pygost/test_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, either version 3 of the License, or
   8 # (at your option) any later version.
   9 #
  10 # This program is distributed in the hope that it will be useful,
  11 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  12 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  13 # GNU General Public License for more details.
  14 #
  15 # You should have received a copy of the GNU General Public License
  16 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
  17
  18 from os import urandom
  19 from unittest import TestCase
  20
  21 from pygost.gost3410 import CURVES
  22 from pygost.gost3410 import GOST3410Curve
  23 from pygost.gost3410 import public_key
  24 from pygost.gost3410 import sign
  25 from pygost.gost3410 import verify
  26 from pygost.utils import bytes2long
  27 from pygost.utils import hexdec
  28 from pygost.utils import long2bytes
  29
  30
  31 class Test341001(TestCase):
  32     def test_rfc(self):
  33         """ Test vector from :rfc:`5832`
  34         """
  35         prv = bytes(bytearray((
  36             0x7A, 0x92, 0x9A, 0xDE, 0x78, 0x9B, 0xB9, 0xBE,
  37             0x10, 0xED, 0x35, 0x9D, 0xD3, 0x9A, 0x72, 0xC1,
  38             0x1B, 0x60, 0x96, 0x1F, 0x49, 0x39, 0x7E, 0xEE,
  39             0x1D, 0x19, 0xCE, 0x98, 0x91, 0xEC, 0x3B, 0x28
  40         )))
  41         pub_x = bytes(bytearray((
  42             0x7F, 0x2B, 0x49, 0xE2, 0x70, 0xDB, 0x6D, 0x90,
  43             0xD8, 0x59, 0x5B, 0xEC, 0x45, 0x8B, 0x50, 0xC5,
  44             0x85, 0x85, 0xBA, 0x1D, 0x4E, 0x9B, 0x78, 0x8F,
  45             0x66, 0x89, 0xDB, 0xD8, 0xE5, 0x6F, 0xD8, 0x0B
  46         )))
  47         pub_y = bytes(bytearray((
  48             0x26, 0xF1, 0xB4, 0x89, 0xD6, 0x70, 0x1D, 0xD1,
  49             0x85, 0xC8, 0x41, 0x3A, 0x97, 0x7B, 0x3C, 0xBB,
  50             0xAF, 0x64, 0xD1, 0xC5, 0x93, 0xD2, 0x66, 0x27,
  51             0xDF, 0xFB, 0x10, 0x1A, 0x87, 0xFF, 0x77, 0xDA
  52         )))
  53         digest = bytes(bytearray((
  54             0x2D, 0xFB, 0xC1, 0xB3, 0x72, 0xD8, 0x9A, 0x11,
  55             0x88, 0xC0, 0x9C, 0x52, 0xE0, 0xEE, 0xC6, 0x1F,
  56             0xCE, 0x52, 0x03, 0x2A, 0xB1, 0x02, 0x2E, 0x8E,
  57             0x67, 0xEC, 0xE6, 0x67, 0x2B, 0x04, 0x3E, 0xE5
  58         )))
  59         signature = bytes(bytearray((
  60             0x41, 0xAA, 0x28, 0xD2, 0xF1, 0xAB, 0x14, 0x82,
  61             0x80, 0xCD, 0x9E, 0xD5, 0x6F, 0xED, 0xA4, 0x19,
  62             0x74, 0x05, 0x35, 0x54, 0xA4, 0x27, 0x67, 0xB8,
  63             0x3A, 0xD0, 0x43, 0xFD, 0x39, 0xDC, 0x04, 0x93,
  64             0x01, 0x45, 0x6C, 0x64, 0xBA, 0x46, 0x42, 0xA1,
  65             0x65, 0x3C, 0x23, 0x5A, 0x98, 0xA6, 0x02, 0x49,
  66             0xBC, 0xD6, 0xD3, 0xF7, 0x46, 0xB6, 0x31, 0xDF,
  67             0x92, 0x80, 0x14, 0xF6, 0xC5, 0xBF, 0x9C, 0x40
  68         )))
  69         prv = bytes2long(prv)
  70         signature = signature[32:] + signature[:32]
  71
