1 | /*
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2 | * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved.
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3 | *
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4 | * Licensed under the OpenSSL license (the "License"). You may not use
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5 | * this file except in compliance with the License. You can obtain a copy
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6 | * in the file LICENSE in the source distribution or at
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7 | * https://www.openssl.org/source/license.html
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8 | */
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9 |
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10 | /* ====================================================================
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11 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
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12 | *
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13 | * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
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14 | * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
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15 | * to the OpenSSL project.
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16 | *
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17 | * The ECC Code is licensed pursuant to the OpenSSL open source
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18 | * license provided below.
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19 | */
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20 |
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21 | #include <assert.h>
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22 | #include <limits.h>
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23 | #include <stdio.h>
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24 | #include "internal/cryptlib.h"
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25 | #include "bn_lcl.h"
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26 |
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27 | #ifndef OPENSSL_NO_EC2M
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28 |
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29 | /*
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30 | * Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should
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31 | * fail.
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32 | */
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33 | # define MAX_ITERATIONS 50
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34 |
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35 | static const BN_ULONG SQR_tb[16] = { 0, 1, 4, 5, 16, 17, 20, 21,
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36 | 64, 65, 68, 69, 80, 81, 84, 85
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37 | };
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38 |
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39 | /* Platform-specific macros to accelerate squaring. */
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40 | # if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
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41 | # define SQR1(w) \
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42 | SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \
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43 | SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \
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44 | SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \
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45 | SQR_tb[(w) >> 36 & 0xF] << 8 | SQR_tb[(w) >> 32 & 0xF]
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46 | # define SQR0(w) \
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47 | SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \
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48 | SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \
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49 | SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \
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50 | SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
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51 | # endif
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52 | # ifdef THIRTY_TWO_BIT
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53 | # define SQR1(w) \
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54 | SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \
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55 | SQR_tb[(w) >> 20 & 0xF] << 8 | SQR_tb[(w) >> 16 & 0xF]
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56 | # define SQR0(w) \
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57 | SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \
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58 | SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
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59 | # endif
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60 |
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61 | # if !defined(OPENSSL_BN_ASM_GF2m)
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62 | /*
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63 | * Product of two polynomials a, b each with degree < BN_BITS2 - 1, result is
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64 | * a polynomial r with degree < 2 * BN_BITS - 1 The caller MUST ensure that
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65 | * the variables have the right amount of space allocated.
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66 | */
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67 | # ifdef THIRTY_TWO_BIT
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68 | static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a,
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69 | const BN_ULONG b)
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70 | {
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71 | register BN_ULONG h, l, s;
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72 | BN_ULONG tab[8], top2b = a >> 30;
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73 | register BN_ULONG a1, a2, a4;
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74 |
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75 | a1 = a & (0x3FFFFFFF);
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76 | a2 = a1 << 1;
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77 | a4 = a2 << 1;
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78 |
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79 | tab[0] = 0;
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80 | tab[1] = a1;
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81 | tab[2] = a2;
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82 | tab[3] = a1 ^ a2;
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83 | tab[4] = a4;
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84 | tab[5] = a1 ^ a4;
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85 | tab[6] = a2 ^ a4;
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86 | tab[7] = a1 ^ a2 ^ a4;
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87 |
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88 | s = tab[b & 0x7];
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89 | l = s;
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90 | s = tab[b >> 3 & 0x7];
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91 | l ^= s << 3;
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92 | h = s >> 29;
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93 | s = tab[b >> 6 & 0x7];
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94 | l ^= s << 6;
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95 | h ^= s >> 26;
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96 | s = tab[b >> 9 & 0x7];
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97 | l ^= s << 9;
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98 | h ^= s >> 23;
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99 | s = tab[b >> 12 & 0x7];
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100 | l ^= s << 12;
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101 | h ^= s >> 20;
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102 | s = tab[b >> 15 & 0x7];
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103 | l ^= s << 15;
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104 | h ^= s >> 17;
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105 | s = tab[b >> 18 & 0x7];
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106 | l ^= s << 18;
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107 | h ^= s >> 14;
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108 | s = tab[b >> 21 & 0x7];
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109 | l ^= s << 21;
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110 | h ^= s >> 11;
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111 | s = tab[b >> 24 & 0x7];
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112 | l ^= s << 24;
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113 | h ^= s >> 8;
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114 | s = tab[b >> 27 & 0x7];
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115 | l ^= s << 27;
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116 | h ^= s >> 5;
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117 | s = tab[b >> 30];
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118 | l ^= s << 30;
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119 | h ^= s >> 2;
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120 |
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121 | /* compensate for the top two bits of a */
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122 |
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123 | if (top2b & 01) {
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124 | l ^= b << 30;
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125 | h ^= b >> 2;
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126 | }
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127 | if (top2b & 02) {
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128 | l ^= b << 31;
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129 | h ^= b >> 1;
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130 | }
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131 |
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132 | *r1 = h;
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133 | *r0 = l;
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134 | }
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135 | # endif
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136 | # if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
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137 | static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a,
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138 | const BN_ULONG b)
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139 | {
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140 | register BN_ULONG h, l, s;
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141 | BN_ULONG tab[16], top3b = a >> 61;
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142 | register BN_ULONG a1, a2, a4, a8;
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143 |
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144 | a1 = a & (0x1FFFFFFFFFFFFFFFULL);
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145 | a2 = a1 << 1;
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146 | a4 = a2 << 1;
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147 | a8 = a4 << 1;
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148 |
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149 | tab[0] = 0;
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150 | tab[1] = a1;
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151 | tab[2] = a2;
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152 | tab[3] = a1 ^ a2;
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153 | tab[4] = a4;
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154 | tab[5] = a1 ^ a4;
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155 | tab[6] = a2 ^ a4;
