e, 0x59, 0x4e, 0x1a, 0x22, 0x97, 0xac, 0xbb, 0xb3, 0x9d, + 0x50, 0x2f, 0x1a, 0x8c, 0x6e, 0xb6, 0xf1, 0xce, 0x22, 0xb3, 0xde, 0x1a, 0x1f, 0x40, 0xcc, 0x24, + 0x55, 0x41, 0x19, 0xa8, 0x31, 0xa9, 0xaa, 0xd6, 0x07, 0x9c, 0xad, 0x88, 0x42, 0x5d, 0xe6, 0xbd, + 0xe1, 0xa9, 0x18, 0x7e, 0xbb, 0x60, 0x92, 0xcf, 0x67, 0xbf, 0x2b, 0x13, 0xfd, 0x65, 0xf2, 0x70, + 0x88, 0xd7, 0x8b, 0x7e, 0x88, 0x3c, 0x87, 0x59, 0xd2, 0xc4, 0xf5, 0xc6, 0x5a, 0xdb, 0x75, 0x53, + 0x87, 0x8a, 0xd5, 0x75, 0xf9, 0xfa, 0xd8, 0x78, 0xe8, 0x0a, 0x0c, 0x9b, 0xa6, 0x3b, 0xcb, 0xcc, + 0x27, 0x32, 0xe6, 0x94, 0x85, 0xbb, 0xc9, 0xc9, 0x0b, 0xfb, 0xd6, 0x24, 0x81, 0xd9, 0x08, 0x9b, + 0xec, 0xcf, 0x80, 0xcf, 0xe2, 0xdf, 0x16, 0xa2, 0xcf, 0x65, 0xbd, 0x92, 0xdd, 0x59, 0x7b, 0x07, + 0x07, 0xe0, 0x91, 0x7a, 0xf4, 0x8b, 0xbb, 0x75, 0xfe, 0xd4, 0x13, 0xd2, 0x38, 0xf5, 0x55, 0x5a, + 0x7a, 0x56, 0x9d, 0x80, 0xc3, 0x41, 0x4a, 0x8d, 0x08, 0x59, 0xdc, 0x65, 0xa4, 0x61, 0x28, 0xba, + 0xb2, 0x7a, 0xf8, 0x7a, 0x71, 0x31, 0x4f, 0x31, 0x8c, 0x78, 0x2b, 0x23, 0xeb, 0xfe, 0x80, 0x8b, + 0x82, 0xb0, 0xce, 0x26, 0x40, 0x1d, 0x2e, 0x22, 0xf0, 0x4d, 0x83, 0xd1, 0x25, 0x5d, 0xc5, 0x1a, + 0xdd, 0xd3, 0xb7, 0x5a, 0x2b, 0x1a, 0xe0, 0x78, 0x45, 0x04, 0xdf, 0x54, 0x3a, 0xf8, 0x96, 0x9b, + 0xe3, 0xea, 0x70, 0x82, 0xff, 0x7f, 0xc9, 0x88, 0x8c, 0x14, 0x4d, 0xa2, 0xaf, 0x58, 0x42, 0x9e, + 0xc9, 0x60, 0x31, 0xdb, 0xca, 0xd3, 0xda, 0xd9, 0xaf, 0x0d, 0xcb, 0xaa, 0xaf, 0x26, 0x8c, 0xb8, + 0xfc, 0xff, 0xea, 0xd9, 0x4f, 0x3c, 0x7c, 0xa4, 0x95, 0xe0, 0x56, 0xa9, 0xb4, 0x7a, 0xcd, 0xb7, + 0x51, 0xfb, 0x73, 0xe6, 0x66, 0xc6, 0xc6, 0x55, 0xad, 0xe8, 0x29, 0x72, 0x97, 0xd0, 0x7a, 0xd1, + 0xba, 0x5e, 0x43, 0xf1, 0xbc, 0xa3, 0x23, 0x01, 0x65, 0x13, 0x39, 0xe2, 0x29, 0x04, 0xcc, 0x8c, + 0x42, 0xf5, 0x8c, 0x30, 0xc0, 0x4a, 0xaf, 0xdb, 0x03, 0x8d, 0xda, 0x08, 0x47, 0xdd, 0x98, 0x8d, + 0xcd, 0xa6, 0xf3, 0xbf, 0xd1, 0x5c, 0x4b, 0x4c, 0x45, 0x25, 0x00, 0x4a, 0xa0, 0x6e, 0xef, 0xf8, + 0xca, 0x61, 0x78, 0x3a, 0xac, 0xec, 0x57, 0xfb, 0x3d, 0x1f, 0x92, 0xb0, 0xfe, 0x2f, 0xd1, 0xa8, + 0x5f, 0x67, 0x24, 0x51, 0x7b, 0x65, 0xe6, 0x14, 0xad, 0x68, 0x08, 0xd6, 0xf6, 0xee, 0x34, 0xdf, + 0xf7, 0x31, 0x0f, 0xdc, 0x82, 0xae, 0xbf, 0xd9, 0x04, 0xb0, 0x1e, 0x1d, 0xc5, 0x4b, 0x29, 0x27, + 0x09, 0x4b, 0x2d, 0xb6, 0x8d, 0x6f, 0x90, 0x3b, 0x68, 0x40, 0x1a, 0xde, 0xbf, 0x5a, 0x7e, 0x08, + 0xd7, 0x8f, 0xf4, 0xef, 0x5d, 0x63, 0x65, 0x3a, 0x65, 0x04, 0x0c, 0xf9, 0xbf, 0xd4, 0xac, 0xa7, + 0x98, 0x4a, 0x74, 0xd3, 0x71, 0x45, 0x98, 0x67, 0x80, 0xfc, 0x0b, 0x16, 0xac, 0x45, 0x16, 0x49, + 0xde, 0x61, 0x88, 0xa7, 0xdb, 0xdf, 0x19, 0x1f, 0x64, 0xb5, 0xfc, 0x5e, 0x2a, 0xb4, 0x7b, 0x57, + 0xf7, 0xf7, 0x27, 0x6c, 0xd4, 0x19, 0xc1, 0x7a, 0x3c, 0xa8, 0xe1, 0xb9, 0x39, 0xae, 0x49, 0xe4, + 0x88, 0xac, 0xba, 0x6b, 0x96, 0x56, 0x10, 0xb5, 0x48, 0x01, 0x09, 0xc8, 0xb1, 0x7b, 0x80, 0xe1, + 0xb7, 0xb7, 0x50, 0xdf, 0xc7, 0x59, 0x8d, 0x5d, 0x50, 0x11, 0xfd, 0x2d, 0xcc, 0x56, 0x00, 0xa3, + 0x2e, 0xf5, 0xb5, 0x2a, 0x1e, 0xcc, 0x82, 0x0e, 0x30, 0x8a, 0xa3, 0x42, 0x72, 0x1a, 0xac, 0x09, + 0x43, 0xbf, 0x66, 0x86, 0xb6, 0x4b, 0x25, 0x79, 0x37, 0x65, 0x04, 0xcc, 0xc4, 0x93, 0xd9, 0x7e, + 0x6a, 0xed, 0x3f, 0xb0, 0xf9, 0xcd, 0x71, 0xa4, 0x3d, 0xd4, 0x97, 0xf0, 0x1f, 0x17, 0xc0, 0xe2, + 0xcb, 0x37, 0x97, 0xaa, 0x2a, 0x2f, 0x25, 0x66, 0x56, 0x16, 0x8e, 0x6c, 0x49, 0x6a, 0xfc, 0x5f, + 0xb9, 0x32, 0x46, 0xf6, 0xb1, 0x11, 0x63, 0x98, 0xa3, 0x46, 0xf1, 0xa6, 0x41, 0xf3, 0xb0, 0x41, + 0xe9, 0x89, 0xf7, 0x91, 0x4f, 0x90, 0xcc, 0x2c, 0x7f, 0xff, 0x35, 0x78, 0x76, 0xe5, 0x06, 0xb5, + 0x0d, 0x33, 0x4b, 0xa7, 0x7c, 0x22, 0x5b, 0xc3, 0x07, 0xba, 0x53, 0x71, 0x52, 0xf3, 0xf1, 0x61, + 0x0e, 0x4e, 0xaf, 0xe5, 0x95, 0xf6, 0xd9, 0xd9, 0x0d, 0x11, 0xfa, 0xa9, 0x33, 0xa1, 0x5e, 0xf1, + 0x36, 0x95, 0x46, 0x86, 0x8a, 0x7f, 0x3a, 0x45, 0xa9, 0x67, 0x68, 0xd4, 0x0f, 0xd9, 0xd0, 0x34, + 0x12, 0xc0, 0x91, 0xc6, 0x31, 0x5c, 0xf4, 0xfd, 0xe7, 0xcb, 0x68, 0x60, 0x69, 0x37, 0x38, 0x0d, + 0xb2, 0xea, 0xaa, 0x70, 0x7b, 0x4c, 0x41, 0x85, 0xc3, 0x2e, 0xdd, 0xcd, 0xd3, 0x06, 0x70, 0x5e, + 0x4d, 0xc1, 0xff, 0xc8, 0x72, 0xee, 0xee, 0x47, 0x5a, 0x64, 0xdf, 0xac, 0x86, 0xab, 0xa4, 0x1c, + 0x06, 0x18, 0x98, 0x3f, 0x87, 0x41, 0xc5, 0xef, 0x68, 0xd3, 0xa1, 0x01, 0xe8, 0xa3, 0xb8, 0xca, + 0xc6, 0x0c, 0x90, 0x5c, 0x15, 0xfc, 0x91, 0x08, 0x40, 0xb9, 0x4c, 0x00, 0xa0, 0xb9, 0xd0, + }, + msgLen: 1023, + sig: []byte{ + 0x0a, 0xab, 0x4c, 0x90, 0x05, 0x01, 0xb3, 0xe2, 0x4d, 0x7c, 0xdf, 0x46, 0x63, 0x32, 0x6a, 0x3a, + 0x87, 0xdf, 0x5e, 0x48, 0x43, 0xb2, 0xcb, 0xdb, 0x67, 0xcb, 0xf6, 0xe4, 0x60, 0xfe, 0xc3, 0x50, + 0xaa, 0x53, 0x71, 0xb1, 0x50, 0x8f, 0x9f, 0x45, 0x28, 0xec, 0xea, 0x23, 0xc4, 0x36, 0xd9, 0x4b, + 0x5e, 0x8f, 0xcd, 0x4f, 0x68, 0x1e, 0x30, 0xa6, 0xac, 0x00, 0xa9, 0x70, 0x4a, 0x18, 0x8a, 0x03, + }, + ph: false, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----TEST sha(abc)", + scheme: "Ed25519Pure", + sk: []byte{ + 0x83, 0x3f, 0xe6, 0x24, 0x09, 0x23, 0x7b, 0x9d, 0x62, 0xec, 0x77, 0x58, 0x75, 0x20, 0x91, 0x1e, + 0x9a, 0x75, 0x9c, 0xec, 0x1d, 0x19, 0x75, 0x5b, 0x7d, 0xa9, 0x01, 0xb9, 0x6d, 0xca, 0x3d, 0x42, + }, + pk: []byte{ + 0xec, 0x17, 0x2b, 0x93, 0xad, 0x5e, 0x56, 0x3b, 0xf4, 0x93, 0x2c, 0x70, 0xe1, 0x24, 0x50, 0x34, + 0xc3, 0x54, 0x67, 0xef, 0x2e, 0xfd, 0x4d, 0x64, 0xeb, 0xf8, 0x19, 0x68, 0x34, 0x67, 0xe2, 0xbf, + }, + msg: []byte{ + 0xdd, 0xaf, 0x35, 0xa1, 0x93, 0x61, 0x7a, 0xba, 0xcc, 0x41, 0x73, 0x49, 0xae, 0x20, 0x41, 0x31, + 0x12, 0xe6, 0xfa, 0x4e, 0x89, 0xa9, 0x7e, 0xa2, 0x0a, 0x9e, 0xee, 0xe6, 0x4b, 0x55, 0xd3, 0x9a, + 0x21, 0x92, 0x99, 0x2a, 0x27, 0x4f, 0xc1, 0xa8, 0x36, 0xba, 0x3c, 0x23, 0xa3, 0xfe, 0xeb, 0xbd, + 0x45, 0x4d, 0x44, 0x23, 0x64, 0x3c, 0xe8, 0x0e, 0x2a, 0x9a, 0xc9, 0x4f, 0xa5, 0x4c, 0xa4, 0x9f, + }, + msgLen: 64, + sig: []byte{ + 0xdc, 0x2a, 0x44, 0x59, 0xe7, 0x36, 0x96, 0x33, 0xa5, 0x2b, 0x1b, 0xf2, 0x77, 0x83, 0x9a, 0x00, + 0x20, 0x10, 0x09, 0xa3, 0xef, 0xbf, 0x3e, 0xcb, 0x69, 0xbe, 0xa2, 0x18, 0x6c, 0x26, 0xb5, 0x89, + 0x09, 0x35, 0x1f, 0xc9, 0xac, 0x90, 0xb3, 0xec, 0xfd, 0xfb, 0xc7, 0xc6, 0x64, 0x31, 0xe0, 0x30, + 0x3d, 0xca, 0x17, 0x9c, 0x13, 0x8a, 0xc1, 0x7a, 0xd9, 0xbe, 0xf1, 0x17, 0x73, 0x31, 0xa7, 0x04, + }, + ph: false, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----TEST abc", + scheme: "Ed25519Ph", + sk: []byte{ + 0x83, 0x3f, 0xe6, 0x24, 0x09, 0x23, 0x7b, 0x9d, 0x62, 0xec, 0x77, 0x58, 0x75, 0x20, 0x91, 0x1e, + 0x9a, 0x75, 0x9c, 0xec, 0x1d, 0x19, 0x75, 0x5b, 0x7d, 0xa9, 0x01, 0xb9, 0x6d, 0xca, 0x3d, 0x42, + }, + pk: []byte{ + 0xec, 0x17, 0x2b, 0x93, 0xad, 0x5e, 0x56, 0x3b, 0xf4, 0x93, 0x2c, 0x70, 0xe1, 0x24, 0x50, 0x34, + 0xc3, 0x54, 0x67, 0xef, 0x2e, 0xfd, 0x4d, 0x64, 0xeb, 0xf8, 0x19, 0x68, 0x34, 0x67, 0xe2, 0xbf, + }, + msg: []byte{ + 0x61, 0x62, 0x63, + }, + msgLen: 3, + sig: []byte{ + 0x98, 0xa7, 0x02, 0x22, 0xf0, 0xb8, 0x12, 0x1a, 0xa9, 0xd3, 0x0f, 0x81, 0x3d, 0x68, 0x3f, 0x80, + 0x9e, 0x46, 0x2b, 0x46, 0x9c, 0x7f, 0xf8, 0x76, 0x39, 0x49, 0x9b, 0xb9, 0x4e, 0x6d, 0xae, 0x41, + 0x31, 0xf8, 0x50, 0x42, 0x46, 0x3c, 0x2a, 0x35, 0x5a, 0x20, 0x03, 0xd0, 0x62, 0xad, 0xf5, 0xaa, + 0xa1, 0x0b, 0x8c, 0x61, 0xe6, 0x36, 0x06, 0x2a, 0xaa, 0xd1, 0x1c, 0x2a, 0x26, 0x08, 0x34, 0x06, + }, + ph: true, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----foo", + scheme: "Ed25519Ctx", + sk: []byte{ + 0x03, 0x05, 0x33, 0x4e, 0x38, 0x1a, 0xf7, 0x8f, 0x14, 0x1c, 0xb6, 0x66, 0xf6, 0x19, 0x9f, 0x57, + 0xbc, 0x34, 0x95, 0x33, 0x5a, 0x25, 0x6a, 0x95, 0xbd, 0x2a, 0x55, 0xbf, 0x54, 0x66, 0x63, 0xf6, + }, + pk: []byte{ + 0xdf, 0xc9, 0x42, 0x5e, 0x4f, 0x96, 0x8f, 0x7f, 0x0c, 0x29, 0xf0, 0x25, 0x9c, 0xf5, 0xf9, 0xae, + 0xd6, 0x85, 0x1c, 0x2b, 0xb4, 0xad, 0x8b, 0xfb, 0x86, 0x0c, 0xfe, 0xe0, 0xab, 0x24, 0x82, 0x92, + }, + msg: []byte{ + 0xf7, 0x26, 0x93, 0x6d, 0x19, 0xc8, 0x00, 0x49, 0x4e, 0x3f, 0xda, 0xff, 0x20, 0xb2, 0x76, 0xa8, + }, + msgLen: 16, + sig: []byte{ + 0x55, 0xa4, 0xcc, 0x2f, 0x70, 0xa5, 0x4e, 0x04, 0x28, 0x8c, 0x5f, 0x4c, 0xd1, 0xe4, 0x5a, 0x7b, + 0xb5, 0x20, 0xb3, 0x62, 0x92, 0x91, 0x18, 0x76, 0xca, 0xda, 0x73, 0x23, 0x19, 0x8d, 0xd8, 0x7a, + 0x8b, 0x36, 0x95, 0x0b, 0x95, 0x13, 0x00, 0x22, 0x90, 0x7a, 0x7f, 0xb7, 0xc4, 0xe9, 0xb2, 0xd5, + 0xf6, 0xcc, 0xa6, 0x85, 0xa5, 0x87, 0xb4, 0xb2, 0x1f, 0x4b, 0x88, 0x8e, 0x4e, 0x7e, 0xdb, 0x0d, + }, + ph: false, + ctx: []byte{ + 0x66, 0x6f, 0x6f, + }, + ctxLen: 3, + }, + { + name: "-----bar", + scheme: "Ed25519Ctx", + sk: []byte{ + 0x03, 0x05, 0x33, 0x4e, 0x38, 0x1a, 0xf7, 0x8f, 0x14, 0x1c, 0xb6, 0x66, 0xf6, 0x19, 0x9f, 0x57, + 0xbc, 0x34, 0x95, 0x33, 0x5a, 0x25, 0x6a, 0x95, 0xbd, 0x2a, 0x55, 0xbf, 0x54, 0x66, 0x63, 0xf6, + }, + pk: []byte{ + 0xdf, 0xc9, 0x42, 0x5e, 0x4f, 0x96, 0x8f, 0x7f, 0x0c, 0x29, 0xf0, 0x25, 0x9c, 0xf5, 0xf9, 0xae, + 0xd6, 0x85, 0x1c, 0x2b, 0xb4, 0xad, 0x8b, 0xfb, 0x86, 0x0c, 0xfe, 0xe0, 0xab, 0x24, 0x82, 0x92, + }, + msg: []byte{ + 0xf7, 0x26, 0x93, 0x6d, 0x19, 0xc8, 0x00, 0x49, 0x4e, 0x3f, 0xda, 0xff, 0x20, 0xb2, 0x76, 0xa8, + }, + msgLen: 16, + sig: []byte{ + 0xfc, 0x60, 0xd5, 0x87, 0x2f, 0xc4, 0x6b, 0x3a, 0xa6, 0x9f, 0x8b, 0x5b, 0x43, 0x51, 0xd5, 0x80, + 0x8f, 0x92, 0xbc, 0xc0, 0x44, 0x60, 0x6d, 0xb0, 0x97, 0xab, 0xab, 0x6d, 0xbc, 0xb1, 0xae, 0xe3, + 0x21, 0x6c, 0x48, 0xe8, 0xb3, 0xb6, 0x64, 0x31, 0xb5, 0xb1, 0x86, 0xd1, 0xd2, 0x8f, 0x8e, 0xe1, + 0x5a, 0x5c, 0xa2, 0xdf, 0x66, 0x68, 0x34, 0x62, 0x91, 0xc2, 0x04, 0x3d, 0x4e, 0xb3, 0xe9, 0x0d, + }, + ph: false, + ctx: []byte{ + 0x62, 0x61, 0x72, + }, + ctxLen: 3, + }, + { + name: "-----foo2", + scheme: "Ed25519Ctx", + sk: []byte{ + 0x03, 0x05, 0x33, 0x4e, 0x38, 0x1a, 0xf7, 0x8f, 0x14, 0x1c, 0xb6, 0x66, 0xf6, 0x19, 0x9f, 0x57, + 0xbc, 0x34, 0x95, 0x33, 0x5a, 0x25, 0x6a, 0x95, 0xbd, 0x2a, 0x55, 0xbf, 0x54, 0x66, 0x63, 0xf6, + }, + pk: []byte{ + 0xdf, 0xc9, 0x42, 0x5e, 0x4f, 0x96, 0x8f, 0x7f, 0x0c, 0x29, 0xf0, 0x25, 0x9c, 0xf5, 0xf9, 0xae, + 0xd6, 0x85, 0x1c, 0x2b, 0xb4, 0xad, 0x8b, 0xfb, 0x86, 0x0c, 0xfe, 0xe0, 0xab, 0x24, 0x82, 0x92, + }, + msg: []byte{ + 0x50, 0x8e, 0x9e, 0x68, 0x82, 0xb9, 0x79, 0xfe, 0xa9, 0x00, 0xf6, 0x2a, 0xdc, 0xea, 0xca, 0x35, + }, + msgLen: 16, + sig: []byte{ + 0x8b, 0x70, 0xc1, 0xcc, 0x83, 0x10, 0xe1, 0xde, 0x20, 0xac, 0x53, 0xce, 0x28, 0xae, 0x6e, 0x72, + 0x07, 0xf3, 0x3c, 0x32, 0x95, 0xe0, 0x3b, 0xb5, 0xc0, 0x73, 0x2a, 0x1d, 0x20, 0xdc, 0x64, 0x90, + 0x89, 0x22, 0xa8, 0xb0, 0x52, 0xcf, 0x99, 0xb7, 0xc4, 0xfe, 0x10, 0x7a, 0x5a, 0xbb, 0x5b, 0x2c, + 0x40, 0x85, 0xae, 0x75, 0x89, 0x0d, 0x02, 0xdf, 0x26, 0x26, 0x9d, 0x89, 0x45, 0xf8, 0x4b, 0x0b, + }, + ph: false, + ctx: []byte{ + 0x66, 0x6f, 0x6f, + }, + ctxLen: 3, + }, + { + name: "-----foo3", + scheme: "Ed25519Ctx", + sk: []byte{ + 0xab, 0x9c, 0x28, 0x53, 0xce, 0x29, 0x7d, 0xda, 0xb8, 0x5c, 0x99, 0x3b, 0x3a, 0xe1, 0x4b, 0xca, + 0xd3, 0x9b, 0x2c, 0x68, 0x2b, 0xea, 0xbc, 0x27, 0xd6, 0xd4, 0xeb, 0x20, 0x71, 0x1d, 0x65, 0x60, + }, + pk: []byte{ + 0x0f, 0x1d, 0x12, 0x74, 0x94, 0x3b, 0x91, 0x41, 0x58, 0x89, 0x15, 0x2e, 0x89, 0x3d, 0x80, 0xe9, + 0x32, 0x75, 0xa1, 0xfc, 0x0b, 0x65, 0xfd, 0x71, 0xb4, 0xb0, 0xdd, 0xa1, 0x0a, 0xd7, 0xd7, 0x72, + }, + msg: []byte{ + 0xf7, 0x26, 0x93, 0x6d, 0x19, 0xc8, 0x00, 0x49, 0x4e, 0x3f, 0xda, 0xff, 0x20, 0xb2, 0x76, 0xa8, + }, + msgLen: 16, + sig: []byte{ + 0x21, 0x65, 0x5b, 0x5f, 0x1a, 0xa9, 0x65, 0x99, 0x6b, 0x3f, 0x97, 0xb3, 0xc8, 0x49, 0xea, 0xfb, + 0xa9, 0x22, 0xa0, 0xa6, 0x29, 0x92, 0xf7, 0x3b, 0x3d, 0x1b, 0x73, 0x10, 0x6a, 0x84, 0xad, 0x85, + 0xe9, 0xb8, 0x6a, 0x7b, 0x60, 0x05, 0xea, 0x86, 0x83, 0x37, 0xff, 0x2d, 0x20, 0xa7, 0xf5, 0xfb, + 0xd4, 0xcd, 0x10, 0xb0, 0xbe, 0x49, 0xa6, 0x8d, 0xa2, 0xb2, 0xe0, 0xdc, 0x0a, 0xd8, 0x96, 0x0f, + }, + ph: false, + ctx: []byte{ + 0x66, 0x6f, 0x6f, + }, + ctxLen: 3, + }, +} + +func (v vector) isPure() bool { return v.scheme == "Ed25519Pure" } +func (v vector) isPreHashed() bool { return v.scheme == "Ed25519Ph" } +func (v vector) hasContext() bool { return v.scheme == "Ed25519Ctx" } +func (v vector) matchMsgLen() bool { return uint(len(v.msg)) == v.msgLen } +func (v vector) matchCtxLen() bool { return uint(len(v.ctx)) == v.ctxLen } + +func (v vector) testPublicKey(t *testing.T) { + keys := ed25519.NewKeyFromSeed(v.sk) + got := keys.Public().(ed25519.PublicKey) + want := v.pk + + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, v.name) + } +} + +func (v vector) testSign(t *testing.T) { + key := ed25519.NewKeyFromSeed(v.sk) + + var got []byte + + if v.ph { + got = ed25519.SignPh(key, v.msg, "") + } else if v.ctxLen > 0 { + got = ed25519.SignWithCtx(key, v.msg, string(v.ctx)) + } else { + got = ed25519.Sign(key, v.msg) + } + + want := v.sig + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, v.name) + } +} + +func (v vector) testVerify(t *testing.T) { + var got bool + if v.ph { + got = ed25519.VerifyPh(v.pk, v.msg, v.sig, "") + } else if v.ctxLen > 0 { + got = ed25519.VerifyWithCtx(v.pk, v.msg, v.sig, string(v.ctx)) + } else { + got = ed25519.Verify(v.pk, v.msg, v.sig) + } + + want := true + + if got != want { + test.ReportError(t, got, want, v.name) + } +} + +func TestEd25519(t *testing.T) { + for _, v := range vectorsEd25519 { + got := (v.isPure() || v.isPreHashed() || v.hasContext()) && v.matchMsgLen() && v.matchCtxLen() + want := true + if got != want { + test.ReportError(t, got, want, v.sk) + } + + v.testPublicKey(t) + v.testSign(t) + v.testVerify(t) + } +} diff --git a/src/circl/sign/ed25519/signapi.go b/src/circl/sign/ed25519/signapi.go new file mode 100644 index 00000000000..af467b4f62a --- /dev/null +++ b/src/circl/sign/ed25519/signapi.go @@ -0,0 +1,87 @@ +package ed25519 + +import ( + "crypto/rand" + "encoding/asn1" + + "circl/sign" +) + +var sch sign.Scheme = &scheme{} + +// Scheme returns a signature interface. +func Scheme() sign.Scheme { return sch } + +type scheme struct{} + +func (*scheme) Name() string { return "Ed25519" } +func (*scheme) PublicKeySize() int { return PublicKeySize } +func (*scheme) PrivateKeySize() int { return PrivateKeySize } +func (*scheme) SignatureSize() int { return SignatureSize } +func (*scheme) SeedSize() int { return SeedSize } +func (*scheme) TLSIdentifier() uint { return 0x0807 } +func (*scheme) SupportsContext() bool { return false } +func (*scheme) Oid() asn1.ObjectIdentifier { + return asn1.ObjectIdentifier{1, 3, 101, 112} +} + +func (*scheme) GenerateKey() (sign.PublicKey, sign.PrivateKey, error) { + return GenerateKey(rand.Reader) +} + +func (*scheme) Sign( + sk sign.PrivateKey, + message []byte, + opts *sign.SignatureOpts, +) []byte { + priv, ok := sk.(PrivateKey) + if !ok { + panic(sign.ErrTypeMismatch) + } + if opts != nil && opts.Context != "" { + panic(sign.ErrContextNotSupported) + } + return Sign(priv, message) +} + +func (*scheme) Verify( + pk sign.PublicKey, + message, signature []byte, + opts *sign.SignatureOpts, +) bool { + pub, ok := pk.(PublicKey) + if !ok { + panic(sign.ErrTypeMismatch) + } + if opts != nil { + if opts.Context != "" { + panic(sign.ErrContextNotSupported) + } + } + return Verify(pub, message, signature) +} + +func (*scheme) DeriveKey(seed []byte) (sign.PublicKey, sign.PrivateKey) { + privateKey := NewKeyFromSeed(seed) + publicKey := make(PublicKey, PublicKeySize) + copy(publicKey, privateKey[SeedSize:]) + return publicKey, privateKey +} + +func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (sign.PublicKey, error) { + if len(buf) < PublicKeySize { + return nil, sign.ErrPubKeySize + } + pub := make(PublicKey, PublicKeySize) + copy(pub, buf[:PublicKeySize]) + return pub, nil +} + +func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (sign.PrivateKey, error) { + if len(buf) < PrivateKeySize { + return nil, sign.ErrPrivKeySize + } + priv := make(PrivateKey, PrivateKeySize) + copy(priv, buf[:PrivateKeySize]) + return priv, nil +} diff --git a/src/circl/sign/ed25519/tables.go b/src/circl/sign/ed25519/tables.go new file mode 100644 index 00000000000..5588d96b5ca --- /dev/null +++ b/src/circl/sign/ed25519/tables.go @@ -0,0 +1,213 @@ +package ed25519 + +import fp "circl/math/fp25519" + +var tabSign = [fxV][fx2w1]pointR3{ + { + pointR3{ + addYX: fp.Elt{0x85, 0x3b, 0x8c, 0xf5, 0xc6, 0x93, 0xbc, 0x2f, 0x19, 0x0e, 0x8c, 0xfb, 0xc6, 0x2d, 0x93, 0xcf, 0xc2, 0x42, 0x3d, 0x64, 0x98, 0x48, 0x0b, 0x27, 0x65, 0xba, 0xd4, 0x33, 0x3a, 0x9d, 0xcf, 0x07}, + subYX: fp.Elt{0x3e, 0x91, 0x40, 0xd7, 0x05, 0x39, 0x10, 0x9d, 0xb3, 0xbe, 0x40, 0xd1, 0x05, 0x9f, 0x39, 0xfd, 0x09, 0x8a, 0x8f, 0x68, 0x34, 0x84, 0xc1, 0xa5, 0x67, 0x12, 0xf8, 0x98, 0x92, 0x2f, 0xfd, 0x44}, + dt2: fp.Elt{0x68, 0xaa, 0x7a, 0x87, 0x05, 0x12, 0xc9, 0xab, 0x9e, 0xc4, 0xaa, 0xcc, 0x23, 0xe8, 0xd9, 0x26, 0x8c, 0x59, 0x43, 0xdd, 0xcb, 0x7d, 0x1b, 0x5a, 0xa8, 0x65, 0x0c, 0x9f, 0x68, 0x7b, 0x11, 0x6f}, + }, + { + addYX: fp.Elt{0x7c, 0xb0, 0x9e, 0xe6, 0xc5, 0xbf, 0xfa, 0x13, 0x8e, 0x0d, 0x22, 0xde, 0xc8, 0xd1, 0xce, 0x52, 0x02, 0xd5, 0x62, 0x31, 0x71, 0x0e, 0x8e, 0x9d, 0xb0, 0xd6, 0x00, 0xa5, 0x5a, 0x0e, 0xce, 0x72}, + subYX: fp.Elt{0x1a, 0x8e, 0x5c, 0xdc, 0xa4, 0xb3, 0x6c, 0x51, 0x18, 0xa0, 0x09, 0x80, 0x9a, 0x46, 0x33, 0xd5, 0xe0, 0x3c, 0x4d, 0x3b, 0xfc, 0x49, 0xa2, 0x43, 0x29, 0xe1, 0x29, 0xa9, 0x93, 0xea, 0x7c, 0x35}, + dt2: fp.Elt{0x08, 0x46, 0x6f, 0x68, 0x7f, 0x0b, 0x7c, 0x9e, 0xad, 0xba, 0x07, 0x61, 0x74, 0x83, 0x2f, 0xfc, 0x26, 0xd6, 0x09, 0xb9, 0x00, 0x34, 0x36, 0x4f, 0x01, 0xf3, 0x48, 0xdb, 0x43, 0xba, 0x04, 0x44}, + }, + { + addYX: fp.Elt{0x4c, 0xda, 0x0d, 0x13, 0x66, 0xfd, 0x82, 0x84, 0x9f, 0x75, 0x5b, 0xa2, 0x17, 0xfe, 0x34, 0xbf, 0x1f, 0xcb, 0xba, 0x90, 0x55, 0x80, 0x83, 0xfd, 0x63, 0xb9, 0x18, 0xf8, 0x5b, 0x5d, 0x94, 0x1e}, + subYX: fp.Elt{0xb9, 0xdb, 0x6c, 0x04, 0x88, 0x22, 0xd8, 0x79, 0x83, 0x2f, 0x8d, 0x65, 0x6b, 0xd2, 0xab, 0x1b, 0xdd, 0x65, 0xe5, 0x93, 0x63, 0xf8, 0xa2, 0xd8, 0x3c, 0xf1, 0x4b, 0xc5, 0x99, 0xd1, 0xf2, 0x12}, + dt2: fp.Elt{0x05, 0x4c, 0xb8, 0x3b, 0xfe, 0xf5, 0x9f, 0x2e, 0xd1, 0xb2, 0xb8, 0xff, 0xfe, 0x6d, 0xd9, 0x37, 0xe0, 0xae, 0xb4, 0x5a, 0x51, 0x80, 0x7e, 0x9b, 0x1d, 0xd1, 0x8d, 0x8c, 0x56, 0xb1, 0x84, 0x35}, + }, + { + addYX: fp.Elt{0x39, 0x71, 0x43, 0x34, 0xe3, 0x42, 0x45, 0xa1, 0xf2, 0x68, 0x71, 0xa7, 0xe8, 0x23, 0xfd, 0x9f, 0x86, 0x48, 0xff, 0xe5, 0x96, 0x74, 0xcf, 0x05, 0x49, 0xe2, 0xb3, 0x6c, 0x17, 0x77, 0x2f, 0x6d}, + subYX: fp.Elt{0x73, 0x3f, 0xc1, 0xc7, 0x6a, 0x66, 0xa1, 0x20, 0xdd, 0x11, 0xfb, 0x7a, 0x6e, 0xa8, 0x51, 0xb8, 0x3f, 0x9d, 0xa2, 0x97, 0x84, 0xb5, 0xc7, 0x90, 0x7c, 0xab, 0x48, 0xd6, 0x84, 0xa3, 0xd5, 0x1a}, + dt2: fp.Elt{0x63, 0x27, 0x3c, 0x49, 0x4b, 0xfc, 0x22, 0xf2, 0x0b, 0x50, 0xc2, 0x0f, 0xb4, 0x1f, 0x31, 0x0c, 0x2f, 0x53, 0xab, 0xaa, 0x75, 0x6f, 0xe0, 0x69, 0x39, 0x56, 0xe0, 0x3b, 0xb7, 0xa8, 0xbf, 0x45}, + }, + }, + { + { + addYX: fp.Elt{0x00, 0x45, 0xd9, 0x0d, 0x58, 0x03, 0xfc, 0x29, 0x93, 0xec, 0xbb, 0x6f, 0xa4, 0x7a, 0xd2, 0xec, 0xf8, 0xa7, 0xe2, 0xc2, 0x5f, 0x15, 0x0a, 0x13, 0xd5, 0xa1, 0x06, 0xb7, 0x1a, 0x15, 0x6b, 0x41}, + subYX: fp.Elt{0x85, 0x8c, 0xb2, 0x17, 0xd6, 0x3b, 0x0a, 0xd3, 0xea, 0x3b, 0x77, 0x39, 0xb7, 0x77, 0xd3, 0xc5, 0xbf, 0x5c, 0x6a, 0x1e, 0x8c, 0xe7, 0xc6, 0xc6, 0xc4, 0xb7, 0x2a, 0x8b, 0xf7, 0xb8, 0x61, 0x0d}, + dt2: fp.Elt{0xb0, 0x36, 0xc1, 0xe9, 0xef, 0xd7, 0xa8, 0x56, 0x20, 0x4b, 0xe4, 0x58, 0xcd, 0xe5, 0x07, 0xbd, 0xab, 0xe0, 0x57, 0x1b, 0xda, 0x2f, 0xe6, 0xaf, 0xd2, 0xe8, 0x77, 0x42, 0xf7, 0x2a, 0x1a, 0x19}, + }, + { + addYX: fp.Elt{0x6a, 0x6d, 0x6d, 0xd1, 0xfa, 0xf5, 0x03, 0x30, 0xbd, 0x6d, 0xc2, 0xc8, 0xf5, 0x38, 0x80, 0x4f, 0xb2, 0xbe, 0xa1, 0x76, 0x50, 0x1a, 0x73, 0xf2, 0x78, 0x2b, 0x8e, 0x3a, 0x1e, 0x34, 0x47, 0x7b}, + subYX: fp.Elt{0xc3, 0x2c, 0x36, 0xdc, 0xc5, 0x45, 0xbc, 0xef, 0x1b, 0x64, 0xd6, 0x65, 0x28, 0xe9, 0xda, 0x84, 0x13, 0xbe, 0x27, 0x8e, 0x3f, 0x98, 0x2a, 0x37, 0xee, 0x78, 0x97, 0xd6, 0xc0, 0x6f, 0xb4, 0x53}, + dt2: fp.Elt{0x58, 0x5d, 0xa7, 0xa3, 0x68, 0xbb, 0x20, 0x30, 0x2e, 0x03, 0xe9, 0xb1, 0xd4, 0x90, 0x72, 0xe3, 0x71, 0xb2, 0x36, 0x3e, 0x73, 0xa0, 0x2e, 0x3d, 0xd1, 0x85, 0x33, 0x62, 0x4e, 0xa7, 0x7b, 0x31}, + }, + { + addYX: fp.Elt{0xbf, 0xc4, 0x38, 0x53, 0xfb, 0x68, 0xa9, 0x77, 0xce, 0x55, 0xf9, 0x05, 0xcb, 0xeb, 0xfb, 0x8c, 0x46, 0xc2, 0x32, 0x7c, 0xf0, 0xdb, 0xd7, 0x2c, 0x62, 0x8e, 0xdd, 0x54, 0x75, 0xcf, 0x3f, 0x33}, + subYX: fp.Elt{0x49, 0x50, 0x1f, 0x4e, 0x6e, 0x55, 0x55, 0xde, 0x8c, 0x4e, 0x77, 0x96, 0x38, 0x3b, 0xfe, 0xb6, 0x43, 0x3c, 0x86, 0x69, 0xc2, 0x72, 0x66, 0x1f, 0x6b, 0xf9, 0x87, 0xbc, 0x4f, 0x37, 0x3e, 0x3c}, + dt2: fp.Elt{0xd2, 0x2f, 0x06, 0x6b, 0x08, 0x07, 0x69, 0x77, 0xc0, 0x94, 0xcc, 0xae, 0x43, 0x00, 0x59, 0x6e, 0xa3, 0x63, 0xa8, 0xdd, 0xfa, 0x24, 0x18, 0xd0, 0x35, 0xc7, 0x78, 0xf7, 0x0d, 0xd4, 0x5a, 0x1e}, + }, + { + addYX: fp.Elt{0x45, 0xc1, 0x17, 0x51, 0xf8, 0xed, 0x7e, 0xc7, 0xa9, 0x1a, 0x11, 0x6e, 0x2d, 0xef, 0x0b, 0xd5, 0x3f, 0x98, 0xb0, 0xa3, 0x9d, 0x65, 0xf1, 0xcd, 0x53, 0x4a, 0x8a, 0x18, 0x70, 0x0a, 0x7f, 0x23}, + subYX: fp.Elt{0xdd, 0xef, 0xbe, 0x3a, 0x31, 0xe0, 0xbc, 0xbe, 0x6d, 0x5d, 0x79, 0x87, 0xd6, 0xbe, 0x68, 0xe3, 0x59, 0x76, 0x8c, 0x86, 0x0e, 0x7a, 0x92, 0x13, 0x14, 0x8f, 0x67, 0xb3, 0xcb, 0x1a, 0x76, 0x76}, + dt2: fp.Elt{0x56, 0x7a, 0x1c, 0x9d, 0xca, 0x96, 0xf9, 0xf9, 0x03, 0x21, 0xd4, 0xe8, 0xb3, 0xd5, 0xe9, 0x52, 0xc8, 0x54, 0x1e, 0x1b, 0x13, 0xb6, 0xfd, 0x47, 0x7d, 0x02, 0x32, 0x33, 0x27, 0xe2, 0x1f, 0x19}, + }, + }, +} + +var tabVerif = [1 << (omegaFix - 2)]pointR3{ + { /* 1P */ + addYX: fp.Elt{0x85, 0x3b, 0x8c, 0xf5, 0xc6, 0x93, 0xbc, 0x2f, 0x19, 0x0e, 0x8c, 0xfb, 0xc6, 0x2d, 0x93, 0xcf, 0xc2, 0x42, 0x3d, 0x64, 0x98, 0x48, 0x0b, 0x27, 0x65, 0xba, 0xd4, 0x33, 0x3a, 0x9d, 0xcf, 0x07}, + subYX: fp.Elt{0x3e, 0x91, 0x40, 0xd7, 0x05, 0x39, 0x10, 0x9d, 0xb3, 0xbe, 0x40, 0xd1, 0x05, 0x9f, 0x39, 0xfd, 0x09, 0x8a, 0x8f, 0x68, 0x34, 0x84, 0xc1, 0xa5, 0x67, 0x12, 0xf8, 0x98, 0x92, 0x2f, 0xfd, 0x44}, + dt2: fp.Elt{0x68, 0xaa, 0x7a, 0x87, 0x05, 0x12, 0xc9, 0xab, 0x9e, 0xc4, 0xaa, 0xcc, 0x23, 0xe8, 0xd9, 0x26, 0x8c, 0x59, 0x43, 0xdd, 0xcb, 0x7d, 0x1b, 0x5a, 0xa8, 0x65, 0x0c, 0x9f, 0x68, 0x7b, 0x11, 0x6f}, + }, + { /* 3P */ + addYX: fp.Elt{0x30, 0x97, 0xee, 0x4c, 0xa8, 0xb0, 0x25, 0xaf, 0x8a, 0x4b, 0x86, 0xe8, 0x30, 0x84, 0x5a, 0x02, 0x32, 0x67, 0x01, 0x9f, 0x02, 0x50, 0x1b, 0xc1, 0xf4, 0xf8, 0x80, 0x9a, 0x1b, 0x4e, 0x16, 0x7a}, + subYX: fp.Elt{0x65, 0xd2, 0xfc, 0xa4, 0xe8, 0x1f, 0x61, 0x56, 0x7d, 0xba, 0xc1, 0xe5, 0xfd, 0x53, 0xd3, 0x3b, 0xbd, 0xd6, 0x4b, 0x21, 0x1a, 0xf3, 0x31, 0x81, 0x62, 0xda, 0x5b, 0x55, 0x87, 0x15, 0xb9, 0x2a}, + dt2: fp.Elt{0x89, 0xd8, 0xd0, 0x0d, 0x3f, 0x93, 0xae, 0x14, 0x62, 0xda, 0x35, 0x1c, 0x22, 0x23, 0x94, 0x58, 0x4c, 0xdb, 0xf2, 0x8c, 0x45, 0xe5, 0x70, 0xd1, 0xc6, 0xb4, 0xb9, 0x12, 0xaf, 0x26, 0x28, 0x5a}, + }, + { /* 5P */ + addYX: fp.Elt{0x33, 0xbb, 0xa5, 0x08, 0x44, 0xbc, 0x12, 0xa2, 0x02, 0xed, 0x5e, 0xc7, 0xc3, 0x48, 0x50, 0x8d, 0x44, 0xec, 0xbf, 0x5a, 0x0c, 0xeb, 0x1b, 0xdd, 0xeb, 0x06, 0xe2, 0x46, 0xf1, 0xcc, 0x45, 0x29}, + subYX: fp.Elt{0xba, 0xd6, 0x47, 0xa4, 0xc3, 0x82, 0x91, 0x7f, 0xb7, 0x29, 0x27, 0x4b, 0xd1, 0x14, 0x00, 0xd5, 0x87, 0xa0, 0x64, 0xb8, 0x1c, 0xf1, 0x3c, 0xe3, 0xf3, 0x55, 0x1b, 0xeb, 0x73, 0x7e, 0x4a, 0x15}, + dt2: fp.Elt{0x85, 0x82, 0x2a, 0x81, 0xf1, 0xdb, 0xbb, 0xbc, 0xfc, 0xd1, 0xbd, 0xd0, 0x07, 0x08, 0x0e, 0x27, 0x2d, 0xa7, 0xbd, 0x1b, 0x0b, 0x67, 0x1b, 0xb4, 0x9a, 0xb6, 0x3b, 0x6b, 0x69, 0xbe, 0xaa, 0x43}, + }, + { /* 7P */ + addYX: fp.Elt{0xbf, 0xa3, 0x4e, 0x94, 0xd0, 0x5c, 0x1a, 0x6b, 0xd2, 0xc0, 0x9d, 0xb3, 0x3a, 0x35, 0x70, 0x74, 0x49, 0x2e, 0x54, 0x28, 0x82, 0x52, 0xb2, 0x71, 0x7e, 0x92, 0x3c, 0x28, 0x69, 0xea, 0x1b, 0x46}, + subYX: fp.Elt{0xb1, 0x21, 0x32, 0xaa, 0x9a, 0x2c, 0x6f, 0xba, 0xa7, 0x23, 0xba, 0x3b, 0x53, 0x21, 0xa0, 0x6c, 0x3a, 0x2c, 0x19, 0x92, 0x4f, 0x76, 0xea, 0x9d, 0xe0, 0x17, 0x53, 0x2e, 0x5d, 0xdd, 0x6e, 0x1d}, + dt2: fp.Elt{0xa2, 0xb3, 0xb8, 0x01, 0xc8, 0x6d, 0x83, 0xf1, 0x9a, 0xa4, 0x3e, 0x05, 0x47, 0x5f, 0x03, 0xb3, 0xf3, 0xad, 0x77, 0x58, 0xba, 0x41, 0x9c, 0x52, 0xa7, 0x90, 0x0f, 0x6a, 0x1c, 0xbb, 0x9f, 0x7a}, + }, + { /* 9P */ + addYX: fp.Elt{0x2f, 0x63, 0xa8, 0xa6, 0x8a, 0x67, 0x2e, 0x9b, 0xc5, 0x46, 0xbc, 0x51, 0x6f, 0x9e, 0x50, 0xa6, 0xb5, 0xf5, 0x86, 0xc6, 0xc9, 0x33, 0xb2, 0xce, 0x59, 0x7f, 0xdd, 0x8a, 0x33, 0xed, 0xb9, 0x34}, + subYX: fp.Elt{0x64, 0x80, 0x9d, 0x03, 0x7e, 0x21, 0x6e, 0xf3, 0x9b, 0x41, 0x20, 0xf5, 0xb6, 0x81, 0xa0, 0x98, 0x44, 0xb0, 0x5e, 0xe7, 0x08, 0xc6, 0xcb, 0x96, 0x8f, 0x9c, 0xdc, 0xfa, 0x51, 0x5a, 0xc0, 0x49}, + dt2: fp.Elt{0x1b, 0xaf, 0x45, 0x90, 0xbf, 0xe8, 0xb4, 0x06, 0x2f, 0xd2, 0x19, 0xa7, 0xe8, 0x83, 0xff, 0xe2, 0x16, 0xcf, 0xd4, 0x93, 0x29, 0xfc, 0xf6, 0xaa, 0x06, 0x8b, 0x00, 0x1b, 0x02, 0x72, 0xc1, 0x73}, + }, + { /* 11P */ + addYX: fp.Elt{0xde, 0x2a, 0x80, 0x8a, 0x84, 0x00, 0xbf, 0x2f, 0x27, 0x2e, 0x30, 0x02, 0xcf, 0xfe, 0xd9, 0xe5, 0x06, 0x34, 0x70, 0x17, 0x71, 0x84, 0x3e, 0x11, 0xaf, 0x8f, 0x6d, 0x54, 0xe2, 0xaa, 0x75, 0x42}, + subYX: fp.Elt{0x48, 0x43, 0x86, 0x49, 0x02, 0x5b, 0x5f, 0x31, 0x81, 0x83, 0x08, 0x77, 0x69, 0xb3, 0xd6, 0x3e, 0x95, 0xeb, 0x8d, 0x6a, 0x55, 0x75, 0xa0, 0xa3, 0x7f, 0xc7, 0xd5, 0x29, 0x80, 0x59, 0xab, 0x18}, + dt2: fp.Elt{0xe9, 0x89, 0x60, 0xfd, 0xc5, 0x2c, 0x2b, 0xd8, 0xa4, 0xe4, 0x82, 0x32, 0xa1, 0xb4, 0x1e, 0x03, 0x22, 0x86, 0x1a, 0xb5, 0x99, 0x11, 0x31, 0x44, 0x48, 0xf9, 0x3d, 0xb5, 0x22, 0x55, 0xc6, 0x3d}, + }, + { /* 13P */ + addYX: fp.Elt{0x6d, 0x7f, 0x00, 0xa2, 0x22, 0xc2, 0x70, 0xbf, 0xdb, 0xde, 0xbc, 0xb5, 0x9a, 0xb3, 0x84, 0xbf, 0x07, 0xba, 0x07, 0xfb, 0x12, 0x0e, 0x7a, 0x53, 0x41, 0xf2, 0x46, 0xc3, 0xee, 0xd7, 0x4f, 0x23}, + subYX: fp.Elt{0x93, 0xbf, 0x7f, 0x32, 0x3b, 0x01, 0x6f, 0x50, 0x6b, 0x6f, 0x77, 0x9b, 0xc9, 0xeb, 0xfc, 0xae, 0x68, 0x59, 0xad, 0xaa, 0x32, 0xb2, 0x12, 0x9d, 0xa7, 0x24, 0x60, 0x17, 0x2d, 0x88, 0x67, 0x02}, + dt2: fp.Elt{0x78, 0xa3, 0x2e, 0x73, 0x19, 0xa1, 0x60, 0x53, 0x71, 0xd4, 0x8d, 0xdf, 0xb1, 0xe6, 0x37, 0x24, 0x33, 0xe5, 0xa7, 0x91, 0xf8, 0x37, 0xef, 0xa2, 0x63, 0x78, 0x09, 0xaa, 0xfd, 0xa6, 0x7b, 0x49}, + }, + { /* 15P */ + addYX: fp.Elt{0xa0, 0xea, 0xcf, 0x13, 0x03, 0xcc, 0xce, 0x24, 0x6d, 0x24, 0x9c, 0x18, 0x8d, 0xc2, 0x48, 0x86, 0xd0, 0xd4, 0xf2, 0xc1, 0xfa, 0xbd, 0xbd, 0x2d, 0x2b, 0xe7, 0x2d, 0xf1, 0x17, 0x29, 0xe2, 0x61}, + subYX: fp.Elt{0x0b, 0xcf, 0x8c, 0x46, 0x86, 0xcd, 0x0b, 0x04, 0xd6, 0x10, 0x99, 0x2a, 0xa4, 0x9b, 0x82, 0xd3, 0x92, 0x51, 0xb2, 0x07, 0x08, 0x30, 0x08, 0x75, 0xbf, 0x5e, 0xd0, 0x18, 0x42, 0xcd, 0xb5, 0x43}, + dt2: fp.Elt{0x16, 0xb5, 0xd0, 0x9b, 0x2f, 0x76, 0x9a, 0x5d, 0xee, 0xde, 0x3f, 0x37, 0x4e, 0xaf, 0x38, 0xeb, 0x70, 0x42, 0xd6, 0x93, 0x7d, 0x5a, 0x2e, 0x03, 0x42, 0xd8, 0xe4, 0x0a, 0x21, 0x61, 0x1d, 0x51}, + }, + { /* 17P */ + addYX: fp.Elt{0x81, 0x9d, 0x0e, 0x95, 0xef, 0x76, 0xc6, 0x92, 0x4f, 0x04, 0xd7, 0xc0, 0xcd, 0x20, 0x46, 0xa5, 0x48, 0x12, 0x8f, 0x6f, 0x64, 0x36, 0x9b, 0xaa, 0xe3, 0x55, 0xb8, 0xdd, 0x24, 0x59, 0x32, 0x6d}, + subYX: fp.Elt{0x87, 0xde, 0x20, 0x44, 0x48, 0x86, 0x13, 0x08, 0xb4, 0xed, 0x92, 0xb5, 0x16, 0xf0, 0x1c, 0x8a, 0x25, 0x2d, 0x94, 0x29, 0x27, 0x4e, 0xfa, 0x39, 0x10, 0x28, 0x48, 0xe2, 0x6f, 0xfe, 0xa7, 0x71}, + dt2: fp.Elt{0x54, 0xc8, 0xc8, 0xa5, 0xb8, 0x82, 0x71, 0x6c, 0x03, 0x2a, 0x5f, 0xfe, 0x79, 0x14, 0xfd, 0x33, 0x0c, 0x8d, 0x77, 0x83, 0x18, 0x59, 0xcf, 0x72, 0xa9, 0xea, 0x9e, 0x55, 0xb6, 0xc4, 0x46, 0x47}, + }, + { /* 19P */ + addYX: fp.Elt{0x2b, 0x9a, 0xc6, 0x6d, 0x3c, 0x7b, 0x77, 0xd3, 0x17, 0xf6, 0x89, 0x6f, 0x27, 0xb2, 0xfa, 0xde, 0xb5, 0x16, 0x3a, 0xb5, 0xf7, 0x1c, 0x65, 0x45, 0xb7, 0x9f, 0xfe, 0x34, 0xde, 0x51, 0x9a, 0x5c}, + subYX: fp.Elt{0x47, 0x11, 0x74, 0x64, 0xc8, 0x46, 0x85, 0x34, 0x49, 0xc8, 0xfc, 0x0e, 0xdd, 0xae, 0x35, 0x7d, 0x32, 0xa3, 0x72, 0x06, 0x76, 0x9a, 0x93, 0xff, 0xd6, 0xe6, 0xb5, 0x7d, 0x49, 0x63, 0x96, 0x21}, + dt2: fp.Elt{0x67, 0x0e, 0xf1, 0x79, 0xcf, 0xf1, 0x10, 0xf5, 0x5b, 0x51, 0x58, 0xe6, 0xa1, 0xda, 0xdd, 0xff, 0x77, 0x22, 0x14, 0x10, 0x17, 0xa7, 0xc3, 0x09, 0xbb, 0x23, 0x82, 0x60, 0x3c, 0x50, 0x04, 0x48}, + }, + { /* 21P */ + addYX: fp.Elt{0xc7, 0x7f, 0xa3, 0x2c, 0xd0, 0x9e, 0x24, 0xc4, 0xab, 0xac, 0x15, 0xa6, 0xe3, 0xa0, 0x59, 0xa0, 0x23, 0x0e, 0x6e, 0xc9, 0xd7, 0x6e, 0xa9, 0x88, 0x6d, 0x69, 0x50, 0x16, 0xa5, 0x98, 0x33, 0x55}, + subYX: fp.Elt{0x75, 0xd1, 0x36, 0x3a, 0xd2, 0x21, 0x68, 0x3b, 0x32, 0x9e, 0x9b, 0xe9, 0xa7, 0x0a, 0xb4, 0xbb, 0x47, 0x8a, 0x83, 0x20, 0xe4, 0x5c, 0x9e, 0x5d, 0x5e, 0x4c, 0xde, 0x58, 0x88, 0x09, 0x1e, 0x77}, + dt2: fp.Elt{0xdf, 0x1e, 0x45, 0x78, 0xd2, 0xf5, 0x12, 0x9a, 0xcb, 0x9c, 0x89, 0x85, 0x79, 0x5d, 0xda, 0x3a, 0x08, 0x95, 0xa5, 0x9f, 0x2d, 0x4a, 0x7f, 0x47, 0x11, 0xa6, 0xf5, 0x8f, 0xd6, 0xd1, 0x5e, 0x5a}, + }, + { /* 23P */ + addYX: fp.Elt{0x83, 0x0e, 0x15, 0xfe, 0x2a, 0x12, 0x95, 0x11, 0xd8, 0x35, 0x4b, 0x7e, 0x25, 0x9a, 0x20, 0xcf, 0x20, 0x1e, 0x71, 0x1e, 0x29, 0xf8, 0x87, 0x73, 0xf0, 0x92, 0xbf, 0xd8, 0x97, 0xb8, 0xac, 0x44}, + subYX: fp.Elt{0x59, 0x73, 0x52, 0x58, 0xc5, 0xe0, 0xe5, 0xba, 0x7e, 0x9d, 0xdb, 0xca, 0x19, 0x5c, 0x2e, 0x39, 0xe9, 0xab, 0x1c, 0xda, 0x1e, 0x3c, 0x65, 0x28, 0x44, 0xdc, 0xef, 0x5f, 0x13, 0x60, 0x9b, 0x01}, + dt2: fp.Elt{0x83, 0x4b, 0x13, 0x5e, 0x14, 0x68, 0x60, 0x1e, 0x16, 0x4c, 0x30, 0x24, 0x4f, 0xe6, 0xf5, 0xc4, 0xd7, 0x3e, 0x1a, 0xfc, 0xa8, 0x88, 0x6e, 0x50, 0x92, 0x2f, 0xad, 0xe6, 0xfd, 0x49, 0x0c, 0x15}, + }, + { /* 25P */ + addYX: fp.Elt{0x38, 0x11, 0x47, 0x09, 0x95, 0xf2, 0x7b, 0x8e, 0x51, 0xa6, 0x75, 0x4f, 0x39, 0xef, 0x6f, 0x5d, 0xad, 0x08, 0xa7, 0x25, 0xc4, 0x79, 0xaf, 0x10, 0x22, 0x99, 0xb9, 0x5b, 0x07, 0x5a, 0x2b, 0x6b}, + subYX: fp.Elt{0x68, 0xa8, 0xdc, 0x9c, 0x3c, 0x86, 0x49, 0xb8, 0xd0, 0x4a, 0x71, 0xb8, 0xdb, 0x44, 0x3f, 0xc8, 0x8d, 0x16, 0x36, 0x0c, 0x56, 0xe3, 0x3e, 0xfe, 0xc1, 0xfb, 0x05, 0x1e, 0x79, 0xd7, 0xa6, 0x78}, + dt2: fp.Elt{0x76, 0xb9, 0xa0, 0x47, 0x4b, 0x70, 0xbf, 0x58, 0xd5, 0x48, 0x17, 0x74, 0x55, 0xb3, 0x01, 0xa6, 0x90, 0xf5, 0x42, 0xd5, 0xb1, 0x1f, 0x2b, 0xaa, 0x00, 0x5d, 0xd5, 0x4a, 0xfc, 0x7f, 0x5c, 0x72}, + }, + { /* 27P */ + addYX: fp.Elt{0xb2, 0x99, 0xcf, 0xd1, 0x15, 0x67, 0x42, 0xe4, 0x34, 0x0d, 0xa2, 0x02, 0x11, 0xd5, 0x52, 0x73, 0x9f, 0x10, 0x12, 0x8b, 0x7b, 0x15, 0xd1, 0x23, 0xa3, 0xf3, 0xb1, 0x7c, 0x27, 0xc9, 0x4c, 0x79}, + subYX: fp.Elt{0xc0, 0x98, 0xd0, 0x1c, 0xf7, 0x2b, 0x80, 0x91, 0x66, 0x63, 0x5e, 0xed, 0xa4, 0x6c, 0x41, 0xfe, 0x4c, 0x99, 0x02, 0x49, 0x71, 0x5d, 0x58, 0xdf, 0xe7, 0xfa, 0x55, 0xf8, 0x25, 0x46, 0xd5, 0x4c}, + dt2: fp.Elt{0x53, 0x50, 0xac, 0xc2, 0x26, 0xc4, 0xf6, 0x4a, 0x58, 0x72, 0xf6, 0x32, 0xad, 0xed, 0x9a, 0xbc, 0x21, 0x10, 0x31, 0x0a, 0xf1, 0x32, 0xd0, 0x2a, 0x85, 0x8e, 0xcc, 0x6f, 0x7b, 0x35, 0x08, 0x70}, + }, + { /* 29P */ + addYX: fp.Elt{0x01, 0x3f, 0x77, 0x38, 0x27, 0x67, 0x88, 0x0b, 0xfb, 0xcc, 0xfb, 0x95, 0xfa, 0xc8, 0xcc, 0xb8, 0xb6, 0x29, 0xad, 0xb9, 0xa3, 0xd5, 0x2d, 0x8d, 0x6a, 0x0f, 0xad, 0x51, 0x98, 0x7e, 0xef, 0x06}, + subYX: fp.Elt{0x34, 0x4a, 0x58, 0x82, 0xbb, 0x9f, 0x1b, 0xd0, 0x2b, 0x79, 0xb4, 0xd2, 0x63, 0x64, 0xab, 0x47, 0x02, 0x62, 0x53, 0x48, 0x9c, 0x63, 0x31, 0xb6, 0x28, 0xd4, 0xd6, 0x69, 0x36, 0x2a, 0xa9, 0x13}, + dt2: fp.Elt{0xe5, 0x7d, 0x57, 0xc0, 0x1c, 0x77, 0x93, 0xca, 0x5c, 0xdc, 0x35, 0x50, 0x1e, 0xe4, 0x40, 0x75, 0x71, 0xe0, 0x02, 0xd8, 0x01, 0x0f, 0x68, 0x24, 0x6a, 0xf8, 0x2a, 0x8a, 0xdf, 0x6d, 0x29, 0x3c}, + }, + { /* 31P */ + addYX: fp.Elt{0x13, 0xa7, 0x14, 0xd9, 0xf9, 0x15, 0xad, 0xae, 0x12, 0xf9, 0x8f, 0x8c, 0xf9, 0x7b, 0x2f, 0xa9, 0x30, 0xd7, 0x53, 0x9f, 0x17, 0x23, 0xf8, 0xaf, 0xba, 0x77, 0x0c, 0x49, 0x93, 0xd3, 0x99, 0x7a}, + subYX: fp.Elt{0x41, 0x25, 0x1f, 0xbb, 0x2e, 0x4d, 0xeb, 0xfc, 0x1f, 0xb9, 0xad, 0x40, 0xc7, 0x10, 0x95, 0xb8, 0x05, 0xad, 0xa1, 0xd0, 0x7d, 0xa3, 0x71, 0xfc, 0x7b, 0x71, 0x47, 0x07, 0x70, 0x2c, 0x89, 0x0a}, + dt2: fp.Elt{0xe8, 0xa3, 0xbd, 0x36, 0x24, 0xed, 0x52, 0x8f, 0x94, 0x07, 0xe8, 0x57, 0x41, 0xc8, 0xa8, 0x77, 0xe0, 0x9c, 0x2f, 0x26, 0x63, 0x65, 0xa9, 0xa5, 0xd2, 0xf7, 0x02, 0x83, 0xd2, 0x62, 0x67, 0x28}, + }, + { /* 33P */ + addYX: fp.Elt{0x25, 0x5b, 0xe3, 0x3c, 0x09, 0x36, 0x78, 0x4e, 0x97, 0xaa, 0x6b, 0xb2, 0x1d, 0x18, 0xe1, 0x82, 0x3f, 0xb8, 0xc7, 0xcb, 0xd3, 0x92, 0xc1, 0x0c, 0x3a, 0x9d, 0x9d, 0x6a, 0x04, 0xda, 0xf1, 0x32}, + subYX: fp.Elt{0xbd, 0xf5, 0x2e, 0xce, 0x2b, 0x8e, 0x55, 0x7c, 0x63, 0xbc, 0x47, 0x67, 0xb4, 0x6c, 0x98, 0xe4, 0xb8, 0x89, 0xbb, 0x3b, 0x9f, 0x17, 0x4a, 0x15, 0x7a, 0x76, 0xf1, 0xd6, 0xa3, 0xf2, 0x86, 0x76}, + dt2: fp.Elt{0x6a, 0x7c, 0x59, 0x6d, 0xa6, 0x12, 0x8d, 0xaa, 0x2b, 0x85, 0xd3, 0x04, 0x03, 0x93, 0x11, 0x8f, 0x22, 0xb0, 0x09, 0xc2, 0x73, 0xdc, 0x91, 0x3f, 0xa6, 0x28, 0xad, 0xa9, 0xf8, 0x05, 0x13, 0x56}, + }, + { /* 35P */ + addYX: fp.Elt{0xd1, 0xae, 0x92, 0xec, 0x8d, 0x97, 0x0c, 0x10, 0xe5, 0x73, 0x6d, 0x4d, 0x43, 0xd5, 0x43, 0xca, 0x48, 0xba, 0x47, 0xd8, 0x22, 0x1b, 0x13, 0x83, 0x2c, 0x4d, 0x5d, 0xe3, 0x53, 0xec, 0xaa}, + subYX: fp.Elt{0xd5, 0xc0, 0xb0, 0xe7, 0x28, 0xcc, 0x22, 0x67, 0x53, 0x5c, 0x07, 0xdb, 0xbb, 0xe9, 0x9d, 0x70, 0x61, 0x0a, 0x01, 0xd7, 0xa7, 0x8d, 0xf6, 0xca, 0x6c, 0xcc, 0x57, 0x2c, 0xef, 0x1a, 0x0a, 0x03}, + dt2: fp.Elt{0xaa, 0xd2, 0x3a, 0x00, 0x73, 0xf7, 0xb1, 0x7b, 0x08, 0x66, 0x21, 0x2b, 0x80, 0x29, 0x3f, 0x0b, 0x3e, 0xd2, 0x0e, 0x52, 0x86, 0xdc, 0x21, 0x78, 0x80, 0x54, 0x06, 0x24, 0x1c, 0x9c, 0xbe, 0x20}, + }, + { /* 37P */ + addYX: fp.Elt{0xa6, 0x73, 0x96, 0x24, 0xd8, 0x87, 0x53, 0xe1, 0x93, 0xe4, 0x46, 0xf5, 0x2d, 0xbc, 0x43, 0x59, 0xb5, 0x63, 0x6f, 0xc3, 0x81, 0x9a, 0x7f, 0x1c, 0xde, 0xc1, 0x0a, 0x1f, 0x36, 0xb3, 0x0a, 0x75}, + subYX: fp.Elt{0x60, 0x5e, 0x02, 0xe2, 0x4a, 0xe4, 0xe0, 0x20, 0x38, 0xb9, 0xdc, 0xcb, 0x2f, 0x3b, 0x3b, 0xb0, 0x1c, 0x0d, 0x5a, 0xf9, 0x9c, 0x63, 0x5d, 0x10, 0x11, 0xe3, 0x67, 0x50, 0x54, 0x4c, 0x76, 0x69}, + dt2: fp.Elt{0x37, 0x10, 0xf8, 0xa2, 0x83, 0x32, 0x8a, 0x1e, 0xf1, 0xcb, 0x7f, 0xbd, 0x23, 0xda, 0x2e, 0x6f, 0x63, 0x25, 0x2e, 0xac, 0x5b, 0xd1, 0x2f, 0xb7, 0x40, 0x50, 0x07, 0xb7, 0x3f, 0x6b, 0xf9, 0x54}, + }, + { /* 39P */ + addYX: fp.Elt{0x79, 0x92, 0x66, 0x29, 0x04, 0xf2, 0xad, 0x0f, 0x4a, 0x72, 0x7d, 0x7d, 0x04, 0xa2, 0xdd, 0x3a, 0xf1, 0x60, 0x57, 0x8c, 0x82, 0x94, 0x3d, 0x6f, 0x9e, 0x53, 0xb7, 0x2b, 0xc5, 0xe9, 0x7f, 0x3d}, + subYX: fp.Elt{0xcd, 0x1e, 0xb1, 0x16, 0xc6, 0xaf, 0x7d, 0x17, 0x79, 0x64, 0x57, 0xfa, 0x9c, 0x4b, 0x76, 0x89, 0x85, 0xe7, 0xec, 0xe6, 0x10, 0xa1, 0xa8, 0xb7, 0xf0, 0xdb, 0x85, 0xbe, 0x9f, 0x83, 0xe6, 0x78}, + dt2: fp.Elt{0x6b, 0x85, 0xb8, 0x37, 0xf7, 0x2d, 0x33, 0x70, 0x8a, 0x17, 0x1a, 0x04, 0x43, 0x5d, 0xd0, 0x75, 0x22, 0x9e, 0xe5, 0xa0, 0x4a, 0xf7, 0x0f, 0x32, 0x42, 0x82, 0x08, 0x50, 0xf3, 0x68, 0xf2, 0x70}, + }, + { /* 41P */ + addYX: fp.Elt{0x47, 0x5f, 0x80, 0xb1, 0x83, 0x45, 0x86, 0x66, 0x19, 0x7c, 0xdd, 0x60, 0xd1, 0xc5, 0x35, 0xf5, 0x06, 0xb0, 0x4c, 0x1e, 0xb7, 0x4e, 0x87, 0xe9, 0xd9, 0x89, 0xd8, 0xfa, 0x5c, 0x34, 0x0d, 0x7c}, + subYX: fp.Elt{0x55, 0xf3, 0xdc, 0x70, 0x20, 0x11, 0x24, 0x23, 0x17, 0xe1, 0xfc, 0xe7, 0x7e, 0xc9, 0x0c, 0x38, 0x98, 0xb6, 0x52, 0x35, 0xed, 0xde, 0x1d, 0xb3, 0xb9, 0xc4, 0xb8, 0x39, 0xc0, 0x56, 0x4e, 0x40}, + dt2: fp.Elt{0x8a, 0x33, 0x78, 0x8c, 0x4b, 0x1f, 0x1f, 0x59, 0xe1, 0xb5, 0xe0, 0x67, 0xb1, 0x6a, 0x36, 0xa0, 0x44, 0x3d, 0x5f, 0xb4, 0x52, 0x41, 0xbc, 0x5c, 0x77, 0xc7, 0xae, 0x2a, 0x76, 0x54, 0xd7, 0x20}, + }, + { /* 43P */ + addYX: fp.Elt{0x58, 0xb7, 0x3b, 0xc7, 0x6f, 0xc3, 0x8f, 0x5e, 0x9a, 0xbb, 0x3c, 0x36, 0xa5, 0x43, 0xe5, 0xac, 0x22, 0xc9, 0x3b, 0x90, 0x7d, 0x4a, 0x93, 0xa9, 0x62, 0xec, 0xce, 0xf3, 0x46, 0x1e, 0x8f, 0x2b}, + subYX: fp.Elt{0x43, 0xf5, 0xb9, 0x35, 0xb1, 0xfe, 0x74, 0x9d, 0x6c, 0x95, 0x8c, 0xde, 0xf1, 0x7d, 0xb3, 0x84, 0xa9, 0x8b, 0x13, 0x57, 0x07, 0x2b, 0x32, 0xe9, 0xe1, 0x4c, 0x0b, 0x79, 0xa8, 0xad, 0xb8, 0x38}, + dt2: fp.Elt{0x5d, 0xf9, 0x51, 0xdf, 0x9c, 0x4a, 0xc0, 0xb5, 0xac, 0xde, 0x1f, 0xcb, 0xae, 0x52, 0x39, 0x2b, 0xda, 0x66, 0x8b, 0x32, 0x8b, 0x6d, 0x10, 0x1d, 0x53, 0x19, 0xba, 0xce, 0x32, 0xeb, 0x9a, 0x04}, + }, + { /* 45P */ + addYX: fp.Elt{0x31, 0x79, 0xfc, 0x75, 0x0b, 0x7d, 0x50, 0xaa, 0xd3, 0x25, 0x67, 0x7a, 0x4b, 0x92, 0xef, 0x0f, 0x30, 0x39, 0x6b, 0x39, 0x2b, 0x54, 0x82, 0x1d, 0xfc, 0x74, 0xf6, 0x30, 0x75, 0xe1, 0x5e, 0x79}, + subYX: fp.Elt{0x7e, 0xfe, 0xdc, 0x63, 0x3c, 0x7d, 0x76, 0xd7, 0x40, 0x6e, 0x85, 0x97, 0x48, 0x59, 0x9c, 0x20, 0x13, 0x7c, 0x4f, 0xe1, 0x61, 0x68, 0x67, 0xb6, 0xfc, 0x25, 0xd6, 0xc8, 0xe0, 0x65, 0xc6, 0x51}, + dt2: fp.Elt{0x81, 0xbd, 0xec, 0x52, 0x0a, 0x5b, 0x4a, 0x25, 0xe7, 0xaf, 0x34, 0xe0, 0x6e, 0x1f, 0x41, 0x5d, 0x31, 0x4a, 0xee, 0xca, 0x0d, 0x4d, 0xa2, 0xe6, 0x77, 0x44, 0xc5, 0x9d, 0xf4, 0x9b, 0xd1, 0x6c}, + }, + { /* 47P */ + addYX: fp.Elt{0x86, 0xc3, 0xaf, 0x65, 0x21, 0x61, 0xfe, 0x1f, 0x10, 0x1b, 0xd5, 0xb8, 0x88, 0x2a, 0x2a, 0x08, 0xaa, 0x0b, 0x99, 0x20, 0x7e, 0x62, 0xf6, 0x76, 0xe7, 0x43, 0x9e, 0x42, 0xa7, 0xb3, 0x01, 0x5e}, + subYX: fp.Elt{0xa3, 0x9c, 0x17, 0x52, 0x90, 0x61, 0x87, 0x7e, 0x85, 0x9f, 0x2c, 0x0b, 0x06, 0x0a, 0x1d, 0x57, 0x1e, 0x71, 0x99, 0x84, 0xa8, 0xba, 0xa2, 0x80, 0x38, 0xe6, 0xb2, 0x40, 0xdb, 0xf3, 0x20, 0x75}, + dt2: fp.Elt{0xa1, 0x57, 0x93, 0xd3, 0xe3, 0x0b, 0xb5, 0x3d, 0xa5, 0x94, 0x9e, 0x59, 0xdd, 0x6c, 0x7b, 0x96, 0x6e, 0x1e, 0x31, 0xdf, 0x64, 0x9a, 0x30, 0x1a, 0x86, 0xc9, 0xf3, 0xce, 0x9c, 0x2c, 0x09, 0x71}, + }, + { /* 49P */ + addYX: fp.Elt{0xcf, 0x1d, 0x05, 0x74, 0xac, 0xd8, 0x6b, 0x85, 0x1e, 0xaa, 0xb7, 0x55, 0x08, 0xa4, 0xf6, 0x03, 0xeb, 0x3c, 0x74, 0xc9, 0xcb, 0xe7, 0x4a, 0x3a, 0xde, 0xab, 0x37, 0x71, 0xbb, 0xa5, 0x73, 0x41}, + subYX: fp.Elt{0x8c, 0x91, 0x64, 0x03, 0x3f, 0x52, 0xd8, 0x53, 0x1c, 0x6b, 0xab, 0x3f, 0xf4, 0x04, 0xb4, 0xa2, 0xa4, 0xe5, 0x81, 0x66, 0x9e, 0x4a, 0x0b, 0x08, 0xa7, 0x7b, 0x25, 0xd0, 0x03, 0x5b, 0xa1, 0x0e}, + dt2: fp.Elt{0x8a, 0x21, 0xf9, 0xf0, 0x31, 0x6e, 0xc5, 0x17, 0x08, 0x47, 0xfc, 0x1a, 0x2b, 0x6e, 0x69, 0x5a, 0x76, 0xf1, 0xb2, 0xf4, 0x68, 0x16, 0x93, 0xf7, 0x67, 0x3a, 0x4e, 0x4a, 0x61, 0x65, 0xc5, 0x5f}, + }, + { /* 51P */ + addYX: fp.Elt{0x8e, 0x98, 0x90, 0x77, 0xe6, 0xe1, 0x92, 0x48, 0x22, 0xd7, 0x5c, 0x1c, 0x0f, 0x95, 0xd5, 0x01, 0xed, 0x3e, 0x92, 0xe5, 0x9a, 0x81, 0xb0, 0xe3, 0x1b, 0x65, 0x46, 0x9d, 0x40, 0xc7, 0x14, 0x32}, + subYX: fp.Elt{0xe5, 0x7a, 0x6d, 0xc4, 0x0d, 0x57, 0x6e, 0x13, 0x8f, 0xdc, 0xf8, 0x54, 0xcc, 0xaa, 0xd0, 0x0f, 0x86, 0xad, 0x0d, 0x31, 0x03, 0x9f, 0x54, 0x59, 0xa1, 0x4a, 0x45, 0x4c, 0x41, 0x1c, 0x71, 0x62}, + dt2: fp.Elt{0x70, 0x17, 0x65, 0x06, 0x74, 0x82, 0x29, 0x13, 0x36, 0x94, 0x27, 0x8a, 0x66, 0xa0, 0xa4, 0x3b, 0x3c, 0x22, 0x5d, 0x18, 0xec, 0xb8, 0xb6, 0xd9, 0x3c, 0x83, 0xcb, 0x3e, 0x07, 0x94, 0xea, 0x5b}, + }, + { /* 53P */ + addYX: fp.Elt{0xf8, 0xd2, 0x43, 0xf3, 0x63, 0xce, 0x70, 0xb4, 0xf1, 0xe8, 0x43, 0x05, 0x8f, 0xba, 0x67, 0x00, 0x6f, 0x7b, 0x11, 0xa2, 0xa1, 0x51, 0xda, 0x35, 0x2f, 0xbd, 0xf1, 0x44, 0x59, 0x78, 0xd0, 0x4a}, + subYX: fp.Elt{0xe4, 0x9b, 0xc8, 0x12, 0x09, 0xbf, 0x1d, 0x64, 0x9c, 0x57, 0x6e, 0x7d, 0x31, 0x8b, 0xf3, 0xac, 0x65, 0xb0, 0x97, 0xf6, 0x02, 0x9e, 0xfe, 0xab, 0xec, 0x1e, 0xf6, 0x48, 0xc1, 0xd5, 0xac, 0x3a}, + dt2: fp.Elt{0x01, 0x83, 0x31, 0xc3, 0x34, 0x3b, 0x8e, 0x85, 0x26, 0x68, 0x31, 0x07, 0x47, 0xc0, 0x99, 0xdc, 0x8c, 0xa8, 0x9d, 0xd3, 0x2e, 0x5b, 0x08, 0x34, 0x3d, 0x85, 0x02, 0xd9, 0xb1, 0x0c, 0xff, 0x3a}, + }, + { /* 55P */ + addYX: fp.Elt{0x05, 0x35, 0xc5, 0xf4, 0x0b, 0x43, 0x26, 0x92, 0x83, 0x22, 0x1f, 0x26, 0x13, 0x9c, 0xe4, 0x68, 0xc6, 0x27, 0xd3, 0x8f, 0x78, 0x33, 0xef, 0x09, 0x7f, 0x9e, 0xd9, 0x2b, 0x73, 0x9f, 0xcf, 0x2c}, + subYX: fp.Elt{0x5e, 0x40, 0x20, 0x3a, 0xeb, 0xc7, 0xc5, 0x87, 0xc9, 0x56, 0xad, 0xed, 0xef, 0x11, 0xe3, 0x8e, 0xf9, 0xd5, 0x29, 0xad, 0x48, 0x2e, 0x25, 0x29, 0x1d, 0x25, 0xcd, 0xf4, 0x86, 0x7e, 0x0e, 0x11}, + dt2: fp.Elt{0xe4, 0xf5, 0x03, 0xd6, 0x9e, 0xd8, 0xc0, 0x57, 0x0c, 0x20, 0xb0, 0xf0, 0x28, 0x86, 0x88, 0x12, 0xb7, 0x3b, 0x2e, 0xa0, 0x09, 0x27, 0x17, 0x53, 0x37, 0x3a, 0x69, 0xb9, 0xe0, 0x57, 0xc5, 0x05}, + }, + { /* 57P */ + addYX: fp.Elt{0xb0, 0x0e, 0xc2, 0x89, 0xb0, 0xbb, 0x76, 0xf7, 0x5c, 0xd8, 0x0f, 0xfa, 0xf6, 0x5b, 0xf8, 0x61, 0xfb, 0x21, 0x44, 0x63, 0x4e, 0x3f, 0xb9, 0xb6, 0x05, 0x12, 0x86, 0x41, 0x08, 0xef, 0x9f, 0x28}, + subYX: fp.Elt{0x6f, 0x7e, 0xc9, 0x1f, 0x31, 0xce, 0xf9, 0xd8, 0xae, 0xfd, 0xf9, 0x11, 0x30, 0x26, 0x3f, 0x7a, 0xdd, 0x25, 0xed, 0x8b, 0xa0, 0x7e, 0x5b, 0xe1, 0x5a, 0x87, 0xe9, 0x8f, 0x17, 0x4c, 0x15, 0x6e}, + dt2: fp.Elt{0xbf, 0x9a, 0xd6, 0xfe, 0x36, 0x63, 0x61, 0xcf, 0x4f, 0xc9, 0x35, 0x83, 0xe7, 0xe4, 0x16, 0x9b, 0xe7, 0x7f, 0x3a, 0x75, 0x65, 0x97, 0x78, 0x13, 0x19, 0xa3, 0x5c, 0xa9, 0x42, 0xf6, 0xfb, 0x6a}, + }, + { /* 59P */ + addYX: fp.Elt{0xcc, 0xa8, 0x13, 0xf9, 0x70, 0x50, 0xe5, 0x5d, 0x61, 0xf5, 0x0c, 0x2b, 0x7b, 0x16, 0x1d, 0x7d, 0x89, 0xd4, 0xea, 0x90, 0xb6, 0x56, 0x29, 0xda, 0xd9, 0x1e, 0x80, 0xdb, 0xce, 0x93, 0xc0, 0x12}, + subYX: fp.Elt{0xc1, 0xd2, 0xf5, 0x62, 0x0c, 0xde, 0xa8, 0x7d, 0x9a, 0x7b, 0x0e, 0xb0, 0xa4, 0x3d, 0xfc, 0x98, 0xe0, 0x70, 0xad, 0x0d, 0xda, 0x6a, 0xeb, 0x7d, 0xc4, 0x38, 0x50, 0xb9, 0x51, 0xb8, 0xb4, 0x0d}, + dt2: fp.Elt{0x0f, 0x19, 0xb8, 0x08, 0x93, 0x7f, 0x14, 0xfc, 0x10, 0xe3, 0x1a, 0xa1, 0xa0, 0x9d, 0x96, 0x06, 0xfd, 0xd7, 0xc7, 0xda, 0x72, 0x55, 0xe7, 0xce, 0xe6, 0x5c, 0x63, 0xc6, 0x99, 0x87, 0xaa, 0x33}, + }, + { /* 61P */ + addYX: fp.Elt{0xb1, 0x6c, 0x15, 0xfc, 0x88, 0xf5, 0x48, 0x83, 0x27, 0x6d, 0x0a, 0x1a, 0x9b, 0xba, 0xa2, 0x6d, 0xb6, 0x5a, 0xca, 0x87, 0x5c, 0x2d, 0x26, 0xe2, 0xa6, 0x89, 0xd5, 0xc8, 0xc1, 0xd0, 0x2c, 0x21}, + subYX: fp.Elt{0xf2, 0x5c, 0x08, 0xbd, 0x1e, 0xf5, 0x0f, 0xaf, 0x1f, 0x3f, 0xd3, 0x67, 0x89, 0x1a, 0xf5, 0x78, 0x3c, 0x03, 0x60, 0x50, 0xe1, 0xbf, 0xc2, 0x6e, 0x86, 0x1a, 0xe2, 0xe8, 0x29, 0x6f, 0x3c, 0x23}, + dt2: fp.Elt{0x81, 0xc7, 0x18, 0x7f, 0x10, 0xd5, 0xf4, 0xd2, 0x28, 0x9d, 0x7e, 0x52, 0xf2, 0xcd, 0x2e, 0x12, 0x41, 0x33, 0x3d, 0x3d, 0x2a, 0x86, 0x0a, 0xa7, 0xe3, 0x4c, 0x91, 0x11, 0x89, 0x77, 0xb7, 0x1d}, + }, + { /* 63P */ + addYX: fp.Elt{0xb6, 0x1a, 0x70, 0xdd, 0x69, 0x47, 0x39, 0xb3, 0xa5, 0x8d, 0xcf, 0x19, 0xd4, 0xde, 0xb8, 0xe2, 0x52, 0xc8, 0x2a, 0xfd, 0x61, 0x41, 0xdf, 0x15, 0xbe, 0x24, 0x7d, 0x01, 0x8a, 0xca, 0xe2, 0x7a}, + subYX: fp.Elt{0x6f, 0xc2, 0x6b, 0x7c, 0x39, 0x52, 0xf3, 0xdd, 0x13, 0x01, 0xd5, 0x53, 0xcc, 0xe2, 0x97, 0x7a, 0x30, 0xa3, 0x79, 0xbf, 0x3a, 0xf4, 0x74, 0x7c, 0xfc, 0xad, 0xe2, 0x26, 0xad, 0x97, 0xad, 0x31}, + dt2: fp.Elt{0x62, 0xb9, 0x20, 0x09, 0xed, 0x17, 0xe8, 0xb7, 0x9d, 0xda, 0x19, 0x3f, 0xcc, 0x18, 0x85, 0x1e, 0x64, 0x0a, 0x56, 0x25, 0x4f, 0xc1, 0x91, 0xe4, 0x83, 0x2c, 0x62, 0xa6, 0x53, 0xfc, 0xd1, 0x1e}, + }, +} diff --git a/src/circl/sign/ed25519/testdata/sign.input.zip b/src/circl/sign/ed25519/testdata/sign.input.zip new file mode 100644 index 00000000000..3ae0512748b Binary files /dev/null and b/src/circl/sign/ed25519/testdata/sign.input.zip differ diff --git a/src/circl/sign/ed25519/testdata/wycheproof_Ed25519.json b/src/circl/sign/ed25519/testdata/wycheproof_Ed25519.json new file mode 100644 index 00000000000..e2a1ae4f28f --- /dev/null +++ b/src/circl/sign/ed25519/testdata/wycheproof_Ed25519.json @@ -0,0 +1,2262 @@ +{ + "algorithm" : "EDDSA", + "generatorVersion" : "0.8rc16", + "numberOfTests" : 145, + "header" : [ + "Test vectors of type EddsaVerify are intended for testing", + "the verification of Eddsa signatures." + ], + "notes" : { + "SignatureMalleability" : "EdDSA signatures are non-malleable, if implemented accordingly. Failing to check the range of S allows to modify signatures. See RFC 8032, Section 5.2.7 and Section 8.4." + }, + "schema" : "eddsa_verify_schema.json", + "testGroups" : [ + { + "jwk" : { + "crv" : "Ed25519", + "d" : "rdS7gQN4W6-axTQljoqvZfXxrbXvXz3xm7gKuYnE1ks", + "kid" : "none", + "kty" : "OKP", + "x" : "fU0Of2FTpptiQrUiq77mhf2kQg-INLEIw72uNp71Sfo" + }, + "key" : { + "curve" : "edwards25519", + "keySize" : 255, + "pk" : "7d4d0e7f6153a69b6242b522abbee685fda4420f8834b108c3bdae369ef549fa", + "sk" : "add4bb8103785baf9ac534258e8aaf65f5f1adb5ef5f3df19bb80ab989c4d64b", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "302a300506032b65700321007d4d0e7f6153a69b6242b522abbee685fda4420f8834b108c3bdae369ef549fa", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEAfU0Of2FTpptiQrUiq77mhf2kQg+INLEIw72uNp71Sfo=\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 1, + "comment" : "", + "msg" : "", + "sig" : "d4fbdb52bfa726b44d1786a8c0d171c3e62ca83c9e5bbe63de0bb2483f8fd6cc1429ab72cafc41ab56af02ff8fcc43b99bfe4c7ae940f60f38ebaa9d311c4007", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 2, + "comment" : "", + "msg" : "78", + "sig" : "d80737358ede548acb173ef7e0399f83392fe8125b2ce877de7975d8b726ef5b1e76632280ee38afad12125ea44b961bf92f1178c9fa819d020869975bcbe109", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 3, + "comment" : "", + "msg" : "54657374", + "sig" : "7c38e026f29e14aabd059a0f2db8b0cd783040609a8be684db12f82a27774ab07a9155711ecfaf7f99f277bad0c6ae7e39d4eef676573336a5c51eb6f946b30d", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 4, + "comment" : "", + "msg" : "48656c6c6f", + "sig" : "1c1ad976cbaae3b31dee07971cf92c928ce2091a85f5899f5e11ecec90fc9f8e93df18c5037ec9b29c07195ad284e63d548cd0a6fe358cc775bd6c1608d2c905", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 5, + "comment" : "", + "msg" : "313233343030", + "sig" : "657c1492402ab5ce03e2c3a7f0384d051b9cf3570f1207fc78c1bcc98c281c2bf0cf5b3a289976458a1be6277a5055545253b45b07dcc1abd96c8b989c00f301", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 6, + "comment" : "", + "msg" : "000000000000000000000000", + "sig" : "d46543bfb892f84ec124dcdfc847034c19363bf3fc2fa89b1267833a14856e52e60736918783f950b6f1dd8d40dc343247cd43ce054c2d68ef974f7ed0f3c60f", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 7, + "comment" : "", + "msg" : "6161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161", + "sig" : "879350045543bc14ed2c08939b68c30d22251d83e018cacbaf0c9d7a48db577e80bdf76ce99e5926762bc13b7b3483260a5ef63d07e34b58eb9c14621ac92f00", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 8, + "comment" : "", + "msg" : "202122232425262728292a2b2c2d2e2f303132333435363738393a3b3c3d3e3f404142434445464748494a4b4c4d4e4f505152535455565758595a5b5c5d5e5f60", + "sig" : "7bdc3f9919a05f1d5db4a3ada896094f6871c1f37afc75db82ec3147d84d6f237b7e5ecc26b59cfea0c7eaf1052dc427b0f724615be9c3d3e01356c65b9b5109", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 9, + "comment" : "", + "msg" : "ffffffffffffffffffffffffffffffff", + "sig" : "5dbd7360e55aa38e855d6ad48c34bd35b7871628508906861a7c4776765ed7d1e13d910faabd689ec8618b78295c8ab8f0e19c8b4b43eb8685778499e943ae04", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 10, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 11, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "00000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 12, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "0000000000000000000000000000000000000000000000000000000000000000ecd3f55c1a631258d69cf7a2def9de1400000000000000000000000000000010", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 13, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "0000000000000000000000000000000000000000000000000000000000000000edd3f55c1a631258d69cf7a2def9de1400000000000000000000000000000010", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 14, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "0000000000000000000000000000000000000000000000000000000000000000edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 15, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "01000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 16, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "01000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 17, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "0100000000000000000000000000000000000000000000000000000000000000ecd3f55c1a631258d69cf7a2def9de1400000000000000000000000000000010", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 18, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "0100000000000000000000000000000000000000000000000000000000000000edd3f55c1a631258d69cf7a2def9de1400000000000000000000000000000010", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 19, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "0100000000000000000000000000000000000000000000000000000000000000edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 20, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "edd3f55c1a631258d69cf7a2def9de14000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 21, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "edd3f55c1a631258d69cf7a2def9de14000000000000000000000000000000100100000000000000000000000000000000000000000000000000000000000000", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 22, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "edd3f55c1a631258d69cf7a2def9de1400000000000000000000000000000010ecd3f55c1a631258d69cf7a2def9de1400000000000000000000000000000010", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 23, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "edd3f55c1a631258d69cf7a2def9de1400000000000000000000000000000010edd3f55c1a631258d69cf7a2def9de1400000000000000000000000000000010", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 24, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "edd3f55c1a631258d69cf7a2def9de1400000000000000000000000000000010edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 25, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f0000000000000000000000000000000000000000000000000000000000000000", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 26, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f0100000000000000000000000000000000000000000000000000000000000000", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 27, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7fecd3f55c1a631258d69cf7a2def9de1400000000000000000000000000000010", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 28, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7fedd3f55c1a631258d69cf7a2def9de1400000000000000000000000000000010", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 29, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7fedffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 30, + "comment" : "empty signature", + "msg" : "54657374", + "sig" : "", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 31, + "comment" : "s missing", + "msg" : "54657374", + "sig" : "7c38e026f29e14aabd059a0f2db8b0cd783040609a8be684db12f82a27774ab0", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 32, + "comment" : "signature too short", + "msg" : "54657374", + "sig" : "7c38e026f29e14aabd059a0f2db8b0cd783040609a8be684db12f82a27774ab07a9155711ecfaf7f99f277bad0c6ae7e39d4eef676573336a5c51eb6f946", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 33, + "comment" : "signature too long", + "msg" : "54657374", + "sig" : "7c38e026f29e14aabd059a0f2db8b0cd783040609a8be684db12f82a27774ab07a9155711ecfaf7f99f277bad0c6ae7e39d4eef676573336a5c51eb6f946b30d2020", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 34, + "comment" : "include pk in signature", + "msg" : "54657374", + "sig" : "7c38e026f29e14aabd059a0f2db8b0cd783040609a8be684db12f82a27774ab07a9155711ecfaf7f99f277bad0c6ae7e39d4eef676573336a5c51eb6f946b30d7d4d0e7f6153a69b6242b522abbee685fda4420f8834b108c3bdae369ef549fa", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 35, + "comment" : "prepending 0 byte to signature", + "msg" : "54657374", + "sig" : "007c38e026f29e14aabd059a0f2db8b0cd783040609a8be684db12f82a27774ab07a9155711ecfaf7f99f277bad0c6ae7e39d4eef676573336a5c51eb6f946b30d", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 36, + "comment" : "prepending 0 byte to s", + "msg" : "54657374", + "sig" : "7c38e026f29e14aabd059a0f2db8b0cd783040609a8be684db12f82a27774ab0007a9155711ecfaf7f99f277bad0c6ae7e39d4eef676573336a5c51eb6f946b30d", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 37, + "comment" : "appending 0 byte to signature", + "msg" : "54657374", + "sig" : "7c38e026f29e14aabd059a0f2db8b0cd783040609a8be684db12f82a27774ab07a9155711ecfaf7f99f277bad0c6ae7e39d4eef676573336a5c51eb6f946b30d00", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 38, + "comment" : "removing 0 byte from signature", + "msg" : "546573743137", + "sig" : 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"szImXPlVlfDJAiFZO1orPFdNYNxjTd_2GG8O7XmAo4M", + "kid" : "none", + "kty" : "OKP", + "x" : "utJlspTtL0IstqFBaUCGI4-_6YdXGqdl2LTzokEFqgE" + }, + "key" : { + "curve" : "edwards25519", + "keySize" : 255, + "pk" : "bad265b294ed2f422cb6a141694086238fbfe987571aa765d8b4f3a24105aa01", + "sk" : "b332265cf95595f0c90221593b5a2b3c574d60dc634ddff6186f0eed7980a383", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "302a300506032b6570032100bad265b294ed2f422cb6a141694086238fbfe987571aa765d8b4f3a24105aa01", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEAutJlspTtL0IstqFBaUCGI4+/6YdXGqdl2LTzokEFqgE=\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 138, + "comment" : "regression test for arithmetic error", + "msg" : "01a2b5f7fee813b4e9bd7fc25137648004795010", + "sig" : "61792c9442bc6338ac41fd42a40bee9b02ec1836503d60ff725128c63d72808880c36e6190b7da525cbee5d12900aa043547dd14a2709ef9e49d628f37f6b70c", + "result" : "valid", + "flags" : [] + } + ] + }, + { + "jwk" : { + "crv" : "Ed25519", + "d" : "-uyXZLNp3w7xCJDdAixQLlUaMiK0PoQpRVSWx2_upF0", + "kid" : "none", + "kty" : "OKP", + "x" : "Cq7ktyPbm1G6fSLrI-uKdqWsAvT8ndBvd76kLh037Fo" + }, + "key" : { + "curve" : "edwards25519", + "keySize" : 255, + "pk" : "0aaee4b723db9b51ba7d22eb23eb8a76a5ac02f4fc9dd06f77bea42e1d37ec5a", + "sk" : "faec9764b369df0ef10890dd022c502e551a3222b43e8429455496c76feea45d", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "302a300506032b65700321000aaee4b723db9b51ba7d22eb23eb8a76a5ac02f4fc9dd06f77bea42e1d37ec5a", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEACq7ktyPbm1G6fSLrI+uKdqWsAvT8ndBvd76kLh037Fo=\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 139, + "comment" : "regression test for arithmetic error", + "msg" : "0fbf5d47cb5d498feace8f98f1896208da38a885", + "sig" : "fa3cd41e3a8c00b19eecd404a63c3cb787cd30de0dfc936966cff2117f5aff18db6bef80fcfd8856f3fb2e9c3dc47593e9471103032af918feee638a33d40505", + "result" : "valid", + "flags" : [] + } + ] + }, + { + "jwk" : { + "crv" : "Ed25519", + "d" : "TrGeJ496MKBqfVXkLER3X0qBt6RcBRKq4CYmLnF3Daw", + "kid" : "none", + "kty" : "OKP", + "x" : "gSNErxWpG6g8LJHpbxcnrA88TEE4W5-oTvo5mtpRaL4" + }, + "key" : { + "curve" : "edwards25519", + "keySize" : 255, + "pk" : "812344af15a91ba83c2c91e96f1727ac0f3c4c41385b9fa84efa399ada5168be", + "sk" : "4eb19e278f7a30a06a7d55e42c44775f4a81b7a45c0512aae026262e71770dac", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "302a300506032b6570032100812344af15a91ba83c2c91e96f1727ac0f3c4c41385b9fa84efa399ada5168be", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEAgSNErxWpG6g8LJHpbxcnrA88TEE4W5+oTvo5mtpRaL4=\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 140, + "comment" : "regression test for arithmetic error", + "msg" : "36e67c1939750bffb3e4ba6cb85562612275e862", + "sig" : "97fbbcd7a1d0eb42d2f8c42448ef35a2c2472740556b645547865330d6c57068af377fced08aaf810c08cd3c43d296f1975710312e9334c98b485f831efa4103", + "result" : "valid", + "flags" : [] + } + ] + }, + { + "jwk" : { + "crv" : "Ed25519", + "d" : "GZjVlJyrNloA-Cjn0XsGxwjTP-8AMdNTpOFb9yIqc7A", + "kid" : "none", + "kty" : "OKP", + "x" : "DuXLVZf7343MxIsBSF45szqhM7UtMNI3QCdyZ8_sPj4" + }, + "key" : { + "curve" : "edwards25519", + "keySize" : 255, + "pk" : "0ee5cb5597fbdf8dccc48b01485e39b33aa133b52d30d23740277267cfec3e3e", + "sk" : "1998d5949cab365a00f828e7d17b06c708d33fef0031d353a4e15bf7222a73b0", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "302a300506032b65700321000ee5cb5597fbdf8dccc48b01485e39b33aa133b52d30d23740277267cfec3e3e", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEADuXLVZf7343MxIsBSF45szqhM7UtMNI3QCdyZ8/sPj4=\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 141, + "comment" : "regression test for arithmetic error", + "msg" : "13945c894c1d3fe8562e8b20e5f0efaa26ade8e3", + "sig" : "d7dbaa337ffd2a5fd8d5fd8ad5aeccc0c0f83795c2c59fe62a40b87903b1ae62ed748a8df5af4d32f9f822a65d0e498b6f40eaf369a9342a1164ee7d08b58103", + "result" : "valid", + "flags" : [] + } + ] + }, + { + "jwk" : { + "crv" : "Ed25519", + "d" : "YWRnYRTGa9mIfaw0HGYgncWHzPDMXNm6_9-skpWgDEo", + "kid" : "none", + "kty" : "OKP", + "x" : "n7od6StgtbRwMIl2PQ1vkSXk3X765B8IoiiCrvloksQ" + }, + "key" : { + "curve" : "edwards25519", + "keySize" : 255, + "pk" : "9fba1de92b60b5b4703089763d0d6f9125e4dd7efae41f08a22882aef96892c4", + "sk" : "6164676114c66bd9887dac341c66209dc587ccf0cc5cd9baffdfac9295a00c4a", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "302a300506032b65700321009fba1de92b60b5b4703089763d0d6f9125e4dd7efae41f08a22882aef96892c4", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEAn7od6StgtbRwMIl2PQ1vkSXk3X765B8IoiiCrvloksQ=\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 142, + "comment" : "regression test for arithmetic error", + "msg" : "4de142af4b8402f80a47fa812df84f42e283cee7", + "sig" : "09a2ed303a2fa7027a1dd7c3b0d25121eeed2b644a2fbc17aa0c8aea4524071ede7e7dd7a536d5497f8165d29e4e1b63200f74bbae39fbbbccb29889c62c1f09", + "result" : "valid", + "flags" : [] + } + ] + }, + { + "jwk" : { + "crv" : "Ed25519", + "d" : "SwvQOgOyAGnMvMIUp0SEc_TnpJH6fOtI3b4kyDxKpLs", + "kid" : "none", + "kty" : "OKP", + "x" : "dYKrG1LhMW5cE2cfQ7Oco2soEzzQgygxvN3QsPIzmMs" + }, + "key" : { + "curve" : "edwards25519", + "keySize" : 255, + "pk" : "7582ab1b52e1316e5c13671f43b39ca36b28133cd0832831bcddd0b0f23398cb", + "sk" : "4b0bd03a03b20069ccbcc214a7448473f4e7a491fa7ceb48ddbe24c83c4aa4bb", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "302a300506032b65700321007582ab1b52e1316e5c13671f43b39ca36b28133cd0832831bcddd0b0f23398cb", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEAdYKrG1LhMW5cE2cfQ7Oco2soEzzQgygxvN3QsPIzmMs=\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 143, + "comment" : "regression test for arithmetic error", + "msg" : "563357f41b8b23b1d83f19f5667177a67da20b18", + "sig" : "e6884a6e6b2e60a0b5862251c001e7c79d581d777d6fc11d218d0aecd79f26a30e2ca22cc7c4674f8b72655bc4ee5cb5494ca07c05177656142ac55cc9d33e02", + "result" : "valid", + "flags" : [] + } + ] + }, + { + "jwk" : { + "crv" : "Ed25519", + "d" : "L854cL4fOS0h-x0jUOx4d9uKqZs1n-W91TOP81p5HRw", + "kid" : "none", + "kty" : "OKP", + "x" : "3S1ni64iLz-26CePCMyeGmYznJJsKawKFvlxf17hjNg" + }, + "key" : { + "curve" : "edwards25519", + "keySize" : 255, + "pk" : "dd2d678bae222f3fb6e8278f08cc9e1a66339c926c29ac0a16f9717f5ee18cd8", + "sk" : "2fce7870be1f392d21fb1d2350ec7877db8aa99b359fe5bdd5338ff35a791d1c", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "302a300506032b6570032100dd2d678bae222f3fb6e8278f08cc9e1a66339c926c29ac0a16f9717f5ee18cd8", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEA3S1ni64iLz+26CePCMyeGmYznJJsKawKFvlxf17hjNg=\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 144, + "comment" : "regression test for arithmetic error", + "msg" : "931bbf9c877a6571cf7d4609fc3eb867edd43f51", + "sig" : "6124c206d864507ea5d984b363b4cf583314db6856a45ded5e61eebff4d5e337e0b4c82b445ae2e52d549d2d961eace2ea01f81158e09a9686baa040db65ad08", + "result" : "valid", + "flags" : [] + } + ] + }, + { + "jwk" : { + "crv" : "Ed25519", + "d" : "qazkIZXduzoW82ayTdnTeooEPtLmAB9UZSKWdQN5Nn0", + "kid" : "none", + "kty" : "OKP", + "x" : "zL58suS8IVzuL4heHSL34NWCsru9eCwQTlSLFS0m_Gk" + }, + "key" : { + "curve" : "edwards25519", + "keySize" : 255, + "pk" : "ccbe7cb2e4bc215cee2f885e1d22f7e0d582b2bbbd782c104e548b152d26fc69", + "sk" : "a9ace42195ddbb3a16f366b24dd9d37a8a043ed2e6001f54652296750379367d", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "302a300506032b6570032100ccbe7cb2e4bc215cee2f885e1d22f7e0d582b2bbbd782c104e548b152d26fc69", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMCowBQYDK2VwAyEAzL58suS8IVzuL4heHSL34NWCsru9eCwQTlSLFS0m/Gk=\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 145, + "comment" : "regression test for arithmetic error", + "msg" : "44530b0b34f598767a7b875b0caee3c7b9c502d1", + "sig" : "cfbd450a2c83cb8436c348822fe3ee347d4ee937b7f2ea11ed755cc52852407c9eec2c1fa30d2f9aef90e89b2cc3bcef2b1b9ca59f712110d19894a9cf6a2802", + "result" : "valid", + "flags" : [] + } + ] + } + ] +} diff --git a/src/circl/sign/ed25519/wycheproof_test.go b/src/circl/sign/ed25519/wycheproof_test.go new file mode 100644 index 00000000000..9b54071743a --- /dev/null +++ b/src/circl/sign/ed25519/wycheproof_test.go @@ -0,0 +1,111 @@ +package ed25519_test + +import ( + "bytes" + "encoding/hex" + "encoding/json" + "io/ioutil" + "os" + "testing" + + "circl/internal/test" + "circl/sign/ed25519" +) + +type group struct { + Key struct { + Curve string `json:"curve"` + Size int `json:"keySize"` + Pk string `json:"pk"` + Sk string `json:"sk"` + Type string `json:"type"` + } `json:"key"` + Type string `json:"type"` + Tests []struct { + TcID int `json:"tcId"` + Comment string `json:"comment"` + Msg string `json:"msg"` + Sig string `json:"sig"` + Result string `json:"result"` + Flags []string `json:"flags"` + } `json:"tests"` +} + +type Wycheproof struct { + Alg string `json:"algorithm"` + Version string `json:"generatorVersion"` + Num int `json:"numberOfTests"` + Groups []group `json:"testGroups"` +} + +func (kat *Wycheproof) readFile(t *testing.T, fileName string) { + jsonFile, err := os.Open(fileName) + if err != nil { + t.Fatalf("File %v can not be opened. Error: %v", fileName, err) + } + defer jsonFile.Close() + input, _ := ioutil.ReadAll(jsonFile) + + err = json.Unmarshal(input, &kat) + if err != nil { + t.Fatalf("File %v can not be loaded. Error: %v", fileName, err) + } +} + +func (kat *Wycheproof) keyPair(t *testing.T) { + for i, g := range kat.Groups { + if g.Key.Curve != "edwards25519" { + t.Errorf("Curve not expected %v", g.Key.Curve) + } + private, _ := hex.DecodeString(g.Key.Sk) + public, _ := hex.DecodeString(g.Key.Pk) + keys := ed25519.NewKeyFromSeed(private) + got := keys.Public().(ed25519.PublicKey) + want := public + + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, i, g.Key.Sk) + } + } +} + +func (kat *Wycheproof) verify(t *testing.T) { + for i, g := range kat.Groups { + for _, gT := range g.Tests { + isValid := gT.Result == "valid" + private, _ := hex.DecodeString(g.Key.Sk) + public, _ := hex.DecodeString(g.Key.Pk) + sig, _ := hex.DecodeString(gT.Sig) + msg, _ := hex.DecodeString(gT.Msg) + + priv := ed25519.NewKeyFromSeed(private) + got := priv.Public().(ed25519.PublicKey) + want := public + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, i, gT.TcID) + } + if isValid { + got := ed25519.Sign(priv, msg) + want := sig + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, i, gT.TcID) + } + } + { + got := ed25519.Verify(priv.Public().(ed25519.PublicKey), msg, sig) + want := isValid + if got != want { + test.ReportError(t, got, want, i, gT.TcID) + } + } + } + } +} + +func TestWycheproof(t *testing.T) { + // Test vectors from Wycheproof v0.4.12 + var kat Wycheproof + kat.readFile(t, "testdata/wycheproof_Ed25519.json") + t.Run("EDDSAKeyPair", kat.keyPair) + t.Run("EDDSAVerify", kat.verify) +} diff --git a/src/circl/sign/ed448/ed448.go b/src/circl/sign/ed448/ed448.go new file mode 100644 index 00000000000..99fced49e68 --- /dev/null +++ b/src/circl/sign/ed448/ed448.go @@ -0,0 +1,410 @@ +// Package ed448 implements Ed448 signature scheme as described in RFC-8032. +// +// This package implements two signature variants. +// +// | Scheme Name | Sign Function | Verification | Context | +// |-------------|-------------------|---------------|-------------------| +// | Ed448 | Sign | Verify | Yes, can be empty | +// | Ed448Ph | SignPh | VerifyPh | Yes, can be empty | +// | All above | (PrivateKey).Sign | VerifyAny | As above | +// +// Specific functions for sign and verify are defined. A generic signing +// function for all schemes is available through the crypto.Signer interface, +// which is implemented by the PrivateKey type. A correspond all-in-one +// verification method is provided by the VerifyAny function. +// +// Both schemes require a context string for domain separation. This parameter +// is passed using a SignerOptions struct defined in this package. +// +// References: +// +// - RFC8032 https://rfc-editor.org/rfc/rfc8032.txt +// - EdDSA for more curves https://eprint.iacr.org/2015/677 +// - High-speed high-security signatures. https://doi.org/10.1007/s13389-012-0027-1 +package ed448 + +import ( + "bytes" + "crypto" + cryptoRand "crypto/rand" + "crypto/subtle" + "errors" + "fmt" + "io" + "strconv" + + "circl/ecc/goldilocks" + "circl/internal/sha3" + "circl/sign" +) + +const ( + // ContextMaxSize is the maximum length (in bytes) allowed for context. + ContextMaxSize = 255 + // PublicKeySize is the length in bytes of Ed448 public keys. + PublicKeySize = 57 + // PrivateKeySize is the length in bytes of Ed448 private keys. + PrivateKeySize = 114 + // SignatureSize is the length in bytes of signatures. + SignatureSize = 114 + // SeedSize is the size, in bytes, of private key seeds. These are the private key representations used by RFC 8032. + SeedSize = 57 +) + +const ( + paramB = 456 / 8 // Size of keys in bytes. + hashSize = 2 * paramB // Size of the hash function's output. +) + +// SignerOptions implements crypto.SignerOpts and augments with parameters +// that are specific to the Ed448 signature schemes. +type SignerOptions struct { + // Hash must be crypto.Hash(0) for both Ed448 and Ed448Ph. + crypto.Hash + + // Context is an optional domain separation string for signing. + // Its length must be less or equal than 255 bytes. + Context string + + // Scheme is an identifier for choosing a signature scheme. + Scheme SchemeID +} + +// SchemeID is an identifier for each signature scheme. +type SchemeID uint + +const ( + ED448 SchemeID = iota + ED448Ph +) + +// PublicKey is the type of Ed448 public keys. +type PublicKey []byte + +// Equal reports whether pub and x have the same value. +func (pub PublicKey) Equal(x crypto.PublicKey) bool { + xx, ok := x.(PublicKey) + return ok && bytes.Equal(pub, xx) +} + +// PrivateKey is the type of Ed448 private keys. It implements crypto.Signer. +type PrivateKey []byte + +// Equal reports whether priv and x have the same value. +func (priv PrivateKey) Equal(x crypto.PrivateKey) bool { + xx, ok := x.(PrivateKey) + return ok && subtle.ConstantTimeCompare(priv, xx) == 1 +} + +// Public returns the PublicKey corresponding to priv. +func (priv PrivateKey) Public() crypto.PublicKey { + publicKey := make([]byte, PublicKeySize) + copy(publicKey, priv[SeedSize:]) + return PublicKey(publicKey) +} + +// Seed returns the private key seed corresponding to priv. It is provided for +// interoperability with RFC 8032. RFC 8032's private keys correspond to seeds +// in this package. +func (priv PrivateKey) Seed() []byte { + seed := make([]byte, SeedSize) + copy(seed, priv[:SeedSize]) + return seed +} + +func (priv PrivateKey) Scheme() sign.Scheme { return sch } + +func (pub PublicKey) Scheme() sign.Scheme { return sch } + +func (priv PrivateKey) MarshalBinary() (data []byte, err error) { + privateKey := make(PrivateKey, PrivateKeySize) + copy(privateKey, priv) + return privateKey, nil +} + +func (pub PublicKey) MarshalBinary() (data []byte, err error) { + publicKey := make(PublicKey, PublicKeySize) + copy(publicKey, pub) + return publicKey, nil +} + +// Sign creates a signature of a message given a key pair. +// This function supports all the two signature variants defined in RFC-8032, +// namely Ed448 (or pure EdDSA) and Ed448Ph. +// The opts.HashFunc() must return zero to the specify Ed448 variant. This can +// be achieved by passing crypto.Hash(0) as the value for opts. +// Use an Options struct to pass a bool indicating that the ed448Ph variant +// should be used. +// The struct can also be optionally used to pass a context string for signing. +func (priv PrivateKey) Sign( + rand io.Reader, + message []byte, + opts crypto.SignerOpts) (signature []byte, err error) { + var ctx string + var scheme SchemeID + + if o, ok := opts.(SignerOptions); ok { + ctx = o.Context + scheme = o.Scheme + } + + switch true { + case scheme == ED448 && opts.HashFunc() == crypto.Hash(0): + return Sign(priv, message, ctx), nil + case scheme == ED448Ph && opts.HashFunc() == crypto.Hash(0): + return SignPh(priv, message, ctx), nil + default: + return nil, errors.New("ed448: bad hash algorithm") + } +} + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) { + if rand == nil { + rand = cryptoRand.Reader + } + + seed := make(PrivateKey, SeedSize) + if _, err := io.ReadFull(rand, seed); err != nil { + return nil, nil, err + } + + privateKey := NewKeyFromSeed(seed) + publicKey := make([]byte, PublicKeySize) + copy(publicKey, privateKey[SeedSize:]) + + return publicKey, privateKey, nil +} + +// NewKeyFromSeed calculates a private key from a seed. It will panic if +// len(seed) is not SeedSize. This function is provided for interoperability +// with RFC 8032. RFC 8032's private keys correspond to seeds in this +// package. +func NewKeyFromSeed(seed []byte) PrivateKey { + privateKey := make([]byte, PrivateKeySize) + newKeyFromSeed(privateKey, seed) + return privateKey +} + +func newKeyFromSeed(privateKey, seed []byte) { + if l := len(seed); l != SeedSize { + panic("ed448: bad seed length: " + strconv.Itoa(l)) + } + + var h [hashSize]byte + H := sha3.NewShake256() + _, _ = H.Write(seed) + _, _ = H.Read(h[:]) + s := &goldilocks.Scalar{} + deriveSecretScalar(s, h[:paramB]) + + copy(privateKey[:SeedSize], seed) + _ = goldilocks.Curve{}.ScalarBaseMult(s).ToBytes(privateKey[SeedSize:]) +} + +func signAll(signature []byte, privateKey PrivateKey, message, ctx []byte, preHash bool) { + if len(ctx) > ContextMaxSize { + panic(fmt.Errorf("ed448: bad context length: " + strconv.Itoa(len(ctx)))) + } + + H := sha3.NewShake256() + var PHM []byte + + if preHash { + var h [64]byte + _, _ = H.Write(message) + _, _ = H.Read(h[:]) + PHM = h[:] + H.Reset() + } else { + PHM = message + } + + // 1. Hash the 57-byte private key using SHAKE256(x, 114). + var h [hashSize]byte + _, _ = H.Write(privateKey[:SeedSize]) + _, _ = H.Read(h[:]) + s := &goldilocks.Scalar{} + deriveSecretScalar(s, h[:paramB]) + prefix := h[paramB:] + + // 2. Compute SHAKE256(dom4(F, C) || prefix || PH(M), 114). + var rPM [hashSize]byte + H.Reset() + + writeDom(&H, ctx, preHash) + + _, _ = H.Write(prefix) + _, _ = H.Write(PHM) + _, _ = H.Read(rPM[:]) + + // 3. Compute the point [r]B. + r := &goldilocks.Scalar{} + r.FromBytes(rPM[:]) + R := (&[paramB]byte{})[:] + if err := (goldilocks.Curve{}.ScalarBaseMult(r).ToBytes(R)); err != nil { + panic(err) + } + // 4. Compute SHAKE256(dom4(F, C) || R || A || PH(M), 114) + var hRAM [hashSize]byte + H.Reset() + + writeDom(&H, ctx, preHash) + + _, _ = H.Write(R) + _, _ = H.Write(privateKey[SeedSize:]) + _, _ = H.Write(PHM) + _, _ = H.Read(hRAM[:]) + + // 5. Compute S = (r + k * s) mod order. + k := &goldilocks.Scalar{} + k.FromBytes(hRAM[:]) + S := &goldilocks.Scalar{} + S.Mul(k, s) + S.Add(S, r) + + // 6. The signature is the concatenation of R and S. + copy(signature[:paramB], R[:]) + copy(signature[paramB:], S[:]) +} + +// Sign signs the message with privateKey and returns a signature. +// This function supports the signature variant defined in RFC-8032: Ed448, +// also known as the pure version of EdDSA. +// It will panic if len(privateKey) is not PrivateKeySize. +func Sign(priv PrivateKey, message []byte, ctx string) []byte { + signature := make([]byte, SignatureSize) + signAll(signature, priv, message, []byte(ctx), false) + return signature +} + +// SignPh creates a signature of a message given a keypair. +// This function supports the signature variant defined in RFC-8032: Ed448ph, +// meaning it internally hashes the message using SHAKE-256. +// Context could be passed to this function, which length should be no more than +// 255. It can be empty. +func SignPh(priv PrivateKey, message []byte, ctx string) []byte { + signature := make([]byte, SignatureSize) + signAll(signature, priv, message, []byte(ctx), true) + return signature +} + +func verify(public PublicKey, message, signature, ctx []byte, preHash bool) bool { + if len(public) != PublicKeySize || + len(signature) != SignatureSize || + len(ctx) > ContextMaxSize || + !isLessThanOrder(signature[paramB:]) { + return false + } + + P, err := goldilocks.FromBytes(public) + if err != nil { + return false + } + + H := sha3.NewShake256() + var PHM []byte + + if preHash { + var h [64]byte + _, _ = H.Write(message) + _, _ = H.Read(h[:]) + PHM = h[:] + H.Reset() + } else { + PHM = message + } + + var hRAM [hashSize]byte + R := signature[:paramB] + + writeDom(&H, ctx, preHash) + + _, _ = H.Write(R) + _, _ = H.Write(public) + _, _ = H.Write(PHM) + _, _ = H.Read(hRAM[:]) + + k := &goldilocks.Scalar{} + k.FromBytes(hRAM[:]) + S := &goldilocks.Scalar{} + S.FromBytes(signature[paramB:]) + + encR := (&[paramB]byte{})[:] + P.Neg() + _ = goldilocks.Curve{}.CombinedMult(S, k, P).ToBytes(encR) + return bytes.Equal(R, encR) +} + +// VerifyAny returns true if the signature is valid. Failure cases are invalid +// signature, or when the public key cannot be decoded. +// This function supports all the two signature variants defined in RFC-8032, +// namely Ed448 (or pure EdDSA) and Ed448Ph. +// The opts.HashFunc() must return zero, this can be achieved by passing +// crypto.Hash(0) as the value for opts. +// Use a SignerOptions struct to pass a context string for signing. +func VerifyAny(public PublicKey, message, signature []byte, opts crypto.SignerOpts) bool { + var ctx string + var scheme SchemeID + if o, ok := opts.(SignerOptions); ok { + ctx = o.Context + scheme = o.Scheme + } + + switch true { + case scheme == ED448 && opts.HashFunc() == crypto.Hash(0): + return Verify(public, message, signature, ctx) + case scheme == ED448Ph && opts.HashFunc() == crypto.Hash(0): + return VerifyPh(public, message, signature, ctx) + default: + return false + } +} + +// Verify returns true if the signature is valid. Failure cases are invalid +// signature, or when the public key cannot be decoded. +// This function supports the signature variant defined in RFC-8032: Ed448, +// also known as the pure version of EdDSA. +func Verify(public PublicKey, message, signature []byte, ctx string) bool { + return verify(public, message, signature, []byte(ctx), false) +} + +// VerifyPh returns true if the signature is valid. Failure cases are invalid +// signature, or when the public key cannot be decoded. +// This function supports the signature variant defined in RFC-8032: Ed448ph, +// meaning it internally hashes the message using SHAKE-256. +// Context could be passed to this function, which length should be no more than +// 255. It can be empty. +func VerifyPh(public PublicKey, message, signature []byte, ctx string) bool { + return verify(public, message, signature, []byte(ctx), true) +} + +func deriveSecretScalar(s *goldilocks.Scalar, h []byte) { + h[0] &= 0xFC // The two least significant bits of the first octet are cleared, + h[paramB-1] = 0x00 // all eight bits the last octet are cleared, and + h[paramB-2] |= 0x80 // the highest bit of the second to last octet is set. + s.FromBytes(h[:paramB]) +} + +// isLessThanOrder returns true if 0 <= x < order and if the last byte of x is zero. +func isLessThanOrder(x []byte) bool { + order := goldilocks.Curve{}.Order() + i := len(order) - 1 + for i > 0 && x[i] == order[i] { + i-- + } + return x[paramB-1] == 0 && x[i] < order[i] +} + +func writeDom(h io.Writer, ctx []byte, preHash bool) { + dom4 := "SigEd448" + _, _ = h.Write([]byte(dom4)) + + if preHash { + _, _ = h.Write([]byte{byte(0x01), byte(len(ctx))}) + } else { + _, _ = h.Write([]byte{byte(0x00), byte(len(ctx))}) + } + _, _ = h.Write(ctx) +} diff --git a/src/circl/sign/ed448/ed448_test.go b/src/circl/sign/ed448/ed448_test.go new file mode 100644 index 00000000000..639c81c8036 --- /dev/null +++ b/src/circl/sign/ed448/ed448_test.go @@ -0,0 +1,325 @@ +package ed448_test + +import ( + "bytes" + "crypto" + "crypto/rand" + "errors" + "fmt" + "testing" + + "circl/internal/test" + "circl/sign/ed448" +) + +type zeroReader struct{} + +func (zeroReader) Read(buf []byte) (int, error) { + for i := range buf { + buf[i] = 0 + } + return len(buf), nil +} + +func TestEqual(t *testing.T) { + public, private, _ := ed448.GenerateKey(rand.Reader) + + if !public.Equal(public) { + t.Errorf("public key is not equal to itself: %q", public) + } + if !public.Equal(crypto.Signer(private).Public()) { + t.Errorf("private.Public() is not Equal to public: %q", public) + } + if !private.Equal(private) { + t.Errorf("private key is not equal to itself: %q", private) + } + + otherPub, otherPriv, _ := ed448.GenerateKey(rand.Reader) + if public.Equal(otherPub) { + t.Errorf("different public keys are Equal") + } + if private.Equal(otherPriv) { + t.Errorf("different private keys are Equal") + } +} + +func TestWrongPublicKey(t *testing.T) { + wrongPublicKeys := [...][ed448.PublicKeySize]byte{ + { // y = p + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + }, + { // y > p + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + }, + { // x^2 = u/v = (y^2-1)/(dy^2-1) is not a quadratic residue + 0xa4, 0x8b, 0xae, 0x31, 0x1b, 0x3a, 0xe5, 0x62, + 0x3d, 0x6f, 0x2d, 0xbe, 0x8b, 0xb4, 0xd3, 0x21, + 0x0f, 0x04, 0x0a, 0x7e, 0xf2, 0x25, 0x87, 0xc3, + 0xc0, 0x1e, 0xe1, 0xf4, 0x6d, 0xc7, 0x28, 0x8f, + 0x8b, 0xb9, 0x9f, 0x3d, 0x02, 0xb0, 0xc0, 0xa8, + 0xe7, 0xe3, 0x4f, 0xb2, 0x82, 0x64, 0x98, 0x4a, + 0x84, 0x73, 0xd7, 0x57, 0x6a, 0x39, 0x90, 0xa3, + }, + { // y = 1 and x^2 = u/v = 0, and the sign of X is 1 + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, + }, + { // y = -1 and x^2 = u/v = 0, and the sign of X is 1 + 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x80, + }, + } + sig := (&[ed448.SignatureSize]byte{})[:] + for _, public := range wrongPublicKeys { + got := ed448.Verify(public[:], []byte(""), sig, "") + want := false + if got != want { + test.ReportError(t, got, want, public) + } + } +} + +func TestSigner(t *testing.T) { + seed := (&[ed448.SeedSize]byte{})[:] + _, _ = rand.Read(seed) + key := ed448.NewKeyFromSeed(seed) + + priv := key.Seed() + if !bytes.Equal(seed, priv) { + got := priv + want := seed + test.ReportError(t, got, want) + } + + signer := crypto.Signer(key) + ops := crypto.Hash(0) + msg := make([]byte, 16) + _, _ = rand.Read(msg) + sig, err := signer.Sign(nil, msg, ops) + if err != nil { + got := err + var want error + test.ReportError(t, got, want) + } + if len(sig) != ed448.SignatureSize { + got := len(sig) + want := ed448.SignatureSize + test.ReportError(t, got, want) + } + + for _, o := range []ed448.SignerOptions{ + {Scheme: ed448.ED448, Hash: crypto.Hash(0), Context: ""}, + {Scheme: ed448.ED448, Hash: crypto.Hash(0), Context: "non-empty"}, + {Scheme: ed448.ED448Ph, Hash: crypto.Hash(0), Context: ""}, + {Scheme: ed448.ED448Ph, Hash: crypto.Hash(0), Context: "non-empty"}, + } { + testSigner(t, key, o) + } +} + +func testSigner(t *testing.T, signer crypto.Signer, ops ed448.SignerOptions) { + msg := make([]byte, 64) + _, _ = rand.Read(msg) + + sig, err := signer.Sign(nil, msg, ops) + if err != nil { + got := err + var want error + test.ReportError(t, got, want, ops) + } + + if len(sig) != ed448.SignatureSize { + got := len(sig) + want := ed448.SignatureSize + test.ReportError(t, got, want, ops) + } + + pubSigner, ok := signer.Public().(ed448.PublicKey) + if !ok { + got := ok + want := true + test.ReportError(t, got, want, ops) + } + + got := ed448.VerifyAny(pubSigner, msg, sig, ops) + want := true + if got != want { + test.ReportError(t, got, want, ops) + } +} + +type badReader struct{} + +func (badReader) Read([]byte) (n int, err error) { return 0, errors.New("cannot read") } + +func TestErrors(t *testing.T) { + t.Run("badHash", func(t *testing.T) { + var msg [16]byte + ops := crypto.SHA224 + _, priv, _ := ed448.GenerateKey(nil) + _, got := priv.Sign(nil, msg[:], ops) + want := errors.New("ed448: bad hash algorithm") + if got.Error() != want.Error() { + test.ReportError(t, got, want) + } + }) + t.Run("badReader", func(t *testing.T) { + _, _, got := ed448.GenerateKey(badReader{}) + want := errors.New("cannot read") + if got.Error() != want.Error() { + test.ReportError(t, got, want) + } + }) + t.Run("wrongSeedSize", func(t *testing.T) { + var seed [256]byte + var want error + got := test.CheckPanic(func() { ed448.NewKeyFromSeed(seed[:]) }) + if got != want { + test.ReportError(t, got, want) + } + }) + t.Run("bigContext", func(t *testing.T) { + var msg [16]byte + var ctx [256]byte + var want error + _, priv, _ := ed448.GenerateKey(nil) + got := test.CheckPanic(func() { ed448.Sign(priv, msg[:], string(ctx[:])) }) + if got != want { + test.ReportError(t, got, want) + } + }) +} + +func BenchmarkKeyGeneration(b *testing.B) { + var zero zeroReader + for i := 0; i < b.N; i++ { + if _, _, err := ed448.GenerateKey(zero); err != nil { + b.Fatal(err) + } + } +} + +func BenchmarkNewKeyFromSeed(b *testing.B) { + seed := make([]byte, ed448.SeedSize) + b.ReportAllocs() + for i := 0; i < b.N; i++ { + _ = ed448.NewKeyFromSeed(seed) + } +} + +func BenchmarkSigning(b *testing.B) { + var zero zeroReader + _, priv, err := ed448.GenerateKey(zero) + if err != nil { + b.Fatal(err) + } + message := []byte("Hello, world!") + ctx := "a context string" + b.ReportAllocs() + b.ResetTimer() + for i := 0; i < b.N; i++ { + ed448.Sign(priv, message, ctx) + } +} + +func BenchmarkVerification(b *testing.B) { + var zero zeroReader + pub, priv, err := ed448.GenerateKey(zero) + if err != nil { + b.Fatal(err) + } + message := []byte("Hello, world!") + ctx := "a context string" + signature := ed448.Sign(priv, message, ctx) + b.ResetTimer() + for i := 0; i < b.N; i++ { + ed448.Verify(pub, message, signature, ctx) + } +} + +func BenchmarkEd448Ph(b *testing.B) { + msg := make([]byte, 128) + _, _ = rand.Read(msg) + + b.Run("Sign", func(b *testing.B) { + _, key, _ := ed448.GenerateKey(rand.Reader) + ctx := "" + b.ResetTimer() + for i := 0; i < b.N; i++ { + _ = ed448.SignPh(key, msg, ctx) + } + }) + b.Run("Verify", func(b *testing.B) { + pub, priv, _ := ed448.GenerateKey(rand.Reader) + ctx := "" + sig := ed448.SignPh(priv, msg, ctx) + b.ResetTimer() + for i := 0; i < b.N; i++ { + ed448.VerifyPh(pub, msg, sig, ctx) + } + }) +} + +func Example_ed448() { + // import "circl/sign/ed448" + // import "crypto/rand" + + // Generating Alice's key pair + pub, priv, err := ed448.GenerateKey(rand.Reader) + if err != nil { + panic("error on generating keys") + } + + // Alice signs a message. + message := []byte("A message to be signed") + ctx := "This is a context string" + signature := ed448.Sign(priv, message, ctx) + + // Anyone can verify the signature using Alice's public key. + ok := ed448.Verify(pub, message, signature, ctx) + fmt.Println(ok) + // Output: true +} + +func ExampleSignPh() { + // import "circl/sign/ed448" + // import "crypto/rand" + + // Generating Alice's key pair + pub, priv, err := ed448.GenerateKey(rand.Reader) + if err != nil { + panic("error on generating keys") + } + + // Alice signs a message. + message := []byte("A message to be signed") + ctx := "This is a context string" + signature := ed448.SignPh(priv, message, ctx) + + // Anyone can verify the signature using Alice's public key. + ok := ed448.VerifyPh(pub, message, signature, ctx) + fmt.Println(ok) + // Output: true +} diff --git a/src/circl/sign/ed448/rfc8032_test.go b/src/circl/sign/ed448/rfc8032_test.go new file mode 100644 index 00000000000..cf5d0f165d2 --- /dev/null +++ b/src/circl/sign/ed448/rfc8032_test.go @@ -0,0 +1,532 @@ +package ed448_test + +import ( + "bytes" + "testing" + + "circl/internal/test" + "circl/sign/ed448" +) + +type vector struct { + name string + scheme string + sk []byte + pk []byte + sig []byte + msg []byte + msgLen uint + ph bool + ctx []byte + ctxLen uint +} + +var vectorsEd448 = [...]vector{ + { + name: "-----Blank", + scheme: "Ed448Pure", + sk: []byte{ + 0x6c, 0x82, 0xa5, 0x62, 0xcb, 0x80, 0x8d, 0x10, 0xd6, 0x32, 0xbe, 0x89, 0xc8, 0x51, 0x3e, 0xbf, + 0x6c, 0x92, 0x9f, 0x34, 0xdd, 0xfa, 0x8c, 0x9f, 0x63, 0xc9, 0x96, 0x0e, 0xf6, 0xe3, 0x48, 0xa3, + 0x52, 0x8c, 0x8a, 0x3f, 0xcc, 0x2f, 0x04, 0x4e, 0x39, 0xa3, 0xfc, 0x5b, 0x94, 0x49, 0x2f, 0x8f, + 0x03, 0x2e, 0x75, 0x49, 0xa2, 0x00, 0x98, 0xf9, 0x5b, + }, + pk: []byte{ + 0x5f, 0xd7, 0x44, 0x9b, 0x59, 0xb4, 0x61, 0xfd, 0x2c, 0xe7, 0x87, 0xec, 0x61, 0x6a, 0xd4, 0x6a, + 0x1d, 0xa1, 0x34, 0x24, 0x85, 0xa7, 0x0e, 0x1f, 0x8a, 0x0e, 0xa7, 0x5d, 0x80, 0xe9, 0x67, 0x78, + 0xed, 0xf1, 0x24, 0x76, 0x9b, 0x46, 0xc7, 0x06, 0x1b, 0xd6, 0x78, 0x3d, 0xf1, 0xe5, 0x0f, 0x6c, + 0xd1, 0xfa, 0x1a, 0xbe, 0xaf, 0xe8, 0x25, 0x61, 0x80, + }, + msg: []byte{}, + msgLen: 0, + ph: false, + sig: []byte{ + 0x53, 0x3a, 0x37, 0xf6, 0xbb, 0xe4, 0x57, 0x25, 0x1f, 0x02, 0x3c, 0x0d, 0x88, 0xf9, 0x76, 0xae, + 0x2d, 0xfb, 0x50, 0x4a, 0x84, 0x3e, 0x34, 0xd2, 0x07, 0x4f, 0xd8, 0x23, 0xd4, 0x1a, 0x59, 0x1f, + 0x2b, 0x23, 0x3f, 0x03, 0x4f, 0x62, 0x82, 0x81, 0xf2, 0xfd, 0x7a, 0x22, 0xdd, 0xd4, 0x7d, 0x78, + 0x28, 0xc5, 0x9b, 0xd0, 0xa2, 0x1b, 0xfd, 0x39, 0x80, 0xff, 0x0d, 0x20, 0x28, 0xd4, 0xb1, 0x8a, + 0x9d, 0xf6, 0x3e, 0x00, 0x6c, 0x5d, 0x1c, 0x2d, 0x34, 0x5b, 0x92, 0x5d, 0x8d, 0xc0, 0x0b, 0x41, + 0x04, 0x85, 0x2d, 0xb9, 0x9a, 0xc5, 0xc7, 0xcd, 0xda, 0x85, 0x30, 0xa1, 0x13, 0xa0, 0xf4, 0xdb, + 0xb6, 0x11, 0x49, 0xf0, 0x5a, 0x73, 0x63, 0x26, 0x8c, 0x71, 0xd9, 0x58, 0x08, 0xff, 0x2e, 0x65, + 0x26, 0x00, + }, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----1 octet", + scheme: "Ed448Pure", + sk: []byte{ + 0xc4, 0xea, 0xb0, 0x5d, 0x35, 0x70, 0x07, 0xc6, 0x32, 0xf3, 0xdb, 0xb4, 0x84, 0x89, 0x92, 0x4d, + 0x55, 0x2b, 0x08, 0xfe, 0x0c, 0x35, 0x3a, 0x0d, 0x4a, 0x1f, 0x00, 0xac, 0xda, 0x2c, 0x46, 0x3a, + 0xfb, 0xea, 0x67, 0xc5, 0xe8, 0xd2, 0x87, 0x7c, 0x5e, 0x3b, 0xc3, 0x97, 0xa6, 0x59, 0x94, 0x9e, + 0xf8, 0x02, 0x1e, 0x95, 0x4e, 0x0a, 0x12, 0x27, 0x4e, + }, + pk: []byte{ + 0x43, 0xba, 0x28, 0xf4, 0x30, 0xcd, 0xff, 0x45, 0x6a, 0xe5, 0x31, 0x54, 0x5f, 0x7e, 0xcd, 0x0a, + 0xc8, 0x34, 0xa5, 0x5d, 0x93, 0x58, 0xc0, 0x37, 0x2b, 0xfa, 0x0c, 0x6c, 0x67, 0x98, 0xc0, 0x86, + 0x6a, 0xea, 0x01, 0xeb, 0x00, 0x74, 0x28, 0x02, 0xb8, 0x43, 0x8e, 0xa4, 0xcb, 0x82, 0x16, 0x9c, + 0x23, 0x51, 0x60, 0x62, 0x7b, 0x4c, 0x3a, 0x94, 0x80, + }, + msg: []byte{ + 0x03, + }, + msgLen: 1, + ph: false, + sig: []byte{ + 0x26, 0xb8, 0xf9, 0x17, 0x27, 0xbd, 0x62, 0x89, 0x7a, 0xf1, 0x5e, 0x41, 0xeb, 0x43, 0xc3, 0x77, + 0xef, 0xb9, 0xc6, 0x10, 0xd4, 0x8f, 0x23, 0x35, 0xcb, 0x0b, 0xd0, 0x08, 0x78, 0x10, 0xf4, 0x35, + 0x25, 0x41, 0xb1, 0x43, 0xc4, 0xb9, 0x81, 0xb7, 0xe1, 0x8f, 0x62, 0xde, 0x8c, 0xcd, 0xf6, 0x33, + 0xfc, 0x1b, 0xf0, 0x37, 0xab, 0x7c, 0xd7, 0x79, 0x80, 0x5e, 0x0d, 0xbc, 0xc0, 0xaa, 0xe1, 0xcb, + 0xce, 0xe1, 0xaf, 0xb2, 0xe0, 0x27, 0xdf, 0x36, 0xbc, 0x04, 0xdc, 0xec, 0xbf, 0x15, 0x43, 0x36, + 0xc1, 0x9f, 0x0a, 0xf7, 0xe0, 0xa6, 0x47, 0x29, 0x05, 0xe7, 0x99, 0xf1, 0x95, 0x3d, 0x2a, 0x0f, + 0xf3, 0x34, 0x8a, 0xb2, 0x1a, 0xa4, 0xad, 0xaf, 0xd1, 0xd2, 0x34, 0x44, 0x1c, 0xf8, 0x07, 0xc0, + 0x3a, 0x00, + }, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----1 octet (with context)", + scheme: "Ed448Pure", + sk: []byte{ + 0xc4, 0xea, 0xb0, 0x5d, 0x35, 0x70, 0x07, 0xc6, 0x32, 0xf3, 0xdb, 0xb4, 0x84, 0x89, 0x92, 0x4d, + 0x55, 0x2b, 0x08, 0xfe, 0x0c, 0x35, 0x3a, 0x0d, 0x4a, 0x1f, 0x00, 0xac, 0xda, 0x2c, 0x46, 0x3a, + 0xfb, 0xea, 0x67, 0xc5, 0xe8, 0xd2, 0x87, 0x7c, 0x5e, 0x3b, 0xc3, 0x97, 0xa6, 0x59, 0x94, 0x9e, + 0xf8, 0x02, 0x1e, 0x95, 0x4e, 0x0a, 0x12, 0x27, 0x4e, + }, + pk: []byte{ + 0x43, 0xba, 0x28, 0xf4, 0x30, 0xcd, 0xff, 0x45, 0x6a, 0xe5, 0x31, 0x54, 0x5f, 0x7e, 0xcd, 0x0a, + 0xc8, 0x34, 0xa5, 0x5d, 0x93, 0x58, 0xc0, 0x37, 0x2b, 0xfa, 0x0c, 0x6c, 0x67, 0x98, 0xc0, 0x86, + 0x6a, 0xea, 0x01, 0xeb, 0x00, 0x74, 0x28, 0x02, 0xb8, 0x43, 0x8e, 0xa4, 0xcb, 0x82, 0x16, 0x9c, + 0x23, 0x51, 0x60, 0x62, 0x7b, 0x4c, 0x3a, 0x94, 0x80, + }, + msg: []byte{ + 0x03, + }, + msgLen: 1, + ph: false, + sig: []byte{ + 0xd4, 0xf8, 0xf6, 0x13, 0x17, 0x70, 0xdd, 0x46, 0xf4, 0x08, 0x67, 0xd6, 0xfd, 0x5d, 0x50, 0x55, + 0xde, 0x43, 0x54, 0x1f, 0x8c, 0x5e, 0x35, 0xab, 0xbc, 0xd0, 0x01, 0xb3, 0x2a, 0x89, 0xf7, 0xd2, + 0x15, 0x1f, 0x76, 0x47, 0xf1, 0x1d, 0x8c, 0xa2, 0xae, 0x27, 0x9f, 0xb8, 0x42, 0xd6, 0x07, 0x21, + 0x7f, 0xce, 0x6e, 0x04, 0x2f, 0x68, 0x15, 0xea, 0x00, 0x0c, 0x85, 0x74, 0x1d, 0xe5, 0xc8, 0xda, + 0x11, 0x44, 0xa6, 0xa1, 0xab, 0xa7, 0xf9, 0x6d, 0xe4, 0x25, 0x05, 0xd7, 0xa7, 0x29, 0x85, 0x24, + 0xfd, 0xa5, 0x38, 0xfc, 0xcb, 0xbb, 0x75, 0x4f, 0x57, 0x8c, 0x1c, 0xad, 0x10, 0xd5, 0x4d, 0x0d, + 0x54, 0x28, 0x40, 0x7e, 0x85, 0xdc, 0xbc, 0x98, 0xa4, 0x91, 0x55, 0xc1, 0x37, 0x64, 0xe6, 0x6c, + 0x3c, 0x00, + }, + ctx: []byte{ + 0x66, 0x6f, 0x6f, + }, + ctxLen: 3, + }, + { + name: "-----11 octets", + scheme: "Ed448Pure", + sk: []byte{ + 0xcd, 0x23, 0xd2, 0x4f, 0x71, 0x42, 0x74, 0xe7, 0x44, 0x34, 0x32, 0x37, 0xb9, 0x32, 0x90, 0xf5, + 0x11, 0xf6, 0x42, 0x5f, 0x98, 0xe6, 0x44, 0x59, 0xff, 0x20, 0x3e, 0x89, 0x85, 0x08, 0x3f, 0xfd, + 0xf6, 0x05, 0x00, 0x55, 0x3a, 0xbc, 0x0e, 0x05, 0xcd, 0x02, 0x18, 0x4b, 0xdb, 0x89, 0xc4, 0xcc, + 0xd6, 0x7e, 0x18, 0x79, 0x51, 0x26, 0x7e, 0xb3, 0x28, + }, + pk: []byte{ + 0xdc, 0xea, 0x9e, 0x78, 0xf3, 0x5a, 0x1b, 0xf3, 0x49, 0x9a, 0x83, 0x1b, 0x10, 0xb8, 0x6c, 0x90, + 0xaa, 0xc0, 0x1c, 0xd8, 0x4b, 0x67, 0xa0, 0x10, 0x9b, 0x55, 0xa3, 0x6e, 0x93, 0x28, 0xb1, 0xe3, + 0x65, 0xfc, 0xe1, 0x61, 0xd7, 0x1c, 0xe7, 0x13, 0x1a, 0x54, 0x3e, 0xa4, 0xcb, 0x5f, 0x7e, 0x9f, + 0x1d, 0x8b, 0x00, 0x69, 0x64, 0x47, 0x00, 0x14, 0x00, + }, + msg: []byte{ + 0x0c, 0x3e, 0x54, 0x40, 0x74, 0xec, 0x63, 0xb0, 0x26, 0x5e, 0x0c, + }, + msgLen: 11, + ph: false, + sig: []byte{ + 0x1f, 0x0a, 0x88, 0x88, 0xce, 0x25, 0xe8, 0xd4, 0x58, 0xa2, 0x11, 0x30, 0x87, 0x9b, 0x84, 0x0a, + 0x90, 0x89, 0xd9, 0x99, 0xaa, 0xba, 0x03, 0x9e, 0xaf, 0x3e, 0x3a, 0xfa, 0x09, 0x0a, 0x09, 0xd3, + 0x89, 0xdb, 0xa8, 0x2c, 0x4f, 0xf2, 0xae, 0x8a, 0xc5, 0xcd, 0xfb, 0x7c, 0x55, 0xe9, 0x4d, 0x5d, + 0x96, 0x1a, 0x29, 0xfe, 0x01, 0x09, 0x94, 0x1e, 0x00, 0xb8, 0xdb, 0xde, 0xea, 0x6d, 0x3b, 0x05, + 0x10, 0x68, 0xdf, 0x72, 0x54, 0xc0, 0xcd, 0xc1, 0x29, 0xcb, 0xe6, 0x2d, 0xb2, 0xdc, 0x95, 0x7d, + 0xbb, 0x47, 0xb5, 0x1f, 0xd3, 0xf2, 0x13, 0xfb, 0x86, 0x98, 0xf0, 0x64, 0x77, 0x42, 0x50, 0xa5, + 0x02, 0x89, 0x61, 0xc9, 0xbf, 0x8f, 0xfd, 0x97, 0x3f, 0xe5, 0xd5, 0xc2, 0x06, 0x49, 0x2b, 0x14, + 0x0e, 0x00, + }, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----12 octets", + scheme: "Ed448Pure", + sk: []byte{ + 0x25, 0x8c, 0xdd, 0x4a, 0xda, 0x32, 0xed, 0x9c, 0x9f, 0xf5, 0x4e, 0x63, 0x75, 0x6a, 0xe5, 0x82, + 0xfb, 0x8f, 0xab, 0x2a, 0xc7, 0x21, 0xf2, 0xc8, 0xe6, 0x76, 0xa7, 0x27, 0x68, 0x51, 0x3d, 0x93, + 0x9f, 0x63, 0xdd, 0xdb, 0x55, 0x60, 0x91, 0x33, 0xf2, 0x9a, 0xdf, 0x86, 0xec, 0x99, 0x29, 0xdc, + 0xcb, 0x52, 0xc1, 0xc5, 0xfd, 0x2f, 0xf7, 0xe2, 0x1b, + }, + pk: []byte{ + 0x3b, 0xa1, 0x6d, 0xa0, 0xc6, 0xf2, 0xcc, 0x1f, 0x30, 0x18, 0x77, 0x40, 0x75, 0x6f, 0x5e, 0x79, + 0x8d, 0x6b, 0xc5, 0xfc, 0x01, 0x5d, 0x7c, 0x63, 0xcc, 0x95, 0x10, 0xee, 0x3f, 0xd4, 0x4a, 0xdc, + 0x24, 0xd8, 0xe9, 0x68, 0xb6, 0xe4, 0x6e, 0x6f, 0x94, 0xd1, 0x9b, 0x94, 0x53, 0x61, 0x72, 0x6b, + 0xd7, 0x5e, 0x14, 0x9e, 0xf0, 0x98, 0x17, 0xf5, 0x80, + }, + msg: []byte{ + 0x64, 0xa6, 0x5f, 0x3c, 0xde, 0xdc, 0xdd, 0x66, 0x81, 0x1e, 0x29, 0x15, + }, + msgLen: 12, + ph: false, + sig: []byte{ + 0x7e, 0xee, 0xab, 0x7c, 0x4e, 0x50, 0xfb, 0x79, 0x9b, 0x41, 0x8e, 0xe5, 0xe3, 0x19, 0x7f, 0xf6, + 0xbf, 0x15, 0xd4, 0x3a, 0x14, 0xc3, 0x43, 0x89, 0xb5, 0x9d, 0xd1, 0xa7, 0xb1, 0xb8, 0x5b, 0x4a, + 0xe9, 0x04, 0x38, 0xac, 0xa6, 0x34, 0xbe, 0xa4, 0x5e, 0x3a, 0x26, 0x95, 0xf1, 0x27, 0x0f, 0x07, + 0xfd, 0xcd, 0xf7, 0xc6, 0x2b, 0x8e, 0xfe, 0xaf, 0x00, 0xb4, 0x5c, 0x2c, 0x96, 0xba, 0x45, 0x7e, + 0xb1, 0xa8, 0xbf, 0x07, 0x5a, 0x3d, 0xb2, 0x8e, 0x5c, 0x24, 0xf6, 0xb9, 0x23, 0xed, 0x4a, 0xd7, + 0x47, 0xc3, 0xc9, 0xe0, 0x3c, 0x70, 0x79, 0xef, 0xb8, 0x7c, 0xb1, 0x10, 0xd3, 0xa9, 0x98, 0x61, + 0xe7, 0x20, 0x03, 0xcb, 0xae, 0x6d, 0x6b, 0x8b, 0x82, 0x7e, 0x4e, 0x6c, 0x14, 0x30, 0x64, 0xff, + 0x3c, 0x00, + }, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----13 octets", + scheme: "Ed448Pure", + sk: []byte{ + 0x7e, 0xf4, 0xe8, 0x45, 0x44, 0x23, 0x67, 0x52, 0xfb, 0xb5, 0x6b, 0x8f, 0x31, 0xa2, 0x3a, 0x10, + 0xe4, 0x28, 0x14, 0xf5, 0xf5, 0x5c, 0xa0, 0x37, 0xcd, 0xcc, 0x11, 0xc6, 0x4c, 0x9a, 0x3b, 0x29, + 0x49, 0xc1, 0xbb, 0x60, 0x70, 0x03, 0x14, 0x61, 0x17, 0x32, 0xa6, 0xc2, 0xfe, 0xa9, 0x8e, 0xeb, + 0xc0, 0x26, 0x6a, 0x11, 0xa9, 0x39, 0x70, 0x10, 0x0e, + }, + pk: []byte{ + 0xb3, 0xda, 0x07, 0x9b, 0x0a, 0xa4, 0x93, 0xa5, 0x77, 0x20, 0x29, 0xf0, 0x46, 0x7b, 0xae, 0xbe, + 0xe5, 0xa8, 0x11, 0x2d, 0x9d, 0x3a, 0x22, 0x53, 0x23, 0x61, 0xda, 0x29, 0x4f, 0x7b, 0xb3, 0x81, + 0x5c, 0x5d, 0xc5, 0x9e, 0x17, 0x6b, 0x4d, 0x9f, 0x38, 0x1c, 0xa0, 0x93, 0x8e, 0x13, 0xc6, 0xc0, + 0x7b, 0x17, 0x4b, 0xe6, 0x5d, 0xfa, 0x57, 0x8e, 0x80, + }, + msg: []byte{ + 0x64, 0xa6, 0x5f, 0x3c, 0xde, 0xdc, 0xdd, 0x66, 0x81, 0x1e, 0x29, 0x15, 0xe7, + }, + msgLen: 13, + ph: false, + sig: []byte{ + 0x6a, 0x12, 0x06, 0x6f, 0x55, 0x33, 0x1b, 0x6c, 0x22, 0xac, 0xd5, 0xd5, 0xbf, 0xc5, 0xd7, 0x12, + 0x28, 0xfb, 0xda, 0x80, 0xae, 0x8d, 0xec, 0x26, 0xbd, 0xd3, 0x06, 0x74, 0x3c, 0x50, 0x27, 0xcb, + 0x48, 0x90, 0x81, 0x0c, 0x16, 0x2c, 0x02, 0x74, 0x68, 0x67, 0x5e, 0xcf, 0x64, 0x5a, 0x83, 0x17, + 0x6c, 0x0d, 0x73, 0x23, 0xa2, 0xcc, 0xde, 0x2d, 0x80, 0xef, 0xe5, 0xa1, 0x26, 0x8e, 0x8a, 0xca, + 0x1d, 0x6f, 0xbc, 0x19, 0x4d, 0x3f, 0x77, 0xc4, 0x49, 0x86, 0xeb, 0x4a, 0xb4, 0x17, 0x79, 0x19, + 0xad, 0x8b, 0xec, 0x33, 0xeb, 0x47, 0xbb, 0xb5, 0xfc, 0x6e, 0x28, 0x19, 0x6f, 0xd1, 0xca, 0xf5, + 0x6b, 0x4e, 0x7e, 0x0b, 0xa5, 0x51, 0x92, 0x34, 0xd0, 0x47, 0x15, 0x5a, 0xc7, 0x27, 0xa1, 0x05, + 0x31, 0x00, + }, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----64 octets", + scheme: "Ed448Pure", + sk: []byte{ + 0xd6, 0x5d, 0xf3, 0x41, 0xad, 0x13, 0xe0, 0x08, 0x56, 0x76, 0x88, 0xba, 0xed, 0xda, 0x8e, 0x9d, + 0xcd, 0xc1, 0x7d, 0xc0, 0x24, 0x97, 0x4e, 0xa5, 0xb4, 0x22, 0x7b, 0x65, 0x30, 0xe3, 0x39, 0xbf, + 0xf2, 0x1f, 0x99, 0xe6, 0x8c, 0xa6, 0x96, 0x8f, 0x3c, 0xca, 0x6d, 0xfe, 0x0f, 0xb9, 0xf4, 0xfa, + 0xb4, 0xfa, 0x13, 0x5d, 0x55, 0x42, 0xea, 0x3f, 0x01, + }, + pk: []byte{ + 0xdf, 0x97, 0x05, 0xf5, 0x8e, 0xdb, 0xab, 0x80, 0x2c, 0x7f, 0x83, 0x63, 0xcf, 0xe5, 0x56, 0x0a, + 0xb1, 0xc6, 0x13, 0x2c, 0x20, 0xa9, 0xf1, 0xdd, 0x16, 0x34, 0x83, 0xa2, 0x6f, 0x8a, 0xc5, 0x3a, + 0x39, 0xd6, 0x80, 0x8b, 0xf4, 0xa1, 0xdf, 0xbd, 0x26, 0x1b, 0x09, 0x9b, 0xb0, 0x3b, 0x3f, 0xb5, + 0x09, 0x06, 0xcb, 0x28, 0xbd, 0x8a, 0x08, 0x1f, 0x00, + }, + msg: []byte{ + 0xbd, 0x0f, 0x6a, 0x37, 0x47, 0xcd, 0x56, 0x1b, 0xdd, 0xdf, 0x46, 0x40, 0xa3, 0x32, 0x46, 0x1a, + 0x4a, 0x30, 0xa1, 0x2a, 0x43, 0x4c, 0xd0, 0xbf, 0x40, 0xd7, 0x66, 0xd9, 0xc6, 0xd4, 0x58, 0xe5, + 0x51, 0x22, 0x04, 0xa3, 0x0c, 0x17, 0xd1, 0xf5, 0x0b, 0x50, 0x79, 0x63, 0x1f, 0x64, 0xeb, 0x31, + 0x12, 0x18, 0x2d, 0xa3, 0x00, 0x58, 0x35, 0x46, 0x11, 0x13, 0x71, 0x8d, 0x1a, 0x5e, 0xf9, 0x44, + }, + msgLen: 64, + ph: false, + sig: []byte{ + 0x55, 0x4b, 0xc2, 0x48, 0x08, 0x60, 0xb4, 0x9e, 0xab, 0x85, 0x32, 0xd2, 0xa5, 0x33, 0xb7, 0xd5, + 0x78, 0xef, 0x47, 0x3e, 0xeb, 0x58, 0xc9, 0x8b, 0xb2, 0xd0, 0xe1, 0xce, 0x48, 0x8a, 0x98, 0xb1, + 0x8d, 0xfd, 0xe9, 0xb9, 0xb9, 0x07, 0x75, 0xe6, 0x7f, 0x47, 0xd4, 0xa1, 0xc3, 0x48, 0x20, 0x58, + 0xef, 0xc9, 0xf4, 0x0d, 0x2c, 0xa0, 0x33, 0xa0, 0x80, 0x1b, 0x63, 0xd4, 0x5b, 0x3b, 0x72, 0x2e, + 0xf5, 0x52, 0xba, 0xd3, 0xb4, 0xcc, 0xb6, 0x67, 0xda, 0x35, 0x01, 0x92, 0xb6, 0x1c, 0x50, 0x8c, + 0xf7, 0xb6, 0xb5, 0xad, 0xad, 0xc2, 0xc8, 0xd9, 0xa4, 0x46, 0xef, 0x00, 0x3f, 0xb0, 0x5c, 0xba, + 0x5f, 0x30, 0xe8, 0x8e, 0x36, 0xec, 0x27, 0x03, 0xb3, 0x49, 0xca, 0x22, 0x9c, 0x26, 0x70, 0x83, + 0x39, 0x00, + }, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----256 octets", + scheme: "Ed448Pure", + sk: []byte{ + 0x2e, 0xc5, 0xfe, 0x3c, 0x17, 0x04, 0x5a, 0xbd, 0xb1, 0x36, 0xa5, 0xe6, 0xa9, 0x13, 0xe3, 0x2a, + 0xb7, 0x5a, 0xe6, 0x8b, 0x53, 0xd2, 0xfc, 0x14, 0x9b, 0x77, 0xe5, 0x04, 0x13, 0x2d, 0x37, 0x56, + 0x9b, 0x7e, 0x76, 0x6b, 0xa7, 0x4a, 0x19, 0xbd, 0x61, 0x62, 0x34, 0x3a, 0x21, 0xc8, 0x59, 0x0a, + 0xa9, 0xce, 0xbc, 0xa9, 0x01, 0x4c, 0x63, 0x6d, 0xf5, + }, + pk: []byte{ + 0x79, 0x75, 0x6f, 0x01, 0x4d, 0xcf, 0xe2, 0x07, 0x9f, 0x5d, 0xd9, 0xe7, 0x18, 0xbe, 0x41, 0x71, + 0xe2, 0xef, 0x24, 0x86, 0xa0, 0x8f, 0x25, 0x18, 0x6f, 0x6b, 0xff, 0x43, 0xa9, 0x93, 0x6b, 0x9b, + 0xfe, 0x12, 0x40, 0x2b, 0x08, 0xae, 0x65, 0x79, 0x8a, 0x3d, 0x81, 0xe2, 0x2e, 0x9e, 0xc8, 0x0e, + 0x76, 0x90, 0x86, 0x2e, 0xf3, 0xd4, 0xed, 0x3a, 0x00, + }, + msg: []byte{ + 0x15, 0x77, 0x75, 0x32, 0xb0, 0xbd, 0xd0, 0xd1, 0x38, 0x9f, 0x63, 0x6c, 0x5f, 0x6b, 0x9b, 0xa7, + 0x34, 0xc9, 0x0a, 0xf5, 0x72, 0x87, 0x7e, 0x2d, 0x27, 0x2d, 0xd0, 0x78, 0xaa, 0x1e, 0x56, 0x7c, + 0xfa, 0x80, 0xe1, 0x29, 0x28, 0xbb, 0x54, 0x23, 0x30, 0xe8, 0x40, 0x9f, 0x31, 0x74, 0x50, 0x41, + 0x07, 0xec, 0xd5, 0xef, 0xac, 0x61, 0xae, 0x75, 0x04, 0xda, 0xbe, 0x2a, 0x60, 0x2e, 0xde, 0x89, + 0xe5, 0xcc, 0xa6, 0x25, 0x7a, 0x7c, 0x77, 0xe2, 0x7a, 0x70, 0x2b, 0x3a, 0xe3, 0x9f, 0xc7, 0x69, + 0xfc, 0x54, 0xf2, 0x39, 0x5a, 0xe6, 0xa1, 0x17, 0x8c, 0xab, 0x47, 0x38, 0xe5, 0x43, 0x07, 0x2f, + 0xc1, 0xc1, 0x77, 0xfe, 0x71, 0xe9, 0x2e, 0x25, 0xbf, 0x03, 0xe4, 0xec, 0xb7, 0x2f, 0x47, 0xb6, + 0x4d, 0x04, 0x65, 0xaa, 0xea, 0x4c, 0x7f, 0xad, 0x37, 0x25, 0x36, 0xc8, 0xba, 0x51, 0x6a, 0x60, + 0x39, 0xc3, 0xc2, 0xa3, 0x9f, 0x0e, 0x4d, 0x83, 0x2b, 0xe4, 0x32, 0xdf, 0xa9, 0xa7, 0x06, 0xa6, + 0xe5, 0xc7, 0xe1, 0x9f, 0x39, 0x79, 0x64, 0xca, 0x42, 0x58, 0x00, 0x2f, 0x7c, 0x05, 0x41, 0xb5, + 0x90, 0x31, 0x6d, 0xbc, 0x56, 0x22, 0xb6, 0xb2, 0xa6, 0xfe, 0x7a, 0x4a, 0xbf, 0xfd, 0x96, 0x10, + 0x5e, 0xca, 0x76, 0xea, 0x7b, 0x98, 0x81, 0x6a, 0xf0, 0x74, 0x8c, 0x10, 0xdf, 0x04, 0x8c, 0xe0, + 0x12, 0xd9, 0x01, 0x01, 0x5a, 0x51, 0xf1, 0x89, 0xf3, 0x88, 0x81, 0x45, 0xc0, 0x36, 0x50, 0xaa, + 0x23, 0xce, 0x89, 0x4c, 0x3b, 0xd8, 0x89, 0xe0, 0x30, 0xd5, 0x65, 0x07, 0x1c, 0x59, 0xf4, 0x09, + 0xa9, 0x98, 0x1b, 0x51, 0x87, 0x8f, 0xd6, 0xfc, 0x11, 0x06, 0x24, 0xdc, 0xbc, 0xde, 0x0b, 0xf7, + 0xa6, 0x9c, 0xcc, 0xe3, 0x8f, 0xab, 0xdf, 0x86, 0xf3, 0xbe, 0xf6, 0x04, 0x48, 0x19, 0xde, 0x11, + }, + msgLen: 256, + ph: false, + sig: []byte{ + 0xc6, 0x50, 0xdd, 0xbb, 0x06, 0x01, 0xc1, 0x9c, 0xa1, 0x14, 0x39, 0xe1, 0x64, 0x0d, 0xd9, 0x31, + 0xf4, 0x3c, 0x51, 0x8e, 0xa5, 0xbe, 0xa7, 0x0d, 0x3d, 0xcd, 0xe5, 0xf4, 0x19, 0x1f, 0xe5, 0x3f, + 0x00, 0xcf, 0x96, 0x65, 0x46, 0xb7, 0x2b, 0xcc, 0x7d, 0x58, 0xbe, 0x2b, 0x9b, 0xad, 0xef, 0x28, + 0x74, 0x39, 0x54, 0xe3, 0xa4, 0x4a, 0x23, 0xf8, 0x80, 0xe8, 0xd4, 0xf1, 0xcf, 0xce, 0x2d, 0x7a, + 0x61, 0x45, 0x2d, 0x26, 0xda, 0x05, 0x89, 0x6f, 0x0a, 0x50, 0xda, 0x66, 0xa2, 0x39, 0xa8, 0xa1, + 0x88, 0xb6, 0xd8, 0x25, 0xb3, 0x30, 0x5a, 0xd7, 0x7b, 0x73, 0xfb, 0xac, 0x08, 0x36, 0xec, 0xc6, + 0x09, 0x87, 0xfd, 0x08, 0x52, 0x7c, 0x1a, 0x8e, 0x80, 0xd5, 0x82, 0x3e, 0x65, 0xca, 0xfe, 0x2a, + 0x3d, 0x00, + }, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----1023 octets", + scheme: "Ed448Pure", + sk: []byte{ + 0x87, 0x2d, 0x09, 0x37, 0x80, 0xf5, 0xd3, 0x73, 0x0d, 0xf7, 0xc2, 0x12, 0x66, 0x4b, 0x37, 0xb8, + 0xa0, 0xf2, 0x4f, 0x56, 0x81, 0x0d, 0xaa, 0x83, 0x82, 0xcd, 0x4f, 0xa3, 0xf7, 0x76, 0x34, 0xec, + 0x44, 0xdc, 0x54, 0xf1, 0xc2, 0xed, 0x9b, 0xea, 0x86, 0xfa, 0xfb, 0x76, 0x32, 0xd8, 0xbe, 0x19, + 0x9e, 0xa1, 0x65, 0xf5, 0xad, 0x55, 0xdd, 0x9c, 0xe8, + }, + pk: []byte{ + 0xa8, 0x1b, 0x2e, 0x8a, 0x70, 0xa5, 0xac, 0x94, 0xff, 0xdb, 0xcc, 0x9b, 0xad, 0xfc, 0x3f, 0xeb, + 0x08, 0x01, 0xf2, 0x58, 0x57, 0x8b, 0xb1, 0x14, 0xad, 0x44, 0xec, 0xe1, 0xec, 0x0e, 0x79, 0x9d, + 0xa0, 0x8e, 0xff, 0xb8, 0x1c, 0x5d, 0x68, 0x5c, 0x0c, 0x56, 0xf6, 0x4e, 0xec, 0xae, 0xf8, 0xcd, + 0xf1, 0x1c, 0xc3, 0x87, 0x37, 0x83, 0x8c, 0xf4, 0x00, + }, + msg: []byte{ + 0x6d, 0xdf, 0x80, 0x2e, 0x1a, 0xae, 0x49, 0x86, 0x93, 0x5f, 0x7f, 0x98, 0x1b, 0xa3, 0xf0, 0x35, + 0x1d, 0x62, 0x73, 0xc0, 0xa0, 0xc2, 0x2c, 0x9c, 0x0e, 0x83, 0x39, 0x16, 0x8e, 0x67, 0x54, 0x12, + 0xa3, 0xde, 0xbf, 0xaf, 0x43, 0x5e, 0xd6, 0x51, 0x55, 0x80, 0x07, 0xdb, 0x43, 0x84, 0xb6, 0x50, + 0xfc, 0xc0, 0x7e, 0x3b, 0x58, 0x6a, 0x27, 0xa4, 0xf7, 0xa0, 0x0a, 0xc8, 0xa6, 0xfe, 0xc2, 0xcd, + 0x86, 0xae, 0x4b, 0xf1, 0x57, 0x0c, 0x41, 0xe6, 0xa4, 0x0c, 0x93, 0x1d, 0xb2, 0x7b, 0x2f, 0xaa, + 0x15, 0xa8, 0xce, 0xdd, 0x52, 0xcf, 0xf7, 0x36, 0x2c, 0x4e, 0x6e, 0x23, 0xda, 0xec, 0x0f, 0xbc, + 0x3a, 0x79, 0xb6, 0x80, 0x6e, 0x31, 0x6e, 0xfc, 0xc7, 0xb6, 0x81, 0x19, 0xbf, 0x46, 0xbc, 0x76, + 0xa2, 0x60, 0x67, 0xa5, 0x3f, 0x29, 0x6d, 0xaf, 0xdb, 0xdc, 0x11, 0xc7, 0x7f, 0x77, 0x77, 0xe9, + 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0xb2, 0x7a, 0xb9, 0x37, + 0xa5, 0x81, 0x5d, 0x16, 0xb5, 0xfa, 0xe4, 0x07, 0xff, 0x18, 0x22, 0x2c, 0x6d, 0x1e, 0xd2, 0x63, + 0xbe, 0x68, 0xc9, 0x5f, 0x32, 0xd9, 0x08, 0xbd, 0x89, 0x5c, 0xd7, 0x62, 0x07, 0xae, 0x72, 0x64, + 0x87, 0x56, 0x7f, 0x9a, 0x67, 0xda, 0xd7, 0x9a, 0xbe, 0xc3, 0x16, 0xf6, 0x83, 0xb1, 0x7f, 0x2d, + 0x02, 0xbf, 0x07, 0xe0, 0xac, 0x8b, 0x5b, 0xc6, 0x16, 0x2c, 0xf9, 0x46, 0x97, 0xb3, 0xc2, 0x7c, + 0xd1, 0xfe, 0xa4, 0x9b, 0x27, 0xf2, 0x3b, 0xa2, 0x90, 0x18, 0x71, 0x96, 0x25, 0x06, 0x52, 0x0c, + 0x39, 0x2d, 0xa8, 0xb6, 0xad, 0x0d, 0x99, 0xf7, 0x01, 0x3f, 0xbc, 0x06, 0xc2, 0xc1, 0x7a, 0x56, + 0x95, 0x00, 0xc8, 0xa7, 0x69, 0x64, 0x81, 0xc1, 0xcd, 0x33, 0xe9, 0xb1, 0x4e, 0x40, 0xb8, 0x2e, + 0x79, 0xa5, 0xf5, 0xdb, 0x82, 0x57, 0x1b, 0xa9, 0x7b, 0xae, 0x3a, 0xd3, 0xe0, 0x47, 0x95, 0x15, + 0xbb, 0x0e, 0x2b, 0x0f, 0x3b, 0xfc, 0xd1, 0xfd, 0x33, 0x03, 0x4e, 0xfc, 0x62, 0x45, 0xed, 0xdd, + 0x7e, 0xe2, 0x08, 0x6d, 0xda, 0xe2, 0x60, 0x0d, 0x8c, 0xa7, 0x3e, 0x21, 0x4e, 0x8c, 0x2b, 0x0b, + 0xdb, 0x2b, 0x04, 0x7c, 0x6a, 0x46, 0x4a, 0x56, 0x2e, 0xd7, 0x7b, 0x73, 0xd2, 0xd8, 0x41, 0xc4, + 0xb3, 0x49, 0x73, 0x55, 0x12, 0x57, 0x71, 0x3b, 0x75, 0x36, 0x32, 0xef, 0xba, 0x34, 0x81, 0x69, + 0xab, 0xc9, 0x0a, 0x68, 0xf4, 0x26, 0x11, 0xa4, 0x01, 0x26, 0xd7, 0xcb, 0x21, 0xb5, 0x86, 0x95, + 0x56, 0x81, 0x86, 0xf7, 0xe5, 0x69, 0xd2, 0xff, 0x0f, 0x9e, 0x74, 0x5d, 0x04, 0x87, 0xdd, 0x2e, + 0xb9, 0x97, 0xca, 0xfc, 0x5a, 0xbf, 0x9d, 0xd1, 0x02, 0xe6, 0x2f, 0xf6, 0x6c, 0xba, 0x87, + }, + msgLen: 1023, + ph: false, + sig: []byte{ + 0xe3, 0x01, 0x34, 0x5a, 0x41, 0xa3, 0x9a, 0x4d, 0x72, 0xff, 0xf8, 0xdf, 0x69, 0xc9, 0x80, 0x75, + 0xa0, 0xcc, 0x08, 0x2b, 0x80, 0x2f, 0xc9, 0xb2, 0xb6, 0xbc, 0x50, 0x3f, 0x92, 0x6b, 0x65, 0xbd, + 0xdf, 0x7f, 0x4c, 0x8f, 0x1c, 0xb4, 0x9f, 0x63, 0x96, 0xaf, 0xc8, 0xa7, 0x0a, 0xbe, 0x6d, 0x8a, + 0xef, 0x0d, 0xb4, 0x78, 0xd4, 0xc6, 0xb2, 0x97, 0x00, 0x76, 0xc6, 0xa0, 0x48, 0x4f, 0xe7, 0x6d, + 0x76, 0xb3, 0xa9, 0x76, 0x25, 0xd7, 0x9f, 0x1c, 0xe2, 0x40, 0xe7, 0xc5, 0x76, 0x75, 0x0d, 0x29, + 0x55, 0x28, 0x28, 0x6f, 0x71, 0x9b, 0x41, 0x3d, 0xe9, 0xad, 0xa3, 0xe8, 0xeb, 0x78, 0xed, 0x57, + 0x36, 0x03, 0xce, 0x30, 0xd8, 0xbb, 0x76, 0x17, 0x85, 0xdc, 0x30, 0xdb, 0xc3, 0x20, 0x86, 0x9e, + 0x1a, 0x00, + }, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----TEST abc", + scheme: "Ed448Ph", + sk: []byte{ + 0x83, 0x3f, 0xe6, 0x24, 0x09, 0x23, 0x7b, 0x9d, 0x62, 0xec, 0x77, 0x58, 0x75, 0x20, 0x91, 0x1e, + 0x9a, 0x75, 0x9c, 0xec, 0x1d, 0x19, 0x75, 0x5b, 0x7d, 0xa9, 0x01, 0xb9, 0x6d, 0xca, 0x3d, 0x42, + 0xef, 0x78, 0x22, 0xe0, 0xd5, 0x10, 0x41, 0x27, 0xdc, 0x05, 0xd6, 0xdb, 0xef, 0xde, 0x69, 0xe3, + 0xab, 0x2c, 0xec, 0x7c, 0x86, 0x7c, 0x6e, 0x2c, 0x49, + }, + pk: []byte{ + 0x25, 0x9b, 0x71, 0xc1, 0x9f, 0x83, 0xef, 0x77, 0xa7, 0xab, 0xd2, 0x65, 0x24, 0xcb, 0xdb, 0x31, + 0x61, 0xb5, 0x90, 0xa4, 0x8f, 0x7d, 0x17, 0xde, 0x3e, 0xe0, 0xba, 0x9c, 0x52, 0xbe, 0xb7, 0x43, + 0xc0, 0x94, 0x28, 0xa1, 0x31, 0xd6, 0xb1, 0xb5, 0x73, 0x03, 0xd9, 0x0d, 0x81, 0x32, 0xc2, 0x76, + 0xd5, 0xed, 0x3d, 0x5d, 0x01, 0xc0, 0xf5, 0x38, 0x80, + }, + msg: []byte{ + 0x61, 0x62, 0x63, + }, + msgLen: 3, + ph: true, + sig: []byte{ + 0x82, 0x2f, 0x69, 0x01, 0xf7, 0x48, 0x0f, 0x3d, 0x5f, 0x56, 0x2c, 0x59, 0x29, 0x94, 0xd9, 0x69, + 0x36, 0x02, 0x87, 0x56, 0x14, 0x48, 0x32, 0x56, 0x50, 0x56, 0x00, 0xbb, 0xc2, 0x81, 0xae, 0x38, + 0x1f, 0x54, 0xd6, 0xbc, 0xe2, 0xea, 0x91, 0x15, 0x74, 0x93, 0x2f, 0x52, 0xa4, 0xe6, 0xca, 0xdd, + 0x78, 0x76, 0x93, 0x75, 0xec, 0x3f, 0xfd, 0x1b, 0x80, 0x1a, 0x0d, 0x9b, 0x3f, 0x40, 0x30, 0xcd, + 0x43, 0x39, 0x64, 0xb6, 0x45, 0x7e, 0xa3, 0x94, 0x76, 0x51, 0x12, 0x14, 0xf9, 0x74, 0x69, 0xb5, + 0x7d, 0xd3, 0x2d, 0xbc, 0x56, 0x0a, 0x9a, 0x94, 0xd0, 0x0b, 0xff, 0x07, 0x62, 0x04, 0x64, 0xa3, + 0xad, 0x20, 0x3d, 0xf7, 0xdc, 0x7c, 0xe3, 0x60, 0xc3, 0xcd, 0x36, 0x96, 0xd9, 0xd9, 0xfa, 0xb9, + 0x0f, 0x00, + }, + ctx: []byte{}, + ctxLen: 0, + }, + { + name: "-----TEST abc (with context)", + scheme: "Ed448Ph", + sk: []byte{ + 0x83, 0x3f, 0xe6, 0x24, 0x09, 0x23, 0x7b, 0x9d, 0x62, 0xec, 0x77, 0x58, 0x75, 0x20, 0x91, 0x1e, + 0x9a, 0x75, 0x9c, 0xec, 0x1d, 0x19, 0x75, 0x5b, 0x7d, 0xa9, 0x01, 0xb9, 0x6d, 0xca, 0x3d, 0x42, + 0xef, 0x78, 0x22, 0xe0, 0xd5, 0x10, 0x41, 0x27, 0xdc, 0x05, 0xd6, 0xdb, 0xef, 0xde, 0x69, 0xe3, + 0xab, 0x2c, 0xec, 0x7c, 0x86, 0x7c, 0x6e, 0x2c, 0x49, + }, + pk: []byte{ + 0x25, 0x9b, 0x71, 0xc1, 0x9f, 0x83, 0xef, 0x77, 0xa7, 0xab, 0xd2, 0x65, 0x24, 0xcb, 0xdb, 0x31, + 0x61, 0xb5, 0x90, 0xa4, 0x8f, 0x7d, 0x17, 0xde, 0x3e, 0xe0, 0xba, 0x9c, 0x52, 0xbe, 0xb7, 0x43, + 0xc0, 0x94, 0x28, 0xa1, 0x31, 0xd6, 0xb1, 0xb5, 0x73, 0x03, 0xd9, 0x0d, 0x81, 0x32, 0xc2, 0x76, + 0xd5, 0xed, 0x3d, 0x5d, 0x01, 0xc0, 0xf5, 0x38, 0x80, + }, + msg: []byte{ + 0x61, 0x62, 0x63, + }, + msgLen: 3, + ph: true, + sig: []byte{ + 0xc3, 0x22, 0x99, 0xd4, 0x6e, 0xc8, 0xff, 0x02, 0xb5, 0x45, 0x40, 0x98, 0x28, 0x14, 0xdc, 0xe9, + 0xa0, 0x58, 0x12, 0xf8, 0x19, 0x62, 0xb6, 0x49, 0xd5, 0x28, 0x09, 0x59, 0x16, 0xa2, 0xaa, 0x48, + 0x10, 0x65, 0xb1, 0x58, 0x04, 0x23, 0xef, 0x92, 0x7e, 0xcf, 0x0a, 0xf5, 0x88, 0x8f, 0x90, 0xda, + 0x0f, 0x6a, 0x9a, 0x85, 0xad, 0x5d, 0xc3, 0xf2, 0x80, 0xd9, 0x12, 0x24, 0xba, 0x99, 0x11, 0xa3, + 0x65, 0x3d, 0x00, 0xe4, 0x84, 0xe2, 0xce, 0x23, 0x25, 0x21, 0x48, 0x1c, 0x86, 0x58, 0xdf, 0x30, + 0x4b, 0xb7, 0x74, 0x5a, 0x73, 0x51, 0x4c, 0xdb, 0x9b, 0xf3, 0xe1, 0x57, 0x84, 0xab, 0x71, 0x28, + 0x4f, 0x8d, 0x07, 0x04, 0xa6, 0x08, 0xc5, 0x4a, 0x6b, 0x62, 0xd9, 0x7b, 0xeb, 0x51, 0x1d, 0x13, + 0x21, 0x00, + }, + ctx: []byte{ + 0x66, 0x6f, 0x6f, + }, + ctxLen: 3, + }, +} + +func (v vector) isPure() bool { return v.scheme == "Ed448Pure" } +func (v vector) isPreHashed() bool { return v.scheme == "Ed448Ph" } +func (v vector) matchMsgLen() bool { return uint(len(v.msg)) == v.msgLen } +func (v vector) matchCtxLen() bool { return uint(len(v.ctx)) == v.ctxLen } + +func (v vector) testPublicKey(t *testing.T) { + keys := ed448.NewKeyFromSeed(v.sk) + got := keys.Public().(ed448.PublicKey) + want := v.pk + + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, v.name) + } +} + +func (v vector) testSign(t *testing.T) { + private := ed448.NewKeyFromSeed(v.sk) + + var got []byte + + if v.ph { + got = ed448.SignPh(private, v.msg, string(v.ctx)) + } else { + got = ed448.Sign(private, v.msg, string(v.ctx)) + } + + want := v.sig + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, v.name) + } +} + +func (v vector) testVerify(t *testing.T) { + var got bool + + if v.ph { + got = ed448.VerifyPh(v.pk, v.msg, v.sig, string(v.ctx)) + } else { + got = ed448.Verify(v.pk, v.msg, v.sig, string(v.ctx)) + } + + want := true + + if got != want { + test.ReportError(t, got, want, v.name) + } +} + +func TestEd448(t *testing.T) { + for _, v := range vectorsEd448 { + got := (v.isPure() || v.isPreHashed()) && v.matchMsgLen() && v.matchCtxLen() + want := true + if got != want { + test.ReportError(t, got, want, v.sk) + } + v.testPublicKey(t) + v.testSign(t) + v.testVerify(t) + } +} diff --git a/src/circl/sign/ed448/signapi.go b/src/circl/sign/ed448/signapi.go new file mode 100644 index 00000000000..aa57e54bea7 --- /dev/null +++ b/src/circl/sign/ed448/signapi.go @@ -0,0 +1,87 @@ +package ed448 + +import ( + "crypto/rand" + "encoding/asn1" + + "circl/sign" +) + +var sch sign.Scheme = &scheme{} + +// Scheme returns a signature interface. +func Scheme() sign.Scheme { return sch } + +type scheme struct{} + +func (*scheme) Name() string { return "Ed448" } +func (*scheme) PublicKeySize() int { return PublicKeySize } +func (*scheme) PrivateKeySize() int { return PrivateKeySize } +func (*scheme) SignatureSize() int { return SignatureSize } +func (*scheme) SeedSize() int { return SeedSize } +func (*scheme) TLSIdentifier() uint { return 0x0808 } +func (*scheme) SupportsContext() bool { return true } +func (*scheme) Oid() asn1.ObjectIdentifier { + return asn1.ObjectIdentifier{1, 3, 101, 113} +} + +func (*scheme) GenerateKey() (sign.PublicKey, sign.PrivateKey, error) { + return GenerateKey(rand.Reader) +} + +func (*scheme) Sign( + sk sign.PrivateKey, + message []byte, + opts *sign.SignatureOpts, +) []byte { + priv, ok := sk.(PrivateKey) + if !ok { + panic(sign.ErrTypeMismatch) + } + ctx := "" + if opts != nil { + ctx = opts.Context + } + return Sign(priv, message, ctx) +} + +func (*scheme) Verify( + pk sign.PublicKey, + message, signature []byte, + opts *sign.SignatureOpts, +) bool { + pub, ok := pk.(PublicKey) + if !ok { + panic(sign.ErrTypeMismatch) + } + ctx := "" + if opts != nil { + ctx = opts.Context + } + return Verify(pub, message, signature, ctx) +} + +func (*scheme) DeriveKey(seed []byte) (sign.PublicKey, sign.PrivateKey) { + privateKey := NewKeyFromSeed(seed) + publicKey := make(PublicKey, PublicKeySize) + copy(publicKey, privateKey[SeedSize:]) + return publicKey, privateKey +} + +func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (sign.PublicKey, error) { + if len(buf) < PublicKeySize { + return nil, sign.ErrPubKeySize + } + pub := make(PublicKey, PublicKeySize) + copy(pub, buf[:PublicKeySize]) + return pub, nil +} + +func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (sign.PrivateKey, error) { + if len(buf) < PrivateKeySize { + return nil, sign.ErrPrivKeySize + } + priv := make(PrivateKey, PrivateKeySize) + copy(priv, buf[:PrivateKeySize]) + return priv, nil +} diff --git a/src/circl/sign/ed448/testdata/wycheproof_Ed448.json b/src/circl/sign/ed448/testdata/wycheproof_Ed448.json new file mode 100644 index 00000000000..6d791044351 --- /dev/null +++ b/src/circl/sign/ed448/testdata/wycheproof_Ed448.json @@ -0,0 +1,908 @@ +{ + "algorithm" : "EDDSA", + "generatorVersion" : "0.8r12", + "numberOfTests" : 86, + "header" : [ + "Test vectors of type EddsaVerify are intended for testing", + "the verification of Eddsa signatures." + ], + "notes" : { + "SignatureMalleability" : "EdDSA signatures are non-malleable, if implemented accordingly. Failing to check the range of S allows to modify signatures. See RFC 8032, Section 5.2.7 and Section 8.4." + }, + "schema" : "eddsa_verify_schema.json", + "testGroups" : [ + { + "jwk" : { + "crv" : "Ed448", + "d" : "iDAeB2UY01N_kwLuD1Ij5LY-HwFgB9PC69_sX3CZfoEZxrrQrnuAP0h5HKjsVJqiobhi96UVkLnV", + "kid" : "none", + "kty" : "OKP", + "x" : "QZYQpTSvEn9YOwSBjNt_D_MAsCXy4BaCvK4z_Wkc7gOVEd8M3caQ7peEJuizjlDOWvfc-6UPcEwA" + }, + "key" : { + "curve" : "edwards448", + "keySize" : 448, + "pk" : "419610a534af127f583b04818cdb7f0ff300b025f2e01682bcae33fd691cee039511df0cddc690ee978426e8b38e50ce5af7dcfba50f704c00", + "sk" : "88301e076518d3537f9302ee0f5223e4b63e1f016007d3c2ebdfec5f70997e8119c6bad0ae7b803f48791ca8ec549aa2a1b862f7a51590b9d5", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "3043300506032b6571033a00419610a534af127f583b04818cdb7f0ff300b025f2e01682bcae33fd691cee039511df0cddc690ee978426e8b38e50ce5af7dcfba50f704c00", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMEMwBQYDK2VxAzoAQZYQpTSvEn9YOwSBjNt/D/MAsCXy4BaCvK4z/Wkc7gOVEd8M3caQ7peEJuizjlDOWvfc+6UPcEwA\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 1, + "comment" : "", + "msg" : "", + "sig" : "cf7953007666e12f73af9ec92e3e018da5ee5a8d5b17f5100a354c58f1d5f4bb37ab835c52f72374c72d612689149cf6d36a70db6dc5a6c400b597348e0e31e51e65bb144e63c892a367b4c055c036aa6cd7e728cdd2a098963bda863903e6dd025b5a5d891209f4e28537694804e50b0800", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 2, + "comment" : "", + "msg" : "78", + "sig" : "c56e94d5c9ca860c244f33db556bf6b3cec38b024b77604a35d6a07211b1316b9a027133c374b86f72665cc45ce01583a2e0f2775c6172da801acef168717cab1196cddfb149359dfef589756257cc2d6b02fc516d8d41b4adaa3f11428f41410ef0dc3c1b008d3d052173d4389508ed0100", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 3, + "comment" : "", + "msg" : "54657374", + "sig" : "5d053ff5b71f6ec3284525d35d77933178c8e19879886d08eccc6c7d27e9e5b5e02537dbc4d4723506e8d171fc1733857573dd02d18f48f28031d67d699a188a9ca46b4eabe2107aef237ca609cb462e24c91d25d286402b6ef7862b78a386950246ff38d6d2f458136d12e3c97fdd982600", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 4, + "comment" : "", + "msg" : "48656c6c6f", + "sig" : "442e33780f199dd7bc71d1335f74df7f3a0ec789e21a175c1bffddb6e50091998d969ac8194b3acefb7702f6c222f84f7eeca3b80406f1fe80687915e7925bf52deb47b6b779e26d30eec7c5fef03580f280a089eefd0bacc9fbbb6a4d73a591d1671d192e6bbcfdb79ad3db5673a1263000", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 5, + "comment" : "", + "msg" : "313233343030", + "sig" : "5db94c53101f521f6c1f43b60ea4d7e06fbd49c2e8afaf4fcc289e645e0880a87b8e55858df4cf2291a7303ffda446b82a117b4dd408cff28060a05236fc9c1682b0e55b60a082c9a57bffe61ef4dda5ce65df539805122b3a09a05976d41ad68ab52df85428152c57da93531e5d16920e00", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 6, + "comment" : "", + "msg" : "000000000000000000000000", + "sig" : "a8ca64d1ab00eae77fd2854d8422db3ae12fca91c14f274f30a44df98590786ec4cbb96a9564fc1b9b16c22d2bd00aa65f0876323729f5ac809fb0b89a4d3f27afbabb596851d835173d60ea34e0875359f3d6adb13cef1395b7eaa5f9147583ff38b4deb183062874915bf194ae61072300", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 7, + "comment" : "", + "msg" : "6161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161", + "sig" : "b205d3e24ccef64c1e86f15f48ddfa682453503489475188b04a8f55860b3c8a9c01e6de820bb7d9b15daff8de25a4a870e987157a115ec1802da0d0606da12842ea7eab658b5eea6dd1f3a641a5174425578003cd318b8d6b8dcb4de954b5078d1912c578ad8281515d6df3672b94173f00", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 8, + "comment" : "", + "msg" : "202122232425262728292a2b2c2d2e2f303132333435363738393a3b3c3d3e3f404142434445464748494a4b4c4d4e4f505152535455565758595a5b5c5d5e5f60", + "sig" : "3492ef66e5fdf1503e9e206c5c2f0d4b7891aad793575527d2251e0df1b97c2feac188bc382ce3c92c4bc36ba2695f32bedadd480eaa932300d0db1f9a9c60844d2ea5aea64933c7be46c4f9d21cb48b39eae23d08496de7ce9501197185cc5d4ff8aa4b018ce7ad321f6a7d778c4a070400", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 9, + "comment" : "", + "msg" : "ffffffffffffffffffffffffffffffff", + "sig" : "545e1905af1b5886552eaf78e17304c6f83fcfb3444df2d1ea056486db615e3bb29131bb0c1fd295364dc515dae581967148eb23c6c9012e806d3623baff00548c648e3cb3756aaaaf659f2fb7dd2e71c7611448593ca63f2a98913ab7f182e6820eaf1334e2745e0e7bc0dccab98de71600", + "result" : "valid", + "flags" : [] + }, + { + "tcId" : 10, + "comment" : "special values for r and s", + "msg" : "3f", + "sig" : "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "result" : "invalid", + "flags" : [] + }, 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"curve" : "edwards448", + "keySize" : 448, + "pk" : "3ba16da0c6f2cc1f30187740756f5e798d6bc5fc015d7c63cc9510ee3fd44adc24d8e968b6e46e6f94d19b945361726bd75e149ef09817f580", + "sk" : "258cdd4ada32ed9c9ff54e63756ae582fb8fab2ac721f2c8e676a72768513d939f63dddb55609133f29adf86ec9929dccb52c1c5fd2ff7e21b", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "3043300506032b6571033a003ba16da0c6f2cc1f30187740756f5e798d6bc5fc015d7c63cc9510ee3fd44adc24d8e968b6e46e6f94d19b945361726bd75e149ef09817f580", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMEMwBQYDK2VxAzoAO6FtoMbyzB8wGHdAdW9eeY1rxfwBXXxjzJUQ7j/UStwk2OlotuRub5TRm5RTYXJr114UnvCYF/WA\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 82, + "comment" : "RFC 8032: 12 bytes", + "msg" : "64a65f3cdedcdd66811e2915", + "sig" : "7eeeab7c4e50fb799b418ee5e3197ff6bf15d43a14c34389b59dd1a7b1b85b4ae90438aca634bea45e3a2695f1270f07fdcdf7c62b8efeaf00b45c2c96ba457eb1a8bf075a3db28e5c24f6b923ed4ad747c3c9e03c7079efb87cb110d3a99861e72003cbae6d6b8b827e4e6c143064ff3c00", + "result" : "valid", + "flags" : [] + } + ] + }, + { + "jwk" : { + "crv" : "Ed448", + "d" : "fvToRUQjZ1L7tWuPMaI6EOQoFPX1XKA3zcwRxkyaOylJwbtgcAMUYRcypsL-qY7rwCZqEak5cBAO", + "kid" : "none", + "kty" : "OKP", + "x" : "s9oHmwqkk6V3ICnwRnuuvuWoES2dOiJTI2HaKU97s4FcXcWeF2tNnzgcoJOOE8bAexdL5l36V46A" + }, + "key" : { + "curve" : "edwards448", + "keySize" : 448, + "pk" : "b3da079b0aa493a5772029f0467baebee5a8112d9d3a22532361da294f7bb3815c5dc59e176b4d9f381ca0938e13c6c07b174be65dfa578e80", + "sk" : "7ef4e84544236752fbb56b8f31a23a10e42814f5f55ca037cdcc11c64c9a3b2949c1bb60700314611732a6c2fea98eebc0266a11a93970100e", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "3043300506032b6571033a00b3da079b0aa493a5772029f0467baebee5a8112d9d3a22532361da294f7bb3815c5dc59e176b4d9f381ca0938e13c6c07b174be65dfa578e80", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMEMwBQYDK2VxAzoAs9oHmwqkk6V3ICnwRnuuvuWoES2dOiJTI2HaKU97s4FcXcWeF2tNnzgcoJOOE8bAexdL5l36V46A\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 83, + "comment" : "RFC 8032: 13 bytes", + "msg" : "64a65f3cdedcdd66811e2915e7", + "sig" : "6a12066f55331b6c22acd5d5bfc5d71228fbda80ae8dec26bdd306743c5027cb4890810c162c027468675ecf645a83176c0d7323a2ccde2d80efe5a1268e8aca1d6fbc194d3f77c44986eb4ab4177919ad8bec33eb47bbb5fc6e28196fd1caf56b4e7e0ba5519234d047155ac727a1053100", + "result" : "valid", + "flags" : [] + } + ] + }, + { + "jwk" : { + "crv" : "Ed448", + "d" : "1l3zQa0T4AhWdoi67dqOnc3BfcAkl06ltCJ7ZTDjOb_yH5nmjKaWjzzKbf4PufT6tPoTXVVC6j8B", + "kid" : "none", + "kty" : "OKP", + "x" : "35cF9Y7bq4Asf4Njz-VWCrHGEywgqfHdFjSDom-KxTo51oCL9KHfvSYbCZuwOz-1CQbLKL2KCB8A" + }, + "key" : { + "curve" : "edwards448", + "keySize" : 448, + "pk" : "df9705f58edbab802c7f8363cfe5560ab1c6132c20a9f1dd163483a26f8ac53a39d6808bf4a1dfbd261b099bb03b3fb50906cb28bd8a081f00", + "sk" : "d65df341ad13e008567688baedda8e9dcdc17dc024974ea5b4227b6530e339bff21f99e68ca6968f3cca6dfe0fb9f4fab4fa135d5542ea3f01", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "3043300506032b6571033a00df9705f58edbab802c7f8363cfe5560ab1c6132c20a9f1dd163483a26f8ac53a39d6808bf4a1dfbd261b099bb03b3fb50906cb28bd8a081f00", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMEMwBQYDK2VxAzoA35cF9Y7bq4Asf4Njz+VWCrHGEywgqfHdFjSDom+KxTo51oCL9KHfvSYbCZuwOz+1CQbLKL2KCB8A\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 84, + "comment" : "RFC 8032: 64 bytes", + "msg" : "bd0f6a3747cd561bdddf4640a332461a4a30a12a434cd0bf40d766d9c6d458e5512204a30c17d1f50b5079631f64eb3112182da3005835461113718d1a5ef944", + "sig" : "554bc2480860b49eab8532d2a533b7d578ef473eeb58c98bb2d0e1ce488a98b18dfde9b9b90775e67f47d4a1c3482058efc9f40d2ca033a0801b63d45b3b722ef552bad3b4ccb667da350192b61c508cf7b6b5adadc2c8d9a446ef003fb05cba5f30e88e36ec2703b349ca229c2670833900", + "result" : "valid", + "flags" : [] + } + ] + }, + { + "jwk" : { + "crv" : "Ed448", + "d" : "LsX-PBcEWr2xNqXmqRPjKrda5otT0vwUm3flBBMtN1abfnZrp0oZvWFiNDohyFkKqc68qQFMY231", + "kid" : "none", + "kty" : "OKP", + "x" : "eXVvAU3P4gefXdnnGL5BceLvJIagjyUYb2v_Q6mTa5v-EkArCK5leYo9geIunsgOdpCGLvPU7ToA" + }, + "key" : { + "curve" : "edwards448", + "keySize" : 448, + "pk" : "79756f014dcfe2079f5dd9e718be4171e2ef2486a08f25186f6bff43a9936b9bfe12402b08ae65798a3d81e22e9ec80e7690862ef3d4ed3a00", + "sk" : "2ec5fe3c17045abdb136a5e6a913e32ab75ae68b53d2fc149b77e504132d37569b7e766ba74a19bd6162343a21c8590aa9cebca9014c636df5", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "3043300506032b6571033a0079756f014dcfe2079f5dd9e718be4171e2ef2486a08f25186f6bff43a9936b9bfe12402b08ae65798a3d81e22e9ec80e7690862ef3d4ed3a00", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMEMwBQYDK2VxAzoAeXVvAU3P4gefXdnnGL5BceLvJIagjyUYb2v/Q6mTa5v+EkArCK5leYo9geIunsgOdpCGLvPU7ToA\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 85, + "comment" : "RFC 8032: 256 bytes", + "msg" : "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", + "sig" : "c650ddbb0601c19ca11439e1640dd931f43c518ea5bea70d3dcde5f4191fe53f00cf966546b72bcc7d58be2b9badef28743954e3a44a23f880e8d4f1cfce2d7a61452d26da05896f0a50da66a239a8a188b6d825b3305ad77b73fbac0836ecc60987fd08527c1a8e80d5823e65cafe2a3d00", + "result" : "valid", + "flags" : [] + } + ] + }, + { + "jwk" : { + "crv" : "Ed448", + "d" : "hy0JN4D103MN98ISZks3uKDyT1aBDaqDgs1Po_d2NOxE3FTxwu2b6ob6-3Yy2L4ZnqFl9a1V3Zzo", + "kid" : "none", + "kty" : "OKP", + "x" : "qBsuinClrJT_28ybrfw_6wgB8lhXi7EUrUTs4ewOeZ2gjv-4HF1oXAxW9k7srvjN8RzDhzeDjPQA" + }, + "key" : { + "curve" : "edwards448", + "keySize" : 448, + "pk" : "a81b2e8a70a5ac94ffdbcc9badfc3feb0801f258578bb114ad44ece1ec0e799da08effb81c5d685c0c56f64eecaef8cdf11cc38737838cf400", + "sk" : "872d093780f5d3730df7c212664b37b8a0f24f56810daa8382cd4fa3f77634ec44dc54f1c2ed9bea86fafb7632d8be199ea165f5ad55dd9ce8", + "type" : "EDDSAKeyPair" + }, + "keyDer" : "3043300506032b6571033a00a81b2e8a70a5ac94ffdbcc9badfc3feb0801f258578bb114ad44ece1ec0e799da08effb81c5d685c0c56f64eecaef8cdf11cc38737838cf400", + "keyPem" : "-----BEGIN PUBLIC KEY-----\nMEMwBQYDK2VxAzoAqBsuinClrJT/28ybrfw/6wgB8lhXi7EUrUTs4ewOeZ2gjv+4HF1oXAxW9k7srvjN8RzDhzeDjPQA\n-----END PUBLIC KEY-----\n", + "type" : "EddsaVerify", + "tests" : [ + { + "tcId" : 86, + "comment" : "RFC 8032: 1023 bytes", + "msg" : "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", + "sig" : "e301345a41a39a4d72fff8df69c98075a0cc082b802fc9b2b6bc503f926b65bddf7f4c8f1cb49f6396afc8a70abe6d8aef0db478d4c6b2970076c6a0484fe76d76b3a97625d79f1ce240e7c576750d295528286f719b413de9ada3e8eb78ed573603ce30d8bb761785dc30dbc320869e1a00", + "result" : "valid", + "flags" : [] + } + ] + } + ] +} diff --git a/src/circl/sign/ed448/wycheproof_test.go b/src/circl/sign/ed448/wycheproof_test.go new file mode 100644 index 00000000000..c40a9caf83c --- /dev/null +++ b/src/circl/sign/ed448/wycheproof_test.go @@ -0,0 +1,113 @@ +package ed448_test + +import ( + "bytes" + "encoding/hex" + "encoding/json" + "io/ioutil" + "os" + "testing" + + "circl/internal/test" + "circl/sign/ed448" +) + +type group struct { + Key struct { + Curve string `json:"curve"` + Size int `json:"keySize"` + Pk string `json:"pk"` + Sk string `json:"sk"` + Type string `json:"type"` + } `json:"key"` + Type string `json:"type"` + Tests []struct { + TcID int `json:"tcId"` + Comment string `json:"comment"` + Msg string `json:"msg"` + Sig string `json:"sig"` + Result string `json:"result"` + Flags []string `json:"flags"` + } `json:"tests"` +} + +type Wycheproof struct { + Alg string `json:"algorithm"` + Version string `json:"generatorVersion"` + Num int `json:"numberOfTests"` + Groups []group `json:"testGroups"` +} + +func (kat *Wycheproof) readFile(t *testing.T, fileName string) { + jsonFile, err := os.Open(fileName) + if err != nil { + t.Fatalf("File %v can not be opened. Error: %v", fileName, err) + } + defer jsonFile.Close() + input, _ := ioutil.ReadAll(jsonFile) + + err = json.Unmarshal(input, &kat) + if err != nil { + t.Fatalf("File %v can not be loaded. Error: %v", fileName, err) + } +} + +func (kat *Wycheproof) keyPair(t *testing.T) { + for i, g := range kat.Groups { + if g.Key.Curve != "edwards448" { + t.Errorf("Curve not expected %v", g.Key.Curve) + } + private, _ := hex.DecodeString(g.Key.Sk) + public, _ := hex.DecodeString(g.Key.Pk) + keys := ed448.NewKeyFromSeed(private) + got := keys.Public().