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 uv2xy
  26 from pygost.gost3410 import verify
  27 from pygost.gost3410 import xy2uv
  28 from pygost.utils import bytes2long
  29 from pygost.utils import hexdec
  30 from pygost.utils import long2bytes
  31
  32
  33 class Test341001(TestCase):
  34     def test_rfc(self):
  35         """ Test vector from :rfc:`5832`
  36         """
  37         prv = bytes(bytearray((
  38             0x7A, 0x92, 0x9A, 0xDE, 0x78, 0x9B, 0xB9, 0xBE,
  39             0x10, 0xED, 0x35, 0x9D, 0xD3, 0x9A, 0x72, 0xC1,
  40             0x1B, 0x60, 0x96, 0x1F, 0x49, 0x39, 0x7E, 0xEE,
  41             0x1D, 0x19, 0xCE, 0x98, 0x91, 0xEC, 0x3B, 0x28
  42         )))
  43         pub_x = bytes(bytearray((
  44             0x7F, 0x2B, 0x49, 0xE2, 0x70, 0xDB, 0x6D, 0x90,
  45             0xD8, 0x59, 0x5B, 0xEC, 0x45, 0x8B, 0x50, 0xC5,
  46             0x85, 0x85, 0xBA, 0x1D, 0x4E, 0x9B, 0x78, 0x8F,
  47             0x66, 0x89, 0xDB, 0xD8, 0xE5, 0x6F, 0xD8, 0x0B
  48         )))
  49         pub_y = bytes(bytearray((
  50             0x26, 0xF1, 0xB4, 0x89, 0xD6, 0x70, 0x1D, 0xD1,
  51             0x85, 0xC8, 0x41, 0x3A, 0x97, 0x7B, 0x3C, 0xBB,
  52             0xAF, 0x64, 0xD1, 0xC5, 0x93, 0xD2, 0x66, 0x27,
  53             0xDF, 0xFB, 0x10, 0x1A, 0x87, 0xFF, 0x77, 0xDA
  54         )))
  55         digest = bytes(bytearray((
  56             0x2D, 0xFB, 0xC1, 0xB3, 0x72, 0xD8, 0x9A, 0x11,
  57             0x88, 0xC0, 0x9C, 0x52, 0xE0, 0xEE, 0xC6, 0x1F,
  58             0xCE, 0x52, 0x03, 0x2A, 0xB1, 0x02, 0x2E, 0x8E,
  59             0x67, 0xEC, 0xE6, 0x67, 0x2B, 0x04, 0x3E, 0xE5
  60         )))
  61         signature = bytes(bytearray((
  62             0x41, 0xAA, 0x28, 0xD2, 0xF1, 0xAB, 0x14, 0x82,
  63             0x80, 0xCD, 0x9E, 0xD5, 0x6F, 0xED, 0xA4, 0x19,
  64             0x74, 0x05, 0x35, 0x54, 0xA4, 0x27, 0x67, 0xB8,
  65             0x3A, 0xD0, 0x43, 0xFD, 0x39, 0xDC, 0x04, 0x93,
  66             0x01, 0x45, 0x6C, 0x64, 0xBA, 0x46, 0x42, 0xA1,
  67             0x65, 0x3C, 0x23, 0x5A, 0x98, 0xA6, 0x02, 0x49,
  68             0xBC, 0xD6, 0xD3, 0xF7, 0x46, 0xB6, 0x31, 0xDF,
  69             0x92, 0x80, 0x14, 0xF6, 0xC5, 0xBF, 0x9C, 0x40
  70         )))
  71         prv = bytes2long(prv)
  72         signature = signature[32:] + signature[:32]
  73
  74         c = CURVES["id-GostR3410-2001-TestParamSet"]
  75         pubX, pubY = public_key(c, prv)
  76         self.assertSequenceEqual(long2bytes(pubX), pub_x)
  77         self.assertSequenceEqual(long2bytes(pubY), pub_y)
  78         s = sign(c, prv, digest)
  79         self.assertTrue(verify(c, (pubX, pubY), digest, s))
  80         self.assertTrue(verify(c, (pubX, pubY), digest, signature))
  81
  82     def test_sequence(self):
  83         c = CURVES["id-GostR3410-2001-TestParamSet"]
  84         prv = bytes2long(urandom(32))
  85         pubX, pubY = public_key(c, prv)
  86         for _ in range(20):
  87             digest = urandom(32)
