pygost/test_gost3410.py

   1 # coding: utf-8
   2 # PyGOST -- Pure Python GOST cryptographic functions library
   3 # Copyright (C) 2015-2021 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 prv_marshal
  23 from pygost.gost3410 import prv_unmarshal
  24 from pygost.gost3410 import public_key
  25 from pygost.gost3410 import sign
  26 from pygost.gost3410 import uv2xy
  27 from pygost.gost3410 import verify
  28 from pygost.gost3410 import xy2uv
  29 from pygost.utils import bytes2long
  30 from pygost.utils import hexdec
  31 from pygost.utils import hexenc
  32 from pygost.utils import long2bytes
  33
  34
  35 class Test341001(TestCase):
  36     def test_rfc(self):
  37         """Test vector from :rfc:`5832`
  38         """
  39         prv = bytes(bytearray((
  40             0x7A, 0x92, 0x9A, 0xDE, 0x78, 0x9B, 0xB9, 0xBE,
  41             0x10, 0xED, 0x35, 0x9D, 0xD3, 0x9A, 0x72, 0xC1,
  42             0x1B, 0x60, 0x96, 0x1F, 0x49, 0x39, 0x7E, 0xEE,
  43             0x1D, 0x19, 0xCE, 0x98, 0x91, 0xEC, 0x3B, 0x28
  44         )))
  45         pub_x = bytes(bytearray((
  46             0x7F, 0x2B, 0x49, 0xE2, 0x70, 0xDB, 0x6D, 0x90,
  47             0xD8, 0x59, 0x5B, 0xEC, 0x45, 0x8B, 0x50, 0xC5,
  48             0x85, 0x85, 0xBA, 0x1D, 0x4E, 0x9B, 0x78, 0x8F,
  49             0x66, 0x89, 0xDB, 0xD8, 0xE5, 0x6F, 0xD8, 0x0B
  50         )))
  51         pub_y = bytes(bytearray((
  52             0x26, 0xF1, 0xB4, 0x89, 0xD6, 0x70, 0x1D, 0xD1,
  53             0x85, 0xC8, 0x41, 0x3A, 0x97, 0x7B, 0x3C, 0xBB,
  54             0xAF, 0x64, 0xD1, 0xC5, 0x93, 0xD2, 0x66, 0x27,
  55             0xDF, 0xFB, 0x10, 0x1A, 0x87, 0xFF, 0x77, 0xDA
  56         )))
  57         digest = bytes(bytearray((
  58             0x2D, 0xFB, 0xC1, 0xB3, 0x72, 0xD8, 0x9A, 0x11,
  59             0x88, 0xC0, 0x9C, 0x52, 0xE0, 0xEE, 0xC6, 0x1F,
  60             0xCE, 0x52, 0x03, 0x2A, 0xB1, 0x02, 0x2E, 0x8E,
  61             0x67, 0xEC, 0xE6, 0x67, 0x2B, 0x04, 0x3E, 0xE5
  62         )))
  63         signature = bytes(bytearray((
  64             0x41, 0xAA, 0x28, 0xD2, 0xF1, 0xAB, 0x14, 0x82,
  65             0x80, 0xCD, 0x9E, 0xD5, 0x6F, 0xED, 0xA4, 0x19,
  66             0x74, 0x05, 0x35, 0x54, 0xA4, 0x27, 0x67, 0xB8,
  67             0x3A, 0xD0, 0x43, 0xFD, 0x39, 0xDC, 0x04, 0x93,
  68             0x01, 0x45, 0x6C, 0x64, 0xBA, 0x46, 0x42, 0xA1,
  69             0x65, 0x3C, 0x23, 0x5A, 0x98, 0xA6, 0x02, 0x49,
  70             0xBC, 0xD6, 0xD3, 0xF7, 0x46, 0xB6, 0x31, 0xDF,
  71             0x92, 0x80, 0x14, 0xF6, 0xC5, 0xBF, 0x9C, 0x40
  72         )))
  73         prv = bytes2long(prv)
  74         signature = signature[32:] + signature[:32]
  75
  76         c = CURVES["id-GostR3410-2001-TestParamSet"]
  77         pubX, pubY = public_key(c, prv)
  78         self.assertSequenceEqual(long2bytes(pubX), pub_x)
  79         self.assertSequenceEqual(long2bytes(pubY), pub_y)
  80         s = sign(c, prv, digest)
  81         self.assertTrue(verify(c, (pubX, pubY), digest, s))
  82         self.assertTrue(verify(c, (pubX, pubY), digest, signature))
  83
  84     def test_sequence(self):
  85         c = CURVES["id-GostR3410-2001-TestParamSet"]
  86         prv = prv_unmarshal(urandom(32))
  87         pubX, pubY = public_key(c, prv_unmarshal(prv_marshal(c, prv)))
  88         for _ in range(20):
  89             digest = urandom(32)
  90             s = sign(c, prv, digest)