(ed448.PublicKey) + want := public + + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, i, g.Key.Sk) + } + } +} + +func (kat *Wycheproof) verify(t *testing.T) { + ctx := []byte{} + + for i, g := range kat.Groups { + for _, gT := range g.Tests { + isValid := gT.Result == "valid" + private, _ := hex.DecodeString(g.Key.Sk) + public, _ := hex.DecodeString(g.Key.Pk) + sig, _ := hex.DecodeString(gT.Sig) + msg, _ := hex.DecodeString(gT.Msg) + + priv := ed448.NewKeyFromSeed(private) + got := priv.Public().(ed448.PublicKey) + want := public + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, i, gT.TcID) + } + if isValid { + got := ed448.Sign(priv, msg, string(ctx)) + want := sig + if !bytes.Equal(got, want) { + test.ReportError(t, got, want, i, gT.TcID) + } + } + { + got := ed448.Verify(priv.Public().(ed448.PublicKey), msg, sig, string(ctx)) + want := isValid + if got != want { + test.ReportError(t, got, want, i, gT.TcID) + } + } + } + } +} + +func TestWycheproof(t *testing.T) { + // Test vectors from Wycheproof v0.4.12 + var kat Wycheproof + kat.readFile(t, "testdata/wycheproof_Ed448.json") + t.Run("EDDSAKeyPair", kat.keyPair) + t.Run("EDDSAVerify", kat.verify) +} diff --git a/src/circl/sign/eddilithium3/eddilithium.go b/src/circl/sign/eddilithium3/eddilithium.go new file mode 100644 index 00000000000..fb84620eaa9 --- /dev/null +++ b/src/circl/sign/eddilithium3/eddilithium.go @@ -0,0 +1,238 @@ +// Package eddilithium3 implements the hybrid signature scheme Ed25519-Dilithium3. +package eddilithium3 + +import ( + "crypto" + cryptoRand "crypto/rand" + "errors" + "io" + + "circl/internal/sha3" + "circl/sign" + "circl/sign/dilithium/mode3" + "circl/sign/ed25519" +) + +const ( + // SeedSize is the length of the seed for NewKeyFromSeed + SeedSize = mode3.SeedSize // = ed25519.SeedSize = 32 + + // PublicKeySize is the length in bytes of the packed public key. + PublicKeySize = mode3.PublicKeySize + ed25519.PublicKeySize + + // PrivateKeySize is the length in bytes of the packed public key. + PrivateKeySize = mode3.PrivateKeySize + ed25519.SeedSize + + // SignatureSize is the length in bytes of the signatures. + SignatureSize = mode3.SignatureSize + ed25519.SignatureSize +) + +// PublicKey is the type of an EdDilithium3 public key. +type PublicKey struct { + e ed25519.PublicKey + d mode3.PublicKey +} + +// PrivateKey is the type of an EdDilithium3 private key. +type PrivateKey struct { + e ed25519.PrivateKey + d mode3.PrivateKey +} + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [SeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + + pk, sk := NewKeyFromSeed(&seed) + return pk, sk, nil +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { + var seed1 [32]byte + var seed2 [ed25519.SeedSize]byte + + // Internally, Ed25519 and Dilithium hash the seeds they are passed again + // with different hash functions, so it would be safe to use exactly the + // same seed for Ed25519 and Dilithium here. However, in general, when + // combining any two signature schemes it might not be the case that this + // is safe. Setting a bad example here isn't worth the tiny gain in + // performance. + + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Read(seed1[:]) + _, _ = h.Read(seed2[:]) + dpk, dsk := mode3.NewKeyFromSeed(&seed1) + esk := ed25519.NewKeyFromSeed(seed2[:]) + + return &PublicKey{esk.Public().(ed25519.PublicKey), *dpk}, &PrivateKey{esk, *dsk} +} + +// SignTo signs the given message and writes the signature into signature. +// It will panic if signature is not of length at least SignatureSize. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + mode3.SignTo( + &sk.d, + msg, + signature[:mode3.SignatureSize], + ) + esig := ed25519.Sign( + sk.e, + msg, + ) + copy(signature[mode3.SignatureSize:], esig[:]) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + if !mode3.Verify( + &pk.d, + msg, + signature[:mode3.SignatureSize], + ) { + return false + } + if !ed25519.Verify( + pk.e, + msg, + signature[mode3.SignatureSize:], + ) { + return false + } + return true +} + +// Unpack unpacks pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + var tmp [mode3.PublicKeySize]byte + copy(tmp[:], buf[:mode3.PublicKeySize]) + pk.d.Unpack(&tmp) + pk.e = make([]byte, ed25519.PublicKeySize) + copy(pk.e, buf[mode3.PublicKeySize:]) +} + +// Unpack sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + var tmp [mode3.PrivateKeySize]byte + copy(tmp[:], buf[:mode3.PrivateKeySize]) + sk.d.Unpack(&tmp) + sk.e = ed25519.NewKeyFromSeed(buf[mode3.PrivateKeySize:]) +} + +// Pack packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + var tmp [mode3.PublicKeySize]byte + pk.d.Pack(&tmp) + copy(buf[:mode3.PublicKeySize], tmp[:]) + copy(buf[mode3.PublicKeySize:], pk.e) +} + +// Pack packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + var tmp [mode3.PrivateKeySize]byte + sk.d.Pack(&tmp) + copy(buf[:mode3.PrivateKeySize], tmp[:]) + copy(buf[mode3.PrivateKeySize:], sk.e.Seed()) +} + +// Bytes packs the public key. +func (pk *PublicKey) Bytes() []byte { + return append(pk.d.Bytes(), pk.e...) +} + +// Bytes packs the private key. +func (sk *PrivateKey) Bytes() []byte { + return append(sk.d.Bytes(), sk.e.Seed()...) +} + +// MarshalBinary packs the public key. +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + return pk.Bytes(), nil +} + +// MarshalBinary packs the private key. +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + return sk.Bytes(), nil +} + +// UnmarshalBinary the public key from data. +func (pk *PublicKey) UnmarshalBinary(data []byte) error { + if len(data) != PublicKeySize { + return errors.New("packed public key must be of eddilithium3.PublicKeySize bytes") + } + var buf [PublicKeySize]byte + copy(buf[:], data) + pk.Unpack(&buf) + return nil +} + +// UnmarshalBinary unpacks the private key from data. +func (sk *PrivateKey) UnmarshalBinary(data []byte) error { + if len(data) != PrivateKeySize { + return errors.New("packed private key must be of eddilithium3.PrivateKeySize bytes") + } + var buf [PrivateKeySize]byte + copy(buf[:], data) + sk.Unpack(&buf) + return nil +} + +func (sk *PrivateKey) Scheme() sign.Scheme { return sch } +func (pk *PublicKey) Scheme() sign.Scheme { return sch } + +func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { + castOther, ok := other.(*PrivateKey) + if !ok { + return false + } + return castOther.e.Equal(sk.e) && castOther.d.Equal(&sk.d) +} + +func (pk *PublicKey) Equal(other crypto.PublicKey) bool { + castOther, ok := other.(*PublicKey) + if !ok { + return false + } + return castOther.e.Equal(pk.e) && castOther.d.Equal(&pk.d) +} + +// Sign signs the given message. +// +// opts.HashFunc() must return zero, which can be achieved by passing +// crypto.Hash(0) for opts. rand is ignored. Will only return an error +// if opts.HashFunc() is non-zero. +// +// This function is used to make PrivateKey implement the crypto.Signer +// interface. The package-level SignTo function might be more convenient +// to use. +func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( + signature []byte, err error) { + var sig [SignatureSize]byte + + if opts.HashFunc() != crypto.Hash(0) { + return nil, errors.New("eddilithium3: cannot sign hashed message") + } + + SignTo(sk, msg, sig[:]) + return sig[:], nil +} + +// Public computes the public key corresponding to this private key. +// +// Returns a *PublicKey. The type crypto.PublicKey is used to make +// PrivateKey implement the crypto.Signer interface. +func (sk *PrivateKey) Public() crypto.PublicKey { + return &PublicKey{ + sk.e.Public().(ed25519.PublicKey), + *sk.d.Public().(*mode3.PublicKey), + } +} diff --git a/src/circl/sign/eddilithium3/eddilithium_test.go b/src/circl/sign/eddilithium3/eddilithium_test.go new file mode 100644 index 00000000000..a4a476ab4bb --- /dev/null +++ b/src/circl/sign/eddilithium3/eddilithium_test.go @@ -0,0 +1,109 @@ +package eddilithium3_test + +import ( + "circl/sign/eddilithium3" + + "encoding/binary" + "testing" +) + +func BenchmarkVerify(b *testing.B) { + // Note that Dilithium precomputes quite a bit during Unpacking/Keygen + // instead of at the moment of verification (as compared to the reference + // implementation. A fair comparison thus should sum verification + // times with unpacking times.) + var seed [32]byte + var msg [8]byte + var sig [eddilithium3.SignatureSize]byte + pk, sk := eddilithium3.NewKeyFromSeed(&seed) + eddilithium3.SignTo(sk, msg[:], sig[:]) + b.ResetTimer() + for i := 0; i < b.N; i++ { + // We should generate a new signature for every verify attempt, + // as this influences the time a little bit. This difference, however, + // is small and generating a new signature in between creates a lot + // pressure on the allocator which makes an accurate measurement hard. + eddilithium3.Verify(pk, msg[:], sig[:]) + } +} + +func BenchmarkSign(b *testing.B) { + // Note that Dilithium precomputes quite a bit during Unpacking/Keygen + // instead of at the moment of signing (as compared to the reference + // implementation. A fair comparison thus should sum sign times with + // unpacking times.) + var seed [32]byte + var msg [8]byte + var sig [eddilithium3.SignatureSize]byte + _, sk := eddilithium3.NewKeyFromSeed(&seed) + b.ResetTimer() + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(msg[:], uint64(i)) + eddilithium3.SignTo(sk, msg[:], sig[:]) + } +} + +func BenchmarkGenerateKey(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + eddilithium3.NewKeyFromSeed(&seed) + } +} + +func BenchmarkPublicFromPrivate(b *testing.B) { + var seed [32]byte + for i := 0; i < b.N; i++ { + b.StopTimer() + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + _, sk := eddilithium3.NewKeyFromSeed(&seed) + b.StartTimer() + sk.Public() + } +} + +func TestSignThenVerifyAndPkSkPacking(t *testing.T) { + var seed [eddilithium3.SeedSize]byte + var sig [eddilithium3.SignatureSize]byte + var msg [8]byte + var pkb [eddilithium3.PublicKeySize]byte + var skb [eddilithium3.PrivateKeySize]byte + var pk2 eddilithium3.PublicKey + var sk2 eddilithium3.PrivateKey + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := eddilithium3.NewKeyFromSeed(&seed) + for j := uint64(0); j < 10; j++ { + binary.LittleEndian.PutUint64(msg[:], j) + eddilithium3.SignTo(sk, msg[:], sig[:]) + if !eddilithium3.Verify(pk, msg[:], sig[:]) { + t.Fatal() + } + } + pk.Pack(&pkb) + pk2.Unpack(&pkb) + if !pk.Equal(&pk2) { + t.Fatal() + } + sk.Pack(&skb) + sk2.Unpack(&skb) + if !sk.Equal(&sk2) { + t.Fatal() + } + } +} + +func TestPublicFromPrivate(t *testing.T) { + var seed [eddilithium3.SeedSize]byte + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := eddilithium3.NewKeyFromSeed(&seed) + pk2 := sk.Public().(*eddilithium3.PublicKey) + var pkb1, pkb2 [eddilithium3.PublicKeySize]byte + pk.Pack(&pkb1) + pk2.Pack(&pkb2) + if pkb1 != pkb2 { + t.Fatal() + } + } +} diff --git a/src/circl/sign/eddilithium3/example_test.go b/src/circl/sign/eddilithium3/example_test.go new file mode 100644 index 00000000000..3837847e0ff --- /dev/null +++ b/src/circl/sign/eddilithium3/example_test.go @@ -0,0 +1,45 @@ +package eddilithium3_test + +import ( + "fmt" + + "circl/sign/eddilithium3" +) + +func Example() { + // Generates a keypair. + pk, sk, err := eddilithium3.GenerateKey(nil) + if err != nil { + panic(err) + } + + // (Alternatively one can derive a keypair from a seed, + // see NewKeyFromSeed().) + + // Packs public and private key + var packedSk [eddilithium3.PrivateKeySize]byte + var packedPk [eddilithium3.PublicKeySize]byte + sk.Pack(&packedSk) + pk.Pack(&packedPk) + + // Load it again + var sk2 eddilithium3.PrivateKey + var pk2 eddilithium3.PublicKey + sk2.Unpack(&packedSk) + pk2.Unpack(&packedPk) + + // Creates a signature on our message with the generated private key. + msg := []byte("Some message") + var signature [eddilithium3.SignatureSize]byte + eddilithium3.SignTo(&sk2, msg, signature[:]) + + // Checks whether a signature is correct + if !eddilithium3.Verify(&pk2, msg, signature[:]) { + panic("incorrect signature") + } + + fmt.Printf("O.K.") + + // Output: + // O.K. +} diff --git a/src/circl/sign/eddilithium3/signapi.go b/src/circl/sign/eddilithium3/signapi.go new file mode 100644 index 00000000000..e2e7c9a3030 --- /dev/null +++ b/src/circl/sign/eddilithium3/signapi.go @@ -0,0 +1,93 @@ +package eddilithium3 + +import ( + "crypto/rand" + "encoding/asn1" + + "circl/sign" +) + +var sch sign.Scheme = &scheme{} + +// Scheme returns a signature interface. +func Scheme() sign.Scheme { return sch } + +type scheme struct{} + +func (*scheme) Name() string { return "Ed25519-Dilithium3" } +func (*scheme) PublicKeySize() int { return PublicKeySize } +func (*scheme) PrivateKeySize() int { return PrivateKeySize } +func (*scheme) SignatureSize() int { return SignatureSize } +func (*scheme) SeedSize() int { return SeedSize } +func (*scheme) TLSIdentifier() uint { return 0xfe61 /* temp*/ } +func (*scheme) SupportsContext() bool { return false } +func (*scheme) Oid() asn1.ObjectIdentifier { + return asn1.ObjectIdentifier{1, 3, 6, 1, 4, 1, 44363, 45, 9} +} + +func (*scheme) GenerateKey() (sign.PublicKey, sign.PrivateKey, error) { + return GenerateKey(rand.Reader) +} + +func (*scheme) Sign( + sk sign.PrivateKey, + message []byte, + opts *sign.SignatureOpts, +) []byte { + priv, ok := sk.(*PrivateKey) + if !ok { + panic(sign.ErrTypeMismatch) + } + if opts != nil && opts.Context != "" { + panic(sign.ErrContextNotSupported) + } + var sig [SignatureSize]byte + SignTo(priv, message, sig[:]) + return sig[:] +} + +func (*scheme) Verify( + pk sign.PublicKey, + message, signature []byte, + opts *sign.SignatureOpts, +) bool { + pub, ok := pk.(*PublicKey) + if !ok { + panic(sign.ErrTypeMismatch) + } + if opts != nil && opts.Context != "" { + panic(sign.ErrContextNotSupported) + } + return Verify(pub, message, signature) +} + +func (*scheme) DeriveKey(seed []byte) (sign.PublicKey, sign.PrivateKey) { + if len(seed) != SeedSize { + panic(sign.ErrSeedSize) + } + var tmp [SeedSize]byte + copy(tmp[:], seed) + return NewKeyFromSeed(&tmp) +} + +func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (sign.PublicKey, error) { + if len(buf) != PublicKeySize { + return nil, sign.ErrPubKeySize + } + var tmp [PublicKeySize]byte + copy(tmp[:], buf) + var ret PublicKey + ret.Unpack(&tmp) + return &ret, nil +} + +func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (sign.PrivateKey, error) { + if len(buf) != PrivateKeySize { + return nil, sign.ErrPrivKeySize + } + var tmp [PrivateKeySize]byte + copy(tmp[:], buf) + var ret PrivateKey + ret.Unpack(&tmp) + return &ret, nil +} diff --git a/src/circl/sign/eddilithium4/eddilithium.go b/src/circl/sign/eddilithium4/eddilithium.go new file mode 100644 index 00000000000..40e714a0769 --- /dev/null +++ b/src/circl/sign/eddilithium4/eddilithium.go @@ -0,0 +1,233 @@ +// Package eddilithium4 implements the hybrid signature scheme Ed448-Dilithium4. +package eddilithium4 + +import ( + "crypto" + cryptoRand "crypto/rand" + "errors" + "io" + + "circl/internal/sha3" + "circl/sign" + "circl/sign/dilithium/mode4" + "circl/sign/ed448" +) + +const ( + // SeedSize is the length of the seed for NewKeyFromSeed + SeedSize = ed448.SeedSize // > mode4.SeedSize + + // PublicKeySize is the length in bytes of the packed public key. + PublicKeySize = mode4.PublicKeySize + ed448.PublicKeySize + + // PrivateKeySize is the length in bytes of the packed public key. + PrivateKeySize = mode4.PrivateKeySize + ed448.SeedSize + + // SignatureSize is the length in bytes of the signatures. + SignatureSize = mode4.SignatureSize + ed448.SignatureSize +) + +// PublicKey is the type of an EdDilithium4 public key. +type PublicKey struct { + e ed448.PublicKey + d mode4.PublicKey +} + +// PrivateKey is the type of an EdDilithium4 private key. +type PrivateKey struct { + e ed448.PrivateKey + d mode4.PrivateKey +} + +// GenerateKey generates a public/private key pair using entropy from rand. +// If rand is nil, crypto/rand.Reader will be used. +func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) { + var seed [SeedSize]byte + if rand == nil { + rand = cryptoRand.Reader + } + _, err := io.ReadFull(rand, seed[:]) + if err != nil { + return nil, nil, err + } + + pk, sk := NewKeyFromSeed(&seed) + return pk, sk, nil +} + +// NewKeyFromSeed derives a public/private key pair using the given seed. +func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) { + var seed1 [32]byte + var seed2 [ed448.SeedSize]byte + + h := sha3.NewShake256() + _, _ = h.Write(seed[:]) + _, _ = h.Read(seed1[:]) + _, _ = h.Read(seed2[:]) + dpk, dsk := mode4.NewKeyFromSeed(&seed1) + esk := ed448.NewKeyFromSeed(seed2[:]) + + return &PublicKey{esk.Public().(ed448.PublicKey), *dpk}, &PrivateKey{esk, *dsk} +} + +// SignTo signs the given message and writes the signature into signature. +// It will panic if signature is not of length at least SignatureSize. +func SignTo(sk *PrivateKey, msg []byte, signature []byte) { + mode4.SignTo( + &sk.d, + msg, + signature[:mode4.SignatureSize], + ) + esig := ed448.Sign( + sk.e, + msg, + "", + ) + copy(signature[mode4.SignatureSize:], esig[:]) +} + +// Verify checks whether the given signature by pk on msg is valid. +func Verify(pk *PublicKey, msg []byte, signature []byte) bool { + if !mode4.Verify( + &pk.d, + msg, + signature[:mode4.SignatureSize], + ) { + return false + } + if !ed448.Verify( + pk.e, + msg, + signature[mode4.SignatureSize:], + "", + ) { + return false + } + return true +} + +// Unpack unpacks pk to the public key encoded in buf. +func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) { + var tmp [mode4.PublicKeySize]byte + copy(tmp[:], buf[:mode4.PublicKeySize]) + pk.d.Unpack(&tmp) + pk.e = make([]byte, ed448.PublicKeySize) + copy(pk.e, buf[mode4.PublicKeySize:]) +} + +// Unpack sets sk to the private key encoded in buf. +func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) { + var tmp [mode4.PrivateKeySize]byte + copy(tmp[:], buf[:mode4.PrivateKeySize]) + sk.d.Unpack(&tmp) + sk.e = ed448.NewKeyFromSeed(buf[mode4.PrivateKeySize:]) +} + +// Pack packs the public key into buf. +func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) { + var tmp [mode4.PublicKeySize]byte + pk.d.Pack(&tmp) + copy(buf[:mode4.PublicKeySize], tmp[:]) + copy(buf[mode4.PublicKeySize:], pk.e) +} + +// Pack packs the private key into buf. +func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) { + var tmp [mode4.PrivateKeySize]byte + sk.d.Pack(&tmp) + copy(buf[:mode4.PrivateKeySize], tmp[:]) + copy(buf[mode4.PrivateKeySize:], sk.e.Seed()) +} + +// Bytes packs the public key. +func (pk *PublicKey) Bytes() []byte { + return append(pk.d.Bytes(), pk.e...) +} + +// Bytes packs the private key. +func (sk *PrivateKey) Bytes() []byte { + return append(sk.d.Bytes(), sk.e.Seed()...) +} + +// MarshalBinary packs the public key. +func (pk *PublicKey) MarshalBinary() ([]byte, error) { + return pk.Bytes(), nil +} + +// MarshalBinary packs the private key. +func (sk *PrivateKey) MarshalBinary() ([]byte, error) { + return sk.Bytes(), nil +} + +// UnmarshalBinary the public key from data. +func (pk *PublicKey) UnmarshalBinary(data []byte) error { + if len(data) != PublicKeySize { + return errors.New("packed public key must be of eddilithium4.PublicKeySize bytes") + } + var buf [PublicKeySize]byte + copy(buf[:], data) + pk.Unpack(&buf) + return nil +} + +// UnmarshalBinary unpacks the private key from data. +func (sk *PrivateKey) UnmarshalBinary(data []byte) error { + if len(data) != PrivateKeySize { + return errors.New("packed private key must be of eddilithium4.PrivateKeySize bytes") + } + var buf [PrivateKeySize]byte + copy(buf[:], data) + sk.Unpack(&buf) + return nil +} + +func (sk *PrivateKey) Scheme() sign.Scheme { return sch } +func (pk *PublicKey) Scheme() sign.Scheme { return sch } + +func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool { + castOther, ok := other.(*PrivateKey) + if !ok { + return false + } + return castOther.e.Equal(sk.e) && castOther.d.Equal(&sk.d) +} + +func (pk *PublicKey) Equal(other crypto.PublicKey) bool { + castOther, ok := other.(*PublicKey) + if !ok { + return false + } + return castOther.e.Equal(pk.e) && castOther.d.Equal(&pk.d) +} + +// Sign signs the given message. +// +// opts.HashFunc() must return zero, which can be achieved by passing +// crypto.Hash(0) for opts. rand is ignored. Will only return an error +// if opts.HashFunc() is non-zero. +// +// This function is used to make PrivateKey implement the crypto.Signer +// interface. The package-level SignTo function might be more convenient +// to use. +func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ( + signature []byte, err error) { + var sig [SignatureSize]byte + + if opts.HashFunc() != crypto.Hash(0) { + return nil, errors.New("eddilithium4: cannot sign hashed message") + } + + SignTo(sk, msg, sig[:]) + return sig[:], nil +} + +// Public computes the public key corresponding to this private key. +// +// Returns a *PublicKey. The type crypto.PublicKey is used to make +// PrivateKey implement the crypto.Signer interface. +func (sk *PrivateKey) Public() crypto.PublicKey { + return &PublicKey{ + sk.e.Public().(ed448.PublicKey), + *sk.d.Public().(*mode4.PublicKey), + } +} diff --git a/src/circl/sign/eddilithium4/eddilithium_test.go b/src/circl/sign/eddilithium4/eddilithium_test.go new file mode 100644 index 00000000000..030ad19f1a4 --- /dev/null +++ b/src/circl/sign/eddilithium4/eddilithium_test.go @@ -0,0 +1,111 @@ +package eddilithium4_test + +import ( + "circl/sign/eddilithium4" + + "encoding/binary" + "testing" +) + +func BenchmarkVerify(b *testing.B) { + // Note that Dilithium precomputes quite a bit during Unpacking/Keygen + // instead of at the moment of verification (as compared to the reference + // implementation. A fair comparison thus should sum verification + // times with unpacking times.) + var seed [57]byte + var msg [8]byte + var sig [eddilithium4.SignatureSize]byte + pk, sk := eddilithium4.NewKeyFromSeed(&seed) + eddilithium4.SignTo(sk, msg[:], sig[:]) + b.ResetTimer() + for i := 0; i < b.N; i++ { + // We should generate a new signature for every verify attempt, + // as this influences the time a little bit. This difference, however, + // is small and generating a new signature in between creates a lot + // pressure on the allocator which makes an accurate measurement hard. + eddilithium4.Verify(pk, msg[:], sig[:]) + } +} + +func BenchmarkSign(b *testing.B) { + // Note that Dilithium precomputes quite a bit during Unpacking/Keygen + // instead of at the moment of signing (as compared to the reference + // implementation. A fair comparison thus should sum sign times with + // unpacking times.) + var seed [57]byte + var msg [8]byte + var sig [eddilithium4.SignatureSize]byte + _, sk := eddilithium4.NewKeyFromSeed(&seed) + b.ResetTimer() + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(msg[:], uint64(i)) + eddilithium4.SignTo(sk, msg[:], sig[:]) + } +} + +func BenchmarkGenerateKey(b *testing.B) { + var seed [57]byte + for i := 0; i < b.N; i++ { + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + eddilithium4.NewKeyFromSeed(&seed) + } +} + +func BenchmarkPublicFromPrivate(b *testing.B) { + var seed [57]byte + for i := 0; i < b.N; i++ { + b.StopTimer() + binary.LittleEndian.PutUint64(seed[:], uint64(i)) + _, sk := eddilithium4.NewKeyFromSeed(&seed) + b.StartTimer() + sk.Public() + } +} + +func TestSignThenVerifyAndPkSkPacking(t *testing.T) { + var seed [eddilithium4.SeedSize]byte + var sig [eddilithium4.SignatureSize]byte + var msg [8]byte + var pkb1, pkb2 [eddilithium4.PublicKeySize]byte + var skb1, skb2 [eddilithium4.PrivateKeySize]byte + var pk2 eddilithium4.PublicKey + var sk2 eddilithium4.PrivateKey + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := eddilithium4.NewKeyFromSeed(&seed) + for j := uint64(0); j < 10; j++ { + binary.LittleEndian.PutUint64(msg[:], j) + eddilithium4.SignTo(sk, msg[:], sig[:]) + if !eddilithium4.Verify(pk, msg[:], sig[:]) { + t.Fatal() + } + } + pk.Pack(&pkb1) + pk2.Unpack(&pkb1) + pk2.Pack(&pkb2) + if pkb1 != pkb2 { + t.Fatal() + } + sk.Pack(&skb1) + sk2.Unpack(&skb1) + sk2.Pack(&skb2) + if skb1 != skb2 { + t.Fatal() + } + } +} + +func TestPublicFromPrivate(t *testing.T) { + var seed [eddilithium4.SeedSize]byte + for i := uint64(0); i < 100; i++ { + binary.LittleEndian.PutUint64(seed[:], i) + pk, sk := eddilithium4.NewKeyFromSeed(&seed) + pk2 := sk.Public().(*eddilithium4.PublicKey) + var pkb1, pkb2 [eddilithium4.PublicKeySize]byte + pk.Pack(&pkb1) + pk2.Pack(&pkb2) + if pkb1 != pkb2 { + t.Fatal() + } + } +} diff --git a/src/circl/sign/eddilithium4/example_test.go b/src/circl/sign/eddilithium4/example_test.go new file mode 100644 index 00000000000..aacfb3325d9 --- /dev/null +++ b/src/circl/sign/eddilithium4/example_test.go @@ -0,0 +1,45 @@ +package eddilithium4_test + +import ( + "fmt" + + "circl/sign/eddilithium4" +) + +func Example() { + // Generates a keypair. + pk, sk, err := eddilithium4.GenerateKey(nil) + if err != nil { + panic(err) + } + + // (Alternatively one can derive a keypair from a seed, + // see NewKeyFromSeed().) + + // Packs public and private key + var packedSk [eddilithium4.PrivateKeySize]byte + var packedPk [eddilithium4.PublicKeySize]byte + sk.Pack(&packedSk) + pk.Pack(&packedPk) + + // Load it again + var sk2 eddilithium4.PrivateKey + var pk2 eddilithium4.PublicKey + sk2.Unpack(&packedSk) + pk2.Unpack(&packedPk) + + // Creates a signature on our message with the generated private key. + msg := []byte("Some message") + var signature [eddilithium4.SignatureSize]byte + eddilithium4.SignTo(&sk2, msg, signature[:]) + + // Checks whether a signature is correct + if !eddilithium4.Verify(&pk2, msg, signature[:]) { + panic("incorrect signature") + } + + fmt.Printf("O.K.") + + // Output: + // O.K. +} diff --git a/src/circl/sign/eddilithium4/signapi.go b/src/circl/sign/eddilithium4/signapi.go new file mode 100644 index 00000000000..377091ce5fd --- /dev/null +++ b/src/circl/sign/eddilithium4/signapi.go @@ -0,0 +1,93 @@ +package eddilithium4 + +import ( + "crypto/rand" + "encoding/asn1" + + "circl/sign" +) + +var sch sign.Scheme = &scheme{} + +// Scheme returns a signature interface. +func Scheme() sign.Scheme { return sch } + +type scheme struct{} + +func (*scheme) Name() string { return "Ed448-Dilithium4" } +func (*scheme) PublicKeySize() int { return PublicKeySize } +func (*scheme) PrivateKeySize() int { return PrivateKeySize } +func (*scheme) SignatureSize() int { return SignatureSize } +func (*scheme) SeedSize() int { return SeedSize } +func (*scheme) TLSIdentifier() uint { return 0xfe62 /* temp */ } +func (*scheme) SupportsContext() bool { return false } +func (*scheme) Oid() asn1.ObjectIdentifier { + return asn1.ObjectIdentifier{1, 3, 6, 1, 4, 1, 44363, 45, 10} +} + +func (*scheme) GenerateKey() (sign.PublicKey, sign.PrivateKey, error) { + return GenerateKey(rand.Reader) +} + +func (*scheme) Sign( + sk sign.PrivateKey, + message []byte, + opts *sign.SignatureOpts, +) []byte { + priv, ok := sk.(*PrivateKey) + if !ok { + panic(sign.ErrTypeMismatch) + } + if opts != nil && opts.Context != "" { + panic(sign.ErrContextNotSupported) + } + var sig [SignatureSize]byte + SignTo(priv, message, sig[:]) + return sig[:] +} + +func (*scheme) Verify( + pk sign.PublicKey, + message, signature []byte, + opts *sign.SignatureOpts, +) bool { + pub, ok := pk.(*PublicKey) + if !ok { + panic(sign.ErrTypeMismatch) + } + if opts != nil && opts.Context != "" { + panic(sign.ErrContextNotSupported) + } + return Verify(pub, message, signature) +} + +func (*scheme) DeriveKey(seed []byte) (sign.PublicKey, sign.PrivateKey) { + if len(seed) != SeedSize { + panic(sign.ErrSeedSize) + } + var tmp [SeedSize]byte + copy(tmp[:], seed) + return NewKeyFromSeed(&tmp) +} + +func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (sign.PublicKey, error) { + if len(buf) != PublicKeySize { + return nil, sign.ErrPubKeySize + } + var tmp [PublicKeySize]byte + copy(tmp[:], buf) + var ret PublicKey + ret.Unpack(&tmp) + return &ret, nil +} + +func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (sign.PrivateKey, error) { + if len(buf) != PrivateKeySize { + return nil, sign.ErrPrivKeySize + } + var tmp [PrivateKeySize]byte + copy(tmp[:], buf) + var ret PrivateKey + ret.Unpack(&tmp) + return &ret, nil +} diff --git a/src/circl/sign/schemes/schemes.go b/src/circl/sign/schemes/schemes.go new file mode 100644 index 00000000000..b211f11d1a7 --- /dev/null +++ b/src/circl/sign/schemes/schemes.go @@ -0,0 +1,45 @@ +// Package schemes contains a register of signature algorithms. +// +// Implemented schemes: +// Ed25519 +// Ed448 +// Ed25519-Dilithium3 +// Ed448-Dilithium4 +package schemes + +import ( + "strings" + + "circl/sign" + "circl/sign/ed25519" + "circl/sign/ed448" + "circl/sign/eddilithium3" + "circl/sign/eddilithium4" +) + +var allSchemes = [...]sign.Scheme{ + ed25519.Scheme(), + ed448.Scheme(), + eddilithium3.Scheme(), + eddilithium4.Scheme(), +} + +var allSchemeNames map[string]sign.Scheme + +func init() { + allSchemeNames = make(map[string]sign.Scheme) + for _, scheme := range allSchemes { + allSchemeNames[strings.ToLower(scheme.Name())] = scheme + } +} + +// ByName returns the scheme with the given name and nil if it is not +// supported. +// +// Names are case insensitive. +func ByName(name string) sign.Scheme { + return allSchemeNames[strings.ToLower(name)] +} + +// All returns all signature schemes supported. +func All() []sign.Scheme { a := allSchemes; return a[:] } diff --git a/src/circl/sign/schemes/schemes_test.go b/src/circl/sign/schemes/schemes_test.go new file mode 100644 index 00000000000..ceb3635b494 --- /dev/null +++ b/src/circl/sign/schemes/schemes_test.go @@ -0,0 +1,120 @@ +package schemes_test + +import ( + "fmt" + "testing" + + "circl/sign" + "circl/sign/schemes" +) + +func TestCaseSensitivity(t *testing.T) { + if schemes.ByName("ed25519") != schemes.ByName("Ed25519") { + t.Fatal() + } +} + +func TestApi(t *testing.T) { + allSchemes := schemes.All() + for _, scheme := range allSchemes { + scheme := scheme + t.Run(scheme.Name(), func(t *testing.T) { + if scheme == nil { + t.Fatal() + } + + pk, sk, err := scheme.GenerateKey() + if err != nil { + t.Fatal() + } + + packedPk, err := pk.MarshalBinary() + if err != nil { + t.Fatal() + } + + if len(packedPk) != scheme.PublicKeySize() { + t.Fatal() + } + + packedSk, err := sk.MarshalBinary() + if err != nil { + t.Fatal(err) + } + + if len(packedSk) != scheme.PrivateKeySize() { + t.Fatal() + } + + pk2, err := scheme.UnmarshalBinaryPublicKey(packedPk) + if err != nil { + t.Fatal(err) + } + + sk2, err := scheme.UnmarshalBinaryPrivateKey(packedSk) + if err != nil { + t.Fatal(err) + } + + if !sk.Equal(sk2) { + t.Fatal() + } + + if !pk.Equal(pk2) { + t.Fatal() + } + + msg := []byte(fmt.Sprintf("Signing with %s", scheme.Name())) + opts := &sign.SignatureOpts{} + if scheme.SupportsContext() { + opts.Context = "A context" + } + sig := scheme.Sign(sk, msg, opts) + + if scheme.SignatureSize() != len(sig) { + t.Fatal() + } + + if !scheme.Verify(pk2, msg, sig, opts) { + t.Fatal() + } + + if scheme.SupportsContext() { + opts2 := opts + opts2.Context = "Wrong context" + if scheme.Verify(pk2, msg, sig, opts2) { + t.Fatal() + } + } + + sig[0]++ + if scheme.Verify(pk2, msg, sig, opts) { + t.Fatal() + } + + scheme2 := schemes.ByName(scheme.Name()) + if scheme2 == nil || scheme2 != scheme { + t.Fatal() + } + + if pk.Scheme() != scheme { + t.Fatal() + } + + if sk.Scheme() != scheme { + t.Fatal() + } + }) + } +} + +func Example() { + for _, sch := range schemes.All() { + fmt.Println(sch.Name()) + } + // Output: + // Ed25519 + // Ed448 + // Ed25519-Dilithium3 + // Ed448-Dilithium4 +} diff --git a/src/circl/sign/sign.go b/src/circl/sign/sign.go new file mode 100644 index 00000000000..0fedb7396e5 --- /dev/null +++ b/src/circl/sign/sign.go @@ -0,0 +1,111 @@ +// Package sign provides unified interfaces for signature schemes. +// +// A register of schemes is available in the package +// +// circl/sign/schemes +package sign + +import ( + "crypto" + "encoding" + "errors" +) + +type SignatureOpts struct { + // If non-empty, includes the given context in the signature if supported + // and will cause an error during signing otherwise. + Context string +} + +// A public key is used to verify a signature set by the corresponding private +// key. +type PublicKey interface { + // Returns the signature scheme for this public key. + Scheme() Scheme + Equal(crypto.PublicKey) bool + encoding.BinaryMarshaler + crypto.PublicKey +} + +// A private key allows one to create signatures. +type PrivateKey interface { + // Returns the signature scheme for this private key. + Scheme() Scheme + + Equal(crypto.PrivateKey) bool + // For compatibility with Go standard library + crypto.Signer + crypto.PrivateKey + encoding.BinaryMarshaler +} + +// A Scheme represents a specific instance of a signature scheme. +type Scheme interface { + // Name of the scheme. + Name() string + + // GenerateKey creates a new key-pair. + GenerateKey() (PublicKey, PrivateKey, error) + + // Creates a signature using the PrivateKey on the given message and + // returns the signature. opts are additional options which can be nil. + // + // Panics if key is nil or wrong type or opts context is not supported. + Sign(sk PrivateKey, message []byte, opts *SignatureOpts) []byte + + // Checks whether the given signature is a valid signature set by + // the private key corresponding to the given public key on the + // given message. opts are additional options which can be nil. + // + // Panics if key is nil or wrong type or opts context is not supported. + Verify(pk PublicKey, message []byte, signature []byte, opts *SignatureOpts) bool + + // Deterministically derives a keypair from a seed. If you're unsure, + // you're better off using GenerateKey(). + // + // Panics if seed is not of length SeedSize(). + DeriveKey(seed []byte) (PublicKey, PrivateKey) + + // Unmarshals a PublicKey from the provided buffer. + UnmarshalBinaryPublicKey([]byte) (PublicKey, error) + + // Unmarshals a PublicKey from the provided buffer. + UnmarshalBinaryPrivateKey([]byte) (PrivateKey, error) + + // Size of binary marshalled public keys. + PublicKeySize() int + + // Size of binary marshalled public keys. + PrivateKeySize() int + + // Size of signatures. + SignatureSize() int + + // Size of seeds. + SeedSize() int + + // Returns whether contexts are supported. + SupportsContext() bool +} + +var ( + // ErrTypeMismatch is the error used if types of, for instance, private + // and public keys don't match. + ErrTypeMismatch = errors.New("types mismatch") + + // ErrSeedSize is the error used if the provided seed is of the wrong + // size. + ErrSeedSize = errors.New("wrong seed size") + + // ErrPubKeySize is the error used if the provided public key is of + // the wrong size. + ErrPubKeySize = errors.New("wrong size for public key") + + // ErrPrivKeySize is the error used if the provided private key is of + // the wrong size. + ErrPrivKeySize = errors.New("wrong size for private key") + + // ErrContextNotSupported is the error used if a context is not + // supported. + ErrContextNotSupported = errors.New("context not supported") +) diff --git a/src/circl/simd/doc.go b/src/circl/simd/doc.go new file mode 100644 index 00000000000..74814ac2d79 --- /dev/null +++ b/src/circl/simd/doc.go @@ -0,0 +1,2 @@ +// Package simd provides parallel implementations of some primitives. +package simd diff --git a/src/circl/simd/keccakf1600/example_test.go b/src/circl/simd/keccakf1600/example_test.go new file mode 100644 index 00000000000..27475855e5f --- /dev/null +++ b/src/circl/simd/keccakf1600/example_test.go @@ -0,0 +1,79 @@ +package keccakf1600_test + +import ( + "encoding/binary" + "fmt" + + "circl/internal/sha3" + "circl/simd/keccakf1600" +) + +func Example() { + // As an example, computes the (first 32 bytes of a) SHAKE-256 stream of + // four short strings at the same time. + msgs := [4][]byte{ + []byte("These are some short"), + []byte("strings of the same "), + []byte("length that fit in a"), + []byte("single block. "), + } + var hashes [4][32]byte + + // The user could branch to a fast non-SIMD implementation if this function + // returns false. + if !keccakf1600.IsEnabledX4() { + // Compute hashes separately using golang.org/x/crypto/sha3 instead + // when a fast four-way implementation is not available. A generic + // keccakf1600 implementation is quite a bit slower than using + // the non-interleaved hashes because of the need to interleave and + // deinterleave the state. + for i := 0; i < 4; i++ { + h := sha3.NewShake256() + _, _ = h.Write(msgs[i]) + _, _ = h.Read(hashes[i][:]) + } + } else { + // f1600 acts on 1600 bits arranged as 25 uint64s. Our fourway f1600 + // acts on four interleaved states; that is a [100]uint64. (A separate + // type is used to ensure that the encapsulated [100]uint64 is aligned + // properly to be used efficiently with vector instructions.) + var perm keccakf1600.StateX4 + state := perm.Initialize() + + // state is initialized with zeroes. As the messages fit within one + // block, we only need to write the messages, domain separators + // and padding. + for i := 0; i < 4; i++ { + // The messages. + state[i] = binary.LittleEndian.Uint64(msgs[i][:8]) + state[4+i] = binary.LittleEndian.Uint64(msgs[i][8:16]) + + // Final bit of the message together with the SHAKE-256 domain + // separator (0b1111) and the start of the padding (0b10....) + state[8+i] = uint64(binary.LittleEndian.Uint32(msgs[i][16:])) | + (uint64(0x1f) << 32) + state[16*4+i] = 0x80 << 56 // end of padding (0b...01) + } + + // Executes the permutation on state. + perm.Permute() + + // As our desired output fits within one block, we can read it without + // repeating the permutation. + for i := 0; i < 4; i++ { + for j := 0; j < 4; j++ { + binary.LittleEndian.PutUint64( + hashes[i][8*j:8*(j+1)], + state[4*j+i], + ) + } + } + } + + fmt.Printf("\n%x\n%x\n%x\n%x\n", hashes[0], hashes[1], hashes[2], hashes[3]) + // Output: + // 9b48efc4f4e562fe28c510b2ad3966b101ac20066dc88117d85a595cc965f7e4 + // 19333d8bb71edce81f0630e4154abea83bf7d2f7e709d62fda878b6e9db9c9c1 + // 28f31cc0b8d95185fbba5c4ed5cd94ed7dba0e13c21ca830d1325a212defdfc5 + // 51392299d6b10e62b98eb02c9540784046cc9c83e46eddd2ce57cddc2037f917 +} diff --git a/src/circl/simd/keccakf1600/f1600x.go b/src/circl/simd/keccakf1600/f1600x.go new file mode 100644 index 00000000000..4550270fb16 --- /dev/null +++ b/src/circl/simd/keccakf1600/f1600x.go @@ -0,0 +1,149 @@ +// Package keccakf1600 provides a two and four-way Keccak-f[1600] permutation in parallel. +// +// Keccak-f[1600] is the permutation underlying several algorithms such as +// Keccak, SHA3 and SHAKE. Running two or four permutations in parallel is +// useful in some scenarios like in hash-based signatures. +// +// Limitations +// +// Note that not all the architectures support SIMD instructions. This package +// uses AVX2 instructions that are available in some AMD64 architectures +// and NEON instructions that are available in some ARM64 architectures. +// +// For those systems not supporting these, the package still provides the +// expected functionality by means of a generic and slow implementation. +// The recommendation is to beforehand verify IsEnabledX4() and IsEnabledX2() +// to determine if the current system supports the SIMD implementation. +package keccakf1600 + +import ( + "unsafe" + + "circl/internal/sha3" + "internal/cpu" +) + +// StateX4 contains state for the four-way permutation including the four +// interleaved [25]uint64 buffers. Call Initialize() before use to initialize +// and get a pointer to the interleaved buffer. +type StateX4 struct { + // Go guarantees a to be aligned on 8 bytes, whereas we need it to be + // aligned on 32 bytes for bet performance. Thus we leave some headroom + // to be able to move the start of the state. + + // 4 x 25 uint64s for the interleaved states and three uint64s headroom + // to fix alignment. + a [103]uint64 + + // Offset into a that is 32 byte aligned. + offset int +} + +// StateX2 contains state for the two-way permutation including the two +// interleaved [25]uint64 buffers. Call Initialize() before use to initialize +// and get a pointer to the interleaved buffer. +type StateX2 struct { + // Go guarantees a to be aligned on 8 bytes, whereas we need it to be + // aligned on 32 bytes for bet performance. Thus we leave some headroom + // to be able to move the start of the state. + + // 2 x 25 uint64s for the interleaved states and three uint64s headroom + // to fix alignment. + a [53]uint64 + + // Offset into a that is 32 byte aligned. + offset int +} + +// IsEnabledX4 returns true if the architecture supports a four-way SIMD +// implementation provided in this package. +func IsEnabledX4() bool { return cpu.X86.HasAVX2 } + +// IsEnabledX2 returns true if the architecture supports a two-way SIMD +// implementation provided in this package. +func IsEnabledX2() bool { + // After Go 1.16 the flag cpu.ARM64.HasSHA3 is no longer exposed. + return false +} + +// Initialize the state and returns the buffer on which the four permutations +// will act: a uint64 slice of length 100. The first permutation will act +// on {a[0], a[4], ..., a[96]}, the second on {a[1], a[5], ..., a[97]}, etc. +func (s *StateX4) Initialize() []uint64 { + rp := unsafe.Pointer(&s.a[0]) + + // uint64s are always aligned by a multiple of 8. Compute the remainder + // of the address modulo 32 divided by 8. + rem := (int(uintptr(rp)&31) >> 3) + + if rem != 0 { + s.offset = 4 - rem + } + + // The slice we return will be aligned on 32 byte boundary. + return s.a[s.offset : s.offset+100] +} + +// Initialize the state and returns the buffer on which the two permutations +// will act: a uint64 slice of length 50. The first permutation will act +// on {a[0], a[2], ..., a[48]} and the second on {a[1], a[3], ..., a[49]}. +func (s *StateX2) Initialize() []uint64 { + rp := unsafe.Pointer(&s.a[0]) + + // uint64s are always aligned by a multiple of 8. Compute the remainder + // of the address modulo 32 divided by 8. + rem := (int(uintptr(rp)&31) >> 3) + + if rem != 0 { + s.offset = 4 - rem + } + + // The slice we return will be aligned on 32 byte boundary. + return s.a[s.offset : s.offset+50] +} + +// Permute performs the four parallel Keccak-f[1600]s interleaved on the slice +// returned from Initialize(). +func (s *StateX4) Permute() { + if IsEnabledX4() { + permuteSIMDx4(s.a[s.offset:]) + } else { + permuteScalarX4(s.a[s.offset:]) // A slower generic implementation. + } +} + +// Permute performs the two parallel Keccak-f[1600]s interleaved on the slice +// returned from Initialize(). +func (s *StateX2) Permute() { + if IsEnabledX2() { + permuteSIMDx2(s.a[s.offset:]) + } else { + permuteScalarX2(s.a[s.offset:]) // A slower generic implementation. + } +} + +func permuteScalarX4(a []uint64) { + var buf [25]uint64 + for i := 0; i < 4; i++ { + for j := 0; j < 25; j++ { + buf[j] = a[4*j+i] + } + sha3.KeccakF1600(&buf) + for j := 0; j < 25; j++ { + a[4*j+i] = buf[j] + } + } +} + +func permuteScalarX2(a []uint64) { + var buf [25]uint64 + for i := 0; i < 2; i++ { + for j := 0; j < 25; j++ { + buf[j] = a[2*j+i] + } + sha3.KeccakF1600(&buf) + for j := 0; j < 25; j++ { + a[2*j+i] = buf[j] + } + } +} diff --git a/src/circl/simd/keccakf1600/f1600x2_arm64.go b/src/circl/simd/keccakf1600/f1600x2_arm64.go new file mode 100644 index 00000000000..dd742dc4d39 --- /dev/null +++ b/src/circl/simd/keccakf1600/f1600x2_arm64.go @@ -0,0 +1,12 @@ +// +build arm64,go1.16 + +package keccakf1600 + +import "circl/internal/sha3" + +func permuteSIMDx2(state []uint64) { f1600x2ARM(&state[0], &sha3.RC) } + +func permuteSIMDx4(state []uint64) { permuteScalarX4(state) } + +//go:noescape +func f1600x2ARM(state *uint64, rc *[24]uint64) diff --git a/src/circl/simd/keccakf1600/f1600x2_arm64.s b/src/circl/simd/keccakf1600/f1600x2_arm64.s new file mode 100644 index 00000000000..1e8547f9b80 --- /dev/null +++ b/src/circl/simd/keccakf1600/f1600x2_arm64.s @@ -0,0 +1,130 @@ +// +build arm64,go1.16 + +// Taken from https://github.com/bwesterb/armed-keccak + +#include "textflag.h" + +// func f1600x2ARM(state *uint64, rc *[24]uint64) +TEXT ·f1600x2ARM(SB), NOSPLIT, $0-16 + MOVD state+0(FP), R0 + MOVD rc+8(FP), R1 + MOVD R0, R2 + MOVD $24, R3 + + VLD1.P 64(R0), [ V0.B16, V1.B16, V2.B16, V3.B16] + VLD1.P 64(R0), [ V4.B16, V5.B16, V6.B16, V7.B16] + VLD1.P 64(R0), [ V8.B16, V9.B16, V10.B16, V11.B16] + VLD1.P 64(R0), [V12.B16, V13.B16, V14.B16, V15.B16] + VLD1.P 64(R0), [V16.B16, V17.B16, V18.B16, V19.B16] + VLD1.P 64(R0), [V20.B16, V21.B16, V22.B16, V23.B16] + VLD1.P (R0), [V24.B16] + +loop: + // Execute theta but without xorring into the state yet. + VEOR3 V10.B16, V5.B16, V0.B16, V25.B16 + VEOR3 V11.B16, V6.B16, V1.B16, V26.B16 + VEOR3 V12.B16, V7.B16, V2.B16, V27.B16 + VEOR3 V13.B16, V8.B16, V3.B16, V28.B16 + VEOR3 V14.B16, V9.B16, V4.B16, V29.B16 + + VEOR3 V20.B16, V15.B16, V25.B16, V25.B16 + VEOR3 V21.B16, V16.B16, V26.B16, V26.B16 + VEOR3 V22.B16, V17.B16, V27.B16, V27.B16 + VEOR3 V23.B16, V18.B16, V28.B16, V28.B16 + VEOR3 V24.B16, V19.B16, V29.B16, V29.B16 + + // Xor parities from step theta into the state at the same time as + // exeuting rho and pi. + VRAX1 V26.D2, V29.D2, V30.D2 + VRAX1 V29.D2, V27.D2, V29.D2 + VRAX1 V27.D2, V25.D2, V27.D2 + VRAX1 V25.D2, V28.D2, V25.D2 + VRAX1 V28.D2, V26.D2, V28.D2 + + VEOR V30.B16, V0.B16, V0.B16 + VMOV V1.B16, V31.B16 + + VXAR $20, V27.D2, V6.D2, V1.D2 + VXAR $44, V25.D2, V9.D2, V6.D2 + VXAR $3 , V28.D2, V22.D2, V9.D2 + VXAR $25, V25.D2, V14.D2, V22.D2 + VXAR $46, V30.D2, V20.D2, V14.D2 + VXAR $2 , V28.D2, V2.D2, V20.D2 + VXAR $21, V28.D2, V12.D2, V2.D2 + VXAR $39, V29.D2, V13.D2, V12.D2 + VXAR $56, V25.D2, V19.D2, V13.D2 + VXAR $8 , V29.D2, V23.D2, V19.D2 + VXAR $23, V30.D2, V15.D2, V23.D2 + VXAR $37, V25.D2, V4.D2, V15.D2 + VXAR $50, V25.D2, V24.D2, V4.D2 + VXAR $62, V27.D2, V21.D2, V24.D2 + VXAR $9 , V29.D2, V8.D2, V21.D2 + VXAR $19, V27.D2, V16.D2, V8.D2 + VXAR $28, V30.D2, V5.D2, V16.D2 + VXAR $36, V29.D2, V3.D2, V5.D2 + VXAR $43, V29.D2, V18.D2, V3.D2 + VXAR $49, V28.D2, V17.D2, V18.D2 + VXAR $54, V27.D2, V11.D2, V17.D2 + VXAR $58, V28.D2, V7.D2, V11.D2 + VXAR $61, V30.D2, V10.D2, V7.D2 + VXAR $63, V27.D2, V31.D2, V10.D2 + + // Chi + VBCAX V1.B16, V2.B16, V0.B16, V25.B16 + VBCAX V2.B16, V3.B16, V1.B16, V26.B16 + VBCAX V3.B16, V4.B16, V2.B16, V2.B16 + VBCAX V4.B16, V0.B16, V3.B16, V3.B16 + VBCAX V0.B16, V1.B16, V4.B16, V4.B16 + VMOV V25.B16, V0.B16 + VMOV V26.B16, V1.B16 + + VBCAX V6.B16, V7.B16, V5.B16, V25.B16 + VBCAX V7.B16, V8.B16, V6.B16, V26.B16 + VBCAX V8.B16, V9.B16, V7.B16, V7.B16 + VBCAX V9.B16, V5.B16, V8.B16, V8.B16 + VBCAX V5.B16, V6.B16, V9.B16, V9.B16 + VMOV V25.B16, V5.B16 + VMOV V26.B16, V6.B16 + + VBCAX V11.B16, V12.B16, V10.B16, V25.B16 + VBCAX V12.B16, V13.B16, V11.B16, V26.B16 + VBCAX V13.B16, V14.B16, V12.B16, V12.B16 + VBCAX V14.B16, V10.B16, V13.B16, V13.B16 + VBCAX V10.B16, V11.B16, V14.B16, V14.B16 + VMOV V25.B16, V10.B16 + VMOV V26.B16, V11.B16 + + VBCAX V16.B16, V17.B16, V15.B16, V25.B16 + VBCAX V17.B16, V18.B16, V16.B16, V26.B16 + VBCAX V18.B16, V19.B16, V17.B16, V17.B16 + VBCAX V19.B16, V15.B16, V18.B16, V18.B16 + VBCAX V15.B16, V16.B16, V19.B16, V19.B16 + VMOV V25.B16, V15.B16 + VMOV V26.B16, V16.B16 + + VBCAX V21.B16, V22.B16, V20.B16, V25.B16 + VBCAX V22.B16, V23.B16, V21.B16, V26.B16 + VBCAX V23.B16, V24.B16, V22.B16, V22.B16 + VBCAX V24.B16, V20.B16, V23.B16, V23.B16 + VBCAX V20.B16, V21.B16, V24.B16, V24.B16 + VMOV V25.B16, V20.B16 + VMOV V26.B16, V21.B16 + + // Iota + VLD1R.P 8(R1), [V25.D2] + VEOR V25.B16, V0.B16, V0.B16 + + SUBS $1, R3, R3 + CBNZ R3, loop + + MOVD R2, R0 + + VST1.P [ V0.B16, V1.B16, V2.B16, V3.B16], 64(R0) + VST1.P [ V4.B16, V5.B16, V6.B16, V7.B16], 64(R0) + VST1.P [ V8.B16, V9.B16, V10.B16, V11.B16], 64(R0) + VST1.P [V12.B16, V13.B16, V14.B16, V15.B16], 64(R0) + VST1.P [V16.B16, V17.B16, V18.B16, V19.B16], 64(R0) + VST1.P [V20.B16, V21.B16, V22.B16, V23.B16], 64(R0) + VST1.P [V24.B16], (R0) + + RET diff --git a/src/circl/simd/keccakf1600/f1600x4_amd64.go b/src/circl/simd/keccakf1600/f1600x4_amd64.go new file mode 100644 index 00000000000..c7c0e2ce4e6 --- /dev/null +++ b/src/circl/simd/keccakf1600/f1600x4_amd64.go @@ -0,0 +1,7 @@ +package keccakf1600 + +import "circl/internal/sha3" + +func permuteSIMDx4(state []uint64) { f1600x4AVX2(&state[0], &sha3.RC) } + +func permuteSIMDx2(state []uint64) { permuteScalarX2(state) } diff --git a/src/circl/simd/keccakf1600/f1600x4_amd64.s b/src/circl/simd/keccakf1600/f1600x4_amd64.s new file mode 100644 index 00000000000..194981f10ac --- /dev/null +++ b/src/circl/simd/keccakf1600/f1600x4_amd64.s @@ -0,0 +1,894 @@ +// Code generated by command: go run src.go -out ../../f1600x4_amd64.s -stubs ../../f1600x4stubs_amd64.go -pkg keccakf1600. DO NOT EDIT. + +// +build amd64 + +#include "textflag.h" + +// func f1600x4AVX2(state *uint64, rc *[24]uint64) +// Requires: AVX, AVX2 +TEXT ·f1600x4AVX2(SB), NOSPLIT, $0-16 + MOVQ state+0(FP), AX + MOVQ rc+8(FP), CX + MOVQ $0x0000000000000006, DX + +loop: + VMOVDQA (AX), Y0 + VMOVDQA 32(AX), Y1 + VMOVDQA 64(AX), Y2 + VMOVDQA 96(AX), Y3 + VMOVDQA 128(AX), Y4 + VPXOR 160(AX), Y0, Y0 + VPXOR 192(AX), Y1, Y1 + VPXOR 224(AX), Y2, Y2 + VPXOR 256(AX), Y3, Y3 + VPXOR 288(AX), Y4, Y4 + VPXOR 320(AX), Y0, Y0 + VPXOR 352(AX), Y1, Y1 + VPXOR 384(AX), Y2, Y2 + VPXOR 416(AX), Y3, Y3 + VPXOR 448(AX), Y4, Y4 + VPXOR 480(AX), Y0, Y0 + VPXOR 512(AX), Y1, Y1 + VPXOR 544(AX), Y2, Y2 + VPXOR 576(AX), Y3, Y3 + VPXOR 608(AX), Y4, Y4 + VPXOR 640(AX), Y0, Y0 + VPXOR 672(AX), Y1, Y1 + VPXOR 704(AX), Y2, Y2 + VPXOR 736(AX), Y3, Y3 + VPXOR 768(AX), Y4, Y4 + VPSLLQ $0x01, Y1, Y5 + VPSLLQ $0x01, Y2, Y6 + VPSLLQ $0x01, Y3, Y7 + VPSLLQ $0x01, Y4, Y8 + VPSLLQ $0x01, Y0, Y9 + VPSRLQ $0x3f, Y1, Y10 + VPSRLQ $0x3f, Y2, Y11 + VPSRLQ $0x3f, Y3, Y12 + VPSRLQ $0x3f, Y4, Y13 + VPSRLQ $0x3f, Y0, Y14 + VPOR Y5, Y10, Y10 + VPOR Y6, Y11, Y11 + VPOR Y7, Y12, Y12 + VPOR Y8, Y13, Y13 + VPOR Y9, Y14, Y14 + VPXOR Y10, Y4, Y10 + VPXOR Y11, Y0, Y11 + VPXOR Y12, Y1, Y12 + VPXOR Y13, Y2, Y13 + VPXOR Y14, Y3, Y14 + VPXOR (AX), Y10, Y0 + VPXOR 192(AX), Y11, Y1 + VPXOR 384(AX), Y12, Y2 + VPXOR 576(AX), Y13, Y3 + VPXOR 768(AX), Y14, Y4 + VPSLLQ $0x2c, Y1, Y6 + VPSLLQ $0x2b, Y2, Y7 + VPSLLQ $0x15, Y3, Y8 + VPSLLQ $0x0e, Y4, Y9 + VPSRLQ $0x14, Y1, Y1 + VPSRLQ $0x15, Y2, Y2 + VPSRLQ $0x2b, Y3, Y3 + VPSRLQ $0x32, Y4, Y4 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VPBROADCASTQ (CX), Y0 + VPXOR Y0, Y5, Y5 + VMOVDQA Y5, (AX) + VMOVDQA Y6, 192(AX) + VMOVDQA Y7, 384(AX) + VMOVDQA Y8, 576(AX) + VMOVDQA Y9, 768(AX) + VPXOR 96(AX), Y13, Y0 + VPXOR 288(AX), Y14, Y1 + VPXOR 320(AX), Y10, Y2 + VPXOR 512(AX), Y11, Y3 + VPXOR 704(AX), Y12, Y4 + VPSLLQ $0x1c, Y0, Y5 + VPSLLQ $0x14, Y1, Y6 + VPSLLQ $0x03, Y2, Y7 + VPSLLQ $0x2d, Y3, Y8 + VPSLLQ $0x3d, Y4, Y9 + VPSRLQ $0x24, Y0, Y0 + VPSRLQ $0x2c, Y1, Y1 + VPSRLQ $0x3d, Y2, Y2 + VPSRLQ $0x13, Y3, Y3 + VPSRLQ $0x03, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 320(AX) + VMOVDQA Y6, 512(AX) + VMOVDQA Y7, 704(AX) + VMOVDQA Y8, 96(AX) + VMOVDQA Y9, 288(AX) + VPXOR 32(AX), Y11, Y0 + VPXOR 224(AX), Y12, Y1 + VPXOR 416(AX), Y13, Y2 + VPXOR 608(AX), Y14, Y3 + VPXOR 640(AX), Y10, Y4 + VPSLLQ $0x01, Y0, Y5 + VPSLLQ $0x06, Y1, Y6 + VPSLLQ $0x19, Y2, Y7 + VPSLLQ $0x08, Y3, Y8 + VPSLLQ $0x12, Y4, Y9 + VPSRLQ $0x3f, Y0, Y0 + VPSRLQ $0x3a, Y1, Y1 + VPSRLQ $0x27, Y2, Y2 + VPSRLQ $0x38, Y3, Y3 + VPSRLQ $0x2e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 640(AX) + VMOVDQA Y6, 32(AX) + VMOVDQA Y7, 224(AX) + VMOVDQA Y8, 416(AX) + VMOVDQA Y9, 608(AX) + VPXOR 128(AX), Y14, Y0 + VPXOR 160(AX), Y10, Y1 + VPXOR 352(AX), Y11, Y2 + VPXOR 544(AX), Y12, Y3 + VPXOR 736(AX), Y13, Y4 + VPSLLQ $0x1b, Y0, Y5 + VPSLLQ $0x24, Y1, Y6 + VPSLLQ $0x0a, Y2, Y7 + VPSLLQ $0x0f, Y3, Y8 + VPSLLQ $0x38, Y4, Y9 + VPSRLQ $0x25, Y0, Y0 + VPSRLQ $0x1c, Y1, Y1 + VPSRLQ $0x36, Y2, Y2 + VPSRLQ $0x31, Y3, Y3 + VPSRLQ $0x08, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 160(AX) + VMOVDQA Y6, 352(AX) + VMOVDQA Y7, 544(AX) + VMOVDQA Y8, 736(AX) + VMOVDQA Y9, 128(AX) + VPXOR 64(AX), Y12, Y0 + VPXOR 256(AX), Y13, Y1 + VPXOR 448(AX), Y14, Y2 + VPXOR 480(AX), Y10, Y3 + VPXOR 672(AX), Y11, Y4 + VPSLLQ $0x3e, Y0, Y5 + VPSLLQ $0x37, Y1, Y6 + VPSLLQ $0x27, Y2, Y7 + VPSLLQ $0x29, Y3, Y8 + VPSLLQ $0x02, Y4, Y9 + VPSRLQ $0x02, Y0, Y0 + VPSRLQ $0x09, Y1, Y1 + VPSRLQ $0x19, Y2, Y2 + VPSRLQ $0x17, Y3, Y3 + VPSRLQ $0x3e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 480(AX) + VMOVDQA Y6, 672(AX) + VMOVDQA Y7, 64(AX) + VMOVDQA Y8, 256(AX) + VMOVDQA Y9, 448(AX) + VMOVDQA (AX), Y0 + VMOVDQA 32(AX), Y1 + VMOVDQA 64(AX), Y2 + VMOVDQA 96(AX), Y3 + VMOVDQA 128(AX), Y4 + VPXOR 160(AX), Y0, Y0 + VPXOR 192(AX), Y1, Y1 + VPXOR 224(AX), Y2, Y2 + VPXOR 256(AX), Y3, Y3 + VPXOR 288(AX), Y4, Y4 + VPXOR 320(AX), Y0, Y0 + VPXOR 352(AX), Y1, Y1 + VPXOR 384(AX), Y2, Y2 + VPXOR 416(AX), Y3, Y3 + VPXOR 448(AX), Y4, Y4 + VPXOR 480(AX), Y0, Y0 + VPXOR 512(AX), Y1, Y1 + VPXOR 544(AX), Y2, Y2 + VPXOR 576(AX), Y3, Y3 + VPXOR 608(AX), Y4, Y4 + VPXOR 640(AX), Y0, Y0 + VPXOR 672(AX), Y1, Y1 + VPXOR 704(AX), Y2, Y2 + VPXOR 736(AX), Y3, Y3 + VPXOR 768(AX), Y4, Y4 + VPSLLQ $0x01, Y1, Y5 + VPSLLQ $0x01, Y2, Y6 + VPSLLQ $0x01, Y3, Y7 + VPSLLQ $0x01, Y4, Y8 + VPSLLQ $0x01, Y0, Y9 + VPSRLQ $0x3f, Y1, Y10 + VPSRLQ $0x3f, Y2, Y11 + VPSRLQ $0x3f, Y3, Y12 + VPSRLQ $0x3f, Y4, Y13 + VPSRLQ $0x3f, Y0, Y14 + VPOR Y5, Y10, Y10 + VPOR Y6, Y11, Y11 + VPOR Y7, Y12, Y12 + VPOR Y8, Y13, Y13 + VPOR Y9, Y14, Y14 + VPXOR Y10, Y4, Y10 + VPXOR Y11, Y0, Y11 + VPXOR Y12, Y1, Y12 + VPXOR Y13, Y2, Y13 + VPXOR Y14, Y3, Y14 + VPXOR (AX), Y10, Y0 + VPXOR 512(AX), Y11, Y1 + VPXOR 224(AX), Y12, Y2 + VPXOR 736(AX), Y13, Y3 + VPXOR 448(AX), Y14, Y4 + VPSLLQ $0x2c, Y1, Y6 + VPSLLQ $0x2b, Y2, Y7 + VPSLLQ $0x15, Y3, Y8 + VPSLLQ $0x0e, Y4, Y9 + VPSRLQ $0x14, Y1, Y1 + VPSRLQ $0x15, Y2, Y2 + VPSRLQ $0x2b, Y3, Y3 + VPSRLQ $0x32, Y4, Y4 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VPBROADCASTQ 8(CX), Y0 + VPXOR Y0, Y5, Y5 + VMOVDQA Y5, (AX) + VMOVDQA Y6, 512(AX) + VMOVDQA Y7, 224(AX) + VMOVDQA Y8, 736(AX) + VMOVDQA Y9, 448(AX) + VPXOR 576(AX), Y13, Y0 + VPXOR 288(AX), Y14, Y1 + VPXOR 640(AX), Y10, Y2 + VPXOR 352(AX), Y11, Y3 + VPXOR 64(AX), Y12, Y4 + VPSLLQ $0x1c, Y0, Y5 + VPSLLQ $0x14, Y1, Y6 + VPSLLQ $0x03, Y2, Y7 + VPSLLQ $0x2d, Y3, Y8 + VPSLLQ $0x3d, Y4, Y9 + VPSRLQ $0x24, Y0, Y0 + VPSRLQ $0x2c, Y1, Y1 + VPSRLQ $0x3d, Y2, Y2 + VPSRLQ $0x13, Y3, Y3 + VPSRLQ $0x03, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 640(AX) + VMOVDQA Y6, 352(AX) + VMOVDQA Y7, 64(AX) + VMOVDQA Y8, 576(AX) + VMOVDQA Y9, 288(AX) + VPXOR 192(AX), Y11, Y0 + VPXOR 704(AX), Y12, Y1 + VPXOR 416(AX), Y13, Y2 + VPXOR 128(AX), Y14, Y3 + VPXOR 480(AX), Y10, Y4 + VPSLLQ $0x01, Y0, Y5 + VPSLLQ $0x06, Y1, Y6 + VPSLLQ $0x19, Y2, Y7 + VPSLLQ $0x08, Y3, Y8 + VPSLLQ $0x12, Y4, Y9 + VPSRLQ $0x3f, Y0, Y0 + VPSRLQ $0x3a, Y1, Y1 + VPSRLQ $0x27, Y2, Y2 + VPSRLQ $0x38, Y3, Y3 + VPSRLQ $0x2e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 480(AX) + VMOVDQA Y6, 192(AX) + VMOVDQA Y7, 704(AX) + VMOVDQA Y8, 416(AX) + VMOVDQA Y9, 128(AX) + VPXOR 768(AX), Y14, Y0 + VPXOR 320(AX), Y10, Y1 + VPXOR 32(AX), Y11, Y2 + VPXOR 544(AX), Y12, Y3 + VPXOR 256(AX), Y13, Y4 + VPSLLQ $0x1b, Y0, Y5 + VPSLLQ $0x24, Y1, Y6 + VPSLLQ $0x0a, Y2, Y7 + VPSLLQ $0x0f, Y3, Y8 + VPSLLQ $0x38, Y4, Y9 + VPSRLQ $0x25, Y0, Y0 + VPSRLQ $0x1c, Y1, Y1 + VPSRLQ $0x36, Y2, Y2 + VPSRLQ $0x31, Y3, Y3 + VPSRLQ $0x08, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 320(AX) + VMOVDQA Y6, 32(AX) + VMOVDQA Y7, 544(AX) + VMOVDQA Y8, 256(AX) + VMOVDQA Y9, 768(AX) + VPXOR 384(AX), Y12, Y0 + VPXOR 96(AX), Y13, Y1 + VPXOR 608(AX), Y14, Y2 + VPXOR 160(AX), Y10, Y3 + VPXOR 672(AX), Y11, Y4 + VPSLLQ $0x3e, Y0, Y5 + VPSLLQ $0x37, Y1, Y6 + VPSLLQ $0x27, Y2, Y7 + VPSLLQ $0x29, Y3, Y8 + VPSLLQ $0x02, Y4, Y9 + VPSRLQ $0x02, Y0, Y0 + VPSRLQ $0x09, Y1, Y1 + VPSRLQ $0x19, Y2, Y2 + VPSRLQ $0x17, Y3, Y3 + VPSRLQ $0x3e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 160(AX) + VMOVDQA Y6, 672(AX) + VMOVDQA Y7, 384(AX) + VMOVDQA Y8, 96(AX) + VMOVDQA Y9, 608(AX) + VMOVDQA (AX), Y0 + VMOVDQA 32(AX), Y1 + VMOVDQA 64(AX), Y2 + VMOVDQA 96(AX), Y3 + VMOVDQA 128(AX), Y4 + VPXOR 160(AX), Y0, Y0 + VPXOR 192(AX), Y1, Y1 + VPXOR 224(AX), Y2, Y2 + VPXOR 256(AX), Y3, Y3 + VPXOR 288(AX), Y4, Y4 + VPXOR 320(AX), Y0, Y0 + VPXOR 352(AX), Y1, Y1 + VPXOR 384(AX), Y2, Y2 + VPXOR 416(AX), Y3, Y3 + VPXOR 448(AX), Y4, Y4 + VPXOR 480(AX), Y0, Y0 + VPXOR 512(AX), Y1, Y1 + VPXOR 544(AX), Y2, Y2 + VPXOR 576(AX), Y3, Y3 + VPXOR 608(AX), Y4, Y4 + VPXOR 640(AX), Y0, Y0 + VPXOR 672(AX), Y1, Y1 + VPXOR 704(AX), Y2, Y2 + VPXOR 736(AX), Y3, Y3 + VPXOR 768(AX), Y4, Y4 + VPSLLQ $0x01, Y1, Y5 + VPSLLQ $0x01, Y2, Y6 + VPSLLQ $0x01, Y3, Y7 + VPSLLQ $0x01, Y4, Y8 + VPSLLQ $0x01, Y0, Y9 + VPSRLQ $0x3f, Y1, Y10 + VPSRLQ $0x3f, Y2, Y11 + VPSRLQ $0x3f, Y3, Y12 + VPSRLQ $0x3f, Y4, Y13 + VPSRLQ $0x3f, Y0, Y14 + VPOR Y5, Y10, Y10 + VPOR Y6, Y11, Y11 + VPOR Y7, Y12, Y12 + VPOR Y8, Y13, Y13 + VPOR Y9, Y14, Y14 + VPXOR Y10, Y4, Y10 + VPXOR Y11, Y0, Y11 + VPXOR Y12, Y1, Y12 + VPXOR Y13, Y2, Y13 + VPXOR Y14, Y3, Y14 + VPXOR (AX), Y10, Y0 + VPXOR 352(AX), Y11, Y1 + VPXOR 704(AX), Y12, Y2 + VPXOR 256(AX), Y13, Y3 + VPXOR 608(AX), Y14, Y4 + VPSLLQ $0x2c, Y1, Y6 + VPSLLQ $0x2b, Y2, Y7 + VPSLLQ $0x15, Y3, Y8 + VPSLLQ $0x0e, Y4, Y9 + VPSRLQ $0x14, Y1, Y1 + VPSRLQ $0x15, Y2, Y2 + VPSRLQ $0x2b, Y3, Y3 + VPSRLQ $0x32, Y4, Y4 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VPBROADCASTQ 16(CX), Y0 + VPXOR Y0, Y5, Y5 + VMOVDQA Y5, (AX) + VMOVDQA Y6, 352(AX) + VMOVDQA Y7, 704(AX) + VMOVDQA Y8, 256(AX) + VMOVDQA Y9, 608(AX) + VPXOR 736(AX), Y13, Y0 + VPXOR 288(AX), Y14, Y1 + VPXOR 480(AX), Y10, Y2 + VPXOR 32(AX), Y11, Y3 + VPXOR 384(AX), Y12, Y4 + VPSLLQ $0x1c, Y0, Y5 + VPSLLQ $0x14, Y1, Y6 + VPSLLQ $0x03, Y2, Y7 + VPSLLQ $0x2d, Y3, Y8 + VPSLLQ $0x3d, Y4, Y9 + VPSRLQ $0x24, Y0, Y0 + VPSRLQ $0x2c, Y1, Y1 + VPSRLQ $0x3d, Y2, Y2 + VPSRLQ $0x13, Y3, Y3 + VPSRLQ $0x03, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 480(AX) + VMOVDQA Y6, 32(AX) + VMOVDQA Y7, 384(AX) + VMOVDQA Y8, 736(AX) + VMOVDQA Y9, 288(AX) + VPXOR 512(AX), Y11, Y0 + VPXOR 64(AX), Y12, Y1 + VPXOR 416(AX), Y13, Y2 + VPXOR 768(AX), Y14, Y3 + VPXOR 160(AX), Y10, Y4 + VPSLLQ $0x01, Y0, Y5 + VPSLLQ $0x06, Y1, Y6 + VPSLLQ $0x19, Y2, Y7 + VPSLLQ $0x08, Y3, Y8 + VPSLLQ $0x12, Y4, Y9 + VPSRLQ $0x3f, Y0, Y0 + VPSRLQ $0x3a, Y1, Y1 + VPSRLQ $0x27, Y2, Y2 + VPSRLQ $0x38, Y3, Y3 + VPSRLQ $0x2e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 160(AX) + VMOVDQA Y6, 512(AX) + VMOVDQA Y7, 64(AX) + VMOVDQA Y8, 416(AX) + VMOVDQA Y9, 768(AX) + VPXOR 448(AX), Y14, Y0 + VPXOR 640(AX), Y10, Y1 + VPXOR 192(AX), Y11, Y2 + VPXOR 544(AX), Y12, Y3 + VPXOR 96(AX), Y13, Y4 + VPSLLQ $0x1b, Y0, Y5 + VPSLLQ $0x24, Y1, Y6 + VPSLLQ $0x0a, Y2, Y7 + VPSLLQ $0x0f, Y3, Y8 + VPSLLQ $0x38, Y4, Y9 + VPSRLQ $0x25, Y0, Y0 + VPSRLQ $0x1c, Y1, Y1 + VPSRLQ $0x36, Y2, Y2 + VPSRLQ $0x31, Y3, Y3 + VPSRLQ $0x08, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 640(AX) + VMOVDQA Y6, 192(AX) + VMOVDQA Y7, 544(AX) + VMOVDQA Y8, 96(AX) + VMOVDQA Y9, 448(AX) + VPXOR 224(AX), Y12, Y0 + VPXOR 576(AX), Y13, Y1 + VPXOR 128(AX), Y14, Y2 + VPXOR 320(AX), Y10, Y3 + VPXOR 672(AX), Y11, Y4 + VPSLLQ $0x3e, Y0, Y5 + VPSLLQ $0x37, Y1, Y6 + VPSLLQ $0x27, Y2, Y7 + VPSLLQ $0x29, Y3, Y8 + VPSLLQ $0x02, Y4, Y9 + VPSRLQ $0x02, Y0, Y0 + VPSRLQ $0x09, Y1, Y1 + VPSRLQ $0x19, Y2, Y2 + VPSRLQ $0x17, Y3, Y3 + VPSRLQ $0x3e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 320(AX) + VMOVDQA Y6, 672(AX) + VMOVDQA Y7, 224(AX) + VMOVDQA Y8, 576(AX) + VMOVDQA Y9, 128(AX) + VMOVDQA (AX), Y0 + VMOVDQA 32(AX), Y1 + VMOVDQA 64(AX), Y2 + VMOVDQA 96(AX), Y3 + VMOVDQA 128(AX), Y4 + VPXOR 160(AX), Y0, Y0 + VPXOR 192(AX), Y1, Y1 + VPXOR 224(AX), Y2, Y2 + VPXOR 256(AX), Y3, Y3 + VPXOR 288(AX), Y4, Y4 + VPXOR 320(AX), Y0, Y0 + VPXOR 352(AX), Y1, Y1 + VPXOR 384(AX), Y2, Y2 + VPXOR 416(AX), Y3, Y3 + VPXOR 448(AX), Y4, Y4 + VPXOR 480(AX), Y0, Y0 + VPXOR 512(AX), Y1, Y1 + VPXOR 544(AX), Y2, Y2 + VPXOR 576(AX), Y3, Y3 + VPXOR 608(AX), Y4, Y4 + VPXOR 640(AX), Y0, Y0 + VPXOR 672(AX), Y1, Y1 + VPXOR 704(AX), Y2, Y2 + VPXOR 736(AX), Y3, Y3 + VPXOR 768(AX), Y4, Y4 + VPSLLQ $0x01, Y1, Y5 + VPSLLQ $0x01, Y2, Y6 + VPSLLQ $0x01, Y3, Y7 + VPSLLQ $0x01, Y4, Y8 + VPSLLQ $0x01, Y0, Y9 + VPSRLQ $0x3f, Y1, Y10 + VPSRLQ $0x3f, Y2, Y11 + VPSRLQ $0x3f, Y3, Y12 + VPSRLQ $0x3f, Y4, Y13 + VPSRLQ $0x3f, Y0, Y14 + VPOR Y5, Y10, Y10 + VPOR Y6, Y11, Y11 + VPOR Y7, Y12, Y12 + VPOR Y8, Y13, Y13 + VPOR Y9, Y14, Y14 + VPXOR Y10, Y4, Y10 + VPXOR Y11, Y0, Y11 + VPXOR Y12, Y1, Y12 + VPXOR Y13, Y2, Y13 + VPXOR Y14, Y3, Y14 + VPXOR (AX), Y10, Y0 + VPXOR 32(AX), Y11, Y1 + VPXOR 64(AX), Y12, Y2 + VPXOR 96(AX), Y13, Y3 + VPXOR 128(AX), Y14, Y4 + VPSLLQ $0x2c, Y1, Y6 + VPSLLQ $0x2b, Y2, Y7 + VPSLLQ $0x15, Y3, Y8 + VPSLLQ $0x0e, Y4, Y9 + VPSRLQ $0x14, Y1, Y1 + VPSRLQ $0x15, Y2, Y2 + VPSRLQ $0x2b, Y3, Y3 + VPSRLQ $0x32, Y4, Y4 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VPBROADCASTQ 24(CX), Y0 + VPXOR Y0, Y5, Y5 + VMOVDQA Y5, (AX) + VMOVDQA Y6, 32(AX) + VMOVDQA Y7, 64(AX) + VMOVDQA Y8, 96(AX) + VMOVDQA Y9, 128(AX) + VPXOR 256(AX), Y13, Y0 + VPXOR 288(AX), Y14, Y1 + VPXOR 160(AX), Y10, Y2 + VPXOR 192(AX), Y11, Y3 + VPXOR 224(AX), Y12, Y4 + VPSLLQ $0x1c, Y0, Y5 + VPSLLQ $0x14, Y1, Y6 + VPSLLQ $0x03, Y2, Y7 + VPSLLQ $0x2d, Y3, Y8 + VPSLLQ $0x3d, Y4, Y9 + VPSRLQ $0x24, Y0, Y0 + VPSRLQ $0x2c, Y1, Y1 + VPSRLQ $0x3d, Y2, Y2 + VPSRLQ $0x13, Y3, Y3 + VPSRLQ $0x03, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 160(AX) + VMOVDQA Y6, 192(AX) + VMOVDQA Y7, 224(AX) + VMOVDQA Y8, 256(AX) + VMOVDQA Y9, 288(AX) + VPXOR 352(AX), Y11, Y0 + VPXOR 384(AX), Y12, Y1 + VPXOR 416(AX), Y13, Y2 + VPXOR 448(AX), Y14, Y3 + VPXOR 320(AX), Y10, Y4 + VPSLLQ $0x01, Y0, Y5 + VPSLLQ $0x06, Y1, Y6 + VPSLLQ $0x19, Y2, Y7 + VPSLLQ $0x08, Y3, Y8 + VPSLLQ $0x12, Y4, Y9 + VPSRLQ $0x3f, Y0, Y0 + VPSRLQ $0x3a, Y1, Y1 + VPSRLQ $0x27, Y2, Y2 + VPSRLQ $0x38, Y3, Y3 + VPSRLQ $0x2e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 320(AX) + VMOVDQA Y6, 352(AX) + VMOVDQA Y7, 384(AX) + VMOVDQA Y8, 416(AX) + VMOVDQA Y9, 448(AX) + VPXOR 608(AX), Y14, Y0 + VPXOR 480(AX), Y10, Y1 + VPXOR 512(AX), Y11, Y2 + VPXOR 544(AX), Y12, Y3 + VPXOR 576(AX), Y13, Y4 + VPSLLQ $0x1b, Y0, Y5 + VPSLLQ $0x24, Y1, Y6 + VPSLLQ $0x0a, Y2, Y7 + VPSLLQ $0x0f, Y3, Y8 + VPSLLQ $0x38, Y4, Y9 + VPSRLQ $0x25, Y0, Y0 + VPSRLQ $0x1c, Y1, Y1 + VPSRLQ $0x36, Y2, Y2 + VPSRLQ $0x31, Y3, Y3 + VPSRLQ $0x08, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 480(AX) + VMOVDQA Y6, 512(AX) + VMOVDQA Y7, 544(AX) + VMOVDQA Y8, 576(AX) + VMOVDQA Y9, 608(AX) + VPXOR 704(AX), Y12, Y0 + VPXOR 736(AX), Y13, Y1 + VPXOR 768(AX), Y14, Y2 + VPXOR 640(AX), Y10, Y3 + VPXOR 672(AX), Y11, Y4 + VPSLLQ $0x3e, Y0, Y5 + VPSLLQ $0x37, Y1, Y6 + VPSLLQ $0x27, Y2, Y7 + VPSLLQ $0x29, Y3, Y8 + VPSLLQ $0x02, Y4, Y9 + VPSRLQ $0x02, Y0, Y0 + VPSRLQ $0x09, Y1, Y1 + VPSRLQ $0x19, Y2, Y2 + VPSRLQ $0x17, Y3, Y3 + VPSRLQ $0x3e, Y4, Y4 + VPOR Y5, Y0, Y0 + VPOR Y6, Y1, Y1 + VPOR Y7, Y2, Y2 + VPOR Y8, Y3, Y3 + VPOR Y9, Y4, Y4 + VPANDN Y2, Y1, Y5 + VPANDN Y3, Y2, Y6 + VPANDN Y4, Y3, Y7 + VPANDN Y0, Y4, Y8 + VPANDN Y1, Y0, Y9 + VPXOR Y0, Y5, Y5 + VPXOR Y1, Y6, Y6 + VPXOR Y2, Y7, Y7 + VPXOR Y3, Y8, Y8 + VPXOR Y4, Y9, Y9 + VMOVDQA Y5, 640(AX) + VMOVDQA Y6, 672(AX) + VMOVDQA Y7, 704(AX) + VMOVDQA Y8, 736(AX) + VMOVDQA Y9, 768(AX) + ADDQ $0x20, CX + SUBQ $0x00000001, DX + JNZ loop + RET diff --git a/src/circl/simd/keccakf1600/f1600x4stubs_amd64.go b/src/circl/simd/keccakf1600/f1600x4stubs_amd64.go new file mode 100644 index 00000000000..2d633dbf49d --- /dev/null +++ b/src/circl/simd/keccakf1600/f1600x4stubs_amd64.go @@ -0,0 +1,8 @@ +// Code generated by command: go run src.go -out ../../f1600x4_amd64.s -stubs ../../f1600x4stubs_amd64.go -pkg keccakf1600. DO NOT EDIT. + +// +build amd64 + +package keccakf1600 + +//go:noescape +func f1600x4AVX2(state *uint64, rc *[24]uint64) diff --git a/src/circl/simd/keccakf1600/f1600x_test.go b/src/circl/simd/keccakf1600/f1600x_test.go new file mode 100644 index 00000000000..09e83bba6dd --- /dev/null +++ b/src/circl/simd/keccakf1600/f1600x_test.go @@ -0,0 +1,98 @@ +package keccakf1600 + +import "testing" + +// From the Keccak code package. +var permutationOfZeroes = [25]uint64{ + 0xF1258F7940E1DDE7, 0x84D5CCF933C0478A, 0xD598261EA65AA9EE, + 0xBD1547306F80494D, 0x8B284E056253D057, 0xFF97A42D7F8E6FD4, + 0x90FEE5A0A44647C4, 0x8C5BDA0CD6192E76, 0xAD30A6F71B19059C, + 0x30935AB7D08FFC64, 0xEB5AA93F2317D635, 0xA9A6E6260D712103, + 0x81A57C16DBCF555F, 0x43B831CD0347C826, 0x01F22F1A11A5569F, + 0x05E5635A21D9AE61, 0x64BEFEF28CC970F2, 0x613670957BC46611, + 0xB87C5A554FD00ECB, 0x8C3EE88A1CCF32C8, 0x940C7922AE3A2614, + 0x1841F924A2C509E4, 0x16F53526E70465C2, 0x75F644E97F30A13B, + 0xEAF1FF7B5CECA249, +} + +func TestKeccakF1600x2(t *testing.T) { + test := func(t *testing.T, f func(s *StateX2, a []uint64)) { + t.Helper() + var state StateX2 + a := state.Initialize() + f(&state, a) + for i := 0; i < 25; i++ { + for j := 0; j < 2; j++ { + if a[2*i+j] != permutationOfZeroes[i] { + t.Fatalf("%X", a) + } + } + } + } + + t.Run("Generic", func(t *testing.T) { + test(t, func(s *StateX2, a []uint64) { permuteScalarX2(a) }) + }) + t.Run("SIMD", func(t *testing.T) { + test(t, func(s *StateX2, a []uint64) { s.Permute() }) + }) +} + +func TestKeccakF1600x4(t *testing.T) { + test := func(t *testing.T, f func(s *StateX4, a []uint64)) { + t.Helper() + var state StateX4 + a := state.Initialize() + f(&state, a) + for i := 0; i < 25; i++ { + for j := 0; j < 4; j++ { + if a[4*i+j] != permutationOfZeroes[i] { + t.Fatal() + } + } + } + } + + t.Run("Generic", func(t *testing.T) { + test(t, func(s *StateX4, a []uint64) { permuteScalarX4(a) }) + }) + t.Run("SIMD", func(t *testing.T) { + test(t, func(s *StateX4, a []uint64) { s.Permute() }) + }) +} + +func BenchmarkF1600x2(b *testing.B) { + benchmark := func(b *testing.B, f func(s *StateX2, a []uint64)) { + var state StateX2 + a := state.Initialize() + + for i := 0; i < b.N; i++ { + f(&state, a) + } + } + + b.Run("Generic", func(b *testing.B) { + benchmark(b, func(s *StateX2, a []uint64) { permuteScalarX2(a) }) + }) + b.Run("SIMD", func(b *testing.B) { + benchmark(b, func(s *StateX2, a []uint64) { s.Permute() }) + }) +} + +func BenchmarkF1600x4(b *testing.B) { + benchmark := func(b *testing.B, f func(s *StateX4, a []uint64)) { + var state StateX4 + a := state.Initialize() + + for i := 0; i < b.N; i++ { + f(&state, a) + } + } + + b.Run("Generic", func(b *testing.B) { + benchmark(b, func(s *StateX4, a []uint64) { permuteScalarX4(a) }) + }) + b.Run("SIMD", func(b *testing.B) { + benchmark(b, func(s *StateX4, a []uint64) { s.Permute() }) + }) +} diff --git a/src/circl/simd/keccakf1600/fallback.go b/src/circl/simd/keccakf1600/fallback.go new file mode 100644 index 00000000000..70b3070bd63 --- /dev/null +++ b/src/circl/simd/keccakf1600/fallback.go @@ -0,0 +1,7 @@ +// +build !amd64,!arm64 arm64,!go1.16 + +package keccakf1600 + +func permuteSIMDx2(state []uint64) { permuteScalarX2(state) } + +func permuteSIMDx4(state []uint64) { permuteScalarX4(state) } diff --git a/src/cmd/go/internal/imports/tags.go b/src/cmd/go/internal/imports/tags.go index 01b448b9142..277c36ab7fe 100644 --- a/src/cmd/go/internal/imports/tags.go +++ b/src/cmd/go/internal/imports/tags.go @@ -39,6 +39,7 @@ func loadTags() map[string]bool { for _, tag := range cfg.BuildContext.ReleaseTags { tags[tag] = true } + tags["cfgo"] = true return tags } diff --git a/src/crypto/kem/kem.go b/src/crypto/kem/kem.go new file mode 100644 index 00000000000..1c49523af29 --- /dev/null +++ b/src/crypto/kem/kem.go @@ -0,0 +1,203 @@ +package kem + +import ( + "circl/dh/sidh" + "circl/kem/schemes" + "errors" + "fmt" + "io" + + "golang.org/x/crypto/cryptobyte" + "golang.org/x/crypto/curve25519" +) + +// ID identifies each type of KEM. +type ID uint16 + +const ( + // KEM25519 is X25519 as a KEM. Not quantum-safe. + KEM25519 ID = 0x01fb + // Kyber512 is a post-quantum KEM, as defined in: https://pq-crystals.org/kyber/ . + Kyber512 ID = 0x01fc + // SIKEp434 is a post-quantum KEM, as defined in: https://sike.org/ . + SIKEp434 ID = 0x01fd +) + +// PrivateKey is a KEM private key. +type PrivateKey struct { + KEMId ID + PrivateKey []byte +} + +// PublicKey is a KEM public key. +type PublicKey struct { + KEMId ID + PublicKey []byte +} + +// MarshalBinary returns the byte representation of a KEM public key. +func (pubKey *PublicKey) MarshalBinary() ([]byte, error) { + var b cryptobyte.Builder + + b.AddUint16(uint16(pubKey.KEMId)) + b.AddBytes(pubKey.PublicKey) + + return b.BytesOrPanic(), nil +} + +// UnmarshalBinary produces a PublicKey from a byte array. +func (pubKey *PublicKey) UnmarshalBinary(raw []byte) error { + s := cryptobyte.String(raw) + + var id uint16 + if !s.ReadUint16(&id) { + return errors.New("crypto/kem: invalid algorithm") + } + + kemID := ID(id) + pubKey.KEMId = kemID + pubKey.PublicKey = raw[2:] + return nil +} + +// GenerateKey generates a keypair for a given KEM. +// It returns a KEM public and private key. +func GenerateKey(rand io.Reader, kemID ID) (*PublicKey, *PrivateKey, error) { + switch kemID { + case Kyber512: + scheme := schemes.ByName("Kyber512") + seed := make([]byte, scheme.SeedSize()) + if _, err := io.ReadFull(rand, seed); err != nil { + return nil, nil, err + } + publicKey, privateKey := scheme.DeriveKeyPair(seed) + pk, _ := publicKey.MarshalBinary() + sk, _ := privateKey.MarshalBinary() + + return &PublicKey{KEMId: kemID, PublicKey: pk}, &PrivateKey{KEMId: kemID, PrivateKey: sk}, nil + case KEM25519: + privateKey := make([]byte, curve25519.ScalarSize) + if _, err := io.ReadFull(rand, privateKey); err != nil { + return nil, nil, err + } + publicKey, err := curve25519.X25519(privateKey, curve25519.Basepoint) + if err != nil { + return nil, nil, err + } + return &PublicKey{KEMId: kemID, PublicKey: publicKey}, &PrivateKey{KEMId: kemID, PrivateKey: privateKey}, nil + case SIKEp434: + privateKey := sidh.NewPrivateKey(sidh.Fp434, sidh.KeyVariantSike) + publicKey := sidh.NewPublicKey(sidh.Fp434, sidh.KeyVariantSike) + if err := privateKey.Generate(rand); err != nil { + return nil, nil, err + } + privateKey.GeneratePublicKey(publicKey) + + pubBytes := make([]byte, publicKey.Size()) + privBytes := make([]byte, privateKey.Size()) + publicKey.Export(pubBytes) + privateKey.Export(privBytes) + return &PublicKey{KEMId: kemID, PublicKey: pubBytes}, &PrivateKey{KEMId: kemID, PrivateKey: privBytes}, nil + default: + return nil, nil, fmt.Errorf("crypto/kem: internal error: unsupported KEM %d", kemID) + } +} + +// Encapsulate returns a shared secret and a ciphertext. +func Encapsulate(rand io.Reader, pk *PublicKey) (sharedSecret []byte, ciphertext []byte, err error) { + switch pk.KEMId { + case Kyber512: + scheme := schemes.ByName("Kyber512") + pub, err := scheme.UnmarshalBinaryPublicKey(pk.PublicKey) + if err != nil { + return nil, nil, err + } + + seed := make([]byte, scheme.EncapsulationSeedSize()) + if _, err := io.ReadFull(rand, seed); err != nil { + return nil, nil, err + } + + ct, ss, err := scheme.EncapsulateDeterministically(pub, seed) + if err != nil { + return nil, nil, err + } + return ss, ct, nil + case KEM25519: + privateKey := make([]byte, curve25519.ScalarSize) + if _, err := io.ReadFull(rand, privateKey); err != nil { + return nil, nil, err + } + ciphertext, err := curve25519.X25519(privateKey, curve25519.Basepoint) + if err != nil { + return nil, nil, err + } + sharedSecret, err := curve25519.X25519(privateKey, pk.PublicKey) + if err != nil { + return nil, nil, err + } + return sharedSecret, ciphertext, nil + case SIKEp434: + kem := sidh.NewSike434(rand) + sikepk := sidh.NewPublicKey(sidh.Fp434, sidh.KeyVariantSike) + err := sikepk.Import(pk.PublicKey) + if err != nil { + return nil, nil, err + } + + ct := make([]byte, kem.CiphertextSize()) + ss := make([]byte, kem.SharedSecretSize()) + err = kem.Encapsulate(ct, ss, sikepk) + if err != nil { + return nil, nil, err + } + return ss, ct, nil + default: + return nil, nil, errors.New("crypto/kem: internal error: unsupported KEM in Encapsulate") + } +} + +// Decapsulate returns the shared secret given the private key and the ciphertext. +func Decapsulate(privateKey *PrivateKey, ciphertext []byte) (sharedSecret []byte, err error) { + switch privateKey.KEMId { + case Kyber512: + scheme := schemes.ByName("Kyber512") + sk, err := scheme.UnmarshalBinaryPrivateKey(privateKey.PrivateKey) + if err != nil { + return nil, err + } + if len(ciphertext) != scheme.CiphertextSize() { + return nil, fmt.Errorf("crypto/kem: ciphertext is of len %d, expected %d", len(ciphertext), scheme.CiphertextSize()) + } + ss, err := scheme.Decapsulate(sk, ciphertext) + if err != nil { + return nil, err + } + return ss, nil + case KEM25519: + sharedSecret, err := curve25519.X25519(privateKey.PrivateKey, ciphertext) + if err != nil { + return nil, err + } + return sharedSecret, nil + case SIKEp434: + kem := sidh.NewSike434(nil) + sikesk := sidh.NewPrivateKey(sidh.Fp434, sidh.KeyVariantSike) + err := sikesk.Import(privateKey.PrivateKey) + if err != nil { + return nil, err + } + + sikepk := sidh.NewPublicKey(sidh.Fp434, sidh.KeyVariantSike) + sikesk.GeneratePublicKey(sikepk) + ss := make([]byte, kem.SharedSecretSize()) + err = kem.Decapsulate(ss, sikesk, sikepk, ciphertext) + if err != nil { + return nil, err + } + + return ss, nil + default: + return nil, errors.New("crypto/kem: internal error: unsupported KEM in Decapsulate") + } +} diff --git a/src/crypto/kem/kem_test.go b/src/crypto/kem/kem_test.go new file mode 100644 index 00000000000..5828c0d6c14 --- /dev/null +++ b/src/crypto/kem/kem_test.go @@ -0,0 +1,57 @@ +package kem + +import ( + "bytes" + "crypto/rand" + "testing" +) + +func TestKemAPI(t *testing.T) { + tests := []struct { + name string + kemID ID + }{ + {"Kem25519", KEM25519}, + {"SIKEp434", SIKEp434}, + {"Kyber512", Kyber512}, + } + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + publicKey, privateKey, err := GenerateKey(rand.Reader, tt.kemID) + if err != nil { + t.Fatal(err) + } + ss, ct, err := Encapsulate(rand.Reader, publicKey) + if err != nil { + t.Fatal(err) + } + + ss2, err := Decapsulate(privateKey, ct) + if err != nil { + t.Fatal(err) + } + if !bytes.Equal(ss, ss2) { + t.Fatal("Decapsulated a differing shared secret") + } + + data, _ := publicKey.MarshalBinary() + pk2 := new(PublicKey) + err = pk2.UnmarshalBinary(data) + if err != nil { + t.Fatal("error unmarshaling") + } + if pk2.KEMId != publicKey.KEMId { + t.Fatal("error unmarshaling: difference in Id") + } + if !bytes.Equal(publicKey.PublicKey, publicKey.PublicKey) { + t.Fatal("error unmarshaling: difference in public keys") + } + }) + } + + // check if a nonexisting kem fails + invalidKemID := ID(0) + if _, _, err := GenerateKey(rand.Reader, invalidKemID); err == nil { + t.Fatal("This KEM ID should've been invalid and failed") + } +} diff --git a/src/crypto/tls/alert.go b/src/crypto/tls/alert.go index 4790b737245..755083b866c 100644 --- a/src/crypto/tls/alert.go +++ b/src/crypto/tls/alert.go @@ -48,6 +48,7 @@ const ( alertUnknownPSKIdentity alert = 115 alertCertificateRequired alert = 116 alertNoApplicationProtocol alert = 120 + alertECHRequired alert = 121 ) var alertText = map[alert]string{ @@ -84,6 +85,7 @@ var alertText = map[alert]string{ alertUnknownPSKIdentity: "unknown PSK identity", alertCertificateRequired: "certificate required", alertNoApplicationProtocol: "no application protocol", + alertECHRequired: "ECH required", } func (e alert) String() string { diff --git a/src/crypto/tls/auth.go b/src/crypto/tls/auth.go index a9df0da6d62..c40fdaec16b 100644 --- a/src/crypto/tls/auth.go +++ b/src/crypto/tls/auth.go @@ -5,11 +5,15 @@ package tls import ( + circlPki "circl/pki" + circlSign "circl/sign" + "bytes" "crypto" "crypto/ecdsa" "crypto/ed25519" "crypto/elliptic" + "crypto/kem" "crypto/rsa" "errors" "fmt" @@ -55,7 +59,17 @@ func verifyHandshakeSignature(sigType uint8, pubkey crypto.PublicKey, hashFunc c return err } default: - return errors.New("internal error: unknown signature type") + scheme := circlSchemeBySigType(sigType) + if scheme == nil { + return errors.New("internal error: unknown signature type") + } + pubKey, ok := pubkey.(circlSign.PublicKey) + if !ok { + return fmt.Errorf("expected a %s public key, got %T", scheme.Name(), pubkey) + } + if !scheme.Verify(pubKey, signed, sig, nil) { + return fmt.Errorf("%s verification failure", scheme.Name()) + } } return nil } @@ -105,8 +119,24 @@ func typeAndHashFromSignatureScheme(signatureAlgorithm SignatureScheme) (sigType sigType = signatureECDSA case Ed25519: sigType = signatureEd25519 + case Ed448: + sigType = signatureEd448 + case KEMTLSWithSIKEp434, KEMTLSWithKyber512: + sigType = authKEMTLS + case PQTLSWithDilithium3: + sigType = signatureEdDilithium3 + case PQTLSWithDilithium4: + sigType = signatureEdDilithium4 default: - return 0, 0, fmt.Errorf("unsupported signature algorithm: %v", signatureAlgorithm) + scheme := circlPki.SchemeByTLSID(uint(signatureAlgorithm)) + if scheme == nil { + return 0, 0, fmt.Errorf("unsupported signature algorithm: %v", signatureAlgorithm) + } + sigType = sigTypeByCirclScheme(scheme) + if sigType == 0 { + return 0, 0, fmt.Errorf("circl scheme %s not supported", + scheme.Name()) + } } switch signatureAlgorithm { case PKCS1WithSHA1, ECDSAWithSHA1: @@ -117,10 +147,18 @@ func typeAndHashFromSignatureScheme(signatureAlgorithm SignatureScheme) (sigType hash = crypto.SHA384 case PKCS1WithSHA512, PSSWithSHA512, ECDSAWithP521AndSHA512: hash = crypto.SHA512 - case Ed25519: + case Ed25519, Ed448: + hash = directSigning + case KEMTLSWithSIKEp434, KEMTLSWithKyber512: + hash = directSigning + case PQTLSWithDilithium3, PQTLSWithDilithium4: hash = directSigning default: - return 0, 0, fmt.Errorf("unsupported signature algorithm: %v", signatureAlgorithm) + scheme := circlPki.SchemeByTLSID(uint(signatureAlgorithm)) + if scheme == nil { + return 0, 0, fmt.Errorf("unsupported signature algorithm: %v", signatureAlgorithm) + } + hash = directSigning } return sigType, hash, nil } @@ -140,6 +178,8 @@ func legacyTypeAndHashFromPublicKey(pub crypto.PublicKey) (sigType uint8, hash c // full signature, and not even OpenSSL bothers with the // complexity, so we can't even test it properly. return 0, 0, fmt.Errorf("tls: Ed25519 public keys are not supported before TLS 1.2") + case circlSign.PublicKey: + return 0, 0, fmt.Errorf("tls: circl public keys are not supported before TLS 1.2") default: return 0, 0, fmt.Errorf("tls: unsupported public key: %T", pub) } @@ -209,6 +249,13 @@ func signatureSchemesForCertificate(version uint16, cert *Certificate) []Signatu } case ed25519.PublicKey: sigAlgs = []SignatureScheme{Ed25519} + case circlSign.PublicKey: + scheme := pub.Scheme() + tlsScheme, ok := scheme.(circlPki.TLSScheme) + if !ok { + return nil + } + sigAlgs = []SignatureScheme{SignatureScheme(tlsScheme.TLSIdentifier())} default: return nil } @@ -225,6 +272,87 @@ func signatureSchemesForCertificate(version uint16, cert *Certificate) []Signatu return sigAlgs } +// signatureSchemeForDelegatedCredential returns the list of supported +// SignatureSchemes for a given delegated credential, based on the public +// key, and optionally filtered by its explicit +// SupportedSignatureAlgorithmsDC. +// +// This function must be kept in sync with supportedSignatureAlgorithmsDC. +func signatureSchemeForDelegatedCredential(version uint16, dc *DelegatedCredential) []SignatureScheme { + pub := dc.cred.publicKey + var sigAlgs []SignatureScheme + + switch pub.(type) { + case *kem.PublicKey: + pk, ok := pub.(*kem.PublicKey) + if !ok { + return nil + } + switch pk.KEMId { + case kem.SIKEp434: + sigAlgs = []SignatureScheme{KEMTLSWithSIKEp434} + case kem.Kyber512: + sigAlgs = []SignatureScheme{KEMTLSWithKyber512} + default: + return nil + } + case *ecdsa.PublicKey: + pk, ok := pub.(*ecdsa.PublicKey) + if !ok { + return nil + } + switch pk.Curve { + case elliptic.P256(): + sigAlgs = []SignatureScheme{ECDSAWithP256AndSHA256} + case elliptic.P384(): + sigAlgs = []SignatureScheme{ECDSAWithP384AndSHA384} + case elliptic.P521(): + sigAlgs = []SignatureScheme{ECDSAWithP521AndSHA512} + default: + return nil + } + case ed25519.PublicKey: + sigAlgs = []SignatureScheme{Ed25519} + case circlSign.PublicKey: + pk, ok := pub.(circlSign.PublicKey) + if !ok { + return nil + } + scheme := pk.Scheme() + tlsScheme, ok := scheme.(circlPki.TLSScheme) + if !ok { + return nil + } + sigAlgs = []SignatureScheme{SignatureScheme(tlsScheme.TLSIdentifier())} + default: + return nil + } + + return sigAlgs +} + +// selectSignatureSchemeDC picks a SignatureScheme from the peer's preference list +// that works with the selected delegated credential. It's only called for protocol +// versions that support delegated credential, so TLS 1.3. +func selectSignatureSchemeDC(vers uint16, dc *DelegatedCredential, peerAlgs []SignatureScheme) (SignatureScheme, error) { + if vers != VersionTLS13 { + return 0, errors.New("unsupported TLS version for dc") + } + + supportedAlgs := signatureSchemeForDelegatedCredential(vers, dc) + if len(supportedAlgs) == 0 { + return 0, errors.New("unsupported scheme for dc") + } + // Pick signature scheme in the peer's preference order, as our + // preference order is not configurable. + for _, preferredAlg := range peerAlgs { + if isSupportedSignatureAlgorithm(preferredAlg, supportedAlgs) { + return preferredAlg, nil + } + } + return 0, errors.New("tls: peer doesn't support any of the delegated credential's signature algorithms") +} + // selectSignatureScheme picks a SignatureScheme from the peer's preference list // that works with the selected certificate. It's only called for protocol // versions that support signature algorithms, so TLS 1.2 and 1.3. diff --git a/src/crypto/tls/auth_test.go b/src/crypto/tls/auth_test.go index c42e3491e46..c885f91e331 100644 --- a/src/crypto/tls/auth_test.go +++ b/src/crypto/tls/auth_test.go @@ -7,6 +7,8 @@ package tls import ( "crypto" "testing" + + circlPki "circl/pki" ) func TestSignatureSelection(t *testing.T) { @@ -161,7 +163,7 @@ func TestSupportedSignatureAlgorithms(t *testing.T) { if sigType == 0 { t.Errorf("%v: missing signature type", sigAlg) } - if hash == 0 && sigAlg != Ed25519 { + if hash == 0 && (sigAlg != Ed25519 && sigType != authKEMTLS) && circlPki.SchemeByTLSID(uint(sigAlg)) == nil { t.Errorf("%v: missing hash", sigAlg) } } diff --git a/src/crypto/tls/common.go b/src/crypto/tls/common.go index eec6e1ebbd9..cba250159f2 100644 --- a/src/crypto/tls/common.go +++ b/src/crypto/tls/common.go @@ -11,6 +11,7 @@ import ( "crypto/ecdsa" "crypto/ed25519" "crypto/elliptic" + "crypto/kem" "crypto/rand" "crypto/rsa" "crypto/sha512" @@ -92,6 +93,8 @@ const ( extensionSignatureAlgorithms uint16 = 13 extensionALPN uint16 = 16 extensionSCT uint16 = 18 + extensionCachedInfo uint16 = 25 + extensionDelegatedCredentials uint16 = 34 extensionSessionTicket uint16 = 35 extensionPreSharedKey uint16 = 41 extensionEarlyData uint16 = 42 @@ -102,6 +105,10 @@ const ( extensionSignatureAlgorithmsCert uint16 = 50 extensionKeyShare uint16 = 51 extensionRenegotiationInfo uint16 = 0xff01 + extensionECH uint16 = 0xfe0a // draft-ietf-tls-esni-10 + extensionECHIsInner uint16 = 0xda09 // draft-ietf-tls-esni-10 + extensionECHOuterExtensions uint16 = 0xfd00 // draft-ietf-tls-esni-10 + extensionPDKKEMTLS uint16 = 0xfd01 // arbitraly chosen ) // TLS signaling cipher suite values @@ -121,8 +128,18 @@ const ( CurveP384 CurveID = 24 CurveP521 CurveID = 25 X25519 CurveID = 29 + SIKEp434 CurveID = CurveID(kem.SIKEp434) + Kyber512 CurveID = CurveID(kem.Kyber512) ) +func (curve CurveID) isKEM() bool { + switch curve { + case SIKEp434, Kyber512: + return true + } + return false +} + // TLS 1.3 Key Share. See RFC 8446, Section 4.2.8. type keyShare struct { group CurveID @@ -166,6 +183,10 @@ const ( signatureRSAPSS signatureECDSA signatureEd25519 + signatureEd448 + signatureEdDilithium3 + signatureEdDilithium4 + authKEMTLS // for the KEMTLS ) // directSigning is a standard Hash value that signals that no pre-hashing @@ -192,6 +213,27 @@ var supportedSignatureAlgorithms = []SignatureScheme{ ECDSAWithSHA1, } +// supportedSignatureAlgorithmsDC contains the signature and hash algorithms that +// the code advertises as supported in a TLS 1.3 ClientHello and in a TLS 1.3 +// CertificateRequest. This excludes 'rsa_pss_rsae_' algorithms. +var supportedSignatureAlgorithmsDC = []SignatureScheme{ + ECDSAWithP256AndSHA256, + Ed25519, + Ed448, + ECDSAWithP384AndSHA384, + ECDSAWithP521AndSHA512, + + // authentication algorithms for KEMTLS. They are restricted for usage with Delegated + // Credentials. + KEMTLSWithKyber512, + KEMTLSWithSIKEp434, + + // authentication algorithms for PQTLS. They are restricted for usage with Delegated + // Credentials. + PQTLSWithDilithium3, + PQTLSWithDilithium4, +} + // helloRetryRequestRandom is set as the Random value of a ServerHello // to signal that the message is actually a HelloRetryRequest. var helloRetryRequestRandom = []byte{ // See RFC 8446, Section 4.1.3. @@ -213,6 +255,49 @@ const ( // include downgrade canaries even if it's using its highers supported version. var testingOnlyForceDowngradeCanary bool +// testingTriggerHRR causes the server to intentionally trigger a +// HelloRetryRequest (HRR). This is useful for testing new TLS features that +// change the HRR codepath. +var testingTriggerHRR bool + +// testingECHTriggerBypassAfterHRR causes the client to bypass ECH after HRR. +// If available, the client will offer ECH in the first CH only. +var testingECHTriggerBypassAfterHRR bool + +// testingECHTriggerBypassBeforeHRR causes the client to bypass ECH before HRR. +// The client will offer ECH in the second CH only. +var testingECHTriggerBypassBeforeHRR bool + +// testingECHIllegalHandleAfterHRR causes the client to illegally change the ECH +// extension after HRR. +var testingECHIllegalHandleAfterHRR bool + +// testingECHTriggerPayloadDecryptError causes the client to to send an +// inauthentic payload. +var testingECHTriggerPayloadDecryptError bool + +// testingECHOuterExtMany causes a client to incorporate a sequence of +// outer extensions into the ClientHelloInner when it offers the ECH extension. +// The "key_share" extension is the only incorporated extension by default. +var testingECHOuterExtMany bool + +// testingECHOuterExtNone causes a client to not use the "outer_extension" +// mechanism for ECH. The "key_shares" extension is incorporated by default. +var testingECHOuterExtNone bool + +// testingECHOuterExtIncorrectOrder causes the client to send the +// "outer_extension" extension in the wrong order when offering the ECH +// extension. +var testingECHOuterExtIncorrectOrder bool + +// testingECHOuterIsInner causes the client to send the "ech_is_inner" extension +// in the ClientHelloOuter. +var testingECHOuterIsInner bool + +// testingECHOuterExtIllegal causes the client to send in its +// "outer_extension" extension the codepoint for the ECH extension. +var testingECHOuterExtIllegal bool + // ConnectionState records basic TLS details about the connection. type ConnectionState struct { // Version is the TLS version used by the connection (e.g. VersionTLS12). @@ -259,6 +344,26 @@ type ConnectionState struct { // (and the peer provided a certificate) or RequireAndVerifyClientCert. VerifiedChains [][]*x509.Certificate + // VerifiedDC indicates that the Delegated Credential sent by the peer (if advertised + // and correctly processed), which has been verified against the leaf certificate, + // has been used. + VerifiedDC bool + + // DidClientAuthentiation states that the connection used client authentication. + DidClientAuthentication bool + + // DidKEMTLS states that the connection was established by using KEMTLS. + DidKEMTLS bool + + // DidPQTLS states that the connection was established by using PQTLS. + DidPQTLS bool + + // CertificateMessage contains the server's Certificate Message. + CertificateMessage []byte + + // CertificateReqMessage contains the server's Certificate Request Message. + CertificateReqMessage []byte + // SignedCertificateTimestamps is a list of SCTs provided by the peer // through the TLS handshake for the leaf certificate, if any. SignedCertificateTimestamps [][]byte @@ -276,6 +381,17 @@ type ConnectionState struct { // RFC 7627, and https://mitls.org/pages/attacks/3SHAKE#channelbindings. TLSUnique []byte + // ECHAccepted is set if the ECH extension was offered by the client and + // accepted by the server. + ECHAccepted bool + + // CFControl is used to pass additional TLS configuration information to + // HTTP requests. + // + // NOTE: This feature is used to implement Cloudflare-internal features. + // This feature is unstable and applications MUST NOT depend on it. + CFControl interface{} + // ekm is a closure exposed via ExportKeyingMaterial. ekm func(label string, context []byte, length int) ([]byte, error) } @@ -388,12 +504,41 @@ const ( // EdDSA algorithms. Ed25519 SignatureScheme = 0x0807 + Ed448 SignatureScheme = 0x0808 // Legacy signature and hash algorithms for TLS 1.2. PKCS1WithSHA1 SignatureScheme = 0x0201 ECDSAWithSHA1 SignatureScheme = 0x0203 + + // KEMTLS algorithms for the Post-Quantum Cryptography experiment. + // NOTE: Do not use outside of the experiment. + KEMTLSWithSIKEp434 SignatureScheme = 0xfe00 + KEMTLSWithKyber512 SignatureScheme = 0xfe01 + + // PQTLS algorithms for the Post-Quantum Cryptography experiment. + // NOTE: Do not use outside of the experiment. + PQTLSWithDilithium3 SignatureScheme = 0xfe61 + PQTLSWithDilithium4 SignatureScheme = 0xfe62 ) +func (scheme SignatureScheme) isKEMTLS() bool { + switch scheme { + case KEMTLSWithSIKEp434, KEMTLSWithKyber512: + return true + default: + return false + } +} + +func (scheme SignatureScheme) isPQTLS() bool { + switch scheme { + case PQTLSWithDilithium3, PQTLSWithDilithium4: + return true + default: + return false + } +} + // ClientHelloInfo contains information from a ClientHello message in order to // guide application logic in the GetCertificate and GetConfigForClient callbacks. type ClientHelloInfo struct { @@ -421,6 +566,13 @@ type ClientHelloInfo struct { // Algorithms Extension is being used (see RFC 5246, Section 7.4.1.4.1). SignatureSchemes []SignatureScheme + // SignatureSchemesDC lists the signature schemes that the client + // is willing to verify when using Delegated Credentials. + // This is and can be different from SignatureSchemes. SignatureSchemesDC + // is set only if the DelegatedCredentials Extension is being used. + // If Delegated Credentials are supported, this list should not be nil. + SignatureSchemesDC []SignatureScheme + // SupportedProtos lists the application protocols supported by the client. // SupportedProtos is set only if the Application-Layer Protocol // Negotiation Extension is being used (see RFC 7301, Section 3.1). @@ -435,6 +587,16 @@ type ClientHelloInfo struct { // might be rejected if used. SupportedVersions []uint16 + // SupportDelegatedCredential is true if the client indicated willingness + // to negotiate the Delegated Credential extension. + SupportsDelegatedCredential bool + + // CachedInformationCert is true if the client has the server's certificate + // message cached for the cached information extension. + CachedInformationCert bool + // CachedInformationCertReq is true if the client has the server's certificate + // request message cached for the cached information extension. + CachedInformationCertReq bool // Conn is the underlying net.Conn for the connection. Do not read // from, or write to, this connection; that will cause the TLS // connection to fail. @@ -455,10 +617,21 @@ type CertificateRequestInfo struct { // empty slice indicates that the server has no preference. AcceptableCAs [][]byte + // SupportDelegatedCredential is true if the server indicated willingness + // to negotiate the Delegated Credential extension. + SupportsDelegatedCredential bool + // SignatureSchemes lists the signature schemes that the server is // willing to verify. SignatureSchemes []SignatureScheme + // SignatureSchemesDC lists the signature schemes that the server + // is willing to verify when using Delegated Credentials. + // This is and can be different from SignatureSchemes. SignatureSchemesDC + // is set only if the DelegatedCredentials Extension is being used. + // If Delegated Credentials are supported, this list should not be nil. + SignatureSchemesDC []SignatureScheme + // Version is the TLS version that was negotiated for this connection. Version uint16 } @@ -501,6 +674,8 @@ type Config struct { // If Rand is nil, TLS uses the cryptographic random reader in package // crypto/rand. // The Reader must be safe for use by multiple goroutines. + // NOTE: it also provides a source of randomness for kemtls encapsulation + // mechanisms. Rand io.Reader // Time returns the current time as the number of seconds since the epoch. @@ -638,7 +813,8 @@ type Config struct { // SessionTicketsDisabled may be set to true to disable session ticket and // PSK (resumption) support. Note that on clients, session ticket support is - // also disabled if ClientSessionCache is nil. + // also disabled if ClientSessionCache is nil. On clients or servers, + // support is disabled if the ECH extension is enabled. SessionTicketsDisabled bool // SessionTicketKey is used by TLS servers to provide session resumption. @@ -688,6 +864,61 @@ type Config struct { // used for debugging. KeyLogWriter io.Writer + // ECHEnabled determines whether the ECH extension is enabled for this + // connection. + ECHEnabled bool + + // ClientECHConfigs are the parameters used by the client when it offers the + // ECH extension. If ECH is enabled, a suitable configuration is found, and + // the client supports TLS 1.3, then it will offer ECH in this handshake. + // Otherwise, if ECH is enabled, it will send a dummy ECH extension. + ClientECHConfigs []ECHConfig + + // ServerECHProvider is the ECH provider used by the client-facing server + // for the ECH extension. If the client offers ECH and TLS 1.3 is + // negotiated, then the provider is used to compute the HPKE context + // (draft-irtf-cfrg-hpke-07), which in turn is used to decrypt the extension + // payload. + ServerECHProvider ECHProvider + + // CFEventHandler, if set, is called by the client and server at various + // points during the handshake to handle specific events. This is used + // primarily for collecting metrics. + // + // NOTE: This feature is used to implement Cloudflare-internal features. + // This feature is unstable and applications MUST NOT depend on it. + CFEventHandler func(event CFEvent) + + // CFControl is used to pass additional TLS configuration information to + // HTTP requests via ConnectionState. + // + // NOTE: This feature is used to implement Cloudflare-internal features. + // This feature is unstable and applications MUST NOT depend on it. + CFControl interface{} + + // SupportDelegatedCredential is true if the client or server is willing + // to negotiate the delegated credential extension. + // This can only be used with TLS 1.3. + // + // See https://tools.ietf.org/html/draft-ietf-tls-subcerts. + SupportDelegatedCredential bool + + // KEMTLSEnabled is true if the client or server is willing + // to start a KEMTLS handshake based on TLS 1.3. + KEMTLSEnabled bool + + // PQTLSEnabled is true if the client or server is willing + // to start a PQTLS handshake (PQ KEMs for confidentiality and PQ Signatures for + // authentication based on TLS 1.3. + PQTLSEnabled bool + + // CachedCert corresponds to a cached server's Certificate message by the + // client. If filled, it will be used by the cached information extension. + CachedCert []byte + // CachedCertReq corresponds to a cached server's Certificate Request message + // by the client. If filled, it will be used by the cached information extension. + CachedCertReq []byte + // mutex protects sessionTicketKeys and autoSessionTicketKeys. mutex sync.RWMutex // sessionTicketKeys contains zero or more ticket keys. If set, it means the @@ -777,6 +1008,16 @@ func (c *Config) Clone() *Config { DynamicRecordSizingDisabled: c.DynamicRecordSizingDisabled, Renegotiation: c.Renegotiation, KeyLogWriter: c.KeyLogWriter, + SupportDelegatedCredential: c.SupportDelegatedCredential, + KEMTLSEnabled: c.KEMTLSEnabled, + PQTLSEnabled: c.PQTLSEnabled, + CachedCert: c.CachedCert, + CachedCertReq: c.CachedCertReq, + ECHEnabled: c.ECHEnabled, + ClientECHConfigs: c.ClientECHConfigs, + ServerECHProvider: c.ServerECHProvider, + CFEventHandler: c.CFEventHandler, + CFControl: c.CFControl, sessionTicketKeys: c.sessionTicketKeys, autoSessionTicketKeys: c.autoSessionTicketKeys, } @@ -953,6 +1194,23 @@ func (c *Config) supportedVersions() []uint16 { return versions } +func (c *Config) supportedVersionsFromMin(minVersion uint16) []uint16 { + versions := make([]uint16, 0, len(supportedVersions)) + for _, v := range supportedVersions { + if c != nil && c.MinVersion != 0 && v < c.MinVersion { + continue + } + if c != nil && c.MaxVersion != 0 && v > c.MaxVersion { + continue + } + if v < minVersion { + continue + } + versions = append(versions, v) + } + return versions +} + func (c *Config) maxSupportedVersion() uint16 { supportedVersions := c.supportedVersions() if len(supportedVersions) == 0 { @@ -976,9 +1234,14 @@ func supportedVersionsFromMax(maxVersion uint16) []uint16 { } var defaultCurvePreferences = []CurveID{X25519, CurveP256, CurveP384, CurveP521} +var defaultKEMPreferences = []CurveID{Kyber512, SIKEp434, X25519, CurveP256, CurveP384, CurveP521} func (c *Config) curvePreferences() []CurveID { if c == nil || len(c.CurvePreferences) == 0 { + if c.KEMTLSEnabled || c.PQTLSEnabled { + return defaultKEMPreferences + } + return defaultCurvePreferences } return c.CurvePreferences @@ -1274,11 +1537,13 @@ func (c *Config) BuildNameToCertificate() { } const ( - keyLogLabelTLS12 = "CLIENT_RANDOM" - keyLogLabelClientHandshake = "CLIENT_HANDSHAKE_TRAFFIC_SECRET" - keyLogLabelServerHandshake = "SERVER_HANDSHAKE_TRAFFIC_SECRET" - keyLogLabelClientTraffic = "CLIENT_TRAFFIC_SECRET_0" - keyLogLabelServerTraffic = "SERVER_TRAFFIC_SECRET_0" + keyLogLabelTLS12 = "CLIENT_RANDOM" + keyLogLabelClientHandshake = "CLIENT_HANDSHAKE_TRAFFIC_SECRET" + keyLogLabelServerHandshake = "SERVER_HANDSHAKE_TRAFFIC_SECRET" + keyLogLabelClientKEMAuthenticatedHandshake = "CLIENT_AUTHENTICATED_HANDSHAKE_TRAFFIC_SECRET" + keyLogLabelServerKEMAuthenticatedHandshake = "SERVER_AUTHENTICATED_HANDSHAKE_TRAFFIC_SECRET" + keyLogLabelClientTraffic = "CLIENT_TRAFFIC_SECRET_0" + keyLogLabelServerTraffic = "SERVER_TRAFFIC_SECRET_0" ) func (c *Config) writeKeyLog(label string, clientRandom, secret []byte) error { @@ -1299,6 +1564,16 @@ func (c *Config) writeKeyLog(label string, clientRandom, secret []byte) error { // and is only for debugging, so a global mutex saves space. var writerMutex sync.Mutex +// A DelegatedCredentialPair contains a Delegated Credential and its +// associated private key. +type DelegatedCredentialPair struct { + // DC is the delegated credential. + DC *DelegatedCredential + // PrivateKey is the private key used to derive the public key of + // contained in DC. PrivateKey must implement crypto.Signer. + PrivateKey crypto.PrivateKey +} + // A Certificate is a chain of one or more certificates, leaf first. type Certificate struct { Certificate [][]byte @@ -1316,6 +1591,21 @@ type Certificate struct { // SignedCertificateTimestamps contains an optional list of Signed // Certificate Timestamps which will be served to clients that request it. SignedCertificateTimestamps [][]byte + // DelegatedCredentials are a list of Delegated Credentials with their + // corresponding private keys, signed by the leaf certificate. + // If there are no delegated credentials, this field is nil. + DelegatedCredentials []DelegatedCredentialPair + // DelegatedCredential is the delegated credential to be used in the + // handshake. + // If there are no delegated credentials, this field is nil. + // NOTE: Do not fill this field, as it will be filled depending on + // the provided list of delegated credentials. + DelegatedCredential []byte + // DelegatedCredentialPrivateKey contains the private key corresponding to the public key in + // the Delegated Credential. + // NOTE: Do not fill this field, as it will be filled depending on + // the provided list of delegated credentials. + DelegatedCredentialPrivateKey crypto.PrivateKey // Leaf is the parsed form of the leaf certificate, which may be initialized // using x509.ParseCertificate to reduce per-handshake processing. If nil, // the leaf certificate will be parsed as needed. diff --git a/src/crypto/tls/common_string.go b/src/crypto/tls/common_string.go index 238108811f2..ed302663a68 100644 --- a/src/crypto/tls/common_string.go +++ b/src/crypto/tls/common_string.go @@ -18,51 +18,44 @@ func _() { _ = x[ECDSAWithP384AndSHA384-1283] _ = x[ECDSAWithP521AndSHA512-1539] _ = x[Ed25519-2055] + _ = x[Ed448-2056] _ = x[PKCS1WithSHA1-513] _ = x[ECDSAWithSHA1-515] + _ = x[KEMTLSWithSIKEp434-65024] + _ = x[KEMTLSWithKyber512-65025] + _ = x[PQTLSWithDilithium3-65121] + _ = x[PQTLSWithDilithium4-65122] } -const ( - _SignatureScheme_name_0 = "PKCS1WithSHA1" - _SignatureScheme_name_1 = "ECDSAWithSHA1" - _SignatureScheme_name_2 = "PKCS1WithSHA256" - _SignatureScheme_name_3 = "ECDSAWithP256AndSHA256" - _SignatureScheme_name_4 = "PKCS1WithSHA384" - _SignatureScheme_name_5 = "ECDSAWithP384AndSHA384" - _SignatureScheme_name_6 = "PKCS1WithSHA512" - _SignatureScheme_name_7 = "ECDSAWithP521AndSHA512" - _SignatureScheme_name_8 = "PSSWithSHA256PSSWithSHA384PSSWithSHA512Ed25519" -) +const _SignatureScheme_name = "PKCS1WithSHA1ECDSAWithSHA1PKCS1WithSHA256ECDSAWithP256AndSHA256PKCS1WithSHA384ECDSAWithP384AndSHA384PKCS1WithSHA512ECDSAWithP521AndSHA512PSSWithSHA256PSSWithSHA384PSSWithSHA512Ed25519Ed448KEMTLSWithSIKEp434KEMTLSWithKyber512PQTLSWithDilithium3PQTLSWithDilithium4" -var ( - _SignatureScheme_index_8 = [...]uint8{0, 13, 26, 39, 46} -) +var _SignatureScheme_map = map[SignatureScheme]string{ + 513: _SignatureScheme_name[0:13], + 515: _SignatureScheme_name[13:26], + 1025: _SignatureScheme_name[26:41], + 1027: _SignatureScheme_name[41:63], + 1281: _SignatureScheme_name[63:78], + 1283: _SignatureScheme_name[78:100], + 1537: _SignatureScheme_name[100:115], + 1539: _SignatureScheme_name[115:137], + 2052: _SignatureScheme_name[137:150], + 2053: _SignatureScheme_name[150:163], + 2054: _SignatureScheme_name[163:176], + 2055: _SignatureScheme_name[176:183], + 2056: _SignatureScheme_name[183:188], + 65024: _SignatureScheme_name[188:206], + 65025: _SignatureScheme_name[206:224], + 65121: _SignatureScheme_name[224:243], + 65122: _SignatureScheme_name[243:262], +} func (i SignatureScheme) String() string { - switch { - case i == 513: - return _SignatureScheme_name_0 - case i == 515: - return _SignatureScheme_name_1 - case i == 1025: - return _SignatureScheme_name_2 - case i == 1027: - return _SignatureScheme_name_3 - case i == 1281: - return _SignatureScheme_name_4 - case i == 1283: - return _SignatureScheme_name_5 - case i == 1537: - return _SignatureScheme_name_6 - case i == 1539: - return _SignatureScheme_name_7 - case 2052 <= i && i <= 2055: - i -= 2052 - return _SignatureScheme_name_8[_SignatureScheme_index_8[i]:_SignatureScheme_index_8[i+1]] - default: - return "SignatureScheme(" + strconv.FormatInt(int64(i), 10) + ")" + if str, ok := _SignatureScheme_map[i]; ok { + return str } + return "SignatureScheme(" + strconv.FormatInt(int64(i), 10) + ")" } + func _() { // An "invalid array index" compiler error signifies that the constant values have changed. // Re-run the stringer command to generate them again. diff --git a/src/crypto/tls/conn.go b/src/crypto/tls/conn.go index 72ad52c194b..5dc38f917a8 100644 --- a/src/crypto/tls/conn.go +++ b/src/crypto/tls/conn.go @@ -8,6 +8,7 @@ package tls import ( "bytes" + "circl/hpke" "crypto/cipher" "crypto/subtle" "crypto/x509" @@ -51,6 +52,15 @@ type Conn struct { // verifiedChains contains the certificate chains that we built, as // opposed to the ones presented by the server. verifiedChains [][]*x509.Certificate + // verifiedDC contains the Delegated Credential sent by the peer (if advertised + // and correctly processed), which has been verified against the leaf certificate. + verifiedDC *DelegatedCredential + // didPQTLS states that the connection was established by using PQTLS. + didPQTLS bool + // didKEMTLS states that the connection was established by using KEMTLS. + didKEMTLS bool + // didClientAuthentication states that the connection used client authentication. + didClientAuthentication bool // serverName contains the server name indicated by the client, if any. serverName string // secureRenegotiation is true if the server echoed the secure @@ -87,6 +97,14 @@ type Conn struct { clientFinished [12]byte serverFinished [12]byte + // certificateMessage contain the Certificate message sent + // by the server in the most recent handshake. + // certificateMessageReq contain the Certificate Request message sent + // by the server in the most recent handshake. + // This is retained to be used as cached information for a new handshake. + certificateMessage []byte + certificateReqMessage []byte + // clientProtocol is the negotiated ALPN protocol. clientProtocol string @@ -114,6 +132,29 @@ type Conn struct { activeCall int32 tmp [16]byte + + // State used for the ECH extension. + ech struct { + sealer hpke.Sealer // The client's HPKE context + opener hpke.Opener // The server's HPKE context + + // The state shared by the client and server. + offered bool // Client offered ECH + greased bool // Client greased ECH + accepted bool // Server accepted ECH + retryConfigs []byte // The retry configurations + + // The client's state, used in case of HRR. + innerRandom []byte // ClientHelloInner.random + publicName string // ECHConfig.contents.public_name + configId uint8 // ECHConfig.contents.key_config.config_id + suite hpkeSymmetricCipherSuite // ClientECH.cipher_suite + dummy []byte // serialized ClientECH when greasing ECH + } + + // Set by the client and server when an HRR message was sent in this + // handshake. + hrrTriggered bool } // Access to net.Conn methods. @@ -691,6 +732,12 @@ func (c *Conn) readRecordOrCCS(expectChangeCipherSpec bool) error { return c.in.setErrorLocked(io.EOF) } if c.vers == VersionTLS13 { + if !c.isClient && c.ech.greased && alert(data[1]) == alertECHRequired { + // This condition indicates that the client intended to offer + // ECH, but did not use a known ECH config. + c.ech.offered = true + c.ech.greased = false + } return c.in.setErrorLocked(&net.OpError{Op: "remote error", Err: alert(data[1])}) } switch data[0] { @@ -1335,6 +1382,29 @@ func (c *Conn) Close() error { if err := c.conn.Close(); err != nil { return err } + + // Resolve ECH status. + if !c.isClient && c.config.MaxVersion < VersionTLS13 { + c.handleCFEvent(CFEventECHServerStatus(echStatusBypassed)) + } else if !c.ech.offered { + if !c.ech.greased { + c.handleCFEvent(CFEventECHClientStatus(echStatusBypassed)) + } else { + c.handleCFEvent(CFEventECHClientStatus(echStatusOuter)) + } + } else { + c.handleCFEvent(CFEventECHClientStatus(echStatusInner)) + if !c.ech.accepted { + if len(c.ech.retryConfigs) > 0 { + c.handleCFEvent(CFEventECHServerStatus(echStatusOuter)) + } else { + c.handleCFEvent(CFEventECHServerStatus(echStatusBypassed)) + } + } else { + c.handleCFEvent(CFEventECHServerStatus(echStatusInner)) + } + } + return alertErr } @@ -1422,8 +1492,18 @@ func (c *Conn) connectionStateLocked() ConnectionState { state.CipherSuite = c.cipherSuite state.PeerCertificates = c.peerCertificates state.VerifiedChains = c.verifiedChains + if c.verifiedDC != nil { + state.VerifiedDC = true + } + state.DidClientAuthentication = c.didClientAuthentication + state.DidKEMTLS = c.didKEMTLS + state.DidPQTLS = c.didPQTLS + state.CertificateMessage = c.certificateMessage + state.CertificateReqMessage = c.certificateReqMessage state.SignedCertificateTimestamps = c.scts state.OCSPResponse = c.ocspResponse + state.ECHAccepted = c.ech.accepted + state.CFControl = c.config.CFControl if !c.didResume && c.vers != VersionTLS13 { if c.clientFinishedIsFirst { state.TLSUnique = c.clientFinished[:] @@ -1469,3 +1549,9 @@ func (c *Conn) VerifyHostname(host string) error { func (c *Conn) handshakeComplete() bool { return atomic.LoadUint32(&c.handshakeStatus) == 1 } + +func (c *Conn) handleCFEvent(event CFEvent) { + if c.config.CFEventHandler != nil { + c.config.CFEventHandler(event) + } +} diff --git a/src/crypto/tls/delegated_credentials.go b/src/crypto/tls/delegated_credentials.go new file mode 100644 index 00000000000..2b59567b7ec --- /dev/null +++ b/src/crypto/tls/delegated_credentials.go @@ -0,0 +1,552 @@ +// Copyright 2020-2021 Cloudflare, Inc. All rights reserved. Use of this source code +// is governed by a BSD-style license that can be found in the LICENSE file. + +package tls + +// Delegated Credentials for TLS +// (https://tools.ietf.org/html/draft-ietf-tls-subcerts) is an IETF Internet +// draft and proposed TLS extension. If the client or server supports this +// extension, then the server or client may use a "delegated credential" as the +// signing key in the handshake. A delegated credential is a short lived +// public/secret key pair delegated to the peer by an entity trusted by the +// corresponding peer. This allows a reverse proxy to terminate a TLS connection +// on behalf of the entity. Credentials can't be revoked; in order to +// mitigate risk in case the reverse proxy is compromised, the credential is only +// valid for a short time (days, hours, or even minutes). + +import ( + "bytes" + "crypto" + "crypto/ecdsa" + "crypto/ed25519" + "crypto/elliptic" + "crypto/kem" + "crypto/rand" + "crypto/x509" + "encoding/binary" + "errors" + "fmt" + "io" + + "circl/sign/schemes" + "time" + + "golang.org/x/crypto/cryptobyte" +) + +const ( + // In the absence of an application profile standard specifying otherwise, + // the maximum validity period is set to 7 days. + dcMaxTTLSeconds = 60 * 60 * 24 * 7 + dcMaxTTL = time.Duration(dcMaxTTLSeconds * time.Second) + dcMaxPubLen = (1 << 24) - 1 // Bytes + dcMaxSignatureLen = (1 << 16) - 1 // Bytes +) + +var extensionDelegatedCredential = []int{1, 3, 6, 1, 4, 1, 44363, 44} + +// isValidForDelegation returns true if a certificate can be used for Delegated +// Credentials. +func isValidForDelegation(cert *x509.Certificate) bool { + // Check that the digitalSignature key usage is set. + // The certificate must contains the digitalSignature KeyUsage. + if (cert.KeyUsage & x509.KeyUsageDigitalSignature) == 0 { + return false + } + + // Check that the certificate has the DelegationUsage extension and that + // it's marked as non-critical (See Section 4.2 of RFC5280). + for _, extension := range cert.Extensions { + if extension.Id.Equal(extensionDelegatedCredential) { + if extension.Critical { + return false + } + return true + } + } + + return false +} + +// isExpired returns true if the credential has expired. The end of the validity +// interval is defined as the delegator certificate's notBefore field ('start') +// plus dc.cred.validTime seconds. This function simply checks that the current time +// ('now') is before the end of the validity interval. +func (dc *DelegatedCredential) isExpired(start, now time.Time) bool { + end := start.Add(dc.cred.validTime) + return !now.Before(end) +} + +// invalidTTL returns true if the credential's validity period is longer than the +// maximum permitted. This is defined by the certificate's notBefore field +// ('start') plus the dc.validTime, minus the current time ('now'). +func (dc *DelegatedCredential) invalidTTL(start, now time.Time) bool { + return dc.cred.validTime > (now.Sub(start) + dcMaxTTL).Round(time.Second) +} + +// credential stores the public components of a Delegated Credential. +type credential struct { + // The amount of time for which the credential is valid. Specifically, the + // the credential expires 'validTime' seconds after the 'notBefore' of the + // delegation certificate. The delegator shall not issue Delegated + // Credentials that are valid for more than 7 days from the current time. + // + // When this data structure is serialized, this value is converted to a + // uint32 representing the duration in seconds. + validTime time.Duration + // The signature scheme associated with the credential public key. + // This is expected to be the same as the CertificateVerify.algorithm + // sent by the client or server. + expCertVerfAlgo SignatureScheme + // The credential's public key. + publicKey crypto.PublicKey +} + +// DelegatedCredential stores a Delegated Credential with the credential and its +// signature. +type DelegatedCredential struct { + // The serialized form of the Delegated Credential. + raw []byte + + // Cred stores the public components of a Delegated Credential. + cred *credential + + // The signature scheme used to sign the Delegated Credential. + algorithm SignatureScheme + + // The Credential's delegation: a signature that binds the credential to + // the end-entity certificate's public key. + signature []byte +} + +// marshalPublicKeyInfo returns a DER encoded PublicKeyInfo +// from a Delegated Credential (as defined in the X.509 standard). +// The following key types are currently supported: *ecdsa.PublicKey +// and ed25519.PublicKey. Unsupported key types result in an error. +// rsa.PublicKey is not supported as defined by the draft. +func (cred *credential) marshalPublicKeyInfo() ([]byte, error) { + switch cred.expCertVerfAlgo { + case ECDSAWithP256AndSHA256, + ECDSAWithP384AndSHA384, + ECDSAWithP521AndSHA512, + Ed25519, Ed448, + KEMTLSWithSIKEp434, KEMTLSWithKyber512, + PQTLSWithDilithium3, PQTLSWithDilithium4: + rawPub, err := x509.MarshalPKIXPublicKey(cred.publicKey) + if err != nil { + return nil, err + } + + return rawPub, nil + default: + return nil, fmt.Errorf("tls: unsupported signature scheme: 0x%04x", cred.expCertVerfAlgo) + } +} + +// marshal encodes the credential struct of the Delegated Credential. +func (cred *credential) marshal() ([]byte, error) { + var b cryptobyte.Builder + + b.AddUint32(uint32(cred.validTime / time.Second)) + b.AddUint16(uint16(cred.expCertVerfAlgo)) + + // Encode the public key + rawPub, err := cred.marshalPublicKeyInfo() + if err != nil { + return nil, err + } + // Assert that the public key encoding is no longer than 2^24-1 bytes. + if len(rawPub) > dcMaxPubLen { + return nil, errors.New("tls: public key length exceeds 2^24-1 limit") + } + + b.AddUint24(uint32(len(rawPub))) + b.AddBytes(rawPub) + + raw := b.BytesOrPanic() + return raw, nil +} + +// unmarshalCredential decodes serialized bytes and returns a credential, if possible. +func unmarshalCredential(raw []byte) (*credential, error) { + if len(raw) < 10 { + return nil, errors.New("tls: Delegated Credential is not valid: invalid length") + } + + s := cryptobyte.String(raw) + var t uint32 + if !s.ReadUint32(&t) { + return nil, errors.New("tls: Delegated Credential is not valid") + } + validTime := time.Duration(t) * time.Second + + var pubAlgo uint16 + if !s.ReadUint16(&pubAlgo) { + return nil, errors.New("tls: Delegated Credential is not valid") + } + algo := SignatureScheme(pubAlgo) + + var pubLen uint32 + s.ReadUint24(&pubLen) + + pubKey, err := x509.ParsePKIXPublicKey(s) + if err != nil { + return nil, err + } + + return &credential{validTime, algo, pubKey}, nil +} + +// getCredentialLen returns the number of bytes comprising the serialized +// credential struct inside the Delegated Credential. +func getCredentialLen(raw []byte) (int, error) { + if len(raw) < 10 { + return 0, errors.New("tls: Delegated Credential is not valid") + } + + var read []byte + s := cryptobyte.String(raw) + s.ReadBytes(&read, 6) + + var pubLen uint32 + s.ReadUint24(&pubLen) + if !(pubLen > 0) { + return 0, errors.New("tls: Delegated Credential is not valid") + } + + raw = raw[6:] + if len(raw) < int(pubLen) { + return 0, errors.New("tls: Delegated Credential is not valid") + } + + return 9 + int(pubLen), nil +} + +// getHash maps the SignatureScheme to its corresponding hash function. +func getHash(scheme SignatureScheme) crypto.Hash { + switch scheme { + case ECDSAWithP256AndSHA256: + return crypto.SHA256 + case ECDSAWithP384AndSHA384: + return crypto.SHA384 + case ECDSAWithP521AndSHA512: + return crypto.SHA512 + case Ed25519: + return directSigning + default: + return 0 //Unknown hash function + } +} + +// getECDSACurve maps the SignatureScheme to its corresponding ecdsa elliptic.Curve. +func getECDSACurve(scheme SignatureScheme) elliptic.Curve { + switch scheme { + case ECDSAWithP256AndSHA256: + return elliptic.P256() + case ECDSAWithP384AndSHA384: + return elliptic.P384() + case ECDSAWithP521AndSHA512: + return elliptic.P521() + default: + return nil + } +} + +// prepareDelegationSignatureInput returns the message that the delegator is going to sign. +func prepareDelegationSignatureInput(hash crypto.Hash, cred *credential, dCert []byte, algo SignatureScheme, isClient bool) ([]byte, error) { + header := make([]byte, 64) + for i := range header { + header[i] = 0x20 + } + + var context string + if !isClient { + context = "TLS, server delegated credentials\x00" + } else { + context = "TLS, client delegated credentials\x00" + } + + rawCred, err := cred.marshal() + if err != nil { + return nil, err + } + + var rawAlgo [2]byte + binary.BigEndian.PutUint16(rawAlgo[:], uint16(algo)) + + if hash == directSigning { + b := &bytes.Buffer{} + b.Write(header) + io.WriteString(b, context) + b.Write(dCert) + b.Write(rawCred) + b.Write(rawAlgo[:]) + return b.Bytes(), nil + } + + h := hash.New() + h.Write(header) + io.WriteString(h, context) + h.Write(dCert) + h.Write(rawCred) + h.Write(rawAlgo[:]) + return h.Sum(nil), nil +} + +// Extract the algorithm used to sign the Delegated Credential from the +// end-entity (leaf) certificate. +func getSignatureAlgorithm(cert *Certificate) (SignatureScheme, error) { + var sigAlgo SignatureScheme + switch sk := cert.PrivateKey.