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156 | tab[7] = a1 ^ a2 ^ a4;
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157 | tab[8] = a8;
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158 | tab[9] = a1 ^ a8;
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159 | tab[10] = a2 ^ a8;
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160 | tab[11] = a1 ^ a2 ^ a8;
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161 | tab[12] = a4 ^ a8;
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162 | tab[13] = a1 ^ a4 ^ a8;
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163 | tab[14] = a2 ^ a4 ^ a8;
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164 | tab[15] = a1 ^ a2 ^ a4 ^ a8;
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165 |
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166 | s = tab[b & 0xF];
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167 | l = s;
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168 | s = tab[b >> 4 & 0xF];
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169 | l ^= s << 4;
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170 | h = s >> 60;
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171 | s = tab[b >> 8 & 0xF];
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172 | l ^= s << 8;
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173 | h ^= s >> 56;
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174 | s = tab[b >> 12 & 0xF];
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175 | l ^= s << 12;
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176 | h ^= s >> 52;
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177 | s = tab[b >> 16 & 0xF];
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178 | l ^= s << 16;
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179 | h ^= s >> 48;
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180 | s = tab[b >> 20 & 0xF];
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181 | l ^= s << 20;
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182 | h ^= s >> 44;
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183 | s = tab[b >> 24 & 0xF];
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184 | l ^= s << 24;
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185 | h ^= s >> 40;
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186 | s = tab[b >> 28 & 0xF];
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187 | l ^= s << 28;
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188 | h ^= s >> 36;
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189 | s = tab[b >> 32 & 0xF];
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190 | l ^= s << 32;
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191 | h ^= s >> 32;
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192 | s = tab[b >> 36 & 0xF];
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193 | l ^= s << 36;
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194 | h ^= s >> 28;
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195 | s = tab[b >> 40 & 0xF];
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196 | l ^= s << 40;
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197 | h ^= s >> 24;
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198 | s = tab[b >> 44 & 0xF];
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199 | l ^= s << 44;
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200 | h ^= s >> 20;
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201 | s = tab[b >> 48 & 0xF];
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202 | l ^= s << 48;
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203 | h ^= s >> 16;
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204 | s = tab[b >> 52 & 0xF];
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205 | l ^= s << 52;
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206 | h ^= s >> 12;
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207 | s = tab[b >> 56 & 0xF];
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208 | l ^= s << 56;
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209 | h ^= s >> 8;
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210 | s = tab[b >> 60];
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211 | l ^= s << 60;
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212 | h ^= s >> 4;
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213 |
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214 | /* compensate for the top three bits of a */
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215 |
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216 | if (top3b & 01) {
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217 | l ^= b << 61;
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218 | h ^= b >> 3;
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219 | }
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220 | if (top3b & 02) {
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221 | l ^= b << 62;
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222 | h ^= b >> 2;
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223 | }
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224 | if (top3b & 04) {
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225 | l ^= b << 63;
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226 | h ^= b >> 1;
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227 | }
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228 |
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229 | *r1 = h;
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230 | *r0 = l;
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231 | }
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232 | # endif
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233 |
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234 | /*
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235 | * Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1,
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236 | * result is a polynomial r with degree < 4 * BN_BITS2 - 1 The caller MUST
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237 | * ensure that the variables have the right amount of space allocated.
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238 | */
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239 | static void bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0,
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240 | const BN_ULONG b1, const BN_ULONG b0)
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241 | {
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242 | BN_ULONG m1, m0;
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243 | /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */
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244 | bn_GF2m_mul_1x1(r + 3, r + 2, a1, b1);
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245 | bn_GF2m_mul_1x1(r + 1, r, a0, b0);
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246 | bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1);
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247 | /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */
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248 | r[2] ^= m1 ^ r[1] ^ r[3]; /* h0 ^= m1 ^ l1 ^ h1; */
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249 | r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0; /* l1 ^= l0 ^ h0 ^ m0; */
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250 | }
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251 | # else
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252 | void bn_GF2m_mul_2x2(BN_ULONG *r, BN_ULONG a1, BN_ULONG a0, BN_ULONG b1,
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253 | BN_ULONG b0);
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254 | # endif
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255 |
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256 | /*
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257 | * Add polynomials a and b and store result in r; r could be a or b, a and b
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258 | * could be equal; r is the bitwise XOR of a and b.
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259 | */
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260 | int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)
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261 | {
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262 | int i;
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263 | const BIGNUM *at, *bt;
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264 |
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265 | bn_check_top(a);
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266 | bn_check_top(b);
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267 |
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268 | if (a->top < b->top) {
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269 | at = b;
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270 | bt = a;
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271 | } else {
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272 | at = a;
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273 | bt = b;
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274 | }
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275 |
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276 | if (bn_wexpand(r, at->top) == NULL)
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277 | return 0;
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278 |
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279 | for (i = 0; i < bt->top; i++) {
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280 | r->d[i] = at->d[i] ^ bt->d[i];
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281 | }
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282 | for (; i < at->top; i++) {
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283 | r->d[i] = at->d[i];
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284 | }
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285 |
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286 | r->top = at->top;
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287 | bn_correct_top(r);
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288 |
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289 | return 1;
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290 | }
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291 |
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292 | /*-
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293 | * Some functions allow for representation of the irreducible polynomials
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294 | * as an int[], say p. The irreducible f(t) is then of the form:
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295 | * t^p[0] + t^p[1] + ... + t^p[k]
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296 | * where m = p[0] > p[1] > ... > p[k] = 0.
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297 | */
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298 |
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299 | /* Performs modular reduction of a and store result in r. r could be a. */
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300 | int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[])
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301 | {
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302 | int j, k;
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303 | int n, dN, d0, d1;
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304 | BN_ULONG zz, *z;
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305 |
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306 | bn_check_top(a);
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307 |
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308 | if (!p[0]) {
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309 | /* reduction mod 1 => return 0 */
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310 | BN_zero(r);
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311 | return 1;
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312 | }
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313 |
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314 | /*
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315 | * Since the algorithm does reduction in the r value, if a != r, copy the
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316 | * contents of a into r so we can do reduction in r.
