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1 /* ********************************************************************* |
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2 * |
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3 * Sun elects to have this file available under and governed by the |
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4 * Mozilla Public License Version 1.1 ("MPL") (see |
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5 * http://www.mozilla.org/MPL/ for full license text). For the avoidance |
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6 * of doubt and subject to the following, Sun also elects to allow |
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7 * licensees to use this file under the MPL, the GNU General Public |
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8 * License version 2 only or the Lesser General Public License version |
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9 * 2.1 only. Any references to the "GNU General Public License version 2 |
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10 * or later" or "GPL" in the following shall be construed to mean the |
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11 * GNU General Public License version 2 only. Any references to the "GNU |
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12 * Lesser General Public License version 2.1 or later" or "LGPL" in the |
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13 * following shall be construed to mean the GNU Lesser General Public |
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14 * License version 2.1 only. However, the following notice accompanied |
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15 * the original version of this file: |
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16 * |
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17 * Version: MPL 1.1/GPL 2.0/LGPL 2.1 |
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18 * |
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19 * The contents of this file are subject to the Mozilla Public License Version |
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20 * 1.1 (the "License"); you may not use this file except in compliance with |
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21 * the License. You may obtain a copy of the License at |
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22 * http://www.mozilla.org/MPL/ |
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23 * |
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24 * Software distributed under the License is distributed on an "AS IS" basis, |
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25 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License |
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26 * for the specific language governing rights and limitations under the |
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27 * License. |
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28 * |
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29 * The Original Code is the elliptic curve math library for binary polynomial field curves. |
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30 * |
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31 * The Initial Developer of the Original Code is |
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32 * Sun Microsystems, Inc. |
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33 * Portions created by the Initial Developer are Copyright (C) 2003 |
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34 * the Initial Developer. All Rights Reserved. |
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35 * |
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36 * Contributor(s): |
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37 * Sheueling Chang-Shantz <sheueling.chang@sun.com>, |
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38 * Stephen Fung <fungstep@hotmail.com>, and |
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39 * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories. |
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40 * |
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41 * Alternatively, the contents of this file may be used under the terms of |
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42 * either the GNU General Public License Version 2 or later (the "GPL"), or |
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43 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), |
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44 * in which case the provisions of the GPL or the LGPL are applicable instead |
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45 * of those above. If you wish to allow use of your version of this file only |
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46 * under the terms of either the GPL or the LGPL, and not to allow others to |
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47 * use your version of this file under the terms of the MPL, indicate your |
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48 * decision by deleting the provisions above and replace them with the notice |
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49 * and other provisions required by the GPL or the LGPL. If you do not delete |
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50 * the provisions above, a recipient may use your version of this file under |
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51 * the terms of any one of the MPL, the GPL or the LGPL. |
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52 * |
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53 *********************************************************************** */ |
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54 /* |
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55 * Copyright 2007 Sun Microsystems, Inc. All rights reserved. |
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56 * Use is subject to license terms. |
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57 */ |
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58 |
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59 #pragma ident "%Z%%M% %I% %E% SMI" |
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60 |
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61 #include "ec2.h" |
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62 #include "mplogic.h" |
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63 #include "mp_gf2m.h" |
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64 #ifndef _KERNEL |
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65 #include <stdlib.h> |
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66 #endif |
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67 |
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68 /* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery |
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69 * projective coordinates. Uses algorithm Mdouble in appendix of Lopez, J. |
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70 * and Dahab, R. "Fast multiplication on elliptic curves over GF(2^m) |
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71 * without precomputation". modified to not require precomputation of |
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72 * c=b^{2^{m-1}}. */ |
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73 static mp_err |
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74 gf2m_Mdouble(mp_int *x, mp_int *z, const ECGroup *group, int kmflag) |
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75 { |
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76 mp_err res = MP_OKAY; |
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77 mp_int t1; |
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78 |
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79 MP_DIGITS(&t1) = 0; |
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80 MP_CHECKOK(mp_init(&t1, kmflag)); |
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81 |
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82 MP_CHECKOK(group->meth->field_sqr(x, x, group->meth)); |
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83 MP_CHECKOK(group->meth->field_sqr(z, &t1, group->meth)); |
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84 MP_CHECKOK(group->meth->field_mul(x, &t1, z, group->meth)); |
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85 MP_CHECKOK(group->meth->field_sqr(x, x, group->meth)); |
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86 MP_CHECKOK(group->meth->field_sqr(&t1, &t1, group->meth)); |
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87 MP_CHECKOK(group->meth-> |
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88 field_mul(&group->curveb, &t1, &t1, group->meth)); |
