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1 /* crypto/bn/bn_mont.c */ |
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2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) |
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3 * All rights reserved. |
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4 * |
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5 * This package is an SSL implementation written |
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6 * by Eric Young (eay@cryptsoft.com). |
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7 * The implementation was written so as to conform with Netscapes SSL. |
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8 * |
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9 * This library is free for commercial and non-commercial use as long as |
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10 * the following conditions are aheared to. The following conditions |
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11 * apply to all code found in this distribution, be it the RC4, RSA, |
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12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation |
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13 * included with this distribution is covered by the same copyright terms |
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14 * except that the holder is Tim Hudson (tjh@cryptsoft.com). |
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15 * |
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16 * Copyright remains Eric Young's, and as such any Copyright notices in |
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17 * the code are not to be removed. |
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18 * If this package is used in a product, Eric Young should be given attribution |
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19 * as the author of the parts of the library used. |
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20 * This can be in the form of a textual message at program startup or |
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21 * in documentation (online or textual) provided with the package. |
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22 * |
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23 * Redistribution and use in source and binary forms, with or without |
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24 * modification, are permitted provided that the following conditions |
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25 * are met: |
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26 * 1. Redistributions of source code must retain the copyright |
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27 * notice, this list of conditions and the following disclaimer. |
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28 * 2. Redistributions in binary form must reproduce the above copyright |
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29 * notice, this list of conditions and the following disclaimer in the |
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30 * documentation and/or other materials provided with the distribution. |
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31 * 3. All advertising materials mentioning features or use of this software |
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32 * must display the following acknowledgement: |
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33 * "This product includes cryptographic software written by |
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34 * Eric Young (eay@cryptsoft.com)" |
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35 * The word 'cryptographic' can be left out if the rouines from the library |
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36 * being used are not cryptographic related :-). |
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37 * 4. If you include any Windows specific code (or a derivative thereof) from |
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38 * the apps directory (application code) you must include an acknowledgement: |
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39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" |
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40 * |
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41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND |
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42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
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43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
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44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
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45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
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46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
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47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
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48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
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49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
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50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
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51 * SUCH DAMAGE. |
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52 * |
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53 * The licence and distribution terms for any publically available version or |
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54 * derivative of this code cannot be changed. i.e. this code cannot simply be |
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55 * copied and put under another distribution licence |
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56 * [including the GNU Public Licence.] |
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57 */ |
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58 /* ==================================================================== |
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59 * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved. |
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60 * |
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61 * Redistribution and use in source and binary forms, with or without |
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62 * modification, are permitted provided that the following conditions |
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63 * are met: |
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64 * |
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65 * 1. Redistributions of source code must retain the above copyright |
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66 * notice, this list of conditions and the following disclaimer. |
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67 * |
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68 * 2. Redistributions in binary form must reproduce the above copyright |
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69 * notice, this list of conditions and the following disclaimer in |
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70 * the documentation and/or other materials provided with the |
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71 * distribution. |
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72 * |
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73 * 3. All advertising materials mentioning features or use of this |
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74 * software must display the following acknowledgment: |
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75 * "This product includes software developed by the OpenSSL Project |
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76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" |
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77 * |
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78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to |
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79 * endorse or promote products derived from this software without |
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80 * prior written permission. For written permission, please contact |
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81 * openssl-core@openssl.org. |
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82 * |
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83 * 5. Products derived from this software may not be called "OpenSSL" |
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84 * nor may "OpenSSL" appear in their names without prior written |
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85 * permission of the OpenSSL Project. |
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86 * |
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87 * 6. Redistributions of any form whatsoever must retain the following |
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88 * acknowledgment: |
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89 * "This product includes software developed by the OpenSSL Project |
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90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" |
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91 * |
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92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
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93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
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94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
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95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
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96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
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97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
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98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
