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, 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
  17 from os import urandom
  18 from unittest import TestCase
  19
  20 from pygost.gost3410 import CURVES
  21 from pygost.gost3410 import GOST3410Curve
  22 from pygost.gost3410 import public_key
  23 from pygost.gost3410 import sign
  24 from pygost.gost3410 import uv2xy
  25 from pygost.gost3410 import verify
  26 from pygost.gost3410 import xy2uv
  27 from pygost.utils import bytes2long
  28 from pygost.utils import hexdec
  29 from pygost.utils import long2bytes
  30
  31
  32 class Test341001(TestCase):
  33     def test_rfc(self):
  34         """ Test vector from :rfc:`5832`
  35         """
  36         prv = bytes(bytearray((
  37             0x7A, 0x92, 0x9A, 0xDE, 0x78, 0x9B, 0xB9, 0xBE,
  38             0x10, 0xED, 0x35, 0x9D, 0xD3, 0x9A, 0x72, 0xC1,
  39             0x1B, 0x60, 0x96, 0x1F, 0x49, 0x39, 0x7E, 0xEE,
  40             0x1D, 0x19, 0xCE, 0x98, 0x91, 0xEC, 0x3B, 0x28
  41         )))
  42         pub_x = bytes(bytearray((
  43             0x7F, 0x2B, 0x49, 0xE2, 0x70, 0xDB, 0x6D, 0x90,
  44             0xD8, 0x59, 0x5B, 0xEC, 0x45, 0x8B, 0x50, 0xC5,
  45             0x85, 0x85, 0xBA, 0x1D, 0x4E, 0x9B, 0x78, 0x8F,
  46             0x66, 0x89, 0xDB, 0xD8, 0xE5, 0x6F, 0xD8, 0x0B
  47         )))
  48         pub_y = bytes(bytearray((
  49             0x26, 0xF1, 0xB4, 0x89, 0xD6, 0x70, 0x1D, 0xD1,
  50             0x85, 0xC8, 0x41, 0x3A, 0x97, 0x7B, 0x3C, 0xBB,
  51             0xAF, 0x64, 0xD1, 0xC5, 0x93, 0xD2, 0x66, 0x27,
  52             0xDF, 0xFB, 0x10, 0x1A, 0x87, 0xFF, 0x77, 0xDA
  53         )))
  54         digest = bytes(bytearray((
  55             0x2D, 0xFB, 0xC1, 0xB3, 0x72, 0xD8, 0x9A, 0x11,
  56             0x88, 0xC0, 0x9C, 0x52, 0xE0, 0xEE, 0xC6, 0x1F,
  57             0xCE, 0x52, 0x03, 0x2A, 0xB1, 0x02, 0x2E, 0x8E,
  58             0x67, 0xEC, 0xE6, 0x67, 0x2B, 0x04, 0x3E, 0xE5
  59         )))
  60         signature = bytes(bytearray((
  61             0x41, 0xAA, 0x28, 0xD2, 0xF1, 0xAB, 0x14, 0x82,
  62             0x80, 0xCD, 0x9E, 0xD5, 0x6F, 0xED, 0xA4, 0x19,
  63             0x74, 0x05, 0x35, 0x54, 0xA4, 0x27, 0x67, 0xB8,
  64             0x3A, 0xD0, 0x43, 0xFD, 0x39, 0xDC, 0x04, 0x93,
  65             0x01, 0x45, 0x6C, 0x64, 0xBA, 0x46, 0x42, 0xA1,
  66             0x65, 0x3C, 0x23, 0x5A, 0x98, 0xA6, 0x02, 0x49,
  67             0xBC, 0xD6, 0xD3, 0xF7, 0x46, 0xB6, 0x31, 0xDF,
  68             0x92, 0x80, 0x14, 0xF6, 0xC5, 0xBF, 0x9C, 0x40
  69         )))
  70         prv = bytes2long(prv)
  71         signature = signature[32:] + signature[:32]
  72
  73         c = CURVES["id-GostR3410-2001-TestParamSet"]
  74         pubX, pubY = public_key(c, prv)
  75         self.assertSequenceEqual(long2bytes(pubX), pub_x)
  76         self.assertSequenceEqual(long2bytes(pubY), pub_y)
  77         s = sign(c, prv, digest)
  78         self.assertTrue(verify(c, (pubX, pubY), digest, s))
  79         self.assertTrue(verify(c, (pubX, pubY), digest, signature))