(type) { + case *ecdsa.PrivateKey: + pk := sk.Public().(*ecdsa.PublicKey) + curveName := pk.Curve.Params().Name + certAlg := cert.Leaf.SignatureAlgorithm + if certAlg == x509.ECDSAWithSHA256 && curveName == "P-256" { + sigAlgo = ECDSAWithP256AndSHA256 + } else if certAlg == x509.ECDSAWithSHA384 && curveName == "P-384" { + sigAlgo = ECDSAWithP384AndSHA384 + } else if certAlg == x509.ECDSAWithSHA512 && curveName == "P-521" { + sigAlgo = ECDSAWithP521AndSHA512 + } else { + return SignatureScheme(0x00), fmt.Errorf("using curve %s for %s is not supported", curveName, cert.Leaf.SignatureAlgorithm) + } + case ed25519.PrivateKey: + sigAlgo = Ed25519 + default: + return SignatureScheme(0x00), fmt.Errorf("tls: unsupported algorithm for Delegated Credential") + } + + return sigAlgo, nil +} + +// NewDelegatedCredential creates a new Delegated Credential using 'cert' for +// delegation, depending if the caller is the client or the server (defined by +// 'isClient'). It generates a public/private key pair for the provided signature +// algorithm ('pubAlgo') and it defines a validity interval (defined +// by 'cert.Leaf.notBefore' and 'validTime'). It signs the Delegated Credential +// using 'cert.PrivateKey'. +func NewDelegatedCredential(cert *Certificate, pubAlgo SignatureScheme, validTime time.Duration, isClient bool) (*DelegatedCredential, crypto.PrivateKey, error) { + // The granularity of DC validity is seconds. + validTime = validTime.Round(time.Second) + + // Parse the leaf certificate if needed. + var err error + if cert.Leaf == nil { + if len(cert.Certificate[0]) == 0 { + return nil, nil, errors.New("tls: missing leaf certificate for Delegated Credential") + } + cert.Leaf, err = x509.ParseCertificate(cert.Certificate[0]) + if err != nil { + return nil, nil, err + } + } + + // Check that the leaf certificate can be used for delegation. + if !isValidForDelegation(cert.Leaf) { + return nil, nil, errors.New("tls: certificate not authorized for delegation") + } + + sigAlgo, err := getSignatureAlgorithm(cert) + if err != nil { + return nil, nil, err + } + + // Generate the Delegated Credential key pair based on the provided scheme + var privK crypto.PrivateKey + var pubK crypto.PublicKey + switch pubAlgo { + case ECDSAWithP256AndSHA256, + ECDSAWithP384AndSHA384, + ECDSAWithP521AndSHA512: + privK, err = ecdsa.GenerateKey(getECDSACurve(pubAlgo), rand.Reader) + if err != nil { + return nil, nil, err + } + pubK = privK.(*ecdsa.PrivateKey).Public() + case Ed25519: + pubK, privK, err = ed25519.GenerateKey(rand.Reader) + if err != nil { + return nil, nil, err + } + case Ed448: + scheme := schemes.ByName("Ed448") + pubK, privK, err = scheme.GenerateKey() + if err != nil { + return nil, nil, err + } + case KEMTLSWithSIKEp434: + pubK, privK, err = kem.GenerateKey(rand.Reader, kem.SIKEp434) + if err != nil { + return nil, nil, err + } + case KEMTLSWithKyber512: + pubK, privK, err = kem.GenerateKey(rand.Reader, kem.Kyber512) + if err != nil { + return nil, nil, err + } + case PQTLSWithDilithium3: + scheme := schemes.ByName("Ed25519-Dilithium3") + pubK, privK, err = scheme.GenerateKey() + if err != nil { + return nil, nil, err + } + case PQTLSWithDilithium4: + scheme := schemes.ByName("Ed448-Dilithium4") + pubK, privK, err = scheme.GenerateKey() + if err != nil { + return nil, nil, err + } + default: + return nil, nil, fmt.Errorf("tls: unsupported algorithm for Delegated Credential: %T", pubAlgo) + } + + // Prepare the credential for signing + hash := getHash(sigAlgo) + credential := &credential{validTime, pubAlgo, pubK} + values, err := prepareDelegationSignatureInput(hash, credential, cert.Leaf.Raw, sigAlgo, isClient) + if err != nil { + return nil, nil, err + } + + var sig []byte + switch sk := cert.PrivateKey.(type) { + case *ecdsa.PrivateKey: + opts := crypto.SignerOpts(hash) + sig, err = sk.Sign(rand.Reader, values, opts) + if err != nil { + return nil, nil, err + } + case ed25519.PrivateKey: + opts := crypto.SignerOpts(hash) + sig, err = sk.Sign(rand.Reader, values, opts) + if err != nil { + return nil, nil, err + } + default: + return nil, nil, fmt.Errorf("tls: unsupported key type for Delegated Credential") + } + + if len(sig) > dcMaxSignatureLen { + return nil, nil, errors.New("tls: unable to create a Delegated Credential") + } + + return &DelegatedCredential{ + cred: credential, + algorithm: sigAlgo, + signature: sig, + }, privK, nil +} + +// Validate validates the Delegated Credential by checking that the signature is +// valid, that it hasn't expired, and that the TTL is valid. It also checks that +// certificate can be used for delegation. +func (dc *DelegatedCredential) Validate(cert *x509.Certificate, isClient bool, now time.Time, certVerifyMsg *certificateVerifyMsg) bool { + if dc.isExpired(cert.NotBefore, now) { + return false + } + + if dc.invalidTTL(cert.NotBefore, now) { + return false + } + + if certVerifyMsg != nil { // could be nil in the kemtls case + if dc.cred.expCertVerfAlgo != certVerifyMsg.signatureAlgorithm { + return false + } + } + + if !isValidForDelegation(cert) { + return false + } + + hash := getHash(dc.algorithm) + in, err := prepareDelegationSignatureInput(hash, dc.cred, cert.Raw, dc.algorithm, isClient) + if err != nil { + return false + } + + switch dc.algorithm { + case ECDSAWithP256AndSHA256, + ECDSAWithP384AndSHA384, + ECDSAWithP521AndSHA512: + pk, ok := cert.PublicKey.(*ecdsa.PublicKey) + if !ok { + return false + } + + return ecdsa.VerifyASN1(pk, in, dc.signature) + case Ed25519: + pk, ok := cert.PublicKey.(ed25519.PublicKey) + if !ok { + return false + } + + return ed25519.Verify(pk, in, dc.signature) + default: + return false + } +} + +// marshal encodes a DelegatedCredential structure. It also sets dc.Raw to that +// encoding. +func (dc *DelegatedCredential) marshal() ([]byte, error) { + if len(dc.signature) > dcMaxSignatureLen { + return nil, errors.New("tls: delegated credential is not valid") + } + + raw, err := dc.cred.marshal() + if err != nil { + return nil, err + } + + var b cryptobyte.Builder + b.AddBytes(raw) + b.AddUint16(uint16(dc.algorithm)) + b.AddUint16(uint16(len(dc.signature))) + b.AddBytes(dc.signature) + + dc.raw = b.BytesOrPanic() + return dc.raw, nil +} + +// unmarshalDelegatedCredential decodes a DelegatedCredential structure. +func unmarshalDelegatedCredential(raw []byte) (*DelegatedCredential, error) { + rawCredentialLen, err := getCredentialLen(raw) + if err != nil { + return nil, err + } + + credential, err := unmarshalCredential(raw[:rawCredentialLen]) + if err != nil { + return nil, err + } + + raw = raw[rawCredentialLen:] + if len(raw) < 4 { + return nil, errors.New("tls: Delegated Credential is not valid") + } + + s := cryptobyte.String(raw) + + var algo uint16 + if !s.ReadUint16(&algo) { + return nil, errors.New("tls: Delegated Credential is not valid") + } + + var rawSignatureLen uint16 + if !s.ReadUint16(&rawSignatureLen) { + return nil, errors.New("tls: Delegated Credential is not valid") + } + + var sig []byte + if !s.ReadBytes(&sig, int(rawSignatureLen)) { + return nil, errors.New("tls: Delegated Credential is not valid") + } + + return &DelegatedCredential{ + cred: credential, + algorithm: SignatureScheme(algo), + signature: sig, + }, nil +} diff --git a/src/crypto/tls/delegated_credentials_test.go b/src/crypto/tls/delegated_credentials_test.go new file mode 100644 index 00000000000..bec7bcf659d --- /dev/null +++ b/src/crypto/tls/delegated_credentials_test.go @@ -0,0 +1,1139 @@ +// Copyright 2020-2021 Cloudflare, Inc. All rights reserved. Use of this source code +// is governed by a BSD-style license that can be found in the LICENSE file. + +package tls + +import ( + "bytes" + "crypto" + "crypto/ecdsa" + "crypto/ed25519" + "crypto/elliptic" + "crypto/x509" + "errors" + "fmt" + "math/rand" + "testing" + "time" +) + +// These test keys were generated with the following program, available in the +// crypto/tls directory: +// +// go run generate_cert.go -ecdsa-curve P256 -host 127.0.0.1 -allowDC +// +var delegatorCertPEMP256 = `-----BEGIN CERTIFICATE----- +MIIBejCCAR+gAwIBAgIQKEg6iMq02QUu7QZSZJ/qjzAKBggqhkjOPQQDAjASMRAw +DgYDVQQKEwdBY21lIENvMB4XDTIxMDIyNzAwMTYwMVoXDTIyMDIyNzAwMTYwMVow +EjEQMA4GA1UEChMHQWNtZSBDbzBZMBMGByqGSM49AgEGCCqGSM49AwEHA0IABJTe +bU0Yny6aMvae3zlNj135l7XSzqPDZjYh1PqIqY/P2N5PPmD06fHQ2D7xZRUw/a5z +W7KMwRVXrvur+TVn4+GjVzBVMA4GA1UdDwEB/wQEAwIHgDATBgNVHSUEDDAKBggr +BgEFBQcDATAMBgNVHRMBAf8EAjAAMA8GCSsGAQQBgtpLLAQCBQAwDwYDVR0RBAgw +BocEfwAAATAKBggqhkjOPQQDAgNJADBGAiEAvkorBgZm6GidD0Z7tcAJWRq+2YOQ +GVclN1Z1CDljQIoCIQDUlTAqDyRpNJ9ntCHEdOQYe1LfAkJHasok5yCRHC1o8w== +-----END CERTIFICATE----- +` + +var delegatorKeyPEMP256 = `-----BEGIN EC PRIVATE KEY----- +MIGHAgEAMBMGByqGSM49AgEGCCqGSM49AwEHBG0wawIBAQQg4OgO7q8sUUZaYjEp +JuLzlXH0qmTZ1k3UHgPYbAmRFOWhRANCAASU3m1NGJ8umjL2nt85TY9d+Ze10s6j +w2Y2IdT6iKmPz9jeTz5g9Onx0Ng+8WUVMP2uc1uyjMEVV677q/k1Z+Ph +-----END EC PRIVATE KEY----- +` + +// go run generate_cert.go -ecdsa-curve P384 -host 127.0.0.1 -allowDC + +var delegatorCertPEMP384 = `-----BEGIN CERTIFICATE----- +MIIBtzCCATygAwIBAgIQYhD6ucKVx53ZfdRCJkPy3DAKBggqhkjOPQQDAzASMRAw +DgYDVQQKEwdBY21lIENvMB4XDTIxMDIyNzAwMTYzOFoXDTIyMDIyNzAwMTYzOFow +EjEQMA4GA1UEChMHQWNtZSBDbzB2MBAGByqGSM49AgEGBSuBBAAiA2IABHNmyki5 +Xxfmxxrk4QRoXfU7hk0o2gJWTkCUAyzlVNcSaUTHub64v2cwn9/LbbooFBlhwz4n +n706yHtzmSQHTkCKmcG2LwS75U+ZajzPXKoSqazGhapBLQb7R7A+uRQGvqNXMFUw +DgYDVR0PAQH/BAQDAgeAMBMGA1UdJQQMMAoGCCsGAQUFBwMBMAwGA1UdEwEB/wQC +MAAwDwYJKwYBBAGC2kssBAIFADAPBgNVHREECDAGhwR/AAABMAoGCCqGSM49BAMD +A2kAMGYCMQDIOr2c+CckkU48HqcFiyzPkYWUUeytqmzOg3QDOu6U0jfmi1Xb9dda +pytx77nIUucCMQDD9uVr1UeKGC3Iv0VIHw+tjBzTUg9iToG+PPIlnP+duIBjFQcl +FkeNmqTC8510USo= +-----END CERTIFICATE----- +` + +var delegatorKeyPEMP384 = `-----BEGIN EC PRIVATE KEY----- +MIG2AgEAMBAGByqGSM49AgEGBSuBBAAiBIGeMIGbAgEBBDA1ouSiH174RBEvZBch +QQnl5iYWTpdCa+EHjexYzhQ9HHMcU7nKCk7OXRod3kAVcUahZANiAARzZspIuV8X +5sca5OEEaF31O4ZNKNoCVk5AlAMs5VTXEmlEx7m+uL9nMJ/fy226KBQZYcM+J5+9 +Osh7c5kkB05AipnBti8Eu+VPmWo8z1yqEqmsxoWqQS0G+0ewPrkUBr4= +-----END EC PRIVATE KEY----- +` + +// go run generate_cert.go -ecdsa-curve P521 -host 127.0.0.1 -allowDC + +var delegatorCertPEMP521 = `-----BEGIN CERTIFICATE----- +MIICATCCAWKgAwIBAgIQJq2J2jQNbTUbhfjk0PT8/TAKBggqhkjOPQQDBDASMRAw +DgYDVQQKEwdBY21lIENvMB4XDTIxMDIyNzAwMTcxN1oXDTIyMDIyNzAwMTcxN1ow +EjEQMA4GA1UEChMHQWNtZSBDbzCBmzAQBgcqhkjOPQIBBgUrgQQAIwOBhgAEAM3n +1xAxRLYhnDNRqc0onmNM9Ik0Jcja6e0bYa9mo0oV/y5DPeML3UJB1CNImFpAkx62 +wLiZmk/BhcPS0EstLAwXATBkb/q0fbKUZXFHd4gr5spRfAosXz5vg1VLeKHqpUku +tyJjgdFvuBZzmp2olqGKbBSKUElvDFkZWkZk5uGEnCsIo1cwVTAOBgNVHQ8BAf8E +BAMCB4AwEwYDVR0lBAwwCgYIKwYBBQUHAwEwDAYDVR0TAQH/BAIwADAPBgkrBgEE +AYLaSywEAgUAMA8GA1UdEQQIMAaHBH8AAAEwCgYIKoZIzj0EAwQDgYwAMIGIAkIB +TVEJrlJkxqs0adMPKg5D1EQDGy4dUz4YSWc0VXFOV7TKFDhjo1Abs3SYNXPsgAgT +Ol8BhJ2gFUhgHBP8BiJqPUYCQgFWXEe6AfKPyAUcNH28pIavfhxeGc0DGE4Xux0w +/vWpDdT89YxJmQC1roSaXRwEW1GBXL41h5rMMklGqkkfnCW2SQ== +-----END CERTIFICATE----- +` + +var delegatorKeyPEMP521 = `-----BEGIN EC PRIVATE KEY----- +MIHuAgEAMBAGByqGSM49AgEGBSuBBAAjBIHWMIHTAgEBBEIA4X72HzMvgBj//dX/ +SLkA2+oQ93l2eB2jXVRFST/mQj5NSSt8TNcIqW+TaxSejst7+jAQgnH2Zrith8zK +r2/Gy/6hgYkDgYYABADN59cQMUS2IZwzUanNKJ5jTPSJNCXI2untG2GvZqNKFf8u +Qz3jC91CQdQjSJhaQJMetsC4mZpPwYXD0tBLLSwMFwEwZG/6tH2ylGVxR3eIK+bK +UXwKLF8+b4NVS3ih6qVJLrciY4HRb7gWc5qdqJahimwUilBJbwxZGVpGZObhhJwr +CA== +-----END EC PRIVATE KEY----- +` + +// go run generate_cert.go -ed25519 -host 127.0.0.1 -allowDC + +var delegatorCertPEMEd25519 = `-----BEGIN CERTIFICATE----- +MIIBOTCB7KADAgECAhEAzk3wRF7IPMF07CnnLbQEbDAFBgMrZXAwEjEQMA4GA1UE +ChMHQWNtZSBDbzAeFw0yMTAyMjcwMDE4MTVaFw0yMjAyMjcwMDE4MTVaMBIxEDAO +BgNVBAoTB0FjbWUgQ28wKjAFBgMrZXADIQD+aRKJTaCG+yEz/w3lLhglSTsxyPl4 +FepwdCUXDxj2oKNXMFUwDgYDVR0PAQH/BAQDAgeAMBMGA1UdJQQMMAoGCCsGAQUF +BwMBMAwGA1UdEwEB/wQCMAAwDwYJKwYBBAGC2kssBAIFADAPBgNVHREECDAGhwR/ +AAABMAUGAytlcANBAO0XGRvpMAdkI8SVheJmr+Oe+BBR3VWyhU9PdIxiWu+v+pjp +UQDJpmto6r3AsriHVw2EIdvONnL1FeNzMX2HRAw= +-----END CERTIFICATE----- +` + +var delegatorKeyPEMEd25519 = `-----BEGIN EC PRIVATE KEY----- +MC4CAQAwBQYDK2VwBCIEILsRn/g0To97rbKf+2zV+sr6ZmrqcEiLRK2/rD7r+xDZ +-----END EC PRIVATE KEY----- +` + +var nonDelegatorCertPEM = `-----BEGIN CERTIFICATE----- +MIIBaDCCAQ6gAwIBAgIQcMnAGu3NQYTGYf2HK+JodTAKBggqhkjOPQQDAjASMRAw +DgYDVQQKEwdBY21lIENvMB4XDTIwMDgxODA1NDg1NloXDTIxMDgxODA1NDg1Nlow +EjEQMA4GA1UEChMHQWNtZSBDbzBZMBMGByqGSM49AgEGCCqGSM49AwEHA0IABPAi +QzOthHUdwLTPo9P7Vk1I2W5RHW5nIkq9zYqqMZ5mHQ6vmmrpklvTNHtY93PlokjN +pnlhzEsxK/QrBoAQ8fajRjBEMA4GA1UdDwEB/wQEAwIFoDATBgNVHSUEDDAKBggr +BgEFBQcDATAMBgNVHRMBAf8EAjAAMA8GA1UdEQQIMAaHBH8AAAEwCgYIKoZIzj0E +AwIDSAAwRQIgbOxx7/KWTD47UTWIBcFB95BPrFp2SaFBUyjhzMDXsQkCIQDnwtye +V1OlcMigjCsQuGRacYFP3f1ASpYVv58t/ZeVCw== +-----END CERTIFICATE----- +` + +var nonDelegatorKeyPEM = `-----BEGIN EC PRIVATE KEY----- +MIGHAgEAMBMGByqGSM49AgEGCCqGSM49AwEHBG0wawIBAQQgD9Q9131NamLDe4ud +dU9rg+gO0vv8lXYErf7P5GQlZD6hRANCAATwIkMzrYR1HcC0z6PT+1ZNSNluUR1u +ZyJKvc2KqjGeZh0Or5pq6ZJb0zR7WPdz5aJIzaZ5YcxLMSv0KwaAEPH2 +-----END EC PRIVATE KEY----- +` + +var ( + dcTestConfig *Config + dcTestCerts map[string]*Certificate + + serverDC []DelegatedCredentialPair + serverKEMDC []DelegatedCredentialPair + serverPQDC []DelegatedCredentialPair + + clientDC []DelegatedCredentialPair + clientKEMDC []DelegatedCredentialPair + clientPQDC []DelegatedCredentialPair + + dcNow time.Time + dcTestDCSignatureScheme = []SignatureScheme{ECDSAWithP256AndSHA256, Ed25519, Ed448, ECDSAWithP384AndSHA384, ECDSAWithP521AndSHA512} + dcTestDCKEMScheme = []SignatureScheme{KEMTLSWithSIKEp434, KEMTLSWithKyber512} + dcTestDCPQScheme = []SignatureScheme{PQTLSWithDilithium3, PQTLSWithDilithium4} +) + +func init() { + dcTestConfig = &Config{ + Time: func() time.Time { + return dcNow + }, + Rand: zeroSource{}, + Certificates: nil, + MinVersion: VersionTLS10, + MaxVersion: VersionTLS13, + CipherSuites: allCipherSuites(), + } + +} + +func initDCTest() { + // Use a static time for testing at which time the test certificates are + // valid. + dcNow = time.Date(2021, time.March, 31, 11, 0, 0, 234234, time.UTC) + + // The certificates of the server. + dcTestCerts = make(map[string]*Certificate) + var err error + + // The delegation P256 certificate. + dcCertP256 := new(Certificate) + *dcCertP256, err = X509KeyPair([]byte(delegatorCertPEMP256), []byte(delegatorKeyPEMP256)) + if err != nil { + panic(err) + } + + dcCertP256.Leaf, err = x509.ParseCertificate(dcCertP256.Certificate[0]) + if err != nil { + panic(err) + } + dcTestCerts["dcP256"] = dcCertP256 + + // The delegation P384 certificate. + dcCertP384 := new(Certificate) + *dcCertP384, err = X509KeyPair([]byte(delegatorCertPEMP384), []byte(delegatorKeyPEMP384)) + if err != nil { + panic(err) + } + + dcCertP384.Leaf, err = x509.ParseCertificate(dcCertP384.Certificate[0]) + if err != nil { + panic(err) + } + dcTestCerts["dcP384"] = dcCertP384 + + // The delegation P521 certificate. + dcCertP521 := new(Certificate) + *dcCertP521, err = X509KeyPair([]byte(delegatorCertPEMP521), []byte(delegatorKeyPEMP521)) + if err != nil { + panic(err) + } + + dcCertP521.Leaf, err = x509.ParseCertificate(dcCertP521.Certificate[0]) + if err != nil { + panic(err) + } + dcTestCerts["dcP521"] = dcCertP521 + + // The delegation Ed25519 certificate. + dcCertEd25519 := new(Certificate) + *dcCertEd25519, err = X509KeyPair([]byte(delegatorCertPEMEd25519), []byte(delegatorKeyPEMEd25519)) + if err != nil { + panic(err) + } + + dcCertEd25519.Leaf, err = x509.ParseCertificate(dcCertEd25519.Certificate[0]) + if err != nil { + panic(err) + } + dcTestCerts["dcEd25519"] = dcCertEd25519 + + // The non-delegation certificate. + noDcCert := new(Certificate) + *noDcCert, err = X509KeyPair([]byte(nonDelegatorCertPEM), []byte(nonDelegatorKeyPEM)) + if err != nil { + panic(err) + } + noDcCert.Leaf, err = x509.ParseCertificate(noDcCert.Certificate[0]) + if err != nil { + panic(err) + } + dcTestCerts["no dc"] = noDcCert + + // The root certificates for the peer. + dcTestConfig.RootCAs = x509.NewCertPool() + + for _, c := range dcTestCerts { + dcRoot, err := x509.ParseCertificate(c.Certificate[len(c.Certificate)-1]) + if err != nil { + panic(err) + } + dcTestConfig.RootCAs.AddCert(dcRoot) + } + + for i := 0; i < len(dcTestDCSignatureScheme); i++ { + dc, priv, err := NewDelegatedCredential(dcCertP256, dcTestDCSignatureScheme[i], dcNow.Sub(dcCertP256.Leaf.NotBefore)+dcMaxTTL, false) + if err != nil { + panic(err) + } + serverDC = append(serverDC, DelegatedCredentialPair{dc, priv}) + + dc, priv, err = NewDelegatedCredential(dcCertP256, dcTestDCSignatureScheme[i], dcNow.Sub(dcCertP256.Leaf.NotBefore)+dcMaxTTL, true) + if err != nil { + panic(err) + } + clientDC = append(clientDC, DelegatedCredentialPair{dc, priv}) + } + + for i := 0; i < len(dcTestDCKEMScheme); i++ { + dc, priv, err := NewDelegatedCredential(dcCertP256, dcTestDCKEMScheme[i], dcNow.Sub(dcCertP256.Leaf.NotBefore)+dcMaxTTL, false) + if err != nil { + panic(err) + } + serverKEMDC = append(serverKEMDC, DelegatedCredentialPair{dc, priv}) + + dc, priv, err = NewDelegatedCredential(dcCertP256, dcTestDCKEMScheme[i], dcNow.Sub(dcCertP256.Leaf.NotBefore)+dcMaxTTL, true) + if err != nil { + panic(err) + } + clientKEMDC = append(clientKEMDC, DelegatedCredentialPair{dc, priv}) + } + + for i := 0; i < len(dcTestDCPQScheme); i++ { + dc, priv, err := NewDelegatedCredential(dcCertP256, dcTestDCPQScheme[i], dcNow.Sub(dcCertP256.Leaf.NotBefore)+dcMaxTTL, false) + if err != nil { + panic(err) + } + serverPQDC = append(serverPQDC, DelegatedCredentialPair{dc, priv}) + + dc, priv, err = NewDelegatedCredential(dcCertP256, dcTestDCPQScheme[i], dcNow.Sub(dcCertP256.Leaf.NotBefore)+dcMaxTTL, true) + if err != nil { + panic(err) + } + clientPQDC = append(clientPQDC, DelegatedCredentialPair{dc, priv}) + } +} + +func publicKeysEqual(publicKey, publicKey2 crypto.PublicKey, algo SignatureScheme) error { + switch publicKey.(type) { + case *ecdsa.PublicKey: + curve := getECDSACurve(algo) + pk := publicKey.(*ecdsa.PublicKey) + pk2 := publicKey2.(*ecdsa.PublicKey) + + serPubKey := elliptic.Marshal(curve, pk.X, pk.Y) + serPubKey2 := elliptic.Marshal(curve, pk2.X, pk2.Y) + if !bytes.Equal(serPubKey2, serPubKey) { + return errors.New("ecdsa public Keys mismatch") + } + case ed25519.PublicKey: + pk := publicKey.(ed25519.PublicKey) + pk2 := publicKey2.(ed25519.PublicKey) + + if !bytes.Equal(pk, pk2) { + return errors.New("ed25519 Public Keys mismatch") + } + } + + return nil +} + +func delegagedCredentialsEqual(dc, dc2 *DelegatedCredential) error { + if dc2.cred.validTime != dc.cred.validTime { + return fmt.Errorf("ValidTime mismatch: got %d; want %d", dc2.cred.validTime, dc.cred.validTime) + } + + if dc2.cred.expCertVerfAlgo != dc.cred.expCertVerfAlgo { + return fmt.Errorf("scheme mismatch: got %04x; want %04x", dc2.cred.expCertVerfAlgo, dc.cred.expCertVerfAlgo) + } + + return publicKeysEqual(dc.cred.publicKey, dc2.cred.publicKey, dc.cred.expCertVerfAlgo) +} + +// Test delegation and validation of credentials. +func TestDelegateCredentialsValidate(t *testing.T) { + initDCTest() + cert := dcTestCerts["dcP384"] + validTime := dcNow.Sub(cert.Leaf.NotBefore) + dcMaxTTL + + delegatedCred, _, err := NewDelegatedCredential(cert, ECDSAWithP384AndSHA384, validTime, false) + if err != nil { + t.Fatal(err) + } else if delegatedCred == nil { + t.Fatal("unable to generate a Delegated Credential") + } + + rand := rand.New(rand.NewSource(time.Now().UnixNano())) + m := &certificateVerifyMsg{} + m.hasSignatureAlgorithm = true + m.signatureAlgorithm = ECDSAWithP384AndSHA384 + m.signature = randomBytes(rand.Intn(15)+1, rand) + + // Valid Delegated Credential + if !delegatedCred.Validate(cert.Leaf, false, dcNow, m) { + t.Error("generated valid Delegated Credential is rendered invalid") + } + + // Expired Delegated Credential + expired := dcNow.Add(dcMaxTTL).Add(time.Nanosecond) + if delegatedCred.Validate(cert.Leaf, false, expired, m) { + t.Error("expired delegated credential is valid; want invalid") + } + + // Test validation of Delegated Credential which TTL is too long + invalidDelegatedCred, _, err := NewDelegatedCredential(cert, ECDSAWithP384AndSHA384, validTime+time.Second, false) + if err != nil { + t.Fatal(err) + } + if invalidDelegatedCred.Validate(cert.Leaf, false, dcNow, m) { + t.Error("Delegated Credential validation with long TTL succeeded; want failure") + } + + shortValidTime := dcNow.Sub(cert.Leaf.NotBefore) + time.Second + + // Test validation of Delegated Credential which TTL is short + delegatedCred, _, err = NewDelegatedCredential(cert, ECDSAWithP384AndSHA384, shortValidTime, false) + if err != nil { + t.Fatal(err) + } + if !delegatedCred.Validate(cert.Leaf, false, dcNow, m) { + t.Error("valid Delegated Credential is invalid; want valid") + } + + delegatedCred.algorithm = ECDSAWithP521AndSHA512 + + // Test signature algorithm binding + if delegatedCred.Validate(cert.Leaf, false, dcNow, m) { + t.Error("Delegated Credential with wrong scheme is valid; want invalid") + } + + delegatedCred.algorithm = ECDSAWithP384AndSHA384 + + // Test delegation certificate binding + cert.Leaf.Raw[0] ^= byte(42) + if delegatedCred.Validate(cert.Leaf, false, dcNow, m) { + t.Error("Delegated Credential with wrong certificate is valid; want invalid") + } + + // Test validation of DC using a certificate that can't delegate. + if delegatedCred.Validate(dcTestCerts["no dc"].Leaf, false, dcNow, m) { + t.Error("Delegated Credential with non-delegation cert is valid; want invalid") + } + + // Test DC with another certificate + cert = dcTestCerts["dcP521"] + validTime = dcNow.Sub(cert.Leaf.NotBefore) + dcMaxTTL + delegatedCred, _, err = NewDelegatedCredential(cert, ECDSAWithP384AndSHA384, validTime, false) + if err != nil { + t.Fatal(err) + } else if delegatedCred == nil { + t.Fatal("unable to generate a Delegated Credential") + } + + // Valid Delegated Credential + if !delegatedCred.Validate(cert.Leaf, false, dcNow, m) { + t.Error("generated valid Delegated Credential is rendered invalid") + } +} + +// Test encoding/decoding of Delegated Credentials. +func TestDelegatedCredentialMarshal(t *testing.T) { + initDCTest() + cert := dcTestCerts["dcEd25519"] + time := dcNow.Sub(cert.Leaf.NotBefore) + dcMaxTTL + + for _, sig := range dcTestDCSignatureScheme { + delegatedCred, _, err := NewDelegatedCredential(cert, sig, time, false) + if err != nil { + t.Fatal(err) + } + + ser, err := delegatedCred.marshal() + if err != nil { + t.Error(err) + } + + delegatedCred2, err := unmarshalDelegatedCredential(ser) + if err != nil { + t.Error(err) + } + + err = delegagedCredentialsEqual(delegatedCred, delegatedCred2) + if err != nil { + t.Error(err) + } + + if delegatedCred.algorithm != delegatedCred2.algorithm { + t.Errorf("scheme mismatch: got %04x; want %04x", delegatedCred2.algorithm, delegatedCred.algorithm) + } + + if !bytes.Equal(delegatedCred2.signature, delegatedCred.signature) { + t.Error("Signature mismatch") + } + } +} + +var dcServerTests = []struct { + clientDCSupport bool + clientMaxVers uint16 + serverMaxVers uint16 + expectSuccess bool + expectDC bool + name string +}{ + {true, VersionTLS13, VersionTLS13, true, true, "tls13: DC client support"}, + {false, VersionTLS13, VersionTLS13, true, false, "DC not client support"}, + {true, VersionTLS12, VersionTLS13, true, false, "client using TLS 1.2. No DC is supported in that version."}, + {true, VersionTLS13, VersionTLS12, true, false, "server using TLS 1.2. No DC is supported in that version."}, + {true, VersionTLS11, VersionTLS13, true, false, "client using TLS 1.1. No DC is supported in that version."}, + {true, VersionTLS13, VersionTLS10, false, false, "server using TLS 1.0. No DC is supported in that version."}, +} + +var dcClientTests = []struct { + serverDCSupport bool + clientMaxVers uint16 + serverMaxVers uint16 + expectSuccess bool + expectDC bool + name string +}{ + {true, VersionTLS13, VersionTLS13, true, true, "tls13: DC server support"}, + {false, VersionTLS13, VersionTLS13, true, false, "DC not server support"}, + {true, VersionTLS12, VersionTLS13, true, false, "client using TLS 1.2. No DC is supported in that version."}, + {true, VersionTLS13, VersionTLS12, true, false, "server using TLS 1.2. No DC is supported in that version."}, + {true, VersionTLS11, VersionTLS13, true, false, "client using TLS 1.1. No DC is supported in that version."}, + {true, VersionTLS13, VersionTLS10, false, false, "server using TLS 1.0. No DC is supported in that version."}, +} + +// dcCount defines the delegated credential to be used as returned by the +// getCertificate or getClientCertificate callback. This allows to use +// delegated credentials with different algorithms at each run of the +// tests. +var dcCount int + +// Checks that the client suppports a version >= 1.3 and accepts Delegated +// Credentials. If so, it returns the delegation certificate; otherwise it +// returns a non-delegated certificate. +func testServerGetCertificate(ch *ClientHelloInfo) (*Certificate, error) { + versOk := false + for _, vers := range ch.SupportedVersions { + versOk = versOk || (vers >= uint16(VersionTLS13)) + } + + if versOk && ch.SupportsDelegatedCredential { + serverCert := dcTestCerts["dcP256"] + serverCert.DelegatedCredentials = serverDC[dcCount:] + return serverCert, nil + } + return dcTestCerts["no dc"], nil + +} + +// Checks that the client suppports a version >= 1.3 and accepts Delegated +// Credentials. If so, it returns the delegation certificate; otherwise it +// returns a non-Delegated certificate. +func testClientGetCertificate(cr *CertificateRequestInfo) (*Certificate, error) { + versOk := false + if cr.Version == VersionTLS13 { + versOk = true + } + + if versOk && cr.SupportsDelegatedCredential { + clientCert := dcTestCerts["dcP256"] + clientCert.DelegatedCredentials = clientDC[dcCount:] + return clientCert, nil + } + return dcTestCerts["no dc"], nil + +} + +// Tests the handshake and one round of application data. Returns true if the +// connection correctly used a Delegated Credential. +func testConnWithDC(t *testing.T, clientMsg, serverMsg string, clientConfig, serverConfig *Config, peer string, kemtls bool, pqtls bool) (usedDC bool, usedKEMTLS bool, usedPQTLS bool, serverState, clientState ConnectionState, err error) { + ln := newLocalListener(t) + defer ln.Close() + + serverCh := make(chan *Conn, 1) + var serverErr error + go func() { + serverConn, err := ln.Accept() + if err != nil { + serverErr = err + serverCh <- nil + return + } + server := Server(serverConn, serverConfig) + if err := server.Handshake(); err != nil { + serverErr = fmt.Errorf("handshake error: %v", err) + serverCh <- nil + return + } + serverCh <- server + }() + + var state ConnectionState + client, err := Dial("tcp", ln.Addr().String(), clientConfig) + if err != nil { + return false, false, false, state, state, err + } + defer client.Close() + + server := <-serverCh + if server == nil { + return false, false, false, state, state, serverErr + } + + bufLen := len(clientMsg) + if len(serverMsg) > len(clientMsg) { + bufLen = len(serverMsg) + } + buf := make([]byte, bufLen) + + client.Write([]byte(clientMsg)) + n, err := server.Read(buf) + if err != nil || n != len(clientMsg) || string(buf[:n]) != clientMsg { + return false, false, false, state, state, fmt.Errorf("Server read = %d, buf= %q; want %d, %s", n, buf, len(clientMsg), clientMsg) + } + + server.Write([]byte(serverMsg)) + n, err = client.Read(buf) + if n != len(serverMsg) || err != nil || string(buf[:n]) != serverMsg { + return false, false, false, state, state, fmt.Errorf("Client read = %d, %v, data %q; want %d, nil, %s", n, err, buf, len(serverMsg), serverMsg) + } + + if kemtls { + if peer == "server" { + return (server.verifiedDC != nil), (server.didKEMTLS && client.didKEMTLS), false, server.ConnectionState(), client.ConnectionState(), nil + } else if peer == "client" { + return (client.verifiedDC != nil), (server.didKEMTLS && client.didKEMTLS), false, server.ConnectionState(), client.ConnectionState(), nil + } else if peer == "both" { + return (client.verifiedDC != nil && server.verifiedDC != nil), (server.didKEMTLS && client.didKEMTLS), false, server.ConnectionState(), client.ConnectionState(), nil + } + } else if pqtls { + if peer == "server" { + return (server.verifiedDC != nil), false, (server.didPQTLS && client.didPQTLS), state, state, nil + } else if peer == "client" { + return (client.verifiedDC != nil), false, (server.didPQTLS && client.didPQTLS), state, state, nil + } else if peer == "both" { + return (client.verifiedDC != nil && server.verifiedDC != nil), false, (server.didPQTLS && client.didPQTLS), state, state, nil + } + + } else { + if peer == "server" { + return (server.verifiedDC != nil), false, false, state, state, nil + } else if peer == "client" { + return (client.verifiedDC != nil), false, false, state, state, nil + } else if peer == "both" { + return (client.verifiedDC != nil && server.verifiedDC != nil), false, false, state, state, nil + } + } + + return false, false, false, state, state, nil +} + +// Test the server authentication with the Delegated Credential extension. +func TestDCHandshakeServerAuth(t *testing.T) { + serverMsg := "hello, client" + clientMsg := "hello, server" + + clientConfig := dcTestConfig.Clone() + serverConfig := dcTestConfig.Clone() + clientConfig.InsecureSkipVerify = true + + for i, test := range dcServerTests { + clientConfig.SupportDelegatedCredential = test.clientDCSupport + + for dcCount = 0; dcCount < len(dcTestDCSignatureScheme); dcCount++ { + initDCTest() + serverConfig.GetCertificate = testServerGetCertificate + clientConfig.MaxVersion = test.clientMaxVers + serverConfig.MaxVersion = test.serverMaxVers + + usedDC, _, _, _, _, err := testConnWithDC(t, clientMsg, serverMsg, clientConfig, serverConfig, "client", false, false) + + if err != nil && test.expectSuccess { + t.Errorf("test #%d (%s) with signature algorithm #%d fails: %s", i, test.name, dcCount, err.Error()) + } else if err == nil && !test.expectSuccess { + t.Errorf("test #%d (%s) with signature algorithm #%d succeeds; expected failure", i, test.name, dcCount) + } + + if usedDC != test.expectDC { + t.Errorf("test #%d (%s) with signature algorithm #%d usedDC = %v; expected %v", i, test.name, dcCount, usedDC, test.expectDC) + } + } + } +} + +// Test the client authentication with the Delegated Credential extension. +func TestDCHandshakeClientAuth(t *testing.T) { + clientMsg := "hello, server" + serverMsg := "hello, client" + + serverConfig := dcTestConfig.Clone() + serverConfig.ClientAuth = RequestClientCert + serverConfig.GetCertificate = testServerGetCertificate + clientConfig := dcTestConfig.Clone() + clientConfig.GetClientCertificate = testClientGetCertificate + + for j, test := range dcClientTests { + serverConfig.SupportDelegatedCredential = test.serverDCSupport + + for dcCount = 0; dcCount < len(dcTestDCSignatureScheme); dcCount++ { + initDCTest() + serverConfig.MaxVersion = test.serverMaxVers + clientConfig.MaxVersion = test.clientMaxVers + + usedDC, _, _, _, _, err := testConnWithDC(t, clientMsg, serverMsg, clientConfig, serverConfig, "server", false, false) + + if err != nil && test.expectSuccess { + t.Errorf("test #%d (%s) with signature algorithm #%d fails: %s", j, test.name, dcCount, err.Error()) + } else if err == nil && !test.expectSuccess { + t.Errorf("test #%d (%s) with signature algorithm #%d succeeds; expected failure", j, test.name, dcCount) + } + + if usedDC != test.expectDC { + t.Errorf("test #%d (%s) with signature algorithm #%d usedDC = %v; expected %v", j, test.name, dcCount, usedDC, test.expectDC) + } + } + } +} + +// Test server and client authentication with the Delegated Credential extension. +func TestDCHandshakeClientAndServerAuth(t *testing.T) { + clientMsg := "hello, server" + serverMsg := "hello, client" + + serverConfig := dcTestConfig.Clone() + serverConfig.ClientAuth = RequestClientCert + serverConfig.GetCertificate = testServerGetCertificate + clientConfig := dcTestConfig.Clone() + clientConfig.GetClientCertificate = testClientGetCertificate + + serverConfig.SupportDelegatedCredential = true + clientConfig.SupportDelegatedCredential = true + + serverConfig.MaxVersion = VersionTLS13 + clientConfig.MaxVersion = VersionTLS13 + + initDCTest() + + usedDC, _, _, _, _, err := testConnWithDC(t, clientMsg, serverMsg, clientConfig, serverConfig, "both", false, false) + + if err != nil { + t.Errorf("test server and client auth fails: %s", err.Error()) + } + + if usedDC != true { + t.Errorf("test server and client auth does not succeed") + } +} + +var dcKEMServerTests = []struct { + clientDCSupport bool + clientMaxVers uint16 + serverMaxVers uint16 + expectSuccess bool + expectDC bool + name string +}{ + {true, VersionTLS13, VersionTLS13, true, true, "tls13: DC client support"}, + {false, VersionTLS13, VersionTLS13, false, false, "DC not client support"}, + {true, VersionTLS12, VersionTLS13, false, false, "client using TLS 1.2. No DC is supported in that version."}, + {true, VersionTLS13, VersionTLS12, false, false, "server using TLS 1.2. No DC is supported in that version."}, + {true, VersionTLS11, VersionTLS13, false, false, "client using TLS 1.1. No DC is supported in that version."}, + {true, VersionTLS13, VersionTLS10, false, false, "server using TLS 1.0. No DC is supported in that version."}, +} + +var dcKEMClientTests = []struct { + serverDCSupport bool + clientMaxVers uint16 + serverMaxVers uint16 + expectSuccess bool + expectDC bool + name string +}{ + {true, VersionTLS13, VersionTLS13, true, true, "tls13: DC server support"}, + {true, VersionTLS13, VersionTLS12, false, false, "server using TLS 1.2. No DC is supported in that version."}, + {true, VersionTLS11, VersionTLS13, false, false, "client using TLS 1.1. No DC is supported in that version."}, + {true, VersionTLS13, VersionTLS10, false, false, "server using TLS 1.0. No DC is supported in that version."}, +} + +// Checks that the client suppports a version >= 1.3 and accepts Delegated +// Credentials with KEMs. If so, it returns the delegation certificate; otherwise it +// returns a non-delegated certificate. +func testServerGetKEMCertificate(ch *ClientHelloInfo) (*Certificate, error) { + versOk := false + for _, vers := range ch.SupportedVersions { + versOk = versOk || (vers >= uint16(VersionTLS13)) + } + + if versOk && ch.SupportsDelegatedCredential { + serverCert := dcTestCerts["dcP256"] + serverCert.DelegatedCredentials = serverKEMDC[dcCount:] + return serverCert, nil + } + return dcTestCerts["no dc"], nil + +} + +// Checks that the client suppports a version >= 1.3 and accepts Delegated +// Credentials with KEMs. If so, it returns the delegation certificate; otherwise it +// returns a non-Delegated certificate. +func testClientGetKEMCertificate(cr *CertificateRequestInfo) (*Certificate, error) { + versOk := false + if cr.Version == VersionTLS13 { + versOk = true + } + + if versOk && cr.SupportsDelegatedCredential { + clientCert := dcTestCerts["dcP256"] + clientCert.DelegatedCredentials = clientKEMDC[dcCount:] + return clientCert, nil + } + return dcTestCerts["no dc"], nil + +} + +// Test the server authentication with the Delegated Credential extension using +// KEMs. +func TestDCKEMHandshakeServerAuth(t *testing.T) { + serverMsg := "hello, client" + clientMsg := "hello, server" + + clientConfig := dcTestConfig.Clone() + serverConfig := dcTestConfig.Clone() + clientConfig.KEMTLSEnabled = true + serverConfig.KEMTLSEnabled = true + clientConfig.CurvePreferences = []CurveID{Kyber512, SIKEp434} + serverConfig.CurvePreferences = []CurveID{Kyber512, SIKEp434} + clientConfig.InsecureSkipVerify = true + + for i, test := range dcKEMServerTests { + clientConfig.SupportDelegatedCredential = test.clientDCSupport + + for dcCount = 0; dcCount < len(dcTestDCKEMScheme); dcCount++ { + initDCTest() + serverConfig.GetCertificate = testServerGetKEMCertificate + clientConfig.MaxVersion = test.clientMaxVers + serverConfig.MaxVersion = test.serverMaxVers + + usedDC, usedKEMTLS, _, _, _, err := testConnWithDC(t, clientMsg, serverMsg, clientConfig, serverConfig, "client", true, false) + + if err != nil && test.expectSuccess { + t.Errorf("test #%d (%s) with kem #%d fails: %s", i, test.name, dcCount, err.Error()) + } else if err == nil && !test.expectSuccess { + t.Errorf("test #%d (%s) with kem #%d succeeds; expected failure", i, test.name, dcCount) + } + + if usedDC != test.expectDC { + t.Errorf("test #%d (%s) with kem #%d usedDC = %v; expected %v", i, test.name, dcCount, usedDC, test.expectDC) + } + + if !usedKEMTLS && test.expectSuccess { + t.Errorf("test #%d (%s) with kem #%d did not use kemtls", i, test.name, dcCount) + } + } + } +} + +// Test the client authentication with the Delegated Credential extension with +// KEMs. +func TestDCKEMHandshakeClientAuth(t *testing.T) { + clientMsg := "hello, server" + serverMsg := "hello, client" + + serverConfig := dcTestConfig.Clone() + serverConfig.ClientAuth = RequestClientCert + serverConfig.GetCertificate = testServerGetKEMCertificate + serverConfig.KEMTLSEnabled = true + serverConfig.CurvePreferences = []CurveID{SIKEp434, Kyber512} + + clientConfig := dcTestConfig.Clone() + clientConfig.GetClientCertificate = testClientGetKEMCertificate + clientConfig.SupportDelegatedCredential = true // to force the sending of a KEM DC + clientConfig.KEMTLSEnabled = true + clientConfig.CurvePreferences = []CurveID{SIKEp434, Kyber512} + + for i, test := range dcKEMClientTests { + serverConfig.SupportDelegatedCredential = test.serverDCSupport + + for dcCount = 0; dcCount < len(dcTestDCKEMScheme); dcCount++ { + initDCTest() + serverConfig.MaxVersion = test.serverMaxVers + clientConfig.MaxVersion = test.clientMaxVers + + usedDC, usedKEMTLS, _, _, _, err := testConnWithDC(t, clientMsg, serverMsg, clientConfig, serverConfig, "server", true, false) + + if err != nil && test.expectSuccess { + t.Errorf("test #%d (%s) with kem algorithm #%d fails: %s", i, test.name, dcCount, err.Error()) + } else if err == nil && !test.expectSuccess { + t.Errorf("test #%d (%s) with kem algorithm #%d succeeds; expected failure", i, test.name, dcCount) + } + + if usedDC != test.expectDC { + t.Errorf("test #%d (%s) with kem algorithm #%d usedDC = %v; expected %v", i, test.name, dcCount, usedDC, test.expectDC) + } + + if !usedKEMTLS && test.expectSuccess { + t.Errorf("test #%d (%s) with kem #%d did not use kemtls", i, test.name, dcCount) + } + } + } +} + +// Test server and client authentication with the Delegated Credential extension with kems. +func TestDCKEMHandshakeClientAndServerAuth(t *testing.T) { + clientMsg := "hello, server" + serverMsg := "hello, client" + + serverConfig := dcTestConfig.Clone() + serverConfig.ClientAuth = RequestClientCert + serverConfig.GetCertificate = testServerGetKEMCertificate + clientConfig := dcTestConfig.Clone() + clientConfig.GetClientCertificate = testClientGetKEMCertificate + clientConfig.KEMTLSEnabled = true + serverConfig.KEMTLSEnabled = true + clientConfig.CurvePreferences = []CurveID{Kyber512} + serverConfig.CurvePreferences = []CurveID{Kyber512} + + serverConfig.SupportDelegatedCredential = true + clientConfig.SupportDelegatedCredential = true + + serverConfig.MaxVersion = VersionTLS13 + clientConfig.MaxVersion = VersionTLS13 + + initDCTest() + + usedDC, usedKEMTLS, _, _, _, err := testConnWithDC(t, clientMsg, serverMsg, clientConfig, serverConfig, "both", true, false) + + if err != nil { + t.Errorf("test server and client auth with kems fails: %s", err.Error()) + } + + if usedDC != true { + t.Errorf("test server and client auth with kems does not succeed") + } + + if !usedKEMTLS { + t.Errorf("test server and client auth with kems did not use kemtls") + } +} + +// Test server and client authentication with the Delegated Credential extension with kems and cached information. +func TestDCKEMCachedInfoHandshakeServerAuth(t *testing.T) { + clientMsg := "hello, server" + serverMsg := "hello, client" + + serverConfig := dcTestConfig.Clone() + serverConfig.GetCertificate = testServerGetKEMCertificate + clientConfig := dcTestConfig.Clone() + clientConfig.GetClientCertificate = testClientGetKEMCertificate + clientConfig.KEMTLSEnabled = true + serverConfig.KEMTLSEnabled = true + clientConfig.CurvePreferences = []CurveID{Kyber512} + serverConfig.CurvePreferences = []CurveID{Kyber512} + + serverConfig.SupportDelegatedCredential = true + clientConfig.SupportDelegatedCredential = true + + serverConfig.MaxVersion = VersionTLS13 + clientConfig.MaxVersion = VersionTLS13 + + initDCTest() + + usedDC, usedKEMTLS, _, _, clientState, err := testConnWithDC(t, clientMsg, serverMsg, clientConfig, serverConfig, "client", true, false) + + if err != nil { + t.Errorf("test server and client auth with kems fails: %s", err.Error()) + } + + if usedDC != true { + t.Errorf("test server and client auth with kems does not succeed") + } + + if !usedKEMTLS { + t.Errorf("test server and client auth with kems did not use kemtls") + } + + clientConfig.CachedCert = clientState.CertificateMessage + clientConfig.CachedCertReq = clientState.CertificateReqMessage + + usedDC, usedKEMTLS, _, _, _, err = testConnWithDC(t, clientMsg, serverMsg, clientConfig, serverConfig, "client", true, false) + + if err != nil { + t.Errorf("test server and client auth with kems fails: %s", err.Error()) + } + + if usedDC != true { + t.Errorf("test server and client auth with kems does not succeed") + } + + if !usedKEMTLS { + t.Errorf("test server and client auth with kems did not use kemtls") + } +} + +var dcPQServerTests = []struct { + clientDCSupport bool + clientMaxVers uint16 + serverMaxVers uint16 + expectSuccess bool + expectDC bool + name string +}{ + {true, VersionTLS13, VersionTLS13, true, true, "tls13: DC client support"}, + {false, VersionTLS13, VersionTLS13, false, false, "DC not client support"}, + {true, VersionTLS12, VersionTLS13, false, false, "client using TLS 1.2. No DC is supported in that version."}, + {true, VersionTLS13, VersionTLS12, false, false, "server using TLS 1.2. No DC is supported in that version."}, + {true, VersionTLS11, VersionTLS13, false, false, "client using TLS 1.1. No DC is supported in that version."}, + {true, VersionTLS13, VersionTLS10, false, false, "server using TLS 1.0. No DC is supported in that version."}, +} + +var dcPQClientTests = []struct { + serverDCSupport bool + clientMaxVers uint16 + serverMaxVers uint16 + expectSuccess bool + expectDC bool + name string +}{ + {true, VersionTLS13, VersionTLS13, true, true, "tls13: DC server support"}, + {true, VersionTLS13, VersionTLS12, false, false, "server using TLS 1.2. No DC is supported in that version."}, + {true, VersionTLS11, VersionTLS13, false, false, "client using TLS 1.1. No DC is supported in that version."}, + {true, VersionTLS13, VersionTLS10, false, false, "server using TLS 1.0. No DC is supported in that version."}, +} + +// Checks that the client suppports a version >= 1.3 and accepts Delegated +// Credentials with KEMs. If so, it returns the delegation certificate; otherwise it +// returns a non-delegated certificate. +func testServerGetPQCertificate(ch *ClientHelloInfo) (*Certificate, error) { + versOk := false + for _, vers := range ch.SupportedVersions { + versOk = versOk || (vers >= uint16(VersionTLS13)) + } + + if versOk && ch.SupportsDelegatedCredential { + serverCert := dcTestCerts["dcP256"] + serverCert.DelegatedCredentials = serverPQDC[dcCount:] + return serverCert, nil + } + return dcTestCerts["no dc"], nil + +} + +// Checks that the client suppports a version >= 1.3 and accepts Delegated +// Credentials with KEMs. If so, it returns the delegation certificate; otherwise it +// returns a non-Delegated certificate. +func testClientGetPQCertificate(cr *CertificateRequestInfo) (*Certificate, error) { + versOk := false + if cr.Version == VersionTLS13 { + versOk = true + } + + if versOk && cr.SupportsDelegatedCredential { + clientCert := dcTestCerts["dcP256"] + clientCert.DelegatedCredentials = clientPQDC[dcCount:] + return clientCert, nil + } + return dcTestCerts["no dc"], nil + +} + +// Test the server authentication with the Delegated Credential extension using +// PQTLS. +func TestDCPQHandshakeServerAuth(t *testing.T) { + serverMsg := "hello, client" + clientMsg := "hello, server" + + clientConfig := dcTestConfig.Clone() + serverConfig := dcTestConfig.Clone() + clientConfig.PQTLSEnabled = true + serverConfig.PQTLSEnabled = true + clientConfig.CurvePreferences = []CurveID{Kyber512, SIKEp434} + serverConfig.CurvePreferences = []CurveID{Kyber512, SIKEp434} + clientConfig.InsecureSkipVerify = true + + for i, test := range dcKEMServerTests { + clientConfig.SupportDelegatedCredential = test.clientDCSupport + + for dcCount = 0; dcCount < len(dcTestDCPQScheme); dcCount++ { + initDCTest() + serverConfig.GetCertificate = testServerGetPQCertificate + clientConfig.MaxVersion = test.clientMaxVers + serverConfig.MaxVersion = test.serverMaxVers + + usedDC, _, usedPQTLS, _, _, err := testConnWithDC(t, clientMsg, serverMsg, clientConfig, serverConfig, "client", false, true) + + if err != nil && test.expectSuccess { + t.Errorf("test #%d (%s) with pq #%d fails: %s", i, test.name, dcCount, err.Error()) + } else if err == nil && !test.expectSuccess { + t.Errorf("test #%d (%s) with pq #%d succeeds; expected failure", i, test.name, dcCount) + } + + if usedDC != test.expectDC { + t.Errorf("test #%d (%s) with pq #%d usedDC = %v; expected %v", i, test.name, dcCount, usedDC, test.expectDC) + } + + if !usedPQTLS && test.expectSuccess { + t.Errorf("test #%d (%s) with pq #%d did not use pqtls", i, test.name, dcCount) + } + } + } +} + +// Test the client authentication with the Delegated Credential extension with +// PQTLS. +func TestDCPQHandshakeClientAuth(t *testing.T) { + clientMsg := "hello, server" + serverMsg := "hello, client" + + serverConfig := dcTestConfig.Clone() + serverConfig.ClientAuth = RequestClientCert + serverConfig.GetCertificate = testServerGetPQCertificate + serverConfig.PQTLSEnabled = true + serverConfig.CurvePreferences = []CurveID{SIKEp434, Kyber512} + + clientConfig := dcTestConfig.Clone() + clientConfig.GetClientCertificate = testClientGetPQCertificate + clientConfig.SupportDelegatedCredential = true // to force the sending of a PQ DC + clientConfig.PQTLSEnabled = true + clientConfig.CurvePreferences = []CurveID{SIKEp434, Kyber512} + + for i, test := range dcPQClientTests { + serverConfig.SupportDelegatedCredential = test.serverDCSupport + + for dcCount = 0; dcCount < len(dcTestDCPQScheme); dcCount++ { + initDCTest() + serverConfig.MaxVersion = test.serverMaxVers + clientConfig.MaxVersion = test.clientMaxVers + + usedDC, _, usedPQTLS, _, _, err := testConnWithDC(t, clientMsg, serverMsg, clientConfig, serverConfig, "server", false, true) + + if err != nil && test.expectSuccess { + t.Errorf("test #%d (%s) with pq algorithm #%d fails: %s", i, test.name, dcCount, err.Error()) + } else if err == nil && !test.expectSuccess { + t.Errorf("test #%d (%s) with pq algorithm #%d succeeds; expected failure", i, test.name, dcCount) + } + + if usedDC != test.expectDC { + t.Errorf("test #%d (%s) with pq algorithm #%d usedDC = %v; expected %v", i, test.name, dcCount, usedDC, test.expectDC) + } + + if !usedPQTLS && test.expectSuccess { + t.Errorf("test #%d (%s) with pqs #%d did not use pqtls", i, test.name, dcCount) + } + } + } +} + +// Test server and client authentication with the Delegated Credential extension with pqtls. +func TestDCPQHandshakeClientAndServerAuth(t *testing.T) { + clientMsg := "hello, server" + serverMsg := "hello, client" + + serverConfig := dcTestConfig.Clone() + serverConfig.ClientAuth = RequestClientCert + serverConfig.GetCertificate = testServerGetPQCertificate + clientConfig := dcTestConfig.Clone() + clientConfig.GetClientCertificate = testClientGetPQCertificate + clientConfig.PQTLSEnabled = true + serverConfig.PQTLSEnabled = true + clientConfig.CurvePreferences = []CurveID{Kyber512} + serverConfig.CurvePreferences = []CurveID{Kyber512} + + serverConfig.SupportDelegatedCredential = true + clientConfig.SupportDelegatedCredential = true + + serverConfig.MaxVersion = VersionTLS13 + clientConfig.MaxVersion = VersionTLS13 + + initDCTest() + + usedDC, _, usedPQTLS, _, _, err := testConnWithDC(t, clientMsg, serverMsg, clientConfig, serverConfig, "both", false, true) + + if err != nil { + t.Errorf("test server and client auth with pqs fails: %s", err.Error()) + } + + if usedDC != true { + t.Errorf("test server and client auth with pqs does not succeed") + } + + if !usedPQTLS { + t.Errorf("test server and client auth with pqs did not use pqtls") + } +} diff --git a/src/crypto/tls/ech.go b/src/crypto/tls/ech.go new file mode 100644 index 00000000000..05ad0a303b2 --- /dev/null +++ b/src/crypto/tls/ech.go @@ -0,0 +1,929 @@ +// Copyright 2020 Cloudflare, Inc. All rights reserved. Use of this source code +// is governed by a BSD-style license that can be found in the LICENSE file. + +package tls + +import ( + "circl/hpke" + "errors" + "fmt" + "io" + + "golang.org/x/crypto/cryptobyte" +) + +const ( + // Constants for TLS operations + echAcceptConfirmationLabel = "ech accept confirmation" + + // Constants for HPKE operations + echHpkeInfoSetup = "tls ech" +) + +// TODO(cjpatton): "[When offering ECH, the client] MUST NOT offer to resume any +// session for TLS 1.2 and below [in ClientHelloInner]." +// +// TODO(cjpatton): "[When offering ECH, the client] MUST NOT include the +// "pre_shared_key" extension [in ClientHelloOuter]." (This is a "don't stick +// out" issue.) +// +// TODO(cjpatton): Implement client-side padding. +func (c *Conn) echOfferOrGrease(helloBase *clientHelloMsg) (hello, helloInner *clientHelloMsg, err error) { + config := c.config + + if !config.ECHEnabled || + (c.hrrTriggered && testingECHTriggerBypassAfterHRR) || + (!c.hrrTriggered && testingECHTriggerBypassBeforeHRR) { + // Bypass ECH. + return helloBase, nil, nil + } + + echConfig := config.echSelectConfig() + if echConfig == nil || config.maxSupportedVersion() < VersionTLS13 { + // Compute artifacts that are reused across HRR. + if c.ech.dummy == nil { + // Serialized ClientECH. + c.ech.dummy, err = echGenerateDummyExt(config.rand()) + if err != nil { + return nil, nil, fmt.Errorf("tls: ech: failed to generate grease ECH: %s", err) + } + } + + // Grease ECH. + helloBase.ech = c.ech.dummy + helloBase.echIsOuter = true + c.ech.offered = false + c.ech.greased = true + helloBase.raw = nil + return helloBase, nil, nil + } + + // Compute artifacts that are reused across HRR. + var enc []byte + if c.ech.sealer == nil { + // HPKE context. + enc, c.ech.sealer, err = echConfig.setupSealer(config.rand()) + if err != nil { + return nil, nil, fmt.Errorf("tls: ech: %s", err) + } + + // ECHConfig.contents.public_name. + c.ech.publicName = string(echConfig.rawPublicName) + + // ECHConfig.contents.key_config.config_id. + c.ech.configId = echConfig.configId + + // ClientHelloInner.random. + c.ech.innerRandom = make([]byte, 32) + if _, err = io.ReadFull(config.rand(), c.ech.innerRandom); err != nil { + return nil, nil, fmt.Errorf("tls: short read from Rand: %s", err) + } + } + + // ClientHelloInner is constructed from helloBase, but uses a fresh "random" + // (helloBase.random is used for ClientHelloOuter) and an empty + // "ech_is_inner" extension indicating that this is the ClientHelloInner. + helloInner = new(clientHelloMsg) + *helloInner = *helloBase + helloInner.random = c.ech.innerRandom + helloInner.echIsInner = true + + // Ensure that only TLS 1.3 and above are offered. + if v := helloInner.supportedVersions; len(v) == 0 || v[len(v)-1] < VersionTLS13 { + return nil, nil, errors.New("tls: ech: only TLS 1.3 is allowed in ClientHelloInner") + } + + // EncodedClientHelloInner is constructed from ClientHelloInner by removing + // extensions that are also used in the ClientHelloOuter. + // + // NOTE(cjpatton): It would be nice to incorporate more extensions, but + // "key_share" is the last extension to appear in the ClientHello before + // "pre_shared_key". As a result, the only contiguous sequence of outer + // extensions that contains "key_share" is "key_share" itself. Note that + // we cannot change the order of extensions in the ClientHello, as the + // unit tests expect "key_share" to be the second to last extension. + outerExtensions := []uint16{extensionKeyShare} + if testingECHOuterExtMany { + // NOTE(cjpatton): Incorporating this particular sequence does not + // yield significant savings. However, it's useful to test that our + // server correctly handles a sequence of compressed extensions and + // not just one. + outerExtensions = []uint16{ + extensionStatusRequest, + extensionSupportedCurves, + extensionSupportedPoints, + } + } else if testingECHOuterExtNone { + outerExtensions = nil + } + encodedHelloInner := echEncodeClientHelloInner(helloInner.marshal(), outerExtensions) + if encodedHelloInner == nil { + return nil, nil, errors.New("tls: ech: encoding of EncodedClientHelloInner failed") + } + + // ClientHelloOuter is constructed by generating a fresh ClientHello and + // copying "key_share", "random", and "sesion_id" from helloBase, setting + // "server_name" to be the client-facing server, and adding the + // "encrypted_client_hello" extension. + hello, _, _, err = c.makeClientHello(config.MinVersion) + if err != nil { + return nil, nil, fmt.Errorf("tls: ech: %s", err) + } + hello.keyShares = helloBase.keyShares + hello.random = helloBase.random + hello.sessionId = helloBase.sessionId + hello.serverName = hostnameInSNI(c.ech.publicName) + hello.echIsOuter = true + if testingECHOuterIsInner { + hello.echIsInner = true + } + + // ClientECH, the payload of the "encrypted_client_hello" extension. + var ech echClient + _, kdfId, aeadId := c.ech.sealer.Suite().Params() + ech.handle.suite.kdfId = uint16(kdfId) + ech.handle.suite.aeadId = uint16(aeadId) + ech.handle.configId = echConfig.configId + ech.handle.enc = enc // Empty after HRR + helloOuterAad := echEncodeClientHelloOuterAAD(hello.marshal(), ech.handle.marshal()) + if helloOuterAad == nil { + return nil, nil, errors.New("tls: ech: encoding of ClientHelloOuterAAD failed") + } + ech.payload, err = c.ech.sealer.Seal(encodedHelloInner, helloOuterAad) + if err != nil { + return nil, nil, fmt.Errorf("tls: ech: seal failed: %s", err) + } + if testingECHTriggerPayloadDecryptError { + ech.payload[0] ^= 0xff // Inauthentic ciphertext + } + hello.ech = ech.marshal() + + // Offer ECH. + c.ech.offered = true + helloInner.raw = nil + hello.raw = nil + return hello, helloInner, nil +} + +func (c *Conn) echAcceptOrReject(hello *clientHelloMsg) (*clientHelloMsg, error) { + config := c.config + p := config.ServerECHProvider + + if !config.echCanAccept() { + // Bypass ECH. + return hello, nil + } + + if hello.echIsInner { + if hello.echIsOuter { + c.sendAlert(alertIllegalParameter) + return hello, errors.New("ech: hello marked as inner and outer") + } + if len(hello.ech) > 0 { + c.sendAlert(alertIllegalParameter) + return hello, errors.New("ech_is_inner: got non-empty payload") + } + // Bypass ECH and continue as backend server. + return hello, nil + } + + if !hello.echIsOuter { + if c.ech.offered { + // This occurs if the server accepted prior to HRR, but the client + // failed to send the ECH extension in the second ClientHelloOuter. This + // would cause ClientHelloOuter to be used after ClientHelloInner, which + // is illegal. + c.sendAlert(alertMissingExtension) + return nil, errors.New("ech: hrr: bypass after offer") + } + // Bypass ECH. + return hello, nil + } + + if c.hrrTriggered && !c.ech.offered && !c.ech.greased { + // The client bypassed ECH prior to HRR, but not after. This could + // cause ClientHelloInner to be used after ClientHelloOuter, which is + // illegal. + c.sendAlert(alertIllegalParameter) + return nil, errors.New("ech: hrr: offer or grease after bypass") + } + + // Parse ClientECH. + ech, err := echUnmarshalClient(hello.ech) + if err != nil { + c.sendAlert(alertIllegalParameter) + return nil, fmt.Errorf("ech: failed to parse extension: %s", err) + } + if c.hrrTriggered && c.ech.offered && + (ech.handle.suite != c.ech.suite || + ech.handle.configId != c.ech.configId || + len(ech.handle.enc) > 0) { + // The context handle shouldn't change across HRR. + c.sendAlert(alertIllegalParameter) + return nil, errors.New("ech: hrr: illegal handle in second hello") + } + c.ech.suite = ech.handle.suite + + // Ask the ECH provider for the HPKE context. + if c.ech.opener == nil { + res := p.GetDecryptionContext(ech.handle.marshal(), extensionECH) + + // Compute retry configurations, skipping those indicating an + // unsupported version. + if len(res.RetryConfigs) > 0 { + configs, err := UnmarshalECHConfigs(res.RetryConfigs) + if err != nil { + c.sendAlert(alertInternalError) + return nil, fmt.Errorf("ech: %s", err) + } + + if len(configs) > 0 { + c.ech.retryConfigs, err = echMarshalConfigs(configs) + if err != nil { + c.sendAlert(alertInternalError) + return nil, fmt.Errorf("ech: %s", err) + } + } + + // Check if the outer SNI matches the public name of any ECH config + // advertised by the client-facing server. As of + // draft-ietf-tls-esni-10, the client is required to use the ECH + // config's public name as the outer SNI. Although there's no real + // reason for the server to enforce this, it worth noting it when it + // happens. + pubNameMatches := false + for _, config := range configs { + if hello.serverName == string(config.rawPublicName) { + pubNameMatches = true + } + } + if !pubNameMatches { + c.handleCFEvent(CFEventECHPublicNameMismatch{}) + } + } + + switch res.Status { + case ECHProviderSuccess: + c.ech.opener, err = hpke.UnmarshalOpener(res.Context) + if err != nil { + c.sendAlert(alertInternalError) + return nil, fmt.Errorf("ech: %s", err) + } + case ECHProviderReject: + // Reject ECH. We do not know at this point whether the client + // intended to offer or grease ECH, so we presume grease until the + // client indicates rejection by sending an "ech_required" alert. + c.ech.greased = true + return hello, nil + case ECHProviderAbort: + c.sendAlert(alert(res.Alert)) + return nil, fmt.Errorf("ech: %s", err) + default: + c.sendAlert(alertInternalError) + return nil, errors.New("ech: unexpected provider status") + } + } + + // EncodedClientHelloInner, the plaintext corresponding to + // ClientECH.payload. + helloOuterAad := echEncodeClientHelloOuterAAD(hello.marshal(), ech.handle.marshal()) + if helloOuterAad == nil { + // This occurs if the ClientHelloOuter is malformed. This values was + // already parsed into `hello`, so this should not happen. + c.sendAlert(alertInternalError) + return nil, fmt.Errorf("ech: failed to encode ClientHelloOuterAAD") + } + rawEncodedHelloInner, err := c.ech.opener.Open(ech.payload, helloOuterAad) + if err != nil { + if c.hrrTriggered && c.ech.accepted { + // Don't reject after accept, as this would result in processing the + // ClientHelloOuter after processing the ClientHelloInner. + c.sendAlert(alertDecryptError) + return nil, fmt.Errorf("ech: hrr: reject after accept: %s", err) + } + // Reject ECH. We do not know at this point whether the client + // intended to offer or grease ECH, so we presume grease until the + // client indicates rejection by sending an "ech_required" alert. + c.ech.greased = true + return hello, nil + } + + // ClientHelloInner, obtained by decoding EncodedClientHelloInner. + rawHelloInner := echDecodeClientHelloInner(rawEncodedHelloInner, hello.marshal(), hello.sessionId) + if rawHelloInner == nil { + c.sendAlert(alertIllegalParameter) + return nil, fmt.Errorf("ech: failed to decode EncodedClientHelloInner") + } + helloInner := new(clientHelloMsg) + if !helloInner.unmarshal(rawHelloInner) { + c.sendAlert(alertIllegalParameter) + return nil, fmt.Errorf("ech: failed to parse ClientHelloInner") + } + + // Accept ECH. + c.ech.offered = true + c.ech.accepted = true + return helloInner, nil +} + +// echClient represents a ClientECH structure, the payload of the client's +// "encrypted_client_hello" extension. +type echClient struct { + raw []byte + + // Parsed from raw + handle echContextHandle + payload []byte +} + +// echUnmarshalClient parses a ClientECH structure. The caller provides the ECH +// version indicated by the client. +func echUnmarshalClient(raw []byte) (*echClient, error) { + // Parse the payload as a ClientECH structure. + ech := new(echClient) + ech.raw = raw + + // Parse the context handle. + s := cryptobyte.String(raw) + if !echReadContextHandle(&s, &ech.handle) { + return nil, fmt.Errorf("error parsing context handle") + } + ech.handle.raw = raw[:len(raw)-len(s)] + + // Parse the payload. + var t cryptobyte.String + if !s.ReadUint16LengthPrefixed(&t) || + !t.ReadBytes(&ech.payload, len(t)) || !s.Empty() { + return nil, fmt.Errorf("error parsing payload") + } + + return ech, nil +} + +func (ech *echClient) marshal() []byte { + if ech.raw != nil { + return ech.raw + } + var b cryptobyte.Builder + b.AddBytes(ech.handle.marshal()) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(ech.payload) + }) + return b.BytesOrPanic() +} + +// echContextHandle represents the prefix of a ClientECH structure used by +// the server to compute the HPKE context. +type echContextHandle struct { + raw []byte + + // Parsed from raw + suite hpkeSymmetricCipherSuite + configId uint8 + enc []byte +} + +func (handle *echContextHandle) marshal() []byte { + if handle.raw != nil { + return handle.raw + } + var b cryptobyte.Builder + b.AddUint16(handle.suite.kdfId) + b.AddUint16(handle.suite.aeadId) + b.AddUint8(handle.configId) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(handle.enc) + }) + return b.BytesOrPanic() +} + +func echReadContextHandle(s *cryptobyte.String, handle *echContextHandle) bool { + var t cryptobyte.String + if !s.ReadUint16(&handle.suite.kdfId) || // cipher_suite.kdf_id + !s.ReadUint16(&handle.suite.aeadId) || // cipher_suite.aead_id + !s.ReadUint8(&handle.configId) || // config_id + !s.ReadUint16LengthPrefixed(&t) || // enc + !t.ReadBytes(&handle.enc, len(t)) { + return false + } + return true +} + +// hpkeSymmetricCipherSuite represents an ECH ciphersuite, a KDF/AEAD algorithm pair. This +// is different from an HPKE ciphersuite, which represents a KEM/KDF/AEAD +// triple. +type hpkeSymmetricCipherSuite struct { + kdfId, aeadId uint16 +} + +// Generates a grease ECH extension using a hard-coded KEM public key. +func echGenerateDummyExt(rand io.Reader) ([]byte, error) { + var err error + var dummyX25519PublicKey = []byte{ + 143, 38, 37, 36, 12, 6, 229, 30, 140, 27, 167, 73, 26, 100, 203, 107, 216, + 81, 163, 222, 52, 211, 54, 210, 46, 37, 78, 216, 157, 97, 241, 244, + } + dummyEncodedHelloInnerLen := 100 // TODO(cjpatton): Compute this correctly. + kem, kdf, aead := defaultHPKESuite.Params() + + pk, err := kem.Scheme().UnmarshalBinaryPublicKey(dummyX25519PublicKey) + if err != nil { + return nil, fmt.Errorf("tls: grease ech: failed to parse dummy public key: %s", err) + } + sender, err := defaultHPKESuite.NewSender(pk, nil) + if err != nil { + return nil, fmt.Errorf("tls: grease ech: failed to create sender: %s", err) + } + + var ech echClient + ech.handle.suite.kdfId = uint16(kdf) + ech.handle.suite.aeadId = uint16(aead) + randomByte := make([]byte, 1) + _, err = io.ReadFull(rand, randomByte) + if err != nil { + return nil, fmt.Errorf("tls: grease ech:: %s", err) + } + ech.handle.configId = randomByte[0] + ech.handle.enc, _, err = sender.Setup(rand) + if err != nil { + return nil, fmt.Errorf("tls: grease ech:: %s", err) + } + ech.payload = make([]byte, dummyEncodedHelloInnerLen+defaultHPKESuiteTagLen) + if _, err = io.ReadFull(rand, ech.payload); err != nil { + return nil, fmt.Errorf("tls: grease ech:: %s", err) + } + return ech.marshal(), nil +} + +// echEncodeClientHelloInner interprets innerData as a ClientHelloInner message +// and transforms it into an EncodedClientHelloInner. Returns nil if parsing +// innerData fails. +// +// outerExtensions specifies the contiguous sequence of extensions that will be +// incorporated using the "ech_outer_extensions" mechanism. +func echEncodeClientHelloInner(innerData []byte, outerExtensions []uint16) []byte { + var ( + errIllegalParameter = errors.New("illegal parameter") + msgType uint8 + legacyVersion uint16 + random []byte + legacySessionId cryptobyte.String + cipherSuites cryptobyte.String + legacyCompressionMethods cryptobyte.String + extensions cryptobyte.String + s cryptobyte.String + b cryptobyte.Builder + ) + + u := cryptobyte.String(innerData) + if !u.ReadUint8(&msgType) || + !u.ReadUint24LengthPrefixed(&s) || !u.Empty() { + return nil + } + + if !s.ReadUint16(&legacyVersion) || + !s.ReadBytes(&random, 32) || + !s.ReadUint8LengthPrefixed(&legacySessionId) || + !s.ReadUint16LengthPrefixed(&cipherSuites) || + !s.ReadUint8LengthPrefixed(&legacyCompressionMethods) { + return nil + } + + if s.Empty() { + // Extensions field must be present in TLS 1.3. + return nil + } + + if !s.ReadUint16LengthPrefixed(&extensions) || !s.Empty() { + return nil + } + + b.AddUint16(legacyVersion) + b.AddBytes(random) + b.AddUint8(0) // 0-length legacy_session_id + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(cipherSuites) + }) + b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(legacyCompressionMethods) + }) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + if testingECHOuterExtIncorrectOrder { + // Replace outer extensions with "outer_extension" extension, but in + // the incorrect order. + echAddOuterExtensions(b, outerExtensions) + } + + for !extensions.Empty() { + var ext uint16 + var extData cryptobyte.String + if !extensions.ReadUint16(&ext) || + !extensions.ReadUint16LengthPrefixed(&extData) { + panic(cryptobyte.BuildError{Err: errIllegalParameter}) + } + + if len(outerExtensions) > 0 && ext == outerExtensions[0] { + if !testingECHOuterExtIncorrectOrder { + // Replace outer extensions with "outer_extension" extension. + echAddOuterExtensions(b, outerExtensions) + } + + // Consume the remaining outer extensions. + for _, outerExt := range outerExtensions[1:] { + if !extensions.ReadUint16(&ext) || + !extensions.ReadUint16LengthPrefixed(&extData) { + panic(cryptobyte.BuildError{Err: errIllegalParameter}) + } + if ext != outerExt { + panic("internal error: malformed ClientHelloInner") + } + } + + } else { + b.AddUint16(ext) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(extData) + }) + } + } + }) + + encodedData, err := b.Bytes() + if err == errIllegalParameter { + return nil // Input malformed + } else if err != nil { + panic(err) // Host encountered internal error + } + + return encodedData +} + +func echAddOuterExtensions(b *cryptobyte.Builder, outerExtensions []uint16) { + b.AddUint16(extensionECHOuterExtensions) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { + for _, outerExt := range outerExtensions { + b.AddUint16(outerExt) + } + if testingECHOuterExtIllegal { + // This is not allowed. + b.AddUint16(extensionECH) + } + }) + }) +} + +// echDecodeClientHelloInner interprets encodedData as an EncodedClientHelloInner +// message and substitutes the "outer_extension" extension with extensions from +// outerData, interpreted as the ClientHelloOuter message. Returns nil if +// parsing encodedData fails. +func echDecodeClientHelloInner(encodedData, outerData, outerSessionId []byte) []byte { + var ( + errIllegalParameter = errors.New("illegal parameter") + legacyVersion uint16 + random []byte + legacySessionId cryptobyte.String + cipherSuites cryptobyte.String + legacyCompressionMethods cryptobyte.String + extensions cryptobyte.String + b cryptobyte.Builder + ) + + s := cryptobyte.String(encodedData) + if !s.ReadUint16(&legacyVersion) || + !s.ReadBytes(&random, 32) || + !s.ReadUint8LengthPrefixed(&legacySessionId) || + !s.ReadUint16LengthPrefixed(&cipherSuites) || + !s.ReadUint8LengthPrefixed(&legacyCompressionMethods) { + return nil + } + + if len(legacySessionId) > 0 { + return nil + } + + if s.Empty() { + // Extensions field must be present in TLS 1.3. + return nil + } + + if !s.ReadUint16LengthPrefixed(&extensions) || !s.Empty() { + return nil + } + + b.AddUint8(typeClientHello) + b.AddUint24LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddUint16(legacyVersion) + b.AddBytes(random) + b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(outerSessionId) // ClientHelloOuter.legacy_session_id + }) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(cipherSuites) + }) + b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(legacyCompressionMethods) + }) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + var handledOuterExtensions bool + for !extensions.Empty() { + var ext uint16 + var extData cryptobyte.String + if !extensions.ReadUint16(&ext) || + !extensions.ReadUint16LengthPrefixed(&extData) { + panic(cryptobyte.BuildError{Err: errIllegalParameter}) + } + + if ext == extensionECHOuterExtensions { + if handledOuterExtensions { + // It is an error to send any extension more than once in a + // single message. + panic(cryptobyte.BuildError{Err: errIllegalParameter}) + } + handledOuterExtensions = true + + // Read the set of outer extension code points. + outer := make(map[uint16]bool) + var outerExtData cryptobyte.String + if !extData.ReadUint8LengthPrefixed(&outerExtData) || + len(outerExtData)%2 != 0 || + !extData.Empty() { + panic(cryptobyte.BuildError{Err: errIllegalParameter}) + } + for !outerExtData.Empty() { + if !outerExtData.ReadUint16(&ext) || + ext == extensionECH { + panic(cryptobyte.BuildError{Err: errIllegalParameter}) + } + // Mark outer extension as not yet incorporated. + outer[ext] = false + } + + // Add the outer extensions from the ClientHelloOuter into the + // ClientHelloInner. + if !processClientHelloExtensions(outerData, func(ext uint16, extData cryptobyte.String) bool { + if _, ok := outer[ext]; ok { + b.AddUint16(ext) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(extData) + }) + // Mark outer extension as incorporated. + outer[ext] = true + } + return true + }) { + panic(cryptobyte.BuildError{Err: errIllegalParameter}) + } + + // Ensure that all outer extensions have been incorporated. + for _, incorporated := range outer { + if !incorporated { + panic(cryptobyte.BuildError{Err: errIllegalParameter}) + } + } + } else { + b.AddUint16(ext) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(extData) + }) + } + } + }) + }) + + innerData, err := b.Bytes() + if err == errIllegalParameter { + return nil // Input malformed + } else if err != nil { + panic(err) // Host encountered internal error + } + + return innerData +} + +// echEncodeClientHelloOuterAAD interprets outerData as ClientHelloOuter and +// handleData as an ECH context handle and maps these to a ClientHelloOuterAAD. +// Returns nil if parsing outerData fails. +func echEncodeClientHelloOuterAAD(outerData, handleData []byte) []byte { + var ( + errIllegalParameter = errors.New("illegal parameter") + msgType uint8 + legacyVersion uint16 + random []byte + legacySessionId cryptobyte.String + cipherSuites cryptobyte.String + legacyCompressionMethods cryptobyte.String + extensions cryptobyte.String + s cryptobyte.String + b cryptobyte.Builder + ) + + u := cryptobyte.String(outerData) + if !u.ReadUint8(&msgType) || + !u.ReadUint24LengthPrefixed(&s) || !u.Empty() { + return nil + } + + if !s.ReadUint16(&legacyVersion) || + !s.ReadBytes(&random, 32) || + !s.ReadUint8LengthPrefixed(&legacySessionId) || + !s.ReadUint16LengthPrefixed(&cipherSuites) || + !s.ReadUint8LengthPrefixed(&legacyCompressionMethods) { + return nil + } + + if s.Empty() { + // Extensions field must be present in TLS 1.3. + return nil + } + + if !s.ReadUint16LengthPrefixed(&extensions) || !s.Empty() { + return nil + } + + b.AddBytes(handleData) + b.AddUint24LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddUint16(legacyVersion) + b.AddBytes(random) + b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(legacySessionId) + }) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(cipherSuites) + }) + b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(legacyCompressionMethods) + }) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + for !extensions.Empty() { + var ext uint16 + var extData cryptobyte.String + if !extensions.ReadUint16(&ext) || + !extensions.ReadUint16LengthPrefixed(&extData) { + panic(cryptobyte.BuildError{Err: errIllegalParameter}) + } + + // Copy all extensions except for ECH. + if ext != extensionECH { + b.AddUint16(ext) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(extData) + }) + } + } + }) + }) + + outerAadData, err := b.Bytes() + if err == errIllegalParameter { + return nil // Input malformed + } else if err != nil { + panic(err) // Host encountered internal error + } + + return outerAadData +} + +// echEncodeServerHelloConf interprets data as a ServerHello message and encodes +// it as a ServerHelloConf. Returns nil if parsing data fails. +func echEncodeServerHelloConf(data []byte) []byte { + var ( + msgType uint8 + legacyVersion uint16 + random []byte + legacySessionId cryptobyte.String + cipherSuite uint16 + legacyCompressionMethod uint8 + extensions cryptobyte.String + s cryptobyte.String + b cryptobyte.Builder + ) + + u := cryptobyte.String(data) + if !u.ReadUint8(&msgType) || + !u.ReadUint24LengthPrefixed(&s) || !u.Empty() { + return nil + } + + if !s.ReadUint16(&legacyVersion) || + !s.ReadBytes(&random, 32) || + !s.ReadUint8LengthPrefixed(&legacySessionId) || + !s.ReadUint16(&cipherSuite) || + !s.ReadUint8(&legacyCompressionMethod) { + return nil + } + + if s.Empty() { + // Extensions field must be present in TLS 1.3. + return nil + } + + if !s.ReadUint16LengthPrefixed(&extensions) || !s.Empty() { + return nil + } + + b.AddUint8(msgType) + b.AddUint24LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddUint16(legacyVersion) + b.AddBytes(random[:24]) + b.AddBytes([]byte{0, 0, 0, 0, 0, 0, 0, 0}) + b.AddUint8LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(legacySessionId) + }) + b.AddUint16(cipherSuite) + b.AddUint8(legacyCompressionMethod) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(extensions) + }) + }) + + return b.BytesOrPanic() +} + +// processClientHelloExtensions interprets data as a ClientHello and applies a +// function proc to each extension. Returns a bool indicating whether parsing +// succeeded. +func processClientHelloExtensions(data []byte, proc func(ext uint16, extData cryptobyte.String) bool) bool { + _, extensionsData := splitClientHelloExtensions(data) + if extensionsData == nil { + return false + } + + s := cryptobyte.String(extensionsData) + if s.Empty() { + // Extensions field not present. + return true + } + + var extensions cryptobyte.String + if !s.ReadUint16LengthPrefixed(&extensions) || !s.Empty() { + return false + } + + for !extensions.Empty() { + var ext uint16 + var extData cryptobyte.String + if !extensions.ReadUint16(&ext) || + !extensions.ReadUint16LengthPrefixed(&extData) { + return false + } + if ok := proc(ext, extData); !ok { + return false + } + } + return true +} + +// splitClientHelloExtensions interprets data as a ClientHello message and +// returns two strings: the first contains the start of the ClientHello up to +// the start of the extensions; and the second is the length-prefixed +// extensions. Returns (nil, nil) if parsing of data fails. +func splitClientHelloExtensions(data []byte) ([]byte, []byte) { + s := cryptobyte.String(data) + + var ignored uint16 + var t cryptobyte.String + if !s.Skip(4) || // message type and uint24 length field + !s.ReadUint16(&ignored) || !s.Skip(32) || // vers, random + !s.ReadUint8LengthPrefixed(&t) { // session_id + return nil, nil + } + + if !s.ReadUint16LengthPrefixed(&t) { // cipher_suites + return nil, nil + } + + if !s.ReadUint8LengthPrefixed(&t) { // compression_methods + return nil, nil + } + + return data[:len(data)-len(s)], s +} + +func (c *Config) echSelectConfig() *ECHConfig { + for _, echConfig := range c.ClientECHConfigs { + if _, err := echConfig.selectSuite(); err == nil && + echConfig.version == extensionECH { + return &echConfig + } + } + return nil +} + +func (c *Config) echCanOffer() bool { + if c == nil { + return false + } + return c.ECHEnabled && + c.echSelectConfig() != nil && + c.maxSupportedVersion() >= VersionTLS13 +} + +func (c *Config) echCanAccept() bool { + if c == nil { + return false + } + return c.ECHEnabled && + c.ServerECHProvider != nil && + c.maxSupportedVersion() >= VersionTLS13 +} diff --git a/src/crypto/tls/ech_config.go b/src/crypto/tls/ech_config.go new file mode 100644 index 00000000000..804e000eb07 --- /dev/null +++ b/src/crypto/tls/ech_config.go @@ -0,0 +1,164 @@ +// Copyright 2020 Cloudflare, Inc. All rights reserved. Use of this source code +// is governed by a BSD-style license that can be found in the LICENSE file. + +package tls + +import ( + "circl/hpke" + "circl/kem" + "errors" + "fmt" + "io" + + "golang.org/x/crypto/cryptobyte" +) + +// ECHConfig represents an ECH configuration. +type ECHConfig struct { + pk kem.PublicKey + raw []byte + + // Parsed from raw + version uint16 + configId uint8 + rawPublicName []byte + rawPublicKey []byte + kemId uint16 + suites []hpkeSymmetricCipherSuite + maxNameLen uint16 + ignoredExtensions []byte +} + +// UnmarshalECHConfigs parses a sequence of ECH configurations. +func UnmarshalECHConfigs(raw []byte) ([]ECHConfig, error) { + var ( + err error + config ECHConfig + t, contents cryptobyte.String + ) + configs := make([]ECHConfig, 0) + s := cryptobyte.String(raw) + if !s.ReadUint16LengthPrefixed(&t) || !s.Empty() { + return configs, errors.New("error parsing configs") + } + raw = raw[2:] +ConfigsLoop: + for !t.Empty() { + l := len(t) + if !t.ReadUint16(&config.version) || + !t.ReadUint16LengthPrefixed(&contents) { + return nil, errors.New("error parsing config") + } + n := l - len(t) + config.raw = raw[:n] + raw = raw[n:] + + if config.version != extensionECH { + continue ConfigsLoop + } + if !readConfigContents(&contents, &config) { + return nil, errors.New("error parsing config contents") + } + + kem := hpke.KEM(config.kemId) + if !kem.IsValid() { + continue ConfigsLoop + } + config.pk, err = kem.Scheme().UnmarshalBinaryPublicKey(config.rawPublicKey) + if err != nil { + return nil, fmt.Errorf("error parsing public key: %s", err) + } + configs = append(configs, config) + } + return configs, nil +} + +func echMarshalConfigs(configs []ECHConfig) ([]byte, error) { + var b cryptobyte.Builder + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + for _, config := range configs { + if config.raw == nil { + panic("config.raw not set") + } + b.AddBytes(config.raw) + } + }) + return b.Bytes() +} + +func readConfigContents(contents *cryptobyte.String, config *ECHConfig) bool { + var t cryptobyte.String + if !contents.ReadUint8(&config.configId) || + !contents.ReadUint16(&config.kemId) || + !contents.ReadUint16LengthPrefixed(&t) || + !t.ReadBytes(&config.rawPublicKey, len(t)) || + !contents.ReadUint16LengthPrefixed(&t) || + len(t)%4 != 0 { + return false + } + + config.suites = nil + for !t.Empty() { + var kdfId, aeadId uint16 + if !t.ReadUint16(&kdfId) || !t.ReadUint16(&aeadId) { + // This indicates an internal bug. + panic("internal error while parsing contents.cipher_suites") + } + config.suites = append(config.suites, hpkeSymmetricCipherSuite{kdfId, aeadId}) + } + + if !contents.ReadUint16(&config.maxNameLen) || + !contents.ReadUint16LengthPrefixed(&t) || + !t.ReadBytes(&config.rawPublicName, len(t)) || + !contents.ReadUint16LengthPrefixed(&t) || + !t.ReadBytes(&config.ignoredExtensions, len(t)) || + !contents.Empty() { + return false + } + return true +} + +// setupSealer generates the client's HPKE context for use with the ECH +// extension. It returns the context and corresponding encapsulated key. +func (config *ECHConfig) setupSealer(rand io.Reader) (enc []byte, sealer hpke.Sealer, err error) { + if config.raw == nil { + panic("config.raw not set") + } + hpkeSuite, err := config.selectSuite() + if err != nil { + return nil, nil, err + } + info := append(append([]byte(echHpkeInfoSetup), 0), config.raw...) + sender, err := hpkeSuite.NewSender(config.pk, info) + if err != nil { + return nil, nil, err + } + return sender.Setup(rand) +} + +// isPeerCipherSuiteSupported returns true if this configuration indicates +// support for the given ciphersuite. +func (config *ECHConfig) isPeerCipherSuiteSupported(suite hpkeSymmetricCipherSuite) bool { + for _, configSuite := range config.suites { + if suite == configSuite { + return true + } + } + return false +} + +// selectSuite returns the first ciphersuite indicated by this +// configuration that is supported by the caller. +func (config *ECHConfig) selectSuite() (hpke.Suite, error) { + for _, suite := range config.suites { + hpkeSuite, err := hpkeAssembleSuite( + config.kemId, + suite.kdfId, + suite.aeadId, + ) + if err == nil { + return hpkeSuite, nil + } + } + return hpke.Suite{}, errors.New("could not negotiate a ciphersuite") +} diff --git a/src/crypto/tls/ech_provider.go b/src/crypto/tls/ech_provider.go new file mode 100644 index 00000000000..5d5a4b96a32 --- /dev/null +++ b/src/crypto/tls/ech_provider.go @@ -0,0 +1,289 @@ +// Copyright 2020 Cloudflare, Inc. All rights reserved. Use of this source code +// is governed by a BSD-style license that can be found in the LICENSE file. + +package tls + +import ( + "circl/hpke" + "circl/kem" + "errors" + "fmt" + + "golang.org/x/crypto/cryptobyte" +) + +// ECHProvider specifies the interface of an ECH service provider that decrypts +// the ECH payload on behalf of the client-facing server. It also defines the +// set of acceptable ECH configurations. +type ECHProvider interface { + // GetDecryptionContext attempts to construct the HPKE context used by the + // client-facing server for decryption. (See draft-irtf-cfrg-hpke-07, + // Section 5.2.) + // + // handle encodes the parameters of the client's "encrypted_client_hello" + // extension that are needed to construct the context. In + // draft-ietf-tls-esni-10, these are the ECH cipher suite, the identity of + // the ECH configuration, and the encapsulated key. + // + // version is the version of ECH indicated by the client. + // + // res.Status == ECHProviderStatusSuccess indicates the call was successful + // and the caller may proceed. res.Context is set. + // + // res.Status == ECHProviderStatusReject indicates the caller must reject + // ECH. res.RetryConfigs may be set. + // + // res.Status == ECHProviderStatusAbort indicates the caller should abort + // the handshake. Note that, in some cases, it's appropriate to reject + // rather than abort. In particular, aborting with "illegal_parameter" might + // "stick out". res.Alert and res.Error are set. + GetDecryptionContext(handle []byte, version uint16) (res ECHProviderResult) +} + +// ECHProviderStatus is the status of the ECH provider's response. +type ECHProviderStatus uint + +const ( + ECHProviderSuccess ECHProviderStatus = 0 + ECHProviderReject = 1 + ECHProviderAbort = 2 +) + +// ECHProviderResult represents the result of invoking the ECH provider. +type ECHProviderResult struct { + Status ECHProviderStatus + + // Alert is the TLS alert sent by the caller when aborting the handshake. + Alert uint8 + + // Error is the error propagated by the caller when aborting the handshake. + Error error + + // RetryConfigs is the sequence of ECH configs to offer to the client for + // retrying the handshake. This may be set in case of success or rejection. + RetryConfigs []byte + + // Context is the server's HPKE context. This is set if ECH is not rejected + // by the provider and no error was reported. The data has the following + // format (in TLS syntax): + // + // enum { sealer(0), opener(1) } HpkeRole; + // + // struct { + // HpkeRole role; + // HpkeKemId kem_id; // as defined in draft-irtf-cfrg-hpke-07 + // HpkeKdfId kdf_id; // as defined in draft-irtf-cfrg-hpke-07 + // HpkeAeadId aead_id; // as defined in draft-irtf-cfrg-hpke-07 + // opaque exporter_secret<0..255>; + // opaque key<0..255>; + // opaque base_nonce<0..255>; + // opaque seq<0..255>; + // } HpkeContext; + Context []byte +} + +// EXP_ECHKeySet implements the ECHProvider interface for a sequence of ECH keys. +// +// NOTE: This API is EXPERIMENTAL and subject to change. +type EXP_ECHKeySet struct { + // The serialized ECHConfigs, in order of the server's preference. + configs []byte + + // Maps a configuration identifier to its secret key. + sk map[uint8]EXP_ECHKey +} + +// EXP_NewECHKeySet constructs an EXP_ECHKeySet. +func EXP_NewECHKeySet(keys []EXP_ECHKey) (*EXP_ECHKeySet, error) { + if len(keys) > 255 { + return nil, fmt.Errorf("tls: ech provider: unable to support more than 255 ECH configurations at once") + } + + keySet := new(EXP_ECHKeySet) + keySet.sk = make(map[uint8]EXP_ECHKey) + configs := make([]byte, 0) + for _, key := range keys { + if _, ok := keySet.sk[key.config.configId]; ok { + return nil, fmt.Errorf("tls: ech provider: ECH config conflict for configId %d", key.config.configId) + } + + keySet.sk[key.config.configId] = key + configs = append(configs, key.config.raw...) + } + + var b cryptobyte.Builder + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(configs) + }) + keySet.configs = b.BytesOrPanic() + + return keySet, nil +} + +// GetDecryptionContext is required by the ECHProvider interface. +func (keySet *EXP_ECHKeySet) GetDecryptionContext(rawHandle []byte, version uint16) (res ECHProviderResult) { + // Propagate retry configurations regardless of the result. The caller sends + // these to the clients only if it rejects. + res.RetryConfigs = keySet.configs + + // Ensure we know how to proceed, i.e., the caller has indicated a supported + // version of ECH. Currently only draft-ietf-tls-esni-10 is supported. + if version != extensionECH { + res.Status = ECHProviderAbort + res.Alert = uint8(alertInternalError) + res.Error = errors.New("version not supported") + return // Abort + } + + // Parse the handle. + s := cryptobyte.String(rawHandle) + handle := new(echContextHandle) + if !echReadContextHandle(&s, handle) || !s.Empty() { + // This is the result of a client-side error. However, aborting with + // "illegal_parameter" would stick out, so we reject instead. + res.Status = ECHProviderReject + res.RetryConfigs = keySet.configs + return // Reject + } + handle.raw = rawHandle + + // Look up the secret key for the configuration indicated by the client. + key, ok := keySet.sk[handle.configId] + if !ok { + res.Status = ECHProviderReject + res.RetryConfigs = keySet.configs + return // Reject + } + + // Ensure that support for the selected ciphersuite is indicated by the + // configuration. + suite := handle.suite + if !key.config.isPeerCipherSuiteSupported(suite) { + // This is the result of a client-side error. However, aborting with + // "illegal_parameter" would stick out, so we reject instead. + res.Status = ECHProviderReject + res.RetryConfigs = keySet.configs + return // Reject + } + + // Ensure the version indicated by the client matches the version supported + // by the configuration. + if version != key.config.version { + // This is the result of a client-side error. However, aborting with + // "illegal_parameter" would stick out, so we reject instead. + res.Status = ECHProviderReject + res.RetryConfigs = keySet.configs + return // Reject + } + + // Compute the decryption context. + opener, err := key.setupOpener(handle.enc, suite) + if err != nil { + res.Status = ECHProviderAbort + res.Alert = uint8(alertInternalError) + res.Error = err + return // Abort + } + + // Serialize the decryption context. + res.Context, err = opener.MarshalBinary() + if err != nil { + res.Status = ECHProviderAbort + res.Alert = uint8(alertInternalError) + res.Error = err + return // Abort + } + + res.Status = ECHProviderSuccess + return // Success +} + +// EXP_ECHKey represents an ECH key and its corresponding configuration. The +// encoding of an ECH Key has the format defined below (in TLS syntax). Note +// that the ECH standard does not specify this format. +// +// struct { +// opaque sk<0..2^16-1>; +// ECHConfig config<0..2^16>; // draft-ietf-tls-esni-10 +// } ECHKey; +type EXP_ECHKey struct { + sk kem.PrivateKey + config ECHConfig +} + +// EXP_UnmarshalECHKeys parses a sequence of ECH keys. +func EXP_UnmarshalECHKeys(raw []byte) ([]EXP_ECHKey, error) { + var ( + err error + key EXP_ECHKey + sk, config, contents cryptobyte.String + ) + s := cryptobyte.String(raw) + keys := make([]EXP_ECHKey, 0) +KeysLoop: + for !s.Empty() { + if !s.ReadUint16LengthPrefixed(&sk) || + !s.ReadUint16LengthPrefixed(&config) { + return nil, errors.New("error parsing key") + } + + key.config.raw = config + if !config.ReadUint16(&key.config.version) || + !config.ReadUint16LengthPrefixed(&contents) || + !config.Empty() { + return nil, errors.New("error parsing config") + } + + if key.config.version != extensionECH { + continue KeysLoop + } + if !readConfigContents(&contents, &key.config) { + return nil, errors.New("error parsing config contents") + } + + for _, suite := range key.config.suites { + if !hpke.KDF(suite.kdfId).IsValid() || + !hpke.AEAD(suite.aeadId).IsValid() { + continue KeysLoop + } + } + + kem := hpke.KEM(key.config.kemId) + if !kem.IsValid() { + continue KeysLoop + } + key.config.pk, err = kem.Scheme().UnmarshalBinaryPublicKey(key.config.rawPublicKey) + if err != nil { + return nil, fmt.Errorf("error parsing public key: %s", err) + } + key.sk, err = kem.Scheme().UnmarshalBinaryPrivateKey(sk) + if err != nil { + return nil, fmt.Errorf("error parsing secret key: %s", err) + } + + keys = append(keys, key) + } + return keys, nil +} + +// setupOpener computes the HPKE context used by the server in the ECH +// extension.i +func (key *EXP_ECHKey) setupOpener(enc []byte, suite hpkeSymmetricCipherSuite) (hpke.Opener, error) { + if key.config.raw == nil { + panic("raw config not set") + } + hpkeSuite, err := hpkeAssembleSuite( + key.config.kemId, + suite.kdfId, + suite.aeadId, + ) + if err != nil { + return nil, err + } + info := append(append([]byte(echHpkeInfoSetup), 0), key.config.raw...) + receiver, err := hpkeSuite.NewReceiver(key.sk, info) + if err != nil { + return nil, err + } + return receiver.Setup(enc) +} diff --git a/src/crypto/tls/ech_test.go b/src/crypto/tls/ech_test.go new file mode 100644 index 00000000000..f4541154e57 --- /dev/null +++ b/src/crypto/tls/ech_test.go @@ -0,0 +1,945 @@ +// Copyright 2020 Cloudflare, Inc. All rights reserved. Use of this source code +// is governed by a BSD-style license that can be found in the LICENSE file. + +package tls + +import ( + "bytes" + "crypto/rand" + "crypto/x509" + "encoding/pem" + "errors" + "fmt" + "testing" + "time" +) + +const ( + echTestBackendServerName = "example.com" + echTestClientFacingServerName = "cloudflare-esni.com" +) + +// The client's root CA certificate. +const echTestCertRootPEM = ` +-----BEGIN CERTIFICATE----- +MIICQTCCAeigAwIBAgIUYGSqOFcpxSleCzSCaveKL8lV4N0wCgYIKoZIzj0EAwIw +fzELMAkGA1UEBhMCVVMxEzARBgNVBAgTCkNhbGlmb3JuaWExFjAUBgNVBAcTDVNh +biBGcmFuY2lzY28xHzAdBgNVBAoTFkludGVybmV0IFdpZGdldHMsIEluYy4xDDAK +BgNVBAsTA1dXVzEUMBIGA1UEAxMLZXhhbXBsZS5jb20wHhcNMjAwOTIyMTcwNjAw +WhcNMjUwOTIxMTcwNjAwWjB/MQswCQYDVQQGEwJVUzETMBEGA1UECBMKQ2FsaWZv +cm5pYTEWMBQGA1UEBxMNU2FuIEZyYW5jaXNjbzEfMB0GA1UEChMWSW50ZXJuZXQg +V2lkZ2V0cywgSW5jLjEMMAoGA1UECxMDV1dXMRQwEgYDVQQDEwtleGFtcGxlLmNv +bTBZMBMGByqGSM49AgEGCCqGSM49AwEHA0IABNcFaBtPRgekRBKTBvuKdTy3raqs +4IizMLFup434MfQ5oH71mYpKndfBzxcZDTMYeocKlt1pVYwvZ3ZdpRsW6yWjQjBA +MA4GA1UdDwEB/wQEAwIBBjAPBgNVHRMBAf8EBTADAQH/MB0GA1UdDgQWBBQ2GJIW ++4m3/qpkage5tEvMg3NwPTAKBggqhkjOPQQDAgNHADBEAiB6J8UqRvdhLOiaDYqH +KG+TuveHOqlfQqQgXo4/hNKMiAIgV79TTPHu+Ymn/tcCy9LVWZcpgnCEjrZi0ou5 +et8BX9s= +-----END CERTIFICATE-----` + +// Certificate of the client-facing server. The server name is +// "cloudflare-esni.com". +const echTestCertClientFacingPEM = ` +-----BEGIN CERTIFICATE----- +MIICIjCCAcigAwIBAgIUCXySp2MadlDlcvFrSm4BtLUY70owCgYIKoZIzj0EAwIw +fzELMAkGA1UEBhMCVVMxEzARBgNVBAgTCkNhbGlmb3JuaWExFjAUBgNVBAcTDVNh +biBGcmFuY2lzY28xHzAdBgNVBAoTFkludGVybmV0IFdpZGdldHMsIEluYy4xDDAK +BgNVBAsTA1dXVzEUMBIGA1UEAxMLZXhhbXBsZS5jb20wHhcNMjAwOTIyMTcxMDAw +WhcNMjEwOTIyMTcxMDAwWjAAMFkwEwYHKoZIzj0CAQYIKoZIzj0DAQcDQgAE7nP/ +Txinb0JPE/xdjv5d3zrWJqXo7qwP67oVaMKJp5ausJ+0IZfiMWz8pa6T7pyyLrC5 +xvQNkfVkpP9/FxmNFaOBoDCBnTAOBgNVHQ8BAf8EBAMCBaAwHQYDVR0lBBYwFAYI +KwYBBQUHAwEGCCsGAQUFBwMCMAwGA1UdEwEB/wQCMAAwHQYDVR0OBBYEFNN7Afv+ +CgPAxRr4QdZn8JFvQ9nTMB8GA1UdIwQYMBaAFDYYkhb7ibf+qmRqB7m0S8yDc3A9 +MB4GA1UdEQQXMBWCE2Nsb3VkZmxhcmUtZXNuaS5jb20wCgYIKoZIzj0EAwIDSAAw +RQIgZ4VlBtjTRludP/JwfaNQyGKZFWFqRsECvGPbk+ZHLZwCIQCTjuMAFrnjf/j5 +3RNw67l7+QQPrmurSO86l1IlDWNtcA== +-----END CERTIFICATE-----` + +// Signing key of the client-facing server. +const echTestKeyClientFacingPEM = ` +-----BEGIN PRIVATE KEY----- +MHcCAQEEIPpCcU8mu+h4xHAm18NJvn73Ko9fjH9QxDCpRt7kCIq9oAoGCCqGSM49 +AwEHoUQDQgAE7nP/Txinb0JPE/xdjv5d3zrWJqXo7qwP67oVaMKJp5ausJ+0IZfi +MWz8pa6T7pyyLrC5xvQNkfVkpP9/FxmNFQ== +-----END PRIVATE KEY-----` + +// Certificate of the backend server. The server name is "example.com". +const echTestCertBackendPEM = ` +-----BEGIN CERTIFICATE----- +MIICGTCCAcCgAwIBAgIUQJSSdOZs9wag1Toanlt9lol0uegwCgYIKoZIzj0EAwIw +fzELMAkGA1UEBhMCVVMxEzARBgNVBAgTCkNhbGlmb3JuaWExFjAUBgNVBAcTDVNh +biBGcmFuY2lzY28xHzAdBgNVBAoTFkludGVybmV0IFdpZGdldHMsIEluYy4xDDAK +BgNVBAsTA1dXVzEUMBIGA1UEAxMLZXhhbXBsZS5jb20wHhcNMjAwOTIyMTcwOTAw +WhcNMjEwOTIyMTcwOTAwWjAAMFkwEwYHKoZIzj0CAQYIKoZIzj0DAQcDQgAElq+q +E01Z87KIPHWdEAk0cWssHkRnS4aQCDfstoxDIWQ4rMwHvrWGFy/vytRwyjhHuX9n +tc5ArCpwbAmY+oW/46OBmDCBlTAOBgNVHQ8BAf8EBAMCBaAwHQYDVR0lBBYwFAYI +KwYBBQUHAwEGCCsGAQUFBwMCMAwGA1UdEwEB/wQCMAAwHQYDVR0OBBYEFPz9Ct9U +EIjBEcUpv/yxHYccUDo1MB8GA1UdIwQYMBaAFDYYkhb7ibf+qmRqB7m0S8yDc3A9 +MBYGA1UdEQQPMA2CC2V4YW1wbGUuY29tMAoGCCqGSM49BAMCA0cAMEQCICDBEzzE +DF529x9Z4BkOKVxNDicfWSjxrcMohevjeCWDAiBaxXS5+6I2fcred0JGMsJgo7ts +S8GYhuKE99mQA0/mug== +-----END CERTIFICATE-----` + +// Signing key of the backend server. +const echTestKeyBackendPEM = ` +-----BEGIN PRIVATE KEY----- +MHcCAQEEIIJsLXmfzw6FDlqyRRLhY6lVB6ws5ewjUQjnS4DXsQ60oAoGCCqGSM49 +AwEHoUQDQgAElq+qE01Z87KIPHWdEAk0cWssHkRnS4aQCDfstoxDIWQ4rMwHvrWG +Fy/vytRwyjhHuX9ntc5ArCpwbAmY+oW/4w== +-----END PRIVATE KEY-----` + +// The ECH keys used by the client-facing server. +const echTestKeys = `-----BEGIN ECH KEYS----- +ACDhS0q2cTU1Qzi6hPM4BQ/HLnbEUZyWdY2GbmS0DVkumgBI/goARAAAIAAgi1Tu +jWJ236k1VAMeRnysKbDigxLpDs/AGdEowK8KiBkABAABAAEAAAATY2xvdWRmbGFy +ZS1lc25pLmNvbQAAACBmNj/zQe6OT/MR/MM39G6kwMJCJEXpdvTAkbdHErlgXwBI +/goARAEAIAAgZ1Ru1uyGX6N9HYs5/pAE3KwUXRDBHD0Bdna8oP4uVEwABAABAAEA +AAATY2xvdWRmbGFyZS1lc25pLmNvbQAA +-----END ECH KEYS-----` + +// A sequence of ECH keys with unsupported versions. +const echTestInvalidVersionKeys = `-----BEGIN ECH KEYS----- +ACDhS0q2cTU1Qzi6hPM4BQ/HLnbEUZyWdY2GbmS0DVkumgBIAfUARAAAIAAgi1Tu +jWJ236k1VAMeRnysKbDigxLpDs/AGdEowK8KiBkABAABAAEAAAATY2xvdWRmbGFy +ZS1lc25pLmNvbQAAACBmNj/zQe6OT/MR/MM39G6kwMJCJEXpdvTAkbdHErlgXwBI +AfUARAEAIAAgZ1Ru1uyGX6N9HYs5/pAE3KwUXRDBHD0Bdna8oP4uVEwABAABAAEA +AAATY2xvdWRmbGFyZS1lc25pLmNvbQAA +-----END ECH KEYS-----` + +// The sequence of ECH configurations corresponding to echTestKeys. +const echTestConfigs = `-----BEGIN ECH CONFIGS----- +AJD+CgBEAAAgACCLVO6NYnbfqTVUAx5GfKwpsOKDEukOz8AZ0SjArwqIGQAEAAEA +AQAAABNjbG91ZGZsYXJlLWVzbmkuY29tAAD+CgBEAQAgACBnVG7W7IZfo30dizn+ +kATcrBRdEMEcPQF2dryg/i5UTAAEAAEAAQAAABNjbG91ZGZsYXJlLWVzbmkuY29t +AAA= +-----END ECH CONFIGS-----` + +// An invalid sequence of ECH configurations. +const echTestStaleConfigs = `-----BEGIN ECH CONFIGS----- +AJD+CgBEAAAgACCNkMISpIMFmPZwDgob/CROvHD93NQFcX4h0SURHTJpRwAEAAEA +AQAAABNjbG91ZGZsYXJlLWVzbmkuY29tAAD+CgBEAQAgACAH4P9K5l9BJ3aG4QUk +fTjMWUoeLQZVdTxp5Qe0FWvDQwAEAAEAAQAAABNjbG91ZGZsYXJlLWVzbmkuY29t +AAA= +-----END ECH CONFIGS-----` + +// echTestProviderAlwaysAbort mocks an ECHProvider that, in response to any +// request, sets an alert and returns an error. The client-facing server must +// abort the handshake. +type echTestProviderAlwaysAbort struct{} + +// Required by the ECHProvider interface. +func (p echTestProviderAlwaysAbort) GetDecryptionContext(_ []byte, _ uint16) (res ECHProviderResult) { + res.Status = ECHProviderAbort + res.Alert = uint8(alertInternalError) + res.Error = errors.New("provider failed") + return // Abort +} + +// echTestProviderAlwaysReject simulates fallover of the ECH provider. In +// response to any query, it rejects without sending retry configurations., in response to any +type echTestProviderAlwaysReject struct{} + +// Required by the ECHProvider interface. +func (p echTestProviderAlwaysReject) GetDecryptionContext(_ []byte, _ uint16) (res ECHProviderResult) { + res.Status = ECHProviderReject + return // Reject without retry configs +} + +func echTestLoadConfigs(pemData string) []ECHConfig { + block, rest := pem.Decode([]byte(pemData)) + if block == nil || block.Type != "ECH CONFIGS" || len(rest) > 0 { + panic("pem decoding fails") + } + + configs, err := UnmarshalECHConfigs(block.Bytes) + if err != nil { + panic(err) + } + + return configs +} + +func echTestLoadKeySet(pemData string) *EXP_ECHKeySet { + block, rest := pem.Decode([]byte(pemData)) + if block == nil || block.Type != "ECH KEYS" || len(rest) > 0 { + panic("pem decoding fails") + } + + keys, err := EXP_UnmarshalECHKeys(block.Bytes) + if err != nil { + panic(err) + } + + keySet, err := EXP_NewECHKeySet(keys) + if err != nil { + panic(err) + } + + return keySet +} + +type echTestCase struct { + name string + + // expected outcomes + expectClientAbort bool // client aborts + expectServerAbort bool // server aborts + expectOffered bool // server indicates that ECH was offered + expectClientBypassed bool // server bypasses ECH + expectServerBypassed bool // server indicates that ECH was bypassed by client + expectAccepted bool // server indicates ECH acceptance + expectRejected bool // server indicates ECH rejection + expectGrease bool // server indicates dummy ECH was detected + expectBackendServerName bool // client verified backend server name + + // client config + clientEnabled bool // client enables ECH + clientStaleConfigs bool // client offers ECH with invalid config + clientNoConfigs bool // client sends dummy ECH if ECH enabled + clientInvalidTLSVersion bool // client does not offer 1.3 + + // server config + serverEnabled bool // server enables ECH + serverProviderAlwaysAbort bool // ECH provider always aborts + serverProviderAlwaysReject bool // ECH provider always rejects + serverProviderInvalidVersion bool // ECH provider uses configs with unsupported version + serverInvalidTLSVersion bool // server does not offer 1.3 + + // code path triggers + triggerHRR bool // server triggers HRR + triggerECHBypassAfterHRR bool // client bypasses after HRR + triggerECHBypassBeforeHRR bool // client bypasses before HRR + triggerIllegalHandleAfterHRR bool // client sends illegal ECH extension after HRR + triggerOuterExtMany bool // client sends many (not just one) outer extensions + triggerOuterExtIncorrectOrder bool // client sends malformed outer extensions + triggerOuterExtIllegal bool // client sends malformed outer extensions + triggerOuterExtNone bool // client does not incorporate outer extensions + triggerOuterIsInner bool // client sends "ech_is_inner" in ClientHelloOuter + triggerPayloadDecryptError bool // client sends inauthentic ciphertext +} + +// TODO(cjpatton): Add test cases for PSK interactions: +// - ECH bypassed, backend server consumes early data (baseline test config) +// - ECH accepted, backend server consumes early data +// - ECH rejected, client-facing server ignores early data intended for backend +var echTestCases = []echTestCase{ + { + // The client offers ECH and it is accepted by the server + name: "success / accepted", + expectOffered: true, + expectAccepted: true, + expectBackendServerName: true, + clientEnabled: true, + serverEnabled: true, + }, + { + // The client bypasses ECH, i.e., it neither offers ECH nor sends a + // dummy ECH extension. + name: "success / bypassed: not offered", + expectClientBypassed: true, + expectBackendServerName: true, + serverEnabled: true, + }, + { + // The client sends dummy (i.e., "GREASEd") ECH. The server sends retry + // configs in case the client meant to offer ECH. The client does not + // signal rejection, so the server concludes ECH was not offered. + name: "success / bypassed: grease", + expectGrease: true, + expectBackendServerName: true, + clientEnabled: true, + clientNoConfigs: true, + serverEnabled: true, + }, + { + // The client sends dummy ECH because it has enabled ECH but not TLS + // 1.3. The server sends retry configs in case the client meant to offer + // ECH. The client does not signal rejection, so the server concludes + // ECH was not offered. + name: "success / bypassed: client invalid version", + expectGrease: true, + expectBackendServerName: true, + clientInvalidTLSVersion: true, + clientEnabled: true, + serverEnabled: true, + }, + { + // The client offers ECH with an invalid (e.g., stale) config. The + // server sends retry configs. The client signals rejection by sending + // an "ech_required" alert. + name: "success / rejected: invalid config", + expectOffered: true, + expectRejected: true, + expectClientAbort: true, + expectServerAbort: true, + clientStaleConfigs: true, + clientEnabled: true, + serverEnabled: true, + }, + { + // The client offers ECH, but the payload is mangled in transit. The + // server sends retry configurations. The client signals rejection by + // sending an "ech_required" alert. + name: "success / rejected: inauthentic ciphertext", + expectOffered: true, + expectRejected: true, + expectClientAbort: true, + expectServerAbort: true, + clientEnabled: true, + serverEnabled: true, + triggerPayloadDecryptError: true, + }, + { + // The client offered ECH, but client-facing server terminates the + // connection without sending retry configurations. The client aborts + // with "ech_required" and regards ECH as securely disabled by the + // server. + name: "success / rejected: not supported by client-facing server", + expectServerBypassed: true, + expectClientAbort: true, + expectServerAbort: true, + clientEnabled: true, + }, + { + // The client offers ECH. The server ECH rejects without sending retry + // configurations, simulating fallover of the ECH provider. The client + // signals rejection. + name: "success / rejected: provider falls over", + expectServerAbort: true, + expectOffered: true, + expectServerBypassed: true, + expectClientAbort: true, + clientEnabled: true, + serverEnabled: true, + serverProviderAlwaysReject: true, + }, + { + // The client offers ECH. The server ECH rejects without sending retry + // configurations because the ECH provider returns configurations with + // unsupported versions only. + name: "success / rejected: provider invalid version", + expectServerAbort: true, + expectOffered: true, + expectServerBypassed: true, + expectClientAbort: true, + clientEnabled: true, + serverEnabled: true, + serverProviderInvalidVersion: true, + }, + { + // The client offers ECH. The server does not support TLS 1.3, so it + // ignores the extension and continues as usual. The client does not + // signal rejection because TLS 1.2 has been negotiated. + name: "success / bypassed: client-facing invalid version", + expectServerBypassed: true, + clientEnabled: true, + serverEnabled: true, + serverInvalidTLSVersion: true, + }, + { + // The client offers ECH. The ECH provider encounters an unrecoverable + // error, causing the server to abort. + name: "server abort: provider hard fails", + expectServerAbort: true, + expectClientAbort: true, + clientEnabled: true, + serverEnabled: true, + serverProviderAlwaysAbort: true, + }, + { + // The client offers ECH, but sends the "ech_is_inner" extension in the + // ClientHelloOuter, causing the server to abort. + name: "server abort: hello marked as inner and outer", + expectServerAbort: true, + expectClientAbort: true, + clientEnabled: true, + serverEnabled: true, + triggerOuterIsInner: true, + }, + { + // The client offers ECH and it is accepted by the server. The HRR code + // path is triggered. + name: "hrr / accepted", + expectOffered: true, + expectAccepted: true, + expectBackendServerName: true, + triggerHRR: true, + clientEnabled: true, + serverEnabled: true, + }, + { + // The client sends a dummy ECH extension. The server sends retry + // configs in case the client meant to offer ECH. The client does not + // signal rejection, so the server concludes ECH was not offered. The + // HRR code path is triggered. + name: "hrr / bypassed: grease", + expectGrease: true, + expectBackendServerName: true, + clientEnabled: true, + clientNoConfigs: true, + serverEnabled: true, + triggerHRR: true, + }, + { + // The client offers ECH with an invalid (e.g., stale) config. The + // server sends retry configs. The client signals rejection. The HRR + // code path is triggered. + name: "hrr / rejected: invalid config", + expectOffered: true, + expectRejected: true, + expectClientAbort: true, + expectServerAbort: true, + clientEnabled: true, + clientStaleConfigs: true, + serverEnabled: true, + triggerHRR: true, + }, + { + // The HRR code path is triggered. The client offered ECH in the second + // CH but not the first. + name: "hrr / server abort: offer after bypass", + expectServerAbort: true, + expectClientAbort: true, + clientEnabled: true, + serverEnabled: true, + triggerHRR: true, + triggerECHBypassBeforeHRR: true, + }, + { + // The HRR code path is triggered. The client offered ECH in the first + // CH but not the second. + name: "hrr / server abort: bypass after offer", + expectOffered: true, + expectAccepted: true, + expectServerAbort: true, + expectClientAbort: true, + clientEnabled: true, + serverEnabled: true, + triggerHRR: true, + triggerECHBypassAfterHRR: true, + }, + { + // The HRR code path is triggered. In the second CH, the value of the + // context handle changes illegally. Specifically, the client sends a + // non-empty "config_id" and "enc". + name: "hrr / server abort: illegal handle", + expectOffered: true, + expectAccepted: true, + expectServerAbort: true, + expectClientAbort: true, + clientEnabled: true, + serverEnabled: true, + triggerHRR: true, + triggerIllegalHandleAfterHRR: true, + }, + { + // The client offers ECH and it is accepted by the server. The client + // incorporates many outer extensions instead of just one (the default + // behavior). + name: "outer extensions, many / accepted", + expectBackendServerName: true, + expectOffered: true, + expectAccepted: true, + clientEnabled: true, + serverEnabled: true, + triggerOuterExtMany: true, + }, + { + // The client offers ECH and it is accepted by the server. The client + // incorporates no outer extensions. + name: "outer extensions, none / accepted", + expectBackendServerName: true, + expectOffered: true, + expectAccepted: true, + clientEnabled: true, + serverEnabled: true, + triggerOuterExtNone: true, + }, + { + // The client offers ECH but does not implement the "outer_extension" + // mechanism correctly. Specifically, it sends them in the wrong order, + // causing the client and server to compute different transcripts. + name: "outer extensions, incorrect order / server abort: incorrect transcript", + expectOffered: true, + expectAccepted: true, + expectServerAbort: true, + expectClientAbort: true, + clientEnabled: true, + serverEnabled: true, + triggerOuterExtIncorrectOrder: true, + }, + { + // The client offers ECH but does not implement the "outer_extension" + // mechanism correctly. Specifically, the "outer extensions" contains + // the codepoint for the ECH extension itself. + name: "outer extensions, illegal: illegal parameter", + expectServerAbort: true, + expectClientAbort: true, + clientEnabled: true, + serverEnabled: true, + triggerOuterExtIllegal: true, + }, +} + +// Returns the base configurations for the client and client-facing server, +func echSetupConnTest() (clientConfig, serverConfig *Config) { + echTestNow := time.Date(2020, time.September, 23, 0, 0, 0, 0, time.UTC) + echTestConfig := &Config{ + Time: func() time.Time { + return echTestNow + }, + Rand: rand.Reader, + CipherSuites: allCipherSuites(), + InsecureSkipVerify: false, + } + + clientFacingCert, err := X509KeyPair([]byte(echTestCertClientFacingPEM), []byte(echTestKeyClientFacingPEM)) + if err != nil { + panic(err) + } + + backendCert, err := X509KeyPair([]byte(echTestCertBackendPEM), []byte(echTestKeyBackendPEM)) + if err != nil { + panic(err) + } + + block, rest := pem.Decode([]byte(echTestCertRootPEM)) + if block == nil || block.Type != "CERTIFICATE" || len(rest) > 0 { + panic("pem decoding fails") + } + + rootCert, err := x509.ParseCertificate(block.Bytes) + if err != nil { + panic(err) + } + + clientConfig = echTestConfig.Clone() + clientConfig.ServerName = echTestBackendServerName + clientConfig.RootCAs = x509.NewCertPool() + clientConfig.RootCAs.AddCert(rootCert) + + serverConfig = echTestConfig.Clone() + serverConfig.GetCertificate = func(info *ClientHelloInfo) (*Certificate, error) { + if info.ServerName == echTestBackendServerName { + return &backendCert, nil + } else if info.ServerName == echTestClientFacingServerName { + return &clientFacingCert, nil + } + return nil, nil + } + return +} + +// echTestResult represents the ECH status and error status of a connection. +type echTestResult struct { + // Operational parameters + clientDone, serverDone bool + // Results + clientStatus CFEventECHClientStatus + serverStatus CFEventECHServerStatus + connState ConnectionState + err error +} + +func (r *echTestResult) eventHandler(event CFEvent) { + switch e := event.(type) { + case CFEventECHClientStatus: + if r.clientDone { + panic("expected at most one client ECH status event") + } + r.clientStatus = e + r.clientDone = true + case CFEventECHServerStatus: + if r.serverDone { + panic("expected at most one server ECH status event") + } + r.serverStatus = e + r.clientDone = true + } +} + +// echTestConn runs the handshake and returns the ECH and error status of the +// client and server. It also returns the server name verified by the client. +func echTestConn(t *testing.T, clientConfig, serverConfig *Config) (clientRes, serverRes echTestResult) { + testMessage := []byte("hey bud") + buf := make([]byte, len(testMessage)) + ln := newLocalListener(t) + defer ln.Close() + + serverCh := make(chan echTestResult, 1) + go func() { + var res echTestResult + serverConfig.CFEventHandler = res.eventHandler + serverConn, err := ln.Accept() + if err != nil { + res.err = err + serverCh <- res + return + } + + server := Server(serverConn, serverConfig) + defer func() { + server.Close() + serverCh <- res + }() + + if err := server.Handshake(); err != nil { + res.err = err + return + } + + if _, err = server.Read(buf); err != nil { + res.err = err + } + + res.connState = server.ConnectionState() + }() + + clientConfig.CFEventHandler = clientRes.eventHandler + client, err := Dial("tcp", ln.Addr().String(), clientConfig) + if err != nil { + serverRes = <-serverCh + clientRes.err = err + return + } + defer client.Close() + + _, err = client.Write(testMessage) + if err != nil { + serverRes = <-serverCh + clientRes.err = err + return + } + + clientRes.connState = client.ConnectionState() + serverRes = <-serverCh + return +} + +func TestECHHandshake(t *testing.T) { + defer func() { + // Reset testing triggers after the test completes. + testingTriggerHRR = false + testingECHTriggerBypassAfterHRR = false + testingECHTriggerBypassBeforeHRR = false + testingECHIllegalHandleAfterHRR = false + testingECHOuterExtMany = false + testingECHOuterExtNone = false + testingECHOuterExtIncorrectOrder = false + testingECHOuterExtIllegal = false + testingECHOuterIsInner = false + testingECHTriggerPayloadDecryptError = false + }() + + staleConfigs := echTestLoadConfigs(echTestStaleConfigs) + configs := echTestLoadConfigs(echTestConfigs) + keySet := echTestLoadKeySet(echTestKeys) + invalidVersionKeySet := echTestLoadKeySet(echTestInvalidVersionKeys) + + clientConfig, serverConfig := echSetupConnTest() + for i, test := range echTestCases { + t.Run(fmt.Sprintf("%02d", i), func(t *testing.T) { + // Configure the client. + n := 0 + if test.clientNoConfigs { + clientConfig.ClientECHConfigs = nil + n++ + } + if test.clientStaleConfigs { + clientConfig.ClientECHConfigs = staleConfigs + n++ + } + if n == 0 { + clientConfig.ClientECHConfigs = configs + } else if n > 1 { + panic("invalid test configuration") + } + + if test.clientEnabled { + clientConfig.ECHEnabled = true + } else { + clientConfig.ECHEnabled = false + } + + if test.clientInvalidTLSVersion { + clientConfig.MinVersion = VersionTLS10 + clientConfig.MaxVersion = VersionTLS12 + } else { + clientConfig.MinVersion = VersionTLS10 + clientConfig.MaxVersion = VersionTLS13 + } + + // Configure the client-facing server. + if test.serverEnabled { + serverConfig.ECHEnabled = true + } else { + serverConfig.ECHEnabled = false + } + + n = 0 + if test.serverProviderAlwaysAbort { + serverConfig.ServerECHProvider = &echTestProviderAlwaysAbort{} + n++ + } + if test.serverProviderAlwaysReject { + serverConfig.ServerECHProvider = &echTestProviderAlwaysReject{} + n++ + } + if test.serverProviderInvalidVersion { + serverConfig.ServerECHProvider = invalidVersionKeySet + n++ + } + if n == 0 { + serverConfig.ServerECHProvider = keySet + } else if n > 1 { + panic("invalid test configuration") + } + + if test.serverInvalidTLSVersion { + serverConfig.MinVersion = VersionTLS10 + serverConfig.MaxVersion = VersionTLS12 + } else { + serverConfig.MinVersion = VersionTLS10 + serverConfig.MaxVersion = VersionTLS13 + } + + testingTriggerHRR = false + if test.triggerHRR { + testingTriggerHRR = true + } + + testingECHTriggerBypassAfterHRR = false + if test.triggerECHBypassAfterHRR { + testingECHTriggerBypassAfterHRR = true + } + + testingECHTriggerBypassBeforeHRR = false + if test.triggerECHBypassBeforeHRR { + testingECHTriggerBypassBeforeHRR = true + } + + testingECHTriggerPayloadDecryptError = false + if test.triggerPayloadDecryptError { + testingECHTriggerPayloadDecryptError = true + } + + n = 0 + testingECHOuterExtMany = false + if test.triggerOuterExtMany { + testingECHOuterExtMany = true + n++ + } + testingECHOuterExtNone = false + if test.triggerOuterExtNone { + testingECHOuterExtNone = true + n++ + } + testingECHOuterExtIncorrectOrder = false + if test.triggerOuterExtIncorrectOrder { + testingECHOuterExtIncorrectOrder = true + n++ + } + testingECHOuterExtIllegal = false + if test.triggerOuterExtIllegal { + testingECHOuterExtIllegal = true + n++ + } + testingECHOuterIsInner = false + if test.triggerOuterIsInner { + testingECHOuterIsInner = true + n++ + } + testingECHIllegalHandleAfterHRR = false + if test.triggerIllegalHandleAfterHRR { + testingECHIllegalHandleAfterHRR = true + n++ + } + if n > 1 { + panic("invalid test configuration") + } + + t.Logf("%s", test.name) + + // Run the handshake. + client, server := echTestConn(t, clientConfig, serverConfig) + if !test.expectClientAbort && client.err != nil { + t.Error("client aborts; want success") + } + + if !test.expectServerAbort && server.err != nil { + t.Error("server aborts; want success") + } + + if test.expectClientAbort && client.err == nil { + t.Error("client succeeds; want abort") + } else { + t.Logf("client err: %s", client.err) + } + + if test.expectServerAbort && server.err == nil { + t.Errorf("server succeeds; want abort") + } else { + t.Logf("server err: %s", server.err) + } + + if got := server.clientStatus.Offered(); got != test.expectOffered { + t.Errorf("got offered=%v; want %v", got, test.expectOffered) + } + + if got := server.clientStatus.Greased(); got != test.expectGrease { + t.Errorf("got grease=%v; want %v", got, test.expectGrease) + } + + if got := server.clientStatus.Bypassed(); got != test.expectClientBypassed && server.err == nil { + t.Errorf("got clientBypassed=%v; want %v", got, test.expectClientBypassed) + } + + if got := server.serverStatus.Bypassed(); got != test.expectServerBypassed && server.err == nil { + t.Errorf("got serverBypassed=%v; want %v", got, test.expectServerBypassed) + } + + if got := server.serverStatus.Accepted(); got != test.expectAccepted { + t.Errorf("got accepted=%v; want %v", got, test.expectAccepted) + } + + if got := server.serverStatus.Rejected(); got != test.expectRejected { + t.Errorf("got rejected=%v; want %v", got, test.expectRejected) + } + + if client.err != nil { + return + } + + if name := client.connState.ServerName; test.expectBackendServerName != (name == echTestBackendServerName) { + t.Errorf("got backend server name=%v; want %v", name == echTestBackendServerName, test.expectBackendServerName) + } + + if client.clientStatus.Greased() != server.clientStatus.Greased() || + client.clientStatus.Bypassed() != server.clientStatus.Bypassed() || + client.serverStatus.Bypassed() != server.serverStatus.Bypassed() || + client.serverStatus.Accepted() != server.serverStatus.Accepted() || + client.serverStatus.Rejected() != server.serverStatus.Rejected() { + t.Error("client and server disagree on ech usage") + t.Errorf("client=%+v", client) + t.Errorf("server=%+v", server) + } + + if accepted := client.connState.ECHAccepted; accepted != client.serverStatus.Accepted() { + t.Errorf("client got ECHAccepted=%v; want %v", accepted, client.serverStatus.Accepted()) + } + + if accepted := server.connState.ECHAccepted; accepted != server.serverStatus.Accepted() { + t.Errorf("server got ECHAccepted=%v; want %v", accepted, server.serverStatus.Accepted()) + } + }) + } +} + +func TestUnmarshalConfigs(t *testing.T) { + block, rest := pem.Decode([]byte(echTestConfigs)) + if block == nil || block.Type != "ECH CONFIGS" || len(rest) > 0 { + t.Fatal("pem decoding fails") + } + + configs, err := UnmarshalECHConfigs(block.Bytes) + if err != nil { + t.Fatal(err) + } + + for _, config := range configs { + if len(config.raw) == 0 { + t.Error("raw config not set") + } + } +} + +func TestUnmarshalKeys(t *testing.T) { + block, rest := pem.Decode([]byte(echTestKeys)) + if block == nil || block.Type != "ECH KEYS" || len(rest) > 0 { + t.Fatal("pem decoding fails") + } + + keys, err := EXP_UnmarshalECHKeys(block.Bytes) + if err != nil { + t.Fatal(err) + } + + for _, key := range keys { + if len(key.config.raw) == 0 { + t.Error("raw config not set") + } + } +} + +func testECHProvider(t *testing.T, p ECHProvider, handle []byte, version uint16, want ECHProviderResult) { + got := p.GetDecryptionContext(handle, version) + if got.Status != want.Status { + t.Errorf("incorrect status: got %+v; want %+v", got.Status, want.Status) + } + if got.Alert != want.Alert { + t.Errorf("incorrect alert: got %+v; want %+v", got.Alert, want.Alert) + } + if got.Error != want.Error { + t.Errorf("incorrect error: got %+v; want %+v", got.Error, want.Error) + } + if !bytes.Equal(got.RetryConfigs, want.RetryConfigs) { + t.Errorf("incorrect retry configs: got %+v; want %+v", got.RetryConfigs, want.RetryConfigs) + } + if !bytes.Equal(got.Context, want.Context) { + t.Errorf("incorrect context: got %+v; want %+v", got.Context, want.Context) + } +} + +func TestECHProvider(t *testing.T) { + p := echTestLoadKeySet(echTestKeys) + t.Run("ok", func(t *testing.T) { + handle := []byte{ + 0, 1, 0, 1, 0, 0, 32, 40, 52, 167, 167, 21, 125, 151, 32, 250, 255, 1, + 125, 206, 103, 62, 96, 189, 112, 126, 48, 221, 41, 198, 146, 100, 149, + 29, 133, 103, 87, 87, 78, + } + context := []byte{ + 1, 0, 32, 0, 1, 0, 1, 32, 36, 168, 201, 89, 6, 5, 216, 41, 55, 71, 51, + 165, 58, 92, 20, 212, 13, 84, 72, 119, 247, 120, 50, 63, 21, 145, 190, + 153, 201, 60, 38, 185, 16, 73, 40, 109, 39, 98, 199, 188, 154, 135, 218, + 81, 43, 179, 83, 22, 108, 12, 225, 52, 73, 49, 74, 108, 22, 100, 11, 244, + 38, 198, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + } + testECHProvider(t, p, handle, extensionECH, ECHProviderResult{ + Status: ECHProviderSuccess, + RetryConfigs: p.configs, + Context: context, + }) + }) + t.Run("invalid config id", func(t *testing.T) { + handle := []byte{ + 0, 1, 0, 1, 255, 202, 62, 220, 1, 243, 58, 0, 32, 40, 52, 167, 167, + 21, 125, 151, 32, 250, 255, 1, 125, 206, 103, 62, 96, 189, 112, 126, + 48, 221, 41, 198, 146, 100, 149, 29, 133, 103, 87, 87, 78, + } + testECHProvider(t, p, handle, extensionECH, ECHProviderResult{ + Status: ECHProviderReject, + RetryConfigs: p.configs, + }) + }) + t.Run("invalid cipher suite", func(t *testing.T) { + handle := []byte{ + 99, 99, 0, 1, 8, 202, 62, 220, 1, 243, 58, 247, 102, 0, 32, 40, 52, + 167, 167, 21, 125, 151, 32, 250, 255, 1, 125, 206, 103, 62, 96, 189, + 112, 126, 48, 221, 41, 198, 146, 100, 149, 29, 133, 103, 87, 87, 78, + } + testECHProvider(t, p, handle, extensionECH, ECHProviderResult{ + Status: ECHProviderReject, + RetryConfigs: p.configs, + }) + }) + t.Run("malformed", func(t *testing.T) { + handle := []byte{ + 0, 1, 0, 1, 8, 202, 62, 220, 1, + } + testECHProvider(t, p, handle, extensionECH, ECHProviderResult{ + Status: ECHProviderReject, + RetryConfigs: p.configs, + }) + }) +} diff --git a/src/crypto/tls/generate_cert.go b/src/crypto/tls/generate_cert.go index 1857185fe4d..22b746859c4 100644 --- a/src/crypto/tls/generate_cert.go +++ b/src/crypto/tls/generate_cert.go @@ -10,6 +10,7 @@ package main import ( + circlSchemes "circl/sign/schemes" "crypto/ecdsa" "crypto/ed25519" "crypto/elliptic" @@ -32,9 +33,11 @@ var ( validFrom = flag.String("start-date", "", "Creation date formatted as Jan 1 15:04:05 2011") validFor = flag.Duration("duration", 365*24*time.Hour, "Duration that certificate is valid for") isCA = flag.Bool("ca", false, "whether this cert should be its own Certificate Authority") + allowDC = flag.Bool("allowDC", false, "whether this cert can be used with Delegated Credentials") rsaBits = flag.Int("rsa-bits", 2048, "Size of RSA key to generate. Ignored if --ecdsa-curve is set") ecdsaCurve = flag.String("ecdsa-curve", "", "ECDSA curve to use to generate a key. Valid values are P224, P256 (recommended), P384, P521") ed25519Key = flag.Bool("ed25519", false, "Generate an Ed25519 key") + circlKey = flag.String("circl", "", "Generate a key supported by Circl") ) func publicKey(priv interface{}) interface{} { @@ -63,6 +66,12 @@ func main() { case "": if *ed25519Key { _, priv, err = ed25519.GenerateKey(rand.Reader) + } else if *circlKey != "" { + scheme := circlSchemes.ByName(*circlKey) + if scheme == nil { + log.Fatalf("No such Circl scheme: %s", scheme) + } + _, priv, err = scheme.GenerateKey() } else { priv, err = rsa.GenerateKey(rand.Reader, *rsaBits) } @@ -132,10 +141,19 @@ func main() { } if *isCA { + if *allowDC { + log.Fatal("Failed to create certificate: ca is not allowed with the dc flag") + } + template.IsCA = true template.KeyUsage |= x509.KeyUsageCertSign } + if *allowDC { + template.AllowDC = true + template.KeyUsage |= x509.KeyUsageDigitalSignature + } + derBytes, err := x509.CreateCertificate(rand.Reader, &template, &template, publicKey(priv), priv) if err != nil { log.Fatalf("Failed to create certificate: %v", err) diff --git a/src/crypto/tls/handshake_client.go b/src/crypto/tls/handshake_client.go index e684b21d527..85f1e577fc8 100644 --- a/src/crypto/tls/handshake_client.go +++ b/src/crypto/tls/handshake_client.go @@ -9,6 +9,7 @@ import ( "crypto" "crypto/ecdsa" "crypto/ed25519" + "crypto/kem" "crypto/rsa" "crypto/subtle" "crypto/x509" @@ -20,6 +21,8 @@ import ( "strings" "sync/atomic" "time" + + circlSign "circl/sign" ) type clientHandshakeState struct { @@ -32,27 +35,63 @@ type clientHandshakeState struct { session *ClientSessionState } -func (c *Conn) makeClientHello() (*clientHelloMsg, ecdheParameters, error) { +// processCachedDelegatedCredentialFromServer unmarshals the cached DelegatedCredential +// offered by the server (if present) and validates it using the peer's +// certificate. +func processCachedDelegatedCredentialFromServer(c *Conn, dcSupport bool, rawDC []byte, certVerifyMsg *certificateVerifyMsg) error { + var dc *DelegatedCredential + var err error + if rawDC != nil { + // Assert that support for the DC extension was indicated by the client. + if !dcSupport { + return errors.New("tls: got Delegated Credential extension without indication") + } + + dc, err = unmarshalDelegatedCredential(rawDC) + if err != nil { + return fmt.Errorf("tls: Delegated Credential: %s", err) + } + + if !isSupportedSignatureAlgorithm(dc.cred.expCertVerfAlgo, supportedSignatureAlgorithmsDC) { + return errors.New("tls: Delegated Credential used with invalid signature algorithm") + } + } + + if dc != nil { + if !dc.Validate(c.peerCertificates[0], false, c.config.time(), certVerifyMsg) { + return errors.New("tls: invalid Delegated Credential") + } + } + + c.verifiedDC = dc + + return nil +} + +// defines the private part to the handshake keyshares +type clientKeySharePrivate interface{} + +func (c *Conn) makeClientHello(minVersion uint16) (*clientHelloMsg, []clientKeySharePrivate, []byte, error) { config := c.config if len(config.ServerName) == 0 && !config.InsecureSkipVerify { - return nil, nil, errors.New("tls: either ServerName or InsecureSkipVerify must be specified in the tls.Config") + return nil, nil, nil, errors.New("tls: either ServerName or InsecureSkipVerify must be specified in the tls.Config") } nextProtosLength := 0 for _, proto := range config.NextProtos { if l := len(proto); l == 0 || l > 255 { - return nil, nil, errors.New("tls: invalid NextProtos value") + return nil, nil, nil, errors.New("tls: invalid NextProtos value") } else { nextProtosLength += 1 + l } } if nextProtosLength > 0xffff { - return nil, nil, errors.New("tls: NextProtos values too large") + return nil, nil, nil, errors.New("tls: NextProtos values too large") } - supportedVersions := config.supportedVersions() + supportedVersions := config.supportedVersionsFromMin(minVersion) if len(supportedVersions) == 0 { - return nil, nil, errors.New("tls: no supported versions satisfy MinVersion and MaxVersion") + return nil, nil, nil, errors.New("tls: no supported versions satisfy MinVersion and MaxVersion") } clientHelloVersion := config.maxSupportedVersion() @@ -63,6 +102,64 @@ func (c *Conn) makeClientHello() (*clientHelloMsg, ecdheParameters, error) { clientHelloVersion = VersionTLS12 } + var cachedCert, cachedCertReq, pdkKEMTLS bool + var ciphertextKEMTLS, sharedSecret []byte + var cachedCertHash, cachedCertReqHash []byte + if len(config.CachedCert) > 0 { + cachedCert = true + cachedCertHash = calculateHashCachedInfo(config.CachedCert) + + if config.KEMTLSEnabled { + certMsg := new(certificateMsgTLS13) + data := append([]byte(nil), config.CachedCert...) + + if !certMsg.unmarshal(data) { + return nil, nil, nil, errors.New("tls: wrong cached certificates message") + } + + if len(certMsg.certificate.Certificate) == 0 { + c.sendAlert(alertDecodeError) + return nil, nil, nil, errors.New("tls: wrong cached certificates message") + } + // do we need to write this? + //hs.transcript.Write(certMsg.marshal()) + + c.scts = certMsg.certificate.SignedCertificateTimestamps + c.ocspResponse = certMsg.certificate.OCSPStaple + + if err := c.verifyServerCertificate(certMsg.certificate.Certificate); err != nil { + return nil, nil, nil, err + } + + if isKEMTLSAuthUsed(c.peerCertificates[0], certMsg.certificate) { + if certMsg.delegatedCredential { + if err := processCachedDelegatedCredentialFromServer(c, config.SupportDelegatedCredential, certMsg.certificate.DelegatedCredential, nil); err != nil { + return nil, nil, nil, err + } + } + pk, ok := c.verifiedDC.cred.publicKey.