  91             self.assertTrue(verify(c, (pubX, pubY), digest, s))
  92
  93
  94 class Test34102012(TestCase):
  95     def test_1(self):
  96         """Test vector from 34.10-2012 standard itself
  97         """
  98         curve = CURVES["id-GostR3410-2001-TestParamSet"]
  99         prv = bytes2long(hexdec("7A929ADE789BB9BE10ED359DD39A72C11B60961F49397EEE1D19CE9891EC3B28"))
 100         digest = hexdec("2DFBC1B372D89A1188C09C52E0EEC61FCE52032AB1022E8E67ECE6672B043EE5")
 101         rand = hexdec("77105C9B20BCD3122823C8CF6FCC7B956DE33814E95B7FE64FED924594DCEAB3")
 102         signature = sign(curve, prv, digest, rand)
 103         r = "41aa28d2f1ab148280cd9ed56feda41974053554a42767b83ad043fd39dc0493"
 104         s = "01456c64ba4642a1653c235a98a60249bcd6d3f746b631df928014f6c5bf9c40"
 105         self.assertSequenceEqual(hexenc(signature), s + r)
 106
 107     def test_2(self):
 108         """Test vector from 34.10-2012 standard itself
 109         """
 110         curve = GOST3410Curve(
 111             p=3623986102229003635907788753683874306021320925534678605086546150450856166624002482588482022271496854025090823603058735163734263822371964987228582907372403,
 112             q=3623986102229003635907788753683874306021320925534678605086546150450856166623969164898305032863068499961404079437936585455865192212970734808812618120619743,
 113             a=7,
 114             b=1518655069210828534508950034714043154928747527740206436194018823352809982443793732829756914785974674866041605397883677596626326413990136959047435811826396,
 115             x=1928356944067022849399309401243137598997786635459507974357075491307766592685835441065557681003184874819658004903212332884252335830250729527632383493573274,
 116             y=2288728693371972859970012155529478416353562327329506180314497425931102860301572814141997072271708807066593850650334152381857347798885864807605098724013854,
 117         )
 118         prv = bytes2long(hexdec("0BA6048AADAE241BA40936D47756D7C93091A0E8514669700EE7508E508B102072E8123B2200A0563322DAD2827E2714A2636B7BFD18AADFC62967821FA18DD4"))
 119         digest = hexdec("3754F3CFACC9E0615C4F4A7C4D8DAB531B09B6F9C170C533A71D147035B0C5917184EE536593F4414339976C647C5D5A407ADEDB1D560C4FC6777D2972075B8C")
 120         rand = hexdec("0359E7F4B1410FEACC570456C6801496946312120B39D019D455986E364F365886748ED7A44B3E794434006011842286212273A6D14CF70EA3AF71BB1AE679F1")
 121         signature = sign(curve, prv, digest, rand)
 122         r = "2f86fa60a081091a23dd795e1e3c689ee512a3c82ee0dcc2643c78eea8fcacd35492558486b20f1c9ec197c90699850260c93bcbcd9c5c3317e19344e173ae36"
 123         s = "1081b394696ffe8e6585e7a9362d26b6325f56778aadbc081c0bfbe933d52ff5823ce288e8c4f362526080df7f70ce406a6eeb1f56919cb92a9853bde73e5b4a"
 124         self.assertSequenceEqual(hexenc(signature), s + r)
 125
 126     def test_gcl3(self):
 127         """Test vector from libgcl3
 128         """
 129         p = bytes2long(bytes(bytearray((
 130             0x45, 0x31, 0xAC, 0xD1, 0xFE, 0x00, 0x23, 0xC7,
 131             0x55, 0x0D, 0x26, 0x7B, 0x6B, 0x2F, 0xEE, 0x80,
 132             0x92, 0x2B, 0x14, 0xB2, 0xFF, 0xB9, 0x0F, 0x04,
 133             0xD4, 0xEB, 0x7C, 0x09, 0xB5, 0xD2, 0xD1, 0x5D,
 134             0xF1, 0xD8, 0x52, 0x74, 0x1A, 0xF4, 0x70, 0x4A,
 135             0x04, 0x58, 0x04, 0x7E, 0x80, 0xE4, 0x54, 0x6D,
 136             0x35, 0xB8, 0x33, 0x6F, 0xAC, 0x22, 0x4D, 0xD8,
 137             0x16, 0x64, 0xBB, 0xF5, 0x28, 0xBE, 0x63, 0x73,
