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1 /* This Source Code Form is subject to the terms of the Mozilla Public |
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2 * License, v. 2.0. If a copy of the MPL was not distributed with this |
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3 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ |
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4 |
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5 #include "ec2.h" |
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6 #include "mp_gf2m.h" |
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7 #include "mp_gf2m-priv.h" |
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8 #include "mpi.h" |
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9 #include "mpi-priv.h" |
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10 #include <stdlib.h> |
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11 |
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12 /* Fast reduction for polynomials over a 233-bit curve. Assumes reduction |
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13 * polynomial with terms {233, 74, 0}. */ |
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14 mp_err |
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15 ec_GF2m_233_mod(const mp_int *a, mp_int *r, const GFMethod *meth) |
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16 { |
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17 mp_err res = MP_OKAY; |
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18 mp_digit *u, z; |
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19 |
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20 if (a != r) { |
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21 MP_CHECKOK(mp_copy(a, r)); |
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22 } |
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23 #ifdef ECL_SIXTY_FOUR_BIT |
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24 if (MP_USED(r) < 8) { |
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25 MP_CHECKOK(s_mp_pad(r, 8)); |
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26 } |
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27 u = MP_DIGITS(r); |
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28 MP_USED(r) = 8; |
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29 |
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30 /* u[7] only has 18 significant bits */ |
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31 z = u[7]; |
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32 u[4] ^= (z << 33) ^ (z >> 41); |
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33 u[3] ^= (z << 23); |
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34 z = u[6]; |
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35 u[4] ^= (z >> 31); |
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36 u[3] ^= (z << 33) ^ (z >> 41); |
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37 u[2] ^= (z << 23); |
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38 z = u[5]; |
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39 u[3] ^= (z >> 31); |
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40 u[2] ^= (z << 33) ^ (z >> 41); |
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41 u[1] ^= (z << 23); |
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42 z = u[4]; |
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43 u[2] ^= (z >> 31); |
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44 u[1] ^= (z << 33) ^ (z >> 41); |
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45 u[0] ^= (z << 23); |
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46 z = u[3] >> 41; /* z only has 23 significant bits */ |
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47 u[1] ^= (z << 10); |
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48 u[0] ^= z; |
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49 /* clear bits above 233 */ |
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50 u[7] = u[6] = u[5] = u[4] = 0; |
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51 u[3] ^= z << 41; |
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52 #else |
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53 if (MP_USED(r) < 15) { |
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54 MP_CHECKOK(s_mp_pad(r, 15)); |
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55 } |
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56 u = MP_DIGITS(r); |
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57 MP_USED(r) = 15; |
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58 |
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59 /* u[14] only has 18 significant bits */ |
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60 z = u[14]; |
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61 u[9] ^= (z << 1); |
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62 u[7] ^= (z >> 9); |
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63 u[6] ^= (z << 23); |
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64 z = u[13]; |
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65 u[9] ^= (z >> 31); |
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66 u[8] ^= (z << 1); |
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67 u[6] ^= (z >> 9); |
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68 u[5] ^= (z << 23); |
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69 z = u[12]; |
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70 u[8] ^= (z >> 31); |
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71 u[7] ^= (z << 1); |
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72 u[5] ^= (z >> 9); |
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73 u[4] ^= (z << 23); |
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74 z = u[11]; |
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75 u[7] ^= (z >> 31); |
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76 u[6] ^= (z << 1); |
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77 u[4] ^= (z >> 9); |
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78 u[3] ^= (z << 23); |
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79 z = u[10]; |
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80 u[6] ^= (z >> 31); |
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81 u[5] ^= (z << 1); |
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82 u[3] ^= (z >> 9); |
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83 u[2] ^= (z << 23); |
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84 z = u[9]; |
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85 u[5] ^= (z >> 31); |
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86 u[4] ^= (z << 1); |
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87 u[2] ^= (z >> 9); |
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88 u[1] ^= (z << 23); |
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89 z = u[8]; |