(*kem.PublicKey) + if !ok { + return nil, nil, nil, errors.New("tls: invalid key") + } + + var err error + var ct []byte + sharedSecret, ct, err = kem.Encapsulate(c.config.rand(), pk) + if err != nil { + return nil, nil, nil, err + } + + pdkKEMTLS = true + ciphertextKEMTLS = ct + } + } + } + + if len(config.CachedCertReq) > 0 { + cachedCertReq = true + cachedCertReqHash = calculateHashCachedInfo(config.CachedCertReq) + } + hello := &clientHelloMsg{ vers: clientHelloVersion, compressionMethods: []uint8{compressionNone}, @@ -76,6 +173,12 @@ func (c *Conn) makeClientHello() (*clientHelloMsg, ecdheParameters, error) { secureRenegotiationSupported: true, alpnProtocols: config.NextProtos, supportedVersions: supportedVersions, + cachedInformationCert: cachedCert, + cachedInformationCertHash: cachedCertHash, + cachedInformationCertReq: cachedCertReq, + cachedInformationCertReqHash: cachedCertReqHash, + pdkKEMTLS: pdkKEMTLS, + ciphertextKEMTLS: ciphertextKEMTLS, } if c.handshakes > 0 { @@ -102,14 +205,14 @@ func (c *Conn) makeClientHello() (*clientHelloMsg, ecdheParameters, error) { _, err := io.ReadFull(config.rand(), hello.random) if err != nil { - return nil, nil, errors.New("tls: short read from Rand: " + err.Error()) + return nil, nil, nil, errors.New("tls: short read from Rand: " + err.Error()) } // A random session ID is used to detect when the server accepted a ticket // and is resuming a session (see RFC 5077). In TLS 1.3, it's always set as // a compatibility measure (see RFC 8446, Section 4.1.2). if _, err := io.ReadFull(config.rand(), hello.sessionId); err != nil { - return nil, nil, errors.New("tls: short read from Rand: " + err.Error()) + return nil, nil, nil, errors.New("tls: short read from Rand: " + err.Error()) } if hello.vers >= VersionTLS12 { @@ -117,21 +220,66 @@ func (c *Conn) makeClientHello() (*clientHelloMsg, ecdheParameters, error) { } var params ecdheParameters + var keyShares []keyShare + var keySharePrivates []clientKeySharePrivate + if hello.supportedVersions[0] == VersionTLS13 { hello.cipherSuites = append(hello.cipherSuites, defaultCipherSuitesTLS13()...) - curveID := config.curvePreferences()[0] - if _, ok := curveForCurveID(curveID); curveID != X25519 && !ok { - return nil, nil, errors.New("tls: CurvePreferences includes unsupported curve") - } - params, err = generateECDHEParameters(config.rand(), curveID) - if err != nil { - return nil, nil, err + if !config.KEMTLSEnabled && !config.PQTLSEnabled { + curveID := config.curvePreferences()[0] + if _, ok := curveForCurveID(curveID); curveID != X25519 && !ok { + return nil, nil, nil, errors.New("tls: CurvePreferences includes unsupported curve") + } + params, err = generateECDHEParameters(config.rand(), curveID) + if err != nil { + return nil, nil, nil, err + } + keyShares = append(keyShares, keyShare{group: curveID, data: params.PublicKey()}) + keySharePrivates = append(keySharePrivates, params) + // TODO: add EXP name + } else if config.KEMTLSEnabled || config.PQTLSEnabled { + var haveECDHE, haveKEM bool + + // loop over supported curves and kems until there is a KEM and an ECDHE curve + for _, curveID := range config.curvePreferences() { + if _, ok := curveForCurveID(curveID); curveID != X25519 && !curveID.isKEM() && !ok { + return nil, nil, nil, errors.New("tls: CurvePreferences includes unsupported curve") + } + + if !curveID.isKEM() && !haveECDHE { + params, err = generateECDHEParameters(config.rand(), curveID) + if err != nil { + return nil, nil, nil, err + } + + keyShares = append(keyShares, keyShare{group: curveID, data: params.PublicKey()}) + keySharePrivates = append(keySharePrivates, params) + haveECDHE = true + } else if curveID.isKEM() && !haveKEM { + kemID := kem.ID(curveID) + pk, sk, err := kem.GenerateKey(config.rand(), kemID) + if err != nil { + return nil, nil, nil, err + } + + keyShares = append(keyShares, keyShare{group: curveID, data: pk.PublicKey}) + keySharePrivates = append(keySharePrivates, sk) + haveKEM = true + } + + if haveECDHE && haveKEM { + break + } + } } - hello.keyShares = []keyShare{{group: curveID, data: params.PublicKey()}} + + hello.keyShares = keyShares + hello.delegatedCredentialSupported = config.SupportDelegatedCredential + hello.supportedSignatureAlgorithmsDC = supportedSignatureAlgorithmsDC } - return hello, params, nil + return hello, keySharePrivates, sharedSecret, nil } func (c *Conn) clientHandshake() (err error) { @@ -139,17 +287,36 @@ func (c *Conn) clientHandshake() (err error) { c.config = defaultConfig() } + handshakeTimings := createTLS13ClientHandshakeTimingInfo(c.config.Time) + // This may be a renegotiation handshake, in which case some fields // need to be reset. c.didResume = false - hello, ecdheParams, err := c.makeClientHello() + // Determine the minimum required version for this handshake. + minVersion := c.config.MinVersion + if c.config.echCanOffer() || len(c.config.CachedCert) > 0 || len(c.config.CachedCertReq) > 0 { + // If the ECH extension or the cached information extension will be offered in this handshake, + // then the ClientHelloInner must not offer TLS 1.2 or below. + minVersion = VersionTLS13 + } + + helloBase, keysharePrivates, ssKEMTLS, err := c.makeClientHello(minVersion) + if err != nil { + return err + } + + hello, helloInner, err := c.echOfferOrGrease(helloBase) if err != nil { return err } - c.serverName = hello.serverName - cacheKey, session, earlySecret, binderKey := c.loadSession(hello) + helloResumed := hello + if c.ech.offered { + helloResumed = helloInner + } + + cacheKey, session, earlySecret, binderKey := c.loadSession(helloResumed) if cacheKey != "" && session != nil { defer func() { // If we got a handshake failure when resuming a session, throw away @@ -168,6 +335,8 @@ func (c *Conn) clientHandshake() (err error) { return err } + handshakeTimings.WriteClientHello = handshakeTimings.elapsedTime() + msg, err := c.readHandshake() if err != nil { return err @@ -183,6 +352,9 @@ func (c *Conn) clientHandshake() (err error) { return err } + // Client already received the serverHello + handshakeTimings.reset() + // If we are negotiating a protocol version that's lower than what we // support, check for the server downgrade canaries. // See RFC 8446, Section 4.1.3. @@ -197,19 +369,25 @@ func (c *Conn) clientHandshake() (err error) { if c.vers == VersionTLS13 { hs := &clientHandshakeStateTLS13{ - c: c, - serverHello: serverHello, - hello: hello, - ecdheParams: ecdheParams, - session: session, - earlySecret: earlySecret, - binderKey: binderKey, + c: c, + serverHello: serverHello, + hello: hello, + helloInner: helloInner, + helloBase: helloBase, + keyShare: keysharePrivates, + session: session, + earlySecret: earlySecret, + binderKey: binderKey, + handshakeTimings: handshakeTimings, + ssKEMTLS: ssKEMTLS, + pdkKEMTLS: hello.pdkKEMTLS, } // In TLS 1.3, session tickets are delivered after the handshake. return hs.handshake() } + c.serverName = hello.serverName hs := &clientHandshakeState{ c: c, serverHello: serverHello, @@ -232,7 +410,7 @@ func (c *Conn) clientHandshake() (err error) { func (c *Conn) loadSession(hello *clientHelloMsg) (cacheKey string, session *ClientSessionState, earlySecret, binderKey []byte) { - if c.config.SessionTicketsDisabled || c.config.ClientSessionCache == nil { + if c.config.SessionTicketsDisabled || c.config.ClientSessionCache == nil || c.config.ECHEnabled { return "", nil, nil, nil } @@ -834,10 +1012,14 @@ func (c *Conn) verifyServerCertificate(certificates [][]byte) error { } if !c.config.InsecureSkipVerify { + dnsName := c.config.ServerName + if c.ech.offered && !c.ech.accepted { + dnsName = c.serverName + } opts := x509.VerifyOptions{ Roots: c.config.RootCAs, CurrentTime: c.config.time(), - DNSName: c.config.ServerName, + DNSName: dnsName, Intermediates: x509.NewCertPool(), } for _, cert := range certs[1:] { @@ -852,7 +1034,7 @@ func (c *Conn) verifyServerCertificate(certificates [][]byte) error { } switch certs[0].PublicKey.(type) { - case *rsa.PublicKey, *ecdsa.PublicKey, ed25519.PublicKey: + case *rsa.PublicKey, *ecdsa.PublicKey, ed25519.PublicKey, circlSign.PublicKey, *kem.PublicKey: break default: c.sendAlert(alertUnsupportedCertificate) @@ -882,8 +1064,10 @@ func (c *Conn) verifyServerCertificate(certificates [][]byte) error { // <= 1.2 CertificateRequest, making an effort to fill in missing information. func certificateRequestInfoFromMsg(vers uint16, certReq *certificateRequestMsg) *CertificateRequestInfo { cri := &CertificateRequestInfo{ - AcceptableCAs: certReq.certificateAuthorities, - Version: vers, + AcceptableCAs: certReq.certificateAuthorities, + Version: vers, + SupportsDelegatedCredential: false, // Not supported in TLS <= 1.2 + SignatureSchemesDC: nil, // Not supported in TLS <= 1.2 } var rsaAvail, ecAvail bool diff --git a/src/crypto/tls/handshake_client_kemtls.go b/src/crypto/tls/handshake_client_kemtls.go new file mode 100644 index 00000000000..d47973ccdf6 --- /dev/null +++ b/src/crypto/tls/handshake_client_kemtls.go @@ -0,0 +1,342 @@ +// Copyright 2020 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package tls + +import ( + "crypto/hmac" + "crypto/kem" + "errors" + "sync/atomic" +) + +func (hs *clientHandshakeStateTLS13) handshakeKEMTLS() error { + c := hs.c + + if hs.pdkKEMTLS { + if err := hs.processKEMTLSServerFinished(); err != nil { + return err + } + if err := hs.sendKEMTLSClientFinished(); err != nil { + return err + } + + if _, err := c.flush(); err != nil { + return err + } + hs.handshakeTimings.reset() + } else { + if err := hs.sendClientKEMCiphertext(); err != nil { + return err + } + + // Send the KEMTLS client certificate if asked for + if err := hs.sendKEMClientCertificate(); err != nil { + return err + } + + if hs.certReq != nil { + if _, err := c.flush(); err != nil { + return err + } + // second round for KEMTLS + hs.handshakeTimings.reset() + } + + if err := hs.readServerKEMCiphertext(); err != nil { + return err + } + + if err := hs.sendKEMTLSClientFinished(); err != nil { + return err + } + + if _, err := c.flush(); err != nil { + return err + } + // thrid round for KEMTLS + hs.handshakeTimings.reset() + if err := hs.processKEMTLSServerFinished(); err != nil { + return err + } + } + + // hs.handshakeTimings.ExperimentName = experimentName(c) + hs.handshakeTimings.finish() + c.handleCFEvent(hs.handshakeTimings) + atomic.StoreUint32(&c.handshakeStatus, 1) + + return nil +} + +func (hs *clientHandshakeStateTLS13) sendClientKEMCiphertext() error { + c := hs.c + var pk *kem.PublicKey + var ok bool + var ahs []byte + + if !(hs.pdkKEMTLS && hs.keyKEMShare) { + if c.verifiedDC != nil && c.verifiedDC.cred.expCertVerfAlgo.isKEMTLS() { + pk, ok = c.verifiedDC.cred.publicKey.(*kem.PublicKey) + if !ok { + c.sendAlert(alertInternalError) + return errors.New("tls: invalid key") + } + } else { + pk, ok = c.peerCertificates[0].PublicKey.(*kem.PublicKey) + if !ok { + c.sendAlert(alertInternalError) + return errors.New("tls: invalid key") + } + } + + ss, ct, err := kem.Encapsulate(hs.c.config.rand(), pk) + if err != nil { + return err + } + + msg := clientKeyExchangeMsg{ + ciphertext: ct, + } + + _, err = c.writeRecord(recordTypeHandshake, msg.marshal()) + if err != nil { + return err + } + + _, err = hs.transcript.Write(msg.marshal()) + if err != nil { + return err + } + hs.handshakeTimings.WriteKEMCiphertext = hs.handshakeTimings.elapsedTime() + + // AHS <- HKDF.Extract(dHS, ss_s) + ahs = hs.suite.extract(ss, hs.suite.deriveSecret(hs.handshakeSecret, "derived", nil)) + } else { + ahs = hs.suite.extract(hs.ssKEMTLS, hs.suite.deriveSecret(hs.handshakeSecret, "derived", nil)) + } + + // CAHTS <- HKDF.Expand(AHS, "c ahs traffic", CH..CKC) + clientSecret := hs.suite.deriveSecret(ahs, + clientAuthenticatedHandshakeTrafficLabel, hs.transcript) + c.out.setTrafficSecret(hs.suite, clientSecret) + // SAHTS <- HKDF.Expand(AHS, "s ahs traffic", CH..CKC) + serverSecret := hs.suite.deriveSecret(ahs, + serverAuthenticatedHandshakeTrafficLabel, hs.transcript) + c.in.setTrafficSecret(hs.suite, serverSecret) + + // dAHS <- HKDF.Expand(AHS, "derived", nil) + hs.handshakeSecret = hs.suite.deriveSecret(ahs, "derived", nil) + + err := c.config.writeKeyLog(keyLogLabelClientKEMAuthenticatedHandshake, hs.hello.random, clientSecret) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + + err = c.config.writeKeyLog(keyLogLabelServerKEMAuthenticatedHandshake, hs.hello.random, serverSecret) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + + return nil +} + +func (hs *clientHandshakeStateTLS13) sendKEMClientCertificate() error { + c := hs.c + + if hs.certReq == nil { + return nil + } + + cri := certificateRequestInfo(hs.certReq, c.vers) + + cert, err := c.getClientCertificate(cri) + if err != nil { + return err + } + + if hs.certReq.supportDelegatedCredential && len(hs.certReq.supportedSignatureAlgorithmsDC) > 0 { + var dcPair *DelegatedCredentialPair + if delegatedCredentialPair, err := getClientDelegatedCredential(cri, cert); err == nil { + if delegatedCredentialPair.DC != nil && delegatedCredentialPair.PrivateKey != nil { + var err error + // Even if the Delegated Credential has already been marshalled, be sure it is the correct one. + if delegatedCredentialPair.DC.raw, err = delegatedCredentialPair.DC.marshal(); err == nil { + dcPair = delegatedCredentialPair + cert.DelegatedCredential = dcPair.DC.raw + cert.DelegatedCredentialPrivateKey = dcPair.PrivateKey + } + } + } + } + + if len(cert.DelegatedCredential) > 0 { + _, ok := cert.DelegatedCredentialPrivateKey.(*kem.PrivateKey) + if !ok { + // it has to be a KEM key + c.sendAlert(alertInternalError) + return errors.New("tls: incorrect delegated credential found") + } + } else if len(cert.Certificate) != 0 { + _, ok := cert.PrivateKey.(*kem.PrivateKey) + if !ok { + // it has to be a KEM key + c.sendAlert(alertInternalError) + return errors.New("tls: incorrect certificate found") + } + } + + certMsg := new(certificateMsgTLS13) + certMsg.certificate = *cert + hs.certKEMTLS = cert + + certMsg.scts = hs.certReq.scts && len(cert.SignedCertificateTimestamps) > 0 + certMsg.ocspStapling = hs.certReq.ocspStapling && len(cert.OCSPStaple) > 0 + certMsg.delegatedCredential = hs.certReq.supportDelegatedCredential && len(cert.DelegatedCredential) > 0 + + hs.transcript.Write(certMsg.marshal()) + if _, err := c.writeRecord(recordTypeHandshake, certMsg.marshal()); err != nil { + return err + } + + hs.handshakeTimings.WriteCertificate = hs.handshakeTimings.elapsedTime() + + return nil +} + +func (hs *clientHandshakeStateTLS13) readServerKEMCiphertext() error { + c := hs.c + + if hs.certReq == nil { + return nil + } + + if len(hs.certKEMTLS.Certificate) == 0 { + return nil + } + + var sk *kem.PrivateKey + var ok, ok1 bool + sk, ok = hs.certKEMTLS.PrivateKey.(*kem.PrivateKey) + if !ok { + sk, ok1 = hs.certKEMTLS.DelegatedCredentialPrivateKey.(*kem.PrivateKey) + if !ok1 { + c.sendAlert(alertInternalError) + return errors.New("crypto/tls: private key unexpectedly of wrong type") + } + } + + msg, err := c.readHandshake() + if err != nil { + return err + } + + kexMsg, ok := msg.(*serverKeyExchangeMsg) + if !ok { + c.sendAlert(alertUnexpectedMessage) + return unexpectedMessageError(kexMsg, msg) + } + hs.transcript.Write(kexMsg.marshal()) + + hs.handshakeTimings.ReadKEMCiphertext = hs.handshakeTimings.elapsedTime() + + ss, err := kem.Decapsulate(sk, kexMsg.key) + if err != nil { + return err + } + + // compute MS + // MS <- HKDF.Extract(dAHS, ssC) + hs.masterSecret = hs.suite.extract(ss, hs.handshakeSecret) + hs.isClientAuthKEMTLS = true + c.didClientAuthentication = true + + return nil +} + +func (hs *clientHandshakeStateTLS13) sendKEMTLSClientFinished() error { + c := hs.c + + if !hs.isClientAuthKEMTLS { + hs.masterSecret = hs.suite.extract(nil, hs.handshakeSecret) + } + // fk_c <- HKDF.Expand(MS, "c finished", nil) + // CF <- HMAC(fk_c, CH..CKC) + finished := &finishedMsg{ + verifyData: hs.suite.finishedHashKEMTLS(hs.masterSecret, "c", hs.transcript), + } + + if _, err := hs.transcript.Write(finished.marshal()); err != nil { + return err + } + if _, err := c.writeRecord(recordTypeHandshake, finished.marshal()); err != nil { + return err + } + + hs.handshakeTimings.WriteClientFinished = hs.handshakeTimings.elapsedTime() + + // CATS <- HKDF.Expand(MS, "c ap traffic", CH..CF) + hs.trafficSecret = hs.suite.deriveSecret(hs.masterSecret, + clientApplicationTrafficLabel, hs.transcript) + + c.out.setTrafficSecret(hs.suite, hs.trafficSecret) + + err := c.config.writeKeyLog(keyLogLabelClientTraffic, hs.hello.random, hs.trafficSecret) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + + return nil +} + +func (hs *clientHandshakeStateTLS13) processKEMTLSServerFinished() error { + c := hs.c + msg, err := c.readHandshake() + if err != nil { + return err + } + + finished, ok := msg.(*finishedMsg) + if !ok { + c.sendAlert(alertUnexpectedMessage) + return unexpectedMessageError(finished, msg) + } + + hs.handshakeTimings.ReadServerFinished = hs.handshakeTimings.elapsedTime() + + // HMAC(fk_s , CH..CF) + expectedMAC := hs.suite.finishedHashKEMTLS(hs.masterSecret, "s", hs.transcript) + if !hmac.Equal(expectedMAC, finished.verifyData) { + c.sendAlert(alertDecryptError) + return errors.New("tls: invalid server finished hash") + } + + if _, err := hs.transcript.Write(finished.marshal()); err != nil { + return err + } + + // SATS <- HKDF.Expand(MS, "s ap traffic", CH..SF) + serverSecret := hs.suite.deriveSecret(hs.masterSecret, + serverApplicationTrafficLabel, hs.transcript) + c.in.setTrafficSecret(hs.suite, serverSecret) + + err = c.config.writeKeyLog(keyLogLabelServerTraffic, hs.hello.random, serverSecret) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + + if !c.config.SessionTicketsDisabled && c.config.ClientSessionCache != nil { + c.resumptionSecret = hs.suite.deriveSecret(hs.masterSecret, + resumptionLabel, hs.transcript) + } + + c.ekm = hs.suite.exportKeyingMaterial(hs.masterSecret, hs.transcript) + c.didKEMTLS = true + + return nil +} diff --git a/src/crypto/tls/handshake_client_tls13.go b/src/crypto/tls/handshake_client_tls13.go index daa5d97fd35..ded608bab49 100644 --- a/src/crypto/tls/handshake_client_tls13.go +++ b/src/crypto/tls/handshake_client_tls13.go @@ -8,8 +8,11 @@ import ( "bytes" "crypto" "crypto/hmac" + "crypto/kem" "crypto/rsa" + "crypto/x509" "errors" + "fmt" "hash" "sync/atomic" "time" @@ -19,19 +22,72 @@ type clientHandshakeStateTLS13 struct { c *Conn serverHello *serverHelloMsg hello *clientHelloMsg - ecdheParams ecdheParameters + helloInner *clientHelloMsg + helloBase *clientHelloMsg + keyShare []clientKeySharePrivate session *ClientSessionState earlySecret []byte binderKey []byte - certReq *certificateRequestMsgTLS13 - usingPSK bool - sentDummyCCS bool - suite *cipherSuiteTLS13 - transcript hash.Hash - masterSecret []byte - trafficSecret []byte // client_application_traffic_secret_0 + certReq *certificateRequestMsgTLS13 + usingPSK bool + sentDummyCCS bool + + keyKEMShare bool + isKEMTLS bool + pdkKEMTLS bool + ssKEMTLS []byte + isClientAuthKEMTLS bool + certKEMTLS *Certificate // only for KEMTLS + + suite *cipherSuiteTLS13 + transcript hash.Hash + transcriptInner hash.Hash + handshakeSecret []byte + masterSecret []byte + trafficSecret []byte // client_application_traffic_secret_0 + + handshakeTimings CFEventTLS13ClientHandshakeTimingInfo +} + +// processDelegatedCredentialFromServer unmarshals the DelegatedCredential +// offered by the server (if present) and validates it using the peer's +// certificate. +func (hs *clientHandshakeStateTLS13) processDelegatedCredentialFromServer(rawDC []byte, certVerifyMsg *certificateVerifyMsg) error { + c := hs.c + + var dc *DelegatedCredential + var err error + if rawDC != nil { + // Assert that support for the DC extension was indicated by the client. + if !hs.hello.delegatedCredentialSupported { + c.sendAlert(alertUnexpectedMessage) + return errors.New("tls: got Delegated Credential extension without indication") + } + + dc, err = unmarshalDelegatedCredential(rawDC) + if err != nil { + c.sendAlert(alertDecodeError) + return fmt.Errorf("tls: Delegated Credential: %s", err) + } + + if !isSupportedSignatureAlgorithm(dc.cred.expCertVerfAlgo, supportedSignatureAlgorithmsDC) { + c.sendAlert(alertIllegalParameter) + return errors.New("tls: Delegated Credential used with invalid signature algorithm") + } + } + + if dc != nil { + if !dc.Validate(c.peerCertificates[0], false, c.config.time(), certVerifyMsg) { + c.sendAlert(alertIllegalParameter) + return errors.New("tls: invalid Delegated Credential") + } + } + + c.verifiedDC = dc + + return nil } // handshake requires hs.c, hs.hello, hs.serverHello, hs.ecdheParams, and, @@ -47,7 +103,7 @@ func (hs *clientHandshakeStateTLS13) handshake() error { } // Consistency check on the presence of a keyShare and its parameters. - if hs.ecdheParams == nil || len(hs.hello.keyShares) != 1 { + if hs.keyShare == nil || len(hs.hello.keyShares) != len(hs.keyShare) { return c.sendAlert(alertInternalError) } @@ -58,6 +114,14 @@ func (hs *clientHandshakeStateTLS13) handshake() error { hs.transcript = hs.suite.hash.New() hs.transcript.Write(hs.hello.marshal()) + // When offering ECH, it is not known whether ECH was accepted until the + // ServerHello is processed. In particular, we do not know at this point if + // the server used the ClientHelloOuter or the ClientHelloInner. + if c.ech.offered { + hs.transcriptInner = hs.suite.hash.New() + hs.transcriptInner.Write(hs.helloInner.marshal()) + } + if bytes.Equal(hs.serverHello.random, helloRetryRequestRandom) { if err := hs.sendDummyChangeCipherSpec(); err != nil { return err @@ -67,8 +131,6 @@ func (hs *clientHandshakeStateTLS13) handshake() error { } } - hs.transcript.Write(hs.serverHello.marshal()) - c.buffering = true if err := hs.processServerHello(); err != nil { return err @@ -85,6 +147,9 @@ func (hs *clientHandshakeStateTLS13) handshake() error { if err := hs.readServerCertificate(); err != nil { return err } + if hs.isKEMTLS { + return hs.handshakeKEMTLS() + } if err := hs.readServerFinished(); err != nil { return err } @@ -94,10 +159,16 @@ func (hs *clientHandshakeStateTLS13) handshake() error { if err := hs.sendClientFinished(); err != nil { return err } + if err := hs.abortIfRequired(); err != nil { + return err + } if _, err := c.flush(); err != nil { return err } + // hs.handshakeTimings.ExperimentName = experimentName(c) + hs.handshakeTimings.finish() + c.handleCFEvent(hs.handshakeTimings) atomic.StoreUint32(&c.handshakeStatus, 1) return nil @@ -174,6 +245,7 @@ func (hs *clientHandshakeStateTLS13) sendDummyChangeCipherSpec() error { // resends hs.hello, and reads the new ServerHello into hs.serverHello. func (hs *clientHandshakeStateTLS13) processHelloRetryRequest() error { c := hs.c + c.hrrTriggered = true // The first ClientHello gets double-hashed into the transcript upon a // HelloRetryRequest. (The idea is that the server might offload transcript @@ -184,6 +256,14 @@ func (hs *clientHandshakeStateTLS13) processHelloRetryRequest() error { hs.transcript.Write(chHash) hs.transcript.Write(hs.serverHello.marshal()) + if c.ech.offered { + chHash = hs.transcriptInner.Sum(nil) + hs.transcriptInner.Reset() + hs.transcriptInner.Write([]byte{typeMessageHash, 0, 0, uint8(len(chHash))}) + hs.transcriptInner.Write(chHash) + hs.transcriptInner.Write(hs.serverHello.marshal()) + } + // The only HelloRetryRequest extensions we support are key_share and // cookie, and clients must abort the handshake if the HRR would not result // in any change in the ClientHello. @@ -193,7 +273,7 @@ func (hs *clientHandshakeStateTLS13) processHelloRetryRequest() error { } if hs.serverHello.cookie != nil { - hs.hello.cookie = hs.serverHello.cookie + hs.helloBase.cookie = hs.serverHello.cookie } if hs.serverHello.serverShare.group != 0 { @@ -206,7 +286,7 @@ func (hs *clientHandshakeStateTLS13) processHelloRetryRequest() error { // share for it this time. if curveID := hs.serverHello.selectedGroup; curveID != 0 { curveOK := false - for _, id := range hs.hello.supportedCurves { + for _, id := range hs.helloBase.supportedCurves { if id == curveID { curveOK = true break @@ -216,25 +296,52 @@ func (hs *clientHandshakeStateTLS13) processHelloRetryRequest() error { c.sendAlert(alertIllegalParameter) return errors.New("tls: server selected unsupported group") } - if hs.ecdheParams.CurveID() == curveID { - c.sendAlert(alertIllegalParameter) - return errors.New("tls: server sent an unnecessary HelloRetryRequest key_share") - } - if _, ok := curveForCurveID(curveID); curveID != X25519 && !ok { - c.sendAlert(alertInternalError) - return errors.New("tls: CurvePreferences includes unsupported curve") + + for _, keyShare := range hs.keyShare { + if ecdheParams, ok := keyShare.(ecdheParameters); ok { + if ecdheParams.CurveID() == curveID { + c.sendAlert(alertIllegalParameter) + return errors.New("tls: server sent an unnecessary HelloRetryRequest key_share") + } + } else if c.config.KEMTLSEnabled || c.config.PQTLSEnabled { + if kemShare, ok := keyShare.(*kem.PrivateKey); ok { + if CurveID(kemShare.KEMId) == curveID { + c.sendAlert(alertIllegalParameter) + return errors.New("tls: server sent an unnecessary HelloRetryRequest key_share") + } + } + } else { + return errors.New("tls: server sent an unnecessary HelloRetryRequest key_share") + } + } - params, err := generateECDHEParameters(c.config.rand(), curveID) - if err != nil { - c.sendAlert(alertInternalError) - return err + + if curveID.isKEM() && (c.config.KEMTLSEnabled || c.config.PQTLSEnabled) { + kemID := kem.ID(curveID) + pk, sk, err := kem.GenerateKey(c.config.rand(), kemID) + if err != nil { + c.sendAlert(alertInternalError) + return errors.New("tls: CurvePreferences includes unsupported kem") + } + hs.keyShare = []clientKeySharePrivate{sk} + hs.helloBase.keyShares = []keyShare{{group: CurveID(pk.KEMId), data: pk.PublicKey}} + } else { + if _, ok := curveForCurveID(curveID); (curveID != X25519 && !curveID.isKEM()) && !ok { + c.sendAlert(alertInternalError) + return errors.New("tls: CurvePreferences includes unsupported curve") + } + params, err := generateECDHEParameters(c.config.rand(), curveID) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + hs.keyShare = []clientKeySharePrivate{params} + hs.helloBase.keyShares = []keyShare{{group: curveID, data: params.PublicKey()}} } - hs.ecdheParams = params - hs.hello.keyShares = []keyShare{{group: curveID, data: params.PublicKey()}} } - hs.hello.raw = nil - if len(hs.hello.pskIdentities) > 0 { + hs.helloBase.raw = nil + if len(hs.helloBase.pskIdentities) > 0 { pskSuite := cipherSuiteTLS13ByID(hs.session.cipherSuite) if pskSuite == nil { return c.sendAlert(alertInternalError) @@ -242,23 +349,42 @@ func (hs *clientHandshakeStateTLS13) processHelloRetryRequest() error { if pskSuite.hash == hs.suite.hash { // Update binders and obfuscated_ticket_age. ticketAge := uint32(c.config.time().Sub(hs.session.receivedAt) / time.Millisecond) - hs.hello.pskIdentities[0].obfuscatedTicketAge = ticketAge + hs.session.ageAdd + hs.helloBase.pskIdentities[0].obfuscatedTicketAge = ticketAge + hs.session.ageAdd transcript := hs.suite.hash.New() transcript.Write([]byte{typeMessageHash, 0, 0, uint8(len(chHash))}) transcript.Write(chHash) transcript.Write(hs.serverHello.marshal()) - transcript.Write(hs.hello.marshalWithoutBinders()) + transcript.Write(hs.helloBase.marshalWithoutBinders()) pskBinders := [][]byte{hs.suite.finishedHash(hs.binderKey, transcript)} - hs.hello.updateBinders(pskBinders) + hs.helloBase.updateBinders(pskBinders) } else { // Server selected a cipher suite incompatible with the PSK. - hs.hello.pskIdentities = nil - hs.hello.pskBinders = nil + hs.helloBase.pskIdentities = nil + hs.helloBase.pskBinders = nil } } - hs.transcript.Write(hs.hello.marshal()) + var err error + hs.hello, hs.helloInner, err = c.echOfferOrGrease(hs.helloBase) + if err != nil { + return err + } + + if testingECHIllegalHandleAfterHRR { + // Triggers a server abort, since the "config_id" and "enc" fields are + // expected to be empty after HRR. + ech, err := echUnmarshalClient(hs.hello.ech) + if err != nil { + return err + } + ech.raw = nil + ech.handle.raw = nil + ech.handle.configId = uint8(0) + ech.handle.enc = []byte{1, 2, 3, 4} + hs.hello.ech = ech.marshal() + } + if _, err := c.writeRecord(recordTypeHandshake, hs.hello.marshal()); err != nil { return err } @@ -279,12 +405,20 @@ func (hs *clientHandshakeStateTLS13) processHelloRetryRequest() error { return err } + hs.transcript.Write(hs.hello.marshal()) + if c.ech.offered { + hs.transcriptInner.Write(hs.helloInner.marshal()) + } return nil } func (hs *clientHandshakeStateTLS13) processServerHello() error { c := hs.c + defer func() { + hs.handshakeTimings.ProcessServerHello = hs.handshakeTimings.elapsedTime() + }() + if bytes.Equal(hs.serverHello.random, helloRetryRequestRandom) { c.sendAlert(alertUnexpectedMessage) return errors.New("tls: server sent two HelloRetryRequest messages") @@ -304,7 +438,28 @@ func (hs *clientHandshakeStateTLS13) processServerHello() error { c.sendAlert(alertIllegalParameter) return errors.New("tls: server did not send a key share") } - if hs.serverHello.serverShare.group != hs.ecdheParams.CurveID() { + + if hs.serverHello.pdkKEMTLS && !hs.hello.pdkKEMTLS { + return errors.New("tls: server using pre-shared KEMTLS and client not") + } + + var found bool + for _, keyShare := range hs.keyShare { + if ecdheParams, ok := keyShare.(ecdheParameters); ok { + if hs.serverHello.serverShare.group == ecdheParams.CurveID() { + found = true + } + } else if c.config.KEMTLSEnabled || c.config.PQTLSEnabled { + kemShare := keyShare.(*kem.PrivateKey) + if CurveID(kemShare.KEMId) == hs.serverHello.serverShare.group { + found = true + } + } else { + found = false + } + } + + if !found { c.sendAlert(alertIllegalParameter) return errors.New("tls: server selected unsupported group") } @@ -342,23 +497,65 @@ func (hs *clientHandshakeStateTLS13) processServerHello() error { func (hs *clientHandshakeStateTLS13) establishHandshakeKeys() error { c := hs.c - sharedKey := hs.ecdheParams.SharedKey(hs.serverHello.serverShare.data) - if sharedKey == nil { - c.sendAlert(alertIllegalParameter) - return errors.New("tls: invalid server key share") + var sharedKey []byte + for _, keyShare := range hs.keyShare { + if params, ok := keyShare.(ecdheParameters); ok && params.CurveID() == hs.serverHello.serverShare.group { + sharedKey = params.SharedKey(hs.serverHello.serverShare.data) + } else if c.config.KEMTLSEnabled || c.config.PQTLSEnabled { + if kemPrivate, ok := keyShare.(*kem.PrivateKey); ok && kemPrivate.KEMId == kem.ID(hs.serverHello.serverShare.group) { + var err error + sharedKey, err = kem.Decapsulate(kemPrivate, hs.serverHello.serverShare.data) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + hs.keyKEMShare = true + } + } } earlySecret := hs.earlySecret if !hs.usingPSK { earlySecret = hs.suite.extract(nil, nil) } - handshakeSecret := hs.suite.extract(sharedKey, + hs.handshakeSecret = hs.suite.extract(sharedKey, hs.suite.deriveSecret(earlySecret, "derived", nil)) - clientSecret := hs.suite.deriveSecret(handshakeSecret, + // If ECH was offered, then determine if it was accepted. + if c.ech.offered { + confTranscript := cloneHash(hs.transcriptInner, hs.suite.hash) + if confTranscript == nil { + c.sendAlert(alertInternalError) + return errors.New("tls: internal error: failed to clone hash") + } + serverHelloConf := echEncodeServerHelloConf(hs.serverHello.marshal()) + if serverHelloConf == nil { + c.sendAlert(alertInternalError) + return errors.New("tls: internal error: failed to encode ServerHelloConf") + } + confTranscript.Write(serverHelloConf) + conf := hs.suite.deriveSecret(hs.handshakeSecret, + echAcceptConfirmationLabel, confTranscript) + if bytes.Equal(hs.serverHello.random[24:], conf[:8]) { + c.ech.accepted = true + hs.hello = hs.helloInner + hs.transcript = hs.transcriptInner + } + } + + hs.transcript.Write(hs.serverHello.marshal()) + + // Resolve the server name now that ECH acceptance has been determined. + // + // NOTE(cjpatton): Currently the client sends the same ALPN extension in the + // ClientHelloInner and ClientHelloOuter. If that changes, then we'll need + // to resolve ALPN here as well. + c.serverName = hs.hello.serverName + + clientSecret := hs.suite.deriveSecret(hs.handshakeSecret, clientHandshakeTrafficLabel, hs.transcript) c.out.setTrafficSecret(hs.suite, clientSecret) - serverSecret := hs.suite.deriveSecret(handshakeSecret, + serverSecret := hs.suite.deriveSecret(hs.handshakeSecret, serverHandshakeTrafficLabel, hs.transcript) c.in.setTrafficSecret(hs.suite, serverSecret) @@ -373,9 +570,6 @@ func (hs *clientHandshakeStateTLS13) establishHandshakeKeys() error { return err } - hs.masterSecret = hs.suite.extract(nil, - hs.suite.deriveSecret(handshakeSecret, "derived", nil)) - return nil } @@ -406,12 +600,72 @@ func (hs *clientHandshakeStateTLS13) readServerParameters() error { c.clientProtocol = encryptedExtensions.alpnProtocol } + // If the server rejects ECH, then it may send retry configurations. If + // present, we must check them for syntactic correctness and abort if they + // are not correct. + if c.ech.offered && len(encryptedExtensions.ech) > 0 { + c.ech.retryConfigs = encryptedExtensions.ech + if _, err = UnmarshalECHConfigs(c.ech.retryConfigs); err != nil { + c.sendAlert(alertIllegalParameter) + return fmt.Errorf("tls: ech: failed to parse retry configs: %s", err) + } + } + + hs.handshakeTimings.ReadEncryptedExtensions = hs.handshakeTimings.elapsedTime() + return nil } +func isKEMTLSAuthUsed(peerCertificate *x509.Certificate, cert Certificate) bool { + if cert.DelegatedCredential != nil { + dCred, err := unmarshalDelegatedCredential(cert.DelegatedCredential) + if err != nil { + return false + } + + if dCred.cred.expCertVerfAlgo.isKEMTLS() { + return true + } + } + + if kemPriv, ok := peerCertificate.PublicKey.(*kem.PublicKey); ok { + if kemPriv.KEMId == kem.SIKEp434 || kemPriv.KEMId == kem.Kyber512 { + return true + } + } + + return false +} + +func isPQTLSAuthUsed(peerCertificate *x509.Certificate, cert Certificate) bool { + if cert.DelegatedCredential != nil { + dCred, err := unmarshalDelegatedCredential(cert.DelegatedCredential) + if err != nil { + return false + } + + if dCred.cred.expCertVerfAlgo.isPQTLS() { + return true + } + } + + if kemPriv, ok := peerCertificate.PublicKey.(*kem.PublicKey); ok { + if kemPriv.KEMId == kem.SIKEp434 || kemPriv.KEMId == kem.Kyber512 { + return true + } + } + + return false +} + func (hs *clientHandshakeStateTLS13) readServerCertificate() error { c := hs.c + if hs.pdkKEMTLS && hs.keyKEMShare { + hs.isKEMTLS = true + return nil + } + // Either a PSK or a certificate is always used, but not both. // See RFC 8446, Section 4.1.1. if hs.usingPSK { @@ -455,6 +709,8 @@ func (hs *clientHandshakeStateTLS13) readServerCertificate() error { } hs.transcript.Write(certMsg.marshal()) + hs.handshakeTimings.ReadCertificate = hs.handshakeTimings.elapsedTime() + c.scts = certMsg.certificate.SignedCertificateTimestamps c.ocspResponse = certMsg.certificate.OCSPStaple @@ -462,38 +718,76 @@ func (hs *clientHandshakeStateTLS13) readServerCertificate() error { return err } - msg, err = c.readHandshake() - if err != nil { - return err + if isPQTLSAuthUsed(c.peerCertificates[0], certMsg.certificate) { + if hs.keyKEMShare { + c.didPQTLS = true + } } - certVerify, ok := msg.(*certificateVerifyMsg) - if !ok { - c.sendAlert(alertUnexpectedMessage) - return unexpectedMessageError(certVerify, msg) - } + if isKEMTLSAuthUsed(c.peerCertificates[0], certMsg.certificate) { + if certMsg.delegatedCredential { + if err := hs.processDelegatedCredentialFromServer(certMsg.certificate.DelegatedCredential, nil); err != nil { + return err + } + } - // See RFC 8446, Section 4.4.3. - if !isSupportedSignatureAlgorithm(certVerify.signatureAlgorithm, supportedSignatureAlgorithms) { - c.sendAlert(alertIllegalParameter) - return errors.New("tls: certificate used with invalid signature algorithm") - } - sigType, sigHash, err := typeAndHashFromSignatureScheme(certVerify.signatureAlgorithm) - if err != nil { - return c.sendAlert(alertInternalError) - } - if sigType == signaturePKCS1v15 || sigHash == crypto.SHA1 { - c.sendAlert(alertIllegalParameter) - return errors.New("tls: certificate used with invalid signature algorithm") - } - signed := signedMessage(sigHash, serverSignatureContext, hs.transcript) - if err := verifyHandshakeSignature(sigType, c.peerCertificates[0].PublicKey, - sigHash, signed, certVerify.signature); err != nil { - c.sendAlert(alertDecryptError) - return errors.New("tls: invalid signature by the server certificate: " + err.Error()) + if hs.keyKEMShare { + hs.isKEMTLS = true + hs.handshakeTimings.ReadCertificateVerify = hs.handshakeTimings.elapsedTime() + } else { + c.sendAlert(alertInternalError) + return errors.New("tls: received a KEM certificate without using KEMTLS") + } + } else { + msg, err = c.readHandshake() + if err != nil { + return err + } + + certVerify, ok := msg.(*certificateVerifyMsg) + if !ok { + c.sendAlert(alertUnexpectedMessage) + return unexpectedMessageError(certVerify, msg) + } + + // See RFC 8446, Section 4.4.3. + if !isSupportedSignatureAlgorithm(certVerify.signatureAlgorithm, supportedSignatureAlgorithms) { + c.sendAlert(alertIllegalParameter) + return errors.New("tls: certificate used with invalid signature algorithm") + } + + sigType, sigHash, err := typeAndHashFromSignatureScheme(certVerify.signatureAlgorithm) + if err != nil { + return c.sendAlert(alertInternalError) + } + if sigType == signaturePKCS1v15 || sigHash == crypto.SHA1 { + c.sendAlert(alertIllegalParameter) + return errors.New("tls: certificate used with invalid signature algorithm") + } + if certMsg.delegatedCredential { + if err := hs.processDelegatedCredentialFromServer(certMsg.certificate.DelegatedCredential, certVerify); err != nil { + return err // alert sent + } + } + + pk := c.peerCertificates[0].PublicKey + if c.verifiedDC != nil { + pk = c.verifiedDC.cred.publicKey + } + + signed := signedMessage(sigHash, serverSignatureContext, hs.transcript) + if err := verifyHandshakeSignature(sigType, pk, + sigHash, signed, certVerify.signature); err != nil { + c.sendAlert(alertDecryptError) + return errors.New("tls: invalid signature by the server certificate: " + err.Error()) + } + + hs.transcript.Write(certVerify.marshal()) + + hs.handshakeTimings.ReadCertificateVerify = hs.handshakeTimings.elapsedTime() } - hs.transcript.Write(certVerify.marshal()) + c.certificateMessage = certMsg.marshal() return nil } @@ -501,6 +795,10 @@ func (hs *clientHandshakeStateTLS13) readServerCertificate() error { func (hs *clientHandshakeStateTLS13) readServerFinished() error { c := hs.c + if hs.isKEMTLS == true { + return nil + } + msg, err := c.readHandshake() if err != nil { return err @@ -512,6 +810,8 @@ func (hs *clientHandshakeStateTLS13) readServerFinished() error { return unexpectedMessageError(finished, msg) } + hs.handshakeTimings.ReadServerFinished = hs.handshakeTimings.elapsedTime() + expectedMAC := hs.suite.finishedHash(c.in.trafficSecret, hs.transcript) if !hmac.Equal(expectedMAC, finished.verifyData) { c.sendAlert(alertDecryptError) @@ -522,6 +822,8 @@ func (hs *clientHandshakeStateTLS13) readServerFinished() error { // Derive secrets that take context through the server Finished. + hs.masterSecret = hs.suite.extract(nil, + hs.suite.deriveSecret(hs.handshakeSecret, "derived", nil)) hs.trafficSecret = hs.suite.deriveSecret(hs.masterSecret, clientApplicationTrafficLabel, hs.transcript) serverSecret := hs.suite.deriveSecret(hs.masterSecret, @@ -544,33 +846,90 @@ func (hs *clientHandshakeStateTLS13) readServerFinished() error { return nil } +func certificateRequestInfo(certReq *certificateRequestMsgTLS13, vers uint16) *CertificateRequestInfo { + cri := &CertificateRequestInfo{ + SupportsDelegatedCredential: certReq.supportDelegatedCredential, + SignatureSchemes: certReq.supportedSignatureAlgorithms, + SignatureSchemesDC: certReq.supportedSignatureAlgorithmsDC, + AcceptableCAs: certReq.certificateAuthorities, + Version: vers, + } + + return cri +} + +// getClientDelegatedCredential will return a Delegated Credential pair (a +// Delegated Credential and its private key) for the given CertificateRequestInfo, +// defaulting to the first element of cert.DelegatedCredentialPair. +// The returned Delegated Credential could be invalid for usage in the handshake. +// Returns an error if there are no delegated credentials or if the one found +// cannot be used for the current connection. +func getClientDelegatedCredential(cri *CertificateRequestInfo, cert *Certificate) (*DelegatedCredentialPair, error) { + if len(cert.DelegatedCredentials) == 0 { + return nil, errors.New("No Delegated Credential found.") + } + + if len(cert.DelegatedCredentials) == 1 { + // There's only one choice, so no point doing any work. + return &cert.DelegatedCredentials[0], nil + } + + for _, dcPair := range cert.DelegatedCredentials { + // If the client sent the signature_algorithms in the DC extension, ensure it supports + // schemes we can use with this delegated credential. + if len(cri.SignatureSchemesDC) > 0 { + if _, err := selectSignatureSchemeDC(VersionTLS13, dcPair.DC, cri.SignatureSchemesDC); err == nil { + return &dcPair, nil + } + } + } + + // No delegated credential can be returned. + return nil, errors.New("No valid Delegated Credential found.") +} + func (hs *clientHandshakeStateTLS13) sendClientCertificate() error { c := hs.c - if hs.certReq == nil { + if hs.certReq == nil || hs.isKEMTLS == true { return nil } - cert, err := c.getClientCertificate(&CertificateRequestInfo{ - AcceptableCAs: hs.certReq.certificateAuthorities, - SignatureSchemes: hs.certReq.supportedSignatureAlgorithms, - Version: c.vers, - }) + cri := certificateRequestInfo(hs.certReq, c.vers) + + cert, err := c.getClientCertificate(cri) if err != nil { return err } + var dcPair *DelegatedCredentialPair + if hs.certReq.supportDelegatedCredential && len(hs.certReq.supportedSignatureAlgorithmsDC) > 0 { + if delegatedCredentialPair, err := getClientDelegatedCredential(cri, cert); err == nil { + if delegatedCredentialPair.DC != nil && delegatedCredentialPair.PrivateKey != nil { + var err error + // Even if the Delegated Credential has already been marshalled, be sure it is the correct one. + if delegatedCredentialPair.DC.raw, err = delegatedCredentialPair.DC.marshal(); err == nil { + dcPair = delegatedCredentialPair + cert.DelegatedCredential = dcPair.DC.raw + } + } + } + } + certMsg := new(certificateMsgTLS13) certMsg.certificate = *cert certMsg.scts = hs.certReq.scts && len(cert.SignedCertificateTimestamps) > 0 certMsg.ocspStapling = hs.certReq.ocspStapling && len(cert.OCSPStaple) > 0 + certMsg.delegatedCredential = hs.certReq.supportDelegatedCredential && len(cert.DelegatedCredential) > 0 hs.transcript.Write(certMsg.marshal()) if _, err := c.writeRecord(recordTypeHandshake, certMsg.marshal()); err != nil { return err } + hs.handshakeTimings.WriteCertificate = hs.handshakeTimings.elapsedTime() + // If we sent an empty certificate message, skip the CertificateVerify. if len(cert.Certificate) == 0 { return nil @@ -579,14 +938,31 @@ func (hs *clientHandshakeStateTLS13) sendClientCertificate() error { certVerifyMsg := new(certificateVerifyMsg) certVerifyMsg.hasSignatureAlgorithm = true - certVerifyMsg.signatureAlgorithm, err = selectSignatureScheme(c.vers, cert, hs.certReq.supportedSignatureAlgorithms) + var sigAlgorithm SignatureScheme + suppSigAlgo := hs.certReq.supportedSignatureAlgorithms + sigAlgorithm, err = selectSignatureScheme(c.vers, cert, suppSigAlgo) if err != nil { + // getClientCertificate returned a certificate incompatible with the // CertificateRequestInfo supported signature algorithms. c.sendAlert(alertHandshakeFailure) return err } + if certMsg.delegatedCredential { + suppSigAlgo = hs.certReq.supportedSignatureAlgorithmsDC + sigAlgorithm, err = selectSignatureSchemeDC(c.vers, dcPair.DC, suppSigAlgo) + if err != nil { + // getDelegatedCredential returned a delegated credential incompatible with the + // CertificateRequestInfo supported signature algorithms. + cert.DelegatedCredential = nil + } else { + cert.DelegatedCredentialPrivateKey = dcPair.PrivateKey + } + } + + certVerifyMsg.signatureAlgorithm = sigAlgorithm + sigType, sigHash, err := typeAndHashFromSignatureScheme(certVerifyMsg.signatureAlgorithm) if err != nil { return c.sendAlert(alertInternalError) @@ -597,11 +973,24 @@ func (hs *clientHandshakeStateTLS13) sendClientCertificate() error { if sigType == signatureRSAPSS { signOpts = &rsa.PSSOptions{SaltLength: rsa.PSSSaltLengthEqualsHash, Hash: sigHash} } - sig, err := cert.PrivateKey.(crypto.Signer).Sign(c.config.rand(), signed, signOpts) - if err != nil { - c.sendAlert(alertInternalError) - return errors.New("tls: failed to sign handshake: " + err.Error()) + + var sig []byte + if len(cert.DelegatedCredential) > 0 { + var err error + sig, err = cert.DelegatedCredentialPrivateKey.(crypto.Signer).Sign(c.config.rand(), signed, signOpts) + if err != nil { + c.sendAlert(alertInternalError) + return errors.New("tls: failed to sign handshake: " + err.Error()) + } + } else { + var err error + sig, err = cert.PrivateKey.(crypto.Signer).Sign(c.config.rand(), signed, signOpts) + if err != nil { + c.sendAlert(alertInternalError) + return errors.New("tls: failed to sign handshake: " + err.Error()) + } } + certVerifyMsg.signature = sig hs.transcript.Write(certVerifyMsg.marshal()) @@ -609,12 +998,21 @@ func (hs *clientHandshakeStateTLS13) sendClientCertificate() error { return err } + c.didClientAuthentication = true + hs.handshakeTimings.WriteCertificateVerify = hs.handshakeTimings.elapsedTime() + + c.certificateReqMessage = hs.certReq.marshal() + return nil } func (hs *clientHandshakeStateTLS13) sendClientFinished() error { c := hs.c + if hs.isKEMTLS == true { + return nil + } + finished := &finishedMsg{ verifyData: hs.suite.finishedHash(c.out.trafficSecret, hs.transcript), } @@ -624,9 +1022,11 @@ func (hs *clientHandshakeStateTLS13) sendClientFinished() error { return err } + hs.handshakeTimings.WriteClientFinished = hs.handshakeTimings.elapsedTime() + c.out.setTrafficSecret(hs.suite, hs.trafficSecret) - if !c.config.SessionTicketsDisabled && c.config.ClientSessionCache != nil { + if !c.config.SessionTicketsDisabled && c.config.ClientSessionCache != nil && !c.config.ECHEnabled { c.resumptionSecret = hs.suite.deriveSecret(hs.masterSecret, resumptionLabel, hs.transcript) } @@ -640,7 +1040,7 @@ func (c *Conn) handleNewSessionTicket(msg *newSessionTicketMsgTLS13) error { return errors.New("tls: received new session ticket from a client") } - if c.config.SessionTicketsDisabled || c.config.ClientSessionCache == nil { + if c.config.SessionTicketsDisabled || c.config.ClientSessionCache == nil || c.config.ECHEnabled { return nil } @@ -683,3 +1083,13 @@ func (c *Conn) handleNewSessionTicket(msg *newSessionTicketMsgTLS13) error { return nil } + +func (hs *clientHandshakeStateTLS13) abortIfRequired() error { + c := hs.c + if c.ech.offered && !c.ech.accepted { + // If ECH was rejected, then abort the handshake. + c.sendAlert(alertECHRequired) + return errors.New("tls: ech: rejected") + } + return nil +} diff --git a/src/crypto/tls/handshake_messages.go b/src/crypto/tls/handshake_messages.go index b5f81e44366..f98c89de9fb 100644 --- a/src/crypto/tls/handshake_messages.go +++ b/src/crypto/tls/handshake_messages.go @@ -81,8 +81,16 @@ type clientHelloMsg struct { sessionTicket []uint8 supportedSignatureAlgorithms []SignatureScheme supportedSignatureAlgorithmsCert []SignatureScheme + supportedSignatureAlgorithmsDC []SignatureScheme secureRenegotiationSupported bool secureRenegotiation []byte + delegatedCredentialSupported bool + cachedInformationCert bool + cachedInformationCertHash []byte + cachedInformationCertReq bool + cachedInformationCertReqHash []byte + pdkKEMTLS bool + ciphertextKEMTLS []byte alpnProtocols []string scts bool supportedVersions []uint16 @@ -92,6 +100,9 @@ type clientHelloMsg struct { pskModes []uint8 pskIdentities []pskIdentity pskBinders [][]byte + ech []byte + echIsInner bool + echIsOuter bool } func (m *clientHelloMsg) marshal() []byte { @@ -121,6 +132,18 @@ func (m *clientHelloMsg) marshal() []byte { bWithoutExtensions := *b b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + if m.echIsOuter { + // draft-ietf-tls-esni-10, "encrypted_client_hello" + b.AddUint16(extensionECH) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(m.ech) + }) + } + if m.echIsInner { + // draft-ietf-tls-esni-10, "ech_is_inner" + b.AddUint16(extensionECHIsInner) + b.AddUint16(0) + } if len(m.serverName) > 0 { // RFC 6066, Section 3 b.AddUint16(extensionServerName) @@ -200,6 +223,39 @@ func (m *clientHelloMsg) marshal() []byte { }) }) } + if m.delegatedCredentialSupported { + if len(m.supportedSignatureAlgorithmsDC) > 0 { + // Draft: https://tools.ietf.org/html/draft-ietf-tls-subcerts-10 + b.AddUint16(extensionDelegatedCredentials) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + for _, sigAlgo := range m.supportedSignatureAlgorithmsDC { + b.AddUint16(uint16(sigAlgo)) + } + }) + }) + } + } + if m.cachedInformationCert { + // RFC: https://tools.ietf.org/html/rfc6066 + b.AddUint16(extensionCachedInfo) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddUint8(1) // CachedInformationType: cert + addBytesWithLength(b, m.cachedInformationCertHash, 32) + if m.cachedInformationCertReq { + b.AddUint8(2) // CachedInformationType: cert_req + addBytesWithLength(b, m.cachedInformationCertReqHash, 32) + } + }) + } + if m.pdkKEMTLS { + b.AddUint16(extensionPDKKEMTLS) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(m.ciphertextKEMTLS) + }) + }) + } if len(m.alpnProtocols) > 0 { // RFC 7301, Section 3.1 b.AddUint16(extensionALPN) @@ -394,6 +450,18 @@ func (m *clientHelloMsg) unmarshal(data []byte) bool { } switch extension { + case extensionECH: + // draft-ietf-tls-esni-10, "encrypted_client_hello" + if !extData.ReadBytes(&m.ech, len(extData)) { + return false + } + m.echIsOuter = true + case extensionECHIsInner: + // draft-ietf-tls-esni-10, "ech_is_inner" + if !extData.ReadBytes(&m.ech, len(extData)) { + return false + } + m.echIsInner = true case extensionServerName: // RFC 6066, Section 3 var nameList cryptobyte.String @@ -523,6 +591,47 @@ func (m *clientHelloMsg) unmarshal(data []byte) bool { len(m.cookie) == 0 { return false } + case extensionDelegatedCredentials: + var sigAndAlgs cryptobyte.String + if !extData.ReadUint16LengthPrefixed(&sigAndAlgs) || sigAndAlgs.Empty() { + return false + } + for !sigAndAlgs.Empty() { + var sigAndAlg uint16 + if !sigAndAlgs.ReadUint16(&sigAndAlg) { + return false + } + m.supportedSignatureAlgorithmsDC = append( + m.supportedSignatureAlgorithmsDC, SignatureScheme(sigAndAlg)) + } + m.delegatedCredentialSupported = true + case extensionCachedInfo: + // RFC 7924, Section 4 + var cachedType uint8 + if extData.ReadUint8(&cachedType) { + if extData.ReadBytes(&m.cachedInformationCertHash, 32) { + m.cachedInformationCert = true + } + } else { + return false + } + + if !extData.Empty() { + if extData.ReadUint8(&cachedType) { + if extData.ReadBytes(&m.cachedInformationCertReqHash, 32) { + m.cachedInformationCertReq = true + } + } else { + return false + } + } + case extensionPDKKEMTLS: + // RFC 8446, Section 4.2.2 + if !readUint16LengthPrefixed(&extData, &m.ciphertextKEMTLS) || + len(m.ciphertextKEMTLS) == 0 { + return false + } + m.pdkKEMTLS = true case extensionKeyShare: // RFC 8446, Section 4.2.8 var clientShares cryptobyte.String @@ -607,6 +716,9 @@ type serverHelloMsg struct { selectedIdentityPresent bool selectedIdentity uint16 supportedPoints []uint8 + cachedInformationCert bool + cachedInformationCertReq bool + pdkKEMTLS bool // HelloRetryRequest extensions cookie []byte @@ -716,6 +828,20 @@ func (m *serverHelloMsg) marshal() []byte { }) }) } + if m.cachedInformationCert { + // RFC: https://tools.ietf.org/html/rfc6066 + b.AddUint16(extensionCachedInfo) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddUint8(1) // CachedInformationType: cert + if m.cachedInformationCertReq { + b.AddUint8(2) // CachedInformationType: cert_req + } + }) + } + if m.pdkKEMTLS { + b.AddUint16(extensionPDKKEMTLS) + b.AddUint16(0) // empty extension_data + } extensionsPresent = len(b.BytesOrPanic()) > 2 }) @@ -826,6 +952,24 @@ func (m *serverHelloMsg) unmarshal(data []byte) bool { len(m.supportedPoints) == 0 { return false } + case extensionCachedInfo: + // RFC 7924, Section 4 + var cachedType uint8 + if extData.ReadUint8(&cachedType) { + m.cachedInformationCert = true + } else { + return false + } + + if !extData.Empty() { + if extData.ReadUint8(&cachedType) { + m.cachedInformationCertReq = true + } else { + return false + } + } + case extensionPDKKEMTLS: + m.pdkKEMTLS = true default: // Ignore unknown extensions. continue @@ -842,6 +986,7 @@ func (m *serverHelloMsg) unmarshal(data []byte) bool { type encryptedExtensionsMsg struct { raw []byte alpnProtocol string + ech []byte } func (m *encryptedExtensionsMsg) marshal() []byte { @@ -863,6 +1008,15 @@ func (m *encryptedExtensionsMsg) marshal() []byte { }) }) } + if len(m.ech) > 0 { + // draft-ietf-tls-esni-10, "encrypted_client_hello" + b.AddUint16(extensionECH) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + // If the client-facing server rejects ECH, then it may + // sends retry configurations here. + b.AddBytes(m.ech) + }) + } }) }) @@ -900,6 +1054,11 @@ func (m *encryptedExtensionsMsg) unmarshal(data []byte) bool { return false } m.alpnProtocol = string(proto) + case extensionECH: + // draft-ietf-tls-esni-10 + if !extData.ReadBytes(&m.ech, len(extData)) { + return false + } default: // Ignore unknown extensions. continue @@ -1054,7 +1213,9 @@ type certificateRequestMsgTLS13 struct { raw []byte ocspStapling bool scts bool + supportDelegatedCredential bool supportedSignatureAlgorithms []SignatureScheme + supportedSignatureAlgorithmsDC []SignatureScheme supportedSignatureAlgorithmsCert []SignatureScheme certificateAuthorities [][]byte } @@ -1085,6 +1246,19 @@ func (m *certificateRequestMsgTLS13) marshal() []byte { b.AddUint16(extensionSCT) b.AddUint16(0) // empty extension_data } + if m.supportDelegatedCredential { + if len(m.supportedSignatureAlgorithmsDC) > 0 { + // Draft: https://tools.ietf.org/html/draft-ietf-tls-subcerts-10 + b.AddUint16(extensionDelegatedCredentials) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + for _, sigAlgo := range m.supportedSignatureAlgorithmsDC { + b.AddUint16(uint16(sigAlgo)) + } + }) + }) + } + } if len(m.supportedSignatureAlgorithms) > 0 { b.AddUint16(extensionSignatureAlgorithms) b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { @@ -1149,6 +1323,20 @@ func (m *certificateRequestMsgTLS13) unmarshal(data []byte) bool { m.ocspStapling = true case extensionSCT: m.scts = true + case extensionDelegatedCredentials: + var sigAndAlgs cryptobyte.String + if !extData.ReadUint16LengthPrefixed(&sigAndAlgs) || sigAndAlgs.Empty() { + return false + } + for !sigAndAlgs.Empty() { + var sigAndAlg uint16 + if !sigAndAlgs.ReadUint16(&sigAndAlg) { + return false + } + m.supportedSignatureAlgorithmsDC = append( + m.supportedSignatureAlgorithmsDC, SignatureScheme(sigAndAlg)) + } + m.supportDelegatedCredential = true case extensionSignatureAlgorithms: var sigAndAlgs cryptobyte.String if !extData.ReadUint16LengthPrefixed(&sigAndAlgs) || sigAndAlgs.Empty() { @@ -1278,10 +1466,11 @@ func (m *certificateMsg) unmarshal(data []byte) bool { } type certificateMsgTLS13 struct { - raw []byte - certificate Certificate - ocspStapling bool - scts bool + raw []byte + certificate Certificate + ocspStapling bool + scts bool + delegatedCredential bool } func (m *certificateMsgTLS13) marshal() []byte { @@ -1301,10 +1490,14 @@ func (m *certificateMsgTLS13) marshal() []byte { if !m.scts { certificate.SignedCertificateTimestamps = nil } + if !m.delegatedCredential { + certificate.DelegatedCredential = nil + } marshalCertificate(b, certificate) }) m.raw = b.BytesOrPanic() + return m.raw } @@ -1316,7 +1509,8 @@ func marshalCertificate(b *cryptobyte.Builder, certificate Certificate) { }) b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { if i > 0 { - // This library only supports OCSP and SCT for leaf certificates. + // This library only supports OCSP, SCT and Delegated Credentials for leaf certificates. + // Delegated Credentials are only supported on the leaf/end-entity certificate. return } if certificate.OCSPStaple != nil { @@ -1340,6 +1534,12 @@ func marshalCertificate(b *cryptobyte.Builder, certificate Certificate) { }) }) } + if certificate.DelegatedCredential != nil { + b.AddUint16(extensionDelegatedCredentials) + b.AddUint16LengthPrefixed(func(b *cryptobyte.Builder) { + b.AddBytes(certificate.DelegatedCredential) + }) + } }) } }) @@ -1359,6 +1559,7 @@ func (m *certificateMsgTLS13) unmarshal(data []byte) bool { m.scts = m.certificate.SignedCertificateTimestamps != nil m.ocspStapling = m.certificate.OCSPStaple != nil + m.delegatedCredential = m.certificate.DelegatedCredential != nil return true } @@ -1410,6 +1611,13 @@ func unmarshalCertificate(s *cryptobyte.String, certificate *Certificate) bool { certificate.SignedCertificateTimestamps = append( certificate.SignedCertificateTimestamps, sct) } + case extensionDelegatedCredentials: + if !extData.ReadBytes(&certificate.DelegatedCredential, len(extData)) { + return false + } + if len(certificate.DelegatedCredential) == 0 { + return false + } default: // Ignore unknown extensions. continue diff --git a/src/crypto/tls/handshake_messages_test.go b/src/crypto/tls/handshake_messages_test.go index bb8aea86700..de813efbefd 100644 --- a/src/crypto/tls/handshake_messages_test.go +++ b/src/crypto/tls/handshake_messages_test.go @@ -152,6 +152,10 @@ func (*clientHelloMsg) Generate(rand *rand.Rand, size int) reflect.Value { if rand.Intn(10) > 5 { m.supportedSignatureAlgorithmsCert = supportedSignatureAlgorithms } + if rand.Intn(10) > 5 { + m.delegatedCredentialSupported = true + m.supportedSignatureAlgorithmsDC = supportedSignatureAlgorithmsDC + } for i := 0; i < rand.Intn(5); i++ { m.alpnProtocols = append(m.alpnProtocols, randomString(rand.Intn(20)+1, rand)) } @@ -368,6 +372,10 @@ func (*certificateRequestMsgTLS13) Generate(rand *rand.Rand, size int) reflect.V if rand.Intn(10) > 5 { m.scts = true } + if rand.Intn(10) > 5 { + m.supportDelegatedCredential = true + m.supportedSignatureAlgorithmsDC = supportedSignatureAlgorithmsDC + } if rand.Intn(10) > 5 { m.supportedSignatureAlgorithms = supportedSignatureAlgorithms } @@ -393,6 +401,10 @@ func (*certificateMsgTLS13) Generate(rand *rand.Rand, size int) reflect.Value { m.ocspStapling = true m.certificate.OCSPStaple = randomBytes(rand.Intn(100)+1, rand) } + if rand.Intn(10) > 5 { + m.delegatedCredential = true + m.certificate.DelegatedCredential = randomBytes(rand.Intn(100)+1, rand) + } if rand.Intn(10) > 5 { m.scts = true for i := 0; i < rand.Intn(2)+1; i++ { diff --git a/src/crypto/tls/handshake_server.go b/src/crypto/tls/handshake_server.go index 9c3e0f636ea..3baa378ba68 100644 --- a/src/crypto/tls/handshake_server.go +++ b/src/crypto/tls/handshake_server.go @@ -5,9 +5,12 @@ package tls import ( + circlSign "circl/sign" + "crypto" "crypto/ecdsa" "crypto/ed25519" + "crypto/kem" "crypto/rsa" "crypto/subtle" "crypto/x509" @@ -45,8 +48,9 @@ func (c *Conn) serverHandshake() error { if c.vers == VersionTLS13 { hs := serverHandshakeStateTLS13{ - c: c, - clientHello: clientHello, + c: c, + clientHello: clientHello, + handshakeTimings: createTLS13ServerHandshakeTimingInfo(c.config.Time), } return hs.handshake() } @@ -135,6 +139,15 @@ func (c *Conn) readClientHello() (*clientHelloMsg, error) { return nil, unexpectedMessageError(clientHello, msg) } + // NOTE(cjpatton): ECH usage is resolved before calling GetConfigForClient() + // or GetCertifciate(). Hence, it is not currently possible to reject ECH if + // we don't recognize the inner SNI. This may or may not be desirable in the + // future. + clientHello, err = c.echAcceptOrReject(clientHello) + if err != nil { + return nil, fmt.Errorf("tls: %s", err) // Alert sent. + } + var configForClient *Config originalConfig := c.config if c.config.GetConfigForClient != nil { @@ -364,7 +377,7 @@ func (hs *serverHandshakeState) cipherSuiteOk(c *cipherSuite) bool { func (hs *serverHandshakeState) checkForResumption() bool { c := hs.c - if c.config.SessionTicketsDisabled { + if c.config.SessionTicketsDisabled || c.config.ECHEnabled { return false } @@ -461,7 +474,7 @@ func (hs *serverHandshakeState) doFullHandshake() error { hs.hello.ocspStapling = true } - hs.hello.ticketSupported = hs.clientHello.ticketSupported && !c.config.SessionTicketsDisabled + hs.hello.ticketSupported = hs.clientHello.ticketSupported && !c.config.SessionTicketsDisabled && !c.config.ECHEnabled hs.hello.cipherSuite = hs.suite.id hs.finishedHash = newFinishedHash(hs.c.vers, hs.suite) @@ -811,7 +824,7 @@ func (c *Conn) processCertsFromClient(certificate Certificate) error { if len(certs) > 0 { switch certs[0].PublicKey.(type) { - case *ecdsa.PublicKey, *rsa.PublicKey, ed25519.PublicKey: + case *ecdsa.PublicKey, *rsa.PublicKey, ed25519.PublicKey, circlSign.PublicKey, *kem.PublicKey: default: c.sendAlert(alertUnsupportedCertificate) return fmt.Errorf("tls: client certificate contains an unsupported public key of type %T", certs[0].PublicKey) @@ -835,14 +848,18 @@ func clientHelloInfo(c *Conn, clientHello *clientHelloMsg) *ClientHelloInfo { } return &ClientHelloInfo{ - CipherSuites: clientHello.cipherSuites, - ServerName: clientHello.serverName, - SupportedCurves: clientHello.supportedCurves, - SupportedPoints: clientHello.supportedPoints, - SignatureSchemes: clientHello.supportedSignatureAlgorithms, - SupportedProtos: clientHello.alpnProtocols, - SupportedVersions: supportedVersions, - Conn: c.conn, - config: c.config, + CipherSuites: clientHello.cipherSuites, + ServerName: clientHello.serverName, + SupportedCurves: clientHello.supportedCurves, + SupportedPoints: clientHello.supportedPoints, + SignatureSchemes: clientHello.supportedSignatureAlgorithms, + SupportedProtos: clientHello.alpnProtocols, + SupportedVersions: supportedVersions, + SupportsDelegatedCredential: clientHello.delegatedCredentialSupported, + SignatureSchemesDC: clientHello.supportedSignatureAlgorithmsDC, + CachedInformationCert: clientHello.cachedInformationCert, + CachedInformationCertReq: clientHello.cachedInformationCertReq, + Conn: c.conn, + config: c.config, } } diff --git a/src/crypto/tls/handshake_server_kemtls.go b/src/crypto/tls/handshake_server_kemtls.go new file mode 100644 index 00000000000..20bd50f00ba --- /dev/null +++ b/src/crypto/tls/handshake_server_kemtls.go @@ -0,0 +1,336 @@ +package tls + +import ( + "crypto/hmac" + "crypto/kem" + "errors" + "sync/atomic" +) + +func (hs *serverHandshakeStateTLS13) handshakeKEMTLS() error { + c := hs.c + + if hs.pdkKEMTLS { + if err := hs.writeKEMTLSServerFinished(); err != nil { + return err + } + if _, err := c.flush(); err != nil { + return err + } + hs.handshakeTimings.reset() + if err := hs.readKEMTLSClientFinished(); err != nil { + return err + } + } else { + if err := hs.readClientKEMCiphertext(); err != nil { + return err + } + if err := hs.readClientKEMCertificate(); err != nil { + return err + } + if err := hs.sendServerKEMCiphertext(); err != nil { + return err + } + if hs.requestClientKEMCert() { + if _, err := c.flush(); err != nil { + return err + } + // thrid round of sending for mKEMTLS + hs.handshakeTimings.reset() + } + if err := hs.readKEMTLSClientFinished(); err != nil { + return err + } + + if err := hs.writeKEMTLSServerFinished(); err != nil { + return err + } + } + + // hs.handshakeTimings.ExperimentName = experimentName(c) + hs.handshakeTimings.finish() + c.handleCFEvent(hs.handshakeTimings) + atomic.StoreUint32(&c.handshakeStatus, 1) + + return nil +} + +func (hs *serverHandshakeStateTLS13) readClientKEMCiphertext() error { + c := hs.c + + var ahs []byte + + if !(hs.pdkKEMTLS && hs.keyKEMShare) { + var sk *kem.PrivateKey + var ok, ok1 bool + sk, ok = hs.cert.PrivateKey.(*kem.PrivateKey) + if !ok { + sk, ok1 = hs.cert.DelegatedCredentialPrivateKey.(*kem.PrivateKey) + if !ok1 { + c.sendAlert(alertInternalError) + return errors.New("crypto/tls: private key unexpectedly of wrong type") + } + } + + msg, err := c.readHandshake() + if err != nil { + return err + } + + kexMsg, ok := msg.(*clientKeyExchangeMsg) + if !ok { + c.sendAlert(alertUnexpectedMessage) + return unexpectedMessageError(kexMsg, msg) + } + + hs.transcript.Write(kexMsg.marshal()) + hs.handshakeTimings.ReadKEMCiphertext = hs.handshakeTimings.elapsedTime() + + ss, err := kem.Decapsulate(sk, kexMsg.ciphertext) + if err != nil { + return err + } + + // derive AHS + // AHS <- HKDF.Extract(dHS, ss_s) + ahs = hs.suite.extract(ss, hs.suite.deriveSecret(hs.handshakeSecret, "derived", nil)) + } else { + ahs = hs.suite.extract(hs.ssKEMTLS, hs.suite.deriveSecret(hs.handshakeSecret, "derived", nil)) + } + + // CAHTS <- HKDF.Expand(AHS, "c ahs traffic", CH..CKC) + clientSecret := hs.suite.deriveSecret(ahs, + clientAuthenticatedHandshakeTrafficLabel, hs.transcript) + c.in.setTrafficSecret(hs.suite, clientSecret) + // SAHTS <- HKDF.Expand(AHS, "s ahs traffic", CH..CKC) + serverSecret := hs.suite.deriveSecret(ahs, + serverAuthenticatedHandshakeTrafficLabel, hs.transcript) + c.out.setTrafficSecret(hs.suite, serverSecret) + + // dAHS <- HKDF.Expand(AHS, "derived", nil) + hs.handshakeSecret = hs.suite.deriveSecret(ahs, "derived", nil) + + err := c.config.writeKeyLog(keyLogLabelClientKEMAuthenticatedHandshake, hs.clientHello.random, clientSecret) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + + err = c.config.writeKeyLog(keyLogLabelServerKEMAuthenticatedHandshake, hs.clientHello.random, serverSecret) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + + return nil +} + +func (hs *serverHandshakeStateTLS13) requestClientKEMCert() bool { + return hs.c.config.ClientAuth >= RequestClientCert && !hs.usingPSK +} + +func (hs *serverHandshakeStateTLS13) readClientKEMCertificate() error { + c := hs.c + + if !hs.requestClientKEMCert() { + // Make sure the connection is still being verified whether or not + // the server requested a client certificate. + if c.config.VerifyConnection != nil { + if err := c.config.VerifyConnection(c.connectionStateLocked()); err != nil { + c.sendAlert(alertBadCertificate) + return err + } + } + return nil + } + + // If we requested a client kem certificate, then the client must send a + // kem certificate message. + msg, err := c.readHandshake() + if err != nil { + return err + } + + certMsg, ok := msg.(*certificateMsgTLS13) + if !ok { + c.sendAlert(alertUnexpectedMessage) + return unexpectedMessageError(certMsg, msg) + } + hs.transcript.Write(certMsg.marshal()) + + hs.handshakeTimings.ReadCertificate = hs.handshakeTimings.elapsedTime() + + if err := c.processCertsFromClient(certMsg.certificate); err != nil { + return err + } + + if c.config.VerifyConnection != nil { + if err := c.config.VerifyConnection(c.connectionStateLocked()); err != nil { + c.sendAlert(alertBadCertificate) + return err + } + } + + if len(certMsg.certificate.Certificate) != 0 { + if certMsg.delegatedCredential { + if err := hs.processDelegatedCredentialFromClient(certMsg.certificate.DelegatedCredential, nil); err != nil { + return err + } + } + + pk := c.peerCertificates[0].PublicKey + if c.verifiedDC != nil { + pk = c.verifiedDC.cred.publicKey + } + + _, ok = pk.(*kem.PublicKey) + if !ok { + // it has to be a KEM key + c.sendAlert(alertInternalError) + return nil + } + } + + return nil +} + +func (hs *serverHandshakeStateTLS13) sendServerKEMCiphertext() error { + c := hs.c + + if !hs.requestClientKEMCert() { + return nil + } + + if len(c.peerCertificates) == 0 { + return nil + } + + var pk *kem.PublicKey + var ok bool + + if c.verifiedDC != nil && c.verifiedDC.cred.expCertVerfAlgo.isKEMTLS() { + pk, ok = c.verifiedDC.cred.publicKey.(*kem.PublicKey) + if !ok { + c.sendAlert(alertInternalError) + return errors.New("tls: invalid key") + } + } else { + pk, ok = c.peerCertificates[0].PublicKey.(*kem.PublicKey) + if !ok { + c.sendAlert(alertInternalError) + return errors.New("tls: invalid key") + } + } + + ss, ct, err := kem.Encapsulate(hs.c.config.rand(), pk) + if err != nil { + return err + } + + msg := serverKeyExchangeMsg{ + raw: nil, + key: ct, + } + + _, err = c.writeRecord(recordTypeHandshake, msg.marshal()) + if err != nil { + return err + } + _, err = hs.transcript.Write(msg.marshal()) + if err != nil { + return err + } + hs.handshakeTimings.WriteKEMCiphertext = hs.handshakeTimings.elapsedTime() + + // MS <- HKDF.Extract(dAHS, ssC) + hs.masterSecret = hs.suite.extract(ss, hs.handshakeSecret) + hs.isClientAuthKEMTLS = true + c.didClientAuthentication = true + + return nil +} + +func (hs *serverHandshakeStateTLS13) readKEMTLSClientFinished() error { + c := hs.c + + msg, err := c.readHandshake() + if err != nil { + return err + } + + finished, ok := msg.(*finishedMsg) + if !ok { + c.sendAlert(alertUnexpectedMessage) + return unexpectedMessageError(finished, msg) + } + + hs.handshakeTimings.ReadClientFinished = hs.handshakeTimings.elapsedTime() + + if !hs.isClientAuthKEMTLS { + // compute MS + // MS <- HKDF.Extract(dAHS, 0) + hs.masterSecret = hs.suite.extract(nil, hs.handshakeSecret) + } + + // fk_s <- HKDF.Expand(MS, "s finished", nil) + expectedMAC := hs.suite.finishedHashKEMTLS(hs.masterSecret, "c", hs.transcript) + if !hmac.Equal(expectedMAC, finished.verifyData) { + c.sendAlert(alertDecryptError) + return errors.New("tls: invalid server finished hash") + } + + if _, err := hs.transcript.Write(finished.marshal()); err != nil { + return err + } + + // CATS <- HKDF.Expand(MS, "c ap traffic", CH..CF) + clientSecret := hs.suite.deriveSecret(hs.masterSecret, clientApplicationTrafficLabel, hs.transcript) + c.in.setTrafficSecret(hs.suite, clientSecret) + + err = c.config.writeKeyLog(keyLogLabelClientTraffic, hs.clientHello.random, clientSecret) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + + return nil +} + +func (hs *serverHandshakeStateTLS13) writeKEMTLSServerFinished() error { + c := hs.c + + finished := &finishedMsg{ + verifyData: hs.suite.finishedHashKEMTLS(hs.masterSecret, "s", hs.transcript), + } + + if _, err := hs.transcript.Write(finished.marshal()); err != nil { + return err + } + if _, err := c.writeRecord(recordTypeHandshake, finished.marshal()); err != nil { + return err + } + + hs.handshakeTimings.WriteServerFinished = hs.handshakeTimings.elapsedTime() + + // SATS <- HKDF.Expand(MS, "s ap traffic", CH..SF) + hs.trafficSecret = hs.suite.deriveSecret(hs.masterSecret, + serverApplicationTrafficLabel, hs.transcript) + + c.out.setTrafficSecret(hs.suite, hs.trafficSecret) + + err := c.config.writeKeyLog(keyLogLabelServerTraffic, hs.clientHello.random, hs.trafficSecret) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + + if !c.config.SessionTicketsDisabled && c.config.ClientSessionCache != nil { + c.resumptionSecret = hs.suite.deriveSecret(hs.masterSecret, + resumptionLabel, hs.transcript) + } + + c.ekm = hs.suite.exportKeyingMaterial(hs.masterSecret, hs.transcript) + c.didKEMTLS = true + + return nil +} diff --git a/src/crypto/tls/handshake_server_tls13.go b/src/crypto/tls/handshake_server_tls13.go index c2c288aed43..1957f815242 100644 --- a/src/crypto/tls/handshake_server_tls13.go +++ b/src/crypto/tls/handshake_server_tls13.go @@ -8,8 +8,10 @@ import ( "bytes" "crypto" "crypto/hmac" + "crypto/kem" "crypto/rsa" "errors" + "fmt" "hash" "io" "sync/atomic" @@ -22,11 +24,18 @@ import ( const maxClientPSKIdentities = 5 type serverHandshakeStateTLS13 struct { - c *Conn - clientHello *clientHelloMsg - hello *serverHelloMsg - sentDummyCCS bool - usingPSK bool + c *Conn + clientHello *clientHelloMsg + hello *serverHelloMsg + sentDummyCCS bool + usingPSK bool + + keyKEMShare bool + isKEMTLS bool + pdkKEMTLS bool + ssKEMTLS []byte + isClientAuthKEMTLS bool + suite *cipherSuiteTLS13 cert *Certificate sigAlg SignatureScheme @@ -37,6 +46,48 @@ type serverHandshakeStateTLS13 struct { trafficSecret []byte // client_application_traffic_secret_0 transcript hash.Hash clientFinished []byte + certReq *certificateRequestMsgTLS13 + + handshakeTimings CFEventTLS13ServerHandshakeTimingInfo +} + +// processDelegatedCredentialFromClient unmarshals the DelegatedCredential +// offered by the client (if present) and validates it using the peer's +// certificate. +func (hs *serverHandshakeStateTLS13) processDelegatedCredentialFromClient(rawDC []byte, certVerifyMsg *certificateVerifyMsg) error { + c := hs.c + + var dc *DelegatedCredential + var err error + if rawDC != nil { + // Assert that the DC extension was indicated by the client. + if !hs.certReq.supportDelegatedCredential { + c.sendAlert(alertUnexpectedMessage) + return errors.New("tls: got Delegated Credential extension without indication") + } + + dc, err = unmarshalDelegatedCredential(rawDC) + if err != nil { + c.sendAlert(alertDecodeError) + return fmt.Errorf("tls: Delegated Credential: %s", err) + } + + if !isSupportedSignatureAlgorithm(dc.cred.expCertVerfAlgo, supportedSignatureAlgorithmsDC) { + c.sendAlert(alertIllegalParameter) + return errors.New("tls: Delegated Credential used with invalid signature algorithm") + } + } + + if dc != nil { + if !dc.Validate(c.peerCertificates[0], true, c.config.time(), certVerifyMsg) { + c.sendAlert(alertIllegalParameter) + return errors.New("tls: invalid Delegated Credential") + } + } + + c.verifiedDC = dc + + return nil } func (hs *serverHandshakeStateTLS13) handshake() error { @@ -59,15 +110,33 @@ func (hs *serverHandshakeStateTLS13) handshake() error { if err := hs.sendServerCertificate(); err != nil { return err } + if hs.isKEMTLS { + // send application data for KEMTLS + if !hs.pdkKEMTLS { + if _, err := c.flush(); err != nil { + return err + } + // second round of sending for KEMTLS + hs.handshakeTimings.reset() + } + + return hs.handshakeKEMTLS() + } if err := hs.sendServerFinished(); err != nil { return err } - // Note that at this point we could start sending application data without - // waiting for the client's second flight, but the application might not - // expect the lack of replay protection of the ClientHello parameters. - if _, err := c.flush(); err != nil { - return err + if !hs.pdkKEMTLS { + // Note that at this point we could start sending application data without + // waiting for the client's second flight, but the application might not + // expect the lack of replay protection of the ClientHello parameters. + if _, err := c.flush(); err != nil { + return err + } + + // second round of TLS1.3, thrid round for KEMTLS and fourth round for mKEMTLS + hs.handshakeTimings.reset() } + if err := hs.readClientCertificate(); err != nil { return err } @@ -75,6 +144,11 @@ func (hs *serverHandshakeStateTLS13) handshake() error { return err } + //hs.handshakeTimings.ExperimentName = experimentName(c) + fmt.Printf("\n %+v \n", hs.handshakeTimings) + hs.handshakeTimings.finish() + c.handleCFEvent(hs.handshakeTimings) + atomic.StoreUint32(&c.handshakeStatus, 1) return nil @@ -122,12 +196,112 @@ func (hs *serverHandshakeStateTLS13) processClientHello() error { return errors.New("tls: TLS 1.3 client supports illegal compression methods") } + if hs.clientHello.cachedInformationCert { + if c.config.KEMTLSEnabled { + // signature_algorithms is required in TLS 1.3. See RFC 8446, Section 4.2.3. + if len(hs.clientHello.supportedSignatureAlgorithms) == 0 { + return c.sendAlert(alertMissingExtension) + } + + certificate, err := c.config.getCertificate(clientHelloInfo(c, hs.clientHello)) + if err != nil { + if err == errNoCertificates { + c.sendAlert(alertUnrecognizedName) + } else { + c.sendAlert(alertInternalError) + } + return err + } + + hs.sigAlg, err = selectSignatureScheme(c.vers, certificate, hs.clientHello.supportedSignatureAlgorithms) + if err != nil { + // getCertificate returned a certificate that is unsupported or + // incompatible with the client's signature algorithms. + c.sendAlert(alertHandshakeFailure) + return err + } + + hs.cert = certificate + + if hs.clientHello.delegatedCredentialSupported && len(hs.clientHello.supportedSignatureAlgorithmsDC) > 0 { + delegatedCredentialPair, err := getDelegatedCredential(clientHelloInfo(c, hs.clientHello), hs.cert) + if err != nil { + // a Delegated Credential was not found. Fallback to the certificate. + return nil + } + + if delegatedCredentialPair.DC != nil && delegatedCredentialPair.PrivateKey != nil { + // Even if the Delegated Credential has already been marshalled, be sure it is the correct one. + delegatedCredentialPair.DC.raw, err = delegatedCredentialPair.DC.marshal() + if err != nil { + // invalid Delegated Credential. Fallback to the certificate. + return nil + } + + hs.sigAlg, err = selectSignatureSchemeDC(c.vers, delegatedCredentialPair.DC, hs.clientHello.supportedSignatureAlgorithmsDC) + if err != nil { + // the Delegated Credential is unsupported or + // incompatible with the client's signature algorithms. + // Fallback to the certificate. + return nil + } + + hs.cert.DelegatedCredentialPrivateKey = delegatedCredentialPair.PrivateKey + hs.cert.DelegatedCredential = delegatedCredentialPair.DC.raw + + certMsg := new(certificateMsgTLS13) + + certMsg.certificate = *hs.cert + certMsg.scts = hs.clientHello.scts && len(hs.cert.SignedCertificateTimestamps) > 0 + certMsg.ocspStapling = hs.clientHello.ocspStapling && len(hs.cert.OCSPStaple) > 0 + certMsg.delegatedCredential = hs.clientHello.delegatedCredentialSupported && len(hs.cert.DelegatedCredential) > 0 + + certMsgRaw := certMsg.marshal() + cachedCertHash := calculateHashCachedInfo(certMsgRaw) + if bytes.Equal(cachedCertHash, hs.clientHello.cachedInformationCertHash) { + hs.hello.cachedInformationCert = true + + if delegatedCredentialPair.DC.cred.expCertVerfAlgo.isKEMTLS() { + sk, ok1 := hs.cert.DelegatedCredentialPrivateKey.(*kem.PrivateKey) + if !ok1 { + c.sendAlert(alertInternalError) + return errors.New("crypto/tls: private key unexpectedly of wrong type") + } + + ss, err := kem.Decapsulate(sk, hs.clientHello.ciphertextKEMTLS) + if err != nil { + return err + } + hs.pdkKEMTLS = true + hs.ssKEMTLS = ss + hs.hello.pdkKEMTLS = true + } + } + } + } + } + } + + if hs.clientHello.cachedInformationCertReq { + cachedCertReqHash := calculateHashCachedInfo(c.config.CachedCertReq) + if bytes.Equal(cachedCertReqHash, hs.clientHello.cachedInformationCertReqHash) { + hs.hello.cachedInformationCertReq = true + } + } + hs.hello.random = make([]byte, 32) if _, err := io.ReadFull(c.config.rand(), hs.hello.random); err != nil { c.sendAlert(alertInternalError) return err } + if hs.clientHello.echIsInner { + // If confirming ECH acceptance, then clear the last 8 bytes of the + // ServerHello.random in preparation for computing the confirmation + // hint. + copy(hs.hello.random[24:], []byte{0, 0, 0, 0, 0, 0, 0, 0}) + } + if len(hs.clientHello.secureRenegotiation) != 0 { c.sendAlert(alertHandshakeFailure) return errors.New("tls: initial handshake had non-empty renegotiation extension") @@ -182,12 +356,43 @@ func (hs *serverHandshakeStateTLS13) processClientHello() error { hs.hello.cipherSuite = hs.suite.id hs.transcript = hs.suite.hash.New() + // Resolve the server's preference for the ECDHE group. + supportedCurves := c.config.curvePreferences() + if testingTriggerHRR { + // A HelloRetryRequest (HRR) is sent if the client does not offer a key + // share for a curve supported by the server. To trigger this condition + // intentionally, we compute the set of ECDHE groups supported by both + // the client and server but for which the client did not offer a key + // share. + m := make(map[CurveID]bool) + for _, serverGroup := range c.config.curvePreferences() { + for _, clientGroup := range hs.clientHello.supportedCurves { + if clientGroup == serverGroup { + m[clientGroup] = true + } + } + } + for _, ks := range hs.clientHello.keyShares { + delete(m, ks.group) + } + supportedCurves = nil + for group := range m { + supportedCurves = append(supportedCurves, group) + } + if len(supportedCurves) == 0 { + // This occurs if the client offered a key share for each mutually + // supported group. + panic("failed to trigger HelloRetryRequest") + } + } + // Pick the ECDHE group in server preference order, but give priority to // groups with a key share, to avoid a HelloRetryRequest round-trip. var selectedGroup CurveID var clientKeyShare *keyShare + GroupSelection: - for _, preferredGroup := range c.config.curvePreferences() { + for _, preferredGroup := range supportedCurves { for _, ks := range hs.clientHello.keyShares { if ks.group == preferredGroup { selectedGroup = ks.group @@ -216,30 +421,45 @@ GroupSelection: clientKeyShare = &hs.clientHello.keyShares[0] } - if _, ok := curveForCurveID(selectedGroup); selectedGroup != X25519 && !ok { - c.sendAlert(alertInternalError) - return errors.New("tls: CurvePreferences includes unsupported curve") - } - params, err := generateECDHEParameters(c.config.rand(), selectedGroup) - if err != nil { - c.sendAlert(alertInternalError) - return err + if selectedGroup.isKEM() && (c.config.KEMTLSEnabled || c.config.PQTLSEnabled) { + sharedKey, ciphertext, err := kem.Encapsulate(c.config.rand(), &kem.PublicKey{KEMId: kem.ID(selectedGroup), PublicKey: clientKeyShare.data}) + if err != nil { + c.sendAlert(alertInternalError) + return errors.New("tls: CurvePreferences includes unsupported curve") + } + hs.hello.serverShare = keyShare{group: selectedGroup, data: ciphertext} + hs.sharedKey = sharedKey + hs.keyKEMShare = true + } else { + if _, ok := curveForCurveID(selectedGroup); (selectedGroup != X25519 && !selectedGroup.isKEM()) && !ok { + c.sendAlert(alertInternalError) + return errors.New("tls: CurvePreferences includes unsupported curve") + } + params, err := generateECDHEParameters(c.config.rand(), selectedGroup) + if err != nil { + c.sendAlert(alertInternalError) + return err + } + hs.hello.serverShare = keyShare{group: selectedGroup, data: params.PublicKey()} + hs.sharedKey = params.SharedKey(clientKeyShare.data) } - hs.hello.serverShare = keyShare{group: selectedGroup, data: params.PublicKey()} - hs.sharedKey = params.SharedKey(clientKeyShare.data) + if hs.sharedKey == nil { c.sendAlert(alertIllegalParameter) return errors.New("tls: invalid client key share") } c.serverName = hs.clientHello.serverName + + hs.handshakeTimings.ProcessClientHello = hs.handshakeTimings.elapsedTime() + return nil } func (hs *serverHandshakeStateTLS13) checkForResumption() error { c := hs.c - if c.config.SessionTicketsDisabled { + if c.config.SessionTicketsDisabled || c.config.ECHEnabled { return nil } @@ -361,6 +581,36 @@ func cloneHash(in hash.Hash, h crypto.Hash) hash.Hash { return out } +// getDelegatedCredential will return a Delegated Credential pair (a Delegated +// Credential and its private key) for the given ClientHelloInfo, defaulting to +// the first element of cert.DelegatedCredentialPair. +// The returned Delegated Credential could be invalid for usage in the handshake. +// Returns an error if there are no delegated credentials or if the one found +// cannot be used for the current connection. +func getDelegatedCredential(clientHello *ClientHelloInfo, cert *Certificate) (*DelegatedCredentialPair, error) { + if len(cert.DelegatedCredentials) == 0 { + return nil, errors.New("No Delegated Credential found.") + } + + if len(cert.DelegatedCredentials) == 1 { + // There's only one choice, so no point doing any work. + return &cert.DelegatedCredentials[0], nil + } + + for _, dcPair := range cert.DelegatedCredentials { + // The client must have sent the signature_algorithms in the DC extension: ensure it supports + // schemes we can use with this delegated credential. + if len(clientHello.SignatureSchemesDC) > 0 { + if _, err := selectSignatureSchemeDC(VersionTLS13, dcPair.DC, clientHello.SignatureSchemesDC); err == nil { + return &dcPair, nil + } + } + } + + // No delegated credential can be returned. + return nil, errors.New("No valid Delegated Credential found.") +} + func (hs *serverHandshakeStateTLS13) pickCertificate() error { c := hs.c @@ -369,6 +619,10 @@ func (hs *serverHandshakeStateTLS13) pickCertificate() error { return nil } + if hs.pdkKEMTLS && hs.keyKEMShare { + return nil + } + // signature_algorithms is required in TLS 1.3. See RFC 8446, Section 4.2.3. if len(hs.clientHello.supportedSignatureAlgorithms) == 0 { return c.sendAlert(alertMissingExtension) @@ -383,6 +637,7 @@ func (hs *serverHandshakeStateTLS13) pickCertificate() error { } return err } + hs.sigAlg, err = selectSignatureScheme(c.vers, certificate, hs.clientHello.supportedSignatureAlgorithms) if err != nil { // getCertificate returned a certificate that is unsupported or @@ -390,8 +645,57 @@ func (hs *serverHandshakeStateTLS13) pickCertificate() error { c.sendAlert(alertHandshakeFailure) return err } + hs.cert = certificate + if hs.clientHello.delegatedCredentialSupported && len(hs.clientHello.supportedSignatureAlgorithmsDC) > 0 { + delegatedCredentialPair, err := getDelegatedCredential(clientHelloInfo(c, hs.clientHello), hs.cert) + if err != nil { + // a Delegated Credential was not found. Fallback to the certificate. + return nil + } + + if delegatedCredentialPair.DC != nil && delegatedCredentialPair.PrivateKey != nil { + // Even if the Delegated Credential has already been marshalled, be sure it is the correct one. + delegatedCredentialPair.DC.raw, err = delegatedCredentialPair.DC.marshal() + if err != nil { + // invalid Delegated Credential. Fallback to the certificate. + return nil + } + + hs.sigAlg, err = selectSignatureSchemeDC(c.vers, delegatedCredentialPair.DC, hs.clientHello.supportedSignatureAlgorithmsDC) + if err != nil { + // the Delegated Credential is unsupported or + // incompatible with the client's signature algorithms. + // Fallback to the certificate. + return nil + } + + hs.cert.DelegatedCredentialPrivateKey = delegatedCredentialPair.PrivateKey + hs.cert.DelegatedCredential = delegatedCredentialPair.DC.raw + if hs.keyKEMShare { + if delegatedCredentialPair.DC.cred.expCertVerfAlgo.isKEMTLS() { + hs.isKEMTLS = true + } else if delegatedCredentialPair.DC.cred.expCertVerfAlgo.isPQTLS() { + c.didPQTLS = true + } else { + return nil + } + } + } + } else { + if hs.keyKEMShare { + if hs.sigAlg.isKEMTLS() { + hs.isKEMTLS = true + } else if hs.sigAlg.isPQTLS() { + c.didPQTLS = true + } else { + c.sendAlert(alertHandshakeFailure) + return err + } + } + } + return nil } @@ -409,6 +713,7 @@ func (hs *serverHandshakeStateTLS13) sendDummyChangeCipherSpec() error { func (hs *serverHandshakeStateTLS13) doHelloRetryRequest(selectedGroup CurveID) error { c := hs.c + c.hrrTriggered = true // The first ClientHello gets double-hashed into the transcript upon a // HelloRetryRequest. See RFC 8446, Section 4.4.1. @@ -448,6 +753,11 @@ func (hs *serverHandshakeStateTLS13) doHelloRetryRequest(selectedGroup CurveID) return unexpectedMessageError(clientHello, msg) } + clientHello, err = c.echAcceptOrReject(clientHello) + if err != nil { + return fmt.Errorf("tls: %s", err) // Alert sent + } + if len(clientHello.keyShares) != 1 || clientHello.keyShares[0].group != selectedGroup { c.sendAlert(alertIllegalParameter) return errors.New("tls: client sent invalid key share in second ClientHello") @@ -476,6 +786,7 @@ func illegalClientHelloChange(ch, ch1 *clientHelloMsg) bool { len(ch.supportedCurves) != len(ch1.supportedCurves) || len(ch.supportedSignatureAlgorithms) != len(ch1.supportedSignatureAlgorithms) || len(ch.supportedSignatureAlgorithmsCert) != len(ch1.supportedSignatureAlgorithmsCert) || + len(ch.supportedSignatureAlgorithmsDC) != len(ch1.supportedSignatureAlgorithmsDC) || len(ch.alpnProtocols) != len(ch1.alpnProtocols) { return true } @@ -504,6 +815,11 @@ func illegalClientHelloChange(ch, ch1 *clientHelloMsg) bool { return true } } + for i := range ch.supportedSignatureAlgorithmsDC { + if ch.supportedSignatureAlgorithmsDC[i] != ch1.supportedSignatureAlgorithmsDC[i] { + return true + } + } for i := range ch.alpnProtocols { if ch.alpnProtocols[i] != ch1.alpnProtocols[i] { return true @@ -520,6 +836,7 @@ func illegalClientHelloChange(ch, ch1 *clientHelloMsg) bool { !bytes.Equal(ch.sessionTicket, ch1.sessionTicket) || ch.secureRenegotiationSupported != ch1.secureRenegotiationSupported || !bytes.Equal(ch.secureRenegotiation, ch1.secureRenegotiation) || + ch.delegatedCredentialSupported != ch1.delegatedCredentialSupported || ch.scts != ch1.scts || !bytes.Equal(ch.cookie, ch1.cookie) || !bytes.Equal(ch.pskModes, ch1.pskModes) @@ -528,23 +845,40 @@ func illegalClientHelloChange(ch, ch1 *clientHelloMsg) bool { func (hs *serverHandshakeStateTLS13) sendServerParameters() error { c := hs.c + earlySecret := hs.earlySecret + if earlySecret == nil { + earlySecret = hs.suite.extract(nil, nil) + } + hs.handshakeSecret = hs.suite.extract(hs.sharedKey, + hs.suite.deriveSecret(earlySecret, "derived", nil)) + + // Confirm ECH acceptance. + if hs.clientHello.echIsInner { + confTranscript := cloneHash(hs.transcript, hs.suite.hash) + if confTranscript == nil { + c.sendAlert(alertInternalError) + return errors.New("tls: internal error: failed to clone hash") + } + confTranscript.Write(hs.clientHello.marshal()) + confTranscript.Write(hs.hello.marshal()) + conf := hs.suite.deriveSecret(hs.handshakeSecret, + echAcceptConfirmationLabel, confTranscript) + copy(hs.hello.random[24:], conf[:8]) + hs.hello.raw = nil + } + hs.transcript.Write(hs.clientHello.marshal()) hs.transcript.Write(hs.hello.marshal()) if _, err := c.writeRecord(recordTypeHandshake, hs.hello.marshal()); err != nil { return err } + hs.handshakeTimings.WriteServerHello = hs.handshakeTimings.elapsedTime() + if err := hs.sendDummyChangeCipherSpec(); err != nil { return err } - earlySecret := hs.earlySecret - if earlySecret == nil { - earlySecret = hs.suite.extract(nil, nil) - } - hs.handshakeSecret = hs.suite.extract(hs.sharedKey, - hs.suite.deriveSecret(earlySecret, "derived", nil)) - clientSecret := hs.suite.deriveSecret(hs.handshakeSecret, clientHandshakeTrafficLabel, hs.transcript) c.in.setTrafficSecret(hs.suite, clientSecret) @@ -572,11 +906,17 @@ func (hs *serverHandshakeStateTLS13) sendServerParameters() error { } } + if !c.ech.accepted && len(c.ech.retryConfigs) > 0 { + encryptedExtensions.ech = c.ech.retryConfigs + } + hs.transcript.Write(encryptedExtensions.marshal()) if _, err := c.writeRecord(recordTypeHandshake, encryptedExtensions.marshal()); err != nil { return err } + hs.handshakeTimings.WriteEncryptedExtensions = hs.handshakeTimings.elapsedTime() + return nil } @@ -592,20 +932,30 @@ func (hs *serverHandshakeStateTLS13) sendServerCertificate() error { return nil } - if hs.requestClientCert() { + if hs.pdkKEMTLS && hs.keyKEMShare { + hs.isKEMTLS = true + return nil + } + + if hs.requestClientCert() || hs.requestClientKEMCert() { // Request a client certificate certReq := new(certificateRequestMsgTLS13) certReq.ocspStapling = true certReq.scts = true + certReq.supportDelegatedCredential = c.config.SupportDelegatedCredential certReq.supportedSignatureAlgorithms = supportedSignatureAlgorithms + certReq.supportedSignatureAlgorithmsDC = supportedSignatureAlgorithmsDC if c.config.ClientCAs != nil { certReq.certificateAuthorities = c.config.ClientCAs.Subjects() } + hs.certReq = certReq hs.transcript.Write(certReq.marshal()) if _, err := c.writeRecord(recordTypeHandshake, certReq.marshal()); err != nil { return err } + + c.certificateReqMessage = certReq.marshal() } certMsg := new(certificateMsgTLS13) @@ -613,42 +963,70 @@ func (hs *serverHandshakeStateTLS13) sendServerCertificate() error { certMsg.certificate = *hs.cert certMsg.scts = hs.clientHello.scts && len(hs.cert.SignedCertificateTimestamps) > 0 certMsg.ocspStapling = hs.clientHello.ocspStapling && len(hs.cert.OCSPStaple) > 0 + certMsg.delegatedCredential = hs.clientHello.delegatedCredentialSupported && len(hs.cert.DelegatedCredential) > 0 hs.transcript.Write(certMsg.marshal()) if _, err := c.writeRecord(recordTypeHandshake, certMsg.marshal()); err != nil { return err } + c.certificateMessage = certMsg.marshal() - certVerifyMsg := new(certificateVerifyMsg) - certVerifyMsg.hasSignatureAlgorithm = true - certVerifyMsg.signatureAlgorithm = hs.sigAlg + hs.handshakeTimings.WriteCertificate = hs.handshakeTimings.elapsedTime() - sigType, sigHash, err := typeAndHashFromSignatureScheme(hs.sigAlg) - if err != nil { - return c.sendAlert(alertInternalError) - } + if !hs.isKEMTLS { + certVerifyMsg := new(certificateVerifyMsg) + certVerifyMsg.hasSignatureAlgorithm = true + certVerifyMsg.signatureAlgorithm = hs.sigAlg - signed := signedMessage(sigHash, serverSignatureContext, hs.transcript) - signOpts := crypto.SignerOpts(sigHash) - if sigType == signatureRSAPSS { - signOpts = &rsa.PSSOptions{SaltLength: rsa.PSSSaltLengthEqualsHash, Hash: sigHash} - } - sig, err := hs.cert.PrivateKey.(crypto.Signer).Sign(c.config.rand(), signed, signOpts) - if err != nil { - public := hs.cert.PrivateKey.(crypto.Signer).Public() - if rsaKey, ok := public.(*rsa.PublicKey); ok && sigType == signatureRSAPSS && - rsaKey.N.BitLen()/8 < sigHash.Size()*2+2 { // key too small for RSA-PSS - c.sendAlert(alertHandshakeFailure) + sigType, sigHash, err := typeAndHashFromSignatureScheme(certVerifyMsg.signatureAlgorithm) + if err != nil { + return c.sendAlert(alertInternalError) + } + + signed := signedMessage(sigHash, serverSignatureContext, hs.transcript) + signOpts := crypto.SignerOpts(sigHash) + if sigType == signatureRSAPSS { + signOpts = &rsa.PSSOptions{SaltLength: rsa.PSSSaltLengthEqualsHash, Hash: sigHash} + } + + var sig []byte + if len(hs.cert.DelegatedCredential) > 0 { + var err error + sig, err = hs.cert.DelegatedCredentialPrivateKey.(crypto.Signer).Sign(c.config.rand(), signed, signOpts) + if err != nil { + public := hs.cert.DelegatedCredentialPrivateKey.(crypto.Signer).Public() + if rsaKey, ok := public.(*rsa.PublicKey); ok && sigType == signatureRSAPSS && + rsaKey.N.BitLen()/8 < sigHash.Size()*2+2 { // key too small for RSA-PSS + c.sendAlert(alertHandshakeFailure) + } else { + c.sendAlert(alertInternalError) + } + return errors.New("tls: failed to sign handshake: " + err.Error()) + } } else { - c.sendAlert(alertInternalError) + var err error + sig, err = hs.cert.PrivateKey.(crypto.Signer).Sign(c.config.rand(), signed, signOpts) + if err != nil { + public := hs.cert.PrivateKey.(crypto.Signer).Public() + if rsaKey, ok := public.(*rsa.PublicKey); ok && sigType == signatureRSAPSS && + rsaKey.N.BitLen()/8 < sigHash.Size()*2+2 { // key too small for RSA-PSS + c.sendAlert(alertHandshakeFailure) + } else { + c.sendAlert(alertInternalError) + } + return errors.New("tls: failed to sign handshake: " + err.Error()) + } } - return errors.New("tls: failed to sign handshake: " + err.Error()) - } - certVerifyMsg.signature = sig + certVerifyMsg.signature = sig - hs.transcript.Write(certVerifyMsg.marshal()) - if _, err := c.writeRecord(recordTypeHandshake, certVerifyMsg.marshal()); err != nil { - return err + hs.transcript.Write(certVerifyMsg.marshal()) + if _, err := c.writeRecord(recordTypeHandshake, certVerifyMsg.marshal()); err != nil { + return err + } + + hs.handshakeTimings.WriteCertificateVerify = hs.handshakeTimings.elapsedTime() + } else { + hs.handshakeTimings.WriteCertificateVerify = hs.handshakeTimings.elapsedTime() } return nil @@ -657,6 +1035,10 @@ func (hs *serverHandshakeStateTLS13) sendServerCertificate() error { func (hs *serverHandshakeStateTLS13) sendServerFinished() error { c := hs.c + if hs.isKEMTLS == true { + return nil + } + finished := &finishedMsg{ verifyData: hs.suite.finishedHash(c.out.trafficSecret, hs.transcript), } @@ -666,6 +1048,8 @@ func (hs *serverHandshakeStateTLS13) sendServerFinished() error { return err } + hs.handshakeTimings.WriteServerFinished = hs.handshakeTimings.elapsedTime() + // Derive secrets that take context through the server Finished. hs.masterSecret = hs.suite.extract(nil, @@ -703,7 +1087,7 @@ func (hs *serverHandshakeStateTLS13) sendServerFinished() error { } func (hs *serverHandshakeStateTLS13) shouldSendSessionTickets() bool { - if hs.c.config.SessionTicketsDisabled { + if hs.c.config.SessionTicketsDisabled || hs.c.config.ECHEnabled { return false } @@ -765,6 +1149,10 @@ func (hs *serverHandshakeStateTLS13) sendSessionTickets() error { func (hs *serverHandshakeStateTLS13) readClientCertificate() error { c := hs.c + if hs.isKEMTLS == true { + return nil + } + if !hs.requestClientCert() { // Make sure the connection is still being verified whether or not // the server requested a client certificate. @@ -803,6 +1191,8 @@ func (hs *serverHandshakeStateTLS13) readClientCertificate() error { } } + hs.handshakeTimings.ReadCertificate = hs.handshakeTimings.elapsedTime() + if len(certMsg.certificate.Certificate) != 0 { msg, err = c.readHandshake() if err != nil { @@ -828,16 +1218,31 @@ func (hs *serverHandshakeStateTLS13) readClientCertificate() error { c.sendAlert(alertIllegalParameter) return errors.New("tls: client certificate used with invalid signature algorithm") } + + if certMsg.delegatedCredential { + if err := hs.processDelegatedCredentialFromClient(certMsg.certificate.DelegatedCredential, certVerify); err != nil { + return err + } + } + + pk := c.peerCertificates[0].PublicKey + if c.verifiedDC != nil { + pk = c.verifiedDC.cred.publicKey + } + signed := signedMessage(sigHash, clientSignatureContext, hs.transcript) - if err := verifyHandshakeSignature(sigType, c.peerCertificates[0].PublicKey, - sigHash, signed, certVerify.signature); err != nil { + if err := verifyHandshakeSignature(sigType, pk, sigHash, signed, certVerify.signature); err != nil { c.sendAlert(alertDecryptError) return errors.New("tls: invalid signature by the client certificate: " + err.Error()) } hs.transcript.Write(certVerify.marshal()) + + c.didClientAuthentication = true } + hs.handshakeTimings.ReadCertificateVerify = hs.handshakeTimings.elapsedTime() + // If we waited until the client certificates to send session tickets, we // are ready to do it now. if err := hs.sendSessionTickets(); err != nil { @@ -850,6 +1255,10 @@ func (hs *serverHandshakeStateTLS13) readClientCertificate() error { func (hs *serverHandshakeStateTLS13) readClientFinished() error { c := hs.c + if hs.isKEMTLS == true { + return nil + } + msg, err := c.readHandshake() if err != nil { return err @@ -866,6 +1275,8 @@ func (hs *serverHandshakeStateTLS13) readClientFinished() error { return errors.New("tls: invalid client finished hash") } + hs.handshakeTimings.ReadClientFinished = hs.handshakeTimings.elapsedTime() + c.in.setTrafficSecret(hs.suite, hs.trafficSecret) return nil diff --git a/src/crypto/tls/hpke.go b/src/crypto/tls/hpke.go new file mode 100644 index 00000000000..a0867497b11 --- /dev/null +++ b/src/crypto/tls/hpke.go @@ -0,0 +1,45 @@ +// Copyright 2020 Cloudflare, Inc. All rights reserved. Use of this source code +// is governed by a BSD-style license that can be found in the LICENSE file. + +package tls + +import ( + "circl/hpke" + "errors" + "fmt" +) + +// The mandatory-to-implement HPKE cipher suite for use with the ECH extension. +var defaultHPKESuite hpke.Suite + +const ( + defaultHPKESuiteTagLen int = 16 // AEAD_AES128GCM +) + +func hpkeAssembleSuite(kemId, kdfId, aeadId uint16) (hpke.Suite, error) { + kem := hpke.KEM(kemId) + if !kem.IsValid() { + return hpke.Suite{}, errors.New("KEM is not supported") + } + kdf := hpke.KDF(kdfId) + if !kdf.IsValid() { + return hpke.Suite{}, errors.New("KDF is not supported") + } + aead := hpke.AEAD(aeadId) + if !aead.IsValid() { + return hpke.Suite{}, errors.New("AEAD is not supported") + } + return hpke.NewSuite(kem, kdf, aead), nil +} + +func init() { + var err error + defaultHPKESuite, err = hpkeAssembleSuite( + uint16(hpke.KEM_X25519_HKDF_SHA256), + uint16(hpke.KDF_HKDF_SHA256), + uint16(hpke.AEAD_AES128GCM), + ) + if err != nil { + panic(fmt.Sprintf("hpke: mandatory-to-implement cipher suite not supported: %s", err)) + } +} diff --git a/src/crypto/tls/key_agreement.go b/src/crypto/tls/key_agreement.go index 7e6534bd465..66760d096f1 100644 --- a/src/crypto/tls/key_agreement.go +++ b/src/crypto/tls/key_agreement.go @@ -106,7 +106,7 @@ func md5SHA1Hash(slices [][]byte) []byte { // the sigType (for earlier TLS versions). For Ed25519 signatures, which don't // do pre-hashing, it returns the concatenation of the slices. func hashForServerKeyExchange(sigType uint8, hashFunc crypto.Hash, version uint16, slices ...[]byte) []byte { - if sigType == signatureEd25519 { + if sigType == signatureEd25519 || circlSchemeBySigType(sigType) != nil { var signed []byte for _, slice := range slices { signed = append(signed, slice...) @@ -145,7 +145,7 @@ type ecdheKeyAgreement struct { func (ka *ecdheKeyAgreement) generateServerKeyExchange(config *Config, cert *Certificate, clientHello *clientHelloMsg, hello *serverHelloMsg) (*serverKeyExchangeMsg, error) { var curveID CurveID for _, c := range clientHello.supportedCurves { - if config.supportsCurve(c) { + if config.supportsCurve(c) && !c.isKEM() { curveID = c break } @@ -154,7 +154,7 @@ func (ka *ecdheKeyAgreement) generateServerKeyExchange(config *Config, cert *Cer if curveID == 0 { return nil, errors.New("tls: no supported elliptic curves offered") } - if _, ok := curveForCurveID(curveID); curveID != X25519 && !ok { + if _, ok := curveForCurveID(curveID); curveID != X25519 && !curveID.isKEM() && !ok { return nil, errors.New("tls: CurvePreferences includes unsupported curve") } diff --git a/src/crypto/tls/key_schedule.go b/src/crypto/tls/key_schedule.go index 314016979af..4817d96b162 100644 --- a/src/crypto/tls/key_schedule.go +++ b/src/crypto/tls/key_schedule.go @@ -21,14 +21,16 @@ import ( // schedule. See RFC 8446, Section 7. const ( - resumptionBinderLabel = "res binder" - clientHandshakeTrafficLabel = "c hs traffic" - serverHandshakeTrafficLabel = "s hs traffic" - clientApplicationTrafficLabel = "c ap traffic" - serverApplicationTrafficLabel = "s ap traffic" - exporterLabel = "exp master" - resumptionLabel = "res master" - trafficUpdateLabel = "traffic upd" + resumptionBinderLabel = "res binder" + clientHandshakeTrafficLabel = "c hs traffic" + serverHandshakeTrafficLabel = "s hs traffic" + clientApplicationTrafficLabel = "c ap traffic" + serverApplicationTrafficLabel = "s ap traffic" + clientAuthenticatedHandshakeTrafficLabel = "c ahs traffic" + serverAuthenticatedHandshakeTrafficLabel = "s ahs traffic" + exporterLabel = "exp master" + resumptionLabel = "res master" + trafficUpdateLabel = "traffic upd" ) // expandLabel implements HKDF-Expand-Label from RFC 8446, Section 7.1. @@ -89,6 +91,14 @@ func (c *cipherSuiteTLS13) finishedHash(baseKey []byte, transcript hash.Hash) [] return verifyData.Sum(nil) } +// finishedHashKEMTLS is the KEMTLS finished hash, depending on the peer role. +func (c *cipherSuiteTLS13) finishedHashKEMTLS(baseKey []byte, role string, transcript hash.Hash) []byte { + finishedKey := c.expandLabel(baseKey, role+" finished", nil, c.hash.Size()) + verifyData := hmac.New(c.hash.New, finishedKey) + verifyData.Write(transcript.Sum(nil)) + return verifyData.Sum(nil) +} + // exportKeyingMaterial implements RFC5705 exporters for TLS 1.3 according to // RFC 8446, Section 7.5. func (c *cipherSuiteTLS13) exportKeyingMaterial(masterSecret []byte, transcript hash.Hash) func(string, []byte, int) ([]byte, error) { diff --git a/src/crypto/tls/metrics_test.go b/src/crypto/tls/metrics_test.go new file mode 100644 index 00000000000..8e0c9f77c2b --- /dev/null +++ b/src/crypto/tls/metrics_test.go @@ -0,0 +1,135 @@ +// Copyright 2020 Cloudflare, Inc. All rights reserved. Use of this source code +// is governed by a BSD-style license that can be found in the LICENSE file. + +package tls + +import ( + "crypto/x509" + "fmt" + "io" + "io/ioutil" + "testing" + "time" +) + +type testTimingInfo struct { + serverTimingInfo CFEventTLS13ServerHandshakeTimingInfo + clientTimingInfo CFEventTLS13ClientHandshakeTimingInfo +} + +func (t testTimingInfo) isMonotonicallyIncreasing() bool { + serverIsMonotonicallyIncreasing := + 0 < t.serverTimingInfo.ProcessClientHello && + t.serverTimingInfo.ProcessClientHello < t.serverTimingInfo.WriteServerHello && + t.serverTimingInfo.WriteServerHello < t.serverTimingInfo.WriteEncryptedExtensions && + t.serverTimingInfo.WriteEncryptedExtensions < t.serverTimingInfo.WriteCertificate && + t.serverTimingInfo.WriteCertificate < t.serverTimingInfo.WriteCertificateVerify && + t.serverTimingInfo.WriteCertificateVerify < t.serverTimingInfo.WriteServerFinished && + 0 < t.serverTimingInfo.ReadCertificate && + t.serverTimingInfo.ReadCertificate < t.serverTimingInfo.ReadCertificateVerify && + t.serverTimingInfo.ReadCertificateVerify < t.serverTimingInfo.ReadClientFinished && + t.serverTimingInfo.ReadClientFinished < t.serverTimingInfo.FullProtocol + + clientIsMonotonicallyIncreasing := + 0 < t.clientTimingInfo.WriteClientHello && + t.clientTimingInfo.ProcessServerHello < t.clientTimingInfo.ReadEncryptedExtensions && + t.clientTimingInfo.ReadEncryptedExtensions < t.clientTimingInfo.ReadCertificate && + t.clientTimingInfo.ReadCertificate < t.clientTimingInfo.ReadCertificateVerify && + t.clientTimingInfo.ReadCertificateVerify < t.clientTimingInfo.ReadServerFinished && + t.clientTimingInfo.ReadServerFinished < t.clientTimingInfo.WriteCertificate && + t.clientTimingInfo.WriteCertificate < t.clientTimingInfo.WriteCertificateVerify && + t.clientTimingInfo.WriteCertificateVerify < t.clientTimingInfo.WriteClientFinished && + t.clientTimingInfo.WriteClientFinished < t.clientTimingInfo.FullProtocol + + return (serverIsMonotonicallyIncreasing && clientIsMonotonicallyIncreasing) +} + +func (r *testTimingInfo) eventHandler(event CFEvent) { + switch e := event.(type) { + case CFEventTLS13ServerHandshakeTimingInfo: + r.serverTimingInfo = e + case CFEventTLS13ClientHandshakeTimingInfo: + r.clientTimingInfo = e + } +} + +func runHandshake(t *testing.T, clientConfig, serverConfig *Config) (timingState testTimingInfo, err error) { + const sentinel = "SENTINEL\n" + c, s := localPipe(t) + errChan := make(chan error) + + clientConfig.CFEventHandler = timingState.eventHandler + serverConfig.CFEventHandler = timingState.eventHandler + + go func() { + cli := Client(c, clientConfig) + err := cli.Handshake() + if err != nil { + errChan <- fmt.Errorf("client: %v", err) + c.Close() + return + } + defer cli.Close() + buf, err := ioutil.ReadAll(cli) + if err != nil { + t.Errorf("failed to call cli.Read: %v", err) + } + if got := string(buf); got != sentinel { + t.Errorf("read %q from TLS connection, but expected %q", got, sentinel) + } + errChan <- nil + }() + + server := Server(s, serverConfig) + err = server.Handshake() + if err == nil { + if _, err := io.WriteString(server, sentinel); err != nil { + t.Errorf("failed to call server.Write: %v", err) + } + if err := server.Close(); err != nil { + t.Errorf("failed to call server.Close: %v", err) + } + err = <-errChan + } else { + s.Close() + <-errChan + } + + return +} + +func TestTLS13HandshakeTiming(t *testing.T) { + issuer, err := x509.ParseCertificate(testRSACertificateIssuer) + if err != nil { + panic(err) + } + rootCAs := x509.NewCertPool() + rootCAs.AddCert(issuer) + + const serverName = "example.golang" + + baseConfig := &Config{ + Time: time.Now, + Rand: zeroSource{}, + Certificates: make([]Certificate, 1), + MaxVersion: VersionTLS13, + RootCAs: rootCAs, + ClientCAs: rootCAs, + ClientAuth: RequireAndVerifyClientCert, + ServerName: serverName, + } + baseConfig.Certificates[0].Certificate = [][]byte{testRSACertificate} + baseConfig.Certificates[0].PrivateKey = testRSAPrivateKey + + clientConfig := baseConfig.Clone() + serverConfig := baseConfig.Clone() + + ts, err := runHandshake(t, clientConfig, serverConfig) + if err != nil { + t.Fatalf("Handshake failed: %v", err) + } + + if !ts.isMonotonicallyIncreasing() { + t.Fatalf("Timing information is not monotonic") + } +} diff --git a/src/crypto/tls/prf.go b/src/crypto/tls/prf.go index 13bfa009ca4..61e7e3bb641 100644 --- a/src/crypto/tls/prf.go +++ b/src/crypto/tls/prf.go @@ -216,11 +216,11 @@ func (h finishedHash) serverSum(masterSecret []byte) []byte { // hashForClientCertificate returns the handshake messages so far, pre-hashed if // necessary, suitable for signing by a TLS client certificate. func (h finishedHash) hashForClientCertificate(sigType uint8, hashAlg crypto.Hash, masterSecret []byte) []byte { - if (h.version >= VersionTLS12 || sigType == signatureEd25519) && h.buffer == nil { + if (h.version >= VersionTLS12 || sigType == signatureEd25519 || circlSchemeBySigType(sigType) != nil) && h.buffer == nil { panic("tls: handshake hash for a client certificate requested after discarding the handshake buffer") } - if sigType == signatureEd25519 { + if sigType == signatureEd25519 || circlSchemeBySigType(sigType) != nil { return h.buffer } @@ -281,3 +281,9 @@ func ekmFromMasterSecret(version uint16, suite *cipherSuite, masterSecret, clien return keyMaterial, nil } } + +func calculateHashCachedInfo(cachedInfo []byte) []byte { + h := crypto.SHA256.New() + h.Write(cachedInfo) + return h.Sum(nil) +} diff --git a/src/crypto/tls/testdata/Client-TLSv10-ClientCert-ECDSA-ECDSA b/src/crypto/tls/testdata/Client-TLSv10-ClientCert-ECDSA-ECDSA index 9de3f1437b4..91813775e8f 100644 --- a/src/crypto/tls/testdata/Client-TLSv10-ClientCert-ECDSA-ECDSA +++ b/src/crypto/tls/testdata/Client-TLSv10-ClientCert-ECDSA-ECDSA @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 01 00 59 02 00 00 55 03 01 94 1f ba 79 da |....Y...U.....y.| -00000010 4b 58 3e 08 2c c5 31 36 a4 7e 32 bf e1 a0 f7 71 |KX>.,.16.~2....q| -00000020 01 48 63 3c 5f cb 08 7a 25 80 c7 20 35 0c c0 8b |.Hc<_..z%.. 5...| -00000030 df 30 fc dc 3d f1 48 96 0d b6 ff a8 cd 35 29 57 |.0..=.H......5)W| -00000040 7d 3f c2 9d e2 32 b1 c2 4c 05 5e 3b c0 09 00 00 |}?...2..L.^;....| +00000000 16 03 01 00 59 02 00 00 55 03 01 de 63 27 0a cf |....Y...U...c'..| +00000010 9a 00 47 fd 2c da fb eb c3 da 39 a9 99 da 8c 1f |..G.,.....9.....| +00000020 c7 1b a7 43 97 01 02 69 92 62 8d 20 6e d6 22 68 |...C...i.b. n."h| +00000030 b1 99 91 fc a5 ee cb ba 3a 0e 1c 02 1f 24 c8 f7 |........:....$..| +00000040 ab ac 12 81 82 03 ef 2f 05 5e a3 20 c0 09 00 00 |......./.^. ....| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 01 02 0e 0b 00 02 0a 00 02 07 00 02 04 30 82 02 |.............0..| 00000070 00 30 82 01 62 02 09 00 b8 bf 2d 47 a0 d2 eb f4 |.0..b.....-G....| @@ -55,18 +56,18 @@ 00000240 13 83 0d 94 06 bb d4 37 7a f6 ec 7a c9 86 2e dd |.......7z..z....| 00000250 d7 11 69 7f 85 7c 56 de fb 31 78 2b e4 c7 78 0d |..i..|V..1x+..x.| 00000260 ae cb be 9e 4e 36 24 31 7b 6a 0f 39 95 12 07 8f |....N6$1{j.9....| -00000270 2a 16 03 01 00 b5 0c 00 00 b1 03 00 1d 20 1a 74 |*............ .t| -00000280 c4 96 9e 65 45 9a 0a 01 7c ed 7b 51 01 d8 ba 5b |...eE...|.{Q...[| -00000290 3e 2f b1 4b 36 69 e8 47 75 7e 27 be b3 2f 00 8b |>/.K6i.Gu~'../..| -000002a0 30 81 88 02 42 01 cb 20 d9 1e ae 05 6f 1f 37 ce |0...B.. ....o.7.| -000002b0 dc 38 20 2f 8f 52 9a 92 f6 80 d6 f9 97 99 a5 8b |.8 /.R..........| -000002c0 6e 73 0b 95 a4 4e 82 67 bd 1a 34 d9 5c 4e b4 d7 |ns...N.g..4.\N..| -000002d0 35 e6 45 81 14 23 9c 4e 5a 4c 1b 93 fd 7f 43 18 |5.E..#.NZL....C.| -000002e0 db 54 4b e0 d1 d3 fa 02 42 00 ab 8e 34 d5 c2 04 |.TK.....B...4...| -000002f0 d0 a4 44 b1 b3 25 a0 af c8 80 b3 88 ae da b3 c6 |..D..%..........| -00000300 4f 57 ae 31 54 c6 d9 ee 4e 21 56 01 cc b9 6a e9 |OW.1T...N!V...j.| -00000310 e9 7e 62 2a 64 0e a4 a0 79 1e a3 64 52 70 b1 a5 |.~b*d...y..dRp..| -00000320 19 2c a4 6d 4b 3b a3 63 ed 56 2f 16 03 01 00 0a |.,.mK;.c.V/.....| +00000270 2a 16 03 01 00 b5 0c 00 00 b1 03 00 1d 20 ac 7b |*............ .{| +00000280 48 31 66 8e ba 38 b2 b6 a9 69 23 4b 9c 0b 37 6b |H1f..8...i#K..7k| +00000290 76 10 ea fa 0d 6a 08 7e 31 d3 e5 62 e5 6e 00 8b |v....j.~1..b.n..| +000002a0 30 81 88 02 42 00 bd 7b fb 48 94 07 17 4d 50 e7 |0...B..{.H...MP.| +000002b0 de 2a bf 57 a9 fc a9 ce 1b a0 73 78 04 36 8a 20 |.