diff --git a/gcrypto/gbls/gblsminsig/signatureproof.go b/gcrypto/gbls/gblsminsig/signatureproof.go
new file mode 100644
index 0000000..05ee732
--- /dev/null
+++ b/gcrypto/gbls/gblsminsig/signatureproof.go
@@ -0,0 +1,388 @@
+package gblsminsig
+
+import (
+	"bytes"
+	"errors"
+	"fmt"
+	"maps"
+	"slices"
+
+	"github.com/bits-and-blooms/bitset"
+	"github.com/gordian-engine/gordian/gcrypto"
+	"github.com/gordian-engine/gordian/gmerkle"
+	blst "github.com/supranational/blst/bindings/go"
+)
+
+type SignatureProof struct {
+	msg []byte
+
+	keys    []PubKey
+	keyTree *gmerkle.Tree[PubKey]
+
+	// string(pubkey bytes) -> index in keys
+	keyIdxs map[string]int
+
+	keyHash string
+
+	// string(possibly aggregated pubkey bytes) -> validated signature for possibly aggregated key
+	sigs map[string][]byte
+
+	// Bits indicating what keys in the keys slice
+	// have representation in the sigs map.
+	// Note that the sigs map is not necessarily fully aggregated yet;
+	// if bits 0 and 1 are set, we may have either separate individual signatures
+	// for keys 0 and 1, or we might have the aggregation of 0 and 1.
+	sigBitset *bitset.BitSet
+}
+
+func NewSignatureProof(msg []byte, trustedKeys []PubKey, pubKeyHash string) (SignatureProof, error) {
+	keyTree, err := gmerkle.NewTree(keyAggScheme{}, trustedKeys)
+	if err != nil {
+		return SignatureProof{}, err
+	}
+
+	keyIdxs := make(map[string]int, len(trustedKeys))
+	for i, k := range trustedKeys {
+		keyIdxs[string(k.PubKeyBytes())] = i
+	}
+
+	return SignatureProof{
+		msg: msg,
+
+		keys:    trustedKeys,
+		keyTree: keyTree,
+
+		keyIdxs: keyIdxs,
+
+		keyHash: pubKeyHash,
+
+		sigs: make(map[string][]byte),
+
+		sigBitset: bitset.New(uint(len(trustedKeys))),
+	}, nil
+}
+
+func (p SignatureProof) Message() []byte {
+	return p.msg
+}
+
+func (p SignatureProof) PubKeyHash() []byte {
+	return []byte(p.keyHash)
+}
+
+// AddSignature adds a signature representing a single key.
+//
+// This should only be called when receiving the local application's signature for a message.
+// Otherwise, use the Merge method to combine incoming proofs with the existing one.
+//
+// If the signature does not match, or if the public key was not one of the candidate keys,
+// an error is returned.
+func (p SignatureProof) AddSignature(sig []byte, key gcrypto.PubKey) error {
+	pubKeyBytes := string(key.PubKeyBytes())
+	i, ok := p.keyIdxs[pubKeyBytes]
+	if !ok {
+		return fmt.Errorf("unknown key %x", pubKeyBytes)
+	}
+
+	pk := p.keys[i]
+	if !pk.Verify(p.msg, sig) {
+		return errors.New("signature validation failed")
+	}
+
+	p.sigs[pubKeyBytes] = sig
+	p.sigBitset.Set(uint(i))
+
+	return nil
+}
+
+func (p SignatureProof) Matches(other gcrypto.CommonMessageSignatureProof) bool {
+	o := other.(SignatureProof)
+
+	if !bytes.Equal(p.msg, o.msg) {
+		return false
+	}
+
+	// Both the tree and the actual keys should be consistent given a key hash,
+	// so only checking the key hash should suffice.
+	if p.keyHash != o.keyHash {
+		return false
+	}
+
+	return true
+}
+
+func (p SignatureProof) Merge(other gcrypto.CommonMessageSignatureProof) gcrypto.SignatureProofMergeResult {
+	o := other.(SignatureProof)
+
+	if !p.Matches(o) {
+		return gcrypto.SignatureProofMergeResult{
+			// Zero value has all false fields.
+		}
+	}
+
+	res := gcrypto.SignatureProofMergeResult{
+		// Assume at the beginning that all of other's signatures are valid.
+		AllValidSignatures: true,
+	}
+
+	// Check if o looks like a strict superset before we modify p.bitset.
+	// If both are empty, call this a strict superset.
+	// Maybe this is the wrong definition and there is a more appropriate word?
+	looksLikeStrictSuperset := (o.sigBitset.None() && p.sigBitset.None()) || o.sigBitset.IsStrictSuperSet(p.sigBitset)
+
+	// We are going to evaluate every incoming signature from other.
