def test_vectors():
sk1 = PrivateKey.from_seed(bytes([1, 2, 3, 4, 5]))
pk1 = sk1.get_public_key()
sig1 = sk1.sign(bytes([7, 8, 9]))
sk2 = PrivateKey.from_seed(bytes([1, 2, 3, 4, 5, 6]))
pk2 = sk2.get_public_key()
sig2 = sk2.sign(bytes([7, 8, 9]))
assert (sk1.serialize() == bytes.fromhex(
"022fb42c08c12de3a6af053880199806532e79515f94e83461612101f9412f9e"))
assert (pk1.get_fingerprint() == 0x26d53247)
assert (pk2.get_fingerprint() == 0x289bb56e)
assert (sig1.serialize() == bytes.fromhex(
"93eb2e1cb5efcfb31f2c08b235e8203a67265bc6a13d9f0ab77727293b74a357ff0459ac210dc851fcb8a60cb7d393a419915cfcf83908ddbeac32039aaa3e8fea82efcb3ba4f740f20c76df5e97109b57370ae32d9b70d256a98942e5806065"
))
assert (sig2.serialize() == bytes.fromhex(
"975b5daa64b915be19b5ac6d47bc1c2fc832d2fb8ca3e95c4805d8216f95cf2bdbb36cc23645f52040e381550727db420b523b57d494959e0e8c0c6060c46cf173872897f14d43b2ac2aec52fc7b46c02c5699ff7a10beba24d3ced4e89c821e"
))
agg_sig = Signature.aggregate([sig1, sig2])
agg_pk = PublicKey.aggregate([pk1, pk2], True)
agg_sk = PrivateKey.aggregate([sk1, sk2], [pk1, pk2], True)
assert (agg_sig.serialize() == bytes.fromhex(
"0a638495c1403b25be391ed44c0ab013390026b5892c796a85ede46310ff7d0e0671f86ebe0e8f56bee80f28eb6d999c0a418c5fc52debac8fc338784cd32b76338d629dc2b4045a5833a357809795ef55ee3e9bee532edfc1d9c443bf5bc658"
))
assert (agg_sk.sign(bytes([7, 8, 9])).serialize() == agg_sig.serialize())
assert (sig1.verify())
assert (agg_sig.verify())
agg_sig.set_aggregation_info(
AggregationInfo.from_msg(agg_pk, bytes([7, 8, 9])))
assert (agg_sig.verify())
sig1.set_aggregation_info(sig2.aggregation_info)
assert (not sig1.verify())
sig3 = sk1.sign(bytes([1, 2, 3]))
sig4 = sk1.sign(bytes([1, 2, 3, 4]))
sig5 = sk2.sign(bytes([1, 2]))
agg_sig2 = Signature.aggregate([sig3, sig4, sig5])
assert (agg_sig2.verify())
assert (agg_sig2.serialize() == bytes.fromhex(
"8b11daf73cd05f2fe27809b74a7b4c65b1bb79cc1066bdf839d96b97e073c1a635d2ec048e0801b4a208118fdbbb63a516bab8755cc8d850862eeaa099540cd83621ff9db97b4ada857ef54c50715486217bd2ecb4517e05ab49380c041e159b"
))
def test2():
seed = bytes([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
seed2 = bytes([1, 20, 102, 229, 1, 157])
sk = PrivateKey.from_seed(seed)
sk_cp = PrivateKey.from_seed(seed)
sk2 = PrivateKey.from_seed(seed2)
pk = sk.get_public_key()
pk2 = sk2.get_public_key()
assert (sk == sk_cp)
assert (sk != sk2)
assert (pk.get_fingerprint() == 0xddad59bb)
sk2_ser = sk2.serialize()
pk2_ser = pk2.serialize()
pk2_copy = PublicKey.from_bytes(pk2_ser)
assert (pk2 == pk2_copy)
assert (pk != pk2)
assert (len(pk2_ser) == 48)
assert (len(sk2_ser) == 32)
message = bytes("this is the message", "utf-8")
sig = sk.sign(message)
sig_ser = sig.serialize()
sig_cp = Signature.from_bytes(sig_ser)
a1 = AggregationInfo.from_msg(pk, message)
sig_cp.set_aggregation_info(a1)
a2 = sig_cp.get_aggregation_info()
assert (a1 == a2)
sig2 = sk2.sign(message)
assert (len(sig_ser) == 96)
assert (sig != sig2)
assert (sig == sig_cp)
sig_agg = Signature.aggregate([sig, sig2])
result = sig_cp.verify()
result2 = sig2.verify()
result3 = sig_agg.verify()
assert (result)
assert (result2)
assert (result3)
sk2 = sk
def sign_prehashed(self, h):
r = hash_to_point_prehashed_Fq2(h).to_jacobian()
aggregation_info = AggregationInfo.from_msg_hash(
self.get_public_key(), h)
return Signature.from_g2(self.value * r, aggregation_info)
def sign(self, m):
r = hash_to_point_Fq2(m).to_jacobian()
aggregation_info = AggregationInfo.from_msg(self.get_public_key(), m)
return Signature.from_g2(self.value * r, aggregation_info)
def test_threshold_instance(T, N):
commitments = []
# fragments[i][j] = fragment held by player i,
# received from player j
fragments = [[None] * N for _ in range(N)]
secrets = []
# Step 1 : PrivateKey.new_threshold
for player in range(N):
secret_key, commi, frags = PrivateKey.new_threshold(T, N)
for target, frag in enumerate(frags):
fragments[target][player] = frag
commitments.append(commi)
secrets.append(secret_key)
# Step 2 : Threshold.verify_secret_fragment
for player_source in range(1, N + 1):
for player_target in range(1, N + 1):
assert Threshold.verify_secret_fragment(
T, fragments[player_target - 1][player_source - 1],
player_target, commitments[player_source - 1])
