2 # PyGOST -- Pure Python GOST cryptographic functions library
3 # Copyright (C) 2015-2022 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
31 def point_size(point):
32 """Determine is it either 256 or 512 bit point
34 return (512 // 8) if point.bit_length() > 256 else (256 // 8)
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
56 :param str name: human-readable curve name
58 def __init__(self, p, q, a, b, x, y, cofactor=1, e=None, d=None, name=None):
65 self.cofactor = cofactor
68 if not self.contains((x, y)):
69 raise ValueError("Invalid parameters")
75 return point_size(self.p)
78 return "<%s: %s>" % (self.__class__.__name__, self.name)
81 """Make positive number
87 def contains(self, point):
88 """Is point on the curve?
90 :type point: (long, long)
94 r2 = ((x * x + self.a) * x + self.b) % self.p
95 return r1 == self.pos(r2)
97 def _add(self, p1x, p1y, p2x, p2y):
98 if p1x == p2x and p1y == p2y:
100 t = ((3 * p1x * p1x + self.a) * modinvert(2 * p1y, self.p)) % self.p
102 tx = self.pos(p2x - p1x) % self.p
103 ty = self.pos(p2y - p1y) % self.p
104 t = (ty * modinvert(tx, self.p)) % self.p
105 tx = self.pos(t * t - p1x - p2x) % self.p
106 ty = self.pos(t * (p1x - tx) - p1y) % self.p
109 def exp(self, degree, x=None, y=None):
115 raise ValueError("Bad degree value")
119 tx, ty = self._add(tx, ty, x, y)
121 x, y = self._add(x, y, x, y)
125 """Compute s/t parameters for twisted Edwards curve points conversion
127 if self.e is None or self.d is None:
128 raise ValueError("Non twisted Edwards curve")
129 if self._st is not None:
132 self.pos(self.e - self.d) * modinvert(4, self.p) % self.p,
133 (self.e + self.d) * modinvert(6, self.p) % self.p,
139 "GostR3410_2001_ParamSet_cc": GOST3410Curve(
140 p=bytes2long(hexdec("C0000000000000000000000000000000000000000000000000000000000003C7")),
141 q=bytes2long(hexdec("5fffffffffffffffffffffffffffffff606117a2f4bde428b7458a54b6e87b85")),
142 a=bytes2long(hexdec("C0000000000000000000000000000000000000000000000000000000000003c4")),
143 b=bytes2long(hexdec("2d06B4265ebc749ff7d0f1f1f88232e81632e9088fd44b7787d5e407e955080c")),
144 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000002")),
145 y=bytes2long(hexdec("a20e034bf8813ef5c18d01105e726a17eb248b264ae9706f440bedc8ccb6b22c")),
147 "id-GostR3410-2001-TestParamSet": GOST3410Curve(
148 p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000431")),
149 q=bytes2long(hexdec("8000000000000000000000000000000150FE8A1892976154C59CFC193ACCF5B3")),
150 a=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000007")),
151 b=bytes2long(hexdec("5FBFF498AA938CE739B8E022FBAFEF40563F6E6A3472FC2A514C0CE9DAE23B7E")),
152 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000002")),
153 y=bytes2long(hexdec("08E2A8A0E65147D4BD6316030E16D19C85C97F0A9CA267122B96ABBCEA7E8FC8")),
155 "id-tc26-gost-3410-12-256-paramSetA": GOST3410Curve(
156 p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD97")),
157 q=bytes2long(hexdec("400000000000000000000000000000000FD8CDDFC87B6635C115AF556C360C67")),
158 a=bytes2long(hexdec("C2173F1513981673AF4892C23035A27CE25E2013BF95AA33B22C656F277E7335")),
159 b=bytes2long(hexdec("295F9BAE7428ED9CCC20E7C359A9D41A22FCCD9108E17BF7BA9337A6F8AE9513")),