  88             s = sign(c, prv, digest, mode=2001)
  89             self.assertTrue(verify(c, (pubX, pubY), digest, s, mode=2001))
  90
  91
  92 class Test34102012(TestCase):
  93     def test_gcl3(self):
  94         """ Test vector from libgcl3
  95         """
  96         p = bytes2long(bytes(bytearray((
  97             0x45, 0x31, 0xAC, 0xD1, 0xFE, 0x00, 0x23, 0xC7,
  98             0x55, 0x0D, 0x26, 0x7B, 0x6B, 0x2F, 0xEE, 0x80,
  99             0x92, 0x2B, 0x14, 0xB2, 0xFF, 0xB9, 0x0F, 0x04,
 100             0xD4, 0xEB, 0x7C, 0x09, 0xB5, 0xD2, 0xD1, 0x5D,
 101             0xF1, 0xD8, 0x52, 0x74, 0x1A, 0xF4, 0x70, 0x4A,
 102             0x04, 0x58, 0x04, 0x7E, 0x80, 0xE4, 0x54, 0x6D,
 103             0x35, 0xB8, 0x33, 0x6F, 0xAC, 0x22, 0x4D, 0xD8,
 104             0x16, 0x64, 0xBB, 0xF5, 0x28, 0xBE, 0x63, 0x73,
 105         ))))
 106         q = bytes2long(bytes(bytearray((
 107             0x45, 0x31, 0xAC, 0xD1, 0xFE, 0x00, 0x23, 0xC7,
 108             0x55, 0x0D, 0x26, 0x7B, 0x6B, 0x2F, 0xEE, 0x80,
 109             0x92, 0x2B, 0x14, 0xB2, 0xFF, 0xB9, 0x0F, 0x04,
 110             0xD4, 0xEB, 0x7C, 0x09, 0xB5, 0xD2, 0xD1, 0x5D,
 111             0xA8, 0x2F, 0x2D, 0x7E, 0xCB, 0x1D, 0xBA, 0xC7,
 112             0x19, 0x90, 0x5C, 0x5E, 0xEC, 0xC4, 0x23, 0xF1,
 113             0xD8, 0x6E, 0x25, 0xED, 0xBE, 0x23, 0xC5, 0x95,
 114             0xD6, 0x44, 0xAA, 0xF1, 0x87, 0xE6, 0xE6, 0xDF,
 115         ))))
 116         a = bytes2long(bytes(bytearray((
 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, 0x00,
 123             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 124             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07,
 125         ))))
 126         b = bytes2long(bytes(bytearray((
 127             0x1C, 0xFF, 0x08, 0x06, 0xA3, 0x11, 0x16, 0xDA,
 128             0x29, 0xD8, 0xCF, 0xA5, 0x4E, 0x57, 0xEB, 0x74,
 129             0x8B, 0xC5, 0xF3, 0x77, 0xE4, 0x94, 0x00, 0xFD,
 130             0xD7, 0x88, 0xB6, 0x49, 0xEC, 0xA1, 0xAC, 0x43,
 131             0x61, 0x83, 0x40, 0x13, 0xB2, 0xAD, 0x73, 0x22,
 132             0x48, 0x0A, 0x89, 0xCA, 0x58, 0xE0, 0xCF, 0x74,
 133             0xBC, 0x9E, 0x54, 0x0C, 0x2A, 0xDD, 0x68, 0x97,
 134             0xFA, 0xD0, 0xA3, 0x08, 0x4F, 0x30, 0x2A, 0xDC,
 135         ))))
 136         x = bytes2long(bytes(bytearray((
 137             0x24, 0xD1, 0x9C, 0xC6, 0x45, 0x72, 0xEE, 0x30,
 138             0xF3, 0x96, 0xBF, 0x6E, 0xBB, 0xFD, 0x7A, 0x6C,
 139             0x52, 0x13, 0xB3, 0xB3, 0xD7, 0x05, 0x7C, 0xC8,
 140             0x25, 0xF9, 0x10, 0x93, 0xA6, 0x8C, 0xD7, 0x62,
 141             0xFD, 0x60, 0x61, 0x12, 0x62, 0xCD, 0x83, 0x8D,
 142             0xC6, 0xB6, 0x0A, 0xA7, 0xEE, 0xE8, 0x04, 0xE2,
 143             0x8B, 0xC8, 0x49, 0x97, 0x7F, 0xAC, 0x33, 0xB4,
 144             0xB5, 0x30, 0xF1, 0xB1, 0x20, 0x24, 0x8A, 0x9A,
 145         ))))
 146         y = bytes2long(bytes(bytearray((
 147             0x2B, 0xB3, 0x12, 0xA4, 0x3B, 0xD2, 0xCE, 0x6E,
 148             0x0D, 0x02, 0x06, 0x13, 0xC8, 0x57, 0xAC, 0xDD,
