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BIP 340: Use synthetic nonces in reference code and test vectors

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This commit is contained in:
Jonas Nick 2020-02-03 21:56:03 +00:00
parent d41e778ca1
commit b6b5f58e6e
3 changed files with 64 additions and 51 deletions
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15
bip-0340/reference.py
View file

@ -51,6 +51,9 @@ def bytes_from_int(x):
def bytes_from_point(P): def bytes_from_point(P):
return bytes_from_int(x(P)) return bytes_from_int(x(P))
def xor_bytes(b0, b1):
return bytes(x ^ y for (x, y) in zip(b0, b1))
def lift_x_square_y(b): def lift_x_square_y(b):
x = int_from_bytes(b) x = int_from_bytes(b)
if x >= p: if x >= p:
@ -90,15 +93,18 @@ def pubkey_gen(seckey):
P = point_mul(G, x) P = point_mul(G, x)
return bytes_from_point(P) return bytes_from_point(P)
def schnorr_sign(msg, seckey0): def schnorr_sign(msg, seckey0, aux_rand):
if len(msg) != 32: if len(msg) != 32:
raise ValueError('The message must be a 32-byte array.') raise ValueError('The message must be a 32-byte array.')
seckey0 = int_from_bytes(seckey0) seckey0 = int_from_bytes(seckey0)
if not (1 <= seckey0 <= n - 1): if not (1 <= seckey0 <= n - 1):
raise ValueError('The secret key must be an integer in the range 1..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, seckey0) P = point_mul(G, seckey0)
seckey = seckey0 if has_even_y(P) else n - seckey0 seckey = seckey0 if has_even_y(P) else n - seckey0
k0 = int_from_bytes(tagged_hash("BIP340/nonce", bytes_from_int(seckey) + bytes_from_point(P) + msg)) % n t = xor_bytes(bytes_from_int(seckey), tagged_hash("BIP340/aux", aux_rand))
k0 = int_from_bytes(tagged_hash("BIP340/nonce", t + bytes_from_point(P) + msg)) % n
if k0 == 0: if k0 == 0:
raise RuntimeError('Failure. This happens only with negligible probability.') raise RuntimeError('Failure. This happens only with negligible probability.')
R = point_mul(G, k0) R = point_mul(G, k0)
@ -137,7 +143,7 @@ def test_vectors():
reader = csv.reader(csvfile) reader = csv.reader(csvfile)
reader.__next__() reader.__next__()
for row in reader: for row in reader:
(index, seckey, pubkey, msg, sig, result, comment) = row (index, seckey, pubkey, aux_rand, msg, sig, result, comment) = row
pubkey = bytes.fromhex(pubkey) pubkey = bytes.fromhex(pubkey)
msg = bytes.fromhex(msg) msg = bytes.fromhex(msg)
sig = bytes.fromhex(sig) sig = bytes.fromhex(sig)
@ -150,7 +156,8 @@ def test_vectors():
print(' * Failed key generation.') print(' * Failed key generation.')
print(' Expected key:', pubkey.hex().upper()) print(' Expected key:', pubkey.hex().upper())
print(' Actual key:', pubkey_actual.hex().upper()) print(' Actual key:', pubkey_actual.hex().upper())
sig_actual = schnorr_sign(msg, seckey) aux_rand = bytes.fromhex(aux_rand)
sig_actual = schnorr_sign(msg, seckey, aux_rand)
if sig == sig_actual: if sig == sig_actual:
print(' * Passed signing test.') print(' * Passed signing test.')
