def __init__(self, n=256, m=512, h=60, d=12, w=16, tau=16, k=32):
self.n = n
self.m = m
self.h = h
self.d = d
self.w = w
self.tau = tau
self.t = 1 << tau
self.k = k
self.Hdigest = lambda r, m: BLAKE(512).digest(r + m)
self.Fa = lambda a, k: BLAKE(256).digest(k + a)
self.Frand = lambda m, k: BLAKE(512).digest(k + m)
C = bytes("expand 32-byte to 64-byte state!", 'latin-1')
perm = ChaCha().permuted
self.Glambda = lambda seed, n: ChaCha(key=seed).keystream(n)
self.F = lambda m: perm(m + C)[:32]
self.H = lambda m1, m2: perm(xor(perm(m1 + C), m2 + bytes(32)))[:32]
self.wots = WOTSplus(n=n, w=w, F=self.F, Gl=self.Glambda)
self.horst = HORST(n=n,
m=m,
k=k,
tau=tau,
F=self.F,
H=self.H,
Gt=self.Glambda)
def __init__(self, n=256, m=512, h=60, d=12, w=16, tau=16, k=32):
"""Initializes SPHINCS (default to SPHINCS-256)
!!Everything after this line is unestable!!
Currently other parameters than SPHINCS-256 can be buggy
n -- length of hash in WOTS / HORST (in bits)
m -- length of message hash (in bits)
h -- height of the hyper-tree
d -- layers of the hyper-tree
w -- Winternitz parameter used for WOTS signature
tau -- layers in the HORST tree (2^tau is no. of secret-key elements)
k -- number of revealed secret-key elements per HORST signature
"""
self.n = n
self.m = m
self.h = h
self.d = d
self.w = w
self.tau = tau
self.t = 1 << tau
self.k = k
self.Hdigest = lambda r, m: BLAKE(512).digest(r + m)
self.Fa = lambda a, k: BLAKE(256).digest(k + a)
self.Frand = lambda m, k: BLAKE(512).digest(k + m)
C = bytes("expand 32-byte to 64-byte state!", 'latin-1')
perm = ChaCha().permuted
self.Glambda = lambda seed, n: ChaCha(key=seed).keystream(n)
self.F = lambda m: perm(m + C)[:32]
self.H = lambda m1, m2: perm(xor(perm(m1 + C), m2 + bytes(32)))[:32]
self.wots = WOTSplus(n=n, w=w, F=self.F, Gl=self.Glambda)
self.horst = HORST(n=n, m=m, k=k, tau=tau,
F=self.F, H=self.H, Gt=self.Glambda)
def test_WOTSplus():
n = 256
m = os.urandom(n // 8)
seed = os.urandom(n // 8)
w = 16
masks = [os.urandom(n // 8) for _ in range(w - 1)]
wots = WOTSplus(n=n, w=w, F=SPHINCS().F, Gl=SPHINCS().Glambda)
pk = wots.keygen(seed, masks)
sig = wots.sign(m, seed, masks)
assert pk == wots.verify(m, sig, masks)
def test_WOTSplus():
n = 256
m = os.urandom(n // 8)
seed = os.urandom(n // 8)
w = 16
masks = [os.urandom(n // 8) for _ in range(w - 1)]
wots = WOTSplus(n=n, w=w, F=SPHINCS().F, Gl=SPHINCS().Glambda)
pk = wots.keygen(seed, masks)
sig = wots.sign(m, seed, masks)
assert pk == wots.verify(m, sig, masks)
def __init__(self, n=256, m=512, h=60, d=12, w=16, tau=16, k=32):
"""Initializes SPHINCS (default to SPHINCS-256)
Currently other parameters than SPHINCS-256 can be buggy
n -- length of hash in WOTS / HORST (in bits)
m -- length of message hash (in bits)
h -- height of the hyper-tree
d -- layers of the hyper-tree
w -- Winternitz parameter used for WOTS signature
tau -- layers in the HORST tree (2^tau is no. of secret-key elements)
k -- number of revealed secret-key elements per HORST signature
"""
self.n = n
self.m = m
self.h = h
self.d = d
self.w = w
self.tau = tau
self.t = 1 << tau
self.k = k
self.Hdigest = lambda r, m: BLAKE(512).digest(r + m)
self.Fa = lambda a, k: BLAKE(256).digest(k + a)
self.Frand = lambda m, k: BLAKE(512).digest(k + m)
C = bytes("expand 32-byte to 64-byte state!", 'latin-1')
perm = ChaCha().permuted
self.Glambda = lambda seed, n: ChaCha(key=seed).keystream(n)
self.F = lambda m: perm(m + C)[:32]
self.H = lambda m1, m2: perm(xor(perm(m1 + C), m2 + bytes(32)))[:32]
self.wots = WOTSplus(n=n, w=w, F=self.F, Gl=self.Glambda)
self.horst = HORST(n=n, m=m, k=k, tau=tau,
F=self.F, H=self.H, Gt=self.Glambda)
class SPHINCS(object):
def __init__(self, n=256, m=512, h=60, d=12, w=16, tau=16, k=32):
"""Initializes SPHINCS (default to SPHINCS-256)
!!Everything after this line is unestable!!
