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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 * Douglas Stebila <douglas@stebila.ca> |
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38 * |
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39 * Alternatively, the contents of this file may be used under the terms of |
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40 * either the GNU General Public License Version 2 or later (the "GPL"), or |
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41 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), |
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42 * in which case the provisions of the GPL or the LGPL are applicable instead |
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43 * of those above. If you wish to allow use of your version of this file only |
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44 * under the terms of either the GPL or the LGPL, and not to allow others to |
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45 * use your version of this file under the terms of the MPL, indicate your |
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46 * decision by deleting the provisions above and replace them with the notice |
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47 * and other provisions required by the GPL or the LGPL. If you do not delete |
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48 * the provisions above, a recipient may use your version of this file under |
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49 * the terms of any one of the MPL, the GPL or the LGPL. |
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50 * |
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51 *********************************************************************** */ |
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52 /* |
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53 * Copyright 2007 Sun Microsystems, Inc. All rights reserved. |
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54 * Use is subject to license terms. |
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55 */ |
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56 |
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57 #pragma ident "%Z%%M% %I% %E% SMI" |
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58 |
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59 #include "ecp.h" |
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60 #include "mpi.h" |
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61 #include "mplogic.h" |
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62 #include "mpi-priv.h" |
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63 #ifndef _KERNEL |
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64 #include <stdlib.h> |
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65 #endif |
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66 |
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67 /* Fast modular reduction for p256 = 2^256 - 2^224 + 2^192+ 2^96 - 1. a can be r. |
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68 * Uses algorithm 2.29 from Hankerson, Menezes, Vanstone. Guide to |
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69 * Elliptic Curve Cryptography. */ |
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70 mp_err |
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71 ec_GFp_nistp256_mod(const mp_int *a, mp_int *r, const GFMethod *meth) |
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72 { |
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73 mp_err res = MP_OKAY; |
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74 mp_size a_used = MP_USED(a); |
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75 int a_bits = mpl_significant_bits(a); |
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76 mp_digit carry; |
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77 |
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78 #ifdef ECL_THIRTY_TWO_BIT |
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79 mp_digit a8=0, a9=0, a10=0, a11=0, a12=0, a13=0, a14=0, a15=0; |
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80 mp_digit r0, r1, r2, r3, r4, r5, r6, r7; |
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81 int r8; /* must be a signed value ! */ |
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82 #else |
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83 mp_digit a4=0, a5=0, a6=0, a7=0; |
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84 mp_digit a4h, a4l, a5h, a5l, a6h, a6l, a7h, a7l; |
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85 mp_digit r0, r1, r2, r3; |
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86 int r4; /* must be a signed value ! */ |
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87 #endif |
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88 /* for polynomials larger than twice the field size |
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89 * use regular reduction */ |
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90 if (a_bits < 256) { |
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91 if (a == r) return MP_OKAY; |
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92 return mp_copy(a,r); |
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93 } |
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94 if (a_bits > 512) { |
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95 MP_CHECKOK(mp_mod(a, &meth->irr, r)); |
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96 } else { |
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97 |
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98 #ifdef ECL_THIRTY_TWO_BIT |
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99 switch (a_used) { |
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100 case 16: |
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101 a15 = MP_DIGIT(a,15); |
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102 case 15: |
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103 a14 = MP_DIGIT(a,14); |
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104 case 14: |
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105 a13 = MP_DIGIT(a,13); |
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106 case 13: |
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107 a12 = MP_DIGIT(a,12); |
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108 case 12: |
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109 a11 = MP_DIGIT(a,11); |
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110 case 11: |
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111 a10 = MP_DIGIT(a,10); |
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112 case 10: |
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113 a9 = MP_DIGIT(a,9); |
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114 case 9: |
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115 a8 = MP_DIGIT(a,8); |
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116 } |
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117 |
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118 r0 = MP_DIGIT(a,0); |