  72         c = CURVES["id-GostR3410-2001-TestParamSet"]
  73         pubX, pubY = public_key(c, prv)
  74         self.assertSequenceEqual(long2bytes(pubX), pub_x)
  75         self.assertSequenceEqual(long2bytes(pubY), pub_y)
  76         s = sign(c, prv, digest)
  77         self.assertTrue(verify(c, (pubX, pubY), digest, s))
  78         self.assertTrue(verify(c, (pubX, pubY), digest, signature))
  79
  80     def test_sequence(self):
  81         c = CURVES["id-GostR3410-2001-TestParamSet"]
  82         prv = bytes2long(urandom(32))
  83         pubX, pubY = public_key(c, prv)
  84         for _ in range(20):
  85             digest = urandom(32)
  86             s = sign(c, prv, digest, mode=2001)
  87             self.assertTrue(verify(c, (pubX, pubY), digest, s, mode=2001))
  88
  89
  90 class Test34102012(TestCase):
  91     def test_gcl3(self):
  92         """ Test vector from libgcl3
  93         """
  94         p = bytes2long(bytes(bytearray((
  95             0x45, 0x31, 0xAC, 0xD1, 0xFE, 0x00, 0x23, 0xC7,
  96             0x55, 0x0D, 0x26, 0x7B, 0x6B, 0x2F, 0xEE, 0x80,
  97             0x92, 0x2B, 0x14, 0xB2, 0xFF, 0xB9, 0x0F, 0x04,
  98             0xD4, 0xEB, 0x7C, 0x09, 0xB5, 0xD2, 0xD1, 0x5D,
  99             0xF1, 0xD8, 0x52, 0x74, 0x1A, 0xF4, 0x70, 0x4A,
 100             0x04, 0x58, 0x04, 0x7E, 0x80, 0xE4, 0x54, 0x6D,
 101             0x35, 0xB8, 0x33, 0x6F, 0xAC, 0x22, 0x4D, 0xD8,
 102             0x16, 0x64, 0xBB, 0xF5, 0x28, 0xBE, 0x63, 0x73,
 103         ))))
 104         q = bytes2long(bytes(bytearray((
 105             0x45, 0x31, 0xAC, 0xD1, 0xFE, 0x00, 0x23, 0xC7,
 106             0x55, 0x0D, 0x26, 0x7B, 0x6B, 0x2F, 0xEE, 0x80,
 107             0x92, 0x2B, 0x14, 0xB2, 0xFF, 0xB9, 0x0F, 0x04,
 108             0xD4, 0xEB, 0x7C, 0x09, 0xB5, 0xD2, 0xD1, 0x5D,
 109             0xA8, 0x2F, 0x2D, 0x7E, 0xCB, 0x1D, 0xBA, 0xC7,
 110             0x19, 0x90, 0x5C, 0x5E, 0xEC, 0xC4, 0x23, 0xF1,
 111             0xD8, 0x6E, 0x25, 0xED, 0xBE, 0x23, 0xC5, 0x95,
 112             0xD6, 0x44, 0xAA, 0xF1, 0x87, 0xE6, 0xE6, 0xDF,
 113         ))))
 114         a = bytes2long(bytes(bytearray((
 115             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 116             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 117             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 118             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 119             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 120             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 121             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 122             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07,
 123         ))))
 124         b = bytes2long(bytes(bytearray((
 125             0x1C, 0xFF, 0x08, 0x06, 0xA3, 0x11, 0x16, 0xDA,
 126             0x29, 0xD8, 0xCF, 0xA5, 0x4E, 0x57, 0xEB, 0x74,
 127             0x8B, 0xC5, 0xF3, 0x77, 0xE4, 0x94, 0x00, 0xFD,
 128             0xD7, 0x88, 0xB6, 0x49, 0xEC, 0xA1, 0xAC, 0x43,