Currently other parameters than SPHINCS-256 can be buggy
n -- length of hash in WOTS / HORST (in bits)
m -- length of message hash (in bits)
h -- height of the hyper-tree
d -- layers of the hyper-tree
w -- Winternitz parameter used for WOTS signature
tau -- layers in the HORST tree (2^tau is no. of secret-key elements)
k -- number of revealed secret-key elements per HORST signature
"""
self.n = n
self.m = m
self.h = h
self.d = d
self.w = w
self.tau = tau
self.t = 1 << tau
self.k = k
self.Hdigest = lambda r, m: BLAKE(512).digest(r + m)
self.Fa = lambda a, k: BLAKE(256).digest(k + a)
self.Frand = lambda m, k: BLAKE(512).digest(k + m)
C = bytes("expand 32-byte to 64-byte state!", 'latin-1')
perm = ChaCha().permuted
self.Glambda = lambda seed, n: ChaCha(key=seed).keystream(n)
self.F = lambda m: perm(m + C)[:32]
self.H = lambda m1, m2: perm(xor(perm(m1 + C), m2 + bytes(32)))[:32]
self.wots = WOTSplus(n=n, w=w, F=self.F, Gl=self.Glambda)
self.horst = HORST(n=n, m=m, k=k, tau=tau,
F=self.F, H=self.H, Gt=self.Glambda)
@classmethod
def address(self, level, subtree, leaf):
t = level | (subtree << 4) | (leaf << 59)
return int.to_bytes(t, length=8, byteorder='little')
#Code to generate leafs
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 wots_path(self, a, SK1, Q, subh):
ta = dict(a)
leafs = []
for subleaf in range(1 << subh):
ta['leaf'] = subleaf
leafs.append(self.wots_leaf(self.address(**ta), SK1, Q))
Qtree = Q[2 * ceil(log(self.wots.l, 2)):]
H = lambda x, y, i: self.H(xor(x, Qtree[2*i]), xor(y, Qtree[2*i+1]))
tree = list(hash_tree(H, leafs))
return auth_path(tree, a['leaf']), root(tree)
##generate the both keys, public and private, calling the functions
def keygen(self):
SK1 = os.urandom(self.n // 8)
SK2 = os.urandom(self.n // 8)
p = max(self.w-1, 2 * (self.h + ceil(log(self.wots.l, 2))), 2*self.tau)
Q = [os.urandom(self.n // 8) for _ in range(p)]
PK1 = self.keygen_pub(SK1, Q)
return (SK1, SK2, Q), (PK1, Q)
#Function to generate the public key
def keygen_pub(self, SK1, Q):
addresses = [self.address(self.d - 1, 0, i)
for i in range(1 << (self.h//self.d))]
leafs = [self.wots_leaf(A, SK1, Q) for A in addresses]
Qtree = Q[2 * ceil(log(self.wots.l, 2)):]
H = lambda x, y, i: self.H(xor(x, Qtree[2*i]), xor(y, Qtree[2*i+1]))
PK1 = root(hash_tree(H, leafs))
return PK1
def sign(self, M, SK):
SK1, SK2, Q = SK
R = self.Frand(M, SK2)
R1, R2 = R[:self.n // 8], R[self.n // 8:]
D = self.Hdigest(R1, M)
i = int.from_bytes(R2, byteorder='big')
i >>= self.n - self.h
subh = self.h // self.d
a = {'level': self.d,
'subtree': i >> subh,
'leaf': i & ((1 << subh) - 1)}
a_horst = self.address(**a)
seed_horst = self.Fa(a_horst, SK1)
sig_horst, pk_horst = self.horst.sign(D, seed_horst, Q)
pk = pk_horst
sig = [i, R1, sig_horst]
for level in range(self.d):
a['level'] = level
a_wots = self.address(**a)
seed_wots = self.Fa(a_wots, SK1)
wots_sig = self.wots.sign(pk, seed_wots, Q)
sig.append(wots_sig)
path, pk = self.wots_path(a, SK1, Q, subh)
sig.append(path)
a['leaf'] = a['subtree'] & ((1 << subh) - 1)
a['subtree'] >>= subh
return tuple(sig)
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 pack(self, x):
if type(x) is bytes:
return x
if type(x) is int: # needed for index i