+	// Our keyTree has already calculated every valid key combination
+	// (which is a subset of every *possible* combination).
+	for otherKey, otherSig := range o.sigs {
+		curSig, ok := p.sigs[otherKey]
+		if !ok {
+			// We don't have this signature.
+			// We are going to evaluate it anyway,
+			// even if we have the parent.
+
+			// Rebuild the key from the compressed bytes.
+			p2a := new(blst.P2Affine)
+			p2a = p2a.Uncompress([]byte(otherKey))
+			pk := PubKey(*p2a)
+
+			// Confirm the we know of the reconstituted key.
+			if idx, _ := p.keyTree.Lookup(pk); idx < 0 {
+				res.AllValidSignatures = false
+				continue
+			}
+
+			// We know the key; confirm the signature is valid.
+			if !pk.Verify(p.msg, []byte(otherSig)) {
+				res.AllValidSignatures = false
+				continue
+			}
+
+			// The signature was valid and we didn't have it, so now add it.
+			p.sigs[otherKey] = otherSig
+			continue
+		}
+
+		// We did have a signature for the key.
+		// Confirm their signature is the same.
+		if !bytes.Equal(curSig, otherSig) {
+			res.AllValidSignatures = false
+		}
+	}
+
+	res.WasStrictSuperset = looksLikeStrictSuperset && res.AllValidSignatures
+	return res
+}
+
+func (p SignatureProof) MergeSparse(s gcrypto.SparseSignatureProof) gcrypto.SignatureProofMergeResult {
+	if s.PubKeyHash != p.keyHash {
+		// Unmergeable.
+		return gcrypto.SignatureProofMergeResult{}
+	}
+
+	res := gcrypto.SignatureProofMergeResult{
+		// Assume all signatures are valid until we encounter an invalid one.
+		AllValidSignatures: true,
+
+		// Whether the signatures were increased, or whether we added a strict superset,
+		// is determined after iterating over the sparse value.
+	}
+
+	addedBS := bitset.New(uint(len(p.keys)))
+	bsBefore := p.sigBitset.Clone()
+
+	for _, ss := range s.Signatures {
+		var incomingSigBitset bitset.BitSet
+		if err := sparseIDToBitset(ss.KeyID, &incomingSigBitset); err != nil {
+			res.AllValidSignatures = false
+			continue
+		}
+
+		if incomingSigBitset.Count() == 0 {
+			// Malicious incoming value?
+			res.AllValidSignatures = false
+			continue
+		}
+
+		if incomingSigBitset.Count() != 1 {
+			// We can't do this yet, because we don't yet have a clean way
+			// to map a bitset into the keyTree.
+			panic(errors.New("TODO: handle merging aggregated keys"))
+		}
+
+		// But the count=1 case is special because we know that is a leaf, unaggregated key.
+		setIdxU, _ := incomingSigBitset.NextSet(0)
+		setIdx := int(setIdxU)
+		if setIdx >= len(p.keys) || setIdx < 0 {
+			res.AllValidSignatures = false
+			continue
+		}
+
+		pk := p.keys[int(setIdxU)]
+		// Do we already have the signature for this key?
+		if haveSig, ok := p.sigs[string(pk.PubKeyBytes())]; ok {
+			// We already have the signature.
+			// Did they send the same bytes we verified earlier?
+			if !bytes.Equal(haveSig, ss.Sig) {
+				res.AllValidSignatures = false
+				continue
+			}
+
+			// They sent a matching signature,
+			// so mark that signature as added.
+			addedBS.Set(setIdxU)
+			continue
+		}
+
+		// We didn't have the signature.
+		// Try adding it directly, which is valid for an unaggregated key.
+		if err := p.AddSignature(ss.Sig, pk); err != nil {
+			res.AllValidSignatures = false
+			continue
+		}
+
+		// It added successfully, mark it so.
+		addedBS.Set(setIdxU)
+	}
+
+	res.IncreasedSignatures = p.sigBitset.Count() > bsBefore.Count()
+	res.WasStrictSuperset = addedBS.IsStrictSuperSet(bsBefore)
+
+	return res
+}
+
+// HasSparseKeyID reports whether the full proof already contains a signature
+// matching the given sparse key ID.
+// If the key ID does not properly map into the set of trusted public keys,
+// the "valid" return parameter will be false.
+func (p SignatureProof) HasSparseKeyID(keyID []byte) (has, valid bool) {
+	var check bitset.BitSet
+	if err := sparseIDToBitset(keyID, &check); err != nil {
+		return false, false
+	}
+
+	// TODO: bounds check on the incoming ID,
+	// to possibly return early with valid=false.