 129             0x61, 0x83, 0x40, 0x13, 0xB2, 0xAD, 0x73, 0x22,
 130             0x48, 0x0A, 0x89, 0xCA, 0x58, 0xE0, 0xCF, 0x74,
 131             0xBC, 0x9E, 0x54, 0x0C, 0x2A, 0xDD, 0x68, 0x97,
 132             0xFA, 0xD0, 0xA3, 0x08, 0x4F, 0x30, 0x2A, 0xDC,
 133         ))))
 134         x = bytes2long(bytes(bytearray((
 135             0x24, 0xD1, 0x9C, 0xC6, 0x45, 0x72, 0xEE, 0x30,
 136             0xF3, 0x96, 0xBF, 0x6E, 0xBB, 0xFD, 0x7A, 0x6C,
 137             0x52, 0x13, 0xB3, 0xB3, 0xD7, 0x05, 0x7C, 0xC8,
 138             0x25, 0xF9, 0x10, 0x93, 0xA6, 0x8C, 0xD7, 0x62,
 139             0xFD, 0x60, 0x61, 0x12, 0x62, 0xCD, 0x83, 0x8D,
 140             0xC6, 0xB6, 0x0A, 0xA7, 0xEE, 0xE8, 0x04, 0xE2,
 141             0x8B, 0xC8, 0x49, 0x97, 0x7F, 0xAC, 0x33, 0xB4,
 142             0xB5, 0x30, 0xF1, 0xB1, 0x20, 0x24, 0x8A, 0x9A,
 143         ))))
 144         y = bytes2long(bytes(bytearray((
 145             0x2B, 0xB3, 0x12, 0xA4, 0x3B, 0xD2, 0xCE, 0x6E,
 146             0x0D, 0x02, 0x06, 0x13, 0xC8, 0x57, 0xAC, 0xDD,
 147             0xCF, 0xBF, 0x06, 0x1E, 0x91, 0xE5, 0xF2, 0xC3,
 148             0xF3, 0x24, 0x47, 0xC2, 0x59, 0xF3, 0x9B, 0x2C,
 149             0x83, 0xAB, 0x15, 0x6D, 0x77, 0xF1, 0x49, 0x6B,
 150             0xF7, 0xEB, 0x33, 0x51, 0xE1, 0xEE, 0x4E, 0x43,
 151             0xDC, 0x1A, 0x18, 0xB9, 0x1B, 0x24, 0x64, 0x0B,
 152             0x6D, 0xBB, 0x92, 0xCB, 0x1A, 0xDD, 0x37, 0x1E,
 153         ))))
 154         prv = bytes(bytearray((
 155             0x0B, 0xA6, 0x04, 0x8A, 0xAD, 0xAE, 0x24, 0x1B,
 156             0xA4, 0x09, 0x36, 0xD4, 0x77, 0x56, 0xD7, 0xC9,
 157             0x30, 0x91, 0xA0, 0xE8, 0x51, 0x46, 0x69, 0x70,
 158             0x0E, 0xE7, 0x50, 0x8E, 0x50, 0x8B, 0x10, 0x20,
 159             0x72, 0xE8, 0x12, 0x3B, 0x22, 0x00, 0xA0, 0x56,
 160             0x33, 0x22, 0xDA, 0xD2, 0x82, 0x7E, 0x27, 0x14,
 161             0xA2, 0x63, 0x6B, 0x7B, 0xFD, 0x18, 0xAA, 0xDF,
 162             0xC6, 0x29, 0x67, 0x82, 0x1F, 0xA1, 0x8D, 0xD4,
 163         )))
 164         pub_x = bytes(bytearray((
 165             0x11, 0x5D, 0xC5, 0xBC, 0x96, 0x76, 0x0C, 0x7B,
 166             0x48, 0x59, 0x8D, 0x8A, 0xB9, 0xE7, 0x40, 0xD4,
 167             0xC4, 0xA8, 0x5A, 0x65, 0xBE, 0x33, 0xC1, 0x81,
 168             0x5B, 0x5C, 0x32, 0x0C, 0x85, 0x46, 0x21, 0xDD,
 169             0x5A, 0x51, 0x58, 0x56, 0xD1, 0x33, 0x14, 0xAF,
 170             0x69, 0xBC, 0x5B, 0x92, 0x4C, 0x8B, 0x4D, 0xDF,
 171             0xF7, 0x5C, 0x45, 0x41, 0x5C, 0x1D, 0x9D, 0xD9,
 172             0xDD, 0x33, 0x61, 0x2C, 0xD5, 0x30, 0xEF, 0xE1,
 173         )))
 174         pub_y = bytes(bytearray((
 175             0x37, 0xC7, 0xC9, 0x0C, 0xD4, 0x0B, 0x0F, 0x56,
 176             0x21, 0xDC, 0x3A, 0xC1, 0xB7, 0x51, 0xCF, 0xA0,
 177             0xE2, 0x63, 0x4F, 0xA0, 0x50, 0x3B, 0x3D, 0x52,
 178             0x63, 0x9F, 0x5D, 0x7F, 0xB7, 0x2A, 0xFD, 0x61,
 179             0xEA, 0x19, 0x94, 0x41, 0xD9, 0x43, 0xFF, 0xE7,
 180             0xF0, 0xC7, 0x0A, 0x27, 0x59, 0xA3, 0xCD, 0xB8,
 181             0x4C, 0x11, 0x4E, 0x1F, 0x93, 0x39, 0xFD, 0xF2,