return int.to_bytes(x, length=(self.h+7)//8, byteorder='little')
return b''.join([self.pack(a) for a in iter(x)])
def unpack(self, sk=None, pk=None, sig=None, byteseq=None):
n = self.n // 8
if sk:
return sk[:n], sk[n:2*n], self.unpack(byteseq=sk[2*n:])
elif pk:
return pk[:n], self.unpack(byteseq=pk[n:])
elif byteseq:
return [byteseq[i:i+n] for i in range(0, len(byteseq), n)]
elif sig:
def prefix(x, n):
return x[:n], x[n:]
i, sig = prefix(sig, (self.h+7)//8)
i = int.from_bytes(i, byteorder='little')
R1, sig = prefix(sig, n)
sig_horst = []
for _ in range(self.k):
sk, sig = prefix(sig, n)
auth, sig = prefix(sig, (self.tau - self.horst.x)*n)
sig_horst.append((sk, self.unpack(byteseq=auth)))
sigma_k, sig = prefix(sig, (1 << self.horst.x) * n)
sig_horst.append(self.unpack(byteseq=sigma_k))
wots = []
for _ in range(self.d):
wots_sig, sig = prefix(sig, self.wots.l*n)
path, sig = prefix(sig, self.h//self.d*n)
wots.append(self.unpack(byteseq=wots_sig))
wots.append(self.unpack(byteseq=path))
return (i, R1, sig_horst) + tuple(wots)
class SPHINCS(object):
def __init__(self, n=256, m=512, h=60, d=12, w=16, tau=16, k=32):
"""Initializes SPHINCS (default to SPHINCS-256)
Currently other parameters than SPHINCS-256 can be buggy
n -- length of hash in WOTS / HORST (in bits)
m -- length of message hash (in bits)
h -- height of the hyper-tree
d -- layers of the hyper-tree
w -- Winternitz parameter used for WOTS signature
tau -- layers in the HORST tree (2^tau is no. of secret-key elements)
k -- number of revealed secret-key elements per HORST signature
"""
self.n = n
self.m = m
self.h = h
self.d = d
self.w = w
self.tau = tau
self.t = 1 << tau
self.k = k
self.Hdigest = lambda r, m: BLAKE(512).digest(r + m)
self.Fa = lambda a, k: BLAKE(256).digest(k + a)
self.Frand = lambda m, k: BLAKE(512).digest(k + m)
C = bytes("expand 32-byte to 64-byte state!", 'latin-1')
perm = ChaCha().permuted
self.Glambda = lambda seed, n: ChaCha(key=seed).keystream(n)
self.F = lambda m: perm(m + C)[:32]
self.H = lambda m1, m2: perm(xor(perm(m1 + C), m2 + bytes(32)))[:32]
self.wots = WOTSplus(n=n, w=w, F=self.F, Gl=self.Glambda)
self.horst = HORST(n=n, m=m, k=k, tau=tau,
F=self.F, H=self.H, Gt=self.Glambda)
@classmethod
def address(self, level, subtree, leaf):
t = level | (subtree << 4) | (leaf << 59)
return int.to_bytes(t, length=8, byteorder='little')
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 wots_path(self, a, SK1, Q, subh):
ta = dict(a)
leafs = []
for subleaf in range(1 << subh):
ta['leaf'] = subleaf
leafs.append(self.wots_leaf(self.address(**ta), SK1, Q))
Qtree = Q[2 * ceil(log(self.wots.l, 2)):]
H = lambda x, y, i: self.H(xor(x, Qtree[2*i]), xor(y, Qtree[2*i+1]))
tree = list(hash_tree(H, leafs))
return auth_path(tree, a['leaf']), root(tree)
def keygen(self):
SK1 = os.urandom(self.n // 8)
SK2 = os.urandom(self.n // 8)
p = max(self.w-1, 2 * (self.h + ceil(log(self.wots.l, 2))), 2*self.tau)
Q = [os.urandom(self.n // 8) for _ in range(p)]
PK1 = self.keygen_pub(SK1, Q)
return (SK1, SK2, Q), (PK1, Q)
def keygen_pub(self, SK1, Q):
addresses = [self.address(self.d - 1, 0, i)
for i in range(1 << (self.h//self.d))]
leafs = [self.wots_leaf(A, SK1, Q) for A in addresses]
Qtree = Q[2 * ceil(log(self.wots.l, 2)):]