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99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
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100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
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101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
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102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
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103 * OF THE POSSIBILITY OF SUCH DAMAGE. |
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104 * ==================================================================== |
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105 * |
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106 * This product includes cryptographic software written by Eric Young |
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107 * (eay@cryptsoft.com). This product includes software written by Tim |
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108 * Hudson (tjh@cryptsoft.com). |
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109 * |
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110 */ |
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111 |
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112 /* |
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113 * Details about Montgomery multiplication algorithms can be found at |
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114 * http://security.ece.orst.edu/publications.html, e.g. |
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115 * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and |
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116 * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf |
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117 */ |
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118 |
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119 #include <stdio.h> |
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120 #include "cryptlib.h" |
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121 #include "bn_lcl.h" |
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122 |
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123 #define MONT_WORD /* use the faster word-based algorithm */ |
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124 |
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125 EXPORT_C int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
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126 BN_MONT_CTX *mont, BN_CTX *ctx) |
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127 { |
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128 BIGNUM *tmp; |
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129 int ret=0; |
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130 |
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131 BN_CTX_start(ctx); |
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132 tmp = BN_CTX_get(ctx); |
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133 if (tmp == NULL) goto err; |
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134 |
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135 bn_check_top(tmp); |
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136 if (a == b) |
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137 { |
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138 if (!BN_sqr(tmp,a,ctx)) goto err; |
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139 } |
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140 else |
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141 { |
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142 if (!BN_mul(tmp,a,b,ctx)) goto err; |
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143 } |
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144 /* reduce from aRR to aR */ |
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145 if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err; |
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146 bn_check_top(r); |
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147 ret=1; |
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148 err: |
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149 BN_CTX_end(ctx); |
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150 return(ret); |
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151 } |
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152 |
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153 EXPORT_C int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont, |
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154 BN_CTX *ctx) |
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155 { |
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156 int retn=0; |
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157 |
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158 #ifdef MONT_WORD |
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159 BIGNUM *n,*r; |
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160 BN_ULONG *ap,*np,*rp,n0,v,*nrp; |
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161 int al,nl,max,i,x,ri; |
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162 |
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163 BN_CTX_start(ctx); |
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164 if ((r = BN_CTX_get(ctx)) == NULL) goto err; |
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165 |
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166 if (!BN_copy(r,a)) goto err; |
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167 n= &(mont->N); |
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168 |
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169 ap=a->d; |
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170 /* mont->ri is the size of mont->N in bits (rounded up |
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171 to the word size) */ |
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172 al=ri=mont->ri/BN_BITS2; |
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173 |
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174 nl=n->top; |
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175 if ((al == 0) || (nl == 0)) { r->top=0; return(1); } |
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176 |
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177 max=(nl+al+1); /* allow for overflow (no?) XXX */ |
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178 if (bn_wexpand(r,max) == NULL) goto err; |
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179 |
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180 r->neg=a->neg^n->neg; |
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181 np=n->d; |
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182 rp=r->d; |
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183 nrp= &(r->d[nl]); |
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184 |
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185 /* clear the top words of T */ |
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186 #if 1 |
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187 for (i=r->top; i<max; i++) /* memset? XXX */ |
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188 r->d[i]=0; |
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189 #else |
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190 memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG)); |
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191 #endif |
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192 |
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193 r->top=max; |
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194 n0=mont->n0; |
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195 |
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196 #ifdef BN_COUNT |
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197 fprintf(stderr,"word BN_from_montgomery %d * %d\n",nl,nl); |
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198 #endif |
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199 for (i=0; i<nl; i++) |
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200 { |
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201 #ifdef __TANDEM |
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202 { |
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203 long long t1; |
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204 long long t2; |
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205 long long t3; |
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206 t1 = rp[0] * (n0 & 0177777); |
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207 t2 = 037777600000l; |
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208 t2 = n0 & t2; |
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209 t3 = rp[0] & 0177777; |
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210 t2 = (t3 * t2) & BN_MASK2; |
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211 t1 = t1 + t2; |
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212 v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1); |
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213 } |
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214 #else |
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215 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2); |
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216 #endif |
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217 nrp++; |
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218 rp++; |
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219 if (((nrp[-1]+=v)&BN_MASK2) >= v) |
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220 continue; |
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221 else |
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222 { |
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223 if (((++nrp[0])&BN_MASK2) != 0) continue; |
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224 if (((++nrp[1])&BN_MASK2) != 0) continue; |
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225 for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ; |
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226 } |
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227 } |
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228 bn_correct_top(r); |
