def attack(faulty_file, sigs_amount, max_iterations=100, seed=0):
"""
Attacks CMSS with faulty signatures.
"""
random.seed(seed)
faulty_sigs = [
bytearray.fromhex(line.rstrip('\n')) for line in open(faulty_file)
]
wots_pk = verify(exp_root, exp_sigma, in_masks_bytes)
faulty_sigs = random.sample(faulty_sigs, sigs_amount)
faulty_sigs = [chunkbytes(fsig, 32) for fsig in faulty_sigs]
faulty_sigs += [exp_sigma]
masks = chunkbytes(in_masks_bytes, 32)
dico = dict()
for i in range(len(wots_pk)):
dico[i] = (w - 1, wots_pk[i])
for sig in faulty_sigs:
for s in range(len(sig)):
for i in range(w - 1):
x = sig[s]
for j in range(w - 1 - i):
x = F(xor(x, masks[i + j]))
if x == wots_pk[s]:
if dico[s][0] > i:
dico[s] = (i, sig[s])
count = 0
sigma = False
address = subtree_A
xorH = lambda x, y, i: H(xor(x, masks[2 * i]), xor(y, masks[2 * i + 1]))
while not sigma:
sk1 = bytearray((random.getrandbits(8) for i in range(n // 8)))
leaves = []
for j in range((1 << h // d)):
address = (address & 0xfffffffffffffff0) | j
leaves += [
wots_leaf(xorH, int.to_bytes(address,
length=8,
byteorder='big'), sk1,
in_masks_bytes)
]
tree = l_tree(xorH, leaves)
sigma = trysign(root(tree), dico, in_masks_bytes)
count += 1
if count > max_iterations:
return (None, -1)
#print("Amount: " + str(count))
#print(''.join([toHexString(s) for s in sigma]))
#print("sk_1: " + toHexString(sk1))
return (dico, count)
def keygen(in_seed, in_masks): """ W-OTS+ key generation algorithm. """ sk = chunkbytes(Gl(in_seed), sphincs_bytes) masks = chunkbytes(in_masks, sphincs_bytes) pk = list(sk) for i in range(0, w-1): for j in range(len(pk)): pk[j] = F(xor(pk[j], masks[i])) return pk
def keygen(self, seed, masks):
assert len(seed) == self.n // 8
assert len(masks) >= 2 * self.tau
sk = self.Gt(seed)
sk = chunkbytes(sk, self.n // 8)
L = list(map(self.F, sk))
H = lambda x, y, i: self.H(xor(x, masks[2*i]), xor(y, masks[2*i+1]))
return root(hash_tree(H, L))
def sign(in_digest, in_seed, in_masks): """ W-OTS+ signing algorithm. """ M = list(int_to_basew(64, int.from_bytes(in_digest, byteorder="big"), 16))[::-1] C = list(int_to_basew(3, sum(15 - M[i] for i in range(len(M))), 16))[::-1] B = M + C sk = chunkbytes(Gl(in_seed), sphincs_bytes) masks = chunkbytes(in_masks, sphincs_bytes) sign = list(sk) for i in range(len(sk)): for j in range(0, B[i]): sign[i] = F(xor(sign[i], masks[j])) return ''.join([toHexString(s) for s in sign])
def keygen(self, seed, masks):
assert len(seed) == self.n // 8
assert len(masks) >= 2 * self.tau
sk = self.Gt(seed)
sk = chunkbytes(sk, self.n // 8)
L = list(map(self.F, sk))
H = lambda x, y, i: self.H(xor(x, masks[2 * i]),
xor(y, masks[2 * i + 1]))
return root(hash_tree(H, L))
def sign(self, m, seed, masks):
assert len(m) == self.m // 8
assert len(seed) == self.n // 8
assert len(masks) >= 2 * self.tau
sk = self.Gt(seed)
sk = chunkbytes(sk, self.n // 8)
L = list(map(self.F, sk))
H = lambda x, y, i: self.H(xor(x, masks[2*i]), xor(y, masks[2*i+1]))
tree = hash_tree(H, L)
trunk = list(itertools.islice(tree, 0, self.tau - self.x))
sigma_k = next(tree)
M = self.message_indices(m)
pk = root(tree)
# the SPHINCS paper suggests to put sigma_k at the end of sigma
# but the reference code places it at the front
return ([(sk[Mi], auth_path(trunk, Mi)) for Mi in M] + [sigma_k], pk)
def verify(in_digest, in_sigs, in_masks): """ W-OTS+ verification algorithm. """ M = list(int_to_basew(64, int.from_bytes(in_digest, byteorder="big"), 16))[::-1] C = list(int_to_basew(3, sum(15 - M[i] for i in range(len(M))), 16))[::-1] B = M + C masks = chunkbytes(in_masks, sphincs_bytes) pk = list(in_sigs) for i in range(len(pk)): for j in range(B[i], w-1): pk[i] = F(xor(pk[i], masks[j])) return pk
def sign(self, m, seed, masks):
assert len(m) == self.m // 8
assert len(seed) == self.n // 8
assert len(masks) >= 2 * self.tau
sk = self.Gt(seed)
sk = chunkbytes(sk, self.n // 8)
L = list(map(self.F, sk))
