def test_construct_root():
H = lambda x, y, i: x - y
minus_tree = list(hash_tree(H, range(16)))
for i in range(16):
leaf = minus_tree[0][i]
path = auth_path(minus_tree, i)
assert construct_root(H, path, leaf, i) == minus_tree[-1][0]
def verify(self, m, sig, masks):
assert len(m) == self.m // 8
assert len(masks) >= 2 * self.tau
M = self.message_indices(m)
H = lambda x, y, i: self.H(xor(x, masks[2*i]), xor(y, masks[2*i+1]))
sigma_k = sig[-1]
for (sk, path), Mi in zip(sig, M):
leaf = self.F(sk)
r = construct_root(H, path, leaf, Mi)
# there is an error in the SPHINCS paper for this formula, as it
# states that y_i = floor(M_i / 2^tau - x)
# rather than y_i = floor(M_i / 2^{tau - x})
yi = Mi // (1 << (self.tau - self.x))
if r != sigma_k[yi]:
return False
Qtop = masks[2*(self.tau - self.x):]
H = lambda x, y, i: self.H(xor(x, Qtop[2*i]), xor(y, Qtop[2*i+1]))
return root(hash_tree(H, sigma_k))
def verify(self, M, sig, PK):
i, R1, sig_horst, *sig = sig
PK1, Q = PK
Qtree = Q[2 * ceil(log(self.wots.l, 2)):]
D = self.Hdigest(R1, M)
pk = pk_horst = self.horst.verify(D, sig_horst, Q)
if pk_horst is False:
return False
subh = self.h // self.d
H = lambda x, y, i: self.H(xor(x, Q[2*i]), xor(y, Q[2*i+1]))
Ht = lambda x, y, i: self.H(xor(x, Qtree[2*i]), xor(y, Qtree[2*i+1]))
for _ in range(self.d):
wots_sig, wots_path, *sig = sig
pk_wots = self.wots.verify(pk, wots_sig, Q)
leaf = root(l_tree(H, pk_wots))
pk = construct_root(Ht, wots_path, leaf, i & 0x1f)
i >>= subh
return PK1 == pk
def verify(self, M, sig, PK):
i, R1, sig_horst, *sig = sig
PK1, Q = PK
Qtree = Q[2 * ceil(log(self.wots.l, 2)):]
D = self.Hdigest(R1, M)
pk = pk_horst = self.horst.verify(D, sig_horst, Q)
if pk_horst is False:
return False
subh = self.h // self.d
H = lambda x, y, i: self.H(xor(x, Q[2*i]), xor(y, Q[2*i+1]))
Ht = lambda x, y, i: self.H(xor(x, Qtree[2*i]), xor(y, Qtree[2*i+1]))
for _ in range(self.d):
wots_sig, wots_path, *sig = sig
pk_wots = self.wots.verify(pk, wots_sig, Q)
leaf = root(l_tree(H, pk_wots))
pk = construct_root(Ht, wots_path, leaf, i & 0x1f)
i >>= subh
return PK1 == pk
def verify(self, m, sig, masks):
assert len(m) == self.m // 8
assert len(masks) >= 2 * self.tau
M = self.message_indices(m)
H = lambda x, y, i: self.H(xor(x, masks[2 * i]),
xor(y, masks[2 * i + 1]))
sigma_k = sig[-1]
for (sk, path), Mi in zip(sig, M):
leaf = self.F(sk)
r = construct_root(H, path, leaf, Mi)
# there is an error in the SPHINCS paper for this formula, as it
# states that y_i = floor(M_i / 2^tau - x)
# rather than y_i = floor(M_i / 2^{tau - x})
yi = Mi // (1 << (self.tau - self.x))
if r != sigma_k[yi]:
return False
Qtop = masks[2 * (self.tau - self.x):]
H = lambda x, y, i: self.H(xor(x, Qtop[2 * i]), xor(
y, Qtop[2 * i + 1]))
return root(hash_tree(H, sigma_k))