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fips204.py
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# fips204.py
# 2024-08-16 Markku-Juhani O. Saarinen <[email protected]> See LICENSE.
# === FIPS 204 implementation https://doi.org/10.6028/NIST.FIPS.204
# ML-DSA / Module-Lattice-Based Digital Signature Standard
# test_mldsa is only used by the unit test in the end
from test_mldsa import test_mldsa
# hash functions
from Crypto.Hash import SHAKE128, SHAKE256
from Crypto.Hash import SHA224, SHA256, SHA384, SHA512
from Crypto.Hash import SHA3_224, SHA3_256, SHA3_384, SHA3_512
ML_DSA_Q = 8380417
ML_DSA_N = 256
# Appendix B - Zetas Array
ML_DSA_ZETAS = [
0, 4808194, 3765607, 3761513, 5178923, 5496691, 5234739, 5178987,
7778734, 3542485, 2682288, 2129892, 3764867, 7375178, 557458, 7159240,
5010068, 4317364, 2663378, 6705802, 4855975, 7946292, 676590, 7044481,
5152541, 1714295, 2453983, 1460718, 7737789, 4795319, 2815639, 2283733,
3602218, 3182878, 2740543, 4793971, 5269599, 2101410, 3704823, 1159875,
394148, 928749, 1095468, 4874037, 2071829, 4361428, 3241972, 2156050,
3415069, 1759347, 7562881, 4805951, 3756790, 6444618, 6663429, 4430364,
5483103, 3192354, 556856, 3870317, 2917338, 1853806, 3345963, 1858416,
3073009, 1277625, 5744944, 3852015, 4183372, 5157610, 5258977, 8106357,
2508980, 2028118, 1937570, 4564692, 2811291, 5396636, 7270901, 4158088,
1528066, 482649, 1148858, 5418153, 7814814, 169688, 2462444, 5046034,
4213992, 4892034, 1987814, 5183169, 1736313, 235407, 5130263, 3258457,
5801164, 1787943, 5989328, 6125690, 3482206, 4197502, 7080401, 6018354,
7062739, 2461387, 3035980, 621164, 3901472, 7153756, 2925816, 3374250,
1356448, 5604662, 2683270, 5601629, 4912752, 2312838, 7727142, 7921254,
348812, 8052569, 1011223, 6026202, 4561790, 6458164, 6143691, 1744507,
1753, 6444997, 5720892, 6924527, 2660408, 6600190, 8321269, 2772600,
1182243, 87208, 636927, 4415111, 4423672, 6084020, 5095502, 4663471,
8352605, 822541, 1009365, 5926272, 6400920, 1596822, 4423473, 4620952,
6695264, 4969849, 2678278, 4611469, 4829411, 635956, 8129971, 5925040,
4234153, 6607829, 2192938, 6653329, 2387513, 4768667, 8111961, 5199961,
3747250, 2296099, 1239911, 4541938, 3195676, 2642980, 1254190, 8368000,
2998219, 141835, 8291116, 2513018, 7025525, 613238, 7070156, 6161950,
7921677, 6458423, 4040196, 4908348, 2039144, 6500539, 7561656, 6201452,
6757063, 2105286, 6006015, 6346610, 586241, 7200804, 527981, 5637006,
6903432, 1994046, 2491325, 6987258, 507927, 7192532, 7655613, 6545891,
5346675, 8041997, 2647994, 3009748, 5767564, 4148469, 749577, 4357667,
3980599, 2569011, 6764887, 1723229, 1665318, 2028038, 1163598, 5011144,
3994671, 8368538, 7009900, 3020393, 3363542, 214880, 545376, 7609976,
3105558, 7277073, 508145, 7826699, 860144, 3430436, 140244, 6866265,
6195333, 3123762, 2358373, 6187330, 5365997, 6663603, 2926054, 7987710,
8077412, 3531229, 4405932, 4606686, 1900052, 7598542, 1054478, 7648983 ]
# zetas = [ (1753 ** self.bitrev8(i)) % ML_DSA_Q for i in range(256) ]
# Sect 4, Table 1. ML-DSA parameter sets
# (d, tau, lam, gam1, gam2, k, ell, eta, beta, omega)
ML_DSA_PARAM = {
"ML-DSA-44" : (13, 39, 128, 2**17, (ML_DSA_Q-1)//88, 4, 4, 2, 78, 80),
"ML-DSA-65" : (13, 49, 192, 2**19, (ML_DSA_Q-1)//32, 6, 5, 4, 196, 55),
"ML-DSA-87" : (13, 60, 256, 2**19, (ML_DSA_Q-1)//32, 8, 7, 2, 120, 75)
}
class ML_DSA:
def __init__(self, param='ML-DSA-65'):
""" Initialize the class with parameters."""