H = lambda x, y, i: self.H(xor(x, Qtree[2*i]), xor(y, Qtree[2*i+1]))
PK1 = root(hash_tree(H, leafs))
return PK1
def sign(self, M, SK):
SK1, SK2, Q = SK
R = self.Frand(M, SK2)
R1, R2 = R[:self.n // 8], R[self.n // 8:]
D = self.Hdigest(R1, M)
i = int.from_bytes(R2, byteorder='big')
i >>= self.n - self.h
subh = self.h // self.d
a = {'level': self.d,
'subtree': i >> subh,
'leaf': i & ((1 << subh) - 1)}
a_horst = self.address(**a)
seed_horst = self.Fa(a_horst, SK1)
sig_horst, pk_horst = self.horst.sign(D, seed_horst, Q)
pk = pk_horst
sig = [i, R1, sig_horst]
for level in range(self.d):
a['level'] = level
a_wots = self.address(**a)
seed_wots = self.Fa(a_wots, SK1)
wots_sig = self.wots.sign(pk, seed_wots, Q)
sig.append(wots_sig)
path, pk = self.wots_path(a, SK1, Q, subh)
sig.append(path)
a['leaf'] = a['subtree'] & ((1 << subh) - 1)
a['subtree'] >>= subh
return tuple(sig)
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 pack(self, x):
if type(x) is bytes:
return x
if type(x) is int: # needed for index i
return int.to_bytes(x, length=(self.h+7)//8, byteorder='little')
return b''.join([self.pack(a) for a in iter(x)])
def unpack(self, sk=None, pk=None, sig=None, byteseq=None):
n = self.n // 8
if sk:
return sk[:n], sk[n:2*n], self.unpack(byteseq=sk[2*n:])
elif pk:
return pk[:n], self.unpack(byteseq=pk[n:])
elif byteseq:
return [byteseq[i:i+n] for i in range(0, len(byteseq), n)]
elif sig:
def prefix(x, n):
return x[:n], x[n:]
i, sig = prefix(sig, (self.h+7)//8)
i = int.from_bytes(i, byteorder='little')
R1, sig = prefix(sig, n)
sig_horst = []
for _ in range(self.k):
sk, sig = prefix(sig, n)
auth, sig = prefix(sig, (self.tau - self.horst.x)*n)
sig_horst.append((sk, self.unpack(byteseq=auth)))
sigma_k, sig = prefix(sig, (1 << self.horst.x) * n)
sig_horst.append(self.unpack(byteseq=sigma_k))
wots = []
for _ in range(self.d):
wots_sig, sig = prefix(sig, self.wots.l*n)
path, sig = prefix(sig, self.h//self.d*n)
wots.append(self.unpack(byteseq=wots_sig))
wots.append(self.unpack(byteseq=path))
return (i, R1, sig_horst) + tuple(wots)
def test_WOTSplus_ref():
"""This test-case is derived from the SPHINCS reference implementation"""
n = 256
m = bytes(range(32))
seed = bytes(range(32, 64))
w = 16
masks = [bytes(range(i, 32 + i)) for i in range(w - 1)]
wots = WOTSplus(n=n, w=w, F=SPHINCS().F, Gl=SPHINCS().Glambda)
pk = wots.keygen(seed, masks)
sig = wots.sign(m, seed, masks)
assert pk == wots.verify(m, sig, masks)
assert sig == [
bytes([
0x11, 0xD8, 0x5B, 0x22, 0xA5, 0xAB, 0x55, 0x9B, 0x5D, 0x10, 0x6F,
0xDC, 0x08, 0x25, 0xDE, 0x67, 0x7C, 0x28, 0x74, 0x0B, 0x05, 0x68,
0x98, 0x99, 0x4E, 0x14, 0x1A, 0xF4, 0xBF, 0x04, 0x6E, 0x73
]),
bytes([
0xAD, 0x43, 0x24, 0x33, 0x86, 0x8F, 0xB9, 0x9F, 0x09, 0xCD, 0xDF,
0x03, 0xE7, 0x0D, 0x5E, 0xDE, 0xDE, 0xCE, 0x9F, 0x8E, 0xE9, 0x17,
0x39, 0xBF, 0xF3, 0x12, 0x7E, 0x1D, 0x66, 0x82, 0x80, 0x8F
]),
bytes([
0xAC, 0x3F, 0x87, 0xCB, 0xAA, 0x4A, 0x31, 0x1D, 0xE1, 0xA5, 0x9C,
0x1D, 0xBA, 0x2C, 0x05, 0x7E, 0xCF, 0x13, 0xEE, 0x87, 0x35, 0xBB,
0xDD, 0xA6, 0xD3, 0x43, 0xD3, 0xCE, 0xC2, 0xB7, 0x3E, 0xE7
]),
bytes([
0xA6, 0x85, 0x62, 0x12, 0x3F, 0xF2, 0xB2, 0x49, 0xF0, 0x21, 0x0A,
0x47, 0xCD, 0xE3, 0x6A, 0x89, 0x32, 0x08, 0x26, 0x91, 0x28, 0x37,