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229 |
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230 /* mont->ri will be a multiple of the word size and below code |
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231 * is kind of BN_rshift(ret,r,mont->ri) equivalent */ |
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232 if (r->top <= ri) |
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233 { |
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234 ret->top=0; |
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235 retn=1; |
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236 goto err; |
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237 } |
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238 al=r->top-ri; |
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239 |
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240 # define BRANCH_FREE 1 |
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241 # if BRANCH_FREE |
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242 if (bn_wexpand(ret,ri) == NULL) goto err; |
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243 x=0-(((al-ri)>>(sizeof(al)*8-1))&1); |
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244 ret->top=x=(ri&~x)|(al&x); /* min(ri,al) */ |
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245 ret->neg=r->neg; |
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246 |
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247 rp=ret->d; |
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248 ap=&(r->d[ri]); |
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249 |
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250 { |
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251 size_t m1,m2; |
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252 |
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253 v=bn_sub_words(rp,ap,np,ri); |
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254 /* this ----------------^^ works even in al<ri case |
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255 * thanks to zealous zeroing of top of the vector in the |
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256 * beginning. */ |
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257 |
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258 /* if (al==ri && !v) || al>ri) nrp=rp; else nrp=ap; */ |
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259 /* in other words if subtraction result is real, then |
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260 * trick unconditional memcpy below to perform in-place |
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261 * "refresh" instead of actual copy. */ |
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262 m1=0-(size_t)(((al-ri)>>(sizeof(al)*8-1))&1); /* al<ri */ |
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263 m2=0-(size_t)(((ri-al)>>(sizeof(al)*8-1))&1); /* al>ri */ |
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264 m1|=m2; /* (al!=ri) */ |
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265 m1|=(0-(size_t)v); /* (al!=ri || v) */ |
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266 m1&=~m2; /* (al!=ri || v) && !al>ri */ |
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267 nrp=(BN_ULONG *)(((size_t)rp&~m1)|((size_t)ap&m1)); |
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268 } |
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269 |
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270 /* 'i<ri' is chosen to eliminate dependency on input data, even |
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271 * though it results in redundant copy in al<ri case. */ |
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272 for (i=0,ri-=4; i<ri; i+=4) |
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273 { |
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274 BN_ULONG t1,t2,t3,t4; |
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275 |
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276 t1=nrp[i+0]; |
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277 t2=nrp[i+1]; |
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278 t3=nrp[i+2]; ap[i+0]=0; |
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279 t4=nrp[i+3]; ap[i+1]=0; |
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280 rp[i+0]=t1; ap[i+2]=0; |
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281 rp[i+1]=t2; ap[i+3]=0; |
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282 rp[i+2]=t3; |
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283 rp[i+3]=t4; |
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284 } |
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285 for (ri+=4; i<ri; i++) |
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286 rp[i]=nrp[i], ap[i]=0; |
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287 bn_correct_top(r); |
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288 bn_correct_top(ret); |
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289 # else |
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290 if (bn_wexpand(ret,al) == NULL) goto err; |
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291 ret->top=al; |
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292 ret->neg=r->neg; |
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293 |
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294 rp=ret->d; |
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295 ap=&(r->d[ri]); |
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296 al-=4; |
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297 for (i=0; i<al; i+=4) |
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298 { |
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299 BN_ULONG t1,t2,t3,t4; |
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300 |
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301 t1=ap[i+0]; |
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302 t2=ap[i+1]; |
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303 t3=ap[i+2]; |
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304 t4=ap[i+3]; |
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305 rp[i+0]=t1; |
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306 rp[i+1]=t2; |
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307 rp[i+2]=t3; |
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308 rp[i+3]=t4; |
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309 } |
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310 al+=4; |
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311 for (; i<al; i++) |
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312 rp[i]=ap[i]; |
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313 #endif |
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314 #else /* !MONT_WORD */ |
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315 BIGNUM *t1,*t2; |
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316 |
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317 BN_CTX_start(ctx); |
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318 t1 = BN_CTX_get(ctx); |
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319 t2 = BN_CTX_get(ctx); |
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320 if (t1 == NULL || t2 == NULL) goto err; |
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321 |
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322 if (!BN_copy(t1,a)) goto err; |
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323 BN_mask_bits(t1,mont->ri); |
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324 |
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325 if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err; |
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326 BN_mask_bits(t2,mont->ri); |
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327 |
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328 if (!BN_mul(t1,t2,&mont->N,ctx)) goto err; |
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329 if (!BN_add(t2,a,t1)) goto err; |
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330 if (!BN_rshift(ret,t2,mont->ri)) goto err; |
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331 #endif /* MONT_WORD */ |
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332 |
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333 #if !defined(BRANCH_FREE) || BRANCH_FREE==0 |
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334 if (BN_ucmp(ret, &(mont->N)) >= 0) |
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335 { |
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336 if (!BN_usub(ret,ret,&(mont->N))) goto err; |
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337 } |
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338 #endif |
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339 retn=1; |
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340 bn_check_top(ret); |
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341 err: |
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342 BN_CTX_end(ctx); |
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343 return(retn); |
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344 } |
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345 |
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346 EXPORT_C BN_MONT_CTX *BN_MONT_CTX_new(void) |
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347 { |
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348 BN_MONT_CTX *ret; |
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349 |
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350 if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL) |
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351 return(NULL); |
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352 |
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353 BN_MONT_CTX_init(ret); |
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354 ret->flags=BN_FLG_MALLOCED; |
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355 return(ret); |
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356 } |
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357 |
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358 EXPORT_C void BN_MONT_CTX_init(BN_MONT_CTX *ctx) |
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359 { |
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360 ctx->ri=0; |
