X-Git-Url: http://www.git.cypherpunks.ru/?p=pygost.git;a=blobdiff_plain;f=pygost%2Fgost3410.py;h=9f0a11e656689745056b8f7c53cdf5c3779201b3;hp=ed84f3efbd88d5895e10b6eb9c669b6cadf06449;hb=2bb1a163d32e4167e6904ff3c6b4cf64ea7287bb;hpb=e28d82ef85c8cadc47c42ecbc345f9b096beff48 diff --git a/pygost/gost3410.py b/pygost/gost3410.py index ed84f3e..9f0a11e 100644 --- a/pygost/gost3410.py +++ b/pygost/gost3410.py @@ -1,11 +1,10 @@ # coding: utf-8 # PyGOST -- Pure Python GOST cryptographic functions library -# Copyright (C) 2015-2016 Sergey Matveev +# Copyright (C) 2015-2020 Sergey Matveev # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by -# the Free Software Foundation, either version 3 of the License, or -# (at your option) any later version. +# the Free Software Foundation, version 3 of the License. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of @@ -35,112 +34,45 @@ MODE2SIZE = { } -DEFAULT_CURVE = "GostR3410_2001_CryptoPro_A_ParamSet" -# Curve parameters are the following: p, q, a, b, x, y -CURVE_PARAMS = { - "GostR3410_2001_ParamSet_cc": ( - "C0000000000000000000000000000000000000000000000000000000000003C7", - "5fffffffffffffffffffffffffffffff606117a2f4bde428b7458a54b6e87b85", - "C0000000000000000000000000000000000000000000000000000000000003c4", - "2d06B4265ebc749ff7d0f1f1f88232e81632e9088fd44b7787d5e407e955080c", - "0000000000000000000000000000000000000000000000000000000000000002", - "a20e034bf8813ef5c18d01105e726a17eb248b264ae9706f440bedc8ccb6b22c", - ), - "GostR3410_2001_TestParamSet": ( - "8000000000000000000000000000000000000000000000000000000000000431", - "8000000000000000000000000000000150FE8A1892976154C59CFC193ACCF5B3", - "0000000000000000000000000000000000000000000000000000000000000007", - "5FBFF498AA938CE739B8E022FBAFEF40563F6E6A3472FC2A514C0CE9DAE23B7E", - "0000000000000000000000000000000000000000000000000000000000000002", - "08E2A8A0E65147D4BD6316030E16D19C85C97F0A9CA267122B96ABBCEA7E8FC8", - ), - "GostR3410_2001_CryptoPro_A_ParamSet": ( - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD97", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF6C611070995AD10045841B09B761B893", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD94", - "00000000000000000000000000000000000000000000000000000000000000a6", - "0000000000000000000000000000000000000000000000000000000000000001", - "8D91E471E0989CDA27DF505A453F2B7635294F2DDF23E3B122ACC99C9E9F1E14", - ), - "GostR3410_2001_CryptoPro_B_ParamSet": ( - "8000000000000000000000000000000000000000000000000000000000000C99", - "800000000000000000000000000000015F700CFFF1A624E5E497161BCC8A198F", - "8000000000000000000000000000000000000000000000000000000000000C96", - "3E1AF419A269A5F866A7D3C25C3DF80AE979259373FF2B182F49D4CE7E1BBC8B", - "0000000000000000000000000000000000000000000000000000000000000001", - "3FA8124359F96680B83D1C3EB2C070E5C545C9858D03ECFB744BF8D717717EFC", - ), - "GostR3410_2001_CryptoPro_C_ParamSet": ( - "9B9F605F5A858107AB1EC85E6B41C8AACF846E86789051D37998F7B9022D759B", - "9B9F605F5A858107AB1EC85E6B41C8AA582CA3511EDDFB74F02F3A6598980BB9", - "9B9F605F5A858107AB1EC85E6B41C8AACF846E86789051D37998F7B9022D7598", - "000000000000000000000000000000000000000000000000000000000000805a", - "0000000000000000000000000000000000000000000000000000000000000000", - "41ECE55743711A8C3CBF3783CD08C0EE4D4DC440D4641A8F366E550DFDB3BB67", - ), - "GostR3410_2001_CryptoPro_XchA_ParamSet": ( - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD97", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF6C611070995AD10045841B09B761B893", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD94", - "00000000000000000000000000