160 x=bytes2long(hexdec("91E38443A5E82C0D880923425712B2BB658B9196932E02C78B2582FE742DAA28")),
161 y=bytes2long(hexdec("32879423AB1A0375895786C4BB46E9565FDE0B5344766740AF268ADB32322E5C")),
164 d=bytes2long(hexdec("0605F6B7C183FA81578BC39CFAD518132B9DF62897009AF7E522C32D6DC7BFFB")),
166 "id-tc26-gost-3410-12-256-paramSetB": GOST3410Curve(
167 p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD97")),
168 q=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF6C611070995AD10045841B09B761B893")),
169 a=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD94")),
170 b=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000a6")),
171 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000001")),
172 y=bytes2long(hexdec("8D91E471E0989CDA27DF505A453F2B7635294F2DDF23E3B122ACC99C9E9F1E14")),
174 "id-tc26-gost-3410-12-256-paramSetC": GOST3410Curve(
175 p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000C99")),
176 q=bytes2long(hexdec("800000000000000000000000000000015F700CFFF1A624E5E497161BCC8A198F")),
177 a=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000C96")),
178 b=bytes2long(hexdec("3E1AF419A269A5F866A7D3C25C3DF80AE979259373FF2B182F49D4CE7E1BBC8B")),
179 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000001")),
180 y=bytes2long(hexdec("3FA8124359F96680B83D1C3EB2C070E5C545C9858D03ECFB744BF8D717717EFC")),
182 "id-tc26-gost-3410-12-256-paramSetD": GOST3410Curve(
183 p=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AACF846E86789051D37998F7B9022D759B")),
184 q=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AA582CA3511EDDFB74F02F3A6598980BB9")),
185 a=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AACF846E86789051D37998F7B9022D7598")),
186 b=bytes2long(hexdec("000000000000000000000000000000000000000000000000000000000000805a")),
187 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000000")),
188 y=bytes2long(hexdec("41ECE55743711A8C3CBF3783CD08C0EE4D4DC440D4641A8F366E550DFDB3BB67")),
190 "id-tc26-gost-3410-12-512-paramSetTest": GOST3410Curve(
191 p=bytes2long(hexdec("4531ACD1FE0023C7550D267B6B2FEE80922B14B2FFB90F04D4EB7C09B5D2D15DF1D852741AF4704A0458047E80E4546D35B8336FAC224DD81664BBF528BE6373")),
192 q=bytes2long(hexdec("4531ACD1FE0023C7550D267B6B2FEE80922B14B2FFB90F04D4EB7C09B5D2D15DA82F2D7ECB1DBAC719905C5EECC423F1D86E25EDBE23C595D644AAF187E6E6DF")),
194 b=bytes2long(hexdec("1CFF0806A31116DA29D8CFA54E57EB748BC5F377E49400FDD788B649ECA1AC4361834013B2AD7322480A89CA58E0CF74BC9E540C2ADD6897FAD0A3084F302ADC")),
195 x=bytes2long(hexdec("24D19CC64572EE30F396BF6EBBFD7A6C5213B3B3D7057CC825F91093A68CD762FD60611262CD838DC6B60AA7EEE804E28BC849977FAC33B4B530F1B120248A9A")),
196 y=bytes2long(hexdec("2BB312A43BD2CE6E0D020613C857ACDDCFBF061E91E5F2C3F32447C259F39B2C83AB156D77F1496BF7EB3351E1EE4E43DC1A18B91B24640B6DBB92CB1ADD371E")),
198 "id-tc26-gost-3410-12-512-paramSetA": GOST3410Curve(
199 p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7")),
200 q=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF27E69532F48D89116FF22B8D4E0560609B4B38ABFAD2B85DCACDB1411F10B275")),
201 a=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC4")),
202 b=bytes2long(hexdec("E8C2505DEDFC86DDC1BD0B2B6667F1DA34B82574761CB0E879BD081CFD0B6265EE3CB090F30D27614CB4574010DA90DD862EF9D4EBEE4761503190785A71C760")),