 138         ))))
 139         q = bytes2long(bytes(bytearray((
 140             0x45, 0x31, 0xAC, 0xD1, 0xFE, 0x00, 0x23, 0xC7,
 141             0x55, 0x0D, 0x26, 0x7B, 0x6B, 0x2F, 0xEE, 0x80,
 142             0x92, 0x2B, 0x14, 0xB2, 0xFF, 0xB9, 0x0F, 0x04,
 143             0xD4, 0xEB, 0x7C, 0x09, 0xB5, 0xD2, 0xD1, 0x5D,
 144             0xA8, 0x2F, 0x2D, 0x7E, 0xCB, 0x1D, 0xBA, 0xC7,
 145             0x19, 0x90, 0x5C, 0x5E, 0xEC, 0xC4, 0x23, 0xF1,
 146             0xD8, 0x6E, 0x25, 0xED, 0xBE, 0x23, 0xC5, 0x95,
 147             0xD6, 0x44, 0xAA, 0xF1, 0x87, 0xE6, 0xE6, 0xDF,
 148         ))))
 149         a = bytes2long(bytes(bytearray((
 150             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 151             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 152             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 153             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 154             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 155             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 156             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 157             0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07,
 158         ))))
 159         b = bytes2long(bytes(bytearray((
 160             0x1C, 0xFF, 0x08, 0x06, 0xA3, 0x11, 0x16, 0xDA,
 161             0x29, 0xD8, 0xCF, 0xA5, 0x4E, 0x57, 0xEB, 0x74,
 162             0x8B, 0xC5, 0xF3, 0x77, 0xE4, 0x94, 0x00, 0xFD,
 163             0xD7, 0x88, 0xB6, 0x49, 0xEC, 0xA1, 0xAC, 0x43,
 164             0x61, 0x83, 0x40, 0x13, 0xB2, 0xAD, 0x73, 0x22,
 165             0x48, 0x0A, 0x89, 0xCA, 0x58, 0xE0, 0xCF, 0x74,
 166             0xBC, 0x9E, 0x54, 0x0C, 0x2A, 0xDD, 0x68, 0x97,
 167             0xFA, 0xD0, 0xA3, 0x08, 0x4F, 0x30, 0x2A, 0xDC,
 168         ))))
 169         x = bytes2long(bytes(bytearray((
 170             0x24, 0xD1, 0x9C, 0xC6, 0x45, 0x72, 0xEE, 0x30,
 171             0xF3, 0x96, 0xBF, 0x6E, 0xBB, 0xFD, 0x7A, 0x6C,
 172             0x52, 0x13, 0xB3, 0xB3, 0xD7, 0x05, 0x7C, 0xC8,
 173             0x25, 0xF9, 0x10, 0x93, 0xA6, 0x8C, 0xD7, 0x62,
 174             0xFD, 0x60, 0x61, 0x12, 0x62, 0xCD, 0x83, 0x8D,
 175             0xC6, 0xB6, 0x0A, 0xA7, 0xEE, 0xE8, 0x04, 0xE2,
 176             0x8B, 0xC8, 0x49, 0x97, 0x7F, 0xAC, 0x33, 0xB4,
 177             0xB5, 0x30, 0xF1, 0xB1, 0x20, 0x24, 0x8A, 0x9A,
 178         ))))
 179         y = bytes2long(bytes(bytearray((
 180             0x2B, 0xB3, 0x12, 0xA4, 0x3B, 0xD2, 0xCE, 0x6E,
 181             0x0D, 0x02, 0x06, 0x13, 0xC8, 0x57, 0xAC, 0xDD,
 182             0xCF, 0xBF, 0x06, 0x1E, 0x91, 0xE5, 0xF2, 0xC3,
 183             0xF3, 0x24, 0x47, 0xC2, 0x59, 0xF3, 0x9B, 0x2C,
 184             0x83, 0xAB, 0x15, 0x6D, 0x77, 0xF1, 0x49, 0x6B,
 185             0xF7, 0xEB, 0x33, 0x51, 0xE1, 0xEE, 0x4E, 0x43,
 186             0xDC, 0x1A, 0x18, 0xB9, 0x1B, 0x24, 0x64, 0x0B,
 187             0x6D, 0xBB, 0x92, 0xCB, 0x1A, 0xDD, 0x37, 0x1E,
 188         ))))
 189         prv = bytes(bytearray((
 190             0x0B, 0xA6, 0x04, 0x8A, 0xAD, 0xAE, 0x24, 0x1B,
 191             0xA4, 0x09, 0x36, 0xD4, 0x77, 0x56, 0xD7, 0xC9,
 192             0x30, 0x91, 0xA0, 0xE8, 0x51, 0x46, 0x69, 0x70,
 193             0x0E, 0xE7, 0x50, 0x8E, 0x50, 0x8B, 0x10, 0x20,
 194             0x72, 0xE8, 0x12, 0x3B, 0x22, 0x00, 0xA0, 0x56,
 195             0x33, 0x22, 0xDA, 0xD2, 0x82, 0x7E, 0x27, 0x14,