  80
  81     def test_sequence(self):
  82         c = CURVES["id-GostR3410-2001-TestParamSet"]
  83         prv = bytes2long(urandom(32))
  84         pubX, pubY = public_key(c, prv)
  85         for _ in range(20):
  86             digest = urandom(32)
  87             s = sign(c, prv, digest, mode=2001)
  88             self.assertTrue(verify(c, (pubX, pubY), digest, s, mode=2001))
  89
  90
  91 class Test34102012(TestCase):
  92     def test_gcl3(self):
  93         """ Test vector from libgcl3
  94         """
  95         p = bytes2long(bytes(bytearray((
  96             0x45, 0x31, 0xAC, 0xD1, 0xFE, 0x00, 0x23, 0xC7,
  97             0x55, 0x0D, 0x26, 0x7B, 0x6B, 0x2F, 0xEE, 0x80,
  98             0x92, 0x2B, 0x14, 0xB2, 0xFF, 0xB9, 0x0F, 0x04,
  99             0xD4, 0xEB, 0x7C, 0x09, 0xB5, 0xD2, 0xD1, 0x5D,
 100             0xF1, 0xD8, 0x52, 0x74, 0x1A, 0xF4, 0x70, 0x4A,
 101             0x04, 0x58, 0x04, 0x7E, 0x80, 0xE4, 0x54, 0x6D,
 102             0x35, 0xB8, 0x33, 0x6F, 0xAC, 0x22, 0x4D, 0xD8,
 103             0x16, 0x64, 0xBB, 0xF5, 0x28, 0xBE, 0x63, 0x73,
 104         ))))
 105         q = bytes2long(bytes(bytearray((
 106             0x45, 0x31, 0xAC, 0xD1, 0xFE, 0x00, 0x23, 0xC7,
 107             0x55, 0x0D, 0x26, 0x7B, 0x6B, 0x2F, 0xEE, 0x80,
 108             0x92, 0x2B, 0x14, 0xB2, 0xFF, 0xB9, 0x0F, 0x04,
 109             0xD4, 0xEB, 0x7C, 0x09, 0xB5, 0xD2, 0xD1, 0x5D,
 110             0xA8, 0x2F, 0x2D, 0x7E, 0xCB, 0x1D, 0xBA, 0xC7,
 111             0x19, 0x90, 0x5C, 0x5E, 0xEC, 0xC4, 0x23, 0xF1,
 112             0xD8, 0x6E, 0x25, 0xED, 0xBE, 0x23, 0xC5, 0x95,
 113             0xD6, 0x44, 0xAA, 0xF1, 0x87, 0xE6, 0xE6, 0xDF,
 114         ))))
 115         a = bytes2long(bytes(bytearray((
 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, 0x00,
 123             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07,
 124         ))))
 125         b = bytes2long(bytes(bytearray((
 126             0x1C, 0xFF, 0x08, 0x06, 0xA3, 0x11, 0x16, 0xDA,
 127             0x29, 0xD8, 0xCF, 0xA5, 0x4E, 0x57, 0xEB, 0x74,
 128             0x8B, 0xC5, 0xF3, 0x77, 0xE4, 0x94, 0x00, 0xFD,
 129             0xD7, 0x88, 0xB6, 0x49, 0xEC, 0xA1, 0xAC, 0x43,
 130             0x61, 0x83, 0x40, 0x13, 0xB2, 0xAD, 0x73, 0x22,
 131             0x48, 0x0A, 0x89, 0xCA, 0x58, 0xE0, 0xCF, 0x74,
 132             0xBC, 0x9E, 0x54, 0x0C, 0x2A, 0xDD, 0x68, 0x97,
 133             0xFA, 0xD0, 0xA3, 0x08, 0x4F, 0x30, 0x2A, 0xDC,
 134         ))))
 135         x = bytes2long(bytes(bytearray((
 136             0x24, 0xD1, 0x9C, 0xC6, 0x45, 0x72, 0xEE, 0x30,
 137             0xF3, 0x96, 0xBF, 0x6E, 0xBB, 0xFD, 0x7A, 0x6C,
 138             0x52, 0x13, 0xB3, 0xB3, 0xD7, 0x05, 0x7C, 0xC8,
 139             0x25, 0xF9, 0x10, 0x93, 0xA6, 0x8C, 0xD7, 0x62,
 140             0xFD, 0x60, 0x61, 0x12, 0x62, 0xCD, 0x83, 0x8D,
 141             0xC6, 0xB6, 0x0A, 0xA7, 0xEE, 0xE8, 0x04, 0xE2,
 142             0x8B, 0xC8, 0x49, 0x97, 0x7F, 0xAC, 0x33, 0xB4,
 143             0xB5, 0x30, 0xF1, 0xB1, 0x20, 0x24, 0x8A, 0x9A,
