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1 /* crypto/bn/bn_lcl.h */ |
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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) 1998-2000 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 #ifndef HEADER_BN_LCL_H |
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113 #define HEADER_BN_LCL_H |
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114 |
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115 #include <openssl/bn.h> |
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116 |
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117 #ifdef __cplusplus |
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118 extern "C" { |
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119 #endif |
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120 |
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121 |
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122 /* |
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123 * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions |
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124 * |
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125 * |
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126 * For window size 'w' (w >= 2) and a random 'b' bits exponent, |
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127 * the number of multiplications is a constant plus on average |
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128 * |
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129 * 2^(w-1) + (b-w)/(w+1); |
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130 * |
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131 * here 2^(w-1) is for precomputing the table (we actually need |
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132 * entries only for windows that have the lowest bit set), and |
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133 * (b-w)/(w+1) is an approximation for the expected number of |
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134 * w-bit windows, not counting the first one. |
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135 * |
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136 * Thus we should use |
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137 * |
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138 * w >= 6 if b > 671 |
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139 * w = 5 if 671 > b > 239 |
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140 * w = 4 if 239 > b > 79 |
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141 * w = 3 if 79 > b > 23 |
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142 * w <= 2 if 23 > b |
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143 * |
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144 * (with draws in between). Very small exponents are often selected |
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145 * with low Hamming weight, so we use w = 1 for b <= 23. |
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146 */ |
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147 #if 1 |
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148 #define BN_window_bits_for_exponent_size(b) \ |
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149 ((b) > 671 ? 6 : \ |
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150 (b) > 239 ? 5 : \ |
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151 (b) > 79 ? 4 : \ |
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152 (b) > 23 ? 3 : 1) |
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153 #else |
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154 /* Old SSLeay/OpenSSL table. |
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155 * Maximum window size was 5, so this table differs for b==1024; |
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156 * but it coincides for other interesting values (b==160, b==512). |
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157 */ |
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158 #define BN_window_bits_for_exponent_size(b) \ |
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159 ((b) > 255 ? 5 : \ |
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160 (b) > 127 ? 4 : \ |
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161 (b) > 17 ? 3 : 1) |
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162 #endif |
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163 |
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164 |
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165 |
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166 /* BN_mod_exp_mont_conttime is based on the assumption that the |
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167 * L1 data cache line width of the target processor is at least |
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168 * the following value. |
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169 */ |
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170 #define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 ) |
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171 #define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1) |
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172 |
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173 /* Window sizes optimized for fixed window size modular exponentiation |
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174 * algorithm (BN_mod_exp_mont_consttime). |
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175 * |
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176 * To achieve the security goals of BN_mode_exp_mont_consttime, the |
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177 * maximum size of the window must not exceed |
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178 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). |
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179 * |
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180 * Window size thresholds are defined for cache line sizes of 32 and 64, |
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181 * cache line sizes where log_2(32)=5 and log_2(64)=6 respectively. A |
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182 * window size of 7 should only be used on processors that have a 128 |
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183 * byte or greater cache line size. |
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184 */ |
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185 #if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64 |
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186 |
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187 # define BN_window_bits_for_ctime_exponent_size(b) \ |
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188 ((b) > 937 ? 6 : \ |
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189 (b) > 306 ? 5 : \ |
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190 (b) > 89 ? 4 : \ |
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191 (b) > 22 ? 3 : 1) |
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192 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6) |
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193 |
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194 #elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32 |
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195 |
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196 # define BN_window_bits_for_ctime_exponent_size(b) \ |
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197 ((b) > 306 ? 5 : \ |
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198 (b) > 89 ? 4 : \ |
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199 (b) > 22 ? 3 : 1) |
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200 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5) |
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201 |
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202 #endif |
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203 |
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204 |
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205 /* Pentium pro 16,16,16,32,64 */ |
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206 /* Alpha 16,16,16,16.64 */ |
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207 #define BN_MULL_SIZE_NORMAL (16) /* 32 */ |
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208 #define BN_MUL_RECURSIVE_SIZE_NORMAL (16) /* 32 less than */ |
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209 #define BN_SQR_RECURSIVE_SIZE_NORMAL (16) /* 32 */ |
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210 #define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32) /* 32 */ |
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211 #define BN_MONT_CTX_SET_SIZE_WORD (64) /* 32 */ |
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212 |
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213 #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC) |
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214 /* |
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215 * BN_UMULT_HIGH section. |
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216 * |
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217 * No, I'm not trying to overwhelm you when stating that the |
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218 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect |
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219 * you to be impressed when I say that if the compiler doesn't |
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220 * support 2*N integer type, then you have to replace every N*N |