 196             0xA2, 0x63, 0x6B, 0x7B, 0xFD, 0x18, 0xAA, 0xDF,
 197             0xC6, 0x29, 0x67, 0x82, 0x1F, 0xA1, 0x8D, 0xD4,
 198         )))
 199         pub_x = bytes(bytearray((
 200             0x11, 0x5D, 0xC5, 0xBC, 0x96, 0x76, 0x0C, 0x7B,
 201             0x48, 0x59, 0x8D, 0x8A, 0xB9, 0xE7, 0x40, 0xD4,
 202             0xC4, 0xA8, 0x5A, 0x65, 0xBE, 0x33, 0xC1, 0x81,
 203             0x5B, 0x5C, 0x32, 0x0C, 0x85, 0x46, 0x21, 0xDD,
 204             0x5A, 0x51, 0x58, 0x56, 0xD1, 0x33, 0x14, 0xAF,
 205             0x69, 0xBC, 0x5B, 0x92, 0x4C, 0x8B, 0x4D, 0xDF,
 206             0xF7, 0x5C, 0x45, 0x41, 0x5C, 0x1D, 0x9D, 0xD9,
 207             0xDD, 0x33, 0x61, 0x2C, 0xD5, 0x30, 0xEF, 0xE1,
 208         )))
 209         pub_y = bytes(bytearray((
 210             0x37, 0xC7, 0xC9, 0x0C, 0xD4, 0x0B, 0x0F, 0x56,
 211             0x21, 0xDC, 0x3A, 0xC1, 0xB7, 0x51, 0xCF, 0xA0,
 212             0xE2, 0x63, 0x4F, 0xA0, 0x50, 0x3B, 0x3D, 0x52,
 213             0x63, 0x9F, 0x5D, 0x7F, 0xB7, 0x2A, 0xFD, 0x61,
 214             0xEA, 0x19, 0x94, 0x41, 0xD9, 0x43, 0xFF, 0xE7,
 215             0xF0, 0xC7, 0x0A, 0x27, 0x59, 0xA3, 0xCD, 0xB8,
 216             0x4C, 0x11, 0x4E, 0x1F, 0x93, 0x39, 0xFD, 0xF2,
 217             0x7F, 0x35, 0xEC, 0xA9, 0x36, 0x77, 0xBE, 0xEC,
 218         )))
 219         digest = bytes(bytearray((
 220             0x37, 0x54, 0xF3, 0xCF, 0xAC, 0xC9, 0xE0, 0x61,
 221             0x5C, 0x4F, 0x4A, 0x7C, 0x4D, 0x8D, 0xAB, 0x53,
 222             0x1B, 0x09, 0xB6, 0xF9, 0xC1, 0x70, 0xC5, 0x33,
 223             0xA7, 0x1D, 0x14, 0x70, 0x35, 0xB0, 0xC5, 0x91,
 224             0x71, 0x84, 0xEE, 0x53, 0x65, 0x93, 0xF4, 0x41,
 225             0x43, 0x39, 0x97, 0x6C, 0x64, 0x7C, 0x5D, 0x5A,
 226             0x40, 0x7A, 0xDE, 0xDB, 0x1D, 0x56, 0x0C, 0x4F,
 227             0xC6, 0x77, 0x7D, 0x29, 0x72, 0x07, 0x5B, 0x8C,
 228         )))
 229         signature = bytes(bytearray((
 230             0x2F, 0x86, 0xFA, 0x60, 0xA0, 0x81, 0x09, 0x1A,
 231             0x23, 0xDD, 0x79, 0x5E, 0x1E, 0x3C, 0x68, 0x9E,
 232             0xE5, 0x12, 0xA3, 0xC8, 0x2E, 0xE0, 0xDC, 0xC2,
 233             0x64, 0x3C, 0x78, 0xEE, 0xA8, 0xFC, 0xAC, 0xD3,
 234             0x54, 0x92, 0x55, 0x84, 0x86, 0xB2, 0x0F, 0x1C,
 235             0x9E, 0xC1, 0x97, 0xC9, 0x06, 0x99, 0x85, 0x02,
 236             0x60, 0xC9, 0x3B, 0xCB, 0xCD, 0x9C, 0x5C, 0x33,
 237             0x17, 0xE1, 0x93, 0x44, 0xE1, 0x73, 0xAE, 0x36,
 238             0x10, 0x81, 0xB3, 0x94, 0x69, 0x6F, 0xFE, 0x8E,
 239             0x65, 0x85, 0xE7, 0xA9, 0x36, 0x2D, 0x26, 0xB6,
 240             0x32, 0x5F, 0x56, 0x77, 0x8A, 0xAD, 0xBC, 0x08,
 241             0x1C, 0x0B, 0xFB, 0xE9, 0x33, 0xD5, 0x2F, 0xF5,
 242             0x82, 0x3C, 0xE2, 0x88, 0xE8, 0xC4, 0xF3, 0x62,
 243             0x52, 0x60, 0x80, 0xDF, 0x7F, 0x70, 0xCE, 0x40,
 244             0x6A, 0x6E, 0xEB, 0x1F, 0x56, 0x91, 0x9C, 0xB9,
 245             0x2A, 0x98, 0x53, 0xBD, 0xE7, 0x3E, 0x5B, 0x4A,
 246         )))
 247         prv = bytes2long(prv)
 248         signature = signature[64:] + signature[:64]
 249         c = GOST3410Curve(p, q, a, b, x, y)
 250         pubX, pubY = public_key(c, prv)
 251         self.assertSequenceEqual(long2bytes(pubX), pub_x)
 252         self.assertSequenceEqual(long2bytes(pubY), pub_y)
 253         s = sign(c, prv, digest)
 254         self.assertTrue(verify(c, (pubX, pubY), digest, s))
 255         self.assertTrue(verify(c, (pubX, pubY), digest, signature))