203 x=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003")),
204 y=bytes2long(hexdec("7503CFE87A836AE3A61B8816E25450E6CE5E1C93ACF1ABC1778064FDCBEFA921DF1626BE4FD036E93D75E6A50E3A41E98028FE5FC235F5B889A589CB5215F2A4")),
206 "id-tc26-gost-3410-12-512-paramSetB": GOST3410Curve(
207 p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006F")),
208 q=bytes2long(hexdec("800000000000000000000000000000000000000000000000000000000000000149A1EC142565A545ACFDB77BD9D40CFA8B996712101BEA0EC6346C54374F25BD")),
209 a=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006C")),
210 b=bytes2long(hexdec("687D1B459DC841457E3E06CF6F5E2517B97C7D614AF138BCBF85DC806C4B289F3E965D2DB1416D217F8B276FAD1AB69C50F78BEE1FA3106EFB8CCBC7C5140116")),
211 x=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002")),
212 y=bytes2long(hexdec("1A8F7EDA389B094C2C071E3647A8940F3C123B697578C213BE6DD9E6C8EC7335DCB228FD1EDF4A39152CBCAAF8C0398828041055F94CEEEC7E21340780FE41BD")),
214 "id-tc26-gost-3410-12-512-paramSetC": GOST3410Curve(
215 p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7")),
216 q=bytes2long(hexdec("3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC98CDBA46506AB004C33A9FF5147502CC8EDA9E7A769A12694623CEF47F023ED")),
217 a=bytes2long(hexdec("DC9203E514A721875485A529D2C722FB187BC8980EB866644DE41C68E143064546E861C0E2C9EDD92ADE71F46FCF50FF2AD97F951FDA9F2A2EB6546F39689BD3")),
218 b=bytes2long(hexdec("B4C4EE28CEBC6C2C8AC12952CF37F16AC7EFB6A9F69F4B57FFDA2E4F0DE5ADE038CBC2FFF719D2C18DE0284B8BFEF3B52B8CC7A5F5BF0A3C8D2319A5312557E1")),
219 x=bytes2long(hexdec("E2E31EDFC23DE7BDEBE241CE593EF5DE2295B7A9CBAEF021D385F7074CEA043AA27272A7AE602BF2A7B9033DB9ED3610C6FB85487EAE97AAC5BC7928C1950148")),
220 y=bytes2long(hexdec("F5CE40D95B5EB899ABBCCFF5911CB8577939804D6527378B8C108C3D2090FF9BE18E2D33E3021ED2EF32D85822423B6304F726AA854BAE07D0396E9A9ADDC40F")),
223 d=bytes2long(hexdec("9E4F5D8C017D8D9F13A5CF3CDF5BFE4DAB402D54198E31EBDE28A0621050439CA6B39E0A515C06B304E2CE43E79E369E91A0CFC2BC2A22B4CA302DBB33EE7550")),
226 CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"] = CURVES["id-tc26-gost-3410-12-256-paramSetB"]
227 CURVES["id-GostR3410-2001-CryptoPro-B-ParamSet"] = CURVES["id-tc26-gost-3410-12-256-paramSetC"]
228 CURVES["id-GostR3410-2001-CryptoPro-C-ParamSet"] = CURVES["id-tc26-gost-3410-12-256-paramSetD"]
229 CURVES["id-GostR3410-2001-CryptoPro-XchA-ParamSet"] = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"]
230 CURVES["id-GostR3410-2001-CryptoPro-XchB-ParamSet"] = CURVES["id-GostR3410-2001-CryptoPro-C-ParamSet"]
231 CURVES["id-tc26-gost-3410-2012-256-paramSetA"] = CURVES["id-tc26-gost-3410-12-256-paramSetA"]
232 CURVES["id-tc26-gost-3410-2012-256-paramSetB"] = CURVES["id-tc26-gost-3410-12-256-paramSetB"]
233 CURVES["id-tc26-gost-3410-2012-256-paramSetC"] = CURVES["id-tc26-gost-3410-12-256-paramSetC"]
234 CURVES["id-tc26-gost-3410-2012-256-paramSetD"] = CURVES["id-tc26-gost-3410-12-256-paramSetD"]
235 CURVES["id-tc26-gost-3410-2012-512-paramSetTest"] = CURVES["id-tc26-gost-3410-12-512-paramSetTest"]
236 CURVES["id-tc26-gost-3410-2012-512-paramSetA"] = CURVES["id-tc26-gost-3410-12-512-paramSetA"]
237 CURVES["id-tc26-gost-3410-2012-512-paramSetB"] = CURVES["id-tc26-gost-3410-12-512-paramSetB"]
