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Diffstat (limited to 'frozen_deps/ecdsa/ecdsa.py')
| -rw-r--r-- | frozen_deps/ecdsa/ecdsa.py | 754 |
1 files changed, 754 insertions, 0 deletions
diff --git a/frozen_deps/ecdsa/ecdsa.py b/frozen_deps/ecdsa/ecdsa.py new file mode 100644 index 0000000..d785a45 --- /dev/null +++ b/frozen_deps/ecdsa/ecdsa.py @@ -0,0 +1,754 @@ +#! /usr/bin/env python + +""" +Implementation of Elliptic-Curve Digital Signatures. + +Classes and methods for elliptic-curve signatures: +private keys, public keys, signatures, +NIST prime-modulus curves with modulus lengths of +192, 224, 256, 384, and 521 bits. + +Example: + + # (In real-life applications, you would probably want to + # protect against defects in SystemRandom.) + from random import SystemRandom + randrange = SystemRandom().randrange + + # Generate a public/private key pair using the NIST Curve P-192: + + g = generator_192 + n = g.order() + secret = randrange( 1, n ) + pubkey = Public_key( g, g * secret ) + privkey = Private_key( pubkey, secret ) + + # Signing a hash value: + + hash = randrange( 1, n ) + signature = privkey.sign( hash, randrange( 1, n ) ) + + # Verifying a signature for a hash value: + + if pubkey.verifies( hash, signature ): + print_("Demo verification succeeded.") + else: + print_("*** Demo verification failed.") + + # Verification fails if the hash value is modified: + + if pubkey.verifies( hash-1, signature ): + print_("**** Demo verification failed to reject tampered hash.") + else: + print_("Demo verification correctly rejected tampered hash.") + +Version of 2009.05.16. + +Revision history: + 2005.12.31 - Initial version. + 2008.11.25 - Substantial revisions introducing new classes. + 2009.05.16 - Warn against using random.randrange in real applications. + 2009.05.17 - Use random.SystemRandom by default. + +Written in 2005 by Peter Pearson and placed in the public domain. +""" + +from six import int2byte, b +from . import ellipticcurve +from . import numbertheory +from .util import bit_length +from ._compat import remove_whitespace + + +class RSZeroError(RuntimeError): + pass + + +class InvalidPointError(RuntimeError): + pass + + +class Signature(object): + """ECDSA signature.""" + + def __init__(self, r, s): + self.r = r + self.s = s + + def recover_public_keys(self, hash, generator): + """Returns two public keys for which the signature is valid + hash is signed hash + generator is the used generator of the signature + """ + curve = generator.curve() + n = generator.order() + r = self.r + s = self.s + e = hash + x = r + + # Compute the curve point with x as x-coordinate + alpha = ( + pow(x, 3, curve.p()) + (curve.a() * x) + curve.b() + ) % curve.p() + beta = numbertheory.square_root_mod_prime(alpha, curve.p()) + y = beta if beta % 2 == 0 else curve.p() - beta + + # Compute the public key + R1 = ellipticcurve.PointJacobi(curve, x, y, 1, n) + Q1 = numbertheory.inverse_mod(r, n) * (s * R1 + (-e % n) * generator) + Pk1 = Public_key(generator, Q1) + + # And the second solution + R2 = ellipticcurve.PointJacobi(curve, x, -y, 1, n) + Q2 = numbertheory.inverse_mod(r, n) * (s * R2 + (-e % n) * generator) + Pk2 = Public_key(generator, Q2) + + return [Pk1, Pk2] + + +class Public_key(object): + """Public key for ECDSA.""" + + def __init__(self, generator, point, verify=True): + """Low