 256
 257     def test_sequence(self):
 258         c = CURVES["id-tc26-gost-3410-12-512-paramSetA"]
 259         prv = bytes2long(urandom(64))
 260         pubX, pubY = public_key(c, prv_unmarshal(prv_marshal(c, prv)))
 261         for _ in range(20):
 262             digest = urandom(64)
 263             s = sign(c, prv, digest)
 264             self.assertTrue(verify(c, (pubX, pubY), digest, s))
 265             self.assertNotIn(b"\x00" * 8, s)
 266
 267
 268 class TestUVXYConversion(TestCase):
 269     """Twisted Edwards to Weierstrass coordinates conversion and vice versa
 270     """
 271     def test_curve1(self):
 272         c = CURVES["id-tc26-gost-3410-2012-256-paramSetA"]
 273         u, v = (0x0D, bytes2long(hexdec("60CA1E32AA475B348488C38FAB07649CE7EF8DBE87F22E81F92B2592DBA300E7")))
 274         self.assertEqual(uv2xy(c, u, v), (c.x, c.y))
 275         self.assertEqual(xy2uv(c, c.x, c.y), (u, v))
 276
 277     def test_curve2(self):
 278         c = CURVES["id-tc26-gost-3410-2012-512-paramSetC"]
 279         u, v = (0x12, bytes2long(hexdec("469AF79D1FB1F5E16B99592B77A01E2A0FDFB0D01794368D9A56117F7B38669522DD4B650CF789EEBF068C5D139732F0905622C04B2BAAE7600303EE73001A3D")))
 280         self.assertEqual(uv2xy(c, u, v), (c.x, c.y))
 281         self.assertEqual(xy2uv(c, c.x, c.y), (u, v))
 282
 283
 284 class Test34102012SESPAKE(TestCase):
 285     """Test vectors for multiplication from :rfc:`8133`
 286     """
 287     def test_curve1(self):
 288         c = CURVES["id-GostR3410-2001-CryptoPro-A-ParamSet"]
 289         q_ind = (
 290             0xA69D51CAF1A309FA9E9B66187759B0174C274E080356F23CFCBFE84D396AD7BB,
 291             0x5D26F29ECC2E9AC0404DCF7986FA55FE94986362170F54B9616426A659786DAC,
 292         )
 293         self.assertEqual(
 294             c.exp(bytes2long(hexdec(
 295                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 296             )[::-1]), x=q_ind[0], y=q_ind[1]),
 297             (
 298                 0x59495655D1E7C7424C622485F575CCF121F3122D274101E8AB734CC9C9A9B45E,
 299                 0x48D1C311D33C9B701F3B03618562A4A07A044E3AF31E3999E67B487778B53C62,
 300             )
 301         )
 302         self.assertEqual(
 303             c.exp(0x1F2538097D5A031FA68BBB43C84D12B3DE47B7061C0D5E24993E0C873CDBA6B3),
 304             (
 305                 0xBBC77CF42DC1E62D06227935379B4AA4D14FEA4F565DDF4CB4FA4D31579F9676,
 306                 0x8E16604A4AFDF28246684D4996274781F6CB80ABBBA1414C1513EC988509DABF,
 307             )
 308         )
 309         self.assertEqual(
 310             c.exp(0xDC497D9EF6324912FD367840EE509A2032AEDB1C0A890D133B45F596FCCBD45D),
 311             (
 312                 0x6097341C1BE388E83E7CA2DF47FAB86E2271FD942E5B7B2EB2409E49F742BC29,
 313                 0xC81AA48BDB4CA6FA0EF18B9788AE25FE30857AA681B3942217F9FED151BAB7D0,
 314             ),
 315         )
 316
 317     def test_curve2(self):
 318         c = CURVES["id-GostR3410-2001-CryptoPro-B-ParamSet"]
 319         q_ind = (
 320             0x3D715A874A4B17CB3B517893A9794A2B36C89D2FFC693F01EE4CC27E7F49E399,
 321             0x1C5A641FCF7CE7E87CDF8CEA38F3DB3096EACE2FAD158384B53953365F4FE7FE,
 322         )
 323         self.assertEqual(
 324             c.exp(bytes2long(hexdec(
 325                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 326             )[::-1]), x=q_ind[0], y=q_ind[1]),
 327             (
