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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 prime 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 * Bodo Moeller <moeller@cdc.informatik.tu-darmstadt.de>, |
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41 * Nils Larsch <nla@trustcenter.de>, and |
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42 * Lenka Fibikova <fibikova@exp-math.uni-essen.de>, the OpenSSL Project |
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43 * |
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44 * Alternatively, the contents of this file may be used under the terms of |
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45 * either the GNU General Public License Version 2 or later (the "GPL"), or |
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46 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), |
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47 * in which case the provisions of the GPL or the LGPL are applicable instead |
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48 * of those above. If you wish to allow use of your version of this file only |
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49 * under the terms of either the GPL or the LGPL, and not to allow others to |
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50 * use your version of this file under the terms of the MPL, indicate your |
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51 * decision by deleting the provisions above and replace them with the notice |
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52 * and other provisions required by the GPL or the LGPL. If you do not delete |
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53 * the provisions above, a recipient may use your version of this file under |
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54 * the terms of any one of the MPL, the GPL or the LGPL. |
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55 * |
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56 *********************************************************************** */ |
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57 /* |
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58 * Copyright 2007 Sun Microsystems, Inc. All rights reserved. |
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59 * Use is subject to license terms. |
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60 */ |
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61 |
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62 #pragma ident "%Z%%M% %I% %E% SMI" |
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63 |
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64 #include "ecp.h" |
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65 #include "mplogic.h" |
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66 #ifndef _KERNEL |
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67 #include <stdlib.h> |
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68 #endif |
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69 |
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70 /* Checks if point P(px, py) is at infinity. Uses affine coordinates. */ |
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71 mp_err |
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72 ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py) |
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73 { |
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74 |
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75 if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) { |
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76 return MP_YES; |
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77 } else { |
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78 return MP_NO; |
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79 } |
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80 |
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81 } |
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82 |
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83 /* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */ |
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84 mp_err |
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85 ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py) |
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86 { |
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87 mp_zero(px); |
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88 mp_zero(py); |
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89 return MP_OKAY; |
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90 } |
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91 |
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92 /* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P, |
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93 * Q, and R can all be identical. Uses affine coordinates. Assumes input |
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94 * is already field-encoded using field_enc, and returns output that is |
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95 * still field-encoded. */ |
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96 mp_err |
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97 ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx, |
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98 const mp_int *qy, mp_int *rx, mp_int *ry, |
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99 const ECGroup *group) |
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100 { |
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101 mp_err res = MP_OKAY; |
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102 mp_int lambda, temp, tempx, tempy; |
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103 |
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104 MP_DIGITS(&lambda) = 0; |
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105 MP_DIGITS(&temp) = 0; |
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106 MP_DIGITS(&tempx) = 0; |
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107 MP_DIGITS(&tempy) = 0; |
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108 MP_CHECKOK(mp_init(&lambda, FLAG(px))); |
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109 MP_CHECKOK(mp_init(&temp, FLAG(px))); |
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110 MP_CHECKOK(mp_init(&tempx, FLAG(px))); |
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111 MP_CHECKOK(mp_init(&tempy, FLAG(px))); |
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112 /* if P = inf, then R = Q */ |
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113 if (ec_GFp_pt_is_inf_aff(px, py) == 0) { |
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114 MP_CHECKOK(mp_copy(qx, rx)); |
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115 MP_CHECKOK(mp_copy(qy, ry)); |
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116 res = MP_OKAY; |
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117 goto CLEANUP; |
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118 } |
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119 /* if Q = inf, then R = P */ |
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120 if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) { |
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121 MP_CHECKOK(mp_copy(px, rx)); |
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122 MP_CHECKOK(mp_copy(py, ry)); |
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123 res = MP_OKAY; |
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124 goto CLEANUP; |
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125 } |
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126 /* if px != qx, then lambda = (py-qy) / (px-qx) */ |
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127 if (mp_cmp(px, qx) != 0) { |
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128 MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth)); |
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129 MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth)); |
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130 MP_CHECKOK(group->meth-> |
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131 field_div(&tempy, &tempx, &lambda, group->meth)); |
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132 } else { |
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133 /* if py != qy or qy = 0, then R = inf */ |
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134 if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) { |
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135 mp_zero(rx); |
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136 mp_zero(ry); |
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137 res = MP_OKAY; |
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138 goto CLEANUP; |
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139 } |
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140 /* lambda = (3qx^2+a) / (2qy) */ |
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141 MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth)); |
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142 MP_CHECKOK(mp_set_int(&temp, 3)); |
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143 if (group->meth->field_enc) { |
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144 MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth)); |
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145 } |
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146 MP_CHECKOK(group->meth-> |
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147 field_mul(&tempx, &temp, &tempx, group->meth)); |
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148 MP_CHECKOK(group->meth-> |
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149 field_add(&tempx, &group->curvea, &tempx, group->meth)); |