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119 r1 = MP_DIGIT(a,1); |
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120 r2 = MP_DIGIT(a,2); |
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121 r3 = MP_DIGIT(a,3); |
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122 r4 = MP_DIGIT(a,4); |
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123 r5 = MP_DIGIT(a,5); |
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124 r6 = MP_DIGIT(a,6); |
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125 r7 = MP_DIGIT(a,7); |
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126 |
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127 /* sum 1 */ |
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128 MP_ADD_CARRY(r3, a11, r3, 0, carry); |
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129 MP_ADD_CARRY(r4, a12, r4, carry, carry); |
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130 MP_ADD_CARRY(r5, a13, r5, carry, carry); |
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131 MP_ADD_CARRY(r6, a14, r6, carry, carry); |
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132 MP_ADD_CARRY(r7, a15, r7, carry, carry); |
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133 r8 = carry; |
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134 MP_ADD_CARRY(r3, a11, r3, 0, carry); |
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135 MP_ADD_CARRY(r4, a12, r4, carry, carry); |
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136 MP_ADD_CARRY(r5, a13, r5, carry, carry); |
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137 MP_ADD_CARRY(r6, a14, r6, carry, carry); |
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138 MP_ADD_CARRY(r7, a15, r7, carry, carry); |
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139 r8 += carry; |
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140 /* sum 2 */ |
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141 MP_ADD_CARRY(r3, a12, r3, 0, carry); |
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142 MP_ADD_CARRY(r4, a13, r4, carry, carry); |
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143 MP_ADD_CARRY(r5, a14, r5, carry, carry); |
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144 MP_ADD_CARRY(r6, a15, r6, carry, carry); |
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145 MP_ADD_CARRY(r7, 0, r7, carry, carry); |
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146 r8 += carry; |
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147 /* combine last bottom of sum 3 with second sum 2 */ |
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148 MP_ADD_CARRY(r0, a8, r0, 0, carry); |
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149 MP_ADD_CARRY(r1, a9, r1, carry, carry); |
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150 MP_ADD_CARRY(r2, a10, r2, carry, carry); |
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151 MP_ADD_CARRY(r3, a12, r3, carry, carry); |
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152 MP_ADD_CARRY(r4, a13, r4, carry, carry); |
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153 MP_ADD_CARRY(r5, a14, r5, carry, carry); |
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154 MP_ADD_CARRY(r6, a15, r6, carry, carry); |
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155 MP_ADD_CARRY(r7, a15, r7, carry, carry); /* from sum 3 */ |
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156 r8 += carry; |
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157 /* sum 3 (rest of it)*/ |
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158 MP_ADD_CARRY(r6, a14, r6, 0, carry); |
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159 MP_ADD_CARRY(r7, 0, r7, carry, carry); |
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160 r8 += carry; |
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161 /* sum 4 (rest of it)*/ |
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162 MP_ADD_CARRY(r0, a9, r0, 0, carry); |
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163 MP_ADD_CARRY(r1, a10, r1, carry, carry); |
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164 MP_ADD_CARRY(r2, a11, r2, carry, carry); |
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165 MP_ADD_CARRY(r3, a13, r3, carry, carry); |
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166 MP_ADD_CARRY(r4, a14, r4, carry, carry); |
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167 MP_ADD_CARRY(r5, a15, r5, carry, carry); |
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168 MP_ADD_CARRY(r6, a13, r6, carry, carry); |
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169 MP_ADD_CARRY(r7, a8, r7, carry, carry); |
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170 r8 += carry; |
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171 /* diff 5 */ |
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172 MP_SUB_BORROW(r0, a11, r0, 0, carry); |
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173 MP_SUB_BORROW(r1, a12, r1, carry, carry); |
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174 MP_SUB_BORROW(r2, a13, r2, carry, carry); |
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175 MP_SUB_BORROW(r3, 0, r3, carry, carry); |
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176 MP_SUB_BORROW(r4, 0, r4, carry, carry); |
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177 MP_SUB_BORROW(r5, 0, r5, carry, carry); |
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178 MP_SUB_BORROW(r6, a8, r6, carry, carry); |
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179 MP_SUB_BORROW(r7, a10, r7, carry, carry); |
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180 r8 -= carry; |
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181 /* diff 6 */ |
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182 MP_SUB_BORROW(r0, a12, r0, 0, carry); |
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183 MP_SUB_BORROW(r1, a13, r1, carry, carry); |
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184 MP_SUB_BORROW(r2, a14, r2, carry, carry); |
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185 MP_SUB_BORROW(r3, a15, r3, carry, carry); |
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186 MP_SUB_BORROW(r4, 0, r4, carry, carry); |
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187 MP_SUB_BORROW(r5, 0, r5, carry, carry); |
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188 MP_SUB_BORROW(r6, a9, r6, carry, carry); |
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189 MP_SUB_BORROW(r7, a11, r7, carry, carry); |
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190 r8 -= carry; |
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191 /* diff 7 */ |
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192 MP_SUB_BORROW(r0, a13, r0, 0, carry); |
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193 MP_SUB_BORROW(r1, a14, r1, carry, carry); |
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194 MP_SUB_BORROW(r2, a15, r2, carry, carry); |
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195 MP_SUB_BORROW(r3, a8, r3, carry, carry); |