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90 u[4] ^= (z >> 31); |
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91 u[3] ^= (z << 1); |
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92 u[1] ^= (z >> 9); |
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93 u[0] ^= (z << 23); |
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94 z = u[7] >> 9; /* z only has 23 significant bits */ |
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95 u[3] ^= (z >> 22); |
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96 u[2] ^= (z << 10); |
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97 u[0] ^= z; |
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98 /* clear bits above 233 */ |
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99 u[14] = u[13] = u[12] = u[11] = u[10] = u[9] = u[8] = 0; |
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100 u[7] ^= z << 9; |
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101 #endif |
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102 s_mp_clamp(r); |
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103 |
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104 CLEANUP: |
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105 return res; |
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106 } |
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107 |
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108 /* Fast squaring for polynomials over a 233-bit curve. Assumes reduction |
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109 * polynomial with terms {233, 74, 0}. */ |
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110 mp_err |
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111 ec_GF2m_233_sqr(const mp_int *a, mp_int *r, const GFMethod *meth) |
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112 { |
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113 mp_err res = MP_OKAY; |
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114 mp_digit *u, *v; |
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115 |
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116 v = MP_DIGITS(a); |
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117 |
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118 #ifdef ECL_SIXTY_FOUR_BIT |
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119 if (MP_USED(a) < 4) { |
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120 return mp_bsqrmod(a, meth->irr_arr, r); |
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121 } |
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122 if (MP_USED(r) < 8) { |
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123 MP_CHECKOK(s_mp_pad(r, 8)); |
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124 } |
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125 MP_USED(r) = 8; |
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126 #else |
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127 if (MP_USED(a) < 8) { |
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128 return mp_bsqrmod(a, meth->irr_arr, r); |
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129 } |
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130 if (MP_USED(r) < 15) { |
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131 MP_CHECKOK(s_mp_pad(r, 15)); |
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132 } |
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133 MP_USED(r) = 15; |
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134 #endif |
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135 u = MP_DIGITS(r); |
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136 |
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137 #ifdef ECL_THIRTY_TWO_BIT |
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138 u[14] = gf2m_SQR0(v[7]); |
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139 u[13] = gf2m_SQR1(v[6]); |
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140 u[12] = gf2m_SQR0(v[6]); |
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141 u[11] = gf2m_SQR1(v[5]); |
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142 u[10] = gf2m_SQR0(v[5]); |
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143 u[9] = gf2m_SQR1(v[4]); |
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144 u[8] = gf2m_SQR0(v[4]); |
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145 #endif |
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146 u[7] = gf2m_SQR1(v[3]); |
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147 u[6] = gf2m_SQR0(v[3]); |
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148 u[5] = gf2m_SQR1(v[2]); |
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149 u[4] = gf2m_SQR0(v[2]); |
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150 u[3] = gf2m_SQR1(v[1]); |
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151 u[2] = gf2m_SQR0(v[1]); |
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152 u[1] = gf2m_SQR1(v[0]); |
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153 u[0] = gf2m_SQR0(v[0]); |
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154 return ec_GF2m_233_mod(r, r, meth); |
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155 |
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156 CLEANUP: |
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157 return res; |
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158 } |
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159 |
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160 /* Fast multiplication for polynomials over a 233-bit curve. Assumes |
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161 * reduction polynomial with terms {233, 74, 0}. */ |
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162 mp_err |
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163 ec_GF2m_233_mul(const mp_int *a, const mp_int *b, mp_int *r, |
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164 const GFMethod *meth) |
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165 { |
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166 mp_err res = MP_OKAY; |
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167 mp_digit a3 = 0, a2 = 0, a1 = 0, a0, b3 = 0, b2 = 0, b1 = 0, b0; |
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168 |
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169 #ifdef ECL_THIRTY_TWO_BIT |
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170 mp_digit a7 = 0, a6 = 0, a5 = 0, a4 = 0, b7 = 0, b6 = 0, b5 = 0, b4 = |
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171 0; |
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172 mp_digit rm[8]; |
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173 #endif |
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174 |
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175 if (a == b) { |
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176 return ec_GF2m_233_sqr(a, r, meth); |
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177 } else { |