0x14, 0x65, 0xED, 0x29, 0xF0, 0x54, 0x55, 0x07, 0xE1, 0xB7
]),
bytes([
0x26, 0x05, 0x52, 0x3F, 0x3B, 0x54, 0xD7, 0x02, 0x2E, 0xFE, 0x6A,
0xC8, 0xD3, 0xEA, 0xA2, 0xAF, 0xD8, 0xDD, 0x02, 0x7A, 0xD9, 0xA3,
0x4B, 0x90, 0x93, 0x26, 0x6F, 0x78, 0x83, 0x98, 0x81, 0xD1
]),
bytes([
0xAD, 0x46, 0xF2, 0xBD, 0x8F, 0xE9, 0xCB, 0xA4, 0x5E, 0x1C, 0x06,
0xB6, 0x35, 0x26, 0x89, 0x4E, 0x1D, 0x79, 0x90, 0xE3, 0x94, 0xDB,
0x34, 0xB5, 0x0C, 0x4C, 0xBA, 0xA7, 0x59, 0xE6, 0x39, 0x9D
]),
bytes([
0x89, 0x18, 0xD4, 0xC5, 0x72, 0xB9, 0xB0, 0xDD, 0xFE, 0x63, 0xAD,
0xD3, 0xCC, 0xB0, 0xFC, 0xD9, 0x21, 0x13, 0x96, 0x0C, 0x1B, 0x0F,
0xDA, 0xD3, 0xC7, 0x06, 0x71, 0x4C, 0x8E, 0xB3, 0x1F, 0x20
]),
bytes([
0xB2, 0xBF, 0x3A, 0x65, 0x25, 0xF0, 0x2F, 0xE5, 0x98, 0x53, 0xC9,
0xED, 0x4D, 0xAE, 0x02, 0x7B, 0x1B, 0x20, 0x81, 0x15, 0x79, 0xEE,
0x6D, 0x1C, 0x2C, 0xF4, 0xDE, 0x23, 0xE7, 0x0D, 0x9B, 0x09
]),
bytes([
0xDD, 0xC5, 0x9B, 0x98, 0x54, 0x74, 0xC0, 0x7C, 0xF1, 0x42, 0xEF,
0x97, 0x45, 0x00, 0x57, 0x89, 0xDF, 0x62, 0x04, 0x2A, 0xB7, 0x05,
0xD8, 0x2B, 0x9B, 0x32, 0x9E, 0x13, 0xAB, 0x3F, 0x60, 0x7C
]),
bytes([
0xD7, 0x62, 0xD7, 0x42, 0x92, 0x13, 0x15, 0x2F, 0xC7, 0x2E, 0xC4,
0x16, 0x4C, 0x4A, 0x20, 0x30, 0x50, 0xF7, 0x81, 0x2A, 0x60, 0x9E,
0x50, 0xFF, 0xDE, 0x0E, 0x9F, 0x57, 0xB3, 0xBB, 0xC6, 0xE2
]),
bytes([
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bytes([
0xC4, 0xCE, 0xFC, 0x80, 0x5F, 0x10, 0x83, 0xA9, 0xE7, 0x9D, 0xB9,
0x03, 0x48, 0x1A, 0x90, 0x44, 0xDB, 0xB7, 0x06, 0x39, 0xD0, 0x6B,
0x96, 0xFE, 0x80, 0x71, 0x16, 0x74, 0x31, 0x79, 0x55, 0x35
]),
bytes([
0xAD, 0x22, 0xB8, 0xB8, 0xC7, 0x2C, 0x5B, 0x9F, 0x1D, 0x24, 0x9A,
0xD4, 0x1D, 0x48, 0x90, 0x5F, 0x4F, 0x70, 0x57, 0x1D, 0xF2, 0x2F,
0x8D, 0xAF, 0xBB, 0x0A, 0xC8, 0x14, 0x09, 0xA8, 0xB0, 0xC5
])
]
def test_WOTSplus_ref():
"""This test-case is derived from the SPHINCS reference implementation"""
n = 256
m = bytes(range(32))
seed = bytes(range(32, 64))
w = 16
masks = [bytes(range(i, 32+i)) for i in range(w - 1)]
wots = WOTSplus(n=n, w=w, F=SPHINCS().F, Gl=SPHINCS().Glambda)
pk = wots.keygen(seed, masks)
sig = wots.sign(m, seed, masks)
assert pk == wots.verify(m, sig, masks)
assert sig == [bytes([0x11, 0xD8, 0x5B, 0x22, 0xA5, 0xAB, 0x55, 0x9B,
0x5D, 0x10, 0x6F, 0xDC, 0x08, 0x25, 0xDE, 0x67,
0x7C, 0x28, 0x74, 0x0B, 0x05, 0x68, 0x98, 0x99,
0x4E, 0x14, 0x1A, 0xF4, 0xBF, 0x04, 0x6E, 0x73]),
bytes([0xAD, 0x43, 0x24, 0x33, 0x86, 0x8F, 0xB9, 0x9F,
0x09, 0xCD, 0xDF, 0x03, 0xE7, 0x0D, 0x5E, 0xDE,
0xDE, 0xCE, 0x9F, 0x8E, 0xE9, 0x17, 0x39, 0xBF,
0xF3, 0x12, 0x7E, 0x1D, 0x66, 0x82, 0x80, 0x8F]),
bytes([0xAC, 0x3F, 0x87, 0xCB, 0xAA, 0x4A, 0x31, 0x1D,
0xE1, 0xA5, 0x9C, 0x1D, 0xBA, 0x2C, 0x05, 0x7E,
0xCF, 0x13, 0xEE, 0x87, 0x35, 0xBB, 0xDD, 0xA6,
0xD3, 0x43, 0xD3, 0xCE, 0xC2, 0xB7, 0x3E, 0xE7]),
bytes([0xA6, 0x85, 0x62, 0x12, 0x3F, 0xF2, 0xB2, 0x49,
0xF0, 0x21, 0x0A, 0x47, 0xCD, 0xE3, 0x6A, 0x89,
0x32, 0x08, 0x26, 0x91, 0x28, 0x37, 0x14, 0x65,
0xED, 0x29, 0xF0, 0x54, 0x55, 0x07, 0xE1, 0xB7]),
bytes([0x26, 0x05, 0x52, 0x3F, 0x3B, 0x54, 0xD7, 0x02,
0x2E, 0xFE, 0x6A, 0xC8, 0xD3, 0xEA, 0xA2, 0xAF,
0xD8, 0xDD, 0x02, 0x7A, 0xD9, 0xA3, 0x4B, 0x90,
0x93, 0x26, 0x6F, 0x78, 0x83, 0x98, 0x81, 0xD1]),
bytes([0xAD, 0x46, 0xF2, 0xBD, 0x8F, 0xE9, 0xCB, 0xA4,