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196 MP_SUB_BORROW(r4, a9, r4, carry, carry); |
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197 MP_SUB_BORROW(r5, a10, r5, carry, carry); |
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198 MP_SUB_BORROW(r6, 0, r6, carry, carry); |
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199 MP_SUB_BORROW(r7, a12, r7, carry, carry); |
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200 r8 -= carry; |
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201 /* diff 8 */ |
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202 MP_SUB_BORROW(r0, a14, r0, 0, carry); |
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203 MP_SUB_BORROW(r1, a15, r1, carry, carry); |
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204 MP_SUB_BORROW(r2, 0, r2, carry, carry); |
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205 MP_SUB_BORROW(r3, a9, r3, carry, carry); |
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206 MP_SUB_BORROW(r4, a10, r4, carry, carry); |
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207 MP_SUB_BORROW(r5, a11, r5, carry, carry); |
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208 MP_SUB_BORROW(r6, 0, r6, carry, carry); |
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209 MP_SUB_BORROW(r7, a13, r7, carry, carry); |
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210 r8 -= carry; |
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211 |
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212 /* reduce the overflows */ |
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213 while (r8 > 0) { |
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214 mp_digit r8_d = r8; |
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215 MP_ADD_CARRY(r0, r8_d, r0, 0, carry); |
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216 MP_ADD_CARRY(r1, 0, r1, carry, carry); |
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217 MP_ADD_CARRY(r2, 0, r2, carry, carry); |
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218 MP_ADD_CARRY(r3, -r8_d, r3, carry, carry); |
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219 MP_ADD_CARRY(r4, MP_DIGIT_MAX, r4, carry, carry); |
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220 MP_ADD_CARRY(r5, MP_DIGIT_MAX, r5, carry, carry); |
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221 MP_ADD_CARRY(r6, -(r8_d+1), r6, carry, carry); |
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222 MP_ADD_CARRY(r7, (r8_d-1), r7, carry, carry); |
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223 r8 = carry; |
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224 } |
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225 |
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226 /* reduce the underflows */ |
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227 while (r8 < 0) { |
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228 mp_digit r8_d = -r8; |
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229 MP_SUB_BORROW(r0, r8_d, r0, 0, carry); |
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230 MP_SUB_BORROW(r1, 0, r1, carry, carry); |
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231 MP_SUB_BORROW(r2, 0, r2, carry, carry); |
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232 MP_SUB_BORROW(r3, -r8_d, r3, carry, carry); |
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233 MP_SUB_BORROW(r4, MP_DIGIT_MAX, r4, carry, carry); |
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234 MP_SUB_BORROW(r5, MP_DIGIT_MAX, r5, carry, carry); |
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235 MP_SUB_BORROW(r6, -(r8_d+1), r6, carry, carry); |
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236 MP_SUB_BORROW(r7, (r8_d-1), r7, carry, carry); |
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237 r8 = -carry; |
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238 } |
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239 if (a != r) { |
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240 MP_CHECKOK(s_mp_pad(r,8)); |
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241 } |
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242 MP_SIGN(r) = MP_ZPOS; |
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243 MP_USED(r) = 8; |
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244 |
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245 MP_DIGIT(r,7) = r7; |
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246 MP_DIGIT(r,6) = r6; |
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247 MP_DIGIT(r,5) = r5; |
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248 MP_DIGIT(r,4) = r4; |
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249 MP_DIGIT(r,3) = r3; |
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250 MP_DIGIT(r,2) = r2; |
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251 MP_DIGIT(r,1) = r1; |
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252 MP_DIGIT(r,0) = r0; |
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253 |
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254 /* final reduction if necessary */ |
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255 if ((r7 == MP_DIGIT_MAX) && |
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256 ((r6 > 1) || ((r6 == 1) && |
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257 (r5 || r4 || r3 || |
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258 ((r2 == MP_DIGIT_MAX) && (r1 == MP_DIGIT_MAX) |
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259 && (r0 == MP_DIGIT_MAX)))))) { |
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260 MP_CHECKOK(mp_sub(r, &meth->irr, r)); |
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261 } |
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262 #ifdef notdef |
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263 |
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264 |
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265 /* smooth the negatives */ |
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266 while (MP_SIGN(r) != MP_ZPOS) { |
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267 MP_CHECKOK(mp_add(r, &meth->irr, r)); |
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268 } |
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269 while (MP_USED(r) > 8) { |
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270 MP_CHECKOK(mp_sub(r, &meth->irr, r)); |
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271 } |
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272 |
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273 /* final reduction if necessary */ |
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274 if (MP_DIGIT(r,7) >= MP_DIGIT(&meth->irr,7)) { |
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275 if (mp_cmp(r,&meth->irr) != MP_LT) { |
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276 MP_CHECKOK(mp_sub(r, &meth->irr, r)); |
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277 } |
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278 } |
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279 #endif |
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280 s_mp_clamp(r); |