000000000000000000000000000000000000a6", - "0000000000000000000000000000000000000000000000000000000000000001", - "8D91E471E0989CDA27DF505A453F2B7635294F2DDF23E3B122ACC99C9E9F1E14", - ), - "GostR3410_2001_CryptoPro_XchB_ParamSet": ( - "9B9F605F5A858107AB1EC85E6B41C8AACF846E86789051D37998F7B9022D759B", - "9B9F605F5A858107AB1EC85E6B41C8AA582CA3511EDDFB74F02F3A6598980BB9", - "9B9F605F5A858107AB1EC85E6B41C8AACF846E86789051D37998F7B9022D7598", - "000000000000000000000000000000000000000000000000000000000000805a", - "0000000000000000000000000000000000000000000000000000000000000000", - "41ECE55743711A8C3CBF3783CD08C0EE4D4DC440D4641A8F366E550DFDB3BB67", - ), - "GostR3410_2012_TC26_ParamSetA": ( - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF27E69532F48D89116FF22B8D4E0560609B4B38ABFAD2B85DCACDB1411F10B275", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC4", - "E8C2505DEDFC86DDC1BD0B2B6667F1DA34B82574761CB0E879BD081CFD0B6265EE3CB090F30D27614CB4574010DA90DD862EF9D4EBEE4761503190785A71C760", - "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003", - "7503CFE87A836AE3A61B8816E25450E6CE5E1C93ACF1ABC1778064FDCBEFA921DF1626BE4FD036E93D75E6A50E3A41E98028FE5FC235F5B889A589CB5215F2A4", - ), - "GostR3410_2012_TC26_ParamSet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} -for c, params in CURVE_PARAMS.items(): - CURVE_PARAMS[c] = [hexdec(param) for param in params] - - class GOST3410Curve(object): """ GOST 34.10 validated curve - >>> p, q, a, b, x, y = CURVE_PARAMS["GostR3410_2001_TestParamSet"] - >>> curve = GOST3410Curve(p, q, a, b, x, y) + >>> curve = CURVES["id-GostR3410-2001-TestParamSet"] >>> prv = prv_unmarshal(urandom(32)) >>> signature = sign(curve, prv, GOST341194(data).digest()) >>> pub = public_key(curve, prv) >>> verify(curve, pub, GOST341194(data).digest(), signature) True + + :param long p: characteristic of the underlying prime field + :param long q: elliptic curve subgroup order + :param long a, b: coefficients of the equation of the elliptic curve in + the canonical form + :param long x, y: the coordinate of the point P (generator of the + subgroup of order q) of the elliptic curve in + the canonical form + :param long e, d: coefficients of the equation of the elliptic curve in + the twisted Edwards form """ - def __init__(self, p, q, a, b, x, y): - self.p = bytes2long(p) - self.q = bytes2long(q) - self.a = bytes2long(a) - self.b = bytes2long(b) - self.x = bytes2long(x) - self.y = bytes2long(y) + def __init__(self, p, q, a, b, x, y, cofactor=1, e=None, d=None): + self.p = p + self.q = q + self.a = a + self.b = b + self.x = x + self.y = y + self.cofactor = cofactor + self.e = e + self.d = d r1 = self.y * self.y % self.p r2 = ((self.x * self.x + self.a) * self.x + self.b) % self.p - if r2 < 0: - r2 += self.p - if r1 != r2: + if r1 != self.pos(r2): raise ValueError("Invalid parameters") + self._st = None - def _pos(self, v): + def pos(self, v): + """Make positive number + """ if v < 0: return v + self.p return v @@ -150,11 +82,11 @@ class GOST3410Curve(object): # double t = ((3 * p1x * p1x + self.a) * modinvert(2 * p1y, self.p)) % self.p else: - tx = self._pos(p2x - p1x) % self.p - ty = self._pos(p2y - p1y) % self.p + tx = self.pos(p2x - p1x) % self.p + ty = self.pos(p2y - p1y) % self.p t = (ty * modinvert(tx, self.p)) % self.p - tx = self._pos(t * t - p1x - p2x) % self.p - ty = self._pos(t * (p1x - tx) - p1y) % self.p + tx = self.pos(t * t - p1x - p2x) % self.p + ty = self.pos(t * (p1x - tx) - p1y) % self.p return tx, ty def exp(self, degree, x=None, y=None): @@ -162,9 +94,9 @@ class GOST3410Curve(object): y = y or self.y tx = x ty = y - degree -= 1 if degree == 0: raise ValueError("Bad degree value") + degree -= 1 while degree != 0: if degree & 1 == 1: tx, ty = self._add(tx, ty, x, y) @@ -172,26 +104,137 @@ class GOST3410Curve(object): x, y = self._add(x, y, x, y) return tx, ty + def st(self): + """Compute s/t parameters for twisted Edwards curve points conversion + """ + if self.e is None or self.d is None: + raise ValueError("non twisted Edwards curve") + if self._st is not None: + return self._st + self._st = ( + self.pos(self.e - self.d) * modinvert(4, self.p) % self.p, + (self.e + self.d) * modinvert(6, self.p) % self.p, + ) + return self._st + -def public_key(curve, private_key): +CURVES = { + "GostR3410_2001_ParamSet_cc": GOST3410Curve( + p=bytes2long(hexdec("C0000000000000000000000000000000000000000000000000000000000003C7")), + q=bytes2long(hexdec("5fffffffffffffffffffffffffffffff606117a2f4bde428b7458a54b6e87b85")), + a=bytes2long(hexdec("C0000000000000000000000000000000000000000000000000000000000003c4")), + b=bytes2long(hexdec("2d06B4265ebc749ff7d0f1f1f88232e81632e9088fd44b7787d5e407e955080c")), + x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000002")), + y=bytes2long(hexdec("a20e034bf8813ef5c18d01105e726a17eb248b264ae9706f440bedc8ccb6b22c")), + ), + "id-GostR3410-2001-TestParamSet": GOST3410Curve( + p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000431")), + q=bytes2long(hexdec("8000000000000000000000000000000150FE8A1892976154C59CFC193ACCF5B3")), + a=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000007")), + b=bytes2long(hexdec("5FBFF498AA938CE739B8E022FBAFEF40563F6E6A3472FC2A514C0CE9DAE23B7E")), + x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000002")), + y=bytes2long(hexdec("08E2A8A0E65147D4BD6316030E16D19C85C97F0A9CA267122B96ABBCEA7E8FC8")), + ), + "id-GostR3410-2001-CryptoPro-A-ParamSet": GOST3410Curve( + p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD97")), + q=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF6C611070995AD10045841B09B761B893")), + a=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD94")), + b=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000a6")), + x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000001")), + y=bytes2long(hexdec("8D91E471E0989CDA27DF505A453F2B7635294F2DDF23E3B122ACC99C9E9F1E14")), + ), + "id-GostR3410-2001-CryptoPro-B-ParamSet": GOST3410Curve( + p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000C99")), + q=bytes2long(hexdec("800000000000000000000000000000015F700CFFF1A624E5E497161BCC8A198F")), + a=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000C96")), + b=bytes2long(hexdec("3E1AF419A269A5F866A7D3C25C3DF80AE979259373FF2B182F49D4CE7E1BBC8B")), + x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000001")), + y=bytes2long(hexdec("3FA8124359F96680B83D1C3EB2C070E5C545C9858D03ECFB744BF8D717717EFC")), + ), + "id-GostR3410-2001-CryptoPro-C-ParamSet": GOST3410Curve( + p=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AACF846E86789051D37998F7B9022D759B")), + q=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AA582CA3511EDDFB74F02F3A6598980BB9")), + a=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AACF846E86789051D37998F7B9022D7598")), + b=bytes2long(hexdec("000000000000000000000000000000000000000000000000000000000000805a")), + x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000000")), + y=bytes2long(hexdec("41ECE55743711A8C3CBF3783CD08C0EE4D4DC440D4641A8F366E550DFDB3BB67")), + ), + "id-tc26-gost-3410-2012-256-paramSetA": GOST3410Curve( + p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD97")), + q=bytes2long(hexdec("400000000000000000000000000000000FD8CDDFC87B6635C115AF556C360C67")), + a=bytes2long(hexdec("C2173F1513981673AF4892C23035A27CE25E2013BF95AA33B22C656F277E7335")), + b=bytes2long(hexdec("295F9BAE7428ED9CCC20E7C359A9D41A22FCCD9108E17BF7BA9337A6F8AE9513")), + x=bytes2long(hexdec("91E38443A5E82C0D880923425712B2BB658B9196932E02C78B2582FE742DAA28")), + y=bytes2long(hexdec("32879423AB1A0375895786C4BB46E9565FDE0B5344766740AF268ADB32322E5C")), + cofactor=4, + e=0x01, + d=bytes2long(hexdec("0605F6B7C183FA81578BC39CFAD518132B9DF62897009AF7E522C32D6DC7BFFB")), + ), + "id-tc26-gost-3410-2012-512-paramSetTest": GOST3410Curve( + p=bytes2long(hexdec("4531ACD1FE0023C7550D267B6B2FEE80922B14B2FFB90F04D4EB7C09B5D2D15DF1D852741AF4704A0458047E80E4546D35B8336FAC224DD81664BBF528BE6373")), + q=bytes2long(hexdec("4531ACD1FE0023C7550D267B6B2FEE80922B14B2FFB90F04D4EB7C09B5D2D15DA82F2D7ECB1DBAC719905C5EECC423F1D86E25EDBE23C595D644AAF187E6E6DF")), + a=7, + b=bytes2long(hexdec("1CFF0806A31116DA29D8CFA54E57EB748BC5F377E49400FDD788B649ECA1AC4361834013B2AD7322480A89CA58E0CF74BC9E540C2ADD6897FAD0A3084F302ADC")), + x=bytes2long(hexdec("24D19CC64572EE30F396BF6EBBFD7A6C5213B3B3D7057CC825F91093A68CD762FD60611262CD838DC6B60AA7EEE804E28BC849977FAC33B4B530F1B120248A9A")), + y=bytes2long(hexdec("2BB312A43BD2CE6E0D020613C857ACDDCFBF061E91E5F2C3F32447C259F39B2C83AB156D77F1496BF7EB3351E1EE4E43DC1A18B91B24640B6DBB92CB1ADD371E")), + ), + "id-tc26-gost-3410-12-512-paramSetA": GOST3410Curve( + p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7")), + q=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF27E69532F48D89116FF22B8D4E0560609B4B38ABFAD2B85DCACDB1411F10B275")), + a=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC4")), + b=bytes2long(hexdec("E8C2505DEDFC86DDC1BD0B2B6667F1DA34B82574761CB0E879BD081CFD0B6265EE3CB090F30D27614CB4574010DA90DD862EF9D4EBEE4761503190785A71C760")), + x=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003")), + y=bytes2long(hexdec("7503CFE87A836AE3A61B8816E25450E6CE5E1C93ACF1ABC1778064FDCBEFA921DF1626BE4FD036E93D75E6A50E3A41E98028FE5FC235F5B889A589CB5215F2A4")), + ), + "id-tc26-gost-3410-12-512-paramSetB": GOST3410Curve( + p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006F")), + q=bytes2long(hexdec("800000000000000000000000000000000000000000000000000000000000000149A1EC142565A545ACFDB77BD9D40CFA8B996712101BEA0EC6346C54374F25BD")), + a=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006C")), + b=bytes2long(hexdec("687D1B459DC841457E3E06CF6F5E2517B97C7D614AF138BCBF85DC806C4B289F3E965D2DB1416D217F8B276FAD1AB69C50F78BEE1FA3106EFB8CCBC7C5140116")), + x=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002")), + y=bytes2long(hexdec("1A8F7EDA389B094C2C071E3647A8940F3C123B697578C213BE6DD9E6C8EC7335DCB228FD1EDF4A39152CBCAAF8C0398828041055F94CEEEC7E21340780FE41BD")), + ), + "id-tc26-gost-3410-2012-512-paramSetC": GOST3410Curve( + p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7")), + q=bytes2long(hexdec("3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC98CDBA46506AB004C33A9FF5147502CC8EDA9E7A769A12694623CEF47F023ED")), + a=bytes2long(hexdec("DC9203E514A721875485A529D2C722FB187BC8980EB866644DE41C68E143064546E861C0E2C9EDD92ADE71F46FCF50FF2AD97F951FDA9F2A2EB6546F39689BD3")), + b=bytes2long(hexdec("B4C4EE28CEBC6C2C8AC12952CF37F16AC7EFB6A9F69F4B57FFDA2E4F0DE5ADE038CBC2FFF719D2C18DE0284B8BFEF3B52B8CC7A5F5BF0A3C8D2319A5312557E1")), + x=bytes2long(hexdec("E2E31EDFC23DE7BDEBE241CE593EF5DE2295B7A9CBAEF021D385F7074CEA043AA27272A7AE602BF2A7B9033DB9ED3610C6FB85487EAE97AAC5BC7928C1950148")), + y=bytes2long(hexdec("F5CE40D95B5EB899ABBCCFF5911CB8577939804D6527378B8C108C3D2090FF9BE18E2D33E3021ED2EF32