 144         ))))
 145         y = bytes2long(bytes(bytearray((
 146             0x2B, 0xB3, 0x12, 0xA4, 0x3B, 0xD2, 0xCE, 0x6E,
 147             0x0D, 0x02, 0x06, 0x13, 0xC8, 0x57, 0xAC, 0xDD,
 148             0xCF, 0xBF, 0x06, 0x1E, 0x91, 0xE5, 0xF2, 0xC3,
 149             0xF3, 0x24, 0x47, 0xC2, 0x59, 0xF3, 0x9B, 0x2C,
 150             0x83, 0xAB, 0x15, 0x6D, 0x77, 0xF1, 0x49, 0x6B,
 151             0xF7, 0xEB, 0x33, 0x51, 0xE1, 0xEE, 0x4E, 0x43,
 152             0xDC, 0x1A, 0x18, 0xB9, 0x1B, 0x24, 0x64, 0x0B,
 153             0x6D, 0xBB, 0x92, 0xCB, 0x1A, 0xDD, 0x37, 0x1E,
 154         ))))
 155         prv = bytes(bytearray((
 156             0x0B, 0xA6, 0x04, 0x8A, 0xAD, 0xAE, 0x24, 0x1B,
 157             0xA4, 0x09, 0x36, 0xD4, 0x77, 0x56, 0xD7, 0xC9,
 158             0x30, 0x91, 0xA0, 0xE8, 0x51, 0x46, 0x69, 0x70,
 159             0x0E, 0xE7, 0x50, 0x8E, 0x50, 0x8B, 0x10, 0x20,
 160             0x72, 0xE8, 0x12, 0x3B, 0x22, 0x00, 0xA0, 0x56,
 161             0x33, 0x22, 0xDA, 0xD2, 0x82, 0x7E, 0x27, 0x14,
 162             0xA2, 0x63, 0x6B, 0x7B, 0xFD, 0x18, 0xAA, 0xDF,
 163             0xC6, 0x29, 0x67, 0x82, 0x1F, 0xA1, 0x8D, 0xD4,
 164         )))
 165         pub_x = bytes(bytearray((
 166             0x11, 0x5D, 0xC5, 0xBC, 0x96, 0x76, 0x0C, 0x7B,
 167             0x48, 0x59, 0x8D, 0x8A, 0xB9, 0xE7, 0x40, 0xD4,
 168             0xC4, 0xA8, 0x5A, 0x65, 0xBE, 0x33, 0xC1, 0x81,
 169             0x5B, 0x5C, 0x32, 0x0C, 0x85, 0x46, 0x21, 0xDD,
 170             0x5A, 0x51, 0x58, 0x56, 0xD1, 0x33, 0x14, 0xAF,
 171             0x69, 0xBC, 0x5B, 0x92, 0x4C, 0x8B, 0x4D, 0xDF,
 172             0xF7, 0x5C, 0x45, 0x41, 0x5C, 0x1D, 0x9D, 0xD9,
 173             0xDD, 0x33, 0x61, 0x2C, 0xD5, 0x30, 0xEF, 0xE1,
 174         )))
 175         pub_y = bytes(bytearray((
 176             0x37, 0xC7, 0xC9, 0x0C, 0xD4, 0x0B, 0x0F, 0x56,
 177             0x21, 0xDC, 0x3A, 0xC1, 0xB7, 0x51, 0xCF, 0xA0,
 178             0xE2, 0x63, 0x4F, 0xA0, 0x50, 0x3B, 0x3D, 0x52,
 179             0x63, 0x9F, 0x5D, 0x7F, 0xB7, 0x2A, 0xFD, 0x61,
 180             0xEA, 0x19, 0x94, 0x41, 0xD9, 0x43, 0xFF, 0xE7,
 181             0xF0, 0xC7, 0x0A, 0x27, 0x59, 0xA3, 0xCD, 0xB8,
 182             0x4C, 0x11, 0x4E, 0x1F, 0x93, 0x39, 0xFD, 0xF2,
 183             0x7F, 0x35, 0xEC, 0xA9, 0x36, 0x77, 0xBE, 0xEC,
 184         )))
 185         digest = bytes(bytearray((
 186             0x37, 0x54, 0xF3, 0xCF, 0xAC, 0xC9, 0xE0, 0x61,
 187             0x5C, 0x4F, 0x4A, 0x7C, 0x4D, 0x8D, 0xAB, 0x53,
 188             0x1B, 0x09, 0xB6, 0xF9, 0xC1, 0x70, 0xC5, 0x33,
 189             0xA7, 0x1D, 0x14, 0x70, 0x35, 0xB0, 0xC5, 0x91,
 190             0x71, 0x84, 0xEE, 0x53, 0x65, 0x93, 0xF4, 0x41,
 191             0x43, 0x39, 0x97, 0x6C, 0x64, 0x7C, 0x5D, 0x5A,
 192             0x40, 0x7A, 0xDE, 0xDB, 0x1D, 0x56, 0x0C, 0x4F,
 193             0xC6, 0x77, 0x7D, 0x29, 0x72, 0x07, 0x5B, 0x8C,
 194         )))
 195         signature = bytes(bytearray((
 196             0x2F, 0x86, 0xFA, 0x60, 0xA0, 0x81, 0x09, 0x1A,