level ECDSA public key object. + + :param generator: the Point that generates the group (the base point) + :param point: the Point that defines the public key + :param bool verify: if True check if point is valid point on curve + + :raises InvalidPointError: if the point parameters are invalid or + point does not lie on the curve + """ + + self.curve = generator.curve() + self.generator = generator + self.point = point + n = generator.order() + p = self.curve.p() + if not (0 <= point.x() < p) or not (0 <= point.y() < p): + raise InvalidPointError( + "The public point has x or y out of range." + ) + if verify and not self.curve.contains_point(point.x(), point.y()): + raise InvalidPointError("Point does not lie on the curve") + if not n: + raise InvalidPointError("Generator point must have order.") + # for curve parameters with base point with cofactor 1, all points + # that are on the curve are scalar multiples of the base point, so + # verifying that is not necessary. See Section 3.2.2.1 of SEC 1 v2 + if ( + verify + and self.curve.cofactor() != 1 + and not n * point == ellipticcurve.INFINITY + ): + raise InvalidPointError("Generator point order is bad.") + + def __eq__(self, other): + if isinstance(other, Public_key): + """Return True if the points are identical, False otherwise.""" + return self.curve == other.curve and self.point == other.point + return NotImplemented + + def verifies(self, hash, signature): + """Verify that signature is a valid signature of hash. + Return True if the signature is valid. + """ + + # From X9.62 J.3.1. + + G = self.generator + n = G.order() + r = signature.r + s = signature.s + if r < 1 or r > n - 1: + return False + if s < 1 or s > n - 1: + return False + c = numbertheory.inverse_mod(s, n) + u1 = (hash * c) % n + u2 = (r * c) % n + if hasattr(G, "mul_add"): + xy = G.mul_add(u1, self.point, u2) + else: + xy = u1 * G + u2 * self.point + v = xy.x() % n + return v == r + + +class Private_key(object): + """Private key for ECDSA.""" + + def __init__(self, public_key, secret_multiplier): + """public_key is of class Public_key; + secret_multiplier is a large integer. + """ + + self.public_key = public_key + self.secret_multiplier = secret_multiplier + + def __eq__(self, other): + if isinstance(other, Private_key): + """Return True if the points are identical, False otherwise.""" + return ( + self.public_key == other.public_key + and self.secret_multiplier == other.secret_multiplier + ) + return NotImplemented + + def sign(self, hash, random_k): + """Return a signature for the provided hash, using the provided + random nonce. It is absolutely vital that random_k be an unpredictable + number in the range [1, self.public_key.point.order()-1]. If + an attacker can guess random_k, he can compute our private key from a + single signature. Also, if an attacker knows a few high-order + bits (or a few low-order bits) of random_k, he can compute our private + key from many signatures. The generation of nonces with adequate + cryptographic strength is very difficult and far beyond the scope + of this comment. + + May raise RuntimeError, in which case retrying with a new + random value k is in order. + """ + + G = self.public_key.generator + n = G.order() + k = random_k % n + # Fix the bit-length of the random nonce, + # so that it doesn't