 182             0x7F, 0x35, 0xEC, 0xA9, 0x36, 0x77, 0xBE, 0xEC,
 183         )))
 184         digest = bytes(bytearray((
 185             0x37, 0x54, 0xF3, 0xCF, 0xAC, 0xC9, 0xE0, 0x61,
 186             0x5C, 0x4F, 0x4A, 0x7C, 0x4D, 0x8D, 0xAB, 0x53,
 187             0x1B, 0x09, 0xB6, 0xF9, 0xC1, 0x70, 0xC5, 0x33,
 188             0xA7, 0x1D, 0x14, 0x70, 0x35, 0xB0, 0xC5, 0x91,
 189             0x71, 0x84, 0xEE, 0x53, 0x65, 0x93, 0xF4, 0x41,
 190             0x43, 0x39, 0x97, 0x6C, 0x64, 0x7C, 0x5D, 0x5A,
 191             0x40, 0x7A, 0xDE, 0xDB, 0x1D, 0x56, 0x0C, 0x4F,
 192             0xC6, 0x77, 0x7D, 0x29, 0x72, 0x07, 0x5B, 0x8C,
 193         )))
 194         signature = bytes(bytearray((
 195             0x2F, 0x86, 0xFA, 0x60, 0xA0, 0x81, 0x09, 0x1A,
 196             0x23, 0xDD, 0x79, 0x5E, 0x1E, 0x3C, 0x68, 0x9E,
 197             0xE5, 0x12, 0xA3, 0xC8, 0x2E, 0xE0, 0xDC, 0xC2,
 198             0x64, 0x3C, 0x78, 0xEE, 0xA8, 0xFC, 0xAC, 0xD3,
 199             0x54, 0x92, 0x55, 0x84, 0x86, 0xB2, 0x0F, 0x1C,
 200             0x9E, 0xC1, 0x97, 0xC9, 0x06, 0x99, 0x85, 0x02,
 201             0x60, 0xC9, 0x3B, 0xCB, 0xCD, 0x9C, 0x5C, 0x33,
 202             0x17, 0xE1, 0x93, 0x44, 0xE1, 0x73, 0xAE, 0x36,
 203             0x10, 0x81, 0xB3, 0x94, 0x69, 0x6F, 0xFE, 0x8E,
 204             0x65, 0x85, 0xE7, 0xA9, 0x36, 0x2D, 0x26, 0xB6,
 205             0x32, 0x5F, 0x56, 0x77, 0x8A, 0xAD, 0xBC, 0x08,
 206             0x1C, 0x0B, 0xFB, 0xE9, 0x33, 0xD5, 0x2F, 0xF5,
 207             0x82, 0x3C, 0xE2, 0x88, 0xE8, 0xC4, 0xF3, 0x62,
 208             0x52, 0x60, 0x80, 0xDF, 0x7F, 0x70, 0xCE, 0x40,
 209             0x6A, 0x6E, 0xEB, 0x1F, 0x56, 0x91, 0x9C, 0xB9,
 210             0x2A, 0x98, 0x53, 0xBD, 0xE7, 0x3E, 0x5B, 0x4A,
 211         )))
 212         prv = bytes2long(prv)
 213         signature = signature[64:] + signature[:64]
 214         c = GOST3410Curve(p, q, a, b, x, y)
 215         pubX, pubY = public_key(c, prv)
 216         self.assertSequenceEqual(long2bytes(pubX), pub_x)
 217         self.assertSequenceEqual(long2bytes(pubY), pub_y)
 218         s = sign(c, prv, digest, mode=2012)
 219         self.assertTrue(verify(c, (pubX, pubY), digest, s, mode=2012))
 220         self.assertTrue(verify(c, (pubX, pubY), digest, signature, mode=2012))
 221
 222     def test_sequence(self):
 223         c = CURVES["id-tc26-gost-3410-12-512-paramSetA"]
 224         prv = bytes2long(urandom(64))
 225         pubX, pubY = public_key(c, prv)
 226         for _ in range(20):
 227             digest = urandom(64)
 228             s = sign(c, prv, digest, mode=2012)
 229             self.assertTrue(verify(c, (pubX, pubY), digest, s, mode=2012))
 230             self.assertNotIn(b"\x00" * 8, s)
 231
 232
 233 class Test34102012SESPAKE(TestCase):
 234     """Test vectors for multiplication from :rfc:`8133`
 235     """
 236     def test_curve1(self):
 237         c = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"]
 238         q_ind = (