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317 | */
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318 | if (a != r) {
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319 | if (!bn_wexpand(r, a->top))
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320 | return 0;
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321 | for (j = 0; j < a->top; j++) {
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322 | r->d[j] = a->d[j];
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323 | }
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324 | r->top = a->top;
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325 | }
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326 | z = r->d;
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327 |
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328 | /* start reduction */
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329 | dN = p[0] / BN_BITS2;
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330 | for (j = r->top - 1; j > dN;) {
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331 | zz = z[j];
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332 | if (z[j] == 0) {
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333 | j--;
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334 | continue;
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335 | }
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336 | z[j] = 0;
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337 |
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338 | for (k = 1; p[k] != 0; k++) {
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339 | /* reducing component t^p[k] */
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340 | n = p[0] - p[k];
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341 | d0 = n % BN_BITS2;
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342 | d1 = BN_BITS2 - d0;
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343 | n /= BN_BITS2;
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344 | z[j - n] ^= (zz >> d0);
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345 | if (d0)
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346 | z[j - n - 1] ^= (zz << d1);
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347 | }
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348 |
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349 | /* reducing component t^0 */
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350 | n = dN;
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351 | d0 = p[0] % BN_BITS2;
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352 | d1 = BN_BITS2 - d0;
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353 | z[j - n] ^= (zz >> d0);
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354 | if (d0)
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355 | z[j - n - 1] ^= (zz << d1);
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356 | }
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357 |
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358 | /* final round of reduction */
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359 | while (j == dN) {
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360 |
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361 | d0 = p[0] % BN_BITS2;
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362 | zz = z[dN] >> d0;
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363 | if (zz == 0)
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364 | break;
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365 | d1 = BN_BITS2 - d0;
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366 |
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367 | /* clear up the top d1 bits */
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368 | if (d0)
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369 | z[dN] = (z[dN] << d1) >> d1;
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370 | else
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371 | z[dN] = 0;
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372 | z[0] ^= zz; /* reduction t^0 component */
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373 |
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374 | for (k = 1; p[k] != 0; k++) {
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375 | BN_ULONG tmp_ulong;
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376 |
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377 | /* reducing component t^p[k] */
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378 | n = p[k] / BN_BITS2;
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379 | d0 = p[k] % BN_BITS2;
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380 | d1 = BN_BITS2 - d0;
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381 | z[n] ^= (zz << d0);
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382 | if (d0 && (tmp_ulong = zz >> d1))
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383 | z[n + 1] ^= tmp_ulong;
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384 | }
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385 |
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386 | }
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387 |
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388 | bn_correct_top(r);
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389 | return 1;
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390 | }
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391 |
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392 | /*
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393 | * Performs modular reduction of a by p and store result in r. r could be a.
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394 | * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper
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395 | * function is only provided for convenience; for best performance, use the
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396 | * BN_GF2m_mod_arr function.
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397 | */
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398 | int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p)
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399 | {
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400 | int ret = 0;
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401 | int arr[6];
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402 | bn_check_top(a);
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403 | bn_check_top(p);
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404 | ret = BN_GF2m_poly2arr(p, arr, OSSL_NELEM(arr));
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405 | if (!ret || ret > (int)OSSL_NELEM(arr)) {
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406 | BNerr(BN_F_BN_GF2M_MOD, BN_R_INVALID_LENGTH);
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407 | return 0;
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408 | }
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409 | ret = BN_GF2m_mod_arr(r, a, arr);
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410 | bn_check_top(r);
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411 | return ret;
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412 | }
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413 |
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414 | /*
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415 | * Compute the product of two polynomials a and b, reduce modulo p, and store
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416 | * the result in r. r could be a or b; a could be b.
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417 | */
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418 | int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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419 | const int p[], BN_CTX *ctx)
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420 | {
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421 | int zlen, i, j, k, ret = 0;
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422 | BIGNUM *s;
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423 | BN_ULONG x1, x0, y1, y0, zz[4];
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424 |
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425 | bn_check_top(a);
|
---|
426 | bn_check_top(b);
|
---|
427 |
|
---|
428 | if (a == b) {
|
---|
429 | return BN_GF2m_mod_sqr_arr(r, a, p, ctx);
|
---|
430 | }
|
---|
431 |
|
---|
432 | BN_CTX_start(ctx);
|
---|
433 | if ((s = BN_CTX_get(ctx)) == NULL)
|
---|
434 | goto err;
|
---|
435 |
|
---|
436 | zlen = a->top + b->top + 4;
|
---|
437 | if (!bn_wexpand(s, zlen))
|
---|
438 | goto err;
|
---|
439 | s->top = zlen;
|
---|
440 |
|
---|
441 | for (i = 0; i < zlen; i++)
|
---|
442 | s->d[i] = 0;
|
---|
443 |
|
---|
444 | for (j = 0; j < b->top; j += 2) {
|
---|
445 | y0 = b->d[j];
|
---|
446 | y1 = ((j + 1) == b->top) ? 0 : b->d[j + 1];
|
---|
447 | for (i = 0; i < a->top; i += 2) {
|
---|
448 | x0 = a->d[i];
|
---|
449 | x1 = ((i + 1) == a->top) ? 0 : a->d[i + 1];
|
---|
450 | bn_GF2m_mul_2x2(zz, x1, x0, y1, y0);
|
---|
451 | for (k = 0; k < 4; k++)
|
---|
452 | s->d[i + j + k] ^= zz[k];
|
---|
453 | }
|
---|
454 | }
|
---|
455 |
|
---|
456 | bn_correct_top(s);
|
---|
457 | if (BN_GF2m_mod_arr(r, s, p))
|
---|
458 | ret = 1;
|
---|
459 | bn_check_top(r);
|
---|
460 |
|
---|
461 | err:
|
---|
462 | BN_CTX_end(ctx);
|
---|
463 | return ret;
|
---|
464 | }
|
---|
465 |
|
---|
466 | /*
|
---|
467 | * Compute the product of two polynomials a and b, reduce modulo p, and store
|
---|
468 | * the result in r. r could be a or b; a could equal b. This function calls
|
---|
469 | * down to the BN_GF2m_mod_mul_arr implementation; this wrapper function is
|
---|
470 | * only provided for convenience; for best performance, use the
|
---|
471 | * BN_GF2m_mod_mul_arr function.
|
---|
472 | */
|
---|
473 | int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
|
---|
474 | const BIGNUM *p, BN_CTX *ctx)
|
---|
475 | {
|
---|
476 | int ret = 0;
|
---|
477 | const int max = BN_num_bits(p) + 1;
|
---|
478 | int *arr = NULL;
|
---|
479 | bn_check_top(a);
|
---|
480 | bn_check_top(b);
|
---|
481 | bn_check_top(p);
|
---|
482 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
|
---|
483 | goto err;
|
---|
484 | ret = BN_GF2m_poly2arr(p, arr, max);
|
---|
485 | if (!ret || ret > max) {
|
---|
486 | BNerr(BN_F_BN_GF2M_MOD_MUL, BN_R_INVALID_LENGTH);
|
---|
487 | goto err;
|
---|
488 | }
|
---|
489 | ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx);
|
---|
490 | bn_check_top(r);
|
---|
491 | err:
|
---|
492 | OPENSSL_free(arr);
|
---|
493 | return ret;
|
---|
494 | }
|
---|
495 |
|
---|
496 | /* Square a, reduce the result mod p, and store it in a. r could be a. */
|
---|
497 | int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
|
---|
498 | BN_CTX *ctx)
|
---|
499 | {
|
---|
500 | int i, ret = 0;
|
---|
501 | BIGNUM *s;
|
---|
502 |
|
---|
503 | bn_check_top(a);
|
---|
504 | BN_CTX_start(ctx);
|
---|
505 | if ((s = BN_CTX_get(ctx)) == NULL)
|
---|
506 | goto err;
|
---|
507 | if (!bn_wexpand(s, 2 * a->top))
|
---|
508 | goto err;
|
---|
509 |
|
---|
510 | for (i = a->top - 1; i >= 0; i--) {
|
---|
511 | s->d[2 * i + 1] = SQR1(a->d[i]);
|
---|
512 | s->d[2 * i] = SQR0(a->d[i]);
|
---|
513 | }
|
---|
514 |
|
---|
515 | s->top = 2 * a->top;
|
---|
516 | bn_correct_top(s);
|
---|
517 | if (!BN_GF2m_mod_arr(r, s, p))
|
---|
518 | goto err;
|
---|
519 | bn_check_top(r);
|
---|
520 | ret = 1;
|
---|
521 | err:
|
---|
522 | BN_CTX_end(ctx);
|
---|
523 | return ret;
|
---|
524 | }
|
---|
525 |
|
---|
526 | /*
|
---|
527 | * Square a, reduce the result mod p, and store it in a. r could be a. This
|
---|
528 | * function calls down to the BN_GF2m_mod_sqr_arr implementation; this
|
---|
529 | * wrapper function is only provided for convenience; for best performance,
|
---|
530 | * use the BN_GF2m_mod_sqr_arr function.
