from typing import Tuple, Optional, Any
import hashlib
import binascii
# Set DEBUG to True to get a detailed debug output including
# intermediate values during key generation, signing, and
# verification. This is implemented via calls to the
# debug_print_vars() function.
#
# If you want to print values on an individual basis, use
# the pretty() function, e.g., print(pretty(foo)).
DEBUG = False
p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
# Points are tuples of X and Y coordinates and the point at infinity is
# represented by the None keyword.
G = (0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798, 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8)
Point = Tuple[int, int]
# This implementation can be sped up by storing the midstate after hashing
# tag_hash instead of rehashing it all the time.
def tagged_hash(tag: str, msg: bytes) -> bytes:
tag_hash = hashlib.sha256(tag.encode()).digest()
return hashlib.sha256(tag_hash + tag_hash + msg).digest()
def is_infinite(P: Optional[Point]) -> bool:
return P is None
def x(P: Point) -> int:
assert not is_infinite(P)
return P[0]
def y(P: Point) -> int:
assert not is_infinite(P)
return P[1]
def point_add(P1: Optional[Point], P2: Optional[Point]) -> Optional[Point]:
if P1 is None:
return P2
if P2 is None:
return P1
if (x(P1) == x(P2)) and (y(P1) != y(P2)):
return None
if P1 == P2:
lam = (3 * x(P1) * x(P1) * pow(2 * y(P1), p - 2, p)) % p
else:
lam = ((y(P2) - y(P1)) * pow(x(P2) - x(P1), p - 2, p)) % p
x3 = (lam * lam - x(P1) - x(P2)) % p
return (x3, (lam * (x(P1) - x3) - y(P1)) % p)
def point_mul(P: Optional[Point], n: int) -> Optional[Point]:
R = None
for i in range(256):
if (n >> i) & 1:
R = point_add(R, P)
P = point_add(P, P)
return R
def bytes_from_int(x: int) -> bytes:
return x.to_bytes(32, byteorder="big")
def bytes_from_point(P: Point) -> bytes:
return bytes_from_int(x(P))
def xor_bytes(b0: bytes, b1: bytes) -> bytes:
return bytes(x ^ y for (x, y) in zip(b0, b1))
def lift_x(x: int) -> Optional[Point]:
if x >= p:
return None
y_sq = (pow(x, 3, p) + 7) % p
y = pow(y_sq, (p + 1) // 4, p)
if pow(y, 2, p) != y_sq:
return None
return (x, y if y & 1 == 0 else p-y)
def int_from_bytes(b: bytes) -> int:
return int.from_bytes(b, byteorder="big")
def hash_sha256(b: bytes) -> bytes:
return hashlib.sha256(b).digest()
def has_even_y(P: Point) -> bool:
assert not is_infinite(P)
return y(P) % 2 == 0
def pubkey_gen(seckey: bytes) -> bytes:
d0 = int_from_bytes(seckey)
if not (1 <= d0 <= n - 1):
raise ValueError('The secret key must be an integer in the range 1..n-1.')
P = point_mul(G, d0)
assert P is not None
return bytes_from_point(P)
def schnorr_sign(msg: bytes, seckey: bytes, aux_rand: bytes) -> bytes:
d0 = int_from_bytes(seckey)
if not (1 <= d0 <= n - 1):
raise ValueError('The secret key must be an integer in the range 1..n-1.')
if len(aux_rand) != 32:
raise ValueError('aux_rand must be 32 bytes instead of %i.' % len(aux_rand))
P = point_mul(G, d0)
assert P is not None
d = d0 if has_even_y(P) else n - d0
t = xor_bytes(bytes_from_int(d), tagged_hash("BIP0340/aux", aux_rand))
k0 = int_from_bytes(tagged_hash("BIP0340/nonce", t + bytes_from_point(P) + msg)) % n
if k0 == 0:
raise RuntimeError('Failure. This happens only with negligible probability.')