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89 MP_CHECKOK(group->meth->field_add(x, &t1, x, group->meth)); |
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90 |
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91 CLEANUP: |
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92 mp_clear(&t1); |
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93 return res; |
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94 } |
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95 |
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96 /* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in |
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97 * Montgomery projective coordinates. Uses algorithm Madd in appendix of |
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98 * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over |
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99 * GF(2^m) without precomputation". */ |
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100 static mp_err |
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101 gf2m_Madd(const mp_int *x, mp_int *x1, mp_int *z1, mp_int *x2, mp_int *z2, |
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102 const ECGroup *group, int kmflag) |
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103 { |
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104 mp_err res = MP_OKAY; |
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105 mp_int t1, t2; |
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106 |
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107 MP_DIGITS(&t1) = 0; |
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108 MP_DIGITS(&t2) = 0; |
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109 MP_CHECKOK(mp_init(&t1, kmflag)); |
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110 MP_CHECKOK(mp_init(&t2, kmflag)); |
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111 |
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112 MP_CHECKOK(mp_copy(x, &t1)); |
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113 MP_CHECKOK(group->meth->field_mul(x1, z2, x1, group->meth)); |
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114 MP_CHECKOK(group->meth->field_mul(z1, x2, z1, group->meth)); |
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115 MP_CHECKOK(group->meth->field_mul(x1, z1, &t2, group->meth)); |
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116 MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth)); |
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117 MP_CHECKOK(group->meth->field_sqr(z1, z1, group->meth)); |
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118 MP_CHECKOK(group->meth->field_mul(z1, &t1, x1, group->meth)); |
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119 MP_CHECKOK(group->meth->field_add(x1, &t2, x1, group->meth)); |
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120 |
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121 CLEANUP: |
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122 mp_clear(&t1); |
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123 mp_clear(&t2); |
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124 return res; |
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125 } |
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126 |
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127 /* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) |
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128 * using Montgomery point multiplication algorithm Mxy() in appendix of |
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129 * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over |
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130 * GF(2^m) without precomputation". Returns: 0 on error 1 if return value |
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131 * should be the point at infinity 2 otherwise */ |
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132 static int |
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133 gf2m_Mxy(const mp_int *x, const mp_int *y, mp_int *x1, mp_int *z1, |
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134 mp_int *x2, mp_int *z2, const ECGroup *group) |
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135 { |
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136 mp_err res = MP_OKAY; |
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137 int ret = 0; |
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138 mp_int t3, t4, t5; |
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139 |
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140 MP_DIGITS(&t3) = 0; |
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141 MP_DIGITS(&t4) = 0; |
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142 MP_DIGITS(&t5) = 0; |
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143 MP_CHECKOK(mp_init(&t3, FLAG(x2))); |
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144 MP_CHECKOK(mp_init(&t4, FLAG(x2))); |
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145 MP_CHECKOK(mp_init(&t5, FLAG(x2))); |
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146 |
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147 if (mp_cmp_z(z1) == 0) { |
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148 mp_zero(x2); |
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149 mp_zero(z2); |
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150 ret = 1; |
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151 goto CLEANUP; |
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152 } |
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153 |
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154 if (mp_cmp_z(z2) == 0) { |
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155 MP_CHECKOK(mp_copy(x, x2)); |
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156 MP_CHECKOK(group->meth->field_add(x, y, z2, group->meth)); |
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157 ret = 2; |
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158 goto CLEANUP; |
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159 } |
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160 |
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161 MP_CHECKOK(mp_set_int(&t5, 1)); |
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162 if (group->meth->field_enc) { |
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163 MP_CHECKOK(group->meth->field_enc(&t5, &t5, group->meth)); |
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164 } |
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165 |
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166 MP_CHECKOK(group->meth->field_mul(z1, z2, &t3, group->meth)); |
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167 |
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168 MP_CHECKOK(group->meth->field_mul(z1, x, z1, group->meth)); |
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169 MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth)); |
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170 MP_CHECKOK(group->meth->field_mul(z2, x, z2, group->meth)); |
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171 MP_CHECKOK(group->meth->field_mul(z2, x1, x1, group->meth)); |
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172 MP_CHECKOK(group->meth->field_add(z2, x2, z2, group->meth)); |
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173 |
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174 MP_CHECKOK(group->meth->field_mul(z2, z1, z2, group->meth)); |
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175 MP_CHECKOK(group->meth->field_sqr(x, &t4, group->meth)); |
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176 MP_CHECKOK(group->meth->field_add(&t4, y, &t4, group->meth)); |
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177 MP_CHECKOK(group->meth->field_mul(&t4, &t3, &t4, group->meth)); |
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178 MP_CHECKOK(group->meth->field_add(&t4, z2, &t4, group->meth)); |
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179 |
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180 MP_CHECKOK(group->meth->field_mul(&t3, x, &t3, group->meth)); |
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181 MP_CHECKOK(group->meth->field_div(&t5, &t3, &t3, group->meth)); |
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182 MP_CHECKOK(group->meth->field_mul(&t3, &t4, &t4, group->meth)); |
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183 MP_CHECKOK(group->meth->field_mul(x1, &t3, x2, group->meth)); |
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184 MP_CHECKOK(group->meth->field_add(x2, x, z2, group->meth)); |
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185 |
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186 MP_CHECKOK(group->meth->field_mul(z2, &t4, z2, group->meth)); |