if param not in ML_DSA_PARAM:
raise ValueError
self.q = ML_DSA_Q
self.n = ML_DSA_N
(self.d, self.tau, self.lam, self.gam1, self.gam2, self.k, self.ell,
self.eta, self.beta, self.omega) = ML_DSA_PARAM[param]
# 3.7 Use of Symmetric Cryptography
def h(self, s, l):
return SHAKE256.new(s).read(l)
# Algorithm 2, ML-DSA.Sign(sk, M, ctx)
def sign(self, sk, m, ctx=b'', rnd=None, param=None):
if param != None:
self.__init__(param)
if len(ctx) > 255:
return None
if rnd == None:
rnd = b'\x00'*32
mp = ( self.integer_to_bytes(0, 1) +
self.integer_to_bytes(len(ctx), 1) + ctx + m )
sig = self.sign_internal(sk, mp, rnd)
return sig
# Algorithm 3, ML-DSA.Verify(pk, M, sigma, ctx)
def verify(self, pk, m, sig, ctx=b'', param=None):
if param != None:
self.__init__(param)
if len(ctx) > 255:
return False
mp = ( self.integer_to_bytes(0, 1) +
self.integer_to_bytes(len(ctx), 1) + ctx + m)
return self.verify_internal(pk, mp, sig)
# shared formatting routine
def hash_ml_dsa_pad(self, m, ctx, ph):
if len(ctx) > 255:
return None
if ph == 'SHA2-256':
oid = bytes([ 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03,
0x04, 0x02, 0x01])
phm = SHA256.new(m).digest()
elif ph == 'SHA2-384':
oid = bytes([ 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03,
0x04, 0x02, 0x02])
phm = SHA384.new(m).digest()
elif ph == 'SHA2-512':
oid = bytes([ 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03,
0x04, 0x02, 0x03])
phm = SHA512.new(m).digest()
elif ph == 'SHA2-224':
oid = bytes([ 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03,
0x04, 0x02, 0x04])
phm = SHA224.new(m).digest()
elif ph == 'SHA2-512/224':
oid = bytes([ 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03,
0x04, 0x02, 0x05])
phm = SHA512.new(m,truncate="224").digest()
elif ph == 'SHA2-512/256':
oid = bytes([ 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03,
0x04, 0x02, 0x06])
phm = SHA512.new(m,truncate="256").digest()
elif ph == 'SHA3-224':
oid = bytes([ 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03,
0x04, 0x02, 0x07])
phm = SHA3_224.new(m).digest()
elif ph == 'SHA3-256':
oid = bytes([ 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03,
0x04, 0x02, 0x08])
phm = SHA3_256.new(m).digest()
elif ph == 'SHA3-384':
oid = bytes([ 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03,
0x04, 0x02, 0x09])
phm = SHA3_384.new(m).digest()
elif ph == 'SHA3-512':
oid = bytes([ 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03,
0x04, 0x02, 0x0A])
phm = SHA3_512.new(m).digest()
elif ph == 'SHAKE-128':
oid = bytes([ 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03,