D85822423B6304F726AA854BAE07D0396E9A9ADDC40F")), + cofactor=4, + e=0x01, + d=bytes2long(hexdec("9E4F5D8C017D8D9F13A5CF3CDF5BFE4DAB402D54198E31EBDE28A0621050439CA6B39E0A515C06B304E2CE43E79E369E91A0CFC2BC2A22B4CA302DBB33EE7550")), + ), +} +CURVES["id-GostR3410-2001-CryptoPro-XchA-ParamSet"] = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"] +CURVES["id-GostR3410-2001-CryptoPro-XchB-ParamSet"] = CURVES["id-GostR3410-2001-CryptoPro-C-ParamSet"] +CURVES["id-tc26-gost-3410-2012-256-paramSetB"] = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"] +CURVES["id-tc26-gost-3410-2012-256-paramSetC"] = CURVES["id-GostR3410-2001-CryptoPro-B-ParamSet"] +CURVES["id-tc26-gost-3410-2012-256-paramSetD"] = CURVES["id-GostR3410-2001-CryptoPro-C-ParamSet"] +DEFAULT_CURVE = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"] + + +def public_key(curve, prv): """ Generate public key from the private one :param GOST3410Curve curve: curve to use - :param long private_key: private key - :return: public key's parts, X and Y + :param long prv: private key + :returns: public key's parts, X and Y :rtype: (long, long) """ - return curve.exp(private_key) + return curve.exp(prv) -def sign(curve, private_key, digest, mode=2001): +def sign(curve, prv, digest, rand=None, mode=2001): """ Calculate signature for provided digest :param GOST3410Curve curve: curve to use - :param long private_key: private key + :param long prv: private key :param digest: digest for signing :type digest: bytes, 32 or 64 bytes - :return: signature + :param rand: optional predefined random data used for k/r generation + :type rand: bytes, 32 or 64 bytes + :returns: signature, BE(S) || BE(R) :rtype: bytes, 64 or 128 bytes """ size = MODE2SIZE[mode] @@ -200,14 +243,18 @@ def sign(curve, private_key, digest, mode=2001): if e == 0: e = 1 while True: - k = bytes2long(urandom(size)) % q + if rand is None: + rand = urandom(size) + elif len(rand) != size: + raise ValueError("rand length != %d" % size) + k = bytes2long(rand) % q if k == 0: continue r, _ = curve.exp(k) r %= q if r == 0: continue - d = private_key * r + d = prv * r k *= e s = (d + k) % q if s == 0: @@ -260,13 +307,13 @@ def verify(curve, pub, digest, signature, mode=2001): return lm == r -def prv_unmarshal(private_key): - """Unmarshal private key +def prv_unmarshal(prv): + """Unmarshal little-endian private key - :param bytes private_key: serialized private key + :param bytes prv: serialized private key :rtype: long """ - return bytes2long(private_key[::-1]) + return bytes2long(prv[::-1]) def pub_marshal(pub, mode=2001): @@ -274,6 +321,7 @@ def pub_marshal(pub, mode=2001): :type pub: (long, long) :rtype: bytes + :returns: LE(X) || LE(Y) """ size = MODE2SIZE[mode] return (long2bytes(pub[1], size) + long2bytes(pub[0], size))[::-1] @@ -282,9 +330,31 @@ def pub_marshal(pub, mode=2001): def pub_unmarshal(pub, mode=2001): """Unmarshal public key + :param pub: LE(X) || LE(Y) :type pub: bytes :rtype: (long, long) """ size = MODE2SIZE[mode] pub = pub[::-1] return (bytes2long(pub[size:]), bytes2long(pub[:size])) + + +def uv2xy(curve, u, v): + """Convert twisted Edwards curve U,V coordinates to Weierstrass X,Y + """ + s, t = curve.st() + k1 = (s * (1 + v)) % curve.p + k2 = curve.pos(1 - v) + x = t + k1 * modinvert(k2, curve.p) + y = k1 * modinvert(u * k2, curve.p) + return x % curve.p, y % curve.p + + +def xy2uv(curve, x, y): + """Convert Weierstrass X,Y coordinates to twisted Edwards curve U,V + """ + s, t = curve.st() + xmt = curve.pos(x - t) + u = xmt * modinvert(y, curve.p) + v = curve.pos(xmt - s) * modinvert(xmt + s, curve.p) + return u % curve.p, v % curve.p