*.W......sx.6. | +000002c0 2f 41 98 e0 33 27 18 33 71 5d 63 04 97 f6 7e ba |/A..3'.3q]c...~.| +000002d0 c5 c0 a6 84 a6 d9 44 79 8c ac 46 90 c6 58 87 11 |......Dy..F..X..| +000002e0 ca c1 8a 7b 96 43 85 02 42 01 14 be e7 ea 3c 8e |...{.C..B.....<.| +000002f0 f9 6e 86 15 0b 51 eb ec 29 6b 1b 3e a2 96 9e 6e |.n...Q..)k.>...n| +00000300 82 ef 5b 28 7b 04 3f b2 30 b2 09 f4 f4 b3 6e d8 |..[({.?.0.....n.| +00000310 d6 88 7c b4 f8 fb 3a 50 6f 2f e5 20 b8 66 4e b6 |..|...:Po/. .fN.| +00000320 7d cd 99 9a 46 4e 89 ec 44 7d 53 16 03 01 00 0a |}...FN..D}S.....| 00000330 0d 00 00 06 03 01 02 40 00 00 16 03 01 00 04 0e |.......@........| 00000340 00 00 00 |...| >>> Flow 3 (client to server) @@ -106,29 +107,29 @@ 00000210 03 01 00 25 10 00 00 21 20 2f e5 7d a3 47 cd 62 |...%...! /.}.G.b| 00000220 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 cf |C.(.._.).0......| 00000230 c2 ed 90 99 5f 58 cb 3b 74 16 03 01 00 90 0f 00 |...._X.;t.......| -00000240 00 8c 00 8a 30 81 87 02 42 01 89 0f 43 df a8 34 |....0...B...C..4| -00000250 dd d7 c9 d4 2b 8d ec 29 77 7b 64 d0 0e 8c e8 2b |....+..)w{d....+| -00000260 e3 25 1c ed 0a 1b 05 e0 66 42 37 c0 e6 fa 3e 81 |.%......fB7...>.| -00000270 ec e1 06 99 f4 62 3f ea 55 79 ae 68 56 9e e3 3c |.....b?.Uy.hV..<| -00000280 83 ba 9b 1c 65 b9 eb a6 e7 f7 4e 02 41 61 2c 52 |....e.....N.Aa,R| -00000290 4c 48 92 b0 93 d8 31 58 c3 90 b0 e3 7d 55 94 fc |LH....1X....}U..| -000002a0 70 bf 18 42 51 73 d0 45 17 2e 0e 00 b0 12 76 0d |p..BQs.E......v.| -000002b0 35 78 cb fd 34 60 36 ff ed 19 ef 0a 1e 21 cc 4c |5x..4`6......!.L| -000002c0 9a ff a0 f7 cf 72 03 cd 00 bb 73 0d 1d e5 14 03 |.....r....s.....| -000002d0 01 00 01 01 16 03 01 00 30 69 76 1f 5b 81 5f 62 |........0iv.[._b| -000002e0 cf d5 d9 2c 19 71 80 d0 2a 97 8a 89 21 7f 6d 02 |...,.q..*...!.m.| -000002f0 b6 01 a4 ed fe 18 9f 34 ae 95 f6 a1 29 0b 9a 1c |.......4....)...| -00000300 04 b6 ce c7 d1 0c 5a b5 3f |......Z.?| +00000240 00 8c 00 8a 30 81 87 02 42 00 ba 52 f9 37 2d 13 |....0...B..R.7-.| +00000250 cc f0 5a f6 0e 76 27 ce 16 36 d7 4c 08 a5 67 04 |..Z..v'..6.L..g.| +00000260 09 49 bd 67 b8 6e ff 09 79 f4 b1 d3 e4 f8 45 2a |.I.g.n..y.....E*| +00000270 ca 18 56 b0 13 c3 ee b6 5c 38 41 ee 85 c3 29 b9 |..V.....\8A...).| +00000280 e9 69 0d d0 f4 04 be 19 c3 e3 a4 02 41 4e 63 36 |.i..........ANc6| +00000290 e8 31 6c c8 fb d8 04 15 14 27 96 93 e3 ce 5e c7 |.1l......'....^.| +000002a0 28 d8 e8 2d 1d 98 f1 2e e5 fa 10 c4 3b c0 12 c8 |(..-........;...| +000002b0 48 cb 25 c5 23 53 f3 fd ec c8 6a 26 45 c4 2b 1c |H.%.#S....j&E.+.| +000002c0 cd bd fb 2f a9 0b ed 90 48 30 1d ec 22 e2 14 03 |.../....H0.."...| +000002d0 01 00 01 01 16 03 01 00 30 fe a7 cf 13 19 d7 8b |........0.......| +000002e0 3b d9 2f ee 06 c7 bc 0d 7e 21 79 49 78 1c 6d 72 |;./.....~!yIx.mr| +000002f0 fe c5 13 04 e2 9b e4 2c 8f b5 e7 1b 1b d0 29 93 |.......,......).| +00000300 7f 2a 29 fb fb fb 54 e0 9d |.*)...T..| >>> Flow 4 (server to client) -00000000 14 03 01 00 01 01 16 03 01 00 30 7d 4b fc 73 20 |..........0}K.s | -00000010 e4 ac c4 39 15 79 e3 89 e1 24 ce 28 30 e5 f1 87 |...9.y...$.(0...| -00000020 cd c0 cc 39 a8 77 3b 06 a5 f9 b0 a1 3d 54 53 3b |...9.w;.....=TS;| -00000030 53 ec ac b2 ea 24 1b 2d 6a ef c3 |S....$.-j..| +00000000 14 03 01 00 01 01 16 03 01 00 30 96 e6 45 8c 03 |..........0..E..| +00000010 73 2b 3a a6 73 b2 40 f6 1b 70 04 36 7b 5b c3 c2 |s+:.s.@..p.6{[..| +00000020 4a 92 ab ad 33 e9 c4 e5 d3 03 2a c3 11 94 85 b7 |J...3.....*.....| +00000030 04 2e 0c 9f ae 3c 95 a5 5a 6a f5 |.....<..Zj.| >>> Flow 5 (client to server) -00000000 17 03 01 00 20 9d 57 d2 4b 5b 7e 7d 7c 28 f7 8e |.... .W.K[~}|(..| -00000010 00 0a b6 1c 3c 6b df 4d 06 c0 f8 db 86 2e 8f 8e |.....9.VN...... .| +00000050 7a 9c c2 b2 d7 e1 a5 f1 af f7 c2 3f e7 8a ad 41 |z..........?...A| +00000060 26 26 04 cc 7d 1b ee b3 56 dc 63 6f 10 69 92 |&&..}...V.co.i.| diff --git a/src/crypto/tls/testdata/Client-TLSv10-ClientCert-ECDSA-RSA b/src/crypto/tls/testdata/Client-TLSv10-ClientCert-ECDSA-RSA index 754b76ece95..7c09f77009c 100644 --- a/src/crypto/tls/testdata/Client-TLSv10-ClientCert-ECDSA-RSA +++ b/src/crypto/tls/testdata/Client-TLSv10-ClientCert-ECDSA-RSA @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 01 00 59 02 00 00 55 03 01 97 0c 7e fc 7f |....Y...U....~..| -00000010 96 47 02 21 a7 19 45 a5 79 5c 5e fc c2 15 b3 fa |.G.!..E.y\^.....| -00000020 84 98 7d 67 65 c8 48 58 a1 5d 67 20 ad 2a c6 b3 |..}ge.HX.]g .*..| -00000030 a4 17 82 12 4a c5 97 af 12 6b 7d f6 9e 49 f1 38 |....J....k}..I.8| -00000040 d0 56 76 bc 81 23 ad 3a 3e 7f bc 2d c0 13 00 00 |.Vv..#.:>..-....| +00000000 16 03 01 00 59 02 00 00 55 03 01 f9 f7 61 b3 a8 |....Y...U....a..| +00000010 28 68 f6 11 94 f6 ea 95 f4 db d1 cc c7 da 4a a0 |(h............J.| +00000020 d3 72 c5 1d 2e 89 17 5e be 20 ea 20 d1 98 c8 b9 |.r.....^. . ....| +00000030 ec 68 c1 a8 22 8b f0 82 36 7d 48 9b 82 7e fd c8 |.h.."...6}H..~..| +00000040 b8 21 49 63 98 77 52 e6 25 38 e0 e1 c0 13 00 00 |.!Ic.wR.%8......| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 01 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,17 +61,17 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 01 00 |.=.`.\!.;.......| -000002c0 aa 0c 00 00 a6 03 00 1d 20 a4 24 f7 67 e3 da fa |........ .$.g...| -000002d0 10 33 95 b4 46 00 c0 3c cd 74 12 e4 a3 3b 01 70 |.3..F..<.t...;.p| -000002e0 fb 98 01 9a e9 2d d0 18 7b 00 80 ce c5 7b 4b 87 |.....-..{....{K.| -000002f0 cd bc 5d 63 09 7e d4 ce 09 53 7a 1b e5 b4 10 54 |..]c.~...Sz....T| -00000300 89 52 ac 82 9c 78 88 ed e8 1a 8c 3a 7a 2c 9a c5 |.R...x.....:z,..| -00000310 2b 97 1c 79 43 bd b1 ee 93 6f 4c 4d fc 3c 47 91 |+..yC....oLM....| +000002f0 db 12 e5 ba 9f b9 b1 e1 4e 1d c7 bc bc d6 84 a8 |........N.......| +00000300 02 99 69 86 ee 50 80 ac 4a e2 10 fa 4d 2f e1 54 |..i..P..J...M/.T| +00000310 a5 54 18 1a 32 0f d8 4b ca f1 15 8f a6 65 3e 1f |.T..2..K.....e>.| +00000320 ef 7b 40 ce f9 30 c3 9b ad b8 f2 fa d4 6a e4 e0 |.{@..0.......j..| +00000330 f5 90 d1 e8 bf 02 b4 d6 65 ce b4 84 cf 32 d8 11 |........e....2..| +00000340 50 e4 80 3d 14 ac 33 0c 0e 49 eb d5 26 c2 67 c5 |P..=..3..I..&.g.| +00000350 6a a1 a1 f3 4c fd 5d 3e 81 60 8f 63 ad c4 31 f4 |j...L.]>.`.c..1.| +00000360 3c 87 76 8a e7 8e a2 fb 5d 85 8b 16 03 01 00 0a |<.v.....].......| 00000370 0d 00 00 06 03 01 02 40 00 00 16 03 01 00 04 0e |.......@........| 00000380 00 00 00 |...| >>> Flow 3 (client to server) @@ -109,30 +110,30 @@ 00000200 e4 fa cc b1 8a ce e2 23 a0 87 f0 e1 67 51 eb 16 |.......#....gQ..| 00000210 03 01 00 25 10 00 00 21 20 2f e5 7d a3 47 cd 62 |...%...! /.}.G.b| 00000220 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 cf |C.(.._.).0......| -00000230 c2 ed 90 99 5f 58 cb 3b 74 16 03 01 00 91 0f 00 |...._X.;t.......| -00000240 00 8d 00 8b 30 81 88 02 42 01 71 f3 c4 3a 85 08 |....0...B.q..:..| -00000250 3b 18 26 48 5c 3f c3 8a 4f e9 d7 29 48 59 1a 35 |;.&H\?..O..)HY.5| -00000260 ee b3 0d 5e 29 03 1d 34 95 0e 40 73 85 13 14 d0 |...^)..4..@s....| -00000270 fb fb 96 77 21 fb d8 43 d7 e2 bf 2c 95 7b 75 5d |...w!..C...,.{u]| -00000280 59 15 81 71 d2 b6 82 96 d9 cc 78 02 42 01 d3 51 |Y..q......x.B..Q| -00000290 af 25 d0 f8 a4 e2 e7 8e 7e 46 56 53 8f d1 09 f6 |.%......~FVS....| -000002a0 76 88 5a 42 83 89 92 7b c7 e4 40 9c 3d 05 ac 43 |v.ZB...{..@.=..C| -000002b0 bf 6e 24 14 fe 36 f8 43 a6 90 8e a1 bd e2 92 84 |.n$..6.C........| -000002c0 60 e3 92 34 1c 7b 53 d5 57 6d 23 32 12 a8 23 14 |`..4.{S.Wm#2..#.| -000002d0 03 01 00 01 01 16 03 01 00 30 6f 06 c7 84 fa 7f |.........0o.....| -000002e0 c9 66 a9 6f 26 37 45 db 42 c8 8f 63 c3 5b 05 07 |.f.o&7E.B..c.[..| -000002f0 ef 07 41 be 71 60 35 d3 16 8f 92 f6 89 cb c7 dc |..A.q`5.........| -00000300 4e 45 61 99 31 45 66 40 36 86 |NEa.1Ef@6.| +00000230 c2 ed 90 99 5f 58 cb 3b 74 16 03 01 00 8f 0f 00 |...._X.;t.......| +00000240 00 8b 00 89 30 81 86 02 41 3b b5 99 1b a9 3a 5d |....0...A;....:]| +00000250 dd 93 c5 f3 29 e8 50 4b d7 90 56 16 26 88 50 c6 |....).PK..V.&.P.| +00000260 ac f0 6b 91 c7 3c 8f f9 22 36 ed a6 92 52 68 cb |..k..<.."6...Rh.| +00000270 af fa 1b d4 27 67 54 ff ef ea 76 84 41 a3 1d 05 |....'gT...v.A...| +00000280 8e 1a 0a 65 16 38 67 5e 49 26 02 41 43 ab 74 de |...e.8g^I&.AC.t.| +00000290 24 36 ec 55 2f 41 ed 83 26 a1 ed 50 fe 95 dc c7 |$6.U/A..&..P....| +000002a0 b8 d0 10 1a 4b 3d 53 31 a5 9e 31 1e 13 4a 82 6f |....K=S1..1..J.o| +000002b0 a8 a6 76 4e 1d 09 d6 e9 38 df f3 f1 1a cc 90 cf |..vN....8.......| +000002c0 44 59 a1 69 7f 73 9f d4 ec 02 99 b5 0e 14 03 01 |DY.i.s..........| +000002d0 00 01 01 16 03 01 00 30 f8 b2 67 bb 31 a5 70 7f |.......0..g.1.p.| +000002e0 b6 cb 57 f8 77 dc 79 b0 fc bb ac 88 e2 82 cd f5 |..W.w.y.........| +000002f0 33 30 06 35 fb 53 0b b1 03 a0 5a 55 5e c0 66 cf |30.5.S....ZU^.f.| +00000300 17 6f 45 91 15 04 c4 1e |.oE.....| >>> Flow 4 (server to client) -00000000 14 03 01 00 01 01 16 03 01 00 30 d3 83 ac 08 7f |..........0.....| -00000010 a1 91 51 7c b7 99 6f 24 cd b1 cd 31 7b 12 20 47 |..Q|..o$...1{. G| -00000020 66 08 22 f6 28 ea 81 fe 92 b5 c8 40 60 bc 5b 19 |f.".(......@`.[.| -00000030 e0 2b d1 26 fd 4c 12 22 c5 13 9a |.+.&.L."...| +00000000 14 03 01 00 01 01 16 03 01 00 30 1b 14 bb 33 ed |..........0...3.| +00000010 c2 a1 97 52 53 02 0f 83 ad 1b 90 14 04 7f a6 22 |...RS.........."| +00000020 35 4c 76 3d 42 e5 07 63 ba 23 05 04 0f 2a c4 bd |5Lv=B..c.#...*..| +00000030 43 32 cc 11 b0 68 2d 9b 52 8b fd |C2...h-.R..| >>> Flow 5 (client to server) -00000000 17 03 01 00 20 79 06 89 7e e0 17 9a e3 dc 4c ee |.... y..~.....L.| -00000010 70 63 13 bc 27 f5 43 fa f8 90 49 d9 89 43 7a 15 |pc..'.C...I..Cz.| -00000020 d4 e2 a8 e6 3e 17 03 01 00 20 ea 84 0e 21 62 d5 |....>.... ...!b.| -00000030 ee 26 5e fc 3e 0c 83 3b 91 01 c4 a7 8e 9b c4 1a |.&^.>..;........| -00000040 86 f8 a0 44 21 44 2f 31 cf a1 15 03 01 00 20 c6 |...D!D/1...... .| -00000050 11 f1 65 ea f3 39 d1 d2 ac 95 1f 81 36 ae db b1 |..e..9......6...| -00000060 88 a8 42 25 86 ec 1b c1 7e 12 60 a9 6b 7f 66 |..B%....~.`.k.f| +00000000 17 03 01 00 20 23 e1 84 5b ad c1 ad 0e a0 fe 38 |.... #..[......8| +00000010 44 ea c5 8c 5d 03 37 5d 7c 66 5e fc 22 df 3b a9 |D...].7]|f^.".;.| +00000020 dd 14 63 b9 cc 17 03 01 00 20 61 c0 9b 9a f5 ed |..c...... a.....| +00000030 11 92 53 38 0e b2 22 10 ce 4a 6a 21 2f a2 22 13 |..S8.."..Jj!/.".| +00000040 4f 9e 77 e3 f5 56 28 06 d5 ef 15 03 01 00 20 9a |O.w..V(....... .| +00000050 8c b5 ba 4d e9 08 a7 7f 38 ec 93 89 9c 55 7a 3b |...M....8....Uz;| +00000060 5f 3b 27 4f 3e 91 2a e8 42 72 ca 93 17 da fe |_;'O>.*.Br.....| diff --git a/src/crypto/tls/testdata/Client-TLSv10-ClientCert-RSA-ECDSA b/src/crypto/tls/testdata/Client-TLSv10-ClientCert-RSA-ECDSA index 641ab1bd156..e9aeb25d1d8 100644 --- a/src/crypto/tls/testdata/Client-TLSv10-ClientCert-RSA-ECDSA +++ b/src/crypto/tls/testdata/Client-TLSv10-ClientCert-RSA-ECDSA @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 01 00 59 02 00 00 55 03 01 3b 4c b9 76 d2 |....Y...U..;L.v.| -00000010 c3 d1 ea 81 71 1a 10 e1 b1 69 5c 54 c2 df 17 0a |....q....i\T....| -00000020 de 41 cb d1 69 c3 9a da 90 fd 25 20 1e 02 11 16 |.A..i.....% ....| -00000030 ab 66 13 56 3d 94 00 a9 80 7c d8 57 12 99 1c 5f |.f.V=....|.W..._| -00000040 7a b2 02 8c 23 f3 76 b8 59 5e 16 dd c0 09 00 00 |z...#.v.Y^......| +00000000 16 03 01 00 59 02 00 00 55 03 01 4f ed ef dc 7c |....Y...U..O...|| +00000010 4e 2f f4 fe c2 c6 b4 aa 1a c7 66 8f 02 95 94 9d |N/........f.....| +00000020 95 0c 58 20 d0 b0 69 e8 00 34 5a 20 9c d9 b1 a8 |..X ..i..4Z ....| +00000030 94 43 eb f5 36 2b 26 37 9d 6d 8a ef 9f 0f c1 45 |.C..6+&7.m.....E| +00000040 ee 4e f8 17 45 ec 74 56 f5 b8 dd bb c0 09 00 00 |.N..E.tV........| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 01 02 0e 0b 00 02 0a 00 02 07 00 02 04 30 82 02 |.............0..| 00000070 00 30 82 01 62 02 09 00 b8 bf 2d 47 a0 d2 eb f4 |.0..b.....-G....| @@ -55,18 +56,18 @@ 00000240 13 83 0d 94 06 bb d4 37 7a f6 ec 7a c9 86 2e dd |.......7z..z....| 00000250 d7 11 69 7f 85 7c 56 de fb 31 78 2b e4 c7 78 0d |..i..|V..1x+..x.| 00000260 ae cb be 9e 4e 36 24 31 7b 6a 0f 39 95 12 07 8f |....N6$1{j.9....| -00000270 2a 16 03 01 00 b5 0c 00 00 b1 03 00 1d 20 16 64 |*............ .d| -00000280 ca 24 70 6f 61 2f 9e 2d 43 0a 73 ac 67 f0 7a e5 |.$poa/.-C.s.g.z.| -00000290 c7 4e c4 1f ad 13 0d eb df ff 0d ff a3 27 00 8b |.N...........'..| -000002a0 30 81 88 02 42 01 1a 33 8b 88 78 ed 5c c1 56 0d |0...B..3..x.\.V.| -000002b0 75 51 69 a0 e7 45 6d ae b0 67 55 3f be 23 3e 92 |uQi..Em..gU?.#>.| -000002c0 fe 26 68 a2 30 84 2f b3 33 66 f6 dd 71 67 99 5e |.&h.0./.3f..qg.^| -000002d0 1c 6f bf 87 ed 33 a0 87 69 f6 35 65 8d cb 3a 7e |.o...3..i.5e..:~| -000002e0 95 a7 a4 40 54 cb 97 02 42 00 a3 fe 50 34 68 9f |...@T...B...P4h.| -000002f0 f2 43 98 23 e4 24 ad 36 e9 d3 e0 75 2c 11 46 6c |.C.#.$.6...u,.Fl| -00000300 48 33 c5 bc 2d 04 ff cc bb ec 38 ec f4 b3 55 31 |H3..-.....8...U1| -00000310 8a 6e 38 a5 6d a0 9c fc f6 98 75 48 c6 79 53 de |.n8.m.....uH.yS.| -00000320 dd 91 49 f0 b6 32 83 45 61 89 4e 16 03 01 00 0a |..I..2.Ea.N.....| +00000270 2a 16 03 01 00 b5 0c 00 00 b1 03 00 1d 20 b6 a6 |*............ ..| +00000280 a2 c2 d0 5f 15 36 f5 d4 0b 3b 5a 52 87 7c 39 06 |..._.6...;ZR.|9.| +00000290 b3 32 88 ba 67 26 00 a4 91 2f b2 56 e3 46 00 8b |.2..g&.../.V.F..| +000002a0 30 81 88 02 42 01 7b eb 50 b7 73 6f 35 56 b1 51 |0...B.{.P.so5V.Q| +000002b0 d2 78 7d b8 49 33 c7 bd c7 cd 70 50 c3 88 63 0a |.x}.I3....pP..c.| +000002c0 24 78 3c 2a 9a 51 23 05 2b 6e 5a 27 f2 8d 5d 66 |$x<*.Q#.+nZ'..]f| +000002d0 ad 6e 77 45 d7 b7 74 bd 5e 1b 0a c1 13 89 93 17 |.nwE..t.^.......| +000002e0 ea 49 cd f2 46 04 15 02 42 01 24 78 8b 1c 81 e6 |.I..F...B.$x....| +000002f0 f5 5a 95 34 ff 52 f8 ac d2 ef b1 57 7c 56 73 ee |.Z.4.R.....W|Vs.| +00000300 70 15 92 c7 68 28 ab 7e 40 3e 03 ba 1e d5 75 9a |p...h(.~@>....u.| +00000310 3f 66 74 33 e0 69 fc 8f a2 87 c9 63 db ed c2 b8 |?ft3.i.....c....| +00000320 f1 e4 8d 57 09 3c 34 bb 56 e9 5f 16 03 01 00 0a |...W.<4.V._.....| 00000330 0d 00 00 06 03 01 02 40 00 00 16 03 01 00 04 0e |.......@........| 00000340 00 00 00 |...| >>> Flow 3 (client to server) @@ -105,29 +106,29 @@ 00000200 e5 35 16 03 01 00 25 10 00 00 21 20 2f e5 7d a3 |.5....%...! /.}.| 00000210 47 cd 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 |G.bC.(.._.).0...| 00000220 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 16 03 01 00 |......._X.;t....| -00000230 86 0f 00 00 82 00 80 90 68 a8 2f 6f 2b 70 e4 25 |........h./o+p.%| -00000240 7d fb b7 85 db 44 ec 1a ad 6d 84 fb 95 21 fa 24 |}....D...m...!.$| -00000250 7b 31 6a 97 4f 06 ee 87 22 c3 7c 81 70 ed e3 2a |{1j.O...".|.p..*| -00000260 d5 2c d1 4e 6d f0 12 52 2f 98 05 08 af 41 fa 87 |.,.Nm..R/....A..| -00000270 d1 62 98 6c 06 47 ec 7a 44 e0 7d ae 7a 7d ef 1b |.b.l.G.zD.}.z}..| -00000280 d5 2c fa 1b 70 a3 fb 9a 5d 8c 60 b4 44 6a e5 b8 |.,..p...].`.Dj..| -00000290 80 4c 29 fc f1 2d f1 11 46 81 c4 01 e4 11 2e 05 |.L)..-..F.......| -000002a0 cb 2b ca d9 4a 14 39 06 93 77 19 db 80 03 82 38 |.+..J.9..w.....8| -000002b0 e5 c1 0f 11 17 47 a7 14 03 01 00 01 01 16 03 01 |.....G..........| -000002c0 00 30 a6 68 28 50 75 6d eb f4 32 c8 a3 57 3f b1 |.0.h(Pum..2..W?.| -000002d0 37 84 8e 7e 1d 1d 93 7d 9f ec ff ac 1c 8d bf 30 |7..~...}.......0| -000002e0 d2 b0 0f 3f 02 c3 ef ac a3 62 94 26 1c 8f 7e 8d |...?.....b.&..~.| -000002f0 74 99 |t.| +00000230 86 0f 00 00 82 00 80 06 cf 29 53 de 70 87 b6 a5 |.........)S.p...| +00000240 69 ec ee 92 9c 18 5c 16 4f e2 c8 91 e6 42 c2 3f |i.....\.O....B.?| +00000250 95 8b 0f 4c 41 61 f5 70 38 d3 91 d2 41 da 46 b0 |...LAa.p8...A.F.| +00000260 ec 69 36 23 8e 6d 05 f5 3c 27 34 55 a9 94 d9 71 |.i6#.m..<'4U...q| +00000270 79 f4 72 f4 f9 f0 f6 65 ba f1 20 ed 6c 5c 5e a4 |y.r....e.. .l\^.| +00000280 2c 2b 65 58 63 6e cb a0 df ea 24 ea e0 4d 15 a0 |,+eXcn....$..M..| +00000290 e6 8c 20 3c 1a 65 dc 3f f4 6d 87 39 d0 0c 2e 90 |.. <.e.?.m.9....| +000002a0 1a bd 74 7c d6 0b 60 c7 71 4b 86 42 5c 83 f0 72 |..t|..`.qK.B\..r| +000002b0 cc 0f 29 d9 1d 3b 23 14 03 01 00 01 01 16 03 01 |..)..;#.........| +000002c0 00 30 17 bd 63 2f aa 09 ab d2 f0 32 b9 7f 75 22 |.0..c/.....2..u"| +000002d0 18 18 a3 68 16 4a 28 12 30 1f 94 0c cf 96 de b3 |...h.J(.0.......| +000002e0 98 2a 9c e6 66 23 c7 cb cd 47 f2 de 5b 2a ba 78 |.*..f#...G..[*.x| +000002f0 f3 83 |..| >>> Flow 4 (server to client) -00000000 14 03 01 00 01 01 16 03 01 00 30 80 3e 0d 50 13 |..........0.>.P.| -00000010 5f 00 ba 2e 47 46 5d 63 1b 72 a8 02 24 1c 3e 1f |_...GF]c.r..$.>.| -00000020 ed e2 3a 45 d7 7d 3a f2 33 97 c3 ab 13 9b 0e 4a |..:E.}:.3......J| -00000030 04 f0 08 48 ab d3 46 0b 40 7d 5c |...H..F.@}\| +00000000 14 03 01 00 01 01 16 03 01 00 30 60 9d 90 60 62 |..........0`..`b| +00000010 2e e4 8f 10 a2 52 83 24 14 26 08 b3 37 59 03 c4 |.....R.$.&..7Y..| +00000020 57 df 3f 34 35 f4 c8 c2 1f 4f 75 17 92 75 37 7e |W.?45....Ou..u7~| +00000030 78 02 1f 36 e2 65 26 77 15 31 6b |x..6.e&w.1k| >>> Flow 5 (client to server) -00000000 17 03 01 00 20 f7 32 e7 36 4f 77 2f 4a 05 fd 27 |.... .2.6Ow/J..'| -00000010 19 57 52 f7 8a 0c 7f fb 14 78 b2 06 bf ca 86 73 |.WR......x.....s| -00000020 32 13 33 04 91 17 03 01 00 20 7e e4 fe c5 6d f7 |2.3...... ~...m.| -00000030 d4 69 30 57 89 a0 76 70 40 a7 b5 17 74 2f 5d 16 |.i0W..vp@...t/].| -00000040 c1 19 30 73 f8 37 c4 10 5b b7 15 03 01 00 20 08 |..0s.7..[..... .| -00000050 41 5e 0b 9f 36 23 bd 9a 09 f7 58 9d a3 d7 26 3a |A^..6#....X...&:| -00000060 f4 5e 6b bf 9c d4 6f 0c d3 9e cd de cb 95 57 |.^k...o.......W| +00000000 17 03 01 00 20 e9 87 5a ae bf 07 8c 64 16 67 ba |.... ..Z....d.g.| +00000010 ec ad 8a c8 dd 17 25 c7 99 bc 36 8c 79 7d fe 62 |......%...6.y}.b| +00000020 8a b4 b2 92 ee 17 03 01 00 20 67 60 54 96 75 35 |......... g`T.u5| +00000030 d4 d3 49 dc f7 44 f5 78 7e 5e e3 5c 06 a3 f4 16 |..I..D.x~^.\....| +00000040 af 4b c1 fc 11 cb bb ec 60 61 15 03 01 00 20 fc |.K......`a.... .| +00000050 b1 31 bc 8e 98 b8 a4 f4 11 bb 79 36 5c 19 81 80 |.1........y6\...| +00000060 aa 13 d4 72 7f 52 db 75 34 82 7e b2 a5 4e 3d |...r.R.u4.~..N=| diff --git a/src/crypto/tls/testdata/Client-TLSv10-ClientCert-RSA-RSA b/src/crypto/tls/testdata/Client-TLSv10-ClientCert-RSA-RSA index c46a9670e84..b9d182043c2 100644 --- a/src/crypto/tls/testdata/Client-TLSv10-ClientCert-RSA-RSA +++ b/src/crypto/tls/testdata/Client-TLSv10-ClientCert-RSA-RSA @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 01 00 59 02 00 00 55 03 01 97 fe 7f 92 37 |....Y...U......7| -00000010 67 99 e0 d8 62 a9 31 80 bd 1f 31 8e 7d 0b 08 0a |g...b.1...1.}...| -00000020 de a5 82 a2 f2 d0 c1 35 66 34 6e 20 39 46 b1 b0 |.......5f4n 9F..| -00000030 6e 2d 0e fe 8c 48 ea ab 1c c4 49 ee f4 21 cf cb |n-...H....I..!..| -00000040 2a 20 57 78 18 99 a1 b9 7f 88 4f 64 c0 13 00 00 |* Wx......Od....| +00000000 16 03 01 00 59 02 00 00 55 03 01 84 54 17 9d c9 |....Y...U...T...| +00000010 ff 38 07 41 35 79 fc a1 b8 b3 33 7e e3 9c 5c 84 |.8.A5y....3~..\.| +00000020 67 79 3c f1 d5 81 58 95 56 07 3b 20 2c 62 a0 54 |gy<...X.V.; ,b.T| +00000030 9f 1f 62 c8 06 17 61 69 6b 49 8a 37 7d 5f 01 87 |..b...aikI.7}_..| +00000040 a6 e3 13 4e 08 49 74 ab 2e 0f f2 18 c0 13 00 00 |...N.It.........| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 01 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,17 +61,17 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 01 00 |.=.`.\!.;.......| -000002c0 aa 0c 00 00 a6 03 00 1d 20 07 80 79 40 4b b1 0e |........ ..y@K..| -000002d0 05 ce e4 ca 9d f5 d7 ad a6 98 f2 40 f9 b9 66 a8 |...........@..f.| -000002e0 04 6e ae b5 da 99 67 09 69 00 80 01 4a f2 c1 c9 |.n....g.i...J...| -000002f0 2f 46 4f b8 9e 8b 2c c4 a1 32 44 3c dc 2c 5e b9 |/FO...,..2D<.,^.| -00000300 76 5f 41 20 23 1b 82 dd ec 37 b4 24 68 6d a7 39 |v_A #....7.$hm.9| -00000310 4f f2 e5 97 09 75 64 2a 64 16 b8 99 04 8a 74 77 |O....ud*d.....tw| -00000320 19 bb 12 5f 27 f6 41 09 f7 2e 1c 33 80 3b 01 57 |..._'.A....3.;.W| -00000330 5c f9 20 6e 0c 48 76 59 e1 8b 1f bb 2a 33 1a 28 |\. n.HvY....*3.(| -00000340 a0 5a 05 44 94 eb 35 62 5e ae 7f e4 01 76 b6 b4 |.Z.D..5b^....v..| -00000350 64 91 bf 25 09 ff 88 8a af 73 00 d0 7e ea 0f ca |d..%.....s..~...| -00000360 4a 2b d4 6f 02 26 98 28 5a ed 11 16 03 01 00 0a |J+.o.&.(Z.......| +000002c0 aa 0c 00 00 a6 03 00 1d 20 db 1a c8 04 8d d7 40 |........ ......@| +000002d0 99 04 ac df 4b ac 04 1a 0a 59 e1 59 4b 77 97 97 |....K....Y.YKw..| +000002e0 80 66 1b ba 95 29 f3 4c 3e 00 80 8d 64 75 3d 11 |.f...).L>...du=.| +000002f0 00 ec 9f 7d de a0 14 46 31 b6 b5 71 7b 5f 34 cc |...}...F1..q{_4.| +00000300 06 59 19 35 4b 59 0d 7b c5 68 27 91 57 70 4d 04 |.Y.5KY.{.h'.WpM.| +00000310 cf 92 1a f1 7e 68 8e 15 70 05 b2 a9 bd 37 9f b4 |....~h..p....7..| +00000320 02 e7 5c 5a 24 47 03 8a 2b 64 df 29 a3 36 bb 57 |..\Z$G..+d.).6.W| +00000330 87 57 e9 00 85 52 88 25 27 92 99 3d a3 3b 19 e7 |.W...R.%'..=.;..| +00000340 c4 21 8c 1a 4d f6 2c ce 0b ee cf ab d5 df bb 21 |.!..M.,........!| +00000350 55 58 bb 34 8b 85 b7 ef c2 c7 47 b5 76 4d 87 5c |UX.4......G.vM.\| +00000360 ad 11 58 b8 33 b8 b1 91 77 d0 21 16 03 01 00 0a |..X.3...w.!.....| 00000370 0d 00 00 06 03 01 02 40 00 00 16 03 01 00 04 0e |.......@........| 00000380 00 00 00 |...| >>> Flow 3 (client to server) @@ -109,29 +110,29 @@ 00000200 e5 35 16 03 01 00 25 10 00 00 21 20 2f e5 7d a3 |.5....%...! /.}.| 00000210 47 cd 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 |G.bC.(.._.).0...| 00000220 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 16 03 01 00 |......._X.;t....| -00000230 86 0f 00 00 82 00 80 81 aa 68 1f a9 a4 de f1 4d |.........h.....M| -00000240 30 9a fe e6 a5 f6 f6 18 b6 3e d2 c7 f1 e6 77 e3 |0........>....w.| -00000250 6a cd 61 01 81 3a 02 31 a5 aa d6 db b6 02 9d 4b |j.a..:.1.......K| -00000260 f5 78 50 c3 95 fe 43 88 33 3a 95 32 bc e8 02 1a |.xP...C.3:.2....| -00000270 e6 f4 d5 54 b9 fc e0 4a 4e f0 92 21 35 4b de c8 |...T...JN..!5K..| -00000280 a4 b0 01 c3 ca 3a 87 ed cb 21 1c ce c2 14 7b 8d |.....:...!....{.| -00000290 90 68 b9 21 49 13 dd cd e7 68 83 41 7c 84 6a 75 |.h.!I....h.A|.ju| -000002a0 76 ee 19 8b fa d5 a6 57 3d a7 f1 f1 6f 11 ca 77 |v......W=...o..w| -000002b0 95 0e b5 c7 3d 99 d4 14 03 01 00 01 01 16 03 01 |....=...........| -000002c0 00 30 5e be 40 82 f8 db 05 20 23 45 a4 42 48 e8 |.0^.@.... #E.BH.| -000002d0 06 69 eb 4c ef 79 53 52 4a 5a 3a ba cc d6 99 59 |.i.L.ySRJZ:....Y| -000002e0 4d c2 b0 34 0f 14 68 03 93 8b a4 95 7e cf 26 f8 |M..4..h.....~.&.| -000002f0 5c 8a |\.| +00000230 86 0f 00 00 82 00 80 a8 5f cf ad 26 d3 85 5f a8 |........_..&.._.| +00000240 51 54 cd d7 a8 04 22 77 26 42 af 41 c3 04 eb 71 |QT...."w&B.A...q| +00000250 8d cc fc ef 79 20 da 01 9b 19 47 db 3e 31 15 55 |....y ....G.>1.U| +00000260 aa fb 07 61 6c 16 d1 32 1a 4a c3 f1 f0 8a 42 33 |...al..2.J....B3| +00000270 c3 bf d6 8a a0 06 f8 84 6b 5b 32 87 e8 85 bd 3c |........k[2....<| +00000280 1a 81 e8 74 2b f5 c9 f8 87 e6 0a bf 16 7d 35 ac |...t+........}5.| +00000290 2e a7 7a 65 50 25 7e 77 03 b8 ef 66 c7 bd 4e d1 |..zeP%~w...f..N.| +000002a0 47 5f 82 9d 58 a3 3e e6 16 3c 2f 11 79 a9 47 13 |G_..X.>..>> Flow 4 (server to client) -00000000 14 03 01 00 01 01 16 03 01 00 30 ef 9b 5c da 0a |..........0..\..| -00000010 2e c4 79 fa ea 8a 9c 78 4a 1f 08 77 56 73 6e fa |..y....xJ..wVsn.| -00000020 3a 5b 3c cd cd e9 0c a8 bb 59 9e 22 ab 67 2c 03 |:[<......Y.".g,.| -00000030 de ad 7c e4 cb 85 d7 8f c1 1c e3 |..|........| +00000000 14 03 01 00 01 01 16 03 01 00 30 88 10 86 5c 0f |..........0...\.| +00000010 95 da aa 48 cc 53 c7 ed 27 a3 98 22 a0 8c 00 fa |...H.S..'.."....| +00000020 8c 61 72 72 53 a4 e9 1f 48 21 db 94 1e 3d 49 4b |.arrS...H!...=IK| +00000030 b7 ae 5a 5f 20 08 64 6b 77 92 e1 |..Z_ .dkw..| >>> Flow 5 (client to server) -00000000 17 03 01 00 20 48 1a 1a 1c 6c 7d 6c 2a e0 b2 e3 |.... H...l}l*...| -00000010 b3 9f ec 39 a8 cd 9a f9 a2 3e 2d 46 3b cf 17 ed |...9.....>-F;...| -00000020 70 99 ce d7 3c 17 03 01 00 20 69 27 e9 89 78 e6 |p...<.... i'..x.| -00000030 64 c0 a9 40 4f 0d 97 53 b2 2e 15 f3 2b 54 3b 77 |d..@O..S....+T;w| -00000040 f2 24 2c 94 dc b3 8b f0 c4 ce 15 03 01 00 20 1b |.$,........... .| -00000050 50 55 83 d8 6b b4 04 b2 f0 2d 1c 9c 0d fa de 58 |PU..k....-.....X| -00000060 cd 0a 1d 55 d6 36 f4 a4 fb cc 55 c5 b1 f3 d3 |...U.6....U....| +00000000 17 03 01 00 20 52 2c e9 3e ea 16 54 c8 5d d5 6c |.... R,.>..T.].l| +00000010 34 73 96 b5 70 b0 b8 19 3d 54 39 c5 ea d8 91 b2 |4s..p...=T9.....| +00000020 b4 a6 06 2b b3 17 03 01 00 20 9f ac 14 90 89 fe |...+..... ......| +00000030 b3 58 83 a4 4d 4d 4f ca 57 e1 f0 ad a6 b4 24 1f |.X..MMO.W.....$.| +00000040 5d 51 52 86 a7 aa 5f 42 cf c7 15 03 01 00 20 69 |]QR..._B...... i| +00000050 ea fa dc fe 4e 3f d7 7b bd b1 aa e5 4a 3a d4 18 |....N?.{....J:..| +00000060 02 82 c9 77 6d 58 b6 98 17 4f c7 85 4e e8 9b |...wmX...O..N..| diff --git a/src/crypto/tls/testdata/Client-TLSv10-ECDHE-ECDSA-AES b/src/crypto/tls/testdata/Client-TLSv10-ECDHE-ECDSA-AES index 7d6683c026a..60bd22853b7 100644 --- a/src/crypto/tls/testdata/Client-TLSv10-ECDHE-ECDSA-AES +++ b/src/crypto/tls/testdata/Client-TLSv10-ECDHE-ECDSA-AES @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 01 00 59 02 00 00 55 03 01 a7 ea 63 8c 7d |....Y...U....c.}| -00000010 54 70 04 d5 5e a2 2e 8b 75 4f 17 c8 a8 8c 3d bc |Tp..^...uO....=.| -00000020 08 aa 82 48 85 ed 1a ff 42 e1 54 20 3b 77 9d 32 |...H....B.T ;w.2| -00000030 4d 60 f2 81 f8 20 aa d2 b0 eb ea 7c 6a 39 52 20 |M`... .....|j9R | -00000040 94 4a 2a 88 05 8a fe 6c 50 5c 95 39 c0 09 00 00 |.J*....lP\.9....| +00000000 16 03 01 00 59 02 00 00 55 03 01 17 04 f1 24 8a |....Y...U.....$.| +00000010 27 77 65 60 02 db 3d 66 c1 9a 30 30 df e9 df cf |'we`..=f..00....| +00000020 60 f2 8e f9 34 24 21 95 0b bd 5d 20 cc f6 58 37 |`...4$!...] ..X7| +00000030 f1 2b 46 91 cc 35 e3 b0 96 b8 82 de 4f f6 3e 07 |.+F..5......O.>.| +00000040 5e 4e a7 da 41 bc ea f6 dc 4f 33 07 c0 09 00 00 |^N..A....O3.....| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 01 02 0e 0b 00 02 0a 00 02 07 00 02 04 30 82 02 |.............0..| 00000070 00 30 82 01 62 02 09 00 b8 bf 2d 47 a0 d2 eb f4 |.0..b.....-G....| @@ -55,37 +56,37 @@ 00000240 13 83 0d 94 06 bb d4 37 7a f6 ec 7a c9 86 2e dd |.......7z..z....| 00000250 d7 11 69 7f 85 7c 56 de fb 31 78 2b e4 c7 78 0d |..i..|V..1x+..x.| 00000260 ae cb be 9e 4e 36 24 31 7b 6a 0f 39 95 12 07 8f |....N6$1{j.9....| -00000270 2a 16 03 01 00 b5 0c 00 00 b1 03 00 1d 20 3a 1f |*............ :.| -00000280 18 e9 f2 09 3e 79 4b a0 62 73 ef 87 0d ea 90 51 |....>yK.bs.....Q| -00000290 7f 9d d2 79 59 e4 11 7f 69 f7 a9 d7 78 7f 00 8b |...yY...i...x...| -000002a0 30 81 88 02 42 01 65 ac eb e6 b0 86 73 95 a4 27 |0...B.e.....s..'| -000002b0 e3 82 55 cf 88 16 80 c2 68 4b 39 77 2a b1 a9 d3 |..U.....hK9w*...| -000002c0 08 d5 ac 77 ce 5b 16 73 2c ad b5 57 2a 7a 75 34 |...w.[.s,..W*zu4| -000002d0 ec 99 23 bd df b2 27 36 5a 4b 40 e0 d3 b0 d2 31 |..#...'6ZK@....1| -000002e0 9b c7 9e 0a cb 5b 69 02 42 00 88 d7 5a 6a 9e 4c |.....[i.B...Zj.L| -000002f0 c5 7b 2c 8e 93 3b 75 27 b4 00 11 88 ba cf 99 8c |.{,..;u'........| -00000300 e5 f2 60 22 de f2 fe 86 a6 48 86 9c 40 31 08 75 |..`".....H..@1.u| -00000310 aa bc 5d 6d fa 2e a4 a9 a1 0d fc e1 d9 5a a1 60 |..]m.........Z.`| -00000320 93 b9 69 c7 c2 3e f5 a9 cb 31 41 16 03 01 00 04 |..i..>...1A.....| -00000330 0e 00 00 00 |....| +00000270 2a 16 03 01 00 b4 0c 00 00 b0 03 00 1d 20 35 57 |*............ 5W| +00000280 ed c1 9b 2c 52 da 42 91 10 08 b5 06 ed 01 ec 5f |...,R.B........_| +00000290 7e 61 31 ed 7d bb 4d 17 52 74 86 51 43 10 00 8a |~a1.}.M.Rt.QC...| +000002a0 30 81 87 02 41 34 48 d9 6e 92 a1 c1 ce 18 30 7a |0...A4H.n.....0z| +000002b0 9b 8e a6 58 af 62 02 4a ab ec 2d 7c 58 fa 45 65 |...X.b.J..-|X.Ee| +000002c0 2c 68 31 ff c4 24 3c 77 e5 2e 8c 0f 76 b8 70 ea |,h1..$>> Flow 3 (client to server) 00000000 16 03 01 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 01 00 01 01 |....._X.;t......| -00000030 16 03 01 00 30 30 25 15 82 a1 7f 11 32 13 52 17 |....00%.....2.R.| -00000040 b8 bd 5b b9 1e 69 88 0b b3 5f 12 40 e3 4b 03 cb |..[..i..._.@.K..| -00000050 cd 07 3c 43 4f ab f7 5d 2c 6a a3 02 a9 64 d0 77 |..>> Flow 4 (server to client) -00000000 14 03 01 00 01 01 16 03 01 00 30 b5 3e 18 97 a1 |..........0.>...| -00000010 ca 2e 7f 5f b9 72 cb aa d4 f6 85 86 d3 27 40 13 |..._.r.......'@.| -00000020 e3 99 35 13 67 a8 9e 6e bb 63 15 97 96 42 e4 b3 |..5.g..n.c...B..| -00000030 fc 15 ee b7 d8 cb a2 64 3d 55 b8 |.......d=U.| +00000000 14 03 01 00 01 01 16 03 01 00 30 fa da 0d c2 5e |..........0....^| +00000010 a7 0d c6 f1 5b 24 5f 7b 7c d3 20 f4 71 8c 23 a8 |....[$_{|. .q.#.| +00000020 bc 3b d2 9a ea ce 03 55 c7 5a 74 31 4c f1 e7 79 |.;.....U.Zt1L..y| +00000030 ee 09 ae 50 39 2f dc ca d6 e7 f8 |...P9/.....| >>> Flow 5 (client to server) -00000000 17 03 01 00 20 12 6c bf f2 39 2d e6 ad a8 38 d5 |.... .l..9-...8.| -00000010 1c ea 5b 79 e5 c7 4a 41 eb 58 70 f0 7d f7 60 e7 |..[y..JA.Xp.}.`.| -00000020 ee 77 98 75 f2 17 03 01 00 20 ac 5e 6d b0 81 0b |.w.u..... .^m...| -00000030 14 ca c2 70 53 d8 6d 55 49 63 da 8a 61 66 80 2d |...pS.mUIc..af.-| -00000040 e4 7c 2e 60 1f eb 3c f2 27 66 15 03 01 00 20 7a |.|.`..<.'f.... z| -00000050 2b 80 f8 00 0f 06 f5 6e fe b7 b7 6b 12 6c 8d 8e |+......n...k.l..| -00000060 c4 11 23 2b a2 bb 16 93 b4 e0 e0 fd 8c 42 db |..#+.........B.| +00000000 17 03 01 00 20 d1 fd 45 6f 97 b8 a0 8c 21 f5 2d |.... ..Eo....!.-| +00000010 23 33 78 d1 d3 96 74 d7 e8 49 ea 63 0f ea ab 6b |#3x...t..I.c...k| +00000020 d6 85 52 5d e8 17 03 01 00 20 5e 47 90 4d 06 65 |..R]..... ^G.M.e| +00000030 49 c7 f8 54 bc f5 49 65 95 bb 0c e7 8d 20 e4 ac |I..T..Ie..... ..| +00000040 1d 68 b3 a3 a5 c1 b1 2f 21 df 15 03 01 00 20 24 |.h...../!..... $| +00000050 47 bb a9 0a ad dc 19 21 12 7a 49 3e 0b 2a 31 0a |G......!.zI>.*1.| +00000060 83 47 03 10 bd 88 87 4b 2e 55 f4 cf ea 84 e9 |.G.....K.U.....| diff --git a/src/crypto/tls/testdata/Client-TLSv10-ECDHE-RSA-AES b/src/crypto/tls/testdata/Client-TLSv10-ECDHE-RSA-AES index c0e842d155c..40f0a32b619 100644 --- a/src/crypto/tls/testdata/Client-TLSv10-ECDHE-RSA-AES +++ b/src/crypto/tls/testdata/Client-TLSv10-ECDHE-RSA-AES @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 01 00 59 02 00 00 55 03 01 16 f4 24 01 94 |....Y...U....$..| -00000010 68 d2 0f 15 4d d6 65 54 84 73 ab 2c b2 11 c5 64 |h...M.eT.s.,...d| -00000020 d8 93 66 50 cd b0 f0 ab 11 5c 72 20 b1 13 c1 f5 |..fP.....\r ....| -00000030 63 ed 70 0b 21 52 85 36 84 99 1d b6 bb dc d3 1c |c.p.!R.6........| -00000040 b3 76 13 d9 ef 47 c4 c0 18 57 23 3b c0 13 00 00 |.v...G...W#;....| +00000000 16 03 01 00 59 02 00 00 55 03 01 17 f2 52 86 71 |....Y...U....R.q| +00000010 a3 cf 0c 9f 5a c0 16 dd 12 ab e8 be 3a 01 38 fb |....Z.......:.8.| +00000020 40 ac 12 d2 45 c9 33 af e1 3e 06 20 c1 0b 00 a3 |@...E.3..>. ....| +00000030 00 ab 3c 37 eb b4 cf 26 2d 36 e3 fc 56 9d a4 26 |..<7...&-6..V..&| +00000040 3d 6a 98 ec a7 c9 ee 1b c3 d4 d6 07 c0 13 00 00 |=j..............| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 01 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,36 +61,36 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 01 00 |.=.`.\!.;.......| -000002c0 aa 0c 00 00 a6 03 00 1d 20 7e aa 30 94 7b fb 09 |........ ~.0.{..| -000002d0 b5 55 ce b3 e9 e0 5b 55 82 f4 e6 7c d0 e4 57 eb |.U....[U...|..W.| -000002e0 9b ec 82 48 d6 0e 2a bb 16 00 80 80 da c5 75 4f |...H..*.......uO| -000002f0 82 95 ee 47 28 af 09 08 d5 13 68 33 5d 91 dd 13 |...G(.....h3]...| -00000300 43 84 e9 54 d9 e7 39 7c 38 74 d5 92 8f 46 37 86 |C..T..9|8t...F7.| -00000310 44 68 ae c7 3a ad e1 33 5f cd d8 c6 a5 7c 5e 83 |Dh..:..3_....|^.| -00000320 44 ba b1 09 44 ec 42 7f 41 80 d6 b6 4c 6d ae 24 |D...D.B.A...Lm.$| -00000330 a9 3b 53 87 2f 3b 3a 1f da 87 2b 7d cf 9e ed a5 |.;S./;:...+}....| -00000340 04 54 ad c2 3c 7b 21 60 55 67 41 47 60 02 1e 62 |.T..<{!`UgAG`..b| -00000350 bb 9f ee 2c 6e 79 20 6e 65 e2 d0 ae 73 70 3e a7 |...,ny ne...sp>.| -00000360 3f 74 96 8e 2a 6e a6 7e 7a e0 e4 16 03 01 00 04 |?t..*n.~z.......| +000002c0 aa 0c 00 00 a6 03 00 1d 20 40 71 36 40 15 13 ea |........ @q6@...| +000002d0 4b 61 35 2d de 19 e8 d5 d3 9d a7 e7 d5 91 b4 5e |Ka5-...........^| +000002e0 d7 83 42 90 a8 38 7b 51 55 00 80 aa 83 e2 86 4d |..B..8{QU......M| +000002f0 fc 83 0f b3 98 0a 62 9e ea 9a 0b 2a 77 16 1e 73 |......b....*w..s| +00000300 6c 3e 6c 81 6e ac a5 a6 0f f7 78 5a 9b c9 ba 88 |l>l.n.....xZ....| +00000310 8a 04 da 62 d8 04 1c c2 4c 52 31 a5 6f a9 79 e1 |...b....LR1.o.y.| +00000320 de 9c d8 d8 14 ff a5 ff a8 36 fc aa 29 79 e6 e6 |.........6..)y..| +00000330 9c dc d3 01 b9 d9 14 b9 6c f0 07 cb 99 6f dc 65 |........l....o.e| +00000340 99 32 83 35 1f e1 bf 12 f3 63 23 98 23 51 ea ad |.2.5.....c#.#Q..| +00000350 06 42 23 c1 0a 83 e0 2e ec 23 f4 e3 5b b7 62 0a |.B#......#..[.b.| +00000360 b3 81 52 a1 11 5a e1 29 ba 44 ba 16 03 01 00 04 |..R..Z.).D......| 00000370 0e 00 00 00 |....| >>> Flow 3 (client to server) 00000000 16 03 01 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 01 00 01 01 |....._X.;t......| -00000030 16 03 01 00 30 5a cb 36 c8 1c 43 a8 e1 88 db c9 |....0Z.6..C.....| -00000040 ae 78 b0 af 97 e4 c3 f6 25 51 8e 4d 57 94 ee ca |.x......%Q.MW...| -00000050 a4 8b 3f 4d 17 75 34 58 c3 fa a6 6f d4 e5 ae 3a |..?M.u4X...o...:| -00000060 cb 5a cb 11 ef |.Z...| +00000030 16 03 01 00 30 af f2 bb e4 8f 0b 87 24 4e 06 0d |....0.......$N..| +00000040 84 28 59 8e 7d 60 f3 e7 a7 de 01 69 5a 7b 43 df |.(Y.}`.....iZ{C.| +00000050 c8 e7 0c 43 3d a3 af 50 46 dd e5 79 70 09 6d 51 |...C=..PF..yp.mQ| +00000060 6b 0a bf b9 ca |k....| >>> Flow 4 (server to client) -00000000 14 03 01 00 01 01 16 03 01 00 30 96 92 50 6f f0 |..........0..Po.| -00000010 d1 ff 7c 39 fb 75 0c 8b c9 d7 29 7d 9d 32 4c 19 |..|9.u....)}.2L.| -00000020 2e 93 ea 11 87 07 fc 5a 7d 3c 30 e1 bd 64 7f 90 |.......Z}<0..d..| -00000030 fd 70 1d 50 eb ec f2 d6 de 09 61 |.p.P......a| +00000000 14 03 01 00 01 01 16 03 01 00 30 30 48 77 84 7b |..........00Hw.{| +00000010 ff e0 6d 1f 15 81 b7 90 f5 af c4 b6 c9 e3 1e c5 |..m.............| +00000020 61 16 e2 2e 6e 80 c4 65 87 29 de 4e 16 2d 2b 72 |a...n..e.).N.-+r| +00000030 50 ae 7d b0 cf 27 ea 52 e3 b6 9f |P.}..'.R...| >>> Flow 5 (client to server) -00000000 17 03 01 00 20 fd a4 ba f1 78 a9 a2 45 d3 d2 5a |.... ....x..E..Z| -00000010 1e 41 6b 89 8d bd a4 21 69 03 a1 7c b8 56 ff df |.Ak....!i..|.V..| -00000020 67 bc 85 5e 21 17 03 01 00 20 a7 6d 4c 11 d0 f3 |g..^!.... .mL...| -00000030 7d e2 f0 69 18 7c 42 71 78 e4 3b 71 7d 13 27 bb |}..i.|Bqx.;q}.'.| -00000040 79 fd d7 b2 d7 28 ca 92 83 f1 15 03 01 00 20 10 |y....(........ .| -00000050 b3 79 d4 1d 70 db b7 6c f2 15 05 3c 4d 65 ba ec |.y..p..l...>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 01 00 59 02 00 00 55 03 01 7a a4 22 4f 19 |....Y...U..z."O.| -00000010 54 37 47 cb e5 dd b4 54 86 9e 9e d6 3f f1 bd ca |T7G....T....?...| -00000020 9a 3e 16 3c 7e 1a 29 22 0d c8 95 20 ac 85 42 c1 |.>.<~.)"... ..B.| -00000030 e7 f3 38 62 38 24 a8 24 d2 67 bd 0d 06 44 74 cf |..8b8$.$.g...Dt.| -00000040 3d a4 37 17 bc 8c 5d 41 9f 5a 74 69 c0 13 00 00 |=.7...]A.Zti....| +00000000 16 03 01 00 59 02 00 00 55 03 01 29 3d 29 97 31 |....Y...U..)=).1| +00000010 c5 fc e8 fe 4e af 6d 56 6b 22 fb 7f 1c 2d d6 ab |....N.mVk"...-..| +00000020 14 22 92 b7 9c 57 d1 56 47 15 89 20 9b 46 c6 14 |."...W.VG.. .F..| +00000030 4b de ec 2f 7b 8c 40 64 f4 9c 75 f4 62 52 62 52 |K../{.@d..u.bRbR| +00000040 93 54 04 ad ce b9 10 b2 cd f8 57 de c0 13 00 00 |.T........W.....| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 01 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,36 +61,36 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 01 00 |.=.`.\!.;.......| -000002c0 aa 0c 00 00 a6 03 00 1d 20 71 52 12 72 a7 56 0b |........ qR.r.V.| -000002d0 51 81 af 9f e1 95 43 44 54 0e 9e 3d cc 6f 3c 4c |Q.....CDT..=.o| -00000360 cb 59 5d 81 da 58 07 83 e7 af 25 16 03 01 00 04 |.Y]..X....%.....| +000002c0 aa 0c 00 00 a6 03 00 1d 20 c0 b7 b5 96 32 29 b7 |........ ....2).| +000002d0 ba 4e 0c 79 02 bc 64 07 fc 6d 02 ee 0f a8 f8 d8 |.N.y..d..m......| +000002e0 c3 8f a4 85 2c 70 3a a9 4a 00 80 94 36 a8 0a 75 |....,p:.J...6..u| +000002f0 d8 4f 7a 2d ba a8 ad 6a a1 77 0b f9 37 de 4c 36 |.Oz-...j.w..7.L6| +00000300 d1 2f 22 a7 2e b4 0e 54 cb 0b ab 12 95 14 1b ef |./"....T........| +00000310 d9 db 00 95 85 bb e6 d8 69 0b c2 42 80 db b8 30 |........i..B...0| +00000320 a7 cd 71 1d bc 50 3f de c7 80 94 6c 62 4b a9 44 |..q..P?....lbK.D| +00000330 0a 92 a3 12 d2 3a 61 86 78 cb a6 65 a0 e3 91 fe |.....:a.x..e....| +00000340 92 7d d2 8e a0 36 20 b8 c2 89 f3 d5 0b 0b 49 25 |.}...6 .......I%| +00000350 0c 1c 43 1d 42 91 b9 8c 44 bc b8 f7 db ef 2f c6 |..C.B...D...../.| +00000360 c6 ed fc 28 6b ff c4 1b 55 c1 71 16 03 01 00 04 |...(k...U.q.....| 00000370 0e 00 00 00 |....| >>> Flow 3 (client to server) 00000000 16 03 01 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 01 00 01 01 |....._X.;t......| -00000030 16 03 01 00 30 c3 26 49 92 5a 8c d0 da 48 ba 60 |....0.&I.Z...H.`| -00000040 29 c0 5c d5 44 04 11 7a 25 b5 d6 9f a4 cf fe bf |).\.D..z%.......| -00000050 33 a7 ba c2 96 2b 4d c1 fb dc 4c ba b8 2b 6f 20 |3....+M...L..+o | -00000060 2d 2a 02 ee 17 |-*...| +00000030 16 03 01 00 30 15 eb 7d a5 60 f4 c7 fb 49 74 82 |....0..}.`...It.| +00000040 30 5e c1 03 07 f2 7a 66 75 11 8a 4d 69 7a b4 5a |0^....zfu..Miz.Z| +00000050 fe 43 64 b4 d6 95 54 be 15 7e 35 52 f6 aa fe 91 |.Cd...T..~5R....| +00000060 7b ce 00 0e 5b |{...[| >>> Flow 4 (server to client) -00000000 14 03 01 00 01 01 16 03 01 00 30 f4 4e 0a ea 58 |..........0.N..X| -00000010 18 c6 9d 5f aa 5d f0 03 d4 63 0d e7 83 cb a8 18 |..._.]...c......| -00000020 06 fa b6 82 da df 16 89 5c 8b 5d 92 87 b1 42 da |........\.]...B.| -00000030 cd 2a ee dc 43 08 f1 0d 1f 18 5c |.*..C.....\| +00000000 14 03 01 00 01 01 16 03 01 00 30 ad a1 da 3b 29 |..........0...;)| +00000010 dc c2 a8 8c 80 bd fd 95 b3 2c 83 2d 13 4f 16 a0 |.........,.-.O..| +00000020 4b c7 c8 71 29 fd 10 ca 77 b8 56 97 08 55 ed c9 |K..q)...w.V..U..| +00000030 e5 80 9d 70 19 8e 88 65 3a 92 2c |...p...e:.,| >>> Flow 5 (client to server) -00000000 17 03 01 00 20 e6 95 10 e0 98 07 9f 2b 42 06 b8 |.... .......+B..| -00000010 2a 6c 5d 4a 95 2a 2c 17 d5 cc 68 42 18 bd 72 58 |*l]J.*,...hB..rX| -00000020 c1 39 73 05 75 17 03 01 00 20 d4 ae 70 ee a0 ed |.9s.u.... ..p...| -00000030 3e dd f9 aa 93 03 ff f5 a4 f6 f3 0d e7 a6 59 a9 |>.............Y.| -00000040 40 b4 f6 ad a5 46 0b eb ee 0e 15 03 01 00 20 7c |@....F........ || -00000050 1a 29 f3 49 60 47 2e 52 ec 00 4a 62 44 30 93 5f |.).I`G.R..JbD0._| -00000060 df 73 2f 44 65 3f 77 c1 3d 04 32 c8 bb 86 ed |.s/De?w.=.2....| +00000000 17 03 01 00 20 56 0a 77 9e d9 c6 8b 90 bb 4f 8e |.... V.w......O.| +00000010 fe 1a 89 a7 11 2f cf 73 ed 60 c2 bf 7c e0 8a 38 |...../.s.`..|..8| +00000020 5b 32 29 aa 41 17 03 01 00 20 18 a4 aa c8 d5 a7 |[2).A.... ......| +00000030 b7 c2 ff 6a 0d 6b 8f 05 6c 4c 46 08 4f 3e 5d 6c |...j.k..lLF.O>]l| +00000040 c5 ad b9 3e f3 17 2e f3 e4 75 15 03 01 00 20 45 |...>.....u.... E| +00000050 4c 0b 48 a2 dc 00 71 30 80 83 15 bf d4 24 80 93 |L.H...q0.....$..| +00000060 99 6f 75 9a 6b 5e 1e 14 22 02 57 da 68 97 f6 |.ou.k^..".W.h..| diff --git a/src/crypto/tls/testdata/Client-TLSv10-RSA-RC4 b/src/crypto/tls/testdata/Client-TLSv10-RSA-RC4 index 1fe13b9f97a..567c8cb80bf 100644 --- a/src/crypto/tls/testdata/Client-TLSv10-RSA-RC4 +++ b/src/crypto/tls/testdata/Client-TLSv10-RSA-RC4 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 01 00 51 02 00 00 4d 03 01 5a 4f 78 41 d5 |....Q...M..ZOxA.| -00000010 86 2f d2 0a c6 05 bc c9 8e cc bd b2 39 ac a5 78 |./..........9..x| -00000020 e3 e5 31 b9 cb 01 af cb ca fc 88 20 c9 61 c6 91 |..1........ .a..| -00000030 b2 e5 70 df ca d0 41 a8 20 61 ab 08 f6 dc fe c0 |..p...A. a......| -00000040 cc ea 1e 80 89 02 6a 26 ea f0 c8 71 00 05 00 00 |......j&...q....| +00000000 16 03 01 00 51 02 00 00 4d 03 01 a7 f4 fa b1 c3 |....Q...M.......| +00000010 56 41 ee 50 d8 06 78 e3 51 7f 91 b1 67 6c 75 eb |VA.P..x.Q...glu.| +00000020 66 8c 79 42 96 3a a8 17 e9 fa 2c 20 11 0f 59 3c |f.yB.:...., ..Y<| +00000030 b5 76 31 d1 d6 86 2f 49 a6 c0 61 68 9f 2a a5 31 |.v1.../I..ah.*.1| +00000040 8a 88 f6 87 a5 2f 8c 5e 58 69 4c ca 00 05 00 00 |...../.^XiL.....| 00000050 05 ff 01 00 01 00 16 03 01 02 59 0b 00 02 55 00 |..........Y...U.| 00000060 02 52 00 02 4f 30 82 02 4b 30 82 01 b4 a0 03 02 |.R..O0..K0......| 00000070 01 02 02 09 00 e8 f0 9d 3f e2 5b ea a6 30 0d 06 |........?.[..0..| @@ -70,15 +71,15 @@ 00000060 c5 70 0f 08 83 48 e9 48 ef 6e 50 8b 05 7e e5 84 |.p...H.H.nP..~..| 00000070 25 fa 55 c7 ae 31 02 27 00 ef 3f 98 86 20 12 89 |%.U..1.'..?.. ..| 00000080 91 59 28 b4 f7 d7 af d2 69 61 35 14 03 01 00 01 |.Y(.....ia5.....| -00000090 01 16 03 01 00 24 48 fd e6 fc 4a 94 33 82 22 ff |.....$H...J.3.".| -000000a0 af c3 44 98 d2 c6 4e 8a 39 43 dd 4b 2a 11 2b 4e |..D...N.9C.K*.+N| -000000b0 5b d9 a4 fc 6c 95 d7 69 05 f9 |[...l..i..| +00000090 01 16 03 01 00 24 81 95 12 51 f1 9f b1 e9 e6 6c |.....$...Q.....l| +000000a0 f3 99 46 e8 06 da 32 95 41 a5 c8 16 ab 4d 1c 14 |..F...2.A....M..| +000000b0 c0 cd 85 4d b8 2d 32 f3 f6 c5 |...M.-2...| >>> Flow 4 (server to client) -00000000 14 03 01 00 01 01 16 03 01 00 24 61 d2 68 5e 12 |..........$a.h^.| -00000010 91 6e 7f fe bf b7 42 58 e9 06 38 09 c1 16 34 e5 |.n....BX..8...4.| -00000020 a1 46 d6 cf 23 ca 48 c1 ed 76 f9 48 a1 9a 2a |.F..#.H..v.H..*| +00000000 14 03 01 00 01 01 16 03 01 00 24 a1 9e 5d a3 28 |..........$..].(| +00000010 89 5c f9 9d 4d 92 e3 2d f5 47 4c 10 7b b7 16 99 |.\..M..-.GL.{...| +00000020 ab cb ca ba 16 ae c6 0a d7 a0 6d e6 ef 61 02 |..........m..a.| >>> Flow 5 (client to server) -00000000 17 03 01 00 1a 3a e1 39 7c fe 25 50 dc 66 3f b6 |.....:.9|.%P.f?.| -00000010 6f fd 79 3b 12 83 af 89 b1 c5 f6 75 56 ad a1 15 |o.y;.......uV...| -00000020 03 01 00 16 07 d1 d3 7a 54 1c 71 0b c8 64 10 46 |.......zT.q..d.F| -00000030 30 d0 bf df 75 a6 dc 10 b1 d1 |0...u.....| +00000000 17 03 01 00 1a a4 17 5d 86 5f 12 6d 11 9b 1f 24 |.......]._.m...$| +00000010 7c bf 02 10 6b 15 c7 de b7 2c e3 c8 50 78 d3 15 ||...k....,..Px..| +00000020 03 01 00 16 78 23 fb 7b 9a 20 d2 97 4a 66 f0 b0 |....x#.{. ..Jf..| +00000030 8b 1a 30 c1 80 95 c4 01 df fb |..0.......| diff --git a/src/crypto/tls/testdata/Client-TLSv11-ECDHE-ECDSA-AES b/src/crypto/tls/testdata/Client-TLSv11-ECDHE-ECDSA-AES index 9d18cd62f78..daf8751fe4a 100644 --- a/src/crypto/tls/testdata/Client-TLSv11-ECDHE-ECDSA-AES +++ b/src/crypto/tls/testdata/Client-TLSv11-ECDHE-ECDSA-AES @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 02 00 59 02 00 00 55 03 02 23 a8 e7 14 3f |....Y...U..#...?| -00000010 64 61 3c ee 80 a2 94 84 ab b8 66 76 30 84 06 78 |da<.......fv0..x| -00000020 96 ba a7 d3 1e 81 1b 16 64 76 88 20 3d 21 21 b3 |........dv. =!!.| -00000030 45 dd fe cb 5b d7 9a 86 39 ee 4f f8 60 eb 95 ea |E...[...9.O.`...| -00000040 ab 64 48 14 74 16 fd e9 47 07 66 60 c0 09 00 00 |.dH.t...G.f`....| +00000000 16 03 02 00 59 02 00 00 55 03 02 77 d6 3f 36 77 |....Y...U..w.?6w| +00000010 f5 77 b8 09 20 83 9d a7 fa 72 54 2e e7 06 df 30 |.w.. ....rT....0| +00000020 91 f4 2c 17 e8 31 bd b3 c0 30 28 20 fd 71 e6 61 |..,..1...0( .q.a| +00000030 38 0e f0 8b 6f d4 8e 9f e0 ce 34 4d 49 39 aa af |8...o.....4MI9..| +00000040 24 bd 5d 8d ab a1 dc d2 da b2 cc b1 c0 09 00 00 |$.].............| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 02 02 0e 0b 00 02 0a 00 02 07 00 02 04 30 82 02 |.............0..| 00000070 00 30 82 01 62 02 09 00 b8 bf 2d 47 a0 d2 eb f4 |.0..b.....-G....| @@ -55,39 +56,39 @@ 00000240 13 83 0d 94 06 bb d4 37 7a f6 ec 7a c9 86 2e dd |.......7z..z....| 00000250 d7 11 69 7f 85 7c 56 de fb 31 78 2b e4 c7 78 0d |..i..|V..1x+..x.| 00000260 ae cb be 9e 4e 36 24 31 7b 6a 0f 39 95 12 07 8f |....N6$1{j.9....| -00000270 2a 16 03 02 00 b4 0c 00 00 b0 03 00 1d 20 a7 a4 |*............ ..| -00000280 33 20 48 6a 74 8e 07 fc c0 b6 10 61 84 d6 67 d1 |3 Hjt......a..g.| -00000290 ae cf 65 36 4d d5 13 a1 07 fc 1f aa 77 44 00 8a |..e6M.......wD..| -000002a0 30 81 87 02 42 01 02 5b f9 4a af 8d 0a d5 a3 de |0...B..[.J......| -000002b0 11 62 d8 f1 db 49 7a 0c 34 3e 2d 61 f9 6f 6b c2 |.b...Iz.4>-a.ok.| -000002c0 1d 32 4b 88 93 9b 22 b0 3d 09 c3 93 9e 25 31 d6 |.2K...".=....%1.| -000002d0 5f 06 3a f0 4a 61 0b 06 03 5d 6c 0e b3 5e 48 5a |_.:.Ja...]l..^HZ| -000002e0 f0 5b 21 48 58 8f b2 02 41 1c 57 f1 51 04 d6 f8 |.[!HX...A.W.Q...| -000002f0 a2 51 e6 e6 3e e0 99 63 aa d2 1c 7b 92 be 44 ec |.Q..>..c...{..D.| -00000300 86 c3 31 fa e7 9b 98 1a 59 a5 93 3e a9 73 f0 ec |..1.....Y..>.s..| -00000310 03 22 37 19 db 78 30 27 ab bf 52 07 6c 3a 79 f5 |."7..x0'..R.l:y.| -00000320 ad 70 59 76 84 44 f0 47 e0 3d 16 03 02 00 04 0e |.pYv.D.G.=......| +00000270 2a 16 03 02 00 b4 0c 00 00 b0 03 00 1d 20 97 d9 |*............ ..| +00000280 56 76 3f 33 c5 d1 3b 84 a3 4b 2f d0 17 5e 8d ea |Vv?3..;..K/..^..| +00000290 bd b0 4f ec a1 e5 a9 55 4a 54 6a fd 07 1f 00 8a |..O....UJTj.....| +000002a0 30 81 87 02 42 01 37 34 a5 a1 76 63 e6 32 53 cc |0...B.74..vc.2S.| +000002b0 d3 be 40 c1 63 22 6e ff 45 51 a0 12 e5 8d 33 33 |..@.c"n.EQ....33| +000002c0 f6 d7 5d d5 88 2d e2 97 9a 23 ef 40 20 b1 ef 95 |..]..-...#.@ ...| +000002d0 75 d3 8d c8 8d f4 70 a0 9a 08 21 74 fa 37 11 da |u.....p...!t.7..| +000002e0 87 95 db 5e 50 72 ca 02 41 3d 6d 92 da 72 b6 c0 |...^Pr..A=m..r..| +000002f0 92 58 66 62 1f fc fa fc 0e 69 89 b5 d2 3a a1 43 |.Xfb.....i...:.C| +00000300 0d d5 0d 84 47 18 a9 7a 41 a0 96 6a f0 92 d5 18 |....G..zA..j....| +00000310 43 61 a1 fb 37 ec dc 17 64 19 90 d2 40 81 60 04 |Ca..7...d...@.`.| +00000320 69 84 87 de 5b 28 97 e7 3c f8 16 03 02 00 04 0e |i...[(..<.......| 00000330 00 00 00 |...| >>> Flow 3 (client to server) 00000000 16 03 02 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 02 00 01 01 |....._X.;t......| 00000030 16 03 02 00 40 00 00 00 00 00 00 00 00 00 00 00 |....@...........| -00000040 00 00 00 00 00 ef 0f 92 ac 11 fe 97 1a 46 69 e4 |.............Fi.| -00000050 b3 26 8d d7 92 46 02 25 5b 2e 86 3e 96 3d 64 ed |.&...F.%[..>.=d.| -00000060 37 92 dd ae a5 a6 9f 03 f0 c2 42 78 9f b9 78 ac |7.........Bx..x.| -00000070 97 ab 82 25 e2 |...%.| +00000040 00 00 00 00 00 22 bd 55 82 cc eb ee b1 27 b5 ed |.....".U.....'..| +00000050 9c 8b 4c ff 29 9f 96 b4 74 87 17 32 88 1a 79 10 |..L.)...t..2..y.| +00000060 15 76 99 69 14 59 f8 12 fa df cc b7 77 f2 9c 77 |.v.i.Y......w..w| +00000070 b5 6d 76 21 a2 |.mv!.| >>> Flow 4 (server to client) -00000000 14 03 02 00 01 01 16 03 02 00 40 df a9 23 37 74 |..........@..#7t| -00000010 47 d8 98 87 53 b4 0a 4d b0 a5 fb cb d6 37 c8 7c |G...S..M.....7.|| -00000020 61 95 81 ef b3 63 78 2b 53 c2 86 fc 39 df c4 5f |a....cx+S...9.._| -00000030 e4 4b af 1d fe bc 4c fe 1b 6a 28 c3 46 6f 24 94 |.K....L..j(.Fo$.| -00000040 a8 bf ef ce e8 e8 ad 2c d9 10 32 |.......,..2| +00000000 14 03 02 00 01 01 16 03 02 00 40 c9 22 47 ac 83 |..........@."G..| +00000010 63 94 57 75 e5 b1 de 1a 74 81 f1 97 47 39 fc e1 |c.Wu....t...G9..| +00000020 9a 2a 15 2e 6f b3 d3 8a d1 66 6d f1 32 12 b4 a6 |.*..o....fm.2...| +00000030 73 ee c7 c1 85 b4 3b c4 28 b9 1b 58 09 6d 0b 1d |s.....;.(..X.m..| +00000040 c3 01 a2 6f 3a b6 c1 cc c1 80 ba |...o:......| >>> Flow 5 (client to server) 00000000 17 03 02 00 30 00 00 00 00 00 00 00 00 00 00 00 |....0...........| -00000010 00 00 00 00 00 34 50 ce 9c 7f f5 2d a2 c1 e4 5c |.....4P....-...\| -00000020 fa d1 a0 f4 38 e8 4f 51 54 36 07 da f1 af 6d ef |....8.OQT6....m.| -00000030 b8 b0 bc bc a6 15 03 02 00 30 00 00 00 00 00 00 |.........0......| -00000040 00 00 00 00 00 00 00 00 00 00 0b d4 8e e8 69 64 |..............id| -00000050 53 38 7c 72 d8 1d 9f d5 8a 83 74 a7 37 6b e2 c0 |S8|r......t.7k..| -00000060 8f 26 e7 5d 0e 06 ae e0 db fb |.&.]......| +00000010 00 00 00 00 00 3c 0a 48 88 c2 b3 41 fd e7 c3 57 |.....<.H...A...W| +00000020 b3 21 e0 80 ee 87 5c f0 de 12 fd 57 22 2d b6 78 |.!....\....W"-.x| +00000030 c0 c3 b0 0f 9e 15 03 02 00 30 00 00 00 00 00 00 |.........0......| +00000040 00 00 00 00 00 00 00 00 00 00 c8 bb 12 d1 8b ed |................| +00000050 df 02 4b 65 ab 98 ec 48 c3 25 06 e3 2c c4 0c 60 |..Ke...H.%..,..`| +00000060 7a 5d 96 c0 11 63 a9 d5 36 77 |z]...c..6w| diff --git a/src/crypto/tls/testdata/Client-TLSv11-ECDHE-RSA-AES b/src/crypto/tls/testdata/Client-TLSv11-ECDHE-RSA-AES index 4cc9610faa9..91890a99f7a 100644 --- a/src/crypto/tls/testdata/Client-TLSv11-ECDHE-RSA-AES +++ b/src/crypto/tls/testdata/Client-TLSv11-ECDHE-RSA-AES @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 02 00 59 02 00 00 55 03 02 6e ff 3b 26 66 |....Y...U..n.;&f| -00000010 7c 32 3f 42 fd 92 7c 12 db 26 b2 45 6e 28 b9 49 ||2?B..|..&.En(.I| -00000020 86 6b 00 54 92 3b 65 a6 02 6d 94 20 ea 44 db 5c |.k.T.;e..m. .D.\| -00000030 d1 39 35 b2 ea 1c 6d 3e 94 bb 47 60 25 1e 9c 74 |.95...m>..G`%..t| -00000040 e7 bd 54 cc 2b 36 14 6a 12 54 5b 6c c0 13 00 00 |..T.+6.j.T[l....| +00000000 16 03 02 00 59 02 00 00 55 03 02 c7 27 0a b6 97 |....Y...U...'...| +00000010 a8 92 c9 66 6b 74 51 8b aa 8d 6d f6 af e3 e0 d9 |...fktQ...m.....| +00000020 c6 a4 7a b6 02 af 10 80 60 07 22 20 b8 56 69 47 |..z.....`." .ViG| +00000030 36 42 b0 7f e1 d2 ca 03 cb 01 05 01 dc 3b 5c 0e |6B...........;\.| +00000040 8f df e7 b3 e1 d6 3e fc 19 c3 8f 02 c0 13 00 00 |......>.........| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 02 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,38 +61,38 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 02 00 |.=.`.\!.;.......| -000002c0 aa 0c 00 00 a6 03 00 1d 20 82 3b d2 56 dd cd d8 |........ .;.V...| -000002d0 e1 98 a7 90 d1 08 2d 37 dc e8 21 cd 29 af 29 a5 |......-7..!.).).| -000002e0 78 8e 59 9e 4c ac c9 d2 4b 00 80 25 20 91 4e 0d |x.Y.L...K..% .N.| -000002f0 74 12 9e 1c 98 fb 5f 4b ad fd c8 68 df 6b 82 98 |t....._K...h.k..| -00000300 a8 7c ee 17 44 47 91 2a 42 c1 82 d0 ce aa cd f8 |.|..DG.*B.......| -00000310 69 1e 85 79 27 fe ef 5a a2 e1 35 30 9a 2d c6 b0 |i..y'..Z..50.-..| -00000320 43 84 39 7f 8d 68 09 d6 6c 1a 84 0f c0 9a c0 9f |C.9..h..l.......| -00000330 64 56 cb fc 32 f2 4a a3 26 e8 c2 5f d7 16 3e 7c |dV..2.J.&.._..>|| -00000340 4e 8b 89 f8 7f f4 c2 26 fe 01 cd 48 b6 61 9c 93 |N......&...H.a..| -00000350 1a bc a1 d1 01 c5 bf ef 43 b4 ca 86 62 37 b4 99 |........C...b7..| -00000360 54 69 db 74 51 92 92 dd c1 b1 75 16 03 02 00 04 |Ti.tQ.....u.....| +000002c0 aa 0c 00 00 a6 03 00 1d 20 24 ce ed 44 cd 10 38 |........ $..D..8| +000002d0 f2 27 1c c9 55 a0 20 e1 09 dd 8a 0b 73 42 1f 54 |.'..U. .....sB.T| +000002e0 3e 49 97 99 e9 da fe b3 11 00 80 8b 43 4d 5e 90 |>I..........CM^.| +000002f0 c2 f0 6a 0a 8f f9 c1 8c 41 cc 9e 53 8e 9e 3e 38 |..j.....A..S..>8| +00000300 54 74 65 d6 14 c1 10 e8 0e b5 26 22 2f 8e 8a e4 |Tte.......&"/...| +00000310 b3 ea 37 aa 86 7f a7 7a 95 91 98 f3 a0 90 87 19 |..7....z........| +00000320 c0 9e c5 ed 84 a7 78 8c d3 b1 84 5e 68 6f bc ac |......x....^ho..| +00000330 84 7c 12 ec e6 d8 17 56 e4 60 ab 05 6b e5 6d f7 |.|.....V.`..k.m.| +00000340 ec cc ac a6 ab 78 fc 2e 46 4f e7 1a 84 8b 4f d7 |.....x..FO....O.| +00000350 b0 83 d7 9d fc e6 a9 b8 cf 17 ca 4f a2 70 90 cf |...........O.p..| +00000360 26 a7 60 35 69 2f 39 fb 6b a9 e3 16 03 02 00 04 |&.`5i/9.k.......| 00000370 0e 00 00 00 |....| >>> Flow 3 (client to server) 00000000 16 03 02 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 02 00 01 01 |....._X.;t......| 00000030 16 03 02 00 40 00 00 00 00 00 00 00 00 00 00 00 |....@...........| -00000040 00 00 00 00 00 c5 bf e6 b3 86 12 92 df 68 fa 75 |.............h.u| -00000050 79 5f ee fe 60 91 d1 fd 8a 48 3b 97 b4 da 7f 58 |y_..`....H;....X| -00000060 3e 7e 40 d7 93 1d 6b e2 0e 2a a4 45 20 e0 9d f9 |>~@...k..*.E ...| -00000070 b6 5e b1 f1 4f |.^..O| +00000040 00 00 00 00 00 62 8b 44 45 f6 55 4e 13 ea 56 5d |.....b.DE.UN..V]| +00000050 5a 43 35 df e4 4f ca 76 94 b5 61 f7 86 55 c9 8f |ZC5..O.v..a..U..| +00000060 32 c8 85 5c c9 c6 56 c6 df c5 36 de 9f f2 e3 b4 |2..\..V...6.....| +00000070 32 42 44 37 af |2BD7.| >>> Flow 4 (server to client) -00000000 14 03 02 00 01 01 16 03 02 00 40 bf 58 92 80 02 |..........@.X...| -00000010 75 91 40 30 35 e0 16 76 f4 97 bd 77 46 a3 a3 4e |u.@05..v...wF..N| -00000020 f1 be 53 eb b8 56 45 b1 71 c9 f8 a9 bf c6 9a 00 |..S..VE.q.......| -00000030 83 46 91 88 d5 7b 72 95 27 33 80 43 3f 3e f6 60 |.F...{r.'3.C?>.`| -00000040 c6 55 90 6a 87 8e 7d 48 27 e2 40 |.U.j..}H'.@| +00000000 14 03 02 00 01 01 16 03 02 00 40 57 5b bd 27 e5 |..........@W[.'.| +00000010 b1 8a 99 9d e1 3d 54 e7 ce cb e3 d4 1c 26 3e ff |.....=T......&>.| +00000020 ba 22 ca 85 3a 6b 1d 0a 87 9a 92 ff 77 f4 69 88 |."..:k......w.i.| +00000030 96 3e 9d 0b a5 11 70 66 d3 7c 74 c0 61 78 9b 3a |.>....pf.|t.ax.:| +00000040 7f 3c 5b ee 11 08 51 a5 05 f4 e4 |.<[...Q....| >>> Flow 5 (client to server) 00000000 17 03 02 00 30 00 00 00 00 00 00 00 00 00 00 00 |....0...........| -00000010 00 00 00 00 00 f5 6b bc 6d 2c 70 b1 c0 f0 ab 78 |......k.m,p....x| -00000020 44 c9 97 f6 59 ef 15 e4 05 cf e0 55 ee a4 68 8c |D...Y......U..h.| -00000030 86 57 82 bd 84 15 03 02 00 30 00 00 00 00 00 00 |.W.......0......| -00000040 00 00 00 00 00 00 00 00 00 00 ef b2 a9 a5 bb a3 |................| -00000050 6e e5 d1 2b ef 83 1d 11 de 29 d2 30 2c fc 78 73 |n..+.....).0,.xs| -00000060 6b 6e 0a d2 55 67 5c d4 58 b3 |kn..Ug\.X.| +00000010 00 00 00 00 00 9f 57 79 18 e7 e5 82 a3 75 7f 54 |......Wy.....u.T| +00000020 71 19 05 d6 ce 39 00 f6 6b 61 0c 10 83 ea db 2b |q....9..ka.....+| +00000030 da 0b 04 54 30 15 03 02 00 30 00 00 00 00 00 00 |...T0....0......| +00000040 00 00 00 00 00 00 00 00 00 00 e9 44 fe 1d 86 26 |...........D...&| +00000050 bd 39 23 e6 ae 23 dc 8f 15 03 1e e0 cb 03 ed 25 |.9#..#.........%| +00000060 e1 20 f5 c4 97 2d 97 09 85 92 |. ...-....| diff --git a/src/crypto/tls/testdata/Client-TLSv11-RSA-RC4 b/src/crypto/tls/testdata/Client-TLSv11-RSA-RC4 index 9dae5dd6d2b..3800507c7e1 100644 --- a/src/crypto/tls/testdata/Client-TLSv11-RSA-RC4 +++ b/src/crypto/tls/testdata/Client-TLSv11-RSA-RC4 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 02 00 51 02 00 00 4d 03 02 96 ca 2a e7 23 |....Q...M....*.#| -00000010 af 2e 45 62 15 fa 5a 84 bc aa 7c 79 03 1b 37 69 |..Eb..Z...|y..7i| -00000020 a0 77 ce 03 81 b7 e5 7d 31 34 6e 20 93 83 5d 7c |.w.....}14n ..]|| -00000030 e8 c7 48 f9 67 ec 97 b1 27 b6 de de 89 07 5a cf |..H.g...'.....Z.| -00000040 44 77 48 4b e9 62 43 e3 87 fd de 87 00 05 00 00 |DwHK.bC.........| +00000000 16 03 02 00 51 02 00 00 4d 03 02 e7 2b 18 8e de |....Q...M...+...| +00000010 7e 22 f4 88 eb 89 05 74 40 7f a8 bb f0 77 46 61 |~".....t@....wFa| +00000020 d8 33 16 24 61 5c 2a e8 7a a2 cf 20 df f8 b0 60 |.3.$a\*.z.. ...`| +00000030 ec 21 2c 66 8a 2b 48 7d 82 5a ac 48 27 55 80 e3 |.!,f.+H}.Z.H'U..| +00000040 7c 11 33 53 8b 15 a3 78 e8 70 8b c0 00 05 00 00 ||.3S...x.p......| 00000050 05 ff 01 00 01 00 16 03 02 02 59 0b 00 02 55 00 |..........Y...U.| 00000060 02 52 00 02 4f 30 82 02 4b 30 82 01 b4 a0 03 02 |.R..O0..K0......| 00000070 01 02 02 09 00 e8 f0 9d 3f e2 5b ea a6 30 0d 06 |........?.[..0..| @@ -70,15 +71,15 @@ 00000060 c5 70 0f 08 83 48 e9 48 ef 6e 50 8b 05 7e e5 84 |.p...H.H.nP..~..| 00000070 25 fa 55 c7 ae 31 02 27 00 ef 3f 98 86 20 12 89 |%.U..1.'..?.. ..| 00000080 91 59 28 b4 f7 d7 af d2 69 61 35 14 03 02 00 01 |.Y(.....ia5.....| -00000090 01 16 03 02 00 24 33 5d 7f cb 6e 36 19 8b db 35 |.....$3]..n6...5| -000000a0 88 16 87 7a 9d 5a 51 27 51 13 17 64 0e 57 d5 e1 |...z.ZQ'Q..d.W..| -000000b0 6e 34 8d e6 99 a8 38 b2 e7 3a |n4....8..:| +00000090 01 16 03 02 00 24 77 f4 62 23 62 e6 e2 6b fc 9b |.....$w.b#b..k..| +000000a0 c2 29 77 67 bb ac 78 cd 20 90 17 b7 9a f1 2d c4 |.)wg..x. .....-.| +000000b0 5e db 21 8f 71 0a 11 6e 48 64 |^.!.q..nHd| >>> Flow 4 (server to client) -00000000 14 03 02 00 01 01 16 03 02 00 24 e0 8b 90 9b 83 |..........$.....| -00000010 f5 3d 00 e9 cf 7b 1d 75 cf c8 16 f2 29 8d de 0b |.=...{.u....)...| -00000020 75 82 b1 c4 6e 1c 1f ab e9 90 74 31 99 f2 ad |u...n.....t1...| +00000000 14 03 02 00 01 01 16 03 02 00 24 ec 8e b9 25 f2 |..........$...%.| +00000010 8c 0c 1d 81 68 50 35 51 69 4a 42 57 8c 01 80 31 |....hP5QiJBW...1| +00000020 85 6e 7e 98 fc b8 e0 44 e9 11 44 6c a7 94 68 |.n~....D..Dl..h| >>> Flow 5 (client to server) -00000000 17 03 02 00 1a ca 2a 95 13 de 40 0d af 44 a4 aa |......*...@..D..| -00000010 9a 35 d7 38 c7 9f 74 4f 3a bf d1 9c cd 9e ee 15 |.5.8..tO:.......| -00000020 03 02 00 16 d3 a4 32 78 a9 00 1b 7a 48 3e 7c 2b |......2x...zH>|+| -00000030 f9 3b 92 32 20 0b f4 16 39 18 |.;.2 ...9.| +00000000 17 03 02 00 1a 93 4b 7b 22 03 68 d4 ae 49 ab 81 |......K{".h..I..| +00000010 98 f8 2d f0 3b aa c8 2d 98 6e b9 4a f5 97 0b 15 |..-.;..-.n.J....| +00000020 03 02 00 16 db 25 8b 2b 6b fa 67 30 3e f9 93 3f |.....%.+k.g0>..?| +00000030 50 37 89 ff 4c c3 29 71 bc ba |P7..L.)q..| diff --git a/src/crypto/tls/testdata/Client-TLSv12-AES128-GCM-SHA256 b/src/crypto/tls/testdata/Client-TLSv12-AES128-GCM-SHA256 index 4412f53c90a..7b22b146d08 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-AES128-GCM-SHA256 +++ b/src/crypto/tls/testdata/Client-TLSv12-AES128-GCM-SHA256 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 51 02 00 00 4d 03 03 1d be be 1e eb |....Q...M.......| -00000010 59 2c d5 07 b9 7a 64 47 95 84 ef cf d9 3e 82 4c |Y,...zdG.....>.L| -00000020 00 c0 0a 69 8a 01 2a b3 42 78 02 20 5e 32 5c 88 |...i..*.Bx. ^2\.| -00000030 50 ed d5 44 41 4f bf a9 4e 49 83 5d aa 7c 2e 5d |P..DAO..NI.].|.]| -00000040 85 e8 64 92 5e 49 5d 8a d0 0e 89 eb 00 9c 00 00 |..d.^I].........| +00000000 16 03 03 00 51 02 00 00 4d 03 03 ae d0 31 95 45 |....Q...M....1.E| +00000010 6c f4 35 a9 da bb 77 6b 67 fb d9 67 1d 25 85 16 |l.5...wkg..g.%..| +00000020 be ed c5 e6 e5 ee 03 a8 7a 50 ed 20 48 6a 6b 45 |........zP. HjkE| +00000030 bf 52 09 aa 65 0e fd 89 df 46 88 21 a2 e9 e0 dc |.R..e....F.!....| +00000040 0a 2b 1d 10 e0 95 a2 11 cf 10 f2 0c 00 9c 00 00 |.+..............| 00000050 05 ff 01 00 01 00 16 03 03 02 59 0b 00 02 55 00 |..........Y...U.| 00000060 02 52 00 02 4f 30 82 02 4b 30 82 01 b4 a0 03 02 |.R..O0..K0......| 00000070 01 02 02 09 00 e8 f0 9d 3f e2 5b ea a6 30 0d 06 |........?.[..0..| @@ -70,17 +71,17 @@ 00000060 c5 70 0f 08 83 48 e9 48 ef 6e 50 8b 05 7e e5 84 |.p...H.H.nP..~..| 00000070 25 fa 55 c7 ae 31 02 27 00 ef 3f 98 86 20 12 89 |%.U..1.'..?.. ..| 00000080 91 59 28 b4 f7 d7 af d2 69 61 35 14 03 03 00 01 |.Y(.....ia5.....| -00000090 01 16 03 03 00 28 00 00 00 00 00 00 00 00 69 38 |.....(........i8| -000000a0 97 84 2e 77 5c b8 58 82 b5 78 85 2e f3 7b 92 81 |...w\.X..x...{..| -000000b0 00 72 91 23 41 ae 59 6c 18 64 f0 62 f2 c9 |.r.#A.Yl.d.b..| +00000090 01 16 03 03 00 28 00 00 00 00 00 00 00 00 d0 4c |.....(.........L| +000000a0 55 b1 06 02 5d 29 6e 16 5e 00 85 d7 06 4d f6 8b |U...])n.^....M..| +000000b0 af c5 95 44 8f c6 8e 06 d4 40 1a 2d c9 a6 |...D.....@.-..| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 28 37 f7 98 2f 78 |..........(7../x| -00000010 54 85 5f 2e cb a9 b7 bf 4b 2d 62 06 e2 32 cd 18 |T._.....K-b..2..| -00000020 de f5 54 c8 e0 54 2d c5 b4 98 07 7e c7 b7 79 a0 |..T..T-....~..y.| -00000030 75 af 5c |u.\| +00000000 14 03 03 00 01 01 16 03 03 00 28 5c 79 2c 38 4f |..........(\y,8O| +00000010 4b c9 54 5c 9b fc 4a 07 6c 2b 2f 8a 4c 08 9d df |K.T\..J.l+/.L...| +00000020 00 74 ba 05 83 af f3 42 49 3f 80 f6 9e be 52 db |.t.....BI?....R.| +00000030 e8 00 cb |...| >>> Flow 5 (client to server) -00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 78 c1 c0 |.............x..| -00000010 7d 1b a8 b2 80 0e a3 64 cf e0 fa 71 9d 37 5d 32 |}......d...q.7]2| -00000020 8d 36 38 15 03 03 00 1a 00 00 00 00 00 00 00 02 |.68.............| -00000030 c2 f3 41 1a 2c a4 4f 48 fa 61 14 40 60 51 e5 99 |..A.,.OH.a.@`Q..| -00000040 c6 e5 |..| +00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 c0 8a 95 |................| +00000010 76 88 19 b9 43 d3 b2 92 63 bb 6d 66 85 ac b0 1f |v...C...c.mf....| +00000020 98 ec 6b 15 03 03 00 1a 00 00 00 00 00 00 00 02 |..k.............| +00000030 37 63 81 d9 8a 57 0c 11 9c fe 47 c9 9b 9d 07 2a |7c...W....G....*| +00000040 30 3b |0;| diff --git a/src/crypto/tls/testdata/Client-TLSv12-AES128-SHA256 b/src/crypto/tls/testdata/Client-TLSv12-AES128-SHA256 index d7568843b48..06404ba62c1 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-AES128-SHA256 +++ b/src/crypto/tls/testdata/Client-TLSv12-AES128-SHA256 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 51 02 00 00 4d 03 03 c3 41 d7 9c 1b |....Q...M...A...| -00000010 9a ff f8 17 af 41 df 8d 96 70 bb b8 f6 9a 4c a2 |.....A...p....L.| -00000020 03 25 31 2c 58 fa 05 5b 12 85 6a 20 18 3c 34 d6 |.%1,X..[..j .<4.| -00000030 08 44 46 a5 5c b1 40 0d 38 33 c0 2d ea a6 46 53 |.DF.\.@.83.-..FS| -00000040 0e 09 39 6f 11 35 02 63 cf 21 74 c2 00 3c 00 00 |..9o.5.c.!t..<..| +00000000 16 03 03 00 51 02 00 00 4d 03 03 e4 96 d5 7c eb |....Q...M.....|.| +00000010 86 62 12 b6 4f da a0 d6 6c a6 65 56 41 42 78 c6 |.b..O...l.eVABx.| +00000020 7c 32 5b eb 08 8d 5f d2 95 94 14 20 85 ca 35 d3 ||2[..._.... ..5.| +00000030 6a b2 f9 29 eb 26 d6 40 2a 92 98 49 d7 17 5d 97 |j..).&.@*..I..].| +00000040 cc e8 05 89 1b 4e 50 06 b5 6c 32 bb 00 3c 00 00 |.....NP..l2..<..| 00000050 05 ff 01 00 01 00 16 03 03 02 59 0b 00 02 55 00 |..........Y...U.| 00000060 02 52 00 02 4f 30 82 02 4b 30 82 01 b4 a0 03 02 |.R..O0..K0......| 00000070 01 02 02 09 00 e8 f0 9d 3f e2 5b ea a6 30 0d 06 |........?.[..0..| @@ -71,25 +72,25 @@ 00000070 25 fa 55 c7 ae 31 02 27 00 ef 3f 98 86 20 12 89 |%.U..1.'..?.. ..| 00000080 91 59 28 b4 f7 d7 af d2 69 61 35 14 03 03 00 01 |.Y(.....ia5.....| 00000090 01 16 03 03 00 50 00 00 00 00 00 00 00 00 00 00 |.....P..........| -000000a0 00 00 00 00 00 00 88 20 99 51 5e fb 72 79 7f f8 |....... .Q^.ry..| -000000b0 b2 a9 56 96 a3 03 1d a0 e0 38 1a be 4c ea 80 f9 |..V......8..L...| -000000c0 c0 ef 45 81 91 7f b9 1b f7 91 3b 4e 05 87 d6 73 |..E.......;N...s| -000000d0 c0 27 94 50 4f 00 ee c1 02 af 5f 6f 4c a5 0e 5b |.'.PO....._oL..[| -000000e0 6c 76 87 28 b4 bf |lv.(..| +000000a0 00 00 00 00 00 00 dd 45 b3 fd 7a 03 ef 42 de e8 |.......E..z..B..| +000000b0 6d 39 37 fa a4 9c 0f df c8 3f b2 02 73 c9 28 02 |m97......?..s.(.| +000000c0 f6 6d e6 56 b7 ac 78 1f 39 bb 04 c2 c9 f8 46 d7 |.m.V..x.9.....F.| +000000d0 ca 26 09 8e 30 21 76 9a 28 da 0f e3 ec bd 30 f5 |.&..0!v.(.....0.| +000000e0 ed 7b 33 52 01 49 |.{3R.I| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 50 93 14 a5 13 16 |..........P.....| -00000010 d7 af 14 81 94 33 2d ae f7 7a b1 b1 a5 38 fb e8 |.....3-..z...8..| -00000020 c8 38 b3 ce f1 eb 70 e7 84 b6 fc 25 25 32 a9 09 |.8....p....%%2..| -00000030 d1 0d 2d 59 57 6d d0 42 e8 c1 81 92 d0 af fb 5a |..-YWm.B.......Z| -00000040 08 7e 0f 3d 10 e5 42 6d 27 cd 8c 32 b2 20 4b 0a |.~.=..Bm'..2. K.| -00000050 75 76 ed 08 54 fe 74 94 72 35 9e |uv..T.t.r5.| +00000000 14 03 03 00 01 01 16 03 03 00 50 fa e4 85 82 d1 |..........P.....| +00000010 45 48 15 51 bd 34 66 82 09 7f 9a 8f eb 6f b4 d7 |EH.Q.4f......o..| +00000020 e5 1e 6d 68 cf 6f 77 58 30 f8 13 7a fd 69 cb 3b |..mh.owX0..z.i.;| +00000030 70 47 8d 61 77 cc 32 41 e1 10 c5 c5 cb 4d 30 89 |pG.aw.2A.....M0.| +00000040 23 68 56 01 09 32 cd 10 05 9a 4a a8 29 f6 11 8e |#hV..2....J.)...| +00000050 82 dd 64 be f9 5d fe f8 b3 25 23 |..d..]...%#| >>> Flow 5 (client to server) 00000000 17 03 03 00 40 00 00 00 00 00 00 00 00 00 00 00 |....@...........| -00000010 00 00 00 00 00 53 91 38 34 33 20 94 0d 76 d7 72 |.....S.843 ..v.r| -00000020 48 f3 17 34 01 ae 0e 89 db 60 f1 4e 64 a5 cf 0c |H..4.....`.Nd...| -00000030 32 52 3f a0 18 f8 c5 57 ed 3a d1 41 19 81 cf 0a |2R?....W.:.A....| -00000040 f2 d8 90 4b ba 15 03 03 00 40 00 00 00 00 00 00 |...K.....@......| -00000050 00 00 00 00 00 00 00 00 00 00 05 2b 31 3c 1b a2 |...........+1<..| -00000060 11 87 5f 0f 49 72 bb 67 e6 75 18 9c b1 f4 6c ed |.._.Ir.g.u....l.| -00000070 4d 01 58 35 30 43 44 e8 ee 1d f2 81 9d 67 6d 77 |M.X50CD......gmw| -00000080 1e 36 61 7f f3 32 3d 60 73 6d |.6a..2=`sm| +00000010 00 00 00 00 00 24 d5 22 c0 a5 1d b8 15 f7 ac 09 |.....$."........| +00000020 ae b6 0e ee 3f 41 8a aa bf 61 44 f8 ff 69 20 6b |....?A...aD..i k| +00000030 36 1d e1 78 40 64 5f d9 8f d0 ca f6 b2 86 8d 08 |6..x@d_.........| +00000040 25 c4 b9 82 28 15 03 03 00 40 00 00 00 00 00 00 |%...(....@......| +00000050 00 00 00 00 00 00 00 00 00 00 c9 17 55 c4 42 da |............U.B.| +00000060 fa 0b 13 c6 05 cf 07 e5 64 63 c1 41 47 b1 b7 03 |........dc.AG...| +00000070 61 5f 02 58 09 3a 12 c8 2a dc 0f 57 f0 2b cb fe |a_.X.:..*..W.+..| +00000080 44 a1 bf 67 3f c2 c5 43 43 60 |D..g?..CC`| diff --git a/src/crypto/tls/testdata/Client-TLSv12-AES256-GCM-SHA384 b/src/crypto/tls/testdata/Client-TLSv12-AES256-GCM-SHA384 index 2f552cbb627..0ac5ea725de 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-AES256-GCM-SHA384 +++ b/src/crypto/tls/testdata/Client-TLSv12-AES256-GCM-SHA384 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 51 02 00 00 4d 03 03 2b 59 94 f3 9e |....Q...M..+Y...| -00000010 23 ae d3 58 82 1f 2e be 38 1d 14 e4 4c a4 b8 ed |#..X....8...L...| -00000020 95 08 b9 44 60 02 4b 0b a9 6e ae 20 9b 43 e5 2a |...D`.K..n. .C.*| -00000030 0f 08 8e a4 c1 c0 15 79 9f af a5 ab a3 67 9d 09 |.......y.....g..| -00000040 23 0e 8e 96 a9 aa 7d 26 74 d8 0c 9a 00 9d 00 00 |#.....}&t.......| +00000000 16 03 03 00 51 02 00 00 4d 03 03 a4 b7 13 2b 05 |....Q...M.....+.| +00000010 d1 6e 6a 25 e2 1a b1 0e 71 80 9b 9b f3 45 b3 8b |.nj%....q....E..| +00000020 cf 90 de 1b 78 04 ad 8e 8a 80 52 20 b4 e0 ef a4 |....x.....R ....| +00000030 2b df 17 9c 6a 62 bf 77 43 60 29 ba 5e 57 b7 4a |+...jb.wC`).^W.J| +00000040 c2 df c8 79 47 90 0a 42 05 56 82 92 00 9d 00 00 |...yG..B.V......| 00000050 05 ff 01 00 01 00 16 03 03 02 59 0b 00 02 55 00 |..........Y...U.| 00000060 02 52 00 02 4f 30 82 02 4b 30 82 01 b4 a0 03 02 |.R..O0..K0......| 00000070 01 02 02 09 00 e8 f0 9d 3f e2 5b ea a6 30 0d 06 |........?.[..0..| @@ -70,17 +71,17 @@ 00000060 c5 70 0f 08 83 48 e9 48 ef 6e 50 8b 05 7e e5 84 |.p...H.H.nP..~..| 00000070 25 fa 55 c7 ae 31 02 27 00 ef 3f 98 86 20 12 89 |%.U..1.'..?.. ..| 00000080 91 59 28 b4 f7 d7 af d2 69 61 35 14 03 03 00 01 |.Y(.....ia5.....| -00000090 01 16 03 03 00 28 00 00 00 00 00 00 00 00 59 fc |.....(........Y.| -000000a0 aa b1 84 ab 09 82 00 88 8e e4 82 6e cd 24 9f b5 |...........n.$..| -000000b0 01 95 d3 c3 f4 a2 16 54 25 91 77 76 fc f0 |.......T%.wv..| +00000090 01 16 03 03 00 28 00 00 00 00 00 00 00 00 d9 b0 |.....(..........| +000000a0 1b 60 aa 10 77 76 95 27 af ff c6 e3 20 92 0c 2c |.`..wv.'.... ..,| +000000b0 b9 3b e6 2a a3 22 eb 3d 23 6a 74 38 07 a7 |.;.*.".=#jt8..| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 28 67 ac 20 d9 b6 |..........(g. ..| -00000010 a9 f0 ec f6 7b 34 31 3a 5e 06 20 0f 5b 32 86 1b |....{41:^. .[2..| -00000020 da 5a c5 54 47 d0 ad 4f 95 2c b5 1f 17 3f ec 17 |.Z.TG..O.,...?..| -00000030 a3 01 fc |...| +00000000 14 03 03 00 01 01 16 03 03 00 28 93 eb dc cf 90 |..........(.....| +00000010 33 92 b4 d9 2f 16 fb 77 8a ce 93 fe 1e 6a da 91 |3.../..w.....j..| +00000020 ec e3 ac c2 6e c9 f1 5d 6b e0 a7 1b 5a 80 c8 4f |....n..]k...Z..O| +00000030 fb 42 3c |.B<| >>> Flow 5 (client to server) -00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 6c 9c 0a |.............l..| -00000010 ae 0b 40 57 8b 24 6d 09 77 ae 2f 14 be 06 26 9e |..@W.$m.w./...&.| -00000020 0a bf 18 15 03 03 00 1a 00 00 00 00 00 00 00 02 |................| -00000030 32 50 20 68 3d 05 68 ed 0c ac 7a db 24 21 7e e0 |2P h=.h...z.$!~.| -00000040 9e f0 |..| +00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 4b f6 c7 |.............K..| +00000010 1a 35 f5 6a ca e4 21 d5 30 a6 44 bc e1 97 90 4f |.5.j..!.0.D....O| +00000020 6d 3b bf 15 03 03 00 1a 00 00 00 00 00 00 00 02 |m;..............| +00000030 d5 b5 08 af 5f 44 d8 14 d8 d0 4b 3c 0e c0 aa ce |...._D....K<....| +00000040 0d 92 |..| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ALPN b/src/crypto/tls/testdata/Client-TLSv12-ALPN index 358b211fc19..05b9b7ff94b 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ALPN +++ b/src/crypto/tls/testdata/Client-TLSv12-ALPN @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 01 0e 01 00 01 0a 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 14 01 00 01 10 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,22 +7,22 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 8f 00 05 00 05 01 00 00 00 00 00 0a 00 |................| +00000080 01 00 00 95 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 10 00 10 00 0e 06 70 72 6f 74 6f |...........proto| -000000d0 32 06 70 72 6f 74 6f 31 00 12 00 00 00 2b 00 09 |2.proto1.....+..| -000000e0 08 03 04 03 03 03 02 03 01 00 33 00 26 00 24 00 |..........3.&.$.| -000000f0 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da ac 5f |.. /.}.G.bC.(.._| -00000100 bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 5f 58 |.).0.........._X| -00000110 cb 3b 74 |.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 10 00 10 00 0e |a.b.............| +000000d0 06 70 72 6f 74 6f 32 06 70 72 6f 74 6f 31 00 12 |.proto2.proto1..| +000000e0 00 00 00 2b 00 09 08 03 04 03 03 03 02 03 01 00 |...+............| +000000f0 33 00 26 00 24 00 1d 00 20 2f e5 7d a3 47 cd 62 |3.&.$... /.}.G.b| +00000100 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 cf |C.(.._.).0......| +00000110 c2 ed 90 99 5f 58 cb 3b 74 |...._X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 66 02 00 00 62 03 03 95 14 55 52 0b |....f...b....UR.| -00000010 e7 c1 15 6b dc 19 3b 17 9e bb 6a b7 61 82 dc 59 |...k..;...j.a..Y| -00000020 d3 a4 7c e1 c3 83 cc e2 e5 56 e0 20 3c 82 0d 54 |..|......V. <..T| -00000030 2b 78 fe 50 cb 4e c1 69 d7 6f b3 9f ac 2e 27 c8 |+x.P.N.i.o....'.| -00000040 c6 7a 70 27 1e 14 67 43 4c f1 7d d7 cc a8 00 00 |.zp'..gCL.}.....| +00000000 16 03 03 00 66 02 00 00 62 03 03 8a 4f 46 9e 95 |....f...b...OF..| +00000010 ed 5f 6e ed 65 7e 5d 34 d1 21 46 f2 35 28 93 10 |._n.e~]4.!F.5(..| +00000020 ff 2b b5 97 c0 4e f8 6f c9 87 2f 20 c2 1a d5 6a |.+...N.o../ ...j| +00000030 5f 3b 61 e0 3b fa 8a e6 a5 be 1a 4a be b9 46 24 |_;a.;......J..F$| +00000040 7e 88 f6 34 d6 e1 f9 89 b0 12 6a 64 cc a8 00 00 |~..4......jd....| 00000050 1a ff 01 00 01 00 00 0b 00 04 03 00 01 02 00 10 |................| 00000060 00 09 00 07 06 70 72 6f 74 6f 31 16 03 03 02 59 |.....proto1....Y| 00000070 0b 00 02 55 00 02 52 00 02 4f 30 82 02 4b 30 82 |...U..R..O0..K0.| @@ -63,31 +63,31 @@ 000002a0 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d ae db 46 |.....@.a.Lr+...F| 000002b0 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db fe 3d 13 |..M...>...B...=.| 000002c0 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 ac 0c 00 |`.\!.;..........| -000002d0 00 a8 03 00 1d 20 c3 e3 43 9c 5d 0f 09 61 ae 18 |..... ..C.]..a..| -000002e0 66 05 b1 7d c1 9f e5 26 9c a7 97 d6 1f 9a 7c ff |f..}...&......|.| -000002f0 8c 34 a1 32 a2 35 08 04 00 80 6c 50 a1 80 d9 20 |.4.2.5....lP... | -00000300 56 08 da d9 5b 77 4d ad 43 66 71 15 ec fe db 02 |V...[wM.Cfq.....| -00000310 fb 40 d8 8d 67 22 e2 1b ec 8d b9 4e ba 65 01 8b |.@..g".....N.e..| -00000320 70 e0 83 bc 06 1b 14 8f 07 cf a6 08 58 c3 77 94 |p...........X.w.| -00000330 0f 94 53 62 54 6c 1f 92 22 9d ae f8 5a ad d5 f3 |..SbTl.."...Z...| -00000340 8a f7 e6 93 8c 0e 48 1b 23 89 d8 bd e9 5c 50 cd |......H.#....\P.| -00000350 07 3d 7e 8e b0 d6 65 44 58 62 03 a1 d9 94 72 f0 |.=~...eDXb....r.| -00000360 25 a9 e0 c1 be ac 32 05 59 f7 7f 6e 13 23 70 5a |%.....2.Y..n.#pZ| -00000370 65 ba a2 d7 da 3c a2 9e 6b 13 16 03 03 00 04 0e |e....<..k.......| +000002d0 00 a8 03 00 1d 20 2d 20 ab db de 27 88 0b 36 e1 |..... - ...'..6.| +000002e0 c7 55 d4 06 93 ac 58 45 1b 95 54 df 8a bc 5e 9a |.U....XE..T...^.| +000002f0 13 5d 7e b8 c2 05 08 04 00 80 70 8b 09 89 43 a5 |.]~.......p...C.| +00000300 a8 0f 8c 4f 78 86 1b 78 c8 56 8e eb 6e 85 e0 96 |...Ox..x.V..n...| +00000310 d0 63 7b 26 25 20 c1 1e b8 70 99 3e 54 b2 4b 4a |.c{&% ...p.>T.KJ| +00000320 4e 9c 7f cb 61 b6 c4 dd b9 b3 a8 aa cc ad b5 fe |N...a...........| +00000330 53 92 de 66 04 4c cd b3 23 6f 33 66 ac 76 01 f2 |S..f.L..#o3f.v..| +00000340 ab f0 e4 4a d7 8e c3 da b1 10 fc a4 51 88 71 d8 |...J........Q.q.| +00000350 37 a0 db 2d 02 d6 5e 31 a0 0c 1f 34 03 0d 09 7a |7..-..^1...4...z| +00000360 f2 b6 97 b4 62 ad 21 2b a9 3c e0 04 82 39 d5 3f |....b.!+.<...9.?| +00000370 9a fc fd e4 76 bd 5c 26 23 d8 16 03 03 00 04 0e |....v.\&#.......| 00000380 00 00 00 |...| >>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| -00000030 16 03 03 00 20 5e 91 45 7d ab 7c b7 6f 57 a6 d0 |.... ^.E}.|.oW..| -00000040 17 83 cb 40 1b 76 6b 5e 80 39 03 2f 6d 2f 10 8e |...@.vk^.9./m/..| -00000050 74 33 12 54 8d |t3.T.| +00000030 16 03 03 00 20 34 b6 f4 69 a6 6a cf f8 bd 12 2a |.... 4..i.j....*| +00000040 49 63 e8 76 ab de 17 ed 4b 30 7c 44 f8 29 ba f0 |Ic.v....K0|D.)..| +00000050 dc ef af 1d bd |.....| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 20 f1 3c 7a 28 eb |.......... .!=.o.3.| +00000020 93 e0 dc 30 0e 86 6b 3e f1 01 b9 |...0..k>...| >>> Flow 5 (client to server) -00000000 17 03 03 00 16 dc f6 18 54 22 e0 9c 08 bf db a8 |........T"......| -00000010 62 2a 64 9e 06 43 0f 22 18 0e 34 15 03 03 00 12 |b*d..C."..4.....| -00000020 20 2f f4 76 cd dc 82 eb 30 f9 e0 42 6b 29 16 ed | /.v....0..Bk)..| -00000030 7c f0 ||.| +00000000 17 03 03 00 16 c6 60 ce 66 d6 d7 52 b9 af 53 24 |......`.f..R..S$| +00000010 b9 f0 11 17 dd f2 a6 6d dd e1 00 15 03 03 00 12 |.......m........| +00000020 a2 b3 0b 85 86 8d 4b e7 1e 0b db 0c 5c 5e b7 99 |......K.....\^..| +00000030 95 54 |.T| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ClientCert-ECDSA-ECDSA b/src/crypto/tls/testdata/Client-TLSv12-ClientCert-ECDSA-ECDSA index e40999fb852..97be6270e17 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ClientCert-ECDSA-ECDSA +++ b/src/crypto/tls/testdata/Client-TLSv12-ClientCert-ECDSA-ECDSA @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 08 a4 b1 ad 21 |....Y...U......!| -00000010 3a 60 7a d3 3b 60 67 48 5d de da ff 3f a8 55 a9 |:`z.;`gH]...?.U.| -00000020 c4 72 69 32 12 c1 d1 4e d4 78 e1 20 6e 9f ed 1e |.ri2...N.x. n...| -00000030 50 9a 31 e2 ae e2 6a f4 01 cc 94 21 25 73 f3 a5 |P.1...j....!%s..| -00000040 f6 28 b3 c6 6b c1 b3 2d fc 0c d3 66 c0 09 00 00 |.(..k..-...f....| +00000000 16 03 03 00 59 02 00 00 55 03 03 c5 ee 77 70 48 |....Y...U....wpH| +00000010 0f ed 48 65 ec b0 ca 4b 38 35 a3 b7 fb 89 b0 1a |..He...K85......| +00000020 8d b1 de 3d 4d ea 92 c2 7b 53 7e 20 94 ef 64 11 |...=M...{S~ ..d.| +00000030 05 1a f4 6b 26 aa 06 b0 26 82 f9 79 82 d4 81 f7 |...k&...&..y....| +00000040 54 0e 26 bb f8 43 4d 5c 62 32 e3 5a c0 09 00 00 |T.&..CM\b2.Z....| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 0e 0b 00 02 0a 00 02 07 00 02 04 30 82 02 |.............0..| 00000070 00 30 82 01 62 02 09 00 b8 bf 2d 47 a0 d2 eb f4 |.0..b.....-G....| @@ -55,18 +56,18 @@ 00000240 13 83 0d 94 06 bb d4 37 7a f6 ec 7a c9 86 2e dd |.......7z..z....| 00000250 d7 11 69 7f 85 7c 56 de fb 31 78 2b e4 c7 78 0d |..i..|V..1x+..x.| 00000260 ae cb be 9e 4e 36 24 31 7b 6a 0f 39 95 12 07 8f |....N6$1{j.9....| -00000270 2a 16 03 03 00 b7 0c 00 00 b3 03 00 1d 20 ec f3 |*............ ..| -00000280 2b 3b be 93 68 53 f2 ab 6c 97 5a fa 9b 8c bf eb |+;..hS..l.Z.....| -00000290 37 6f af d7 b8 02 f3 8c 0b f9 75 29 11 32 04 03 |7o........u).2..| -000002a0 00 8b 30 81 88 02 42 01 9d 90 aa b3 19 d2 9d cf |..0...B.........| -000002b0 92 c1 64 05 89 db d0 dd 80 f3 a4 7e 09 ec 36 22 |..d........~..6"| -000002c0 95 79 c4 36 0e 21 80 7d 4b 72 a5 38 a4 b0 a7 5f |.y.6.!.}Kr.8..._| -000002d0 fb ae f7 66 23 82 91 c2 f8 95 df 60 ce dc e8 1a |...f#......`....| -000002e0 3f 2b 2c fa 5e 58 67 98 78 02 42 00 fa 88 7f ae |?+,.^Xg.x.B.....| -000002f0 00 55 2c a1 c2 47 ed c8 11 74 64 e7 c6 30 63 fb |.U,..G...td..0c.| -00000300 bb 42 2a 02 9b 80 60 88 e7 3f af 17 a3 7f 1e f6 |.B*...`..?......| -00000310 31 9c 1f 8c 89 e5 a0 b1 01 2a 4e d8 d2 1e 9f 11 |1........*N.....| -00000320 f5 e3 35 38 3e b0 da 30 f1 fb ed e5 d1 16 03 03 |..58>..0........| +00000270 2a 16 03 03 00 b7 0c 00 00 b3 03 00 1d 20 66 13 |*............ f.| +00000280 86 ed 87 52 0d 3d af 67 6d 69 aa a8 f0 31 39 03 |...R.=.gmi...19.| +00000290 28 25 d8 88 99 49 a0 7b f8 92 22 26 85 1c 04 03 |(%...I.{.."&....| +000002a0 00 8b 30 81 88 02 42 01 e7 94 8c b1 4d 73 3f 46 |..0...B.....Ms?F| +000002b0 27 92 bc 48 6a 12 2a 6f be fc 3b 4e 61 5f 70 1d |'..Hj.*o..;Na_p.| +000002c0 fa 55 18 f7 57 bc 21 15 57 f6 c9 03 53 1d 0c f2 |.U..W.!.W...S...| +000002d0 b4 5d 61 65 f8 31 1d b9 77 f2 9e 28 f7 05 f3 34 |.]ae.1..w..(...4| +000002e0 0e a7 2c 98 28 b1 ac a8 cf 02 42 00 d9 1c 1f 71 |..,.(.....B....q| +000002f0 a4 7b 8a f0 c2 57 a1 17 98 48 e4 c5 a2 2c 2c f8 |.{...W...H...,,.| +00000300 dc c3 b2 6d f6 d5 31 42 f9 77 f3 9a 21 1a af ac |...m..1B.w..!...| +00000310 71 ee be 36 a2 33 81 97 44 b6 09 30 35 86 67 a6 |q..6.3..D..05.g.| +00000320 8d d1 7c 09 7b 7f f9 16 fb 8b 3b 1b 47 16 03 03 |..|.{.....;.G...| 00000330 00 3a 0d 00 00 36 03 01 02 40 00 2e 04 03 05 03 |.:...6...@......| 00000340 06 03 08 07 08 08 08 09 08 0a 08 0b 08 04 08 05 |................| 00000350 08 06 04 01 05 01 06 01 03 03 02 03 03 01 02 01 |................| @@ -108,32 +109,32 @@ 00000200 e4 fa cc b1 8a ce e2 23 a0 87 f0 e1 67 51 eb 16 |.......#....gQ..| 00000210 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd 62 |...%...! /.}.G.b| 00000220 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 cf |C.(.._.).0......| -00000230 c2 ed 90 99 5f 58 cb 3b 74 16 03 03 00 93 0f 00 |...._X.;t.......| -00000240 00 8f 04 03 00 8b 30 81 88 02 42 01 e6 0a ff de |......0...B.....| -00000250 af a6 d2 7a 5f 4e f8 eb c8 19 74 53 5c e8 bc 2d |...z_N....tS\..-| -00000260 72 24 11 d2 11 ec ec cd a1 9c 3d 10 a2 de f8 8b |r$........=.....| -00000270 22 98 d3 33 c2 13 3b 93 89 ae ca a6 a8 94 70 fe |"..3..;.......p.| -00000280 76 2f 04 bc ac fb 66 79 3b 76 7f 6d 96 02 42 01 |v/....fy;v.m..B.| -00000290 df f6 30 14 7c 7e a1 0b f6 b8 8b d7 75 b8 bd 0e |..0.|~......u...| -000002a0 63 8a bd 8b ec 75 70 db d9 37 d7 53 f3 8b a2 ae |c....up..7.S....| -000002b0 60 96 69 74 eb bb 3d a6 9a 7d 46 51 73 ff 78 cf |`.it..=..}FQs.x.| -000002c0 7f 49 d9 27 5e 9f f9 d2 11 cc 0e e4 dc 04 fe d5 |.I.'^...........| -000002d0 d2 14 03 03 00 01 01 16 03 03 00 40 00 00 00 00 |...........@....| -000002e0 00 00 00 00 00 00 00 00 00 00 00 00 7a db 34 e9 |............z.4.| -000002f0 98 f8 c1 f0 38 c3 33 22 5c c3 45 b0 a3 10 3c 77 |....8.3"\.E...>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 40 18 c0 f3 96 7b |..........@....{| -00000010 45 91 6d 5b 1c 67 4f 37 74 b7 db 72 45 57 09 25 |E.m[.gO7t..rEW.%| -00000020 4a 14 68 4d 78 6c c7 15 6a b1 57 e6 ff 53 c4 58 |J.hMxl..j.W..S.X| -00000030 41 c5 6b 08 3c 5a 8c b9 04 d0 27 62 ee a6 e3 36 |A.k.>> Flow 5 (client to server) 00000000 17 03 03 00 30 00 00 00 00 00 00 00 00 00 00 00 |....0...........| -00000010 00 00 00 00 00 a6 c2 ef 07 bb 38 4a e4 8f 0c 12 |..........8J....| -00000020 19 1a 96 62 22 57 57 a2 b5 b3 06 70 95 28 a7 f7 |...b"WW....p.(..| -00000030 0d 42 69 37 7f 15 03 03 00 30 00 00 00 00 00 00 |.Bi7.....0......| -00000040 00 00 00 00 00 00 00 00 00 00 04 ed 3e 68 40 eb |............>h@.| -00000050 a0 7e 57 da 27 e7 f5 e8 6c e5 6d 58 c8 a5 18 47 |.~W.'...l.mX...G| -00000060 92 5a 43 90 de 07 9e 9a 3b cc |.ZC.....;.| +00000010 00 00 00 00 00 40 86 f6 cf aa b0 31 58 e0 e5 51 |.....@.....1X..Q| +00000020 ff 25 30 fd 0f dc 58 b7 9c 58 05 b9 a1 73 4c fa |.%0...X..X...sL.| +00000030 ac 80 44 f6 f9 15 03 03 00 30 00 00 00 00 00 00 |..D......0......| +00000040 00 00 00 00 00 00 00 00 00 00 e5 5a 81 c4 80 c7 |...........Z....| +00000050 61 a0 14 c4 6f c2 19 1a 0a 7a c3 88 d2 a4 3f f8 |a...o....z....?.| +00000060 33 0e bf 68 6f 08 26 e2 7d 4a |3..ho.&.}J| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ClientCert-ECDSA-RSA b/src/crypto/tls/testdata/Client-TLSv12-ClientCert-ECDSA-RSA index f5fae453a86..d369f6a4e56 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ClientCert-ECDSA-RSA +++ b/src/crypto/tls/testdata/Client-TLSv12-ClientCert-ECDSA-RSA @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 be ba ac 2a 81 |....Y...U.....*.| -00000010 33 b1 6e 4d 8b 9b 29 f9 16 86 bc cd b2 03 50 72 |3.nM..).......Pr| -00000020 91 9a 93 f9 e1 d6 27 55 8b b8 6c 20 84 c2 21 9e |......'U..l ..!.| -00000030 60 aa b3 f0 ec 2f 66 0d 59 31 02 08 9e 68 68 c0 |`..../f.Y1...hh.| -00000040 58 9a 8e 6c 25 ce 4d e3 3f 9d dc 91 c0 2f 00 00 |X..l%.M.?..../..| +00000000 16 03 03 00 59 02 00 00 55 03 03 00 7e 73 6e dc |....Y...U...~sn.| +00000010 56 8e 73 50 5b a0 5a 82 b5 c5 ff 3b eb 91 f2 f5 |V.sP[.Z....;....| +00000020 cf 5d 8e 77 1d ef d8 5f f7 d8 75 20 d7 2d 01 56 |.].w..._..u .-.V| +00000030 59 73 5a d1 c4 db d9 85 dc 53 c5 dd ef b3 06 43 |YsZ......S.....C| +00000040 e8 7b 2c 08 6e bb 36 90 8e 79 e0 69 c0 2f 00 00 |.{,.n.6..y.i./..| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,17 +61,17 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 ac 0c 00 00 a8 03 00 1d 20 82 89 54 65 64 97 8d |........ ..Ted..| -000002d0 e8 63 a2 5b 4f 16 56 7c cf 8b 0a 75 46 52 7e b6 |.c.[O.V|...uFR~.| -000002e0 99 2a e9 52 1f 11 46 85 36 08 04 00 80 cd a5 84 |.*.R..F.6.......| -000002f0 ff 9a 79 b5 04 85 88 fb 1e 1c d6 6b 78 e8 4d a5 |..y........kx.M.| -00000300 10 38 25 8e 8d de 71 51 b5 fd a6 2a f8 8b 5c 6d |.8%...qQ...*..\m| -00000310 1e 88 f7 d8 12 24 ff f7 7e dd 05 1c bf 71 7d 4f |.....$..~....q}O| -00000320 26 2f 2e 27 d8 e1 a8 8b d2 42 2b a6 d9 4e e6 60 |&/.'.....B+..N.`| -00000330 48 57 38 5d 3b f3 94 74 2c 8f ba e0 84 54 1c c0 |HW8];..t,....T..| -00000340 10 51 a0 31 1a d0 ec 72 01 f1 d3 65 73 c7 40 25 |.Q.1...r...es.@%| -00000350 af cd 10 18 29 2c 1a 52 e0 c9 a6 de 85 8c 96 e6 |....),.R........| -00000360 7d 85 0a 64 86 59 39 25 8f 8c 36 4c 37 16 03 03 |}..d.Y9%..6L7...| +000002c0 ac 0c 00 00 a8 03 00 1d 20 82 2e 3b 44 da bb 0f |........ ..;D...| +000002d0 4a 32 d1 8a c0 e5 b9 10 3a 35 06 85 ba db ca 5a |J2......:5.....Z| +000002e0 2a 5c 0c c5 45 c3 66 47 55 08 04 00 80 da 78 ad |*\..E.fGU.....x.| +000002f0 33 9c bf b1 1d cd 15 a2 35 66 39 54 c1 e6 3c 5e |3.......5f9T..<^| +00000300 1f 68 0d 18 54 51 01 a9 6e 34 46 1e 7f 35 2f b4 |.h..TQ..n4F..5/.| +00000310 1a 30 48 2f a8 13 25 85 1b 87 f1 f9 ab 19 bf 49 |.0H/..%........I| +00000320 7a e8 dd 1f 44 86 7a 24 50 aa b3 1e 4f 7b ae bf |z...D.z$P...O{..| +00000330 ea a1 ef 6c 37 f2 2c 7a db 05 ba 06 3c f2 4d 04 |...l7.,z....<.M.| +00000340 3e 3b 82 26 ad db 80 0f 1e 52 53 54 0f 54 5c fa |>;.&.....RST.T\.| +00000350 58 d5 bb b4 11 5f 56 20 b1 24 9f d0 0d b9 83 c4 |X...._V .$......| +00000360 ce 48 a5 71 e7 6b 93 1e 25 e6 7e 60 c2 16 03 03 |.H.q.k..%.~`....| 00000370 00 3a 0d 00 00 36 03 01 02 40 00 2e 04 03 05 03 |.:...6...@......| 00000380 06 03 08 07 08 08 08 09 08 0a 08 0b 08 04 08 05 |................| 00000390 08 06 04 01 05 01 06 01 03 03 02 03 03 01 02 01 |................| @@ -112,28 +113,28 @@ 00000200 e4 fa cc b1 8a ce e2 23 a0 87 f0 e1 67 51 eb 16 |.......#....gQ..| 00000210 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd 62 |...%...! /.}.G.b| 00000220 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 cf |C.(.._.).0......| -00000230 c2 ed 90 99 5f 58 cb 3b 74 16 03 03 00 92 0f 00 |...._X.;t.......| -00000240 00 8e 04 03 00 8a 30 81 87 02 41 72 16 75 7d 08 |......0...Ar.u}.| -00000250 42 7b 33 e7 59 51 ef 3c 54 e7 81 e4 10 31 ab 5d |B{3.YQ....<..........| +00000260 5e 88 0f 9f 03 2f 92 a5 9c 00 b1 af 04 b3 61 b2 |^..../........a.| +00000270 eb b5 39 a9 01 2a 11 54 53 89 94 6c 51 72 a2 16 |..9..*.TS..lQr..| +00000280 f1 1a 6b ce cd 8f 88 59 2f d4 ea 02 b4 02 42 01 |..k....Y/.....B.| +00000290 05 54 4d 19 a1 de 75 90 d6 b6 23 84 7a b3 75 2c |.TM...u...#.z.u,| +000002a0 a8 89 7f ce 73 85 d0 11 9c be f5 7d 78 e0 8d e1 |....s......}x...| +000002b0 f9 a6 6a e6 6e 78 be 1e d0 6b 30 db f8 ba 3d fd |..j.nx...k0...=.| +000002c0 af 06 e9 47 e9 7c ea 32 46 f2 e0 35 0d ee a5 2d |...G.|.2F..5...-| +000002d0 00 14 03 03 00 01 01 16 03 03 00 28 00 00 00 00 |...........(....| +000002e0 00 00 00 00 ec 7d a7 6b 24 ea 04 db c4 8a d2 fa |.....}.k$.......| +000002f0 aa cc f8 3d bc 5d 7d 47 49 1b 37 74 06 ae fd be |...=.]}GI.7t....| +00000300 07 c0 ea 5d |...]| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 28 b8 e9 dd 30 75 |..........(...0u| -00000010 40 7d 71 76 db 9a 95 92 81 02 3a 9e 36 d5 15 ca |@}qv......:.6...| -00000020 5d 63 a1 0f 8c 53 c9 1c 37 56 b2 0d 54 15 a2 dc |]c...S..7V..T...| -00000030 03 d6 2e |...| +00000000 14 03 03 00 01 01 16 03 03 00 28 cc 0e a0 ed 17 |..........(.....| +00000010 84 cd 5b cf 24 c0 9d 2a af 76 75 2b 26 39 3d db |..[.$..*.vu+&9=.| +00000020 78 1e ed 30 81 e3 9a 78 f9 07 f9 07 90 58 ea 74 |x..0...x.....X.t| +00000030 be 48 57 |.HW| >>> Flow 5 (client to server) -00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 01 85 96 |................| -00000010 67 b2 4b d3 e3 27 80 9f 2d a8 f4 bf 47 91 58 6e |g.K..'..-...G.Xn| -00000020 47 d8 98 15 03 03 00 1a 00 00 00 00 00 00 00 02 |G...............| -00000030 36 54 82 d1 a2 0f 2a c3 53 f6 09 d0 5c 78 46 97 |6T....*.S...\xF.| -00000040 20 41 | A| +00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 77 56 f2 |.............wV.| +00000010 ba 08 c8 93 d5 5a c2 e2 65 5e 5e c9 12 44 e3 df |.....Z..e^^..D..| +00000020 f5 f9 ba 15 03 03 00 1a 00 00 00 00 00 00 00 02 |................| +00000030 96 b8 5c a9 61 56 e0 11 9d ce b0 47 dd 4b 5e 05 |..\.aV.....G.K^.| +00000040 4e 20 |N | diff --git a/src/crypto/tls/testdata/Client-TLSv12-ClientCert-Ed25519 b/src/crypto/tls/testdata/Client-TLSv12-ClientCert-Ed25519 index e415b126e56..4e95c14925e 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ClientCert-Ed25519 +++ b/src/crypto/tls/testdata/Client-TLSv12-ClientCert-Ed25519 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 1c 50 4e 50 35 |....Y...U...PNP5| -00000010 51 02 a9 62 ba 82 a5 d3 fa 40 4e f3 28 9b 50 a6 |Q..b.....@N.(.P.| -00000020 f0 75 30 e9 fe be a3 42 1d 1c f5 20 9e 88 46 57 |.u0....B... ..FW| -00000030 c5 b4 a3 a3 fc 88 bb e0 1c 5e ea 77 a0 75 93 5a |.........^.w.u.Z| -00000040 6d 4c c7 57 6f 3a 05 af 3f 3f ac 75 cc a8 00 00 |mL.Wo:..??.u....| +00000000 16 03 03 00 59 02 00 00 55 03 03 de bc 1c f0 a4 |....Y...U.......| +00000010 a0 ca 32 f8 05 b4 ac d5 6a d7 db 61 48 ec ac d0 |..2.....j..aH...| +00000020 fb c5 02 e7 15 60 be 54 d6 2c 23 20 59 9b f4 8e |.....`.T.,# Y...| +00000030 58 ea d5 bb 15 e8 79 e1 1c 3f b3 08 72 e8 c3 5c |X.....y..?..r..\| +00000040 e6 16 d8 97 01 42 bd be 2d 4d 62 f4 cc a8 00 00 |.....B..-Mb.....| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,17 +61,17 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 ac 0c 00 00 a8 03 00 1d 20 82 c1 f5 7b 68 eb 7a |........ ...{h.z| -000002d0 cf 02 c9 95 28 4b 31 76 a9 84 93 a9 1f 5b f4 2a |....(K1v.....[.*| -000002e0 5c a5 31 94 5f f0 e0 ed 2e 08 04 00 80 7a 99 38 |\.1._........z.8| -000002f0 7f d0 25 4b bf a9 e0 2b db ce 17 9d 30 4b 82 9e |..%K...+....0K..| -00000300 b1 50 84 fc dd b0 a8 5c 39 20 00 40 5b 92 dc 7c |.P.....\9 .@[..|| -00000310 25 3b 53 7d 5a 4b ad 05 6f 3a 4f e5 84 b6 3a e2 |%;S}ZK..o:O...:.| -00000320 fb bf cb c8 94 39 a5 28 ad c8 5f 94 53 90 0e 61 |.....9.(.._.S..a| -00000330 af f2 92 2c 3b ec 3c bf 1d d3 8b a5 65 58 5b bf |...,;.<.....eX[.| -00000340 5a 21 3d cd 40 7c 9e 1d e9 62 3c 67 71 7c ec b4 |Z!=.@|...b....| +000002c0 ac 0c 00 00 a8 03 00 1d 20 e3 86 c2 33 d1 24 89 |........ ...3.$.| +000002d0 90 2b ca c7 e9 bf a5 a2 2d a7 e1 1b 39 7b 3f 37 |.+......-...9{?7| +000002e0 40 2a ff dc 44 08 90 69 1d 08 04 00 80 24 99 a6 |@*..D..i.....$..| +000002f0 47 b9 09 c4 02 ee 4a fa 6c c7 41 fb e4 8b e7 72 |G.....J.l.A....r| +00000300 32 96 bd 34 2a 72 76 c0 e3 5e d9 f1 f3 38 0b e7 |2..4*rv..^...8..| +00000310 58 e4 a6 2d dd dd b3 3f 66 7e 02 75 ce 72 14 97 |X..-...?f~.u.r..| +00000320 14 b7 75 39 cd 3a 60 0a eb 5a 88 db d2 0c 7b b4 |..u9.:`..Z....{.| +00000330 1e 9c f4 b3 b6 6c 2c d6 89 c4 f8 f3 8f 5c a7 e7 |.....l,......\..| +00000340 05 71 92 81 f1 1b b7 fa df 5b a6 5d a0 8d 97 f6 |.q.......[.]....| +00000350 93 0d 7d 14 f1 05 fb a5 9b 8a b6 e8 34 43 66 d4 |..}.........4Cf.| +00000360 b8 dc 48 29 c7 ea 69 f1 52 41 c5 b7 e0 16 03 03 |..H)..i.RA......| 00000370 00 3a 0d 00 00 36 03 01 02 40 00 2e 04 03 05 03 |.:...6...@......| 00000380 06 03 08 07 08 08 08 09 08 0a 08 0b 08 04 08 05 |................| 00000390 08 06 04 01 05 01 06 01 03 03 02 03 03 01 02 01 |................| @@ -100,20 +101,20 @@ 00000140 08 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 |.....%...! /.}.G| 00000150 cd 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af |.bC.(.._.).0....| 00000160 c4 cf c2 ed 90 99 5f 58 cb 3b 74 16 03 03 00 48 |......_X.;t....H| -00000170 0f 00 00 44 08 07 00 40 af a6 03 14 53 7a 4f 75 |...D...@....SzOu| -00000180 9d cc 2f e3 e7 2a 51 16 16 b0 1d 28 e0 2a 59 f0 |../..*Q....(.*Y.| -00000190 3c df cc 18 dd b8 ef d1 9f 9d 03 8e 59 00 27 d1 |<...........Y.'.| -000001a0 39 2f 3b 33 53 1f b2 f0 22 1d 06 f6 50 0b a7 98 |9/;3S..."...P...| -000001b0 cc fa 78 53 bf 8e ff 0b 14 03 03 00 01 01 16 03 |..xS............| -000001c0 03 00 20 e5 81 3e a3 34 29 52 14 19 49 cf 04 82 |.. ..>.4)R..I...| -000001d0 8b e7 83 aa 6c db 96 ec 97 29 b4 a3 db 87 21 2e |....l....)....!.| -000001e0 a5 c0 66 |..f| +00000170 0f 00 00 44 08 07 00 40 de 00 e6 5f f4 59 97 97 |...D...@..._.Y..| +00000180 23 1e 0f d8 b0 79 ab 71 34 35 68 c2 0e db df 48 |#....y.q45h....H| +00000190 c1 37 20 6c 54 90 50 f5 ad 6c 65 a2 1a 19 16 e7 |.7 lT.P..le.....| +000001a0 bb 81 0f 2d 73 4b 45 71 3c 52 c6 51 1c d7 6b f7 |...-sKEq>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 20 84 67 d4 ce cf |.......... .g...| -00000010 fb 54 2c dc f7 53 31 8a aa 03 60 37 3d 33 f2 79 |.T,..S1...`7=3.y| -00000020 d0 65 2e 3f 0e f9 1a d3 6e 6d 8e |.e.?....nm.| +00000000 14 03 03 00 01 01 16 03 03 00 20 ad ee ac 81 e6 |.......... .....| +00000010 71 68 16 ff c6 cc f4 e0 81 9b 1c 62 d4 69 47 df |qh.........b.iG.| +00000020 f7 c7 9c fb be 69 65 1c 77 7a a4 |.....ie.wz.| >>> Flow 5 (client to server) -00000000 17 03 03 00 16 e5 b7 4c 92 05 fc 81 cf 11 ef cd |.......L........| -00000010 0f 4b df ef a1 54 ae 26 4e ec aa 15 03 03 00 12 |.K...T.&N.......| -00000020 0a f3 5b 06 63 84 a6 eb d4 73 94 db fe d8 e0 ae |..[.c....s......| -00000030 d6 fc |..| +00000000 17 03 03 00 16 0f 19 65 02 7e ea 9c e0 c3 64 b1 |.......e.~....d.| +00000010 12 b5 4c 65 62 86 68 3b 7b fd c9 15 03 03 00 12 |..Leb.h;{.......| +00000020 05 d0 e2 86 df 61 28 36 9f 49 69 73 2b 52 11 b9 |.....a(6.Iis+R..| +00000030 18 4d |.M| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-AES256-GCM-SHA384 b/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-AES256-GCM-SHA384 index 3975b072c95..8056220c58a 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-AES256-GCM-SHA384 +++ b/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-AES256-GCM-SHA384 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 d4 20 b3 4c 6a |....Y...U... .Lj| -00000010 69 44 3f f7 ab 15 35 85 ca 71 02 b0 70 18 8e d6 |iD?...5..q..p...| -00000020 61 d5 34 08 42 de cf a1 57 32 96 20 8c b4 72 dd |a.4.B...W2. ..r.| -00000030 63 93 e6 13 9d 4a ec 75 d9 a1 a6 9e 5e 02 f5 63 |c....J.u....^..c| -00000040 29 1a 78 9f 94 9f 6c 58 b5 91 ae 63 c0 30 00 00 |).x...lX...c.0..| +00000000 16 03 03 00 59 02 00 00 55 03 03 94 63 1a 7a d2 |....Y...U...c.z.| +00000010 0f 99 b7 3e c2 90 14 73 5f d9 15 30 48 86 af ca |...>...s_..0H...| +00000020 f7 92 ff 84 01 ab 8f bb 13 1d a9 20 79 a9 24 65 |........... y.$e| +00000030 03 d6 49 02 6d db 63 34 08 1c 4a 2f 37 6d 8a 61 |..I.m.c4..J/7m.a| +00000040 ff 1f d7 7a 09 2e c8 ae a0 f6 f7 bd c0 30 00 00 |...z.........0..| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,17 +61,17 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 ac 0c 00 00 a8 03 00 1d 20 a2 bd 95 3e 0c 9f ad |........ ...>...| -000002d0 11 59 e0 6a c1 21 0c 6c 86 cc f1 ce bd a0 30 5d |.Y.j.!.l......0]| -000002e0 53 1e 75 f9 55 af 49 7b 31 08 04 00 80 d4 8b 11 |S.u.U.I{1.......| -000002f0 ca 22 14 79 a3 e8 b6 c7 d0 d6 1b 17 42 93 47 30 |.".y........B.G0| -00000300 ab 50 0e c9 0c 92 88 96 b4 63 4e 4e ac 7f dd c8 |.P.......cNN....| -00000310 8f 85 07 5b 95 c5 0a c0 4e 6d 4f 51 ba d8 d7 db |...[....NmOQ....| -00000320 14 70 80 4f 68 d9 b4 39 e7 48 27 21 76 4c 79 a4 |.p.Oh..9.H'!vLy.| -00000330 60 91 d7 2f 75 69 04 1a da 71 ff b8 4d 78 d8 e7 |`../ui...q..Mx..| -00000340 ca f2 f2 1e 71 21 b3 a0 44 a7 6c 99 16 a1 c9 f8 |....q!..D.l.....| -00000350 f0 de e8 99 12 7b 3d a2 e3 15 fa 63 62 e9 1b 72 |.....{=....cb..r| -00000360 c8 bb 27 38 4a 48 66 1d dd fb ef 6f d1 16 03 03 |..'8JHf....o....| +000002c0 ac 0c 00 00 a8 03 00 1d 20 4b 8e 9f 8d 3c d9 a1 |........ K...<..| +000002d0 bd 49 ea 69 b1 08 bb d3 92 0e e4 8f ed bc 18 f5 |.I.i............| +000002e0 3b 25 3d 39 ab 51 fd b3 49 08 04 00 80 b1 f9 94 |;%=9.Q..I.......| +000002f0 17 4b 9b ab c7 e2 5c 37 a0 eb e5 72 44 ed ef 31 |.K....\7...rD..1| +00000300 15 56 9f 5c e5 f0 04 dd 71 b1 ff ee 20 9b 07 de |.V.\....q... ...| +00000310 7b 2f ba f0 1e 6c d4 f5 8d e5 bc bf 85 c5 25 7b |{/...l........%{| +00000320 f9 fb 2d 34 f1 cb 61 28 c3 89 8d ce 13 df 85 f9 |..-4..a(........| +00000330 ee 0a c7 1f 6c cc 8a 5a cf e8 cc 90 21 0c 3d de |....l..Z....!.=.| +00000340 51 d3 0b cf 4e 7c 70 07 3b ee f8 80 97 25 19 41 |Q...N|p.;....%.A| +00000350 b1 11 20 ef 22 83 5f fe 46 19 77 6c b1 d2 57 6b |.. ."._.F.wl..Wk| +00000360 9b 9d 49 f9 63 68 b0 4c 26 ce d5 63 31 16 03 03 |..I.ch.L&..c1...| 00000370 00 3a 0d 00 00 36 03 01 02 40 00 2e 04 03 05 03 |.:...6...@......| 00000380 06 03 08 07 08 08 08 09 08 0a 08 0b 08 04 08 05 |................| 00000390 08 06 04 01 05 01 06 01 03 03 02 03 03 01 02 01 |................| @@ -112,26 +113,26 @@ 00000200 e5 35 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 |.5....%...! /.}.| 00000210 47 cd 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 |G.bC.(.._.).0...| 00000220 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 16 03 03 00 |......._X.;t....| -00000230 88 0f 00 00 84 08 04 00 80 2e bf 05 22 82 a7 d6 |............"...| -00000240 e9 08 ff 9b 10 d3 4a 6c c4 73 5c 78 88 05 0c 15 |......Jl.s\x....| -00000250 b7 8c 78 49 64 2d 58 67 ef 8f db c0 67 fa 32 6e |..xId-Xg....g.2n| -00000260 65 45 90 a0 69 5c fb ba e0 16 1c d4 81 1d 24 89 |eE..i\........$.| -00000270 35 27 14 15 19 0b 86 ee 6a f2 b4 a5 27 61 5f 1f |5'......j...'a_.| -00000280 cc 47 7c 01 ed a9 ff ed 61 45 3f 53 1c 82 c8 cd |.G|.....aE?S....| -00000290 48 e4 89 82 12 d7 d2 ff fa 32 b3 e6 9d ce 75 75 |H........2....uu| -000002a0 d1 cd b2 a8 56 a6 a6 63 da 8d ed 27 13 01 9a 56 |....V..c...'...V| -000002b0 a2 26 b4 6c af 27 f6 4f 1b 14 03 03 00 01 01 16 |.&.l.'.O........| -000002c0 03 03 00 28 00 00 00 00 00 00 00 00 f0 e8 32 33 |...(..........23| -000002d0 50 df 73 17 3c 58 f2 c9 30 2e 5d e9 00 4f 4b 33 |P.s..6.X| +00000230 88 0f 00 00 84 08 04 00 80 4e 7e e6 78 e6 9e 19 |.........N~.x...| +00000240 c1 bb 85 46 75 53 a7 0c f2 e1 9d 00 3a b6 ac 30 |...FuS......:..0| +00000250 44 c7 38 7a b7 46 8a c2 87 34 5e c9 ed cd 6e cf |D.8z.F...4^...n.| +00000260 74 14 8a 76 78 32 89 92 7a b5 f0 ab 1b 5d fb 0d |t..vx2..z....]..| +00000270 fa df c4 0d c1 6e 2a 2f 02 39 f2 d0 29 f6 fd 43 |.....n*/.9..)..C| +00000280 31 f7 31 46 17 05 77 f8 c1 00 08 80 2c b8 eb 32 |1.1F..w.....,..2| +00000290 96 5d c6 1b d0 a8 4c 60 d3 36 3c e3 98 61 77 84 |.]....L`.6<..aw.| +000002a0 8e ba 5c f9 1c 37 9a 77 f2 53 b9 ff 4d bd 01 2e |..\..7.w.S..M...| +000002b0 37 e7 e2 fd 07 0a 0d b4 aa 14 03 03 00 01 01 16 |7...............| +000002c0 03 03 00 28 00 00 00 00 00 00 00 00 e5 8c 9d 4b |...(...........K| +000002d0 10 ec f8 85 12 74 4f ad 5d 61 5e 69 c7 4d 5a 63 |.....tO.]a^i.MZc| +000002e0 a5 57 64 5e 1a ff 22 0f cc d7 fc 24 |.Wd^.."....$| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 28 14 ce b1 86 0e |..........(.....| -00000010 9f ce 73 25 44 b7 3e a9 25 db a8 93 d9 39 33 75 |..s%D.>.%....93u| -00000020 2f a9 7f 97 6a 76 28 fe e2 84 5f 1e 84 66 b4 c8 |/...jv(..._..f..| -00000030 45 e7 64 |E.d| +00000000 14 03 03 00 01 01 16 03 03 00 28 6f 8a 03 7a 3e |..........(o..z>| +00000010 5d 92 d5 52 41 87 51 57 84 f8 06 d8 33 06 2d 13 |]..RA.QW....3.-.| +00000020 bf 21 a1 ee 94 5c 08 be 7e 89 0e 6c ac dc 18 21 |.!...\..~..l...!| +00000030 98 0b 1a |...| >>> Flow 5 (client to server) -00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 3b 17 73 |.............;.s| -00000010 78 d6 3a b4 6d 3a 61 52 f6 a5 8c dd 18 3e ff 04 |x.:.m:aR.....>..| -00000020 d9 3f 22 15 03 03 00 1a 00 00 00 00 00 00 00 02 |.?".............| -00000030 32 8d 5d 07 14 a9 d2 1c dd 1e 2f 3d 89 a9 8f 1d |2.]......./=....| -00000040 08 0f |..| +00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 e5 be 31 |...............1| +00000010 93 e2 2f fe 7e b3 e2 95 77 69 40 9a cc 32 7f 79 |../.~...wi@..2.y| +00000020 30 88 02 15 03 03 00 1a 00 00 00 00 00 00 00 02 |0...............| +00000030 be 47 1a 94 f6 5b 7d 0e 52 03 a9 b5 8c 89 8e 31 |.G...[}.R......1| +00000040 45 77 |Ew| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-ECDSA b/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-ECDSA index 2d608a78245..d9dcf3d5626 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-ECDSA +++ b/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-ECDSA @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 3c ba b1 d8 8d |....Y...U..<....| -00000010 f5 52 f4 a4 70 fc 12 54 20 85 eb 23 bc b8 0b e0 |.R..p..T ..#....| -00000020 80 b6 ab 9b c5 34 84 57 bc ae 95 20 e3 51 8d 40 |.....4.W... .Q.@| -00000030 93 cc 9f e4 fd 77 82 c8 12 54 6a 23 08 db ff e5 |.....w...Tj#....| -00000040 87 8d 72 41 60 51 6a 11 5f 0a 9a d2 c0 09 00 00 |..rA`Qj._.......| +00000000 16 03 03 00 59 02 00 00 55 03 03 a7 29 a5 f1 46 |....Y...U...)..F| +00000010 0d 82 c6 cf 46 c7 6a e7 1d 5b 76 4b 59 4d 4b 9c |....F.j..[vKYMK.| +00000020 48 78 2f 96 ca 03 31 ee dc a1 3d 20 8f 78 25 7f |Hx/...1...= .x%.| +00000030 97 ea d7 75 cb 63 c7 22 34 dc e3 98 9e 39 1d 35 |...u.c."4....9.5| +00000040 ab 45 52 f0 07 b2 38 be 61 e8 37 35 c0 09 00 00 |.ER...8.a.75....| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 0e 0b 00 02 0a 00 02 07 00 02 04 30 82 02 |.............0..| 00000070 00 30 82 01 62 02 09 00 b8 bf 2d 47 a0 d2 eb f4 |.0..b.....-G....| @@ -55,18 +56,18 @@ 00000240 13 83 0d 94 06 bb d4 37 7a f6 ec 7a c9 86 2e dd |.......7z..z....| 00000250 d7 11 69 7f 85 7c 56 de fb 31 78 2b e4 c7 78 0d |..i..|V..1x+..x.| 00000260 ae cb be 9e 4e 36 24 31 7b 6a 0f 39 95 12 07 8f |....N6$1{j.9....| -00000270 2a 16 03 03 00 b7 0c 00 00 b3 03 00 1d 20 86 f3 |*............ ..| -00000280 1e c5 fb 1f 91 44 0e e5 e4 3e 0a cd 75 a2 fb 4c |.....D...>..u..L| -00000290 a2 b9 07 f7 33 ce cc cd 61 a5 8c ba 6a 35 04 03 |....3...a...j5..| -000002a0 00 8b 30 81 88 02 42 01 f4 8d 4f 3e c8 73 b5 b4 |..0...B...O>.s..| -000002b0 b5 2b ac 2a 27 68 56 a1 45 ce b6 1d c6 37 ce de |.+.*'hV.E....7..| -000002c0 bd 96 90 5e e2 1c c8 84 b2 84 57 25 81 d4 c3 7a |...^......W%...z| -000002d0 db b2 3d 24 2b 17 3a 4a 7e 92 1a bb 0c fb b6 05 |..=$+.:J~.......| -000002e0 cd 0e 85 4c 3d 4b 24 2a 2a 02 42 00 f6 91 d6 82 |...L=K$**.B.....| -000002f0 9e 81 98 5f 64 59 ce 16 85 fc 65 19 0c 50 ca ea |..._dY....e..P..| -00000300 8a ba 1e 61 a8 71 cf 2c eb 94 24 ac 34 75 6e 5c |...a.q.,..$.4un\| -00000310 dc 92 ba b8 bd 42 75 ef 6d 67 5f 06 5c e3 6c c2 |.....Bu.mg_.\.l.| -00000320 aa 5e 29 25 66 00 68 c8 5d 9c 6f bb e0 16 03 03 |.^)%f.h.].o.....| +00000270 2a 16 03 03 00 b7 0c 00 00 b3 03 00 1d 20 2f 01 |*............ /.| +00000280 dc 54 52 ea 1b b8 36 0c 5d 3b 3a eb 6e 5b f7 3e |.TR...6.];:.n[.>| +00000290 e3 fa f3 c7 d0 ec d3 97 be f8 01 44 aa 2b 04 03 |...........D.+..| +000002a0 00 8b 30 81 88 02 42 01 a2 b9 27 d7 b7 74 6a a4 |..0...B...'..tj.| +000002b0 2f 17 c7 97 2a 14 94 92 44 a7 1c aa 31 ff 02 f5 |/...*...D...1...| +000002c0 df 47 47 f0 76 db 08 9f 0c 28 5c 1c 06 91 ed 44 |.GG.v....(\....D| +000002d0 7e 22 5f ff 7c 52 aa ab fb 87 6c 21 a0 f9 d7 34 |~"_.|R....l!...4| +000002e0 9a 36 cb d9 d7 b2 f0 09 c9 02 42 01 d9 7e e1 b9 |.6........B..~..| +000002f0 cc 80 44 a9 1a c6 94 99 3d a6 72 3b 5c 39 32 04 |..D.....=.r;\92.| +00000300 a4 5c d5 90 c1 7b 9d d5 98 26 38 26 5b e6 1c f1 |.\...{...&8&[...| +00000310 da 41 16 36 48 c2 be aa 01 c4 3d f0 f6 e4 9a 6f |.A.6H.....=....o| +00000320 b4 b2 83 c5 67 cf 1c 1c 20 4f 91 47 07 16 03 03 |....g... O.G....| 00000330 00 3a 0d 00 00 36 03 01 02 40 00 2e 04 03 05 03 |.:...6...@......| 00000340 06 03 08 07 08 08 08 09 08 0a 08 0b 08 04 08 05 |................| 00000350 08 06 04 01 05 01 06 01 03 03 02 03 03 01 02 01 |................| @@ -108,31 +109,31 @@ 00000200 e5 35 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 |.5....%...! /.}.| 00000210 47 cd 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 |G.bC.(.._.).0...| 00000220 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 16 03 03 00 |......._X.;t....| -00000230 88 0f 00 00 84 08 04 00 80 53 85 ea dc a6 86 2d |.........S.....-| -00000240 e7 8c 0b 68 f9 57 7f f5 77 d8 fe 35 28 91 e7 2f |...h.W..w..5(../| -00000250 8a 2c 36 cf d7 8c 9f 3d f2 e2 99 41 11 b2 3c a2 |.,6....=...A..<.| -00000260 5e f3 68 1f b5 d4 f8 90 8a e2 5e 02 48 00 2b eb |^.h.......^.H.+.| -00000270 f0 e6 8c 28 af 11 80 82 ea 35 06 fd 0a 5f d7 1a |...(.....5..._..| -00000280 e9 63 29 08 8c aa 18 1e 7c 08 81 21 c8 aa 86 b1 |.c).....|..!....| -00000290 cf 94 db f6 8d 15 dc cc ae cf 41 2c 32 b1 3f 0c |..........A,2.?.| -000002a0 96 0e 5c ed 82 74 cc fc 35 f4 38 80 29 00 c1 3a |..\..t..5.8.)..:| -000002b0 70 d4 07 07 9c 49 9e 7b 91 14 03 03 00 01 01 16 |p....I.{........| +00000230 88 0f 00 00 84 08 04 00 80 7d fc b7 17 32 a9 aa |.........}...2..| +00000240 21 70 dc 23 a7 f4 87 fe d2 f1 dd 15 48 56 ea 3a |!p.#........HV.:| +00000250 a2 fb 76 0e 5b f7 ac 13 35 0b 4a 7f f7 b6 71 db |..v.[...5.J...q.| +00000260 77 55 bd de 2a 52 b0 ae 6e 9c 8f 65 2e 8f cf 05 |wU..*R..n..e....| +00000270 18 4d f0 c4 1c 78 5f 62 09 64 28 22 06 1c 9a 03 |.M...x_b.d("....| +00000280 eb 4f b8 c3 7d 5c 37 b6 a5 d0 2c fa 08 31 ed 3a |.O..}\7...,..1.:| +00000290 a6 e9 c2 04 5f 0f 31 54 38 ee 07 ba 0a 69 ab df |...._.1T8....i..| +000002a0 ec f5 d0 e1 cb 17 af 48 84 7c 58 8f 77 32 bd d7 |.......H.|X.w2..| +000002b0 7e ac 3f be f6 ae 0c be 6f 14 03 03 00 01 01 16 |~.?.....o.......| 000002c0 03 03 00 40 00 00 00 00 00 00 00 00 00 00 00 00 |...@............| -000002d0 00 00 00 00 f3 da dc d7 12 d6 f6 19 75 a8 02 68 |............u..h| -000002e0 57 0e e1 90 75 d1 fc b8 32 a3 34 16 d6 8d 2a f5 |W...u...2.4...*.| -000002f0 65 f2 a7 67 2c 2c a4 73 6a b6 f2 ad 2d 7f 8a ce |e..g,,.sj...-...| -00000300 a7 12 16 97 |....| +000002d0 00 00 00 00 e3 19 d0 4e e8 da b9 20 a0 d9 3a ff |.......N... ..:.| +000002e0 7c a6 f6 a5 c9 fe 61 fe 86 62 ec 2a fd de 7c ec ||.....a..b.*..|.| +000002f0 be 38 fa 59 a8 12 28 cc 4f 43 fa 15 fd 49 f7 db |.8.Y..(.OC...I..| +00000300 83 9f 84 cc |....| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 40 dc 11 a1 a2 fb |..........@.....| -00000010 55 0c 9e e0 e2 55 1a ca cd 5b df 1f 39 9e 08 51 |U....U...[..9..Q| -00000020 bd 6b 72 40 93 f8 23 7a 32 9d 85 18 20 b7 39 b0 |.kr@..#z2... .9.| -00000030 03 d3 10 6a 8e 66 6d e6 d5 38 03 c6 e5 b8 dc d7 |...j.fm..8......| -00000040 3c 27 1d d2 a9 59 f9 18 7d 15 90 |<'...Y..}..| +00000000 14 03 03 00 01 01 16 03 03 00 40 2e 4b 13 61 0e |..........@.K.a.| +00000010 b0 a0 61 ce b4 04 9f 8b 0b 75 33 f6 93 1b 00 8f |..a......u3.....| +00000020 ec 28 fc d8 d4 d3 8c 8d 66 32 40 8f 38 4f b4 01 |.(......f2@.8O..| +00000030 65 35 9d ab db 7a 9b be c0 57 7c 1b 73 ee 99 de |e5...z...W|.s...| +00000040 4e 5c 42 03 38 d2 59 67 c8 09 d0 |N\B.8.Yg...| >>> Flow 5 (client to server) 00000000 17 03 03 00 30 00 00 00 00 00 00 00 00 00 00 00 |....0...........| -00000010 00 00 00 00 00 c2 92 ee 96 31 60 90 d5 ee a6 1c |.........1`.....| -00000020 ed 3c 03 40 8c e7 0c db 7f b0 11 dc 7e 58 e1 aa |.<.@........~X..| -00000030 4c d7 68 2a 91 15 03 03 00 30 00 00 00 00 00 00 |L.h*.....0......| -00000040 00 00 00 00 00 00 00 00 00 00 b6 61 51 ac 66 a5 |...........aQ.f.| -00000050 d1 ef d3 ee c8 d3 48 72 d5 e0 ef 7d ca 6a ec b2 |......Hr...}.j..| -00000060 77 ff 2d a8 32 6d be 6e a7 42 |w.-.2m.n.B| +00000010 00 00 00 00 00 c0 47 e7 58 eb 46 e4 6d 05 af 84 |......G.X.F.m...| +00000020 4f 77 c6 22 28 92 58 3a 2d 64 d6 6a 73 19 f5 c3 |Ow."(.X:-d.js...| +00000030 6e 31 f5 82 90 15 03 03 00 30 00 00 00 00 00 00 |n1.......0......| +00000040 00 00 00 00 00 00 00 00 00 00 2d 63 52 df 2c 6f |..........-cR.,o| +00000050 f2 0b 11 1a 39 ca 1a 87 7e 45 26 43 d8 78 93 a9 |....9...~E&C.x..| +00000060 da a0 7c 26 87 49 31 2a 3e 42 |..|&.I1*>B| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-RSA b/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-RSA index cdc71041fbb..ac6c834bb7f 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-RSA +++ b/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-RSA @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 f3 28 ca c9 ac |....Y...U...(...| -00000010 29 bb 15 80 56 d2 37 09 fa 7d 23 04 d4 79 e7 1d |)...V.7..}#..y..| -00000020 bb 4e c5 60 c8 44 39 02 6a e9 e0 20 b5 ae 39 87 |.N.`.D9.j.. ..9.| -00000030 4e 24 2f 33 02 fe 72 d6 2a 4d 0c 8c da 36 7b 28 |N$/3..r.*M...6{(| -00000040 3c 06 aa b2 60 68 91 7a ae d8 7b e2 c0 2f 00 00 |<...`h.z..{../..| +00000000 16 03 03 00 59 02 00 00 55 03 03 e2 9a e1 34 0d |....Y...U.....4.| +00000010 fb 94 84 1a eb 02 cc f3 28 52 a6 43 2b c9 4a 97 |........(R.C+.J.| +00000020 df 73 e7 d2 71 2c 77 33 8c 69 14 20 69 03 8a 58 |.s..q,w3.i. i..X| +00000030 4d 93 dd 29 dd 12 04 4d 85 22 98 aa 75 b2 a4 69 |M..)...M."..u..i| +00000040 f0 ca 9e 68 87 82 83 c3 3e c9 c4 ba c0 2f 00 00 |...h....>..../..| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,17 +61,17 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 ac 0c 00 00 a8 03 00 1d 20 d4 df 5d 10 ee ba a6 |........ ..]....| -000002d0 51 d7 1b fb bf ed bc d6 b9 34 44 e7 af 23 0e 9b |Q........4D..#..| -000002e0 45 af ba 7a 89 63 03 a9 4c 08 04 00 80 30 2c 0f |E..z.c..L....0,.| -000002f0 2e d9 e4 1d c2 90 01 1c cc cf d4 fe 06 6d c3 aa |.............m..| -00000300 59 d9 d9 bc 16 2f 2c b1 be 90 a3 93 a7 be bc 4d |Y..../,........M| -00000310 d8 f4 ac 21 36 59 a8 21 94 ef d3 c4 53 14 34 18 |...!6Y.!....S.4.| -00000320 c9 10 d5 77 fd 1e ad 15 0f 23 d7 73 90 7a c0 7b |...w.....#.s.z.{| -00000330 b3 b2 e2 df 15 42 35 ce 38 05 52 02 77 b7 b2 2b |.....B5.8.R.w..+| -00000340 6b 88 6a ce d4 20 99 9d e4 fe e8 38 1e 01 b7 78 |k.j.. .....8...x| -00000350 3c ea ac 8e ef 2f 7e e8 22 08 78 42 b7 db 84 80 |<..../~.".xB....| -00000360 8c 61 8a c5 cc d7 1f 6a 8d 5c 1d 2d 0d 16 03 03 |.a.....j.\.-....| +000002c0 ac 0c 00 00 a8 03 00 1d 20 e0 3c d0 b9 11 a0 6c |........ .<....l| +000002d0 7f 27 de d6 7b 4f 8d c6 fc 41 5d 10 cc dd ab 1d |.'..{O...A].....| +000002e0 a8 ed af 41 c0 06 c7 e2 2e 08 04 00 80 61 6b 9c |...A.........ak.| +000002f0 d9 48 e9 cb 65 7f ed 76 36 76 ee 71 55 39 0a 3f |.H..e..v6v.qU9.?| +00000300 33 fb c6 4c 20 c2 49 8e 9f 82 f2 b2 ff 3a 45 ef |3..L .I......:E.| +00000310 e5 66 a3 cb f4 4d 6f 51 f9 25 e4 d5 49 c9 f7 ce |.f...MoQ.%..I...| +00000320 20 d2 bb 41 c0 bd be 5e ca 6f cc 25 ca 7b 42 43 | ..A...^.o.%.{BC| +00000330 3c c1 02 73 66 84 0a a5 07 b6 b5 d4 74 13 d0 03 |<..sf.......t...| +00000340 87 27 45 67 9a 6b 02 0e 5f 4e 92 8f 32 58 9a 9a |.'Eg.k.._N..2X..| +00000350 6b 19 2a eb cd e7 6b 28 59 b5 e8 dc b2 38 4c 1b |k.*...k(Y....8L.| +00000360 36 d7 8f a5 da 4e ff 1d 2b f6 6a 73 8d 16 03 03 |6....N..+.js....| 00000370 00 3a 0d 00 00 36 03 01 02 40 00 2e 04 03 05 03 |.:...6...@......| 00000380 06 03 08 07 08 08 08 09 08 0a 08 0b 08 04 08 05 |................| 00000390 08 06 04 01 05 01 06 01 03 03 02 03 03 01 02 01 |................| @@ -112,26 +113,26 @@ 00000200 e5 35 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 |.5....%...! /.}.| 00000210 47 cd 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 |G.bC.(.._.).0...| 00000220 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 16 03 03 00 |......._X.;t....| -00000230 88 0f 00 00 84 08 04 00 80 b8 96 b3 c8 66 a9 fb |.............f..| -00000240 da 1b 82 65 9d 57 e5 e5 e5 60 c9 43 df 6e 99 53 |...e.W...`.C.n.S| -00000250 45 95 b8 58 d1 19 05 50 e1 a7 3c e8 07 ad 57 09 |E..X...P..<...W.| -00000260 9c 95 13 ea 80 24 53 56 b1 13 2d 59 9d e9 60 0f |.....$SV..-Y..`.| -00000270 75 97 d3 4f 82 3a b5 41 3e 90 75 ea 28 97 00 e7 |u..O.:.A>.u.(...| -00000280 74 c9 04 1d d0 16 ba 40 75 9c ae a0 bd 00 b1 a9 |t......@u.......| -00000290 86 d5 1a f2 30 45 72 99 ea b2 eb 61 b1 63 72 c5 |....0Er....a.cr.| -000002a0 ad b1 60 a8 fa bd 95 95 17 03 4c 8e 87 4b 44 e5 |..`.......L..KD.| -000002b0 ec f3 e0 48 33 b8 a9 74 78 14 03 03 00 01 01 16 |...H3..tx.......| -000002c0 03 03 00 28 00 00 00 00 00 00 00 00 e6 a6 db ee |...(............| -000002d0 7d fb 48 9f 81 a6 78 6a db a1 9a bb c8 da 7b b2 |}.H...xj......{.| -000002e0 6a 01 66 fb 85 a7 2f 35 40 77 b6 b2 |j.f.../5@w..| +00000230 88 0f 00 00 84 08 04 00 80 03 bd ea 7f 2e bd c2 |................| +00000240 5e 4f 2e a5 78 60 9b 9e e5 cb 73 d3 5e 5e c9 b9 |^O..x`....s.^^..| +00000250 10 89 ef ae 40 46 c0 0b d0 ce 00 c4 ac 48 e9 67 |....@F.......H.g| +00000260 ba 2a 83 8c a8 14 2e 52 01 14 36 b2 aa f4 c9 ca |.*.....R..6.....| +00000270 e1 3b fb 85 bb ad 54 eb ab 3e b7 00 af 13 71 ce |.;....T..>....q.| +00000280 1b b9 04 b7 c4 15 a9 f5 d2 41 16 60 ea ba 3b c1 |.........A.`..;.| +00000290 04 fb f9 3f 15 0a 5f 09 31 19 59 b0 69 98 c3 70 |...?.._.1.Y.i..p| +000002a0 9d fc 5f 67 75 41 b2 d9 ab bb 0f 0c 14 b6 2a dd |.._guA........*.| +000002b0 e8 35 3e 3a 78 38 16 dd 16 14 03 03 00 01 01 16 |.5>:x8..........| +000002c0 03 03 00 28 00 00 00 00 00 00 00 00 1e 0f ef 34 |...(...........4| +000002d0 86 04 b7 77 c4 e3 b8 3d 5c f4 16 13 f3 08 52 1e |...w...=\.....R.| +000002e0 3c 37 60 b1 c7 52 ef 10 96 4a c1 8d |<7`..R...J..| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 28 b3 9c 30 b6 a2 |..........(..0..| -00000010 cb cf 75 38 10 e7 80 39 0e 87 39 9c d9 da 2c 53 |..u8...9..9...,S| -00000020 1a 64 2d 33 ff 21 25 e9 3c f2 ec 6d a4 59 f4 30 |.d-3.!%.<..m.Y.0| -00000030 ea 41 24 |.A$| +00000000 14 03 03 00 01 01 16 03 03 00 28 90 76 7b bf 93 |..........(.v{..| +00000010 64 8b 3c 80 3e fc 25 ee 86 40 f1 86 de 6e 50 2c |d.<.>.%..@...nP,| +00000020 45 a4 b8 64 78 49 60 45 77 b1 16 17 e6 48 7b 4c |E..dxI`Ew....H{L| +00000030 39 b6 9d |9..| >>> Flow 5 (client to server) -00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 65 72 8f |.............er.| -00000010 4a 5f 08 c1 f9 37 5d 30 bc c6 e6 5f a8 23 35 69 |J_...7]0..._.#5i| -00000020 d3 3c 7a 15 03 03 00 1a 00 00 00 00 00 00 00 02 |.>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 97 f2 cb de f1 |....Y...U.......| -00000010 bb cf 9a 6c 6d 7e e2 94 af 9d 0b ed 02 cf fc b2 |...lm~..........| -00000020 80 b2 7b 41 2c a6 83 e7 52 62 93 20 63 23 7f 48 |..{A,...Rb. c#.H| -00000030 be c1 7f d3 75 34 fe 3a ad 27 f5 99 b0 73 91 df |....u4.:.'...s..| -00000040 b3 e9 82 95 cd 1b f9 08 b6 3d 4f 9b c0 2f 00 00 |.........=O../..| +00000000 16 03 03 00 59 02 00 00 55 03 03 55 bb e3 16 65 |....Y...U..U...e| +00000010 a0 9d d2 17 44 3a e7 74 ed 74 6e 82 b6 44 cf c9 |....D:.t.tn..D..| +00000020 61 a5 10 2a f8 ae 24 6a 0b 7a 8f 20 8d fa 31 fc |a..*..$j.z. ..1.| +00000030 7c 01 30 b9 68 e9 db ff 14 af 13 94 03 f5 17 66 ||.0.h..........f| +00000040 e0 6d c9 00 d9 3f cd c2 63 95 95 fe c0 2f 00 00 |.m...?..c..../..| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,17 +61,17 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 ac 0c 00 00 a8 03 00 1d 20 f8 3a 6c 5b 6f 88 48 |........ .:l[o.H| -000002d0 19 c5 a2 e7 4a d9 6d 21 56 23 63 1b 1f 95 aa bc |....J.m!V#c.....| -000002e0 33 ac aa 3b bb f8 35 ba 1a 04 01 00 80 98 6d 7b |3..;..5.......m{| -000002f0 7d 40 13 81 6b 70 ec ac 60 ee 1d 3e 37 36 bc f4 |}@..kp..`..>76..| -00000300 c1 9f 3c 13 b7 06 3d 38 be 4f 8c 3e e2 2e f2 b5 |..<...=8.O.>....| -00000310 de 16 ec a0 5b 64 00 5c c3 50 cc 79 a2 f7 e0 8d |....[d.\.P.y....| -00000320 68 e6 6b 1b b8 57 a4 15 d0 2c d7 4a be 97 26 26 |h.k..W...,.J..&&| -00000330 8c 5c 4e 26 36 96 48 b5 0f 88 7b 37 43 e4 d1 24 |.\N&6.H...{7C..$| -00000340 01 3c 70 38 99 c6 e2 2f 66 e7 db 57 30 f2 72 d0 |.>> Flow 3 (client to server) @@ -109,26 +110,26 @@ 00000200 e5 35 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 |.5....%...! /.}.| 00000210 47 cd 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 |G.bC.(.._.).0...| 00000220 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 16 03 03 00 |......._X.;t....| -00000230 88 0f 00 00 84 04 01 00 80 a8 12 9d 84 c2 17 0a |................| -00000240 03 ae bd 87 9a b6 6f 65 2f 7a 04 1f 69 2a 41 f4 |......oe/z..i*A.| -00000250 d0 9a 4d a4 5b 6e d2 d3 42 c3 77 4f 04 28 ce e6 |..M.[n..B.wO.(..| -00000260 d4 25 c5 81 1b 78 91 e9 1e 93 90 57 b2 58 6f 26 |.%...x.....W.Xo&| -00000270 ed 20 15 62 ff e9 c6 c1 52 4a 9a 05 a6 cd 17 22 |. .b....RJ....."| -00000280 75 c8 81 da a4 96 af c6 83 b5 5c 81 93 59 44 26 |u.........\..YD&| -00000290 5b 03 59 9d ab 93 ee c7 37 61 74 e7 4a 22 1c ec |[.Y.....7at.J"..| -000002a0 96 fb a2 c9 ea 2d 4b 8d d3 a7 e4 60 57 10 be b7 |.....-K....`W...| -000002b0 60 80 4f ee 8e 21 6b a2 13 14 03 03 00 01 01 16 |`.O..!k.........| -000002c0 03 03 00 28 00 00 00 00 00 00 00 00 16 82 4a c0 |...(..........J.| -000002d0 98 7b 62 3e 9b da a9 ac 31 f2 32 a9 23 13 2f e3 |.{b>....1.2.#./.| -000002e0 77 c9 1e ca 39 9f 4c 8a 10 58 33 67 |w...9.L..X3g| +00000230 88 0f 00 00 84 04 01 00 80 52 ae 04 3c 1c 34 2d |.........R..<.4-| +00000240 f6 8b c6 f6 6b 48 67 08 e7 96 03 2e 1c 5d 99 c3 |....kHg......]..| +00000250 8e b4 ee 4c 7f 73 ab 56 78 19 28 40 df 7a 96 bd |...L.s.Vx.(@.z..| +00000260 e5 5f 7a f3 7a 1f 5a fe c8 1b d8 ae 95 b4 8c 50 |._z.z.Z........P| +00000270 89 ca f1 d3 84 18 07 d7 4f ab 77 e0 d9 ce a5 87 |........O.w.....| +00000280 07 1f 61 c7 03 d4 67 d7 e3 96 65 ae ce ec 5c b7 |..a...g...e...\.| +00000290 8b 56 5c 30 5f 47 59 d2 5b 24 ae 8e 7d 17 61 6b |.V\0_GY.[$..}.ak| +000002a0 0b 3a 52 96 0b 10 e4 f8 20 c1 d3 76 14 ac 45 c5 |.:R..... ..v..E.| +000002b0 ae f0 95 62 d8 3f f5 5c 5f 14 03 03 00 01 01 16 |...b.?.\_.......| +000002c0 03 03 00 28 00 00 00 00 00 00 00 00 b6 b0 2a f0 |...(..........*.| +000002d0 2a 27 bc 1c e1 34 59 ff 88 76 61 7d c7 de 36 cc |*'...4Y..va}..6.| +000002e0 1e 11 99 a0 1f 5e 2b 28 86 bf 9e 1b |.....^+(....| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 28 8e 56 d0 9c 38 |..........(.V..8| -00000010 4f d9 df 12 9b dd 96 05 94 77 2f 6d 24 a8 cb 56 |O........w/m$..V| -00000020 91 f9 bc ec 00 b5 cc 71 c4 f4 36 42 be 68 37 78 |.......q..6B.h7x| -00000030 8f 6e 8c |.n.| +00000000 14 03 03 00 01 01 16 03 03 00 28 83 8d 2f 30 0a |..........(../0.| +00000010 f4 74 ff 13 16 80 a7 26 4c 25 90 75 3e 23 e3 f6 |.t.....&L%.u>#..| +00000020 eb 01 76 fe 0a 71 e7 41 02 45 da 57 3a 9e 67 00 |..v..q.A.E.W:.g.| +00000030 89 84 7d |..}| >>> Flow 5 (client to server) -00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 1c 19 9e |................| -00000010 a5 40 f6 d7 8b 80 23 8a 0b fa 14 65 08 6a 3c 66 |.@....#....e.j..D| +00000020 b6 d3 2d 15 03 03 00 1a 00 00 00 00 00 00 00 02 |..-.............| +00000030 d0 86 d3 eb a6 d1 0f b5 22 c5 ee b0 4d 76 9f 40 |........"...Mv.@| +00000040 7c 8b ||.| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-RSAPSS b/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-RSAPSS index 3f740807f6a..410dd3e35e9 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-RSAPSS +++ b/src/crypto/tls/testdata/Client-TLSv12-ClientCert-RSA-RSAPSS @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 29 bc e2 fe ae |....Y...U..)....| -00000010 0a db 37 e6 39 d5 48 24 3d 0f e5 d7 6b a3 69 dd |..7.9.H$=...k.i.| -00000020 ce 09 fd 28 03 c2 7e 38 db c9 ec 20 d2 5e 3f 94 |...(..~8... .^?.| -00000030 b0 2c 5e 4c 77 c2 94 c3 f2 a9 d0 91 4f 96 45 0e |.,^Lw.......O.E.| -00000040 d3 34 fc 9f e0 a5 e6 fc 1e 8a c1 00 c0 2f 00 00 |.4.........../..| +00000000 16 03 03 00 59 02 00 00 55 03 03 39 b0 78 c5 b4 |....Y...U..9.x..| +00000010 32 16 6f 41 13 05 be c5 c6 04 ea 2a 11 72 d3 1f |2.oA.......*.r..| +00000020 6e bf 89 89 48 20 0e 1d 9a 44 77 20 e8 5b a7 6e |n...H ...Dw .[.n| +00000030 7a fb 95 52 09 ec a7 95 a5 2c 52 d6 7e 28 d8 4e |z..R.....,R.~(.N| +00000040 96 95 16 c8 e7 5e af 80 b0 9b 9a 22 c0 2f 00 00 |.....^....."./..| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 66 0b 00 02 62 00 02 5f 00 02 5c 30 82 02 |..f...b.._..\0..| 00000070 58 30 82 01 8d a0 03 02 01 02 02 11 00 f2 99 26 |X0.............&| @@ -61,17 +62,17 @@ 000002a0 11 89 66 79 d1 8e 88 0e 0b a0 9e 30 2a c0 67 ef |..fy.......0*.g.| 000002b0 ca 46 02 88 e9 53 81 22 69 22 97 ad 80 93 d4 f7 |.F...S."i"......| 000002c0 dd 70 14 24 d7 70 0a 46 a1 16 03 03 00 ac 0c 00 |.p.$.p.F........| -000002d0 00 a8 03 00 1d 20 9e e4 39 3a b3 d5 f9 51 16 d4 |..... ..9:...Q..| -000002e0 a8 e1 0a 6d ad 3c ca 01 97 d6 a1 ce 03 2a 67 4a |...m.<.......*gJ| -000002f0 49 06 eb ed c6 24 08 04 00 80 b3 b7 9e fd 97 9b |I....$..........| -00000300 b0 d6 35 89 21 53 ff a8 4b 59 59 26 37 ac 2f 36 |..5.!S..KYY&7./6| -00000310 27 3d 5a 04 3f 50 ed 36 e0 5f 1a d7 1b 36 47 94 |'=Z.?P.6._...6G.| -00000320 45 ec 8c 0b 8f 0f fc df ec 3c 56 f0 d0 28 45 94 |E........#......| 00000380 00 00 08 01 01 00 02 08 04 00 00 16 03 03 00 04 |................| 00000390 0e 00 00 00 |....| >>> Flow 3 (client to server) @@ -117,26 +118,26 @@ 00000270 10 00 00 21 20 2f e5 7d a3 47 cd 62 43 15 28 da |...! /.}.G.bC.(.| 00000280 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| 00000290 5f 58 cb 3b 74 16 03 03 00 88 0f 00 00 84 08 04 |_X.;t...........| -000002a0 00 80 a6 6b 99 15 5e 97 33 4f a8 0e 59 af 15 22 |...k..^.3O..Y.."| -000002b0 f3 6e be 02 6e e4 20 d5 81 c0 b4 74 5a e2 20 32 |.n..n. ....tZ. 2| -000002c0 2b 7f 9c e6 94 32 4d 30 bf 93 86 9b 75 4d f1 9f |+....2M0....uM..| -000002d0 e4 48 28 00 27 fa 7c 45 2e fe d7 0b dc 03 c4 6b |.H(.'.|E.......k| -000002e0 42 ad a2 32 d7 9d ea d6 52 05 3f ed 87 fd b9 9d |B..2....R.?.....| -000002f0 58 fd d6 9f 28 6d 45 07 de 5b 4a 8e f4 4d 19 0b |X...(mE..[J..M..| -00000300 cf 4e 64 75 73 ae cd e9 ae f9 af 27 d0 b9 eb 4c |.Ndus......'...L| -00000310 98 ad 66 6d 4e bf 2c 39 87 f3 72 3e 4e bc a1 8f |..fmN.,9..r>N...| -00000320 a8 1e 14 03 03 00 01 01 16 03 03 00 28 00 00 00 |............(...| -00000330 00 00 00 00 00 04 3c cc ae cd 19 52 6b 1e 0e cc |......<....Rk...| -00000340 dd a9 ac 2f 2a c6 94 4c 09 f3 ee 2f b5 5a 13 1e |.../*..L.../.Z..| -00000350 4f 54 a0 ae c2 |OT...| +000002a0 00 80 8f 53 4a 89 09 a1 b4 4a f1 d6 b8 9e 00 9c |...SJ....J......| +000002b0 87 74 4d 70 46 de 8d 89 a8 68 68 9d a3 2d d9 54 |.tMpF....hh..-.T| +000002c0 43 d4 f0 67 0a a7 44 39 4e 2c 92 fe ba 12 21 f9 |C..g..D9N,....!.| +000002d0 2d e0 3a e4 2a b0 72 93 0f eb 27 43 3b b2 47 d1 |-.:.*.r...'C;.G.| +000002e0 49 9f e1 79 8f f8 51 c3 51 6b 45 3b 8d 25 64 ad |I..y..Q.QkE;.%d.| +000002f0 5c f2 ca f1 89 dd ab 55 f2 99 5a 7d f2 5b b2 08 |\......U..Z}.[..| +00000300 22 83 55 ff 6e 78 08 9a 7b 15 fc fc cf f5 18 1c |".U.nx..{.......| +00000310 ba 14 eb 5d 6b 35 08 95 5d 60 12 12 9c 92 d1 f4 |...]k5..]`......| +00000320 9b c0 14 03 03 00 01 01 16 03 03 00 28 00 00 00 |............(...| +00000330 00 00 00 00 00 4a 07 ef fb b0 9b 52 05 13 11 de |.....J.....R....| +00000340 21 46 4a d9 18 c3 c1 10 97 78 d1 e6 16 e9 90 a2 |!FJ......x......| +00000350 42 08 11 eb 07 |B....| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 28 6d 44 cb 35 8b |..........(mD.5.| -00000010 15 5c f9 f8 1e ae 4f 8c 8c d9 90 9e 6c cf 13 f6 |.\....O.....l...| -00000020 12 29 f5 f7 d6 ff da e2 48 7d 68 ec ad 1a 6c 39 |.)......H}h...l9| -00000030 c5 77 6c |.wl| +00000000 14 03 03 00 01 01 16 03 03 00 28 21 7c c3 2b 12 |..........(!|.+.| +00000010 37 a3 8d 5c 86 04 31 dd da d9 65 59 e9 2e bd 88 |7..\..1...eY....| +00000020 6a 83 9c f2 80 e7 4b 58 b2 92 c2 64 38 63 66 f2 |j.....KX...d8cf.| +00000030 54 c5 16 |T..| >>> Flow 5 (client to server) -00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 2a ce da |.............*..| -00000010 11 1c 7d 49 0d aa 44 d4 d6 d4 7f 64 2b 49 47 20 |..}I..D....d+IG | -00000020 5a 21 bb 15 03 03 00 1a 00 00 00 00 00 00 00 02 |Z!..............| -00000030 fc 10 75 a7 22 f9 74 1c 3a d2 b2 a8 04 2d 37 5f |..u.".t.:....-7_| -00000040 c2 76 |.v| +00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 5c bc af |.............\..| +00000010 d6 61 03 a4 fe dd f6 0f 21 f7 57 82 bf 91 d4 1d |.a......!.W.....| +00000020 7a fd be 15 03 03 00 1a 00 00 00 00 00 00 00 02 |z...............| +00000030 e6 e4 df c9 1e 71 be 1e f5 c8 c3 15 68 1a 87 f0 |.....q......h...| +00000040 70 45 |pE| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES index 95781c6853b..46f690e823a 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES +++ b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 eb a2 77 eb b6 |....Y...U....w..| -00000010 1e e4 5c 2c ed 5a dc 93 1b 7e 8a 75 a1 8c ac a6 |..\,.Z...~.u....| -00000020 69 13 f6 f6 a4 69 07 93 99 cf 12 20 37 d7 f8 26 |i....i..... 7..&| -00000030 46 ea 3a 21 03 d0 25 0f 22 84 8d 24 2f 98 3d 42 |F.:!..%."..$/.=B| -00000040 eb 47 1d de 0c 12 ab 95 7a 55 46 f7 c0 09 00 00 |.G......zUF.....| +00000000 16 03 03 00 59 02 00 00 55 03 03 37 82 24 98 f9 |....Y...U..7.$..