0x5E, 0x1C, 0x06, 0xB6, 0x35, 0x26, 0x89, 0x4E,
0x1D, 0x79, 0x90, 0xE3, 0x94, 0xDB, 0x34, 0xB5,
0x0C, 0x4C, 0xBA, 0xA7, 0x59, 0xE6, 0x39, 0x9D]),
bytes([0x89, 0x18, 0xD4, 0xC5, 0x72, 0xB9, 0xB0, 0xDD,
0xFE, 0x63, 0xAD, 0xD3, 0xCC, 0xB0, 0xFC, 0xD9,
0x21, 0x13, 0x96, 0x0C, 0x1B, 0x0F, 0xDA, 0xD3,
0xC7, 0x06, 0x71, 0x4C, 0x8E, 0xB3, 0x1F, 0x20]),
bytes([0xB2, 0xBF, 0x3A, 0x65, 0x25, 0xF0, 0x2F, 0xE5,
0x98, 0x53, 0xC9, 0xED, 0x4D, 0xAE, 0x02, 0x7B,
0x1B, 0x20, 0x81, 0x15, 0x79, 0xEE, 0x6D, 0x1C,
0x2C, 0xF4, 0xDE, 0x23, 0xE7, 0x0D, 0x9B, 0x09]),
bytes([0xDD, 0xC5, 0x9B, 0x98, 0x54, 0x74, 0xC0, 0x7C,
0xF1, 0x42, 0xEF, 0x97, 0x45, 0x00, 0x57, 0x89,
0xDF, 0x62, 0x04, 0x2A, 0xB7, 0x05, 0xD8, 0x2B,
0x9B, 0x32, 0x9E, 0x13, 0xAB, 0x3F, 0x60, 0x7C]),
bytes([0xD7, 0x62, 0xD7, 0x42, 0x92, 0x13, 0x15, 0x2F,
0xC7, 0x2E, 0xC4, 0x16, 0x4C, 0x4A, 0x20, 0x30,
0x50, 0xF7, 0x81, 0x2A, 0x60, 0x9E, 0x50, 0xFF,
0xDE, 0x0E, 0x9F, 0x57, 0xB3, 0xBB, 0xC6, 0xE2]),
bytes([0x79, 0x61, 0xA7, 0xD7, 0x22, 0x00, 0x40, 0x3A,
0x3B, 0x4C, 0x70, 0x33, 0x15, 0x2D, 0xB0, 0x09,
0x9C, 0x46, 0xEF, 0xEF, 0xEB, 0xA9, 0x42, 0x9D,
0xCC, 0xA8, 0x0E, 0x13, 0xD4, 0xC5, 0x06, 0x5F]),
bytes([0x44, 0xAB, 0xEF, 0x27, 0x43, 0xCE, 0xC1, 0xDC,
0xF2, 0x0A, 0xDE, 0x53, 0x82, 0x12, 0xE7, 0x37,
0xBA, 0x0A, 0xC7, 0xCF, 0xAC, 0x2B, 0x39, 0x08,
0xC2, 0x92, 0x76, 0xDB, 0x08, 0x8D, 0x4A, 0x4F]),
bytes([0x0C, 0x3D, 0x04, 0x7B, 0x76, 0xE3, 0x30, 0xA5,
0x71, 0x49, 0x56, 0xB3, 0xB6, 0xF9, 0x9F, 0x9E,
0xE1, 0xC1, 0x84, 0xB5, 0xB5, 0xB3, 0xF9, 0xFC,
0xBC, 0x4D, 0xC8, 0x78, 0xA5, 0x99, 0x20, 0x54]),
bytes([0x76, 0x89, 0x21, 0xFC, 0x2B, 0x08, 0xF6, 0x50,
0x7D, 0x44, 0x29, 0x40, 0xF1, 0xDA, 0x5A, 0x3F,
0xEC, 0x11, 0xAE, 0x00, 0x07, 0x7A, 0x6C, 0x73,
0xF2, 0xD8, 0x92, 0x09, 0x7F, 0xF5, 0x95, 0x94]),
bytes([0xD4, 0x53, 0x75, 0x89, 0xCF, 0xF3, 0x5D, 0x10,
0xD9, 0x8F, 0x5D, 0x9A, 0x39, 0xEB, 0x44, 0x6C,
0x21, 0x46, 0xA7, 0xF6, 0x54, 0xC3, 0xE7, 0xDE,
0x6A, 0x1D, 0x9F, 0x6D, 0xA5, 0x24, 0xA0, 0xB5]),
bytes([0xA8, 0x47, 0x1B, 0x7C, 0xF9, 0x70, 0x8E, 0x8E,
0x57, 0x10, 0x93, 0x33, 0xF0, 0x50, 0x60, 0xCF,
0x3D, 0xE9, 0x3C, 0xCF, 0x5B, 0x42, 0x39, 0x75,
0x64, 0xD1, 0xA5, 0x09, 0x8C, 0xBA, 0xD2, 0x5E]),
bytes([0x07, 0x11, 0xA9, 0x75, 0x19, 0xEA, 0x9C, 0x02,
0xC4, 0xFC, 0xBF, 0x12, 0xD2, 0x74, 0xF6, 0x22,
0xF6, 0x56, 0xE5, 0x9B, 0x86, 0x66, 0xE2, 0x20,
0xDE, 0xCD, 0xE8, 0x4E, 0x20, 0xC1, 0x04, 0x50]),
bytes([0x99, 0x52, 0xFD, 0x64, 0x4E, 0x01, 0xC7, 0xB4,
0x76, 0xF6, 0xBC, 0xD3, 0x81, 0xDA, 0xA1, 0x82,
0x7D, 0xEE, 0x01, 0x98, 0x80, 0x98, 0xED, 0x3E,
0xC8, 0xB2, 0xC3, 0x39, 0xF6, 0x1A, 0xF1, 0xA6]),
bytes([0x5B, 0x43, 0x17, 0x14, 0x35, 0xCD, 0x8F, 0x4D,
0xF0, 0x5C, 0x3D, 0x57, 0xD0, 0x41, 0x6C, 0xB2,
0x61, 0xB6, 0x17, 0xF2, 0xE9, 0xE6, 0x46, 0x4E,
0x92, 0xCD, 0x49, 0x96, 0x3D, 0x55, 0x1D, 0xFE]),
bytes([0xFA, 0x17, 0xE0, 0x74, 0xD1, 0x70, 0x61, 0x52,
0xB9, 0x7C, 0xB8, 0x23, 0x4B, 0x67, 0x69, 0xBA,
0x7B, 0x8F, 0xCA, 0x69, 0x2A, 0x8E, 0x8B, 0x4F,
0x99, 0xEF, 0x51, 0x5A, 0x90, 0x48, 0x3A, 0x9A]),
bytes([0x3D, 0x6B, 0x23, 0x8F, 0xE0, 0xEE, 0xB5, 0x1C,
0x5D, 0x38, 0x14, 0x98, 0x09, 0xF3, 0x1B, 0xBF,
0xFE, 0x17, 0xC8, 0xB1, 0x8E, 0x20, 0xC5, 0x5D,
0xF4, 0xB1, 0x19, 0x36, 0x18, 0x2C, 0xE0, 0xBE]),
bytes([0x7C, 0x74, 0xD6, 0x2A, 0x3D, 0x8D, 0xF3, 0x35,