 239             0xA69D51CAF1A309FA9E9B66187759B0174C274E080356F23CFCBFE84D396AD7BB,
 240             0x5D26F29ECC2E9AC0404DCF7986FA55FE94986362170F54B9616426A659786DAC,
 241         )
 242         self.assertEqual(
 243             c.exp(bytes2long(hexdec(
 244                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 245             )[::-1]), x=q_ind[0], y=q_ind[1]),
 246             (
 247                 0x59495655D1E7C7424C622485F575CCF121F3122D274101E8AB734CC9C9A9B45E,
 248                 0x48D1C311D33C9B701F3B03618562A4A07A044E3AF31E3999E67B487778B53C62,
 249             )
 250         )
 251         self.assertEqual(
 252             c.exp(0x1F2538097D5A031FA68BBB43C84D12B3DE47B7061C0D5E24993E0C873CDBA6B3),
 253             (
 254                 0xBBC77CF42DC1E62D06227935379B4AA4D14FEA4F565DDF4CB4FA4D31579F9676,
 255                 0x8E16604A4AFDF28246684D4996274781F6CB80ABBBA1414C1513EC988509DABF,
 256             )
 257         )
 258         self.assertEqual(
 259             c.exp(0xDC497D9EF6324912FD367840EE509A2032AEDB1C0A890D133B45F596FCCBD45D),
 260             (
 261                 0x6097341C1BE388E83E7CA2DF47FAB86E2271FD942E5B7B2EB2409E49F742BC29,
 262                 0xC81AA48BDB4CA6FA0EF18B9788AE25FE30857AA681B3942217F9FED151BAB7D0,
 263             ),
 264         )
 265
 266     def test_curve2(self):
 267         c = CURVES["id-GostR3410-2001-CryptoPro-B-ParamSet"]
 268         q_ind = (
 269             0x3D715A874A4B17CB3B517893A9794A2B36C89D2FFC693F01EE4CC27E7F49E399,
 270             0x1C5A641FCF7CE7E87CDF8CEA38F3DB3096EACE2FAD158384B53953365F4FE7FE,
 271         )
 272         self.assertEqual(
 273             c.exp(bytes2long(hexdec(
 274                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 275             )[::-1]), x=q_ind[0], y=q_ind[1]),
 276             (
 277                 0x6DC2AE26BC691FCA5A73D9C452790D15E34BA5404D92955B914C8D2662ABB985,
 278                 0x3B02AAA9DD65AE30C335CED12F3154BBAC059F66B088306747453EDF6E5DB077,
 279             )
 280         )
 281         self.assertEqual(
 282             c.exp(0x499D72B90299CAB0DA1F8BE19D9122F622A13B32B730C46BD0664044F2144FAD),
 283             (
 284                 0x61D6F916DB717222D74877F179F7EBEF7CD4D24D8C1F523C048E34A1DF30F8DD,
 285                 0x3EC48863049CFCFE662904082E78503F4973A4E105E2F1B18C69A5E7FB209000,
 286             )
 287         )
 288         self.assertEqual(
 289             c.exp(0x0F69FF614957EF83668EDC2D7ED614BE76F7B253DB23C5CC9C52BF7DF8F4669D),
 290             (
 291                 0x33BC6F7E9C0BA10CFB2B72546C327171295508EA97F8C8BA9F890F2478AB4D6C,
 292                 0x75D57B396C396F492F057E9222CCC686437A2AAD464E452EF426FC8EEED1A4A6,
 293             ),
 294         )
 295
 296     def test_curve3(self):
 297         c = CURVES["id-GostR3410-2001-CryptoPro-C-ParamSet"]
 298         q_ind = (
 299             0x1E36383E43BB6CFA2917167D71B7B5DD3D6D462B43D7C64282AE67DFBEC2559D,
 300             0x137478A9F721C73932EA06B45CF72E37EB78A63F29A542E563C614650C8B6399,