|
---|
531 | */
|
---|
532 | int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
|
---|
533 | {
|
---|
534 | int ret = 0;
|
---|
535 | const int max = BN_num_bits(p) + 1;
|
---|
536 | int *arr = NULL;
|
---|
537 |
|
---|
538 | bn_check_top(a);
|
---|
539 | bn_check_top(p);
|
---|
540 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
|
---|
541 | goto err;
|
---|
542 | ret = BN_GF2m_poly2arr(p, arr, max);
|
---|
543 | if (!ret || ret > max) {
|
---|
544 | BNerr(BN_F_BN_GF2M_MOD_SQR, BN_R_INVALID_LENGTH);
|
---|
545 | goto err;
|
---|
546 | }
|
---|
547 | ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx);
|
---|
548 | bn_check_top(r);
|
---|
549 | err:
|
---|
550 | OPENSSL_free(arr);
|
---|
551 | return ret;
|
---|
552 | }
|
---|
553 |
|
---|
554 | /*
|
---|
555 | * Invert a, reduce modulo p, and store the result in r. r could be a. Uses
|
---|
556 | * Modified Almost Inverse Algorithm (Algorithm 10) from Hankerson, D.,
|
---|
557 | * Hernandez, J.L., and Menezes, A. "Software Implementation of Elliptic
|
---|
558 | * Curve Cryptography Over Binary Fields".
|
---|
559 | */
|
---|
560 | int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
|
---|
561 | {
|
---|
562 | BIGNUM *b, *c = NULL, *u = NULL, *v = NULL, *tmp;
|
---|
563 | int ret = 0;
|
---|
564 |
|
---|
565 | bn_check_top(a);
|
---|
566 | bn_check_top(p);
|
---|
567 |
|
---|
568 | BN_CTX_start(ctx);
|
---|
569 |
|
---|
570 | if ((b = BN_CTX_get(ctx)) == NULL)
|
---|
571 | goto err;
|
---|
572 | if ((c = BN_CTX_get(ctx)) == NULL)
|
---|
573 | goto err;
|
---|
574 | if ((u = BN_CTX_get(ctx)) == NULL)
|
---|
575 | goto err;
|
---|
576 | if ((v = BN_CTX_get(ctx)) == NULL)
|
---|
577 | goto err;
|
---|
578 |
|
---|
579 | if (!BN_GF2m_mod(u, a, p))
|
---|
580 | goto err;
|
---|
581 | if (BN_is_zero(u))
|
---|
582 | goto err;
|
---|
583 |
|
---|
584 | if (!BN_copy(v, p))
|
---|
585 | goto err;
|
---|
586 | # if 0
|
---|
587 | if (!BN_one(b))
|
---|
588 | goto err;
|
---|
589 |
|
---|
590 | while (1) {
|
---|
591 | while (!BN_is_odd(u)) {
|
---|
592 | if (BN_is_zero(u))
|
---|
593 | goto err;
|
---|
594 | if (!BN_rshift1(u, u))
|
---|
595 | goto err;
|
---|
596 | if (BN_is_odd(b)) {
|
---|
597 | if (!BN_GF2m_add(b, b, p))
|
---|
598 | goto err;
|
---|
599 | }
|
---|
600 | if (!BN_rshift1(b, b))
|
---|
601 | goto err;
|
---|
602 | }
|
---|
603 |
|
---|
604 | if (BN_abs_is_word(u, 1))
|
---|
605 | break;
|
---|
606 |
|
---|
607 | if (BN_num_bits(u) < BN_num_bits(v)) {
|
---|
608 | tmp = u;
|
---|
609 | u = v;
|
---|
610 | v = tmp;
|
---|
611 | tmp = b;
|
---|
612 | b = c;
|
---|
613 | c = tmp;
|
---|
614 | }
|
---|
615 |
|
---|
616 | if (!BN_GF2m_add(u, u, v))
|
---|
617 | goto err;
|
---|
618 | if (!BN_GF2m_add(b, b, c))
|
---|
619 | goto err;
|
---|
620 | }
|
---|
621 | # else
|
---|
622 | {
|
---|
623 | int i;
|
---|
624 | int ubits = BN_num_bits(u);
|
---|
625 | int vbits = BN_num_bits(v); /* v is copy of p */
|
---|
626 | int top = p->top;
|
---|
627 | BN_ULONG *udp, *bdp, *vdp, *cdp;
|
---|
628 |
|
---|
629 | if (!bn_wexpand(u, top))
|
---|
630 | goto err;
|
---|
631 | udp = u->d;
|
---|
632 | for (i = u->top; i < top; i++)
|
---|
633 | udp[i] = 0;
|
---|
634 | u->top = top;
|
---|
635 | if (!bn_wexpand(b, top))
|
---|
636 | goto err;
|
---|
637 | bdp = b->d;
|
---|
638 | bdp[0] = 1;
|
---|
639 | for (i = 1; i < top; i++)
|
---|
640 | bdp[i] = 0;
|
---|
641 | b->top = top;
|
---|
642 | if (!bn_wexpand(c, top))
|
---|
643 | goto err;
|
---|
644 | cdp = c->d;
|
---|
645 | for (i = 0; i < top; i++)
|
---|
646 | cdp[i] = 0;
|
---|
647 | c->top = top;
|
---|
648 | vdp = v->d; /* It pays off to "cache" *->d pointers,
|
---|
649 | * because it allows optimizer to be more
|
---|
650 | * aggressive. But we don't have to "cache"
|
---|
651 | * p->d, because *p is declared 'const'... */
|
---|
652 | while (1) {
|
---|
653 | while (ubits && !(udp[0] & 1)) {
|
---|
654 | BN_ULONG u0, u1, b0, b1, mask;
|
---|
655 |
|
---|
656 | u0 = udp[0];
|
---|
657 | b0 = bdp[0];
|
---|
658 | mask = (BN_ULONG)0 - (b0 & 1);
|
---|
659 | b0 ^= p->d[0] & mask;
|
---|
660 | for (i = 0; i < top - 1; i++) {