else: else:

32
bip-0340/test-vectors.csv
View file

@ -1,16 +1,16 @@
index,secret key,public key,message,signature,verification result,comment index,secret key,public key,aux_rand,message,signature,verification result,comment
0,0000000000000000000000000000000000000000000000000000000000000003,F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9,0000000000000000000000000000000000000000000000000000000000000000,514F0E96BB9AD56A245A7F4ED1030D4DE3FB0F5DE285116514292B2F910C979201D5C686A9D968E169C3ED1C2249C81F2BD27D53C42D15FA275EA6445389410A,TRUE, 0,0000000000000000000000000000000000000000000000000000000000000003,F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9,0000000000000000000000000000000000000000000000000000000000000000,0000000000000000000000000000000000000000000000000000000000000000,067E337AD551B2276EC705E43F0920926A9CE08AC68159F9D258C9BBA412781C9F059FCDF4824F13B3D7C1305316F956704BB3FEA2C26142E18ACD90A90C947E,TRUE,
1,B7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,74556372D3369E8C53E6B84B5D7EE9AE0220EB37A6EA5501EF828FBFBA90A864092EF727796DACA51118BE8FBD70B3EC50536E65DB6F3B3B3FE1049862018B02,TRUE, 1,B7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,0000000000000000000000000000000000000000000000000000000000000001,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,0E12B8C520948A776753A96F21ABD7FDC2D7D0C0DDC90851BE17B04E75EF86A47EF0DA46C4DC4D0D1BCB8668C2CE16C54C7C23A6716EDE303AF86774917CF928,TRUE,
2,C90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C9,DD308AFEC5777E13121FA72B9CC1B7CC0139715309B086C960E18FD969774EB8,7E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C,FAD73AE779EDD67BA40772867FEF9F20F151EB4BFDDECC53B90DD3017FC5D6035670DB8C83BA96EAF51C069B2AA7CEEF556787AE897F84F8D822C4ED7115B851,TRUE, 2,C90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C9,DD308AFEC5777E13121FA72B9CC1B7CC0139715309B086C960E18FD969774EB8,C87AA53824B4D7AE2EB035A2B5BBBCCC080E76CDC6D1692C4B0B62D798E6D906,7E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C,FC012F9FB8FE00A358F51EF93DCE0DC0C895F6E9A87C6C4905BC820B0C3677616B8737D14E703AF8E16E22E5B8F26227D41E5128F82D86F747244CC289C74D1D,TRUE,
3,0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710,25D1DFF95105F5253C4022F628A996AD3A0D95FBF21D468A1B33F8C160D8F517,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,60DC1A7E50D2269424060FF66361601075EB4B516DE89BF1D91B1D6AD78900DACDA5AC4B697491430CAA7604C8D819B2150DEC26E8D01E2981DDA071D7556CD3,TRUE,test fails if msg is reduced modulo p or n 3,0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710,25D1DFF95105F5253C4022F628A996AD3A0D95FBF21D468A1B33F8C160D8F517,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,FC132D4E426DFF535AEC0FA7083AC5118BC1D5FFFD848ABD8290C23F271CA0DD11AEDCEA3F55DA9BD677FE29C9DDA0CF878BCE43FDE0E313D69D1AF7A5AE8369,TRUE,test fails if msg is reduced modulo p or n
4,,D69C3509BB99E412E68B0FE8544E72837DFA30746D8BE2AA65975F29D22DC7B9,4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703,00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C630EC50E5363E227ACAC6F542CE1C0B186657E0E0D1A6FFE283A33438DE4738419,TRUE, 4,,D69C3509BB99E412E68B0FE8544E72837DFA30746D8BE2AA65975F29D22DC7B9,,4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703,00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C630EC50E5363E227ACAC6F542CE1C0B186657E0E0D1A6FFE283A33438DE4738419,TRUE,
5,,EEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,74556372D3369E8C53E6B84B5D7EE9AE0220EB37A6EA5501EF828FBFBA90A864092EF727796DACA51118BE8FBD70B3EC50536E65DB6F3B3B3FE1049862018B02,FALSE,public key not on the curve 5,,EEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,7036D6BFE1837AE919631039A2CF652A295DFAC9A8BBB0806014B2F48DD7C807941607B563ABBA414287F374A332BA3636DE009EE1EF551A17796B72B68B8A24,FALSE,public key not on the curve
6,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F995A579DA959FA739FCE39E8BD16FECB5CDCF97060B2C73CDE60E87ABCA1AA5D9,FALSE,has_square_y(R) is false 6,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F995A579DA959FA739FCE39E8BD16FECB5CDCF97060B2C73CDE60E87ABCA1AA5D9,FALSE,has_square_y(R) is false