R = point_mul(G, k0)
assert R is not None
k = n - k0 if not has_even_y(R) else k0
e = int_from_bytes(tagged_hash("BIP0340/challenge", bytes_from_point(R) + bytes_from_point(P) + msg)) % n
sig = bytes_from_point(R) + bytes_from_int((k + e * d) % n)
debug_print_vars()
if not schnorr_verify(msg, bytes_from_point(P), sig):
raise RuntimeError('The created signature does not pass verification.')
return sig
def schnorr_verify(msg: bytes, pubkey: bytes, sig: bytes) -> bool:
if len(pubkey) != 32:
raise ValueError('The public key must be a 32-byte array.')
if len(sig) != 64:
raise ValueError('The signature must be a 64-byte array.')
P = lift_x(int_from_bytes(pubkey))
r = int_from_bytes(sig[0:32])
s = int_from_bytes(sig[32:64])
if (P is None) or (r >= p) or (s >= n):
debug_print_vars()
return False
e = int_from_bytes(tagged_hash("BIP0340/challenge", sig[0:32] + pubkey + msg)) % n
R = point_add(point_mul(G, s), point_mul(P, n - e))
if (R is None) or (not has_even_y(R)) or (x(R) != r):
debug_print_vars()
return False
debug_print_vars()
return True
#
# The following code is only used to verify the test vectors.
#
import csv
import os
import sys
def test_vectors() -> bool:
all_passed = True
with open(os.path.join(sys.path[0], 'test-vectors.csv'), newline='') as csvfile:
reader = csv.reader(csvfile)
reader.__next__()
for row in reader:
(index, seckey_hex, pubkey_hex, aux_rand_hex, msg_hex, sig_hex, result_str, comment) = row
pubkey = bytes.fromhex(pubkey_hex)
msg = bytes.fromhex(msg_hex)
sig = bytes.fromhex(sig_hex)
result = result_str == 'TRUE'
print('\nTest vector', ('#' + index).rjust(3, ' ') + ':')
if seckey_hex != '':
seckey = bytes.fromhex(seckey_hex)
pubkey_actual = pubkey_gen(seckey)
if pubkey != pubkey_actual:
print(' * Failed key generation.')
print(' Expected key:', pubkey.hex().upper())
print(' Actual key:', pubkey_actual.hex().upper())
aux_rand = bytes.fromhex(aux_rand_hex)
try:
sig_actual = schnorr_sign(msg, seckey, aux_rand)
if sig == sig_actual:
print(' * Passed signing test.')
else:
print(' * Failed signing test.')
print(' Expected signature:', sig.hex().upper())
print(' Actual signature:', sig_actual.hex().upper())
all_passed = False
except RuntimeError as e:
print(' * Signing test raised exception:', e)
all_passed = False
result_actual = schnorr_verify(msg, pubkey, sig)
if result == result_actual:
print(' * Passed verification test.')
else:
print(' * Failed verification test.')
print(' Expected verification result:', result)
print(' Actual verification result:', result_actual)
if comment:
print(' Comment:', comment)
all_passed = False
print()
if all_passed:
print('All test vectors passed.')
else:
print('Some test vectors failed.')
return all_passed
#
# The following code is only used for debugging
#
import inspect
def pretty(v: Any) -> Any:
if isinstance(v, bytes):
return '0x' + v.hex()
if isinstance(v, int):
return pretty(bytes_from_int(v))
if isinstance(v, tuple):
return tuple(map(pretty, v))
return v
def debug_print_vars() -> None:
if DEBUG:
current_frame = inspect.currentframe()
assert current_frame is not None
frame = current_frame.f_back
assert frame is not None
print(' Variables in function ', frame.f_code.co_name, ' at line ', frame.f_lineno, ':', sep='')
for var_name, var_val in frame.f_locals.items():
print(' ' + var_name.rjust(11, ' '), '==', pretty(var_val))
if __name__ == '__main__':
test_vectors()