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
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
57 def __init__(self, p, q, a, b, x, y, cofactor=1, e=None, d=None):
64 self.cofactor = cofactor
67 if not self.contains((x, y)):
68 raise ValueError("Invalid parameters")
73 return point_size(self.p)
76 """Make positive number
82 def contains(self, point):
83 """Is point on the curve?
85 :type point: (long, long)
89 r2 = ((x * x + self.a) * x + self.b) % self.p
90 return r1 == self.pos(r2)
92 def _add(self, p1x, p1y, p2x, p2y):
93 if p1x == p2x and p1y == p2y:
95 t = ((3 * p1x * p1x + self.a) * modinvert(2 * p1y, self.p)) % self.p
97 tx = self.pos(p2x - p1x) % self.p
98 ty = self.pos(p2y - p1y) % self.p
99 t = (ty * modinvert(tx, self.p)) % self.p
100 tx = self.pos(t * t - p1x - p2x) % self.p
101 ty = self.pos(t * (p1x - tx) - p1y) % self.p
104 def exp(self, degree, x=None, y=None):
110 raise ValueError("Bad degree value")
114 tx, ty = self._add(tx, ty, x, y)
116 x, y = self._add(x, y, x, y)
120 """Compute s/t parameters for twisted Edwards curve points conversion
122 if self.e is None or self.d is None:
123 raise ValueError("Non twisted Edwards curve")
124 if self._st is not None:
127 self.pos(self.e - self.d) * modinvert(4, self.p) % self.p,
128 (self.e + self.d) * modinvert(6, self.p) % self.p,
134 "GostR3410_2001_ParamSet_cc": GOST3410Curve(
135 p=bytes2long(hexdec("C0000000000000000000000000000000000000000000000000000000000003C7")),
136 q=bytes2long(hexdec("5fffffffffffffffffffffffffffffff606117a2f4bde428b7458a54b6e87b85")),
137 a=bytes2long(hexdec("C0000000000000000000000000000000000000000000000000000000000003c4")),
138 b=bytes2long(hexdec("2d06B4265ebc749ff7d0f1f1f88232e81632e9088fd44b7787d5e407e955080c")),
139 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000002")),
140 y=bytes2long(hexdec("a20e034bf8813ef5c18d01105e726a17eb248b264ae9706f440bedc8ccb6b22c")),
142 "id-GostR3410-2001-TestParamSet": GOST3410Curve(
143 p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000431")),
144 q=bytes2long(hexdec("8000000000000000000000000000000150FE8A1892976154C59CFC193ACCF5B3")),
145 a=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000007")),
146 b=bytes2long(hexdec("5FBFF498AA938CE739B8E022FBAFEF40563F6E6A3472FC2A514C0CE9DAE23B7E")),
147 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000002")),
148 y=bytes2long(hexdec("08E2A8A0E65147D4BD6316030E16D19C85C97F0A9CA267122B96ABBCEA7E8FC8")),
150 "id-GostR3410-2001-CryptoPro-A-ParamSet": GOST3410Curve(
151 p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD97")),
152 q=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF6C611070995AD10045841B09B761B893")),
153 a=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD94")),
154 b=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000a6")),
155 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000001")),
156 y=bytes2long(hexdec("8D91E471E0989CDA27DF505A453F2B7635294F2DDF23E3B122ACC99C9E9F1E14")),
158 "id-GostR3410-2001-CryptoPro-B-ParamSet": GOST3410Curve(
159 p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000C99")),
160 q=bytes2long(hexdec("800000000000000000000000000000015F700CFFF1A624E5E497161BCC8A198F")),
161 a=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000C96")),
162 b=bytes2long(hexdec("3E1AF419A269A5F866A7D3C25C3DF80AE979259373FF2B182F49D4CE7E1BBC8B")),
163 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000001")),
164 y=bytes2long(hexdec("3FA8124359F96680B83D1C3EB2C070E5C545C9858D03ECFB744BF8D717717EFC")),
166 "id-GostR3410-2001-CryptoPro-C-ParamSet": GOST3410Curve(
167 p=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AACF846E86789051D37998F7B9022D759B")),
168 q=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AA582CA3511EDDFB74F02F3A6598980BB9")),
169 a=bytes2long(hexdec("9B9F605F5A858107AB1EC85E6B41C8AACF846E86789051D37998F7B9022D7598")),