leak via timing. + # This does not change that ks = k mod n + ks = k + n + kt = ks + n + if bit_length(ks) == bit_length(n): + p1 = kt * G + else: + p1 = ks * G + r = p1.x() % n + if r == 0: + raise RSZeroError("amazingly unlucky random number r") + s = ( + numbertheory.inverse_mod(k, n) + * (hash + (self.secret_multiplier * r) % n) + ) % n + if s == 0: + raise RSZeroError("amazingly unlucky random number s") + return Signature(r, s) + + +def int_to_string(x): + """Convert integer x into a string of bytes, as per X9.62.""" + assert x >= 0 + if x == 0: + return b("\0") + result = [] + while x: + ordinal = x & 0xFF + result.append(int2byte(ordinal)) + x >>= 8 + + result.reverse() + return b("").join(result) + + +def string_to_int(s): + """Convert a string of bytes into an integer, as per X9.62.""" + result = 0 + for c in s: + if not isinstance(c, int): + c = ord(c) + result = 256 * result + c + return result + + +def digest_integer(m): + """Convert an integer into a string of bytes, compute + its SHA-1 hash, and convert the result to an integer.""" + # + # I don't expect this function to be used much. I wrote + # it in order to be able to duplicate the examples + # in ECDSAVS. + # + from hashlib import sha1 + + return string_to_int(sha1(int_to_string(m)).digest()) + + +def point_is_valid(generator, x, y): + """Is (x,y) a valid public key based on the specified generator?""" + + # These are the tests specified in X9.62. + + n = generator.order() + curve = generator.curve() + p = curve.p() + if not (0 <= x < p) or not (0 <= y < p): + return False + if not curve.contains_point(x, y): + return False + if ( + curve.cofactor() != 1 + and not n * ellipticcurve.PointJacobi(curve, x, y, 1) + == ellipticcurve.INFINITY + ): + return False + return True + + +# NIST Curve P-192: +_p = 6277101735386680763835789423207666416083908700390324961279 +_r = 6277101735386680763835789423176059013767194773182842284081 +# s = 0x3045ae6fc8422f64ed579528d38120eae12196d5L +# c = 0x3099d2bbbfcb2538542dcd5fb078b6ef5f3d6fe2c745de65L +_b = int( + remove_whitespace( + """ + 64210519 E59C80E7 0FA7E9AB 72243049 FEB8DEEC C146B9B1""" + ), + 16, +) +_Gx = int( + remove_whitespace( + """ + 188DA80E B03090F6 7CBF20EB 43A18800 F4FF0AFD 82FF1012""" + ), + 16, +) +_Gy = int( + remove_whitespace( + """ + 07192B95 FFC8DA78 631011ED 6B24CDD5 73F977A1 1E794811""" + ), + 16, +) + +curve_192 = ellipticcurve.CurveFp(_p, -3, _b, 1) +generator_192 = ellipticcurve.PointJacobi( + curve_192, _Gx, _Gy, 1, _r, generator=True +) + + +# NIST Curve P-224: +_p = int( + remove_whitespace( + """ + 2695994666715063979466701508701963067355791626002630814351 + 0066298881""" + ) +) +_r = int( + remove_whitespace( + """ + 2695994666715063979466701508701962594045780771442439172168 + 2722368061""" + ) +) +# s = 0xbd71344799d5c7fcdc45b59fa3b9ab8f6a948bc5L +# c = 0x5b056c7e11dd68f40469ee7f3c7a7d74f7d121116506d031218291fbL +_b = int( + remove_whitespace( + """ + B4050A85 0C04B3AB F5413256 5044B0B7 D7BFD8BA 270B3943 + 2355FFB4""" + ), + 16, +) +_Gx = int( + remove_whitespace( + """ + B70E0CBD 6BB4BF7F 321390B9 4A03C1D3 56C21122 343280D6 + 115C1D21""" + ), + 16, +) +_Gy = int( + remove_whitespace( + """ + BD376388 B5F723FB 4C22DFE6 CD4375A0 5A074764 44D58199 + 85007E34""" + ), + 16, +) + +curve_224 = ellipticcurve.CurveFp(_p, -3, _b, 