0x5A, 0xFD, 0xBB, 0x95, 0x4F, 0xF2, 0x7A, 0xAA,
0x5D, 0xCE, 0x50, 0x2B, 0x52, 0xBE, 0xF6, 0x98,
0x71, 0x8A, 0x16, 0xEB, 0xD6, 0xAD, 0x03, 0x0D]),
bytes([0xE3, 0x64, 0x01, 0x35, 0xB6, 0x81, 0x9E, 0xB2,
0xE0, 0x41, 0x0A, 0xBA, 0xCD, 0x14, 0x29, 0xED,
0xB8, 0x94, 0x3C, 0x6D, 0x2D, 0x63, 0x21, 0x16,
0x18, 0x9A, 0x2F, 0x50, 0x7B, 0x0D, 0xE8, 0x9F]),
bytes([0x70, 0xD6, 0x41, 0x70, 0xAF, 0x00, 0x83, 0x0A,
0x46, 0x9E, 0xCD, 0x86, 0xA4, 0xE2, 0xBE, 0xEA,
0xCD, 0x9F, 0xB9, 0x91, 0x14, 0x89, 0xED, 0x4E,
0x63, 0x60, 0x7E, 0x09, 0xEA, 0xB3, 0x73, 0x8D]),
bytes([0xDF, 0x04, 0x52, 0x09, 0x59, 0xD6, 0x26, 0xAE,
0x6E, 0xDD, 0xCF, 0x32, 0xDF, 0x8E, 0x08, 0x28,
0xA4, 0x45, 0x19, 0x3C, 0xFE, 0xAF, 0x1F, 0xA8,
0x9B, 0x99, 0x3C, 0xD3, 0x9F, 0x01, 0x02, 0x9A]),
bytes([0x47, 0x3C, 0x4A, 0xE6, 0x41, 0x0B, 0xFB, 0x91,
0xAE, 0xF5, 0xA9, 0xA1, 0x19, 0x01, 0xB1, 0x2D,
0xBB, 0xDA, 0xB7, 0x09, 0x33, 0xE6, 0x0D, 0x00,
0xD1, 0xA1, 0x79, 0xC3, 0xA3, 0xFB, 0x26, 0x05]),
bytes([0x31, 0x7F, 0x64, 0x5A, 0x5B, 0x2D, 0xA6, 0x9D,
0x76, 0xF9, 0x84, 0x53, 0x3E, 0x77, 0x0A, 0xB8,
0x91, 0x98, 0x64, 0x8A, 0x15, 0x2A, 0xF6, 0xDA,
0x23, 0xD0, 0x2E, 0xAF, 0x37, 0x3C, 0xDB, 0xE9]),
bytes([0x60, 0x09, 0xB4, 0x02, 0x5B, 0x3A, 0x3D, 0xB9,
0xE8, 0x8D, 0x40, 0x62, 0x5A, 0x48, 0xFC, 0x00,
0x64, 0x1B, 0x1B, 0x4E, 0x31, 0x1D, 0xFD, 0x90,
0x43, 0xAA, 0x69, 0x9A, 0xBE, 0x18, 0x3F, 0x76]),
bytes([0xB3, 0x4D, 0xED, 0xFF, 0x07, 0x77, 0xE5, 0xAD,
0xB5, 0x26, 0xC2, 0xF9, 0x2C, 0x57, 0x69, 0x7C,
0x5C, 0xBC, 0x59, 0x07, 0x18, 0x1A, 0x5F, 0xF3,
0x05, 0xD9, 0x70, 0x0B, 0x87, 0x65, 0xFF, 0x7D]),
bytes([0x7C, 0x1B, 0xC6, 0x30, 0xF6, 0x45, 0x9D, 0x88,
0x69, 0xF3, 0x4C, 0xC0, 0x3A, 0xD7, 0xC9, 0xA8,
0x7D, 0x41, 0xA8, 0x9D, 0x13, 0x50, 0x21, 0xF4,
0xC4, 0x02, 0xD8, 0xB7, 0x29, 0xB2, 0x8C, 0x5C]),
bytes([0xC3, 0x5F, 0xE3, 0xE7, 0xC2, 0x33, 0x6E, 0x36,
0x72, 0x85, 0xA2, 0x3B, 0x6E, 0x1D, 0x96, 0x7A,
0xD6, 0x8A, 0xA7, 0x24, 0x72, 0xAA, 0x1A, 0xB7,
0x61, 0x90, 0x54, 0x6B, 0x0F, 0xAA, 0x64, 0x24]),
bytes([0xA0, 0xCF, 0x1F, 0xBD, 0x0B, 0x9B, 0xE7, 0xE5,
0x3E, 0xE7, 0xB4, 0x6E, 0x54, 0xDA, 0x5F, 0x4D,
0xA2, 0x78, 0xAE, 0x50, 0xA2, 0x6A, 0x22, 0x60,
0x34, 0x9C, 0x77, 0xF2, 0xEF, 0x26, 0xF9, 0x14]),
bytes([0x5C, 0x42, 0x0B, 0x50, 0x21, 0xAF, 0x47, 0x02,
0x49, 0x51, 0x4B, 0xD9, 0x38, 0x74, 0x53, 0x5E,
0xD3, 0xEB, 0xC5, 0x89, 0x52, 0xCF, 0xA7, 0xD8,
0x9B, 0x34, 0x58, 0x62, 0x37, 0x56, 0x31, 0x75]),
bytes([0x57, 0xBB, 0x89, 0x88, 0xC8, 0x52, 0xEA, 0xB4,
0xF4, 0xF6, 0x4C, 0xAF, 0x87, 0xFF, 0xA2, 0xA4,
0x80, 0x4E, 0x12, 0xE1, 0x2B, 0xE6, 0xCB, 0xE5,
0x65, 0xC5, 0xC7, 0x46, 0x9E, 0x0B, 0xE3, 0x28]),
bytes([0x02, 0x38, 0x6B, 0xCB, 0x64, 0xDA, 0x26, 0xEB,
0x69, 0xB6, 0x7B, 0xC8, 0xCF, 0xA9, 0xDE, 0xC5,
0x66, 0x02, 0x98, 0xAF, 0x68, 0xD6, 0x5E, 0x99,
0xB8, 0xC9, 0xC3, 0xC3, 0x4E, 0x62, 0x9D, 0x26]),
bytes([0x46, 0x5C, 0xCC, 0x08, 0x70, 0x49, 0xCD, 0x00,
0x12, 0x59, 0xF7, 0x14, 0x12, 0x53, 0x03, 0xA4,
0x40, 0xD7, 0x3D, 0x0E, 0xC2, 0x79, 0xF1, 0x90,
0xFB, 0x3B, 0x88, 0x07, 0x13, 0xC9, 0x8A, 0x3C]),
bytes([0x6E, 0xA7, 0x31, 0x5E, 0x36, 0xBB, 0x31, 0xBC,
0x51, 0x1D, 0xBF, 0x01, 0x96, 0x65, 0x90, 0xA9,
0x96, 0xF1, 0x1C, 0x2A, 0xE6, 0xEB, 0xAA, 0x97,
0xC7, 0x61, 0x68, 0xE0, 0x52, 0x82, 0xA3, 0xC5]),
bytes([0x63, 0x09, 0x85, 0xCC, 0x33, 0x86, 0x11, 0xA2,
