diff options
Diffstat (limited to 'bip-schnorr')
-rw-r--r-- | bip-schnorr/reference.py | 169 | ||||
-rw-r--r-- | bip-schnorr/test-vectors.csv | 16 | ||||
-rw-r--r-- | bip-schnorr/test-vectors.py | 241 |
3 files changed, 0 insertions, 426 deletions
diff --git a/bip-schnorr/reference.py b/bip-schnorr/reference.py deleted file mode 100644 index f2a944f..0000000 --- a/bip-schnorr/reference.py +++ /dev/null @@ -1,169 +0,0 @@ -import hashlib -import binascii - -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) - -# 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): - 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] - -def y(P): - return P[1] - -def point_add(P1, P2): - 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, n): - 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): - return x.to_bytes(32, byteorder="big") - -def bytes_from_point(P): - return bytes_from_int(x(P)) - -def point_from_bytes(b): - x = int_from_bytes(b) - 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] - -def int_from_bytes(b): - return int.from_bytes(b, byteorder="big") - -def hash_sha256(b): - return hashlib.sha256(b).digest() - -def is_square(x): - return pow(x, (p - 1) // 2, p) == 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) - if not (1 <= x <= n - 1): - raise ValueError('The secret key must be an integer in the range 1..n-1.') - P = point_mul(G, x) - return bytes_from_point(P) - -def schnorr_sign(msg, seckey0): - 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): - 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 k0 == 0: - raise RuntimeError('Failure. This happens only with negligible probability.') - R = point_mul(G, 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) - -def schnorr_verify(msg, pubkey, sig): - 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 - r = int_from_bytes(sig[0:32]) - s = int_from_bytes(sig[32:64]) - if (r >= p or s >= n): - 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 has_square_y(R) or x(R) != r: - return False - return True - -# -# The following code is only used to verify the test vectors. -# -import csv - -def test_vectors(): - all_passed = True - with open('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) - 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()) - 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 - -if __name__ == '__main__': - test_vectors() diff --git a/bip-schnorr/test-vectors.csv b/bip-schnorr/test-vectors.csv deleted file mode 100644 index 3970803..0000000 --- a/bip-schnorr/test-vectors.csv +++ /dev/null @@ -1,16 +0,0 @@ -index,secret key,public key,message,signature,verification result,comment
-0,0000000000000000000000000000000000000000000000000000000000000001,79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,0000000000000000000000000000000000000000000000000000000000000000,528F745793E8472C0329742A463F59E58F3A3F1A4AC09C28F6F8514D4D0322A258BD08398F82CF67B812AB2C7717CE566F877C2F8795C846146978E8F04782AE,TRUE,
-1,B7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,667C2F778E0616E611BD0C14B8A600C5884551701A949EF0EBFD72D452D64E844160BCFC3F466ECB8FACD19ADE57D8699D74E7207D78C6AEDC3799B52A8E0598,TRUE,
-2,C90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C9,DD308AFEC5777E13121FA72B9CC1B7CC0139715309B086C960E18FD969774EB8,5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C,2D941B38E32624BF0AC7669C0971B990994AF6F9B18426BF4F4E7EC10E6CDF386CF646C6DDAFCFA7F1993EEB2E4D66416AEAD1DDAE2F22D63CAD901412D116C6,TRUE,
-3,0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710,25D1DFF95105F5253C4022F628A996AD3A0D95FBF21D468A1B33F8C160D8F517,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,8BD2C11604B0A87A443FCC2E5D90E5328F934161B18864FB48CE10CB59B45FB9B5B2A0F129BD88F5BDC05D5C21E5C57176B913002335784F9777A24BD317CD36,TRUE,test fails if msg is reduced modulo p or n
-4,,D69C3509BB99E412E68B0FE8544E72837DFA30746D8BE2AA65975F29D22DC7B9,4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703,00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C63EE374AC7FAE927D334CCB190F6FB8FD27A2DDC639CCEE46D43F113A4035A2C7F,TRUE,
-5,,EEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,667C2F778E0616E611BD0C14B8A600C5884551701A949EF0EBFD72D452D64E844160BCFC3F466ECB8FACD19ADE57D8699D74E7207D78C6AEDC3799B52A8E0598,FALSE,public key not on the curve
-6,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9935554D1AA5F0374E5CDAACB3925035C7C169B27C4426DF0A6B19AF3BAEAB138,FALSE,has_square_y(R) is false
-7,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,10AC49A6A2EBF604189C5F40FC75AF2D42D77DE9A2782709B1EB4EAF1CFE9108D7003B703A3499D5E29529D39BA040A44955127140F81A8A89A96F992AC0FE79,FALSE,negated message
-8,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,667C2F778E0616E611BD0C14B8A600C5884551701A949EF0EBFD72D452D64E84BE9F4303C0B9913470532E6521A827951D39F5C631CFD98CE39AC4D7A5A83BA9,FALSE,negated s value