1) +generator_224 = ellipticcurve.PointJacobi( + curve_224, _Gx, _Gy, 1, _r, generator=True +) + +# NIST Curve P-256: +_p = int( + remove_whitespace( + """ + 1157920892103562487626974469494075735300861434152903141955 + 33631308867097853951""" + ) +) +_r = int( + remove_whitespace( + """ + 115792089210356248762697446949407573529996955224135760342 + 422259061068512044369""" + ) +) +# s = 0xc49d360886e704936a6678e1139d26b7819f7e90L +# c = 0x7efba1662985be9403cb055c75d4f7e0ce8d84a9c5114abcaf3177680104fa0dL +_b = int( + remove_whitespace( + """ + 5AC635D8 AA3A93E7 B3EBBD55 769886BC 651D06B0 CC53B0F6 + 3BCE3C3E 27D2604B""" + ), + 16, +) +_Gx = int( + remove_whitespace( + """ + 6B17D1F2 E12C4247 F8BCE6E5 63A440F2 77037D81 2DEB33A0 + F4A13945 D898C296""" + ), + 16, +) +_Gy = int( + remove_whitespace( + """ + 4FE342E2 FE1A7F9B 8EE7EB4A 7C0F9E16 2BCE3357 6B315ECE + CBB64068 37BF51F5""" + ), + 16, +) + +curve_256 = ellipticcurve.CurveFp(_p, -3, _b, 1) +generator_256 = ellipticcurve.PointJacobi( + curve_256, _Gx, _Gy, 1, _r, generator=True +) + +# NIST Curve P-384: +_p = int( + remove_whitespace( + """ + 3940200619639447921227904010014361380507973927046544666794 + 8293404245721771496870329047266088258938001861606973112319""" + ) +) +_r = int( + remove_whitespace( + """ + 3940200619639447921227904010014361380507973927046544666794 + 6905279627659399113263569398956308152294913554433653942643""" + ) +) +# s = 0xa335926aa319a27a1d00896a6773a4827acdac73L +# c = int(remove_whitespace( +# """ +# 79d1e655 f868f02f ff48dcde e14151dd b80643c1 406d0ca1 +# 0dfe6fc5 2009540a 495e8042 ea5f744f 6e184667 cc722483""" +# ), 16) +_b = int( + remove_whitespace( + """ + B3312FA7 E23EE7E4 988E056B E3F82D19 181D9C6E FE814112 + 0314088F 5013875A C656398D 8A2ED19D 2A85C8ED D3EC2AEF""" + ), + 16, +) +_Gx = int( + remove_whitespace( + """ + AA87CA22 BE8B0537 8EB1C71E F320AD74 6E1D3B62 8BA79B98 + 59F741E0 82542A38 5502F25D BF55296C 3A545E38 72760AB7""" + ), + 16, +) +_Gy = int( + remove_whitespace( + """ + 3617DE4A 96262C6F 5D9E98BF 9292DC29 F8F41DBD 289A147C + E9DA3113 B5F0B8C0 0A60B1CE 1D7E819D 7A431D7C 90EA0E5F""" + ), + 16, +) + +curve_384 = ellipticcurve.CurveFp(_p, -3, _b, 1) +generator_384 = ellipticcurve.PointJacobi( + curve_384, _Gx, _Gy, 1, _r, generator=True +) + +# NIST Curve P-521: +_p = int( + "686479766013060971498190079908139321726943530014330540939" + "446345918554318339765605212255964066145455497729631139148" + "0858037121987999716643812574028291115057151" +) +_r = int( + "686479766013060971498190079908139321726943530014330540939" + "446345918554318339765539424505774633321719753296399637136" + "3321113864768612440380340372808892707005449" +) +# s = 0xd09e8800291cb85396cc6717393284aaa0da64baL +# c = int(remove_whitespace( +# """ +# 0b4 8bfa5f42 0a349495 39d2bdfc 264eeeeb 077688e4 +# 4fbf0ad8 f6d0edb3 7bd6b533 28100051 8e19f1b9 ffbe0fe9 +# ed8a3c22 00b8f875 e523868c 70c1e5bf 55bad637""" +# ), 16) +_b = int( + remove_whitespace( + """ + 051 953EB961 8E1C9A1F 929A21A0 B68540EE A2DA725B + 99B315F3 B8B48991 8EF109E1 56193951 EC7E937B 1652C0BD + 3BB1BF07 3573DF88 3D2C34F1 EF451FD4 6B503F00""" + ), + 16, +) +_Gx = int( + remove_whitespace( + """ + C6 858E06B7 0404E9CD 9E3ECB66 2395B442 9C648139 + 053FB521 F828AF60 6B4D3DBA A14B5E77 EFE75928 FE1DC127 + A2FFA8DE 3348B3C1 856A429B F97E7E31 C2E5BD66""" + ), + 