 149             0xCF, 0xBF, 0x06, 0x1E, 0x91, 0xE5, 0xF2, 0xC3,
 150             0xF3, 0x24, 0x47, 0xC2, 0x59, 0xF3, 0x9B, 0x2C,
 151             0x83, 0xAB, 0x15, 0x6D, 0x77, 0xF1, 0x49, 0x6B,
 152             0xF7, 0xEB, 0x33, 0x51, 0xE1, 0xEE, 0x4E, 0x43,
 153             0xDC, 0x1A, 0x18, 0xB9, 0x1B, 0x24, 0x64, 0x0B,
 154             0x6D, 0xBB, 0x92, 0xCB, 0x1A, 0xDD, 0x37, 0x1E,
 155         ))))
 156         prv = bytes(bytearray((
 157             0x0B, 0xA6, 0x04, 0x8A, 0xAD, 0xAE, 0x24, 0x1B,
 158             0xA4, 0x09, 0x36, 0xD4, 0x77, 0x56, 0xD7, 0xC9,
 159             0x30, 0x91, 0xA0, 0xE8, 0x51, 0x46, 0x69, 0x70,
 160             0x0E, 0xE7, 0x50, 0x8E, 0x50, 0x8B, 0x10, 0x20,
 161             0x72, 0xE8, 0x12, 0x3B, 0x22, 0x00, 0xA0, 0x56,
 162             0x33, 0x22, 0xDA, 0xD2, 0x82, 0x7E, 0x27, 0x14,
 163             0xA2, 0x63, 0x6B, 0x7B, 0xFD, 0x18, 0xAA, 0xDF,
 164             0xC6, 0x29, 0x67, 0x82, 0x1F, 0xA1, 0x8D, 0xD4,
 165         )))
 166         pub_x = bytes(bytearray((
 167             0x11, 0x5D, 0xC5, 0xBC, 0x96, 0x76, 0x0C, 0x7B,
 168             0x48, 0x59, 0x8D, 0x8A, 0xB9, 0xE7, 0x40, 0xD4,
 169             0xC4, 0xA8, 0x5A, 0x65, 0xBE, 0x33, 0xC1, 0x81,
 170             0x5B, 0x5C, 0x32, 0x0C, 0x85, 0x46, 0x21, 0xDD,
 171             0x5A, 0x51, 0x58, 0x56, 0xD1, 0x33, 0x14, 0xAF,
 172             0x69, 0xBC, 0x5B, 0x92, 0x4C, 0x8B, 0x4D, 0xDF,
 173             0xF7, 0x5C, 0x45, 0x41, 0x5C, 0x1D, 0x9D, 0xD9,
 174             0xDD, 0x33, 0x61, 0x2C, 0xD5, 0x30, 0xEF, 0xE1,
 175         )))
 176         pub_y = bytes(bytearray((
 177             0x37, 0xC7, 0xC9, 0x0C, 0xD4, 0x0B, 0x0F, 0x56,
 178             0x21, 0xDC, 0x3A, 0xC1, 0xB7, 0x51, 0xCF, 0xA0,
 179             0xE2, 0x63, 0x4F, 0xA0, 0x50, 0x3B, 0x3D, 0x52,
 180             0x63, 0x9F, 0x5D, 0x7F, 0xB7, 0x2A, 0xFD, 0x61,
 181             0xEA, 0x19, 0x94, 0x41, 0xD9, 0x43, 0xFF, 0xE7,
 182             0xF0, 0xC7, 0x0A, 0x27, 0x59, 0xA3, 0xCD, 0xB8,
 183             0x4C, 0x11, 0x4E, 0x1F, 0x93, 0x39, 0xFD, 0xF2,
 184             0x7F, 0x35, 0xEC, 0xA9, 0x36, 0x77, 0xBE, 0xEC,
 185         )))
 186         digest = bytes(bytearray((
 187             0x37, 0x54, 0xF3, 0xCF, 0xAC, 0xC9, 0xE0, 0x61,
 188             0x5C, 0x4F, 0x4A, 0x7C, 0x4D, 0x8D, 0xAB, 0x53,
 189             0x1B, 0x09, 0xB6, 0xF9, 0xC1, 0x70, 0xC5, 0x33,
 190             0xA7, 0x1D, 0x14, 0x70, 0x35, 0xB0, 0xC5, 0x91,
 191             0x71, 0x84, 0xEE, 0x53, 0x65, 0x93, 0xF4, 0x41,
 192             0x43, 0x39, 0x97, 0x6C, 0x64, 0x7C, 0x5D, 0x5A,
 193             0x40, 0x7A, 0xDE, 0xDB, 0x1D, 0x56, 0x0C, 0x4F,
 194             0xC6, 0x77, 0x7D, 0x29, 0x72, 0x07, 0x5B, 0x8C,
 195         )))
 196         signature = bytes(bytearray((
 197             0x2F, 0x86, 0xFA, 0x60, 0xA0, 0x81, 0x09, 0x1A,
 198             0x23, 0xDD, 0x79, 0x5E, 0x1E, 0x3C, 0x68, 0x9E,
 199             0xE5, 0x12, 0xA3, 0xC8, 0x2E, 0xE0, 0xDC, 0xC2,
 200             0x64, 0x3C, 0x78, 0xEE, 0xA8, 0xFC, 0xAC, 0xD3,