 197             0x23, 0xDD, 0x79, 0x5E, 0x1E, 0x3C, 0x68, 0x9E,
 198             0xE5, 0x12, 0xA3, 0xC8, 0x2E, 0xE0, 0xDC, 0xC2,
 199             0x64, 0x3C, 0x78, 0xEE, 0xA8, 0xFC, 0xAC, 0xD3,
 200             0x54, 0x92, 0x55, 0x84, 0x86, 0xB2, 0x0F, 0x1C,
 201             0x9E, 0xC1, 0x97, 0xC9, 0x06, 0x99, 0x85, 0x02,
 202             0x60, 0xC9, 0x3B, 0xCB, 0xCD, 0x9C, 0x5C, 0x33,
 203             0x17, 0xE1, 0x93, 0x44, 0xE1, 0x73, 0xAE, 0x36,
 204             0x10, 0x81, 0xB3, 0x94, 0x69, 0x6F, 0xFE, 0x8E,
 205             0x65, 0x85, 0xE7, 0xA9, 0x36, 0x2D, 0x26, 0xB6,
 206             0x32, 0x5F, 0x56, 0x77, 0x8A, 0xAD, 0xBC, 0x08,
 207             0x1C, 0x0B, 0xFB, 0xE9, 0x33, 0xD5, 0x2F, 0xF5,
 208             0x82, 0x3C, 0xE2, 0x88, 0xE8, 0xC4, 0xF3, 0x62,
 209             0x52, 0x60, 0x80, 0xDF, 0x7F, 0x70, 0xCE, 0x40,
 210             0x6A, 0x6E, 0xEB, 0x1F, 0x56, 0x91, 0x9C, 0xB9,
 211             0x2A, 0x98, 0x53, 0xBD, 0xE7, 0x3E, 0x5B, 0x4A,
 212         )))
 213         prv = bytes2long(prv)
 214         signature = signature[64:] + signature[:64]
 215         c = GOST3410Curve(p, q, a, b, x, y)
 216         pubX, pubY = public_key(c, prv)
 217         self.assertSequenceEqual(long2bytes(pubX), pub_x)
 218         self.assertSequenceEqual(long2bytes(pubY), pub_y)
 219         s = sign(c, prv, digest, mode=2012)
 220         self.assertTrue(verify(c, (pubX, pubY), digest, s, mode=2012))
 221         self.assertTrue(verify(c, (pubX, pubY), digest, signature, mode=2012))
 222
 223     def test_sequence(self):
 224         c = CURVES["id-tc26-gost-3410-12-512-paramSetA"]
 225         prv = bytes2long(urandom(64))
 226         pubX, pubY = public_key(c, prv)
 227         for _ in range(20):
 228             digest = urandom(64)
 229             s = sign(c, prv, digest, mode=2012)
 230             self.assertTrue(verify(c, (pubX, pubY), digest, s, mode=2012))
 231             self.assertNotIn(b"\x00" * 8, s)
 232
 233
 234 class TestUVXYConversion(TestCase):
 235     """Twisted Edwards to Weierstrass coordinates conversion and vice versa
 236     """
 237     def test_curve1(self):
 238         c = CURVES["id-tc26-gost-3410-2012-256-paramSetA"]
 239         u, v = (0x0D, bytes2long(hexdec("60CA1E32AA475B348488C38FAB07649CE7EF8DBE87F22E81F92B2592DBA300E7")))
 240         self.assertEqual(uv2xy(c, u, v), (c.x, c.y))
 241         self.assertEqual(xy2uv(c, c.x, c.y), (u, v))
 242
 243     def test_curve2(self):
 244         c = CURVES["id-tc26-gost-3410-2012-512-paramSetC"]
 245         u, v = (0x12, bytes2long(hexdec("469AF79D1FB1F5E16B99592B77A01E2A0FDFB0D01794368D9A56117F7B38669522DD4B650CF789EEBF068C5D139732F0905622C04B2BAAE7600303EE73001A3D")))
 246         self.assertEqual(uv2xy(c, u, v), (c.x, c.y))
 247         self.assertEqual(xy2uv(c, c.x, c.y), (u, v))
 248
 249
 250 class Test34102012SESPAKE(TestCase):
 251     """Test vectors for multiplication from :rfc:`8133`
 252     """
 253     def test_curve1(self):
 254         c = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"]
