pygost/gost3410.py

   1 # coding: utf-8
   2 # PyGOST -- Pure Python GOST cryptographic functions library
   3 # Copyright (C) 2015-2020 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 def point_size(point):
  32     """Determine is it either 256 or 512 bit point
  33     """
  34     return (512 // 8) if point.bit_length() > 256 else (256 // 8)
  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, cofactor=1, 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.cofactor = cofactor
  65         self.e = e
  66         self.d = d
  67         if not self.contains((x, y)):
  68             raise ValueError("Invalid parameters")
  69         self._st = None
  70
  71     @property
  72     def point_size(self):
  73         return point_size(self.p)
  74
  75     def pos(self, v):
  76         """Make positive number
  77         """
  78         if v < 0:
  79             return v + self.p
  80         return v
  81
  82     def contains(self, point):
  83         """Is point on the curve?
  84
  85         :type point: (long, long)
  86         """
  87         x, y = point
  88         r1 = y * y % self.p
  89         r2 = ((x * x + self.a) * x + self.b) % self.p
  90         return r1 == self.pos(r2)
  91
  92     def _add(self, p1x, p1y, p2x, p2y):
  93         if p1x == p2x and p1y == p2y:
  94             # double
  95             t = ((3 * p1x * p1x + self.a) * modinvert(2 * p1y, self.p)) % self.p
  96         else:
  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
 102         return tx, ty
 103
 104     def exp(self, degree, x=None, y=None):
 105         x = x or self.x
 106         y = y or self.y
 107         tx = x
 108         ty = y
 109         if degree == 0:
 110             raise ValueError("Bad degree value")
 111         degree -= 1
 112         while degree != 0:
 113             if degree & 1 == 1:
 114                 tx, ty = self._add(tx, ty, x, y)
 115             degree = degree >> 1
 116             x, y = self._add(x, y, x, y)
 117         return tx, ty
 118
 119     def st(self):
 120         """Compute s/t parameters for twisted Edwards curve points conversion
 121         """
 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:
 125             return self._st
 126         self._st = (
 127             self.pos(self.e - self.d) * modinvert(4, self.p) % self.p,
 128             (self.e + self.d) * modinvert(6, self.p) % self.p,
 129         )
 130         return self._st
 131
 132
 133 CURVES = {
 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")),
 141     ),
 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")),
 149     ),
 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")),
 157     ),
 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")),
 165     ),
 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")),
 173     ),
 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")),
 181         cofactor=4,
 182         e=0x01,
 183         d=bytes2long(hexdec("0605F6B7C183FA81578BC39CFAD518132B9DF62897009AF7E522C32D6DC7BFFB")),
 184     ),
 185     "id-tc26-gost-3410-2012-512-paramSetTest": GOST3410Curve(
 186         p=bytes2long(hexdec("4531ACD1FE0023C7550D267B6B2FEE80922B14B2FFB90F04D4EB7C09B5D2D15DF1D852741AF4704A0458047E80E4546D35B8336FAC224DD81664BBF528BE6373")),
 187         q=bytes2long(hexdec("4531ACD1FE0023C7550D267B6B2FEE80922B14B2FFB90F04D4EB7C09B5D2D15DA82F2D7ECB1DBAC719905C5EECC423F1D86E25EDBE23C595D644AAF187E6E6DF")),
 188         a=7,
 189         b=bytes2long(hexdec("1CFF0806A31116DA29D8CFA54E57EB748BC5F377E49400FDD788B649ECA1AC4361834013B2AD7322480A89CA58E0CF74BC9E540C2ADD6897FAD0A3084F302ADC")),
 190         x=bytes2long(hexdec("24D19CC64572EE30F396BF6EBBFD7A6C5213B3B3D7057CC825F91093A68CD762FD60611262CD838DC6B60AA7EEE804E28BC849977FAC33B4B530F1B120248A9A")),
 191         y=bytes2long(hexdec("2BB312A43BD2CE6E0D020613C857ACDDCFBF061E91E5F2C3F32447C259F39B2C83AB156D77F1496BF7EB3351E1EE4E43DC1A18B91B24640B6DBB92CB1ADD371E")),
 192     ),