|
---|
661 | u1 = udp[i + 1];
|
---|
662 | udp[i] = ((u0 >> 1) | (u1 << (BN_BITS2 - 1))) & BN_MASK2;
|
---|
663 | u0 = u1;
|
---|
664 | b1 = bdp[i + 1] ^ (p->d[i + 1] & mask);
|
---|
665 | bdp[i] = ((b0 >> 1) | (b1 << (BN_BITS2 - 1))) & BN_MASK2;
|
---|
666 | b0 = b1;
|
---|
667 | }
|
---|
668 | udp[i] = u0 >> 1;
|
---|
669 | bdp[i] = b0 >> 1;
|
---|
670 | ubits--;
|
---|
671 | }
|
---|
672 |
|
---|
673 | if (ubits <= BN_BITS2) {
|
---|
674 | if (udp[0] == 0) /* poly was reducible */
|
---|
675 | goto err;
|
---|
676 | if (udp[0] == 1)
|
---|
677 | break;
|
---|
678 | }
|
---|
679 |
|
---|
680 | if (ubits < vbits) {
|
---|
681 | i = ubits;
|
---|
682 | ubits = vbits;
|
---|
683 | vbits = i;
|
---|
684 | tmp = u;
|
---|
685 | u = v;
|
---|
686 | v = tmp;
|
---|
687 | tmp = b;
|
---|
688 | b = c;
|
---|
689 | c = tmp;
|
---|
690 | udp = vdp;
|
---|
691 | vdp = v->d;
|
---|
692 | bdp = cdp;
|
---|
693 | cdp = c->d;
|
---|
694 | }
|
---|
695 | for (i = 0; i < top; i++) {
|
---|
696 | udp[i] ^= vdp[i];
|
---|
697 | bdp[i] ^= cdp[i];
|
---|
698 | }
|
---|
699 | if (ubits == vbits) {
|
---|
700 | BN_ULONG ul;
|
---|
701 | int utop = (ubits - 1) / BN_BITS2;
|
---|
702 |
|
---|
703 | while ((ul = udp[utop]) == 0 && utop)
|
---|
704 | utop--;
|
---|
705 | ubits = utop * BN_BITS2 + BN_num_bits_word(ul);
|
---|
706 | }
|
---|
707 | }
|
---|
708 | bn_correct_top(b);
|
---|
709 | }
|
---|
710 | # endif
|
---|
711 |
|
---|
712 | if (!BN_copy(r, b))
|
---|
713 | goto err;
|
---|
714 | bn_check_top(r);
|
---|
715 | ret = 1;
|
---|
716 |
|
---|
717 | err:
|
---|
718 | # ifdef BN_DEBUG /* BN_CTX_end would complain about the
|
---|
719 | * expanded form */
|
---|
720 | bn_correct_top(c);
|
---|
721 | bn_correct_top(u);
|
---|
722 | bn_correct_top(v);
|
---|
723 | # endif
|
---|
724 | BN_CTX_end(ctx);
|
---|
725 | return ret;
|
---|
726 | }
|
---|
727 |
|
---|
728 | /*
|
---|
729 | * Invert xx, reduce modulo p, and store the result in r. r could be xx.
|
---|
730 | * This function calls down to the BN_GF2m_mod_inv implementation; this
|
---|
731 | * wrapper function is only provided for convenience; for best performance,
|
---|
732 | * use the BN_GF2m_mod_inv function.
|
---|
733 | */
|
---|
734 | int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[],
|
---|
735 | BN_CTX *ctx)
|
---|
736 | {
|
---|
737 | BIGNUM *field;
|
---|
738 | int ret = 0;
|
---|
739 |
|
---|
740 | bn_check_top(xx);
|
---|
741 | BN_CTX_start(ctx);
|
---|
742 | if ((field = BN_CTX_get(ctx)) == NULL)
|
---|
743 | goto err;
|
---|
744 | if (!BN_GF2m_arr2poly(p, field))
|
---|
745 | goto err;
|
---|
746 |
|
---|
747 | ret = BN_GF2m_mod_inv(r, xx, field, ctx);
|
---|
748 | bn_check_top(r);
|
---|
749 |
|
---|
750 | err:
|
---|
751 | BN_CTX_end(ctx);
|
---|
752 | return ret;
|
---|
753 | }
|
---|
754 |
|
---|
755 | # ifndef OPENSSL_SUN_GF2M_DIV
|
---|
756 | /*
|
---|
757 | * Divide y by x, reduce modulo p, and store the result in r. r could be x
|
---|
758 | * or y, x could equal y.
|
---|
759 | */
|
---|
760 | int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x,
|
---|
761 | const BIGNUM *p, BN_CTX *ctx)
|
---|
762 | {
|
---|
763 | BIGNUM *xinv = NULL;
|
---|
764 | int ret = 0;
|
---|
765 |
|
---|
766 | bn_check_top(y);
|
---|
767 | bn_check_top(x);
|
---|
768 | bn_check_top(p);
|
---|
769 |
|
---|
770 | BN_CTX_start(ctx);
|
---|
771 | xinv = BN_CTX_get(ctx);
|
---|
772 | if (xinv == NULL)
|
---|
773 | goto err;
|
---|
774 |
|
---|
775 | if (!BN_GF2m_mod_inv(xinv, x, p, ctx))
|
---|
776 | goto err;
|
---|
777 | if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx))
|
---|
778 | goto err;
|
---|
779 | bn_check_top(r);
|
---|
780 | ret = 1;
|
---|
781 |
|
---|
782 | err:
|
---|
783 | BN_CTX_end(ctx);
|
---|
784 | return ret;
|
---|
785 | }
|
---|
786 | # else
|
---|
787 | /*
|
---|
788 | * Divide y by x, reduce modulo p, and store the result in r. r could be x
|
---|
789 | * or y, x could equal y. Uses algorithm Modular_Division_GF(2^m) from
|
---|
790 | * Chang-Shantz, S. "From Euclid's GCD to Montgomery Multiplication to the
|
---|
791 | * Great Divide".