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187 MP_CHECKOK(group->meth->field_add(z2, y, z2, group->meth)); |
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188 |
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189 ret = 2; |
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190 |
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191 CLEANUP: |
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192 mp_clear(&t3); |
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193 mp_clear(&t4); |
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194 mp_clear(&t5); |
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195 if (res == MP_OKAY) { |
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196 return ret; |
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197 } else { |
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198 return 0; |
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199 } |
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200 } |
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201 |
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202 /* Computes R = nP based on algorithm 2P of Lopex, J. and Dahab, R. "Fast |
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203 * multiplication on elliptic curves over GF(2^m) without |
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204 * precomputation". Elliptic curve points P and R can be identical. Uses |
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205 * Montgomery projective coordinates. */ |
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206 mp_err |
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207 ec_GF2m_pt_mul_mont(const mp_int *n, const mp_int *px, const mp_int *py, |
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208 mp_int *rx, mp_int *ry, const ECGroup *group) |
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209 { |
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210 mp_err res = MP_OKAY; |
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211 mp_int x1, x2, z1, z2; |
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212 int i, j; |
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213 mp_digit top_bit, mask; |
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214 |
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215 MP_DIGITS(&x1) = 0; |
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216 MP_DIGITS(&x2) = 0; |
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217 MP_DIGITS(&z1) = 0; |
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218 MP_DIGITS(&z2) = 0; |
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219 MP_CHECKOK(mp_init(&x1, FLAG(n))); |
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220 MP_CHECKOK(mp_init(&x2, FLAG(n))); |
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221 MP_CHECKOK(mp_init(&z1, FLAG(n))); |
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222 MP_CHECKOK(mp_init(&z2, FLAG(n))); |
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223 |
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224 /* if result should be point at infinity */ |
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225 if ((mp_cmp_z(n) == 0) || (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES)) { |
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226 MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry)); |
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227 goto CLEANUP; |
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228 } |
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229 |
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230 MP_CHECKOK(mp_copy(px, &x1)); /* x1 = px */ |
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231 MP_CHECKOK(mp_set_int(&z1, 1)); /* z1 = 1 */ |
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232 MP_CHECKOK(group->meth->field_sqr(&x1, &z2, group->meth)); /* z2 = |
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233 * x1^2 = |
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234 * px^2 */ |
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235 MP_CHECKOK(group->meth->field_sqr(&z2, &x2, group->meth)); |
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236 MP_CHECKOK(group->meth->field_add(&x2, &group->curveb, &x2, group->meth)); /* x2 |
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237 * = |
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238 * px^4 |
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239 * + |
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240 * b |
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241 */ |
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242 |
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243 /* find top-most bit and go one past it */ |
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244 i = MP_USED(n) - 1; |
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245 j = MP_DIGIT_BIT - 1; |
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246 top_bit = 1; |
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247 top_bit <<= MP_DIGIT_BIT - 1; |
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248 mask = top_bit; |
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249 while (!(MP_DIGITS(n)[i] & mask)) { |
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250 mask >>= 1; |
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251 j--; |
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252 } |
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253 mask >>= 1; |
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254 j--; |
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255 |
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256 /* if top most bit was at word break, go to next word */ |
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257 if (!mask) { |
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258 i--; |
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259 j = MP_DIGIT_BIT - 1; |
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260 mask = top_bit; |
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261 } |
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262 |
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263 for (; i >= 0; i--) { |
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264 for (; j >= 0; j--) { |
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265 if (MP_DIGITS(n)[i] & mask) { |
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266 MP_CHECKOK(gf2m_Madd(px, &x1, &z1, &x2, &z2, group, FLAG(n))); |
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267 MP_CHECKOK(gf2m_Mdouble(&x2, &z2, group, FLAG(n))); |
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268 } else { |
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269 MP_CHECKOK(gf2m_Madd(px, &x2, &z2, &x1, &z1, group, FLAG(n))); |
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270 MP_CHECKOK(gf2m_Mdouble(&x1, &z1, group, FLAG(n))); |
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271 } |
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272 mask >>= 1; |
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273 } |
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274 j = MP_DIGIT_BIT - 1; |
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275 mask = top_bit; |
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276 } |
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277 |
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278 /* convert out of "projective" coordinates */ |
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279 i = gf2m_Mxy(px, py, &x1, &z1, &x2, &z2, group); |
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280 if (i == 0) { |
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281 res = MP_BADARG; |
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282 goto CLEANUP; |
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283 } else if (i == 1) { |
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284 MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry)); |
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285 } else { |
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286 MP_CHECKOK(mp_copy(&x2, rx)); |
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287 MP_CHECKOK(mp_copy(&z2, ry)); |
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288 } |
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289 |
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290 CLEANUP: |
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291 mp_clear(&x1); |
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292 mp_clear(&x2); |
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293 mp_clear(&z1); |
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294 mp_clear(&z2); |
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295 return res; |
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296 } |