diff options
Diffstat (limited to 'bip-schnorr')
| -rw-r--r-- | bip-schnorr/reference.py | 17 | ||||
| -rw-r--r-- | bip-schnorr/test-vectors.py | 19 |
2 files changed, 19 insertions, 17 deletions
diff --git a/bip-schnorr/reference.py b/bip-schnorr/reference.py index e5d9557..7de37c2 100644 --- a/bip-schnorr/reference.py +++ b/bip-schnorr/reference.py @@ -11,6 +11,9 @@ def tagged_hash(tag, msg): tag_hash = hashlib.sha256(tag.encode()).digest() return hashlib.sha256(tag_hash + tag_hash + msg).digest() +def is_infinity(P): + return P is None + def x(P): return P[0] @@ -59,11 +62,11 @@ def int_from_bytes(b): def hash_sha256(b): return hashlib.sha256(b).digest() -def jacobi(x): - return pow(x, (p - 1) // 2, p) +def is_square(x): + return pow(x, (p - 1) // 2, p) == 1 -def is_quad(x): - return jacobi(x) == 1 +def has_square_y(P): + return not is_infinity(P) and is_square(y(P)) def pubkey_gen(seckey): x = int_from_bytes(seckey) @@ -79,12 +82,12 @@ def schnorr_sign(msg, seckey0): if not (1 <= seckey0 <= 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 is_quad(y(P)) else n - 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 k0 == 0: raise RuntimeError('Failure. This happens only with negligible probability.') R = point_mul(G, k0) - k = n - k0 if not is_quad(y(R)) else k0 + 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) @@ -104,7 +107,7 @@ def schnorr_verify(msg, pubkey, sig): return False e = int_from_bytes(tagged_hash("BIPSchnorr", sig[0:32] + pubkey + msg)) % n R = point_add(point_mul(G, s), point_mul(P, n - e)) - if R is None or not is_quad(y(R)) or x(R) != r: + if R is None or not has_square_y(R) or x(R) != r: return False return True diff --git a/bip-schnorr/test-vectors.py b/bip-schnorr/test-vectors.py index 52e3b05..768d9f1 100644 --- a/bip-schnorr/test-vectors.py +++ b/bip-schnorr/test-vectors.py @@ -30,10 +30,10 @@ def vector2(): msg = bytes_from_int(0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C) sig = schnorr_sign(msg, seckey) - # This singature vector would not verify if the implementer checked the - # jacobi symbol of the X coordinate of R instead of the Y coordinate. + # This signature vector would not verify if the implementer checked the + # squareness of the X coordinate of R instead of the Y coordinate. R = point_from_bytes(sig[0:32]) - assert(jacobi(R[0]) != 1) + assert(not is_square(R[0])) return (bytes_from_int(seckey), pubkey_gen(seckey), msg, sig, "TRUE", None) @@ -43,15 +43,14 @@ def vector3(): sig = schnorr_sign(msg, seckey) return (bytes_from_int(seckey), pubkey_gen(seckey), msg, sig, "TRUE", "test fails if msg is reduced modulo p or n") -# Signs with a given nonce. Results in an invalid signature if y(kG) is not a -# quadratic residue. +# Signs with a given nonce. Results in an invalid signature if y(kG) is not a square def schnorr_sign_fixed_nonce(msg, seckey0, k): if len(msg) != 32: raise ValueError('The message must be a 32-byte array.') if not (1 <= seckey0 <= 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 (jacobi(P[1]) == 1) else n - seckey0 + seckey = seckey0 if has_square_y(P) else n - seckey0 R = point_mul(G, k) 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) @@ -84,9 +83,9 @@ def vector6(): k = 3 sig = schnorr_sign_fixed_nonce(msg, seckey, k) - # Y coordinate of R is not a quadratic residue + # Y coordinate of R is not a square R = point_mul(G, k) - assert(jacobi(R[1]) != 1) + assert(not has_square_y(R)) return (None, pubkey_gen(seckey), msg, sig, "FALSE", "incorrect R residuosity") @@ -121,7 +120,7 @@ def vector9(): sig = schnorr_sign_fixed_nonce(msg, seckey, k) bytes_from_point.__code__ = bytes_from_point_tmp - return (None, pubkey_gen(seckey), msg, sig, "FALSE", "sG - eP is infinite. Test fails in single verification if jacobi(y(inf)) is defined as 1 and x(inf) as 0") + return (None, pubkey_gen(seckey), msg, sig, "FALSE", "sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 0") def bytes_from_point_inf1(P): if P == None: @@ -140,7 +139,7 @@ def vector10(): sig = schnorr_sign_fixed_nonce(msg, seckey, k) bytes_from_point.__code__ = bytes_from_point_tmp - return (None, pubkey_gen(seckey), msg, sig, "FALSE", "sG - eP is infinite. Test fails in single verification if jacobi(y(inf)) is defined as 1 and x(inf) as 1") + return (None, pubkey_gen(seckey), msg, sig, "FALSE", "sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 1") # It's cryptographically impossible to create a test vector that fails if run # in an implementation which merely misses the check that sig[0:32] is an X |