# Step 3 : master_pubkey = PublicKey.aggregate(...)
# secret_share = PrivateKey.aggregate(...)
master_pubkey = PublicKey.aggregate(
[PublicKey.from_g1(cpoly[0].to_jacobian()) for cpoly in commitments],
False)
secret_shares = [
PrivateKey.aggregate(map(PrivateKey, row), None, False)
for row in fragments
]
master_privkey = PrivateKey.aggregate(secrets, None, False)
msg = 'Test'
signature_actual = master_privkey.sign(msg)
# Step 4 : sig_share = secret_share.sign_threshold(...)
# Check every combination of T players
for X in combinations(range(1, N + 1), T):
# X: a list of T indices like [1, 2, 5]
# Check underlying secret key is correct
r = Threshold.interpolate_at_zero(
X, [secret_shares[x - 1].value for x in X])
secret_cand = PrivateKey(r)
assert secret_cand == master_privkey
# Check signatures
signature_shares = [
secret_shares[x - 1].sign_threshold(msg, x, X) for x in X
]
signature_cand = Signature.aggregate_sigs_simple(signature_shares)
assert signature_cand == signature_actual
# Check that the signature actually verifies the message
agg_info = AggregationInfo.from_msg(master_pubkey, msg)
signature_actual.set_aggregation_info(agg_info)
assert signature_actual.verify()
# Step 4b : Alternatively, we can add the lagrange coefficients
# to 'unit' signatures.
for X in combinations(range(1, N + 1), T):
# X: a list of T indices like [1, 2, 5]
# Check signatures
signature_shares = [secret_shares[x - 1].sign(msg) for x in X]
signature_cand = Threshold.aggregate_unit_sigs(signature_shares, X, T)
assert signature_cand == signature_actual
def test1():
seed = bytes([
0, 50, 6, 244, 24, 199, 1, 25, 52, 88, 192, 19, 18, 12, 89, 6, 220, 18,
102, 58, 209, 82, 12, 62, 89, 110, 182, 9, 44, 20, 254, 22
])
sk = PrivateKey.from_seed(seed)
pk = sk.get_public_key()
msg = bytes([100, 2, 254, 88, 90, 45, 23])
sig = sk.sign(msg)
sk_bytes = sk.serialize()
pk_bytes = pk.serialize()
sig_bytes = sig.serialize()
sk = PrivateKey.from_bytes(sk_bytes)
pk = PublicKey.from_bytes(pk_bytes)
sig = Signature.from_bytes(sig_bytes)
sig.set_aggregation_info(AggregationInfo.from_msg(pk, msg))
ok = sig.verify()
assert (ok)
seed = bytes([1]) + seed[1:]
sk1 = PrivateKey.from_seed(seed)
seed = bytes([2]) + seed[1:]
sk2 = PrivateKey.from_seed(seed)
pk1 = sk1.get_public_key()
sig1 = sk1.sign(msg)
pk2 = sk2.get_public_key()
sig2 = sk2.sign(msg)
agg_sig = Signature.aggregate([sig1, sig2])
agg_pubkey = PublicKey.aggregate([pk1, pk2])
agg_sig.set_aggregation_info(AggregationInfo.from_msg(agg_pubkey, msg))
assert (agg_sig.verify())
seed = bytes([3]) + seed[1:]
sk3 = PrivateKey.from_seed(seed)
pk3 = sk3.get_public_key()
msg2 = bytes([100, 2, 254, 88, 90, 45, 23])
sig1 = sk1.sign(msg)
sig2 = sk2.sign(msg)
sig3 = sk3.sign(msg2)
agg_sig_l = Signature.aggregate([sig1, sig2])
agg_sig_final = Signature.aggregate([agg_sig_l, sig3])
sig_bytes = agg_sig_final.serialize()
agg_sig_final = Signature.from_bytes(sig_bytes)
a1 = AggregationInfo.from_msg(pk1, msg)
a2 = AggregationInfo.from_msg(pk2, msg)
a3 = AggregationInfo.from_msg(pk3, msg2)
a1a2 = AggregationInfo.merge_infos([a1, a2])
a_final = AggregationInfo.merge_infos([a1a2, a3])
print(a_final)
agg_sig_final.set_aggregation_info(a_final)
ok = agg_sig_final.verify()
ok = agg_sig_l.verify()
agg_sig_final = agg_sig_final.divide_by([agg_sig_l])
ok = agg_sig_final.verify()
agg_sk = PrivateKey.aggregate([sk1, sk2], [pk1, pk2])
agg_sk.sign(msg)
seed = bytes([
1, 50, 6, 244, 24, 199, 1, 25, 52, 88, 192, 19, 18, 12, 89, 6, 220, 18,
102, 58, 209, 82, 12, 62, 89, 110, 182, 9, 44, 20, 254, 22
])
esk = ExtendedPrivateKey.from_seed(seed)