16, +) +_Gy = int( + remove_whitespace( + """ + 118 39296A78 9A3BC004 5C8A5FB4 2C7D1BD9 98F54449 + 579B4468 17AFBD17 273E662C 97EE7299 5EF42640 C550B901 + 3FAD0761 353C7086 A272C240 88BE9476 9FD16650""" + ), + 16, +) + +curve_521 = ellipticcurve.CurveFp(_p, -3, _b, 1) +generator_521 = ellipticcurve.PointJacobi( + curve_521, _Gx, _Gy, 1, _r, generator=True +) + +# Certicom secp256-k1 +_a = 0x0000000000000000000000000000000000000000000000000000000000000000 +_b = 0x0000000000000000000000000000000000000000000000000000000000000007 +_p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F +_Gx = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798 +_Gy = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8 +_r = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 + +curve_secp256k1 = ellipticcurve.CurveFp(_p, _a, _b, 1) +generator_secp256k1 = ellipticcurve.PointJacobi( + curve_secp256k1, _Gx, _Gy, 1, _r, generator=True +) + +# Brainpool P-160-r1 +_a = 0x340E7BE2A280EB74E2BE61BADA745D97E8F7C300 +_b = 0x1E589A8595423412134FAA2DBDEC95C8D8675E58 +_p = 0xE95E4A5F737059DC60DFC7AD95B3D8139515620F +_Gx = 0xBED5AF16EA3F6A4F62938C4631EB5AF7BDBCDBC3 +_Gy = 0x1667CB477A1A8EC338F94741669C976316DA6321 +_q = 0xE95E4A5F737059DC60DF5991D45029409E60FC09 + +curve_brainpoolp160r1 = ellipticcurve.CurveFp(_p, _a, _b, 1) +generator_brainpoolp160r1 = ellipticcurve.PointJacobi( + curve_brainpoolp160r1, _Gx, _Gy, 1, _q, generator=True +) + +# Brainpool P-192-r1 +_a = 0x6A91174076B1E0E19C39C031FE8685C1CAE040E5C69A28EF +_b = 0x469A28EF7C28CCA3DC721D044F4496BCCA7EF4146FBF25C9 +_p = 0xC302F41D932A36CDA7A3463093D18DB78FCE476DE1A86297 +_Gx = 0xC0A0647EAAB6A48753B033C56CB0F0900A2F5C4853375FD6 +_Gy = 0x14B690866ABD5BB88B5F4828C1490002E6773FA2FA299B8F +_q = 0xC302F41D932A36CDA7A3462F9E9E916B5BE8F1029AC4ACC1 + +curve_brainpoolp192r1 = ellipticcurve.CurveFp(_p, _a, _b, 1) +generator_brainpoolp192r1 = ellipticcurve.PointJacobi( + curve_brainpoolp192r1, _Gx, _Gy, 1, _q, generator=True +) + +# Brainpool P-224-r1 +_a = 0x68A5E62CA9CE6C1C299803A6C1530B514E182AD8B0042A59CAD29F43 +_b = 0x2580F63CCFE44138870713B1A92369E33E2135D266DBB372386C400B +_p = 0xD7C134AA264366862A18302575D1D787B09F075797DA89F57EC8C0FF +_Gx = 0x0D9029AD2C7E5CF4340823B2A87DC68C9E4CE3174C1E6EFDEE12C07D +_Gy = 0x58AA56F772C0726F24C6B89E4ECDAC24354B9E99CAA3F6D3761402CD +_q = 0xD7C134AA264366862A18302575D0FB98D116BC4B6DDEBCA3A5A7939F + +curve_brainpoolp224r1 = ellipticcurve.CurveFp(_p, _a, _b, 1) +generator_brainpoolp224r1 = ellipticcurve.PointJacobi( + curve_brainpoolp224r1, _Gx, _Gy, 1, _q, generator=True +) + +# Brainpool P-256-r1 +_a = 0x7D5A0975FC2C3057EEF67530417AFFE7FB8055C126DC5C6CE94A4B44F330B5D9 +_b = 0x26DC5C6CE94A4B44F330B5D9BBD77CBF958416295CF7E1CE6BCCDC18FF8C07B6 +_p = 0xA9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377 +_Gx = 0x8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262 +_Gy = 0x547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997 +_q = 0xA9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7 + +curve_brainpoolp256r1 = ellipticcurve.CurveFp(_p, _a, _b, 1) +generator_brainpoolp256r1 = ellipticcurve.PointJacobi( + curve_brainpoolp256r1, _Gx, _Gy, 1, _q, generator=True +) + +# Brainpool P-320-r1 +_a = int( + remove_whitespace( + """ + 3EE30B568FBAB0F883CCEBD46D3F3BB8A2A73513F5EB79DA66190EB085FFA9 + F492F375A97D860EB4""" + ), + 16, +) +_b = int( + remove_whitespace( + """ + 520883949DFDBC42D3AD198640688A6FE13F41349554B49ACC31DCCD884539 + 816F5EB4AC8FB1F1A6""" + ), + 16, +) +_p = int( + remove_whitespace( + """ + D35E472036BC4FB7E13C785ED201E065F98FCFA6F6F40DEF4F92B9EC7893EC + 28FCD412B1F1B32E27""" + ), + 16, +) +_Gx = int( + remove_whitespace( + """ + 43BD7E9AFB53D8B85289BCC48EE5BFE6F20137D10A087EB6E7871E2A10A599 + C710AF8D0D39E20611""" + ), + 16, +) +_Gy = int( + remove_whitespace( + """ + 14FDD05545EC1CC8AB4093247F77275E0743FFED117182EAA9C77877AAAC6A + C7D35245D1692E8EE1""" + ), + 16, +) +_q = int( + remove_whitespace( + """ + D35E472036BC4FB7E13C785ED201E065F98FCFA5B68F12A32D482EC7EE8658 + E98691555B44C59311""" + ), + 16, +) + +curve_brainpoolp320r1 = ellipticcurve.CurveFp(_p, _a, _b, 1) +generator_brainpoolp320r1 = ellipticcurve.PointJacobi( + curve_brainpoolp320r1, _Gx, _Gy, 1, _q, generator=True +) + +# Brainpool P-384-r1 +_a = int( + remove_whitespace( + """ + 7BC382C63D8C150C3C72080ACE05AFA0C2BEA28E4FB22787139165EFBA91F9 + 0F8AA5814A503AD4EB04A8C7DD22CE2826""" + ), + 16, +) +_b = int( + remove_whitespace( + """ + 04A8C7DD22CE28268B39B55416F0447C2FB77DE107DCD2A62E880EA53EEB62 + D57CB4390295DBC9943AB78696FA504C11""" + ), + 16, +) +_p = int( + remove_whitespace( + """ + 8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB711 + 23ACD3A729901D1A71874700133107EC53""" + ), + 16, +) +_Gx = int( + remove_whitespace( + """ + 1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10 + E8E826E03436D646AAEF87B2E247D4AF1E""" + ), + 16, +) +_Gy = int( + remove_whitespace( + """ + 8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF991292 + 80E4646217791811142820341263C5315""" + ), + 16, +) +_q = int( + remove_whitespace( + """ + 8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425 + A7CF3AB6AF6B7FC3103B883202E9046565""" + ), + 16, +) + +curve_brainpoolp384r1 = ellipticcurve.CurveFp(_p, _a, _b, 1) +generator_brainpoolp384r1 = ellipticcurve.PointJacobi( + curve_brainpoolp384r1, _Gx, _Gy, 1, _q, generator=True +) + +# Brainpool P-512-r1 +_a = int( + remove_whitespace( + """ + 7830A3318B603B89E2327145AC234CC594CBDD8D3DF91610A83441CAEA9863 + BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CA""" + ), + 16, +) +_b = int( + remove_whitespace( + """ + 3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117 + A72BF2C7B9E7C1AC4D77FC94CADC083E67984050B75EBAE5DD2809BD638016F723""" + ), + 16, +) +_p = int( + remove_whitespace( + """ + AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308 + 717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3""" + ), + 16, +) +_Gx = int( + remove_whitespace( + """ + 81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D009 + 8EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F822""" + ), + 16, +) +_Gy = int( + remove_whitespace( + """ + 7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F81 + 11B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892""" + ), + 16, +) +_q = int( + remove_whitespace( + """ + AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308 + 70553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069""" + ), + 16, +) + +curve_brainpoolp512r1 = ellipticcurve.CurveFp(_p, _a, _b, 1) +generator_brainpoolp512r1 = ellipticcurve.PointJacobi( + curve_brainpoolp512r1, _Gx, _Gy, 1, _q, generator=True +) |