7,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,0B3E00AF0641F28B4B52F7E7AD3DDEB9BD313F9E382563BA9C9A8274F45D3D72D8F733F2901432C8DD99C739B0C1EE4030E79A94318278EC4E7160A65CDE8015,FALSE,negated message 7,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,F8704654F4687B7365ED32E796DE92761390A3BCC495179BFE073817B7ED32824E76B987F7C1F9A751EF5C343F7645D3CFFC7D570B9A7192EBF1898E1344E3BF,FALSE,negated message
8,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,74556372D3369E8C53E6B84B5D7EE9AE0220EB37A6EA5501EF828FBFBA90A864F6D108D88692535AEEE74170428F4C126A5B6E80D3D965007FF159F46E34B63F,FALSE,negated s value 8,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,7036D6BFE1837AE919631039A2CF652A295DFAC9A8BBB0806014B2F48DD7C8076BE9F84A9C5445BEBD780C8B5CCD45C883D0DC47CD594B21A858F31A19AAB71D,FALSE,negated s value
9,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,00000000000000000000000000000000000000000000000000000000000000009915EE59F07F9DBBAEDC31BFCC9B34AD49DE669CD24773BCED77DDA36D073EC8,FALSE,sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 0 9,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,00000000000000000000000000000000000000000000000000000000000000009915EE59F07F9DBBAEDC31BFCC9B34AD49DE669CD24773BCED77DDA36D073EC8,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,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,0000000000000000000000000000000000000000000000000000000000000001C7EC918B2B9CF34071BB54BED7EB4BB6BAB148E9A7E36E6B228F95DFA08B43EC,FALSE,sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 1 10,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,0000000000000000000000000000000000000000000000000000000000000001C7EC918B2B9CF34071BB54BED7EB4BB6BAB148E9A7E36E6B228F95DFA08B43EC,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,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D092EF727796DACA51118BE8FBD70B3EC50536E65DB6F3B3B3FE1049862018B02,FALSE,sig[0:32] is not an X coordinate on the curve 11,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D941607B563ABBA414287F374A332BA3636DE009EE1EF551A17796B72B68B8A24,FALSE,sig[0:32] is not an X coordinate on the curve
12,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F092EF727796DACA51118BE8FBD70B3EC50536E65DB6F3B3B3FE1049862018B02,FALSE,sig[0:32] is equal to field size 12,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F941607B563ABBA414287F374A332BA3636DE009EE1EF551A17796B72B68B8A24,FALSE,sig[0:32] is equal to field size
13,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,74556372D3369E8C53E6B84B5D7EE9AE0220EB37A6EA5501EF828FBFBA90A864FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,FALSE,sig[32:64] is equal to curve order 13,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,7036D6BFE1837AE919631039A2CF652A295DFAC9A8BBB0806014B2F48DD7C807FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,FALSE,sig[32:64] is equal to curve order
14,,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC30,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,74556372D3369E8C53E6B84B5D7EE9AE0220EB37A6EA5501EF828FBFBA90A864092EF727796DACA51118BE8FBD70B3EC50536E65DB6F3B3B3FE1049862018B02,FALSE,public key is not a valid X coordinate because it exceeds the field size 14,,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC30,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,7036D6BFE1837AE919631039A2CF652A295DFAC9A8BBB0806014B2F48DD7C807941607B563ABBA414287F374A332BA3636DE009EE1EF551A17796B72B68B8A24,FALSE,public key is not a valid X coordinate because it exceeds the field size

1 index secret key public key aux_rand message signature verification result comment
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
5 3 0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710 25D1DFF95105F5253C4022F628A996AD3A0D95FBF21D468A1B33F8C160D8F517 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF 60DC1A7E50D2269424060FF66361601075EB4B516DE89BF1D91B1D6AD78900DACDA5AC4B697491430CAA7604C8D819B2150DEC26E8D01E2981DDA071D7556CD3 FC132D4E426DFF535AEC0FA7083AC5118BC1D5FFFD848ABD8290C23F271CA0DD11AEDCEA3F55DA9BD677FE29C9DDA0CF878BCE43FDE0E313D69D1AF7A5AE8369 TRUE test fails if msg is reduced modulo p or n