epk = esk.get_extended_public_key()
sk_child = esk.private_child(0).private_child(5)
pk_child = epk.public_child(0).public_child(5)
buffer1 = pk_child.serialize()
buffer2 = sk_child.serialize()
print(len(buffer1), buffer1)
print(len(buffer2), buffer2)
assert (sk_child.get_extended_public_key() == pk_child)
def aggregate(signatures):
"""
Aggregates many (aggregate) signatures, using a combination of simple
and secure aggregation. Signatures are grouped based on which ones
share common messages, and these are all merged securely.
"""
public_keys = [] # List of lists
message_hashes = [] # List of lists
for signature in signatures:
if signature.aggregation_info.empty():
raise Exception(
"Each signature must have a valid aggregation " + "info")
public_keys.append(signature.aggregation_info.public_keys)
message_hashes.append(signature.aggregation_info.message_hashes)
# Find colliding vectors, save colliding messages
messages_set = set()
colliding_messages_set = set()
for msg_vector in message_hashes:
messages_set_local = set()
for msg in msg_vector:
if msg in messages_set and msg not in messages_set_local:
colliding_messages_set.add(msg)
messages_set.add(msg)
messages_set_local.add(msg)
if len(colliding_messages_set) == 0:
# There are no colliding messages between the groups, so we
# will just aggregate them all simply. Note that we assume
# that every group is a valid aggregate signature. If an invalid
# or insecure signature is given, and invalid signature will
# be created. We don't verify for performance reasons.
final_sig = Signature.aggregate_sigs_simple(signatures)
aggregation_infos = [sig.aggregation_info for sig in signatures]
final_agg_info = AggregationInfo.merge_infos(aggregation_infos)
final_sig.set_aggregation_info(final_agg_info)
return final_sig
# There are groups that share messages, therefore we need
# to use a secure form of aggregation. First we find which
# groups collide, and securely aggregate these. Then, we
# use simple aggregation at the end.
colliding_sigs = []
non_colliding_sigs = []
colliding_message_hashes = [] # List of lists
colliding_public_keys = [] # List of lists
for i in range(len(signatures)):
group_collides = False
for msg in message_hashes[i]:
if msg in colliding_messages_set:
group_collides = True
colliding_sigs.append(signatures[i])
colliding_message_hashes.append(message_hashes[i])
colliding_public_keys.append(public_keys[i])
break
if not group_collides:
non_colliding_sigs.append(signatures[i])
# Arrange all signatures, sorted by their aggregation info
colliding_sigs.sort(key=lambda s: s.aggregation_info)
# Arrange all public keys in sorted order, by (m, pk)
sort_keys_sorted = []
for i in range(len(colliding_public_keys)):
for j in range(len(colliding_public_keys[i])):
sort_keys_sorted.append((colliding_message_hashes[i][j],
colliding_public_keys[i][j]))
sort_keys_sorted.sort()
sorted_public_keys = [pk for (mh, pk) in sort_keys_sorted]
computed_Ts = BLS.hash_pks(len(colliding_sigs), sorted_public_keys)
# Raise each sig to a power of each t,
# and multiply all together into agg_sig
ec = sorted_public_keys[0].value.ec
agg_sig = JacobianPoint(Fq2.one(ec.q), Fq2.one(ec.q), Fq2.zero(ec.q),
True, ec)
for i, signature in enumerate(colliding_sigs):
agg_sig += signature.value * computed_Ts[i]
for signature in non_colliding_sigs:
agg_sig += signature.value
final_sig = Signature.from_g2(agg_sig)
aggregation_infos = [sig.aggregation_info for sig in signatures]
final_agg_info = AggregationInfo.merge_infos(aggregation_infos)
final_sig.set_aggregation_info(final_agg_info)
return final_sig