|
---|
792 | */
|
---|
793 | int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x,
|
---|
794 | const BIGNUM *p, BN_CTX *ctx)
|
---|
795 | {
|
---|
796 | BIGNUM *a, *b, *u, *v;
|
---|
797 | int ret = 0;
|
---|
798 |
|
---|
799 | bn_check_top(y);
|
---|
800 | bn_check_top(x);
|
---|
801 | bn_check_top(p);
|
---|
802 |
|
---|
803 | BN_CTX_start(ctx);
|
---|
804 |
|
---|
805 | a = BN_CTX_get(ctx);
|
---|
806 | b = BN_CTX_get(ctx);
|
---|
807 | u = BN_CTX_get(ctx);
|
---|
808 | v = BN_CTX_get(ctx);
|
---|
809 | if (v == NULL)
|
---|
810 | goto err;
|
---|
811 |
|
---|
812 | /* reduce x and y mod p */
|
---|
813 | if (!BN_GF2m_mod(u, y, p))
|
---|
814 | goto err;
|
---|
815 | if (!BN_GF2m_mod(a, x, p))
|
---|
816 | goto err;
|
---|
817 | if (!BN_copy(b, p))
|
---|
818 | goto err;
|
---|
819 |
|
---|
820 | while (!BN_is_odd(a)) {
|
---|
821 | if (!BN_rshift1(a, a))
|
---|
822 | goto err;
|
---|
823 | if (BN_is_odd(u))
|
---|
824 | if (!BN_GF2m_add(u, u, p))
|
---|
825 | goto err;
|
---|
826 | if (!BN_rshift1(u, u))
|
---|
827 | goto err;
|
---|
828 | }
|
---|
829 |
|
---|
830 | do {
|
---|
831 | if (BN_GF2m_cmp(b, a) > 0) {
|
---|
832 | if (!BN_GF2m_add(b, b, a))
|
---|
833 | goto err;
|
---|
834 | if (!BN_GF2m_add(v, v, u))
|
---|
835 | goto err;
|
---|
836 | do {
|
---|
837 | if (!BN_rshift1(b, b))
|
---|
838 | goto err;
|
---|
839 | if (BN_is_odd(v))
|
---|
840 | if (!BN_GF2m_add(v, v, p))
|
---|
841 | goto err;
|
---|
842 | if (!BN_rshift1(v, v))
|
---|
843 | goto err;
|
---|
844 | } while (!BN_is_odd(b));
|
---|
845 | } else if (BN_abs_is_word(a, 1))
|
---|
846 | break;
|
---|
847 | else {
|
---|
848 | if (!BN_GF2m_add(a, a, b))
|
---|
849 | goto err;
|
---|
850 | if (!BN_GF2m_add(u, u, v))
|
---|
851 | goto err;
|
---|
852 | do {
|
---|
853 | if (!BN_rshift1(a, a))
|
---|
854 | goto err;
|
---|
855 | if (BN_is_odd(u))
|
---|
856 | if (!BN_GF2m_add(u, u, p))
|
---|
857 | goto err;
|
---|
858 | if (!BN_rshift1(u, u))
|
---|
859 | goto err;
|
---|
860 | } while (!BN_is_odd(a));
|
---|
861 | }
|
---|
862 | } while (1);
|
---|
863 |
|
---|
864 | if (!BN_copy(r, u))
|
---|
865 | goto err;
|
---|
866 | bn_check_top(r);
|
---|
867 | ret = 1;
|
---|
868 |
|
---|
869 | err:
|
---|
870 | BN_CTX_end(ctx);
|
---|
871 | return ret;
|
---|
872 | }
|
---|
873 | # endif
|
---|
874 |
|
---|
875 | /*
|
---|
876 | * Divide yy by xx, reduce modulo p, and store the result in r. r could be xx
|
---|
877 | * * or yy, xx could equal yy. This function calls down to the
|
---|
878 | * BN_GF2m_mod_div implementation; this wrapper function is only provided for
|
---|
879 | * convenience; for best performance, use the BN_GF2m_mod_div function.
|
---|
880 | */
|
---|
881 | int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx,
|
---|
882 | const int p[], BN_CTX *ctx)
|
---|
883 | {
|
---|
884 | BIGNUM *field;
|
---|
885 | int ret = 0;
|
---|
886 |
|
---|
887 | bn_check_top(yy);
|
---|
888 | bn_check_top(xx);
|
---|
889 |
|
---|
890 | BN_CTX_start(ctx);
|
---|
891 | if ((field = BN_CTX_get(ctx)) == NULL)
|
---|
892 | goto err;
|
---|
893 | if (!BN_GF2m_arr2poly(p, field))
|
---|
894 | goto err;
|
---|
895 |
|
---|
896 | ret = BN_GF2m_mod_div(r, yy, xx, field, ctx);
|
---|
897 | bn_check_top(r);
|
---|
898 |
|
---|
899 | err:
|
---|
900 | BN_CTX_end(ctx);
|
---|
901 | return ret;
|
---|
902 | }
|
---|
903 |
|
---|
904 | /*
|
---|
905 | * Compute the bth power of a, reduce modulo p, and store the result in r. r
|
---|
906 | * could be a. Uses simple square-and-multiply algorithm A.5.1 from IEEE
|
---|
907 | * P1363.
|
---|
908 | */
|
---|
909 | int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
|
---|
910 | const int p[], BN_CTX *ctx)
|
---|
911 | {
|
---|
912 | int ret = 0, i, n;
|
---|
913 | BIGNUM *u;
|
---|
914 |
|
---|
915 | bn_check_top(a);
|
---|
916 | bn_check_top(b);
|
---|
917 |
|
---|
918 | if (BN_is_zero(b))
|
---|
919 | return (BN_one(r));
|
---|
920 |
|
---|
921 | if (BN_abs_is_word(b, 1))
|
---|
922 | return (BN_copy(r, a) != NULL);
|
---|
923 |
|
---|
924 | BN_CTX_start(ctx);
|
---|
925 | if ((u = BN_CTX_get(ctx)) == NULL)
|
---|
926 | goto err;
|
---|
927 |
|
---|
928 | if (!BN_GF2m_mod_arr(u, a, p))
|
---|
929 | goto err;
|
---|
930 |
|
---|
931 | n = BN_num_bits(b) - 1;
|
---|
932 | for (i = n - 1; i >= 0; i--) {
|
---|
933 | if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx))
|
---|
934 | goto err;
|
---|
935 | if (BN_is_bit_set(b, i)) {
|
---|
936 | if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx))
|
---|
937 | goto err;
|
---|
938 | }
|
---|
939 | }
|
---|
940 | if (!BN_copy(r, u))
|
---|
941 | goto err;
|
---|
942 | bn_check_top(r);
|
---|
943 | ret = 1;
|
---|
944 | err:
|
---|
945 | BN_CTX_end(ctx);
|
---|
946 | return ret;
|
---|
947 | }
|
---|
948 |
|
---|
949 | /*
|
---|
950 | * Compute the bth power of a, reduce modulo p, and store the result in r. r
|
---|
951 | * could be a. This function calls down to the BN_GF2m_mod_exp_arr
|
---|
952 | * implementation; this wrapper function is only provided for convenience;
|
---|
953 | * for best performance, use the BN_GF2m_mod_exp_arr function.