| +00000010 5d aa 41 32 e5 67 0f 8e d5 11 09 b6 98 06 8d 6a |].A2.g.........j| +00000020 96 17 cd 3b 66 40 ef 99 c6 d6 52 20 73 6f 80 f5 |...;f@....R so..| +00000030 10 8b 11 23 4e 6b 0d c3 ea e0 da 02 be fc 11 27 |...#Nk.........'| +00000040 8a b0 6c 46 71 56 44 69 50 ec 4e f5 c0 09 00 00 |..lFqVDiP.N.....| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 0e 0b 00 02 0a 00 02 07 00 02 04 30 82 02 |.............0..| 00000070 00 30 82 01 62 02 09 00 b8 bf 2d 47 a0 d2 eb f4 |.0..b.....-G....| @@ -55,39 +56,39 @@ 00000240 13 83 0d 94 06 bb d4 37 7a f6 ec 7a c9 86 2e dd |.......7z..z....| 00000250 d7 11 69 7f 85 7c 56 de fb 31 78 2b e4 c7 78 0d |..i..|V..1x+..x.| 00000260 ae cb be 9e 4e 36 24 31 7b 6a 0f 39 95 12 07 8f |....N6$1{j.9....| -00000270 2a 16 03 03 00 b7 0c 00 00 b3 03 00 1d 20 90 68 |*............ .h| -00000280 81 8b 1d 7f d5 69 36 d3 4e 63 40 fa 3a 21 ee a4 |.....i6.Nc@.:!..| -00000290 c7 b4 09 bc 34 51 89 df d5 d2 79 51 34 32 04 03 |....4Q....yQ42..| -000002a0 00 8b 30 81 88 02 42 01 b4 69 6b 1c e6 35 99 81 |..0...B..ik..5..| -000002b0 fb aa cb b4 2d e9 e0 48 6a 6c 5e 14 54 77 b7 9d |....-..Hjl^.Tw..| -000002c0 df a3 c2 1b 53 8c d2 46 6d 2e ae 83 3a db 7c 86 |....S..Fm...:.|.| -000002d0 4a 45 c7 51 cd 30 d6 8c f5 4f ea 37 cb 1e 27 18 |JE.Q.0...O.7..'.| -000002e0 ba df d5 5f 11 ae 0e af 75 02 42 01 2b 37 2e 6d |..._....u.B.+7.m| -000002f0 7c 11 57 b7 b7 8b 90 73 cd e0 c9 38 3c ee aa d5 ||.W....s...8<...| -00000300 f2 cd ff b9 66 6a be 62 70 74 ee a4 f4 e3 fb 4f |....fj.bpt.....O| -00000310 ed 2e d5 a7 b5 a4 53 c8 1b 17 9e e9 48 e1 dd a6 |......S.....H...| -00000320 e8 6a 05 cf 73 b2 85 11 13 37 be e0 26 16 03 03 |.j..s....7..&...| -00000330 00 04 0e 00 00 00 |......| +00000270 2a 16 03 03 00 b6 0c 00 00 b2 03 00 1d 20 d1 6c |*............ .l| +00000280 75 ba f5 41 b8 0e 92 fe cb 0a 7e 8a fc 5a a6 9f |u..A......~..Z..| +00000290 a9 3e b9 db 37 86 5b 16 36 9b eb cf ee 69 04 03 |.>..7.[.6....i..| +000002a0 00 8a 30 81 87 02 41 71 50 84 52 af ae 91 63 8d |..0...AqP.R...c.| +000002b0 ae bd 7c b6 b8 ab f4 0d 89 39 dd 61 7d 0e 59 a6 |..|......9.a}.Y.| +000002c0 83 42 5a a2 06 16 4d 2d 17 08 b5 9a 91 a4 0c 95 |.BZ...M-........| +000002d0 d6 5f e5 e7 d9 93 9d 20 2a 9a a1 75 31 19 5e 82 |._..... *..u1.^.| +000002e0 6c 3a 26 36 05 bb 67 42 02 42 01 dc b6 d6 fe 34 |l:&6..gB.B.....4| +000002f0 2a 88 77 e2 9e 48 32 ca fe 99 72 56 47 4a c7 59 |*.w..H2...rVGJ.Y| +00000300 96 fa 5e 21 76 ce ba 75 11 d3 a4 a8 ca 68 f8 eb |..^!v..u.....h..| +00000310 8a 43 f6 d3 0e 0d 19 da 65 84 e3 12 be 3b c7 e2 |.C......e....;..| +00000320 48 c1 90 9d 96 7d ac 60 0d 01 5c e8 16 03 03 00 |H....}.`..\.....| +00000330 04 0e 00 00 00 |.....| >>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| 00000030 16 03 03 00 40 00 00 00 00 00 00 00 00 00 00 00 |....@...........| -00000040 00 00 00 00 00 7f 83 b7 cd 14 66 fb c3 2a f9 9f |..........f..*..| -00000050 79 ec 40 e5 dd 15 46 f3 25 8d dd b2 8e d5 78 97 |y.@...F.%.....x.| -00000060 e5 d6 4e 1a 2e 35 21 b2 aa ac 28 6f 2c 36 a6 6e |..N..5!...(o,6.n| -00000070 44 92 84 1b b9 |D....| +00000040 00 00 00 00 00 ce 1b 8e 84 37 1d 41 a0 84 93 88 |.........7.A....| +00000050 d1 ad 2c 7d 8e bf 77 20 42 3a be fe 45 29 c0 b3 |..,}..w B:..E)..| +00000060 7f a9 35 2b 4c 42 aa a2 8e 52 f1 a1 a0 69 fc 03 |..5+LB...R...i..| +00000070 7d 76 c5 c8 6f |}v..o| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 40 db ee f8 c1 0e |..........@.....| -00000010 7f 23 b4 cb e6 db 03 2a fb 68 40 78 85 03 9e dc |.#.....*.h@x....| -00000020 ac f8 f0 b5 65 8d 7c 01 4a ce 86 29 a9 c5 c3 b2 |....e.|.J..)....| -00000030 12 8d d1 58 af e7 21 75 e4 be f3 c0 03 55 f8 bb |...X..!u.....U..| -00000040 71 bd 85 ee 46 87 a0 32 75 ee 4c |q...F..2u.L| +00000000 14 03 03 00 01 01 16 03 03 00 40 23 c9 a6 0e 9c |..........@#....| +00000010 16 db 20 e1 e1 46 70 c4 50 47 8d 19 0a 33 23 2a |.. ..Fp.PG...3#*| +00000020 5b f3 12 78 62 9e de fc bb 98 fd 0c ef 9a f0 6b |[..xb..........k| +00000030 29 06 8a 7a 97 39 c8 56 ca 19 b0 7e ab 67 5d 58 |)..z.9.V...~.g]X| +00000040 18 af 9c 40 77 3e 68 b3 3b 26 9a |...@w>h.;&.| >>> Flow 5 (client to server) 00000000 17 03 03 00 30 00 00 00 00 00 00 00 00 00 00 00 |....0...........| -00000010 00 00 00 00 00 48 95 f8 a1 0e a7 d0 50 dd cf 8f |.....H......P...| -00000020 c4 af ec 49 89 bf 5d 8b a0 d0 60 7b 38 5a 83 e4 |...I..]...`{8Z..| -00000030 72 47 7f 81 bd 15 03 03 00 30 00 00 00 00 00 00 |rG.......0......| -00000040 00 00 00 00 00 00 00 00 00 00 48 06 f1 30 61 dd |..........H..0a.| -00000050 e2 97 aa 9c 5f a7 07 bb 44 a4 fb d6 6a 7c aa f5 |...._...D...j|..| -00000060 16 ae 38 1a 98 e5 f5 28 c2 57 |..8....(.W| +00000010 00 00 00 00 00 2a a1 02 72 cd 55 e7 43 e6 16 53 |.....*..r.U.C..S| +00000020 88 91 3e e4 cc ae 4d e2 22 ab 78 59 5e 32 c5 40 |..>...M.".xY^2.@| +00000030 db 4a 2c 92 90 15 03 03 00 30 00 00 00 00 00 00 |.J,......0......| +00000040 00 00 00 00 00 00 00 00 00 00 b3 d0 dc f3 e9 b5 |................| +00000050 a1 36 b9 bf 44 5d ee 83 40 c5 21 f7 61 a0 b0 7d |.6..D]..@.!.a..}| +00000060 8c 0c 96 d6 51 a1 fe 08 9f 25 |....Q....%| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES-GCM b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES-GCM index 7214747d15e..64305aea2e6 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES-GCM +++ b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES-GCM @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 c9 a1 8b 70 59 |....Y...U.....pY| -00000010 8b 88 41 56 b7 bc 9a 1f 50 57 46 7d 79 d8 ef b2 |..AV....PWF}y...| -00000020 15 3f ad ad bb 48 09 ce e1 c2 2c 20 84 43 65 e7 |.?...H...., .Ce.| -00000030 3f 2f d8 13 9a 79 ac 54 ee b9 13 a1 7c a7 05 f7 |?/...y.T....|...| -00000040 c8 b4 fc bd 20 40 17 ca 15 cd 91 1e c0 2b 00 00 |.... @.......+..| +00000000 16 03 03 00 59 02 00 00 55 03 03 1f da 30 68 6e |....Y...U....0hn| +00000010 dd b8 c1 80 c1 12 c0 16 35 3b 8e f7 12 e1 cb b3 |........5;......| +00000020 c1 1f dc 67 84 94 ff a8 f3 b6 ca 20 28 db 1e 50 |...g....... (..P| +00000030 48 32 39 1e 82 c5 0a 37 b3 c7 60 88 c6 4f b6 96 |H29....7..`..O..| +00000040 70 cf da 55 d3 3a 15 02 f2 ed 49 96 c0 2b 00 00 |p..U.:....I..+..| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 0e 0b 00 02 0a 00 02 07 00 02 04 30 82 02 |.............0..| 00000070 00 30 82 01 62 02 09 00 b8 bf 2d 47 a0 d2 eb f4 |.0..b.....-G....| @@ -55,34 +56,34 @@ 00000240 13 83 0d 94 06 bb d4 37 7a f6 ec 7a c9 86 2e dd |.......7z..z....| 00000250 d7 11 69 7f 85 7c 56 de fb 31 78 2b e4 c7 78 0d |..i..|V..1x+..x.| 00000260 ae cb be 9e 4e 36 24 31 7b 6a 0f 39 95 12 07 8f |....N6$1{j.9....| -00000270 2a 16 03 03 00 b7 0c 00 00 b3 03 00 1d 20 58 f9 |*............ X.| -00000280 2e 03 90 fa 3d 33 0d 3e e1 3a b1 5a 45 ec 5c ee |....=3.>.:.ZE.\.| -00000290 9f 47 51 4b 93 89 33 11 e0 63 86 fd b2 3b 04 03 |.GQK..3..c...;..| -000002a0 00 8b 30 81 88 02 42 01 c2 fa 7b f8 ed 6b a5 0f |..0...B...{..k..| -000002b0 33 87 02 35 5b 8e 5d 31 5e 92 df c2 90 ae 58 24 |3..5[.]1^.....X$| -000002c0 43 0f ba e3 b8 77 12 7a 97 c3 77 15 62 d3 f2 cc |C....w.z..w.b...| -000002d0 10 cd a9 be b6 b2 37 93 b1 ce 8b b2 6c fa 93 74 |......7.....l..t| -000002e0 5e 14 8e ba 9e d7 66 48 b8 02 42 01 8e 9a 10 1d |^.....fH..B.....| -000002f0 7d e0 d3 cf 0d d0 3c bc 34 1c 16 20 85 50 03 3f |}.....<.4.. .P.?| -00000300 e1 6d a3 a0 d4 6e d8 fd 7e df b4 c1 84 29 c3 68 |.m...n..~....).h| -00000310 c2 01 dd 77 fc 2c a5 8f 3b 74 c6 e4 32 20 b7 a0 |...w.,..;t..2 ..| -00000320 8c 1b 2d 93 6a 9c 8a ed 21 b5 9a e0 cb 16 03 03 |..-.j...!.......| +00000270 2a 16 03 03 00 b7 0c 00 00 b3 03 00 1d 20 16 7e |*............ .~| +00000280 b8 86 3b 99 63 37 d3 60 8b a2 84 ed e1 2c 38 93 |..;.c7.`.....,8.| +00000290 b6 cc fb 59 95 f9 ef b0 89 da 1a 04 fa 71 04 03 |...Y.........q..| +000002a0 00 8b 30 81 88 02 42 01 3a db 0e ed 72 a0 d9 e6 |..0...B.:...r...| +000002b0 2a 81 ff a4 74 49 ed 02 6d ba c8 bd 82 9a 1e 83 |*...tI..m.......| +000002c0 32 3c 8b e3 4c dc 7f 77 a5 77 56 01 df 72 cb 00 |2<..L..w.wV..r..| +000002d0 c2 f8 bc 11 09 82 dd 2b 68 79 13 45 ff 54 99 df |.......+hy.E.T..| +000002e0 1d 15 25 78 53 eb f1 00 3a 02 42 01 55 67 57 ea |..%xS...:.B.UgW.| +000002f0 7c ce cb 76 69 02 6d 1d 80 72 3c 6f bd d7 3c a7 ||..vi.m..r>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| -00000030 16 03 03 00 28 00 00 00 00 00 00 00 00 c2 14 2d |....(..........-| -00000040 fc d7 a2 cb 18 b9 2a ae 38 70 b7 78 7c 88 97 d3 |......*.8p.x|...| -00000050 ff 7f df 12 23 96 ab 4d 6c 5c 67 72 c4 |....#..Ml\gr.| +00000030 16 03 03 00 28 00 00 00 00 00 00 00 00 4b 8e 00 |....(........K..| +00000040 44 bf cd d5 4c 14 0e 87 aa 7c 8b a7 39 a6 e4 ed |D...L....|..9...| +00000050 bc e0 03 44 98 c9 c7 73 1d 21 7a 64 0c |...D...s.!zd.| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 28 2a dd b3 5b c6 |..........(*..[.| -00000010 76 e7 c0 ac 8c 70 77 d6 d8 4e 79 4a 04 3d 91 a9 |v....pw..NyJ.=..| -00000020 ad 79 ef c9 22 78 17 9e ef b0 03 c8 e6 85 b7 8c |.y.."x..........| -00000030 e5 74 95 |.t.| +00000000 14 03 03 00 01 01 16 03 03 00 28 0e de af 82 c9 |..........(.....| +00000010 87 66 1e 67 f7 4d 77 8e 8a fd c4 f8 50 32 63 14 |.f.g.Mw.....P2c.| +00000020 38 04 fa 28 4e 9f dd f0 5b fa 3c ed c4 76 c3 1f |8..(N...[.<..v..| +00000030 5c cb 21 |\.!| >>> Flow 5 (client to server) -00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 84 b5 0f |................| -00000010 1f ed f9 4c 0d a1 f3 7b 8e 23 87 65 b1 39 98 50 |...L...{.#.e.9.P| -00000020 3d ff 1b 15 03 03 00 1a 00 00 00 00 00 00 00 02 |=...............| -00000030 aa 34 cc f1 4a d3 de 4c 42 bc 2c 0f 3e 71 af 6b |.4..J..LB.,.>q.k| -00000040 3c fc |<.| +00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 2b 89 d5 |.............+..| +00000010 d9 34 98 0a 1f d6 d8 d1 4d bd 20 e1 45 04 9e 1f |.4......M. .E...| +00000020 71 8c c8 15 03 03 00 1a 00 00 00 00 00 00 00 02 |q...............| +00000030 92 5e 79 50 7c 19 b1 26 eb 52 c2 10 75 0b a0 43 |.^yP|..&.R..u..C| +00000040 45 d0 |E.| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES128-SHA256 b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES128-SHA256 index 96f6218a35d..c0e908e9cc2 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES128-SHA256 +++ b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES128-SHA256 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 87 87 6f ce 44 |....Y...U....o.D| -00000010 94 5f 2f cc 94 03 50 68 a7 4f 37 70 8a d4 cf e3 |._/...Ph.O7p....| -00000020 23 7f 11 f5 93 c7 3f 96 87 49 45 20 9c d4 96 b2 |#.....?..IE ....| -00000030 dc 8c 16 c5 fb cc 2f 8e 0e a5 ef a3 ea cf 57 d0 |....../.......W.| -00000040 09 70 bd 16 c4 d9 e4 1b a0 40 f7 f3 c0 23 00 00 |.p.......@...#..| +00000000 16 03 03 00 59 02 00 00 55 03 03 5b 5d 5d 8a 4c |....Y...U..[]].L| +00000010 ba a9 b4 79 dd 3b d5 02 d8 f2 de f7 85 73 16 17 |...y.;.......s..| +00000020 e9 49 d5 56 a7 82 98 fa 0d 7d ce 20 e1 fc 99 42 |.I.V.....}. ...B| +00000030 f7 f3 40 c9 dc d7 60 57 3b 21 5d 54 d0 86 fc 74 |..@...`W;!]T...t| +00000040 07 77 b2 f4 b6 d9 90 b5 a9 38 84 38 c0 23 00 00 |.w.......8.8.#..| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 0e 0b 00 02 0a 00 02 07 00 02 04 30 82 02 |.............0..| 00000070 00 30 82 01 62 02 09 00 b8 bf 2d 47 a0 d2 eb f4 |.0..b.....-G....| @@ -55,43 +56,43 @@ 00000240 13 83 0d 94 06 bb d4 37 7a f6 ec 7a c9 86 2e dd |.......7z..z....| 00000250 d7 11 69 7f 85 7c 56 de fb 31 78 2b e4 c7 78 0d |..i..|V..1x+..x.| 00000260 ae cb be 9e 4e 36 24 31 7b 6a 0f 39 95 12 07 8f |....N6$1{j.9....| -00000270 2a 16 03 03 00 b6 0c 00 00 b2 03 00 1d 20 3f a6 |*............ ?.| -00000280 d1 0d ae 8d c0 06 14 ca da 2c 69 1c f1 84 c4 dd |.........,i.....| -00000290 14 f4 0e a6 ce b5 d6 37 9d 9f a5 ba 7b 74 04 03 |.......7....{t..| -000002a0 00 8a 30 81 87 02 42 00 b5 2b 9a 32 9d af b9 cc |..0...B..+.2....| -000002b0 0d b6 f1 9b 87 35 af d7 dc 04 0f 1b 04 d7 fa 62 |.....5.........b| -000002c0 20 bd 2c 31 41 17 e7 c0 ea 22 78 e4 de 37 14 a8 | .,1A...."x..7..| -000002d0 f9 f3 f1 3e 0c 55 59 b3 e3 0e 31 26 ce d0 c1 19 |...>.UY...1&....| -000002e0 b8 17 07 2a 23 98 7b 17 0f 02 41 41 d5 51 80 4d |...*#.{...AA.Q.M| -000002f0 8a 14 56 b1 39 7b 8b 37 24 ef e0 ec 43 44 5a cc |..V.9{.7$...CDZ.| -00000300 9b ab dc 63 e7 cc 7b 29 c0 66 ae 9c 23 c5 1b 98 |...c..{).f..#...| -00000310 6e 35 64 97 12 43 16 73 a6 6b c8 09 2c 26 7c f5 |n5d..C.s.k..,&|.| -00000320 b1 1f 9f 55 04 9e 53 33 c1 89 7a d0 16 03 03 00 |...U..S3..z.....| -00000330 04 0e 00 00 00 |.....| +00000270 2a 16 03 03 00 b7 0c 00 00 b3 03 00 1d 20 b4 e2 |*............ ..| +00000280 7e 17 88 04 39 06 9e 01 38 92 d5 e7 d5 3a 52 f0 |~...9...8....:R.| +00000290 e3 c9 43 6d 7f 66 76 f4 47 1a af ac 42 7a 04 03 |..Cm.fv.G...Bz..| +000002a0 00 8b 30 81 88 02 42 01 00 dc 63 78 49 3d 35 e7 |..0...B...cxI=5.| +000002b0 dc 48 b0 84 81 94 7c 5a b1 bc 8c 49 8f bd 7f 18 |.H....|Z...I....| +000002c0 7c 59 4d 1c 1a 27 a1 2a ac 5b 73 57 49 25 c9 2e ||YM..'.*.[sWI%..| +000002d0 fa 5d d5 f9 c7 99 5e bc 1a f0 0d 98 85 15 09 a6 |.]....^.........| +000002e0 b2 b1 f9 41 93 0d 46 2f 0a 02 42 01 d9 35 e3 27 |...A..F/..B..5.'| +000002f0 aa 57 29 2f e0 0c de 44 51 e3 0b eb 25 4c 02 84 |.W)/...DQ...%L..| +00000300 d3 f2 11 7c 08 d9 03 7e 66 91 32 ef d9 3c f8 89 |...|...~f.2..<..| +00000310 35 4a 84 02 61 ff 91 5b 2a d1 82 ee b7 82 d8 24 |5J..a..[*......$| +00000320 6b 5c 1a c9 22 d5 c1 6b c4 97 14 6a e2 16 03 03 |k\.."..k...j....| +00000330 00 04 0e 00 00 00 |......| >>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| 00000030 16 03 03 00 50 00 00 00 00 00 00 00 00 00 00 00 |....P...........| -00000040 00 00 00 00 00 d3 72 3f 9d 37 ba 97 55 83 b4 f0 |......r?.7..U...| -00000050 ad 0b f0 48 98 16 05 f1 b5 6e da a4 79 e4 d9 8e |...H.....n..y...| -00000060 62 af b9 a1 d1 a4 5c 04 d2 b1 86 32 af 64 ac 89 |b.....\....2.d..| -00000070 d3 47 5f 61 ae f4 21 5b 8d 4b ff 74 c1 b8 9c de |.G_a..![.K.t....| -00000080 fd 74 a0 99 c1 |.t...| +00000040 00 00 00 00 00 63 47 df 33 dd 2f 30 01 5c 87 67 |.....cG.3./0.\.g| +00000050 10 e4 0a 04 ef 97 ba fb cb 29 43 b7 a5 cd 29 0c |.........)C...).| +00000060 c3 8c 31 bf 87 f9 14 ab 53 ae a3 07 9e e9 72 c5 |..1.....S.....r.| +00000070 b3 9f b5 70 1d 74 7b aa a2 04 07 74 7e 79 3c f0 |...p.t{....t~y<.| +00000080 ee 26 57 e4 65 |.&W.e| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 50 09 3b 3e 7e 2e |..........P.;>~.| -00000010 d8 46 04 ac b0 3d c9 7e ec 28 8c bd 6c 0f a8 b5 |.F...=.~.(..l...| -00000020 af 8c 86 ed 64 81 6c d4 98 9e 56 2a 48 0d 03 40 |....d.l...V*H..@| -00000030 64 3e 25 58 6f 03 6a 4e be a2 11 6f 6f e7 2f c2 |d>%Xo.jN...oo./.| -00000040 8f 78 c4 11 a1 07 21 91 9d 34 01 08 39 0d 07 d2 |.x....!..4..9...| -00000050 d4 a2 cc 2f 25 ea ee 8d 8b 91 f9 |.../%......| +00000000 14 03 03 00 01 01 16 03 03 00 50 fd c7 a3 f6 1e |..........P.....| +00000010 7e 81 c1 90 f0 39 c7 0a bf 9a 27 35 bf 78 7b 19 |~....9....'5.x{.| +00000020 42 61 c0 30 dc a6 87 80 9a a1 a3 88 bc 9f e7 b5 |Ba.0............| +00000030 26 f8 60 df 3b 62 c8 a4 23 f4 d3 54 ce 7e a5 37 |&.`.;b..#..T.~.7| +00000040 92 3f 0b 54 95 01 03 c3 30 f8 9f 5a 01 45 8e f1 |.?.T....0..Z.E..| +00000050 2a ca 8e 45 f7 c0 d2 a7 44 06 60 |*..E....D.`| >>> Flow 5 (client to server) 00000000 17 03 03 00 40 00 00 00 00 00 00 00 00 00 00 00 |....@...........| -00000010 00 00 00 00 00 1d 76 4c fb 46 f8 02 9a bc 07 8d |......vL.F......| -00000020 b0 52 40 44 58 da ad be 3c a6 d7 44 0f 59 98 f3 |.R@DX...<..D.Y..| -00000030 ae 5c d2 04 bb 07 ee f6 99 9d 2c 14 44 3b 90 bc |.\........,.D;..| -00000040 2b e9 bc 37 59 15 03 03 00 40 00 00 00 00 00 00 |+..7Y....@......| -00000050 00 00 00 00 00 00 00 00 00 00 c4 ef 97 87 35 a2 |..............5.| -00000060 2f cc c2 6f 3d d5 f5 6f fd 74 56 50 37 f8 10 e8 |/..o=..o.tVP7...| -00000070 36 f5 fb 6f 7b 5d 20 07 0d 2f 72 46 a7 3a e0 de |6..o{] ../rF.:..| -00000080 39 b3 76 0e 4f c0 e7 85 4b bb |9.v.O...K.| +00000010 00 00 00 00 00 f0 3a bf be 28 56 73 60 e0 16 99 |......:..(Vs`...| +00000020 ea b7 f5 b5 0d 77 ee 2b e1 8a f4 47 48 14 de e1 |.....w.+...GH...| +00000030 e1 65 72 7c 9c 52 a2 02 69 6e 8d 4d 48 e8 61 05 |.er|.R..in.MH.a.| +00000040 bd 6a 5f b2 7a 15 03 03 00 40 00 00 00 00 00 00 |.j_.z....@......| +00000050 00 00 00 00 00 00 00 00 00 00 b2 a2 db 45 da d7 |.............E..| +00000060 45 df 9f 7b df d3 c6 d2 83 8f 90 15 dd 13 4a e3 |E..{..........J.| +00000070 33 bf 17 43 47 11 48 9b 2f e0 4e 49 3c 1e 9d a4 |3..CG.H./.NI<...| +00000080 1d 0c d5 8e 31 19 64 49 13 51 |....1.dI.Q| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES256-GCM-SHA384 b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES256-GCM-SHA384 index 90a1639e990..e6b17fe9660 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES256-GCM-SHA384 +++ b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-AES256-GCM-SHA384 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 b8 16 bd ae 15 |....Y...U.......| -00000010 a3 33 52 cc 60 dc 6c fe 7c f3 82 b9 1e 13 ab 87 |.3R.`.l.|.......| -00000020 22 d8 c3 38 dc 8a 76 bb a0 a3 fd 20 8a d1 92 d1 |"..8..v.... ....| -00000030 d6 f3 76 e0 e2 76 32 95 32 a0 eb 5b dc e4 42 81 |..v..v2.2..[..B.| -00000040 14 bb 58 ab b8 e8 9d ee fa 32 58 05 c0 2c 00 00 |..X......2X..,..| +00000000 16 03 03 00 59 02 00 00 55 03 03 09 26 6c b6 48 |....Y...U...&l.H| +00000010 c1 56 0f 9c 49 b9 3f 59 a4 d1 3b 7a f9 52 04 7d |.V..I.?Y..;z.R.}| +00000020 f1 e0 45 c2 ef 8c 16 3d 79 2b fd 20 b2 14 24 ce |..E....=y+. ..$.| +00000030 a8 46 c8 fd 94 b3 b2 29 ab 4c da a0 d5 1e c4 7d |.F.....).L.....}| +00000040 98 52 3b c7 da 3a b6 af 22 29 8b 31 c0 2c 00 00 |.R;..:..").1.,..| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 0e 0b 00 02 0a 00 02 07 00 02 04 30 82 02 |.............0..| 00000070 00 30 82 01 62 02 09 00 b8 bf 2d 47 a0 d2 eb f4 |.0..b.....-G....| @@ -55,34 +56,34 @@ 00000240 13 83 0d 94 06 bb d4 37 7a f6 ec 7a c9 86 2e dd |.......7z..z....| 00000250 d7 11 69 7f 85 7c 56 de fb 31 78 2b e4 c7 78 0d |..i..|V..1x+..x.| 00000260 ae cb be 9e 4e 36 24 31 7b 6a 0f 39 95 12 07 8f |....N6$1{j.9....| -00000270 2a 16 03 03 00 b6 0c 00 00 b2 03 00 1d 20 5c 9b |*............ \.| -00000280 9b 29 5c 83 36 b8 20 47 2b 04 0d 1b ab f5 f7 81 |.)\.6. G+.......| -00000290 aa 89 b4 93 37 aa 28 4e 44 e1 22 26 b6 46 04 03 |....7.(ND."&.F..| -000002a0 00 8a 30 81 87 02 42 01 2c 87 df 1f 07 86 36 c8 |..0...B.,.....6.| -000002b0 f6 aa 41 c1 8e 99 6e 12 08 5f e2 62 4b 3a 9b ad |..A...n.._.bK:..| -000002c0 e8 26 1c 95 f9 62 c6 f6 c7 e4 f7 db 3b 23 e5 4f |.&...b......;#.O| -000002d0 03 a1 c6 89 74 cb bd 2a 4e 47 3f 0f bf 28 bb 6d |....t..*NG?..(.m| -000002e0 c0 c6 53 4c 02 0b 9a 30 2d 02 41 0c 6f 26 a5 4c |..SL...0-.A.o&.L| -000002f0 b6 6c 8c ab 82 32 19 a0 f0 1b 41 2d 9d 1d 12 1b |.l...2....A-....| -00000300 91 62 6a 3d 17 92 79 f6 59 45 21 2f 6b d0 cb 7b |.bj=..y.YE!/k..{| -00000310 22 b3 79 80 90 90 81 97 06 c8 59 fd 8b 40 f9 ec |".y.......Y..@..| -00000320 80 58 db fc 5e a2 67 9a 96 01 53 d4 16 03 03 00 |.X..^.g...S.....| -00000330 04 0e 00 00 00 |.....| +00000270 2a 16 03 03 00 b7 0c 00 00 b3 03 00 1d 20 3c 6b |*............ >> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| -00000030 16 03 03 00 28 00 00 00 00 00 00 00 00 17 be e6 |....(...........| -00000040 ba 39 2d 82 38 6e 09 2c 1c ef d5 1f ad 8e e0 47 |.9-.8n.,.......G| -00000050 2d bc 74 f8 3b ed 86 89 9e e9 a5 01 40 |-.t.;.......@| +00000030 16 03 03 00 28 00 00 00 00 00 00 00 00 90 77 e2 |....(.........w.| +00000040 93 66 4c bb 7e af cd c7 ee cc 49 e5 bb e8 45 3a |.fL.~.....I...E:| +00000050 42 51 72 17 8a cb 53 a2 6e a5 14 cf ea |BQr...S.n....| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 28 42 3b b0 5e 66 |..........(B;.^f| -00000010 3e ef a5 3d 49 64 42 34 b1 21 d6 43 d3 f6 f5 84 |>..=IdB4.!.C....| -00000020 21 96 b4 7b ed 73 b5 23 b6 40 cf 86 ab 71 59 58 |!..{.s.#.@...qYX| -00000030 3a bf 79 |:.y| +00000000 14 03 03 00 01 01 16 03 03 00 28 d5 bd d4 73 39 |..........(...s9| +00000010 f7 e7 cf e8 4d 93 23 e0 50 39 07 36 bd 32 a8 72 |....M.#.P9.6.2.r| +00000020 14 74 1d 53 a5 a0 9c f1 90 a0 82 14 ef 98 43 9a |.t.S..........C.| +00000030 c7 e6 a2 |...| >>> Flow 5 (client to server) -00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 8d 3c f7 |..............<.| -00000010 9e da 91 15 35 10 5f a4 29 32 3f 6a 8c 1d bc 13 |....5._.)2?j....| -00000020 8a 35 2b 15 03 03 00 1a 00 00 00 00 00 00 00 02 |.5+.............| -00000030 1f b3 e3 e3 24 ac 7a a6 ee 81 e7 cc 9e 70 34 2c |....$.z......p4,| -00000040 d2 28 |.(| +00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 22 8a b5 |............."..| +00000010 90 76 1f 68 e9 72 20 03 a8 38 26 71 19 fe c1 59 |.v.h.r ..8&q...Y| +00000020 71 90 4d 15 03 03 00 1a 00 00 00 00 00 00 00 02 |q.M.............| +00000030 60 82 f2 76 13 6f 3a 13 44 09 ff 45 a4 b1 23 3c |`..v.o:.D..E..#<| +00000040 40 e0 |@.| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-CHACHA20-POLY1305 b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-CHACHA20-POLY1305 index 1b3c37be241..33f3acfba4d 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-CHACHA20-POLY1305 +++ b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-ECDSA-CHACHA20-POLY1305 @@ -1,24 +1,24 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 d0 01 00 00 cc 03 03 00 00 00 00 00 |................| +00000000 16 03 01 00 d6 01 00 00 d2 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000040 00 00 00 00 00 00 00 00 00 00 00 00 00 08 cc a9 |................| -00000050 13 01 13 03 13 02 01 00 00 7b 00 05 00 05 01 00 |.........{......| +00000050 13 01 13 03 13 02 01 00 00 81 00 05 00 05 01 00 |................| 00000060 00 00 00 00 0a 00 0a 00 08 00 1d 00 17 00 18 00 |................| -00000070 19 00 0b 00 02 01 00 00 0d 00 1a 00 18 08 04 04 |................| +00000070 19 00 0b 00 02 01 00 00 0d 00 20 00 1e 08 04 04 |.......... .....| 00000080 03 08 07 08 05 08 06 04 01 05 01 06 01 05 03 06 |................| -00000090 03 02 01 02 03 ff 01 00 01 00 00 12 00 00 00 2b |...............+| -000000a0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| -000000b0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| -000000c0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| -000000d0 5f 58 cb 3b 74 |_X.;t| +00000090 03 02 01 02 03 fe 61 fe 62 08 08 ff 01 00 01 00 |......a.b.......| +000000a0 00 12 00 00 00 2b 00 09 08 03 04 03 03 03 02 03 |.....+..........| +000000b0 01 00 33 00 26 00 24 00 1d 00 20 2f e5 7d a3 47 |..3.&.$... /.}.G| +000000c0 cd 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af |.bC.(.._.).0....| +000000d0 c4 cf c2 ed 90 99 5f 58 cb 3b 74 |......_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 ea 73 50 31 e4 |....Y...U...sP1.| -00000010 7a c7 e2 05 23 a0 22 e3 1a cd 6d b5 0f e7 f2 5e |z...#."...m....^| -00000020 d6 cb 6c 70 05 04 a9 63 4a a3 fc 20 a2 c5 68 f2 |..lp...cJ.. ..h.| -00000030 9b 56 6e 83 66 c1 7f 85 02 b6 6d 37 12 0f 12 5a |.Vn.f.....m7...Z| -00000040 41 7e c3 c9 44 85 3c 00 50 6f c7 f9 cc a9 00 00 |A~..D.<.Po......| +00000000 16 03 03 00 59 02 00 00 55 03 03 d7 12 11 69 43 |....Y...U.....iC| +00000010 93 3b 99 0c 56 01 39 5f 80 d9 bb 12 43 89 2f 4d |.;..V.9_....C./M| +00000020 71 de 0e bf 92 6e 56 2a ab 53 cc 20 9a a7 8b 79 |q....nV*.S. ...y| +00000030 d6 6e e0 a2 e5 3c 37 49 ca b2 b4 ee b4 eb 9d 63 |.n...<7I.......c| +00000040 14 a9 c9 5f 0e 27 7f 45 bb 4d 0a 73 cc a9 00 00 |..._.'.E.M.s....| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 0e 0b 00 02 0a 00 02 07 00 02 04 30 82 02 |.............0..| 00000070 00 30 82 01 62 02 09 00 b8 bf 2d 47 a0 d2 eb f4 |.0..b.....-G....| @@ -53,32 +53,32 @@ 00000240 13 83 0d 94 06 bb d4 37 7a f6 ec 7a c9 86 2e dd |.......7z..z....| 00000250 d7 11 69 7f 85 7c 56 de fb 31 78 2b e4 c7 78 0d |..i..|V..1x+..x.| 00000260 ae cb be 9e 4e 36 24 31 7b 6a 0f 39 95 12 07 8f |....N6$1{j.9....| -00000270 2a 16 03 03 00 b7 0c 00 00 b3 03 00 1d 20 a4 6a |*............ .j| -00000280 0d ab f2 7c 1a 31 2a 7d 51 b7 fe 69 cd 59 f5 c1 |...|.1*}Q..i.Y..| -00000290 10 94 a0 b2 6f 6f c4 48 48 9b 20 1e 46 2a 04 03 |....oo.HH. .F*..| -000002a0 00 8b 30 81 88 02 42 00 84 2a 96 88 a4 7a 86 7f |..0...B..*...z..| -000002b0 cf 86 20 37 17 de 54 0c c2 89 5e 27 f4 3b a4 ec |.. 7..T...^'.;..| -000002c0 ce 25 34 4e c7 a8 7d f5 56 6d 96 2c d0 53 ae 42 |.%4N..}.Vm.,.S.B| -000002d0 b5 87 a9 20 9c 4f c9 67 7e ca f6 fc 2f 61 72 35 |... .O.g~.../ar5| -000002e0 78 fe 54 32 1e a1 90 88 c2 02 42 01 a6 7b 98 de |x.T2......B..{..| -000002f0 fd 01 4b 4a 8f 1a e8 18 dd 07 bb 0b 38 41 7f 22 |..KJ........8A."| -00000300 62 3b 7e 37 67 b7 18 46 a7 32 43 1b c9 a9 8a a6 |b;~7g..F.2C.....| -00000310 d7 8a 2f 7b c5 14 f3 33 96 fe 0a fc 22 d0 a5 02 |../{...3...."...| -00000320 37 a5 31 5f b9 6b d2 3b f6 d0 d1 7b a1 16 03 03 |7.1_.k.;...{....| +00000270 2a 16 03 03 00 b7 0c 00 00 b3 03 00 1d 20 04 75 |*............ .u| +00000280 b0 7b eb a9 d6 2d b7 23 96 13 62 4e 3b 62 cc 70 |.{...-.#..bN;b.p| +00000290 b3 f0 ed e9 00 bd 93 b2 af c2 ce 8a dd 53 04 03 |.............S..| +000002a0 00 8b 30 81 88 02 42 00 f4 46 68 93 e5 3d 18 bb |..0...B..Fh..=..| +000002b0 3b ab 9f 96 2d 81 de 41 9d 8f 77 3e 73 bc 74 c2 |;...-..A..w>s.t.| +000002c0 37 63 50 0e 82 f8 43 0d da ba 17 d8 8f 8e c8 63 |7cP...C........c| +000002d0 18 74 f9 ec e5 93 e6 43 fb b5 13 c7 9d 45 e6 3b |.t.....C.....E.;| +000002e0 cd 93 0d f0 af b5 3c 6a 18 02 42 00 d1 16 b0 ab |......>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| -00000030 16 03 03 00 20 f5 a0 28 0a 7e d4 8b a2 b6 e1 af |.... ..(.~......| -00000040 83 e2 50 e8 fc 7e f0 59 21 ed 3d 0d a8 ef a9 b1 |..P..~.Y!.=.....| -00000050 5a 13 2a 1b 2c |Z.*.,| +00000030 16 03 03 00 20 09 06 28 1e db e6 ec 2e 39 5b 39 |.... ..(.....9[9| +00000040 22 da 4b 3c a4 38 ce 61 7b 40 59 27 74 50 78 e3 |".K<.8.a{@Y'tPx.| +00000050 e3 df 47 55 9d |..GU.| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 20 44 15 68 4d e0 |.......... D.hM.| -00000010 3b 34 c5 77 b2 25 f2 e9 35 75 08 f5 a9 53 c9 65 |;4.w.%..5u...S.e| -00000020 19 36 49 fe 43 e4 f5 48 ac 7c d7 |.6I.C..H.|.| +00000000 14 03 03 00 01 01 16 03 03 00 20 d0 36 fe 1a a6 |.......... .6...| +00000010 fc ce 0d 08 6f d1 03 09 95 7e 30 2e 3e 85 1b cc |....o....~0.>...| +00000020 fb bd 80 e9 7a ac 82 2e 94 c6 32 |....z.....2| >>> Flow 5 (client to server) -00000000 17 03 03 00 16 f7 fd 2a 83 90 01 f3 d2 82 dc bd |.......*........| -00000010 6c 33 31 a3 92 0f a4 f5 9c fa f4 15 03 03 00 12 |l31.............| -00000020 9e 60 18 02 f1 0d 2f f5 5f 68 69 ae 62 93 04 6a |.`..../._hi.b..j| -00000030 41 f0 |A.| +00000000 17 03 03 00 16 e5 5a 41 27 e1 4e f5 8f 27 23 6a |......ZA'.N..'#j| +00000010 ab 2a 79 d4 eb 81 25 42 91 ec 47 15 03 03 00 12 |.*y...%B..G.....| +00000020 2a 1c 99 f8 43 e3 75 94 57 9b 69 e6 66 c9 4f e2 |*...C.u.W.i.f.O.| +00000030 d1 bc |..| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-RSA-AES b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-RSA-AES index eff5b979f97..9ceb0d9c7bc 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-RSA-AES +++ b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-RSA-AES @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 f1 07 97 47 f7 |....Y...U.....G.| -00000010 b8 42 f5 ce 2b b5 ec 5a d3 74 f1 fa 1f ea ec 6d |.B..+..Z.t.....m| -00000020 49 4e cf 2e 47 8b 2e 80 9b 8a ed 20 89 ca 35 4a |IN..G...... ..5J| -00000030 f4 35 5e b7 ed b2 96 ad e1 66 1d 43 9d 07 ba ed |.5^......f.C....| -00000040 ff 9d 47 65 c8 7d 91 32 4b 88 4d 83 c0 13 00 00 |..Ge.}.2K.M.....| +00000000 16 03 03 00 59 02 00 00 55 03 03 3d 4b 8e 08 fa |....Y...U..=K...| +00000010 29 ab c7 87 02 db e7 12 20 c8 7b 88 8c 04 b5 4c |)....... .{....L| +00000020 1c d9 2f b0 d0 f5 f4 bf 9e 67 81 20 16 0b 82 06 |../......g. ....| +00000030 0f dc 7c a9 8a 51 1f f5 ae 3b 06 57 48 ec 48 87 |..|..Q...;.WH.H.| +00000040 0d 0c c0 14 03 f5 af 6f a7 48 54 fc c0 13 00 00 |.......o.HT.....| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,38 +61,38 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 ac 0c 00 00 a8 03 00 1d 20 78 22 92 20 a9 be 78 |........ x". ..x| -000002d0 12 0f e6 83 13 3d 13 91 16 11 ca 26 9f b7 37 d5 |.....=.....&..7.| -000002e0 f0 97 f9 f2 01 fd 08 4f 42 08 04 00 80 2c f1 4e |.......OB....,.N| -000002f0 79 63 f2 d9 54 1c 0c 56 fd 56 4d e0 37 ee 5d bb |yc..T..V.VM.7.].| -00000300 22 90 fd ee d9 0f e6 d9 85 41 b9 8d d6 76 5f 05 |"........A...v_.| -00000310 1b 8c d7 4e c5 e8 4e 69 b9 5d de 73 c0 ed 4f 3e |...N..Ni.].s..O>| -00000320 09 9d b0 10 d6 61 87 d8 f9 c2 5b 48 f9 ef dd 65 |.....a....[H...e| -00000330 e6 f8 b0 d2 71 f6 e9 ae b1 c0 ea 90 dc 33 c6 72 |....q........3.r| -00000340 3e 9f 31 d4 ae 78 23 54 7a 4f 02 69 72 c1 06 2f |>.1..x#TzO.ir../| -00000350 3f 3c 7b f2 d8 17 40 a6 95 6d 46 62 6b 54 f1 cf |?<{...@..mFbkT..| -00000360 60 08 63 89 f7 a5 2a 52 3b 0e 0c d6 34 16 03 03 |`.c...*R;...4...| +000002c0 ac 0c 00 00 a8 03 00 1d 20 86 2c 0b 8c 09 ca b2 |........ .,.....| +000002d0 97 eb 0e 54 64 91 29 e8 6b fb c3 bc 14 17 cb 98 |...Td.).k.......| +000002e0 f1 78 4b a8 8d 64 31 06 0f 08 04 00 80 00 05 bb |.xK..d1.........| +000002f0 4a d6 5b 17 4c f1 ba 54 5a 90 25 78 55 cf a9 ea |J.[.L..TZ.%xU...| +00000300 5e 84 62 fb cd 55 bc 63 70 32 72 8b a1 92 53 a1 |^.b..U.cp2r...S.| +00000310 74 9d 31 d6 b5 72 3a 18 6e 69 de 89 11 66 3f 37 |t.1..r:.ni...f?7| +00000320 7a a7 9e fd ad 29 71 38 d9 18 b2 cc 10 54 d2 77 |z....)q8.....T.w| +00000330 43 ba a0 40 4c f2 85 a1 59 eb 34 cb 44 6b b0 7c |C..@L...Y.4.Dk.|| +00000340 f4 a5 ac be 91 95 44 c1 17 7d ac 02 4d 6c 18 ea |......D..}..Ml..| +00000350 2b d3 ac 07 cf f7 e4 65 72 f2 40 10 87 12 0d 03 |+......er.@.....| +00000360 20 db 81 6b 01 22 51 83 fd 30 31 43 b2 16 03 03 | ..k."Q..01C....| 00000370 00 04 0e 00 00 00 |......| >>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| 00000030 16 03 03 00 40 00 00 00 00 00 00 00 00 00 00 00 |....@...........| -00000040 00 00 00 00 00 96 55 d3 bd a1 b6 de 93 68 19 ed |......U......h..| -00000050 4a 3a cc 42 7c c4 41 1e b5 37 65 d5 84 10 60 3d |J:.B|.A..7e...`=| -00000060 e9 57 29 28 79 54 da 6c 1b 36 6b b1 75 f4 bb 32 |.W)(yT.l.6k.u..2| -00000070 47 8d de c8 7d |G...}| +00000040 00 00 00 00 00 d6 ae 15 88 93 d4 57 31 1c 13 ce |...........W1...| +00000050 ea 77 96 68 21 d5 4f 56 22 fe 31 1a 33 47 44 ed |.w.h!.OV".1.3GD.| +00000060 2c e2 06 43 51 d4 9b 36 f1 68 3c 95 30 0f 36 ae |,..CQ..6.h<.0.6.| +00000070 7c a9 23 1d 16 ||.#..| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 40 db ed ec 54 4a |..........@...TJ| -00000010 20 d8 a7 ee 12 04 e2 e4 95 b4 a4 a7 e1 80 c8 40 | ..............@| -00000020 81 00 6d 3e 58 26 7c d4 26 84 86 ee b4 fc c5 50 |..m>X&|.&......P| -00000030 46 31 e7 4c 1e fd ed 10 7e 72 45 18 43 db 4c 0d |F1.L....~rE.C.L.| -00000040 b5 49 6c 31 04 f0 85 a7 f8 02 e1 |.Il1.......| +00000000 14 03 03 00 01 01 16 03 03 00 40 b6 86 ea e7 0d |..........@.....| +00000010 bb 14 af 56 cd 5e 9b 58 f8 ab dd 97 bd 43 79 d2 |...V.^.X.....Cy.| +00000020 9e 59 d5 e2 2a bc eb 5d 69 59 6c f8 d8 de 80 d5 |.Y..*..]iYl.....| +00000030 bf 35 ca fe e7 d5 ca 57 c4 26 5b ff 2c 8c d2 2a |.5.....W.&[.,..*| +00000040 c0 15 b7 be 1f 18 cb 67 2e bb 21 |.......g..!| >>> Flow 5 (client to server) 00000000 17 03 03 00 30 00 00 00 00 00 00 00 00 00 00 00 |....0...........| -00000010 00 00 00 00 00 90 f7 06 a7 05 8d de 51 21 88 95 |............Q!..| -00000020 47 61 fb 8d a9 c9 6d 59 ca 92 8d 07 8b 9d 82 4e |Ga....mY.......N| -00000030 fd e9 ae 3d b0 15 03 03 00 30 00 00 00 00 00 00 |...=.....0......| -00000040 00 00 00 00 00 00 00 00 00 00 12 77 0c 5f 12 4b |...........w._.K| -00000050 96 ab 64 58 6e f5 82 09 6c 18 ae 1f a2 fb 0a 3b |..dXn...l......;| -00000060 71 17 25 8b c8 72 d0 13 fb e8 |q.%..r....| +00000010 00 00 00 00 00 01 66 c3 81 55 cb d0 d8 1d b3 db |......f..U......| +00000020 bc 22 12 48 d8 2d 47 f2 75 08 1e ab b6 a8 84 a2 |.".H.-G.u.......| +00000030 24 00 15 09 e3 15 03 03 00 30 00 00 00 00 00 00 |$........0......| +00000040 00 00 00 00 00 00 00 00 00 00 a4 80 d4 e0 87 32 |...............2| +00000050 45 69 44 28 88 19 24 9e ec ca 02 df d6 48 3e 57 |EiD(..$......H>W| +00000060 7a b0 c6 c9 2a ef 9f df 36 dd |z...*...6.| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-RSA-AES128-SHA256 b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-RSA-AES128-SHA256 index 4f8f49eb6a0..1f4644ab778 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-RSA-AES128-SHA256 +++ b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-RSA-AES128-SHA256 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 9e d4 c1 3e c6 |....Y...U.....>.| -00000010 3d 44 eb a7 b8 c5 c8 e0 ab 16 06 83 67 5e b2 d6 |=D..........g^..| -00000020 67 50 4b f3 24 17 97 19 76 7e 71 20 5a 2b dc 15 |gPK.$...v~q Z+..| -00000030 87 37 be bb c7 9c 38 cd 3e 55 4e 33 32 a0 01 1b |.7....8.>UN32...| -00000040 79 13 87 6a 19 09 42 4c fb 59 97 a8 c0 27 00 00 |y..j..BL.Y...'..| +00000000 16 03 03 00 59 02 00 00 55 03 03 2f a7 6a 8f 66 |....Y...U../.j.f| +00000010 14 37 3a 6c c8 a6 8b d7 55 9a 2d d8 ef 37 19 f1 |.7:l....U.-..7..| +00000020 b7 33 86 7d 8e ba f1 1f 83 88 a6 20 8e 85 7a 53 |.3.}....... ..zS| +00000030 8d 4f 8e 01 23 da 79 d8 56 79 ab 56 91 c9 0e 4c |.O..#.y.Vy.V...L| +00000040 ad fd 80 0e 3d f6 0b 76 b9 21 a7 92 c0 27 00 00 |....=..v.!...'..| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,42 +61,42 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 ac 0c 00 00 a8 03 00 1d 20 57 62 97 e9 c8 c6 17 |........ Wb.....| -000002d0 73 d2 9e 31 a6 f8 be 03 65 86 af 6b e2 64 bf 7c |s..1....e..k.d.|| -000002e0 4a f1 b9 fb 84 21 10 76 66 08 04 00 80 2d 08 24 |J....!.vf....-.$| -000002f0 06 2a a3 c5 28 c4 22 5b fe 79 4f 91 56 9e 40 6f |.*..(."[.yO.V.@o| -00000300 e6 0c e8 70 e0 35 9e 55 91 51 86 ec ad ff 6b 3f |...p.5.U.Q....k?| -00000310 a7 19 fa 6f 74 47 8a 86 04 b5 8a f0 0a d5 e5 5f |...otG........._| -00000320 ea 30 cc 79 77 3d ac 99 da 41 7f 25 3b da cd da |.0.yw=...A.%;...| -00000330 aa 4e 2a 54 b5 d3 13 4f e4 e9 cb 76 86 fb 0b b5 |.N*T...O...v....| -00000340 0d a3 be ab d2 e6 6e f6 77 7c 60 a7 50 56 43 60 |......n.w|`.PVC`| -00000350 95 ba 95 c4 b5 1a 8d 6a f7 a5 9f 03 27 93 9f 23 |.......j....'..#| -00000360 44 27 88 f0 d5 51 0f ba 43 84 5c 02 14 16 03 03 |D'...Q..C.\.....| +000002c0 ac 0c 00 00 a8 03 00 1d 20 59 cc a6 a8 b4 05 10 |........ Y......| +000002d0 00 0d 14 4f ec 26 d8 fb 9e a7 c3 74 8e d8 ca 66 |...O.&.....t...f| +000002e0 e4 e1 96 f0 8a ef 95 63 46 08 04 00 80 ad 32 e6 |.......cF.....2.| +000002f0 39 ef 4c b3 25 8d d1 26 2f de 32 aa 56 00 80 d5 |9.L.%..&/.2.V...| +00000300 8a b4 45 f9 cc 29 40 b2 20 f9 d1 57 f0 17 98 06 |..E..)@. ..W....| +00000310 ba 53 e0 59 75 70 7a ac ec 5a 74 ac fa 30 c5 74 |.S.Yupz..Zt..0.t| +00000320 d3 43 f9 bc 6f 7d 71 ff c5 3d fe 98 64 aa 67 cd |.C..o}q..=..d.g.| +00000330 84 f7 af cb de f6 bb a1 65 62 c5 07 08 2b 7b 0d |........eb...+{.| +00000340 8d e4 16 97 9a 01 55 82 7d b7 a0 23 71 0a 81 f3 |......U.}..#q...| +00000350 e4 6b 14 16 51 84 08 db 21 09 d1 0f bc 2f 60 11 |.k..Q...!..../`.| +00000360 5c eb a0 15 8c a7 27 dd 2d 80 82 58 5b 16 03 03 |\.....'.-..X[...| 00000370 00 04 0e 00 00 00 |......| >>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| 00000030 16 03 03 00 50 00 00 00 00 00 00 00 00 00 00 00 |....P...........| -00000040 00 00 00 00 00 02 19 fd 3e 06 0d 12 0d 03 42 da |........>.....B.| -00000050 76 6f e2 e3 96 eb 42 d9 96 b7 0b ae d6 a0 06 fa |vo....B.........| -00000060 57 4e ff 62 85 dd 3f ab 63 f9 73 87 8d 71 6a c6 |WN.b..?.c.s..qj.| -00000070 f4 ef ce f5 55 5b d2 1f b5 33 fd 12 32 bd 5e 1e |....U[...3..2.^.| -00000080 d5 32 91 9a ae |.2...| +00000040 00 00 00 00 00 95 9c 80 38 ba 7e b1 d4 59 71 ea |........8.~..Yq.| +00000050 8b 5b c2 0b 10 bb 52 07 e3 11 66 e3 f8 be 89 0a |.[....R...f.....| +00000060 25 35 09 4e e9 eb 1e 17 ff 89 96 65 b9 8e ea 25 |%5.N.......e...%| +00000070 b7 8a a8 e5 29 f7 24 03 43 61 50 cd de a3 46 31 |....).$.CaP...F1| +00000080 30 4e aa e3 0a |0N...| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 50 77 80 95 42 a3 |..........Pw..B.| -00000010 2b 1c 16 0f 3b f4 78 2a bd ab 6e d1 33 1e 0e a5 |+...;.x*..n.3...| -00000020 c7 f4 e9 92 82 00 da 44 0f b6 4e f9 1f ef 67 3b |.......D..N...g;| -00000030 de 5c dc 93 07 68 99 1a 70 7f 92 a7 d7 da f3 60 |.\...h..p......`| -00000040 cf d5 f1 f0 5e 75 68 a1 0b 32 eb d2 96 de e6 34 |....^uh..2.....4| -00000050 c3 e3 26 43 1f a2 8d e7 1b fc 76 |..&C......v| +00000000 14 03 03 00 01 01 16 03 03 00 50 0e ae f5 ea fe |..........P.....| +00000010 a0 c2 6f 72 25 b3 0a 1f 88 05 a3 0e 75 15 3c bc |..or%.......u.<.| +00000020 c6 af 4d d2 44 3e 27 5c 8c ad 7a 69 8a 36 99 19 |..M.D>'\..zi.6..| +00000030 23 0b 4e 7c ef 13 ff b9 04 da e6 43 65 f3 25 0f |#.N|.......Ce.%.| +00000040 0b 64 a4 8e 57 51 0c e6 f4 85 0f d1 4b 27 99 1c |.d..WQ......K'..| +00000050 35 8f bc 90 ae 54 3a 02 f7 7b 69 |5....T:..{i| >>> Flow 5 (client to server) 00000000 17 03 03 00 40 00 00 00 00 00 00 00 00 00 00 00 |....@...........| -00000010 00 00 00 00 00 f8 35 11 b8 23 cf d9 ec a7 d3 b9 |......5..#......| -00000020 60 1e 34 01 20 49 73 ec 72 78 58 24 3b fc a8 42 |`.4. Is.rxX$;..B| -00000030 b2 a9 69 69 40 65 5a c2 8b 9f 0b 0e 70 ab ac 22 |..ii@eZ.....p.."| -00000040 1a ac d6 04 06 15 03 03 00 40 00 00 00 00 00 00 |.........@......| -00000050 00 00 00 00 00 00 00 00 00 00 fe ed 19 a0 84 06 |................| -00000060 8b f0 e8 4e 30 7a 3c 89 a0 a8 59 74 a5 92 73 f3 |...N0z<...Yt..s.| -00000070 df 1b f0 c6 5a 95 d5 1c b6 57 4a 1b 8f 24 59 87 |....Z....WJ..$Y.| -00000080 b4 2b 7f 6f 89 03 e8 6d e5 d9 |.+.o...m..| +00000010 00 00 00 00 00 10 18 2b dc 81 92 0a c2 55 aa 52 |.......+.....U.R| +00000020 da 07 52 dc f5 ca 78 eb b2 de 53 66 ef e4 97 89 |..R...x...Sf....| +00000030 1f 20 68 76 27 30 2a 26 06 7b 25 d4 f7 57 b8 06 |. hv'0*&.{%..W..| +00000040 58 ab c3 36 c0 15 03 03 00 40 00 00 00 00 00 00 |X..6.....@......| +00000050 00 00 00 00 00 00 00 00 00 00 e7 94 35 0a 20 41 |............5. A| +00000060 da df a2 9e 11 54 90 ab 8f 94 d9 c8 24 28 e1 4f |.....T......$(.O| +00000070 e6 5c 69 34 3f 9d 89 bd 4a d7 7c b0 b3 69 6c 0f |.\i4?...J.|..il.| +00000080 87 d7 98 0e e9 20 00 88 50 bd |..... ..P.| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-RSA-CHACHA20-POLY1305 b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-RSA-CHACHA20-POLY1305 index 38fb4a0be7c..c8530c15c44 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ECDHE-RSA-CHACHA20-POLY1305 +++ b/src/crypto/tls/testdata/Client-TLSv12-ECDHE-RSA-CHACHA20-POLY1305 @@ -1,24 +1,24 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 d0 01 00 00 cc 03 03 00 00 00 00 00 |................| +00000000 16 03 01 00 d6 01 00 00 d2 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000040 00 00 00 00 00 00 00 00 00 00 00 00 00 08 cc a8 |................| -00000050 13 01 13 03 13 02 01 00 00 7b 00 05 00 05 01 00 |.........{......| +00000050 13 01 13 03 13 02 01 00 00 81 00 05 00 05 01 00 |................| 00000060 00 00 00 00 0a 00 0a 00 08 00 1d 00 17 00 18 00 |................| -00000070 19 00 0b 00 02 01 00 00 0d 00 1a 00 18 08 04 04 |................| +00000070 19 00 0b 00 02 01 00 00 0d 00 20 00 1e 08 04 04 |.......... .....| 00000080 03 08 07 08 05 08 06 04 01 05 01 06 01 05 03 06 |................| -00000090 03 02 01 02 03 ff 01 00 01 00 00 12 00 00 00 2b |...............+| -000000a0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| -000000b0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| -000000c0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| -000000d0 5f 58 cb 3b 74 |_X.;t| +00000090 03 02 01 02 03 fe 61 fe 62 08 08 ff 01 00 01 00 |......a.b.......| +000000a0 00 12 00 00 00 2b 00 09 08 03 04 03 03 03 02 03 |.....+..........| +000000b0 01 00 33 00 26 00 24 00 1d 00 20 2f e5 7d a3 47 |..3.&.$... /.}.G| +000000c0 cd 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af |.bC.(.._.).0....| +000000d0 c4 cf c2 ed 90 99 5f 58 cb 3b 74 |......_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 4e fb dc 04 6f |....Y...U..N...o| -00000010 5a 52 37 a3 55 58 26 e5 cd a0 67 4c 0f 87 1a 3a |ZR7.UX&...gL...:| -00000020 f6 84 33 2f 2e 52 d0 48 7c 5b 64 20 6e d0 bc ca |..3/.R.H|[d n...| -00000030 c9 a5 87 8d 99 c5 ec 85 84 89 f0 22 ab 63 55 f4 |...........".cU.| -00000040 70 d7 02 93 b5 fe d7 38 fb c1 b2 da cc a8 00 00 |p......8........| +00000000 16 03 03 00 59 02 00 00 55 03 03 8b 6f 39 b0 1c |....Y...U...o9..| +00000010 ca a8 57 f6 29 4b aa ad 18 5d a2 e4 e2 32 27 95 |..W.)K...]...2'.| +00000020 1f 7e 74 84 06 20 c4 19 76 de 96 20 42 b0 09 f9 |.~t.. ..v.. B...| +00000030 27 56 b6 d4 c7 01 20 bd f2 bf 4c 98 c6 ad 0c 37 |'V.... ...L....7| +00000040 a4 40 f6 3e a4 fd da 3f 2c fd 59 1f cc a8 00 00 |.@.>...?,.Y.....| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -58,31 +58,31 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 ac 0c 00 00 a8 03 00 1d 20 fc 4b 92 ab d2 cb 4f |........ .K....O| -000002d0 61 aa 86 12 1a 1d 75 be 31 dd b8 ee 6c a6 db bd |a.....u.1...l...| -000002e0 0b ea b2 d5 27 49 42 eb 5a 08 04 00 80 02 ad 71 |....'IB.Z......q| -000002f0 e2 e8 f6 44 3c a6 18 6f 76 ee 9a eb 0e d9 ff cb |...D<..ov.......| -00000300 6d 1e 64 dd 29 1d 8c c8 f6 14 40 c0 12 46 74 4c |m.d.).....@..FtL| -00000310 41 2d 71 5f 9c b7 86 0b fc 66 1e 14 cb 26 d0 d7 |A-q_.....f...&..| -00000320 21 b4 bd c2 04 38 77 90 6a f0 01 18 bd 1c 17 45 |!....8w.j......E| -00000330 7e 38 46 4c 2e 97 ba 11 01 1f 20 cc df f2 6b 5b |~8FL...... ...k[| -00000340 a7 29 c0 52 52 9c 2f 23 bd 1c 72 c2 f2 99 d1 dc |.).RR./#..r.....| -00000350 6a 6c ac 8e 87 8a 00 74 47 2e 99 8d 3f 79 04 60 |jl.....tG...?y.`| -00000360 5e dc ba 86 1c f4 f9 03 22 38 96 a7 b3 16 03 03 |^......."8......| +000002c0 ac 0c 00 00 a8 03 00 1d 20 98 f5 d8 73 66 f6 7f |........ ...sf..| +000002d0 d6 f4 d5 0c b5 f4 a7 2f 2c 48 d0 76 2f b7 20 93 |......./,H.v/. .| +000002e0 6f 76 7c 16 d8 1d 72 c3 1c 08 04 00 80 a0 fe b6 |ov|...r.........| +000002f0 46 cd 2c dd 7a 3a 5b 10 37 0f ce 37 da 83 86 2e |F.,.z:[.7..7....| +00000300 13 c9 87 34 54 ef b9 70 9e 3f c2 6c db 66 9b 29 |...4T..p.?.l.f.)| +00000310 48 d9 2a b7 33 ce 5c e4 8e d1 c2 df a5 9c 08 73 |H.*.3.\........s| +00000320 4c ae 8c bc a7 32 cf 80 7b 40 6e 62 27 63 20 c4 |L....2..{@nb'c .| +00000330 a7 22 57 ee 72 2b 1b f5 c1 22 fa 5c 21 ea 7c 95 |."W.r+...".\!.|.| +00000340 bd 8b ab c5 06 87 b0 28 88 42 c3 0e 57 15 01 47 |.......(.B..W..G| +00000350 74 93 8b 81 c0 b7 3e 4a 00 8b 79 0b c9 d4 ec 07 |t.....>J..y.....| +00000360 62 eb 93 aa cb df 2a 54 49 aa a6 e7 03 16 03 03 |b.....*TI.......| 00000370 00 04 0e 00 00 00 |......| >>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| -00000030 16 03 03 00 20 0a 17 ee 70 8c 50 24 7c 00 b9 6f |.... ...p.P$|..o| -00000040 82 71 ed 2b 8c 0b 4b ff bb 38 bc 12 7e 0c a5 3e |.q.+..K..8..~..>| -00000050 71 a2 ad f8 52 |q...R| +00000030 16 03 03 00 20 d8 1e 11 d0 07 a4 7c 53 d5 74 0d |.... ......|S.t.| +00000040 ad 03 d4 ca e4 92 93 e8 12 f4 bf c5 7e b9 3d ee |............~.=.| +00000050 e9 ed e4 ea 01 |.....| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 20 e9 87 55 12 a8 |.......... ..U..| -00000010 ad 68 42 0c 60 12 be 2f 2c e5 00 2d 01 cf 86 a2 |.hB.`../,..-....| -00000020 1b 06 b3 86 bf 88 48 73 7a d3 cc |......Hsz..| +00000000 14 03 03 00 01 01 16 03 03 00 20 3c a1 72 44 6b |.......... <.rDk| +00000010 18 0a 9f aa 78 72 a4 c3 25 26 82 ae 56 e1 c0 e9 |....xr..%&..V...| +00000020 23 d0 d0 53 0f c3 7b 6a f3 b2 78 |#..S..{j..x| >>> Flow 5 (client to server) -00000000 17 03 03 00 16 96 75 4c c6 ba b1 ad ae 2f 44 9d |......uL...../D.| -00000010 10 c3 ef e5 dc fb 0a 3e af 6b 6a 15 03 03 00 12 |.......>.kj.....| -00000020 30 13 8f e5 a1 0f 38 67 b9 53 4e 6a 66 ec ee 45 |0.....8g.SNjf..E| -00000030 c2 b2 |..| +00000000 17 03 03 00 16 15 87 ff 2f 31 67 02 10 1a 6a e6 |......../1g...j.| +00000010 b2 8f 6f 17 94 54 ac ff 30 f6 dd 15 03 03 00 12 |..o..T..0.......| +00000020 58 df 0c 63 3f 9b b4 69 4d 63 3b 37 7b 46 fa 89 |X..c?..iMc;7{F..| +00000030 d6 e0 |..| diff --git a/src/crypto/tls/testdata/Client-TLSv12-Ed25519 b/src/crypto/tls/testdata/Client-TLSv12-Ed25519 index 35513adb842..8a0c89da8ac 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-Ed25519 +++ b/src/crypto/tls/testdata/Client-TLSv12-Ed25519 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 66 49 2a a6 a4 |....Y...U..fI*..| -00000010 75 60 58 bb 5f 5e 82 cd e5 c0 9f 6d a4 fd 39 3b |u`X._^.....m..9;| -00000020 d9 17 80 14 89 ea 51 c1 b0 43 d6 20 b2 6b 72 81 |......Q..C. .kr.| -00000030 f6 63 20 22 e2 b6 d2 61 aa 87 b6 67 ae 56 78 44 |.c "...a...g.VxD| -00000040 5d 10 8c cf ea 32 cf 9e 92 e5 59 70 cc a9 00 00 |]....2....Yp....| +00000000 16 03 03 00 59 02 00 00 55 03 03 d1 78 d5 a8 ef |....Y...U...x...| +00000010 93 84 e1 23 fc f9 79 e2 23 69 28 c4 c2 f2 76 7f |...#..y.#i(...v.| +00000020 3c 00 10 27 63 bc 0c e9 37 cd eb 20 d3 98 4c fd |<..'c...7.. ..L.| +00000030 d6 e4 43 03 ca f4 3d 7d 52 2c 15 a6 f9 50 f3 49 |..C...=}R,...P.I| +00000040 85 4c 6e c5 12 c8 bb 5f d3 02 9b 0f cc a9 00 00 |.Ln...._........| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 01 3c 0b 00 01 38 00 01 35 00 01 32 30 82 01 |..<...8..5..20..| 00000070 2e 30 81 e1 a0 03 02 01 02 02 10 0f 43 1c 42 57 |.0..........C.BW| @@ -42,27 +43,27 @@ 00000170 90 95 39 e5 0d c1 55 ff 2c 16 b7 1d fc ab 7d 4d |..9...U.,.....}M| 00000180 d4 e0 93 13 d0 a9 42 e0 b6 6b fe 5d 67 48 d7 9f |......B..k.]gH..| 00000190 50 bc 6c cd 4b 03 83 7c f2 08 58 cd ac cf 0c 16 |P.l.K..|..X.....| -000001a0 03 03 00 6c 0c 00 00 68 03 00 1d 20 c4 8c b8 a2 |...l...h... ....| -000001b0 32 92 b8 22 1f 4c f1 96 00 64 35 47 4e f8 3d 08 |2..".L...d5GN.=.| -000001c0 83 12 fe 95 a8 e4 8e c9 30 27 5c 39 08 07 00 40 |........0'\9...@| -000001d0 7f 90 cf e0 87 69 e3 50 e6 fa 5e 28 a1 0f 79 0a |.....i.P..^(..y.| -000001e0 6e cf f4 87 e8 2f 55 b2 dd cb 5e 8f 9a 14 bd c2 |n..../U...^.....| -000001f0 2b 2b 2d ed 72 40 23 5d 6d f4 89 3a ff 09 82 ec |++-.r@#]m..:....| -00000200 b6 4b 27 9a 08 ea e9 73 94 b4 31 1f e1 39 86 0e |.K'....s..1..9..| +000001a0 03 03 00 6c 0c 00 00 68 03 00 1d 20 13 3d 70 03 |...l...h... .=p.| +000001b0 5d f8 ed 0d e2 d8 32 20 f2 8a 44 12 c2 c6 6c 25 |].....2 ..D...l%| +000001c0 02 3c 89 4a 97 72 77 a1 1d f5 48 42 08 07 00 40 |.<.J.rw...HB...@| +000001d0 6d 02 b5 86 ed 0e a6 d3 d2 99 af ec 85 90 d4 75 |m..............u| +000001e0 d0 1f 23 0d a0 8d 4d 08 f0 d6 d5 c3 72 f4 73 2a |..#...M.....r.s*| +000001f0 1b e0 4b c9 49 ec 34 72 58 30 bd d0 e8 2f 73 e2 |..K.I.4rX0.../s.| +00000200 ad a0 ae 06 99 7a 6d 90 06 b2 1d 39 bd d8 05 02 |.....zm....9....| 00000210 16 03 03 00 04 0e 00 00 00 |.........| >>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| -00000030 16 03 03 00 20 8f 97 36 bd 59 ef 8e 2f 11 28 b0 |.... ..6.Y../.(.| -00000040 d7 20 79 bf 04 07 45 f9 89 de b0 c7 55 1a ad 80 |. y...E.....U...| -00000050 0f 8c ef 1d c6 |.....| +00000030 16 03 03 00 20 1f ea af 73 91 4f f9 a6 05 69 60 |.... ...s.O...i`| +00000040 50 e2 9a 4c 50 ae 18 2d c4 25 de a0 f7 b1 4f c3 |P..LP..-.%....O.| +00000050 97 54 b1 0b 7a |.T..z| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 20 47 6c 1f 86 47 |.......... Gl..G| -00000010 72 03 94 e0 43 f8 e5 ca 03 7d f5 d5 dd 70 05 f5 |r...C....}...p..| -00000020 98 5d 51 b4 11 49 71 7a fd 37 9a |.]Q..Iqz.7.| +00000000 14 03 03 00 01 01 16 03 03 00 20 e0 35 a6 14 a1 |.......... .5...| +00000010 5c 09 3c 29 69 0d 9f cc fb cb 0a 3a 7c 45 bf bb |\.<)i......:|E..| +00000020 dd 9c 70 e8 19 5d 03 98 d0 c1 4a |..p..]....J| >>> Flow 5 (client to server) -00000000 17 03 03 00 16 b7 a2 f5 8e 7c d3 7d 61 af 29 1c |.........|.}a.).| -00000010 77 0c 8d b4 5b d3 be 77 a6 a5 99 15 03 03 00 12 |w...[..w........| -00000020 d8 23 dc a8 99 fe 1c 6e f2 2f 41 8e df 40 11 4f |.#.....n./A..@.O| -00000030 6b 92 |k.| +00000000 17 03 03 00 16 dd 4f 40 12 b6 04 02 51 6c 01 4c |......O@....Ql.L| +00000010 cd d2 72 df 01 26 8d c9 d3 cc d2 15 03 03 00 12 |..r..&..........| +00000020 d9 17 20 b5 46 c7 59 4a 2c b9 3b 0d 4c a6 d2 01 |.. .F.YJ,.;.L...| +00000030 fe c5 |..| diff --git a/src/crypto/tls/testdata/Client-TLSv12-ExportKeyingMaterial b/src/crypto/tls/testdata/Client-TLSv12-ExportKeyingMaterial index c900aa6d5e1..58624258a48 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-ExportKeyingMaterial +++ b/src/crypto/tls/testdata/Client-TLSv12-ExportKeyingMaterial @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 7c c1 7b 30 03 |....Y...U..|.{0.| -00000010 3c d7 63 5f 47 1c b1 13 56 56 b4 fd 55 e2 27 3e |<.c_G...VV..U.'>| -00000020 39 bb ce 9b 5b 2c 1e 17 33 e1 da 20 65 8b 26 42 |9...[,..3.. e.&B| -00000030 a4 38 29 c7 9a 25 13 fc 1d 69 cb 10 63 c6 26 fc |.8)..%...i..c.&.| -00000040 f4 46 64 31 28 06 b3 a5 a4 c2 f6 5a cc a8 00 00 |.Fd1(......Z....| +00000000 16 03 03 00 59 02 00 00 55 03 03 b2 36 13 c0 db |....Y...U...6...| +00000010 2b 1b 40 f2 9e 8e ef 60 cc 2a 7c 97 d7 13 13 96 |+.@....`.*|.....| +00000020 f6 3a 98 f8 fc 82 de 52 b2 01 df 20 e7 ac 8d 36 |.:.....R... ...6| +00000030 7c 58 2e 64 0d 90 dc a3 23 b6 87 e7 b7 a6 0e 32 ||X.d....#......2| +00000040 ff 42 dc f3 57 85 12 2c 9e f0 8e dc cc a8 00 00 |.B..W..,........| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,31 +61,31 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 ac 0c 00 00 a8 03 00 1d 20 f7 a2 97 2f 50 e4 e2 |........ .../P..| -000002d0 fa ef 80 67 78 1c aa 6c 03 aa 05 3b 6f 98 97 11 |...gx..l...;o...| -000002e0 7e 55 3d 50 f3 a9 9b 21 65 08 04 00 80 34 4a 4b |~U=P...!e....4JK| -000002f0 4b 6e 86 01 1b 6b 8e 3e 84 01 75 b8 05 c3 b2 52 |Kn...k.>..u....R| -00000300 16 ee ac 61 83 dd 09 32 d5 55 6a 5d d6 6b 4a 1a |...a...2.Uj].kJ.| -00000310 2b f7 09 33 6f 3d 4f c1 e3 aa 03 27 fe af cd 6d |+..3o=O....'...m| -00000320 b8 76 00 02 42 98 e6 f6 b7 ed fb 35 35 29 23 b1 |.v..B......55)#.| -00000330 4d 48 0a ba a1 1b e3 8e a2 cb 80 11 ec 92 20 df |MH............ .| -00000340 1f a4 5e 5d 70 85 8e 5d 85 62 81 1f b3 3a 0d 8d |..^]p..].b...:..| -00000350 9a 07 d3 99 a5 3c 6c c2 52 08 f0 be 50 ed d2 4d |.......qT\Um..>.....| +00000320 85 5c 33 f2 f0 7d fb 35 1b 22 e1 4b d1 43 d8 ae |.\3..}.5.".K.C..| +00000330 db 6d 1b fe 12 7f 43 e8 5c 6b d5 e0 53 3e b8 9f |.m....C.\k..S>..| +00000340 83 6e e6 56 6d 5e 18 a4 f0 2a de 4a 9b b2 a0 86 |.n.Vm^...*.J....| +00000350 55 c2 07 6c 5d 2b 0c ec 47 b1 56 fc 5e 20 2b 15 |U..l]+..G.V.^ +.| +00000360 f2 bb ce 98 3a 3f 19 68 49 bb c8 bc 8e 16 03 03 |....:?.hI.......| 00000370 00 04 0e 00 00 00 |......| >>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| -00000030 16 03 03 00 20 30 8b ea ef 6c 35 97 5b 26 5f ef |.... 0...l5.[&_.| -00000040 bc 28 fd e9 23 73 bb b3 ae 41 0c be 5f 83 a5 f7 |.(..#s...A.._...| -00000050 96 07 8d 81 67 |....g| +00000030 16 03 03 00 20 85 6f 02 54 c0 bb 39 e5 ba ea 49 |.... .o.T..9...I| +00000040 c2 15 bf ca fd d1 87 8c e2 f0 f6 d1 0e 96 2e 3d |...............=| +00000050 dc 07 a0 a4 27 |....'| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 20 29 fa a8 de f2 |.......... )....| -00000010 8f 94 16 fc be 84 93 e9 34 98 c2 44 08 9b 2e 37 |........4..D...7| -00000020 1f 41 61 53 fa 9c 23 ff d8 6d c3 |.AaS..#..m.| +00000000 14 03 03 00 01 01 16 03 03 00 20 46 e7 ae 80 0e |.......... F....| +00000010 df 7c 96 f5 db a3 2c c6 2a 31 f9 71 44 3b 25 c8 |.|....,.*1.qD;%.| +00000020 d1 ee ad d9 7c 4b a5 e2 56 3d b9 |....|K..V=.| >>> Flow 5 (client to server) -00000000 17 03 03 00 16 ab 6d 32 1c 16 cc 29 b1 21 4c b1 |......m2...).!L.| -00000010 74 4c 50 e3 1f c5 f1 05 6a 8a 92 15 03 03 00 12 |tLP.....j.......| -00000020 18 88 3d 23 81 d7 ba c5 1e 9a c4 3a 1b c8 cd 5b |..=#.......:...[| -00000030 c5 fa |..| +00000000 17 03 03 00 16 6b 74 2b 06 24 89 38 b8 ae 45 9e |.....kt+.$.8..E.| +00000010 4d 3c 55 07 48 f1 d5 27 73 2e 4d 15 03 03 00 12 |M>> Flow 1 (client to server) -00000000 16 03 01 01 15 01 00 01 11 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 1b 01 00 01 17 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,22 +7,22 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 96 00 05 00 05 01 00 00 00 00 00 0a 00 |................| -00000090 04 00 02 00 17 00 0b 00 02 01 00 00 0d 00 1a 00 |................| -000000a0 18 08 04 04 03 08 07 08 05 08 06 04 01 05 01 06 |................| -000000b0 01 05 03 06 03 02 01 02 03 ff 01 00 01 00 00 12 |................| -000000c0 00 00 00 2b 00 09 08 03 04 03 03 03 02 03 01 00 |...+............| -000000d0 33 00 47 00 45 00 17 00 41 04 1e 18 37 ef 0d 19 |3.G.E...A...7...| -000000e0 51 88 35 75 71 b5 e5 54 5b 12 2e 8f 09 67 fd a7 |Q.5uq..T[....g..| -000000f0 24 20 3e b2 56 1c ce 97 28 5e f8 2b 2d 4f 9e f1 |$ >.V...(^.+-O..| -00000100 07 9f 6c 4b 5b 83 56 e2 32 42 e9 58 b6 d7 49 a6 |..lK[.V.2B.X..I.| -00000110 b5 68 1a 41 03 56 6b dc 5a 89 |.h.A.Vk.Z.| +00000080 01 00 00 9c 00 05 00 05 01 00 00 00 00 00 0a 00 |................| +00000090 04 00 02 00 17 00 0b 00 02 01 00 00 0d 00 20 00 |.............. .| +000000a0 1e 08 04 04 03 08 07 08 05 08 06 04 01 05 01 06 |................| +000000b0 01 05 03 06 03 02 01 02 03 fe 61 fe 62 08 08 ff |..........a.b...| +000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| +000000d0 03 03 02 03 01 00 33 00 47 00 45 00 17 00 41 04 |......3.G.E...A.| +000000e0 1e 18 37 ef 0d 19 51 88 35 75 71 b5 e5 54 5b 12 |..7...Q.5uq..T[.| +000000f0 2e 8f 09 67 fd a7 24 20 3e b2 56 1c ce 97 28 5e |...g..$ >.V...(^| +00000100 f8 2b 2d 4f 9e f1 07 9f 6c 4b 5b 83 56 e2 32 42 |.+-O....lK[.V.2B| +00000110 e9 58 b6 d7 49 a6 b5 68 1a 41 03 56 6b dc 5a 89 |.X..I..h.A.Vk.Z.| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 b8 7d f5 69 c3 |....Y...U...}.i.| -00000010 6a ca 8b df f3 30 2c 39 47 2e 74 2e 4f 89 4c 1e |j....0,9G.t.O.L.| -00000020 f0 eb 10 0e 06 1d 2c 4e de 2e 8f 20 6c a0 5b 66 |......,N... l.[f| -00000030 fc a6 05 df 29 6b ce 72 92 e7 d7 78 f5 46 38 f9 |....)k.r...x.F8.| -00000040 91 1c 9a 08 4c b1 9a 41 e5 0c d2 cd c0 2f 00 00 |....L..A...../..| +00000000 16 03 03 00 59 02 00 00 55 03 03 c7 2c fe 84 bc |....Y...U...,...| +00000010 a4 2a 42 11 a2 66 58 8f c0 e1 c8 73 da d7 94 c8 |.*B..fX....s....| +00000020 6c 43 e8 6e c0 e0 3f 42 dd d4 a4 20 13 4e 56 35 |lC.n..?B... .NV5| +00000030 14 54 97 22 38 6d d6 fc 22 17 e8 d3 d8 5d 12 22 |.T."8m.."....]."| +00000040 9e c7 c1 e5 fc 53 8c 3f 24 05 d4 be c0 2f 00 00 |.....S.?$..../..| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -62,19 +62,19 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 cd 0c 00 00 c9 03 00 17 41 04 3e 87 67 8b 87 08 |........A.>.g...| -000002d0 fe 4e 4c c3 6b 42 4b 97 ad f4 1c 83 35 72 db 4f |.NL.kBK.....5r.O| -000002e0 39 83 ea 14 69 bb 8c 87 58 c5 a4 a8 8c d7 9d af |9...i...X.......| -000002f0 7a 5e 58 59 31 4d f2 01 4a 23 51 24 1b 04 0c e3 |z^XY1M..J#Q$....| -00000300 94 9e 1b 6c ad aa 83 fd 2d 36 08 04 00 80 ab e9 |...l....-6......| -00000310 ff 6d 7a cd 3b a7 da ff d5 bd 27 49 68 53 f5 45 |.mz.;.....'IhS.E| -00000320 c3 dd 5b a2 99 fb 8f 24 37 49 d3 08 87 d1 06 98 |..[....$7I......| -00000330 39 72 25 78 b3 05 fb a2 c9 ac f9 c8 f7 fc ea 8a |9r%x............| -00000340 98 ce 78 83 64 f6 e0 c7 44 62 af a7 d5 26 df f1 |..x.d...Db...&..| -00000350 2c cc ce 11 8b 03 4a e1 81 54 3f e1 6e 52 c9 1a |,.....J..T?.nR..| -00000360 d8 95 52 e0 3f a5 e3 c8 12 9a c7 57 5d 46 7a ce |..R.?......W]Fz.| -00000370 56 8a 90 0f 0d 1b ba 58 cf 1c a3 4b 39 5a 08 ee |V......X...K9Z..| -00000380 8a 61 bb 0f 7d f7 0e f2 1f 73 e0 c8 6f 54 16 03 |.a..}....s..oT..| +000002c0 cd 0c 00 00 c9 03 00 17 41 04 6e 5a 7b 43 16 a9 |........A.nZ{C..| +000002d0 ea 61 fd 21 c7 d9 e4 a0 48 5a a3 a2 6b a2 03 f6 |.a.!....HZ..k...| +000002e0 44 63 6d af 59 59 a8 46 b2 c2 25 a2 21 cf 3e ad |Dcm.YY.F..%.!.>.| +000002f0 30 35 d2 1f d7 64 f8 8b 1a 83 43 24 48 72 ca ad |05...d....C$Hr..| +00000300 9e 67 0e 68 cd 3e ea a6 a4 c6 08 04 00 80 28 d2 |.g.h.>........(.| +00000310 64 ff 1f 04 2d 1f 96 9f e2 a6 88 27 b7 d3 a5 7f |d...-......'....| +00000320 8c 09 8f 92 57 87 b2 bd 11 e9 08 9e ee 29 83 2f |....W........)./| +00000330 94 7b 3b 5c 8b 26 27 93 8f 22 d3 8f 53 40 b4 53 |.{;\.&'.."..S@.S| +00000340 2b ec f5 02 d6 83 79 be 10 5b 50 a9 0b 2f 39 0f |+.....y..[P../9.| +00000350 ad 01 2d 4e 4e 2a 02 3c 06 53 fb 69 ac 34 65 f4 |..-NN*.<.S.i.4e.| +00000360 ae d7 98 3b 85 b9 b1 45 85 b0 1b af dc 86 bb 25 |...;...E.......%| +00000370 e8 e2 12 c8 44 83 e2 25 a5 22 76 45 71 f9 a7 e4 |....D..%."vEq...| +00000380 f8 39 de 94 b7 db 20 6e 7d e8 6e 80 8b 34 16 03 |.9.... n}.n..4..| 00000390 03 00 04 0e 00 00 00 |.......| >>> Flow 3 (client to server) 00000000 16 03 03 00 46 10 00 00 42 41 04 1e 18 37 ef 0d |....F...BA...7..| @@ -82,17 +82,17 @@ 00000020 a7 24 20 3e b2 56 1c ce 97 28 5e f8 2b 2d 4f 9e |.$ >.V...(^.+-O.| 00000030 f1 07 9f 6c 4b 5b 83 56 e2 32 42 e9 58 b6 d7 49 |...lK[.V.2B.X..I| 00000040 a6 b5 68 1a 41 03 56 6b dc 5a 89 14 03 03 00 01 |..h.A.Vk.Z......| -00000050 01 16 03 03 00 28 00 00 00 00 00 00 00 00 b8 16 |.....(..........| -00000060 ce 7d df 64 13 07 9e d8 37 bb 3f 9c 9e 2b 3c 0e |.}.d....7.?..+<.| -00000070 26 a7 9d 32 e5 44 b8 d6 66 bc 05 7b 27 7a |&..2.D..f..{'z| +00000050 01 16 03 03 00 28 00 00 00 00 00 00 00 00 9f 17 |.....(..........| +00000060 19 4f e0 e4 e0 af c5 64 71 75 2c fd 89 da 02 45 |.O.....dqu,....E| +00000070 93 31 12 52 5b e8 99 48 81 a4 72 7d 0f 6f |.1.R[..H..r}.o| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 28 c0 73 5c 27 1b |..........(.s\'.| -00000010 19 d0 66 68 ea c5 ad 7d a8 03 37 d2 9a ff 00 c4 |..fh...}..7.....| -00000020 70 65 98 3b 88 59 c0 ca e3 c0 d6 32 0e 8d 15 3c |pe.;.Y.....2...<| -00000030 e2 c3 f3 |...| +00000000 14 03 03 00 01 01 16 03 03 00 28 bf db dd 46 6d |..........(...Fm| +00000010 b7 35 b9 f0 99 41 b9 d4 c1 0d d7 c0 c6 c4 14 4f |.5...A.........O| +00000020 fd 43 f7 72 ae 70 e9 fc 59 80 d8 2a 16 d2 77 19 |.C.r.p..Y..*..w.| +00000030 b1 3a 67 |.:g| >>> Flow 5 (client to server) -00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 28 ef 47 |.............(.G| -00000010 ad 7f 40 4b 34 78 f3 1e 01 a7 f4 20 0a d5 c1 41 |..@K4x..... ...A| -00000020 f7 be 41 15 03 03 00 1a 00 00 00 00 00 00 00 02 |..A.............| -00000030 fb fc eb 14 f2 a6 e7 2e 80 d6 93 31 25 01 e9 d2 |...........1%...| -00000040 c3 ae |..| +00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 f9 e4 58 |...............X| +00000010 1f 57 ec 4b 00 88 43 30 ee ca 88 45 17 33 bd cd |.W.K..C0...E.3..| +00000020 66 93 73 15 03 03 00 1a 00 00 00 00 00 00 00 02 |f.s.............| +00000030 ee 3f 79 3e 97 f6 b0 9d c5 13 fe 8e 3d c2 6b a3 |.?y>........=.k.| +00000040 88 13 |..| diff --git a/src/crypto/tls/testdata/Client-TLSv12-RSA-RC4 b/src/crypto/tls/testdata/Client-TLSv12-RSA-RC4 index ab2c4eb14d8..4fd7ea6a758 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-RSA-RC4 +++ b/src/crypto/tls/testdata/Client-TLSv12-RSA-RC4 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 51 02 00 00 4d 03 03 34 50 1f 52 15 |....Q...M..4P.R.| -00000010 85 c7 85 2c 4d a9 b2 0c 49 e5 a3 ea 57 21 96 39 |...,M...I...W!.9| -00000020 db c9 97 b6 c4 d0 81 9a 39 a3 e8 20 59 f5 b9 db |........9.. Y...| -00000030 58 2e ef 1c b3 85 96 27 6a 23 71 3f 5c 72 ce cf |X......'j#q?\r..| -00000040 c5 b7 fe 05 00 f4 65 06 54 c1 2e 7c 00 05 00 00 |......e.T..|....| +00000000 16 03 03 00 51 02 00 00 4d 03 03 f8 4b 13 f3 20 |....Q...M...K.. | +00000010 30 5e 64 97 04 98 61 6e 69 7b d0 41 05 4f e8 ea |0^d...ani{.A.O..| +00000020 46 2c b3 54 f4 a7 03 e5 87 2c 5a 20 62 d5 58 55 |F,.T.....,Z b.XU| +00000030 93 31 5a fa 65 50 ad 9d 8b f6 8d db 41 75 90 a5 |.1Z.eP......Au..| +00000040 17 d9 5b 45 f4 42 11 a7 c2 0d c9 13 00 05 00 00 |..[E.B..........| 00000050 05 ff 01 00 01 00 16 03 03 02 59 0b 00 02 55 00 |..........Y...U.| 00000060 02 52 00 02 4f 30 82 02 4b 30 82 01 b4 a0 03 02 |.R..O0..K0......| 00000070 01 02 02 09 00 e8 f0 9d 3f e2 5b ea a6 30 0d 06 |........?.[..0..| @@ -70,15 +71,15 @@ 00000060 c5 70 0f 08 83 48 e9 48 ef 6e 50 8b 05 7e e5 84 |.p...H.H.nP..~..| 00000070 25 fa 55 c7 ae 31 02 27 00 ef 3f 98 86 20 12 89 |%.U..1.'..?.. ..| 00000080 91 59 28 b4 f7 d7 af d2 69 61 35 14 03 03 00 01 |.Y(.....ia5.....| -00000090 01 16 03 03 00 24 ab 48 84 ae 77 f9 8b 82 44 52 |.....$.H..w...DR| -000000a0 3e 65 94 27 cc f2 08 a7 f2 e5 21 0c 02 d0 89 ac |>e.'......!.....| -000000b0 50 be 69 57 c9 7c a0 f2 7f 6d |P.iW.|...m| +00000090 01 16 03 03 00 24 ca ed 08 ea 45 2a a7 f0 ab 08 |.....$....E*....| +000000a0 c8 ff ed c5 08 4d 2f 1d c8 35 74 61 0d 6f 92 c9 |.....M/..5ta.o..| +000000b0 53 25 93 6e 99 b4 3c 0b 91 24 |S%.n..<..$| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 24 61 94 21 65 0f |..........$a.!e.| -00000010 10 ba 0c a6 d9 e3 08 54 86 ae f9 64 c7 e7 f4 4b |.......T...d...K| -00000020 aa f5 19 ca 2a 0d 50 88 85 42 32 14 04 29 d9 |....*.P..B2..).| +00000000 14 03 03 00 01 01 16 03 03 00 24 17 86 70 b3 7c |..........$..p.|| +00000010 06 f8 3a 5b ea 8b c6 c8 98 c3 18 e4 99 8f 05 1c |..:[............| +00000020 e6 1a b1 20 31 0b f4 ad d8 22 47 64 f4 05 a9 |... 1...."Gd...| >>> Flow 5 (client to server) -00000000 17 03 03 00 1a cb 1d 43 67 de 7a 20 c7 ed 46 99 |.......Cg.z ..F.| -00000010 86 1f b9 61 9f c6 34 9a 07 37 3c 94 45 b4 40 15 |...a..4..7<.E.@.| -00000020 03 03 00 16 4e ac d3 12 23 b4 33 bc 5b 03 91 7e |....N...#.3.[..~| -00000030 d9 d0 7f d7 48 3e 8c 16 16 ec |....H>....| +00000000 17 03 03 00 1a 9d 21 96 cd c1 89 b9 6f 5a 9a e0 |......!.....oZ..| +00000010 26 60 93 ff a8 a2 6a d2 01 dd be d7 4e 37 f0 15 |&`....j.....N7..| +00000020 03 03 00 16 0f 9c c4 e5 dc c1 1c 0a 45 32 1d d2 |............E2..| +00000030 2a fb d2 59 17 69 78 a0 a7 6a |*..Y.ix..j| diff --git a/src/crypto/tls/testdata/Client-TLSv12-RenegotiateOnce b/src/crypto/tls/testdata/Client-TLSv12-RenegotiateOnce index 48a99eda155..38e08f07033 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-RenegotiateOnce +++ b/src/crypto/tls/testdata/Client-TLSv12-RenegotiateOnce @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 f1 d8 72 0c 79 |....Y...U....r.y| -00000010 e2 ca 92 11 1c 30 cc 45 00 9b ea 3d a3 ed 23 d5 |.....0.E...=..#.| -00000020 22 f0 da 9c 03 32 7b c3 13 d3 df 20 8f 7a 61 43 |"....2{.... .zaC| -00000030 cb 72 46 5e c1 39 78 42 32 97 cc 2b 90 2e 53 59 |.rF^.9xB2..+..SY| -00000040 31 38 ec 7b 2b 8a f3 80 e0 03 f0 0e cc a8 00 00 |18.{+...........| +00000000 16 03 03 00 59 02 00 00 55 03 03 98 94 40 cb 60 |....Y...U....@.`| +00000010 7b 16 05 6c 06 29 ea a5 dc 72 ff 3f 03 54 3a 8e |{..l.)...r.?.T:.| +00000020 7c 94 11 56 97 db 33 e3 82 cd ec 20 8f e2 9c 88 ||..V..3.... ....| +00000030 3f d1 a2 bb b6 bb 0b 5f 19 c3 23 13 2a d9 04 cd |?......_..#.*...| +00000040 e5 f3 7d 88 c8 55 f7 3e 1b 86 c4 e5 cc a8 00 00 |..}..U.>........| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,185 +61,186 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 ac 0c 00 00 a8 03 00 1d 20 96 cb 1d cd f6 2f ff |........ ...../.| -000002d0 fe 32 ef d6 18 a2 6b 57 66 cd 3d 50 42 56 dc a4 |.2....kWf.=PBV..| -000002e0 5f fe e4 91 ce d1 17 34 3c 08 04 00 80 b1 47 de |_......4<.....G.| -000002f0 b3 19 b0 fd 02 35 eb 3c a1 04 d3 6b 53 84 20 c7 |.....5.<...kS. .| -00000300 08 4b 96 12 23 ae bf ca a8 83 1d 90 16 ae d3 7c |.K..#..........|| -00000310 fa 1b b4 f0 bb bb 4e 3f 70 13 2f 40 6c d4 76 61 |......N?p./@l.va| -00000320 5b 23 85 3f e7 37 ef e1 55 47 8d 01 e1 24 22 7f |[#.?.7..UG...$".| -00000330 a4 2c 6f 97 47 5f d6 69 bf b4 db 4b b8 a1 ad 66 |.,o.G_.i...K...f| -00000340 5f d5 5d b6 06 ac 93 ed d7 06 cb b5 a4 d4 4b a7 |_.]...........K.| -00000350 7b de f7 73 60 af ad 23 f4 6a f1 bf 2a ee 5b 4e |{..s`..#.j..*.[N| -00000360 83 94 d7 95 3b e5 5e a5 3d 1a 0a 7a 9e 16 03 03 |....;.^.=..z....| +000002c0 ac 0c 00 00 a8 03 00 1d 20 b8 7d 4b 03 c2 6b 43 |........ .}K..kC| +000002d0 e2 c4 6f 3e 49 09 09 1d f8 a8 06 8e c7 7d 62 ad |..o>I........}b.| +000002e0 8a 60 9d b9 ed 46 3c d4 03 08 04 00 80 58 fb c4 |.`...F<......X..| +000002f0 e4 0e 7b 54 46 d2 d1 98 b3 75 0f e2 78 bc 44 89 |..{TF....u..x.D.| +00000300 fb 74 47 15 8b fe 2f 89 04 fb d4 8d ba df 34 24 |.tG.../.......4$| +00000310 f0 a8 26 1f 0e 6f b2 f7 20 bf c6 11 83 8e 62 7f |..&..o.. .....b.| +00000320 56 5e 36 97 a3 f1 3a 81 06 4d c4 c2 bb e3 80 aa |V^6...:..M......| +00000330 7f f2 41 58 8e e7 19 da 03 73 01 31 f1 b0 bf e2 |..AX.....s.1....| +00000340 8a 73 fc 09 26 2b 12 d3 07 bd bf 21 fd 7a 2f b8 |.s..&+.....!.z/.| +00000350 05 db c8 e7 4e 88 17 1a 65 47 f8 71 c5 91 15 47 |....N...eG.q...G| +00000360 54 bd cf a7 dc f9 4b 93 d1 cd 57 bc 7b 16 03 03 |T.....K...W.{...| 00000370 00 04 0e 00 00 00 |......| >>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| -00000030 16 03 03 00 20 f2 6f 2e 79 5c db 90 b8 2e cf 59 |.... .o.y\.....Y| -00000040 0a 56 69 86 f1 71 0c ff a9 7c 0b a0 e7 c9 8d 17 |.Vi..q...|......| -00000050 65 ad a5 6c 82 |e..l.| +00000030 16 03 03 00 20 9b 6c 14 75 9a 5c ba 07 48 75 ba |.... .l.u.\..Hu.| +00000040 f7 37 50 b7 4b 8e 73 cf 0d 75 5e ad 7c ac 84 e4 |.7P.K.s..u^.|...| +00000050 ea 0c 5d ce 72 |..].r| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 20 d5 90 08 84 71 |.......... ....q| -00000010 bc 09 48 be ad 59 11 76 c6 39 bb 94 8c 60 80 29 |..H..Y.v.9...`.)| -00000020 44 1a 0d fe 5c 00 4c bc 47 3c 1e |D...\.L.G<.| +00000000 14 03 03 00 01 01 16 03 03 00 20 65 ef 4e 87 51 |.......... e.N.Q| +00000010 f2 95 98 46 ef 0b 44 81 c4 52 eb 51 bf 40 29 19 |...F..D..R.Q.@).| +00000020 b7 34 38 73 a1 d4 ac 5c 05 87 12 |.48s...\...| >>> Flow 5 (client to server) -00000000 17 03 03 00 16 42 cd 1c e5 91 35 b0 c1 4d df e4 |.....B....5..M..| -00000010 b0 ca f3 8a 7a 41 85 31 7a 7d 59 |....zA.1z}Y| +00000000 17 03 03 00 16 36 e0 de e1 5d 42 a5 95 a2 60 9f 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a3 3a 7c b7 02 cc 76 25 1d |a.S7yW..:|...v%.| -000003f0 96 8b dd 9e 32 8b 1a 9e 37 b1 1a b8 f2 4f ef 3c |....2...7....O.<| -00000400 78 e1 b9 07 16 03 03 00 14 bf da c1 d4 16 fd 48 |x..............H| -00000410 a9 ad 59 6d 8c dc e1 6c fd 73 ca 9c 1b |..Ym...l.s...| +00000000 16 03 03 00 81 3d 56 b0 8a 0d 84 ad f4 e7 53 5e |.....=V.......S^| +00000010 e6 f6 c8 b5 2f f9 5f d8 b4 d1 51 f9 ae 5b 2d 82 |..../._...Q..[-.| +00000020 e6 7a 10 f6 5d f1 a1 f0 04 58 82 6a fb 5e b0 63 |.z..]....X.j.^.c| +00000030 01 78 0f a3 76 7e d5 17 22 92 92 0e 50 33 93 1d |.x..v~.."...P3..| +00000040 55 ef 27 7c 82 28 4e f2 c2 8c 11 d5 4d 5f 5a db |U.'|.(N.....M_Z.| +00000050 53 40 86 5f a4 b1 50 08 51 c6 12 e2 f4 a0 08 83 |S@._..P.Q.......| +00000060 84 65 60 74 af 85 b3 fb 96 66 7b ad 2a a5 4c 46 |.e`t.....f{.*.LF| +00000070 65 2a 6b 5d f0 43 75 1a be 41 46 78 5c e2 2c e7 |e*k].Cu..AFx\.,.| +00000080 29 1e 31 fd d8 02 16 03 03 02 69 ea b4 d4 5a 44 |).1.......i...ZD| +00000090 8f 00 9f ac 8a c3 e6 a5 7c b9 0d a6 1e a8 49 50 |........|.....IP| +000000a0 fc 7e 41 1d 98 ab c8 7f a4 c6 b7 c7 fb ca 53 ee |.~A...........S.| +000000b0 c2 8b 2f ec 4b 50 dd ed 4c dc 3c 5d fe 7a 38 36 |../.KP..L.<].z86| +000000c0 a2 1d ad cf a1 d6 d1 a1 5c 89 f6 6f f0 ca 33 2b |........\..o..3+| +000000d0 28 5e e4 08 7b ba a9 12 8d 6d f5 62 35 a8 68 40 |(^..{....m.b5.h@| +000000e0 41 f5 9d 16 8d cd ba 8d 26 9d 5e cb e0 19 0a f8 |A.......&.^.....| +000000f0 c0 f1 05 f7 b9 a9 28 10 32 35 a2 4f 4e f3 b6 06 |......(.25.ON...| +00000100 b3 a4 e4 23 81 85 26 3b 58 74 9d c8 ef 51 7d 90 |...#..&;Xt...Q}.| +00000110 99 44 8b 95 53 e8 e3 56 44 01 c2 37 07 d1 8e 36 |.D..S..VD..7...6| +00000120 56 1b f6 58 af 44 e1 da 40 85 ed 25 03 79 ac 5c |V..X.D..@..%.y.\| +00000130 ab 1b 1c ce 58 ec e0 58 3d bf 18 4d 5b b5 29 d2 |....X..X=..M[.).| +00000140 c1 f2 e1 5d 0b 4c 23 65 fe 09 23 11 e3 03 48 80 |...].L#e..#...H.| +00000150 25 71 4d 27 fe 3b a5 86 f1 09 34 4f 3b bb a5 9c |%qM'.;....4O;...| +00000160 c4 d2 8d f8 1a c7 96 e6 63 c8 ac 06 94 df cf f4 |........c.......| +00000170 62 cb e2 bd a8 8d 91 72 b4 c4 30 b1 3e c9 85 cd |b......r..0.>...| +00000180 ab bd bf 48 38 76 27 e5 be a0 1e 8e 38 8d b8 83 |...H8v'.....8...| +00000190 b6 c2 f4 33 1b 10 5d 35 95 46 8b c1 cd 74 ca e2 |...3..]5.F...t..| +000001a0 c4 cd 81 ca c7 27 bd e7 d5 4a e2 fc c2 ea 6d 45 |.....'...J....mE| +000001b0 3d 16 43 77 b1 f2 e5 6a 88 c9 34 da cb 9e fd 68 |=.Cw...j..4....h| +000001c0 bf 7e db 88 b7 61 17 f4 77 45 74 6d ca 40 e0 6b |.~...a..wEtm.@.k| +000001d0 65 d1 ee de fa b3 a7 41 f3 f7 e1 c4 16 88 cc 8b |e......A........| +000001e0 8f d7 0a 88 87 1b b3 60 ce 5e 8c 32 06 dd e5 cd |.......`.^.2....| +000001f0 5c d3 6b bc 8b d3 c9 3f 87 c2 5a 15 2e 51 24 75 |\.k....?..Z..Q$u| +00000200 70 6c b4 e9 f6 df 08 24 d9 e2 6e 95 d8 6d eb 03 |pl.....$..n..m..| +00000210 2c 19 f8 1a a3 d9 0c 65 3e 8e 6b 15 d7 6d 32 ea |,......e>.k..m2.| +00000220 9e c3 d7 d6 53 54 6d 0d 36 82 59 94 da 93 24 14 |....STm.6.Y...$.| +00000230 d2 52 e7 1a 43 c1 d9 9a ff 1d 79 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36 8c 18 1e af 34 a6 4d c9 21 a0 |....e6....4.M.!.| +00000120 12 67 4f fd b0 ab 4b 6a c9 db 3e 58 3c 8a 6f 70 |.gO...Kj..>X<.op| +00000130 ed d4 10 3b e8 b2 b5 98 45 66 c5 ab d9 2b 90 1b |...;....Ef...+..| +00000140 07 eb 82 90 08 61 40 bd 4d a8 84 8e a2 c3 f0 e7 |.....a@.M.......| +00000150 a1 7c d5 fa 7e 32 4f 21 aa 56 69 82 b9 95 a9 a7 |.|..~2O!.Vi.....| +00000160 bf f0 8c bd e7 0a 09 eb 0b 4e 49 25 08 26 86 a2 |.........NI%.&..| +00000170 a7 45 e0 18 bb 7c 9a 81 7a 2b 9e e5 4f 7f 75 0e |.E...|..z+..O.u.| +00000180 16 cd 2f 55 8c 2f 71 d7 71 b6 d2 62 72 31 ea 7c |../U./q.q..br1.|| +00000190 34 aa d3 4c f9 3c 23 9f 29 e8 43 d2 56 23 02 c5 |4..L.<#.).C.V#..| +000001a0 45 54 09 72 e0 89 f6 e1 c0 23 58 9d de a6 cb 8e |ET.r.....#X.....| +000001b0 1d d3 03 d7 1d c6 02 9c 3e 16 92 73 f1 bc ee a1 |........>..s....| +000001c0 ae fa 57 86 27 01 2e ad 37 6e 90 96 e9 b8 3c 56 |..W.'...7n......@6|.s;B| +00000200 97 a6 be 6b 43 b3 70 ed 1d f4 cb 39 5d 85 bc e0 |...kC.p....9]...| +00000210 3d 9e 02 47 ca 3d c4 aa 2b 49 29 e8 47 e9 f8 e0 |=..G.=..+I).G...| +00000220 43 ab 83 20 fa 28 dc 99 c5 6d 7c 34 4f da 4c 27 |C.. .(...m|4O.L'| +00000230 f9 6b 39 6a 8c d5 66 9d a6 18 da c1 2a fc 34 c6 |.k9j..f.....*.4.| +00000240 b7 de ce 51 d4 ee d8 2f 25 26 7f 43 20 a8 2b bd |...Q.../%&.C .+.| +00000250 73 4d 33 7b 9e b2 a3 85 60 44 a6 ce 7c d8 b5 38 |sM3{....`D..|..8| +00000260 73 90 82 ea 0c 45 40 2c f7 e2 ad ae f3 41 16 03 |s....E@,.....A..| +00000270 03 00 35 ab 86 d3 1e 58 85 06 11 db be 23 13 b7 |..5....X.....#..| +00000280 13 f2 a5 c1 71 48 ab 67 0e 34 07 dd ec ef 6d 83 |....qH.g.4....m.| +00000290 49 56 2b ff 8f 02 13 78 e3 7b b3 6a 1f 57 46 54 |IV+....x.{.j.WFT| +000002a0 59 38 d2 dd ee 7c 76 e1 16 03 03 00 98 2d a3 d5 |Y8...|v......-..| +000002b0 89 f8 f9 6b 55 5e 78 ba 6a 29 2e 3c c8 ac 3f f4 |...kU^x.j).<..?.| +000002c0 c9 6b e3 86 7d d4 0b 9e d9 70 e0 fb 25 5a 62 7b |.k..}....p..%Zb{| +000002d0 38 cc cb 58 16 84 7d 86 54 2d de 3a 23 ce b0 a8 |8..X..}.T-.:#...| +000002e0 fa a9 e1 72 8a b5 a7 cf ff 76 37 4a 58 9e ff 7c |...r.....v7JX..|| +000002f0 ec 47 35 70 70 36 6b c1 b2 4e 74 9f 04 35 6c 06 |.G5pp6k..Nt..5l.| +00000300 4b c2 8a 95 84 09 a3 00 3b f6 24 d9 81 30 6c d6 |K.......;.$..0l.| +00000310 26 16 ab 50 02 41 93 00 1d ca ca 33 d6 8d 68 37 |&..P.A.....3..h7| +00000320 00 22 e5 d9 f4 22 a1 02 18 2b 35 f8 a2 47 03 26 |."..."...+5..G.&| +00000330 0f 26 9d 43 6b 78 16 17 9a a9 6a ac c5 32 28 8e |.&.Ckx....j..2(.| +00000340 8f 7e 38 5a c9 14 03 03 00 11 71 55 3f 87 b5 e1 |.~8Z......qU?...| +00000350 09 94 30 ca 34 97 c5 01 b8 4c 3f 16 03 03 00 20 |..0.4....L?.... | +00000360 5a 5f a3 64 31 f3 56 e7 8a d2 95 e4 f3 f9 10 78 |Z_.d1.V........x| +00000370 48 4a e5 0d 11 b2 ef 5a a1 db b8 e2 ff b9 52 f2 |HJ.....Z......R.| >>> Flow 10 (server to client) -00000000 14 03 03 00 11 45 8e f9 74 04 d0 44 c6 94 80 60 |.....E..t..D...`| -00000010 c1 50 7d b2 64 76 16 03 03 00 20 d5 65 8a b9 26 |.P}.dv.... .e..&| -00000020 54 70 26 de c6 8a 8f 61 a3 b1 9e 8b 49 40 f7 24 |Tp&....a....I@.$| -00000030 4f 75 e0 94 e6 e7 68 51 38 8a 37 17 03 03 00 19 |Ou....hQ8.7.....| -00000040 42 7e 5a e2 46 7b ba 7d 0d 07 20 2a c0 56 fe aa |B~Z.F{.}.. *.V..| -00000050 01 eb ca d2 29 1d ff 85 10 |....)....| +00000000 14 03 03 00 11 00 65 41 e8 ef db 97 da 21 43 96 |......eA.....!C.| +00000010 c3 99 f6 ee 51 d9 16 03 03 00 20 9d 2d 5a e1 0a |....Q..... .-Z..| +00000020 1e 37 42 90 17 84 ba 09 69 4c 2b 77 68 9b 87 65 |.7B.....iL+wh..e| +00000030 bc c3 df 43 44 15 62 3e cb 26 55 17 03 03 00 19 |...CD.b>.&U.....| +00000040 5d 2b 1f ed 88 2b 3b b5 fa 52 3c 45 1a 13 23 87 |]+...+;..R>> Flow 11 (client to server) -00000000 15 03 03 00 12 1d 01 c7 d5 d5 d1 ce 8c 52 15 8f |.............R..| -00000010 75 1e 97 fa 38 5c 65 |u...8\e| +00000000 15 03 03 00 12 25 53 9c b7 f2 c8 d4 52 85 bf 93 |.....%S.....R...| +00000010 1f d8 7a d6 ea 08 e3 |..z....| diff --git a/src/crypto/tls/testdata/Client-TLSv12-RenegotiateTwice b/src/crypto/tls/testdata/Client-TLSv12-RenegotiateTwice index 006e2d7cef8..6e2f288cca0 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-RenegotiateTwice +++ b/src/crypto/tls/testdata/Client-TLSv12-RenegotiateTwice @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 47 d0 f5 d9 f0 |....Y...U..G....| -00000010 59 d1 bf 28 d0 39 36 c0 bc d1 25 fd 5a 63 18 06 |Y..(.96...%.Zc..| -00000020 1e 8a 5c a6 6f d0 f9 b4 02 23 e1 20 df a0 2a 74 |..\.o....#. ..*t| -00000030 1a 52 8b d9 90 01 c2 86 69 12 b8 13 58 aa 59 b0 |.R......i...X.Y.| -00000040 66 79 ff 01 9b 9a 72 1c a6 83 e6 91 cc a8 00 00 |fy....r.........| +00000000 16 03 03 00 59 02 00 00 55 03 03 90 ca c9 b4 3a |....Y...U......:| +00000010 06 58 7d 40 cb b9 b0 62 73 8c 03 98 52 7b c1 30 |.X}@...bs...R{.0| +00000020 d9 d0 cc 7d 23 83 6a 0b cc e7 63 20 29 36 70 8e |...}#.j...c )6p.| +00000030 b1 f5 e3 e1 0e 02 4a d6 22 eb 63 3c bb b1 1a 81 |......J.".c<....| +00000040 82 03 fc 72 3a b4 0c 3e 72 cf d0 1e cc a8 00 00 |...r:..>r.......| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,284 +61,286 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 ac 0c 00 00 a8 03 00 1d 20 20 97 bd 85 2f cb 85 |........ .../..| -000002d0 be a8 9c e3 ae 6b 23 a5 5b 18 65 5c f5 cc 24 2b |.....k#.[.e\..$+| -000002e0 34 2c 5f c8 4d e9 86 35 0b 08 04 00 80 d2 b6 ee |4,_.M..5........| -000002f0 86 76 aa 1d 9c 1c ee ef 0e 59 63 1d ec f1 cf a1 |.v.......Yc.....| -00000300 f3 5b 6d da 99 9c 40 07 bf 28 ad 72 cd 80 6c 9d |.[m...@..(.r..l.| -00000310 bf a2 20 33 2d d0 67 ef 90 28 88 2b d0 8e c6 9d |.. 3-.g..(.+....| -00000320 87 7a 18 8f 80 ce 25 92 13 8d ef 38 0a 14 f9 67 |.z....%....8...g| -00000330 88 94 ef af 97 d2 21 90 9e 24 2f af 1e bb fa 10 |......!..$/.....| -00000340 4c a7 9f f5 27 63 e6 d8 1a 86 53 c6 3c 15 a8 6c |L...'c....S.<..l| -00000350 b9 bc 8f c4 38 1a 4b 34 36 ec af b2 1e d0 bf 58 |....8.K46......X| -00000360 74 36 ad fb e4 f0 fd 9d 6d 01 cf 51 6c 16 03 03 |t6......m..Ql...| +000002c0 ac 0c 00 00 a8 03 00 1d 20 ac f9 73 ff a4 25 a6 |........ ..s..%.| +000002d0 93 df 82 5a 21 3c 5d fc 19 ca 00 75 c2 cb fa 95 |...Z!<]....u....| +000002e0 ad c8 fe f6 d6 9f 3c 4b 3c 08 04 00 80 bc 07 6b |.......P..6| +00000340 16 8b f0 85 2f 08 49 c7 ba 40 e6 ad 15 64 82 6e |..../.I..@...d.n| +00000350 a3 a0 0c 54 4d d2 8c 80 3b 8e 08 39 01 51 20 06 |...TM...;..9.Q .| +00000360 17 99 98 aa 80 bd dd ec 97 8b d0 d7 bb 16 03 03 |................| 00000370 00 04 0e 00 00 00 |......| >>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| -00000030 16 03 03 00 20 e8 d5 df da 49 9a 94 10 30 90 81 |.... ....I...0..| -00000040 c6 19 54 d4 0d e2 0d e0 d9 a3 c0 21 7f a6 d1 cc |..T........!....| -00000050 ea 75 2e 17 01 |.u...| +00000030 16 03 03 00 20 0f 02 ef ff 39 17 cf ee e3 2e cb |.... ....9......| +00000040 3f 88 17 70 07 03 c7 1f 93 f8 d3 68 70 8c 96 aa |?..p.......hp...| +00000050 fe 93 1e 64 6f |...do| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 20 f3 92 03 fb 7b |.......... ....{| -00000010 0f 32 0b 5b dd 9e eb c3 26 2c 92 4d 58 35 a8 96 |.2.[....&,.MX5..| -00000020 74 d6 d8 0f 61 b2 7d b6 8d ec e6 |t...a.}....| +00000000 14 03 03 00 01 01 16 03 03 00 20 ea a8 ad 11 19 |.......... .....| +00000010 c9 b9 c7 6e 66 f6 a3 00 31 ee 8e 67 04 2c 05 ae |...nf...1..g.,..| +00000020 2a e7 86 9e 74 a8 ca 6c 46 a4 ec |*...t..lF..| >>> Flow 5 (client to server) -00000000 17 03 03 00 16 ab 69 44 d0 fe 95 93 ae f9 1b d7 |......iD........| -00000010 33 6c 59 a5 41 cc d2 1b ca 2c 63 |3lY.A....,c| +00000000 17 03 03 00 16 49 80 66 a0 36 d6 75 5b dd 2b 31 |.....I.f.6.u[.+1| +00000010 43 9b 6d 51 06 16 d9 72 c4 e3 23 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|K...........-]..| -00000090 37 f8 fc 89 24 ea c4 b8 87 f4 f4 f0 4b cd db e2 |7...$.......K...| -000000a0 15 03 95 1e c1 10 7c e8 6d 99 6c e0 bc e1 0a a5 |......|.m.l.....| -000000b0 d8 36 eb 59 93 6d 1c 96 1c 61 1b 11 36 04 58 6b |.6.Y.m...a..6.Xk| -000000c0 c5 b0 fb 8e 9f 21 4a 25 a1 59 ee 5d 1b e3 e3 98 |.....!J%.Y.]....| -000000d0 71 0a d8 3f 18 f2 b2 1c 6f ec 6d 87 13 b9 d3 25 |q..?....o.m....%| -000000e0 53 c1 00 78 be 99 82 f6 27 05 24 01 10 1c 59 19 |S..x....'.$...Y.| -000000f0 94 6a af 7e e5 ae c5 03 14 04 e2 fe 5e 59 e8 e0 |.j.~........^Y..| -00000100 45 3d af c0 40 ea 84 0a 13 9c d3 0f d4 69 3f 3e |E=..@........i?>| -00000110 97 83 ac b5 b9 07 56 9a 19 44 ca |......V..D.| +00000000 16 03 03 01 1c 25 68 1f dd 6c 4d 02 76 cd f0 50 |.....%h..lM.v..P| +00000010 35 a2 0d 77 aa ca 43 c8 93 c1 1b 6e c2 88 b6 5f |5..w..C....n..._| +00000020 d4 d5 a0 9a c5 a1 09 ef 53 47 f3 7a 19 0b c6 a5 |........SG.z....| +00000030 0c f5 90 39 b8 cd 92 0d 03 a8 39 08 42 ce 41 40 |...9......9.B.A@| 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41 e6 3a |..k}.,.n.O...A.:| +000002d0 9d 0b 8a 1e 90 3a c9 8a 69 60 3b 32 00 75 0d a8 |.....:..i`;2.u..| +000002e0 b8 76 05 a5 23 99 2a a0 49 c7 49 5a 7a 5a 29 5d |.v..#.*.I.IZzZ)]| +000002f0 ef ee 91 bd 16 03 03 00 bc 5a fa bb 7b 77 b6 34 |.........Z..{w.4| +00000300 38 37 8d 7b 8b e0 cd fa 2e 91 52 74 ba 9c 0e bf |87.{......Rt....| +00000310 29 45 ad 9f 84 af 3a 88 e7 fe c1 cf db 38 4a 35 |)E....:......8J5| +00000320 63 b6 5f 62 f8 1d 34 40 03 72 62 55 c3 f6 3c 4b |c._b..4@.rbU..[...+..0.CY.-| +00000350 b6 c3 4e 65 d3 81 22 ad d2 66 72 56 44 c0 c5 fe |..Ne.."..frVD...| +00000360 08 e0 b7 00 4e 03 e8 94 62 00 43 b9 18 ff fd 43 |....N...b.C....C| +00000370 e7 3c 6a 01 88 2d 4b 27 06 e6 c3 d1 0d 22 c1 60 |..&.....C.| >>> Flow 13 (client to server) -00000000 16 03 03 00 35 a4 b8 43 07 6e 71 c9 b4 fa e1 9c |....5..C.nq.....| -00000010 a7 9d 0b 47 d8 ea 8b bd ea c2 f5 bf 36 fa 88 95 |...G........6...| -00000020 3b 98 b3 7e 19 21 9b 0f 58 76 e8 de 5b 24 d3 b5 |;..~.!..Xv..[$..| -00000030 81 bd 11 ce 86 02 b0 d1 3b ac 14 03 03 00 11 3f |........;......?| -00000040 4e a4 96 06 71 44 5f 57 30 5e 1a bc 22 8d 42 97 |N...qD_W0^..".B.| -00000050 16 03 03 00 20 23 e7 90 a5 0a 32 b4 69 06 d7 77 |.... #....2.i..w| -00000060 df ef f6 2f b8 d8 22 39 08 4f 39 02 e0 7f 62 93 |.../.."9.O9...b.| -00000070 02 b9 8e a5 b6 |.....| +00000000 16 03 03 00 35 c1 81 14 20 7c 44 9c f1 88 f0 49 |....5... |D....I| +00000010 22 e6 c6 10 d3 37 bb bc 8d 0a fe c3 35 cc c3 af |"....7......5...| +00000020 e3 2d 61 64 97 57 b0 0f 8d 1f 9f ae f4 7a 35 85 |.-ad.W.......z5.| +00000030 e2 81 1e 3a 6d b6 a7 d7 34 92 14 03 03 00 11 e3 |...:m...4.......| +00000040 f0 e6 ec 46 91 82 c3 81 93 75 6b e4 66 1c d9 4c |...F.....uk.f..L| +00000050 16 03 03 00 20 79 f9 0e 3a b5 36 d0 9f 8c 5a 8e |.... y..:.6...Z.| +00000060 2c 16 9f 9d 48 c8 d1 e8 5e 4f b5 70 a8 02 c6 6b |,...H...^O.p...k| +00000070 41 a0 82 bf 19 |A....| >>> Flow 14 (server to client) -00000000 14 03 03 00 11 0e 2d 1e 73 95 29 15 86 03 a2 da |......-.s.).....| -00000010 6c f4 d2 02 2c 57 16 03 03 00 20 cd a2 f5 b6 da |l...,W.... .....| -00000020 0c 35 45 96 54 c3 96 5d d8 e6 03 49 7b 5c d4 6f |.5E.T..]...I{\.o| -00000030 02 da 27 9e 2f a7 09 57 1b de 7b 17 03 03 00 19 |..'./..W..{.....| -00000040 18 06 7d aa 5c 93 a9 b3 d3 14 0b 76 78 a2 57 73 |..}.\......vx.Ws| -00000050 2f a3 4f 66 c4 b3 ee 21 95 |/.Of...!.| +00000000 14 03 03 00 11 28 b7 5d 06 32 1a a2 ab 4d de 93 |.....(.].2...M..| +00000010 bd 66 38 e9 31 bc 16 03 03 00 20 5f 44 a4 90 d5 |.f8.1..... _D...| +00000020 a0 24 e4 26 9b 17 c3 10 8c 2d c2 a4 b2 18 ff 6b |.$.&.....-.....k| +00000030 86 2d 74 89 29 3a 6d 42 25 f4 2e 17 03 03 00 19 |.-t.):mB%.......| +00000040 a6 3a fc e1 33 2f e2 67 6e 50 73 49 6e 30 3c 05 |.:..3/.gnPsIn0<.| +00000050 38 7b 8e a8 ab 60 48 1c 24 |8{...`H.$| >>> Flow 15 (client to server) -00000000 15 03 03 00 12 55 f7 2f b2 a2 e7 59 6c f6 a9 2d |.....U./...Yl..-| -00000010 d1 17 88 01 49 c6 f2 |....I..| +00000000 15 03 03 00 12 5c c9 57 f2 8b ce 9c 53 08 57 fd |.....\.W....S.W.| +00000010 0d df ef b5 12 b7 2f |....../| diff --git a/src/crypto/tls/testdata/Client-TLSv12-RenegotiateTwiceRejected b/src/crypto/tls/testdata/Client-TLSv12-RenegotiateTwiceRejected index 441fa0fd2aa..075858a8fb2 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-RenegotiateTwiceRejected +++ b/src/crypto/tls/testdata/Client-TLSv12-RenegotiateTwiceRejected @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 bb ec 39 c5 f2 |....Y...U....9..| -00000010 dd a8 26 56 80 09 60 f5 d8 0a 93 6d 08 c4 30 c2 |..&V..`....m..0.| -00000020 cf 0c 44 86 49 a3 19 84 20 38 98 20 0d 8b 81 b5 |..D.I... 8. ....| -00000030 a7 42 37 27 1b 9c be 36 8f 9b 49 31 4f 73 67 a7 |.B7'...6..I1Osg.| -00000040 78 9f 46 e5 9e 3b 45 ff e9 16 11 ca cc a8 00 00 |x.F..;E.........| +00000000 16 03 03 00 59 02 00 00 55 03 03 e8 3e ed 97 18 |....Y...U...>...| +00000010 26 6a e6 ef 4f ea af 98 74 6d d2 f9 0f d2 b8 1c |&j..O...tm......| +00000020 4c 02 a5 a9 c0 f3 30 96 ea b4 53 20 40 15 3f cc |L.....0...S @.?.| +00000030 16 d6 a5 b0 fe a5 77 65 60 2f c9 bd b8 74 91 43 |......we`/...t.C| +00000040 d9 df 69 50 9f 5a 8b 95 c3 cf ef 5c cc a8 00 00 |..iP.Z.....\....| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,188 +61,189 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 ac 0c 00 00 a8 03 00 1d 20 2f ad 87 a5 c9 9e c7 |........ /......| -000002d0 f6 f1 05 9a 44 97 57 34 6b 3a 30 54 4c 0e 47 5e |....D.W4k:0TL.G^| -000002e0 16 d3 c9 c2 25 a8 47 e5 63 08 04 00 80 9f 54 b4 |....%.G.c.....T.| -000002f0 c1 aa bb 15 07 5c b1 52 ef bd 26 fa ec ce 70 31 |.....\.R..&...p1| -00000300 90 fb f5 4d d2 26 0c 64 6f b3 9f 7f 27 c7 a5 b2 |...M.&.do...'...| -00000310 d1 6d cf 0e 9c 91 e3 c4 20 f7 e3 ae 95 ff 6d ce |.m...... .....m.| -00000320 80 b5 30 89 6c a2 dd 31 26 5b 24 19 7a 30 f7 43 |..0.l..1&[$.z0.C| -00000330 71 a8 e9 1a 27 ee 46 86 44 56 b1 f3 2e e1 bd d5 |q...'.F.DV......| -00000340 79 99 34 0c 9b 01 e6 bb 0f ad 96 4a 68 0f 10 79 |y.4........Jh..y| -00000350 e9 91 7f 06 e6 02 32 ba 8c b6 a2 0c 4b 6d 09 f6 |......2.....Km..| -00000360 28 8f 94 e8 10 e1 ca 48 6c de 56 c2 5c 16 03 03 |(......Hl.V.\...| +000002c0 ac 0c 00 00 a8 03 00 1d 20 84 c8 b0 e3 24 80 91 |........ ....$..| +000002d0 32 6e 14 2e 0a 03 c8 6e bc ee b3 03 9d f6 5f c1 |2n.....n......_.| +000002e0 bc 9e ad 01 05 b9 c7 e2 17 08 04 00 80 d7 27 9b |..............'.| +000002f0 23 b5 5b 84 38 11 be 15 4e c5 9c 9d 54 2d a9 35 |#.[.8...N...T-.5| +00000300 52 75 e2 51 cd f3 90 3e db a3 27 47 f2 92 de 0d |Ru.Q...>..'G....| +00000310 27 45 6d 4b 32 60 60 11 39 ab 27 71 f4 76 7f 66 |'EmK2``.9.'q.v.f| +00000320 de 34 24 d1 b7 ec f5 b4 ed c4 6f 1a 6f 8d 33 ce |.4$.......o.o.3.| +00000330 2e 3d 09 f8 30 1d a3 69 e3 52 d7 e1 fc 64 c4 c5 |.=..0..i.R...d..| +00000340 32 66 4b 47 8a c4 3a f6 c5 79 62 d0 fc 4e 1b a9 |2fKG..:..yb..N..| +00000350 e4 eb 86 80 a6 ff 66 31 30 6e e8 26 9e 4d e7 7d |......f10n.&.M.}| +00000360 b6 8c e9 1e aa 21 e1 e7 a3 b2 83 6f 6b 16 03 03 |.....!.....ok...| 00000370 00 04 0e 00 00 00 |......| >>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| -00000030 16 03 03 00 20 d5 77 86 8e 32 60 6b 0f 0f 36 33 |.... .w..2`k..63| -00000040 89 fe 51 b8 69 3a 1f 37 b3 d1 eb 43 ab e0 f6 db |..Q.i:.7...C....| -00000050 8b 9d 3c 0d 9a |..<..| +00000030 16 03 03 00 20 4c 29 1c 10 e6 5c 55 6c 75 cc 5d |.... L)...\Ulu.]| +00000040 53 c0 69 20 68 c3 62 e1 85 1d b0 d9 a7 35 70 47 |S.i h.b......5pG| +00000050 6a d2 e0 26 87 |j..&.| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 20 ed 78 35 a3 71 |.......... .x5.q| -00000010 34 a9 40 b2 be 15 dc a9 10 86 e0 de 94 23 e9 51 |4.@..........#.Q| -00000020 2c 01 1e 34 19 07 53 20 59 ac f9 |,..4..S Y..| +00000000 14 03 03 00 01 01 16 03 03 00 20 a9 90 a3 f4 27 |.......... ....'| +00000010 bf 7b bb a4 3c ab 35 e2 d7 a3 8f 10 f5 1d ac 6c |.{..<.5........l| +00000020 f2 6d d1 19 96 1b 24 10 00 31 d3 |.m....$..1.| >>> Flow 5 (client to server) -00000000 17 03 03 00 16 f3 a2 5f da 1c 09 70 76 af 14 83 |......._...pv...| -00000010 e5 7f 6f c9 9a 61 7f d9 e6 86 3c |..o..a....<| +00000000 17 03 03 00 16 d6 e2 7a 07 c6 75 5e 2c cb 48 aa |.......z..u^,.H.| +00000010 92 9a 08 1b e2 61 e3 92 2b 36 3c |.....a..+6<| >>> Flow 6 (server to client) -00000000 16 03 03 00 14 71 23 15 46 93 87 94 38 01 d0 1b |.....q#.F...8...| -00000010 1a 34 db 58 17 d0 ac 62 87 |.4.X...b.| +00000000 16 03 03 00 14 c2 16 75 9a 6b d5 05 ee af 65 8a |.......u.k....e.| +00000010 02 8e 50 30 d9 7c 73 4f c8 |..P0.|sO.| >>> Flow 7 (client to server) -00000000 16 03 03 01 16 46 70 b5 5f 98 fc af a8 cb d6 7c |.....Fp._......|| -00000010 8c 1e 60 c3 68 25 20 7b 95 9a 0c 04 b3 2c 52 b2 |..`.h% {.....,R.| -00000020 30 f9 db cf 64 48 0a 46 9b 7a 11 76 11 5c 22 0c |0...dH.F.z.v.\".| -00000030 ef fa e6 6e a1 90 29 b3 64 aa ff 4d cb 7d 4d 91 |...n..).d..M.}M.| -00000040 c0 05 99 a0 3d 25 b2 1e 7c c4 d2 94 6b bf f0 f7 |....=%..|...k...| -00000050 0f 6a 3b 4c 66 c7 8a 26 9e 4f 79 68 50 5c f9 92 |.j;Lf..&.OyhP\..| -00000060 97 e1 a5 86 aa f2 e9 d5 8a a1 96 a7 37 82 71 7d |............7.q}| -00000070 7d 7e b6 77 a3 3d 84 40 58 0d 66 cd 52 6c 9b 18 |}~.w.=.@X.f.Rl..| -00000080 e2 c4 f0 dc 3d 9e 0e b8 49 ca 64 f3 71 c5 24 34 |....=...I.d.q.$4| -00000090 e7 ca c3 87 f6 b9 2c 6a 95 12 4d 9d 4a 4d fe 8a |......,j..M.JM..| -000000a0 51 16 6e c9 00 64 c0 d1 da ae e6 14 66 d2 a8 80 |Q.n..d......f...| -000000b0 35 ae 86 f6 64 f8 56 87 8a 40 46 43 ae d1 d1 fb |5...d.V..@FC....| -000000c0 64 1d 00 a1 3d e9 d9 7a b5 fb 71 2a db 76 5a 74 |d...=..z..q*.vZt| -000000d0 03 c3 79 df e6 90 e9 7e de f9 0e 70 7a 65 3c 68 |..y....~...pze| -00000100 cc f9 8d a6 56 37 0d ff 92 8f 1b 36 b3 3d 0b f5 |....V7.....6.=..| -00000110 5b fb fb 1e 4d c8 cb 84 39 5b 87 |[...M...9[.| +00000000 16 03 03 01 1c df de 55 d6 2e 06 26 26 12 ee 56 |.......U...&&..V| +00000010 9a 0e e7 43 c7 41 1f cb 18 07 5b 2f 2f ae 4b 1e |...C.A....[//.K.| +00000020 bc 04 a5 c9 67 97 6b 22 47 40 89 77 4b 8e 9c 8a |....g.k"G@.wK...| +00000030 f8 3e c6 57 b3 e9 56 4f 30 19 53 96 a5 02 29 ef |.>.W..VO0.S...).| +00000040 19 ef f8 86 0a f7 5e 56 2e bd ee 0a 7b 7c 95 fb |......^V....{|..| +00000050 1b 5d ba 2c 71 23 98 26 1e 74 7f 0a fb 17 b5 80 |.].,q#.&.t......| +00000060 87 54 ec de 85 77 f0 4b b4 6b ae 6e 02 03 ac 18 |.T...w.K.k.n....| +00000070 7e 93 7f 91 00 ef 78 48 08 69 08 2a 47 35 23 2a |~.....xH.i.*G5#*| +00000080 e1 1f 8c 34 43 54 dc 31 07 ee 5b 40 2d fe 3f e2 |...4CT.1..[@-.?.| +00000090 9e 47 d0 44 27 3c 3f 27 98 c8 8b 18 a3 93 f3 b6 |.G.D'>> Flow 8 (server to client) -00000000 16 03 03 00 81 25 44 f6 91 ed d5 01 fa 88 d6 74 |.....%D........t| -00000010 f7 cd 6d ba 85 76 1d bd ef 7b 31 51 db b4 42 a3 |..m..v...{1Q..B.| -00000020 0a 89 3f 47 dc ca 18 39 84 5d 5a 4e d2 cd ba 75 |..?G...9.]ZN...u| -00000030 b9 75 53 28 8c 85 6e 84 02 39 0a d2 59 ee ac 2f |.uS(..n..9..Y../| -00000040 fe a3 e4 fb 8c a1 72 e3 9f 28 8b 13 92 a8 5b 70 |......r..(....[p| -00000050 24 f0 1b 6d 19 aa f1 b2 bf 8a 1f e2 3a 3e 3f e2 |$..m........:>?.| -00000060 57 16 12 9e e8 21 11 66 b9 96 71 36 46 e1 2e fc |W....!.f..q6F...| -00000070 1e 40 a2 e2 6a 4d 4b 91 7a 50 0b d0 87 d1 04 16 |.@..jMK.zP......| -00000080 2f 47 4d f2 c9 68 16 03 03 02 69 9a 28 7b f7 fc |/GM..h....i.({..| -00000090 8b e7 2b 40 88 1c 30 c1 5a f6 1d 51 a9 a8 5e 70 |..+@..0.Z..Q..^p| -000000a0 73 1c 43 a7 3c 11 7e d5 92 78 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8b 78 72 98 7b f6 69 e5 57 83 1d |..~f..xr.{.i.W..| >>> Flow 10 (server to client) -00000000 14 03 03 00 11 00 e4 ef 62 c1 c0 72 f3 98 4d 5a |........b..r..MZ| -00000010 6a c8 7e 29 92 b8 16 03 03 00 20 ff 7e fc cb b5 |j.~)...... .~...| -00000020 07 5f ea 8a 89 2a 46 1b c6 33 41 fe f9 f4 1e 3a |._...*F..3A....:| -00000030 9d 8b 1d 8f 9b 7b 89 07 b4 e8 59 17 03 03 00 19 |.....{....Y.....| -00000040 a3 ba 0c 9b 54 cd 59 6a e1 db 33 80 38 a9 95 a1 |....T.Yj..3.8...| -00000050 95 5b a5 5f ad 3c d0 52 f7 16 03 03 00 14 e6 22 |.[._.<.R......."| -00000060 84 a7 02 10 1e ee 58 88 a5 b8 e8 bf 0a 9b 61 46 |......X.......aF| -00000070 0c ae |..| +00000000 14 03 03 00 11 74 5e 9a 15 15 ea 29 5b 3b 65 10 |.....t^....)[;e.| +00000010 dc 55 35 e6 06 2b 16 03 03 00 20 31 f8 fb ed 18 |.U5..+.... 1....| +00000020 33 8d 04 13 0d f1 32 28 37 07 b7 7f 5c 7a 72 8e |3.....2(7...\zr.| +00000030 89 b1 30 31 1e e9 b7 da a3 52 cf 17 03 03 00 19 |..01.....R......| +00000040 de ee 68 e9 bf a7 44 16 2f b1 63 86 d8 5a ac 9c |..h...D./.c..Z..| +00000050 12 11 19 d0 0b 42 5b 65 7f 16 03 03 00 14 41 fd |.....B[e......A.| +00000060 7f 3c 9a 8e 58 4a 43 2f 36 ff 2a 16 4f 5c 3f eb |.<..XJC/6.*.O\?.| +00000070 b0 9d |..| >>> Flow 11 (client to server) -00000000 15 03 03 00 12 7f 90 91 7b 93 4e 24 25 5e cb 35 |........{.N$%^.5| -00000010 2c eb ee 29 6a b3 a3 15 03 03 00 12 3d b7 30 fe |,..)j.......=.0.| -00000020 63 90 c3 2d 17 a0 e1 ed 8d bb a4 f6 f6 17 |c..-..........| +00000000 15 03 03 00 12 05 9b cd 8b 34 b7 8f 36 a5 b4 94 |.........4..6...| +00000010 10 94 7b 7d fe bb ad 15 03 03 00 12 dd a0 76 3f |..{}..........v?| +00000020 87 90 fd a6 2f e0 8c f3 53 8c cf e6 b3 30 |..../...S....0| diff --git a/src/crypto/tls/testdata/Client-TLSv12-RenegotiationRejected b/src/crypto/tls/testdata/Client-TLSv12-RenegotiationRejected index 3502977efa6..c786898b3f2 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-RenegotiationRejected +++ b/src/crypto/tls/testdata/Client-TLSv12-RenegotiationRejected @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 9c d0 eb d6 42 |....Y...U......B| -00000010 2e ff 6e 5a 19 33 6d 12 97 56 56 2b f5 1b 86 c8 |..nZ.3m..VV+....| -00000020 38 83 59 37 ac 17 46 ed 73 53 43 20 e4 94 9b 71 |8.Y7..F.sSC ...q| -00000030 f4 94 d9 d9 3a a1 e1 99 1e b4 a5 55 46 88 e0 0a |....:......UF...| -00000040 af 0a 0e ff 81 10 e2 e0 63 21 ae 2a cc a8 00 00 |........c!.*....| +00000000 16 03 03 00 59 02 00 00 55 03 03 32 cc a3 4f 3a |....Y...U..2..O:| +00000010 60 77 69 7f 97 c4 08 f6 72 3c fc ba 66 db cd 17 |`wi.....r<..f...| +00000020 24 cd 25 84 4e 47 d9 7b 09 d6 22 20 40 23 b7 d8 |$.%.NG.{.." @#..| +00000030 de 66 07 be c2 15 b1 59 6c e8 bf 91 4a 00 4d ed |.f.....Yl...J.M.| +00000040 8b c2 0f 50 42 01 3f 15 f6 d3 21 ff cc a8 00 00 |...PB.?...!.....| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,36 +61,36 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 ac 0c 00 00 a8 03 00 1d 20 9b 89 08 0d ea c2 d3 |........ .......| -000002d0 4f 73 77 a0 e3 0e 1a 68 13 2c 5c a5 ec 39 75 1b |Osw....h.,\..9u.| -000002e0 c2 95 fe b8 fe 58 f4 bb 16 08 04 00 80 d4 e8 d3 |.....X..........| -000002f0 d4 5b 1f ee ff 60 f5 86 b1 f4 06 c0 a8 ab 90 b0 |.[...`..........| -00000300 26 15 d5 4e 3f d6 a5 e2 a3 3a e0 0f 9a 92 bd 96 |&..N?....:......| -00000310 9d 98 15 f3 95 82 a9 5d 9f 1d 9b 4f 2e 77 58 40 |.......]...O.wX@| -00000320 58 3d fd 8f a6 09 1c fa 61 77 2e 87 df e7 76 8b |X=......aw....v.| -00000330 bf f1 dd 29 f8 70 c0 6d db e5 a0 55 92 77 44 75 |...).p.m...U.wDu| -00000340 d9 95 a6 17 67 93 47 8e 1f 61 50 65 31 94 d3 79 |....g.G..aPe1..y| -00000350 5f 25 a6 f0 3e 19 9a c8 ad b9 1a af 5b 50 2c 97 |_%..>.......[P,.| -00000360 78 1e 71 3a e0 fa 7c 44 1e d1 32 56 4e 16 03 03 |x.q:..|D..2VN...| +000002c0 ac 0c 00 00 a8 03 00 1d 20 fb 37 61 9a dd a9 99 |........ .7a....| +000002d0 4f a5 2d 4d e5 93 70 91 be 11 3d cc 66 d1 f6 4d |O.-M..p...=.f..M| +000002e0 f7 45 75 c9 27 fe 13 1c 04 08 04 00 80 58 c3 2c |.Eu.'........X.,| +000002f0 73 09 15 3c 4f 44 07 d9 7c 11 20 2f 0b e5 77 02 |s..=..*D| +00000350 91 6e 83 13 94 75 55 73 c2 fc ae dd 3b 44 01 93 |.n...uUs....;D..| +00000360 c3 d3 21 36 7e ee 2d 3c 75 e5 8c e6 13 16 03 03 |..!6~.->> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| -00000030 16 03 03 00 20 88 fe 97 82 bd a7 99 c6 a6 2f c1 |.... ........./.| -00000040 1a a8 54 8c e5 c6 39 0a 6b 07 9b 1a 05 f4 fb e3 |..T...9.k.......| -00000050 67 f5 c8 6e 17 |g..n.| +00000030 16 03 03 00 20 e7 43 cd 94 5d 17 64 66 97 4f 60 |.... .C..].df.O`| +00000040 a0 1f 5a 4f f5 75 8f 93 8e 7a 44 2e d6 03 80 d6 |..ZO.u...zD.....| +00000050 25 06 52 69 25 |%.Ri%| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 20 3b 6d ac 1c 8b |.......... ;m...| -00000010 1b 46 3a 4e 03 75 51 9e 99 6e 5a a8 4f 07 91 a3 |.F:N.uQ..nZ.O...| -00000020 18 2c bf 88 92 17 e5 13 65 a3 6c |.,......e.l| +00000000 14 03 03 00 01 01 16 03 03 00 20 e7 25 f6 37 44 |.......... .%.7D| +00000010 d0 12 f4 fb 21 ef 3b 8b ad ac 48 4d 39 08 8e 20 |....!.;...HM9.. | +00000020 8c ab 07 9b b5 99 06 9a c8 0c c5 |...........| >>> Flow 5 (client to server) -00000000 17 03 03 00 16 c7 94 fc be 3d 73 fd ec ce b2 f6 |.........=s.....| -00000010 bf 17 bf 52 3e b4 98 39 43 c0 0a |...R>..9C..| +00000000 17 03 03 00 16 7c 2e b4 a0 ee 6e 1b cb 99 3c de |.....|....n...<.| +00000010 17 b9 23 ce a8 45 8b 55 74 bc dc |..#..E.Ut..| >>> Flow 6 (server to client) -00000000 16 03 03 00 14 cf 01 f5 e6 eb 60 e3 49 c4 fb 84 |..........`.I...| -00000010 e1 11 69 e1 91 c0 02 d2 e3 |..i......| +00000000 16 03 03 00 14 5b 11 6b 18 97 aa 21 56 09 20 1f |.....[.k...!V. .| +00000010 71 f6 7d e3 7f 85 8c 53 7e |q.}....S~| >>> Flow 7 (client to server) -00000000 15 03 03 00 12 4d 7f de 01 23 f7 3f 0d e6 1a f1 |.....M...#.?....| -00000010 19 a2 cd 58 1a 25 f5 15 03 03 00 12 95 78 52 00 |...X.%.......xR.| -00000020 65 aa 6d 77 5a 66 d5 95 c4 5a 9b 1b 05 b2 |e.mwZf...Z....| +00000000 15 03 03 00 12 ce c0 d2 da 23 4b 12 c2 f5 a9 df |.........#K.....| +00000010 03 05 fb 9b e8 17 29 15 03 03 00 12 34 45 6a ac |......).....4Ej.| +00000020 af 6a b9 e6 d2 9d 5e 11 eb 93 0e 0e 1e 47 |.j....^......G| diff --git a/src/crypto/tls/testdata/Client-TLSv12-SCT b/src/crypto/tls/testdata/Client-TLSv12-SCT index d12e263e153..988a2e2a1c4 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-SCT +++ b/src/crypto/tls/testdata/Client-TLSv12-SCT @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,21 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 01 c6 02 00 01 c2 03 03 d8 a9 75 cc 9a |.............u..| -00000010 81 df 5a a0 3b ba 51 74 52 50 72 08 35 02 35 77 |..Z.;.QtRPr.5.5w| -00000020 28 ff 44 e6 d9 c6 8b f8 54 67 b4 20 62 80 60 cc |(.D.....Tg. b.`.| -00000030 09 90 52 66 75 72 a2 c5 dc 8d 18 ce 9a d5 7e cd |..Rfur........~.| -00000040 a5 36 2a 2e 65 72 6f f0 dd b0 8c 14 cc a8 00 01 |.6*.ero.........| +00000000 16 03 03 01 c6 02 00 01 c2 03 03 7a e6 8c be 07 |...........z....| +00000010 fd 4d 8a 55 3e d9 00 d0 88 22 b2 bc 76 37 8a 8b |.M.U>...."..v7..| +00000020 16 6b 3d 79 12 08 7f 8d c0 e8 83 20 f8 e3 cf 6f |.k=y....... ...o| +00000030 04 0a 05 23 4f 03 08 aa 00 f2 6b 9b 3c 36 77 26 |...#O.....k.<6w&| +00000040 89 bb e1 1d 81 14 18 54 b8 47 7a 13 cc a8 00 01 |.......T.Gz.....| 00000050 7a 00 12 01 69 01 67 00 75 00 a4 b9 09 90 b4 18 |z...i.g.u.......| 00000060 58 14 87 bb 13 a2 cc 67 70 0a 3c 35 98 04 f9 1b |X......gp.<5....| 00000070 df b8 e3 77 cd 0e c8 0d dc 10 00 00 01 47 97 99 |...w.........G..| @@ -83,31 +84,31 @@ 00000400 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d ae db 46 |.....@.a.Lr+...F| 00000410 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db fe 3d 13 |..M...>...B...=.| 00000420 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 ac 0c 00 |`.\!.;..........| -00000430 00 a8 03 00 1d 20 cd 2a 10 ee 97 4a 83 7b 0e 6d |..... .*...J.{.m| -00000440 e7 00 5a ce bc d8 1c 57 fa f6 ec 52 0d 0f be 6d |..Z....W...R...m| -00000450 c8 5d 27 3c 8c 1b 08 04 00 80 a9 4c bb 3a 0a d7 |.]'<.......L.:..| -00000460 db 72 3d 88 49 a6 0b f7 dc d5 e1 d0 07 e8 6c fa |.r=.I.........l.| -00000470 b0 5e 0b 13 27 29 6f 1f 1e b9 05 60 16 cc ea 7b |.^..')o....`...{| -00000480 46 d7 12 58 03 43 b0 fe 8e 7b 83 3b ee 11 78 8c |F..X.C...{.;..x.| -00000490 60 0f 9c 76 63 60 01 78 a0 9b 19 b9 32 99 a9 9d |`..vc`.x....2...| -000004a0 42 b8 1f f1 8b 87 07 32 fa 5e 74 d5 3e 5e ba 21 |B......2.^t.>^.!| -000004b0 ff 63 b7 c6 68 bc b3 f9 52 1a ea 23 c7 f2 ec ff |.c..h...R..#....| -000004c0 d4 10 0d f8 76 2f bc 0d e5 12 7f ee d3 8d 9e 6b |....v/.........k| -000004d0 5e 22 78 d6 fa 5e 6a 53 16 44 16 03 03 00 04 0e |^"x..^jS.D......| +00000430 00 a8 03 00 1d 20 17 43 54 89 3e b8 74 5b 66 cd |..... .CT.>.t[f.| +00000440 5f 28 dd 1e e5 8f 2e f2 e2 2f 8a 0a ca ea 3e 8f |_(......./....>.| +00000450 8a af 2e 6d ab 3d 08 04 00 80 3c b2 0e bb 41 5a |...m.=....<...AZ| +00000460 65 1d e4 7e e6 0c e5 f4 28 7b fc a5 42 83 84 5d |e..~....({..B..]| +00000470 73 f7 57 ce 01 f1 af 82 69 a1 95 37 97 f6 1f d5 |s.W.....i..7....| +00000480 2a c6 a3 83 d7 66 c4 e8 57 3a 7f 60 87 cd a8 cf |*....f..W:.`....| +00000490 ff 9c bf ea cb 45 bf 64 70 cb 30 a2 97 b5 06 26 |.....E.dp.0....&| +000004a0 dc 71 ca d1 24 18 bd a5 0d 57 b8 ee 75 ea 1d 60 |.q..$....W..u..`| +000004b0 16 60 d0 9f 4d 9d 73 3d bf fc 67 5d d0 9c fe 72 |.`..M.s=..g]...r| +000004c0 32 fb 49 b4 42 4c ae a8 ed 05 7e 07 0d 1c 7e 54 |2.I.BL....~...~T| +000004d0 22 7a 27 a1 f1 48 c0 d8 5b cc 16 03 03 00 04 0e |"z'..H..[.......| 000004e0 00 00 00 |...| >>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| -00000030 16 03 03 00 20 5c 1a 1b 0e 7e 83 4f 9b f6 8e 9f |.... \...~.O....| -00000040 ca 95 86 c3 7b 60 73 d3 8d 3c 6d 18 6a eb 70 a3 |....{`s..>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 20 1f a2 50 dd c5 |.......... ..P..| -00000010 ba 96 4a 63 e1 cc b6 45 77 09 c1 49 cb 5f eb 4b |..Jc...Ew..I._.K| -00000020 38 9b b1 40 1c af b1 a2 dc 7c ba |8..@.....|.| +00000000 14 03 03 00 01 01 16 03 03 00 20 30 5f d8 71 86 |.......... 0_.q.| +00000010 79 ec 3e a0 fc 4a 52 08 1f 9b c5 5c 57 74 f2 1f |y.>..JR....\Wt..| +00000020 c1 f7 97 60 0a 60 39 f6 42 ae f4 |...`.`9.B..| >>> Flow 5 (client to server) -00000000 17 03 03 00 16 e7 54 f6 bf 56 39 57 c4 b2 ac f2 |......T..V9W....| -00000010 b1 f4 b1 2f ad ae d7 87 21 ff 1c 15 03 03 00 12 |.../....!.......| -00000020 5d b6 56 77 55 99 b6 7b a4 0b d8 8e 8d 93 b6 35 |].VwU..{.......5| -00000030 ce 9a |..| +00000000 17 03 03 00 16 72 fa 8d 52 6c 26 f6 ae dd a6 90 |.....r..Rl&.....| +00000010 11 87 da 7b f4 71 ad b7 c6 84 cd 15 03 03 00 12 |...{.q..........| +00000020 b7 fa 56 d2 a4 84 fb 33 64 f5 18 8e 67 ea 0b d2 |..V....3d...g...| +00000030 d4 c5 |..| diff --git a/src/crypto/tls/testdata/Client-TLSv12-X25519-ECDHE b/src/crypto/tls/testdata/Client-TLSv12-X25519-ECDHE index d58a32f2b37..8aa322d52d8 100644 --- a/src/crypto/tls/testdata/Client-TLSv12-X25519-ECDHE +++ b/src/crypto/tls/testdata/Client-TLSv12-X25519-ECDHE @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 f4 01 00 00 f0 03 03 00 00 00 00 00 |................| +00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,20 +7,20 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 75 00 05 00 05 01 00 00 00 00 00 0a 00 |...u............| -00000090 04 00 02 00 1d 00 0b 00 02 01 00 00 0d 00 1a 00 |................| -000000a0 18 08 04 04 03 08 07 08 05 08 06 04 01 05 01 06 |................| -000000b0 01 05 03 06 03 02 01 02 03 ff 01 00 01 00 00 12 |................| -000000c0 00 00 00 2b 00 09 08 03 04 03 03 03 02 03 01 00 |...+............| -000000d0 33 00 26 00 24 00 1d 00 20 2f e5 7d a3 47 cd 62 |3.&.$... /.}.G.b| -000000e0 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 cf |C.(.._.).0......| -000000f0 c2 ed 90 99 5f 58 cb 3b 74 |...._X.;t| +00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000090 04 00 02 00 1d 00 0b 00 02 01 00 00 0d 00 20 00 |.............. .| +000000a0 1e 08 04 04 03 08 07 08 05 08 06 04 01 05 01 06 |................| +000000b0 01 05 03 06 03 02 01 02 03 fe 61 fe 62 08 08 ff |..........a.b...| +000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| +000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| +000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| +000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 59 02 00 00 55 03 03 e0 c7 ce be 3a |....Y...U......:| -00000010 a6 34 5f b7 c5 ec f1 f3 09 df 4d db 39 60 71 93 |.4_.......M.9`q.| -00000020 db 7c 30 e0 81 93 f0 19 57 6b 6b 20 9e 4b e2 1e |.|0.....Wkk .K..| -00000030 27 8d d3 f6 0c f3 3d bc 67 3e 79 33 fd c9 cc 55 |'.....=.g>y3...U| -00000040 36 55 a5 aa 89 94 fe b2 51 cf 24 56 c0 2f 00 00 |6U......Q.$V./..| +00000000 16 03 03 00 59 02 00 00 55 03 03 7c 84 a2 1f f5 |....Y...U..|....| +00000010 ed 1d 8a b0 31 68 01 25 d1 29 73 83 65 e7 ae ad |....1h.%.)s.e...| +00000020 3a 2e 62 26 c7 36 84 9e 41 78 8c 20 8d d6 1a cf |:.b&.6..Ax. ....| +00000030 20 65 4d 3c 7c 45 ea a2 0b d3 ce e1 8c 24 02 ac | eM<|E.......$..| +00000040 01 ef 7e 52 d5 07 8b 06 c2 24 bc 3c c0 2f 00 00 |..~R.....$.<./..| 00000050 0d ff 01 00 01 00 00 0b 00 04 03 00 01 02 16 03 |................| 00000060 03 02 59 0b 00 02 55 00 02 52 00 02 4f 30 82 02 |..Y...U..R..O0..| 00000070 4b 30 82 01 b4 a0 03 02 01 02 02 09 00 e8 f0 9d |K0..............| @@ -60,33 +60,33 @@ 00000290 77 8d 0c 1c f1 0f a1 d8 40 83 61 c9 4c 72 2b 9d |w.......@.a.Lr+.| 000002a0 ae db 46 06 06 4d f4 c1 b3 3e c0 d1 bd 42 d4 db |..F..M...>...B..| 000002b0 fe 3d 13 60 84 5c 21 d3 3b e9 fa e7 16 03 03 00 |.=.`.\!.;.......| -000002c0 ac 0c 00 00 a8 03 00 1d 20 9b 73 58 2f 9a aa 8b |........ .sX/...| -000002d0 3e 80 1c b1 8e e5 d4 54 c2 d0 b1 94 16 86 e2 4b |>......T.......K| -000002e0 9c ab d7 ce 2c e5 26 20 04 08 04 00 80 d8 c0 18 |....,.& ........| -000002f0 90 8e 06 d8 d6 4c af a1 ae 5e ca 4b a1 18 bb 31 |.....L...^.K...1| -00000300 f5 3a 75 c3 d7 73 69 a7 e0 0f 8e f2 c5 92 0a bd |.:u..si.........| -00000310 7f 91 36 6c 01 c3 eb 08 9a 3b 25 2c bd 86 88 05 |..6l.....;%,....| -00000320 64 e0 38 5b 75 01 10 1f 1b d5 34 09 04 2e 34 6d |d.8[u.....4...4m| -00000330 71 d2 6c b6 f3 7a 1e ed a9 9d 28 60 13 fc 02 6f |q.l..z....(`...o| -00000340 f6 17 99 52 7b 19 60 e5 a6 11 d4 b3 4c 52 03 b5 |...R{.`.....LR..| -00000350 3e 28 91 c6 66 87 25 df 10 c6 cf b9 5f 92 0e d7 |>(..f.%....._...| -00000360 b6 19 f0 19 b9 f6 e9 e9 24 74 35 3b c6 16 03 03 |........$t5;....| +000002c0 ac 0c 00 00 a8 03 00 1d 20 0a 64 f2 e6 ec 58 68 |........ .d...Xh| +000002d0 7b 13 97 52 45 a2 8f cf ed 93 e9 fa 00 c2 d1 11 |{..RE...........| +000002e0 5b 9c 09 90 d5 cf 81 3e 2f 08 04 00 80 8e 9e a7 |[......>/.......| +000002f0 98 25 f1 eb a2 e3 dc cd 44 3e 24 bf 9d 95 a3 6c |.%......D>$....l| +00000300 d2 ea bf 47 7c fa 90 de 5a ea 8c f6 83 4b c3 92 |...G|...Z....K..| +00000310 6a d5 ce 27 8d 84 b7 6e 3c bf 3f a5 97 ad 61 ef |j..'...n<.?...a.| +00000320 3a 92 db 70 7b 3d f0 af e5 28 c8 96 98 b4 bd ed |:..p{=...(......| +00000330 55 ed fe c4 c9 38 65 a2 67 d7 43 a4 01 52 00 18 |U....8e.g.C..R..| +00000340 2c 0c a6 37 fb 36 34 f6 9c b8 11 e9 fa a6 e5 d5 |,..7.64.........| +00000350 e0 22 7b 1e 15 e0 33 97 ab 60 f5 15 8b 7c 25 06 |."{...3..`...|%.| +00000360 f8 fe 63 64 16 d0 e5 0f 40 94 b0 0d df 16 03 03 |..cd....@.......| 00000370 00 04 0e 00 00 00 |......| >>> Flow 3 (client to server) 00000000 16 03 03 00 25 10 00 00 21 20 2f e5 7d a3 47 cd |....%...! /.}.G.| 00000010 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 |bC.(.._.).0.....| 00000020 cf c2 ed 90 99 5f 58 cb 3b 74 14 03 03 00 01 01 |....._X.;t......| -00000030 16 03 03 00 28 00 00 00 00 00 00 00 00 01 e4 5a |....(..........Z| -00000040 e9 dc dd 98 cd 5f d2 d2 eb 84 12 c9 96 ca 91 d7 |....._..........| -00000050 ae f4 db 44 a4 37 f3 a3 b2 8d db ed 3d |...D.7......=| +00000030 16 03 03 00 28 00 00 00 00 00 00 00 00 ce 1a b6 |....(...........| +00000040 76 9d b0 34 f2 7e d8 48 34 81 f3 31 32 0a b1 b4 |v..4.~.H4..12...| +00000050 fe ee 4a 24 98 16 cd 64 c5 67 47 e1 41 |..J$...d.gG.A| >>> Flow 4 (server to client) -00000000 14 03 03 00 01 01 16 03 03 00 28 c2 2d 32 ba 46 |..........(.-2.F| -00000010 27 8d 87 13 7f b9 49 04 64 2f 6e cc 32 81 f8 3c |'.....I.d/n.2..<| -00000020 7f 0f 19 13 5c 11 33 a1 05 5f 91 bc 97 30 64 84 |....\.3.._...0d.| -00000030 57 69 90 |Wi.| +00000000 14 03 03 00 01 01 16 03 03 00 28 f1 8f b9 88 82 |..........(.....| +00000010 76 41 a4 76 ba 3b 28 19 68 61 9e 5e a6 ac 1f 16 |vA.v.;(.ha.^....| +00000020 f5 14 01 8e 6a 39 d7 67 d1 2a 12 b4 5c da 65 27 |....j9.g.*..\.e'| +00000030 bb 30 88 |.0.| >>> Flow 5 (client to server) -00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 fd 0f a5 |................| -00000010 74 98 c4 98 ee 67 74 d4 c1 d4 fe d3 c7 e2 1b 2c |t....gt........,| -00000020 e5 3c be 15 03 03 00 1a 00 00 00 00 00 00 00 02 |.<..............| -00000030 f8 d4 60 41 13 6a 9c e3 0e 56 e2 ab 96 45 7e 06 |..`A.j...V...E~.| -00000040 87 63 |.c| +00000000 17 03 03 00 1e 00 00 00 00 00 00 00 01 83 d1 38 |...............8| +00000010 d1 f5 2a 47 e4 46 20 1f 14 61 10 5d 4d 60 e5 d8 |..*G.F ..a.]M`..| +00000020 ae 26 59 15 03 03 00 1a 00 00 00 00 00 00 00 02 |.&Y.............| +00000030 22 fb e1 53 ef c4 fb f5 9a 81 69 35 33 14 46 ac |"..S......i53.F.| +00000040 5c 8e |\.| diff --git a/src/crypto/tls/testdata/Client-TLSv13-AES128-SHA256 b/src/crypto/tls/testdata/Client-TLSv13-AES128-SHA256 index 4273484ca71..8158e3692d9 100644 --- a/src/crypto/tls/testdata/Client-TLSv13-AES128-SHA256 +++ b/src/crypto/tls/testdata/Client-TLSv13-AES128-SHA256 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,84 +7,85 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 7a 02 00 00 76 03 03 f7 30 f3 d1 e7 |....z...v...0...| -00000010 eb 94 97 a2 c6 d5 be 74 e0 6c 08 80 2f ad 11 6b |.......t.l../..k| -00000020 b3 ce 22 59 06 a9 eb 41 9c 97 a8 20 00 00 00 00 |.."Y...A... ....| +00000000 16 03 03 00 7a 02 00 00 76 03 03 32 21 56 66 57 |....z...v..2!VfW| +00000010 d3 ab f7 5f 92 a3 cf fb 0f 37 45 d3 d6 6c 70 a0 |..._.....7E..lp.| +00000020 ab 32 42 7b d7 d1 d1 6f 25 67 c1 20 00 00 00 00 |.2B{...o%g. ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000040 00 00 00 00 00 00 00 00 00 00 00 00 13 01 00 00 |................| -00000050 2e 00 2b 00 02 03 04 00 33 00 24 00 1d 00 20 c0 |..+.....3.$... .| -00000060 47 7e ad a1 41 53 e5 25 ec 74 46 bc 9e 80 08 3b |G~..AS.%.tF....;| -00000070 0b f5 7e fb 71 1f 00 d5 4b 27 51 22 4a 5e 5f 14 |..~.q...K'Q"J^_.| -00000080 03 03 00 01 01 17 03 03 00 17 e9 e8 56 00 26 9e |............V.&.| -00000090 92 60 84 6c 07 3d b1 ef e4 63 51 ba 48 ee d7 fe |.`.l.=...cQ.H...| -000000a0 57 17 03 03 02 6d 2e d4 bb bf a2 e8 3b 84 47 2e |W....m......;.G.| -000000b0 22 66 c1 98 ea 11 6b a3 4d 1b 64 c0 02 32 76 9b |"f....k.M.d..2v.| -000000c0 29 8a 4a 96 68 5b d1 fd a0 0f a6 9b 70 20 c7 08 |).J.h[......p ..| -000000d0 7b 25 07 d1 54 8c b1 bb 4e ba 32 65 2c 1e 16 29 |{%..T...N.2e,..)| -000000e0 e7 d2 df e3 84 60 e1 43 07 99 35 4d 95 7c 27 96 |.....`.C..5M.|'.| -000000f0 be f4 bf 0a e9 3b 9d 60 7a 6e 34 82 1f 03 ca 17 |.....;.`zn4.....| -00000100 ac d1 a1 b5 dc 3f 20 7b 42 f6 94 43 60 ff 3f 1b |.....? {B..C`.?.| -00000110 b1 2e 2d 71 55 07 fb 65 40 56 59 82 1e 31 83 c9 |..-qU..e@VY..1..| -00000120 35 6c 28 ad c1 bd 88 55 1b b6 1e 89 af 64 7f 11 |5l(....U.....d..| -00000130 53 80 3a 62 ef 34 a7 d0 ce 38 9b 19 d6 5f 78 0d |S.:b.4...8..._x.| -00000140 66 73 b2 bd b6 a6 f8 70 c8 40 f9 aa a2 86 f4 48 |fs.....p.@.....H| -00000150 0d 6c 54 67 c6 3c 91 97 ff 94 4d 9a 01 d5 e1 c9 |.lTg.<....M.....| -00000160 8f 27 d3 8d b3 72 cd 34 eb 7a 6d 48 84 f3 8b 84 |.'...r.4.zmH....| -00000170 34 d2 68 bd 26 bc 6d e5 46 41 cc 86 d4 7a b6 31 |4.h.&.m.FA...z.1| -00000180 05 b3 bc a4 fe e1 5c d4 eb 8b fe 64 0e be 89 c4 |......\....d....| -00000190 ce e0 49 a0 ba 7a 83 b6 fb 31 17 42 fd b4 e3 59 |..I..z...1.B...Y| -000001a0 48 df f6 a8 e4 5c d1 77 77 cb c2 31 85 8a 26 65 |H....\.ww..1..&e| -000001b0 20 fa 05 90 ae 66 95 7a 75 4b bc 93 15 dd a0 13 | ....f.zuK......| -000001c0 61 d5 99 fb b2 27 bd ec fd 10 b5 d2 c7 18 ac b9 |a....'..........| -000001d0 bd bc 35 72 d0 42 6c f7 5a e0 67 46 45 10 f7 50 |..5r.Bl.Z.gFE..P| -000001e0 e4 14 47 ac 39 5a 05 38 b9 25 4a 43 fa 57 b2 51 |..G.9Z.8.%JC.W.Q| -000001f0 b7 3e f7 ef d5 b5 de 2e 2f 5c d0 d7 00 23 ac 4b |.>....../\...#.K| -00000200 65 8d 6c f4 ab 6f ef 1e c2 66 c5 b2 cb 1a 51 4c |e.l..o...f....QL| -00000210 ef 96 8f 28 65 2f 50 9c 91 1f 73 87 fc 81 db 90 |...(e/P...s.....| -00000220 16 69 00 06 98 6b 00 33 41 e1 e6 12 89 cb c9 f3 |.i...k.3A.......| -00000230 23 2c 28 83 00 ca 4f 42 f5 26 bc 94 39 3b 18 31 |#,(...OB.&..9;.1| -00000240 41 a9 19 4a 60 e8 de 8f 1d d0 e8 96 77 c0 49 bd |A..J`.......w.I.| -00000250 a2 98 bd b1 0a 6f bd 27 79 1d c4 33 50 37 a8 eb |.....o.'y..3P7..| -00000260 a5 4e 59 87 58 cd f0 a0 34 4e 2b 9d ee 03 e4 8a |.NY.X...4N+.....| -00000270 24 94 86 11 e1 94 f0 2b 3e 27 9a 92 1c 17 d3 96 |$......+>'......| -00000280 c0 71 ab ee 75 5f 99 ca 0e 42 65 5d ed 48 0c 7a |.q..u_...Be].H.z| -00000290 95 8a d9 da f7 60 ee de 46 f2 f4 7a d6 ce 38 41 |.....`..F..z..8A| -000002a0 fa e8 1f 3e 77 be 02 53 0c 33 96 5b 0d 38 bb 08 |...>w..S.3.[.8..| -000002b0 5e 92 1a 81 f1 be c7 9a e2 02 80 09 3b b7 62 b0 |^...........;.b.| -000002c0 7c a7 85 3a d9 52 34 23 4f a3 04 e7 35 98 9e 18 ||..:.R4#O...5...| -000002d0 13 0b 71 12 6d a4 2e 11 bf 39 8c 94 ef 15 96 27 |..q.m....9.....'| -000002e0 9e be 81 d9 55 5a 8b 14 c5 49 dd 6e 6e 7b 6b c2 |....UZ...I.nn{k.| -000002f0 f3 7d ef 24 88 b9 eb a6 15 3e aa a8 3e eb 37 54 |.}.$.....>..>.7T| -00000300 fc 86 9f 51 30 5f 9c a5 fc 7a af f6 1b a5 a4 27 |...Q0_...z.....'| -00000310 51 78 f7 17 03 03 00 99 79 14 63 10 91 cd 73 f5 |Qx......y.c...s.| -00000320 a8 62 c3 92 a3 04 c2 3d 58 5e d3 6e 93 eb 9b b1 |.b.....=X^.n....| -00000330 11 f0 3c c6 96 9f c6 c8 9b de 2c d5 12 c2 bd d1 |..<.......,.....| -00000340 2a 68 89 4a 07 1e 23 d2 45 ca a1 0f 92 71 b7 f7 |*h.J..#.E....q..| -00000350 d0 2f 2a be d0 5e 0c 5d 13 8f b0 7f df b8 52 2e |./*..^.]......R.| -00000360 7a 5e c8 eb 84 06 46 81 d0 f7 09 18 52 fb ce fd |z^....F.....R...| -00000370 22 d8 74 71 e8 7d 41 5f 3a 5d e5 f9 bb e6 99 03 |".tq.}A_:]......| -00000380 32 d1 58 e8 5a 58 d8 b2 39 61 01 33 72 7d d2 11 |2.X.ZX..9a.3r}..| -00000390 8f f7 58 55 c8 f2 64 63 33 9b 78 36 bf 9b 8b 40 |..XU..dc3.x6...@| -000003a0 8c ec 7b a2 bb 51 ed b1 fe 74 c2 c9 1f b4 2b cb |..{..Q...t....+.| -000003b0 fd 17 03 03 00 35 75 46 88 74 06 9b 5e 88 c2 0d |.....5uF.t..^...| -000003c0 fc 7d 29 bd 6c 1c 23 2f 06 3f 14 b1 55 e4 98 b1 |.}).l.#/.?..U...| -000003d0 ed c3 9a ed ea be 29 60 15 ac 80 c7 a8 f7 9b ce |......)`........| -000003e0 f3 79 b3 be ad ff ab b4 a7 45 57 |.y.......EW| +00000050 2e 00 2b 00 02 03 04 00 33 00 24 00 1d 00 20 4c |..+.....3.$... L| +00000060 2d a1 0d c0 12 61 0f f7 34 85 8f 64 2b 33 cb 98 |-....a..4..d+3..| +00000070 3d 88 b8 90 22 fb 81 2e aa a8 74 76 3b 10 68 14 |=...".....tv;.h.| +00000080 03 03 00 01 01 17 03 03 00 17 71 a7 f3 c4 55 f5 |..........q...U.| +00000090 08 8a 3d ed 30 43 25 6a 2c b0 79 c8 da cb 7a 78 |..=.0C%j,.y...zx| +000000a0 dd 17 03 03 02 6d e3 6a 2f 3b 3d bd 98 5d 96 17 |.....m.j/;=..]..| +000000b0 6f 95 77 b7 f6 f2 c1 44 74 e7 4a a2 9b 2d 41 35 |o.w....Dt.J..-A5| +000000c0 1d b4 ec 37 c2 6d 35 66 b1 7d 07 49 24 3d 51 81 |...7.m5f.}.I$=Q.| +000000d0 c2 44 8a a0 a1 1a 41 ca dd 56 21 a0 77 18 5f 38 |.D....A..V!.w._8| +000000e0 5f a4 fa 8f 5c 8b 59 ff 45 2b f9 c4 5d 81 16 c7 |_...\.Y.E+..]...| +000000f0 bf a7 5e a6 b5 f8 71 3f cf 46 03 b1 96 55 7e ca |..^...q?.F...U~.| +00000100 6e 87 e0 85 44 5a 19 44 b7 d5 23 d6 2f b7 cf e5 |n...DZ.D..#./...| +00000110 de e6 a3 80 84 95 e1 b7 30 b6 0e ba 6d d0 ee 96 |........0...m...| +00000120 39 7f e0 8a e7 94 fd 17 be d6 33 8b 62 51 b5 75 |9.........3.bQ.u| +00000130 e0 70 5c f1 f1 d4 d3 bd 97 5c 05 37 79 f3 d8 14 |.p\......\.7y...| +00000140 18 57 d6 8a 7a b0 5a 92 da 3f 82 34 1a 05 33 ce |.W..z.Z..?.4..3.| +00000150 91 df 0e 32 f5 f0 4e b3 e6 b6 bf 97 97 d6 07 bb |...2..N.........| +00000160 70 58 83 05 0f cf cb 22 2f 36 2e 42 03 66 04 86 |pX....."/6.B.f..| +00000170 17 b5 16 96 08 96 2f 3f e8 8a c3 bd 65 d0 04 cd |....../?....e...| +00000180 68 a6 b1 f4 c7 f7 e1 4f 84 4a 40 68 23 4f 57 ce |h......O.J@h#OW.| +00000190 5f 11 73 bb 53 8d ed d8 0b d6 70 40 83 70 49 d6 |_.s.S.....p@.pI.| +000001a0 95 b0 10 8e 7e f0 c3 07 ec 32 6a bf 33 a4 aa 95 |....~....2j.3...| +000001b0 62 30 34 f6 1a fd 38 17 c6 b4 3e e6 be bc dd 6c |b04...8...>....l| +000001c0 8f 7f be 38 c9 3d 57 6c 2e 48 06 15 fc ca ad d8 |...8.=Wl.H......| +000001d0 56 1e c6 a7 57 df a5 9d 89 22 4b 7b 06 0d 1b 10 |V...W...."K{....| +000001e0 5d 1a 14 c4 0a 15 c0 28 f3 97 6c 03 d6 dc 08 83 |]......(..l.....| +000001f0 e2 d4 e0 93 93 82 b1 ac c3 9b 05 d7 1d 05 3c 56 |..............'..."|.I| +00000240 eb 3b 98 5c 3e 1f 7b 5e e6 d4 aa fe 1f 0c cb 04 |.;.\>.{^........| +00000250 14 f9 ed 12 d6 49 9d 6d 12 e8 db 4d 9c 1e 49 1e |.....I.m...M..I.| +00000260 2e f5 95 72 d3 d4 9c d8 a1 7b a8 68 43 c3 18 6a |...r.....{.hC..j| +00000270 6a 54 36 26 71 e3 60 4e 50 4a 25 2b ad 12 52 5b |jT6&q.`NPJ%+..R[| +00000280 4c 7c c0 a8 6e 58 15 79 cf ca 5e e4 8a 7f 38 5f |L|..nX.y..^...8_| +00000290 9f c2 70 e0 9f 2f b9 c2 25 ad 43 4d 1d 5f 31 11 |..p../..%.CM._1.| +000002a0 64 0e f6 ee 93 6a 9b 79 f3 9b 3a 60 2e 67 e5 6a |d....j.y..:`.g.j| +000002b0 4c 70 75 20 f8 5c a8 e1 ca b7 07 fa 8c 1c 01 c2 |Lpu .\..........| +000002c0 f0 be 18 c5 a7 73 a0 01 eb 36 82 d7 4c d2 17 b6 |.....s...6..L...| +000002d0 ca 58 dc b9 ac bb 1e 5b 57 bb 2f fb ce 44 d0 0b |.X.....[W./..D..| +000002e0 49 8c 57 75 cc b9 2b 8e b8 93 65 75 2c 71 55 13 |I.Wu..+...eu,qU.| +000002f0 5d 8f 7e 74 4e 38 2d dc ff a4 75 06 3f 46 ac bd |].~tN8-...u.?F..| +00000300 3e b5 d5 bc d2 73 c6 7d 36 76 cf d5 85 9a 60 82 |>....s.}6v....`.| +00000310 ab 8e 50 17 03 03 00 99 f0 f7 90 9d bf 9f bb 9c |..P.............| +00000320 36 2f 5a 81 e1 07 04 4f 1a a5 42 ea 06 18 34 51 |6/Z....O..B...4Q| +00000330 2b d9 61 9f c3 28 c7 e1 75 49 51 2c f6 31 11 42 |+.a..(..uIQ,.1.B| +00000340 96 95 8d 3d 2d 17 e0 0b 88 d0 94 dc fe 15 55 24 |...=-.........U$| +00000350 05 02 63 bf d4 12 03 76 24 fe 01 11 ab 3d 8c 9f |..c....v$....=..| +00000360 8e a1 cf 6e 33 21 4c 7c a1 8b 49 52 be e8 17 4d |...n3!L|..IR...M| +00000370 94 4b 34 3e dd f4 99 a2 a6 e3 00 8e 19 73 00 44 |.K4>.........s.D| +00000380 a9 3b 15 07 76 27 6c 4b 80 47 51 aa 66 86 5f a9 |.;..v'lK.GQ.f._.| +00000390 75 24 fd 3b 89 41 43 ab f7 e9 9b b2 7c ec 66 e1 |u$.;.AC.....|.f.| +000003a0 af 4c 36 3b 4e 6b f9 be f9 9a 1b 0d 49 e4 3f c6 |.L6;Nk......I.?.| +000003b0 a8 17 03 03 00 35 44 b7 aa bb f4 d3 40 1d ed eb |.....5D.....@...| +000003c0 52 e8 af 01 a1 6d 1f 65 56 5a bb 3d a8 85 7e 24 |R....m.eVZ.=..~$| +000003d0 e2 c8 02 12 59 2d 49 df 1f c5 f9 a2 ec f5 99 c1 |....Y-I.........| +000003e0 1e 16 34 43 a5 1f df 3e df e2 10 |..4C...>...| >>> Flow 3 (client to server) -00000000 14 03 03 00 01 01 17 03 03 00 35 b5 22 19 23 49 |..........5.".#I| -00000010 48 33 a5 f3 b2 72 2b 31 ab 89 27 f9 eb 1b b7 b1 |H3...r+1..'.....| -00000020 bc 2b 99 9e 73 24 42 c4 2a 68 2c 76 e1 45 61 09 |.+..s$B.*h,v.Ea.| -00000030 18 c7 44 45 9a 05 86 4c 90 c1 41 c6 fd 6a c2 95 |..DE...L..A..j..| -00000040 17 03 03 00 17 ee 18 4e d9 94 15 50 a9 99 4a 82 |.......N...P..J.| -00000050 10 13 26 7b 74 10 db ef fe b8 96 f6 17 03 03 00 |..&{t...........| -00000060 13 2a 4c 52 8d c3 c5 af d0 cd 5a 7d 0d a5 59 90 |.*LR......Z}..Y.| -00000070 ce 59 3b af |.Y;.| +00000000 14 03 03 00 01 01 17 03 03 00 35 66 49 60 ff 38 |..........5fI`.8| +00000010 e6 1e 3a 25 ab 71 80 7c d1 f1 75 5c 95 be 6d f7 |..:%.q.|..u\..m.| +00000020 23 92 11 14 e7 90 df 57 ba 5a 69 65 85 b1 ad cd |#......W.Zie....| +00000030 9b f8 f7 9b 47 2f 41 42 01 62 35 89 d8 bd de c1 |....G/AB.b5.....| +00000040 17 03 03 00 17 46 6b 07 52 b8 8e 37 d3 cc c5 34 |.....Fk.R..7...4| +00000050 69 c7 6e a8 ad 0f 44 d8 e4 ce 7d 8d 17 03 03 00 |i.n...D...}.....| +00000060 13 70 b3 6c d7 c5 91 6d d7 87 e3 78 86 b6 bc 81 |.p.l...m...x....| +00000070 82 ca 89 f0 |....| diff --git a/src/crypto/tls/testdata/Client-TLSv13-AES256-SHA384 b/src/crypto/tls/testdata/Client-TLSv13-AES256-SHA384 index 7fecc79add7..0e53c916c0d 100644 --- a/src/crypto/tls/testdata/Client-TLSv13-AES256-SHA384 +++ b/src/crypto/tls/testdata/Client-TLSv13-AES256-SHA384 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,86 +7,87 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 7a 02 00 00 76 03 03 dd df 8d 85 da |....z...v.......| -00000010 3c 99 a3 0c 01 90 5f ec b8 3d 28 ce e4 32 c0 e8 |<....._..=(..2..| -00000020 fe 77 03 ad 0f e1 33 1f dc 89 cb 20 00 00 00 00 |.w....3.... ....| +00000000 16 03 03 00 7a 02 00 00 76 03 03 f9 40 27 c9 cf |....z...v...@'..| +00000010 04 7e ac 2c 6a d4 00 d1 be fb 27 87 3e e9 2c ba |.~.,j.....'.>.,.| +00000020 2c 9a ae 04 25 a1 71 59 98 9e 52 20 00 00 00 00 |,...%.qY..R ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000040 00 00 00 00 00 00 00 00 00 00 00 00 13 02 00 00 |................| -00000050 2e 00 2b 00 02 03 04 00 33 00 24 00 1d 00 20 03 |..+.....3.$... .| -00000060 6b 91 90 36 f0 54 da 66 8e 47 9b 26 9f 9f ae 30 |k..6.T.f.G.&...0| -00000070 69 9e a2 6a 70 fb ef b2 f1 76 2b 32 90 0e 63 14 |i..jp....v+2..c.| -00000080 03 03 00 01 01 17 03 03 00 17 46 47 2e ae ea 9b |..........FG....| -00000090 78 7b 0c d4 74 e2 b5 bf 7b 64 da c3 d3 c9 55 7f |x{..t...{d....U.| -000000a0 e3 17 03 03 02 6d a8 c1 57 27 66 9d 16 f6 4f 1b |.....m..W'f...O.| -000000b0 17 b6 5d 8c 3c fe f5 d5 4a d3 c6 8d e2 a8 2d d0 |..].<...J.....-.| -000000c0 01 8d db 18 e8 c8 69 74 eb 81 9e 97 20 01 60 d5 |......it.... .`.| -000000d0 96 d1 8f 9c de 09 ff 1d e7 45 97 97 36 fa 89 77 |.........E..6..w| -000000e0 88 20 30 c6 5b 42 d6 0e 85 9a 11 43 60 a1 86 34 |. 0.[B.....C`..4| -000000f0 22 47 25 23 a5 35 87 a9 74 5d fe eb c9 70 32 44 |"G%#.5..t]...p2D| -00000100 17 60 55 99 7a 93 b5 92 8b 66 31 ce dc e0 39 f2 |.`U.z....f1...9.| -00000110 6a b3 db 43 5d 3f ba e5 12 12 1f 0e 3c 35 3b 72 |j..C]?......<5;r| -00000120 9f 9d 69 d5 d6 cb ac b5 9e f4 af f5 74 68 67 f4 |..i.........thg.| -00000130 e9 5f a4 4a d7 27 5b a5 2a 39 b7 30 49 4d 64 bb |._.J.'[.*9.0IMd.| -00000140 5d 89 10 ff a6 2c 42 a1 4a 2a 0c 28 c6 cd 4a e8 |]....,B.J*.(..J.| -00000150 7d 24 d0 75 ff 61 08 3f 3b 05 ec f3 d6 61 ed 43 |}$.u.a.?;....a.C| -00000160 08 5e 07 1c f2 15 96 22 2a c0 3c 5f 04 d1 17 82 |.^....."*.<_....| -00000170 ea ee ee c7 49 cc 3e e4 65 15 97 6e 6f 36 24 a9 |....I.>.e..no6$.| -00000180 27 34 3a 75 dc 07 1e 4c f1 29 d1 e3 22 31 7d 84 |'4:u...L.).."1}.| -00000190 a8 2a 7f 37 03 ab 13 ae 15 e2 74 50 bd 54 5b 32 |.*.7......tP.T[2| -000001a0 ea 75 10 ed 39 5c 69 90 f6 74 09 53 c1 ce 44 49 |.u..9\i..t.S..DI| -000001b0 64 fb f2 c6 bd 93 b2 07 06 96 94 04 a5 9e ed 67 |d..............g| -000001c0 10 cb 01 fc 85 45 d7 22 76 3c c6 2f 14 4c 31 e1 |.....E."v<./.L1.| -000001d0 73 81 7b 8b 6b 54 d6 34 15 d2 eb d0 03 10 c7 3d |s.{.kT.4.......=| -000001e0 f5 07 48 cc 72 9b e9 48 ee 13 9f 80 b5 13 86 77 |..H.r..H.......w| -000001f0 33 91 79 6f f2 13 17 68 ca 72 6b 0d 93 9a 20 30 |3.yo...h.rk... 0| -00000200 70 c3 30 ab 13 7e 14 39 97 4b ce c5 3d 8b 03 7f |p.0..~.9.K..=...| -00000210 cd 4b 67 c4 c5 79 0c bb cd ba 17 c5 d5 15 51 cb |.Kg..y........Q.| -00000220 ac b7 f7 19 43 ff f5 c4 09 8c 44 67 ca e6 a1 5f |....C.....Dg..._| -00000230 1d 27 29 63 f2 0d 75 6d b7 62 52 c9 1d 8e 0e 3b |.')c..um.bR....;| -00000240 6c cb 04 3e f7 13 74 bb 03 35 2e 4e 41 9a b7 72 |l..>..t..5.NA..r| -00000250 15 ed 02 79 c7 bc 38 b3 65 75 0a 8e 82 dc d4 79 |...y..8.eu.....y| -00000260 1c 10 3f 78 8c be 78 b0 73 18 cc 52 1d 3b 91 66 |..?x..x.s..R.;.f| -00000270 33 fe 63 b2 ec 19 92 44 8f 06 4e 20 85 94 5c b4 |3.c....D..N ..\.| -00000280 ad 22 16 a0 b3 76 03 dc 62 e9 0c ac 8c e1 67 c9 |."...v..b.....g.| -00000290 d8 6f 40 51 b5 39 9a 61 b6 63 e0 d5 60 6a 27 78 |.o@Q.9.a.c..`j'x| -000002a0 62 ec 94 1c 75 2c 38 f2 a6 f2 f0 c4 8f 98 ad cc |b...u,8.........| -000002b0 2e ce 7d 13 76 f4 4f 94 78 3f 85 cf ea 52 c4 6e |..}.v.O.x?...R.n| -000002c0 16 65 f9 48 5e f9 0b 07 bc 3e 38 91 06 e1 b0 76 |.e.H^....>8....v| -000002d0 82 60 25 03 36 9c 3e 5e 54 73 8d cf df 91 19 33 |.`%.6.>^Ts.....3| -000002e0 a7 18 96 d4 86 ea 7c 00 88 e6 a3 fe ea a1 14 db |......|.........| -000002f0 ae da 07 ef 1e 6f 16 bb ad fb c0 f4 60 2f 75 5c |.....o......`/u\| -00000300 a4 43 a0 fc 3c d6 5e 89 cf 6e 1a c6 de 61 65 34 |.C..<.^..n...ae4| -00000310 03 e5 cd 17 03 03 00 99 0a f3 a2 45 fe 53 22 37 |...........E.S"7| -00000320 cd 31 9d 67 31 56 f9 99 c2 d1 bc 6d 47 de 9a e7 |.1.g1V.....mG...| -00000330 67 c0 89 84 ac bf 27 b5 32 f0 e9 a5 9d f2 e0 ad |g.....'.2.......| -00000340 fd 12 6a a4 5d 50 4c b9 ed f1 f4 0e c0 c0 6c c4 |..j.]PL.......l.| -00000350 39 9b 10 02 fa 10 64 a6 8b af 9d 6e d9 40 6d 0c |9.....d....n.@m.| -00000360 b0 6c b8 8d d5 b0 14 f0 ed 85 d6 66 8f 6f 61 43 |.l.........f.oaC| -00000370 49 dd 95 08 94 2e a8 a6 19 b9 7b 6b 99 09 af 4c |I.........{k...L| -00000380 5f 41 48 da 10 b6 cf ee 68 b6 6e 03 d7 29 93 8e |_AH.....h.n..)..| -00000390 1a ab d1 ad d4 bf 33 2a 53 87 92 05 d1 1a de c0 |......3*S.......| -000003a0 aa ef b9 9c 4d 2d f6 b1 72 60 22 80 bb 46 24 75 |....M-..r`"..F$u| -000003b0 35 17 03 03 00 45 46 9e b3 7f d0 82 b6 ef 45 1f |5....EF.......E.| -000003c0 18 6d 3b b6 23 f5 c9 f4 54 e3 08 d0 8b 30 c7 31 |.m;.#...T....0.1| -000003d0 af 98 26 69 b7 6e 08 1d 1f be 1a 7e 5b 97 91 28 |..