H = lambda x, y, i: self.H(xor(x, masks[2 * i]),
xor(y, masks[2 * i + 1]))
tree = hash_tree(H, L)
trunk = list(itertools.islice(tree, 0, self.tau - self.x))
sigma_k = next(tree)
M = self.message_indices(m)
pk = root(tree)
# the SPHINCS paper suggests to put sigma_k at the end of sigma
# but the reference code places it at the front
return ([(sk[Mi], auth_path(trunk, Mi)) for Mi in M] + [sigma_k], pk)
def trysign(in_digest, dico, in_masks): """ Attempts to produce a W-OTS+ signature with the dictionary of secret values. """ M = list(int_to_basew(64, int.from_bytes(in_digest, byteorder="big"), 16))[::-1] C = list(int_to_basew(3, sum(15 - M[i] for i in range(len(M))), 16))[::-1] B = M + C masks = chunkbytes(in_masks, sphincs_bytes) sig = [] for i in range(len(B)): if dico[i][0] <= B[i]: sig += [dico[i][1]] for j in range(dico[i][0], B[i]): sig[i] = F(xor(sig[i], masks[j])) else: return False return sig
from bytes_utils import xor, chunkbytes
from blake import BLAKE
def toByteArray(string): return bytes(string, "latin-1")
def toHexString(bytes): return ''.join('{:02x}'.format(x) for x in bytes)
in_sk = "Cé qu'è lainô, le Maitre dé bataille, Que se moqué et se ri dé c"
in_masks = "anaille, A bin fai vi, pè on desande nai, Qu'il étivé patron dé Genevoi. I son vegnu le doze de dessanbro, Pè onna nai asse naire que d'ancro; Y étivé l'an mil si san et dou, Qu'i veniron parla ou pou troi tou. Pè onna nai qu'étive la pe naire, I veniron; y n'étai pas pè bairè: Y étivé pè pilli nou maison, Et no tüa sans aucuna raison Petis et grans, ossis an sevegnance: Pè on matin d'onna bella demanze, Et pè on zeur qu'y fassive bin frai, Sans le bon Di, nos étivon to prai! On vo dera qu'étai cela canaille. - Lou Savoyar contre noutra mouraille Trai eitiellé on dressia et plianta, Et par iqué dou san y son monta. Etian antra, veniron u courdegarda, Yo i firon onna ruda montada. Is avion tenaillé et marté Qu'étivon fai avoi du boun acié, Pè arraci lou cliou et lé saraille, To lou verreu et tota la féraille Qu'on rancontré an dé pari andrai, Et qu'on bouté pè n'eitre pas surprai. On eitablio is avivon forcia; Et d'on petar qu'is avivon teria, I coudavon deiza eitre à sevau: I n'étivon pas assé monta yo. Sen Altessé dessu Pincha étive. Yon d'antre leu s'ancoru pè li dire Q"
in_sk1_bytes = toByteArray(in_sk[:32])
in_sk2_bytes = toByteArray(in_sk[32:])
in_masks_bytes = toByteArray(in_masks)
exp_root = bytearray.fromhex("0b87b5678179f3c3614ce6181380ee0b434eb7f2aefb9af73e2bcd379b341c95")
exp_sigma = chunkbytes(bytearray.fromhex("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"), 32)
subtree_A = int("07c1d4f115363236", 16)
target_A = int("103e0ea788a9b191", 16)
Glambda = lambda seed, n: ChaCha(key=seed).keystream(n)
Gl = lambda seed: Glambda(seed=seed, n=67*32)
perm = ChaCha().permuted
F = lambda m: perm(m + toByteArray("expand 32-byte to 64-byte state!"))[:32]
H = lambda m1, m2: perm(xor(perm(m1 + toByteArray("expand 32-byte to 64-byte state!")), m2 + bytes(32)))[:32]
Fa = lambda a, k: BLAKE(256).digest(k + a)
Frand = lambda m, k: BLAKE(512).digest(k + m)
n = 256
l = 64 + 3
def message_indices(self, m):
M = chunkbytes(m, self.tau // 8)
# the reference implementation uses 'idx = m[2*i] + (m[2*i+1]<<8)'
# which suggests using little-endian byte order
M = [int.from_bytes(Mi, byteorder='little') for Mi in M]
return M
def sign(self, m, seed, masks):
sk = self.Gl(seed)
sk = chunkbytes(sk, self.n // 8)
B = self.chainlengths(m)
return self.chains(sk, masks, [range(0, b) for b in B])
def keygen(self, seed, masks):
sk = self.Gl(seed)
sk = chunkbytes(sk, self.n // 8)
return self.chains(sk, masks, [range(0, self.w - 1)] * self.l)
def message_indices(self, m):
M = chunkbytes(m, self.tau // 8)
# the reference implementation uses 'idx = m[2*i] + (m[2*i+1]<<8)'
# which suggests using little-endian byte order
M = [int.from_bytes(Mi, byteorder='little') for Mi in M]
return M