|
---|
954 | */
|
---|
955 | int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
|
---|
956 | const BIGNUM *p, BN_CTX *ctx)
|
---|
957 | {
|
---|
958 | int ret = 0;
|
---|
959 | const int max = BN_num_bits(p) + 1;
|
---|
960 | int *arr = NULL;
|
---|
961 | bn_check_top(a);
|
---|
962 | bn_check_top(b);
|
---|
963 | bn_check_top(p);
|
---|
964 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
|
---|
965 | goto err;
|
---|
966 | ret = BN_GF2m_poly2arr(p, arr, max);
|
---|
967 | if (!ret || ret > max) {
|
---|
968 | BNerr(BN_F_BN_GF2M_MOD_EXP, BN_R_INVALID_LENGTH);
|
---|
969 | goto err;
|
---|
970 | }
|
---|
971 | ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx);
|
---|
972 | bn_check_top(r);
|
---|
973 | err:
|
---|
974 | OPENSSL_free(arr);
|
---|
975 | return ret;
|
---|
976 | }
|
---|
977 |
|
---|
978 | /*
|
---|
979 | * Compute the square root of a, reduce modulo p, and store the result in r.
|
---|
980 | * r could be a. Uses exponentiation as in algorithm A.4.1 from IEEE P1363.
|
---|
981 | */
|
---|
982 | int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[],
|
---|
983 | BN_CTX *ctx)
|
---|
984 | {
|
---|
985 | int ret = 0;
|
---|
986 | BIGNUM *u;
|
---|
987 |
|
---|
988 | bn_check_top(a);
|
---|
989 |
|
---|
990 | if (!p[0]) {
|
---|
991 | /* reduction mod 1 => return 0 */
|
---|
992 | BN_zero(r);
|
---|
993 | return 1;
|
---|
994 | }
|
---|
995 |
|
---|
996 | BN_CTX_start(ctx);
|
---|
997 | if ((u = BN_CTX_get(ctx)) == NULL)
|
---|
998 | goto err;
|
---|
999 |
|
---|
1000 | if (!BN_set_bit(u, p[0] - 1))
|
---|
1001 | goto err;
|
---|
1002 | ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx);
|
---|
1003 | bn_check_top(r);
|
---|
1004 |
|
---|
1005 | err:
|
---|
1006 | BN_CTX_end(ctx);
|
---|
1007 | return ret;
|
---|
1008 | }
|
---|
1009 |
|
---|
1010 | /*
|
---|
1011 | * Compute the square root of a, reduce modulo p, and store the result in r.
|
---|
1012 | * r could be a. This function calls down to the BN_GF2m_mod_sqrt_arr
|
---|
1013 | * implementation; this wrapper function is only provided for convenience;
|
---|
1014 | * for best performance, use the BN_GF2m_mod_sqrt_arr function.
|
---|
1015 | */
|
---|
1016 | int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
|
---|
1017 | {
|
---|
1018 | int ret = 0;
|
---|
1019 | const int max = BN_num_bits(p) + 1;
|
---|
1020 | int *arr = NULL;
|
---|
1021 | bn_check_top(a);
|
---|
1022 | bn_check_top(p);
|
---|
1023 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
|
---|
1024 | goto err;
|
---|
1025 | ret = BN_GF2m_poly2arr(p, arr, max);
|
---|
1026 | if (!ret || ret > max) {
|
---|
1027 | BNerr(BN_F_BN_GF2M_MOD_SQRT, BN_R_INVALID_LENGTH);
|
---|
1028 | goto err;
|
---|
1029 | }
|
---|
1030 | ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx);
|
---|
1031 | bn_check_top(r);
|
---|
1032 | err:
|
---|
1033 | OPENSSL_free(arr);
|
---|
1034 | return ret;
|
---|
1035 | }
|
---|
1036 |
|
---|
1037 | /*
|
---|
1038 | * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns
|
---|
1039 | * 0. Uses algorithms A.4.7 and A.4.6 from IEEE P1363.