 301         )
 302         self.assertEqual(
 303             c.exp(bytes2long(hexdec(
 304                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 305             )[::-1]), x=q_ind[0], y=q_ind[1]),
 306             (
 307                 0x945821DAF91E158B839939630655A3B21FF3E146D27041E86C05650EB3B46B59,
 308                 0x3A0C2816AC97421FA0E879605F17F0C9C3EB734CFF196937F6284438D70BDC48,
 309             )
 310         )
 311         self.assertEqual(
 312             c.exp(0x3A54AC3F19AD9D0B1EAC8ACDCEA70E581F1DAC33D13FEAFD81E762378639C1A8),
 313             (
 314                 0x96B7F09C94D297C257A7DA48364C0076E59E48D221CBA604AE111CA3933B446A,
 315                 0x54E4953D86B77ECCEB578500931E822300F7E091F79592CA202A020D762C34A6,
 316             )
 317         )
 318         self.assertEqual(
 319             c.exp(0x448781782BF7C0E52A1DD9E6758FD3482D90D3CFCCF42232CF357E59A4D49FD4),
 320             (
 321                 0x4B9C0AB55A938121F282F48A2CC4396EB16E7E0068B495B0C1DD4667786A3EB7,
 322                 0x223460AA8E09383E9DF9844C5A0F2766484738E5B30128A171B69A77D9509B96,
 323             ),
 324         )
 325
 326     def test_curve4(self):
 327         c = CURVES["id-tc26-gost-3410-12-512-paramSetA"]
 328         q_ind = (
 329             0x2A17F8833A32795327478871B5C5E88AEFB91126C64B4B8327289BEA62559425D18198F133F400874328B220C74497CD240586CB249E158532CB8090776CD61C,
 330             0x728F0C4A73B48DA41CE928358FAD26B47A6E094E9362BAE82559F83CDDC4EC3A4676BD3707EDEAF4CD85E99695C64C241EDC622BE87DC0CF87F51F4367F723C5,
 331         )
 332         self.assertEqual(
 333             c.exp(bytes2long(hexdec(
 334                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F181270671C6213E3930EFDDA26451792C6208122EE60D200520D695DFD9F5F0FD5ABA702"
 335             )[::-1]), x=q_ind[0], y=q_ind[1]),
 336             (
 337                 0x0C0AB53D0E0A9C607CAD758F558915A0A7DC5DC87B45E9A58FDDF30EC3385960283E030CD322D9E46B070637785FD49D2CD711F46807A24C40AF9A42C8E2D740,
 338                 0xDF93A8012B86D3A3D4F8A4D487DA15FC739EB31B20B3B0E8C8C032AAF8072C6337CF7D5B404719E5B4407C41D9A3216A08CA69C271484E9ED72B8AAA52E28B8B,
 339             )
 340         )
 341         self.assertEqual(
 342             c.exp(0x3CE54325DB52FE798824AEAD11BB16FA766857D04A4AF7D468672F16D90E7396046A46F815693E85B1CE5464DA9270181F82333B0715057BBE8D61D400505F0E),
 343             (
 344                 0xB93093EB0FCC463239B7DF276E09E592FCFC9B635504EA4531655D76A0A3078E2B4E51CFE2FA400CC5DE9FBE369DB204B3E8ED7EDD85EE5CCA654C1AED70E396,
 345                 0x809770B8D910EA30BD2FA89736E91DC31815D2D9B31128077EEDC371E9F69466F497DC64DD5B1FADC587F860EE256109138C4A9CD96B628E65A8F590520FC882,
 346             )
 347         )
 348         self.assertEqual(
 349             c.exp(0xB5C286A79AA8E97EC0E19BC1959A1D15F12F8C97870BA9D68CC12811A56A3BB11440610825796A49D468CDC9C2D02D76598A27973D5960C5F50BCE28D8D345F4),
 350             (
