2 # PyGOST -- Pure Python GOST cryptographic functions library
3 # Copyright (C) 2015-2020 Sergey Matveev <stargrave@stargrave.org>
5 # This program is free software: you can redistribute it and/or modify
6 # it under the terms of the GNU General Public License as published by
7 # the Free Software Foundation, version 3 of the License.
9 # This program is distributed in the hope that it will be useful,
10 # but WITHOUT ANY WARRANTY; without even the implied warranty of
11 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 # GNU General Public License for more details.
14 # You should have received a copy of the GNU General Public License
15 # along with this program. If not, see <http://www.gnu.org/licenses/>.
16 """ GOST R 34.10 public-key signature function.
18 This is implementation of GOST R 34.10-2001 (:rfc:`5832`), GOST R
19 34.10-2012 (:rfc:`7091`). The difference between 2001 and 2012 is the
20 key, digest and signature lengths.
23 from os import urandom
25 from pygost.utils import bytes2long
26 from pygost.utils import hexdec
27 from pygost.utils import long2bytes
28 from pygost.utils import modinvert
37 class GOST3410Curve(object):
38 """ GOST 34.10 validated curve
40 >>> curve = CURVES["id-GostR3410-2001-TestParamSet"]
41 >>> prv = prv_unmarshal(urandom(32))
42 >>> signature = sign(curve, prv, GOST341194(data).digest())
43 >>> pub = public_key(curve, prv)
44 >>> verify(curve, pub, GOST341194(data).digest(), signature)
47 :param long p: characteristic of the underlying prime field
48 :param long q: elliptic curve subgroup order
49 :param long a, b: coefficients of the equation of the elliptic curve in
51 :param long x, y: the coordinate of the point P (generator of the
52 subgroup of order q) of the elliptic curve in
54 :param long e, d: coefficients of the equation of the elliptic curve in
55 the twisted Edwards form
57 def __init__(self, p, q, a, b, x, y, e=None, d=None):
66 r1 = self.y * self.y % self.p
67 r2 = ((self.x * self.x + self.a) * self.x + self.b) % self.p
68 if r1 != self.pos(r2):
69 raise ValueError("Invalid parameters")
73 """Make positive number
79 def _add(self, p1x, p1y, p2x, p2y):
80 if p1x == p2x and p1y == p2y:
82 t = ((3 * p1x * p1x + self.a) * modinvert(2 * p1y, self.p)) % self.p
84 tx = self.pos(p2x - p1x) % self.p
85 ty = self.pos(p2y - p1y) % self.p
86 t = (ty * modinvert(tx, self.p)) % self.p
87 tx = self.pos(t * t - p1x - p2x) % self.p
88 ty = self.pos(t * (p1x - tx) - p1y) % self.p
91 def exp(self, degree, x=None, y=None):
97 raise ValueError("Bad degree value")
101 tx, ty = self._add(tx, ty, x, y)
103 x, y = self._add(x, y, x, y)
107 """Compute s/t parameters for twisted Edwards curve points conversion
109 if self.e is None or self.d is None:
110 raise ValueError("non twisted Edwards curve")
111 if self._st is not None:
114 self.pos(self.e - self.d) * modinvert(4, self.p) % self.p,
115 (self.e + self.d) * modinvert(6, self.p) % self.p,
121 "GostR3410_2001_ParamSet_cc": GOST3410Curve(
122 p=bytes2long(hexdec("C0000000000000000000000000000000000000000000000000000000000003C7")),
123 q=bytes2long(hexdec("5fffffffffffffffffffffffffffffff606117a2f4bde428b7458a54b6e87b85")),
124 a=bytes2long(hexdec("C0000000000000000000000000000000000000000000000000000000000003c4")),
125 b=bytes2long(hexdec("2d06B4265ebc749ff7d0f1f1f88232e81632e9088fd44b7787d5e407e955080c")),
126 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000002")),
127 y=bytes2long(hexdec("a20e034bf8813ef5c18d01105e726a17eb248b264ae9706f440bedc8ccb6b22c")),
129 "id-GostR3410-2001-TestParamSet": GOST3410Curve(
130 p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000431")),
131 q=bytes2long(hexdec("8000000000000000000000000000000150FE8A1892976154C59CFC193ACCF5B3")),
132 a=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000007")),
133 b=bytes2long(hexdec("5FBFF498AA938CE739B8E022FBAFEF40563F6E6A3472FC2A514C0CE9DAE23B7E")),
134 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000002")),