0x04, 0x02, 0x0B])
phm = SHAKE128.new(m).read(256 // 8)
elif ph == 'SHAKE-256':
oid = bytes([ 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03,
0x04, 0x02, 0x0C])
phm = SHAKE256.new(m).read(512 // 8)
else:
return None
mp = ( self.integer_to_bytes(1, 1) +
self.integer_to_bytes(len(ctx), 1) +
ctx + oid + phm )
return mp
# Algorithm 4, HashML-DSA.Sign(sk, M, ctx, PH)
def hash_ml_dsa_sign(self, sk, m, ctx=b'', ph='SHA2-512', rnd=None, param=None):
if param != None:
self.__init__(param)
if len(ctx) > 255:
return None
if rnd == None:
rnd = b'\x00'*32
mp = self.hash_ml_dsa_pad(m, ctx, ph)
if mp == None:
return None
sig = self.sign_internal(sk, mp, rnd)
return sig
# Algorithm 5, HashML-DSA.Verify(pk, M, sig, ctx, PH)
def hash_ml_dsa_verify(self, pk, m, sig, ctx=b'', ph='SHA2-512', param=None):
if param != None:
self.__init__(param)
mp = self.hash_ml_dsa_pad(m, ctx, ph)
if mp == None:
return False
return self.verify_internal(pk, mp, sig)
# Algorithm 6, ML-DSA.KeyGen_internal(xi)
def keygen_internal(self, xi, param=None):
if param != None:
self.__init__(param)
# print('# keygen_internal()', param)
# print('# seed:', xi.hex())
se = self.h(xi +
self.integer_to_bytes(self.k, 1) +
self.integer_to_bytes(self.ell, 1), 128 )
rho = se[0:32]
rhop = se[32:96]
kk = se[96:128]
# print('# rho:', rho.hex())
# print('# rhoPrime:', rhop.hex())
# print('# k:', kk.hex())
ah = self.expand_a(rho)
# print('# aHat:', ah)
(s1, s2) = self.expand_s(rhop)
# print('# s1:', s1)
# print('# s2:', s2)
s1h = [ self.ntt(v) for v in s1 ]
# print('# s1Hat:', s1h)
t = self.matrix_vector_ntt(ah, s1h)
# print('# aHat*s1Hat:', t)
t = [ self.add(self.ntt_inverse(t[i]), s2[i])
for i in range(self.k) ]
# print('# t:', t)
(t1, t0) = self.power2round(t)
# print('# t0:', t0)
# print('# t1:', t1)
pk = self.pk_encode(rho, t1)
# print('# pk:', pk.hex())
tr = self.h(pk, 64)
# print('# tr:', tr.hex())
sk = self.sk_encode(rho, kk, tr, s1, s2, t0)
# print('# sk:', sk.hex())
return pk, sk
# Algorithm 7, ML-DSA.Sign_internal(sk, M', rnd)
def sign_internal(self, sk, mp, rnd, param=None, mu=None):
if param != None:
self.__init__(param)
(rho, kk, tr, s1, s2, t0) = self.sk_decode(sk)
# print('# sign_internal()', param)
# print('# rho:', rho.hex())
# print('# tr:', tr.hex())
# print('# rnd:', rnd.hex())
s1h = [ self.ntt(s1i) for s1i in s1 ]
# print('# s1Hat:', s1h)
s2h = [ self.ntt(s2i) for s2i in s2 ]
# print('# s2Hat:', s2h)
t0h = [ self.ntt(t0i) for t0i in t0 ]
# print('# t0Hat:', t0h)
ah = self.expand_a(rho)