 255         q_ind = (
 256             0xA69D51CAF1A309FA9E9B66187759B0174C274E080356F23CFCBFE84D396AD7BB,
 257             0x5D26F29ECC2E9AC0404DCF7986FA55FE94986362170F54B9616426A659786DAC,
 258         )
 259         self.assertEqual(
 260             c.exp(bytes2long(hexdec(
 261                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 262             )[::-1]), x=q_ind[0], y=q_ind[1]),
 263             (
 264                 0x59495655D1E7C7424C622485F575CCF121F3122D274101E8AB734CC9C9A9B45E,
 265                 0x48D1C311D33C9B701F3B03618562A4A07A044E3AF31E3999E67B487778B53C62,
 266             )
 267         )
 268         self.assertEqual(
 269             c.exp(0x1F2538097D5A031FA68BBB43C84D12B3DE47B7061C0D5E24993E0C873CDBA6B3),
 270             (
 271                 0xBBC77CF42DC1E62D06227935379B4AA4D14FEA4F565DDF4CB4FA4D31579F9676,
 272                 0x8E16604A4AFDF28246684D4996274781F6CB80ABBBA1414C1513EC988509DABF,
 273             )
 274         )
 275         self.assertEqual(
 276             c.exp(0xDC497D9EF6324912FD367840EE509A2032AEDB1C0A890D133B45F596FCCBD45D),
 277             (
 278                 0x6097341C1BE388E83E7CA2DF47FAB86E2271FD942E5B7B2EB2409E49F742BC29,
 279                 0xC81AA48BDB4CA6FA0EF18B9788AE25FE30857AA681B3942217F9FED151BAB7D0,
 280             ),
 281         )
 282
 283     def test_curve2(self):
 284         c = CURVES["id-GostR3410-2001-CryptoPro-B-ParamSet"]
 285         q_ind = (
 286             0x3D715A874A4B17CB3B517893A9794A2B36C89D2FFC693F01EE4CC27E7F49E399,
 287             0x1C5A641FCF7CE7E87CDF8CEA38F3DB3096EACE2FAD158384B53953365F4FE7FE,
 288         )
 289         self.assertEqual(
 290             c.exp(bytes2long(hexdec(
 291                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 292             )[::-1]), x=q_ind[0], y=q_ind[1]),
 293             (
 294                 0x6DC2AE26BC691FCA5A73D9C452790D15E34BA5404D92955B914C8D2662ABB985,
 295                 0x3B02AAA9DD65AE30C335CED12F3154BBAC059F66B088306747453EDF6E5DB077,
 296             )
 297         )
 298         self.assertEqual(
 299             c.exp(0x499D72B90299CAB0DA1F8BE19D9122F622A13B32B730C46BD0664044F2144FAD),
 300             (
 301                 0x61D6F916DB717222D74877F179F7EBEF7CD4D24D8C1F523C048E34A1DF30F8DD,
 302                 0x3EC48863049CFCFE662904082E78503F4973A4E105E2F1B18C69A5E7FB209000,
 303             )
 304         )
 305         self.assertEqual(
 306             c.exp(0x0F69FF614957EF83668EDC2D7ED614BE76F7B253DB23C5CC9C52BF7DF8F4669D),
 307             (
 308                 0x33BC6F7E9C0BA10CFB2B72546C327171295508EA97F8C8BA9F890F2478AB4D6C,
 309                 0x75D57B396C396F492F057E9222CCC686437A2AAD464E452EF426FC8EEED1A4A6,
 310             ),
 311         )
 312
 313     def test_curve3(self):
 314         c = CURVES["id-GostR3410-2001-CryptoPro-C-ParamSet"]
 315         q_ind = (
 316             0x1E36383E43BB6CFA2917167D71B7B5DD3D6D462B43D7C64282AE67DFBEC2559D,