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221 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts |
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222 * and additions which unavoidably results in severe performance |
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223 * penalties. Of course provided that the hardware is capable of |
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224 * producing 2*N result... That's when you normally start |
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225 * considering assembler implementation. However! It should be |
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226 * pointed out that some CPUs (most notably Alpha, PowerPC and |
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227 * upcoming IA-64 family:-) provide *separate* instruction |
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228 * calculating the upper half of the product placing the result |
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229 * into a general purpose register. Now *if* the compiler supports |
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230 * inline assembler, then it's not impossible to implement the |
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231 * "bignum" routines (and have the compiler optimize 'em) |
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232 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH |
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233 * macro is about:-) |
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234 * |
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235 * <appro@fy.chalmers.se> |
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236 */ |
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237 # if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT)) |
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238 # if defined(__DECC) |
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239 # include <c_asm.h> |
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240 # define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b)) |
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241 # elif defined(__GNUC__) |
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242 # define BN_UMULT_HIGH(a,b) ({ \ |
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243 register BN_ULONG ret; \ |
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244 asm ("umulh %1,%2,%0" \ |
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245 : "=r"(ret) \ |
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246 : "r"(a), "r"(b)); \ |
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247 ret; }) |
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248 # endif /* compiler */ |
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249 # elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG) |
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250 # if defined(__GNUC__) |
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251 # define BN_UMULT_HIGH(a,b) ({ \ |
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252 register BN_ULONG ret; \ |
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253 asm ("mulhdu %0,%1,%2" \ |
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254 : "=r"(ret) \ |
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255 : "r"(a), "r"(b)); \ |
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256 ret; }) |
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257 # endif /* compiler */ |
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258 # elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG) |
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259 # if defined(__GNUC__) |
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260 # define BN_UMULT_HIGH(a,b) ({ \ |
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261 register BN_ULONG ret,discard; \ |
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262 asm ("mulq %3" \ |
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263 : "=a"(discard),"=d"(ret) \ |
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264 : "a"(a), "g"(b) \ |
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265 : "cc"); \ |
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266 ret; }) |
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267 # define BN_UMULT_LOHI(low,high,a,b) \ |
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268 asm ("mulq %3" \ |
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269 : "=a"(low),"=d"(high) \ |
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270 : "a"(a),"g"(b) \ |
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271 : "cc"); |
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272 # endif |
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273 # elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT) |
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274 # if defined(_MSC_VER) && _MSC_VER>=1400 |
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275 unsigned __int64 __umulh (unsigned __int64 a,unsigned __int64 b); |
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276 unsigned __int64 _umul128 (unsigned __int64 a,unsigned __int64 b, |
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277 unsigned __int64 *h); |
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278 # pragma intrinsic(__umulh,_umul128) |
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279 # define BN_UMULT_HIGH(a,b) __umulh((a),(b)) |
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280 # define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high))) |
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281 # endif |
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282 # endif /* cpu */ |
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283 #endif /* OPENSSL_NO_ASM */ |
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284 |
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285 /************************************************************* |
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286 * Using the long long type |
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287 */ |
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288 #define Lw(t) (((BN_ULONG)(t))&BN_MASK2) |
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289 #define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2) |
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290 |
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291 #ifdef BN_DEBUG_RAND |
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292 #define bn_clear_top2max(a) \ |
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293 { \ |
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294 int ind = (a)->dmax - (a)->top; \ |
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295 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \ |
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296 for (; ind != 0; ind--) \ |
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297 *(++ftl) = 0x0; \ |
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298 } |
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299 #else |
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300 #define bn_clear_top2max(a) |
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301 #endif |
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302 |
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303 #ifdef BN_LLONG |
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304 #define mul_add(r,a,w,c) { \ |
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305 BN_ULLONG t; \ |
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306 t=(BN_ULLONG)w * (a) + (r) + (c); \ |
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307 (r)= Lw(t); \ |
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308 (c)= Hw(t); \ |
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309 } |
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310 |
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311 #define mul(r,a,w,c) { \ |
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312 BN_ULLONG t; \ |
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313 t=(BN_ULLONG)w * (a) + (c); \ |
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314 (r)= Lw(t); \ |
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315 (c)= Hw(t); \ |
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316 } |
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317 |
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318 #define sqr(r0,r1,a) { \ |
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319 BN_ULLONG t; \ |
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320 t=(BN_ULLONG)(a)*(a); \ |
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321 (r0)=Lw(t); \ |
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322 (r1)=Hw(t); \ |
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323 } |
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324 |
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325 #elif defined(BN_UMULT_LOHI) |
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326 #define mul_add(r,a,w,c) { \ |
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327 BN_ULONG high,low,ret,tmp=(a); \ |
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328 ret = (r); \ |
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329 BN_UMULT_LOHI(low,high,w,tmp); \ |
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330 ret += (c); \ |
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331 (c) = (ret<(c))?1:0; \ |
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332 (c) += high; \ |
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333 ret += low; \ |