# print('# aHat:', ah)
if mu == None:
mu = self.h(tr + mp, 64)
# print('# mu:', mu.hex())
rhopp = self.h(kk + rnd + mu, 64)
# print('# rhoPrime:', rhopp.hex())
kappa = 0
(z, h) = (None, None)
while (z, h) == (None, None):
y = self.expand_mask(rhopp, kappa)
# print('# y:', y)
yh = [ self.ntt(yi) for yi in y ]
# print('# NTT(y):', yh)
w = self.matrix_vector_ntt(ah, yh)
# print('# aHat*NTT(y):', w)
w = [ self.ntt_inverse(wi) for wi in w ]
# print('# w:', w)
w1 = self.high_bits(w)
# print('# w1:', w1)
w1t = self.w1_encode(w1)
# print('# w1Encode:', w1t.hex())
ct = self.h(mu + w1t, self.lam // 4)
# print('# cTilde:', ct.hex())
c = self.sample_in_ball(ct)
# print('# c:', c)
ch = self.ntt(c)
# print('# cHat:', ch)
cs1 = [ self.ntt_inverse(self.mul_ntt(ch, s1i)) for s1i in s1h ]
# print('# cs1:', cs1)
cs2 = [ self.ntt_inverse(self.mul_ntt(ch, s2i)) for s2i in s2h ]
# print('# cs2:', cs2)
z = [ self.add(y[i], cs1[i]) for i in range(self.ell) ]
# print('# z:', z)
r0 = [ self.sub(w[i], cs2[i]) for i in range(self.k) ]
r0 = self.low_bits(r0)
# print('# r0:', r0)
z_norm = self.inf_norm(z)
# print('# ||z||:', z_norm)
r0_norm = self.inf_norm(r0)
# print('# ||r0||:', r0_norm)
if (z_norm >= self.gam1 - self.beta or
r0_norm >= self.gam2 - self.beta):
# print('# norm check fail')
(z, h) = (None, None)
else:
ct0 = [ self.ntt_inverse(self.mul_ntt(ch, t0i))
for t0i in t0h ]
# print('# ct0:', ct0)
ct0n = [ self.neg(ct0i) for ct0i in ct0 ]
# print('# -ct0:', ct0n)
h_r = [ self.add(self.sub(w[i], cs2[i]), ct0[i])
for i in range(self.k) ]
# print('# w - cs2 + ct0:', h_r)
h = self.make_hint(ct0n, h_r)
# print('# h', h)
h_wt = self.weight(h)
# print('# ||h||:', h_wt)
ct0_norm = self.inf_norm(ct0)
# print('# ||ct0||:', ct0_norm)
if ct0_norm >= self.gam2 or h_wt > self.omega:
(z, h) = (None, None)
kappa += self.ell
z = [ [ self.modpm(x, self.q) for x in zi ] for zi in z ]
sig = self.sig_encode(ct, z, h)
# print('# sig:', sig.hex())
return sig
# Algorithm 8, ML-DSA.Verify_internal(pk, M', sigma)
def verify_internal(self, pk, mp, sig, param=None, mu=None):
if param != None:
self.__init__(param)
(rho, t1) = self.pk_decode(pk)
(ct, z, h) = self.sig_decode(sig)
# print('# rho:', rho.hex())
# print('# t1:', t1)
# print('# cTilde:', ct.hex())
# print('# z:', z)
if h == None:
return False
ah = self.expand_a(rho)
# print('# aHat:', ah)
tr = self.h(pk, 64)
# print('# tr:', tr.hex())
if mu == None:
mu = self.h(tr + mp, 64)
# print('# mu:', mu.hex())
c = self.sample_in_ball(ct)
# print('# c:', c)
zh = [ self.ntt(zi) for zi in z ]