 328                 0x6DC2AE26BC691FCA5A73D9C452790D15E34BA5404D92955B914C8D2662ABB985,
 329                 0x3B02AAA9DD65AE30C335CED12F3154BBAC059F66B088306747453EDF6E5DB077,
 330             )
 331         )
 332         self.assertEqual(
 333             c.exp(0x499D72B90299CAB0DA1F8BE19D9122F622A13B32B730C46BD0664044F2144FAD),
 334             (
 335                 0x61D6F916DB717222D74877F179F7EBEF7CD4D24D8C1F523C048E34A1DF30F8DD,
 336                 0x3EC48863049CFCFE662904082E78503F4973A4E105E2F1B18C69A5E7FB209000,
 337             )
 338         )
 339         self.assertEqual(
 340             c.exp(0x0F69FF614957EF83668EDC2D7ED614BE76F7B253DB23C5CC9C52BF7DF8F4669D),
 341             (
 342                 0x33BC6F7E9C0BA10CFB2B72546C327171295508EA97F8C8BA9F890F2478AB4D6C,
 343                 0x75D57B396C396F492F057E9222CCC686437A2AAD464E452EF426FC8EEED1A4A6,
 344             ),
 345         )
 346
 347     def test_curve3(self):
 348         c = CURVES["id-GostR3410-2001-CryptoPro-C-ParamSet"]
 349         q_ind = (
 350             0x1E36383E43BB6CFA2917167D71B7B5DD3D6D462B43D7C64282AE67DFBEC2559D,
 351             0x137478A9F721C73932EA06B45CF72E37EB78A63F29A542E563C614650C8B6399,
 352         )
 353         self.assertEqual(
 354             c.exp(bytes2long(hexdec(
 355                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 356             )[::-1]), x=q_ind[0], y=q_ind[1]),
 357             (
 358                 0x945821DAF91E158B839939630655A3B21FF3E146D27041E86C05650EB3B46B59,
 359                 0x3A0C2816AC97421FA0E879605F17F0C9C3EB734CFF196937F6284438D70BDC48,
 360             )
 361         )
 362         self.assertEqual(
 363             c.exp(0x3A54AC3F19AD9D0B1EAC8ACDCEA70E581F1DAC33D13FEAFD81E762378639C1A8),
 364             (
 365                 0x96B7F09C94D297C257A7DA48364C0076E59E48D221CBA604AE111CA3933B446A,
 366                 0x54E4953D86B77ECCEB578500931E822300F7E091F79592CA202A020D762C34A6,
 367             )
 368         )
 369         self.assertEqual(
 370             c.exp(0x448781782BF7C0E52A1DD9E6758FD3482D90D3CFCCF42232CF357E59A4D49FD4),
 371             (
 372                 0x4B9C0AB55A938121F282F48A2CC4396EB16E7E0068B495B0C1DD4667786A3EB7,
 373                 0x223460AA8E09383E9DF9844C5A0F2766484738E5B30128A171B69A77D9509B96,
 374             ),
 375         )
 376
 377     def test_curve4(self):
 378         c = CURVES["id-tc26-gost-3410-12-512-paramSetA"]
 379         q_ind = (
 380             0x2A17F8833A32795327478871B5C5E88AEFB91126C64B4B8327289BEA62559425D18198F133F400874328B220C74497CD240586CB249E158532CB8090776CD61C,
 381             0x728F0C4A73B48DA41CE928358FAD26B47A6E094E9362BAE82559F83CDDC4EC3A4676BD3707EDEAF4CD85E99695C64C241EDC622BE87DC0CF87F51F4367F723C5,
 382         )
 383         self.assertEqual(
 384             c.exp(bytes2long(hexdec(
 385                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F181270671C6213E3930EFDDA26451792C6208122EE60D200520D695DFD9F5F0FD5ABA702"
 386             )[::-1]), x=q_ind[0], y=q_ind[1]),
 387             (
 388                 0x0C0AB53D0E0A9C607CAD758F558915A0A7DC5DC87B45E9A58FDDF30EC3385960283E030CD322D9E46B070637785FD49D2CD711F46807A24C40AF9A42C8E2D740,
 389                 0xDF93A8012B86D3A3D4F8A4D487DA15FC739EB31B20B3B0E8C8C032AAF8072C6337CF7D5B404719E5B4407C41D9A3216A08CA69C271484E9ED72B8AAA52E28B8B,
 390             )
 391         )