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361 BN_init(&(ctx->RR)); |
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362 BN_init(&(ctx->N)); |
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363 BN_init(&(ctx->Ni)); |
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364 ctx->flags=0; |
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365 } |
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366 |
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367 EXPORT_C void BN_MONT_CTX_free(BN_MONT_CTX *mont) |
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368 { |
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369 if(mont == NULL) |
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370 return; |
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371 |
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372 BN_free(&(mont->RR)); |
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373 BN_free(&(mont->N)); |
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374 BN_free(&(mont->Ni)); |
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375 if (mont->flags & BN_FLG_MALLOCED) |
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376 OPENSSL_free(mont); |
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377 } |
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378 |
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379 EXPORT_C int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) |
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380 { |
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381 int ret = 0; |
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382 BIGNUM *Ri,*R; |
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383 |
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384 BN_CTX_start(ctx); |
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385 if((Ri = BN_CTX_get(ctx)) == NULL) goto err; |
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386 R= &(mont->RR); /* grab RR as a temp */ |
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387 if (!BN_copy(&(mont->N),mod)) goto err; /* Set N */ |
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388 mont->N.neg = 0; |
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389 |
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390 #ifdef MONT_WORD |
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391 { |
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392 BIGNUM tmod; |
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393 BN_ULONG buf[2]; |
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394 |
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395 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2; |
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396 BN_zero(R); |
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397 if (!(BN_set_bit(R,BN_BITS2))) goto err; /* R */ |
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398 |
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399 buf[0]=mod->d[0]; /* tmod = N mod word size */ |
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400 buf[1]=0; |
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401 tmod.d=buf; |
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402 tmod.top = buf[0] != 0 ? 1 : 0; |
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403 tmod.dmax=2; |
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404 tmod.neg=0; |
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405 /* Ri = R^-1 mod N*/ |
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406 if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL) |
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407 goto err; |
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408 if (!BN_lshift(Ri,Ri,BN_BITS2)) goto err; /* R*Ri */ |
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409 if (!BN_is_zero(Ri)) |
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410 { |
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411 if (!BN_sub_word(Ri,1)) goto err; |
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412 } |
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413 else /* if N mod word size == 1 */ |
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414 { |
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415 if (!BN_set_word(Ri,BN_MASK2)) goto err; /* Ri-- (mod word size) */ |
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416 } |
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417 if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err; |
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418 /* Ni = (R*Ri-1)/N, |
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419 * keep only least significant word: */ |
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420 mont->n0 = (Ri->top > 0) ? Ri->d[0] : 0; |
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421 } |
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422 #else /* !MONT_WORD */ |
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423 { /* bignum version */ |
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424 mont->ri=BN_num_bits(&mont->N); |
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425 BN_zero(R); |
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426 if (!BN_set_bit(R,mont->ri)) goto err; /* R = 2^ri */ |
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427 /* Ri = R^-1 mod N*/ |
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428 if ((BN_mod_inverse(Ri,R,&mont->N,ctx)) == NULL) |
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429 goto err; |
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430 if (!BN_lshift(Ri,Ri,mont->ri)) goto err; /* R*Ri */ |
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431 if (!BN_sub_word(Ri,1)) goto err; |
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432 /* Ni = (R*Ri-1) / N */ |
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433 if (!BN_div(&(mont->Ni),NULL,Ri,&mont->N,ctx)) goto err; |
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434 } |
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435 #endif |
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436 |
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437 /* setup RR for conversions */ |
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438 BN_zero(&(mont->RR)); |
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439 if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err; |
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440 if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err; |
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441 |
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442 ret = 1; |
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443 err: |
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444 BN_CTX_end(ctx); |
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445 return ret; |
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446 } |
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447 |
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448 EXPORT_C BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from) |
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449 { |
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450 if (to == from) return(to); |
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451 |
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452 if (!BN_copy(&(to->RR),&(from->RR))) return NULL; |
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453 if (!BN_copy(&(to->N),&(from->N))) return NULL; |
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454 if (!BN_copy(&(to->Ni),&(from->Ni))) return NULL; |
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455 to->ri=from->ri; |
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456 to->n0=from->n0; |
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457 return(to); |
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458 } |
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459 |
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460 EXPORT_C BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock, |
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461 const BIGNUM *mod, BN_CTX *ctx) |
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462 { |
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463 int got_write_lock = 0; |
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464 BN_MONT_CTX *ret; |
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465 |
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466 CRYPTO_r_lock(lock); |
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467 if (!*pmont) |
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468 { |
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469 CRYPTO_r_unlock(lock); |
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470 CRYPTO_w_lock(lock); |
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471 got_write_lock = 1; |
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472 |
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473 if (!*pmont) |
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474 { |
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475 ret = BN_MONT_CTX_new(); |
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476 if (ret && !BN_MONT_CTX_set(ret, mod, ctx)) |
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477 BN_MONT_CTX_free(ret); |
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478 else |
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479 *pmont = ret; |
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480 } |
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481 } |
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482 |
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483 ret = *pmont; |
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484 |
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485 if (got_write_lock) |
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486 CRYPTO_w_unlock(lock); |
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487 else |
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488 CRYPTO_r_unlock(lock); |
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489 |
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490 return ret; |
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491 } |