# print('# zHat:', zh)
wp = self.matrix_vector_ntt(ah, zh)
# print('# aHat*NTT(z):', wp)
th = [ self.ntt([ x << self.d for x in t1i ]) for t1i in t1 ]
# print('# NTT(t1*2^d):', th)
ch = self.ntt(c)
# print('# NTT(c):', ch)
th = [ self.mul_ntt(ch, thi) for thi in th ]
# print('# NTT(c)*NTT(t1*2^d):', th)
wp = [ self.ntt_inverse(self.sub(wp[i], th[i]))
for i in range(self.k) ]
# print('# wPrimeApprox:', wp)
w1p = self.use_hint(h, wp)
# print('# w1Prime;', w1p)
ctp = self.h(mu + self.w1_encode(w1p), self.lam // 4)
# print('# cTildePrime:', ctp.hex())
z_norm = self.inf_norm(z)
# print('# ||z||:', z_norm)
return z_norm < self.gam1 - self.beta and ct == ctp
# Algorithm 9, IntegerToBits(x, alpha)
def integer_to_bits(self, x, alpha):
y = bytearray(alpha)
for i in range(alpha):
y[i] = x & 1
x >>= 1
return y
# Algorithm 10, BitsToInteger(y, alpha)
def bits_to_integer(self, y, alpha):
x = 0
for i in range(1, alpha + 1):
x = 2*x + y[alpha - i]
return x
# Algorithm 11, IntegerToBytes(x, alpha)
def integer_to_bytes(self, x, alpha):
y = bytearray(alpha)
for i in range(alpha):
y[i] = x & 0xff
x >>= 8
return y
# Algorithm 12, BitsToBytes(y)
def bits_to_bytes(self, y):
alpha = len(y)
z = bytearray(alpha // 8)
for i in range(0, alpha, 8):
x = 0
for j in range(8):
x += y[i + j] << j
z[i // 8] = x
return z
# Algorithm 13, BytesToBits(z)
def bytes_to_bits(self, z):
alpha = len(z)
y = bytearray(8*alpha)
for i in range(alpha):
x = z[i]
for j in range(8):
y[8*i + j] = (x >> j) & 1
return y
# Algorithm 14, CoeffFromThreeBytes(b0, b1, b2)
def coeff_from_three_bytes(self, b0, b1, b2):
if b2 > 127:
b2 -= 128
z = (b2 << 16) + (b1 << 8) + b0
if z < self.q:
return z
else:
return None
# Algorithm 15, CoeffFromHalfByte(b)
def coeff_from_half_byte(self, b):
if self.eta == 2 and b < 15:
return 2 - (b % 5)
elif self.eta == 4 and b < 9:
return 4 - b
else:
return None
# Algorithm 16, SimpleBitPack(w, b)
def simple_bit_pack(self, w, b):
z = bytearray(0)
bitlen_b = int(b).bit_length()
for i in range(256):
z += self.integer_to_bits(w[i], bitlen_b)
return self.bits_to_bytes(z)
# Algorithm 17, BitPack(w, a, b)
def bit_pack(self, w, a, b):
c = int(a + b).bit_length()
z = bytearray(0)
for wi in w:
z += self.integer_to_bits(b - wi, c)
return self.bits_to_bytes(z)
# Algorithm 18, SimpleBitUnpack(v, b)
def simple_bit_unpack(self, v, b):
c = int(b).bit_length()
z = self.bytes_to_bits(v)
w = [None]*256
for i in range(256):
w[i] = self.bits_to_integer(z[i*c : (i+1)*c ], c)
return w
# Algorithm 19, BitUnpack(v, a, b)
def bit_unpack(self, v, a, b):