+
+	return p.sigBitset.IsSuperSet(&check), true
+}
+
+func (p SignatureProof) AsSparse() gcrypto.SparseSignatureProof {
+	outPubKeys := p.keyTree.BitSetToIDs(p.sigBitset)
+
+	sparseSigs := make([]gcrypto.SparseSignature, len(outPubKeys))
+
+	for i, pubKey := range outPubKeys {
+		sig := p.sigs[string(pubKey.PubKeyBytes())]
+		// TODO: handle failed lookup by aggregating appropriately,
+		// e.g. if we have 0 and 1 and this is looking for 01.
+
+		sparseSigs[i] = gcrypto.SparseSignature{
+			KeyID: bitsetToSparseID(p.sigBitset),
+			Sig:   sig,
+		}
+	}
+
+	return gcrypto.SparseSignatureProof{
+		PubKeyHash: p.keyHash,
+		Signatures: sparseSigs,
+	}
+}
+
+func (p SignatureProof) Clone() gcrypto.CommonMessageSignatureProof {
+	sigs := make(map[string][]byte, len(p.sigs))
+	for k, v := range p.sigs {
+		sigs[k] = bytes.Clone(v)
+	}
+	return SignatureProof{
+		msg:     bytes.Clone(p.msg),
+		keys:    slices.Clone(p.keys),
+		keyTree: p.keyTree, // TODO: this needs to be cloned
+
+		keyIdxs: maps.Clone(p.keyIdxs),
+
+		keyHash: p.keyHash,
+
+		sigs: sigs,
+
+		sigBitset: p.sigBitset.Clone(),
+	}
+}
+
+func (p SignatureProof) Derive() gcrypto.CommonMessageSignatureProof {
+	return SignatureProof{
+		msg:  bytes.Clone(p.msg),
+		keys: slices.Clone(p.keys),
+
+		keyTree: p.keyTree, // TODO: this needs to be cloned
+
+		keyIdxs: maps.Clone(p.keyIdxs),
+
+		keyHash: p.keyHash,
+
+		sigs: make(map[string][]byte),
+
+		sigBitset: bitset.New(uint(len(p.keys))),
+	}
+}
+
+func (p SignatureProof) SignatureBitSet() *bitset.BitSet {
+	return p.sigBitset
+}
+
+type keyAggScheme struct{}
+
+func (s keyAggScheme) BranchFactor() uint8 {
+	return 2
+}
+
+// BranchID aggregates the children.
+func (s keyAggScheme) BranchID(depth, rowIdx int, childIDs []PubKey) (PubKey, error) {
+	keyAgg := new(blst.P2Aggregate)
+
+	compressed := make([][]byte, len(childIDs))
+	for i, c := range childIDs {
+		compressed[i] = c.PubKeyBytes()
+	}
+
+	if !keyAgg.AggregateCompressed(compressed, true) {
+		return PubKey{}, errors.New("failed to aggregate keys")
+	}
+
+	aff := keyAgg.ToAffine()
+	return PubKey(*aff), nil
+}
+
+// LeafID returns the unmodified leafData.
+func (s keyAggScheme) LeafID(idx int, leafData PubKey) (PubKey, error) {
+	return leafData, nil
+}
+
+// bitsetToSparseID returns a byte slice the bits
+// representing a possibly aggregated key.
+//
+// This is an unoptimized implementation;
+// we can instead encode two values:
+// the first set bit and the run of set bits.
+// If we used uint8, we would be limited to 256 validators,
+// so encoding this as a pair of uint16 values,
+// which will be 32 bits, which is 8 bytes.
+// This uses less space than an encoded bitset with more than 32 validators.
+//
+// Also, this should encode to an existing slice to avoid
+// allocating a new slice every time.