 317             0x137478A9F721C73932EA06B45CF72E37EB78A63F29A542E563C614650C8B6399,
 318         )
 319         self.assertEqual(
 320             c.exp(bytes2long(hexdec(
 321                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 322             )[::-1]), x=q_ind[0], y=q_ind[1]),
 323             (
 324                 0x945821DAF91E158B839939630655A3B21FF3E146D27041E86C05650EB3B46B59,
 325                 0x3A0C2816AC97421FA0E879605F17F0C9C3EB734CFF196937F6284438D70BDC48,
 326             )
 327         )
 328         self.assertEqual(
 329             c.exp(0x3A54AC3F19AD9D0B1EAC8ACDCEA70E581F1DAC33D13FEAFD81E762378639C1A8),
 330             (
 331                 0x96B7F09C94D297C257A7DA48364C0076E59E48D221CBA604AE111CA3933B446A,
 332                 0x54E4953D86B77ECCEB578500931E822300F7E091F79592CA202A020D762C34A6,
 333             )
 334         )
 335         self.assertEqual(
 336             c.exp(0x448781782BF7C0E52A1DD9E6758FD3482D90D3CFCCF42232CF357E59A4D49FD4),
 337             (
 338                 0x4B9C0AB55A938121F282F48A2CC4396EB16E7E0068B495B0C1DD4667786A3EB7,
 339                 0x223460AA8E09383E9DF9844C5A0F2766484738E5B30128A171B69A77D9509B96,
 340             ),
 341         )
 342
 343     def test_curve4(self):
 344         c = CURVES["id-tc26-gost-3410-12-512-paramSetA"]
 345         q_ind = (
 346             0x2A17F8833A32795327478871B5C5E88AEFB91126C64B4B8327289BEA62559425D18198F133F400874328B220C74497CD240586CB249E158532CB8090776CD61C,
 347             0x728F0C4A73B48DA41CE928358FAD26B47A6E094E9362BAE82559F83CDDC4EC3A4676BD3707EDEAF4CD85E99695C64C241EDC622BE87DC0CF87F51F4367F723C5,
 348         )
 349         self.assertEqual(
 350             c.exp(bytes2long(hexdec(
 351                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F181270671C6213E3930EFDDA26451792C6208122EE60D200520D695DFD9F5F0FD5ABA702"
 352             )[::-1]), x=q_ind[0], y=q_ind[1]),
 353             (
 354                 0x0C0AB53D0E0A9C607CAD758F558915A0A7DC5DC87B45E9A58FDDF30EC3385960283E030CD322D9E46B070637785FD49D2CD711F46807A24C40AF9A42C8E2D740,
 355                 0xDF93A8012B86D3A3D4F8A4D487DA15FC739EB31B20B3B0E8C8C032AAF8072C6337CF7D5B404719E5B4407C41D9A3216A08CA69C271484E9ED72B8AAA52E28B8B,
 356             )
 357         )
 358         self.assertEqual(
 359             c.exp(0x3CE54325DB52FE798824AEAD11BB16FA766857D04A4AF7D468672F16D90E7396046A46F815693E85B1CE5464DA9270181F82333B0715057BBE8D61D400505F0E),
 360             (
 361                 0xB93093EB0FCC463239B7DF276E09E592FCFC9B635504EA4531655D76A0A3078E2B4E51CFE2FA400CC5DE9FBE369DB204B3E8ED7EDD85EE5CCA654C1AED70E396,
 362                 0x809770B8D910EA30BD2FA89736E91DC31815D2D9B31128077EEDC371E9F69466F497DC64DD5B1FADC587F860EE256109138C4A9CD96B628E65A8F590520FC882,
 363             )
 364         )
 365         self.assertEqual(
 366             c.exp(0xB5C286A79AA8E97EC0E19BC1959A1D15F12F8C97870BA9D68CC12811A56A3BB11440610825796A49D468CDC9C2D02D76598A27973D5960C5F50BCE28D8D345F4),
 367             (