c = int(a + b).bit_length()
z = self.bytes_to_bits(v)
w = []
for i in range(256):
w += [ b - self.bits_to_integer(z[i*c:(i+1)*c], c) ]
return w
# Algorithm 20, HintBitPack(h)
def hint_bit_pack(self, h):
idx = 0
y = bytearray(self.omega + self.k)
for i in range(self.k):
for j in range(256):
if h[i][j] != 0:
y[idx] = j
idx += 1
y[self.omega + i] = idx
return y
# Algorithm 21, HintBitPack(h)
def hint_bit_unpack(self, y):
idx = 0
h = [ [0]*256 for _ in range(self.k) ]
for i in range(self.k):
if y[self.omega + i] < idx or y[self.omega + i] > self.omega:
return None
first = idx
while idx < y[self.omega + i]:
if idx > first:
if y[idx - 1] >= y[idx]:
return None
h[i][y[idx]] = 1
idx += 1
for i in range(idx, self.omega):
if y[i] != 0:
return None
return h
# Algorithm 22, pkEncode(rho, t1)
def pk_encode(self, rho, t1):
pk = rho
b = 2**(int(self.q-1).bit_length() - self.d) - 1
for t1i in t1:
pk += self.simple_bit_pack(t1i, b)
return pk
# Algorithm 23, pkDecode(pk)
def pk_decode(self, pk):
rho = pk[0:32]
bitlen_b = int(self.q - 1).bit_length() - self.d
b = 2 ** bitlen_b - 1
t1 = []
for i in range(self.k):
zi = pk[32 + 32*bitlen_b*i: 32 + 32*bitlen_b*(i + 1)]
t1 += [ self.simple_bit_unpack(zi, b) ]
return (rho, t1)
# Algorithm 24, skEncode(rho, K, tr, s1, s2, t0)
def sk_encode(self, rho, kk, tr, s1, s2, t0):
sk = rho + kk + tr
for s1i in s1:
sk += self.bit_pack(s1i, self.eta, self.eta)
for s2i in s2:
sk += self.bit_pack(s2i, self.eta, self.eta)
for t0i in t0:
sk += self.bit_pack(t0i, 2**(self.d-1)-1, 2**(self.d-1))
return sk
# Algorithm 25, skDecode(sk)
def sk_decode(self, sk):
rho = sk[0:32]
kk = sk[32:64]
tr = sk[64:128]
pt = 128
le = 32*int(2*self.eta).bit_length()
s1 = []
for i in range(self.ell):
yi = sk[pt : pt + le]
pt += le
s1 += [ self.bit_unpack(yi, self.eta, self.eta) ]
s2 = []
for i in range(self.k):
zi = sk[pt : pt + le]
pt += le
s2 += [ self.bit_unpack(zi, self.eta, self.eta) ]
ld = 32*self.d
t0 = []
for i in range(self.k):
wi = sk[pt : pt + ld]
pt += ld
t0 += [ self.bit_unpack(wi, 2**(self.d-1) - 1, 2**(self.d-1)) ]
return (rho, kk, tr, s1, s2, t0)
# Algorithm 26, sigEncode(c~, z, h)
def sig_encode(self, ct, z, h):
sig = ct
for i in range(self.ell):
sig += self.bit_pack(z[i], self.gam1 - 1, self.gam1)
sig += self.hint_bit_pack(h)
return sig
# Algorithm 27, sigDecode(sig)
def sig_decode(self, sig):
bl = 32*(1 + int(self.gam1-1).bit_length())
cl = self.lam // 4
ct = sig[0 : cl]
z = []
for i in range(self.ell):
xi = sig[cl + bl*i : cl + bl*(i+1)]
z += [ self.bit_unpack(xi, self.gam1 - 1, self.gam1) ]
