# coding: utf-8
# PyGOST -- Pure Python GOST cryptographic functions library
-# Copyright (C) 2015-2016 Sergey Matveev <stargrave@stargrave.org>
+# Copyright (C) 2015-2020 Sergey Matveev <stargrave@stargrave.org>
#
# 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
}
-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_ParamSetB": (
- "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006F",
- "800000000000000000000000000000000000000000000000000000000000000149A1EC142565A545ACFDB77BD9D40CFA8B996712101BEA0EC6346C54374F25BD",
- "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006C",
- "687D1B459DC841457E3E06CF6F5E2517B97C7D614AF138BCBF85DC806C4B289F3E965D2DB1416D217F8B276FAD1AB69C50F78BEE1FA3106EFB8CCBC7C5140116",
- "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002",
- "1A8F7EDA389B094C2C071E3647A8940F3C123B697578C213BE6DD9E6C8EC7335DCB228FD1EDF4A39152CBCAAF8C0398828041055F94CEEEC7E21340780FE41BD"
- ),
-}
-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
# 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):
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)
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]
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:
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):
:type pub: (long, long)
:rtype: bytes
+ :returns: LE(X) || LE(Y)
"""
size = MODE2SIZE[mode]
return (long2bytes(pub[1], size) + long2bytes(pub[0], size))[::-1]
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