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281 #else |
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282 switch (a_used) { |
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283 case 8: |
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284 a7 = MP_DIGIT(a,7); |
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285 case 7: |
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286 a6 = MP_DIGIT(a,6); |
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287 case 6: |
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288 a5 = MP_DIGIT(a,5); |
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289 case 5: |
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290 a4 = MP_DIGIT(a,4); |
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291 } |
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292 a7l = a7 << 32; |
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293 a7h = a7 >> 32; |
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294 a6l = a6 << 32; |
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295 a6h = a6 >> 32; |
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296 a5l = a5 << 32; |
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297 a5h = a5 >> 32; |
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298 a4l = a4 << 32; |
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299 a4h = a4 >> 32; |
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300 r3 = MP_DIGIT(a,3); |
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301 r2 = MP_DIGIT(a,2); |
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302 r1 = MP_DIGIT(a,1); |
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303 r0 = MP_DIGIT(a,0); |
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304 |
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305 /* sum 1 */ |
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306 MP_ADD_CARRY(r1, a5h << 32, r1, 0, carry); |
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307 MP_ADD_CARRY(r2, a6, r2, carry, carry); |
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308 MP_ADD_CARRY(r3, a7, r3, carry, carry); |
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309 r4 = carry; |
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310 MP_ADD_CARRY(r1, a5h << 32, r1, 0, carry); |
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311 MP_ADD_CARRY(r2, a6, r2, carry, carry); |
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312 MP_ADD_CARRY(r3, a7, r3, carry, carry); |
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313 r4 += carry; |
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314 /* sum 2 */ |
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315 MP_ADD_CARRY(r1, a6l, r1, 0, carry); |
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316 MP_ADD_CARRY(r2, a6h | a7l, r2, carry, carry); |
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317 MP_ADD_CARRY(r3, a7h, r3, carry, carry); |
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318 r4 += carry; |
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319 MP_ADD_CARRY(r1, a6l, r1, 0, carry); |
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320 MP_ADD_CARRY(r2, a6h | a7l, r2, carry, carry); |
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321 MP_ADD_CARRY(r3, a7h, r3, carry, carry); |
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322 r4 += carry; |
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323 |
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324 /* sum 3 */ |
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325 MP_ADD_CARRY(r0, a4, r0, 0, carry); |
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326 MP_ADD_CARRY(r1, a5l >> 32, r1, carry, carry); |
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327 MP_ADD_CARRY(r2, 0, r2, carry, carry); |
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328 MP_ADD_CARRY(r3, a7, r3, carry, carry); |
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329 r4 += carry; |
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330 /* sum 4 */ |
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331 MP_ADD_CARRY(r0, a4h | a5l, r0, 0, carry); |
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332 MP_ADD_CARRY(r1, a5h|(a6h<<32), r1, carry, carry); |
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333 MP_ADD_CARRY(r2, a7, r2, carry, carry); |
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334 MP_ADD_CARRY(r3, a6h | a4l, r3, carry, carry); |
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335 r4 += carry; |
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336 /* diff 5 */ |
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337 MP_SUB_BORROW(r0, a5h | a6l, r0, 0, carry); |
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338 MP_SUB_BORROW(r1, a6h, r1, carry, carry); |
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339 MP_SUB_BORROW(r2, 0, r2, carry, carry); |
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340 MP_SUB_BORROW(r3, (a4l>>32)|a5l,r3, carry, carry); |
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341 r4 -= carry; |
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342 /* diff 6 */ |
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343 MP_SUB_BORROW(r0, a6, r0, 0, carry); |
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344 MP_SUB_BORROW(r1, a7, r1, carry, carry); |
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345 MP_SUB_BORROW(r2, 0, r2, carry, carry); |
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346 MP_SUB_BORROW(r3, a4h|(a5h<<32),r3, carry, carry); |
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347 r4 -= carry; |
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348 /* diff 7 */ |
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349 MP_SUB_BORROW(r0, a6h|a7l, r0, 0, carry); |
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350 MP_SUB_BORROW(r1, a7h|a4l, r1, carry, carry); |
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351 MP_SUB_BORROW(r2, a4h|a5l, r2, carry, carry); |
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352 MP_SUB_BORROW(r3, a6l, r3, carry, carry); |
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353 r4 -= carry; |
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354 /* diff 8 */ |
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355 MP_SUB_BORROW(r0, a7, r0, 0, carry); |
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356 MP_SUB_BORROW(r1, a4h<<32, r1, carry, carry); |
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357 MP_SUB_BORROW(r2, a5, r2, carry, carry); |
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358 MP_SUB_BORROW(r3, a6h<<32, r3, carry, carry); |
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359 r4 -= carry; |
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360 |
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361 /* reduce the overflows */ |
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362 while (r4 > 0) { |
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363 mp_digit r4_long = r4; |
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364 mp_digit r4l = (r4_long << 32); |