170 b=bytes2long(hexdec("000000000000000000000000000000000000000000000000000000000000805a")),
171 x=bytes2long(hexdec("0000000000000000000000000000000000000000000000000000000000000000")),
172 y=bytes2long(hexdec("41ECE55743711A8C3CBF3783CD08C0EE4D4DC440D4641A8F366E550DFDB3BB67")),
174 "id-tc26-gost-3410-2012-256-paramSetA": GOST3410Curve(
175 p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD97")),
176 q=bytes2long(hexdec("400000000000000000000000000000000FD8CDDFC87B6635C115AF556C360C67")),
177 a=bytes2long(hexdec("C2173F1513981673AF4892C23035A27CE25E2013BF95AA33B22C656F277E7335")),
178 b=bytes2long(hexdec("295F9BAE7428ED9CCC20E7C359A9D41A22FCCD9108E17BF7BA9337A6F8AE9513")),
179 x=bytes2long(hexdec("91E38443A5E82C0D880923425712B2BB658B9196932E02C78B2582FE742DAA28")),
180 y=bytes2long(hexdec("32879423AB1A0375895786C4BB46E9565FDE0B5344766740AF268ADB32322E5C")),
183 d=bytes2long(hexdec("0605F6B7C183FA81578BC39CFAD518132B9DF62897009AF7E522C32D6DC7BFFB")),
185 "id-tc26-gost-3410-2012-512-paramSetTest": GOST3410Curve(
186 p=bytes2long(hexdec("4531ACD1FE0023C7550D267B6B2FEE80922B14B2FFB90F04D4EB7C09B5D2D15DF1D852741AF4704A0458047E80E4546D35B8336FAC224DD81664BBF528BE6373")),
187 q=bytes2long(hexdec("4531ACD1FE0023C7550D267B6B2FEE80922B14B2FFB90F04D4EB7C09B5D2D15DA82F2D7ECB1DBAC719905C5EECC423F1D86E25EDBE23C595D644AAF187E6E6DF")),
189 b=bytes2long(hexdec("1CFF0806A31116DA29D8CFA54E57EB748BC5F377E49400FDD788B649ECA1AC4361834013B2AD7322480A89CA58E0CF74BC9E540C2ADD6897FAD0A3084F302ADC")),
190 x=bytes2long(hexdec("24D19CC64572EE30F396BF6EBBFD7A6C5213B3B3D7057CC825F91093A68CD762FD60611262CD838DC6B60AA7EEE804E28BC849977FAC33B4B530F1B120248A9A")),
191 y=bytes2long(hexdec("2BB312A43BD2CE6E0D020613C857ACDDCFBF061E91E5F2C3F32447C259F39B2C83AB156D77F1496BF7EB3351E1EE4E43DC1A18B91B24640B6DBB92CB1ADD371E")),
193 "id-tc26-gost-3410-12-512-paramSetA": GOST3410Curve(
194 p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7")),
195 q=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF27E69532F48D89116FF22B8D4E0560609B4B38ABFAD2B85DCACDB1411F10B275")),
196 a=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC4")),
197 b=bytes2long(hexdec("E8C2505DEDFC86DDC1BD0B2B6667F1DA34B82574761CB0E879BD081CFD0B6265EE3CB090F30D27614CB4574010DA90DD862EF9D4EBEE4761503190785A71C760")),
198 x=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003")),
199 y=bytes2long(hexdec("7503CFE87A836AE3A61B8816E25450E6CE5E1C93ACF1ABC1778064FDCBEFA921DF1626BE4FD036E93D75E6A50E3A41E98028FE5FC235F5B889A589CB5215F2A4")),
201 "id-tc26-gost-3410-12-512-paramSetB": GOST3410Curve(
202 p=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006F")),
203 q=bytes2long(hexdec("800000000000000000000000000000000000000000000000000000000000000149A1EC142565A545ACFDB77BD9D40CFA8B996712101BEA0EC6346C54374F25BD")),
204 a=bytes2long(hexdec("8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006C")),
205 b=bytes2long(hexdec("687D1B459DC841457E3E06CF6F5E2517B97C7D614AF138BCBF85DC806C4B289F3E965D2DB1416D217F8B276FAD1AB69C50F78BEE1FA3106EFB8CCBC7C5140116")),
206 x=bytes2long(hexdec("00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002")),
207 y=bytes2long(hexdec("1A8F7EDA389B094C2C071E3647A8940F3C123B697578C213BE6DD9E6C8EC7335DCB228FD1EDF4A39152CBCAAF8C0398828041055F94CEEEC7E21340780FE41BD")),
209 "id-tc26-gost-3410-2012-512-paramSetC": GOST3410Curve(
210 p=bytes2long(hexdec("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFDC7")),
211 q=bytes2long(hexdec("3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC98CDBA46506AB004C33A9FF5147502CC8EDA9E7A769A12694623CEF47F023ED")),
212 a=bytes2long(hexdec("DC9203E514A721875485A529D2C722FB187BC8980EB866644DE41C68E143064546E861C0E2C9EDD92ADE71F46FCF50FF2AD97F951FDA9F2A2EB6546F39689BD3")),