-9,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,000000000000000000000000000000000000000000000000000000000000000099D2F0EBC2996808208633CD9926BF7EC3DAB73DAAD36E85B3040A698E6D1CE0,FALSE,sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 0
-10,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,000000000000000000000000000000000000000000000000000000000000000124E81D89F01304695CE943F7D5EBD00EF726A0864B4FF33895B4E86BEADC5456,FALSE,sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 1
-11,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D4160BCFC3F466ECB8FACD19ADE57D8699D74E7207D78C6AEDC3799B52A8E0598,FALSE,sig[0:32] is not an X coordinate on the curve
-12,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F4160BCFC3F466ECB8FACD19ADE57D8699D74E7207D78C6AEDC3799B52A8E0598,FALSE,sig[0:32] is equal to field size
-13,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,667C2F778E0616E611BD0C14B8A600C5884551701A949EF0EBFD72D452D64E84FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,FALSE,sig[32:64] is equal to curve order
-14,,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC30,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,667C2F778E0616E611BD0C14B8A600C5884551701A949EF0EBFD72D452D64E844160BCFC3F466ECB8FACD19ADE57D8699D74E7207D78C6AEDC3799B52A8E0598,FALSE,public key is not a valid X coordinate because it exceeds the field size
diff --git a/bip-schnorr/test-vectors.py b/bip-schnorr/test-vectors.py deleted file mode 100644 index 195b61b..0000000 --- a/bip-schnorr/test-vectors.py +++ /dev/null @@ -1,241 +0,0 @@ -import sys -from reference import * - -def vector0(): - seckey = bytes_from_int(1) - msg = bytes_from_int(0) - sig = schnorr_sign(msg, seckey) - pubkey = pubkey_gen(seckey) - - # The point reconstructed from the public key has an even Y coordinate. - pubkey_point = point_from_bytes(pubkey) - assert(pubkey_point[1] & 1 == 0) - - return (seckey, pubkey, msg, sig, "TRUE", None) - -def vector1(): - seckey = bytes_from_int(0xB7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF) - msg = bytes_from_int(0x243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89) - sig = schnorr_sign(msg, seckey) - pubkey = pubkey_gen(seckey) - - # The point reconstructed from the public key has an odd Y coordinate. - pubkey_point = point_from_bytes(pubkey) - assert(pubkey_point[1] & 1 == 1) - - return (seckey, pubkey, msg, sig, "TRUE", None) - -def vector2(): - seckey = bytes_from_int(0xC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C9) - msg = bytes_from_int(0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C) - sig = schnorr_sign(msg, seckey) - - # 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(not is_square(R[0])) - - return (seckey, pubkey_gen(seckey), msg, sig, "TRUE", None) - -def vector3(): - seckey = bytes_from_int(0x0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710) - msg = bytes_from_int(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF) - sig = schnorr_sign(msg, seckey) - return (seckey, pubkey_gen(seckey), msg, sig, "TRUE", "test fails if msg is reduced modulo p or n") - -# Signs with a given nonce. This can be INSECURE and is only INTENDED FOR -# GENERATING TEST VECTORS. Results in an invalid signature if y(kG) is not -# square. -def insecure_schnorr_sign_fixed_nonce(msg, seckey0, k): - 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): - 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 - 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) - -# Creates a singature with a small x(R) by using k = 1/2 -def vector4(): - one_half = 0x7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0 - seckey = bytes_from_int(0x763758E5CBEEDEE4F7D3FC86F531C36578933228998226672F13C4F0EBE855EB) - msg = bytes_from_int(0x4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703) - sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, one_half) - return (None, pubkey_gen(seckey), msg, sig, "TRUE", None) - -default_seckey = bytes_from_int(0xB7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF) -default_msg = bytes_from_int(0x243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89) - -# Public key is not on the curve -def vector5(): - # This creates a dummy signature that doesn't have anything to do with the - # public key. - seckey = default_seckey - msg = default_msg - sig = schnorr_sign(msg, seckey) - - pubkey = bytes_from_int(0xEEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34) - assert(point_from_bytes(pubkey) is None) - - return (None, pubkey, msg, sig, "FALSE", "public key not on the curve") - -def vector6(): - seckey = default_seckey - msg = default_msg - k = 3 - sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, k) - - # Y coordinate of R is not a square - R = point_mul(G, k) - assert(not has_square_y(R)) - - return (None, pubkey_gen(seckey), msg, sig, "FALSE", "has_square_y(R) is false") - -def vector7(): - seckey = default_seckey - msg = int_from_bytes(default_msg) - neg_msg = bytes_from_int(n - msg) - sig = schnorr_sign(neg_msg, seckey) - return (None, pubkey_gen(seckey), bytes_from_int(msg), sig, "FALSE", "negated message") - -def vector8(): - seckey = default_seckey - msg = default_msg - sig = schnorr_sign(msg, seckey) - sig = sig[0:32] + bytes_from_int(n - int_from_bytes(sig[32:64])) - return (None, pubkey_gen(seckey), msg, sig, "FALSE", "negated s value") - -def bytes_from_point_inf0(P): - if P == None: - return bytes_from_int(0) - return bytes_from_int(P[0]) - -def vector9(): - seckey = default_seckey - msg = default_msg - - # Override bytes_from_point in schnorr_sign to allow creating a signature - # with k = 0. - k = 0 - bytes_from_point_tmp = bytes_from_point.__code__ - bytes_from_point.__code__ = bytes_from_point_inf0.__code__ - sig = insecure_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 has_square_y(inf) is defined as true and x(inf) as 0") - -def bytes_from_point_inf1(P): - if P == None: - return bytes_from_int(1) - return bytes_from_int(P[0]) - -def vector10(): - seckey = default_seckey - msg = default_msg - - # Override bytes_from_point in schnorr_sign to allow creating a signature - # with k = 0. - k = 0 - bytes_from_point_tmp = bytes_from_point.__code__ - bytes_from_point.__code__ = bytes_from_point_inf1.__code__ - sig = insecure_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 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 -# coordinate on the curve. This test vector just increases test coverage. -def vector11(): - seckey = default_seckey - msg = default_msg - sig = schnorr_sign(msg, seckey) - - # Replace R's X coordinate with an X coordinate that's not on the curve - x_not_on_curve = bytes_from_int(0x4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D) - assert(point_from_bytes(x_not_on_curve) is None) - sig = x_not_on_curve + sig[32:64] - - return (None, pubkey_gen(seckey), msg, sig, "FALSE", "sig[0:32] is not an X coordinate on the curve") - -# 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 smaller -# than the field size. This test vector just increases test coverage. -def vector12(): - seckey = default_seckey - msg = default_msg - sig = schnorr_sign(msg, seckey) - - # Replace R's X coordinate with an X coordinate that's equal to field size - sig = bytes_from_int(p) + sig[32:64] - - return (None, pubkey_gen(seckey), msg, sig, "FALSE", "sig[0:32] is equal to field size") - -# It's cryptographically impossible to create a test vector that fails if run -# in an implementation which merely misses the check that sig[32:64] is smaller -# than the curve order. This test vector just increases test coverage. -def vector13(): - seckey = default_seckey - msg = default_msg - sig = schnorr_sign(msg, seckey) - - # Replace s with a number that's equal to the curve order - sig = sig[0:32] + bytes_from_int(n) - - return (None, pubkey_gen(seckey), msg, sig, "FALSE", "sig[32:64] is equal to curve order") - -# Test out of range pubkey -# It's cryptographically impossible to create a test vector that fails if run -# in an implementation which accepts out of range pubkeys because we can't find -# a secret key for such a public key and therefore can not create a signature. -# This test vector just increases test coverage. -def vector14(): - # This creates a dummy signature that doesn't have anything to do with the - # public key. - seckey = default_seckey - msg = default_msg - sig = schnorr_sign(msg, seckey) - - pubkey_int = p + 1 - pubkey = bytes_from_int(pubkey_int) - assert(point_from_bytes(pubkey) is None) - # If an implementation would reduce a given public key modulo p then the - # pubkey would be valid - assert(point_from_bytes(bytes_from_int(pubkey_int % p)) is not None) - - return (None, pubkey, msg, sig, "FALSE", "public key is not a valid X coordinate because it exceeds the field size") - -vectors = [ - vector0(), - vector1(), - vector2(), - vector3(), - vector4(), - vector5(), - vector6(), - vector7(), - vector8(), - vector9(), - vector10(), - vector11(), - vector12(), - vector13(), - vector14() - ] - -# Converts the byte strings of a test vector into hex strings -def bytes_to_hex(seckey, pubkey, msg, sig, result, comment): - return (seckey.hex().upper() if seckey is not None else None, pubkey.hex().upper(), msg.hex().upper(), sig.hex().upper(), result, comment) - -vectors = list(map(lambda vector: bytes_to_hex(vector[0], vector[1], vector[2], vector[3], vector[4], vector[5]), vectors)) - -def print_csv(vectors): - writer = csv.writer(sys.stdout) - writer.writerow(("index", "secret key", "public key", "message", "signature", "verification result", "comment")) - for (i,v) in enumerate(vectors): - writer.writerow((i,)+v) - -print_csv(vectors) |