|
---|
1040 | */
|
---|
1041 | int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[],
|
---|
1042 | BN_CTX *ctx)
|
---|
1043 | {
|
---|
1044 | int ret = 0, count = 0, j;
|
---|
1045 | BIGNUM *a, *z, *rho, *w, *w2, *tmp;
|
---|
1046 |
|
---|
1047 | bn_check_top(a_);
|
---|
1048 |
|
---|
1049 | if (!p[0]) {
|
---|
1050 | /* reduction mod 1 => return 0 */
|
---|
1051 | BN_zero(r);
|
---|
1052 | return 1;
|
---|
1053 | }
|
---|
1054 |
|
---|
1055 | BN_CTX_start(ctx);
|
---|
1056 | a = BN_CTX_get(ctx);
|
---|
1057 | z = BN_CTX_get(ctx);
|
---|
1058 | w = BN_CTX_get(ctx);
|
---|
1059 | if (w == NULL)
|
---|
1060 | goto err;
|
---|
1061 |
|
---|
1062 | if (!BN_GF2m_mod_arr(a, a_, p))
|
---|
1063 | goto err;
|
---|
1064 |
|
---|
1065 | if (BN_is_zero(a)) {
|
---|
1066 | BN_zero(r);
|
---|
1067 | ret = 1;
|
---|
1068 | goto err;
|
---|
1069 | }
|
---|
1070 |
|
---|
1071 | if (p[0] & 0x1) { /* m is odd */
|
---|
1072 | /* compute half-trace of a */
|
---|
1073 | if (!BN_copy(z, a))
|
---|
1074 | goto err;
|
---|
1075 | for (j = 1; j <= (p[0] - 1) / 2; j++) {
|
---|
1076 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
|
---|
1077 | goto err;
|
---|
1078 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
|
---|
1079 | goto err;
|
---|
1080 | if (!BN_GF2m_add(z, z, a))
|
---|
1081 | goto err;
|
---|
1082 | }
|
---|
1083 |
|
---|
1084 | } else { /* m is even */
|
---|
1085 |
|
---|
1086 | rho = BN_CTX_get(ctx);
|
---|
1087 | w2 = BN_CTX_get(ctx);
|
---|
1088 | tmp = BN_CTX_get(ctx);
|
---|
1089 | if (tmp == NULL)
|
---|
1090 | goto err;
|
---|
1091 | do {
|
---|
1092 | if (!BN_rand(rho, p[0], BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
|
---|
1093 | goto err;
|
---|
1094 | if (!BN_GF2m_mod_arr(rho, rho, p))
|
---|
1095 | goto err;
|
---|
1096 | BN_zero(z);
|
---|
1097 | if (!BN_copy(w, rho))
|
---|
1098 | goto err;
|
---|
1099 | for (j = 1; j <= p[0] - 1; j++) {
|
---|
1100 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
|
---|
1101 | goto err;
|
---|
1102 | if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx))
|
---|
1103 | goto err;
|
---|
1104 | if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx))
|
---|
1105 | goto err;
|
---|
1106 | if (!BN_GF2m_add(z, z, tmp))
|
---|
1107 | goto err;
|
---|
1108 | if (!BN_GF2m_add(w, w2, rho))
|
---|
1109 | goto err;
|
---|
1110 | }
|
---|
1111 | count++;
|
---|
1112 | } while (BN_is_zero(w) && (count < MAX_ITERATIONS));
|
---|
1113 | if (BN_is_zero(w)) {
|
---|
1114 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_TOO_MANY_ITERATIONS);
|
---|
1115 | goto err;
|
---|
1116 | }
|
---|
1117 | }
|
---|
1118 |
|
---|
1119 | if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx))
|
---|
1120 | goto err;
|
---|
1121 | if (!BN_GF2m_add(w, z, w))
|
---|
1122 | goto err;
|
---|
1123 | if (BN_GF2m_cmp(w, a)) {
|
---|
1124 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_NO_SOLUTION);
|
---|
1125 | goto err;
|
---|
1126 | }
|
---|
1127 |
|
---|
1128 | if (!BN_copy(r, z))
|
---|
1129 | goto err;
|
---|
1130 | bn_check_top(r);
|
---|
1131 |
|
---|
1132 | ret = 1;
|
---|
1133 |
|
---|
1134 | err:
|
---|
1135 | BN_CTX_end(ctx);
|
---|
1136 | return ret;
|
---|
1137 | }
|
---|
1138 |
|
---|
1139 | /*
|
---|
1140 | * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns
|
---|
1141 | * 0. This function calls down to the BN_GF2m_mod_solve_quad_arr
|
---|
1142 | * implementation; this wrapper function is only provided for convenience;
|
---|
1143 | * for best performance, use the BN_GF2m_mod_solve_quad_arr function.
|
---|
1144 | */
|
---|
1145 | int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
|
---|
1146 | BN_CTX *ctx)
|
---|
1147 | {
|
---|
1148 | int ret = 0;
|
---|
1149 | const int max = BN_num_bits(p) + 1;
|
---|
1150 | int *arr = NULL;
|
---|
1151 | bn_check_top(a);
|
---|
1152 | bn_check_top(p);
|
---|
1153 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
|
---|
1154 | goto err;
|
---|
1155 | ret = BN_GF2m_poly2arr(p, arr, max);
|
---|
1156 | if (!ret || ret > max) {
|
---|
1157 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD, BN_R_INVALID_LENGTH);
|
---|
1158 | goto err;
|
---|
1159 | }
|
---|
1160 | ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx);
|
---|
1161 | bn_check_top(r);
|
---|
1162 | err:
|
---|
1163 | OPENSSL_free(arr);
|
---|
1164 | return ret;
|
---|
1165 | }
|
---|
1166 |
|
---|
1167 | /*
|
---|
1168 | * Convert the bit-string representation of a polynomial ( \sum_{i=0}^n a_i *
|
---|
1169 | * x^i) into an array of integers corresponding to the bits with non-zero
|
---|
1170 | * coefficient. Array is terminated with -1. Up to max elements of the array
|
---|
1171 | * will be filled. Return value is total number of array elements that would
|
---|
1172 | * be filled if array was large enough.
|
---|
1173 | */
|
---|
1174 | int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max)
|
---|
1175 | {
|
---|
1176 | int i, j, k = 0;
|
---|
1177 | BN_ULONG mask;
|
---|
1178 |
|
---|
1179 | if (BN_is_zero(a))
|
---|
1180 | return 0;
|
---|
1181 |
|
---|
1182 | for (i = a->top - 1; i >= 0; i--) {
|
---|
1183 | if (!a->d[i])
|
---|
1184 | /* skip word if a->d[i] == 0 */
|
---|
1185 | continue;
|
---|
1186 | mask = BN_TBIT;
|
---|
1187 | for (j = BN_BITS2 - 1; j >= 0; j--) {
|
---|
1188 | if (a->d[i] & mask) {
|
---|
1189 | if (k < max)
|
---|
1190 | p[k] = BN_BITS2 * i + j;
|
---|
1191 | k++;
|
---|
1192 | }
|
---|
1193 | mask >>= 1;
|
---|
1194 | }
|
---|
1195 | }
|
---|
1196 |
|
---|
1197 | if (k < max) {
|
---|
1198 | p[k] = -1;
|
---|
1199 | k++;
|
---|
1200 | }
|
---|
1201 |
|
---|
1202 | return k;
|
---|
1203 | }
|
---|
1204 |
|
---|
1205 | /*
|
---|
1206 | * Convert the coefficient array representation of a polynomial to a
|
---|
1207 | * bit-string. The array must be terminated by -1.
|
---|
1208 | */
|
---|
1209 | int BN_GF2m_arr2poly(const int p[], BIGNUM *a)
|
---|
1210 | {
|
---|
1211 | int i;
|
---|
1212 |
|
---|
1213 | bn_check_top(a);
|
---|
1214 | BN_zero(a);
|
---|
1215 | for (i = 0; p[i] != -1; i++) {
|
---|
1216 | if (BN_set_bit(a, p[i]) == 0)
|
---|
1217 | return 0;
|
---|
1218 | }
|
---|
1219 | bn_check_top(a);
|
---|
1220 |
|
---|
1221 | return 1;
|
---|
1222 | }
|
---|
1223 |
|
---|
1224 | #endif
|
---|