 201             0x54, 0x92, 0x55, 0x84, 0x86, 0xB2, 0x0F, 0x1C,
 202             0x9E, 0xC1, 0x97, 0xC9, 0x06, 0x99, 0x85, 0x02,
 203             0x60, 0xC9, 0x3B, 0xCB, 0xCD, 0x9C, 0x5C, 0x33,
 204             0x17, 0xE1, 0x93, 0x44, 0xE1, 0x73, 0xAE, 0x36,
 205             0x10, 0x81, 0xB3, 0x94, 0x69, 0x6F, 0xFE, 0x8E,
 206             0x65, 0x85, 0xE7, 0xA9, 0x36, 0x2D, 0x26, 0xB6,
 207             0x32, 0x5F, 0x56, 0x77, 0x8A, 0xAD, 0xBC, 0x08,
 208             0x1C, 0x0B, 0xFB, 0xE9, 0x33, 0xD5, 0x2F, 0xF5,
 209             0x82, 0x3C, 0xE2, 0x88, 0xE8, 0xC4, 0xF3, 0x62,
 210             0x52, 0x60, 0x80, 0xDF, 0x7F, 0x70, 0xCE, 0x40,
 211             0x6A, 0x6E, 0xEB, 0x1F, 0x56, 0x91, 0x9C, 0xB9,
 212             0x2A, 0x98, 0x53, 0xBD, 0xE7, 0x3E, 0x5B, 0x4A,
 213         )))
 214         prv = bytes2long(prv)
 215         signature = signature[64:] + signature[:64]
 216         c = GOST3410Curve(p, q, a, b, x, y)
 217         pubX, pubY = public_key(c, prv)
 218         self.assertSequenceEqual(long2bytes(pubX), pub_x)
 219         self.assertSequenceEqual(long2bytes(pubY), pub_y)
 220         s = sign(c, prv, digest, mode=2012)
 221         self.assertTrue(verify(c, (pubX, pubY), digest, s, mode=2012))
 222         self.assertTrue(verify(c, (pubX, pubY), digest, signature, mode=2012))
 223
 224     def test_sequence(self):
 225         c = CURVES["id-tc26-gost-3410-12-512-paramSetA"]
 226         prv = bytes2long(urandom(64))
 227         pubX, pubY = public_key(c, prv)
 228         for _ in range(20):
 229             digest = urandom(64)
 230             s = sign(c, prv, digest, mode=2012)
 231             self.assertTrue(verify(c, (pubX, pubY), digest, s, mode=2012))
 232             self.assertNotIn(b"\x00" * 8, s)
 233
 234
 235 class TestUVXYConversion(TestCase):
 236     """Twisted Edwards to Weierstrass coordinates conversion and vice versa
 237     """
 238     def test_curve1(self):
 239         c = CURVES["id-tc26-gost-3410-2012-256-paramSetA"]
 240         u, v = (0x0D, bytes2long(hexdec("60CA1E32AA475B348488C38FAB07649CE7EF8DBE87F22E81F92B2592DBA300E7")))
 241         self.assertEqual(uv2xy(c, u, v), (c.x, c.y))
 242         self.assertEqual(xy2uv(c, c.x, c.y), (u, v))
 243
 244     def test_curve2(self):
 245         c = CURVES["id-tc26-gost-3410-2012-512-paramSetC"]
 246         u, v = (0x12, bytes2long(hexdec("469AF79D1FB1F5E16B99592B77A01E2A0FDFB0D01794368D9A56117F7B38669522DD4B650CF789EEBF068C5D139732F0905622C04B2BAAE7600303EE73001A3D")))
 247         self.assertEqual(uv2xy(c, u, v), (c.x, c.y))
 248         self.assertEqual(xy2uv(c, c.x, c.y), (u, v))
 249
 250
 251 class Test34102012SESPAKE(TestCase):
 252     """Test vectors for multiplication from :rfc:`8133`
 253     """
 254     def test_curve1(self):
 255         c = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"]
 256         q_ind = (
 257             0xA69D51CAF1A309FA9E9B66187759B0174C274E080356F23CFCBFE84D396AD7BB,
