diff options
Diffstat (limited to 'bip-0340/reference.py')
| -rw-r--r-- | bip-0340/reference.py | 186 |
1 files changed, 128 insertions, 58 deletions
diff --git a/bip-0340/reference.py b/bip-0340/reference.py index f2a944f..f24963c 100644 --- a/bip-0340/reference.py +++ b/bip-0340/reference.py @@ -1,6 +1,16 @@ +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 @@ -8,50 +18,55 @@ n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 # 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, msg): +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_infinity(P): +def is_infinity(P: Optional[Point]) -> bool: return P is None -def x(P): +def x(P: Point) -> int: return P[0] -def y(P): +def y(P: Point) -> int: return P[1] -def point_add(P1, P2): - if (P1 is None): +def point_add(P1: Optional[Point], P2: Optional[Point]) -> Optional[Point]: + if P1 is None: return P2 - if (P2 is None): + if P2 is None: return P1 - if (x(P1) == x(P2) and y(P1) != y(P2)): + if (x(P1) == x(P2)) and (y(P1) != y(P2)): return None - if (P1 == P2): + 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, n): +def point_mul(P: Optional[Point], n: int) -> Optional[Point]: R = None for i in range(256): - if ((n >> i) & 1): + if (n >> i) & 1: R = point_add(R, P) P = point_add(P, P) return R -def bytes_from_int(x): +def bytes_from_int(x: int) -> bytes: return x.to_bytes(32, byteorder="big") -def bytes_from_point(P): +def bytes_from_point(P: Point) -> bytes: return bytes_from_int(x(P)) -def point_from_bytes(b): +def xor_bytes(b0: bytes, b1: bytes) -> bytes: + return bytes(x ^ y for (x, y) in zip(b0, b1)) + +def lift_x_square_y(b: bytes) -> Optional[Point]: x = int_from_bytes(b) if x >= p: return None @@ -59,94 +74,125 @@ def point_from_bytes(b): y = pow(y_sq, (p + 1) // 4, p) if pow(y, 2, p) != y_sq: return None - return [x, y] + return (x, y) + +def lift_x_even_y(b: bytes) -> Optional[Point]: + P = lift_x_square_y(b) + if P is None: + return None + else: + return (x(P), y(P) if y(P) % 2 == 0 else p - y(P)) -def int_from_bytes(b): +def int_from_bytes(b: bytes) -> int: return int.from_bytes(b, byteorder="big") -def hash_sha256(b): +def hash_sha256(b: bytes) -> bytes: return hashlib.sha256(b).digest() -def is_square(x): - return pow(x, (p - 1) // 2, p) == 1 +def is_square(x: int) -> bool: + return int(pow(x, (p - 1) // 2, p)) == 1 -def has_square_y(P): - return not is_infinity(P) and is_square(y(P)) +def has_square_y(P: Optional[Point]) -> bool: + infinity = is_infinity(P) + if infinity: return False + assert P is not None + return is_square(y(P)) -def pubkey_gen(seckey): - x = int_from_bytes(seckey) - if not (1 <= x <= n - 1): +def has_even_y(P: Point) -> bool: + 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, x) + P = point_mul(G, d0) + assert P is not None return bytes_from_point(P) -def schnorr_sign(msg, seckey0): +def schnorr_sign(msg: bytes, seckey: bytes, aux_rand: bytes) -> bytes: if len(msg) != 32: raise ValueError('The message must be a 32-byte array.') - seckey0 = int_from_bytes(seckey0) - if not (1 <= seckey0 <= n - 1): + 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, seckey0) - seckey = seckey0 if has_square_y(P) else n - seckey0 - k0 = int_from_bytes(tagged_hash("BIPSchnorrDerive", bytes_from_int(seckey) + msg)) % n + 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("BIP340/aux", aux_rand)) + k0 = int_from_bytes(tagged_hash("BIP340/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_square_y(R) else k0 - e = int_from_bytes(tagged_hash("BIPSchnorr", bytes_from_point(R) + bytes_from_point(P) + msg)) % n - return bytes_from_point(R) + bytes_from_int((k + e * seckey) % n) - -def schnorr_verify(msg, pubkey, sig): + e = int_from_bytes(tagged_hash("BIP340/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(msg) != 32: raise ValueError('The message must be a 32-byte array.') 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 = point_from_bytes(pubkey) - if (P is None): - return False + P = lift_x_even_y(pubkey) r = int_from_bytes(sig[0:32]) s = int_from_bytes(sig[32:64]) - if (r >= p or s >= n): + if (P is None) or (r >= p) or (s >= n): + debug_print_vars() return False - e = int_from_bytes(tagged_hash("BIPSchnorr", sig[0:32] + pubkey + msg)) % n + e = int_from_bytes(tagged_hash("BIP340/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_square_y(R) or x(R) != r: + if (R is None) or (not has_square_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(): +def test_vectors() -> bool: all_passed = True - with open('test-vectors.csv', newline='') as csvfile: + 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, pubkey, msg, sig, result, comment) = row - pubkey = bytes.fromhex(pubkey) - msg = bytes.fromhex(msg) - sig = bytes.fromhex(sig) - result = result == 'TRUE' - print('\nTest vector #%-3i: ' % int(index)) - if seckey != '': - seckey = bytes.fromhex(seckey) + (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()) - sig_actual = schnorr_sign(msg, seckey) - 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()) + 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: @@ -165,5 +211,29 @@ def test_vectors(): 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() |