y = sig[cl + bl*self.ell : cl + bl*self.ell + self.omega + self.k]
h = self.hint_bit_unpack(y)
return (ct, z, h)
# Algorithm 28, w1Encode(w1)
def w1_encode(self, w1):
w1t = b''
b = (self.q - 1) // (2*self.gam2) - 1
for w1i in w1:
w1t += self.simple_bit_pack(w1i, b)
return w1t
# Algorithm 29, SampleInBall(rho)
def sample_in_ball(self, rho):
c = [0]*256
xof = SHAKE256.new(rho)
s = xof.read(8)
h = self.bytes_to_bits(s)
for i in range(256-self.tau, 256):
j = xof.read(1)[0]
while j > i:
j = xof.read(1)[0]
c[i] = c[j]
c[j] = (-1)**h[i + self.tau - 256]
return c
# Algorithm 30, RejNTTPoly(rho):
def rej_ntt_poly(self, rho):
j = 0
#print('self.rej_ntt_poly', len(rho), rho.hex())
g = SHAKE128.new(rho)
a = [None]*256
while j < 256:
s = g.read(3)
a[j] = self.coeff_from_three_bytes(s[0], s[1], s[2])
if a[j] != None:
j += 1
return a
# Algorithm 31, RejBoundedPoly(rho)
def rej_bounded_poly(self, rho):
j = 0
h = SHAKE256.new(rho)
a = [None]*256
while j < 256:
z = h.read(1)[0]
z0 = self.coeff_from_half_byte(z % 16)
z1 = self.coeff_from_half_byte(z // 16)
if z0 != None:
a[j] = z0
j += 1
if z1 != None and j < 256:
a[j] = z1
j += 1
return a
# Algorithm 32, ExpandA(rho)
def expand_a(self, rho):
a = [ [None]*self.ell for _ in range(self.k) ]
for r in range(self.k):
for s in range(self.ell):
rhop = rho + self.integer_to_bytes(s, 1) + self.integer_to_bytes(r, 1)
a[r][s] = self.rej_ntt_poly(rhop)
return a
# Algorithm 33, ExpandS(rho)
def expand_s(self, rho):
s1 = []
for r in range(self.ell):
s1 += [ self.rej_bounded_poly(rho +
self.integer_to_bytes(r, 2)) ]
s2 = []
for r in range(self.k):
s2 += [ self.rej_bounded_poly(rho +
self.integer_to_bytes(r + self.ell, 2)) ]
return (s1, s2)
# Algorithm 34, ExpandMask(rho, mu)
def expand_mask(self, rho, mu):
c = 1 + int(self.gam1 - 1).bit_length()
y = []
for r in range(self.ell):
rhop = rho + self.integer_to_bytes(mu + r, 2)
v = self.h(rhop, 32*c)
y += [ self.bit_unpack(v, self.gam1 - 1, self.gam1) ]
return y
"""2.3 Mathematical Symbols:
If alpha is a positive integer and m in Z or m in Z_alpha, then
m mod^{+-} alpha denotes the unique element m' in Z in the
range -ceil(alpha/2) < m' <= floor(alpha/2) such that m and m' are
congruent modulo alpha.
NOTE: This is *not* two's complement sign extension as it includes
+alpha/2 and excludes -alpha/2. Hence the negations here.
"""
def modpm(self, m, alpha):
return -((alpha // 2 - m) % alpha) + (alpha // 2)
def inf_norm(self, x):
if type(x) == list:
y = 0
for xi in x:
y = max(y, self.inf_norm(xi))
return y
else:
return abs(self.modpm(x, self.q))