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365 MP_ADD_CARRY(r0, r4_long, r0, 0, carry); |
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366 MP_ADD_CARRY(r1, -r4l, r1, carry, carry); |
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367 MP_ADD_CARRY(r2, MP_DIGIT_MAX, r2, carry, carry); |
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368 MP_ADD_CARRY(r3, r4l-r4_long-1,r3, carry, carry); |
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369 r4 = carry; |
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370 } |
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371 |
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372 /* reduce the underflows */ |
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373 while (r4 < 0) { |
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374 mp_digit r4_long = -r4; |
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375 mp_digit r4l = (r4_long << 32); |
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376 MP_SUB_BORROW(r0, r4_long, r0, 0, carry); |
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377 MP_SUB_BORROW(r1, -r4l, r1, carry, carry); |
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378 MP_SUB_BORROW(r2, MP_DIGIT_MAX, r2, carry, carry); |
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379 MP_SUB_BORROW(r3, r4l-r4_long-1,r3, carry, carry); |
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380 r4 = -carry; |
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381 } |
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382 |
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383 if (a != r) { |
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384 MP_CHECKOK(s_mp_pad(r,4)); |
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385 } |
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386 MP_SIGN(r) = MP_ZPOS; |
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387 MP_USED(r) = 4; |
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388 |
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389 MP_DIGIT(r,3) = r3; |
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390 MP_DIGIT(r,2) = r2; |
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391 MP_DIGIT(r,1) = r1; |
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392 MP_DIGIT(r,0) = r0; |
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393 |
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394 /* final reduction if necessary */ |
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395 if ((r3 > 0xFFFFFFFF00000001ULL) || |
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396 ((r3 == 0xFFFFFFFF00000001ULL) && |
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397 (r2 || (r1 >> 32)|| |
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398 (r1 == 0xFFFFFFFFULL && r0 == MP_DIGIT_MAX)))) { |
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399 /* very rare, just use mp_sub */ |
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400 MP_CHECKOK(mp_sub(r, &meth->irr, r)); |
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401 } |
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402 |
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403 s_mp_clamp(r); |
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404 #endif |
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405 } |
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406 |
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407 CLEANUP: |
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408 return res; |
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409 } |
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410 |
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411 /* Compute the square of polynomial a, reduce modulo p256. Store the |
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412 * result in r. r could be a. Uses optimized modular reduction for p256. |
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413 */ |
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414 mp_err |
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415 ec_GFp_nistp256_sqr(const mp_int *a, mp_int *r, const GFMethod *meth) |
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416 { |
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417 mp_err res = MP_OKAY; |
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418 |
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419 MP_CHECKOK(mp_sqr(a, r)); |
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420 MP_CHECKOK(ec_GFp_nistp256_mod(r, r, meth)); |
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421 CLEANUP: |
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422 return res; |
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423 } |
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424 |
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425 /* Compute the product of two polynomials a and b, reduce modulo p256. |
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426 * Store the result in r. r could be a or b; a could be b. Uses |
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427 * optimized modular reduction for p256. */ |
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428 mp_err |
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429 ec_GFp_nistp256_mul(const mp_int *a, const mp_int *b, mp_int *r, |
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430 const GFMethod *meth) |
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431 { |
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432 mp_err res = MP_OKAY; |
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433 |
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434 MP_CHECKOK(mp_mul(a, b, r)); |
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435 MP_CHECKOK(ec_GFp_nistp256_mod(r, r, meth)); |
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436 CLEANUP: |
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437 return res; |
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438 } |
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439 |
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440 /* Wire in fast field arithmetic and precomputation of base point for |
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441 * named curves. */ |
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442 mp_err |
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443 ec_group_set_gfp256(ECGroup *group, ECCurveName name) |
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444 { |
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445 if (name == ECCurve_NIST_P256) { |
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446 group->meth->field_mod = &ec_GFp_nistp256_mod; |
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447 group->meth->field_mul = &ec_GFp_nistp256_mul; |
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448 group->meth->field_sqr = &ec_GFp_nistp256_sqr; |
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449 } |
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450 return MP_OKAY; |
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451 } |