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150 MP_CHECKOK(mp_set_int(&temp, 2)); |
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151 if (group->meth->field_enc) { |
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152 MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth)); |
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153 } |
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154 MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth)); |
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155 MP_CHECKOK(group->meth-> |
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156 field_div(&tempx, &tempy, &lambda, group->meth)); |
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157 } |
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158 /* rx = lambda^2 - px - qx */ |
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159 MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth)); |
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160 MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth)); |
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161 MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth)); |
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162 /* ry = (x1-x2) * lambda - y1 */ |
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163 MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth)); |
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164 MP_CHECKOK(group->meth-> |
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165 field_mul(&tempy, &lambda, &tempy, group->meth)); |
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166 MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth)); |
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167 MP_CHECKOK(mp_copy(&tempx, rx)); |
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168 MP_CHECKOK(mp_copy(&tempy, ry)); |
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169 |
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170 CLEANUP: |
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171 mp_clear(&lambda); |
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172 mp_clear(&temp); |
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173 mp_clear(&tempx); |
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174 mp_clear(&tempy); |
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175 return res; |
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176 } |
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177 |
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178 /* Computes R = P - Q. Elliptic curve points P, Q, and R can all be |
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179 * identical. Uses affine coordinates. Assumes input is already |
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180 * field-encoded using field_enc, and returns output that is still |
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181 * field-encoded. */ |
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182 mp_err |
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183 ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx, |
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184 const mp_int *qy, mp_int *rx, mp_int *ry, |
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185 const ECGroup *group) |
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186 { |
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187 mp_err res = MP_OKAY; |
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188 mp_int nqy; |
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189 |
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190 MP_DIGITS(&nqy) = 0; |
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191 MP_CHECKOK(mp_init(&nqy, FLAG(px))); |
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192 /* nqy = -qy */ |
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193 MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth)); |
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194 res = group->point_add(px, py, qx, &nqy, rx, ry, group); |
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195 CLEANUP: |
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196 mp_clear(&nqy); |
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197 return res; |
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198 } |
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199 |
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200 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses |
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201 * affine coordinates. Assumes input is already field-encoded using |
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202 * field_enc, and returns output that is still field-encoded. */ |
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203 mp_err |
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204 ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx, |
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205 mp_int *ry, const ECGroup *group) |
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206 { |
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207 return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group); |
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208 } |
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209 |
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210 /* by default, this routine is unused and thus doesn't need to be compiled */ |
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211 #ifdef ECL_ENABLE_GFP_PT_MUL_AFF |
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212 /* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and |
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213 * R can be identical. Uses affine coordinates. Assumes input is already |
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214 * field-encoded using field_enc, and returns output that is still |
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215 * field-encoded. */ |
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216 mp_err |
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217 ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py, |
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218 mp_int *rx, mp_int *ry, const ECGroup *group) |
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219 { |
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220 mp_err res = MP_OKAY; |
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221 mp_int k, k3, qx, qy, sx, sy; |
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222 int b1, b3, i, l; |
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223 |
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224 MP_DIGITS(&k) = 0; |
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225 MP_DIGITS(&k3) = 0; |
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226 MP_DIGITS(&qx) = 0; |
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227 MP_DIGITS(&qy) = 0; |
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228 MP_DIGITS(&sx) = 0; |
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229 MP_DIGITS(&sy) = 0; |
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230 MP_CHECKOK(mp_init(&k)); |
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231 MP_CHECKOK(mp_init(&k3)); |
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232 MP_CHECKOK(mp_init(&qx)); |
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233 MP_CHECKOK(mp_init(&qy)); |
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234 MP_CHECKOK(mp_init(&sx)); |
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235 MP_CHECKOK(mp_init(&sy)); |
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236 |
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237 /* if n = 0 then r = inf */ |
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238 if (mp_cmp_z(n) == 0) { |
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239 mp_zero(rx); |
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240 mp_zero(ry); |
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241 res = MP_OKAY; |
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242 goto CLEANUP; |
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243 } |
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244 /* Q = P, k = n */ |
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245 MP_CHECKOK(mp_copy(px, &qx)); |
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246 MP_CHECKOK(mp_copy(py, &qy)); |
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247 MP_CHECKOK(mp_copy(n, &k)); |
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248 /* if n < 0 then Q = -Q, k = -k */ |
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249 if (mp_cmp_z(n) < 0) { |
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250 MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth)); |
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251 MP_CHECKOK(mp_neg(&k, &k)); |
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252 } |
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253 #ifdef ECL_DEBUG /* basic double and add method */ |
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254 l = mpl_significant_bits(&k) - 1; |
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255 MP_CHECKOK(mp_copy(&qx, &sx)); |
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256 MP_CHECKOK(mp_copy(&qy, &sy)); |
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257 for (i = l - 1; i >= 0; i--) { |
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258 /* S = 2S */ |
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259 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group)); |
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260 /* if k_i = 1, then S = S + Q */ |
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261 if (mpl_get_bit(&k, i) != 0) { |
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262 MP_CHECKOK(group-> |