 392         self.assertEqual(
 393             c.exp(0x3CE54325DB52FE798824AEAD11BB16FA766857D04A4AF7D468672F16D90E7396046A46F815693E85B1CE5464DA9270181F82333B0715057BBE8D61D400505F0E),
 394             (
 395                 0xB93093EB0FCC463239B7DF276E09E592FCFC9B635504EA4531655D76A0A3078E2B4E51CFE2FA400CC5DE9FBE369DB204B3E8ED7EDD85EE5CCA654C1AED70E396,
 396                 0x809770B8D910EA30BD2FA89736E91DC31815D2D9B31128077EEDC371E9F69466F497DC64DD5B1FADC587F860EE256109138C4A9CD96B628E65A8F590520FC882,
 397             )
 398         )
 399         self.assertEqual(
 400             c.exp(0xB5C286A79AA8E97EC0E19BC1959A1D15F12F8C97870BA9D68CC12811A56A3BB11440610825796A49D468CDC9C2D02D76598A27973D5960C5F50BCE28D8D345F4),
 401             (
 402                 0x238B38644E440452A99FA6B93D9FD7DA0CB83C32D3C1E3CFE5DF5C3EB0F9DB91E588DAEDC849EA2FB867AE855A21B4077353C0794716A6480995113D8C20C7AF,
 403                 0xB2273D5734C1897F8D15A7008B862938C8C74CA7E877423D95243EB7EBD02FD2C456CF9FC956F078A59AA86F19DD1075E5167E4ED35208718EA93161C530ED14,
 404             ),
 405         )
 406
 407     def test_curve5(self):
 408         c = CURVES["id-tc26-gost-3410-12-512-paramSetB"]
 409         q_ind = (
 410             0x7E1FAE8285E035BEC244BEF2D0E5EBF436633CF50E55231DEA9C9CF21D4C8C33DF85D4305DE92971F0A4B4C07E00D87BDBC720EB66E49079285AAF12E0171149,
 411             0x2CC89998B875D4463805BA0D858A196592DB20AB161558FF2F4EF7A85725D20953967AE621AFDEAE89BB77C83A2528EF6FCE02F68BDA4679D7F2704947DBC408,
 412         )
 413         self.assertEqual(
 414             c.exp(bytes2long(hexdec(
 415                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F181270671C6213E3930EFDDA26451792C6208122EE60D200520D695DFD9F5F0FD5ABA702"
 416             )[::-1]), x=q_ind[0], y=q_ind[1]),
 417             (
 418                 0x7D03E65B8050D1E12CBB601A17B9273B0E728F5021CD47C8A4DD822E4627BA5F9C696286A2CDDA9A065509866B4DEDEDC4A118409604AD549F87A60AFA621161,
 419                 0x16037DAD45421EC50B00D50BDC6AC3B85348BC1D3A2F85DB27C3373580FEF87C2C743B7ED30F22BE22958044E716F93A61CA3213A361A2797A16A3AE62957377,
 420             )
 421         )
 422         self.assertEqual(
 423             c.exp(0x715E893FA639BF341296E0623E6D29DADF26B163C278767A7982A989462A3863FE12AEF8BD403D59C4DC4720570D4163DB0805C7C10C4E818F9CB785B04B9997),
 424             (
 425                 0x10C479EA1C04D3C2C02B0576A9C42D96226FF033C1191436777F66916030D87D02FB93738ED7669D07619FFCE7C1F3C4DB5E5DF49E2186D6FA1E2EB5767602B9,
 426                 0x039F6044191404E707F26D59D979136A831CCE43E1C5F0600D1DDF8F39D0CA3D52FBD943BF04DDCED1AA2CE8F5EBD7487ACDEF239C07D015084D796784F35436,
 427             )
 428         )
 429         self.assertEqual(
 430             c.exp(0x30FA8C2B4146C2DBBE82BED04D7378877E8C06753BD0A0FF71EBF2BEFE8DA8F3DC0836468E2CE7C5C961281B6505140F8407413F03C2CB1D201EA1286CE30E6D),
 431             (
 432                 0x34C0149E7BB91AE377B02573FCC48AF7BFB7B16DEB8F9CE870F384688E3241A3A868588CC0EF4364CCA67D17E3260CD82485C202ADC76F895D5DF673B1788E67,
 433                 0x608E944929BD643569ED5189DB871453F13333A1EAF82B2FE1BE8100E775F13DD9925BD317B63BFAF05024D4A738852332B64501195C1B2EF789E34F23DDAFC5,
 434             ),
 435         )
 436
 437     def test_curve6(self):
 438         c = CURVES["id-tc26-gost-3410-2012-256-paramSetA"]
 439         q_ind = (
 440             0xB51ADF93A40AB15792164FAD3352F95B66369EB2A4EF5EFAE32829320363350E,