# Algorithm 35, Power2Round(r)
# "PowerTwoRound is applied componentwise."
def power2round(self, r):
r0vv = []
r1vv = []
for rr in r:
r0v = []
r1v = []
for rx in rr:
rp = rx % self.q
r0 = self.modpm(rp, 1 << self.d)
r1 = (rp - r0) >> self.d
r0v += [ r0 ]
r1v += [ r1 ]
r0vv += [ r0v ]
r1vv += [ r1v ]
return r1vv, r0vv
# Algorithm 36, Decompose(r)
def decompose(self, r):
rp = r % self.q
r0 = self.modpm(rp, 2*self.gam2)
if rp - r0 == self.q - 1:
r1 = 0
r0 -= 1
else:
r1 = (rp - r0) // (2*self.gam2)
return (r1, r0)
# Algorithm 37, HighBits(r)
def high_bits(self, r):
r1vv = []
for rr in r:
r1v = []
for rx in rr:
(r1, r0) = self.decompose(rx)
r1v += [ r1 ]
r1vv += [ r1v ]
return r1vv
# Algorithm 38, LowBits(r)
def low_bits(self, r):
r0vv = []
for rr in r:
r0v = []
for rx in rr:
(r1, r0) = self.decompose(rx)
r0v += [ r0 ]
r0vv += [ r0v ]
return r0vv
# Algorithm 39, MakeHint(z, r)
def make_hint(self, z, r):
r1 = self.high_bits(r)
v1 = self.high_bits(self.add(r, z))
return self.neq(r1, v1)
# Algorithm 40, UseHint(h, r)
def use_hint(self, h, r):
if type(h[0]) == list:
return [ self.use_hint(h[i], r[i]) for i in range(len(h)) ]
m = (self.q - 1) // (2*self.gam2)
r1v = []
for i in range(256):
(r1, r0) = self.decompose(r[i])
if h[i] == 1 and r0 > 0:
r1 = (r1 + 1) % m
if h[i] == 1 and r0 <= 0:
r1 = (r1 - 1) % m
r1v += [ r1 ]
return r1v
# Algorithm 41, NTT(w)
def ntt(self, w):
w = w.copy()
m = 0
le = 128
while le >= 1:
st = 0
while st < 256:
m += 1
z = ML_DSA_ZETAS[m]
for j in range(st, st + le):
t = (z*w[j + le]) % self.q
w[j + le] = (w[j] - t) % self.q
w[j] = (w[j] + t) % self.q
st = st + 2*le
le = le // 2
return w
# Algorithm 42, NTT^-1(w)
def ntt_inverse(self, w):
w = w.copy()
m = 256
le = 1
while le < 256:
st = 0
while st < 256:
m -= 1
z = -ML_DSA_ZETAS[m]
for j in range(st, st + le):
t = w[j]
w[j] = (t + w[j + le]) % self.q
w[j + le] = (t - w[j + le]) % self.q
w[j + le] = (z*w[j + le]) % self.q
st = st + 2*le
le = 2*le
f = 8347681
w = [ (f*w[j]) % self.q for j in range(256) ]
return w
# Algorithm 43, BitRev8(m)
def bitrev8(self, m):
b = self.integer_to_bits(m, 8)
brev = [ b[7 - i] for i in range(8) ]
r = self.bits_to_integer(brev, 8)
return r
# Algorithm 44, AddNTT(a, b)
def add(self, a, b):
if type(a) == list:
return [ self.add(a[i], b[i]) for i in range(len(a)) ]
else:
return (a + b) % self.q
# negation
def neg(self, a):
if type(a) == list:
return [ self.neg(a[i]) for i in range(len(a)) ]
else:
return (-a) % self.q
# subtraction
def sub(self, a, b):
if type(a) == list:
return [ self.sub(a[i], b[i]) for i in range(len(a)) ]
else:
return (a - b) % self.q
# not equivalent
def neq(self, a, b):
if type(a) == list:
return [ self.neq(a[i], b[i]) for i in range(len(a)) ]
elif a == b:
return 0
else:
return 1
# weigth (number of nonzero entries)
def weight(self, a):
if type(a) == list:
w = 0
for ai in a:
w += self.weight(ai)
return w
elif a == 0:
return 0
else:
return 1
# Algorithm 45, MulNTT(a, b)
def mul_ntt(self, a, b):
return [ (a[i]*b[i]) % self.q for i in range(256) ]
# Algorithm 48, MatrixVectorNTT(M^, v^)
def matrix_vector_ntt(self, m, v):
w = [ [0]*256 for _ in range(self.k) ]
for i in range(self.k):
for j in range(self.ell):
w[i] = self.add(w[i], self.mul_ntt(m[i][j], v[j]))
return w
# run the test on these functions
if __name__ == '__main__':
ml_dsa = ML_DSA()
test_mldsa( ml_dsa, '(fips204.py)')