6 4 D69C3509BB99E412E68B0FE8544E72837DFA30746D8BE2AA65975F29D22DC7B9 4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703 00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C630EC50E5363E227ACAC6F542CE1C0B186657E0E0D1A6FFE283A33438DE4738419 TRUE
7 5 EEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34 243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89 74556372D3369E8C53E6B84B5D7EE9AE0220EB37A6EA5501EF828FBFBA90A864092EF727796DACA51118BE8FBD70B3EC50536E65DB6F3B3B3FE1049862018B02 7036D6BFE1837AE919631039A2CF652A295DFAC9A8BBB0806014B2F48DD7C807941607B563ABBA414287F374A332BA3636DE009EE1EF551A17796B72B68B8A24 FALSE public key not on the curve
8 6 DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89 F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F995A579DA959FA739FCE39E8BD16FECB5CDCF97060B2C73CDE60E87ABCA1AA5D9 FALSE has_square_y(R) is false
9 7 DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89 0B3E00AF0641F28B4B52F7E7AD3DDEB9BD313F9E382563BA9C9A8274F45D3D72D8F733F2901432C8DD99C739B0C1EE4030E79A94318278EC4E7160A65CDE8015 F8704654F4687B7365ED32E796DE92761390A3BCC495179BFE073817B7ED32824E76B987F7C1F9A751EF5C343F7645D3CFFC7D570B9A7192EBF1898E1344E3BF FALSE negated message
10 8 DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89 74556372D3369E8C53E6B84B5D7EE9AE0220EB37A6EA5501EF828FBFBA90A864F6D108D88692535AEEE74170428F4C126A5B6E80D3D965007FF159F46E34B63F 7036D6BFE1837AE919631039A2CF652A295DFAC9A8BBB0806014B2F48DD7C8076BE9F84A9C5445BEBD780C8B5CCD45C883D0DC47CD594B21A858F31A19AAB71D FALSE negated s value
11 9 DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89 00000000000000000000000000000000000000000000000000000000000000009915EE59F07F9DBBAEDC31BFCC9B34AD49DE669CD24773BCED77DDA36D073EC8 FALSE sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 0
12 10 DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89 0000000000000000000000000000000000000000000000000000000000000001C7EC918B2B9CF34071BB54BED7EB4BB6BAB148E9A7E36E6B228F95DFA08B43EC FALSE sG - eP is infinite. Test fails in single verification if has_square_y(inf) is defined as true and x(inf) as 1
13 11 DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89 4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D092EF727796DACA51118BE8FBD70B3EC50536E65DB6F3B3B3FE1049862018B02 4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D941607B563ABBA414287F374A332BA3636DE009EE1EF551A17796B72B68B8A24 FALSE sig[0:32] is not an X coordinate on the curve
14 12 DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F092EF727796DACA51118BE8FBD70B3EC50536E65DB6F3B3B3FE1049862018B02 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F941607B563ABBA414287F374A332BA3636DE009EE1EF551A17796B72B68B8A24 FALSE sig[0:32] is equal to field size
15 13 DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89 74556372D3369E8C53E6B84B5D7EE9AE0220EB37A6EA5501EF828FBFBA90A864FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 7036D6BFE1837AE919631039A2CF652A295DFAC9A8BBB0806014B2F48DD7C807FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 FALSE sig[32:64] is equal to curve order
16 14 FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC30 243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89 74556372D3369E8C53E6B84B5D7EE9AE0220EB37A6EA5501EF828FBFBA90A864092EF727796DACA51118BE8FBD70B3EC50536E65DB6F3B3B3FE1049862018B02 7036D6BFE1837AE919631039A2CF652A295DFAC9A8BBB0806014B2F48DD7C807941607B563ABBA414287F374A332BA3636DE009EE1EF551A17796B72B68B8A24 FALSE public key is not a valid X coordinate because it exceeds the field size

68
bip-0340/test-vectors.py
View file

@ -4,7 +4,8 @@ from reference import *
def vector0(): def vector0():
seckey = bytes_from_int(3) seckey = bytes_from_int(3)
msg = bytes_from_int(0) msg = bytes_from_int(0)
sig = schnorr_sign(msg, seckey) aux_rand = bytes_from_int(0)
sig = schnorr_sign(msg, seckey, aux_rand)
pubkey = pubkey_gen(seckey) pubkey = pubkey_gen(seckey)