0xB4, 0xD3, 0xF0, 0x58, 0xFC, 0x92, 0xDF, 0xB4,
0x63, 0xBE, 0x67, 0x20, 0x2D, 0x3D, 0xA7, 0x9A,
0xFA, 0x36, 0xAA, 0x4B, 0xD4, 0x17, 0x8D, 0x07]),
bytes([0xC1, 0x15, 0xEB, 0x3B, 0xD0, 0xAF, 0xE3, 0xEA,
0xB0, 0x84, 0x68, 0xCF, 0xC5, 0x90, 0xCF, 0x27,
0x0C, 0x17, 0x38, 0xAC, 0x80, 0x0A, 0x11, 0xBD,
0x77, 0xB9, 0x7F, 0x95, 0xF1, 0xC6, 0x72, 0xC6]),
bytes([0x77, 0x95, 0xF9, 0x30, 0x58, 0x10, 0x33, 0xC1,
0x7B, 0x65, 0xFF, 0xB5, 0x76, 0xAB, 0x41, 0xE6,
0xE1, 0x2A, 0xE9, 0xEF, 0xAF, 0x93, 0xE3, 0xD9,
0x83, 0x3F, 0x7E, 0xF1, 0x1A, 0x1A, 0x2E, 0xB2]),
bytes([0x04, 0xBF, 0x7D, 0x84, 0x2C, 0xCD, 0x7A, 0x43,
0x64, 0x7C, 0xB6, 0x8C, 0xB7, 0x03, 0xDB, 0x81,
0xAE, 0x04, 0xE5, 0xEE, 0x2F, 0x6B, 0x13, 0x74,
0x00, 0x2C, 0x8E, 0xE7, 0x97, 0x17, 0x3A, 0x12]),
bytes([0xDC, 0xF2, 0xA1, 0xAA, 0xA9, 0xE1, 0x14, 0xF9,
0x3A, 0x55, 0xE1, 0xF2, 0x75, 0xB9, 0xC2, 0x37,
0xA9, 0x6C, 0x36, 0x2D, 0x47, 0xBC, 0xFF, 0x22,
0x2C, 0xFC, 0xDF, 0x83, 0x73, 0x09, 0x5D, 0x8A]),
bytes([0x55, 0x5C, 0xDA, 0x71, 0x22, 0x0B, 0x66, 0x54,
0xF9, 0x95, 0x73, 0xC4, 0xF4, 0x75, 0xC7, 0x9E,
0x43, 0xFB, 0x41, 0xFD, 0xC2, 0x25, 0xB5, 0xA7,
0xD4, 0x07, 0xAC, 0xBF, 0xBF, 0x88, 0xBB, 0x79]),
bytes([0xCE, 0x7E, 0x1C, 0xA5, 0x43, 0x9C, 0xFF, 0x25,
0x65, 0xC2, 0x31, 0x22, 0x40, 0x07, 0xCF, 0x00,
0xA3, 0x6B, 0x86, 0x6F, 0xB8, 0x48, 0x8B, 0x11,
0xA5, 0xAC, 0x19, 0x69, 0x8C, 0x8D, 0x66, 0xC5]),
bytes([0xA2, 0xDF, 0x74, 0x94, 0xA6, 0x1E, 0x73, 0x14,
0xB1, 0xD3, 0x4F, 0xDD, 0x1A, 0xF8, 0xF1, 0x4F,
0x01, 0x66, 0x1A, 0x63, 0xF7, 0x15, 0xDD, 0x05,
0x6C, 0xD6, 0xE8, 0xC8, 0xBD, 0xDD, 0xB7, 0x30]),
bytes([0x6F, 0x1B, 0xDD, 0xF8, 0xF0, 0x87, 0x2E, 0xE8,
0x25, 0x1D, 0x7A, 0x7E, 0x95, 0x6D, 0xA8, 0x9A,
0x26, 0x4F, 0xCE, 0x8D, 0x0D, 0x38, 0xFB, 0x11,
0x96, 0x90, 0x56, 0x7E, 0x6F, 0x47, 0x43, 0x80]),
bytes([0x71, 0xCD, 0x2A, 0xDB, 0x3A, 0x0A, 0x29, 0xD1,
0xC2, 0xD9, 0x33, 0x64, 0xDC, 0x6D, 0x82, 0x5A,
0x8F, 0x69, 0x99, 0x88, 0xBF, 0x9E, 0xBA, 0xC5,
0x97, 0x13, 0xA4, 0xD1, 0x3D, 0xCB, 0x85, 0x34]),
bytes([0xAC, 0xAA, 0x9F, 0x1D, 0xD7, 0xE4, 0xC0, 0x59,
0xC7, 0xD6, 0xC4, 0xAE, 0xB7, 0x1F, 0x87, 0x52,
0xDB, 0x7E, 0xB2, 0xED, 0x93, 0xB2, 0x11, 0x73,
0x3B, 0x94, 0x45, 0xCB, 0xF2, 0xE3, 0xD8, 0xF7]),
bytes([0xFA, 0x3F, 0x55, 0x92, 0x6F, 0xDA, 0x24, 0x2A,
0xE5, 0x20, 0x00, 0x63, 0xCA, 0xAC, 0x73, 0x66,
0x65, 0x81, 0xE5, 0x9D, 0x2C, 0xEB, 0xF5, 0xBB,
0xA9, 0x2E, 0x8B, 0xA4, 0x55, 0x4F, 0xE4, 0x70]),
bytes([0x45, 0xE9, 0xA6, 0x9E, 0x95, 0x1A, 0x21, 0x31,
0xF2, 0xE0, 0x27, 0xE1, 0xC7, 0xE8, 0xC9, 0xE2,
0xFE, 0x05, 0x7C, 0x7A, 0x10, 0x82, 0x29, 0xA5,
0x22, 0x5E, 0xD0, 0x21, 0xCA, 0x89, 0xC6, 0xEB]),
bytes([0xAD, 0x62, 0xAB, 0x67, 0x46, 0x05, 0x20, 0x7E,
0x82, 0xFF, 0x9D, 0xD9, 0x6F, 0x47, 0xF2, 0x53,
0x46, 0x9D, 0x08, 0x44, 0xB4, 0x73, 0x35, 0x5A,
0x2A, 0xF4, 0x54, 0xCD, 0xAE, 0x6A, 0xA2, 0x97]),
bytes([0xD1, 0x1D, 0x65, 0xF6, 0x64, 0x68, 0x3E, 0x3E,
0xC5, 0x10, 0x9D, 0x24, 0x06, 0xD4, 0xCC, 0x8F,
0x63, 0x06, 0xF4, 0xD7, 0x22, 0x0C, 0x44, 0xEB,
0xDE, 0x0E, 0x6C, 0xDA, 0xA5, 0x04, 0xDE, 0x13]),
bytes([0x63, 0x2F, 0x27, 0x19, 0xBE, 0x41, 0x2B, 0xA6,
0xA8, 0x60, 0xDF, 0x7D, 0x08, 0xE6, 0x6B, 0x82,
0xC3, 0xD0, 0xE3, 0x30, 0x3D, 0xEF, 0x0E, 0x43,
0x1F, 0x64, 0xDF, 0xB7, 0xBA, 0xA7, 0x0A, 0x3D]),
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