 258             0x5D26F29ECC2E9AC0404DCF7986FA55FE94986362170F54B9616426A659786DAC,
 259         )
 260         self.assertEqual(
 261             c.exp(bytes2long(hexdec(
 262                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 263             )[::-1]), x=q_ind[0], y=q_ind[1]),
 264             (
 265                 0x59495655D1E7C7424C622485F575CCF121F3122D274101E8AB734CC9C9A9B45E,
 266                 0x48D1C311D33C9B701F3B03618562A4A07A044E3AF31E3999E67B487778B53C62,
 267             )
 268         )
 269         self.assertEqual(
 270             c.exp(0x1F2538097D5A031FA68BBB43C84D12B3DE47B7061C0D5E24993E0C873CDBA6B3),
 271             (
 272                 0xBBC77CF42DC1E62D06227935379B4AA4D14FEA4F565DDF4CB4FA4D31579F9676,
 273                 0x8E16604A4AFDF28246684D4996274781F6CB80ABBBA1414C1513EC988509DABF,
 274             )
 275         )
 276         self.assertEqual(
 277             c.exp(0xDC497D9EF6324912FD367840EE509A2032AEDB1C0A890D133B45F596FCCBD45D),
 278             (
 279                 0x6097341C1BE388E83E7CA2DF47FAB86E2271FD942E5B7B2EB2409E49F742BC29,
 280                 0xC81AA48BDB4CA6FA0EF18B9788AE25FE30857AA681B3942217F9FED151BAB7D0,
 281             ),
 282         )
 283
 284     def test_curve2(self):
 285         c = CURVES["id-GostR3410-2001-CryptoPro-B-ParamSet"]
 286         q_ind = (
 287             0x3D715A874A4B17CB3B517893A9794A2B36C89D2FFC693F01EE4CC27E7F49E399,
 288             0x1C5A641FCF7CE7E87CDF8CEA38F3DB3096EACE2FAD158384B53953365F4FE7FE,
 289         )
 290         self.assertEqual(
 291             c.exp(bytes2long(hexdec(
 292                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 293             )[::-1]), x=q_ind[0], y=q_ind[1]),
 294             (
 295                 0x6DC2AE26BC691FCA5A73D9C452790D15E34BA5404D92955B914C8D2662ABB985,
 296                 0x3B02AAA9DD65AE30C335CED12F3154BBAC059F66B088306747453EDF6E5DB077,
 297             )
 298         )
 299         self.assertEqual(
 300             c.exp(0x499D72B90299CAB0DA1F8BE19D9122F622A13B32B730C46BD0664044F2144FAD),
 301             (
 302                 0x61D6F916DB717222D74877F179F7EBEF7CD4D24D8C1F523C048E34A1DF30F8DD,
 303                 0x3EC48863049CFCFE662904082E78503F4973A4E105E2F1B18C69A5E7FB209000,
 304             )
 305         )
 306         self.assertEqual(
 307             c.exp(0x0F69FF614957EF83668EDC2D7ED614BE76F7B253DB23C5CC9C52BF7DF8F4669D),
 308             (
 309                 0x33BC6F7E9C0BA10CFB2B72546C327171295508EA97F8C8BA9F890F2478AB4D6C,
 310                 0x75D57B396C396F492F057E9222CCC686437A2AAD464E452EF426FC8EEED1A4A6,
 311             ),
 312         )
 313
 314     def test_curve3(self):
 315         c = CURVES["id-GostR3410-2001-CryptoPro-C-ParamSet"]
 316         q_ind = (
 317             0x1E36383E43BB6CFA2917167D71B7B5DD3D6D462B43D7C64282AE67DFBEC2559D,
 318             0x137478A9F721C73932EA06B45CF72E37EB78A63F29A542E563C614650C8B6399,
 319         )
 320         self.assertEqual(