213 b=bytes2long(hexdec("B4C4EE28CEBC6C2C8AC12952CF37F16AC7EFB6A9F69F4B57FFDA2E4F0DE5ADE038CBC2FFF719D2C18DE0284B8BFEF3B52B8CC7A5F5BF0A3C8D2319A5312557E1")),
214 x=bytes2long(hexdec("E2E31EDFC23DE7BDEBE241CE593EF5DE2295B7A9CBAEF021D385F7074CEA043AA27272A7AE602BF2A7B9033DB9ED3610C6FB85487EAE97AAC5BC7928C1950148")),
215 y=bytes2long(hexdec("F5CE40D95B5EB899ABBCCFF5911CB8577939804D6527378B8C108C3D2090FF9BE18E2D33E3021ED2EF32D85822423B6304F726AA854BAE07D0396E9A9ADDC40F")),
218 d=bytes2long(hexdec("9E4F5D8C017D8D9F13A5CF3CDF5BFE4DAB402D54198E31EBDE28A0621050439CA6B39E0A515C06B304E2CE43E79E369E91A0CFC2BC2A22B4CA302DBB33EE7550")),
221 CURVES["id-GostR3410-2001-CryptoPro-XchA-ParamSet"] = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"]
222 CURVES["id-GostR3410-2001-CryptoPro-XchB-ParamSet"] = CURVES["id-GostR3410-2001-CryptoPro-C-ParamSet"]
223 CURVES["id-tc26-gost-3410-2012-256-paramSetB"] = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"]
224 CURVES["id-tc26-gost-3410-2012-256-paramSetC"] = CURVES["id-GostR3410-2001-CryptoPro-B-ParamSet"]
225 CURVES["id-tc26-gost-3410-2012-256-paramSetD"] = CURVES["id-GostR3410-2001-CryptoPro-C-ParamSet"]
226 DEFAULT_CURVE = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"]
229 def public_key(curve, prv):
230 """Generate public key from the private one
232 :param GOST3410Curve curve: curve to use
233 :param long prv: private key
234 :returns: public key's parts, X and Y
237 return curve.exp(prv)
240 def sign(curve, prv, digest, rand=None):
241 """Calculate signature for provided digest
243 :param GOST3410Curve curve: curve to use
244 :param long prv: private key
245 :param digest: digest for signing
246 :type digest: bytes, 32 or 64 bytes
247 :param rand: optional predefined random data used for k/r generation
248 :type rand: bytes, 32 or 64 bytes
249 :returns: signature, BE(S) || BE(R)
250 :rtype: bytes, 64 or 128 bytes
252 size = curve.point_size
254 e = bytes2long(digest) % q
260 elif len(rand) != size:
261 raise ValueError("rand length != %d" % size)
262 k = bytes2long(rand) % q
275 return long2bytes(s, size) + long2bytes(r, size)
278 def verify(curve, pub, digest, signature):
279 """Verify provided digest with the signature
281 :param GOST3410Curve curve: curve to use
282 :type pub: (long, long)
283 :param digest: digest needed to check
284 :type digest: bytes, 32 or 64 bytes
285 :param signature: signature to verify with
286 :type signature: bytes, 64 or 128 bytes
289 size = curve.point_size
290 if len(signature) != size * 2:
291 raise ValueError("Invalid signature length")
294 s = bytes2long(signature[:size])
295 r = bytes2long(signature[size:])
296 if r <= 0 or r >= q or s <= 0 or s >= q:
298 e = bytes2long(digest) % curve.q
304 p1x, p1y = curve.exp(z1)
305 q1x, q1y = curve.exp(z2, pub[0], pub[1])
309 lm = modinvert(lm, p)
318 # This is not constant time comparison!
322 def prv_unmarshal(prv):
323 """Unmarshal little-endian private key
325 :param bytes prv: serialized private key
328 return bytes2long(prv[::-1])
331 def pub_marshal(pub):
332 """Marshal public key
334 :type pub: (long, long)
336 :returns: LE(X) || LE(Y)
338 size = point_size(pub[0])
339 return (long2bytes(pub[1], size) + long2bytes(pub[0], size))[::-1]
342 def pub_unmarshal(pub):
343 """Unmarshal public key
345 :param pub: LE(X) || LE(Y)
351 return (bytes2long(pub[size:]), bytes2long(pub[:size]))
354 def uv2xy(curve, u, v):
355 """Convert twisted Edwards curve U,V coordinates to Weierstrass X,Y
358 k1 = (s * (1 + v)) % curve.p
359 k2 = curve.pos(1 - v)
360 x = t + k1 * modinvert(k2, curve.p)
361 y = k1 * modinvert(u * k2, curve.p)
362 return x % curve.p, y % curve.p
365 def xy2uv(curve, x, y):
366 """Convert Weierstrass X,Y coordinates to twisted Edwards curve U,V
369 xmt = curve.pos(x - t)
370 u = xmt * modinvert(y, curve.p)
371 v = curve.pos(xmt - s) * modinvert(xmt + s, curve.p)
372 return u % curve.p, v % curve.p