&i.n.....~[..(| -000003e0 fa b7 78 05 ee 3f a1 9e a0 79 fc 45 51 4c 96 fb |..x..?...y.EQL..| -000003f0 03 46 24 7d fe ec a4 40 51 d6 73 |.F$}...@Q.s| +00000050 2e 00 2b 00 02 03 04 00 33 00 24 00 1d 00 20 dd |..+.....3.$... .| +00000060 7d 5d 73 30 62 54 5d 2b 8c da 7c 7e f5 4f 96 8c |}]s0bT]+..|~.O..| +00000070 3b f2 72 32 e0 b5 49 2a b3 db c5 b9 31 c8 51 14 |;.r2..I*....1.Q.| +00000080 03 03 00 01 01 17 03 03 00 17 0d 0f 90 b0 0a 6c |...............l| +00000090 4b d8 f4 9f e9 c4 63 bc 1f 44 ea 2d 11 a3 b5 d9 |K.....c..D.-....| +000000a0 99 17 03 03 02 6d bf c6 29 37 89 68 ca 67 82 ad |.....m..)7.h.g..| +000000b0 cd 4c 0e 58 20 c1 04 91 a7 e5 ba 37 e9 cf 89 99 |.L.X ......7....| +000000c0 16 82 16 9a ad 5f 57 8b 4c dc 9a 63 04 69 19 69 |....._W.L..c.i.i| +000000d0 f9 a7 bc 33 1a 41 37 90 18 de c5 42 a6 7b 9a b6 |...3.A7....B.{..| +000000e0 78 c0 81 b7 74 3e 11 7b 10 05 c2 19 30 4b 01 af |x...t>.{....0K..| +000000f0 d0 22 83 3e 5d 68 29 b0 50 86 7e 32 83 8b 7c e1 |.".>]h).P.~2..|.| +00000100 78 c3 69 d2 24 a9 4b 75 a5 c5 d1 d4 27 07 28 bf |x.i.$.Ku....'.(.| +00000110 81 20 60 ef 3e 87 2b 9b 5a 53 2a 5f 70 d6 6c 53 |. `.>.+.ZS*_p.lS| +00000120 f4 68 99 53 ec 97 93 57 51 2b db 3d 4a 9f e6 6a |.h.S...WQ+.=J..j| +00000130 50 e4 ed bb dd be 4e c1 23 c8 2a e3 01 0d 32 5f |P.....N.#.*...2_| +00000140 f1 ae b1 f5 75 c0 88 f4 86 80 b9 4b bd b3 4b 33 |....u......K..K3| +00000150 3d e2 b4 c2 e0 b5 2a d1 63 3b 67 2a 1c b5 c2 aa |=.....*.c;g*....| +00000160 80 71 7e 63 56 c1 c4 c7 88 33 4f 5b 49 96 98 6e |.q~cV....3O[I..n| +00000170 c4 1c bd 03 cb 43 b2 16 d2 ab 0c 39 fd 13 f8 c9 |.....C.....9....| +00000180 2d 92 47 20 8c 92 ad 8a 87 45 71 6c 49 29 06 d2 |-.G .....EqlI)..| +00000190 48 6e 44 e3 97 cf c0 51 38 51 f1 35 29 78 ca 45 |HnD....Q8Q.5)x.E| +000001a0 f8 cb 56 02 43 ef ca a9 08 7f a5 82 23 cc a9 00 |..V.C.......#...| +000001b0 3a 49 e1 98 45 f6 34 42 56 dd e9 ff 15 36 56 98 |:I..E.4BV....6V.| +000001c0 45 a0 1a 11 c9 eb 69 f8 9b 5e 8b bf 2d 8b be cd |E.....i..^..-...| +000001d0 50 0a 01 03 6e bb ea 64 a0 a1 5d 1f 61 3e d8 d6 |P...n..d..].a>..| +000001e0 1a 00 3c 65 64 df 1c 2f 01 2b 3b c4 36 85 98 6d |..>> Flow 3 (client to server) -00000000 14 03 03 00 01 01 17 03 03 00 45 44 15 b9 ed d8 |..........ED....| -00000010 10 2c 88 80 79 f3 38 a4 bc 42 9b 22 09 44 d9 19 |.,..y.8..B.".D..| -00000020 e1 0a ec 15 aa d5 15 e9 19 6d b8 6b 71 63 86 ce |.........m.kqc..| -00000030 e7 16 0d 8e 3f 9a 3b 52 25 1e 96 f6 d9 d1 6c dd |....?.;R%.....l.| -00000040 e3 20 e9 97 f9 60 81 f5 4a b2 26 b5 d3 9e 84 46 |. ...`..J.&....F| -00000050 17 03 03 00 17 de 4a e9 44 21 88 ef ce 78 35 6d |......J.D!...x5m| -00000060 b2 e4 78 47 39 8d 1f fd 9b 2d a4 47 17 03 03 00 |..xG9....-.G....| -00000070 13 98 f9 1c 9c d4 b1 42 f7 e7 a1 9b 6d b1 b1 cb |.......B....m...| -00000080 86 e3 c2 27 |...'| +00000000 14 03 03 00 01 01 17 03 03 00 45 d6 41 e2 72 0c |..........E.A.r.| +00000010 14 a6 a4 71 c6 d2 47 d1 03 7e 04 e6 4d 69 8e d0 |...q..G..~..Mi..| +00000020 d6 f8 55 32 fe 54 f3 e5 be 22 af ae a2 b2 6c 58 |..U2.T..."....lX| +00000030 71 4a 73 85 5f 9f 09 69 7e 8c 75 61 86 0b 6c 6d |qJs._..i~.ua..lm| +00000040 b3 98 0d 97 7c 39 2e c7 81 f5 c7 4d 53 09 af aa |....|9.....MS...| +00000050 17 03 03 00 17 d6 39 0c 75 a1 fb 4c 88 99 d0 c0 |......9.u..L....| +00000060 d8 4d b1 31 16 9c 18 35 85 c3 ed 6f 17 03 03 00 |.M.1...5...o....| +00000070 13 5a f5 57 bf 1e f3 c5 b0 9b b7 4b 64 9c 38 90 |.Z.W.......Kd.8.| +00000080 c6 f2 7f 13 |....| diff --git a/src/crypto/tls/testdata/Client-TLSv13-ALPN b/src/crypto/tls/testdata/Client-TLSv13-ALPN index 0ac9b36933c..427c6e55e56 100644 --- a/src/crypto/tls/testdata/Client-TLSv13-ALPN +++ b/src/crypto/tls/testdata/Client-TLSv13-ALPN @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 01 0e 01 00 01 0a 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 14 01 00 01 10 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,87 +7,87 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 8f 00 05 00 05 01 00 00 00 00 00 0a 00 |................| +00000080 01 00 00 95 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 10 00 10 00 0e 06 70 72 6f 74 6f |...........proto| -000000d0 32 06 70 72 6f 74 6f 31 00 12 00 00 00 2b 00 09 |2.proto1.....+..| -000000e0 08 03 04 03 03 03 02 03 01 00 33 00 26 00 24 00 |..........3.&.$.| -000000f0 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da ac 5f |.. /.}.G.bC.(.._| -00000100 bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 5f 58 |.).0.........._X| -00000110 cb 3b 74 |.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 10 00 10 00 0e |a.b.............| +000000d0 06 70 72 6f 74 6f 32 06 70 72 6f 74 6f 31 00 12 |.proto2.proto1..| +000000e0 00 00 00 2b 00 09 08 03 04 03 03 03 02 03 01 00 |...+............| +000000f0 33 00 26 00 24 00 1d 00 20 2f e5 7d a3 47 cd 62 |3.&.$... /.}.G.b| +00000100 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 cf |C.(.._.).0......| +00000110 c2 ed 90 99 5f 58 cb 3b 74 |...._X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 7a 02 00 00 76 03 03 23 c5 c4 0c 4a |....z...v..#...J| -00000010 d2 5f 0b f6 ea 21 7a d1 a0 7d 21 26 b5 a3 94 ca |._...!z..}!&....| -00000020 91 6c 13 58 60 4f 39 cc 1a f7 c0 20 00 00 00 00 |.l.X`O9.... ....| +00000000 16 03 03 00 7a 02 00 00 76 03 03 60 c2 ba 68 ed |....z...v..`..h.| +00000010 91 b6 36 3d b1 e8 87 61 b1 e7 73 dc 72 ec cf ea |..6=...a..s.r...| +00000020 27 18 be b3 00 bb 05 cd d8 34 b5 20 00 00 00 00 |'........4. ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000040 00 00 00 00 00 00 00 00 00 00 00 00 13 01 00 00 |................| -00000050 2e 00 2b 00 02 03 04 00 33 00 24 00 1d 00 20 f9 |..+.....3.$... .| -00000060 64 7e 54 8f 64 ec 3d 7c 17 f1 96 3c 44 ca cd d7 |d~T.d.=|.....| +00000350 26 af 9e 72 77 f8 84 7e f3 25 e8 04 4c 1e 26 f5 |&..rw..~.%..L.&.| +00000360 36 9b 39 01 35 03 1e 1f c7 d4 ca ae d8 9f 4f a7 |6.9.5.........O.| +00000370 16 c2 7c 18 04 20 7a 56 fb 06 7c b8 62 c8 cf 19 |..|.. zV..|.b...| +00000380 e1 f3 cd e2 30 29 5d 77 c0 2b 17 03 d2 49 94 31 |....0)]w.+...I.1| +00000390 95 81 6e 7d a4 49 c2 df 92 d5 32 f3 3a 2a db 35 |..n}.I....2.:*.5| +000003a0 19 b9 69 d8 c4 ef d0 f5 59 20 2d f8 69 e1 ba 02 |..i.....Y -.i...| +000003b0 78 b9 1f 4c 1a 79 61 23 03 de 32 b5 05 5c 17 03 |x..L.ya#..2..\..| +000003c0 03 00 35 92 fc a5 f8 83 64 2e fe 83 67 12 8a d9 |..5.....d...g...| +000003d0 46 30 8d aa 7c 20 be 13 f1 1d 80 57 04 29 61 39 |F0..| .....W.)a9| +000003e0 53 13 26 31 84 ab 6e dc d1 2d e9 51 41 51 50 e4 |S.&1..n..-.QAQP.| +000003f0 41 e7 f0 46 45 e0 dc 03 |A..FE...| >>> Flow 3 (client to server) -00000000 14 03 03 00 01 01 17 03 03 00 35 3e e7 50 e1 d1 |..........5>.P..| -00000010 4d 9f 84 fe ca 83 c4 3b a6 86 45 c2 7e e7 af 00 |M......;..E.~...| -00000020 db e6 23 3c 06 b8 a3 1e 36 2e ab 45 7e d8 07 8c |..#<....6..E~...| -00000030 66 bf 5a 0f ff e6 3f 09 a4 d3 cf 74 1c d6 cf c7 |f.Z...?....t....| -00000040 17 03 03 00 17 4c db af a7 f3 73 b3 84 b9 a7 d1 |.....L....s.....| -00000050 1c 2f cb 27 d8 ba 2c c6 84 48 88 18 17 03 03 00 |./.'..,..H......| -00000060 13 a3 41 6f fb da f5 5a 4d 85 0c e0 ff 3a fb 91 |..Ao...ZM....:..| -00000070 e2 5e ab 96 |.^..| +00000000 14 03 03 00 01 01 17 03 03 00 35 6c 9a b7 a4 14 |..........5l....| +00000010 f0 ac 2e 6d 6e d5 67 da 48 bc 52 10 af 76 1a 74 |...mn.g.H.R..v.t| +00000020 41 b1 32 d0 ac de 61 73 20 40 c4 d6 2a 1f de 8c |A.2...as @..*...| +00000030 3b cf df ec 97 dc 1d 76 73 88 f8 46 a8 71 8b af |;......vs..F.q..| +00000040 17 03 03 00 17 12 a8 a4 f8 06 e5 19 2e 60 45 e6 |.............`E.| +00000050 79 29 b4 63 85 a0 f6 88 13 b4 3e 44 17 03 03 00 |y).c......>D....| +00000060 13 ed a2 8a 80 8c 7a da 83 3f 3e 51 a1 40 49 48 |......z..?>Q.@IH| +00000070 39 6b 30 64 |9k0d| diff --git a/src/crypto/tls/testdata/Client-TLSv13-CHACHA20-SHA256 b/src/crypto/tls/testdata/Client-TLSv13-CHACHA20-SHA256 index 6d7b508fd34..8360d25dbef 100644 --- a/src/crypto/tls/testdata/Client-TLSv13-CHACHA20-SHA256 +++ b/src/crypto/tls/testdata/Client-TLSv13-CHACHA20-SHA256 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,84 +7,85 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 7a 02 00 00 76 03 03 43 b1 e8 d9 c3 |....z...v..C....| -00000010 22 a0 a3 08 df 7f 37 34 7a fe 7a 47 98 ee ed 51 |".....74z.zG...Q| -00000020 c2 ae 5c c6 b1 43 3d ff f7 91 68 20 00 00 00 00 |..\..C=...h ....| +00000000 16 03 03 00 7a 02 00 00 76 03 03 4b a4 b4 05 a8 |....z...v..K....| +00000010 d4 42 51 8b 64 1a 48 82 a5 2e 57 3c ad c1 e0 6e |.BQ.d.H...W<...n| +00000020 f0 00 b1 c7 73 df ff a1 6a 3b b2 20 00 00 00 00 |....s...j;. ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000040 00 00 00 00 00 00 00 00 00 00 00 00 13 03 00 00 |................| -00000050 2e 00 2b 00 02 03 04 00 33 00 24 00 1d 00 20 63 |..+.....3.$... c| -00000060 0f 66 ec 2d fa 67 d4 eb 94 47 8d 88 0b eb ed ec |.f.-.g...G......| -00000070 5b ac 22 f7 46 85 c5 1c 2b 5e e8 57 e2 d3 6f 14 |[.".F...+^.W..o.| -00000080 03 03 00 01 01 17 03 03 00 17 d0 f8 1f 06 59 8d |..............Y.| -00000090 a0 40 21 8f 3e 36 3b 1d 6a 6e f7 77 44 fb b3 8e |.@!.>6;.jn.wD...| -000000a0 e2 17 03 03 02 6d 22 6b 63 ae 47 fd 66 f9 95 f6 |.....m"kc.G.f...| -000000b0 63 ea e8 16 61 a3 64 82 39 82 76 1c 2c 04 9b 29 |c...a.d.9.v.,..)| -000000c0 0f 8a ff 77 9b e6 2c ce 04 09 5f 91 f3 b6 2e 8d |...w..,..._.....| -000000d0 be 42 94 7e 5a 28 4b 9f e9 7b 38 0a 3c de 90 77 |.B.~Z(K..{8.<..w| -000000e0 c1 bf 97 bf 35 6c 77 98 4b 38 b4 8d 7f 1f 4b c0 |....5lw.K8....K.| -000000f0 23 c5 73 08 90 fa 21 5c cd cb 84 5b 0e 89 86 ce |#.s...!\...[....| -00000100 83 78 d5 1c 2b b9 b1 24 45 ad ab 9c 68 9f c2 28 |.x..+..$E...h..(| -00000110 40 d6 c2 ac a2 0c 86 cd 75 92 43 d5 22 3f 61 9d |@.......u.C."?a.| -00000120 e8 56 b8 7c 71 db 25 cc 2e 74 52 74 da 6b d4 a1 |.V.|q.%..tRt.k..| -00000130 2c 32 d2 d8 9c 74 41 9d 78 98 94 3b 87 99 8e 17 |,2...tA.x..;....| -00000140 df df d6 c3 6d ef 58 13 5c 1e 20 2d ed 77 bd 5c |....m.X.\. -.w.\| -00000150 d6 5c 9a 6d 0f 19 77 e1 4f 79 b0 ed 9d 0b f5 e8 |.\.m..w.Oy......| -00000160 42 d0 f4 90 88 97 a9 84 af 92 3c 41 fe fd 67 6e |B.........R...| -000002d0 fc ba 9c f0 82 13 ba 25 11 c7 5d 38 00 cf 83 14 |.......%..]8....| -000002e0 30 a9 72 48 d1 e8 4e 1b ed 04 ed cf b7 5b 2e 72 |0.rH..N......[.r| -000002f0 1c a2 03 ae 60 54 d6 cf 2f fb 11 a3 b1 8d d6 47 |....`T../......G| -00000300 e8 9f 96 08 90 ae 3c 3c c0 8c d8 c4 ef 30 18 ea |......<<.....0..| -00000310 2a 1a 15 17 03 03 00 99 85 b3 e4 18 6f 8d 34 c7 |*...........o.4.| -00000320 3d 66 49 b8 f6 f5 aa 7a e1 ca ba cb 48 53 15 bb |=fI....z....HS..| -00000330 e9 ec 74 91 c3 b5 d3 6b bc 84 81 d8 e1 a4 31 62 |..t....k......1b| -00000340 d5 19 6d 2f 15 4c f3 8a 3b ec 41 12 89 be d3 cc |..m/.L..;.A.....| -00000350 ab 08 59 a7 79 5d 77 14 ce b1 98 b4 ce 71 7b ad |..Y.y]w......q{.| -00000360 ba 41 3a 7f 9a f8 23 5c c6 fb b5 7b cc eb 0e 7a |.A:...#\...{...z| -00000370 ee af 3d ff 4d 03 ba c2 2a af ac fd b5 e8 5b 43 |..=.M...*.....[C| -00000380 3e 37 ef 84 3d 66 af 3c 8e 1d 0d 36 bd df 25 dc |>7..=f.<...6..%.| -00000390 74 89 9c e6 da 18 c4 c8 b5 6c 3c 4c a6 ac 10 28 |t........l.9\\.rrA ...%.7| +000000a0 32 17 03 03 02 6d 8e bf 7b ee 4a b5 07 e0 ca a8 |2....m..{.J.....| +000000b0 36 9f 35 a3 f3 51 db fb 87 a6 c7 59 07 16 fa f6 |6.5..Q.....Y....| +000000c0 21 20 66 6a 99 b9 2a 52 f2 24 73 cb 03 db 1f c4 |! fj..*R.$s.....| +000000d0 c3 b7 a7 b4 17 dc 11 43 f3 2a 5d af a8 5c d3 6a |.......C.*]..\.j| +000000e0 8e ad e8 38 88 4b 60 9c 76 e9 84 60 18 2a 5f d0 |...8.K`.v..`.*_.| +000000f0 01 5a 05 f9 78 0f 38 25 1f e9 71 35 3c 23 3c ba |.Z..x.8%..q5<#<.| +00000100 0a 28 3a da 85 b2 9c 9e f1 9e cf 9b 0d 63 85 04 |.(:..........c..| +00000110 d5 6b b4 3b a1 f8 1d 60 e0 d3 cd 38 cb 3f 27 00 |.k.;...`...8.?'.| +00000120 37 81 b2 0a 9c 6e 61 42 d1 1a a8 80 48 d2 96 46 |7....naB....H..F| +00000130 59 cf 5e 7e 46 c4 69 30 56 84 2c e9 18 4a 34 64 |Y.^~F.i0V.,..J4d| +00000140 ba 24 e5 ea 04 24 41 f1 cd 8b 8d 03 ac 78 9b 41 |.$...$A......x.A| +00000150 3f 09 c2 55 de b3 8d 84 6a 8d c8 14 ba de 07 06 |?..U....j.......| +00000160 25 81 15 d0 c5 a0 1c a4 15 ef c4 5e f7 e5 98 0a |%..........^....| +00000170 76 b1 bf 7a 0d cf 72 54 57 1f e5 c9 69 f9 18 b1 |v..z..rTW...i...| +00000180 f4 67 9f ac f4 54 dc 79 d2 6b f8 e3 c5 e1 81 72 |.g...T.y.k.....r| +00000190 8d a9 0c e2 92 2c 47 f6 f1 b0 d4 69 0e 23 a1 e2 |.....,G....i.#..| +000001a0 63 33 57 a6 d0 d5 b5 d3 31 f9 e6 ad d2 32 77 bb |c3W.....1....2w.| +000001b0 cd 31 d3 1b bf cc 16 e8 5e 49 e3 00 66 40 3a 3e |.1......^I..f@:>| +000001c0 67 9d b0 90 9d 6d 03 4a 08 fa e9 08 76 77 98 79 |g....m.J....vw.y| +000001d0 84 d1 b0 9b 4e 8c 66 25 4f 2a 38 bd 05 8d 07 d1 |....N.f%O*8.....| +000001e0 c6 e5 42 68 94 55 b0 c4 a4 82 fb 35 08 dd 8d da |..Bh.U.....5....| +000001f0 0c ab 1c e6 b7 7c 32 78 87 70 00 c3 be 88 f8 18 |.....|2x.p......| +00000200 66 1a d1 20 ea 5a 42 fb 84 d3 25 49 a9 ac 6f 47 |f.. .ZB...%I..oG| +00000210 71 e1 15 4d 05 15 64 8b 6b ca 6e c8 dc 82 52 eb |q..M..d.k.n...R.| +00000220 76 d2 71 f3 7f 1a 56 d5 2b ce 54 4b eb 8a cd 62 |v.q...V.+.TK...b| +00000230 25 17 95 2f 86 87 65 0d fc 6d dd 97 76 b4 7e 62 |%../..e..m..v.~b| +00000240 65 71 b7 b0 a2 bc d8 e5 6e 37 0e 83 a5 75 a9 98 |eq......n7...u..| +00000250 43 a3 7b 96 e8 c2 a1 0a 9c 2e 06 2a d3 32 45 03 |C.{........*.2E.| +00000260 1b 14 ac a8 ba 80 75 d0 22 1d 8f 8b 00 36 b3 80 |......u."....6..| +00000270 54 64 93 b4 ae 40 c1 93 ec 41 ba 88 e5 ff 74 24 |Td...@...A....t$| +00000280 88 d1 10 54 8b fd 31 38 74 a0 df a4 41 bb 87 44 |...T..18t...A..D| +00000290 4b f3 db 34 aa 79 3a 10 a4 2e 90 b0 a8 d0 93 96 |K..4.y:.........| +000002a0 6c b8 39 e3 90 df 59 74 d4 80 5c 0c 22 82 ca 71 |l.9...Yt..\."..q| +000002b0 05 ae e4 75 63 bb 23 11 6f 58 a0 77 9f 2b 6c d9 |...uc.#.oX.w.+l.| +000002c0 ec be eb da a4 c2 f4 b3 2c 0d 9b f8 b1 29 bf b5 |........,....)..| +000002d0 8c 22 d7 93 2e 85 7e b2 88 11 31 cd c6 5c dd b6 |."....~...1..\..| +000002e0 46 26 d8 d8 60 bc 56 77 ab d7 89 80 cd 0b 99 27 |F&..`.Vw.......'| +000002f0 a1 eb 45 df 30 e8 32 4f 67 ba 8c 85 24 ad 8d a4 |..E.0.2Og...$...| +00000300 18 f7 99 b8 41 77 c7 71 8f 50 db 85 e5 16 c3 40 |....Aw.q.P.....@| +00000310 de 86 3f 17 03 03 00 99 87 74 5e 08 46 86 36 82 |..?......t^.F.6.| +00000320 e3 23 76 c1 7d 55 45 f4 f5 fe 2c 04 e3 4a c1 3d |.#v.}UE...,..J.=| +00000330 20 d6 c5 1c d1 d1 a8 b5 44 76 3f e5 c3 22 9f bd | .......Dv?.."..| +00000340 1d a0 06 04 02 a4 6f 27 6a d6 48 4d 57 0e f2 51 |......o'j.HMW..Q| +00000350 79 5e a6 a5 08 71 8a 33 46 b4 2f 32 64 d2 7d ce |y^...q.3F./2d.}.| +00000360 86 9e 8d 3a bc e4 72 bc 09 94 0e 28 5d 53 d4 f7 |...:..r....(]S..| +00000370 7e 63 0d 66 e3 cb 27 92 8e af e4 0c 3e 1f 38 44 |~c.f..'.....>.8D| +00000380 b4 c9 cf aa 99 9b a8 7e 1b 9f 15 e9 ce ab ba 8b |.......~........| +00000390 40 ee b6 ef 9c 3f 8f a9 59 5a e4 68 5a fe ff dc |@....?..YZ.hZ...| +000003a0 b2 5c d7 52 df 93 4f 61 fc b5 fe 59 5a e6 39 23 |.\.R..Oa...YZ.9#| +000003b0 c6 17 03 03 00 35 c3 83 c8 d2 92 92 68 a1 4d 99 |.....5......h.M.| +000003c0 58 7f b8 56 d6 f5 56 ee 73 e5 9e 42 a4 b9 25 1c |X..V..V.s..B..%.| +000003d0 1c 68 14 0b 25 f5 f3 cd 5f 59 27 ac 53 b3 22 94 |.h..%..._Y'.S.".| +000003e0 3a b2 d6 2e 6e 58 9f f5 89 8a 24 |:...nX....$| >>> Flow 3 (client to server) -00000000 14 03 03 00 01 01 17 03 03 00 35 55 88 37 f3 ee |..........5U.7..| -00000010 c5 1b 20 ac fe bc a3 f8 c9 59 3f 5f c0 81 40 8f |.. ......Y?_..@.| -00000020 1e a9 44 c8 10 16 69 8a 76 45 17 51 06 9e f0 55 |..D...i.vE.Q...U| -00000030 a2 f2 56 98 7d a1 4d 95 5a c3 1f 51 cf 31 20 ca |..V.}.M.Z..Q.1 .| -00000040 17 03 03 00 17 81 2a 8e 32 29 ec 9b 92 c3 fd 98 |......*.2)......| -00000050 64 aa 47 2a a5 0c d6 77 7f b1 8f 12 17 03 03 00 |d.G*...w........| -00000060 13 60 8c fb 98 e1 03 b6 20 c8 45 4e d9 4b a8 17 |.`...... .EN.K..| -00000070 10 79 5f b6 |.y_.| +00000000 14 03 03 00 01 01 17 03 03 00 35 4e 10 cd 88 f6 |..........5N....| +00000010 8a 03 95 91 70 75 bf 5b fd 62 58 b1 6d 64 d0 13 |....pu.[.bX.md..| +00000020 b3 49 68 89 1f 12 23 4b 1c 3c b5 2a 0b db 18 fc |.Ih...#K.<.*....| +00000030 d3 d8 73 f3 24 44 e2 d7 5c ed 36 f6 f0 19 c8 df |..s.$D..\.6.....| +00000040 17 03 03 00 17 15 49 3a 44 9c ef 1a 2f 0d 82 e5 |......I:D.../...| +00000050 40 5c 60 9c 94 9b 98 e7 d4 92 fa f5 17 03 03 00 |@\`.............| +00000060 13 bc df af 9f 03 d9 53 c7 90 c3 56 aa 62 7a 40 |.......S...V.bz@| +00000070 a7 2b 7f ed |.+..| diff --git a/src/crypto/tls/testdata/Client-TLSv13-ClientCert-ECDSA-RSA b/src/crypto/tls/testdata/Client-TLSv13-ClientCert-ECDSA-RSA index c8e95c85dfc..053b9696732 100644 --- a/src/crypto/tls/testdata/Client-TLSv13-ClientCert-ECDSA-RSA +++ b/src/crypto/tls/testdata/Client-TLSv13-ClientCert-ECDSA-RSA @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,133 +7,134 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 7a 02 00 00 76 03 03 98 9a 92 3f c6 |....z...v.....?.| -00000010 67 f5 96 5b 2f 5e 70 89 2d f6 1e ce 6f 6a e5 91 |g..[/^p.-...oj..| -00000020 4b 4b 6f 98 cc f7 78 4a b1 54 4a 20 00 00 00 00 |KKo...xJ.TJ ....| +00000000 16 03 03 00 7a 02 00 00 76 03 03 57 6e 3b 6f 07 |....z...v..Wn;o.| +00000010 19 3d 4b 5c cb b3 ca 51 b6 74 04 5a af 78 c4 c0 |.=K\...Q.t.Z.x..| +00000020 ec 7b 2e 0a 28 74 7b 23 a4 e5 15 20 00 00 00 00 |.{..(t{#... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000040 00 00 00 00 00 00 00 00 00 00 00 00 13 01 00 00 |................| -00000050 2e 00 2b 00 02 03 04 00 33 00 24 00 1d 00 20 58 |..+.....3.$... X| -00000060 96 37 c3 41 35 73 13 21 fc 31 e3 09 33 48 15 be |.7.A5s.!.1..3H..| -00000070 31 fb 57 61 b2 c9 60 31 2d 68 83 d5 7c d1 3a 14 |1.Wa..`1-h..|.:.| -00000080 03 03 00 01 01 17 03 03 00 17 1d ce 7d b7 ca e3 |............}...| -00000090 10 82 cb f6 1d 52 61 41 29 57 e3 7e e5 88 5c 47 |.....RaA)W.~..\G| -000000a0 16 17 03 03 00 42 1b 49 e1 4a d7 73 57 cd e9 b7 |.....B.I.J.sW...| -000000b0 e2 47 d3 74 21 6a 14 1d 1b 8d f5 aa 4c 1b f8 61 |.G.t!j......L..a| -000000c0 8c 3a e4 2e 9d ff 3f 7d b2 4d 79 6e 1d 02 05 ce |.:....?}.Myn....| -000000d0 c3 ad e6 f9 2b 2b dd 75 3b 6f 3e 0b 29 07 09 74 |....++.u;o>.)..t| -000000e0 d1 37 68 9b 8a b6 8d 2b 17 03 03 02 6d d1 1b 9f |.7h....+....m...| -000000f0 75 ba cf 2d 10 4b f0 4e 09 58 fa ff 06 e8 c9 d5 |u..-.K.N.X......| -00000100 a0 51 c8 d4 6f b2 c5 c1 d5 f3 ff 12 1f 43 d8 74 |.Q..o........C.t| -00000110 33 d9 9b e5 f3 34 26 0e 89 dc 00 54 67 17 d2 f3 |3....4&....Tg...| -00000120 c9 9e be f8 4c 77 8a 63 b1 64 5a b4 d7 57 d2 89 |....Lw.c.dZ..W..| -00000130 ce 68 d1 f7 93 01 6c 36 b7 c9 4d 50 d0 4b df 5e |.h....l6..MP.K.^| -00000140 8a bb 6c d9 54 57 9b b9 c9 ec d8 49 c7 51 3c e5 |..l.TW.....I.Q<.| -00000150 7b fb 48 0f fd 1b dd 0f 57 d3 a8 ee f6 51 ba 78 |{.H.....W....Q.x| -00000160 c0 60 f1 d9 c1 d2 65 b4 a7 98 99 fb 64 83 4c 2c |.`....e.....d.L,| -00000170 a6 e9 19 ef 0e 88 68 f8 21 a4 2b bd 95 e9 52 d5 |......h.!.+...R.| -00000180 fb 12 d3 36 06 a2 13 f9 e2 35 6a 06 dd 49 d9 42 |...6.....5j..I.B| -00000190 89 d9 f0 24 5c 36 b8 6d 95 35 21 b3 9c 3b ee 08 |...$\6.m.5!..;..| -000001a0 06 06 4d aa 74 eb fc 1b c1 fd cf 07 24 74 44 2d |..M.t.......$tD-| -000001b0 54 d5 c5 d3 4e c4 eb 09 6e 90 8f 3d c0 c5 1c 21 |T...N...n..=...!| -000001c0 7c 32 1b bc 4b 85 2b f0 b0 f5 cd 61 3d dd 31 03 ||2..K.+....a=.1.| -000001d0 5e e0 5e 06 1a 37 61 1a 58 fa ed e8 cf 0c 4f da |^.^..7a.X.....O.| -000001e0 73 69 42 3a f4 ed dc ad e5 e7 9b fd 54 16 77 85 |siB:........T.w.| -000001f0 ae 84 41 10 be 84 ad 28 ef e6 13 2a e9 9f 9f 2f |..A....(...*.../| -00000200 c5 d0 65 c6 f5 58 b3 39 9b 5e 07 ba 95 be 5e 75 |..e..X.9.^....^u| -00000210 68 17 ba 9d 2a 69 6d b8 ed d4 4b 6a ce 30 b1 82 |h...*im...Kj.0..| -00000220 ae ec 68 9a 26 13 6b 05 38 0f 38 c9 94 01 d0 0b |..h.&.k.8.8.....| -00000230 7b bb ca 70 86 6c e4 f1 eb 81 05 25 33 c0 3e e3 |{..p.l.....%3.>.| -00000240 2a 25 8e 32 eb d5 03 c7 c4 d8 22 22 ef 99 5a a3 |*%.2......""..Z.| -00000250 01 6a b5 65 9a 55 6e fb 84 83 aa 43 ae 4a 3e da |.j.e.Un....C.J>.| -00000260 40 7e 09 e1 3b 15 ad 33 66 5a 3d 30 62 72 86 54 |@~..;..3fZ=0br.T| -00000270 cd a2 6a bf 82 61 17 87 84 c5 3f f3 1e 86 a2 b1 |..j..a....?.....| -00000280 2c 1a f9 ba 8c a2 21 5b 93 b2 16 b4 81 ae 7d 98 |,.....![......}.| -00000290 d6 db 0a 56 14 c9 f7 48 c1 c7 3c 7e 63 8e bc 50 |...V...H..<~c..P| -000002a0 6a 64 e1 1d 04 ba d3 cc 6a 61 60 4b d2 97 d5 ba |jd......ja`K....| -000002b0 23 1a 69 76 86 db 96 39 04 f6 ec e9 96 79 6a 25 |#.iv...9.....yj%| -000002c0 ff 39 dd 19 08 34 4d c3 f6 7c 91 f2 6b 3a e1 0f |.9...4M..|..k:..| -000002d0 66 6d 14 5d 82 21 0b e3 e0 c3 f1 a1 70 e1 2c bc |fm.].!......p.,.| -000002e0 fb 54 aa 85 3c a0 7c 9a 35 00 e2 a1 4f 83 3e f1 |.T..<.|.5...O.>.| -000002f0 64 83 ab c5 e6 31 c7 00 eb 36 f1 bc 41 f3 eb d4 |d....1...6..A...| -00000300 97 30 4d 7f d2 d1 e7 1a 9e a2 53 31 35 6a 16 d1 |.0M.......S15j..| -00000310 65 be d7 d3 93 2a be d2 27 dc 1b 8c 09 16 30 d4 |e....*..'.....0.| -00000320 cb eb e0 bb 42 50 ff 59 c3 81 81 36 88 09 c2 23 |....BP.Y...6...#| -00000330 dc dd 80 63 bb 78 19 6b 6a 70 4b b5 17 bf ed 6c |...c.x.kjpK....l| -00000340 58 f1 15 a9 16 66 c8 45 f5 5f 99 05 b1 3b be e6 |X....f.E._...;..| -00000350 66 d7 45 df 19 16 9d c7 dd 4d 17 03 03 00 99 38 |f.E......M.....8| -00000360 70 9e 16 94 07 67 7c ce 90 67 99 46 5e d9 61 b5 |p....g|..g.F^.a.| -00000370 9b b8 31 fc cc 80 a3 07 30 c9 f5 f9 90 fb e2 0d |..1.....0.......| -00000380 dc 93 ab de 38 25 83 f8 77 0c 94 53 75 68 c7 71 |....8%..w..Suh.q| -00000390 72 6f 61 77 a7 d7 c7 ed 5c d3 08 18 9f 64 f4 6e 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|-M.5^.Q..<6F*.".| +000002f0 02 1c ed cb a0 04 dd 01 a7 2d ea f9 42 4e ea c9 |.........-..BN..| +00000300 2e 23 ff 3f ea 82 88 9c 6c 0a cf 8e 17 03 03 00 |.#.?....l.......| +00000310 17 7c 54 f2 49 ab ad 87 23 6f 72 fa d5 29 41 22 |.|T.I...#or..)A"| +00000320 11 29 56 4b 36 99 14 e8 17 03 03 00 13 fc 80 4d |.)VK6..........M| +00000330 19 20 1d 69 a8 bf 6a 2a 43 e4 b1 2d f2 b6 ab 17 |. .i..j*C..-....| diff --git a/src/crypto/tls/testdata/Client-TLSv13-ClientCert-Ed25519 b/src/crypto/tls/testdata/Client-TLSv13-ClientCert-Ed25519 index 26f76bc1b12..cc1a6406e72 100644 --- a/src/crypto/tls/testdata/Client-TLSv13-ClientCert-Ed25519 +++ b/src/crypto/tls/testdata/Client-TLSv13-ClientCert-Ed25519 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,116 +7,117 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 7a 02 00 00 76 03 03 a5 5b a0 2c f5 |....z...v...[.,.| -00000010 57 cc 49 88 64 7d ea 7c ee 61 cf fc 94 9f d4 5c |W.I.d}.|.a.....\| -00000020 bb 83 80 5a f5 7c a3 fc 0a c8 61 20 00 00 00 00 |...Z.|....a ....| +00000000 16 03 03 00 7a 02 00 00 76 03 03 39 ef 52 65 c8 |....z...v..9.Re.| +00000010 0b bd d6 c1 94 49 20 1f f2 d4 b5 af f4 1c f8 a6 |.....I .........| +00000020 7a 9d 50 ab 32 3a 15 52 b3 4c 45 20 00 00 00 00 |z.P.2:.R.LE ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000040 00 00 00 00 00 00 00 00 00 00 00 00 13 01 00 00 |................| -00000050 2e 00 2b 00 02 03 04 00 33 00 24 00 1d 00 20 fe |..+.....3.$... .| -00000060 e1 43 bd 10 b3 f6 3b 4d 7c 46 8f a3 bc 7d 08 08 |.C....;M|F...}..| -00000070 22 ed aa 9b 7b 89 f3 87 13 7e fe 6c b0 db 3f 14 |"...{....~.l..?.| -00000080 03 03 00 01 01 17 03 03 00 17 2b ce 52 22 34 c5 |..........+.R"4.| -00000090 d9 2c ae d0 23 4d 0c 6e b4 f0 c8 58 11 22 54 bb |.,..#M.n...X."T.| -000000a0 15 17 03 03 00 42 96 b4 72 be f0 6b d3 b0 82 7c |.....B..r..k...|| -000000b0 dc d2 67 69 2c d4 40 a1 7a 3d 9a 39 a5 29 ca 64 |..gi,.@.z=.9.).d| -000000c0 c5 0b d2 ba 7c c3 73 e2 93 0d 44 e3 64 ce ec b2 |....|.s...D.d...| -000000d0 90 ae e2 df 18 f8 f5 93 5f 91 80 c2 b4 00 e7 de |........_.......| -000000e0 f5 3f 4d c8 de 4c 5f f0 17 03 03 02 6d c6 df 33 |.?M..L_.....m..3| -000000f0 1e 12 40 02 7f 46 67 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ea 66 dd dd 86 f5 03 |U....l....f.....| -00000380 12 08 9d b4 07 48 eb 8b 45 f1 35 b1 31 bd 5d f3 |.....H..E.5.1.].| -00000390 e2 34 73 9a e5 87 b7 8b 0b 8b ab 7e 05 db 56 db |.4s........~..V.| -000003a0 4f 4c 52 1a 3b 5d 4c 53 b1 49 40 81 5e 73 af 26 |OLR.;]LS.I@.^s.&| -000003b0 21 e6 e3 5c 4a a6 f6 07 56 de f5 76 5c 67 d8 d5 |!..\J...V..v\g..| -000003c0 eb f3 6a fb 6d b7 00 bc 6b 28 c9 63 4d 58 76 97 |..j.m...k(.cMXv.| -000003d0 aa 51 2b f3 03 9c 70 3b 3e b2 a4 16 a0 a0 e0 43 |.Q+...p;>......C| -000003e0 77 da 88 2d 48 3b 07 e2 8d a6 e2 80 85 68 ac dc |w..-H;.......h..| -000003f0 ce 66 2f 97 20 9e 4e 33 17 03 03 00 35 f6 ce 98 |.f/. .N3....5...| -00000400 8b 01 f5 75 8e 98 42 02 b1 b8 90 f3 08 96 e8 5a |...u..B........Z| -00000410 d4 7c ef d1 62 1e b3 36 39 d9 b2 59 1f 1f cc 74 |.|..b..69..Y...t| -00000420 f2 a8 62 11 00 28 31 fa d9 5a 27 10 7b 93 ff de |..b..(1..Z'.{...| -00000430 a0 ec |..| +00000050 2e 00 2b 00 02 03 04 00 33 00 24 00 1d 00 20 f7 |..+.....3.$... .| +00000060 60 ba d2 86 4e 37 c1 c8 5a fe 4f 72 4a e6 d4 22 |`...N7..Z.OrJ.."| +00000070 73 6d 80 1a da f2 c9 8f 9a 9f 28 d7 f4 59 03 14 |sm........(..Y..| +00000080 03 03 00 01 01 17 03 03 00 17 82 84 14 f4 03 87 |................| +00000090 89 bc 41 c7 5e 17 ba fa fa 3f d9 af 22 42 fa 65 |..A.^....?.."B.e| +000000a0 73 17 03 03 00 42 a0 56 43 d6 cc f6 c9 f9 83 7b |s....B.VC......{| +000000b0 49 56 1a 87 81 85 40 51 75 5a ee 38 f0 02 fd eb |IV....@QuZ.8....| +000000c0 95 97 ae 34 8f 43 83 31 bd d0 81 5e e5 dd 94 d0 |...4.C.1...^....| +000000d0 77 6c 85 ba f7 0a d3 68 d4 4d 84 23 0b b9 43 22 |wl.....h.M.#..C"| +000000e0 98 6a 41 6a a2 d2 00 79 17 03 03 02 6d 24 17 31 |.jAj...y....m$.1| +000000f0 bb e2 97 55 6e 31 05 57 bd dc a5 2e d5 b3 66 c8 |...Un1.W......f.| +00000100 f8 5c 14 e5 59 b2 f2 ea 70 4c bf 4c 34 a7 aa 0f |.\..Y...pL.L4...| +00000110 3b 89 08 ff e2 88 58 58 90 90 2f 7e 31 58 8b fa |;.....XX../~1X..| +00000120 12 de 5f b3 80 81 6f 43 12 b5 62 2c 91 2c 77 6b |.._...oC..b,.,wk| +00000130 b8 54 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e3 b7 3a d9 20 eb 9c e6 fe cd 55 00 42 1f |N...:. .....U.B.| +00000210 03 8a c4 5f f1 50 f8 14 67 1c 58 cc cb 46 4f 81 |..._.P..g.X..FO.| +00000220 03 d8 5e 11 71 c2 86 83 0e 97 d1 e5 2c b7 d9 5a |..^.q.......,..Z| +00000230 08 f7 ae c5 75 49 29 19 27 00 a3 54 12 7a d6 2a |....uI).'..T.z.*| +00000240 94 f1 64 cd f1 01 fa a7 32 2e fa 9d d4 e8 e5 1c |..d.....2.......| +00000250 f9 93 96 0d 8f c1 2e 7f a8 9b 9c 55 cd 15 c4 c9 |...........U....| +00000260 81 f1 fe e8 af 8d c8 5f 59 d2 f6 78 ab 44 18 1b |......._Y..x.D..| +00000270 e6 cf 7f 96 c1 5a 49 4d 74 37 69 20 d9 6b 80 c3 |.....ZIMt7i .k..| +00000280 df ec 59 b2 0b 50 ac cb 61 d9 d9 bb 22 a7 5e 9c |..Y..P..a...".^.| +00000290 a2 f8 c8 fe 7a b4 dc d9 da 51 13 f2 47 54 01 55 |....z....Q..GT.U| +000002a0 40 11 9b e3 06 69 a8 48 d2 c5 af 2f 38 bb 60 1d |@....i.H.../8.`.| +000002b0 74 8d f8 55 2d 87 42 66 31 6e 11 79 04 f3 7f e0 |t..U-.Bf1n.y....| +000002c0 97 3d b5 e9 b7 c0 8a 69 dc af f1 99 79 3e ac 73 |.=.....i....y>.s| +000002d0 22 28 71 4b 8f 98 53 b3 2b ce 84 2c 4e 3c 35 85 |"(qK..S.+..,N<5.| +000002e0 1c cb 4a 16 eb 66 f7 e4 6e 89 55 26 71 04 ed da |..J..f..n.U&q...| +000002f0 e8 d7 05 d4 99 27 a3 6e 3a 36 05 08 ff c7 18 19 |.....'.n:6......| +00000300 06 d7 11 bd e6 a2 20 79 20 49 0e ed 66 64 27 24 |...... y I..fd'$| +00000310 c3 c4 a6 ba 27 c4 86 6d d2 c0 39 60 a4 40 57 06 |....'..m..9`.@W.| +00000320 71 51 90 23 26 a3 72 9c ab 7d d5 c6 1a 49 4b 01 |qQ.#&.r..}...IK.| +00000330 2b b2 44 73 bb 6c af f2 a8 24 dc be 7e c3 9d 28 |+.Ds.l...$..~..(| +00000340 c1 5e 60 b3 34 92 b9 42 4a 05 82 ea 13 68 f9 28 |.^`.4..BJ....h.(| +00000350 20 c4 c0 96 ac 63 95 82 96 50 17 03 03 00 99 eb | ....c...P......| +00000360 d6 1a 78 84 ad 9e eb c4 0b 1c 04 bc 76 11 7e 6c |..x.........v.~l| +00000370 04 83 50 b0 d5 f7 1e 61 c3 23 37 01 fb ea 84 57 |..P....a.#7....W| +00000380 1a b2 17 d8 97 41 0f 80 54 e0 c2 0b b9 db d6 1b |.....A..T.......| +00000390 71 58 56 32 5f cc 98 e3 19 c4 1c 6e 76 9a 84 17 |qXV2_......nv...| +000003a0 97 54 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-00000090 00 00 5a f0 07 0a f5 66 46 86 94 8c 0b 62 1c fd |..Z....fF....b..| -000000a0 cc cf fd 5d 06 96 1e 21 9e 20 d5 07 5f 5a 00 9f |...]...!. .._Z..| -000000b0 6f 80 36 5e aa 56 d0 07 00 20 08 55 48 fe 6c a1 |o.6^.V... .UH.l.| -000000c0 b1 22 f3 94 54 7e 7e d5 e9 f0 71 69 01 fc bd 14 |."..T~~...qi....| -000000d0 a1 de 38 e4 b4 02 88 3e 66 77 3b f7 aa cd 57 a3 |..8....>fw;...W.| -000000e0 cf 6a 40 7d 93 75 79 3b 95 07 33 69 b2 8d 2a 37 |.j@}.uy;..3i..*7| -000000f0 94 d3 8d d5 b5 8a f0 94 8d 1e b4 9e 02 4f 7d 83 |.............O}.| -00000100 05 c6 c7 c8 a0 74 f1 88 f7 68 bf 4b e4 18 3b 6f |.....t...h.K..;o| -00000110 0c 6c a6 e7 75 50 b9 f6 68 2e 05 67 a3 47 df 22 |.l..uP..h..g.G."| -00000120 fa ae c1 4f a8 3d f3 bb dc 66 c3 b6 98 b7 8c 5b |...O.=...f.....[| -00000130 48 51 57 d7 43 b2 13 25 9e d5 82 6c 70 5c 42 53 |HQW.C..%...lp\BS| -00000140 a9 e8 8a 12 26 cd 3a f8 f8 e5 97 84 55 89 09 d4 |....&.:.....U...| -00000150 d4 20 40 d7 2d 6f 66 36 63 f6 53 17 03 03 00 59 |. @.-of6c.S....Y| -00000160 2f f6 22 ce f3 86 f8 ee b1 f6 49 de c8 bf 91 9c |/.".......I.....| -00000170 bc 2f fa 75 af 51 bc ee b7 a5 a9 82 35 3b 83 9d |./.u.Q......5;..| -00000180 3d 9f 57 10 07 4b af 01 66 f0 39 dd f0 4a a7 90 |=.W..K..f.9..J..| -00000190 f3 6c 28 97 80 0d a5 74 2d 22 a3 81 cd 64 2b 1a |.l(....t-"...d+.| -000001a0 d1 4e 2d 9e 8e 69 38 f8 11 9c 17 1f e6 c9 01 4e |.N-..i8........N| -000001b0 48 1f 80 43 26 d4 5a 82 30 17 03 03 00 35 e9 25 |H..C&.Z.0....5.%| -000001c0 b9 01 8e 0d 51 be 9d d1 b4 2b 0a ee 36 69 85 1a |....Q....+..6i..| -000001d0 10 a8 ff 36 e7 21 b7 f2 54 75 ca 07 52 88 48 d0 |...6.!..Tu..R.H.| -000001e0 ad 67 0b 92 52 70 fa 14 bc 7e 1d 43 f0 a2 7b df |.g..Rp...~.C..{.| -000001f0 ac 0c 19 17 03 03 00 17 98 76 d7 52 06 90 ef 00 |.........v.R....| -00000200 21 5e ec ed 0e 35 77 ef 5c f1 32 58 33 0f 06 17 |!^...5w.\.2X3...| -00000210 03 03 00 13 05 fb b3 c3 4d b5 a4 9c 52 ea bc d2 |........M...R...| -00000220 86 08 26 b8 df 5c 4c |..&..\L| +00000000 14 03 03 00 01 01 17 03 03 01 50 91 c4 28 45 d6 |..........P..(E.| +00000010 75 d9 6a 6e 53 d3 9a 02 43 af ef 38 8f 32 c4 05 |u.jnS...C..8.2..| +00000020 0c 2e 3f ec ad f5 51 cc d3 ef b6 59 c3 49 6d ea |..?...Q....Y.Im.| +00000030 7a d9 5e 19 d2 d5 4b 36 f6 a4 6b 5a 12 59 65 47 |z.^...K6..kZ.YeG| +00000040 da a4 e6 a1 68 15 25 9f 3e f1 94 56 f8 8b a1 fe |....h.%.>..V....| +00000050 af 41 ff 24 f3 34 23 df 5e 6c 1f be e4 0a 6c 64 |.A.$.4#.^l....ld| +00000060 15 c0 3d f7 04 be 77 e0 47 55 c0 56 78 35 43 95 |..=...w.GU.Vx5C.| +00000070 16 1d 10 a8 1b 14 c6 4d 63 02 9d 26 0a 57 92 c4 |.......Mc..&.W..| +00000080 0d 8a f6 29 76 15 83 9a b1 92 af e2 ca 98 36 9a |...)v.........6.| +00000090 db f9 99 a2 15 55 e3 87 1d 4c ed 41 b0 86 80 75 |.....U...L.A...u| +000000a0 c2 43 4b 44 b6 43 be f2 4e ce 4b 31 bb d5 5e be |.CKD.C..N.K1..^.| +000000b0 70 1f 24 96 21 a7 e8 58 30 65 50 ba 5d 15 ee 91 |p.$.!..X0eP.]...| +000000c0 f0 9b 2d e0 e2 c0 ef 15 51 bb f5 59 9c bb 44 eb |..-.....Q..Y..D.| +000000d0 6c be 1d 9c 33 af 71 db 82 35 05 8f 2b 9e 90 76 |l...3.q..5..+..v| +000000e0 f8 de 9f 0c 37 6d 35 b0 e7 df d2 27 1c e7 04 9d |....7m5....'....| +000000f0 38 b1 9d c5 eb 92 80 ec 6f 7e 97 15 0c 29 df 38 |8.......o~...).8| +00000100 8e 4a c2 1d 8b ce 39 24 1f fd e6 88 05 5b ca 0d |.J....9$.....[..| +00000110 16 46 50 f5 7e 1d 8c 30 da 9c 41 f5 d4 52 80 e4 |.FP.~..0..A..R..| +00000120 99 1a f4 0b 12 85 2b b0 c6 19 33 e2 5d 5e 55 8e |......+...3.]^U.| +00000130 00 5b 5e aa db ef f9 fd 2a 63 26 da 55 3e 47 d1 |.[^.....*c&.U>G.| +00000140 31 b3 83 ca b9 fb ed af f1 11 bc fd 2f 22 b7 2b |1.........../".+| +00000150 bf c8 11 07 e2 e2 41 42 ec de d1 17 03 03 00 59 |......AB.......Y| +00000160 e1 ea 82 cc db a9 d0 df dc 98 14 66 ee 17 72 61 |...........f..ra| +00000170 2e 88 b6 a3 48 b3 1c 22 35 09 8f e7 63 94 ba cc |....H.."5...c...| +00000180 5a 8f 3f 67 27 95 fc 8f f9 c4 a0 44 cb bb ba de |Z.?g'......D....| +00000190 1b ce 7a 37 6c b6 95 bb c4 62 f2 d9 84 2b c1 e8 |..z7l....b...+..| +000001a0 19 e5 c2 d9 df 16 12 40 00 6b 0e 99 ef 0d d0 0e |.......@.k......| +000001b0 1f b7 8e b8 b7 a2 86 31 91 17 03 03 00 35 11 b7 |.......1.....5..| +000001c0 08 5e 8b 8f 16 92 33 73 25 d1 94 a0 28 1e a0 33 |.^....3s%...(..3| +000001d0 be 25 cd e9 eb 0d 29 4d ea 63 e1 44 60 88 26 f0 |.%....)M.c.D`.&.| +000001e0 c4 8a ee 9d fe 1c ec 37 1f 19 f6 f5 fd 35 7b 86 |.......7.....5{.| +000001f0 af 79 1b 17 03 03 00 17 7f de 37 0f fa 4f ac 15 |.y........7..O..| +00000200 82 fd 7e 84 72 03 30 5a 6e b8 c6 ed 31 6f 18 17 |..~.r.0Zn...1o..| +00000210 03 03 00 13 6a 30 db 1f cf b1 46 55 5e 62 a4 7d |....j0....FU^b.}| +00000220 67 d5 16 ef 5e 28 28 |g...^((| diff --git a/src/crypto/tls/testdata/Client-TLSv13-ClientCert-RSA-ECDSA b/src/crypto/tls/testdata/Client-TLSv13-ClientCert-RSA-ECDSA index 09de5cca834..019f8952bc8 100644 --- a/src/crypto/tls/testdata/Client-TLSv13-ClientCert-RSA-ECDSA +++ b/src/crypto/tls/testdata/Client-TLSv13-ClientCert-RSA-ECDSA @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 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|-:gWn.yM..k.1.#.| +00000170 af e9 6b 41 2d 95 7b ff 0c 5e 6e 76 74 b0 03 56 |..kA-.{..^nvt..V| +00000180 50 1c d5 20 78 31 19 e4 26 b8 76 ce c4 cd 1e b3 |P.. x1..&.v.....| +00000190 35 0a ac 49 e6 67 70 03 99 4e 07 0d a3 9e 6b 98 |5..I.gp..N....k.| +000001a0 65 4c 30 e0 5e 98 8a 90 06 92 73 bc c0 e8 11 06 |eL0.^.....s.....| +000001b0 35 d3 d9 cb b8 59 8d 83 0f f3 3e d8 19 43 50 71 |5....Y....>..CPq| +000001c0 cf a4 98 0c 6a 90 d3 28 ce d9 05 50 e3 b1 51 06 |....j..(...P..Q.| +000001d0 fd 03 27 f7 57 51 d8 38 c7 ac 5a c9 29 55 b2 90 |..'.WQ.8..Z.)U..| +000001e0 89 46 66 0a 8a 9a 3e 4b c0 9b d8 cb 5f 12 5d ef |.Ff...>K...._.].| +000001f0 79 20 b7 b8 5a 6c 7e b4 de 79 9a 1b 81 4c 1f e5 |y ..Zl~..y...L..| +00000200 7a cb be 9b 2c cd 5b e2 97 e2 0c a5 a9 1b 7e c0 |z...,.[.......~.| +00000210 99 e6 b1 8c f3 f9 eb d1 15 1b 23 aa 17 03 03 00 |..........#.....| +00000220 99 b8 55 c2 3b a6 a9 36 22 19 9f 77 89 93 1b 84 |..U.;..6"..w....| +00000230 2d 67 fb 23 07 7c c7 44 7e 9f ca 80 bf aa 50 ba |-g.#.|.D~.....P.| +00000240 fe 7f a9 ca af 46 fb f9 69 a4 07 85 df d8 21 47 |.....F..i.....!G| +00000250 cb 2f 43 5e f5 b5 b7 f1 25 b4 1d d0 33 a4 45 de |./C^....%...3.E.| +00000260 76 c5 4e 30 87 76 2d ba fa 91 f5 07 85 38 bb 70 |v.N0.v-......8.p| +00000270 38 6d 97 7c 77 a9 22 60 dd f2 42 bc 60 89 ff 3f |8m.|w."`..B.`..?| +00000280 bf 31 d7 81 0b 26 09 75 be d9 c8 5d f6 28 cc ca |.1...&.u...].(..| +00000290 37 68 0c 81 78 4a 70 a6 cf 96 04 92 58 de 4d 24 |7h..xJp.....X.M$| +000002a0 b2 84 94 ed 7f b6 37 b5 f4 33 94 75 05 e5 68 fe |......7..3.u..h.| +000002b0 bd 39 be d2 e0 83 a1 32 41 70 17 03 03 00 35 54 |.9.....2Ap....5T| +000002c0 d6 fb 9d 58 e9 86 5d b0 ca 0f f3 cd 9c 4c d8 88 |...X..]......L..| +000002d0 28 ff 6c c9 1d 85 8d e9 72 56 1a f9 48 78 60 ad |(.l.....rV..Hx`.| +000002e0 6f 96 18 40 bd 6b 34 c0 ea 66 62 45 71 85 ec 8d |o..@.k4..fbEq...| +000002f0 09 ac cb 82 17 03 03 00 17 44 fd 91 ed 48 30 60 |.........D...H0`| +00000300 13 e1 d4 b2 6f a7 8e 0f 4f 49 89 f6 8e 2e 71 a0 |....o...OI....q.| +00000310 17 03 03 00 13 45 45 f9 5c 9f e7 48 40 4d 05 0a |.....EE.\..H@M..| +00000320 e4 08 31 6d bc d2 5f a0 |..1m.._.| diff --git a/src/crypto/tls/testdata/Client-TLSv13-ClientCert-RSA-RSAPSS b/src/crypto/tls/testdata/Client-TLSv13-ClientCert-RSA-RSAPSS index 9488dd6b66d..11513ab4891 100644 --- a/src/crypto/tls/testdata/Client-TLSv13-ClientCert-RSA-RSAPSS +++ b/src/crypto/tls/testdata/Client-TLSv13-ClientCert-RSA-RSAPSS @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,137 +7,138 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 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8c 2f 60 76 4f 7b 33 b3 7e 9f 1b b6 59 6c 6d |f./`vO{3.~...Ylm| +00000210 24 c0 b0 39 b3 30 de f0 52 e4 7f ee 6f f9 0f d3 |$..9.0..R...o...| +00000220 3d dd 98 b6 48 6a b9 c9 fa 38 49 46 c8 84 e2 d8 |=...Hj...8IF....| +00000230 b4 03 1c 2b 3a b2 37 8d 7a 7e 06 24 1c 22 f2 1e |...+:.7.z~.$."..| +00000240 4a 3c ed 91 20 bd c5 e9 c7 6d 77 45 83 74 eb e7 |J<.. ....mwE.t..| +00000250 30 d0 ec d5 10 ad 0f 5d 34 e6 51 20 55 22 4d 44 |0......]4.Q U"MD| +00000260 3b 78 63 42 a8 71 21 6a 0b c6 d7 f1 5f e6 08 89 |;xcB.q!j...._...| +00000270 f2 e6 17 10 a8 77 82 9a af ec d8 3c 59 4f 29 25 |.....w......:....G..| +000002a0 72 dd 8b 40 97 af 49 70 09 95 97 98 e8 ca ab 4b |r..@..Ip.......K| +000002b0 ce 33 e3 5b 5a ad bd be 8c 4c 5e 39 57 5c 77 fa |.3.[Z....L^9W\w.| +000002c0 fc 67 f8 28 93 98 2f e1 17 03 03 00 a4 09 c8 b8 |.g.(../.........| +000002d0 0c ca 4e 7a ff 99 39 c5 d5 10 37 e0 7b 04 03 c5 |..Nz..9...7.{...| +000002e0 58 de 62 35 5c c8 93 92 b2 9b b3 80 07 c5 dd 80 |X.b5\...........| +000002f0 cc 2f 14 33 3f 65 73 bf 49 8a a7 9c 2a ab a9 28 |./.3?es.I...*..(| +00000300 36 35 49 e5 3a 35 b2 66 f5 66 fd bb eb 65 62 55 |65I.:5.f.f...ebU| +00000310 8d 63 b5 e8 7f 30 ed f0 0b b1 0e c6 b6 e8 59 4c |.c...0........YL| +00000320 39 28 36 2f b5 4e 3b cf 4a 09 f9 ff c2 6e a4 af |9(6/.N;.J....n..| +00000330 0c 07 d1 4c 44 69 84 7b 5c da 27 69 c7 d5 7c 88 |...LDi.{\.'i..|.| +00000340 23 fe ff 50 b9 13 df 1d 4e 21 ac 14 84 98 ba f2 |#..P....N!......| +00000350 65 82 fd eb f2 72 7c 73 77 27 8b fc 5c db e2 31 |e....r|sw'..\..1| +00000360 cc f1 85 ba 68 4a 76 e4 d1 47 27 74 f6 b1 99 0e |....hJv..G't....| +00000370 36 17 03 03 00 35 90 d6 b3 06 40 da 48 59 98 19 |6....5....@.HY..| +00000380 89 09 8f 1d 3e 24 01 1e 23 c1 7b 52 41 f0 2a c6 |....>$..#.{RA.*.| +00000390 8e 33 c5 1f 9b 29 02 a8 c7 3b 83 2e d3 92 a5 a0 |.3...)...;......| +000003a0 7e ac 23 04 4d c0 53 59 0a 91 1b |~.#.M.SY...| >>> Flow 3 (client to server) -00000000 14 03 03 00 01 01 17 03 03 00 35 10 bd 5d 23 36 |..........5..]#6| -00000010 58 43 f4 bb 5e 4e ee 43 fd 0e a1 d9 de 81 99 54 |XC..^N.C.......T| -00000020 de 6e 82 33 71 8a 45 a7 35 f1 cd fb 5f bf 46 20 |.n.3q.E.5..._.F | -00000030 a5 79 d6 87 aa f4 29 51 02 f5 4e 69 ef a5 d7 d6 |.y....)Q..Ni....| -00000040 17 03 03 00 17 21 1f 90 0b 01 63 89 6a af 53 72 |.....!....c.j.Sr| -00000050 51 c0 11 01 7b 09 dd 40 82 dd e1 32 17 03 03 00 |Q...{..@...2....| -00000060 13 93 5d c1 19 16 5c 17 1a 7b 92 a0 9b f5 14 57 |..]...\..{.....W| -00000070 85 39 4a ac |.9J.| +00000000 14 03 03 00 01 01 17 03 03 00 35 10 e0 01 ca f7 |..........5.....| +00000010 4d 2b cb 95 a5 ac 48 e6 92 34 28 39 4f 5b c7 e5 |M+....H..4(9O[..| +00000020 5b a8 a1 6a f1 0a a6 21 77 92 ef fa f5 cc 41 55 |[..j...!w.....AU| +00000030 bd 5b 6d 68 80 22 e7 1b 2a 29 bb ef dc ed 37 b6 |.[mh."..*)....7.| +00000040 17 03 03 00 17 a1 5b 8f 83 06 c8 f6 8b 42 d0 c0 |......[......B..| +00000050 fd 36 c0 26 8e 04 89 61 2b d1 1b 7f 17 03 03 00 |.6.&...a+.......| +00000060 13 33 f1 a9 7e 1d 21 da e4 29 74 46 76 61 31 ce |.3..~.!..)tFva1.| +00000070 f6 b1 5b cd |..[.| diff --git a/src/crypto/tls/testdata/Client-TLSv13-Ed25519 b/src/crypto/tls/testdata/Client-TLSv13-Ed25519 index 0b4a17af3a2..b3bd6f8298f 100644 --- a/src/crypto/tls/testdata/Client-TLSv13-Ed25519 +++ b/src/crypto/tls/testdata/Client-TLSv13-Ed25519 @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,62 +7,63 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 7a 02 00 00 76 03 03 a8 21 4e 51 6a |....z...v...!NQj| -00000010 ce ba 17 cc 2d 25 b3 31 59 6a 3f 81 eb e6 ac a0 |....-%.1Yj?.....| -00000020 91 d9 ef 76 a1 5f bb 63 ab 2c 6b 20 00 00 00 00 |...v._.c.,k ....| +00000000 16 03 03 00 7a 02 00 00 76 03 03 53 04 82 7c f6 |....z...v..S..|.| +00000010 e4 8a 60 60 6e 26 7e 0a 78 c1 03 01 b8 b6 84 cc |..``n&~.x.......| +00000020 d5 48 a9 ea 34 7e 40 9c 51 07 bc 20 00 00 00 00 |.H..4~@.Q.. ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000040 00 00 00 00 00 00 00 00 00 00 00 00 13 01 00 00 |................| -00000050 2e 00 2b 00 02 03 04 00 33 00 24 00 1d 00 20 81 |..+.....3.$... .| -00000060 4c a8 07 aa 6b 4a f9 44 77 78 a9 57 d0 07 55 07 |L...kJ.Dwx.W..U.| -00000070 9a c2 8e 33 bf c4 09 ee 49 51 5c fe f1 7b 30 14 |...3....IQ\..{0.| -00000080 03 03 00 01 01 17 03 03 00 17 5a 22 a1 07 01 ea |..........Z"....| -00000090 97 bd 5a 59 3a 21 de 9c 45 0c 41 ff 34 45 35 ab |..ZY:!..E.A.4E5.| -000000a0 25 17 03 03 01 50 a1 8c 19 e7 0c 69 d3 e0 f6 53 |%....P.....i...S| -000000b0 95 15 13 4c e3 c3 3f 35 d9 73 c9 fe 24 b0 14 5f |...L..?5.s..$.._| -000000c0 b6 9e 94 20 cf 80 f7 88 7c 0f be 4c 70 16 00 2a |... ....|..Lp..*| -000000d0 55 02 aa a9 4b 7f a7 a5 b8 46 09 9e 18 78 78 66 |U...K....F...xxf| -000000e0 22 c2 31 19 12 f7 e4 7e f3 26 39 7d cd 5e 74 24 |".1....~.&9}.^t$| -000000f0 fb 75 7d b7 2c b5 fb e0 49 bd da 96 e1 c3 63 8f |.u}.,...I.....c.| -00000100 e3 28 43 bb 32 a7 fd 9c ab 54 ba ce 07 4a 23 35 |.(C.2....T...J#5| -00000110 a4 3a ff 43 40 19 ef 38 07 02 ba d6 c4 f0 bf 63 |.:.C@..8.......c| -00000120 aa b3 ea 55 d0 e1 a9 f3 cb 04 6b 1b 8d 35 3a f8 |...U......k..5:.| -00000130 0b 1c 40 99 fe b0 04 5f d1 5b 3f 4b be fe b5 96 |..@...._.[?K....| -00000140 f0 49 3d bf a5 92 f3 bd a6 4c 47 24 f8 b5 7c 45 |.I=......LG$..|E| -00000150 47 85 9b 08 a1 da 51 7a ce 3f 32 66 de 89 c0 c3 |G.....Qz.?2f....| -00000160 ac da 73 0d 15 14 18 e6 a0 7d 07 26 44 df 55 b7 |..s......}.&D.U.| -00000170 6e 4e fa c0 f5 5e 42 3a d9 29 d3 1d e6 cf 3c 8c |nN...^B:.)....<.| -00000180 6d c1 d9 f9 04 f0 57 dc 47 4e d1 e2 a1 f1 a1 c9 |m.....W.GN......| -00000190 2e da 97 4d 65 65 04 54 e7 80 f1 88 b2 34 26 61 |...Mee.T.....4&a| -000001a0 77 8a 1f bb 82 7f 4b ce b3 5a 55 60 e1 3a ef 95 |w.....K..ZU`.:..| -000001b0 bd 34 fc ef 2b 18 4b bb 8a cf ba 3a 69 43 f4 59 |.4..+.K....:iC.Y| -000001c0 98 a1 95 a3 22 f6 b5 1a 84 83 cf cb 90 eb 28 29 |....".........()| -000001d0 b3 84 e1 0d 37 9e 98 96 91 73 f1 7f d7 9b 71 38 |....7....s....q8| -000001e0 6e bc 2e 60 2d 27 0c 18 fd 2a b8 76 01 33 2f 95 |n..`-'...*.v.3/.| -000001f0 6e 0b bf 2b 26 5e 17 03 03 00 59 ed 43 2f e8 df |n..+&^....Y.C/..| -00000200 f3 2f 91 f3 dc 1b aa ff d3 3b 28 1f 78 21 fb e2 |./.......;(.x!..| -00000210 7d 6e 03 09 98 c1 23 09 d7 45 da b8 e0 5a e5 27 |}n....#..E...Z.'| -00000220 38 9a 2f da 9b d3 04 35 f5 b9 31 b0 c0 1f 8a 1e |8./....5..1.....| -00000230 d8 8a 19 f1 38 af a6 74 ac e5 b4 0d 45 83 b4 59 |....8..t....E..Y| -00000240 83 42 97 14 23 55 71 ef 66 8c 35 69 3f 2c 88 63 |.B..#Uq.f.5i?,.c| -00000250 8d 3b 05 fe 17 03 03 00 35 47 82 ec 22 f4 86 6a |.;......5G.."..j| -00000260 b7 c1 d8 64 3b 42 f4 ca 5c 3d ba a3 6a ea 77 6a |...d;B..\=..j.wj| -00000270 d6 52 e3 b0 42 fb c2 f1 2c b1 ef 44 ed 11 29 6d |.R..B...,..D..)m| -00000280 2b 6f 13 0f 42 48 a0 2e 5b ba a1 93 6b de |+o..BH..[...k.| +00000050 2e 00 2b 00 02 03 04 00 33 00 24 00 1d 00 20 eb |..+.....3.$... .| +00000060 17 f8 ff f0 83 82 37 4a cf 66 0c 2c 92 63 d2 ee |......7J.f.,.c..| +00000070 e3 fa fa 0b 54 f3 7a 93 93 06 2a 1f f0 26 3b 14 |....T.z...*..&;.| +00000080 03 03 00 01 01 17 03 03 00 17 df 45 b6 6c e5 fe |...........E.l..| +00000090 9c 99 ca 87 1f f5 66 33 60 9c 35 f6 a2 c4 6a b6 |......f3`.5...j.| +000000a0 17 17 03 03 01 50 04 67 b5 b3 09 8e 2e 13 d5 8c |.....P.g........| +000000b0 9e 37 b7 80 cc 79 69 a8 46 50 ea 79 79 b6 ea 5f |.7...yi.FP.yy.._| +000000c0 f9 70 29 08 63 c9 4a 5d 3c aa 24 8a 69 5d 3f 15 |.p).c.J]<.$.i]?.| +000000d0 ff 0d 05 22 13 ef 97 c0 4d 7d 3e 06 b3 36 f6 97 |..."....M}>..6..| +000000e0 d4 10 01 12 3e 69 76 47 df 4e 2a ab 8a 7d 0e 46 |....>ivG.N*..}.F| +000000f0 a4 48 25 7d a2 7f 83 2f 6e c9 9b 8a 46 00 6b 68 |.H%}.../n...F.kh| +00000100 98 1a 51 89 91 29 0a d1 73 6c e9 af 5f b1 4d 3e |..Q..)..sl.._.M>| +00000110 a4 27 8a 2b 55 2a 79 bb 7d 88 a9 93 5c 18 28 2f |.'.+U*y.}...\.(/| +00000120 a1 aa d8 8c 6c 8e 6b 8d 1f 57 8a a9 22 a8 03 5d |....l.k..W.."..]| +00000130 b7 db f4 a4 00 83 d4 49 28 67 a3 7e dc 47 c5 2d |.......I(g.~.G.-| +00000140 0c 90 48 06 66 d7 4f fc e9 e7 c1 7c 43 4a 05 eb |..H.f.O....|CJ..| +00000150 b8 ee 5f 0f 87 de 98 bb 1d 51 3a 10 6d 8a 99 2b |.._......Q:.m..+| +00000160 1c 52 96 4b 63 ab 0f ea f8 86 1f d3 1a 32 bf 79 |.R.Kc........2.y| +00000170 7a 1f 75 09 d7 0f 9c 47 71 cb 67 c2 72 c6 2e 8b |z.u....Gq.g.r...| +00000180 26 ef 32 00 8c 0d 0e b3 9a f4 5f c7 7e b3 58 50 |&.2......._.~.XP| +00000190 79 0e 4b 93 83 31 14 ca dd e4 86 dc 12 3f b7 e0 |y.K..1.......?..| +000001a0 eb 73 2d 9d 57 cd 0d eb 02 7f 1d 96 bb 97 f7 d1 |.s-.W...........| +000001b0 d8 56 77 81 39 c1 ef 6e 64 3d 8c 62 39 73 da c4 |.Vw.9..nd=.b9s..| +000001c0 50 ce 0b b9 70 30 1f 76 37 7a c9 5a a7 49 5b c3 |P...p0.v7z.Z.I[.| +000001d0 2d 00 3d fe 77 18 64 04 f7 2d b8 e9 06 8d 7b 37 |-.=.w.d..-....{7| +000001e0 5f 76 4f 91 33 7b 09 0c bf fc c8 d1 6e 79 a9 0f |_vO.3{......ny..| +000001f0 cf db cf a2 be fd 17 03 03 00 59 7b 08 b1 2a ae |..........Y{..*.| +00000200 97 dd 93 84 78 b6 9a 13 6b c4 d3 1c eb d9 c0 f3 |....x...k.......| +00000210 a4 8c ac fb bb 8e c7 3b 27 cc c0 d7 01 18 e7 1e |.......;'.......| +00000220 12 ec 76 54 52 eb fd e0 cd 85 0d 6c 52 7f b8 14 |..vTR......lR...| +00000230 19 48 29 77 71 3b d3 ce cb 55 1c 6b 2b aa 1a a7 |.H)wq;...U.k+...| +00000240 52 35 6f 52 f4 36 34 e1 b1 54 7e 86 8f 03 fd 16 |R5oR.64..T~.....| +00000250 ea 9f a4 6a 17 03 03 00 35 16 31 24 cd 72 3e 0b |...j....5.1$.r>.| +00000260 5e fa f4 73 96 12 3c 9d e8 bd 21 1f 06 06 fb 71 |^..s..<...!....q| +00000270 24 7c 26 62 3d d0 f9 fb f4 30 07 27 ab 3e 54 8e |$|&b=....0.'.>T.| +00000280 4a bf 9f a9 74 b5 ce a2 16 6a 69 a9 c5 33 |J...t....ji..3| >>> Flow 3 (client to server) -00000000 14 03 03 00 01 01 17 03 03 00 35 11 45 8f b2 e0 |..........5.E...| -00000010 87 3d 09 94 93 16 19 04 3d 84 6c e5 14 5e c6 8b |.=......=.l..^..| -00000020 73 1a 53 4c d0 f4 11 27 0c 0d 05 c7 9d ba d0 04 |s.SL...'........| -00000030 37 ed 8b 8a 65 34 54 b1 07 36 92 8c 8c a8 30 b7 |7...e4T..6....0.| -00000040 17 03 03 00 17 ea fc b8 84 8d f0 9d 8e 1c 2c 65 |..............,e| -00000050 10 a8 69 7f dd 3c a4 80 45 5d c3 38 17 03 03 00 |..i..<..E].8....| -00000060 13 15 4b b7 23 2f 55 b0 ae d3 3f f6 68 c9 b2 ef |..K.#/U...?.h...| -00000070 d7 e2 18 49 |...I| +00000000 14 03 03 00 01 01 17 03 03 00 35 ad ca 92 a0 d6 |..........5.....| +00000010 9a 4e 88 ae 6d f5 c9 20 11 d7 1b 81 b5 83 c8 62 |.N..m.. .......b| +00000020 65 4c 79 86 9f 6b aa 84 d7 73 01 70 db f2 f2 cd |eLy..k...s.p....| +00000030 0b d8 a4 b8 cc 03 bb 0c 9d 3d 83 ee f3 f1 db 3b |.........=.....;| +00000040 17 03 03 00 17 37 8e 77 a5 33 c1 66 dc f0 ee b7 |.....7.w.3.f....| +00000050 2a 36 b9 67 1b 95 02 62 54 f4 5f 94 17 03 03 00 |*6.g...bT._.....| +00000060 13 f7 74 48 62 8a 09 33 04 02 1c a2 e5 2e d5 fe |..tHb..3........| +00000070 f1 bc 5d 2b |..]+| diff --git a/src/crypto/tls/testdata/Client-TLSv13-ExportKeyingMaterial b/src/crypto/tls/testdata/Client-TLSv13-ExportKeyingMaterial index b30641131ea..0408d892c4d 100644 --- a/src/crypto/tls/testdata/Client-TLSv13-ExportKeyingMaterial +++ b/src/crypto/tls/testdata/Client-TLSv13-ExportKeyingMaterial @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,84 +7,85 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 7a 02 00 00 76 03 03 6d fb 70 07 b4 |....z...v..m.p..| -00000010 2d 14 d1 d1 88 17 6a a3 b1 c1 e7 23 4b 06 c4 fa |-.....j....#K...| -00000020 4a 0e e1 2c ce 5a d5 c7 8c ab f2 20 00 00 00 00 |J..,.Z..... ....| +00000000 16 03 03 00 7a 02 00 00 76 03 03 21 c4 39 aa bf |....z...v..!.9..| +00000010 5f d9 83 0d 5d 33 60 37 8c b2 ff 0d 78 e3 42 87 |_...]3`7....x.B.| +00000020 9d 6a 32 90 7b de 78 e6 e2 00 93 20 00 00 00 00 |.j2.{.x.... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000040 00 00 00 00 00 00 00 00 00 00 00 00 13 01 00 00 |................| -00000050 2e 00 2b 00 02 03 04 00 33 00 24 00 1d 00 20 4e |..+.....3.$... 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+00000270 d2 6b ee 74 eb e6 35 9c 95 ad cb b5 96 0e 6a 90 |.k.t..5.......j.| +00000280 85 ff 3e b7 e5 82 45 59 d3 c3 76 21 3f ba 80 ac |..>...EY..v!?...| +00000290 ce a0 0a 75 12 7d d3 5d a2 28 79 40 dd 4b 58 f8 |...u.}.].(y@.KX.| +000002a0 87 9d fd 4a 96 b1 a3 70 27 23 0d 06 3b 47 83 b7 |...J...p'#..;G..| +000002b0 4c 1f 82 7e d0 07 38 2c 62 f6 de 90 29 f3 7c 94 |L..~..8,b...).|.| +000002c0 4e ea 5e 66 11 1f 27 35 23 de a2 09 3f 34 83 2a |N.^f..'5#...?4.*| +000002d0 08 1a 6e e9 c1 a0 38 18 53 92 16 07 ab 19 ea 93 |..n...8.S.......| +000002e0 cd 9f f1 bb f0 4b 2b 2f 5b fa e3 f9 c5 cc f1 02 |.....K+/[.......| +000002f0 f6 47 70 50 03 98 36 c9 cd fd 1a 01 20 6d 12 0b |.GpP..6..... m..| +00000300 7e b9 ba 76 aa 44 19 97 3b b0 6f 20 b4 e0 fc a7 |~..v.D..;.o ....| +00000310 a9 1f eb 17 03 03 00 99 44 85 f9 ed c9 ea 2e 88 |........D.......| +00000320 4b fa a9 76 68 8f e3 f1 9c 62 7f 91 cc f6 80 12 |K..vh....b......| +00000330 7a 0b f7 4a 93 68 14 c6 cf e2 7c 6f 02 5d e5 dc |z..J.h....|o.]..| +00000340 89 a0 23 71 d1 86 c4 9c 66 86 45 73 54 5f c3 6d |..#q....f.EsT_.m| +00000350 22 01 43 b2 46 c3 bc ff 8d 82 ae f1 72 f7 0b 33 |".C.F.......r..3| +00000360 3c 8e a3 67 d9 69 0f be ce 5c 08 4d d1 14 2d 93 |<..g.i...\.M..-.| +00000370 c9 af 66 1c 55 b3 89 3d 14 15 f0 60 80 2d 9f b0 |..f.U..=...`.-..| +00000380 b3 6a 84 7a 2b 52 cb df 04 d0 96 d3 48 ca 9f c8 |.j.z+R......H...| +00000390 18 a8 a8 50 12 14 7f 2a e9 4c 96 6f 57 9d 66 5c |...P...*.L.oW.f\| +000003a0 ba a0 2d e1 52 37 b5 c1 9b 76 43 b2 e8 84 53 3c |..-.R7...vC...S<| +000003b0 be 17 03 03 00 35 8f 39 78 66 11 c2 24 c6 1a 79 |.....5.9xf..$..y| +000003c0 c4 4f de 76 87 d1 24 c9 d0 4f d0 be d8 72 bf ed |.O.v..$..O...r..| +000003d0 78 28 05 cf e4 72 6d 35 88 07 1b ce ac c6 d0 8a |x(...rm5........| +000003e0 75 a5 fd a1 9e 06 1c 38 47 0e 93 |u......8G..| >>> Flow 3 (client to server) -00000000 14 03 03 00 01 01 17 03 03 00 35 02 ed 34 8f 83 |..........5..4..| -00000010 44 27 8b 71 af c1 06 33 0b 25 aa 22 85 96 41 75 |D'.q...3.%."..Au| -00000020 4f fe 46 82 ba 95 91 4c cc a9 99 60 5c f7 72 7f |O.F....L...`\.r.| -00000030 e4 1f e4 99 6a c2 25 db d0 11 5d fc d6 28 8f 56 |....j.%...]..(.V| -00000040 17 03 03 00 17 fe e8 cf ed a0 7a ce 77 57 e6 aa |..........z.wW..| -00000050 f0 ce 6d 2f 5c e5 1f 7d 37 c8 91 cf 17 03 03 00 |..m/\..}7.......| -00000060 13 a4 a9 4c b5 33 38 4a 1e b7 65 9d 72 85 1b 79 |...L.38J..e.r..y| -00000070 79 87 e3 bf |y...| +00000000 14 03 03 00 01 01 17 03 03 00 35 69 03 1d cc 94 |..........5i....| +00000010 59 f8 91 58 29 4e 88 e1 88 44 2b 93 b4 6a 9a 76 |Y..X)N...D+..j.v| +00000020 a3 fb 58 64 2a d4 95 d9 3a 5d 60 48 8a 52 60 3d |..Xd*...:]`H.R`=| +00000030 01 c3 b6 9f c1 12 fe f6 6f 1c 31 03 21 61 e4 e0 |........o.1.!a..| +00000040 17 03 03 00 17 85 08 f1 af 00 7c e1 b9 f6 ad a3 |..........|.....| +00000050 e0 b1 24 c4 e5 34 49 19 37 53 f8 dd 17 03 03 00 |..$..4I.7S......| +00000060 13 4d d3 16 f0 be e1 13 2d b8 99 7d 95 f8 c7 b4 |.M......-..}....| +00000070 b8 1c 81 5e |...^| diff --git a/src/crypto/tls/testdata/Client-TLSv13-HelloRetryRequest b/src/crypto/tls/testdata/Client-TLSv13-HelloRetryRequest index 10e13ec33d9..88fb3b7775b 100644 --- a/src/crypto/tls/testdata/Client-TLSv13-HelloRetryRequest +++ b/src/crypto/tls/testdata/Client-TLSv13-HelloRetryRequest @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 f6 01 00 00 f2 03 03 00 00 00 00 00 |................| +00000000 16 03 01 00 fc 01 00 00 f8 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,14 +7,15 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 77 00 05 00 05 01 00 00 00 00 00 0a 00 |...w............| +00000080 01 00 00 7d 00 05 00 05 01 00 00 00 00 00 0a 00 |...}............| 00000090 06 00 04 00 1d 00 17 00 0b 00 02 01 00 00 0d 00 |................| -000000a0 1a 00 18 08 04 04 03 08 07 08 05 08 06 04 01 05 |................| -000000b0 01 06 01 05 03 06 03 02 01 02 03 ff 01 00 01 00 |................| -000000c0 00 12 00 00 00 2b 00 09 08 03 04 03 03 03 02 03 |.....+..........| -000000d0 01 00 33 00 26 00 24 00 1d 00 20 2f e5 7d a3 47 |..3.&.$... /.}.G| -000000e0 cd 62 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af |.bC.(.._.).0....| -000000f0 c4 cf c2 ed 90 99 5f 58 cb 3b 74 |......_X.;t| +000000a0 20 00 1e 08 04 04 03 08 07 08 05 08 06 04 01 05 | ...............| +000000b0 01 06 01 05 03 06 03 02 01 02 03 fe 61 fe 62 08 |............a.b.| +000000c0 08 ff 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 |...........+....| +000000d0 04 03 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 |........3.&.$...| +000000e0 20 2f e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 | /.}.G.bC.(.._.)| +000000f0 07 30 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b |.0.........._X.;| +00000100 74 |t| >>> Flow 2 (server to client) 00000000 16 03 03 00 58 02 00 00 54 03 03 cf 21 ad 74 e5 |....X...T...!.t.| 00000010 9a 61 11 be 1d 8c 02 1e 65 b8 91 c2 a2 11 16 7a |.a......e......z| @@ -24,7 +25,7 @@ 00000050 0c 00 2b 00 02 03 04 00 33 00 02 00 17 14 03 03 |..+.....3.......| 00000060 00 01 01 |...| >>> Flow 3 (client to server) -00000000 14 03 03 00 01 01 16 03 03 01 17 01 00 01 13 03 |................| +00000000 14 03 03 00 01 01 16 03 03 01 1d 01 00 01 19 03 |................| 00000010 03 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000030 00 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |. ..............| @@ -32,88 +33,88 @@ 00000050 00 00 00 32 cc a8 cc a9 c0 2f c0 2b c0 30 c0 2c |...2...../.+.0.,| 00000060 c0 27 c0 13 c0 23 c0 09 c0 14 c0 0a 00 9c 00 9d |.'...#..........| 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-00000120 5a 89 |Z.| +000000c0 03 fe 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 |..a.b...........| +000000d0 00 2b 00 09 08 03 04 03 03 03 02 03 01 00 33 00 |.+............3.| +000000e0 47 00 45 00 17 00 41 04 1e 18 37 ef 0d 19 51 88 |G.E...A...7...Q.| +000000f0 35 75 71 b5 e5 54 5b 12 2e 8f 09 67 fd a7 24 20 |5uq..T[....g..$ | +00000100 3e b2 56 1c ce 97 28 5e f8 2b 2d 4f 9e f1 07 9f |>.V...(^.+-O....| +00000110 6c 4b 5b 83 56 e2 32 42 e9 58 b6 d7 49 a6 b5 68 |lK[.V.2B.X..I..h| +00000120 1a 41 03 56 6b dc 5a 89 |.A.Vk.Z.| >>> Flow 4 (server to client) -00000000 16 03 03 00 9b 02 00 00 97 03 03 b5 7c 4a c4 82 |............|J..| -00000010 67 2c 0d e4 cf 12 5a 8c fc 44 10 da 7e ef ec ae |g,....Z..D..~...| -00000020 bc 59 6c 7d 62 b1 d8 95 5d 9d 3b 20 00 00 00 00 |.Yl}b...].; ....| +00000000 16 03 03 00 9b 02 00 00 97 03 03 6a 2a 6d 32 a5 |...........j*m2.| +00000010 14 5d 5d 56 e4 88 02 0e a0 82 48 8d 15 a7 ff 4a |.]]V......H....J| +00000020 dd ec 96 7f a8 fe d7 b5 4b 8f 09 20 00 00 00 00 |........K.. ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000040 00 00 00 00 00 00 00 00 00 00 00 00 13 01 00 00 |................| 00000050 4f 00 2b 00 02 03 04 00 33 00 45 00 17 00 41 04 |O.+.....3.E...A.| -00000060 51 c8 a4 d2 63 ec a1 b7 72 7e 42 30 8e d2 eb b0 |Q...c...r~B0....| -00000070 3c e0 06 d0 69 39 b7 55 ee 47 c3 b3 b6 56 2d df |<...i9.U.G...V-.| -00000080 3e 0c 1c 92 cf f6 c4 52 13 90 fa e6 52 13 e6 6d |>......R....R..m| -00000090 35 46 de 60 05 a1 85 a9 ec 86 dc da 19 4d 21 67 |5F.`.........M!g| -000000a0 17 03 03 00 17 d7 59 69 75 49 13 ac 27 ad 1c a9 |......YiuI..'...| -000000b0 17 68 46 77 a2 22 0a f5 6f ce 70 67 17 03 03 02 |.hFw."..o.pg....| -000000c0 6d ee 92 51 b3 07 0f 46 be 24 a1 12 02 7e d1 d4 |m..Q...F.$...~..| -000000d0 b1 2e f5 87 f5 96 ed 00 77 f1 ad 1b 8e cd 1d 01 |........w.......| -000000e0 41 78 6a ff 68 9f 6d ac fe 92 8a c5 43 d2 c9 1d |Axj.h.m.....C...| -000000f0 a8 d8 0f 00 7e c1 06 a9 16 ba 13 94 e7 d9 cd e1 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|c..{..%+...f....| -000001d0 4a 95 64 3d 9f c2 e9 eb 7c 59 72 1c 52 68 fa 5a |J.d=....|Yr.Rh.Z| -000001e0 b3 d6 9e dc 51 d6 ac 0b 34 f1 66 42 4b 99 1d cb |....Q...4.fBK...| -000001f0 94 f4 08 c6 57 f9 97 87 54 9c 3b ba 4e 21 c7 b3 |....W...T.;.N!..| -00000200 a0 d9 41 33 22 c4 3f a4 29 e4 7a 3c a1 86 e0 65 |..A3".?.).z<...e| -00000210 f4 ff 67 c5 32 ae 16 01 67 8e 16 d7 28 5e b3 19 |..g.2...g...(^..| -00000220 c6 18 c7 27 0d 01 8e 04 87 fb 6b f9 72 ee 00 ff |...'......k.r...| -00000230 25 f9 c5 dd bc 30 45 63 2d 4d 2d 9d ea 7f 54 aa |%....0Ec-M-...T.| -00000240 ac 9e d8 a2 ae c2 e3 64 b7 3d 54 56 67 39 e8 96 |.......d.=TVg9..| -00000250 a5 5d fd 1e 01 2a 0c 7d ee f1 4e fc 1b 19 f9 ef |.]...*.}..N.....| -00000260 60 dd e1 b2 94 f3 5f 54 d4 05 f7 86 83 6f 97 43 |`....._T.....o.C| -00000270 4e 30 c1 49 cc 5e 98 10 5c 4e 32 84 97 70 c8 b9 |N0.I.^..\N2..p..| -00000280 6d 0b c2 23 ab f9 e8 85 6f 0a 2a 99 e7 12 33 e8 |m..#....o.*...3.| -00000290 f2 62 6f 65 0c 3d ff 9f e6 15 eb 1d 24 0e e9 8a |.boe.=......$...| -000002a0 28 e0 09 31 23 a4 5c 2c 25 49 b4 0c 5f 18 e1 12 |(..1#.\,%I.._...| -000002b0 82 16 6e 79 68 21 fb 5a 68 73 dd f7 2f aa e2 f9 |..nyh!.Zhs../...| -000002c0 85 8d af c6 84 50 af 84 95 12 c8 32 a6 eb f0 93 |.....P.....2....| -000002d0 a2 bd 97 d3 ba 76 a8 2e a2 44 2f 98 23 ca 78 cd |.....v...D/.#.x.| -000002e0 7a 5f bf ab 19 00 72 b5 b3 e0 a7 b5 da 47 05 c8 |z_....r......G..| -000002f0 44 0b 6c 7f 0b 4c 99 79 3c 47 7e e9 25 bd a8 4d |D.l..L.yOh.'.%..| -00000390 1f 89 9e 21 34 97 b9 7e 6e 2a c2 df 47 22 7d a6 |...!4..~n*..G"}.| -000003a0 aa 7a 4a fd 11 b0 73 10 f5 16 8b 2c 3a af a6 7a |.zJ...s....,:..z| -000003b0 cc 3d 4b f0 36 43 60 db 53 2a 4e 2c 1b 2c 0a 54 |.=K.6C`.S*N,.,.T| -000003c0 01 ff ad 7e 93 a8 d0 76 da 5a 88 88 17 03 03 00 |...~...v.Z......| -000003d0 35 d0 36 70 7c 4c 6a 10 bd 43 50 2c 47 74 f9 ed |5.6p|Lj..CP,Gt..| -000003e0 9f 0b d7 33 82 74 2f fd 81 4d 08 d6 cf f4 13 4e |...3.t/..M.....N| -000003f0 de ec 84 bf 79 35 ee 72 8a a3 d0 61 29 94 ad 79 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b7 c1 58 86 1b 5c 31 94 8c 26 61 f3 48 |~.|..X..\1..&a.H| +00000200 a3 c4 42 c5 89 39 6d 13 48 e9 eb 38 e3 67 dc 15 |..B..9m.H..8.g..| +00000210 90 ce 60 11 5a 3f 0d de c4 5d 05 c3 d3 1c cb 2d |..`.Z?...].....-| +00000220 9f 3f 2e 77 cb 7f bb 8d 85 4d d3 02 37 27 76 84 |.?.w.....M..7'v.| +00000230 8e 9a cc 5d 22 c1 4d 7e 00 a1 af e6 a3 0f ff 07 |...]".M~........| +00000240 e7 ac fc 0d c2 cf 82 63 22 fd b3 94 00 e2 58 e8 |.......c".....X.| +00000250 bb d6 26 a8 01 94 85 e3 0e 6b 0e 4d e7 0a 48 e4 |..&......k.M..H.| +00000260 03 3b b0 3a 35 50 5e 54 92 35 2a 54 fd 13 47 76 |.;.:5P^T.5*T..Gv| +00000270 1e 9b ea 97 25 20 10 63 88 03 89 15 17 78 d8 6b |....% .c.....x.k| +00000280 3b 82 4a d3 1c 04 dd 7f 77 bf 2d a4 02 fe 3d 06 |;.J.....w.-...=.| +00000290 4e 79 a8 48 fb 13 6f f4 ca 89 1d ab ce a8 4e 05 |Ny.H..o.......N.| +000002a0 36 6f 20 7e 40 a0 cd ea dc 5f 79 34 f7 bd dd 4c |6o ~@...._y4...L| +000002b0 49 67 c1 ab 50 7a 7f 9f 8c 5b 7b 3f f7 36 65 4f |Ig..Pz...[{?.6eO| +000002c0 88 9d 7a 26 5b 12 82 c7 41 f7 10 2e 67 b9 6e 46 |..z&[...A...g.nF| +000002d0 ce df 87 65 bf 1c 57 d9 5c bd 40 12 4a 84 bc fd |...e..W.\.@.J...| +000002e0 a1 d1 97 3a 7e f7 f1 d5 72 21 d1 ad 09 73 7e 89 |...:~...r!...s~.| +000002f0 26 5f 18 49 a1 f9 ae 5c 56 9b a6 3f a0 dd ee ab |&_.I...\V..?....| +00000300 f1 7e 57 b8 36 ec b6 9b 09 ae 98 f6 e2 66 ee c4 |.~W.6........f..| +00000310 34 0b 8d 0e 6c 66 a7 a5 a4 0d f2 f3 b4 b1 ef 11 |4...lf..........| +00000320 ca 8b 02 00 75 31 c5 3e d9 7d a8 4b 94 d7 17 03 |....u1.>.}.K....| +00000330 03 00 99 c0 22 4e 1f d8 9f f7 39 1c 6b 33 26 f9 |...."N....9.k3&.| +00000340 a7 0f 0e 70 77 03 b1 37 26 6d e7 a2 6c 8b 1f 11 |...pw..7&m..l...| +00000350 71 15 a9 d1 8f f2 b9 8b e6 d6 68 ba d1 ad 53 83 |q.........h...S.| +00000360 98 93 ed 0a cb 79 0c 4b c4 aa ee e2 55 4c 4c 92 |.....y.K....ULL.| +00000370 99 cb 61 25 14 de c3 82 a0 23 0a 90 f8 13 8c 43 |..a%.....#.....C| +00000380 17 1c e5 56 0d 21 d7 58 50 df ea d8 12 cd ef c7 |...V.!.XP.......| +00000390 46 f8 49 92 f7 eb 3d 29 d4 72 ef 0c 46 f0 6a aa |F.I...=).r..F.j.| +000003a0 73 73 94 84 ef ad 58 a5 74 18 2a f1 a7 31 5a 6c |ss....X.t.*..1Zl| +000003b0 8c ca 2f 99 58 b9 b1 54 e4 2b cc ac 53 bd 27 bd |../.X..T.+..S.'.| +000003c0 b9 01 41 37 4d b7 2f 03 f4 14 32 c3 17 03 03 00 |..A7M./...2.....| +000003d0 35 a8 76 c5 67 1c 67 c8 c8 be bd ef d7 e6 be 67 |5.v.g.g........g| +000003e0 9f 64 5e 83 a6 2d f6 06 41 e6 1d 4f e6 f1 b7 97 |.d^..-..A..O....| +000003f0 91 a0 11 6d 92 1c c7 fb d8 7b 7e e2 62 a8 5c 81 |...m.....{~.b.\.| +00000400 6e ba 6e f4 c5 7f |n.n...| >>> Flow 5 (client to server) -00000000 17 03 03 00 35 4b f7 dd b6 64 32 61 42 e7 b2 93 |....5K...d2aB...| -00000010 b8 4b dd 7c 25 c6 57 5b 68 d5 f2 d9 27 85 ee cf |.K.|%.W[h...'...| -00000020 09 44 79 8d 8e 14 0f 84 44 e5 16 a9 bf d9 14 bb |.Dy.....D.......| -00000030 22 73 c7 a9 24 c1 dd 38 1e 63 17 03 03 00 17 63 |"s..$..8.c.....c| -00000040 56 45 91 62 9c 00 4b d6 ae f4 dc 17 a2 89 55 0d |VE.b..K.......U.| -00000050 c3 d4 f3 12 8b bf 17 03 03 00 13 1f ac ed f8 80 |................| -00000060 31 7f 75 9f 6c a1 48 6e 20 89 b8 45 08 33 |1.u.l.Hn ..E.3| +00000000 17 03 03 00 35 0c 6d 39 41 20 1b a5 34 1e fc 04 |....5.m9A ..4...| +00000010 32 6a 25 28 be 0a b9 57 2d a3 18 5b 0f f4 6f 0d |2j%(...W-..[..o.| +00000020 49 e3 ea ae ce 0e c6 08 51 70 0b 39 cf 58 ef 1b |I.......Qp.9.X..| +00000030 49 7c 26 1c b4 41 78 5b 5a b4 17 03 03 00 17 76 |I|&..Ax[Z......v| +00000040 cf e5 42 3c 99 2c 4a 04 96 6c dc e6 a1 1c 84 33 |..B<.,J..l.....3| +00000050 e2 c8 96 62 31 d3 17 03 03 00 13 2b 36 fd 7d 11 |...b1......+6.}.| +00000060 2a c8 58 80 68 2e 09 94 e7 0b 32 5a d9 5c |*.X.h.....2Z.\| diff --git a/src/crypto/tls/testdata/Client-TLSv13-KeyUpdate b/src/crypto/tls/testdata/Client-TLSv13-KeyUpdate index d1efba928c5..b52de8198ec 100644 --- a/src/crypto/tls/testdata/Client-TLSv13-KeyUpdate +++ b/src/crypto/tls/testdata/Client-TLSv13-KeyUpdate @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 00 01 00 00 fc 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,96 +7,97 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000080 01 00 00 81 00 05 00 05 01 00 00 00 00 00 0a 00 |................| 00000090 0a 00 08 00 1d 00 17 00 18 00 19 00 0b 00 02 01 |................| -000000a0 00 00 0d 00 1a 00 18 08 04 04 03 08 07 08 05 08 |................| -000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 ff |................| -000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| -000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| -000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| -000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| +000000a0 00 00 0d 00 20 00 1e 08 04 04 03 08 07 08 05 08 |.... ...........| +000000b0 06 04 01 05 01 06 01 05 03 06 03 02 01 02 03 fe |................| +000000c0 61 fe 62 08 08 ff 01 00 01 00 00 12 00 00 00 2b |a.b............+| +000000d0 00 09 08 03 04 03 03 03 02 03 01 00 33 00 26 00 |............3.&.| +000000e0 24 00 1d 00 20 2f e5 7d a3 47 cd 62 43 15 28 da |$... /.}.G.bC.(.| +000000f0 ac 5f bb 29 07 30 ff f6 84 af c4 cf c2 ed 90 99 |._.).0..........| +00000100 5f 58 cb 3b 74 |_X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 7a 02 00 00 76 03 03 a2 49 b5 61 fe |....z...v...I.a.| -00000010 e3 52 ca 87 58 57 0f ec bc 71 51 a9 50 7c ac 5e |.R..XW...qQ.P|.^| -00000020 af 4e 47 56 81 6c 92 d9 10 3d d0 20 00 00 00 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fa |R.:&]G.k...tP.n.| -000000d0 1b 3f 17 3b 21 f7 fa f7 c7 c3 e3 14 05 09 76 b2 |.?.;!.........v.| -000000e0 27 66 bc 42 7e 49 4b ff 3a f1 3f a3 1a d4 9e 03 |'f.B~IK.:.?.....| -000000f0 3f b6 a8 87 98 50 f3 d8 cb 8b a2 e9 2a ea ff bc |?....P......*...| -00000100 50 18 d0 57 58 c5 e9 c8 96 67 01 8b e2 a3 f4 77 |P..WX....g.....w| -00000110 5e 1d 93 89 b6 f6 57 7d 93 b6 62 86 0a 21 18 56 |^.....W}..b..!.V| -00000120 8c 14 25 df 47 1a b3 23 e6 99 d1 fc dc 07 0a 38 |..%.G..#.......8| -00000130 9a 05 c8 3f 23 5c c5 d3 c4 48 fb b2 fd 9f 83 37 |...?#\...H.....7| -00000140 1d 0c 85 9c 2b e6 ae 42 aa ad d4 5a 9e 49 89 b7 |....+..B...Z.I..| -00000150 b0 c2 c5 ec 42 89 88 87 6e 54 3d 73 b2 f1 5f 0f |....B...nT=s.._.| -00000160 4b 49 3f 6b a3 8f 5f 99 bf fe af e9 25 ac 27 b7 |KI?k.._.....%.'.| -00000170 e7 96 bb 4a c8 e8 9e f1 2c 23 c2 e7 96 ba b4 fe |...J....,#......| -00000180 d5 94 b5 72 82 bd 7f c2 e1 af b4 bd db c7 15 20 |...r........... | -00000190 85 60 bb 02 f6 4b ef 09 3e a1 4e b9 77 64 0a 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|.Z..U..e..0...E3| +00000070 5c 96 19 ab 2b 93 6a 44 95 a7 b4 71 66 25 60 14 |\...+.jD...qf%`.| +00000080 03 03 00 01 01 17 03 03 00 17 bf cb c6 b0 27 53 |..............'S| +00000090 c5 06 d0 9b f5 54 8e ac a2 07 d7 06 50 b5 05 5f |.....T......P.._| +000000a0 54 17 03 03 02 6d 74 98 8f 37 97 77 f6 ec b3 2e |T....mt..7.w....| +000000b0 06 88 e5 e2 6a e8 dd 56 d0 ae e6 fd 64 73 8e 1d |....j..V....ds..| +000000c0 00 4b 85 a6 20 96 2a 21 ee 4b 0e 49 b9 64 b2 8f |.K.. .*!.K.I.d..| +000000d0 99 27 ed a5 82 40 99 b1 9b 72 35 f4 ab ad 90 ac |.'...@...r5.....| +000000e0 43 0a 35 96 30 5f 40 16 51 e7 5f c5 06 df 68 13 |C.5.0_@.Q._...h.| +000000f0 91 1b e4 da 1e 89 0c f3 d6 87 a6 0d 39 08 cc db |............9...| +00000100 fb 30 d4 7f 27 e5 c4 b3 6a 09 b9 f5 c5 0f 00 1b |.0..'...j.......| +00000110 b3 9c a0 0e 28 52 92 e6 34 b8 11 24 55 1c 49 96 |....(R..4..$U.I.| +00000120 a5 7f 00 dc 7a e7 38 fc 98 e3 b3 ec 54 73 45 62 |....z.8.....TsEb| +00000130 43 4b 47 fe 65 4f da 43 fa 6b 9a 6e 87 ed ec 9d |CKG.eO.C.k.n....| +00000140 f3 d0 a6 69 5e 98 0d 6b ae f7 aa 8d 60 e0 46 79 |...i^..k....`.Fy| +00000150 72 6f c1 b0 44 21 6a 62 c3 3a 7f bb f6 ab 16 4a |ro..D!jb.:.....J| +00000160 4c 3c 35 d4 d4 9f 6b 45 f2 a6 3c b7 e0 6e 80 8a |L<5...kE..<..n..| +00000170 93 0c d7 2d 9c 03 f4 92 06 61 59 34 f0 7d 27 1f |...-.....aY4.}'.| +00000180 38 a9 e9 78 f2 b2 3d a7 12 c4 0e ca c7 a1 85 5d |8..x..=........]| +00000190 fd 31 3f ee 31 4e c3 78 0d 10 46 5f 71 fe 7b 92 |.1?.1N.x..F_q.{.| +000001a0 88 0c 0d 1b 54 8a 2d e7 01 7b 77 07 b8 56 d9 d5 |....T.-..{w..V..| +000001b0 3c 76 a3 bc 67 75 a2 96 b3 ae b0 72 80 06 e8 6f |>> Flow 3 (client to server) -00000000 14 03 03 00 01 01 17 03 03 00 35 4d ad c5 c7 cc |..........5M....| -00000010 5a 34 8a f8 5f 71 83 af fa 94 df 2a 94 a0 c4 8e |Z4.._q.....*....| -00000020 5e 00 f7 02 e1 30 62 a5 49 27 58 0b 1f fa 46 98 |^....0b.I'X...F.| -00000030 f0 b8 6f 42 e3 3a 7f 26 77 b6 46 8f ab c6 5d d6 |..oB.:.&w.F...].| -00000040 17 03 03 00 17 90 81 68 7a 48 8d 3b 59 9e 11 6f |.......hzH.;Y..o| -00000050 86 b5 24 e4 d9 e0 60 9f c2 4f 3d 33 |..$...`..O=3| +00000000 14 03 03 00 01 01 17 03 03 00 35 06 03 8b 82 ad |..........5.....| +00000010 01 7e 18 0e 0d 82 ad cb 02 c9 c6 14 2e 3c 02 e2 |.~...........<..| +00000020 4d b5 98 ab a2 05 cc 19 db 8f 83 d0 58 9f 94 61 |M...........X..a| +00000030 66 7e 88 53 82 15 e1 f3 2a f0 89 d5 ab 2a 18 95 |f~.S....*....*..| +00000040 17 03 03 00 17 a9 ea 25 81 ff 26 37 db ad 07 9a |.......%..&7....| +00000050 88 5c 18 2c ae 80 73 2a ea a1 f0 ec |.\.,..s*....| >>> Flow 4 (server to client) -00000000 17 03 03 00 16 94 83 fa cc 66 b4 60 c0 c7 6d b3 |.........f.`..m.| -00000010 6e 8c 84 9d 89 76 61 3d 69 fd 29 |n....va=i.)| +00000000 17 03 03 00 16 a2 b2 37 5e 98 79 be 40 26 fc a8 |.......7^.y.@&..| +00000010 9c 83 51 a2 1c de ef af 35 ac 3c |..Q.....5.<| >>> Flow 5 (client to server) -00000000 17 03 03 00 16 60 cb 39 3d 7d 79 01 88 93 bd bf |.....`.9=}y.....| -00000010 23 3b d1 f3 a4 5e 78 ea cd 0f 5e |#;...^x...^| +00000000 17 03 03 00 16 5c e9 7f 66 e9 de 07 82 f2 3d 68 |.....\..f.....=h| +00000010 f1 b6 de c8 bc e1 7c ca 1b 77 0c |......|..w.| >>> Flow 6 (server to client) -00000000 17 03 03 00 1a 88 13 b4 f1 5f cc 63 1e 99 9f 85 |........._.c....| -00000010 60 ff 0e 97 13 59 64 2a c3 0d 2b ac ca a2 25 |`....Yd*..+...%| +00000000 17 03 03 00 1a 1e 84 5c b8 7d f2 ba 09 29 0e ea |.......\.}...)..| +00000010 f8 ce 60 58 4b 1e 12 f2 ff 66 fe 85 16 0e 66 |..`XK....f....f| >>> Flow 7 (client to server) -00000000 17 03 03 00 1d 4f f2 48 ea b8 d6 75 8e 97 ab 54 |.....O.H...u...T| -00000010 29 57 50 5b 59 40 59 d3 7a 3c 01 43 6a 33 30 bb |)WP[Y@Y.z<.Cj30.| -00000020 d4 40 17 03 03 00 13 18 fc b7 ac eb e7 52 6d f0 |.@...........Rm.| -00000030 d4 d3 03 c6 5f 4e ea e3 7b 4e |...._N..{N| +00000000 17 03 03 00 1d 71 58 8d da 90 05 62 e5 07 50 04 |.....qX....b..P.| +00000010 74 5a ca e0 dc b9 d9 18 5f a0 cd 3b bc 1d 9f 28 |tZ......_..;...(| +00000020 12 71 17 03 03 00 13 26 ec 8a f5 19 fe 6d af 32 |.q.....&.....m.2| +00000030 19 b9 73 69 3d 59 92 97 88 5f |..si=Y..._| diff --git a/src/crypto/tls/testdata/Client-TLSv13-P256-ECDHE b/src/crypto/tls/testdata/Client-TLSv13-P256-ECDHE index e6d81184e10..fa8eecc7c87 100644 --- a/src/crypto/tls/testdata/Client-TLSv13-P256-ECDHE +++ b/src/crypto/tls/testdata/Client-TLSv13-P256-ECDHE @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 01 15 01 00 01 11 03 03 00 00 00 00 00 |................| +00000000 16 03 01 01 1b 01 00 01 17 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,88 +7,88 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 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|.x.!.Q...`...I;.| +00000230 a7 82 51 bb e1 35 ca 4a e5 f7 cf 1c 1e b2 b0 50 |..Q..5.J.......P| +00000240 4a 95 e4 18 e5 66 87 c0 06 9d cf 43 f1 dd 27 69 |J....f.....C..'i| +00000250 24 7c dd ad 3c c5 a8 26 5f a2 17 2f da 78 1b 2d |$|..<..&_../.x.-| +00000260 d7 c7 8d 29 ad 44 d3 a4 92 15 7b 12 99 75 90 32 |...).D....{..u.2| +00000270 90 b7 50 69 87 c6 d3 01 6a 8f 7b 93 0e 11 5e d1 |..Pi....j.{...^.| +00000280 f6 1d fe 40 47 3f 2d d0 7e 9d dd dc ec e7 c1 70 |...@G?-.~......p| +00000290 99 1b 68 1d 3c d4 da 5c c9 e0 78 79 e7 65 e6 3d |..h.<..\..xy.e.=| +000002a0 ff 9f 2b 4c 53 d1 85 0e ed 0b c9 d9 27 c9 b3 77 |..+LS.......'..w| +000002b0 82 b6 f2 06 9f 77 ca c3 ac 81 eb 9f bd 53 59 05 |.....w.......SY.| +000002c0 81 83 f5 fe 44 cb 57 66 dc 2c 52 22 28 f1 4a f5 |....D.Wf.,R"(.J.| +000002d0 26 4c a9 0b 71 1a 9a fc 16 73 0b de d8 46 bf 8e |&L..q....s...F..| +000002e0 d1 41 f1 c6 24 55 a3 50 88 60 25 cc 5d 0f 6c e9 |.A..$U.P.`%.].l.| +000002f0 bf 50 2b a2 a8 57 fe 20 c2 db c4 63 d2 2d e0 97 |.P+..W. ...c.-..| +00000300 bd 36 ca af 81 6f 29 fe 8e e0 ad 4f e8 fb 14 06 |.6...o)....O....| +00000310 f0 16 73 b9 38 b7 0a 70 7b ff 25 0b 74 be 8d 12 |..s.8..p{.%.t...| +00000320 a4 c1 e0 46 21 9a 79 87 34 cd 7e 07 96 5a 01 27 |...F!.y.4.~..Z.'| +00000330 0a 3b 9f b7 17 03 03 00 99 be 00 e8 69 81 30 da |.;..........i.0.| +00000340 0b 72 95 28 1a e9 f2 b8 de 3d d1 d8 9b 77 0b 0f |.r.(.....=...w..| +00000350 46 b5 65 af ce 1f 20 77 c4 1e 4b d0 d5 7a 86 c7 |F.e... w..K..z..| +00000360 d5 15 64 47 dd c2 be 24 be 6c c5 c5 d0 72 34 30 |..dG...$.l...r40| +00000370 99 71 9c 5e 27 82 b2 0e da 36 40 4f bd 33 d4 7f |.q.^'....6@O.3..| +00000380 60 26 47 40 16 c1 06 cf 13 09 bc a6 17 73 98 b1 |`&G@.........s..| +00000390 92 4a de 39 4f 1e 0d f5 18 1a f3 0c bf 29 51 f9 |.J.9O........)Q.| +000003a0 16 e9 e8 43 57 57 07 ca a0 03 18 14 aa 5e 9d 9c |...CWW.......^..| +000003b0 76 9b 88 4c 92 3b 18 c4 51 cc 8a 10 87 4c 6a 45 |v..L.;..Q....LjE| +000003c0 68 d9 86 50 97 81 a4 46 61 28 84 d9 0d e5 65 fc |h..P...Fa(....e.| +000003d0 36 c8 17 03 03 00 35 0f 98 b3 f8 67 dc 66 56 f7 |6.....5....g.fV.| +000003e0 b1 cb f4 dd a8 ce 5d be b2 5e 03 13 ef 99 fe cc |......]..^......| +000003f0 cd f8 d5 5e 30 e5 c4 75 85 0e a4 b0 cb bc f5 9a |...^0..u........| +00000400 20 62 64 53 fc 41 7d ce 93 07 53 d7 | bdS.A}...S.| >>> Flow 3 (client to server) -00000000 14 03 03 00 01 01 17 03 03 00 35 ba 59 57 3e a3 |..........5.YW>.| -00000010 cd 02 7f 7c c2 16 f5 6b ec 42 66 aa a2 7a 3d 47 |...|...k.Bf..z=G| -00000020 43 c9 02 4b a3 72 d0 4d fa f8 32 28 1a 19 16 6a |C..K.r.M..2(...j| -00000030 7c 0e 4a 75 80 94 34 fe 30 7b d0 52 15 48 10 30 ||.Ju..4.0{.R.H.0| -00000040 17 03 03 00 17 5d de 53 df 00 21 ca 6d 69 ff 45 |.....].S..!.mi.E| -00000050 2e 53 57 db 3f 8d d8 6c 5a e1 f8 cc 17 03 03 00 |.SW.?..lZ.......| -00000060 13 43 d9 94 95 41 af 1d 80 a7 f2 28 2a 44 50 8d |.C...A.....(*DP.| -00000070 41 8f 82 09 |A...| +00000000 14 03 03 00 01 01 17 03 03 00 35 71 a7 b4 b8 9d |..........5q....| +00000010 fe e8 89 34 e1 09 bf dd 09 70 66 5b 68 c5 d0 70 |...4.....pf[h..p| +00000020 b2 29 15 8b bd 12 b0 3b 7e 3f e4 61 bb 38 fb 50 |.).....;~?.a.8.P| +00000030 cb 42 34 f6 fa 3b e1 d6 d2 95 52 da bd 21 99 cf |.B4..;....R..!..| +00000040 17 03 03 00 17 df 38 76 c7 b8 58 9a 88 c3 82 5a |......8v..X....Z| +00000050 66 83 7a 10 5d c8 e8 44 01 3c cf 6b 17 03 03 00 |f.z.]..D.<.k....| +00000060 13 ba 4d a6 32 12 9d 24 8e 05 8f 78 09 b9 55 8e |..M.2..$...x..U.| +00000070 67 c1 0e 66 |g..f| diff --git a/src/crypto/tls/testdata/Client-TLSv13-X25519-ECDHE b/src/crypto/tls/testdata/Client-TLSv13-X25519-ECDHE index 4e3eb760e69..49fbea486ec 100644 --- a/src/crypto/tls/testdata/Client-TLSv13-X25519-ECDHE +++ b/src/crypto/tls/testdata/Client-TLSv13-X25519-ECDHE @@ -1,5 +1,5 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 f4 01 00 00 f0 03 03 00 00 00 00 00 |................| +00000000 16 03 01 00 fa 01 00 00 f6 03 03 00 00 00 00 00 |................| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000020 00 00 00 00 00 00 00 00 00 00 00 20 00 00 00 00 |........... ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| @@ -7,84 +7,84 @@ 00000050 cc a9 c0 2f c0 2b c0 30 c0 2c c0 27 c0 13 c0 23 |.../.+.0.,.'...#| 00000060 c0 09 c0 14 c0 0a 00 9c 00 9d 00 3c 00 2f 00 35 |...........<./.5| 00000070 c0 12 00 0a 00 05 c0 11 c0 07 13 01 13 03 13 02 |................| -00000080 01 00 00 75 00 05 00 05 01 00 00 00 00 00 0a 00 |...u............| -00000090 04 00 02 00 1d 00 0b 00 02 01 00 00 0d 00 1a 00 |................| -000000a0 18 08 04 04 03 08 07 08 05 08 06 04 01 05 01 06 |................| -000000b0 01 05 03 06 03 02 01 02 03 ff 01 00 01 00 00 12 |................| -000000c0 00 00 00 2b 00 09 08 03 04 03 03 03 02 03 01 00 |...+............| -000000d0 33 00 26 00 24 00 1d 00 20 2f e5 7d a3 47 cd 62 |3.&.$... /.}.G.b| -000000e0 43 15 28 da ac 5f bb 29 07 30 ff f6 84 af c4 cf |C.(.._.).0......| -000000f0 c2 ed 90 99 5f 58 cb 3b 74 |...._X.;t| +00000080 01 00 00 7b 00 05 00 05 01 00 00 00 00 00 0a 00 |...{............| +00000090 04 00 02 00 1d 00 0b 00 02 01 00 00 0d 00 20 00 |.............. .| +000000a0 1e 08 04 04 03 08 07 08 05 08 06 04 01 05 01 06 |................| +000000b0 01 05 03 06 03 02 01 02 03 fe 61 fe 62 08 08 ff |..........a.b...| +000000c0 01 00 01 00 00 12 00 00 00 2b 00 09 08 03 04 03 |.........+......| +000000d0 03 03 02 03 01 00 33 00 26 00 24 00 1d 00 20 2f |......3.&.$... /| +000000e0 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| +000000f0 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 |.........._X.;t| >>> Flow 2 (server to client) -00000000 16 03 03 00 7a 02 00 00 76 03 03 5d 2e e6 ba 34 |....z...v..]...4| -00000010 6c 42 bb 48 58 fe c5 f0 95 f9 34 11 04 b5 2a f4 |lB.HX.....4...*.| -00000020 f1 16 41 db 14 a0 19 d8 43 7c 09 20 00 00 00 00 |..A.....C|. ....| +00000000 16 03 03 00 7a 02 00 00 76 03 03 b6 2f 04 f6 51 |....z...v.../..Q| +00000010 f2 22 78 92 1a 4d 33 ff fd 95 27 3a 01 b0 b0 e3 |."x..M3...':....| +00000020 fb 4d 28 11 f2 75 50 a1 b4 44 3f 20 00 00 00 00 |.M(..uP..D? ....| 00000030 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| 00000040 00 00 00 00 00 00 00 00 00 00 00 00 13 01 00 00 |................| -00000050 2e 00 2b 00 02 03 04 00 33 00 24 00 1d 00 20 82 |..+.....3.$... .| -00000060 de 1b d1 83 7a e1 46 cc c7 36 15 62 48 07 6b f6 |....z.F..6.bH.k.| -00000070 eb 0a 53 a3 34 cd 34 ee cc 0c d0 c9 02 d5 38 14 |..S.4.4.......8.| -00000080 03 03 00 01 01 17 03 03 00 17 3d 0c 61 12 1b 55 |..........=.a..U| -00000090 6e f4 13 59 c8 4a e7 12 63 5d bf be 34 9f d7 2a |n..Y.J..c]..4..*| -000000a0 c2 17 03 03 02 6d 82 e8 43 93 e4 80 4d a7 d2 cf |.....m..C...M...| -000000b0 43 9d 71 8d cc 78 e8 e9 58 7e 28 53 57 6d 95 1e |C.q..x..X~(SWm..| -000000c0 fb 98 05 ec 66 47 d9 a1 6a b5 f4 28 09 4a 6c 4c |....fG..j..(.JlL| -000000d0 ee a0 1a 86 e7 29 c0 0e d8 e0 ca 2d bb 50 e4 34 |.....).....-.P.4| -000000e0 8d 66 be 54 b5 df 94 fc 69 0e a6 9a 76 8b 8f f5 |.f.T....i...v...| -000000f0 a9 01 1a 1d 8d b0 ae a9 0c 10 58 13 f9 91 80 43 |..........X....C| -00000100 69 f8 3f 03 14 8e 73 1a ce 52 72 86 3d 60 8b 0f |i.?...s..Rr.=`..| -00000110 38 e7 4b 43 f0 b3 4b 12 3a a7 cd 4b ac ef 7d fb |8.KC..K.:..K..}.| -00000120 27 3a 38 36 ad a5 90 eb 57 80 47 99 bc c6 58 55 |':86....W.G...XU| -00000130 15 6f 53 f7 83 ca 2b 89 ae be 23 9a 83 3c 6b b1 |.oS...+...#....| +000000a0 42 17 03 03 02 6d 2c 0b 01 0e 4d 53 bf ca b2 73 |B....m,...MS...s| +000000b0 75 6d 28 b8 3d 70 29 a7 5d 61 0b a0 5f ba aa 00 |um(.=p).]a.._...| +000000c0 e0 47 7b 20 9b b0 d0 a8 95 b5 37 a9 42 63 cc cb |.G{ ......7.Bc..| +000000d0 99 0e 30 30 8c 0a 0d d3 80 99 45 ba f2 62 7a 03 |..00......E..bz.| +000000e0 e4 9c 7f d4 85 ac 60 b9 4b 72 31 22 33 d2 70 72 |......`.Kr1"3.pr| +000000f0 be 0b 0d 12 f3 10 56 ca eb 20 87 b4 fe 5b 0f fe |......V.. ...[..| +00000100 f4 95 3f d9 f1 4b 75 03 99 02 a1 16 ff 92 9f 1b |..?..Ku.........| +00000110 e7 25 bc 02 5c 76 72 22 db 31 38 71 65 ea 43 40 |.%..\vr".18qe.C@| +00000120 16 77 51 de 4a ff 5d 13 f1 71 35 e9 3f e5 0e da |.wQ.J.]..q5.?...| +00000130 43 a9 73 9e 87 25 67 d3 85 c6 ad 51 5e 68 f9 a9 |C.s..%g....Q^h..| +00000140 6b d8 bc 4f a9 32 e2 44 e2 06 5c ae 4d a9 e7 09 |k..O.2.D..\.M...| +00000150 ae 6b d0 ea 30 7b 9d fb e0 f2 7e 68 e5 ef 67 31 |.k..0{....~h..g1| +00000160 2c 64 eb 91 35 a5 81 c9 18 50 d4 ff 28 f7 c9 ba |,d..5....P..(...| +00000170 34 8e f4 97 d9 ca 56 9b 23 39 8a 0c af 58 5b 3e |4.....V.#9...X[>| +00000180 46 65 6c b2 90 c2 9d 89 9f 8a 79 1f b6 2a 83 d5 |Fel.......y..*..| +00000190 51 da 46 5a 6f 94 06 60 01 e1 ad 2e 77 bd ea ae |Q.FZo..`....w...| +000001a0 73 43 ec 28 4c 52 bb cb a7 ae a3 c6 7c 7d 40 9f |sC.(LR......|}@.| +000001b0 96 b8 da ba 5a db b6 83 76 a0 80 6e ff ed 07 3e |....Z...v..n...>| +000001c0 e3 0c 0f cd 1f 06 b1 45 e6 80 e5 35 a5 0c 29 7f |.......E...5..).| +000001d0 35 1a ce 36 58 bd 0a 54 6c 63 3f ec 27 dc 18 e5 |5..6X..Tlc?.'...| +000001e0 6f c8 97 53 88 85 ca f3 f7 ab 8c 3e a7 71 6f 91 |o..S.......>.qo.| +000001f0 36 ef 48 be 14 13 a8 f6 35 61 db f0 5f b0 9d c7 |6.H.....5a.._...| +00000200 38 ad b6 d6 3e 02 a7 5c c9 83 2d c2 a3 f4 09 00 |8...>..\..-.....| +00000210 c3 f5 3a f7 f2 21 84 42 ec ce ea b1 51 07 70 f8 |..:..!.B....Q.p.| +00000220 55 52 ee b0 c6 4e cf 8d d4 3d 2e cb d6 87 f8 f1 |UR...N...=......| +00000230 1e 81 a2 0c ab b5 33 44 a6 e0 19 a4 ab 7f 8e 5f |......3D......._| +00000240 0f 52 36 10 23 49 73 f7 81 a7 47 9b 82 30 b5 fc |.R6.#Is...G..0..| +00000250 dc 02 5d df 2f 5b 04 64 c6 78 4b fc 57 2b 97 bf |..]./[.d.xK.W+..| +00000260 14 dd 4d d5 7d 16 59 21 d7 09 4f 79 9b 4a 6e a3 |..M.}.Y!..Oy.Jn.| +00000270 4d 7d b5 b1 54 fc f6 80 af 3a e0 68 93 c9 c6 30 |M}..T....:.h...0| +00000280 f2 f5 52 cd 1c 7a 0f c7 fa 03 e9 ae c1 d5 f6 71 |..R..z.........q| +00000290 4f bb 6c ec 46 b0 2a b6 29 da 71 59 5d 25 42 5d |O.l.F.*.).qY]%B]| +000002a0 47 17 b8 d1 e8 61 69 51 01 df ce c9 e1 a6 2f e6 |G....aiQ....../.| +000002b0 a8 a9 f1 02 60 44 0e 8e 35 91 60 ac 32 13 2e d4 |....`D..5.`.2...| +000002c0 69 f4 b7 88 79 5b 8c bb 04 1a 0e 94 95 bb 7a 08 |i...y[........z.| +000002d0 f4 2e 25 31 d0 11 27 46 e7 9d ef ac 68 d9 a9 d8 |..%1..'F....h...| +000002e0 39 8e cb 3b fa 07 02 a9 72 56 fb 1e ed 7d 0f 4b |9..;....rV...}.K| +000002f0 cb 95 ef 8f e8 06 09 14 3e a0 62 ef 83 28 9c 67 |........>.b..(.g| +00000300 3f bb cc 7c 8b 94 38 1b 37 b3 16 d9 91 c6 9c 9a |?..|..8.7.......| +00000310 b6 ab 79 17 03 03 00 99 66 27 09 b8 57 f5 e0 1b |..y.....f'..W...| +00000320 5f 42 50 ad 3e 46 1e 58 e7 fc fd 9a 1a 0b 98 49 |_BP.>F.X.......I| +00000330 2f e6 de 6c aa 36 cd 25 e6 b0 e7 cc 6d e5 0a 9b |/..l.6.%....m...| +00000340 b6 12 4d 2c cc 36 1c 86 99 3e ca 14 07 17 fe 3f |..M,.6...>.....?| +00000350 20 43 9d 1f 54 38 f0 99 24 4b 6b af b5 0f 72 3f | C..T8..$Kk...r?| +00000360 e5 99 2f 91 dd 42 a3 63 9b 80 6d fb 17 3c be 1f |../..B.c..m..<..| +00000370 bd 12 ff 38 85 e3 b4 79 17 81 09 81 dd dc ae 27 |...8...y.......'| +00000380 2e 2e a7 a8 76 e3 78 b1 85 92 62 2d f7 68 45 2a |....v.x...b-.hE*| +00000390 cf e2 91 02 d9 1c 12 14 46 d7 33 64 1c 70 d1 dd |........F.3d.p..| +000003a0 66 c1 19 3e 29 df 1f 00 68 e0 f3 50 80 33 6d 99 |f..>)...h..P.3m.| +000003b0 89 17 03 03 00 35 4b 1c 4f ed 92 51 08 9b 5a 58 |.....5K.O..Q..ZX| +000003c0 04 3b 3d 7e c1 d9 f3 a2 01 b6 a0 ce 8f 59 eb c3 |.;=~.........Y..| +000003d0 4f c8 97 12 a1 b0 81 4e 7d 49 ab 5a cc c7 18 67 |O......N}I.Z...g| +000003e0 8a 00 79 6f d9 19 d5 9a 62 23 71 |..yo....b#q| >>> Flow 3 (client to server) -00000000 14 03 03 00 01 01 17 03 03 00 35 7d 5e 95 38 a2 |..........5}^.8.| -00000010 d3 f4 04 59 57 2a 1a 86 ac 12 8e 17 88 fb 52 25 |...YW*........R%| -00000020 1d 19 2c c5 ac 57 c9 bf af 07 e7 c1 4d f3 dd f0 |..,..W......M...| -00000030 13 ad a1 73 07 32 a4 c5 7c 9e ad 5a 88 59 57 4b |...s.2..|..Z.YWK| -00000040 17 03 03 00 17 e2 65 4f bd 1f bb 00 a1 6b ae a4 |......eO.....k..| -00000050 9d d3 d2 6e 7b 62 b5 09 19 d6 8f 1b 17 03 03 00 |...n{b..........| -00000060 13 96 de 94 2b a7 bb c5 4b 7e 02 b2 27 07 4d 49 |....+...K~..'.MI| -00000070 32 2b 83 48 |2+.H| +00000000 14 03 03 00 01 01 17 03 03 00 35 30 2d 51 90 ab |..........50-Q..| +00000010 94 49 1a ac 50 7e e8 2d e0 b5 d7 91 b2 c9 3e af |.I..P~.-......>.| +00000020 a3 ba 44 d1 f2 e9 c4 94 07 5e 24 3d e7 78 92 72 |..D......^$=.x.r| +00000030 66 ee 7c 43 8a 13 aa 78 36 f5 55 8c 35 f4 5d e2 |f.|C...x6.U.5.].| +00000040 17 03 03 00 17 4f 81 1c 2c bd f7 52 90 9b 99 dc |.....O..,..R....| +00000050 1f 24 b2 6d 28 32 ce c3 c9 1f 83 73 17 03 03 00 |.$.m(2.....s....| +00000060 13 ce a7 7c 2a cd 55 52 bc 03 bc 44 37 c6 e0 a1 |...|*.UR...D7...| +00000070 84 60 35 35 |.`55| diff --git a/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndECDSAGiven b/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndECDSAGiven index 3d1ceaf9038..58241e97eec 100644 --- a/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndECDSAGiven +++ b/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndECDSAGiven @@ -1,7 +1,7 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 6d 01 00 00 69 03 03 b0 00 44 aa 86 |....m...i....D..| -00000010 30 87 8e 3f f1 89 9a 4a f6 4c 3b 11 f3 4f e9 9f |0..?...J.L;..O..| -00000020 00 22 47 82 26 57 c7 d0 f9 59 6f 00 00 04 00 2f |."G.&W...Yo..../| +00000000 16 03 01 00 6d 01 00 00 69 03 03 2e 12 ce ae 93 |....m...i.......| +00000010 a4 45 04 1a e9 2a d4 6d 4e 80 d6 b1 39 2c e3 77 |.E...*.mN...9,.w| +00000020 4e f8 0f 8b eb c2 ad 68 dd 60 d9 00 00 04 00 2f |N......h.`...../| 00000030 00 ff 01 00 00 3c 00 16 00 00 00 17 00 00 00 0d |.....<..........| 00000040 00 30 00 2e 04 03 05 03 06 03 08 07 08 08 08 09 |.0..............| 00000050 08 0a 08 0b 08 04 08 05 08 06 04 01 05 01 06 01 |................| @@ -49,10 +49,10 @@ 00000260 f1 6c 04 ed 73 bb b3 43 77 8d 0c 1c f1 0f a1 d8 |.l..s..Cw.......| 00000270 40 83 61 c9 4c 72 2b 9d ae db 46 06 06 4d f4 c1 |@.a.Lr+...F..M..| 00000280 b3 3e c0 d1 bd 42 d4 db fe 3d 13 60 84 5c 21 d3 |.>...B...=.`.\!.| -00000290 3b e9 fa e7 16 03 03 00 23 0d 00 00 1f 02 01 40 |;.......#......@| -000002a0 00 18 08 04 04 03 08 07 08 05 08 06 04 01 05 01 |................| -000002b0 06 01 05 03 06 03 02 01 02 03 00 00 16 03 03 00 |................| -000002c0 04 0e 00 00 00 |.....| +00000290 3b e9 fa e7 16 03 03 00 29 0d 00 00 25 02 01 40 |;.......)...%..@| +000002a0 00 1e 08 04 04 03 08 07 08 05 08 06 04 01 05 01 |................| +000002b0 06 01 05 03 06 03 02 01 02 03 fe 61 fe 62 08 08 |...........a.b..| +000002c0 00 00 16 03 03 00 04 0e 00 00 00 |...........| >>> Flow 3 (client to server) 00000000 16 03 03 02 0a 0b 00 02 06 00 02 03 00 02 00 30 |...............0| 00000010 82 01 fc 30 82 01 5e 02 09 00 9a 30 84 6c 26 35 |...0..^....0.l&5| @@ -87,40 +87,40 @@ 000001e0 be e8 91 b3 da 1a f5 5d a3 23 f5 26 8b 45 70 8d |.......].#.&.Ep.| 000001f0 65 62 9b 7e 01 99 3d 18 f6 10 9a 38 61 9b 2e 57 |eb.~..=....8a..W| 00000200 e4 fa cc b1 8a ce e2 23 a0 87 f0 e1 67 51 eb 16 |.......#....gQ..| -00000210 03 03 00 86 10 00 00 82 00 80 10 ab 2f 0f b9 29 |............/..)| -00000220 9f 26 36 09 00 96 9a 3d 2a 01 50 03 f3 d6 ac fc |.&6....=*.P.....| -00000230 40 76 96 d0 e6 a6 67 89 24 b0 56 80 58 5e 6d 03 |@v....g.$.V.X^m.| -00000240 e3 0f dc 61 d1 de 25 95 8a 54 9f 5b 3e f2 31 dd |...a..%..T.[>.1.| -00000250 14 2a e2 de 7b 70 66 b5 ed 95 d9 cc 6f c0 b3 a1 |.*..{pf.....o...| -00000260 bb 41 b2 0f 7d e8 ce b5 11 eb 99 e2 ce c0 33 bc |.A..}.........3.| -00000270 6a 67 10 84 d2 dd ac 15 8f 8e aa 2b 1a 7b ca d3 |jg.........+.{..| -00000280 bb 4b 92 c4 b9 2b 08 c1 0d b2 cf 96 63 64 9d 12 |.K...+......cd..| -00000290 a6 93 cd 21 3b bc 8e 94 72 76 16 03 03 00 93 0f |...!;...rv......| -000002a0 00 00 8f 04 03 00 8b 30 81 88 02 42 00 d5 05 54 |.......0...B...T| -000002b0 b2 68 a5 04 d6 3c 7b 7d c1 be e3 d1 b4 25 42 d6 |.h...<{}.....%B.| -000002c0 2a 3a 2e ea 73 0d 57 ba 0f 96 78 66 c2 c5 d7 57 |*:..s.W...xf...W| -000002d0 79 9c 22 8b 76 e9 45 ff ef 92 e9 43 3e b8 8b b4 |y.".v.E....C>...| -000002e0 cf 3f 67 aa 70 d1 e8 a2 1c a8 3d 24 a2 78 02 42 |.?g.p.....=$.x.B| -000002f0 01 b2 17 64 66 2f 2e 0d 2d b9 1d 67 45 de 48 9e |...df/..-..gE.H.| -00000300 32 f2 1f 79 38 39 b8 bb 8b 7f 82 e9 46 fd 9b 1b |2..y89......F...| -00000310 b3 dd a4 9c 15 b2 a2 88 4c f7 42 a2 62 92 c0 d0 |........L.B.b...| -00000320 a1 78 aa 8b 2d 78 4f 02 5a f7 eb ca c7 34 fc b6 |.x..-xO.Z....4..| -00000330 6c 6e 14 03 03 00 01 01 16 03 03 00 40 bd 47 9b |ln..........@.G.| -00000340 ce 31 2c 09 d3 a8 2c bb 28 0c e8 bd 01 a9 54 34 |.1,...,.(.....T4| -00000350 a5 74 af e0 d2 38 f3 1b fa d0 2b a6 39 24 ae de |.t...8....+.9$..| -00000360 0a cf 4b c0 a2 3b bf 80 23 71 0a 60 ca 94 b7 23 |..K..;..#q.`...#| -00000370 80 e3 89 89 42 74 0b a1 c6 f6 d2 c0 79 |....Bt......y| +00000210 03 03 00 86 10 00 00 82 00 80 0d 47 fa 02 55 0e |...........G..U.| +00000220 68 34 b2 f4 97 16 cc d8 d8 39 23 8a 90 09 3b 70 |h4.......9#...;p| +00000230 76 1a fa 3d 58 86 f5 2d 0f d3 3c 1f 4b 8c 03 08 |v..=X..-..<.K...| +00000240 f4 ad 5f dc 4c 8e 1e 6e 88 db c5 e0 9b ba 84 15 |.._.L..n........| +00000250 db 85 67 04 a1 e7 15 ef 41 9e aa f7 3b b8 f8 54 |..g.....A...;..T| +00000260 3c 72 84 a8 e4 3d 6b 2c 70 03 89 7f 78 79 6e ee |....aU....| +00000320 75 7d 89 ec ac 6e 53 18 2f 7b fd a1 41 f4 c0 ad |u}...nS./{..A...| +00000330 ed 14 03 03 00 01 01 16 03 03 00 40 b7 b5 d4 ba |...........@....| +00000340 10 a3 fe a6 c8 0a 35 fe 7c 07 a7 fe 45 ac ec e2 |......5.|...E...| +00000350 a8 6a d2 46 f0 ce 70 43 fb a5 c4 d5 8f d0 15 e2 |.j.F..pC........| +00000360 a3 ff 43 ee 09 f9 f4 c2 64 60 2b af eb ee 8f af |..C.....d`+.....| +00000370 dc 03 dd 29 cf 0c 6e f4 b4 df 2e f7 |...)..n.....| >>> Flow 4 (server to client) 00000000 14 03 03 00 01 01 16 03 03 00 40 00 00 00 00 00 |..........@.....| -00000010 00 00 00 00 00 00 00 00 00 00 00 54 52 4a 33 9e |...........TRJ3.| -00000020 bb 59 7e 21 03 a6 23 bd 68 18 43 b5 c5 c5 37 a2 |.Y~!..#.h.C...7.| -00000030 6f ac 8c 78 c5 cf 8f e6 01 df 17 53 45 6f 1a e0 |o..x.......SEo..| -00000040 9c 4a 3d 2c cb 0d 55 7d 32 81 ec 17 03 03 00 40 |.J=,..U}2......@| +00000010 00 00 00 00 00 00 00 00 00 00 00 76 48 4f 08 4f |...........vHO.O| +00000020 29 70 80 84 a0 09 d5 f8 4a 38 1d f0 8e 39 1c ce |)p......J8...9..| +00000030 e7 9c 4c ba 04 58 60 fb ff 96 c5 34 47 fc 63 0f |..L..X`....4G.c.| +00000040 db 36 ef fd 7e 08 c4 5a 9d 7e 99 17 03 03 00 40 |.6..~..Z.~.....@| 00000050 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| -00000060 ba 75 93 00 86 1c bc 66 9e 27 2f 2b 5a 68 0e 44 |.u.....f.'/+Zh.D| -00000070 81 15 0d 67 e6 ee 7a 43 08 78 93 71 91 00 56 0e |...g..zC.x.q..V.| -00000080 c6 e1 73 4b af 2f e6 e0 92 4d e5 35 ea 53 7c 45 |..sK./...M.5.S|E| +00000060 da 1d 10 05 da c8 00 0c 1a d9 94 8c a9 d7 40 38 |..............@8| +00000070 9a cc b0 c0 48 e0 e6 0f f9 81 2a d2 5c dd 99 14 |....H.....*.\...| +00000080 c4 48 ad 54 4c c7 02 7e ac c1 d3 cf 55 a7 12 b9 |.H.TL..~....U...| 00000090 15 03 03 00 30 00 00 00 00 00 00 00 00 00 00 00 |....0...........| -000000a0 00 00 00 00 00 8d 7e 99 bb 93 bd 5d ba 31 b0 0d |......~....].1..| -000000b0 1f 76 95 50 7c 1e 24 62 9d 05 65 3f ee b7 c2 24 |.v.P|.$b..e?...$| -000000c0 13 60 43 69 3a |.`Ci:| +000000a0 00 00 00 00 00 58 2c 48 53 cd f2 51 f3 20 45 b1 |.....X,HS..Q. E.| +000000b0 60 44 0b 8f 7b 21 dd 15 4b 85 6f 5a 25 83 82 93 |`D..{!..K.oZ%...| +000000c0 c1 95 27 3e b7 |..'>.| diff --git a/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndEd25519Given b/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndEd25519Given index 1c3b08f06fa..f12bc0276f5 100644 --- a/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndEd25519Given +++ b/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndEd25519Given @@ -1,7 +1,7 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 6d 01 00 00 69 03 03 aa ad c9 dc 56 |....m...i......V| -00000010 79 2e da 42 a6 b2 9e 0a 85 a6 1b e0 5e cd 4e f5 |y..B........^.N.| -00000020 93 93 0c d5 62 a8 53 17 10 f7 e6 00 00 04 00 2f |....b.S......../| +00000000 16 03 01 00 6d 01 00 00 69 03 03 d5 77 47 d2 82 |....m...i...wG..| +00000010 17 ca 91 e7 c1 1d 0b c6 92 89 de 03 60 b6 aa 0d |............`...| +00000020 59 3f 24 dc 15 96 06 ba 8a b0 d6 00 00 04 00 2f |Y?$............/| 00000030 00 ff 01 00 00 3c 00 16 00 00 00 17 00 00 00 0d |.....<..........| 00000040 00 30 00 2e 04 03 05 03 06 03 08 07 08 08 08 09 |.0..............| 00000050 08 0a 08 0b 08 04 08 05 08 06 04 01 05 01 06 01 |................| @@ -49,10 +49,10 @@ 00000260 f1 6c 04 ed 73 bb b3 43 77 8d 0c 1c f1 0f a1 d8 |.l..s..Cw.......| 00000270 40 83 61 c9 4c 72 2b 9d ae db 46 06 06 4d f4 c1 |@.a.Lr+...F..M..| 00000280 b3 3e c0 d1 bd 42 d4 db fe 3d 13 60 84 5c 21 d3 |.>...B...=.`.\!.| -00000290 3b e9 fa e7 16 03 03 00 23 0d 00 00 1f 02 01 40 |;.......#......@| -000002a0 00 18 08 04 04 03 08 07 08 05 08 06 04 01 05 01 |................| -000002b0 06 01 05 03 06 03 02 01 02 03 00 00 16 03 03 00 |................| -000002c0 04 0e 00 00 00 |.....| +00000290 3b e9 fa e7 16 03 03 00 29 0d 00 00 25 02 01 40 |;.......)...%..@| +000002a0 00 1e 08 04 04 03 08 07 08 05 08 06 04 01 05 01 |................| +000002b0 06 01 05 03 06 03 02 01 02 03 fe 61 fe 62 08 08 |...........a.b..| +000002c0 00 00 16 03 03 00 04 0e 00 00 00 |...........| >>> Flow 3 (client to server) 00000000 16 03 03 01 3c 0b 00 01 38 00 01 35 00 01 32 30 |....<...8..5..20| 00000010 82 01 2e 30 81 e1 a0 03 02 01 02 02 10 17 d1 81 |...0............| @@ -74,36 +74,36 @@ 00000110 8a 4e 34 40 39 d6 b3 10 dc 19 fe a0 22 71 b3 f5 |.N4@9......."q..| 00000120 8f a1 58 0d cd f4 f1 85 24 bf e6 3d 14 df df ed |..X.....$..=....| 00000130 0e e1 17 d8 11 a2 60 d0 8a 37 23 2a c2 46 aa 3a |......`..7#*.F.:| -00000140 08 16 03 03 00 86 10 00 00 82 00 80 14 f2 ac 22 |..............."| -00000150 fb 0b f8 03 a7 cf 23 d5 ea 9f b0 f2 64 ae 41 fe |......#.....d.A.| -00000160 33 f7 54 69 f5 41 b7 c1 91 6d 2b 3e 14 2a f6 c8 |3.Ti.A...m+>.*..| -00000170 96 45 00 28 13 f5 2f de 35 f9 64 89 5c 99 3e 89 |.E.(../.5.d.\.>.| -00000180 06 ff 59 56 69 db 5f 6e 02 84 dd 1c 44 7b 86 e8 |..YVi._n....D{..| -00000190 e3 d9 03 f1 16 9e 06 23 00 43 91 ec a9 dd da a4 |.......#.C......| -000001a0 ac fe 5b f8 62 f9 76 19 38 83 54 b4 8c 0b 02 f0 |..[.b.v.8.T.....| -000001b0 fa 7a 8e 2e da 9d e1 4a c6 51 92 9b f6 4b a1 31 |.z.....J.Q...K.1| -000001c0 c9 64 b2 a6 9a 01 52 86 b3 7a 43 17 16 03 03 00 |.d....R..zC.....| -000001d0 48 0f 00 00 44 08 07 00 40 29 35 71 34 aa b1 f1 |H...D...@)5q4...| -000001e0 64 08 4e 06 43 db 00 f7 f5 98 8e b6 51 d7 c4 b5 |d.N.C.......Q...| -000001f0 2b fa 56 8b bd 7b 18 f2 81 e9 2f 81 82 d8 90 e7 |+.V..{..../.....| -00000200 5b bc 72 7e f7 97 43 df cd 07 bf 7b ae 60 08 8b |[.r~..C....{.`..| -00000210 0a 71 c5 bf f0 7a 3e cc 0b 14 03 03 00 01 01 16 |.q...z>.........| -00000220 03 03 00 40 85 4f e0 c0 f3 3e a4 51 68 d6 ec 1b |...@.O...>.Qh...| -00000230 f1 4b 3e 0e 13 84 87 e3 3c 9a 5f 67 75 3a ad 08 |.K>.....<._gu:..| -00000240 be 29 15 b0 1f 62 27 fd d8 dd 58 b1 65 e7 e2 db |.)...b'...X.e...| -00000250 fe 55 a5 2d 2e 71 59 07 ad 12 12 80 12 bb 26 36 |.U.-.qY.......&6| -00000260 93 fb ea b1 |....| +00000140 08 16 03 03 00 86 10 00 00 82 00 80 42 fe 7f 60 |............B..`| +00000150 76 89 08 e1 84 cf d5 95 ce aa 32 58 5c 16 73 d0 |v.........2X\.s.| +00000160 2c c7 c9 24 e8 5a e1 11 0c 6a 15 c1 52 3f 5f 54 |,..$.Z...j..R?_T| +00000170 db 9c f3 a3 e6 97 ab 97 1c c4 a2 16 a6 85 1a 2e |................| +00000180 f1 36 4e 8e 89 a9 57 16 ae 34 8d ab 2f ab 65 18 |.6N...W..4../.e.| +00000190 23 57 28 a8 ea 4d b8 09 54 de c9 2a d2 46 b7 93 |#W(..M..T..*.F..| +000001a0 66 5b 24 e2 1a ca e8 45 20 9f fa b3 6f 0f 47 0c |f[$....E ...o.G.| +000001b0 09 99 54 38 8e 7f 57 88 87 ec 86 e4 1c e9 86 5e |..T8..W........^| +000001c0 8b 97 07 72 54 04 b7 ef 65 7f 86 ef 16 03 03 00 |...rT...e.......| +000001d0 48 0f 00 00 44 08 07 00 40 a2 a6 b5 d9 20 3f cd |H...D...@.... ?.| +000001e0 fe e6 ba b9 21 3c 3e b7 a8 f9 7b ab 5f 9b df 12 |....!<>...{._...| +000001f0 c9 a1 fe ae 46 3f f3 4d c7 01 c7 4c 0d 87 2d 9b |....F?.M...L..-.| +00000200 15 75 4e 32 11 9e 43 6d 54 23 17 fe b8 d9 9f 72 |.uN2..CmT#.....r| +00000210 00 42 89 98 70 49 0a 40 08 14 03 03 00 01 01 16 |.B..pI.@........| +00000220 03 03 00 40 90 d6 7f dc 40 3e 85 0a 70 5e 4a 65 |...@....@>..p^Je| +00000230 bf b4 f1 19 5e 79 24 fc 97 63 51 a3 42 44 17 01 |....^y$..cQ.BD..| +00000240 e0 73 15 26 ad 35 d1 03 42 63 ba 16 a0 70 49 ef |.s.&.5..Bc...pI.| +00000250 7d ce 34 a9 28 10 10 55 32 6d 56 d2 46 81 9b 40 |}.4.(..U2mV.F..@| +00000260 4f 9a 99 ab |O...| >>> Flow 4 (server to client) 00000000 14 03 03 00 01 01 16 03 03 00 40 00 00 00 00 00 |..........@.....| -00000010 00 00 00 00 00 00 00 00 00 00 00 f4 ed 23 ce da |.............#..| -00000020 73 5f ef 6b a2 82 3d a5 c6 f1 fd 8f a0 47 4e 34 |s_.k..=......GN4| -00000030 f9 7c d0 67 49 00 11 c3 76 83 23 3f 99 41 d5 5c |.|.gI...v.#?.A.\| -00000040 aa 9f 97 66 b7 0a 59 ba f3 40 83 17 03 03 00 40 |...f..Y..@.....@| +00000010 00 00 00 00 00 00 00 00 00 00 00 f6 d7 a7 9d 29 |...............)| +00000020 99 20 f9 5a 0c 6e 33 f1 4e 5b e6 e8 56 ea 28 ca |. .Z.n3.N[..V.(.| +00000030 1b a8 b3 0a 0f ec e5 be c6 fe 94 09 f8 05 0f 18 |................| +00000040 32 4b d5 46 32 01 59 64 3f b7 e4 17 03 03 00 40 |2K.F2.Yd?......@| 00000050 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| -00000060 82 66 85 d7 47 a6 5a 19 4f 89 5c 56 43 cb 6a bd |.f..G.Z.O.\VC.j.| -00000070 1b ae 46 40 7d e8 a9 7b 57 04 91 8b d5 de 24 f1 |..F@}..{W.....$.| -00000080 c0 df 37 45 e9 af d7 c5 1c e7 ee 80 0d 61 2a 7f |..7E.........a*.| +00000060 9a 84 8a 6e f8 25 2c 1b 9f 8f 6d f3 ec 7e 81 7a |...n.%,...m..~.z| +00000070 da 10 3d bd 86 ae 3c 9f 5c f6 71 24 33 4a 30 54 |..=...<.\.q$3J0T| +00000080 35 fc 4b 6f 0e 6a 8a 95 6c cd b0 cb 8c 7e 60 06 |5.Ko.j..l....~`.| 00000090 15 03 03 00 30 00 00 00 00 00 00 00 00 00 00 00 |....0...........| -000000a0 00 00 00 00 00 5a 97 f3 38 e5 3a f1 07 79 b7 eb |.....Z..8.:..y..| -000000b0 ed 85 57 3a 96 16 51 38 85 86 ec 1b 9b 48 82 9c |..W:..Q8.....H..| -000000c0 05 bf 4d e5 fb |..M..| +000000a0 00 00 00 00 00 fd 8e a6 2a 05 f9 71 12 07 ac d7 |........*..q....| +000000b0 0e 13 30 bc e5 75 e4 79 df 81 5c 57 8e 3c e5 58 |..0..u.y..\W.<.X| +000000c0 21 01 38 43 87 |!.8C.| diff --git a/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndGiven b/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndGiven index 3dec0deeb16..951c40afbe5 100644 --- a/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndGiven +++ b/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndGiven @@ -1,7 +1,7 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 6d 01 00 00 69 03 03 e7 7e 1f 56 df |....m...i...~.V.| -00000010 f1 1b e5 92 47 3b fb 25 a6 57 7d 13 47 08 f0 0f |....G;.%.W}.G...| -00000020 5b 64 64 00 d3 25 33 e5 a5 5b e3 00 00 04 00 2f |[dd..%3..[...../| +00000000 16 03 01 00 6d 01 00 00 69 03 03 a1 c3 e0 96 ea |....m...i.......| +00000010 eb ad 43 f4 d4 30 bd a0 d0 93 c8 cb b1 6c e5 22 |..C..0.......l."| +00000020 0b 1f c7 e2 5e cd e1 24 4b 5a 13 00 00 04 00 2f |....^..$KZ...../| 00000030 00 ff 01 00 00 3c 00 16 00 00 00 17 00 00 00 0d |.....<..........| 00000040 00 30 00 2e 04 03 05 03 06 03 08 07 08 08 08 09 |.0..............| 00000050 08 0a 08 0b 08 04 08 05 08 06 04 01 05 01 06 01 |................| @@ -49,10 +49,10 @@ 00000260 f1 6c 04 ed 73 bb b3 43 77 8d 0c 1c f1 0f a1 d8 |.l..s..Cw.......| 00000270 40 83 61 c9 4c 72 2b 9d ae db 46 06 06 4d f4 c1 |@.a.Lr+...F..M..| 00000280 b3 3e c0 d1 bd 42 d4 db fe 3d 13 60 84 5c 21 d3 |.>...B...=.`.\!.| -00000290 3b e9 fa e7 16 03 03 00 23 0d 00 00 1f 02 01 40 |;.......#......@| -000002a0 00 18 08 04 04 03 08 07 08 05 08 06 04 01 05 01 |................| -000002b0 06 01 05 03 06 03 02 01 02 03 00 00 16 03 03 00 |................| -000002c0 04 0e 00 00 00 |.....| +00000290 3b e9 fa e7 16 03 03 00 29 0d 00 00 25 02 01 40 |;.......)...%..@| +000002a0 00 1e 08 04 04 03 08 07 08 05 08 06 04 01 05 01 |................| +000002b0 06 01 05 03 06 03 02 01 02 03 fe 61 fe 62 08 08 |...........a.b..| +000002c0 00 00 16 03 03 00 04 0e 00 00 00 |...........| >>> Flow 3 (client to server) 00000000 16 03 03 01 fd 0b 00 01 f9 00 01 f6 00 01 f3 30 |...............0| 00000010 82 01 ef 30 82 01 58 a0 03 02 01 02 02 10 5c 19 |...0..X.......\.| @@ -86,40 +86,40 @@ 000001d0 ac 11 b1 28 56 be 1d cd 61 62 84 09 bf d6 80 c6 |...(V...ab......| 000001e0 45 8d 82 2c b4 d8 83 9b db c9 22 b7 2a 12 11 7b |E..,......".*..{| 000001f0 fa 02 3b c1 c9 ff ea c9 9d a8 49 d3 95 d7 d5 0e |..;.......I.....| -00000200 e5 35 16 03 03 00 86 10 00 00 82 00 80 7f 38 c9 |.5............8.| -00000210 56 ed de 7d a6 2c dc cc 24 61 ea d3 8a fc b8 18 |V..}.,..$a......| -00000220 b8 e5 50 3e c3 d1 ca cf f7 0c d9 9b 22 d8 6d 0f |..P>........".m.| -00000230 71 e7 dd 7c 24 84 c6 f1 6a ac a0 3d ea d7 65 24 |q..|$...j..=..e$| -00000240 d7 3a 17 d5 b7 ec f7 03 bc 58 3a 01 d5 08 27 25 |.:.......X:...'%| -00000250 b9 2f 3b 96 cb d5 7c 12 20 f4 f1 91 58 13 fb 50 |./;...|. ...X..P| -00000260 f8 d5 5c e4 43 85 e8 41 37 3e ff fa a6 64 92 4d |..\.C..A7>...d.M| -00000270 bd d4 96 59 bd 94 f1 95 21 ad 75 1e 0d a2 8d 30 |...Y....!.u....0| -00000280 a3 82 f4 56 0f ba 5d 40 32 7f 0c 5f 5a 16 03 03 |...V..]@2.._Z...| -00000290 00 88 0f 00 00 84 08 04 00 80 39 b4 f4 68 e9 96 |..........9..h..| -000002a0 01 53 95 31 26 fa 3c 70 46 9f ba 62 b4 37 ea a6 |.S.1&..Gy..^p| -000002f0 30 8c 11 3f 27 43 4f 5d 81 89 83 39 9d fe 0c c3 |0..?'CO]...9....| -00000300 af 40 8d 2a 41 bf 57 67 7a df b4 89 29 10 9a 84 |.@.*A.Wgz...)...| -00000310 ff 8c 2f 58 1a 0a b9 62 4e 8e 14 03 03 00 01 01 |../X...bN.......| -00000320 16 03 03 00 40 7c 7a 79 ae 84 60 b8 95 83 30 78 |....@|zy..`...0x| -00000330 e9 6e 02 36 52 85 5a 6a a7 b5 f5 6d 4d a9 09 9d |.n.6R.Zj...mM...| -00000340 43 9d 46 da d0 cf 75 25 49 e1 79 0b 23 2d 85 c2 |C.F...u%I.y.#-..| -00000350 fd 5d 90 08 f5 75 81 ab 01 a0 f4 93 12 87 fb e3 |.]...u..........| -00000360 9b 99 4d fa c5 |..M..| +00000200 e5 35 16 03 03 00 86 10 00 00 82 00 80 67 71 9e |.5...........gq.| +00000210 9c e5 a7 ee 24 e8 a2 0d eb 46 84 de e5 61 84 56 |....$....F...a.V| +00000220 1c f3 b7 65 cd af 4e c6 0f 55 0e e6 cb 91 d8 b1 |...e..N..U......| +00000230 21 85 fa d6 46 16 42 61 58 88 13 f7 10 42 55 42 |!...F.BaX....BUB| +00000240 e5 9f 65 bb 99 04 b0 94 bd 12 37 8f d6 23 59 cc |..e.......7..#Y.| +00000250 24 7c 1b 35 be c0 a3 63 40 74 b1 e1 e1 53 83 a6 |$|.5...c@t...S..| +00000260 7d bc 85 76 4f 08 d6 5e 5a 44 05 6a 60 0b 4e 90 |}..vO..^ZD.j`.N.| +00000270 3d a5 08 25 af fd e4 cd 96 2f b1 db 76 13 e5 3c |=..%...../..v..<| +00000280 92 b8 89 03 91 e8 4f 9e 72 85 5c 9b 6d 16 03 03 |......O.r.\.m...| +00000290 00 88 0f 00 00 84 08 04 00 80 10 b9 b8 79 48 3d |.............yH=| +000002a0 a2 64 85 da d5 20 a0 73 be 51 68 da 58 e2 5a 36 |.d... .s.Qh.X.Z6| +000002b0 7b 4a 50 0c 94 5e da 40 0d 8f ee 8a 45 95 d2 35 |{JP..^.@....E..5| +000002c0 cf e5 87 75 a4 65 e7 1b a4 9e f3 1e ec 10 dd 2f |...u.e........./| +000002d0 1d 94 85 5f 99 41 49 d2 34 44 36 06 bf 3b af d3 |..._.AI.4D6..;..| +000002e0 66 b4 a1 5b df 33 0e d7 00 fc 40 1c 28 70 0e bc |f..[.3....@.(p..| +000002f0 e5 3f d0 82 86 31 9b 9a e1 67 00 b1 19 fe 4e a3 |.?...1...g....N.| +00000300 4c 33 14 4f 0b 8a bd dd 2a 8a eb 10 66 ac 53 9e |L3.O....*...f.S.| +00000310 82 dc 0e b2 64 47 12 3f 82 93 14 03 03 00 01 01 |....dG.?........| +00000320 16 03 03 00 40 d9 d1 b3 59 64 bb e0 1a 53 a4 de |....@...Yd...S..| +00000330 0f 9a eb 15 3c 97 48 d0 95 65 b6 25 1f dd 0c 7e |....<.H..e.%...~| +00000340 ea 02 a2 9a 9f 6a a3 b3 49 8f a4 2f 80 bc 06 54 |.....j..I../...T| +00000350 61 f4 07 d5 3f 5c 0d 8d f8 74 aa c3 5f b3 73 cd |a...?\...t.._.s.| +00000360 a0 61 cb 0a 8c |.a...| >>> Flow 4 (server to client) 00000000 14 03 03 00 01 01 16 03 03 00 40 00 00 00 00 00 |..........@.....| -00000010 00 00 00 00 00 00 00 00 00 00 00 48 61 67 c0 1e |...........Hag..| -00000020 09 79 82 cc 55 60 fa e5 bd 1a 1d 14 d3 25 e6 4b |.y..U`.......%.K| -00000030 b7 a6 47 64 01 65 12 b3 37 42 1a 13 d9 90 12 7e |..Gd.e..7B.....~| -00000040 ea d8 30 39 e2 25 5e 9a 05 61 11 17 03 03 00 40 |..09.%^..a.....@| +00000010 00 00 00 00 00 00 00 00 00 00 00 e4 6c 6c 34 ee |............ll4.| +00000020 24 99 16 4f 05 87 11 e0 fa 62 ef dd 03 9d 01 58 |$..O.....b.....X| +00000030 f1 b4 c8 8f f1 ff ce 5a 43 59 c2 6c bb 62 41 b9 |.......ZCY.l.bA.| +00000040 c8 95 2b 13 39 fa 97 9c 2e af d6 17 03 03 00 40 |..+.9..........@| 00000050 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| -00000060 cf c5 73 08 e9 15 25 b6 d8 e3 fa 0c a1 25 33 75 |..s...%......%3u| -00000070 8a 2e 66 03 c2 2d 50 c7 e1 10 b4 2a 0c 88 87 90 |..f..-P....*....| -00000080 04 4a 80 26 85 4b fd 9a 4f 0e b1 2c f0 18 57 f5 |.J.&.K..O..,..W.| +00000060 ce 79 bc 52 f1 f8 c9 20 10 3b c2 fd f4 69 cf 13 |.y.R... .;...i..| +00000070 b6 80 87 11 31 e9 0b 66 6b 63 0e 61 0e 35 9d de |....1..fkc.a.5..| +00000080 43 bd 40 94 55 7e 67 41 db de 42 78 cd 69 68 45 |C.@.U~gA..Bx.ihE| 00000090 15 03 03 00 30 00 00 00 00 00 00 00 00 00 00 00 |....0...........| -000000a0 00 00 00 00 00 ce e0 a1 71 be 3d 1e b0 bd 06 4c |........q.=....L| -000000b0 1f 5b 10 8d 77 18 e0 c5 81 c9 4e 1b 3b 96 f6 6d |.[..w.....N.;..m| -000000c0 88 03 53 54 30 |..ST0| +000000a0 00 00 00 00 00 f2 19 81 09 54 d5 80 ac e4 b4 eb |.........T......| +000000b0 d6 10 20 7b f9 44 4a 72 ed 2f 4a c5 55 26 f2 46 |.. {.DJr./J.U&.F| +000000c0 e4 99 3a 68 2a |..:h*| diff --git a/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndPKCS1v15Given b/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndPKCS1v15Given index 8efbc912d95..b2bb3c23034 100644 --- a/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndPKCS1v15Given +++ b/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedAndPKCS1v15Given @@ -1,7 +1,7 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 6d 01 00 00 69 03 03 4c 65 99 ab e0 |....m...i..Le...| -00000010 4b 0a 08 f5 06 20 f9 3d 96 4f 05 e3 58 6f 41 50 |K.... .=.O..XoAP| -00000020 c1 5f e8 a8 0a 5f 8f f2 de 7f 16 00 00 04 00 2f |._..._........./| +00000000 16 03 01 00 6d 01 00 00 69 03 03 34 6a c0 48 ba |....m...i..4j.H.| +00000010 77 0c fd 11 72 9d 91 e2 fe c5 a1 0f e2 a8 a7 62 |w...r..........b| +00000020 ae 68 f8 1b 7f 8d 59 ec d1 27 0d 00 00 04 00 2f |.h....Y..'...../| 00000030 00 ff 01 00 00 3c 00 16 00 00 00 17 00 00 00 0d |.....<..........| 00000040 00 30 00 2e 04 03 05 03 06 03 08 07 08 08 08 09 |.0..............| 00000050 08 0a 08 0b 08 04 08 05 08 06 04 01 05 01 06 01 |................| @@ -49,10 +49,10 @@ 00000260 f1 6c 04 ed 73 bb b3 43 77 8d 0c 1c f1 0f a1 d8 |.l..s..Cw.......| 00000270 40 83 61 c9 4c 72 2b 9d ae db 46 06 06 4d f4 c1 |@.a.Lr+...F..M..| 00000280 b3 3e c0 d1 bd 42 d4 db fe 3d 13 60 84 5c 21 d3 |.>...B...=.`.\!.| -00000290 3b e9 fa e7 16 03 03 00 23 0d 00 00 1f 02 01 40 |;.......#......@| -000002a0 00 18 08 04 04 03 08 07 08 05 08 06 04 01 05 01 |................| -000002b0 06 01 05 03 06 03 02 01 02 03 00 00 16 03 03 00 |................| -000002c0 04 0e 00 00 00 |.....| +00000290 3b e9 fa e7 16 03 03 00 29 0d 00 00 25 02 01 40 |;.......)...%..@| +000002a0 00 1e 08 04 04 03 08 07 08 05 08 06 04 01 05 01 |................| +000002b0 06 01 05 03 06 03 02 01 02 03 fe 61 fe 62 08 08 |...........a.b..| +000002c0 00 00 16 03 03 00 04 0e 00 00 00 |...........| >>> Flow 3 (client to server) 00000000 16 03 03 01 fd 0b 00 01 f9 00 01 f6 00 01 f3 30 |...............0| 00000010 82 01 ef 30 82 01 58 a0 03 02 01 02 02 10 5c 19 |...0..X.......\.| @@ -86,40 +86,40 @@ 000001d0 ac 11 b1 28 56 be 1d cd 61 62 84 09 bf d6 80 c6 |...(V...ab......| 000001e0 45 8d 82 2c b4 d8 83 9b db c9 22 b7 2a 12 11 7b |E..,......".*..{| 000001f0 fa 02 3b c1 c9 ff ea c9 9d a8 49 d3 95 d7 d5 0e |..;.......I.....| -00000200 e5 35 16 03 03 00 86 10 00 00 82 00 80 41 62 b4 |.5...........Ab.| -00000210 fb 81 80 58 e3 0d c7 b2 c0 55 ee 5b 1a ba 2d 8f |...X.....U.[..-.| -00000220 9f 79 24 0a d5 be c7 2b 55 ec 51 6d b9 78 63 85 |.y$....+U.Qm.xc.| -00000230 82 d2 ea 02 0c 06 fe 05 fd ed 08 be 71 99 5f 53 |............q._S| -00000240 94 85 01 ff ba 2a ee 14 cb 99 0a df 1e 67 0d 95 |.....*.......g..| -00000250 63 8d 1f 96 41 75 f9 5d 1a 21 03 6c e3 eb 4f 5e |c...Au.].!.l..O^| -00000260 28 c3 4d bb 6d 29 33 bc 24 75 8c 3b f2 c4 6b f5 |(.M.m)3.$u.;..k.| -00000270 86 db 40 59 34 43 fb a9 1e ea 6f 3f 0e b4 35 39 |..@Y4C....o?..59| -00000280 52 d8 0f 85 ed 3b 52 b6 5b 7f b0 bf c3 16 03 03 |R....;R.[.......| -00000290 00 88 0f 00 00 84 04 01 00 80 52 85 ca 08 7d 07 |..........R...}.| -000002a0 bc d8 0c a4 b8 36 01 c0 b8 8a 18 ba d8 d4 a3 fa |.....6..........| -000002b0 fd 32 e2 00 72 e5 d2 c8 5a 59 6b 5e 6e df 35 da |.2..r...ZYk^n.5.| -000002c0 c7 1e ee af 87 4b d6 30 7e 27 1c 76 70 28 79 ac |.....K.0~'.vp(y.| -000002d0 7f 31 bc 44 55 3c 15 61 d2 0d 24 9c 48 43 9f 12 |.1.DU<.a..$.HC..| -000002e0 a6 74 5c 2f 5b 4e 96 4a 47 b4 6b 7c fa da 37 96 |.t\/[N.JG.k|..7.| -000002f0 ec 46 7d 05 be 24 8f cf 11 31 ab 4c 5b c7 3e 94 |.F}..$...1.L[.>.| -00000300 9a 2a 39 e8 fe aa aa ee e3 00 a3 a8 1e 75 4a 21 |.*9..........uJ!| -00000310 b4 ad 24 8f ee e8 30 85 b1 28 14 03 03 00 01 01 |..$...0..(......| -00000320 16 03 03 00 40 71 47 13 68 49 74 9c 2a 81 35 94 |....@qG.hIt.*.5.| -00000330 52 f6 44 44 67 3b 62 e1 ef 34 18 e7 8a 56 71 88 |R.DDg;b..4...Vq.| -00000340 83 7e 67 28 20 18 b1 c5 8a c8 8b 6a fe ee bf da |.~g( ......j....| -00000350 5f 6e cd fa a8 5c af 5c 3c 83 80 78 f3 fe 1b dc |_n...\.\<..x....| -00000360 95 fe 22 16 82 |.."..| +00000200 e5 35 16 03 03 00 86 10 00 00 82 00 80 5f 05 c8 |.5..........._..| +00000210 7e 71 5b fa 77 dd d9 2c 07 4b e8 07 14 c2 0e 63 |~q[.w..,.K.....c| +00000220 91 1e 98 97 18 c2 94 b2 74 14 49 3d 42 1f c5 54 |........t.I=B..T| +00000230 7d ef 29 43 0a d1 86 fe 1e 6c c7 69 81 d8 55 0e |}.)C.....l.i..U.| +00000240 e0 e8 20 b8 7e 57 12 cc 23 98 f3 fb c7 f1 91 da |.. .~W..#.......| +00000250 04 82 46 41 36 f6 58 5b 25 5a f6 8e aa 4c 66 59 |..FA6.X[%Z...LfY| +00000260 ea 62 f9 c0 3e ed a8 6d 5f ce a1 6c 65 c5 05 cb |.b..>..m_..le...| +00000270 e8 8f f2 f9 93 29 b8 ff 7a e7 ed 23 1a d1 38 2b |.....)..z..#..8+| +00000280 c9 7a af f0 a2 33 14 fa e0 74 1b c3 07 16 03 03 |.z...3...t......| +00000290 00 88 0f 00 00 84 04 01 00 80 22 4c ae 8a d2 11 |.........."L....| +000002a0 e6 a8 9c 4e e5 cc 7a 58 83 80 ce cc 1a be d3 e2 |...N..zX........| +000002b0 67 04 c8 30 f9 85 5a 75 9b c0 d7 0b e8 86 7c e2 |g..0..Zu......|.| +000002c0 1e 44 ab da 34 41 f4 27 86 ed fc 2a d0 ad a6 b9 |.D..4A.'...*....| +000002d0 f9 b0 1f a6 37 d1 16 51 64 59 84 a1 a8 de 54 78 |....7..QdY....Tx| +000002e0 71 94 a2 61 e7 ac 9d 1d d3 bb ba fd 97 a1 23 0e |q..a..........#.| +000002f0 69 b5 f3 09 96 3f f6 fb c3 bc 2e 72 e3 b5 d2 45 |i....?.....r...E| +00000300 af 03 8c 49 95 10 b6 bd 62 3d 31 56 39 d9 0f 83 |...I....b=1V9...| +00000310 83 36 1d 29 d0 0d fb 6f 36 2e 14 03 03 00 01 01 |.6.)...o6.......| +00000320 16 03 03 00 40 6e 0c 83 37 81 e4 b0 3d 12 f7 ca |....@n..7...=...| +00000330 19 7f 1c f0 29 b7 06 7a fe 89 70 13 2a 6d 46 54 |....)..z..p.*mFT| +00000340 d9 b7 a2 ef ea f9 a4 d5 27 97 f2 43 09 3a a9 22 |........'..C.:."| +00000350 63 a5 16 67 62 ef 86 41 20 21 f9 1e 0d 5e be 05 |c..gb..A !...^..| +00000360 76 f6 06 74 ee |v..t.| >>> Flow 4 (server to client) 00000000 14 03 03 00 01 01 16 03 03 00 40 00 00 00 00 00 |..........@.....| -00000010 00 00 00 00 00 00 00 00 00 00 00 20 f7 51 8f 23 |........... .Q.#| -00000020 08 8d 67 5d 12 06 b0 48 81 2d 0c ba 88 03 88 31 |..g]...H.-.....1| -00000030 d0 ab 63 0d 9f 28 60 21 0a a3 58 47 c2 04 cc f1 |..c..(`!..XG....| -00000040 50 0d 88 b2 e5 54 50 26 e6 6e ed 17 03 03 00 40 |P....TP&.n.....@| +00000010 00 00 00 00 00 00 00 00 00 00 00 2e f4 f9 ea e1 |................| +00000020 36 2c 86 67 52 93 62 99 b2 aa a1 df 04 10 2d 3a |6,.gR.b.......-:| +00000030 77 88 b4 41 0d 8d 5f e6 0d af 66 64 20 e9 a3 e4 |w..A.._...fd ...| +00000040 a5 6c c0 1b 6f 42 8c de ec e9 f0 17 03 03 00 40 |.l..oB.........@| 00000050 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| -00000060 fa 4d e5 00 14 2c 65 82 5d 1b bf 99 6a 54 16 98 |.M...,e.]...jT..| -00000070 ef 55 15 00 f9 c4 3e 61 88 83 63 fd 60 66 f1 87 |.U....>a..c.`f..| -00000080 fa c4 45 ae de b8 0a 36 75 f5 b2 b6 f5 d8 9b df |..E....6u.......| +00000060 f5 c8 90 ba 51 60 eb 57 3b fd 8e 57 86 e6 97 86 |....Q`.W;..W....| +00000070 c6 8b 91 de e9 19 f2 1d cc 4e 0d ff c0 31 25 bd |.........N...1%.| +00000080 f3 e6 0b c0 d9 ea 32 7d a1 a3 a4 63 af a0 8d ce |......2}...c....| 00000090 15 03 03 00 30 00 00 00 00 00 00 00 00 00 00 00 |....0...........| -000000a0 00 00 00 00 00 54 cc c0 15 e5 6d 62 4d 13 54 e8 |.....T....mbM.T.| -000000b0 fa cf 76 a6 de d6 48 f8 0d ef 30 b7 12 05 cf 75 |..v...H...0....u| -000000c0 8b 00 9e d5 63 |....c| +000000a0 00 00 00 00 00 5f cf 25 0f 97 a4 db 27 d3 ff c6 |....._.%....'...| +000000b0 29 47 ff bb 80 73 d5 43 f7 be 45 38 91 11 dd 0e |)G...s.C..E8....| +000000c0 f3 40 9d b7 c7 |.@...| diff --git a/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedNotGiven b/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedNotGiven index a81c1731535..c98cbfb1a10 100644 --- a/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedNotGiven +++ b/src/crypto/tls/testdata/Server-TLSv12-ClientAuthRequestedNotGiven @@ -1,7 +1,7 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 6d 01 00 00 69 03 03 be a7 a4 6c f7 |....m...i.....l.| -00000010 f6 b4 f2 64 5d 0e 36 b6 05 f5 f1 c9 fe 3c c2 8e |...d].6......<..| -00000020 c4 b7 18 68 b9 0c 1d 51 50 2f 1e 00 00 04 00 2f |...h...QP/...../| +00000000 16 03 01 00 6d 01 00 00 69 03 03 7f 8e a8 8f 5d |....m...i......]| +00000010 13 84 9e ad a7 3b a5 6c b0 d1 d3 33 71 38 6f e8 |.....;.l...3q8o.| +00000020 e9 19 a6 a1 23 40 cb 17 61 93 6b 00 00 04 00 2f |....#@..a.k..../| 00000030 00 ff 01 00 00 3c 00 16 00 00 00 17 00 00 00 0d |.....<..........| 00000040 00 30 00 2e 04 03 05 03 06 03 08 07 08 08 08 09 |.0..............| 00000050 08 0a 08 0b 08 04 08 05 08 06 04 01 05 01 06 01 |................| @@ -49,37 +49,37 @@ 00000260 f1 6c 04 ed 73 bb b3 43 77 8d 0c 1c f1 0f a1 d8 |.l..s..Cw.......| 00000270 40 83 61 c9 4c 72 2b 9d ae db 46 06 06 4d f4 c1 |@.a.Lr+...F..M..| 00000280 b3 3e c0 d1 bd 42 d4 db fe 3d 13 60 84 5c 21 d3 |.>...B...=.`.\!.| -00000290 3b e9 fa e7 16 03 03 00 23 0d 00 00 1f 02 01 40 |;.......#......@| -000002a0 00 18 08 04 04 03 08 07 08 05 08 06 04 01 05 01 |................| -000002b0 06 01 05 03 06 03 02 01 02 03 00 00 16 03 03 00 |................| -000002c0 04 0e 00 00 00 |.....| +00000290 3b e9 fa e7 16 03 03 00 29 0d 00 00 25 02 01 40 |;.......)...%..@| +000002a0 00 1e 08 04 04 03 08 07 08 05 08 06 04 01 05 01 |................| +000002b0 06 01 05 03 06 03 02 01 02 03 fe 61 fe 62 08 08 |...........a.b..| +000002c0 00 00 16 03 03 00 04 0e 00 00 00 |...........| >>> Flow 3 (client to server) 00000000 16 03 03 00 07 0b 00 00 03 00 00 00 16 03 03 00 |................| -00000010 86 10 00 00 82 00 80 a9 b6 12 e2 84 71 62 7a 20 |............qbz | -00000020 63 80 99 c6 ee f7 61 f9 74 d6 0b ab 31 74 69 ca |c.....a.t...1ti.| -00000030 94 20 9e 1b 0e 52 45 c4 f4 b3 cb fb a4 07 61 6f |. ...RE.......ao| -00000040 a1 5a 84 4c 4f f6 4a e4 bc c5 c2 b0 ee 8a 30 5b |.Z.LO.J.......0[| -00000050 10 e0 ed d3 4c b7 32 8c ed 3f 89 a7 a7 95 60 86 |....L.2..?....`.| -00000060 97 1a ae ab 2f 5c e6 6d 1b c3 35 bd f5 c1 f0 1a |..../\.m..5.....| -00000070 d4 70 e5 00 f2 d4 d1 20 6a 82 db e7 52 ca 88 e5 |.p..... j...R...| -00000080 2d cc 79 0c f6 09 84 65 f0 30 41 67 10 0a 48 d1 |-.y....e.0Ag..H.| -00000090 09 3e 56 7a aa 57 bc 14 03 03 00 01 01 16 03 03 |.>Vz.W..........| -000000a0 00 40 e6 0a 91 5f 30 f8 52 75 94 8e ab 82 ec 1d |.@..._0.Ru......| -000000b0 b7 a1 1c 18 1a aa 1c f8 73 93 0e 20 ad 68 a7 65 |........s.. .h.e| -000000c0 86 c9 f5 90 f9 b2 fd d1 32 94 52 6e 82 9b b9 45 |........2.Rn...E| -000000d0 97 52 4b 1e c2 31 a6 2e c8 b3 1a 62 22 83 8f df |.RK..1.....b"...| -000000e0 d7 06 |..| +00000010 86 10 00 00 82 00 80 22 89 ca 93 8f 3b 25 04 29 |......."....;%.)| +00000020 3d 70 25 23 3e 46 d4 84 49 73 00 c7 e5 0c d9 8a |=p%#>F..Is......| +00000030 88 61 7a 1d c9 0e 19 b0 65 f5 ab ba 58 c1 e2 41 |.az.....e...X..A| +00000040 19 2a 60 3a 6f 7c cd 7d dc b9 9e fd 55 38 b7 b3 |.*`:o|.}....U8..| +00000050 ad 4a 7c df de 80 fc 9d 1f 38 00 a4 62 7d f1 22 |.J|......8..b}."| +00000060 08 51 b8 f6 88 f2 06 2f ce 8c 3f 78 d0 a7 71 31 |.Q...../..?x..q1| +00000070 85 83 3f 26 d8 41 20 e9 6d 2f 95 2a 5d f4 10 a9 |..?&.A .m/.*]...| +00000080 e0 6a b9 db 4e 6e 1c 19 fe 79 9e 40 55 b5 28 49 |.j..Nn...y.@U.(I| +00000090 7b 0b bf e5 a7 5c 27 14 03 03 00 01 01 16 03 03 |{....\'.........| +000000a0 00 40 e7 9d ea 73 04 72 5f d4 da c6 58 a4 0e b6 |.@...s.r_...X...| +000000b0 33 48 93 ff 0e e4 99 29 a6 23 54 93 ae 65 64 a1 |3H.....).#T..ed.| +000000c0 f2 62 31 c4 bb f0 30 fb 5c e3 30 3a 4e 0a f0 7d |.b1...0.\.0:N..}| +000000d0 09 ad 98 ea 26 17 cf a6 ee 6d c1 73 02 08 09 23 |....&....m.s...#| +000000e0 22 48 |"H| >>> Flow 4 (server to client) 00000000 14 03 03 00 01 01 16 03 03 00 40 00 00 00 00 00 |..........@.....| -00000010 00 00 00 00 00 00 00 00 00 00 00 b0 2c 61 79 87 |............,ay.| -00000020 59 d4 9e 4d e7 56 4a 34 ba 78 d5 06 98 a2 92 35 |Y..M.VJ4.x.....5| -00000030 a1 fc 57 5a 6e d3 0f 44 08 1c a1 7b 3c d3 f1 86 |..WZn..D...{<...| -00000040 a2 04 04 5e 1b 7c 00 4f 51 71 73 17 03 03 00 40 |...^.|.OQqs....@| +00000010 00 00 00 00 00 00 00 00 00 00 00 13 a3 51 fb 70 |.............Q.p| +00000020 88 49 20 51 c7 e2 19 43 61 be 16 2f 51 98 1b 99 |.I Q...Ca../Q...| +00000030 dc 1d 99 f4 ea 76 a3 59 14 18 f2 c6 c0 19 42 61 |.....v.Y......Ba| +00000040 9d e6 d8 63 23 f0 d9 56 ad 33 2c 17 03 03 00 40 |...c#..V.3,....@| 00000050 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| -00000060 aa 5c 1a 9a 70 bc b3 fb 70 07 0b 24 cb 95 84 61 |.\..p...p..$...a| -00000070 96 ed d8 97 2f d6 79 51 ed cd 67 44 e5 d4 a3 57 |..../.yQ..gD...W| -00000080 95 f6 c8 31 a8 95 c2 07 a4 ce 1c fc 4a dc 93 d9 |...1........J...| +00000060 e9 03 08 52 f3 04 44 89 0e ac 29 d7 74 f5 7d 88 |...R..D...).t.}.| +00000070 c7 ce b1 44 d9 05 da 62 f4 4b 3d aa 27 73 d1 c1 |...D...b.K=.'s..| +00000080 3f f5 68 c1 b0 83 2a 47 0f d8 3b 31 ba d2 88 7b |?.h...*G..;1...{| 00000090 15 03 03 00 30 00 00 00 00 00 00 00 00 00 00 00 |....0...........| -000000a0 00 00 00 00 00 ae dd c4 f4 04 d3 b1 1a 8a 56 f7 |..............V.| -000000b0 73 c9 d5 aa 6c 59 d7 66 77 34 64 2d 19 79 13 80 |s...lY.fw4d-.y..| -000000c0 98 60 6d f4 d9 |.`m..| +000000a0 00 00 00 00 00 05 7e ee 78 66 d4 22 ff 96 36 18 |......~.xf."..6.| +000000b0 9b 0b c5 44 d0 ac 03 07 b6 03 48 13 ad ad 75 a2 |...D......H...u.| +000000c0 b5 78 e0 2f 05 |.x./.| diff --git a/src/crypto/tls/testdata/Server-TLSv13-ClientAuthRequestedAndECDSAGiven b/src/crypto/tls/testdata/Server-TLSv13-ClientAuthRequestedAndECDSAGiven index 0b6eaf43810..36dd1561a5b 100644 --- a/src/crypto/tls/testdata/Server-TLSv13-ClientAuthRequestedAndECDSAGiven +++ b/src/crypto/tls/testdata/Server-TLSv13-ClientAuthRequestedAndECDSAGiven @@ -1,179 +1,180 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 ca 01 00 00 c6 03 03 54 78 64 8e b6 |...........Txd..| -00000010 69 c6 1c 8a 69 eb 09 ef 32 59 f9 9f 63 ac 6e 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|.tw...T....,...+| -000002a0 dc 02 32 01 ad 96 5c a0 87 3c 55 dd ee 4d cb fd |..2...\.......B2| +00000320 a7 dc 48 91 3b 1c ab ad 3b d1 b9 09 ef 14 1e 4e |..H.;...;......N| +00000330 06 0c 4a 43 54 b5 6f c7 42 55 d5 a1 c5 2c 24 25 |..JCT.o.BU...,$%| +00000340 0e 18 a7 4d ca 21 29 b3 2a 9e 9d cf d4 40 0f 0e |...M.!).*....@..| +00000350 3d e2 05 e1 e4 88 ba 75 52 84 43 ce 17 03 03 00 |=......uR.C.....| +00000360 99 bc d9 77 e9 6f 3f 67 55 90 62 8d cd 31 9d c0 |...w.o?gU.b..1..| +00000370 f0 2f 08 56 9f 4e 08 ae c3 05 50 3e 33 9b bb 8f |./.V.N....P>3...| +00000380 01 d1 34 1d 68 46 14 68 8f 59 86 02 da 03 9c 04 |..4.hF.h.Y......| +00000390 f0 4b 06 d6 74 ab fe 87 99 7d e0 51 2b 7c 97 54 |.K..t....}.Q+|.T| +000003a0 35 88 05 16 9f 8e b4 50 a0 8c ca b0 e0 5c fb 8d |5......P.....\..| +000003b0 53 3c 09 ff 2b 12 f1 b3 d5 b9 66 cb 57 4b c7 cf |S<..+.....f.WK..| +000003c0 30 68 3a 62 15 9b 43 4b 53 80 c3 ed e6 98 9b f6 |0h:b..CKS.......| +000003d0 94 25 18 11 93 13 6c ec f2 09 08 5d e1 75 28 68 |.%....l....].u(h| +000003e0 5f 81 8a 30 80 2e 5d 33 8e b3 17 bf ba 53 80 66 |_..0..]3.....S.f| +000003f0 13 c6 df 77 28 48 47 30 e4 21 17 03 03 00 35 50 |...w(HG0.!....5P| +00000400 e5 c6 2a b1 3d 8f 99 25 5e 52 e0 b5 c6 b7 fc cb |..*.=..%^R......| +00000410 14 a2 07 79 a4 9f 8e 4e 0c 51 17 d8 8a c3 02 53 |...y...N.Q.....S| +00000420 4e ce 48 9e 13 47 ba a5 79 06 7b d6 8f 3a b6 bf |N.H..G..y.{..:..| +00000430 78 2e 61 5d |x.a]| >>> Flow 3 (client to server) -00000000 14 03 03 00 01 01 17 03 03 01 50 d8 03 a6 37 13 |..........P...7.| -00000010 5f fb 65 9f 33 33 79 ae 89 c3 de ea 4b 55 e2 b3 |_.e.33y.....KU..| -00000020 13 07 0d 95 c6 f7 79 74 ad 8a 42 dd 78 55 a5 01 |......yt..B.xU..| -00000030 69 f2 11 cf 72 de 85 04 56 78 9c ba 21 77 b8 76 |i...r...Vx..!w.v| -00000040 e3 58 23 3d 2b 8a ee a4 5c 52 60 4b 50 0d c4 83 |.X#=+...\R`KP...| -00000050 a1 8d 06 82 68 99 34 65 7a 7b 55 8e 46 04 47 55 |....h.4ez{U.F.GU| -00000060 4d 42 02 41 b6 e4 dd a4 33 6a 04 97 e6 4a 80 3a |MB.A....3j...J.:| -00000070 e1 7e 0a a5 4f 0c f9 de 7a 91 96 4f 6a 6a 8a 4b |.~..O...z..Ojj.K| -00000080 fd 24 b9 bf e7 d5 5a 27 17 18 45 77 1d e2 c9 ea |.$....Z'..Ew....| -00000090 23 57 c4 e1 30 9e de d2 bd 0c 28 59 dc a1 12 d9 |#W..0.....(Y....| -000000a0 ee 2e 43 4b 83 fc d7 6c a4 e7 47 c4 14 c1 1f ee |..CK...l..G.....| -000000b0 79 60 26 86 73 5c ec c9 c0 ec f9 c9 38 98 2d ba |y`&.s\......8.-.| -000000c0 10 83 1b fe 8f cf 59 77 f0 60 fe c0 d0 7e 0f 2d |......Yw.`...~.-| -000000d0 69 04 dd 79 49 c5 b1 d9 9b 48 ad de 55 cf d3 47 |i..yI....H..U..G| -000000e0 9b eb 64 ae ed cb b0 48 78 a9 27 24 b8 8d 53 36 |..d....Hx.'$..S6| -000000f0 b7 0f 82 1c ee 11 4b 5a 98 1d 21 73 b4 f4 06 ce |......KZ..!s....| -00000100 50 bc 36 27 e1 87 70 04 68 1b 30 3a 86 68 b3 71 |P.6'..p.h.0:.h.q| -00000110 8c 57 69 60 d6 a8 bd fa 13 46 2b 52 00 dc 45 53 |.Wi`.....F+R..ES| -00000120 06 79 5b 96 78 69 d0 a8 cd 2d 39 8c 11 12 9f 65 |.y[.xi...-9....e| -00000130 72 01 5e b4 c5 df bc 9d a2 7f 00 a7 cc 95 3b 0b 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41 d2 e9 f2 a4 c0 6a d3 81 |.%f....A.....j..| +00000020 f0 a9 6b 32 62 23 71 6b 8f 4e 8c e2 f4 99 5e 45 |..k2b#qk.N....^E| +00000030 d4 49 8c cc a7 e9 02 00 ff f7 26 e4 c4 8e 45 0f |.I........&...E.| +00000040 e7 32 fa cf 5a 3f 9e f6 6c b3 2c 6b 90 99 f0 ba |.2..Z?..l.,k....| +00000050 d8 ab 2e 7e a0 4f af 68 31 92 c6 0c 3c 1b 6c 35 |...~.O.h1...<.l5| +00000060 c6 7d be 9c e9 0e ab f4 9a c9 43 79 64 7d f1 08 |.}........Cyd}..| +00000070 2a 7a 4c 8b 2e fa f1 20 3f af e2 b2 92 63 ff f0 |*zL.... ?....c..| +00000080 9f 42 94 14 c3 f2 88 5d 79 95 9f a7 c8 a1 54 9f |.B.....]y.....T.| +00000090 6f be 9e 9b bc 5e 01 6b 15 5e 00 1f 39 b9 55 f4 |o....^.k.^..9.U.| +000000a0 31 d8 14 79 65 19 03 31 50 79 e0 56 fa 03 85 44 |1..ye..1Py.V...D| +000000b0 de 67 64 13 52 92 c6 8e 82 ab e5 d0 15 d6 91 22 |.gd.R.........."| +000000c0 87 ca 15 2d 29 7a f5 c7 c8 3a 48 4e fb 82 bc fb |...-)z...:HN....| +000000d0 6b 83 39 48 59 f7 49 9a 39 5b 03 03 43 ec 5b da |k.9HY.I.9[..C.[.| +000000e0 23 58 cf 39 f8 19 f0 e7 79 98 38 ce 49 b4 b7 b9 |#X.9....y.8.I...| +000000f0 ae e8 c6 c7 a4 f6 6d 25 f2 ed fe 05 95 e0 58 1f |......m%......X.| +00000100 53 24 54 67 36 23 2f 48 3e 6c 73 b5 92 2c 97 5a |S$Tg6#/H>ls..,.Z| +00000110 e9 e0 2f 1b f9 01 9d 5e be 50 f2 b6 c5 b5 33 c0 |../....^.P....3.| +00000120 45 42 f3 17 9a d8 72 ee 08 d1 69 5c de 92 cc 03 |EB....r...i\....| +00000130 0b a5 99 80 b0 43 81 d5 2b e6 1d 74 ec 00 df 38 |.....C..+..t...8| +00000140 a2 be 7b 8e 48 0a 8d 79 bf 79 04 dd f1 c8 a2 50 |..{.H..y.y.....P| +00000150 5c 9e b0 d4 30 6e 3b 11 03 48 76 17 03 03 00 59 |\...0n;..Hv....Y| +00000160 ea 2b 3d 52 27 eb 11 14 37 48 52 12 e0 16 6c e0 |.+=R'...7HR...l.| +00000170 99 61 c3 a2 64 4e 0c 79 bf 9d 3a d4 a9 f7 c3 2d |.a..dN.y..:....-| +00000180 4f 32 e6 5c 53 3b 9a 5f 10 36 41 e4 27 a2 b3 ed |O2.\S;._.6A.'...| +00000190 07 7c f8 ba 2c fe df 19 6e f2 09 1b f3 26 ed fb |.|..,...n....&..| +000001a0 63 21 cf 4c 63 5a 70 2b 21 05 bf a4 44 a9 0a 58 |c!.LcZp+!...D..X| +000001b0 d8 18 cc 53 79 29 2d 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64 85 |...q~.K{...w.8d.