pygost/gost3410.py

   1 # coding: utf-8
   2 # PyGOST -- Pure Python GOST cryptographic functions library
   3 # Copyright (C) 2015-2019 Sergey Matveev <stargrave@stargrave.org>
   4 #
   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.
   8 #
   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.
  13 #
  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.
  17
  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.
  21 """
  22
  23 from os import urandom
  24
  25 from pygost.utils import bytes2long
  26 from pygost.utils import hexdec
  27 from pygost.utils import long2bytes
  28 from pygost.utils import modinvert
  29
  30
  31 MODE2SIZE = {
  32     2001: 32,
  33     2012: 64,
  34 }
  35
  36
  37 class GOST3410Curve(object):
  38     """ GOST 34.10 validated curve
  39
  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)
  45     True
  46
  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
  50                       the canonical form
  51     :param long x, y: the coordinate of the point P (generator of the
  52                       subgroup of order q) of the elliptic curve in
  53                       the canonical form
  54     :param long e, d: coefficients of the equation of the elliptic curve in
  55                       the twisted Edwards form
  56     """
  57     def __init__(self, p, q, a, b, x, y, e=None, d=None):
  58         self.p = p
  59         self.q = q
  60         self.a = a
  61         self.b = b
  62         self.x = x
  63         self.y = y
  64         self.e = e
  65         self.d = d
  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")
  70         self._st = None
  71
  72     def pos(self, v):
  73         """Make positive number
  74         """
  75         if v < 0:
  76             return v + self.p
  77         return v
  78
  79     def _add(self, p1x, p1y, p2x, p2y):
  80         if p1x == p2x and p1y == p2y:
  81             # double
  82             t = ((3 * p1x * p1x + self.a) * modinvert(2 * p1y, self.p)) % self.p
  83         else:
  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
  89         return tx, ty
  90
  91     def exp(self, degree, x=None, y=None):
  92         x = x or self.x
  93         y = y or self.y
  94         tx = x
  95         ty = y
  96         if degree == 0:
  97             raise ValueError("Bad degree value")
  98         degree -= 1
  99         while degree != 0:
 100             if degree & 1 == 1:
 101                 tx, ty = self._add(tx, ty, x, y)
 102             degree = degree >> 1
 103             x, y = self._add(x, y, x, y)
 104         return tx, ty
 105
 106     def st(self):
 107         """Compute s/t parameters for twisted Edwards curve points conversion
 108         """
 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:
 112             return self._st
 113         self._st = (
 114             self.pos(self.e - self.d) * modinvert(4, self.p) % self.p,
 115             (self.e + self.d) * modinvert(6, self.p) % self.p,
 116         )
 117         return self._st
 118
 119
 120 CURVES = {
 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")),
 128     ),
 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")),
 136     ),
 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")),
 144     ),
 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")),
 152     ),
 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")),
 160     ),
 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")),
 168         e=0x01,
 169         d=bytes2long(hexdec("0605F6B7C183FA81578BC39CFAD518132B9DF62897009AF7E522C32D6DC7BFFB")),
 170     ),
 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")),
 178     ),
 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")),
 186     ),
 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")),
 194         e=0x01,
 195         d=bytes2long(hexdec("9E4F5D8C017D8D9F13A5CF3CDF5BFE4DAB402D54198E31EBDE28A0621050439CA6B39E0A515C06B304E2CE43E79E369E91A0CFC2BC2A22B4CA302DBB33EE7550")),
 196     ),
 197 }
 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"]
 204
 205
 206 def public_key(curve, prv):
 207     """ Generate public key from the private one
 208
 209     :param GOST3410Curve curve: curve to use
 210     :param long prv: private key
 211     :returns: public key's parts, X and Y
 212     :rtype: (long, long)
 213     """
 214     return curve.exp(prv)
 215
 216
 217 def sign(curve, prv, digest, mode=2001):
 218     """ Calculate signature for provided digest
 219
 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
 224     :returns: signature
 225     :rtype: bytes, 64 or 128 bytes
 226     """
 227     size = MODE2SIZE[mode]
 228     q = curve.q
 229     e = bytes2long(digest) % q
 230     if e == 0:
 231         e = 1
 232     while True:
 233         k = bytes2long(urandom(size)) % q
 234         if k == 0:
 235             continue
 236         r, _ = curve.exp(k)
 237         r %= q
 238         if r == 0:
 239             continue
 240         d = prv * r
 241         k *= e
 242         s = (d + k) % q
 243         if s == 0:
 244             continue
 245         break
 246     return long2bytes(s, size) + long2bytes(r, size)
 247
 248
 249 def verify(curve, pub, digest, signature, mode=2001):
 250     """ Verify provided digest with the signature
 251
 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
 258     :rtype: bool
 259     """
 260     size = MODE2SIZE[mode]
 261     if len(signature) != size * 2:
 262         raise ValueError("Invalid signature length")
 263     q = curve.q
 264     p = curve.p
 265     s = bytes2long(signature[:size])
 266     r = bytes2long(signature[size:])
 267     if r <= 0 or r >= q or s <= 0 or s >= q:
 268         return False
 269     e = bytes2long(digest) % curve.q
 270     if e == 0:
 271         e = 1
 272     v = modinvert(e, q)
 273     z1 = s * v % q
 274     z2 = q - r * v % q
 275     p1x, p1y = curve.exp(z1)
 276     q1x, q1y = curve.exp(z2, pub[0], pub[1])
 277     lm = q1x - p1x
 278     if lm < 0:
 279         lm += p
 280     lm = modinvert(lm, p)
 281     z1 = q1y - p1y
 282     lm = lm * z1 % p
 283     lm = lm * lm % p
 284     lm = lm - p1x - q1x
 285     lm = lm % p
 286     if lm < 0:
 287         lm += p
 288     lm %= q
 289     # This is not constant time comparison!
 290     return lm == r
 291
 292
 293 def prv_unmarshal(prv):
 294     """Unmarshal private key
 295
 296     :param bytes prv: serialized private key
 297     :rtype: long
 298     """
 299     return bytes2long(prv[::-1])
 300
 301
 302 def pub_marshal(pub, mode=2001):
 303     """Marshal public key
 304
 305     :type pub: (long, long)
 306     :rtype: bytes
 307     """
 308     size = MODE2SIZE[mode]
 309     return (long2bytes(pub[1], size) + long2bytes(pub[0], size))[::-1]
 310
 311
 312 def pub_unmarshal(pub, mode=2001):
 313     """Unmarshal public key
 314
 315     :type pub: bytes
 316     :rtype: (long, long)
 317     """
 318     size = MODE2SIZE[mode]
 319     pub = pub[::-1]
 320     return (bytes2long(pub[size:]), bytes2long(pub[:size]))
 321
 322
 323 def uv2xy(curve, u, v):
 324     """Convert twisted Edwards curve U,V coordinates to Weierstrass X,Y
 325     """
 326     s, t = curve.st()
 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
 332
 333
 334 def xy2uv(curve, x, y):
 335     """Convert Weierstrass X,Y coordinates to twisted Edwards curve U,V
 336     """
 337     s, t = curve.st()
 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