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178 switch (MP_USED(a)) { |
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179 #ifdef ECL_THIRTY_TWO_BIT |
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180 case 8: |
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181 a7 = MP_DIGIT(a, 7); |
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182 case 7: |
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183 a6 = MP_DIGIT(a, 6); |
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184 case 6: |
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185 a5 = MP_DIGIT(a, 5); |
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186 case 5: |
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187 a4 = MP_DIGIT(a, 4); |
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188 #endif |
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189 case 4: |
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190 a3 = MP_DIGIT(a, 3); |
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191 case 3: |
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192 a2 = MP_DIGIT(a, 2); |
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193 case 2: |
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194 a1 = MP_DIGIT(a, 1); |
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195 default: |
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196 a0 = MP_DIGIT(a, 0); |
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197 } |
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198 switch (MP_USED(b)) { |
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199 #ifdef ECL_THIRTY_TWO_BIT |
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200 case 8: |
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201 b7 = MP_DIGIT(b, 7); |
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202 case 7: |
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203 b6 = MP_DIGIT(b, 6); |
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204 case 6: |
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205 b5 = MP_DIGIT(b, 5); |
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206 case 5: |
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207 b4 = MP_DIGIT(b, 4); |
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208 #endif |
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209 case 4: |
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210 b3 = MP_DIGIT(b, 3); |
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211 case 3: |
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212 b2 = MP_DIGIT(b, 2); |
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213 case 2: |
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214 b1 = MP_DIGIT(b, 1); |
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215 default: |
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216 b0 = MP_DIGIT(b, 0); |
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217 } |
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218 #ifdef ECL_SIXTY_FOUR_BIT |
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219 MP_CHECKOK(s_mp_pad(r, 8)); |
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220 s_bmul_4x4(MP_DIGITS(r), a3, a2, a1, a0, b3, b2, b1, b0); |
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221 MP_USED(r) = 8; |
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222 s_mp_clamp(r); |
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223 #else |
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224 MP_CHECKOK(s_mp_pad(r, 16)); |
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225 s_bmul_4x4(MP_DIGITS(r) + 8, a7, a6, a5, a4, b7, b6, b5, b4); |
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226 s_bmul_4x4(MP_DIGITS(r), a3, a2, a1, a0, b3, b2, b1, b0); |
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227 s_bmul_4x4(rm, a7 ^ a3, a6 ^ a2, a5 ^ a1, a4 ^ a0, b7 ^ b3, |
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228 b6 ^ b2, b5 ^ b1, b4 ^ b0); |
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229 rm[7] ^= MP_DIGIT(r, 7) ^ MP_DIGIT(r, 15); |
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230 rm[6] ^= MP_DIGIT(r, 6) ^ MP_DIGIT(r, 14); |
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231 rm[5] ^= MP_DIGIT(r, 5) ^ MP_DIGIT(r, 13); |
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232 rm[4] ^= MP_DIGIT(r, 4) ^ MP_DIGIT(r, 12); |
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233 rm[3] ^= MP_DIGIT(r, 3) ^ MP_DIGIT(r, 11); |
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234 rm[2] ^= MP_DIGIT(r, 2) ^ MP_DIGIT(r, 10); |
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235 rm[1] ^= MP_DIGIT(r, 1) ^ MP_DIGIT(r, 9); |
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236 rm[0] ^= MP_DIGIT(r, 0) ^ MP_DIGIT(r, 8); |
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237 MP_DIGIT(r, 11) ^= rm[7]; |
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238 MP_DIGIT(r, 10) ^= rm[6]; |
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239 MP_DIGIT(r, 9) ^= rm[5]; |
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240 MP_DIGIT(r, 8) ^= rm[4]; |
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241 MP_DIGIT(r, 7) ^= rm[3]; |
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242 MP_DIGIT(r, 6) ^= rm[2]; |
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243 MP_DIGIT(r, 5) ^= rm[1]; |
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244 MP_DIGIT(r, 4) ^= rm[0]; |
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245 MP_USED(r) = 16; |
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246 s_mp_clamp(r); |
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247 #endif |
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248 return ec_GF2m_233_mod(r, r, meth); |
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249 } |
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250 |
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251 CLEANUP: |
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252 return res; |
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253 } |
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254 |
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255 /* Wire in fast field arithmetic for 233-bit curves. */ |
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256 mp_err |
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257 ec_group_set_gf2m233(ECGroup *group, ECCurveName name) |
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258 { |
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259 group->meth->field_mod = &ec_GF2m_233_mod; |
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260 group->meth->field_mul = &ec_GF2m_233_mul; |
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261 group->meth->field_sqr = &ec_GF2m_233_sqr; |
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262 return MP_OKAY; |
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263 } |