 368                 0x238B38644E440452A99FA6B93D9FD7DA0CB83C32D3C1E3CFE5DF5C3EB0F9DB91E588DAEDC849EA2FB867AE855A21B4077353C0794716A6480995113D8C20C7AF,
 369                 0xB2273D5734C1897F8D15A7008B862938C8C74CA7E877423D95243EB7EBD02FD2C456CF9FC956F078A59AA86F19DD1075E5167E4ED35208718EA93161C530ED14,
 370             ),
 371         )
 372
 373     def test_curve5(self):
 374         c = CURVES["id-tc26-gost-3410-12-512-paramSetB"]
 375         q_ind = (
 376             0x7E1FAE8285E035BEC244BEF2D0E5EBF436633CF50E55231DEA9C9CF21D4C8C33DF85D4305DE92971F0A4B4C07E00D87BDBC720EB66E49079285AAF12E0171149,
 377             0x2CC89998B875D4463805BA0D858A196592DB20AB161558FF2F4EF7A85725D20953967AE621AFDEAE89BB77C83A2528EF6FCE02F68BDA4679D7F2704947DBC408,
 378         )
 379         self.assertEqual(
 380             c.exp(bytes2long(hexdec(
 381                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F181270671C6213E3930EFDDA26451792C6208122EE60D200520D695DFD9F5F0FD5ABA702"
 382             )[::-1]), x=q_ind[0], y=q_ind[1]),
 383             (
 384                 0x7D03E65B8050D1E12CBB601A17B9273B0E728F5021CD47C8A4DD822E4627BA5F9C696286A2CDDA9A065509866B4DEDEDC4A118409604AD549F87A60AFA621161,
 385                 0x16037DAD45421EC50B00D50BDC6AC3B85348BC1D3A2F85DB27C3373580FEF87C2C743B7ED30F22BE22958044E716F93A61CA3213A361A2797A16A3AE62957377,
 386             )
 387         )
 388         self.assertEqual(
 389             c.exp(0x715E893FA639BF341296E0623E6D29DADF26B163C278767A7982A989462A3863FE12AEF8BD403D59C4DC4720570D4163DB0805C7C10C4E818F9CB785B04B9997),
 390             (
 391                 0x10C479EA1C04D3C2C02B0576A9C42D96226FF033C1191436777F66916030D87D02FB93738ED7669D07619FFCE7C1F3C4DB5E5DF49E2186D6FA1E2EB5767602B9,
 392                 0x039F6044191404E707F26D59D979136A831CCE43E1C5F0600D1DDF8F39D0CA3D52FBD943BF04DDCED1AA2CE8F5EBD7487ACDEF239C07D015084D796784F35436,
 393             )
 394         )
 395         self.assertEqual(
 396             c.exp(0x30FA8C2B4146C2DBBE82BED04D7378877E8C06753BD0A0FF71EBF2BEFE8DA8F3DC0836468E2CE7C5C961281B6505140F8407413F03C2CB1D201EA1286CE30E6D),
 397             (
 398                 0x34C0149E7BB91AE377B02573FCC48AF7BFB7B16DEB8F9CE870F384688E3241A3A868588CC0EF4364CCA67D17E3260CD82485C202ADC76F895D5DF673B1788E67,
 399                 0x608E944929BD643569ED5189DB871453F13333A1EAF82B2FE1BE8100E775F13DD9925BD317B63BFAF05024D4A738852332B64501195C1B2EF789E34F23DDAFC5,
 400             ),
 401         )
 402
 403     def test_curve6(self):
 404         c = CURVES["id-tc26-gost-3410-2012-256-paramSetA"]
 405         q_ind = (
 406             0xB51ADF93A40AB15792164FAD3352F95B66369EB2A4EF5EFAE32829320363350E,
 407             0x74A358CC08593612F5955D249C96AFB7E8B0BB6D8BD2BBE491046650D822BE18,
 408         )
 409         self.assertEqual(
 410             c.exp(bytes2long(hexdec(
 411                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 412             )[::-1]), x=q_ind[0], y=q_ind[1]),
 413             (