 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")),
 200     ),
 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")),
 208     ),
 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")),
 216         cofactor=4,
 217         e=0x01,
 218         d=bytes2long(hexdec("9E4F5D8C017D8D9F13A5CF3CDF5BFE4DAB402D54198E31EBDE28A0621050439CA6B39E0A515C06B304E2CE43E79E369E91A0CFC2BC2A22B4CA302DBB33EE7550")),
 219     ),
 220 }
 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"]
 227
 228
 229 def public_key(curve, prv):
 230     """Generate public key from the private one
 231
 232     :param GOST3410Curve curve: curve to use
 233     :param long prv: private key
 234     :returns: public key's parts, X and Y
 235     :rtype: (long, long)
 236     """
 237     return curve.exp(prv)
 238
 239
 240 def sign(curve, prv, digest, rand=None):
 241     """Calculate signature for provided digest
 242
 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
 251     """
 252     size = curve.point_size
 253     q = curve.q
 254     e = bytes2long(digest) % q
 255     if e == 0:
 256         e = 1
 257     while True:
 258         if rand is None:
 259             rand = urandom(size)
 260         elif len(rand) != size:
 261             raise ValueError("rand length != %d" % size)
 262         k = bytes2long(rand) % q
 263         if k == 0:
 264             continue
 265         r, _ = curve.exp(k)
 266         r %= q
 267         if r == 0:
 268             continue
 269         d = prv * r
 270         k *= e
 271         s = (d + k) % q
 272         if s == 0:
 273             continue
 274         break
 275     return long2bytes(s, size) + long2bytes(r, size)
 276
 277
 278 def verify(curve, pub, digest, signature):
 279     """Verify provided digest with the signature
 280
 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
 287     :rtype: bool
 288     """
 289     size = curve.point_size
 290     if len(signature) != size * 2:
 291         raise ValueError("Invalid signature length")
 292     q = curve.q
 293     p = curve.p
 294     s = bytes2long(signature[:size])
 295     r = bytes2long(signature[size:])
 296     if r <= 0 or r >= q or s <= 0 or s >= q:
 297         return False
 298     e = bytes2long(digest) % curve.q
 299     if e == 0:
 300         e = 1
 301     v = modinvert(e, q)
 302     z1 = s * v % q
 303     z2 = q - r * v % q
 304     p1x, p1y = curve.exp(z1)
 305     q1x, q1y = curve.exp(z2, pub[0], pub[1])
 306     lm = q1x - p1x
 307     if lm < 0:
 308         lm += p
 309     lm = modinvert(lm, p)
 310     z1 = q1y - p1y
 311     lm = lm * z1 % p
 312     lm = lm * lm % p
 313     lm = lm - p1x - q1x
 314     lm = lm % p
 315     if lm < 0:
 316         lm += p
 317     lm %= q
 318     # This is not constant time comparison!
 319     return lm == r
 320
 321
 322 def prv_unmarshal(prv):
 323     """Unmarshal little-endian private key
 324
 325     :param bytes prv: serialized private key
 326     :rtype: long
 327     """
 328     return bytes2long(prv[::-1])
 329
 330
 331 def pub_marshal(pub):
 332     """Marshal public key
 333
 334     :type pub: (long, long)
 335     :rtype: bytes
 336     :returns: LE(X) || LE(Y)
 337     """
 338     size = point_size(pub[0])
 339     return (long2bytes(pub[1], size) + long2bytes(pub[0], size))[::-1]
 340
 341
 342 def pub_unmarshal(pub):
 343     """Unmarshal public key
 344
 345     :param pub: LE(X) || LE(Y)
 346     :type pub: bytes
 347     :rtype: (long, long)
 348     """
 349     size = len(pub) // 2
 350     pub = pub[::-1]
 351     return (bytes2long(pub[size:]), bytes2long(pub[:size]))
 352
 353
 354 def uv2xy(curve, u, v):
 355     """Convert twisted Edwards curve U,V coordinates to Weierstrass X,Y
 356     """
 357     s, t = curve.st()
 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
 363
 364
 365 def xy2uv(curve, x, y):
 366     """Convert Weierstrass X,Y coordinates to twisted Edwards curve U,V
 367     """
 368     s, t = curve.st()
 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