+func bitsetToSparseID(bs *bitset.BitSet) []byte {
+	b, err := bs.MarshalBinary()
+	if err != nil {
+		panic(fmt.Errorf("failed to encode bitset: %w", err))
+	}
+
+	return b
+}
+
+func sparseIDToBitset(id []byte, dst *bitset.BitSet) error {
+	if err := dst.UnmarshalBinary(id); err != nil {
+		return fmt.Errorf("failed to parse sparse ID: %w", err)
+	}
+
+	return nil
+}
diff --git a/gcrypto/gbls/gblsminsig/signatureproof_test.go b/gcrypto/gbls/gblsminsig/signatureproof_test.go
new file mode 100644
index 0000000..bf685ad
--- /dev/null
+++ b/gcrypto/gbls/gblsminsig/signatureproof_test.go
@@ -0,0 +1,151 @@
+package gblsminsig_test
+
+import (
+	"context"
+	"testing"
+
+	"github.com/gordian-engine/gordian/gcrypto/gbls/gblsminsig"
+	"github.com/stretchr/testify/require"
+)
+
+var (
+	testSigners [16]gblsminsig.Signer
+	testPubKeys [16]gblsminsig.PubKey
+)
+
+func init() {
+	for i := range testSigners {
+		ikm := [32]byte{}
+		for j := range ikm {
+			ikm[j] = byte(i)
+		}
+
+		s, err := gblsminsig.NewSigner(ikm[:])
+		if err != nil {
+			panic(err)
+		}
+
+		testSigners[i] = s
+
+		testPubKeys[i] = s.PubKey().(gblsminsig.PubKey)
+	}
+}
+
+func TestSignatureProof_AddSignature(t *testing.T) {
+	t.Parallel()
+
+	msg := []byte("hello")
+
+	proof, err := gblsminsig.NewSignatureProof(msg, testPubKeys[:], "ignored")
+	require.NoError(t, err)
+
+	ctx := context.Background()
+
+	sig0, err := testSigners[0].Sign(ctx, msg)
+	require.NoError(t, err)
+
+	require.NoError(t, proof.AddSignature(sig0, testPubKeys[0]))
+}
+
+func TestSignatureProof_AsSparse(t *testing.T) {
+	t.Parallel()
+
+	msg := []byte("hello")
+
+	const hash = "fake_hash"
+	proof, err := gblsminsig.NewSignatureProof(msg, testPubKeys[:], hash)
+	require.NoError(t, err)
+
+	ctx := context.Background()
+
+	sig0, err := testSigners[0].Sign(ctx, msg)
+	require.NoError(t, err)
+
+	require.NoError(t, proof.AddSignature(sig0, testPubKeys[0]))
+
+	sp := proof.AsSparse()
+	require.Equal(t, hash, sp.PubKeyHash)
+	require.Len(t, sp.Signatures, 1)
+	require.Equal(t, sig0, sp.Signatures[0].Sig)
+
+	// Not asserting anything about the sparse signature ID
+	// until we use the optimized encoding.
+	// See the unexported bitsetToSparseID function.
+}
+
+func TestSignatureProof_MergeSparse_disjoint(t *testing.T) {
+	t.Parallel()
+
+	msg := []byte("hello")
+
+	const hash = "fake_hash"
+	proof0, err := gblsminsig.NewSignatureProof(msg, testPubKeys[:], hash)
+	require.NoError(t, err)
+
+	ctx := context.Background()
+
+	sig0, err := testSigners[0].Sign(ctx, msg)
+	require.NoError(t, err)
+
+	require.NoError(t, proof0.AddSignature(sig0, testPubKeys[0]))
+
+	proof2, err := gblsminsig.NewSignatureProof(msg, testPubKeys[:], hash)
+	require.NoError(t, err)
+
+	sig2, err := testSigners[2].Sign(ctx, msg)
+	require.NoError(t, err)
+
+	require.NoError(t, proof2.AddSignature(sig2, testPubKeys[2]))
+
+	res := proof0.MergeSparse(proof2.AsSparse())
+	require.True(t, res.AllValidSignatures)
+	require.True(t, res.IncreasedSignatures)
+	require.False(t, res.WasStrictSuperset)
+
+	bs0 := proof0.SignatureBitSet()
+	require.Equal(t, uint(2), bs0.Count())
+	require.True(t, bs0.Test(0))
+	require.True(t, bs0.Test(2))
+}
+
+// TODO: test for Merged sparse signature, once mergeable.
+
+func TestSignatureProof_HasSparseKeyID(t *testing.T) {
+	t.Parallel()
+
+	msg := []byte("hello")
+
+	const hash = "fake_hash"
+	proof0, err := gblsminsig.NewSignatureProof(msg, testPubKeys[:], hash)
+	require.NoError(t, err)
+
+	ctx := context.Background()
+
+	sig0, err := testSigners[0].Sign(ctx, msg)
+	require.NoError(t, err)
+
+	require.NoError(t, proof0.AddSignature(sig0, testPubKeys[0]))
+
+	sp0 := proof0.AsSparse()
+	has, valid := proof0.HasSparseKeyID(sp0.Signatures[0].KeyID)
+	require.True(t, valid)
+	require.True(t, has)
+
+	proof1, err := gblsminsig.NewSignatureProof(msg, testPubKeys[:], hash)
+	require.NoError(t, err)
+
+	// New proof doesn't have the other signature yet, of course.
+	has, valid = proof1.HasSparseKeyID(sp0.Signatures[0].KeyID)
+	require.True(t, valid)
+	require.False(t, has)
+
+	sig1, err := testSigners[1].Sign(ctx, msg)
+	require.NoError(t, err)
+
+	require.NoError(t, proof1.AddSignature(sig1, testPubKeys[1]))
+
+	sp1 := proof1.AsSparse()
+	has, valid = proof1.HasSparseKeyID(sp1.Signatures[0].KeyID)
+	require.True(t, valid)
+	require.True(t, has)
+}