135 y=bytes2long(hexdec("08E2A8A0E65147D4BD6316030E16D19C85C97F0A9CA267122B96ABBCEA7E8FC8")),
137 "id-GostR3410-2001-CryptoPro-A-ParamSet": GOST3410Curve(
138 p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD97")),
139 q=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF6C611070995AD10045841B09B761B893")),
140 a=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD94")),
141 b=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000a6")),
142 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000001")),
143 y=bytes2long(hexdec("8D91E471E0989CDA27DF505A453F2B7635294F2DDF23E3B122ACC99C9E9F1E14")),
145 "id-GostR3410-2001-CryptoPro-B-ParamSet": GOST3410Curve(
146 p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000C99")),
147 q=bytes2long(hexdec("800000000000000000000000000000015F700CFFF1A624E5E497161BCC8A198F")),
148 a=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000C96")),
149 b=bytes2long(hexdec("3E1AF419A269A5F866A7D3C25C3DF80AE979259373FF2B182F49D4CE7E1BBC8B")),
150 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000001")),
151 y=bytes2long(hexdec("3FA8124359F96680B83D1C3EB2C070E5C545C9858D03ECFB744BF8D717717EFC")),
153 "id-GostR3410-2001-CryptoPro-C-ParamSet": GOST3410Curve(
154 p=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AACF846E86789051D37998F7B9022D759B")),
155 q=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AA582CA3511EDDFB74F02F3A6598980BB9")),
156 a=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AACF846E86789051D37998F7B9022D7598")),
157 b=bytes2long(hexdec("000000000000000000000000000000000000000000000000000000000000805a")),
158 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000000")),
159 y=bytes2long(hexdec("41ECE55743711A8C3CBF3783CD08C0EE4D4DC440D4641A8F366E550DFDB3BB67")),
161 "id-tc26-gost-3410-2012-256-paramSetA": GOST3410Curve(
162 p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD97")),
163 q=bytes2long(hexdec("400000000000000000000000000000000FD8CDDFC87B6635C115AF556C360C67")),
164 a=bytes2long(hexdec("C2173F1513981673AF4892C23035A27CE25E2013BF95AA33B22C656F277E7335")),
165 b=bytes2long(hexdec("295F9BAE7428ED9CCC20E7C359A9D41A22FCCD9108E17BF7BA9337A6F8AE9513")),
166 x=bytes2long(hexdec("91E38443A5E82C0D880923425712B2BB658B9196932E02C78B2582FE742DAA28")),
167 y=bytes2long(hexdec("32879423AB1A0375895786C4BB46E9565FDE0B5344766740AF268ADB32322E5C")),
169 d=bytes2long(hexdec("0605F6B7C183FA81578BC39CFAD518132B9DF62897009AF7E522C32D6DC7BFFB")),
171 "id-tc26-gost-3410-12-512-paramSetA": GOST3410Curve(
172 p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7")),
173 q=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF27E69532F48D89116FF22B8D4E0560609B4B38ABFAD2B85DCACDB1411F10B275")),
174 a=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC4")),
175 b=bytes2long(hexdec("E8C2505DEDFC86DDC1BD0B2B6667F1DA34B82574761CB0E879BD081CFD0B6265EE3CB090F30D27614CB4574010DA90DD862EF9D4EBEE4761503190785A71C760")),
176 x=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003")),
177 y=bytes2long(hexdec("7503CFE87A836AE3A61B8816E25450E6CE5E1C93ACF1ABC1778064FDCBEFA921DF1626BE4FD036E93D75E6A50E3A41E98028FE5FC235F5B889A589CB5215F2A4")),
179 "id-tc26-gost-3410-12-512-paramSetB": GOST3410Curve(
180 p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006F")),
181 q=bytes2long(hexdec("800000000000000000000000000000000000000000000000000000000000000149A1EC142565A545ACFDB77BD9D40CFA8B996712101BEA0EC6346C54374F25BD")),
182 a=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006C")),
183 b=bytes2long(hexdec("687D1B459DC841457E3E06CF6F5E2517B97C7D614AF138BCBF85DC806C4B289F3E965D2DB1416D217F8B276FAD1AB69C50F78BEE1FA3106EFB8CCBC7C5140116")),
184 x=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002")),
185 y=bytes2long(hexdec("1A8F7EDA389B094C2C071E3647A8940F3C123B697578C213BE6DD9E6C8EC7335DCB228FD1EDF4A39152CBCAAF8C0398828041055F94CEEEC7E21340780FE41BD")),
187 "id-tc26-gost-3410-2012-512-paramSetC": GOST3410Curve(
188 p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7")),