 414                 0xDBF99827078956812FA48C6E695DF589DEF1D18A2D4D35A96D75BF6854237629,
 415                 0x9FDDD48BFBC57BEE1DA0CFF282884F284D471B388893C48F5ECB02FC18D67589,
 416             )
 417         )
 418         self.assertEqual(
 419             c.exp(0x147B72F6684FB8FD1B418A899F7DBECAF5FCE60B13685BAA95328654A7F0707F),
 420             (
 421                 0x33FBAC14EAE538275A769417829C431BD9FA622B6F02427EF55BD60EE6BC2888,
 422                 0x22F2EBCF960A82E6CDB4042D3DDDA511B2FBA925383C2273D952EA2D406EAE46,
 423             )
 424         )
 425         self.assertEqual(
 426             c.exp(0x30D5CFADAA0E31B405E6734C03EC4C5DF0F02F4BA25C9A3B320EE6453567B4CB),
 427             (
 428                 0x2B2D89FAB735433970564F2F28CFA1B57D640CB902BC6334A538F44155022CB2,
 429                 0x10EF6A82EEF1E70F942AA81D6B4CE5DEC0DDB9447512962874870E6F2849A96F,
 430             ),
 431         )
 432
 433     def test_curve7(self):
 434         c = CURVES["id-tc26-gost-3410-2012-512-paramSetC"]
 435         q_ind = (
 436             0x489C91784E02E98F19A803ABCA319917F37689E5A18965251CE2FF4E8D8B298F5BA7470F9E0E713487F96F4A8397B3D09A270C9D367EB5E0E6561ADEEB51581D,
 437             0x684EA885ACA64EAF1B3FEE36C0852A3BE3BD8011B0EF18E203FF87028D6EB5DB2C144A0DCC71276542BFD72CA2A43FA4F4939DA66D9A60793C704A8C94E16F18,
 438         )
 439         self.assertEqual(
 440             c.exp(bytes2long(hexdec(
 441                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F181270671C6213E3930EFDDA26451792C6208122EE60D200520D695DFD9F5F0FD5ABA702"
 442             )[::-1]), x=q_ind[0], y=q_ind[1]),
 443             (
 444                 0x0185AE6271A81BB7F236A955F7CAA26FB63849813C0287D96C83A15AE6B6A86467AB13B6D88CE8CD7DC2E5B97FF5F28FAC2C108F2A3CF3DB5515C9E6D7D210E8,
 445                 0xED0220F92EF771A71C64ECC77986DB7C03D37B3E2AB3E83F32CE5E074A762EC08253C9E2102B87532661275C4B1D16D2789CDABC58ACFDF7318DE70AB64F09B8,
 446             )
 447         )
 448         self.assertEqual(
 449             c.exp(0x332F930421D14CFE260042159F18E49FD5A54167E94108AD80B1DE60B13DE7999A34D611E63F3F870E5110247DF8EC7466E648ACF385E52CCB889ABF491EDFF0),
 450             (
 451                 0x561655966D52952E805574F4281F1ED3A2D498932B00CBA9DECB42837F09835BFFBFE2D84D6B6B242FE7B57F92E1A6F2413E12DDD6383E4437E13D72693469AD,
 452                 0xF6B18328B2715BD7F4178615273A36135BC0BF62F7D8BB9F080164AD36470AD03660F51806C64C6691BADEF30F793720F8E3FEAED631D6A54A4C372DCBF80E82,
 453             )
 454         )
 455         self.assertEqual(
 456             c.exp(0x38481771E7D054F96212686B613881880BD8A6C89DDBC656178F014D2C093432A033EE10415F13A160D44C2AD61E6E2E05A7F7EC286BCEA3EA4D4D53F8634FA2),
 457             (
 458                 0xB7C5818687083433BC1AFF61CB5CA79E38232025E0C1F123B8651E62173CE6873F3E6FFE7281C2E45F4F524F66B0C263616ED08FD210AC4355CA3292B51D71C3,
 459                 0x497F14205DBDC89BDDAF50520ED3B1429AD30777310186BE5E68070F016A44E0C766DB08E8AC23FBDFDE6D675AA4DF591EB18BA0D348DF7AA40973A2F1DCFA55,
 460             ),
 461         )