 321             c.exp(bytes2long(hexdec(
 322                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 323             )[::-1]), x=q_ind[0], y=q_ind[1]),
 324             (
 325                 0x945821DAF91E158B839939630655A3B21FF3E146D27041E86C05650EB3B46B59,
 326                 0x3A0C2816AC97421FA0E879605F17F0C9C3EB734CFF196937F6284438D70BDC48,
 327             )
 328         )
 329         self.assertEqual(
 330             c.exp(0x3A54AC3F19AD9D0B1EAC8ACDCEA70E581F1DAC33D13FEAFD81E762378639C1A8),
 331             (
 332                 0x96B7F09C94D297C257A7DA48364C0076E59E48D221CBA604AE111CA3933B446A,
 333                 0x54E4953D86B77ECCEB578500931E822300F7E091F79592CA202A020D762C34A6,
 334             )
 335         )
 336         self.assertEqual(
 337             c.exp(0x448781782BF7C0E52A1DD9E6758FD3482D90D3CFCCF42232CF357E59A4D49FD4),
 338             (
 339                 0x4B9C0AB55A938121F282F48A2CC4396EB16E7E0068B495B0C1DD4667786A3EB7,
 340                 0x223460AA8E09383E9DF9844C5A0F2766484738E5B30128A171B69A77D9509B96,
 341             ),
 342         )
 343
 344     def test_curve4(self):
 345         c = CURVES["id-tc26-gost-3410-12-512-paramSetA"]
 346         q_ind = (
 347             0x2A17F8833A32795327478871B5C5E88AEFB91126C64B4B8327289BEA62559425D18198F133F400874328B220C74497CD240586CB249E158532CB8090776CD61C,
 348             0x728F0C4A73B48DA41CE928358FAD26B47A6E094E9362BAE82559F83CDDC4EC3A4676BD3707EDEAF4CD85E99695C64C241EDC622BE87DC0CF87F51F4367F723C5,
 349         )
 350         self.assertEqual(
 351             c.exp(bytes2long(hexdec(
 352                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F181270671C6213E3930EFDDA26451792C6208122EE60D200520D695DFD9F5F0FD5ABA702"
 353             )[::-1]), x=q_ind[0], y=q_ind[1]),
 354             (
 355                 0x0C0AB53D0E0A9C607CAD758F558915A0A7DC5DC87B45E9A58FDDF30EC3385960283E030CD322D9E46B070637785FD49D2CD711F46807A24C40AF9A42C8E2D740,
 356                 0xDF93A8012B86D3A3D4F8A4D487DA15FC739EB31B20B3B0E8C8C032AAF8072C6337CF7D5B404719E5B4407C41D9A3216A08CA69C271484E9ED72B8AAA52E28B8B,
 357             )
 358         )
 359         self.assertEqual(
 360             c.exp(0x3CE54325DB52FE798824AEAD11BB16FA766857D04A4AF7D468672F16D90E7396046A46F815693E85B1CE5464DA9270181F82333B0715057BBE8D61D400505F0E),
 361             (
 362                 0xB93093EB0FCC463239B7DF276E09E592FCFC9B635504EA4531655D76A0A3078E2B4E51CFE2FA400CC5DE9FBE369DB204B3E8ED7EDD85EE5CCA654C1AED70E396,
 363                 0x809770B8D910EA30BD2FA89736E91DC31815D2D9B31128077EEDC371E9F69466F497DC64DD5B1FADC587F860EE256109138C4A9CD96B628E65A8F590520FC882,
 364             )
 365         )
 366         self.assertEqual(
 367             c.exp(0xB5C286A79AA8E97EC0E19BC1959A1D15F12F8C97870BA9D68CC12811A56A3BB11440610825796A49D468CDC9C2D02D76598A27973D5960C5F50BCE28D8D345F4),
 368             (
 369                 0x238B38644E440452A99FA6B93D9FD7DA0CB83C32D3C1E3CFE5DF5C3EB0F9DB91E588DAEDC849EA2FB867AE855A21B4077353C0794716A6480995113D8C20C7AF,