189 q=bytes2long(hexdec("3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC98CDBA46506AB004C33A9FF5147502CC8EDA9E7A769A12694623CEF47F023ED")),
190 a=bytes2long(hexdec("DC9203E514A721875485A529D2C722FB187BC8980EB866644DE41C68E143064546E861C0E2C9EDD92ADE71F46FCF50FF2AD97F951FDA9F2A2EB6546F39689BD3")),
191 b=bytes2long(hexdec("B4C4EE28CEBC6C2C8AC12952CF37F16AC7EFB6A9F69F4B57FFDA2E4F0DE5ADE038CBC2FFF719D2C18DE0284B8BFEF3B52B8CC7A5F5BF0A3C8D2319A5312557E1")),
192 x=bytes2long(hexdec("E2E31EDFC23DE7BDEBE241CE593EF5DE2295B7A9CBAEF021D385F7074CEA043AA27272A7AE602BF2A7B9033DB9ED3610C6FB85487EAE97AAC5BC7928C1950148")),
193 y=bytes2long(hexdec("F5CE40D95B5EB899ABBCCFF5911CB8577939804D6527378B8C108C3D2090FF9BE18E2D33E3021ED2EF32D85822423B6304F726AA854BAE07D0396E9A9ADDC40F")),
195 d=bytes2long(hexdec("9E4F5D8C017D8D9F13A5CF3CDF5BFE4DAB402D54198E31EBDE28A0621050439CA6B39E0A515C06B304E2CE43E79E369E91A0CFC2BC2A22B4CA302DBB33EE7550")),
198 CURVES["id-GostR3410-2001-CryptoPro-XchA-ParamSet"] = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"]
199 CURVES["id-GostR3410-2001-CryptoPro-XchB-ParamSet"] = CURVES["id-GostR3410-2001-CryptoPro-C-ParamSet"]
200 CURVES["id-tc26-gost-3410-2012-256-paramSetB"] = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"]
201 CURVES["id-tc26-gost-3410-2012-256-paramSetC"] = CURVES["id-GostR3410-2001-CryptoPro-B-ParamSet"]
202 CURVES["id-tc26-gost-3410-2012-256-paramSetD"] = CURVES["id-GostR3410-2001-CryptoPro-C-ParamSet"]
203 DEFAULT_CURVE = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"]
206 def public_key(curve, prv):
207 """ Generate public key from the private one
209 :param GOST3410Curve curve: curve to use
210 :param long prv: private key
211 :returns: public key's parts, X and Y
214 return curve.exp(prv)
217 def sign(curve, prv, digest, mode=2001):
218 """ Calculate signature for provided digest
220 :param GOST3410Curve curve: curve to use
221 :param long prv: private key
222 :param digest: digest for signing
223 :type digest: bytes, 32 or 64 bytes
225 :rtype: bytes, 64 or 128 bytes
227 size = MODE2SIZE[mode]
229 e = bytes2long(digest) % q
233 k = bytes2long(urandom(size)) % q
246 return long2bytes(s, size) + long2bytes(r, size)
249 def verify(curve, pub, digest, signature, mode=2001):
250 """ Verify provided digest with the signature
252 :param GOST3410Curve curve: curve to use
253 :type pub: (long, long)
254 :param digest: digest needed to check
255 :type digest: bytes, 32 or 64 bytes
256 :param signature: signature to verify with
257 :type signature: bytes, 64 or 128 bytes
260 size = MODE2SIZE[mode]
261 if len(signature) != size * 2:
262 raise ValueError("Invalid signature length")
265 s = bytes2long(signature[:size])
266 r = bytes2long(signature[size:])
267 if r <= 0 or r >= q or s <= 0 or s >= q:
269 e = bytes2long(digest) % curve.q
275 p1x, p1y = curve.exp(z1)
276 q1x, q1y = curve.exp(z2, pub[0], pub[1])
280 lm = modinvert(lm, p)
289 # This is not constant time comparison!
293 def prv_unmarshal(prv):
294 """Unmarshal private key
296 :param bytes prv: serialized private key
299 return bytes2long(prv[::-1])
302 def pub_marshal(pub, mode=2001):
303 """Marshal public key
305 :type pub: (long, long)
308 size = MODE2SIZE[mode]
309 return (long2bytes(pub[1], size) + long2bytes(pub[0], size))[::-1]
312 def pub_unmarshal(pub, mode=2001):
313 """Unmarshal public key
318 size = MODE2SIZE[mode]
320 return (bytes2long(pub[size:]), bytes2long(pub[:size]))
323 def uv2xy(curve, u, v):
324 """Convert twisted Edwards curve U,V coordinates to Weierstrass X,Y
327 k1 = (s * (1 + v)) % curve.p
328 k2 = curve.pos(1 - v)
329 x = t + k1 * modinvert(k2, curve.p)
330 y = k1 * modinvert(u * k2, curve.p)
331 return x % curve.p, y % curve.p
334 def xy2uv(curve, x, y):
335 """Convert Weierstrass X,Y coordinates to twisted Edwards curve U,V
338 xmt = curve.pos(x - t)
339 u = xmt * modinvert(y, curve.p)
340 v = curve.pos(xmt - s) * modinvert(xmt + s, curve.p)
341 return u % curve.p, v % curve.p