# We should have at least one test vector where the seckey needs to be # We should have at least one test vector where the seckey needs to be
@ -21,18 +22,21 @@ def vector0():
pubkey_point = lift_x_even_y(pubkey) pubkey_point = lift_x_even_y(pubkey)
assert(not has_square_y(pubkey_point)) assert(not has_square_y(pubkey_point))
return (seckey, pubkey, msg, sig, "TRUE", None) return (seckey, pubkey, aux_rand, msg, sig, "TRUE", None)
def vector1(): def vector1():
seckey = bytes_from_int(0xB7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF) seckey = bytes_from_int(0xB7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF)
msg = bytes_from_int(0x243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89) msg = bytes_from_int(0x243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89)
sig = schnorr_sign(msg, seckey) aux_rand = bytes_from_int(1)
return (seckey, pubkey_gen(seckey), msg, sig, "TRUE", None)
sig = schnorr_sign(msg, seckey, aux_rand)
return (seckey, pubkey_gen(seckey), aux_rand, msg, sig, "TRUE", None)
def vector2(): def vector2():
seckey = bytes_from_int(0xC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C9) seckey = bytes_from_int(0xC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C9)
msg = bytes_from_int(0x7E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C) msg = bytes_from_int(0x7E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C)
sig = schnorr_sign(msg, seckey) aux_rand = bytes_from_int(0xC87AA53824B4D7AE2EB035A2B5BBBCCC080E76CDC6D1692C4B0B62D798E6D906)
sig = schnorr_sign(msg, seckey, aux_rand)
# The point reconstructed from the public key has a square Y coordinate. # The point reconstructed from the public key has a square Y coordinate.
pubkey = pubkey_gen(seckey) pubkey = pubkey_gen(seckey)
@ -44,7 +48,7 @@ def vector2():
R = lift_x_square_y(sig[0:32]) R = lift_x_square_y(sig[0:32])
assert(not is_square(R[0])) assert(not is_square(R[0]))
return (seckey, pubkey, msg, sig, "TRUE", None) return (seckey, pubkey, aux_rand, msg, sig, "TRUE", None)
def vector3(): def vector3():
seckey = bytes_from_int(0x0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710) seckey = bytes_from_int(0x0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710)
@ -55,8 +59,10 @@ def vector3():
assert(y(P) % 2 != 0) assert(y(P) % 2 != 0)
msg = bytes_from_int(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF) msg = bytes_from_int(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
sig = schnorr_sign(msg, seckey) aux_rand = bytes_from_int(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
return (seckey, pubkey_gen(seckey), msg, sig, "TRUE", "test fails if msg is reduced modulo p or n")
sig = schnorr_sign(msg, seckey, aux_rand)
return (seckey, pubkey_gen(seckey), aux_rand, 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 # 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 # GENERATING TEST VECTORS. Results in an invalid signature if y(kG) is not
@ -79,10 +85,11 @@ def vector4():
seckey = bytes_from_int(0x763758E5CBEEDEE4F7D3FC86F531C36578933228998226672F13C4F0EBE855EB) seckey = bytes_from_int(0x763758E5CBEEDEE4F7D3FC86F531C36578933228998226672F13C4F0EBE855EB)
msg = bytes_from_int(0x4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703) msg = bytes_from_int(0x4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703)
sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, one_half) sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, one_half)
return (None, pubkey_gen(seckey), msg, sig, "TRUE", None) return (None, pubkey_gen(seckey), None, msg, sig, "TRUE", None)
default_seckey = bytes_from_int(0xB7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF) default_seckey = bytes_from_int(0xB7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF)
default_msg = bytes_from_int(0x243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89) default_msg = bytes_from_int(0x243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89)
default_aux_rand = bytes_from_int(0xC87AA53824B4D7AE2EB035A2B5BBBCCC080E76CDC6D1692C4B0B62D798E6D906)
# Public key is not on the curve # Public key is not on the curve
def vector5(): def vector5():
@ -90,12 +97,12 @@ def vector5():