 370                 0xB2273D5734C1897F8D15A7008B862938C8C74CA7E877423D95243EB7EBD02FD2C456CF9FC956F078A59AA86F19DD1075E5167E4ED35208718EA93161C530ED14,
 371             ),
 372         )
 373
 374     def test_curve5(self):
 375         c = CURVES["id-tc26-gost-3410-12-512-paramSetB"]
 376         q_ind = (
 377             0x7E1FAE8285E035BEC244BEF2D0E5EBF436633CF50E55231DEA9C9CF21D4C8C33DF85D4305DE92971F0A4B4C07E00D87BDBC720EB66E49079285AAF12E0171149,
 378             0x2CC89998B875D4463805BA0D858A196592DB20AB161558FF2F4EF7A85725D20953967AE621AFDEAE89BB77C83A2528EF6FCE02F68BDA4679D7F2704947DBC408,
 379         )
 380         self.assertEqual(
 381             c.exp(bytes2long(hexdec(
 382                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F181270671C6213E3930EFDDA26451792C6208122EE60D200520D695DFD9F5F0FD5ABA702"
 383             )[::-1]), x=q_ind[0], y=q_ind[1]),
 384             (
 385                 0x7D03E65B8050D1E12CBB601A17B9273B0E728F5021CD47C8A4DD822E4627BA5F9C696286A2CDDA9A065509866B4DEDEDC4A118409604AD549F87A60AFA621161,
 386                 0x16037DAD45421EC50B00D50BDC6AC3B85348BC1D3A2F85DB27C3373580FEF87C2C743B7ED30F22BE22958044E716F93A61CA3213A361A2797A16A3AE62957377,
 387             )
 388         )
 389         self.assertEqual(
 390             c.exp(0x715E893FA639BF341296E0623E6D29DADF26B163C278767A7982A989462A3863FE12AEF8BD403D59C4DC4720570D4163DB0805C7C10C4E818F9CB785B04B9997),
 391             (
 392                 0x10C479EA1C04D3C2C02B0576A9C42D96226FF033C1191436777F66916030D87D02FB93738ED7669D07619FFCE7C1F3C4DB5E5DF49E2186D6FA1E2EB5767602B9,
 393                 0x039F6044191404E707F26D59D979136A831CCE43E1C5F0600D1DDF8F39D0CA3D52FBD943BF04DDCED1AA2CE8F5EBD7487ACDEF239C07D015084D796784F35436,
 394             )
 395         )
 396         self.assertEqual(
 397             c.exp(0x30FA8C2B4146C2DBBE82BED04D7378877E8C06753BD0A0FF71EBF2BEFE8DA8F3DC0836468E2CE7C5C961281B6505140F8407413F03C2CB1D201EA1286CE30E6D),
 398             (
 399                 0x34C0149E7BB91AE377B02573FCC48AF7BFB7B16DEB8F9CE870F384688E3241A3A868588CC0EF4364CCA67D17E3260CD82485C202ADC76F895D5DF673B1788E67,
 400                 0x608E944929BD643569ED5189DB871453F13333A1EAF82B2FE1BE8100E775F13DD9925BD317B63BFAF05024D4A738852332B64501195C1B2EF789E34F23DDAFC5,
 401             ),
 402         )
 403
 404     def test_curve6(self):
 405         c = CURVES["id-tc26-gost-3410-2012-256-paramSetA"]
 406         q_ind = (
 407             0xB51ADF93A40AB15792164FAD3352F95B66369EB2A4EF5EFAE32829320363350E,
 408             0x74A358CC08593612F5955D249C96AFB7E8B0BB6D8BD2BBE491046650D822BE18,
 409         )
 410         self.assertEqual(
 411             c.exp(bytes2long(hexdec(
 412                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 413             )[::-1]), x=q_ind[0], y=q_ind[1]),
 414             (
 415                 0xDBF99827078956812FA48C6E695DF589DEF1D18A2D4D35A96D75BF6854237629,