 351                 0x238B38644E440452A99FA6B93D9FD7DA0CB83C32D3C1E3CFE5DF5C3EB0F9DB91E588DAEDC849EA2FB867AE855A21B4077353C0794716A6480995113D8C20C7AF,
 352                 0xB2273D5734C1897F8D15A7008B862938C8C74CA7E877423D95243EB7EBD02FD2C456CF9FC956F078A59AA86F19DD1075E5167E4ED35208718EA93161C530ED14,
 353             ),
 354         )
 355
 356     def test_curve5(self):
 357         c = CURVES["id-tc26-gost-3410-12-512-paramSetB"]
 358         q_ind = (
 359             0x7E1FAE8285E035BEC244BEF2D0E5EBF436633CF50E55231DEA9C9CF21D4C8C33DF85D4305DE92971F0A4B4C07E00D87BDBC720EB66E49079285AAF12E0171149,
 360             0x2CC89998B875D4463805BA0D858A196592DB20AB161558FF2F4EF7A85725D20953967AE621AFDEAE89BB77C83A2528EF6FCE02F68BDA4679D7F2704947DBC408,
 361         )
 362         self.assertEqual(
 363             c.exp(bytes2long(hexdec(
 364                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F181270671C6213E3930EFDDA26451792C6208122EE60D200520D695DFD9F5F0FD5ABA702"
 365             )[::-1]), x=q_ind[0], y=q_ind[1]),
 366             (
 367                 0x7D03E65B8050D1E12CBB601A17B9273B0E728F5021CD47C8A4DD822E4627BA5F9C696286A2CDDA9A065509866B4DEDEDC4A118409604AD549F87A60AFA621161,
 368                 0x16037DAD45421EC50B00D50BDC6AC3B85348BC1D3A2F85DB27C3373580FEF87C2C743B7ED30F22BE22958044E716F93A61CA3213A361A2797A16A3AE62957377,
 369             )
 370         )
 371         self.assertEqual(
 372             c.exp(0x715E893FA639BF341296E0623E6D29DADF26B163C278767A7982A989462A3863FE12AEF8BD403D59C4DC4720570D4163DB0805C7C10C4E818F9CB785B04B9997),
 373             (
 374                 0x10C479EA1C04D3C2C02B0576A9C42D96226FF033C1191436777F66916030D87D02FB93738ED7669D07619FFCE7C1F3C4DB5E5DF49E2186D6FA1E2EB5767602B9,
 375                 0x039F6044191404E707F26D59D979136A831CCE43E1C5F0600D1DDF8F39D0CA3D52FBD943BF04DDCED1AA2CE8F5EBD7487ACDEF239C07D015084D796784F35436,
 376             )
 377         )
 378         self.assertEqual(
 379             c.exp(0x30FA8C2B4146C2DBBE82BED04D7378877E8C06753BD0A0FF71EBF2BEFE8DA8F3DC0836468E2CE7C5C961281B6505140F8407413F03C2CB1D201EA1286CE30E6D),
 380             (
 381                 0x34C0149E7BB91AE377B02573FCC48AF7BFB7B16DEB8F9CE870F384688E3241A3A868588CC0EF4364CCA67D17E3260CD82485C202ADC76F895D5DF673B1788E67,
 382                 0x608E944929BD643569ED5189DB871453F13333A1EAF82B2FE1BE8100E775F13DD9925BD317B63BFAF05024D4A738852332B64501195C1B2EF789E34F23DDAFC5,
 383             ),
 384         )
 385
 386     def test_curve6(self):
 387         c = CURVES["id-tc26-gost-3410-2012-256-paramSetA"]
 388         q_ind = (
 389             0xB51ADF93A40AB15792164FAD3352F95B66369EB2A4EF5EFAE32829320363350E,
 390             0x74A358CC08593612F5955D249C96AFB7E8B0BB6D8BD2BBE491046650D822BE18,
 391         )
 392         self.assertEqual(
 393             c.exp(bytes2long(hexdec(
 394                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 395             )[::-1]), x=q_ind[0], y=q_ind[1]),
 396             (
 397                 0xDBF99827078956812FA48C6E695DF589DEF1D18A2D4D35A96D75BF6854237629,