| -00000160 5c 3d af fc e3 17 46 e7 c5 71 c9 63 bf 03 ae 35 |\=....F..q.c...5| -00000170 7b 60 61 5d 5a 7b 57 88 79 82 55 68 45 a1 59 bc |{`a]Z{W.y.UhE.Y.| -00000180 e5 3b 5a 31 32 5c 24 13 e3 fc b7 53 41 76 1d 24 |.;Z12\$....SAv.$| -00000190 7f 08 89 c6 f0 b9 57 3a 4d 91 66 66 e4 57 33 51 |......W:M.ff.W3Q| -000001a0 1d b9 1e c5 68 9a 6a 74 1e c3 16 de 15 92 e3 d0 |....h.jt........| -000001b0 0a 64 a4 64 e8 c4 a5 9c 55 30 a9 c3 b0 53 72 54 |.d.d....U0...SrT| -000001c0 75 d7 a0 7a 54 85 6e 9a 4d ff 9f 13 3c b9 42 17 |u..zT.n.M...<.B.| -000001d0 03 03 00 1e 6f 06 3f 1c da f6 55 50 05 de 38 9d |....o.?...UP..8.| -000001e0 07 00 bb 28 32 a5 3f 04 22 4c 6e f2 ea 3a e0 cc |...(2.?."Ln..:..| -000001f0 5d 5b 17 03 03 00 13 3b b8 7c df 14 b4 ba fa 6e |][.....;.|.....n| -00000200 2e 61 d6 6b bf b5 ad c2 35 73 |.a.k....5s| +00000000 17 03 03 01 ca ed 03 5c 29 0d f1 07 d6 54 2a d1 |.......\)....T*.| +00000010 d8 93 d4 a2 bb 51 f1 8f 03 87 ee d0 62 6c ea 2e |.....Q......bl..| +00000020 42 79 d1 37 f3 b1 75 1b d6 9b 1a a8 be 17 06 28 |By.7..u........(| +00000030 78 1f 29 46 07 1f b9 39 79 8f cc 5a 2a 87 bb 80 |x.)F...9y..Z*...| +00000040 fe d2 ac c7 76 0d 1d 6b 5e 56 0f 46 c3 e6 ed 75 |....v..k^V.F...u| +00000050 f2 87 73 27 d3 60 81 41 77 2d c5 2c 27 91 50 1a |..s'.`.Aw-.,'.P.| +00000060 7a 78 9c 8f 1c ec c5 3a b1 c2 4c 25 09 db 72 bf |zx.....:..L%..r.| +00000070 14 43 02 06 94 57 2f 9d e4 a5 39 53 a3 82 ac b1 |.C...W/...9S....| +00000080 41 3c af 35 d5 61 95 95 b7 3a e2 34 af 99 c4 20 |A<.5.a...:.4... | +00000090 50 0d 1d a1 a9 4b f0 41 95 1f 9b e8 24 a9 1d 0f |P....K.A....$...| +000000a0 c4 ec f3 4a b8 f8 81 5d 77 84 f5 21 04 aa 7b 66 |...J...]w..!..{f| +000000b0 18 15 df f7 91 1b f7 06 14 de 00 bc f1 a8 0e 90 |................| +000000c0 9c df bd 6c 92 64 80 9d 9e 87 ac 1e 7a c1 db 0a |...l.d......z...| +000000d0 d9 2b f7 fd b2 74 db 63 32 19 85 34 91 13 2c 98 |.+...t.c2..4..,.| +000000e0 f1 ac 0a f8 a6 a1 86 4a dc 35 4f 7f 73 62 d6 5e |.......J.5O.sb.^| +000000f0 f4 48 06 88 66 70 fb b0 46 c5 b2 ae fd d3 d6 35 |.H..fp..F......5| +00000100 61 97 cb 7b 2a 9c b2 67 82 cc c7 70 70 69 84 92 |a..{*..g...ppi..| +00000110 83 f6 62 ce 95 ce 65 68 dc ad bf dd d6 b4 93 36 |..b...eh.......6| +00000120 87 be 44 d2 fb 9a 64 3e 70 ae 3c 16 97 f8 bb b1 |..D...d>p.<.....| +00000130 91 f4 1e 60 84 fb 2c f2 39 d5 58 47 ec 1d 1c de |...`..,.9.XG....| +00000140 21 9f 16 25 5f 46 e4 d6 e7 f6 4a 1e c8 8b d1 01 |!..%_F....J.....| +00000150 c3 6d 97 64 e2 aa d8 f3 60 c8 2e 30 81 ab 0e e9 |.m.d....`..0....| +00000160 52 96 f1 ed 61 49 e0 25 73 39 96 a7 1d fd a5 d2 |R...aI.%s9......| +00000170 7f 2e 19 6c 89 8d f0 03 48 c9 68 d8 09 2f 90 33 |...l....H.h../.3| +00000180 94 f9 fb 9c f7 e2 e8 42 c5 bb f6 63 d8 2a e7 dd |.......B...c.*..| +00000190 15 aa bb f2 cb 27 f9 00 3e 5d 89 3a d6 19 15 71 |.....'..>].:...q| +000001a0 86 65 65 91 35 b8 a3 ee fe 3f 86 a8 5a 9a b0 5b |.ee.5....?..Z..[| +000001b0 01 11 81 5c 7f 94 91 52 5a ac 50 e8 f5 15 52 0a |...\...RZ.P...R.| +000001c0 03 b8 40 04 d1 89 e0 6d 0d 33 bf ea ed 39 42 17 |..@....m.3...9B.| +000001d0 03 03 00 1e c7 73 e5 b8 3e 6d bf ef 3a d8 9b ba |.....s..>m..:...| +000001e0 1f 28 a0 68 3e 6c a3 58 76 4a b0 48 2b 4d b2 2f |.(.h>l.XvJ.H+M./| +000001f0 4a f0 17 03 03 00 13 a6 66 28 39 c6 46 bb 6d c7 |J.......f(9.F.m.| +00000200 9a a5 6d 8f 56 f3 bf de b3 8b |..m.V.....| diff --git a/src/crypto/tls/testdata/Server-TLSv13-ClientAuthRequestedAndGiven b/src/crypto/tls/testdata/Server-TLSv13-ClientAuthRequestedAndGiven index 800f99916c0..36a91b5edf6 100644 --- a/src/crypto/tls/testdata/Server-TLSv13-ClientAuthRequestedAndGiven +++ b/src/crypto/tls/testdata/Server-TLSv13-ClientAuthRequestedAndGiven @@ -1,177 +1,178 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 ca 01 00 00 c6 03 03 c8 2f b4 54 5b |............/.T[| -00000010 11 8a 88 a9 a2 9b bf 66 f2 b4 e5 fb 32 af d6 dd |.......f....2...| -00000020 6c 6c 99 4f d6 48 cd eb 63 6e 1d 20 bb 0a 48 2e |ll.O.H..cn. ..H.| -00000030 45 4e 86 2d ae d6 fb 3e 0c 3e 9f a3 17 4a e3 39 |EN.-...>.>...J.9| -00000040 58 a7 92 92 cb 30 03 0d be b5 79 a5 00 04 13 01 |X....0....y.....| +00000000 16 03 01 00 ca 01 00 00 c6 03 03 22 61 05 f6 33 |..........."a..3| +00000010 9e 22 f6 3a 2e a8 ef 4e bd 10 7a 95 9f 10 02 e5 |.".:...N..z.....| +00000020 8d 59 f3 1e b1 c9 f4 3d b6 dc 7f 20 6f cb 76 af |.Y.....=... o.v.| +00000030 99 99 32 43 54 64 c5 b1 55 d2 db 0f 6c 1d 35 e0 |..2CTd..U...l.5.| +00000040 78 e3 87 65 41 ae f4 8d 43 a5 57 a2 00 04 13 01 |x..eA...C.W.....| 00000050 00 ff 01 00 00 79 00 0b 00 04 03 00 01 02 00 0a |.....y..........| 00000060 00 0c 00 0a 00 1d 00 17 00 1e 00 19 00 18 00 16 |................| 00000070 00 00 00 17 00 00 00 0d 00 1e 00 1c 04 03 05 03 |................| 00000080 06 03 08 07 08 08 08 09 08 0a 08 0b 08 04 08 05 |................| 00000090 08 06 04 01 05 01 06 01 00 2b 00 03 02 03 04 00 |.........+......| -000000a0 2d 00 02 01 01 00 33 00 26 00 24 00 1d 00 20 f0 |-.....3.&.$... .| -000000b0 8e 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|.(.V...i|.....H_| -00000040 4e 78 87 14 38 f8 fa 3c 17 97 f9 de 38 3b cf 0f |Nx..8..<....8;..| -00000050 d9 dd 41 0a bb 65 ca a7 0b fd a5 11 c2 c3 6a b8 |..A..e........j.| -00000060 5a e1 68 a1 8d f8 35 9d c6 e1 3e e1 03 a9 06 ee |Z.h...5...>.....| -00000070 1f 92 ca b5 f4 df 3e e5 69 63 9e a2 ea 5e b8 d9 |......>.ic...^..| -00000080 26 31 9e 25 de a8 ea 44 1a c0 86 0b 38 75 04 dc |&1.%...D....8u..| -00000090 2d 37 ad 40 e3 2f d1 b0 9e 9e 64 57 8b 31 20 d6 |-7.@./....dW.1 .| -000000a0 16 64 fd 1b c1 01 58 af 4b 88 49 23 7a f6 a2 15 |.d....X.K.I#z...| -000000b0 ca 02 4b d6 6d 7c f8 7a c9 c0 0d 32 6e 1d 83 ca |..K.m|.z...2n...| -000000c0 47 e5 6f 86 a0 f7 8b 50 1d 91 ec fa 2b 4a 72 f7 |G.o....P....+Jr.| -000000d0 a0 09 f1 65 fb 81 32 d2 a0 be 18 07 9f 5d 89 98 |...e..2......]..| -000000e0 08 09 a6 1d 9a 5a 10 67 81 58 82 00 9d 01 48 a8 |.....Z.g.X....H.| -000000f0 5b df 54 b3 cd 84 87 e0 41 e6 1e 47 46 33 56 0c |[.T.....A..GF3V.| -00000100 67 82 b9 bc 28 68 f3 5b 51 a8 c0 0e 43 14 62 bb |g...(h.[Q...C.b.| -00000110 8a bd 3f 4d d6 33 c4 76 4f c1 06 f8 9b bf 64 41 |..?M.3.vO.....dA| -00000120 6c e5 40 8d 93 4a 6b 6f fe 72 6b db ac 35 b4 fc |l.@..Jko.rk..5..| -00000130 84 13 fa 8a 7d 35 e3 73 12 eb 1a 5f a9 e2 28 53 |....}5.s..._..(S| -00000140 0c 6d 41 ec 4b 76 f5 d9 48 2a c2 85 2a 1f 7d 61 |.mA.Kv..H*..*.}a| -00000150 f6 1f 27 ef 47 c9 c7 b3 19 5c 07 d5 18 ec fd 3e |..'.G....\.....>| -00000160 78 41 cb a4 3a 47 22 cf 7e 7e 17 be 27 c4 90 ce |xA..:G".~~..'...| -00000170 2a cb cd ed 0f a3 bf 1e 4c 62 7a 80 ff 21 38 c5 |*.......Lbz..!8.| -00000180 c2 37 9f 62 4b d8 c0 9e df ae 3c 69 cd 25 f5 65 |.7.bK......*.;..S.....>..| +000001a0 3c 79 f0 2a 8b a8 c8 15 9c 1a aa fc b0 35 14 60 |.04....| +000001d0 21 79 d9 5c bb 9b 26 7f d1 28 1d b5 21 b8 ea 7a |!y.\..&..(..!..z| +000001e0 bd ca ff 0b 23 55 17 cc 31 2d ee 44 f1 3a 09 fe |....#U..1-.D.:..| +000001f0 b2 64 92 c4 31 6d 44 d2 54 3c e0 13 f6 6f 7b 6f |.d..1mD.T<...o{o| +00000200 7a e1 94 7d 72 25 0b ff d1 e7 c4 dc a8 2a a6 e4 |z..}r%.......*..| +00000210 52 b0 a5 d2 67 3a 0d d8 49 3d 71 ec ed 29 dd 5f |R...g:..I=q..)._| +00000220 60 93 34 4f 8b 43 d1 0c d3 9d 3e 67 eb e7 5c a7 |`.4O.C....>g..\.| +00000230 82 7a e1 64 35 72 30 24 72 21 e5 ef e2 d0 09 0e |.z.d5r0$r!......| +00000240 a4 7e 59 8b 24 7e 33 28 96 e2 e8 18 19 2e 26 e0 |.~Y.$~3(......&.| +00000250 c3 7f 8b 5d fe 52 fd 14 b5 27 62 89 00 15 e9 4a |...].R...'b....J| +00000260 1f 9b db ce b9 8b 08 46 9c 32 59 ef 6b fd 86 48 |.......F.2Y.k..H| +00000270 68 0b 1b f9 be 18 49 6a 3f ca 9b 2d ef b9 8f a9 |h.....Ij?..-....| +00000280 17 69 9f 23 04 e3 ac 10 e8 96 c3 52 00 14 68 67 |.i.#.......R..hg| +00000290 17 03 03 00 1e fd b1 7f 65 cf 8e 81 4a aa 4d 3f |........e...J.M?| +000002a0 d1 6c 7c 57 45 c5 af 4f 21 ed ff ad bf 25 ec 78 |.l|WE..O!....%.x| +000002b0 d0 7d 10 17 03 03 00 13 9e aa fc 24 58 be ec f6 |.}.........$X...| +000002c0 62 ba 19 e9 7a 3e 66 bf bb 7e 07 |b...z>f..~.| diff --git a/src/crypto/tls/testdata/Server-TLSv13-ClientAuthRequestedNotGiven b/src/crypto/tls/testdata/Server-TLSv13-ClientAuthRequestedNotGiven index fb2fb34d541..8acf69b2c77 100644 --- a/src/crypto/tls/testdata/Server-TLSv13-ClientAuthRequestedNotGiven +++ b/src/crypto/tls/testdata/Server-TLSv13-ClientAuthRequestedNotGiven @@ -1,104 +1,105 @@ >>> Flow 1 (client to server) -00000000 16 03 01 00 ca 01 00 00 c6 03 03 15 b6 db 09 24 |...............$| -00000010 50 ea d6 f7 ae d7 32 2f 72 25 23 db 11 ad 6f c1 |P.....2/r%#...o.| -00000020 5d 62 af e7 93 63 1a 8b f3 82 80 20 5f 15 2e 86 |]b...c..... _...| -00000030 86 2c 2e 2f 82 11 3c d2 9f 00 32 d4 3d 05 04 fa |.,./..<...2.=...| -00000040 36 41 8d dc 30 ce a6 2b 6e d4 3c 9c 00 04 13 01 |6A..0..+n.<.....| +00000000 16 03 01 00 ca 01 00 00 c6 03 03 2f cf 74 ea 4a |.........../.t.J| +00000010 69 06 51 85 47 b0 7d 47 67 0f 14 ac 4d 51 dd c3 |i.Q.G.}Gg...MQ..| +00000020 b2 20 4d e4 d5 7b 51 9f 73 bb 9b 20 65 a9 b6 65 |. M..{Q.s.. e..e| +00000030 37 97 40 71 50 68 2b d4 ea 3f b5 c1 5f b4 06 25 |7.@qPh+..?.._..%| +00000040 fe 0d 80 47 91 c5 63 44 b2 9c cf 65 00 04 13 01 |...G..cD...e....| 00000050 00 ff 01 00 00 79 00 0b 00 04 03 00 01 02 00 0a |.....y..........| 00000060 00 0c 00 0a 00 1d 00 17 00 1e 00 19 00 18 00 16 |................| 00000070 00 00 00 17 00 00 00 0d 00 1e 00 1c 04 03 05 03 |................| 00000080 06 03 08 07 08 08 08 09 08 0a 08 0b 08 04 08 05 |................| 00000090 08 06 04 01 05 01 06 01 00 2b 00 03 02 03 04 00 |.........+......| -000000a0 2d 00 02 01 01 00 33 00 26 00 24 00 1d 00 20 98 |-.....3.&.$... .| -000000b0 b7 40 03 d8 a3 4c 9e 16 82 77 16 9b c1 17 3a 2a |.@...L...w....:*| -000000c0 fc 25 73 5d 2d 5c dc 15 78 36 12 7a 28 f2 0e |.%s]-\..x6.z(..| +000000a0 2d 00 02 01 01 00 33 00 26 00 24 00 1d 00 20 b3 |-.....3.&.$... .| +000000b0 5a b6 ce 96 a9 d3 b2 a2 64 7c 7a be c2 d3 96 ab |Z.......d|z.....| +000000c0 ce 3f 74 0a fa a5 fb 04 d0 a8 b5 05 48 25 67 |.?t.........H%g| >>> Flow 2 (server to client) 00000000 16 03 03 00 7a 02 00 00 76 03 03 00 00 00 00 00 |....z...v.......| 00000010 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |................| -00000020 00 00 00 00 00 00 00 00 00 00 00 20 5f 15 2e 86 |........... _...| -00000030 86 2c 2e 2f 82 11 3c d2 9f 00 32 d4 3d 05 04 fa |.,./..<...2.=...| -00000040 36 41 8d dc 30 ce a6 2b 6e d4 3c 9c 13 01 00 00 |6A..0..+n.<.....| +00000020 00 00 00 00 00 00 00 00 00 00 00 20 65 a9 b6 65 |........... e..e| +00000030 37 97 40 71 50 68 2b d4 ea 3f b5 c1 5f b4 06 25 |7.@qPh+..?.._..%| +00000040 fe 0d 80 47 91 c5 63 44 b2 9c cf 65 13 01 00 00 |...G..cD...e....| 00000050 2e 00 2b 00 02 03 04 00 33 00 24 00 1d 00 20 2f |..+.....3.$... /| 00000060 e5 7d a3 47 cd 62 43 15 28 da ac 5f bb 29 07 30 |.}.G.bC.(.._.).0| 00000070 ff f6 84 af c4 cf c2 ed 90 99 5f 58 cb 3b 74 14 |.........._X.;t.| -00000080 03 03 00 01 01 17 03 03 00 17 14 12 e8 30 75 5a |.............0uZ| -00000090 a4 27 7d 83 2e 51 0e 48 14 7b 53 0c 65 24 71 c5 |.'}..Q.H.{S.e$q.| -000000a0 44 17 03 03 00 3e 34 38 ac c0 b5 05 e1 03 e1 a3 |D....>48........| -000000b0 d3 42 ec e3 94 96 e7 a3 05 d8 44 ca 1d 89 b6 6f |.B........D....o| -000000c0 52 ce 3c 7d 61 f1 b4 a2 83 31 ab cf e7 ca 53 57 |R.<}a....1....SW| -000000d0 b8 eb f4 7a 8a 7c ce 31 fe a4 b6 c7 a5 ed f2 2d |...z.|.1.......-| -000000e0 da 36 d6 49 17 03 03 02 6d 2c b4 e1 f3 87 4e c7 |.6.I....m,....N.| -000000f0 ab db ea fa 0d 31 20 f2 1e 63 1d 10 bd 61 98 a2 |.....1 ..c...a..| -00000100 50 8d 12 0d c8 5c f8 e4 97 9c 5f f3 47 f4 60 a5 |P....\...._.G.`.| -00000110 59 16 a2 27 06 94 80 93 af 1e 9d c0 9a 23 20 bf |Y..'.........# .| -00000120 a4 5a 26 2c 37 86 d8 8a b7 e2 bd e2 4f ab 53 65 |.Z&,7.......O.Se| -00000130 bd 34 2c 1a 88 72 bf 8f 20 0c e2 51 0f ea 3f 47 |.4,..r.. ..Q..?G| -00000140 dc 0e cd 21 3c d0 cc 7d 38 b8 b9 1b 20 67 83 a9 |...!<..}8... g..| -00000150 af 4c f7 7b c0 d9 00 5c 66 e3 d7 2e 3b 6a b5 9c |.L.{...\f...;j..| -00000160 6e f6 ed 96 25 3c ce ea db fa 85 ba e2 d8 4c 95 |n...%<........L.| -00000170 92 06 0a 38 19 7f 52 30 2b ef fc 23 c6 b3 e5 d1 |...8..R0+..#....| -00000180 83 2e 56 65 d6 ef 06 3a 71 d6 39 e9 16 62 65 78 |..Ve...:q.9..bex| -00000190 59 c1 9f 7f 99 be c2 b9 0b 56 0a db 26 ec 16 15 |Y........V..&...| -000001a0 be 27 cb bb cf 4a 9c a1 fd 5c 7d 5d c6 df a2 ed |.'...J...\}]....| -000001b0 f1 70 74 03 40 7c 8f af ea 3c 6a c7 c6 30 98 4c |.pt.@|....| +000001b0 05 dc 5e 27 43 76 21 f7 6c a2 9d 7c 82 6f fa 65 |..^'Cv!.l..|.o.e| +000001c0 b4 ae e3 89 80 be b9 c4 e7 b1 b0 61 e3 fb 32 72 |...........a..2r| +000001d0 e7 b7 85 d5 88 f7 7a cf 89 59 10 78 11 2b c0 a6 |......z..Y.x.+..| +000001e0 f4 6c f1 02 d0 ec 3f d6 32 e8 1a 4a e3 6f 2d 7d |.l....?.2..J.o-}| +000001f0 40 b1 fb 0a da bf 83 d5 47 c8 1c 27 1b cc 10 d4 |@.......G..'....| +00000200 c2 34 f3 1c 9e 3a ef 95 1e 91 e4 37 08 be 16 ba |.4...:.....7....| +00000210 a3 76 85 45 c5 1b b9 37 d3 0e a0 90 51 c3 f8 8e |.v.E...7....Q...| +00000220 8b c7 91 93 5b ad 99 8b 49 6e 6f 39 c1 98 4d bb |....[...Ino9..M.| +00000230 51 c0 ac 1e b6 ba bd 9e 5d f5 cb f2 ab 6f 86 fa |Q.......]....o..| +00000240 6e 93 91 36 70 1d b3 e0 a1 10 53 fb 67 9a 15 a8 |n..6p.....S.g...| +00000250 d1 f0 c8 32 63 83 06 f7 cf 61 9f 01 99 66 9e bf |...2c....a...f..| +00000260 c3 6d f4 a3 23 9b 6d f7 85 5b 4b 82 a9 50 2d 28 |.m..#.m..[K..P-(| +00000270 c5 89 4a ee c0 73 d4 33 ce 3c 08 f4 38 60 17 8a |..J..s.3.<..8`..| +00000280 e0 dd a6 ad ca 62 bf 50 51 5b 63 6f 07 a2 7a 1f |.....b.PQ[co..z.| +00000290 b7 5e 43 24 ad 56 73 ec 96 6d 75 fc a3 3c e4 d4 |.^C$.Vs..mu..<..| +000002a0 4d 03 c7 f5 e2 85 a6 ea 61 10 a9 c3 9d b4 19 c3 |M.......a.......| +000002b0 da f8 31 e2 7d 13 47 43 2c a4 b6 7a 1a 7f d3 60 |..1.}.GC,..z...`| +000002c0 01 1f 86 49 ef 0f 31 00 b4 c5 57 15 05 8a c4 7c |...I..1...W....|| +000002d0 f2 7e db 35 af d4 13 59 e6 63 96 b5 2c a7 e4 90 |.~.5...Y.c..,...| +000002e0 a5 a5 1a ef cd 43 48 6e fc e3 8c 91 aa 75 d1 75 |.....CHn.....u.u| +000002f0 2a 51 74 b5 1e 83 de aa 27 2a c6 04 fb 9c 23 5f |*Qt.....'*....#_| +00000300 b0 d2 c4 d4 af 81 10 bd 05 00 cd 8e 6c f8 12 34 |............l..4| +00000310 9f 90 ef de 15 7b a2 ad 28 fe 68 57 b1 f1 72 7e |.....{..(.hW..r~| +00000320 f1 8a c4 e5 e5 7e ba 3c e2 91 3d 6a 5c 44 3d ab |.....~.<..=j\D=.| +00000330 63 43 5d 36 20 ad 3d 2c e0 52 86 68 af 4e a3 c3 |cC]6 .=,.R.h.N..| +00000340 c0 7c 71 b4 04 0a 9e 2a b6 ad 17 06 56 51 14 56 |.|q....*....VQ.V| +00000350 c6 9f 39 60 5e a3 4a c5 c5 51 f6 82 17 03 03 00 |..9`^.J..Q......| +00000360 99 20 dd 68 f7 6c 50 7e c4 f6 03 6f 0f a6 d8 1e |. .h.lP~...o....| +00000370 f2 7d ba 98 ed 64 0a 9e 60 96 09 cb a8 07 ea 59 |.}...d..`......Y| +00000380 ae 70 bf f7 b3 cf 81 54 4d 29 8a 4d 1a 47 35 af |.p.....TM).M.G5.| +00000390 d6 46 ca 04 8a 1e b7 4f f7 03 66 08 12 57 45 06 |.F.....O..f..WE.| +000003a0 57 2d 9f 2a b3 50 35 74 f0 62 27 18 37 53 cf 6c |W-.*.P5t.b'.7S.l| +000003b0 72 1d 2e ed b5 88 ca 93 44 87 d3 7e 3b f4 8f d4 |r.......D..~;...| +000003c0 28 d5 4e f5 7b 48 e7 52 f7 fd 84 73 34 bc 4c dd |(.N.{H.R...s4.L.| +000003d0 e6 09 4b 68 d1 f7 7e 9a fb 31 ef 77 9d 3e 96 15 |..Kh..~..1.w.>..| +000003e0 dd 25 b0 d4 27 8b 9a 47 6d 17 8d 2a 23 ef c5 cb |.%..'..Gm..*#...| +000003f0 1d 42 94 82 c8 46 a6 2b b8 de 17 03 03 00 35 cf |.B...F.+......5.| +00000400 1f f7 44 67 c4 e6 17 93 d8 5f 59 62 0a 46 d9 7d |..Dg....._Yb.F.}| +00000410 3b 0b 05 4f b0 a7 7b 74 6d f4 da 52 52 76 89 4c |;..O..{tm..RRv.L| +00000420 dc a8 dc fb 99 c2 d0 86 17 27 c5 16 fa 0a d7 b8 |.........'......| +00000430 d8 e6 9e ec |....| >>> Flow 3 (client to server) -00000000 14 03 03 00 01 01 17 03 03 00 19 83 88 d2 c3 d4 |................| -00000010 a8 98 6c 8f fa 1b 52 a5 83 58 e3 62 89 3e 22 a3 |..l...R..X.b.>".| -00000020 37 b8 ee 13 17 03 03 00 35 b5 5f aa fd ca 85 74 |7.......5._....t| -00000030 ee c6 06 d9 2e d8 4f 7d 87 a2 b7 20 80 a5 3b 97 |......O}... ..;.| -00000040 41 bc 80 20 af b5 c4 66 26 2e 39 fd 81 e0 1a a0 |A.. ...f&.9.....| -00000050 6f c3 08 d0 23 c2 27 49 91 58 77 15 2d 49 |o...#.'I.Xw.-I| +00000000 14 03 03 00 01 01 17 03 03 00 19 e8 f2 9f cf 1d |................| +00000010 d9 2e ad d3 3f 6f 2d b3 e1 1e f1 d7 cc fc 0b 63 |....?o-........c| +00000020 c0 e1 a4 ec 17 03 03 00 35 3c 7c a4 22 a5 1f cd |........5<|."...| +00000030 ab 1a ce 3f 76 29 2d 8f 04 a9 9b bd f9 b7 bb c4 |...?v)-.........| +00000040 3f ba fb 8d 1c 8e 80 35 ce 77 02 f8 26 42 1c 7c |?......5.w..&B.|| +00000050 67 74 61 35 64 a7 27 24 b6 5a d1 0f 56 7a |gta5d.'$.Z..Vz| >>> Flow 4 (server to client) -00000000 17 03 03 00 93 10 f4 e9 f1 51 30 25 9e f0 c4 d2 |.........Q0%....| -00000010 b8 f4 4b ad dd 89 ad ab 1a 39 88 44 98 a2 53 4e |..K......9.D..SN| -00000020 1c e9 bb 4a b7 c1 d8 cc bc 76 e6 a8 e6 41 b9 42 |...J.....v...A.B| -00000030 c8 7a 0a f4 35 73 cc 9f 9d 30 ff 4e e3 44 89 a5 |.z..5s...0.N.D..| -00000040 d0 2b 88 36 0a 87 72 b4 bf 48 6a 4e 2e 03 1a 96 |.+.6..r..HjN....| -00000050 1e 01 07 90 61 b0 f1 c5 58 e0 48 30 db d6 e9 5c |....a...X.H0...\| -00000060 88 05 0d 47 fc d1 33 6e 7e c4 fb 81 e3 80 ce 67 |...G..3n~......g| -00000070 93 59 5e 68 39 6c b2 c3 c3 56 09 61 e5 a1 d6 d9 |.Y^h9l...V.a....| -00000080 95 3a 70 6a 5c 4a 51 24 d9 e7 ed 88 7f 6c 32 0a |.:pj\JQ$.....l2.| -00000090 2d 5d 79 40 75 c9 b9 d4 17 03 03 00 1e 24 cc 07 |-]y@u........$..| -000000a0 53 2b 27 c1 36 47 88 b8 3c 91 9e 8b 13 da 9d 3c |S+'.6G..<......<| -000000b0 f9 65 9d 78 ed 92 36 11 41 fe 42 17 03 03 00 13 |.e.x..6.A.B.....| -000000c0 2b 52 80 d0 d5 39 77 77 38 ad e0 ad 78 f8 0a 59 |+R...9ww8...x..Y| -000000d0 96 18 7e |..~| +00000000 17 03 03 00 93 c9 dc 93 00 07 3a 67 39 76 6b ed |..........:g9vk.| +00000010 21 7c 66 68 b9 2f 88 35 86 ba 7b a0 7a a1 57 52 |!|fh./.5..{.z.WR| +00000020 96 51 38 2d 1e dc 09 35 7a 29 5d 75 bb bf ce f8 |.Q8-...5z)]u....| +00000030 79 8c 19 f2 eb f5 01 50 6e 63 cb c8 c2 77 63 31 |y......Pnc...wc1| +00000040 04 21 f8 16 37 86 13 f6 6f 91 3c e3 f8 43 b4 39 |.!..7...o.<..C.9| +00000050 33 16 10 8b 8e 5a a4 f2 29 3c 8c fe c9 c3 20 77 |3....Z..)<.... w| +00000060 81 00 1a a0 5c 84 bd fc 1d f2 37 e5 13 36 14 de |....\.....7..6..| +00000070 75 6a 75 4e 39 81 e0 71 30 16 96 44 08 9c ba 8b |ujuN9..q0..D....| +00000080 d9 6d 97 16 29 db a6 ca 86 dd 57 a1 91 a8 88 00 |.m..).....W.....| +00000090 60 3b ca 0f c3 98 42 60 17 03 03 00 1e 9e 4e 56 |`;....B`......NV| +000000a0 ce 3d 2d ce 00 d7 7c 0e 41 07 f1 02 95 6a 94 78 |.=-...|.A....j.x| +000000b0 f8 3c 25 c7 d1 82 57 9c 89 5d 4a 17 03 03 00 13 |.<%...W..]J.....| +000000c0 b4 6a 72 ea ba 94 4e 58 76 f8 7a cd 33 10 e2 5f |.jr...NXv.z.3.._| +000000d0 ef ec c8 |...| diff --git a/src/crypto/tls/tls.go b/src/crypto/tls/tls.go index a389873d32e..0cab274de24 100644 --- a/src/crypto/tls/tls.go +++ b/src/crypto/tls/tls.go @@ -4,14 +4,63 @@ // Package tls partially implements TLS 1.2, as specified in RFC 5246, // and TLS 1.3, as specified in RFC 8446. +// +// This package implements the "Encrypted ClientHello (ECH)" extension, as +// specified by draft-ietf-tls-esni-10. This extension allows the client to +// encrypt its ClientHello to the public key of an ECH-service provider, known +// as the client-facing server. If successful, then the client-facing server +// forwards the decrypted ClientHello to the intended recipient, known as the +// backend server. The goal of this mechanism is to ensure that connections made +// to backend servers are indistinguishable from one another. +// +// This package implements the "Delegated Credentials" extension, as +// specified by draft-ietf-tls-subcerts-10. This extension allows the usage +// of a limited delegation mechanism that allows a TLS peer to issue its own +// credentials within the scope of a certificate issued by an external +// CA. These credentials only enable the recipient of the delegation to +// speak for names that the CA has authorized. If the client or server supports +// this extension, then the server or client may use a "delegated credential" +// as the signing key in the handshake. A delegated credential is a short lived +// public/secret key pair delegated to the peer by an entity trusted by the +// corresponding peer. This allows a reverse proxy to terminate a TLS connection +// on behalf of the entity. Credentials can't be revoked; in order to +// mitigate risk in case the reverse proxy is compromised, the credential is only +// valid for a short time (days, hours, or even minutes). package tls +// BUG(cjpatton): In order to achieve its security goal, the ECH extension +// requires padding in order to ensure that the length of handshake messages +// doesn't depend on who terminates the connection. This package does not yet +// implement client- or server-side padding: see +// https://github.com/tlswg/draft-ietf-tls-esni/issues/264. + +// BUG(cjpatton): Another goal of the ECH extension is that connections that +// middleboxes shouldn't differentiate between the real ECH protocol and the +// "grease ECH" protocol wherein the client generates a dummy ECH extension, +// which the server is expected to ignore. The ECH specification is subject to +// change as this "don't stick out" property is worked out in more detail. + +// BUG(cjpatton): The interaction of the ECH extension with PSK has not yet been +// fully vetted. For now, the server disables session tickets if ECH is enabled. + +// BUG(cjpatton): Upon ECH rejection, if retry configurations are provided, then +// the client is expected to retry the connection. Otherwise, it may regard ECH +// as being securely disabled by the client-facing server. The client in this +// package does not attempt to retry the handshake. + +// BUG(cjpatton): If the client offers the ECH extension and the client-facing +// server rejects it, then only the client-facing server is authenticated. In +// particular, the client is expected to respond to a CertificateRequest with an +// empty certificate. This package does not yet implement this behavior. + // BUG(agl): The crypto/tls package only implements some countermeasures // against Lucky13 attacks on CBC-mode encryption, and only on SHA1 // variants. See http://www.isg.rhul.ac.uk/tls/TLStiming.pdf and // https://www.imperialviolet.org/2013/02/04/luckythirteen.html. import ( + circlSign "circl/sign" + "bytes" "context" "crypto" @@ -357,6 +406,17 @@ func X509KeyPair(certPEMBlock, keyPEMBlock []byte) (Certificate, error) { if !bytes.Equal(priv.Public().(ed25519.PublicKey), pub) { return fail(errors.New("tls: private key does not match public key")) } + case circlSign.PublicKey: + priv, ok := cert.PrivateKey.(circlSign.PrivateKey) + if !ok { + return fail(errors.New("tls: private key type does not match public key type")) + } + pkBytes, err := priv.Public().(circlSign.PublicKey).MarshalBinary() + pkBytes2, err2 := pub.MarshalBinary() + + if err != nil || err2 != nil || !bytes.Equal(pkBytes, pkBytes2) { + return fail(errors.New("tls: private key does not match public key")) + } default: return fail(errors.New("tls: unknown public key algorithm")) } @@ -373,7 +433,7 @@ func parsePrivateKey(der []byte) (crypto.PrivateKey, error) { } if key, err := x509.ParsePKCS8PrivateKey(der); err == nil { switch key := key.(type) { - case *rsa.PrivateKey, *ecdsa.PrivateKey, ed25519.PrivateKey: + case *rsa.PrivateKey, *ecdsa.PrivateKey, ed25519.PrivateKey, circlSign.PrivateKey: return key, nil default: return nil, errors.New("tls: found unknown private key type in PKCS#8 wrapping") diff --git a/src/crypto/tls/tls_cf.go b/src/crypto/tls/tls_cf.go new file mode 100644 index 00000000000..50f166c1736 --- /dev/null +++ b/src/crypto/tls/tls_cf.go @@ -0,0 +1,273 @@ +// Copyright 2021 Cloudflare, Inc. All rights reserved. Use of this source code +// is governed by a BSD-style license that can be found in the LICENSE file. + +package tls + +import ( + circlPki "circl/pki" + circlSign "circl/sign" + + "circl/sign/ed448" + "circl/sign/eddilithium3" + "circl/sign/eddilithium4" + "time" +) + +const ( + // Constants for ECH status events. + echStatusBypassed = 1 + iota + echStatusInner + echStatusOuter +) + +// To add a signature scheme from Circl +// +// 1. make sure it implements TLSScheme and CertificateScheme, +// 2. follow the instructions in crypto/x509/x509_cf.go +// 3. add a signature to the iota in common.go +// 4. add row in the circlSchemes lists below + +var circlSchemes = [...]struct { + sigType uint8 + scheme circlSign.Scheme +}{ + {signatureEdDilithium3, eddilithium3.Scheme()}, + {signatureEdDilithium4, eddilithium4.Scheme()}, + {signatureEd448, ed448.Scheme()}, +} + +func circlSchemeBySigType(sigType uint8) circlSign.Scheme { + for _, cs := range circlSchemes { + if cs.sigType == sigType { + return cs.scheme + } + } + return nil +} + +func sigTypeByCirclScheme(scheme circlSign.Scheme) uint8 { + for _, cs := range circlSchemes { + if cs.scheme == scheme { + return cs.sigType + } + } + return 0 +} + +func init() { + for _, cs := range circlSchemes { + supportedSignatureAlgorithms = append(supportedSignatureAlgorithms, + SignatureScheme(cs.scheme.(circlPki.TLSScheme).TLSIdentifier())) + } +} + +// CFEvent is a value emitted at various points in the handshake that is +// handled by the callback Config.CFEventHandler. +type CFEvent interface { + Name() string +} + +func experimentName(c *Conn) string { + // Reports the experiment number + exp := "exp" + alg := "" + switch true { + case c.didKEMTLS: + exp += "3" + alg += c.verifiedDC.algorithm.String() + break + case c.didPQTLS: + exp += "2" + alg += c.verifiedDC.algorithm.String() + break + case c.verifiedDC != nil: + exp += "1" + alg += c.verifiedDC.algorithm.String() + break + case c.verifiedDC == nil: + exp += "0" + alg = CipherSuiteName(c.cipherSuite) + break + default: + break + } + return exp + "_" + alg +} + +// CFEventTLS13ClientHandshakeTimingInfo carries intra-stack time durations for +// TLS 1.3 client-state machine changes. It can be used for tracking metrics +// during a connection. Some durations may be sensitive, such as the amount of +// time to process a particular handshake message, so this event should only be +// used for experimental purposes. +type CFEventTLS13ClientHandshakeTimingInfo struct { + timer func() time.Time + start time.Time + total time.Time + WriteClientHello time.Duration + ProcessServerHello time.Duration + ReadEncryptedExtensions time.Duration + ReadCertificate time.Duration + ReadCertificateVerify time.Duration + + ReadServerFinished time.Duration + WriteCertificate time.Duration + WriteCertificateVerify time.Duration + WriteClientFinished time.Duration + + WriteKEMCiphertext time.Duration + ReadKEMCiphertext time.Duration + FullProtocol time.Duration + + ExperimentName string +} + +// Name is required by the CFEvent interface. +func (e CFEventTLS13ClientHandshakeTimingInfo) Name() string { + return "TLS13ClientHandshakeTimingInfo" +} + +func (e CFEventTLS13ClientHandshakeTimingInfo) elapsedTime() time.Duration { + if e.timer == nil { + return 0 + } + return e.timer().Sub(e.start) +} + +func (e *CFEventTLS13ClientHandshakeTimingInfo) reset() { + e.start = e.timer() +} + +func (e *CFEventTLS13ClientHandshakeTimingInfo) finish() { + e.FullProtocol = e.timer().Sub(e.total) +} + +func createTLS13ClientHandshakeTimingInfo(timerFunc func() time.Time) CFEventTLS13ClientHandshakeTimingInfo { + timer := time.Now + if timerFunc != nil { + timer = timerFunc + } + now := timer() + return CFEventTLS13ClientHandshakeTimingInfo{ + timer: timer, + start: now, + total: now, + } +} + +// CFEventTLS13ServerHandshakeTimingInfo carries intra-stack time durations +// for TLS 1.3 state machine changes. It can be used for tracking metrics during a +// connection. Some durations may be sensitive, such as the amount of time to +// process a particular handshake message, so this event should only be used +// for experimental purposes. +type CFEventTLS13ServerHandshakeTimingInfo struct { + timer func() time.Time + start time.Time + total time.Time + ProcessClientHello time.Duration + WriteServerHello time.Duration + WriteEncryptedExtensions time.Duration + WriteCertificate time.Duration + WriteCertificateVerify time.Duration + + WriteServerFinished time.Duration + ReadCertificate time.Duration + ReadCertificateVerify time.Duration + ReadClientFinished time.Duration + + ReadKEMCiphertext time.Duration + WriteKEMCiphertext time.Duration + FullProtocol time.Duration + + ExperimentName string +} + +// Name is required by the CFEvent interface. +func (e CFEventTLS13ServerHandshakeTimingInfo) Name() string { + return "TLS13ServerHandshakeTimingInfo" +} + +func (e CFEventTLS13ServerHandshakeTimingInfo) elapsedTime() time.Duration { + if e.timer == nil { + return 0 + } + return e.timer().Sub(e.start) +} + +func (e *CFEventTLS13ServerHandshakeTimingInfo) reset() { + e.start = e.timer() +} + +func (e *CFEventTLS13ServerHandshakeTimingInfo) finish() { + e.FullProtocol = e.timer().Sub(e.total) +} + +func createTLS13ServerHandshakeTimingInfo(timerFunc func() time.Time) CFEventTLS13ServerHandshakeTimingInfo { + timer := time.Now + if timerFunc != nil { + timer = timerFunc + } + now := timer() + return CFEventTLS13ServerHandshakeTimingInfo{ + timer: timer, + start: now, + total: now, + } +} + +// CFEventECHClientStatus is emitted once it is known whether the client +// bypassed, offered, or greased ECH. +type CFEventECHClientStatus int + +// Bypassed returns true if the client bypassed ECH. +func (e CFEventECHClientStatus) Bypassed() bool { + return e == echStatusBypassed +} + +// Offered returns true if the client offered ECH. +func (e CFEventECHClientStatus) Offered() bool { + return e == echStatusInner +} + +// Greased returns true if the client greased ECH. +func (e CFEventECHClientStatus) Greased() bool { + return e == echStatusOuter +} + +// Name is required by the CFEvent interface. +func (e CFEventECHClientStatus) Name() string { + return "ech client status" +} + +// CFEventECHServerStatus is emitted once it is known whether the client +// bypassed, offered, or greased ECH. +type CFEventECHServerStatus int + +// Bypassed returns true if the client bypassed ECH. +func (e CFEventECHServerStatus) Bypassed() bool { + return e == echStatusBypassed +} + +// Accepted returns true if the client offered ECH. +func (e CFEventECHServerStatus) Accepted() bool { + return e == echStatusInner +} + +// Rejected returns true if the client greased ECH. +func (e CFEventECHServerStatus) Rejected() bool { + return e == echStatusOuter +} + +// Name is required by the CFEvent interface. +func (e CFEventECHServerStatus) Name() string { + return "ech server status" +} + +// CFEventECHPublicNameMismatch is emitted if the outer SNI does not match +// match the public name of the ECH configuration. Note that we do not record +// the outer SNI in order to avoid collecting this potentially sensitive data. +type CFEventECHPublicNameMismatch struct{} + +// Name is required by the CFEvent interface. +func (e CFEventECHPublicNameMismatch) Name() string { + return "ech public name does not match outer sni" +} diff --git a/src/crypto/tls/tls_cf_test.go b/src/crypto/tls/tls_cf_test.go new file mode 100644 index 00000000000..53c3becf3df --- /dev/null +++ b/src/crypto/tls/tls_cf_test.go @@ -0,0 +1,19 @@ +package tls + +import ( + "testing" +) + +type testCFControl struct { + flags uint64 +} + +// Check that CFControl is correctly propagated from Config to ConnectionState. +func TestPropagateCFControl(t *testing.T) { + want := uint64(23) + s := Server(nil, &Config{CFControl: &testCFControl{want}}) + got := s.ConnectionState().CFControl.(*testCFControl).flags + if got != want { + t.Errorf("failed to propagate CFControl: got %v; want %v", got, want) + } +} diff --git a/src/crypto/tls/tls_test.go b/src/crypto/tls/tls_test.go index 9995538871e..eb3be3d3c58 100644 --- a/src/crypto/tls/tls_test.go +++ b/src/crypto/tls/tls_test.go @@ -789,7 +789,7 @@ func TestCloneNonFuncFields(t *testing.T) { switch fn := typ.Field(i).Name; fn { case "Rand": f.Set(reflect.ValueOf(io.Reader(os.Stdin))) - case "Time", "GetCertificate", "GetConfigForClient", "VerifyPeerCertificate", "VerifyConnection", "GetClientCertificate": + case "Time", "GetCertificate", "GetConfigForClient", "VerifyPeerCertificate", "VerifyConnection", "GetClientCertificate", "ServerECHProvider", "CFEventHandler": // DeepEqual can't compare functions. If you add a // function field to this list, you must also change // TestCloneFuncFields to ensure that the func field is @@ -816,6 +816,16 @@ func TestCloneNonFuncFields(t *testing.T) { f.Set(reflect.ValueOf(true)) case "MinVersion", "MaxVersion": f.Set(reflect.ValueOf(uint16(VersionTLS12))) + case "KEMTLSEnabled": + f.Set(reflect.ValueOf(false)) + case "PQTLSEnabled": + f.Set(reflect.ValueOf(false)) + case "SupportDelegatedCredential": + f.Set(reflect.ValueOf(true)) + case "CachedCert": + f.Set(reflect.ValueOf([]byte{})) + case "CachedCertReq": + f.Set(reflect.ValueOf([]byte{})) case "SessionTicketKey": f.Set(reflect.ValueOf([32]byte{})) case "CipherSuites": @@ -826,6 +836,12 @@ func TestCloneNonFuncFields(t *testing.T) { f.Set(reflect.ValueOf(RenegotiateOnceAsClient)) case "mutex", "autoSessionTicketKeys", "sessionTicketKeys": continue // these are unexported fields that are handled separately + case "ClientECHConfigs": + f.Set(reflect.ValueOf([]ECHConfig{ECHConfig{}})) + case "ECHEnabled": + f.Set(reflect.ValueOf(true)) + case "CFControl": + f.Set(reflect.ValueOf(&testCFControl{23})) default: t.Errorf("all fields must be accounted for, but saw unknown field %q", fn) } @@ -1474,3 +1490,87 @@ func TestPKCS1OnlyCert(t *testing.T) { t.Error(err) } } + +func TestKEMEphemeralTLS13(t *testing.T) { + tests := []CurveID{ + SIKEp434, + Kyber512, + } + + for _, kem := range tests { + clientConfig := testConfig.Clone() + clientConfig.CurvePreferences = []CurveID{kem} + clientConfig.MinVersion = VersionTLS13 + clientConfig.MaxVersion = VersionTLS13 + clientConfig.KEMTLSEnabled = true + + serverConfig := testConfig.Clone() + + if _, _, err := testHandshake(t, clientConfig, serverConfig); err == nil { + t.Fatal("Should have failed to connect with KEM-only client") + } + + clientConfig = testConfig.Clone() + clientConfig.KEMTLSEnabled = false + + serverConfig = testConfig.Clone() + serverConfig.KEMTLSEnabled = true + serverConfig.MinVersion = VersionTLS13 + serverConfig.MaxVersion = VersionTLS13 + serverConfig.CurvePreferences = []CurveID{kem} + + if _, _, err := testHandshake(t, clientConfig, serverConfig); err == nil { + t.Fatal("Should have failed to connect with KEM-only server") + } + + clientConfig.CurvePreferences = []CurveID{X25519} + if _, _, err := testHandshake(t, clientConfig, serverConfig); err == nil { + t.Fatal("Still connected with KEM-only server and no-KEM Client") + } + + serverConfig = testConfig.Clone() + serverConfig.KEMTLSEnabled = true + serverConfig.CurvePreferences = []CurveID{kem} + + clientConfig = testConfig.Clone() + clientConfig.KEMTLSEnabled = true + clientConfig.CurvePreferences = []CurveID{kem} + clientConfig.MaxVersion = VersionTLS12 + + if _, _, err := testHandshake(t, clientConfig, serverConfig); err == nil { + t.Fatal("Still connected with KEM-only server and TLS 1.2 Client") + } + } +} + +func TestChachedInformationTLS13(t *testing.T) { + clientConfig := testConfig.Clone() + clientConfig.MinVersion = VersionTLS13 + clientConfig.MaxVersion = VersionTLS13 + + serverConfig := testConfig.Clone() + serverConfig.ClientAuth = RequestClientCert + + serverState, clientState, err := testHandshake(t, clientConfig, serverConfig) + if err != nil { + t.Fatal("Should have succedeed") + } + + if len(serverState.CertificateMessage) < 0 || len(clientState.CertificateMessage) < 0 { + t.Fatal("Should have saved the Certificate Message") + } + + if len(serverState.CertificateReqMessage) < 0 || len(clientState.CertificateReqMessage) < 0 { + t.Fatal("Should have saved the Certificate Request Message") + } + + serverConfig.CachedCert = serverState.CertificateMessage + serverConfig.CachedCertReq = serverState.CertificateReqMessage + clientConfig.CachedCert = clientState.CertificateMessage + clientConfig.CachedCertReq = clientState.CertificateReqMessage + + _, _, err = testHandshake(t, clientConfig, serverConfig) + if err != nil { + t.Fatal("Should have succedeed") + } +} diff --git a/src/crypto/x509/pkcs8.go b/src/crypto/x509/pkcs8.go index a5ee4cfbfef..42843ae9675 100644 --- a/src/crypto/x509/pkcs8.go +++ b/src/crypto/x509/pkcs8.go @@ -12,6 +12,9 @@ import ( "encoding/asn1" "errors" "fmt" + + circlPki "circl/pki" + circlSign "circl/sign" ) // pkcs8 reflects an ASN.1, PKCS #8 PrivateKey. See @@ -75,7 +78,22 @@ func ParsePKCS8PrivateKey(der []byte) (key interface{}, err error) { return ed25519.NewKeyFromSeed(curvePrivateKey), nil default: - return nil, fmt.Errorf("x509: PKCS#8 wrapping contained private key with unknown algorithm: %v", privKey.Algo.Algorithm) + scheme := circlPki.SchemeByOid(privKey.Algo.Algorithm) + if scheme == nil { + return nil, fmt.Errorf("x509: PKCS#8 wrapping contained private key with unknown algorithm: %v", privKey.Algo.Algorithm) + } + if l := len(privKey.Algo.Parameters.FullBytes); l != 0 { + return nil, fmt.Errorf("x509: invalid %s private key parameters", scheme.Name()) + } + var packedSk []byte + if _, err := asn1.Unmarshal(privKey.PrivateKey, &packedSk); err != nil { + return nil, fmt.Errorf("x509: invalid %s private key: %v", scheme.Name(), err) + } + sk, err := scheme.UnmarshalBinaryPrivateKey(packedSk) + if err != nil { + return nil, fmt.Errorf("x509: invalid %s private key: %v", scheme.Name(), err) + } + return sk, nil } } @@ -128,6 +146,22 @@ func MarshalPKCS8PrivateKey(key interface{}) ([]byte, error) { } privKey.PrivateKey = curvePrivateKey + case circlSign.PrivateKey: + scheme, ok := k.Scheme().(circlPki.CertificateScheme) + if !ok { + return nil, fmt.Errorf( + "x509: circl private key is not CertificateScheme") + } + privKey.Algo = pkix.AlgorithmIdentifier{ + Algorithm: scheme.Oid(), + } + bytes, _ := k.MarshalBinary() + packedSk, err := asn1.Marshal(bytes) + if err != nil { + return nil, fmt.Errorf("x509: failed to marshal private key: %v", err) + } + privKey.PrivateKey = packedSk + default: return nil, fmt.Errorf("x509: unknown key type while marshaling PKCS#8: %T", key) } diff --git a/src/crypto/x509/verify_test.go b/src/crypto/x509/verify_test.go index 8e0a7bef475..f7caf53d0ae 100644 --- a/src/crypto/x509/verify_test.go +++ b/src/crypto/x509/verify_test.go @@ -1883,7 +1883,7 @@ func TestValidHostname(t *testing.T) { } } -func generateCert(cn string, isCA bool, issuer *Certificate, issuerKey crypto.PrivateKey) (*Certificate, crypto.PrivateKey, error) { +func generateCert(cn string, isCA bool, isDC bool, issuer *Certificate, issuerKey crypto.PrivateKey) (*Certificate, crypto.PrivateKey, error) { priv, err := ecdsa.GenerateKey(elliptic.P256(), rand.Reader) if err != nil { return nil, nil, err @@ -1902,6 +1902,7 @@ func generateCert(cn string, isCA bool, issuer *Certificate, issuerKey crypto.Pr ExtKeyUsage: []ExtKeyUsage{ExtKeyUsageServerAuth}, BasicConstraintsValid: true, IsCA: isCA, + AllowDC: isDC, } if issuer == nil { issuer = template @@ -1929,21 +1930,21 @@ func TestPathologicalChain(t *testing.T) { // path building worst behavior. roots, intermediates := NewCertPool(), NewCertPool() - parent, parentKey, err := generateCert("Root CA", true, nil, nil) + parent, parentKey, err := generateCert("Root CA", true, false, nil, nil) if err != nil { t.Fatal(err) } roots.AddCert(parent) for i := 1; i < 100; i++ { - parent, parentKey, err = generateCert("Intermediate CA", true, parent, parentKey) + parent, parentKey, err = generateCert("Intermediate CA", true, false, parent, parentKey) if err != nil { t.Fatal(err) } intermediates.AddCert(parent) } - leaf, _, err := generateCert("Leaf", false, parent, parentKey) + leaf, _, err := generateCert("Leaf", false, true, parent, parentKey) if err != nil { t.Fatal(err) } @@ -1967,7 +1968,7 @@ func TestLongChain(t *testing.T) { roots, intermediates := NewCertPool(), NewCertPool() - parent, parentKey, err := generateCert("Root CA", true, nil, nil) + parent, parentKey, err := generateCert("Root CA", true, false, nil, nil) if err != nil { t.Fatal(err) } @@ -1975,14 +1976,14 @@ func TestLongChain(t *testing.T) { for i := 1; i < 15; i++ { name := fmt.Sprintf("Intermediate CA #%d", i) - parent, parentKey, err = generateCert(name, true, parent, parentKey) + parent, parentKey, err = generateCert(name, true, false, parent, parentKey) if err != nil { t.Fatal(err) } intermediates.AddCert(parent) } - leaf, _, err := generateCert("Leaf", false, parent, parentKey) + leaf, _, err := generateCert("Leaf", false, true, parent, parentKey) if err != nil { t.Fatal(err) } diff --git a/src/crypto/x509/x509.go b/src/crypto/x509/x509.go index 8c0299b11e9..24d2dfc97ce 100644 --- a/src/crypto/x509/x509.go +++ b/src/crypto/x509/x509.go @@ -12,6 +12,7 @@ import ( "crypto/ecdsa" "crypto/ed25519" "crypto/elliptic" + "crypto/kem" "crypto/rsa" "crypto/sha1" "crypto/x509/pkix" @@ -34,6 +35,9 @@ import ( _ "crypto/sha256" _ "crypto/sha512" + circlPki "circl/pki" + circlSign "circl/sign" + "golang.org/x/crypto/cryptobyte" cryptobyte_asn1 "golang.org/x/crypto/cryptobyte/asn1" ) @@ -100,6 +104,17 @@ func marshalPublicKey(pub interface{}) (publicKeyBytes []byte, publicKeyAlgorith case ed25519.PublicKey: publicKeyBytes = pub publicKeyAlgorithm.Algorithm = oidPublicKeyEd25519 + case circlSign.PublicKey: + scheme, ok := pub.Scheme().(circlPki.CertificateScheme) + if !ok { + return nil, pkix.AlgorithmIdentifier{}, errors.New( + "x509: circl scheme is not CertificateScheme") + } + publicKeyBytes, _ = pub.MarshalBinary() + publicKeyAlgorithm.Algorithm = scheme.Oid() + case *kem.PublicKey: + publicKeyBytes, _ = pub.MarshalBinary() + publicKeyAlgorithm.Algorithm = oidPublicKeyKEMTLS default: return nil, pkix.AlgorithmIdentifier{}, fmt.Errorf("x509: unsupported public key type: %T", pub) } @@ -199,6 +214,9 @@ const ( SHA384WithRSAPSS SHA512WithRSAPSS PureEd25519 + PureEd448 + PureEdDilithium3 + PureEdDilithium4 ) func (algo SignatureAlgorithm) isRSAPSS() bool { @@ -227,13 +245,21 @@ const ( DSA // Unsupported. ECDSA Ed25519 + Ed448 + EdDilithium3 + EdDilithium4 + KEMTLS ) var publicKeyAlgoName = [...]string{ - RSA: "RSA", - DSA: "DSA", - ECDSA: "ECDSA", - Ed25519: "Ed25519", + RSA: "RSA", + DSA: "DSA", + ECDSA: "ECDSA", + Ed25519: "Ed25519", + Ed448: "Ed448", + EdDilithium3: "Ed25519-Dilithium3", + EdDilithium4: "Ed448-Dilithium4", + KEMTLS: "KEMTLS", } func (algo PublicKeyAlgorithm) String() string { @@ -378,7 +404,7 @@ type pssParameters struct { } func getSignatureAlgorithmFromAI(ai pkix.AlgorithmIdentifier) SignatureAlgorithm { - if ai.Algorithm.Equal(oidSignatureEd25519) { + if ai.Algorithm.Equal(oidSignatureEd25519) || circlPki.SchemeByOid(ai.Algorithm) != nil { // RFC 8410, Section 3 // > For all of the OIDs, the parameters MUST be absent. if len(ai.Parameters.FullBytes) != 0 { @@ -448,10 +474,14 @@ func getSignatureAlgorithmFromAI(ai pkix.AlgorithmIdentifier) SignatureAlgorithm // id-ecPublicKey OBJECT IDENTIFIER ::= { // iso(1) member-body(2) us(840) ansi-X9-62(10045) keyType(2) 1 } var ( - oidPublicKeyRSA = asn1.ObjectIdentifier{1, 2, 840, 113549, 1, 1, 1} - oidPublicKeyDSA = asn1.ObjectIdentifier{1, 2, 840, 10040, 4, 1} - oidPublicKeyECDSA = asn1.ObjectIdentifier{1, 2, 840, 10045, 2, 1} - oidPublicKeyEd25519 = oidSignatureEd25519 + oidPublicKeyRSA = asn1.ObjectIdentifier{1, 2, 840, 113549, 1, 1, 1} + oidPublicKeyDSA = asn1.ObjectIdentifier{1, 2, 840, 10040, 4, 1} + oidPublicKeyECDSA = asn1.ObjectIdentifier{1, 2, 840, 10045, 2, 1} + oidPublicKeyEd25519 = oidSignatureEd25519 + oidPublicKeyEd448 = asn1.ObjectIdentifier{1, 3, 101, 113} + oidPublicKeyEdDilithium3 = asn1.ObjectIdentifier{1, 3, 6, 1, 4, 1, 44363, 45, 9} // Cloudflare OID + oidPublicKeyEdDilithium4 = asn1.ObjectIdentifier{1, 3, 6, 1, 4, 1, 44363, 45, 10} // Cloudflare OID + oidPublicKeyKEMTLS = asn1.ObjectIdentifier{1, 3, 6, 1, 4, 1, 44363, 45, 11} // Cloudflare OID ) func getPublicKeyAlgorithmFromOID(oid asn1.ObjectIdentifier) PublicKeyAlgorithm { @@ -464,8 +494,21 @@ func getPublicKeyAlgorithmFromOID(oid asn1.ObjectIdentifier) PublicKeyAlgorithm return ECDSA case oid.Equal(oidPublicKeyEd25519): return Ed25519 + case oid.Equal(oidPublicKeyEd448): + return Ed448 + case oid.Equal(oidPublicKeyEdDilithium3): + return EdDilithium3 + case oid.Equal(oidPublicKeyEdDilithium4): + return EdDilithium4 + case oid.Equal(oidPublicKeyKEMTLS): + return KEMTLS + default: + scheme := circlPki.SchemeByOid(oid) + if scheme == nil { + return UnknownPublicKeyAlgorithm + } + return PublicKeyAlgorithmByCirclScheme(scheme) } - return UnknownPublicKeyAlgorithm } // RFC 5480, 2.1.1.1. Named Curve @@ -676,6 +719,9 @@ type Certificate struct { BasicConstraintsValid bool IsCA bool + // AllowDC indicates if the certificate can be used for delegated credentials. + AllowDC bool + // MaxPathLen and MaxPathLenZero indicate the presence and // value of the BasicConstraints' "pathLenConstraint". // @@ -822,7 +868,7 @@ func checkSignature(algo SignatureAlgorithm, signed, signature []byte, publicKey switch hashType { case crypto.Hash(0): - if pubKeyAlgo != Ed25519 { + if pubKeyAlgo != Ed25519 && CirclSchemeByPublicKeyAlgorithm(pubKeyAlgo) == nil { return ErrUnsupportedAlgorithm } case crypto.MD5: @@ -862,6 +908,19 @@ func checkSignature(algo SignatureAlgorithm, signed, signature []byte, publicKey return errors.New("x509: Ed25519 verification failure") } return + case circlSign.PublicKey: + scheme := pub.Scheme() + expectedAlg := PublicKeyAlgorithmByCirclScheme(scheme) + if expectedAlg == UnknownPublicKeyAlgorithm { + return ErrUnsupportedAlgorithm + } + if expectedAlg != pubKeyAlgo { + return signaturePublicKeyAlgoMismatchError(pubKeyAlgo, pub) + } + if !scheme.Verify(pub, signed, signature, nil) { + return fmt.Errorf("x509: %s verification failed", scheme.Name()) + } + return } return ErrUnsupportedAlgorithm } @@ -1011,7 +1070,27 @@ func parsePublicKey(algo PublicKeyAlgorithm, keyData *publicKeyInfo) (interface{ pub := make([]byte, ed25519.PublicKeySize) copy(pub, asn1Data) return ed25519.PublicKey(pub), nil + case KEMTLS: + pub := new(kem.PublicKey) + err := pub.UnmarshalBinary(keyData.PublicKey.Bytes) + if err != nil { + return nil, errors.New("x509: wrong KEM identifier") + } + return pub, nil default: + if scheme := CirclSchemeByPublicKeyAlgorithm(algo); scheme != nil { + if len(keyData.Algorithm.Parameters.FullBytes) != 0 { + return nil, fmt.Errorf( + "x509: %skey encoded with illegal parameters", + scheme.Name(), + ) + } + pub, err := scheme.UnmarshalBinaryPublicKey(asn1Data) + if err != nil { + return nil, fmt.Errorf("x509: %s: %v", scheme.Name(), err) + } + return pub, nil + } return nil, nil } } @@ -1449,6 +1528,18 @@ func parseCertificate(in *certificate) (*Certificate, error) { out.IssuingCertificateURL = append(out.IssuingCertificateURL, string(v.Location.Bytes)) } } + } else if e.Id.Equal(oidExtensionDelegatedCredential) { + if !out.IsCA { + if out.KeyUsage == KeyUsageDigitalSignature { + val := asn1.RawValue{} + if rest, err := asn1.Unmarshal(e.Value, &val); err != nil { + return nil, err + } else if len(rest) != 0 { + return nil, errors.New("x509: trailing data after X.509 authority information") + } + out.AllowDC = true + } + } } else { // Unknown extensions are recorded if critical. unhandled = true @@ -1623,6 +1714,7 @@ var ( oidExtensionCRLDistributionPoints = []int{2, 5, 29, 31} oidExtensionAuthorityInfoAccess = []int{1, 3, 6, 1, 5, 5, 7, 1, 1} oidExtensionCRLNumber = []int{2, 5, 29, 20} + oidExtensionDelegatedCredential = []int{1, 3, 6, 1, 4, 1, 44363, 44} ) var ( @@ -1687,7 +1779,7 @@ func isIA5String(s string) error { } func buildCertExtensions(template *Certificate, subjectIsEmpty bool, authorityKeyId []byte, subjectKeyId []byte) (ret []pkix.Extension, err error) { - ret = make([]pkix.Extension, 10 /* maximum number of elements. */) + ret = make([]pkix.Extension, 11 /* maximum number of elements. */) n := 0 if template.KeyUsage != 0 && @@ -1725,6 +1817,16 @@ func buildCertExtensions(template *Certificate, subjectIsEmpty bool, authorityKe n++ } + // This extension is not critical + if template.KeyUsage == KeyUsageDigitalSignature && template.AllowDC && !template.IsCA && !oidInExtensions(oidExtensionDelegatedCredential, template.ExtraExtensions) { + ret[n].Id = oidExtensionDelegatedCredential + ret[n].Value, err = asn1.Marshal(asn1.NullRawValue) + if err != nil { + return + } + n++ + } + if len(authorityKeyId) > 0 && !oidInExtensions(oidExtensionAuthorityKeyId, template.ExtraExtensions) { ret[n].Id = oidExtensionAuthorityKeyId ret[n].Value, err = asn1.Marshal(authKeyId{authorityKeyId}) @@ -2041,9 +2143,21 @@ func signingParamsForPublicKey(pub interface{}, requestedSigAlgo SignatureAlgori case ed25519.PublicKey: pubType = Ed25519 sigAlgo.Algorithm = oidSignatureEd25519 - + case circlSign.PublicKey: + scheme := pub.Scheme() + certScheme, ok := scheme.(circlPki.CertificateScheme) + if !ok { + err = errors.New("x509: circl scheme is not CertificateScheme") + return + } + pubType = PublicKeyAlgorithmByCirclScheme(scheme) + if pubType == UnknownPublicKeyAlgorithm { + err = errors.New("x509: particular circl scheme not supported") + return + } + sigAlgo.Algorithm = certScheme.Oid() default: - err = errors.New("x509: only RSA, ECDSA and Ed25519 keys supported") + err = errors.New("x509: only RSA, ECDSA, Ed25519 and circl keys supported") } if err != nil { @@ -2062,7 +2176,8 @@ func signingParamsForPublicKey(pub interface{}, requestedSigAlgo SignatureAlgori return } sigAlgo.Algorithm, hashFunc = details.oid, details.hash - if hashFunc == 0 && pubType != Ed25519 { + if hashFunc == 0 && (pubType != Ed25519 && + CirclSchemeByPublicKeyAlgorithm(pubType) == nil) { err = errors.New("x509: cannot sign with hash function requested") return } @@ -2101,6 +2216,7 @@ var emptyASN1Subject = []byte{0x30, 0} // - ExtraExtensions // - IPAddresses // - IsCA +// - AllowDC // - IssuingCertificateURL // - KeyUsage // - MaxPathLen diff --git a/src/crypto/x509/x509_cf.go b/src/crypto/x509/x509_cf.go new file mode 100644 index 00000000000..b093fd51efc --- /dev/null +++ b/src/crypto/x509/x509_cf.go @@ -0,0 +1,77 @@ +package x509 + +import ( + circlPki "circl/pki" + circlSign "circl/sign" + + "circl/sign/ed448" + "circl/sign/eddilithium3" + "circl/sign/eddilithium4" + + "crypto" + "encoding/asn1" +) + +// To add a signature scheme from Circl +// +// 1. make sure it implements CertificateScheme, +// 2. add SignatureAlgorithm and PublicKeyAlgorithm constants in x509.go +// 3. add row in circlSchemes below +// 4. update publicKeyAlgoName in x509.go + +var circlSchemes = [...]struct { + sga SignatureAlgorithm + alg PublicKeyAlgorithm + scheme circlSign.Scheme +}{ + {PureEd448, Ed448, ed448.Scheme()}, + {PureEdDilithium3, EdDilithium3, eddilithium3.Scheme()}, + {PureEdDilithium4, EdDilithium4, eddilithium4.Scheme()}, +} + +func CirclSchemeByPublicKeyAlgorithm(alg PublicKeyAlgorithm) circlSign.Scheme { + for _, cs := range circlSchemes { + if cs.alg == alg { + return cs.scheme + } + } + return nil +} + +func SignatureAlgorithmByCirclScheme(scheme circlSign.Scheme) SignatureAlgorithm { + for _, cs := range circlSchemes { + if cs.scheme == scheme { + return cs.sga + } + } + return UnknownSignatureAlgorithm +} + +func PublicKeyAlgorithmByCirclScheme(scheme circlSign.Scheme) PublicKeyAlgorithm { + for _, cs := range circlSchemes { + if cs.scheme == scheme { + return cs.alg + } + } + return UnknownPublicKeyAlgorithm +} + +func init() { + for _, cs := range circlSchemes { + signatureAlgorithmDetails = append(signatureAlgorithmDetails, + struct { + algo SignatureAlgorithm + name string + oid asn1.ObjectIdentifier + pubKeyAlgo PublicKeyAlgorithm + hash crypto.Hash + }{ + cs.sga, + cs.scheme.Name(), + cs.scheme.(circlPki.CertificateScheme).Oid(), + cs.alg, + crypto.Hash(0), + }, + ) + } +} diff --git a/src/crypto/x509/x509_test.go b/src/crypto/x509/x509_test.go index 51dda16815b..9bbd63147fb 100644 --- a/src/crypto/x509/x509_test.go +++ b/src/crypto/x509/x509_test.go @@ -595,6 +595,25 @@ func TestCreateSelfSignedCertificate(t *testing.T) { {"Ed25519", ed25519Pub, ed25519Priv, true, PureEd25519}, } + for _, cs := range circlSchemes { + pk, sk, err := cs.scheme.GenerateKey() + if err != nil { + t.Fatal() + } + tests = append(tests, struct { + name string + pub, priv interface{} + checkSig bool + sigAlgo SignatureAlgorithm + }{ + cs.scheme.Name(), + pk, + sk, + true, + cs.sga, + }) + } + testExtKeyUsage := []ExtKeyUsage{ExtKeyUsageClientAuth, ExtKeyUsageServerAuth} testUnknownExtKeyUsage := []asn1.ObjectIdentifier{[]int{1, 2, 3}, []int{2, 59, 1}} extraExtensionData := []byte("extra extension") @@ -1896,6 +1915,48 @@ func TestISOOIDInCertificate(t *testing.T) { } } +const certIsDCOID = ` +-----BEGIN CERTIFICATE----- +MIIFRjCCBMugAwIBAgIQDGevB+lY0o/OecHFSJ6YnTAKBggqhkjOPQQDAzBMMQsw +CQYDVQQGEwJVUzEVMBMGA1UEChMMRGlnaUNlcnQgSW5jMSYwJAYDVQQDEx1EaWdp +Q2VydCBFQ0MgU2VjdXJlIFNlcnZlciBDQTAeFw0xOTAzMjYwMDAwMDBaFw0yMTAz +MzAxMjAwMDBaMGoxCzAJBgNVBAYTAlVTMRMwEQYDVQQIEwpDYWxpZm9ybmlhMRYw +FAYDVQQHEw1TYW4gRnJhbmNpc2NvMRkwFwYDVQQKExBDbG91ZGZsYXJlLCBJbmMu +MRMwEQYDVQQDEwprYzJrZG0uY29tMFkwEwYHKoZIzj0CAQYIKoZIzj0DAQcDQgAE +d4azI83Bw0fcPgfoeiZpZZnwGuxjBjv++wzE0zAj8vNiUkKxOWSQiGNLn+xlWUpL +lw9djRN1rLmVmn2gb9GgdKOCA28wggNrMB8GA1UdIwQYMBaAFKOd5h/52jlPwG7o +kcuVpdox4gqfMB0GA1UdDgQWBBSfcb7fS3fUFAyB91fRcwoDPtgtJjAjBgNVHREE +HDAaggprYzJrZG0uY29tggwqLmtjMmtkbS5jb20wDgYDVR0PAQH/BAQDAgeAMB0G +A1UdJQQWMBQGCCsGAQUFBwMBBggrBgEFBQcDAjBpBgNVHR8EYjBgMC6gLKAqhiho +dHRwOi8vY3JsMy5kaWdpY2VydC5jb20vc3NjYS1lY2MtZzEuY3JsMC6gLKAqhiho +dHRwOi8vY3JsNC5kaWdpY2VydC5jb20vc3NjYS1lY2MtZzEuY3JsMEwGA1UdIARF +MEMwNwYJYIZIAYb9bAEBMCowKAYIKwYBBQUHAgEWHGh0dHBzOi8vd3d3LmRpZ2lj +ZXJ0LmNvbS9DUFMwCAYGZ4EMAQICMHsGCCsGAQUFBwEBBG8wbTAkBggrBgEFBQcw +AYYYaHR0cDovL29jc3AuZGlnaWNlcnQuY29tMEUGCCsGAQUFBzAChjlodHRwOi8v +Y2FjZXJ0cy5kaWdpY2VydC5jb20vRGlnaUNlcnRFQ0NTZWN1cmVTZXJ2ZXJDQS5j +cnQwDAYDVR0TAQH/BAIwADAPBgkrBgEEAYLaSywEAgUAMIIBfgYKKwYBBAHWeQIE +AgSCAW4EggFqAWgAdgC72d+8H4pxtZOUI5eqkntHOFeVCqtS6BqQlmQ2jh7RhQAA +AWm5hYJ5AAAEAwBHMEUCICiGfq+hSThRL2m8H0awoDR8OpnEHNkF0nI6nL5yYL/j +AiEAxwebGs/T6Es0YarPzoQJrVZqk+sHH/t+jrSrKd5TDjcAdgCHdb/nWXz4jEOZ +X73zbv9WjUdWNv9KtWDBtOr/XqCDDwAAAWm5hYNgAAAEAwBHMEUCIQD9OWA8KGL6 +bxDKfgIleHJWB0iWieRs88VgJyfAg/aFDgIgQ/OsdSF9XOy1foqge0DTDM2FExuw +0JR0AGZWXoNtJzMAdgBElGUusO7Or8RAB9io/ijA2uaCvtjLMbU/0zOWtbaBqAAA +AWm5hYHgAAAEAwBHMEUCIQC4vua1n3BqthEqpA/VBTcsNwMtAwpCuac2IhJ9wx6X +/AIgb+o00k28JQo9TMpP4vzJ3BD3HXWSNc2Zizbq7mkUQYMwCgYIKoZIzj0EAwMD +aQAwZgIxAJsX7d0SuA8ddf/m7IWfNfs3MQfJyGkEezMJX1t6sRso5z50SS12LpXe +muGa1FE2ZgIxAL+CDUF5pz7mhrAEIjQ1MqlpF9tH40dJGvYZZQ3W23cMzSkDfvlt +y5S4RfWHIIPjbw== +-----END CERTIFICATE-----` + +func TestIsDCOIDInCertificate(t *testing.T) { + block, _ := pem.Decode([]byte(certIsDCOID)) + if cert, err := ParseCertificate(block.Bytes); err != nil { + t.Errorf("certificate with DC OID failed to parse: %s", err) + } else if cert.SignatureAlgorithm == UnknownSignatureAlgorithm { + t.Errorf("DC OID not recognised in certificate") + } +} + // certMultipleRDN contains a RelativeDistinguishedName with two elements (the // common name and serial number). This particular certificate was the first // such certificate in the “Pilot” Certificate Transparency log. diff --git a/src/go/build/build.go b/src/go/build/build.go index 217fadf5bd4..c22d778a943 100644 --- a/src/go/build/build.go +++ b/src/go/build/build.go @@ -1879,6 +1879,9 @@ func (ctxt *Context) match(name string, allTags map[string]bool) bool { if ctxt.CgoEnabled && name == "cgo" { return true } + if name == "cfgo" { + return true + } if name == ctxt.GOOS || name == ctxt.GOARCH || name == ctxt.Compiler { return true } diff --git a/src/go/build/deps_test.go b/src/go/build/deps_test.go index c97c668cc49..219fbf201f7 100644 --- a/src/go/build/deps_test.go +++ b/src/go/build/deps_test.go @@ -402,8 +402,11 @@ var depsRules = ` < golang.org/x/crypto/curve25519 < crypto/dsa, crypto/elliptic, crypto/rsa < crypto/ecdsa + < crypto/kem < CRYPTO-MATH; + CRYPTO < golang.org/x/crypto/sha3; + CGO, net !< CRYPTO-MATH; # TLS, Prince of Dependencies. @@ -576,11 +579,15 @@ func TestDependencies(t *testing.T) { var bad []string for _, imp := range imports { sawImport[pkg][imp] = true - if !ok[imp] { + // TODO(anY): Remove this exception for circl/ and add CIRCL to the + // dependency graph specified by `depsRules`. + if !ok[imp] && !strings.HasPrefix(imp, "circl/") { bad = append(bad, imp) } } - if bad != nil { + // TODO(anY): Remove this exception for circl/ and add CIRCL to the + // dependency graph specified by `depsRules`. + if bad != nil && !strings.HasPrefix(pkg, "circl") { t.Errorf("unexpected dependency: %s imports %v", pkg, bad) } } diff --git a/src/vendor/golang.org/x/crypto/sha3/doc.go b/src/vendor/golang.org/x/crypto/sha3/doc.go new file mode 100644 index 00000000000..c2fef30afff --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/doc.go @@ -0,0 +1,66 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Package sha3 implements the SHA-3 fixed-output-length hash functions and +// the SHAKE variable-output-length hash functions defined by FIPS-202. +// +// Both types of hash function use the "sponge" construction and the Keccak +// permutation. For a detailed specification see http://keccak.noekeon.org/ +// +// +// Guidance +// +// If you aren't sure what function you need, use SHAKE256 with at least 64 +// bytes of output. The SHAKE instances are faster than the SHA3 instances; +// the latter have to allocate memory to conform to the hash.Hash interface. +// +// If you need a secret-key MAC (message authentication code), prepend the +// secret key to the input, hash with SHAKE256 and read at least 32 bytes of +// output. +// +// +// Security strengths +// +// The SHA3-x (x equals 224, 256, 384, or 512) functions have a security +// strength against preimage attacks of x bits. Since they only produce "x" +// bits of output, their collision-resistance is only "x/2" bits. +// +// The SHAKE-256 and -128 functions have a generic security strength of 256 and +// 128 bits against all attacks, provided that at least 2x bits of their output +// is used. Requesting more than 64 or 32 bytes of output, respectively, does +// not increase the collision-resistance of the SHAKE functions. +// +// +// The sponge construction +// +// A sponge builds a pseudo-random function from a public pseudo-random +// permutation, by applying the permutation to a state of "rate + capacity" +// bytes, but hiding "capacity" of the bytes. +// +// A sponge starts out with a zero state. To hash an input using a sponge, up +// to "rate" bytes of the input are XORed into the sponge's state. The sponge +// is then "full" and the permutation is applied to "empty" it. This process is +// repeated until all the input has been "absorbed". The input is then padded. +// The digest is "squeezed" from the sponge in the same way, except that output +// is copied out instead of input being XORed in. +// +// A sponge is parameterized by its generic security strength, which is equal +// to half its capacity; capacity + rate is equal to the permutation's width. +// Since the KeccakF-1600 permutation is 1600 bits (200 bytes) wide, this means +// that the security strength of a sponge instance is equal to (1600 - bitrate) / 2. +// +// +// Recommendations +// +// The SHAKE functions are recommended for most new uses. They can produce +// output of arbitrary length. SHAKE256, with an output length of at least +// 64 bytes, provides 256-bit security against all attacks. The Keccak team +// recommends it for most applications upgrading from SHA2-512. (NIST chose a +// much stronger, but much slower, sponge instance for SHA3-512.) +// +// The SHA-3 functions are "drop-in" replacements for the SHA-2 functions. +// They produce output of the same length, with the same security strengths +// against all attacks. This means, in particular, that SHA3-256 only has +// 128-bit collision resistance, because its output length is 32 bytes. +package sha3 // import "golang.org/x/crypto/sha3" diff --git a/src/vendor/golang.org/x/crypto/sha3/hashes.go b/src/vendor/golang.org/x/crypto/sha3/hashes.go new file mode 100644 index 00000000000..0d8043fd2a1 --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/hashes.go @@ -0,0 +1,97 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// This file provides functions for creating instances of the SHA-3 +// and SHAKE hash functions, as well as utility functions for hashing +// bytes. + +import ( + "hash" +) + +// New224 creates a new SHA3-224 hash. +// Its generic security strength is 224 bits against preimage attacks, +// and 112 bits against collision attacks. +func New224() hash.Hash { + if h := new224Asm(); h != nil { + return h + } + return &state{rate: 144, outputLen: 28, dsbyte: 0x06} +} + +// New256 creates a new SHA3-256 hash. +// Its generic security strength is 256 bits against preimage attacks, +// and 128 bits against collision attacks. +func New256() hash.Hash { + if h := new256Asm(); h != nil { + return h + } + return &state{rate: 136, outputLen: 32, dsbyte: 0x06} +} + +// New384 creates a new SHA3-384 hash. +// Its generic security strength is 384 bits against preimage attacks, +// and 192 bits against collision attacks. +func New384() hash.Hash { + if h := new384Asm(); h != nil { + return h + } + return &state{rate: 104, outputLen: 48, dsbyte: 0x06} +} + +// New512 creates a new SHA3-512 hash. +// Its generic security strength is 512 bits against preimage attacks, +// and 256 bits against collision attacks. +func New512() hash.Hash { + if h := new512Asm(); h != nil { + return h + } + return &state{rate: 72, outputLen: 64, dsbyte: 0x06} +} + +// NewLegacyKeccak256 creates a new Keccak-256 hash. +// +// Only use this function if you require compatibility with an existing cryptosystem +// that uses non-standard padding. All other users should use New256 instead. +func NewLegacyKeccak256() hash.Hash { return &state{rate: 136, outputLen: 32, dsbyte: 0x01} } + +// NewLegacyKeccak512 creates a new Keccak-512 hash. +// +// Only use this function if you require compatibility with an existing cryptosystem +// that uses non-standard padding. All other users should use New512 instead. +func NewLegacyKeccak512() hash.Hash { return &state{rate: 72, outputLen: 64, dsbyte: 0x01} } + +// Sum224 returns the SHA3-224 digest of the data. +func Sum224(data []byte) (digest [28]byte) { + h := New224() + h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum256 returns the SHA3-256 digest of the data. +func Sum256(data []byte) (digest [32]byte) { + h := New256() + h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum384 returns the SHA3-384 digest of the data. +func Sum384(data []byte) (digest [48]byte) { + h := New384() + h.Write(data) + h.Sum(digest[:0]) + return +} + +// Sum512 returns the SHA3-512 digest of the data. +func Sum512(data []byte) (digest [64]byte) { + h := New512() + h.Write(data) + h.Sum(digest[:0]) + return +} diff --git a/src/vendor/golang.org/x/crypto/sha3/hashes_generic.go b/src/vendor/golang.org/x/crypto/sha3/hashes_generic.go new file mode 100644 index 00000000000..f455147d212 --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/hashes_generic.go @@ -0,0 +1,27 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build gccgo appengine !s390x + +package sha3 + +import ( + "hash" +) + +// new224Asm returns an assembly implementation of SHA3-224 if available, +// otherwise it returns nil. +func new224Asm() hash.Hash { return nil } + +// new256Asm returns an assembly implementation of SHA3-256 if available, +// otherwise it returns nil. +func new256Asm() hash.Hash { return nil } + +// new384Asm returns an assembly implementation of SHA3-384 if available, +// otherwise it returns nil. +func new384Asm() hash.Hash { return nil } + +// new512Asm returns an assembly implementation of SHA3-512 if available, +// otherwise it returns nil. +func new512Asm() hash.Hash { return nil } diff --git a/src/vendor/golang.org/x/crypto/sha3/keccakf.go b/src/vendor/golang.org/x/crypto/sha3/keccakf.go new file mode 100644 index 00000000000..46d03ed385d --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/keccakf.go @@ -0,0 +1,412 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build !amd64 appengine gccgo + +package sha3 + +// rc stores the round constants for use in the ι step. +var rc = [24]uint64{ + 0x0000000000000001, + 0x0000000000008082, + 0x800000000000808A, + 0x8000000080008000, + 0x000000000000808B, + 0x0000000080000001, + 0x8000000080008081, + 0x8000000000008009, + 0x000000000000008A, + 0x0000000000000088, + 0x0000000080008009, + 0x000000008000000A, + 0x000000008000808B, + 0x800000000000008B, + 0x8000000000008089, + 0x8000000000008003, + 0x8000000000008002, + 0x8000000000000080, + 0x000000000000800A, + 0x800000008000000A, + 0x8000000080008081, + 0x8000000000008080, + 0x0000000080000001, + 0x8000000080008008, +} + +// keccakF1600 applies the Keccak permutation to a 1600b-wide +// state represented as a slice of 25 uint64s. +func keccakF1600(a *[25]uint64) { + // Implementation translated from Keccak-inplace.c + // in the keccak reference code. + var t, bc0, bc1, bc2, bc3, bc4, d0, d1, d2, d3, d4 uint64 + + for i := 0; i < 24; i += 4 { + // Combines the 5 steps in each round into 2 steps. + // Unrolls 4 rounds per loop and spreads some steps across rounds. + + // Round 1 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[6] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[12] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[18] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[24] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ rc[i] + a[6] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[16] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[22] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[3] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[10] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[1] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[7] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[19] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[20] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[11] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[23] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[4] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[5] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[2] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[8] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[14] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[15] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + // Round 2 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[16] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[7] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[23] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[14] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ rc[i+1] + a[16] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[11] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[2] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[18] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[20] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[6] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[22] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[4] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[15] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[1] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[8] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[24] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[10] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[12] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[3] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[19] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[5] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + // Round 3 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[11] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[22] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[8] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[19] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ rc[i+2] + a[11] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[1] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[12] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[23] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[15] = bc0 ^ (bc2 &^ bc1) + a[1] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[16] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[2] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[24] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[5] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[6] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[3] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[14] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[20] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[7] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[18] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[4] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[10] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + // Round 4 + bc0 = a[0] ^ a[5] ^ a[10] ^ a[15] ^ a[20] + bc1 = a[1] ^ a[6] ^ a[11] ^ a[16] ^ a[21] + bc2 = a[2] ^ a[7] ^ a[12] ^ a[17] ^ a[22] + bc3 = a[3] ^ a[8] ^ a[13] ^ a[18] ^ a[23] + bc4 = a[4] ^ a[9] ^ a[14] ^ a[19] ^ a[24] + d0 = bc4 ^ (bc1<<1 | bc1>>63) + d1 = bc0 ^ (bc2<<1 | bc2>>63) + d2 = bc1 ^ (bc3<<1 | bc3>>63) + d3 = bc2 ^ (bc4<<1 | bc4>>63) + d4 = bc3 ^ (bc0<<1 | bc0>>63) + + bc0 = a[0] ^ d0 + t = a[1] ^ d1 + bc1 = t<<44 | t>>(64-44) + t = a[2] ^ d2 + bc2 = t<<43 | t>>(64-43) + t = a[3] ^ d3 + bc3 = t<<21 | t>>(64-21) + t = a[4] ^ d4 + bc4 = t<<14 | t>>(64-14) + a[0] = bc0 ^ (bc2 &^ bc1) ^ rc[i+3] + a[1] = bc1 ^ (bc3 &^ bc2) + a[2] = bc2 ^ (bc4 &^ bc3) + a[3] = bc3 ^ (bc0 &^ bc4) + a[4] = bc4 ^ (bc1 &^ bc0) + + t = a[5] ^ d0 + bc2 = t<<3 | t>>(64-3) + t = a[6] ^ d1 + bc3 = t<<45 | t>>(64-45) + t = a[7] ^ d2 + bc4 = t<<61 | t>>(64-61) + t = a[8] ^ d3 + bc0 = t<<28 | t>>(64-28) + t = a[9] ^ d4 + bc1 = t<<20 | t>>(64-20) + a[5] = bc0 ^ (bc2 &^ bc1) + a[6] = bc1 ^ (bc3 &^ bc2) + a[7] = bc2 ^ (bc4 &^ bc3) + a[8] = bc3 ^ (bc0 &^ bc4) + a[9] = bc4 ^ (bc1 &^ bc0) + + t = a[10] ^ d0 + bc4 = t<<18 | t>>(64-18) + t = a[11] ^ d1 + bc0 = t<<1 | t>>(64-1) + t = a[12] ^ d2 + bc1 = t<<6 | t>>(64-6) + t = a[13] ^ d3 + bc2 = t<<25 | t>>(64-25) + t = a[14] ^ d4 + bc3 = t<<8 | t>>(64-8) + a[10] = bc0 ^ (bc2 &^ bc1) + a[11] = bc1 ^ (bc3 &^ bc2) + a[12] = bc2 ^ (bc4 &^ bc3) + a[13] = bc3 ^ (bc0 &^ bc4) + a[14] = bc4 ^ (bc1 &^ bc0) + + t = a[15] ^ d0 + bc1 = t<<36 | t>>(64-36) + t = a[16] ^ d1 + bc2 = t<<10 | t>>(64-10) + t = a[17] ^ d2 + bc3 = t<<15 | t>>(64-15) + t = a[18] ^ d3 + bc4 = t<<56 | t>>(64-56) + t = a[19] ^ d4 + bc0 = t<<27 | t>>(64-27) + a[15] = bc0 ^ (bc2 &^ bc1) + a[16] = bc1 ^ (bc3 &^ bc2) + a[17] = bc2 ^ (bc4 &^ bc3) + a[18] = bc3 ^ (bc0 &^ bc4) + a[19] = bc4 ^ (bc1 &^ bc0) + + t = a[20] ^ d0 + bc3 = t<<41 | t>>(64-41) + t = a[21] ^ d1 + bc4 = t<<2 | t>>(64-2) + t = a[22] ^ d2 + bc0 = t<<62 | t>>(64-62) + t = a[23] ^ d3 + bc1 = t<<55 | t>>(64-55) + t = a[24] ^ d4 + bc2 = t<<39 | t>>(64-39) + a[20] = bc0 ^ (bc2 &^ bc1) + a[21] = bc1 ^ (bc3 &^ bc2) + a[22] = bc2 ^ (bc4 &^ bc3) + a[23] = bc3 ^ (bc0 &^ bc4) + a[24] = bc4 ^ (bc1 &^ bc0) + } +} diff --git a/src/vendor/golang.org/x/crypto/sha3/keccakf_amd64.go b/src/vendor/golang.org/x/crypto/sha3/keccakf_amd64.go new file mode 100644 index 00000000000..78867958502 --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/keccakf_amd64.go @@ -0,0 +1,13 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build amd64,!appengine,!gccgo + +package sha3 + +// This function is implemented in keccakf_amd64.s. + +//go:noescape + +func keccakF1600(a *[25]uint64) diff --git a/src/vendor/golang.org/x/crypto/sha3/keccakf_amd64.s b/src/vendor/golang.org/x/crypto/sha3/keccakf_amd64.s new file mode 100644 index 00000000000..d9819089f53 --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/keccakf_amd64.s @@ -0,0 +1,390 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build amd64,!appengine,!gccgo + +// This code was translated into a form compatible with 6a from the public +// domain sources at https://github.com/gvanas/KeccakCodePackage + +// Offsets in state +#define _ba (0*8) +#define _be (1*8) +#define _bi (2*8) +#define _bo (3*8) +#define _bu (4*8) +#define _ga (5*8) +#define _ge (6*8) +#define _gi (7*8) +#define _go (8*8) +#define _gu (9*8) +#define _ka (10*8) +#define _ke (11*8) +#define _ki (12*8) +#define _ko (13*8) +#define _ku (14*8) +#define _ma (15*8) +#define _me (16*8) +#define _mi (17*8) +#define _mo (18*8) +#define _mu (19*8) +#define _sa (20*8) +#define _se (21*8) +#define _si (22*8) +#define _so (23*8) +#define _su (24*8) + +// Temporary registers +#define rT1 AX + +// Round vars +#define rpState DI +#define rpStack SP + +#define rDa BX +#define rDe CX +#define rDi DX +#define rDo R8 +#define rDu R9 + +#define rBa R10 +#define rBe R11 +#define rBi R12 +#define rBo R13 +#define rBu R14 + +#define rCa SI +#define rCe BP +#define rCi rBi +#define rCo rBo +#define rCu R15 + +#define MOVQ_RBI_RCE MOVQ rBi, rCe +#define XORQ_RT1_RCA XORQ rT1, rCa +#define XORQ_RT1_RCE XORQ rT1, rCe +#define XORQ_RBA_RCU XORQ rBa, rCu +#define XORQ_RBE_RCU XORQ rBe, rCu +#define XORQ_RDU_RCU XORQ rDu, rCu +#define XORQ_RDA_RCA XORQ rDa, rCa +#define XORQ_RDE_RCE XORQ rDe, rCe + +#define mKeccakRound(iState, oState, rc, B_RBI_RCE, G_RT1_RCA, G_RT1_RCE, G_RBA_RCU, K_RT1_RCA, K_RT1_RCE, K_RBA_RCU, M_RT1_RCA, M_RT1_RCE, M_RBE_RCU, S_RDU_RCU, S_RDA_RCA, S_RDE_RCE) \ + /* Prepare round */ \ + MOVQ rCe, rDa; \ + ROLQ $1, rDa; \ + \ + MOVQ _bi(iState), rCi; \ + XORQ _gi(iState), rDi; \ + XORQ rCu, rDa; \ + XORQ _ki(iState), rCi; \ + XORQ _mi(iState), rDi; \ + XORQ rDi, rCi; \ + \ + MOVQ rCi, rDe; \ + ROLQ $1, rDe; \ + \ + MOVQ _bo(iState), rCo; \ + XORQ _go(iState), rDo; \ + XORQ rCa, rDe; \ + XORQ _ko(iState), rCo; \ + XORQ _mo(iState), rDo; \ + XORQ rDo, rCo; \ + \ + MOVQ rCo, rDi; \ + ROLQ $1, rDi; \ + \ + MOVQ rCu, rDo; \ + XORQ rCe, rDi; \ + ROLQ $1, rDo; \ + \ + MOVQ rCa, rDu; \ + XORQ rCi, rDo; \ + ROLQ $1, rDu; \ + \ + /* Result b */ \ + MOVQ _ba(iState), rBa; \ + MOVQ _ge(iState), rBe; \ + XORQ rCo, rDu; \ + MOVQ _ki(iState), rBi; \ + MOVQ _mo(iState), rBo; \ + MOVQ _su(iState), rBu; \ + XORQ rDe, rBe; \ + ROLQ $44, rBe; \ + XORQ rDi, rBi; \ + XORQ rDa, rBa; \ + ROLQ $43, rBi; \ + \ + MOVQ rBe, rCa; \ + MOVQ rc, rT1; \ + ORQ rBi, rCa; \ + XORQ rBa, rT1; \ + XORQ rT1, rCa; \ + MOVQ rCa, _ba(oState); \ + \ + XORQ rDu, rBu; \ + ROLQ $14, rBu; \ + MOVQ rBa, rCu; \ + ANDQ rBe, rCu; \ + XORQ rBu, rCu; \ + MOVQ rCu, _bu(oState); \ + \ + XORQ rDo, rBo; \ + ROLQ $21, rBo; \ + MOVQ rBo, rT1; \ + ANDQ rBu, rT1; \ + XORQ rBi, rT1; \ + MOVQ rT1, _bi(oState); \ + \ + NOTQ rBi; \ + ORQ rBa, rBu; \ + ORQ rBo, rBi; \ + XORQ rBo, rBu; \ + XORQ rBe, rBi; \ + MOVQ rBu, _bo(oState); \ + MOVQ rBi, _be(oState); \ + B_RBI_RCE; \ + \ + /* Result g */ \ + MOVQ _gu(iState), rBe; \ + XORQ rDu, rBe; \ + MOVQ _ka(iState), rBi; \ + ROLQ $20, rBe; \ + XORQ rDa, rBi; \ + ROLQ $3, rBi; \ + MOVQ _bo(iState), rBa; \ + MOVQ rBe, rT1; \ + ORQ rBi, rT1; \ + XORQ rDo, rBa; \ + MOVQ _me(iState), rBo; \ + MOVQ _si(iState), rBu; \ + ROLQ $28, rBa; \ + XORQ rBa, rT1; \ + MOVQ rT1, _ga(oState); \ + G_RT1_RCA; \ + \ + XORQ rDe, rBo; \ + ROLQ $45, rBo; \ + MOVQ rBi, rT1; \ + ANDQ rBo, rT1; \ + XORQ rBe, rT1; \ + MOVQ rT1, _ge(oState); \ + G_RT1_RCE; \ + \ + XORQ rDi, rBu; \ + ROLQ $61, rBu; \ + MOVQ rBu, rT1; \ + ORQ rBa, rT1; \ + XORQ rBo, rT1; \ + MOVQ rT1, _go(oState); \ + \ + ANDQ rBe, rBa; \ + XORQ rBu, rBa; \ + MOVQ rBa, _gu(oState); \ + NOTQ rBu; \ + G_RBA_RCU; \ + \ + ORQ rBu, rBo; \ + XORQ rBi, rBo; \ + MOVQ rBo, _gi(oState); \ + \ + /* Result k */ \ + MOVQ _be(iState), rBa; \ + MOVQ _gi(iState), rBe; \ + MOVQ _ko(iState), rBi; \ + MOVQ _mu(iState), rBo; \ + MOVQ _sa(iState), rBu; \ + XORQ rDi, rBe; \ + ROLQ $6, rBe; \ + XORQ rDo, rBi; \ + ROLQ $25, rBi; \ + MOVQ rBe, rT1; \ + ORQ rBi, rT1; \ + XORQ rDe, rBa; \ + ROLQ $1, rBa; \ + XORQ rBa, rT1; \ + MOVQ rT1, _ka(oState); \ + K_RT1_RCA; \ + \ + XORQ rDu, rBo; \ + ROLQ $8, rBo; \ + MOVQ rBi, rT1; \ + ANDQ rBo, rT1; \ + XORQ rBe, rT1; \ + MOVQ rT1, _ke(oState); \ + K_RT1_RCE; \ + \ + XORQ rDa, rBu; \ + ROLQ $18, rBu; \ + NOTQ rBo; \ + MOVQ rBo, rT1; \ + ANDQ rBu, rT1; \ + XORQ rBi, rT1; \ + MOVQ rT1, _ki(oState); \ + \ + MOVQ rBu, rT1; \ + ORQ rBa, rT1; \ + XORQ rBo, rT1; \ + MOVQ rT1, _ko(oState); \ + \ + ANDQ rBe, rBa; \ + XORQ rBu, rBa; \ + MOVQ rBa, _ku(oState); \ + K_RBA_RCU; \ + \ + /* Result m */ \ + MOVQ _ga(iState), rBe; \ + XORQ rDa, rBe; \ + MOVQ _ke(iState), rBi; \ + ROLQ $36, rBe; \ + XORQ rDe, rBi; \ + MOVQ _bu(iState), rBa; \ + ROLQ $10, rBi; \ + MOVQ rBe, rT1; \ + MOVQ _mi(iState), rBo; \ + ANDQ rBi, rT1; \ + XORQ rDu, rBa; \ + MOVQ _so(iState), rBu; \ + ROLQ $27, rBa; \ + XORQ rBa, rT1; \ + MOVQ rT1, _ma(oState); \ + M_RT1_RCA; \ + \ + XORQ rDi, rBo; \ + ROLQ $15, rBo; \ + MOVQ rBi, rT1; \ + ORQ rBo, rT1; \ + XORQ rBe, rT1; \ + MOVQ rT1, _me(oState); \ + M_RT1_RCE; \ + \ + XORQ rDo, rBu; \ + ROLQ $56, rBu; \ + NOTQ rBo; \ + MOVQ rBo, rT1; \ + ORQ rBu, rT1; \ + XORQ rBi, rT1; \ + MOVQ rT1, _mi(oState); \ + \ + ORQ rBa, rBe; \ + XORQ rBu, rBe; \ + MOVQ rBe, _mu(oState); \ + \ + ANDQ rBa, rBu; \ + XORQ rBo, rBu; \ + MOVQ rBu, _mo(oState); \ + M_RBE_RCU; \ + \ + /* Result s */ \ + MOVQ _bi(iState), rBa; \ + MOVQ _go(iState), rBe; \ + MOVQ _ku(iState), rBi; \ + XORQ rDi, rBa; \ + MOVQ _ma(iState), rBo; \ + ROLQ $62, rBa; \ + XORQ rDo, rBe; \ + MOVQ _se(iState), rBu; \ + ROLQ $55, rBe; \ + \ + XORQ rDu, rBi; \ + MOVQ rBa, rDu; \ + XORQ rDe, rBu; \ + ROLQ $2, rBu; \ + ANDQ rBe, rDu; \ + XORQ rBu, rDu; \ + MOVQ rDu, _su(oState); \ + \ + ROLQ $39, rBi; \ + S_RDU_RCU; \ + NOTQ rBe; \ + XORQ rDa, rBo; \ + MOVQ rBe, rDa; \ + ANDQ rBi, rDa; \ + XORQ rBa, rDa; \ + MOVQ rDa, _sa(oState); \ + S_RDA_RCA; \ + \ + ROLQ $41, rBo; \ + MOVQ rBi, rDe; \ + ORQ rBo, rDe; \ + XORQ rBe, rDe; \ + MOVQ rDe, _se(oState); \ + S_RDE_RCE; \ + \ + MOVQ rBo, rDi; \ + MOVQ rBu, rDo; \ + ANDQ rBu, rDi; \ + ORQ rBa, rDo; \ + XORQ rBi, rDi; \ + XORQ rBo, rDo; \ + MOVQ rDi, _si(oState); \ + MOVQ rDo, _so(oState) \ + +// func keccakF1600(a *[25]uint64) +TEXT ·keccakF1600(SB), 0, $200-8 + MOVQ a+0(FP), rpState + + // Convert the user state into an internal state + NOTQ _be(rpState) + NOTQ _bi(rpState) + NOTQ _go(rpState) + NOTQ _ki(rpState) + NOTQ _mi(rpState) + NOTQ _sa(rpState) + + // Execute the KeccakF permutation + MOVQ _ba(rpState), rCa + MOVQ _be(rpState), rCe + MOVQ _bu(rpState), rCu + + XORQ _ga(rpState), rCa + XORQ _ge(rpState), rCe + XORQ _gu(rpState), rCu + + XORQ _ka(rpState), rCa + XORQ _ke(rpState), rCe + XORQ _ku(rpState), rCu + + XORQ _ma(rpState), rCa + XORQ _me(rpState), rCe + XORQ _mu(rpState), rCu + + XORQ _sa(rpState), rCa + XORQ _se(rpState), rCe + MOVQ _si(rpState), rDi + MOVQ _so(rpState), rDo + XORQ _su(rpState), rCu + + mKeccakRound(rpState, rpStack, $0x0000000000000001, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x0000000000008082, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x800000000000808a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000080008000, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000000000808b, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x0000000080000001, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000080008081, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000008009, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000000000008a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x0000000000000088, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x0000000080008009, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x000000008000000a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000008000808b, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x800000000000008b, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000000008089, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000008003, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000000008002, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000000080, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x000000000000800a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x800000008000000a, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x8000000080008081, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000000008080, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpState, rpStack, $0x0000000080000001, MOVQ_RBI_RCE, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBA_RCU, XORQ_RT1_RCA, XORQ_RT1_RCE, XORQ_RBE_RCU, XORQ_RDU_RCU, XORQ_RDA_RCA, XORQ_RDE_RCE) + mKeccakRound(rpStack, rpState, $0x8000000080008008, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP, NOP) + + // Revert the internal state to the user state + NOTQ _be(rpState) + NOTQ _bi(rpState) + NOTQ _go(rpState) + NOTQ _ki(rpState) + NOTQ _mi(rpState) + NOTQ _sa(rpState) + + RET diff --git a/src/vendor/golang.org/x/crypto/sha3/register.go b/src/vendor/golang.org/x/crypto/sha3/register.go new file mode 100644 index 00000000000..3cf6a22e093 --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/register.go @@ -0,0 +1,18 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build go1.4 + +package sha3 + +import ( + "crypto" +) + +func init() { + crypto.RegisterHash(crypto.SHA3_224, New224) + crypto.RegisterHash(crypto.SHA3_256, New256) + crypto.RegisterHash(crypto.SHA3_384, New384) + crypto.RegisterHash(crypto.SHA3_512, New512) +} diff --git a/src/vendor/golang.org/x/crypto/sha3/sha3.go b/src/vendor/golang.org/x/crypto/sha3/sha3.go new file mode 100644 index 00000000000..ba269a07300 --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/sha3.go @@ -0,0 +1,193 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// spongeDirection indicates the direction bytes are flowing through the sponge. +type spongeDirection int + +const ( + // spongeAbsorbing indicates that the sponge is absorbing input. + spongeAbsorbing spongeDirection = iota + // spongeSqueezing indicates that the sponge is being squeezed. + spongeSqueezing +) + +const ( + // maxRate is the maximum size of the internal buffer. SHAKE-256 + // currently needs the largest buffer. + maxRate = 168 +) + +type state struct { + // Generic sponge components. + a [25]uint64 // main state of the hash + buf []byte // points into storage + rate int // the number of bytes of state to use + + // dsbyte contains the "domain separation" bits and the first bit of + // the padding. Sections 6.1 and 6.2 of [1] separate the outputs of the + // SHA-3 and SHAKE functions by appending bitstrings to the message. + // Using a little-endian bit-ordering convention, these are "01" for SHA-3 + // and "1111" for SHAKE, or 00000010b and 00001111b, respectively. Then the + // padding rule from section 5.1 is applied to pad the message to a multiple + // of the rate, which involves adding a "1" bit, zero or more "0" bits, and + // a final "1" bit. We merge the first "1" bit from the padding into dsbyte, + // giving 00000110b (0x06) and 00011111b (0x1f). + // [1] http://csrc.nist.gov/publications/drafts/fips-202/fips_202_draft.pdf + // "Draft FIPS 202: SHA-3 Standard: Permutation-Based Hash and + // Extendable-Output Functions (May 2014)" + dsbyte byte + + storage storageBuf + + // Specific to SHA-3 and SHAKE. + outputLen int // the default output size in bytes + state spongeDirection // whether the sponge is absorbing or squeezing +} + +// BlockSize returns the rate of sponge underlying this hash function. +func (d *state) BlockSize() int { return d.rate } + +// Size returns the output size of the hash function in bytes. +func (d *state) Size() int { return d.outputLen } + +// Reset clears the internal state by zeroing the sponge state and +// the byte buffer, and setting Sponge.state to absorbing. +func (d *state) Reset() { + // Zero the permutation's state. + for i := range d.a { + d.a[i] = 0 + } + d.state = spongeAbsorbing + d.buf = d.storage.asBytes()[:0] +} + +func (d *state) clone() *state { + ret := *d + if ret.state == spongeAbsorbing { + ret.buf = ret.storage.asBytes()[:len(ret.buf)] + } else { + ret.buf = ret.storage.asBytes()[d.rate-cap(d.buf) : d.rate] + } + + return &ret +} + +// permute applies the KeccakF-1600 permutation. It handles +// any input-output buffering. +func (d *state) permute() { + switch d.state { + case spongeAbsorbing: + // If we're absorbing, we need to xor the input into the state + // before applying the permutation. + xorIn(d, d.buf) + d.buf = d.storage.asBytes()[:0] + keccakF1600(&d.a) + case spongeSqueezing: + // If we're squeezing, we need to apply the permutatin before + // copying more output. + keccakF1600(&d.a) + d.buf = d.storage.asBytes()[:d.rate] + copyOut(d, d.buf) + } +} + +// pads appends the domain separation bits in dsbyte, applies +// the multi-bitrate 10..1 padding rule, and permutes the state. +func (d *state) padAndPermute(dsbyte byte) { + if d.buf == nil { + d.buf = d.storage.asBytes()[:0] + } + // Pad with this instance's domain-separator bits. We know that there's + // at least one byte of space in d.buf because, if it were full, + // permute would have been called to empty it. dsbyte also contains the + // first one bit for the padding. See the comment in the state struct. + d.buf = append(d.buf, dsbyte) + zerosStart := len(d.buf) + d.buf = d.storage.asBytes()[:d.rate] + for i := zerosStart; i < d.rate; i++ { + d.buf[i] = 0 + } + // This adds the final one bit for the padding. Because of the way that + // bits are numbered from the LSB upwards, the final bit is the MSB of + // the last byte. + d.buf[d.rate-1] ^= 0x80 + // Apply the permutation + d.permute() + d.state = spongeSqueezing + d.buf = d.storage.asBytes()[:d.rate] + copyOut(d, d.buf) +} + +// Write absorbs more data into the hash's state. It produces an error +// if more data is written to the ShakeHash after writing +func (d *state) Write(p []byte) (written int, err error) { + if d.state != spongeAbsorbing { + panic("sha3: write to sponge after read") + } + if d.buf == nil { + d.buf = d.storage.asBytes()[:0] + } + written = len(p) + + for len(p) > 0 { + if len(d.buf) == 0 && len(p) >= d.rate { + // The fast path; absorb a full "rate" bytes of input and apply the permutation. + xorIn(d, p[:d.rate]) + p = p[d.rate:] + keccakF1600(&d.a) + } else { + // The slow path; buffer the input until we can fill the sponge, and then xor it in. + todo := d.rate - len(d.buf) + if todo > len(p) { + todo = len(p) + } + d.buf = append(d.buf, p[:todo]...) + p = p[todo:] + + // If the sponge is full, apply the permutation. + if len(d.buf) == d.rate { + d.permute() + } + } + } + + return +} + +// Read squeezes an arbitrary number of bytes from the sponge. +func (d *state) Read(out []byte) (n int, err error) { + // If we're still absorbing, pad and apply the permutation. + if d.state == spongeAbsorbing { + d.padAndPermute(d.dsbyte) + } + + n = len(out) + + // Now, do the squeezing. + for len(out) > 0 { + n := copy(out, d.buf) + d.buf = d.buf[n:] + out = out[n:] + + // Apply the permutation if we've squeezed the sponge dry. + if len(d.buf) == 0 { + d.permute() + } + } + + return +} + +// Sum applies padding to the hash state and then squeezes out the desired +// number of output bytes. +func (d *state) Sum(in []byte) []byte { + // Make a copy of the original hash so that caller can keep writing + // and summing. + dup := d.clone() + hash := make([]byte, dup.outputLen) + dup.Read(hash) + return append(in, hash...) +} diff --git a/src/vendor/golang.org/x/crypto/sha3/sha3_s390x.go b/src/vendor/golang.org/x/crypto/sha3/sha3_s390x.go new file mode 100644 index 00000000000..259ff4dada0 --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/sha3_s390x.go @@ -0,0 +1,284 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build !gccgo,!appengine + +package sha3 + +// This file contains code for using the 'compute intermediate +// message digest' (KIMD) and 'compute last message digest' (KLMD) +// instructions to compute SHA-3 and SHAKE hashes on IBM Z. + +import ( + "hash" + + "golang.org/x/sys/cpu" +) + +// codes represent 7-bit KIMD/KLMD function codes as defined in +// the Principles of Operation. +type code uint64 + +const ( + // function codes for KIMD/KLMD + sha3_224 code = 32 + sha3_256 = 33 + sha3_384 = 34 + sha3_512 = 35 + shake_128 = 36 + shake_256 = 37 + nopad = 0x100 +) + +// kimd is a wrapper for the 'compute intermediate message digest' instruction. +// src must be a multiple of the rate for the given function code. +//go:noescape +func kimd(function code, chain *[200]byte, src []byte) + +// klmd is a wrapper for the 'compute last message digest' instruction. +// src padding is handled by the instruction. +//go:noescape +func klmd(function code, chain *[200]byte, dst, src []byte) + +type asmState struct { + a [200]byte // 1600 bit state + buf []byte // care must be taken to ensure cap(buf) is a multiple of rate + rate int // equivalent to block size + storage [3072]byte // underlying storage for buf + outputLen int // output length if fixed, 0 if not + function code // KIMD/KLMD function code + state spongeDirection // whether the sponge is absorbing or squeezing +} + +func newAsmState(function code) *asmState { + var s asmState + s.function = function + switch function { + case sha3_224: + s.rate = 144 + s.outputLen = 28 + case sha3_256: + s.rate = 136 + s.outputLen = 32 + case sha3_384: + s.rate = 104 + s.outputLen = 48 + case sha3_512: + s.rate = 72 + s.outputLen = 64 + case shake_128: + s.rate = 168 + case shake_256: + s.rate = 136 + default: + panic("sha3: unrecognized function code") + } + + // limit s.buf size to a multiple of s.rate + s.resetBuf() + return &s +} + +func (s *asmState) clone() *asmState { + c := *s + c.buf = c.storage[:len(s.buf):cap(s.buf)] + return &c +} + +// copyIntoBuf copies b into buf. It will panic if there is not enough space to +// store all of b. +func (s *asmState) copyIntoBuf(b []byte) { + bufLen := len(s.buf) + s.buf = s.buf[:len(s.buf)+len(b)] + copy(s.buf[bufLen:], b) +} + +// resetBuf points buf at storage, sets the length to 0 and sets cap to be a +// multiple of the rate. +func (s *asmState) resetBuf() { + max := (cap(s.storage) / s.rate) * s.rate + s.buf = s.storage[:0:max] +} + +// Write (via the embedded io.Writer interface) adds more data to the running hash. +// It never returns an error. +func (s *asmState) Write(b []byte) (int, error) { + if s.state != spongeAbsorbing { + panic("sha3: write to sponge after read") + } + length := len(b) + for len(b) > 0 { + if len(s.buf) == 0 && len(b) >= cap(s.buf) { + // Hash the data directly and push any remaining bytes + // into the buffer. + remainder := len(b) % s.rate + kimd(s.function, &s.a, b[:len(b)-remainder]) + if remainder != 0 { + s.copyIntoBuf(b[len(b)-remainder:]) + } + return length, nil + } + + if len(s.buf) == cap(s.buf) { + // flush the buffer + kimd(s.function, &s.a, s.buf) + s.buf = s.buf[:0] + } + + // copy as much as we can into the buffer + n := len(b) + if len(b) > cap(s.buf)-len(s.buf) { + n = cap(s.buf) - len(s.buf) + } + s.copyIntoBuf(b[:n]) + b = b[n:] + } + return length, nil +} + +// Read squeezes an arbitrary number of bytes from the sponge. +func (s *asmState) Read(out []byte) (n int, err error) { + n = len(out) + + // need to pad if we were absorbing + if s.state == spongeAbsorbing { + s.state = spongeSqueezing + + // write hash directly into out if possible + if len(out)%s.rate == 0 { + klmd(s.function, &s.a, out, s.buf) // len(out) may be 0 + s.buf = s.buf[:0] + return + } + + // write hash into buffer + max := cap(s.buf) + if max > len(out) { + max = (len(out)/s.rate)*s.rate + s.rate + } + klmd(s.function, &s.a, s.buf[:max], s.buf) + s.buf = s.buf[:max] + } + + for len(out) > 0 { + // flush the buffer + if len(s.buf) != 0 { + c := copy(out, s.buf) + out = out[c:] + s.buf = s.buf[c:] + continue + } + + // write hash directly into out if possible + if len(out)%s.rate == 0 { + klmd(s.function|nopad, &s.a, out, nil) + return + } + + // write hash into buffer + s.resetBuf() + if cap(s.buf) > len(out) { + s.buf = s.buf[:(len(out)/s.rate)*s.rate+s.rate] + } + klmd(s.function|nopad, &s.a, s.buf, nil) + } + return +} + +// Sum appends the current hash to b and returns the resulting slice. +// It does not change the underlying hash state. +func (s *asmState) Sum(b []byte) []byte { + if s.outputLen == 0 { + panic("sha3: cannot call Sum on SHAKE functions") + } + + // Copy the state to preserve the original. + a := s.a + + // Hash the buffer. Note that we don't clear it because we + // aren't updating the state. + klmd(s.function, &a, nil, s.buf) + return append(b, a[:s.outputLen]...) +} + +// Reset resets the Hash to its initial state. +func (s *asmState) Reset() { + for i := range s.a { + s.a[i] = 0 + } + s.resetBuf() + s.state = spongeAbsorbing +} + +// Size returns the number of bytes Sum will return. +func (s *asmState) Size() int { + return s.outputLen +} + +// BlockSize returns the hash's underlying block size. +// The Write method must be able to accept any amount +// of data, but it may operate more efficiently if all writes +// are a multiple of the block size. +func (s *asmState) BlockSize() int { + return s.rate +} + +// Clone returns a copy of the ShakeHash in its current state. +func (s *asmState) Clone() ShakeHash { + return s.clone() +} + +// new224Asm returns an assembly implementation of SHA3-224 if available, +// otherwise it returns nil. +func new224Asm() hash.Hash { + if cpu.S390X.HasSHA3 { + return newAsmState(sha3_224) + } + return nil +} + +// new256Asm returns an assembly implementation of SHA3-256 if available, +// otherwise it returns nil. +func new256Asm() hash.Hash { + if cpu.S390X.HasSHA3 { + return newAsmState(sha3_256) + } + return nil +} + +// new384Asm returns an assembly implementation of SHA3-384 if available, +// otherwise it returns nil. +func new384Asm() hash.Hash { + if cpu.S390X.HasSHA3 { + return newAsmState(sha3_384) + } + return nil +} + +// new512Asm returns an assembly implementation of SHA3-512 if available, +// otherwise it returns nil. +func new512Asm() hash.Hash { + if cpu.S390X.HasSHA3 { + return newAsmState(sha3_512) + } + return nil +} + +// newShake128Asm returns an assembly implementation of SHAKE-128 if available, +// otherwise it returns nil. +func newShake128Asm() ShakeHash { + if cpu.S390X.HasSHA3 { + return newAsmState(shake_128) + } + return nil +} + +// newShake256Asm returns an assembly implementation of SHAKE-256 if available, +// otherwise it returns nil. +func newShake256Asm() ShakeHash { + if cpu.S390X.HasSHA3 { + return newAsmState(shake_256) + } + return nil +} diff --git a/src/vendor/golang.org/x/crypto/sha3/sha3_s390x.s b/src/vendor/golang.org/x/crypto/sha3/sha3_s390x.s new file mode 100644 index 00000000000..8a4458f63f9 --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/sha3_s390x.s @@ -0,0 +1,33 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build !gccgo,!appengine + +#include "textflag.h" + +// func kimd(function code, chain *[200]byte, src []byte) +TEXT ·kimd(SB), NOFRAME|NOSPLIT, $0-40 + MOVD function+0(FP), R0 + MOVD chain+8(FP), R1 + LMG src+16(FP), R2, R3 // R2=base, R3=len + +continue: + WORD $0xB93E0002 // KIMD --, R2 + BVS continue // continue if interrupted + MOVD $0, R0 // reset R0 for pre-go1.8 compilers + RET + +// func klmd(function code, chain *[200]byte, dst, src []byte) +TEXT ·klmd(SB), NOFRAME|NOSPLIT, $0-64 + // TODO: SHAKE support + MOVD function+0(FP), R0 + MOVD chain+8(FP), R1 + LMG dst+16(FP), R2, R3 // R2=base, R3=len + LMG src+40(FP), R4, R5 // R4=base, R5=len + +continue: + WORD $0xB93F0024 // KLMD R2, R4 + BVS continue // continue if interrupted + MOVD $0, R0 // reset R0 for pre-go1.8 compilers + RET diff --git a/src/vendor/golang.org/x/crypto/sha3/sha3_test.go b/src/vendor/golang.org/x/crypto/sha3/sha3_test.go new file mode 100644 index 00000000000..83bd6195d6c --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/sha3_test.go @@ -0,0 +1,490 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// Tests include all the ShortMsgKATs provided by the Keccak team at +// https://github.com/gvanas/KeccakCodePackage +// +// They only include the zero-bit case of the bitwise testvectors +// published by NIST in the draft of FIPS-202. + +import ( + "bytes" + "compress/flate" + "encoding/hex" + "encoding/json" + "fmt" + "hash" + "math/rand" + "os" + "strings" + "testing" +) + +const ( + testString = "brekeccakkeccak koax koax" + katFilename = "testdata/keccakKats.json.deflate" +) + +// testDigests contains functions returning hash.Hash instances +// with output-length equal to the KAT length for SHA-3, Keccak +// and SHAKE instances. +var testDigests = map[string]func() hash.Hash{ + "SHA3-224": New224, + "SHA3-256": New256, + "SHA3-384": New384, + "SHA3-512": New512, + "Keccak-256": NewLegacyKeccak256, + "Keccak-512": NewLegacyKeccak512, +} + +// testShakes contains functions that return sha3.ShakeHash instances for +// with output-length equal to the KAT length. +var testShakes = map[string]struct { + constructor func(N []byte, S []byte) ShakeHash + defAlgoName string + defCustomStr string +}{ + // NewCShake without customization produces same result as SHAKE + "SHAKE128": {NewCShake128, "", ""}, + "SHAKE256": {NewCShake256, "", ""}, + "cSHAKE128": {NewCShake128, "CSHAKE128", "CustomStrign"}, + "cSHAKE256": {NewCShake256, "CSHAKE256", "CustomStrign"}, +} + +// decodeHex converts a hex-encoded string into a raw byte string. +func decodeHex(s string) []byte { + b, err := hex.DecodeString(s) + if err != nil { + panic(err) + } + return b +} + +// structs used to marshal JSON test-cases. +type KeccakKats struct { + Kats map[string][]struct { + Digest string `json:"digest"` + Length int64 `json:"length"` + Message string `json:"message"` + + // Defined only for cSHAKE + N string `json:"N"` + S string `json:"S"` + } +} + +func testUnalignedAndGeneric(t *testing.T, testf func(impl string)) { + xorInOrig, copyOutOrig := xorIn, copyOut + xorIn, copyOut = xorInGeneric, copyOutGeneric + testf("generic") + if xorImplementationUnaligned != "generic" { + xorIn, copyOut = xorInUnaligned, copyOutUnaligned + testf("unaligned") + } + xorIn, copyOut = xorInOrig, copyOutOrig +} + +// TestKeccakKats tests the SHA-3 and Shake implementations against all the +// ShortMsgKATs from https://github.com/gvanas/KeccakCodePackage +// (The testvectors are stored in keccakKats.json.deflate due to their length.) +func TestKeccakKats(t *testing.T) { + testUnalignedAndGeneric(t, func(impl string) { + // Read the KATs. + deflated, err := os.Open(katFilename) + if err != nil { + t.Errorf("error opening %s: %s", katFilename, err) + } + file := flate.NewReader(deflated) + dec := json.NewDecoder(file) + var katSet KeccakKats + err = dec.Decode(&katSet) + if err != nil { + t.Errorf("error decoding KATs: %s", err) + } + + for algo, function := range testDigests { + d := function() + for _, kat := range katSet.Kats[algo] { + d.Reset() + in, err := hex.DecodeString(kat.Message) + if err != nil { + t.Errorf("error decoding KAT: %s", err) + } + d.Write(in[:kat.Length/8]) + got := strings.ToUpper(hex.EncodeToString(d.Sum(nil))) + if got != kat.Digest { + t.Errorf("function=%s, implementation=%s, length=%d\nmessage:\n %s\ngot:\n %s\nwanted:\n %s", + algo, impl, kat.Length, kat.Message, got, kat.Digest) + t.Logf("wanted %+v", kat) + t.FailNow() + } + continue + } + } + + for algo, v := range testShakes { + for _, kat := range katSet.Kats[algo] { + N, err := hex.DecodeString(kat.N) + if err != nil { + t.Errorf("error decoding KAT: %s", err) + } + + S, err := hex.DecodeString(kat.S) + if err != nil { + t.Errorf("error decoding KAT: %s", err) + } + d := v.constructor(N, S) + in, err := hex.DecodeString(kat.Message) + if err != nil { + t.Errorf("error decoding KAT: %s", err) + } + + d.Write(in[:kat.Length/8]) + out := make([]byte, len(kat.Digest)/2) + d.Read(out) + got := strings.ToUpper(hex.EncodeToString(out)) + if got != kat.Digest { + t.Errorf("function=%s, implementation=%s, length=%d N:%s\n S:%s\nmessage:\n %s \ngot:\n %s\nwanted:\n %s", + algo, impl, kat.Length, kat.N, kat.S, kat.Message, got, kat.Digest) + t.Logf("wanted %+v", kat) + t.FailNow() + } + continue + } + } + }) +} + +// TestKeccak does a basic test of the non-standardized Keccak hash functions. +func TestKeccak(t *testing.T) { + tests := []struct { + fn func() hash.Hash + data []byte + want string + }{ + { + NewLegacyKeccak256, + []byte("abc"), + "4e03657aea45a94fc7d47ba826c8d667c0d1e6e33a64a036ec44f58fa12d6c45", + }, + { + NewLegacyKeccak512, + []byte("abc"), + "18587dc2ea106b9a1563e32b3312421ca164c7f1f07bc922a9c83d77cea3a1e5d0c69910739025372dc14ac9642629379540c17e2a65b19d77aa511a9d00bb96", + }, + } + + for _, u := range tests { + h := u.fn() + h.Write(u.data) + got := h.Sum(nil) + want := decodeHex(u.want) + if !bytes.Equal(got, want) { + t.Errorf("unexpected hash for size %d: got '%x' want '%s'", h.Size()*8, got, u.want) + } + } +} + +// TestUnalignedWrite tests that writing data in an arbitrary pattern with +// small input buffers. +func TestUnalignedWrite(t *testing.T) { + testUnalignedAndGeneric(t, func(impl string) { + buf := sequentialBytes(0x10000) + for alg, df := range testDigests { + d := df() + d.Reset() + d.Write(buf) + want := d.Sum(nil) + d.Reset() + for i := 0; i < len(buf); { + // Cycle through offsets which make a 137 byte sequence. + // Because 137 is prime this sequence should exercise all corner cases. + offsets := [17]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1} + for _, j := range offsets { + if v := len(buf) - i; v < j { + j = v + } + d.Write(buf[i : i+j]) + i += j + } + } + got := d.Sum(nil) + if !bytes.Equal(got, want) { + t.Errorf("Unaligned writes, implementation=%s, alg=%s\ngot %q, want %q", impl, alg, got, want) + } + } + + // Same for SHAKE + for alg, df := range testShakes { + want := make([]byte, 16) + got := make([]byte, 16) + d := df.constructor([]byte(df.defAlgoName), []byte(df.defCustomStr)) + + d.Reset() + d.Write(buf) + d.Read(want) + d.Reset() + for i := 0; i < len(buf); { + // Cycle through offsets which make a 137 byte sequence. + // Because 137 is prime this sequence should exercise all corner cases. + offsets := [17]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1} + for _, j := range offsets { + if v := len(buf) - i; v < j { + j = v + } + d.Write(buf[i : i+j]) + i += j + } + } + d.Read(got) + if !bytes.Equal(got, want) { + t.Errorf("Unaligned writes, implementation=%s, alg=%s\ngot %q, want %q", impl, alg, got, want) + } + } + }) +} + +// TestAppend checks that appending works when reallocation is necessary. +func TestAppend(t *testing.T) { + testUnalignedAndGeneric(t, func(impl string) { + d := New224() + + for capacity := 2; capacity <= 66; capacity += 64 { + // The first time around the loop, Sum will have to reallocate. + // The second time, it will not. + buf := make([]byte, 2, capacity) + d.Reset() + d.Write([]byte{0xcc}) + buf = d.Sum(buf) + expected := "0000DF70ADC49B2E76EEE3A6931B93FA41841C3AF2CDF5B32A18B5478C39" + if got := strings.ToUpper(hex.EncodeToString(buf)); got != expected { + t.Errorf("got %s, want %s", got, expected) + } + } + }) +} + +// TestAppendNoRealloc tests that appending works when no reallocation is necessary. +func TestAppendNoRealloc(t *testing.T) { + testUnalignedAndGeneric(t, func(impl string) { + buf := make([]byte, 1, 200) + d := New224() + d.Write([]byte{0xcc}) + buf = d.Sum(buf) + expected := "00DF70ADC49B2E76EEE3A6931B93FA41841C3AF2CDF5B32A18B5478C39" + if got := strings.ToUpper(hex.EncodeToString(buf)); got != expected { + t.Errorf("%s: got %s, want %s", impl, got, expected) + } + }) +} + +// TestSqueezing checks that squeezing the full output a single time produces +// the same output as repeatedly squeezing the instance. +func TestSqueezing(t *testing.T) { + testUnalignedAndGeneric(t, func(impl string) { + for algo, v := range testShakes { + d0 := v.constructor([]byte(v.defAlgoName), []byte(v.defCustomStr)) + d0.Write([]byte(testString)) + ref := make([]byte, 32) + d0.Read(ref) + + d1 := v.constructor([]byte(v.defAlgoName), []byte(v.defCustomStr)) + d1.Write([]byte(testString)) + var multiple []byte + for range ref { + one := make([]byte, 1) + d1.Read(one) + multiple = append(multiple, one...) + } + if !bytes.Equal(ref, multiple) { + t.Errorf("%s (%s): squeezing %d bytes one at a time failed", algo, impl, len(ref)) + } + } + }) +} + +// sequentialBytes produces a buffer of size consecutive bytes 0x00, 0x01, ..., used for testing. +// +// The alignment of each slice is intentionally randomized to detect alignment +// issues in the implementation. See https://golang.org/issue/37644. +// Ideally, the compiler should fuzz the alignment itself. +// (See https://golang.org/issue/35128.) +func sequentialBytes(size int) []byte { + alignmentOffset := rand.Intn(8) + result := make([]byte, size+alignmentOffset)[alignmentOffset:] + for i := range result { + result[i] = byte(i) + } + return result +} + +func TestReset(t *testing.T) { + out1 := make([]byte, 32) + out2 := make([]byte, 32) + + for _, v := range testShakes { + // Calculate hash for the first time + c := v.constructor(nil, []byte{0x99, 0x98}) + c.Write(sequentialBytes(0x100)) + c.Read(out1) + + // Calculate hash again + c.Reset() + c.Write(sequentialBytes(0x100)) + c.Read(out2) + + if !bytes.Equal(out1, out2) { + t.Error("\nExpected:\n", out1, "\ngot:\n", out2) + } + } +} + +func TestClone(t *testing.T) { + out1 := make([]byte, 16) + out2 := make([]byte, 16) + + // Test for sizes smaller and larger than block size. + for _, size := range []int{0x1, 0x100} { + in := sequentialBytes(size) + for _, v := range testShakes { + h1 := v.constructor(nil, []byte{0x01}) + h1.Write([]byte{0x01}) + + h2 := h1.Clone() + + h1.Write(in) + h1.Read(out1) + + h2.Write(in) + h2.Read(out2) + + if !bytes.Equal(out1, out2) { + t.Error("\nExpected:\n", hex.EncodeToString(out1), "\ngot:\n", hex.EncodeToString(out2)) + } + } + } +} + +// BenchmarkPermutationFunction measures the speed of the permutation function +// with no input data. +func BenchmarkPermutationFunction(b *testing.B) { + b.SetBytes(int64(200)) + var lanes [25]uint64 + for i := 0; i < b.N; i++ { + keccakF1600(&lanes) + } +} + +// benchmarkHash tests the speed to hash num buffers of buflen each. +func benchmarkHash(b *testing.B, h hash.Hash, size, num int) { + b.StopTimer() + h.Reset() + data := sequentialBytes(size) + b.SetBytes(int64(size * num)) + b.StartTimer() + + var state []byte + for i := 0; i < b.N; i++ { + for j := 0; j < num; j++ { + h.Write(data) + } + state = h.Sum(state[:0]) + } + b.StopTimer() + h.Reset() +} + +// benchmarkShake is specialized to the Shake instances, which don't +// require a copy on reading output. +func benchmarkShake(b *testing.B, h ShakeHash, size, num int) { + b.StopTimer() + h.Reset() + data := sequentialBytes(size) + d := make([]byte, 32) + + b.SetBytes(int64(size * num)) + b.StartTimer() + + for i := 0; i < b.N; i++ { + h.Reset() + for j := 0; j < num; j++ { + h.Write(data) + } + h.Read(d) + } +} + +func BenchmarkSha3_512_MTU(b *testing.B) { benchmarkHash(b, New512(), 1350, 1) } +func BenchmarkSha3_384_MTU(b *testing.B) { benchmarkHash(b, New384(), 1350, 1) } +func BenchmarkSha3_256_MTU(b *testing.B) { benchmarkHash(b, New256(), 1350, 1) } +func BenchmarkSha3_224_MTU(b *testing.B) { benchmarkHash(b, New224(), 1350, 1) } + +func BenchmarkShake128_MTU(b *testing.B) { benchmarkShake(b, NewShake128(), 1350, 1) } +func BenchmarkShake256_MTU(b *testing.B) { benchmarkShake(b, NewShake256(), 1350, 1) } +func BenchmarkShake256_16x(b *testing.B) { benchmarkShake(b, NewShake256(), 16, 1024) } +func BenchmarkShake256_1MiB(b *testing.B) { benchmarkShake(b, NewShake256(), 1024, 1024) } + +func BenchmarkSha3_512_1MiB(b *testing.B) { benchmarkHash(b, New512(), 1024, 1024) } + +func Example_sum() { + buf := []byte("some data to hash") + // A hash needs to be 64 bytes long to have 256-bit collision resistance. + h := make([]byte, 64) + // Compute a 64-byte hash of buf and put it in h. + ShakeSum256(h, buf) + fmt.Printf("%x\n", h) + // Output: 0f65fe41fc353e52c55667bb9e2b27bfcc8476f2c413e9437d272ee3194a4e3146d05ec04a25d16b8f577c19b82d16b1424c3e022e783d2b4da98de3658d363d +} + +func Example_mac() { + k := []byte("this is a secret key; you should generate a strong random key that's at least 32 bytes long") + buf := []byte("and this is some data to authenticate") + // A MAC with 32 bytes of output has 256-bit security strength -- if you use at least a 32-byte-long key. + h := make([]byte, 32) + d := NewShake256() + // Write the key into the hash. + d.Write(k) + // Now write the data. + d.Write(buf) + // Read 32 bytes of output from the hash into h. + d.Read(h) + fmt.Printf("%x\n", h) + // Output: 78de2974bd2711d5549ffd32b753ef0f5fa80a0db2556db60f0987eb8a9218ff +} + +func ExampleNewCShake256() { + out := make([]byte, 32) + msg := []byte("The quick brown fox jumps over the lazy dog") + + // Example 1: Simple cshake + c1 := NewCShake256([]byte("NAME"), []byte("Partition1")) + c1.Write(msg) + c1.Read(out) + fmt.Println(hex.EncodeToString(out)) + + // Example 2: Different customization string produces different digest + c1 = NewCShake256([]byte("NAME"), []byte("Partition2")) + c1.Write(msg) + c1.Read(out) + fmt.Println(hex.EncodeToString(out)) + + // Example 3: Longer output length produces longer digest + out = make([]byte, 64) + c1 = NewCShake256([]byte("NAME"), []byte("Partition1")) + c1.Write(msg) + c1.Read(out) + fmt.Println(hex.EncodeToString(out)) + + // Example 4: Next read produces different result + c1.Read(out) + fmt.Println(hex.EncodeToString(out)) + + // Output: + //a90a4c6ca9af2156eba43dc8398279e6b60dcd56fb21837afe6c308fd4ceb05b + //a8db03e71f3e4da5c4eee9d28333cdd355f51cef3c567e59be5beb4ecdbb28f0 + //a90a4c6ca9af2156eba43dc8398279e6b60dcd56fb21837afe6c308fd4ceb05b9dd98c6ee866ca7dc5a39d53e960f400bcd5a19c8a2d6ec6459f63696543a0d8 + //85e73a72228d08b46515553ca3a29d47df3047e5d84b12d6c2c63e579f4fd1105716b7838e92e981863907f434bfd4443c9e56ea09da998d2f9b47db71988109 +} diff --git a/src/vendor/golang.org/x/crypto/sha3/shake.go b/src/vendor/golang.org/x/crypto/sha3/shake.go new file mode 100644 index 00000000000..d7be2954ab2 --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/shake.go @@ -0,0 +1,173 @@ +// Copyright 2014 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +// This file defines the ShakeHash interface, and provides +// functions for creating SHAKE and cSHAKE instances, as well as utility +// functions for hashing bytes to arbitrary-length output. +// +// +// SHAKE implementation is based on FIPS PUB 202 [1] +// cSHAKE implementations is based on NIST SP 800-185 [2] +// +// [1] https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf +// [2] https://doi.org/10.6028/NIST.SP.800-185 + +import ( + "encoding/binary" + "io" +) + +// ShakeHash defines the interface to hash functions that +// support arbitrary-length output. +type ShakeHash interface { + // Write absorbs more data into the hash's state. It panics if input is + // written to it after output has been read from it. + io.Writer + + // Read reads more output from the hash; reading affects the hash's + // state. (ShakeHash.Read is thus very different from Hash.Sum) + // It never returns an error. + io.Reader + + // Clone returns a copy of the ShakeHash in its current state. + Clone() ShakeHash + + // Reset resets the ShakeHash to its initial state. + Reset() +} + +// cSHAKE specific context +type cshakeState struct { + *state // SHA-3 state context and Read/Write operations + + // initBlock is the cSHAKE specific initialization set of bytes. It is initialized + // by newCShake function and stores concatenation of N followed by S, encoded + // by the method specified in 3.3 of [1]. + // It is stored here in order for Reset() to be able to put context into + // initial state. + initBlock []byte +} + +// Consts for configuring initial SHA-3 state +const ( + dsbyteShake = 0x1f + dsbyteCShake = 0x04 + rate128 = 168 + rate256 = 136 +) + +func bytepad(input []byte, w int) []byte { + // leftEncode always returns max 9 bytes + buf := make([]byte, 0, 9+len(input)+w) + buf = append(buf, leftEncode(uint64(w))...) + buf = append(buf, input...) + padlen := w - (len(buf) % w) + return append(buf, make([]byte, padlen)...) +} + +func leftEncode(value uint64) []byte { + var b [9]byte + binary.BigEndian.PutUint64(b[1:], value) + // Trim all but last leading zero bytes + i := byte(1) + for i < 8 && b[i] == 0 { + i++ + } + // Prepend number of encoded bytes + b[i-1] = 9 - i + return b[i-1:] +} + +func newCShake(N, S []byte, rate int, dsbyte byte) ShakeHash { + c := cshakeState{state: &state{rate: rate, dsbyte: dsbyte}} + + // leftEncode returns max 9 bytes + c.initBlock = make([]byte, 0, 9*2+len(N)+len(S)) + c.initBlock = append(c.initBlock, leftEncode(uint64(len(N)*8))...) + c.initBlock = append(c.initBlock, N...) + c.initBlock = append(c.initBlock, leftEncode(uint64(len(S)*8))...) + c.initBlock = append(c.initBlock, S...) + c.Write(bytepad(c.initBlock, c.rate)) + return &c +} + +// Reset resets the hash to initial state. +func (c *cshakeState) Reset() { + c.state.Reset() + c.Write(bytepad(c.initBlock, c.rate)) +} + +// Clone returns copy of a cSHAKE context within its current state. +func (c *cshakeState) Clone() ShakeHash { + b := make([]byte, len(c.initBlock)) + copy(b, c.initBlock) + return &cshakeState{state: c.clone(), initBlock: b} +} + +// Clone returns copy of SHAKE context within its current state. +func (c *state) Clone() ShakeHash { + return c.clone() +} + +// NewShake128 creates a new SHAKE128 variable-output-length ShakeHash. +// Its generic security strength is 128 bits against all attacks if at +// least 32 bytes of its output are used. +func NewShake128() ShakeHash { + if h := newShake128Asm(); h != nil { + return h + } + return &state{rate: rate128, dsbyte: dsbyteShake} +} + +// NewShake256 creates a new SHAKE256 variable-output-length ShakeHash. +// Its generic security strength is 256 bits against all attacks if +// at least 64 bytes of its output are used. +func NewShake256() ShakeHash { + if h := newShake256Asm(); h != nil { + return h + } + return &state{rate: rate256, dsbyte: dsbyteShake} +} + +// NewCShake128 creates a new instance of cSHAKE128 variable-output-length ShakeHash, +// a customizable variant of SHAKE128. +// N is used to define functions based on cSHAKE, it can be empty when plain cSHAKE is +// desired. S is a customization byte string used for domain separation - two cSHAKE +// computations on same input with different S yield unrelated outputs. +// When N and S are both empty, this is equivalent to NewShake128. +func NewCShake128(N, S []byte) ShakeHash { + if len(N) == 0 && len(S) == 0 { + return NewShake128() + } + return newCShake(N, S, rate128, dsbyteCShake) +} + +// NewCShake256 creates a new instance of cSHAKE256 variable-output-length ShakeHash, +// a customizable variant of SHAKE256. +// N is used to define functions based on cSHAKE, it can be empty when plain cSHAKE is +// desired. S is a customization byte string used for domain separation - two cSHAKE +// computations on same input with different S yield unrelated outputs. +// When N and S are both empty, this is equivalent to NewShake256. +func NewCShake256(N, S []byte) ShakeHash { + if len(N) == 0 && len(S) == 0 { + return NewShake256() + } + return newCShake(N, S, rate256, dsbyteCShake) +} + +// ShakeSum128 writes an arbitrary-length digest of data into hash. +func ShakeSum128(hash, data []byte) { + h := NewShake128() + h.Write(data) + h.Read(hash) +} + +// ShakeSum256 writes an arbitrary-length digest of data into hash. +func ShakeSum256(hash, data []byte) { + h := NewShake256() + h.Write(data) + h.Read(hash) +} diff --git a/src/vendor/golang.org/x/crypto/sha3/shake_generic.go b/src/vendor/golang.org/x/crypto/sha3/shake_generic.go new file mode 100644 index 00000000000..add4e733967 --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/shake_generic.go @@ -0,0 +1,19 @@ +// Copyright 2017 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build gccgo appengine !s390x + +package sha3 + +// newShake128Asm returns an assembly implementation of SHAKE-128 if available, +// otherwise it returns nil. +func newShake128Asm() ShakeHash { + return nil +} + +// newShake256Asm returns an assembly implementation of SHAKE-256 if available, +// otherwise it returns nil. +func newShake256Asm() ShakeHash { + return nil +} diff --git a/src/vendor/golang.org/x/crypto/sha3/testdata/keccakKats.json.deflate b/src/vendor/golang.org/x/crypto/sha3/testdata/keccakKats.json.deflate new file mode 100644 index 00000000000..7a94c2f8bce Binary files /dev/null and b/src/vendor/golang.org/x/crypto/sha3/testdata/keccakKats.json.deflate differ diff --git a/src/vendor/golang.org/x/crypto/sha3/xor.go b/src/vendor/golang.org/x/crypto/sha3/xor.go new file mode 100644 index 00000000000..079b650141c --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/xor.go @@ -0,0 +1,23 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build !amd64,!386,!ppc64le appengine + +package sha3 + +// A storageBuf is an aligned array of maxRate bytes. +type storageBuf [maxRate]byte + +func (b *storageBuf) asBytes() *[maxRate]byte { + return (*[maxRate]byte)(b) +} + +var ( + xorIn = xorInGeneric + copyOut = copyOutGeneric + xorInUnaligned = xorInGeneric + copyOutUnaligned = copyOutGeneric +) + +const xorImplementationUnaligned = "generic" diff --git a/src/vendor/golang.org/x/crypto/sha3/xor_generic.go b/src/vendor/golang.org/x/crypto/sha3/xor_generic.go new file mode 100644 index 00000000000..fd35f02ef6e --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/xor_generic.go @@ -0,0 +1,28 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package sha3 + +import "encoding/binary" + +// xorInGeneric xors the bytes in buf into the state; it +// makes no non-portable assumptions about memory layout +// or alignment. +func xorInGeneric(d *state, buf []byte) { + n := len(buf) / 8 + + for i := 0; i < n; i++ { + a := binary.LittleEndian.Uint64(buf) + d.a[i] ^= a + buf = buf[8:] + } +} + +// copyOutGeneric copies ulint64s to a byte buffer. +func copyOutGeneric(d *state, b []byte) { + for i := 0; len(b) >= 8; i++ { + binary.LittleEndian.PutUint64(b, d.a[i]) + b = b[8:] + } +} diff --git a/src/vendor/golang.org/x/crypto/sha3/xor_unaligned.go b/src/vendor/golang.org/x/crypto/sha3/xor_unaligned.go new file mode 100644 index 00000000000..5f19cdff391 --- /dev/null +++ b/src/vendor/golang.org/x/crypto/sha3/xor_unaligned.go @@ -0,0 +1,67 @@ +// Copyright 2015 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// +build amd64 386 ppc64le +// +build !appengine + +package sha3 + +import "unsafe" + +// A storageBuf is an aligned array of maxRate bytes. +type storageBuf [maxRate / 8]uint64 + +func (b *storageBuf) asBytes() *[maxRate]byte { + return (*[maxRate]byte)(unsafe.Pointer(b)) +} + +// xorInUnaligned uses unaligned reads and writes to update d.a to contain d.a +// XOR buf. +func xorInUnaligned(d *state, buf []byte) { + n := len(buf) + bw := (*[maxRate / 8]uint64)(unsafe.Pointer(&buf[0]))[: n/8 : n/8] + if n >= 72 { + d.a[0] ^= bw[0] + d.a[1] ^= bw[1] + d.a[2] ^= bw[2] + d.a[3] ^= bw[3] + d.a[4] ^= bw[4] + d.a[5] ^= bw[5] + d.a[6] ^= bw[6] + d.a[7] ^= bw[7] + d.a[8] ^= bw[8] + } + if n >= 104 { + d.a[9] ^= bw[9] + d.a[10] ^= bw[10] + d.a[11] ^= bw[11] + d.a[12] ^= bw[12] + } + if n >= 136 { + d.a[13] ^= bw[13] + d.a[14] ^= bw[14] + d.a[15] ^= bw[15] + d.a[16] ^= bw[16] + } + if n >= 144 { + d.a[17] ^= bw[17] + } + if n >= 168 { + d.a[18] ^= bw[18] + d.a[19] ^= bw[19] + d.a[20] ^= bw[20] + } +} + +func copyOutUnaligned(d *state, buf []byte) { + ab := (*[maxRate]uint8)(unsafe.Pointer(&d.a[0])) + copy(buf, ab[:]) +} + +var ( + xorIn = xorInUnaligned + copyOut = copyOutUnaligned +) + +const xorImplementationUnaligned = "unaligned"