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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 163-bit curve. Assumes reduction |
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13 * polynomial with terms {163, 7, 6, 3, 0}. */ |
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14 mp_err |
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15 ec_GF2m_163_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) < 6) { |
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25 MP_CHECKOK(s_mp_pad(r, 6)); |
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26 } |
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27 u = MP_DIGITS(r); |
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28 MP_USED(r) = 6; |
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29 |
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30 /* u[5] only has 6 significant bits */ |
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31 z = u[5]; |
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32 u[2] ^= (z << 36) ^ (z << 35) ^ (z << 32) ^ (z << 29); |
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33 z = u[4]; |
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34 u[2] ^= (z >> 28) ^ (z >> 29) ^ (z >> 32) ^ (z >> 35); |
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35 u[1] ^= (z << 36) ^ (z << 35) ^ (z << 32) ^ (z << 29); |
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36 z = u[3]; |
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37 u[1] ^= (z >> 28) ^ (z >> 29) ^ (z >> 32) ^ (z >> 35); |
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38 u[0] ^= (z << 36) ^ (z << 35) ^ (z << 32) ^ (z << 29); |
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39 z = u[2] >> 35; /* z only has 29 significant bits */ |
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40 u[0] ^= (z << 7) ^ (z << 6) ^ (z << 3) ^ z; |
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41 /* clear bits above 163 */ |
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42 u[5] = u[4] = u[3] = 0; |
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43 u[2] ^= z << 35; |
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44 #else |
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45 if (MP_USED(r) < 11) { |
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46 MP_CHECKOK(s_mp_pad(r, 11)); |
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47 } |
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48 u = MP_DIGITS(r); |
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49 MP_USED(r) = 11; |
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50 |
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51 /* u[11] only has 6 significant bits */ |
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52 z = u[10]; |
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53 u[5] ^= (z << 4) ^ (z << 3) ^ z ^ (z >> 3); |
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54 u[4] ^= (z << 29); |
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55 z = u[9]; |
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56 u[5] ^= (z >> 28) ^ (z >> 29); |
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57 u[4] ^= (z << 4) ^ (z << 3) ^ z ^ (z >> 3); |
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58 u[3] ^= (z << 29); |
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59 z = u[8]; |
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60 u[4] ^= (z >> 28) ^ (z >> 29); |
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61 u[3] ^= (z << 4) ^ (z << 3) ^ z ^ (z >> 3); |
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62 u[2] ^= (z << 29); |
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63 z = u[7]; |
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64 u[3] ^= (z >> 28) ^ (z >> 29); |
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65 u[2] ^= (z << 4) ^ (z << 3) ^ z ^ (z >> 3); |
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66 u[1] ^= (z << 29); |
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67 z = u[6]; |
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68 u[2] ^= (z >> 28) ^ (z >> 29); |
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69 u[1] ^= (z << 4) ^ (z << 3) ^ z ^ (z >> 3); |
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70 u[0] ^= (z << 29); |
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71 z = u[5] >> 3; /* z only has 29 significant bits */ |
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72 u[1] ^= (z >> 25) ^ (z >> 26); |
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73 u[0] ^= (z << 7) ^ (z << 6) ^ (z << 3) ^ z; |
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74 /* clear bits above 163 */ |
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75 u[11] = u[10] = u[9] = u[8] = u[7] = u[6] = 0; |
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76 u[5] ^= z << 3; |
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77 #endif |
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78 s_mp_clamp(r); |
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79 |
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80 CLEANUP: |
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81 return res; |
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82 } |
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83 |
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84 /* Fast squaring for polynomials over a 163-bit curve. Assumes reduction |
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85 * polynomial with terms {163, 7, 6, 3, 0}. */ |
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86 mp_err |
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87 ec_GF2m_163_sqr(const mp_int *a, mp_int *r, const GFMethod *meth) |
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88 { |
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89 mp_err res = MP_OKAY; |
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90 mp_digit *u, *v; |
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91 |
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92 v = MP_DIGITS(a); |
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93 |
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94 #ifdef ECL_SIXTY_FOUR_BIT |
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95 if (MP_USED(a) < 3) { |
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96 return mp_bsqrmod(a, meth->irr_arr, r); |
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97 } |
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98 if (MP_USED(r) < 6) { |
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99 MP_CHECKOK(s_mp_pad(r, 6)); |
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100 } |
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101 MP_USED(r) = 6; |
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102 #else |
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103 if (MP_USED(a) < 6) { |
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104 return mp_bsqrmod(a, meth->irr_arr, r); |
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105 } |
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106 if (MP_USED(r) < 12) { |
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107 MP_CHECKOK(s_mp_pad(r, 12)); |
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108 } |
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109 MP_USED(r) = 12; |
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110 #endif |
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111 u = MP_DIGITS(r); |
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112 |
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113 #ifdef ECL_THIRTY_TWO_BIT |
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114 u[11] = gf2m_SQR1(v[5]); |
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115 u[10] = gf2m_SQR0(v[5]); |
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116 u[9] = gf2m_SQR1(v[4]); |
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117 u[8] = gf2m_SQR0(v[4]); |
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118 u[7] = gf2m_SQR1(v[3]); |
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119 u[6] = gf2m_SQR0(v[3]); |
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120 #endif |