 441             0x74A358CC08593612F5955D249C96AFB7E8B0BB6D8BD2BBE491046650D822BE18,
 442         )
 443         self.assertEqual(
 444             c.exp(bytes2long(hexdec(
 445                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F18127067"
 446             )[::-1]), x=q_ind[0], y=q_ind[1]),
 447             (
 448                 0xDBF99827078956812FA48C6E695DF589DEF1D18A2D4D35A96D75BF6854237629,
 449                 0x9FDDD48BFBC57BEE1DA0CFF282884F284D471B388893C48F5ECB02FC18D67589,
 450             )
 451         )
 452         self.assertEqual(
 453             c.exp(0x147B72F6684FB8FD1B418A899F7DBECAF5FCE60B13685BAA95328654A7F0707F),
 454             (
 455                 0x33FBAC14EAE538275A769417829C431BD9FA622B6F02427EF55BD60EE6BC2888,
 456                 0x22F2EBCF960A82E6CDB4042D3DDDA511B2FBA925383C2273D952EA2D406EAE46,
 457             )
 458         )
 459         self.assertEqual(
 460             c.exp(0x30D5CFADAA0E31B405E6734C03EC4C5DF0F02F4BA25C9A3B320EE6453567B4CB),
 461             (
 462                 0x2B2D89FAB735433970564F2F28CFA1B57D640CB902BC6334A538F44155022CB2,
 463                 0x10EF6A82EEF1E70F942AA81D6B4CE5DEC0DDB9447512962874870E6F2849A96F,
 464             ),
 465         )
 466
 467     def test_curve7(self):
 468         c = CURVES["id-tc26-gost-3410-2012-512-paramSetC"]
 469         q_ind = (
 470             0x489C91784E02E98F19A803ABCA319917F37689E5A18965251CE2FF4E8D8B298F5BA7470F9E0E713487F96F4A8397B3D09A270C9D367EB5E0E6561ADEEB51581D,
 471             0x684EA885ACA64EAF1B3FEE36C0852A3BE3BD8011B0EF18E203FF87028D6EB5DB2C144A0DCC71276542BFD72CA2A43FA4F4939DA66D9A60793C704A8C94E16F18,
 472         )
 473         self.assertEqual(
 474             c.exp(bytes2long(hexdec(
 475                 "BD04673F7149B18E98155BD1E2724E71D0099AA25174F792D3326C6F181270671C6213E3930EFDDA26451792C6208122EE60D200520D695DFD9F5F0FD5ABA702"
 476             )[::-1]), x=q_ind[0], y=q_ind[1]),
 477             (
 478                 0x0185AE6271A81BB7F236A955F7CAA26FB63849813C0287D96C83A15AE6B6A86467AB13B6D88CE8CD7DC2E5B97FF5F28FAC2C108F2A3CF3DB5515C9E6D7D210E8,
 479                 0xED0220F92EF771A71C64ECC77986DB7C03D37B3E2AB3E83F32CE5E074A762EC08253C9E2102B87532661275C4B1D16D2789CDABC58ACFDF7318DE70AB64F09B8,
 480             )
 481         )
 482         self.assertEqual(
 483             c.exp(0x332F930421D14CFE260042159F18E49FD5A54167E94108AD80B1DE60B13DE7999A34D611E63F3F870E5110247DF8EC7466E648ACF385E52CCB889ABF491EDFF0),
 484             (
 485                 0x561655966D52952E805574F4281F1ED3A2D498932B00CBA9DECB42837F09835BFFBFE2D84D6B6B242FE7B57F92E1A6F2413E12DDD6383E4437E13D72693469AD,
 486                 0xF6B18328B2715BD7F4178615273A36135BC0BF62F7D8BB9F080164AD36470AD03660F51806C64C6691BADEF30F793720F8E3FEAED631D6A54A4C372DCBF80E82,
 487             )
 488         )
 489         self.assertEqual(
 490             c.exp(0x38481771E7D054F96212686B613881880BD8A6C89DDBC656178F014D2C093432A033EE10415F13A160D44C2AD61E6E2E05A7F7EC286BCEA3EA4D4D53F8634FA2),
 491             (
 492                 0xB7C5818687083433BC1AFF61CB5CA79E38232025E0C1F123B8651E62173CE6873F3E6FFE7281C2E45F4F524F66B0C263616ED08FD210AC4355CA3292B51D71C3,
 493                 0x497F14205DBDC89BDDAF50520ED3B1429AD30777310186BE5E68070F016A44E0C766DB08E8AC23FBDFDE6D675AA4DF591EB18BA0D348DF7AA40973A2F1DCFA55,
 494             ),
 495         )