def wots_leaf(self, address, SK1, masks):
seed = self.Fa(address, SK1)
pk_A = self.wots.keygen(seed, masks)
def H(x, y, i):
return self.H(xor(x, masks[2 * i]), xor(y, masks[2 * i + 1]))
return root(l_tree(H, pk_A))
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 wots_leaf(self, address, SK1, masks):
seed = self.Fa(address, SK1)
pk_A = self.wots.keygen(seed, masks)
H = lambda x, y, i: self.H(xor(x, masks[2*i]), xor(y, masks[2*i+1]))
return root(l_tree(H, pk_A))
def test_sum_l_tree():
sum_tree = list(l_tree(lambda x, y, i: x + y, range(20)))
assert sum_tree[-1][0] == sum(range(20))
def test_right_tree():
max_tree = list(l_tree(lambda x, y, i: y, range(20)))
assert max_tree[-1][0] == max(range(20))
def test_left_tree():
min_tree = list(l_tree(lambda x, y, i: x, range(20)))
assert min_tree[-1][0] == min(range(20))