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121 u[5] = gf2m_SQR1(v[2]); |
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122 u[4] = gf2m_SQR0(v[2]); |
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123 u[3] = gf2m_SQR1(v[1]); |
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124 u[2] = gf2m_SQR0(v[1]); |
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125 u[1] = gf2m_SQR1(v[0]); |
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126 u[0] = gf2m_SQR0(v[0]); |
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127 return ec_GF2m_163_mod(r, r, meth); |
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128 |
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129 CLEANUP: |
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130 return res; |
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131 } |
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132 |
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133 /* Fast multiplication for polynomials over a 163-bit curve. Assumes |
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134 * reduction polynomial with terms {163, 7, 6, 3, 0}. */ |
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135 mp_err |
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136 ec_GF2m_163_mul(const mp_int *a, const mp_int *b, mp_int *r, |
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137 const GFMethod *meth) |
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138 { |
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139 mp_err res = MP_OKAY; |
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140 mp_digit a2 = 0, a1 = 0, a0, b2 = 0, b1 = 0, b0; |
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141 |
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142 #ifdef ECL_THIRTY_TWO_BIT |
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143 mp_digit a5 = 0, a4 = 0, a3 = 0, b5 = 0, b4 = 0, b3 = 0; |
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144 mp_digit rm[6]; |
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145 #endif |
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146 |
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147 if (a == b) { |
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148 return ec_GF2m_163_sqr(a, r, meth); |
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149 } else { |
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150 switch (MP_USED(a)) { |
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151 #ifdef ECL_THIRTY_TWO_BIT |
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152 case 6: |
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153 a5 = MP_DIGIT(a, 5); |
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154 case 5: |
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155 a4 = MP_DIGIT(a, 4); |
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156 case 4: |
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157 a3 = MP_DIGIT(a, 3); |
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158 #endif |
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159 case 3: |
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160 a2 = MP_DIGIT(a, 2); |
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161 case 2: |
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162 a1 = MP_DIGIT(a, 1); |
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163 default: |
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164 a0 = MP_DIGIT(a, 0); |
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165 } |
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166 switch (MP_USED(b)) { |
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167 #ifdef ECL_THIRTY_TWO_BIT |
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168 case 6: |
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169 b5 = MP_DIGIT(b, 5); |
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170 case 5: |
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171 b4 = MP_DIGIT(b, 4); |
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172 case 4: |
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173 b3 = MP_DIGIT(b, 3); |
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174 #endif |
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175 case 3: |
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176 b2 = MP_DIGIT(b, 2); |
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177 case 2: |
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178 b1 = MP_DIGIT(b, 1); |
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179 default: |
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180 b0 = MP_DIGIT(b, 0); |
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181 } |
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182 #ifdef ECL_SIXTY_FOUR_BIT |
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183 MP_CHECKOK(s_mp_pad(r, 6)); |
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184 s_bmul_3x3(MP_DIGITS(r), a2, a1, a0, b2, b1, b0); |
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185 MP_USED(r) = 6; |
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186 s_mp_clamp(r); |
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187 #else |
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188 MP_CHECKOK(s_mp_pad(r, 12)); |
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189 s_bmul_3x3(MP_DIGITS(r) + 6, a5, a4, a3, b5, b4, b3); |
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190 s_bmul_3x3(MP_DIGITS(r), a2, a1, a0, b2, b1, b0); |
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191 s_bmul_3x3(rm, a5 ^ a2, a4 ^ a1, a3 ^ a0, b5 ^ b2, b4 ^ b1, |
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192 b3 ^ b0); |
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193 rm[5] ^= MP_DIGIT(r, 5) ^ MP_DIGIT(r, 11); |
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194 rm[4] ^= MP_DIGIT(r, 4) ^ MP_DIGIT(r, 10); |
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195 rm[3] ^= MP_DIGIT(r, 3) ^ MP_DIGIT(r, 9); |
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196 rm[2] ^= MP_DIGIT(r, 2) ^ MP_DIGIT(r, 8); |
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197 rm[1] ^= MP_DIGIT(r, 1) ^ MP_DIGIT(r, 7); |
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198 rm[0] ^= MP_DIGIT(r, 0) ^ MP_DIGIT(r, 6); |
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199 MP_DIGIT(r, 8) ^= rm[5]; |
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200 MP_DIGIT(r, 7) ^= rm[4]; |
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201 MP_DIGIT(r, 6) ^= rm[3]; |
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202 MP_DIGIT(r, 5) ^= rm[2]; |
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203 MP_DIGIT(r, 4) ^= rm[1]; |
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204 MP_DIGIT(r, 3) ^= rm[0]; |
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205 MP_USED(r) = 12; |
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206 s_mp_clamp(r); |
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207 #endif |
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208 return ec_GF2m_163_mod(r, r, meth); |
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209 } |
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210 |
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211 CLEANUP: |
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212 return res; |
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213 } |
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214 |
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215 /* Wire in fast field arithmetic for 163-bit curves. */ |
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216 mp_err |
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217 ec_group_set_gf2m163(ECGroup *group, ECCurveName name) |
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218 { |
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219 group->meth->field_mod = &ec_GF2m_163_mod; |
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220 group->meth->field_mul = &ec_GF2m_163_mul; |
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221 group->meth->field_sqr = &ec_GF2m_163_sqr; |
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222 return MP_OKAY; |
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223 } |