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263 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group)); |
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264 } |
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265 } |
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266 #else /* double and add/subtract method from |
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267 * standard */ |
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268 /* k3 = 3 * k */ |
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269 MP_CHECKOK(mp_set_int(&k3, 3)); |
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270 MP_CHECKOK(mp_mul(&k, &k3, &k3)); |
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271 /* S = Q */ |
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272 MP_CHECKOK(mp_copy(&qx, &sx)); |
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273 MP_CHECKOK(mp_copy(&qy, &sy)); |
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274 /* l = index of high order bit in binary representation of 3*k */ |
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275 l = mpl_significant_bits(&k3) - 1; |
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276 /* for i = l-1 downto 1 */ |
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277 for (i = l - 1; i >= 1; i--) { |
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278 /* S = 2S */ |
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279 MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group)); |
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280 b3 = MP_GET_BIT(&k3, i); |
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281 b1 = MP_GET_BIT(&k, i); |
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282 /* if k3_i = 1 and k_i = 0, then S = S + Q */ |
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283 if ((b3 == 1) && (b1 == 0)) { |
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284 MP_CHECKOK(group-> |
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285 point_add(&sx, &sy, &qx, &qy, &sx, &sy, group)); |
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286 /* if k3_i = 0 and k_i = 1, then S = S - Q */ |
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287 } else if ((b3 == 0) && (b1 == 1)) { |
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288 MP_CHECKOK(group-> |
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289 point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group)); |
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290 } |
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291 } |
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292 #endif |
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293 /* output S */ |
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294 MP_CHECKOK(mp_copy(&sx, rx)); |
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295 MP_CHECKOK(mp_copy(&sy, ry)); |
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296 |
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297 CLEANUP: |
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298 mp_clear(&k); |
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299 mp_clear(&k3); |
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300 mp_clear(&qx); |
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301 mp_clear(&qy); |
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302 mp_clear(&sx); |
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303 mp_clear(&sy); |
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304 return res; |
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305 } |
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306 #endif |
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307 |
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308 /* Validates a point on a GFp curve. */ |
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309 mp_err |
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310 ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group) |
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311 { |
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312 mp_err res = MP_NO; |
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313 mp_int accl, accr, tmp, pxt, pyt; |
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314 |
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315 MP_DIGITS(&accl) = 0; |
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316 MP_DIGITS(&accr) = 0; |
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317 MP_DIGITS(&tmp) = 0; |
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318 MP_DIGITS(&pxt) = 0; |
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319 MP_DIGITS(&pyt) = 0; |
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320 MP_CHECKOK(mp_init(&accl, FLAG(px))); |
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321 MP_CHECKOK(mp_init(&accr, FLAG(px))); |
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322 MP_CHECKOK(mp_init(&tmp, FLAG(px))); |
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323 MP_CHECKOK(mp_init(&pxt, FLAG(px))); |
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324 MP_CHECKOK(mp_init(&pyt, FLAG(px))); |
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325 |
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326 /* 1: Verify that publicValue is not the point at infinity */ |
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327 if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) { |
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328 res = MP_NO; |
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329 goto CLEANUP; |
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330 } |
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331 /* 2: Verify that the coordinates of publicValue are elements |
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332 * of the field. |
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333 */ |
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334 if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) || |
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335 (MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) { |
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336 res = MP_NO; |
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337 goto CLEANUP; |
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338 } |
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339 /* 3: Verify that publicValue is on the curve. */ |
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340 if (group->meth->field_enc) { |
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341 group->meth->field_enc(px, &pxt, group->meth); |
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342 group->meth->field_enc(py, &pyt, group->meth); |
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343 } else { |
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344 mp_copy(px, &pxt); |
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345 mp_copy(py, &pyt); |
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346 } |
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347 /* left-hand side: y^2 */ |
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348 MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) ); |
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349 /* right-hand side: x^3 + a*x + b */ |
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350 MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) ); |
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351 MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) ); |
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352 MP_CHECKOK( group->meth->field_mul(&group->curvea, &pxt, &tmp, group->meth) ); |
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353 MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) ); |
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354 MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) ); |
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355 /* check LHS - RHS == 0 */ |
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356 MP_CHECKOK( group->meth->field_sub(&accl, &accr, &accr, group->meth) ); |
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357 if (mp_cmp_z(&accr) != 0) { |
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358 res = MP_NO; |
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359 goto CLEANUP; |
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360 } |
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361 /* 4: Verify that the order of the curve times the publicValue |
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362 * is the point at infinity. |
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363 */ |
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364 MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) ); |
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365 if (ec_GFp_pt_is_inf_aff(&pxt, &pyt) != MP_YES) { |
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366 res = MP_NO; |
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367 goto CLEANUP; |
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368 } |
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369 |
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370 res = MP_YES; |
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371 |
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372 CLEANUP: |
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373 mp_clear(&accl); |
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374 mp_clear(&accr); |
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375 mp_clear(&tmp); |
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376 mp_clear(&pxt); |
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377 mp_clear(&pyt); |
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378 return res; |
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379 } |