 398                 0x9FDDD48BFBC57BEE1DA0CFF282884F284D471B388893C48F5ECB02FC18D67589,
 399             )
 400         )
 401         self.assertEqual(
 402             c.exp(0x147B72F6684FB8FD1B418A899F7DBECAF5FCE60B13685BAA95328654A7F0707F),
 403             (
 404                 0x33FBAC14EAE538275A769417829C431BD9FA622B6F02427EF55BD60EE6BC2888,
 405                 0x22F2EBCF960A82E6CDB4042D3DDDA511B2FBA925383C2273D952EA2D406EAE46,
 406             )
 407         )
 408         self.assertEqual(
 409             c.exp(0x30D5CFADAA0E31B405E6734C03EC4C5DF0F02F4BA25C9A3B320EE6453567B4CB),
 410             (
 411                 0x2B2D89FAB735433970564F2F28CFA1B57D640CB902BC6334A538F44155022CB2,
 412                 0x10EF6A82EEF1E70F942AA81D6B4CE5DEC0DDB9447512962874870E6F2849A96F,
 413             ),
 414         )
 415
 416     def test_curve7(self):
 417         c = CURVES["id-tc26-gost-3410-2012-512-paramSetC"]
 418         q_ind = (
 419             0x489C91784E02E98F19A803ABCA319917F37689E5A18965251CE2FF4E8D8B298F5BA7470F9E0E713487F96F4A8397B3D09A270C9D367EB5E0E6561ADEEB51581D,
 420             0x684EA885ACA64EAF1B3FEE36C0852A3BE3BD8011B0EF18E203FF87028D6EB5DB2C144A0DCC71276542BFD72CA2A43FA4F4939DA66D9A60793C704A8C94E16F18,
 421         )
 422         self.assertEqual(
 423             c.exp(bytes2long(hexdec(
 424                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F181270671C6213E3930EFDDA26451792C6208122EE60D200520D695DFD9F5F0FD5ABA702"
 425             )[::-1]), x=q_ind[0], y=q_ind[1]),
 426             (
 427                 0x0185AE6271A81BB7F236A955F7CAA26FB63849813C0287D96C83A15AE6B6A86467AB13B6D88CE8CD7DC2E5B97FF5F28FAC2C108F2A3CF3DB5515C9E6D7D210E8,
 428                 0xED0220F92EF771A71C64ECC77986DB7C03D37B3E2AB3E83F32CE5E074A762EC08253C9E2102B87532661275C4B1D16D2789CDABC58ACFDF7318DE70AB64F09B8,
 429             )
 430         )
 431         self.assertEqual(
 432             c.exp(0x332F930421D14CFE260042159F18E49FD5A54167E94108AD80B1DE60B13DE7999A34D611E63F3F870E5110247DF8EC7466E648ACF385E52CCB889ABF491EDFF0),
 433             (
 434                 0x561655966D52952E805574F4281F1ED3A2D498932B00CBA9DECB42837F09835BFFBFE2D84D6B6B242FE7B57F92E1A6F2413E12DDD6383E4437E13D72693469AD,
 435                 0xF6B18328B2715BD7F4178615273A36135BC0BF62F7D8BB9F080164AD36470AD03660F51806C64C6691BADEF30F793720F8E3FEAED631D6A54A4C372DCBF80E82,
 436             )
 437         )
 438         self.assertEqual(
 439             c.exp(0x38481771E7D054F96212686B613881880BD8A6C89DDBC656178F014D2C093432A033EE10415F13A160D44C2AD61E6E2E05A7F7EC286BCEA3EA4D4D53F8634FA2),
 440             (
 441                 0xB7C5818687083433BC1AFF61CB5CA79E38232025E0C1F123B8651E62173CE6873F3E6FFE7281C2E45F4F524F66B0C263616ED08FD210AC4355CA3292B51D71C3,
 442                 0x497F14205DBDC89BDDAF50520ED3B1429AD30777310186BE5E68070F016A44E0C766DB08E8AC23FBDFDE6D675AA4DF591EB18BA0D348DF7AA40973A2F1DCFA55,
 443             ),
 444         )