# public key. # public key.
seckey = default_seckey seckey = default_seckey
msg = default_msg msg = default_msg
sig = schnorr_sign(msg, seckey) sig = schnorr_sign(msg, seckey, default_aux_rand)
pubkey = bytes_from_int(0xEEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34) pubkey = bytes_from_int(0xEEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34)
assert(lift_x_even_y(pubkey) is None) assert(lift_x_even_y(pubkey) is None)
return (None, pubkey, msg, sig, "FALSE", "public key not on the curve") return (None, pubkey, None, msg, sig, "FALSE", "public key not on the curve")
def vector6(): def vector6():
seckey = default_seckey seckey = default_seckey
@ -107,21 +114,21 @@ def vector6():
R = point_mul(G, k) R = point_mul(G, k)
assert(not has_square_y(R)) assert(not has_square_y(R))
return (None, pubkey_gen(seckey), msg, sig, "FALSE", "has_square_y(R) is false") return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "has_square_y(R) is false")
def vector7(): def vector7():
seckey = default_seckey seckey = default_seckey
msg = int_from_bytes(default_msg) msg = int_from_bytes(default_msg)
neg_msg = bytes_from_int(n - msg) neg_msg = bytes_from_int(n - msg)
sig = schnorr_sign(neg_msg, seckey) sig = schnorr_sign(neg_msg, seckey, default_aux_rand)
return (None, pubkey_gen(seckey), bytes_from_int(msg), sig, "FALSE", "negated message") return (None, pubkey_gen(seckey), None, bytes_from_int(msg), sig, "FALSE", "negated message")
def vector8(): def vector8():
seckey = default_seckey seckey = default_seckey
msg = default_msg msg = default_msg
sig = schnorr_sign(msg, seckey) sig = schnorr_sign(msg, seckey, default_aux_rand)
sig = sig[0:32] + bytes_from_int(n - int_from_bytes(sig[32:64])) 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") return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "negated s value")
def bytes_from_point_inf0(P): def bytes_from_point_inf0(P):
if P == None: if P == None:
@ -140,7 +147,7 @@ def vector9():
sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, k) sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, k)
bytes_from_point.__code__ = bytes_from_point_tmp 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") return (None, pubkey_gen(seckey), None, 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): def bytes_from_point_inf1(P):
if P == None: if P == None:
@ -159,7 +166,7 @@ def vector10():
sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, k) sig = insecure_schnorr_sign_fixed_nonce(msg, seckey, k)
bytes_from_point.__code__ = bytes_from_point_tmp 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") return (None, pubkey_gen(seckey), None, 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 # 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 # in an implementation which merely misses the check that sig[0:32] is an X
@ -167,14 +174,14 @@ def vector10():
def vector11(): def vector11():
seckey = default_seckey seckey = default_seckey
msg = default_msg msg = default_msg
sig = schnorr_sign(msg, seckey) sig = schnorr_sign(msg, seckey, default_aux_rand)
# Replace R's X coordinate with an X coordinate that's not on the curve # Replace R's X coordinate with an X coordinate that's not on the curve
x_not_on_curve = bytes_from_int(0x4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D) x_not_on_curve = bytes_from_int(0x4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D)
assert(lift_x_square_y(x_not_on_curve) is None) assert(lift_x_square_y(x_not_on_curve) is None)
sig = x_not_on_curve + sig[32:64] 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") return (None, pubkey_gen(seckey), None, 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 # 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 # in an implementation which merely misses the check that sig[0:32] is smaller