238 CURVES["id-tc26-gost-3410-2012-512-paramSetC"] = CURVES["id-tc26-gost-3410-12-512-paramSetC"]
239 for _name, _curve in CURVES.items():
241 DEFAULT_CURVE = CURVES["id-tc26-gost-3410-12-256-paramSetB"]
244 def public_key(curve, prv):
245 """Generate public key from the private one
247 :param GOST3410Curve curve: curve to use
248 :param long prv: private key
249 :returns: public key's parts, X and Y
252 return curve.exp(prv)
255 def sign(curve, prv, digest, rand=None):
256 """Calculate signature for provided digest
258 :param GOST3410Curve curve: curve to use
259 :param long prv: private key
260 :param digest: digest for signing
261 :type digest: bytes, 32 or 64 bytes
262 :param rand: optional predefined random data used for k/r generation
263 :type rand: bytes, 32 or 64 bytes
264 :returns: signature, BE(S) || BE(R)
265 :rtype: bytes, 64 or 128 bytes
267 size = curve.point_size
269 e = bytes2long(digest) % q
275 elif len(rand) != size:
276 raise ValueError("rand length != %d" % size)
277 k = bytes2long(rand) % q
290 return long2bytes(s, size) + long2bytes(r, size)
293 def verify(curve, pub, digest, signature):
294 """Verify provided digest with the signature
296 :param GOST3410Curve curve: curve to use
297 :type pub: (long, long)
298 :param digest: digest needed to check
299 :type digest: bytes, 32 or 64 bytes
300 :param signature: signature to verify with
301 :type signature: bytes, 64 or 128 bytes
304 size = curve.point_size
305 if len(signature) != size * 2:
306 raise ValueError("Invalid signature length")
309 s = bytes2long(signature[:size])
310 r = bytes2long(signature[size:])
311 if r <= 0 or r >= q or s <= 0 or s >= q:
313 e = bytes2long(digest) % curve.q
319 p1x, p1y = curve.exp(z1)
320 q1x, q1y = curve.exp(z2, pub[0], pub[1])
324 lm = modinvert(lm, p)
333 # This is not constant time comparison!
337 def prv_unmarshal(prv):
338 """Unmarshal little-endian private key
340 :param bytes prv: serialized private key
343 It is advisable to use :py:func:`pygost.gost3410.prv_marshal` to
344 assure that key i in curve's Q field for better compatibility with
345 some implementations.
347 return bytes2long(prv[::-1])
350 def prv_marshal(curve, prv):
351 """Marshal little-endian private key
353 :param GOST3410Curve curve: curve to use
354 :param long prv: serialized private key
357 Key is in curve's Q field.
359 return long2bytes(prv % curve.q, point_size(prv))[::-1]
362 def pub_marshal(pub):
363 """Marshal public key
365 :type pub: (long, long)
367 :returns: LE(X) || LE(Y)
369 size = point_size(pub[0])
370 return (long2bytes(pub[1], size) + long2bytes(pub[0], size))[::-1]
373 def pub_unmarshal(pub):
374 """Unmarshal public key
376 :param pub: LE(X) || LE(Y)
382 return (bytes2long(pub[size:]), bytes2long(pub[:size]))
385 def uv2xy(curve, u, v):
386 """Convert twisted Edwards curve U,V coordinates to Weierstrass X,Y
389 k1 = (s * (1 + v)) % curve.p
390 k2 = curve.pos(1 - v)
391 x = t + k1 * modinvert(k2, curve.p)
392 y = k1 * modinvert(u * k2, curve.p)
393 return x % curve.p, y % curve.p
396 def xy2uv(curve, x, y):
397 """Convert Weierstrass X,Y coordinates to twisted Edwards curve U,V
400 xmt = curve.pos(x - t)
401 u = xmt * modinvert(y, curve.p)
402 v = curve.pos(xmt - s) * modinvert(xmt + s, curve.p)
403 return u % curve.p, v % curve.p