 416                 0x9FDDD48BFBC57BEE1DA0CFF282884F284D471B388893C48F5ECB02FC18D67589,
 417             )
 418         )
 419         self.assertEqual(
 420             c.exp(0x147B72F6684FB8FD1B418A899F7DBECAF5FCE60B13685BAA95328654A7F0707F),
 421             (
 422                 0x33FBAC14EAE538275A769417829C431BD9FA622B6F02427EF55BD60EE6BC2888,
 423                 0x22F2EBCF960A82E6CDB4042D3DDDA511B2FBA925383C2273D952EA2D406EAE46,
 424             )
 425         )
 426         self.assertEqual(
 427             c.exp(0x30D5CFADAA0E31B405E6734C03EC4C5DF0F02F4BA25C9A3B320EE6453567B4CB),
 428             (
 429                 0x2B2D89FAB735433970564F2F28CFA1B57D640CB902BC6334A538F44155022CB2,
 430                 0x10EF6A82EEF1E70F942AA81D6B4CE5DEC0DDB9447512962874870E6F2849A96F,
 431             ),
 432         )
 433
 434     def test_curve7(self):
 435         c = CURVES["id-tc26-gost-3410-2012-512-paramSetC"]
 436         q_ind = (
 437             0x489C91784E02E98F19A803ABCA319917F37689E5A18965251CE2FF4E8D8B298F5BA7470F9E0E713487F96F4A8397B3D09A270C9D367EB5E0E6561ADEEB51581D,
 438             0x684EA885ACA64EAF1B3FEE36C0852A3BE3BD8011B0EF18E203FF87028D6EB5DB2C144A0DCC71276542BFD72CA2A43FA4F4939DA66D9A60793C704A8C94E16F18,
 439         )
 440         self.assertEqual(
 441             c.exp(bytes2long(hexdec(
 442                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F181270671C6213E3930EFDDA26451792C6208122EE60D200520D695DFD9F5F0FD5ABA702"
 443             )[::-1]), x=q_ind[0], y=q_ind[1]),
 444             (
 445                 0x0185AE6271A81BB7F236A955F7CAA26FB63849813C0287D96C83A15AE6B6A86467AB13B6D88CE8CD7DC2E5B97FF5F28FAC2C108F2A3CF3DB5515C9E6D7D210E8,
 446                 0xED0220F92EF771A71C64ECC77986DB7C03D37B3E2AB3E83F32CE5E074A762EC08253C9E2102B87532661275C4B1D16D2789CDABC58ACFDF7318DE70AB64F09B8,
 447             )
 448         )
 449         self.assertEqual(
 450             c.exp(0x332F930421D14CFE260042159F18E49FD5A54167E94108AD80B1DE60B13DE7999A34D611E63F3F870E5110247DF8EC7466E648ACF385E52CCB889ABF491EDFF0),
 451             (
 452                 0x561655966D52952E805574F4281F1ED3A2D498932B00CBA9DECB42837F09835BFFBFE2D84D6B6B242FE7B57F92E1A6F2413E12DDD6383E4437E13D72693469AD,
 453                 0xF6B18328B2715BD7F4178615273A36135BC0BF62F7D8BB9F080164AD36470AD03660F51806C64C6691BADEF30F793720F8E3FEAED631D6A54A4C372DCBF80E82,
 454             )
 455         )
 456         self.assertEqual(
 457             c.exp(0x38481771E7D054F96212686B613881880BD8A6C89DDBC656178F014D2C093432A033EE10415F13A160D44C2AD61E6E2E05A7F7EC286BCEA3EA4D4D53F8634FA2),
 458             (
 459                 0xB7C5818687083433BC1AFF61CB5CA79E38232025E0C1F123B8651E62173CE6873F3E6FFE7281C2E45F4F524F66B0C263616ED08FD210AC4355CA3292B51D71C3,
 460                 0x497F14205DBDC89BDDAF50520ED3B1429AD30777310186BE5E68070F016A44E0C766DB08E8AC23FBDFDE6D675AA4DF591EB18BA0D348DF7AA40973A2F1DCFA55,
 461             ),
 462         )