@ -182,12 +189,12 @@ def vector11():
def vector12(): def vector12():
seckey = default_seckey seckey = default_seckey
msg = default_msg msg = default_msg
sig = schnorr_sign(msg, seckey) sig = schnorr_sign(msg, seckey, default_aux_rand)
# Replace R's X coordinate with an X coordinate that's equal to field size # Replace R's X coordinate with an X coordinate that's equal to field size
sig = bytes_from_int(p) + sig[32:64] sig = bytes_from_int(p) + sig[32:64]
return (None, pubkey_gen(seckey), msg, sig, "FALSE", "sig[0:32] is equal to field size") return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "sig[0:32] is equal to field size")
# It's cryptographically impossible to create a test vector that fails if run # 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 # in an implementation which merely misses the check that sig[32:64] is smaller
@ -195,12 +202,12 @@ def vector12():
def vector13(): def vector13():
seckey = default_seckey seckey = default_seckey
msg = default_msg msg = default_msg
sig = schnorr_sign(msg, seckey) sig = schnorr_sign(msg, seckey, default_aux_rand)
# Replace s with a number that's equal to the curve order # Replace s with a number that's equal to the curve order
sig = sig[0:32] + bytes_from_int(n) sig = sig[0:32] + bytes_from_int(n)
return (None, pubkey_gen(seckey), msg, sig, "FALSE", "sig[32:64] is equal to curve order") return (None, pubkey_gen(seckey), None, msg, sig, "FALSE", "sig[32:64] is equal to curve order")
# Test out of range pubkey # Test out of range pubkey
# It's cryptographically impossible to create a test vector that fails if run # It's cryptographically impossible to create a test vector that fails if run
@ -212,8 +219,7 @@ def vector14():
# public key. # public key.
seckey = default_seckey seckey = default_seckey
msg = default_msg msg = default_msg
sig = schnorr_sign(msg, seckey) sig = schnorr_sign(msg, seckey, default_aux_rand)
pubkey_int = p + 1 pubkey_int = p + 1
pubkey = bytes_from_int(pubkey_int) pubkey = bytes_from_int(pubkey_int)
assert(lift_x_even_y(pubkey) is None) assert(lift_x_even_y(pubkey) is None)
@ -221,7 +227,7 @@ def vector14():
# pubkey would be valid # pubkey would be valid
assert(lift_x_even_y(bytes_from_int(pubkey_int % p)) is not None) assert(lift_x_even_y(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") return (None, pubkey, None, msg, sig, "FALSE", "public key is not a valid X coordinate because it exceeds the field size")
vectors = [ vectors = [
vector0(), vector0(),
@ -242,14 +248,14 @@ vectors = [
] ]
# Converts the byte strings of a test vector into hex strings # Converts the byte strings of a test vector into hex strings
def bytes_to_hex(seckey, pubkey, msg, sig, result, comment): def bytes_to_hex(seckey, pubkey, aux_rand, 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) return (seckey.hex().upper() if seckey is not None else None, pubkey.hex().upper(), aux_rand.hex().upper() if aux_rand is not None else None, 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)) vectors = list(map(lambda vector: bytes_to_hex(vector[0], vector[1], vector[2], vector[3], vector[4], vector[5], vector[6]), vectors))
def print_csv(vectors): def print_csv(vectors):
writer = csv.writer(sys.stdout) writer = csv.writer(sys.stdout)
writer.writerow(("index", "secret key", "public key", "message", "signature", "verification result", "comment")) writer.writerow(("index", "secret key", "public key", "aux_rand", "message", "signature", "verification result", "comment"))
for (i,v) in enumerate(vectors): for (i,v) in enumerate(vectors):
writer.writerow((i,)+v) writer.writerow((i,)+v)