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334 (c) += (ret<low)?1:0; \ |
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335 (r) = ret; \ |
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336 } |
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337 |
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338 #define mul(r,a,w,c) { \ |
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339 BN_ULONG high,low,ret,ta=(a); \ |
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340 BN_UMULT_LOHI(low,high,w,ta); \ |
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341 ret = low + (c); \ |
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342 (c) = high; \ |
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343 (c) += (ret<low)?1:0; \ |
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344 (r) = ret; \ |
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345 } |
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346 |
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347 #define sqr(r0,r1,a) { \ |
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348 BN_ULONG tmp=(a); \ |
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349 BN_UMULT_LOHI(r0,r1,tmp,tmp); \ |
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350 } |
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351 |
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352 #elif defined(BN_UMULT_HIGH) |
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353 #define mul_add(r,a,w,c) { \ |
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354 BN_ULONG high,low,ret,tmp=(a); \ |
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355 ret = (r); \ |
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356 high= BN_UMULT_HIGH(w,tmp); \ |
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357 ret += (c); \ |
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358 low = (w) * tmp; \ |
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359 (c) = (ret<(c))?1:0; \ |
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360 (c) += high; \ |
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361 ret += low; \ |
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362 (c) += (ret<low)?1:0; \ |
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363 (r) = ret; \ |
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364 } |
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365 |
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366 #define mul(r,a,w,c) { \ |
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367 BN_ULONG high,low,ret,ta=(a); \ |
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368 low = (w) * ta; \ |
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369 high= BN_UMULT_HIGH(w,ta); \ |
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370 ret = low + (c); \ |
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371 (c) = high; \ |
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372 (c) += (ret<low)?1:0; \ |
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373 (r) = ret; \ |
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374 } |
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375 |
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376 #define sqr(r0,r1,a) { \ |
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377 BN_ULONG tmp=(a); \ |
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378 (r0) = tmp * tmp; \ |
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379 (r1) = BN_UMULT_HIGH(tmp,tmp); \ |
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380 } |
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381 |
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382 #else |
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383 /************************************************************* |
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384 * No long long type |
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385 */ |
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386 |
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387 #define LBITS(a) ((a)&BN_MASK2l) |
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388 #define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l) |
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389 #define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2) |
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390 |
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391 #define LLBITS(a) ((a)&BN_MASKl) |
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392 #define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl) |
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393 #define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2) |
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394 |
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395 #define mul64(l,h,bl,bh) \ |
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396 { \ |
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397 BN_ULONG m,m1,lt,ht; \ |
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398 \ |
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399 lt=l; \ |
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400 ht=h; \ |
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401 m =(bh)*(lt); \ |
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402 lt=(bl)*(lt); \ |
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403 m1=(bl)*(ht); \ |
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404 ht =(bh)*(ht); \ |
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405 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \ |
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406 ht+=HBITS(m); \ |
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407 m1=L2HBITS(m); \ |
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408 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \ |
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409 (l)=lt; \ |
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410 (h)=ht; \ |
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411 } |
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412 |
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413 #define sqr64(lo,ho,in) \ |
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414 { \ |
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415 BN_ULONG l,h,m; \ |
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416 \ |
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417 h=(in); \ |
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418 l=LBITS(h); \ |
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419 h=HBITS(h); \ |
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420 m =(l)*(h); \ |
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421 l*=l; \ |
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422 h*=h; \ |
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423 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \ |
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424 m =(m&BN_MASK2l)<<(BN_BITS4+1); \ |
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425 l=(l+m)&BN_MASK2; if (l < m) h++; \ |
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426 (lo)=l; \ |
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427 (ho)=h; \ |
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428 } |
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429 |
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430 #define mul_add(r,a,bl,bh,c) { \ |
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431 BN_ULONG l,h; \ |
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432 \ |
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433 h= (a); \ |
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434 l=LBITS(h); \ |
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435 h=HBITS(h); \ |
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436 mul64(l,h,(bl),(bh)); \ |
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437 \ |
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438 /* non-multiply part */ \ |
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439 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ |
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440 (c)=(r); \ |
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441 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \ |
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442 (c)=h&BN_MASK2; \ |
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443 (r)=l; \ |
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444 } |
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445 |
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446 #define mul(r,a,bl,bh,c) { \ |
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447 BN_ULONG l,h; \ |
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448 \ |
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449 h= (a); \ |
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450 l=LBITS(h); \ |
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451 h=HBITS(h); \ |
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452 mul64(l,h,(bl),(bh)); \ |
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453 \ |
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454 /* non-multiply part */ \ |
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455 l+=(c); if ((l&BN_MASK2) < (c)) h++; \ |
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456 (c)=h&BN_MASK2; \ |
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457 (r)=l&BN_MASK2; \ |
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458 } |
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459 #endif /* !BN_LLONG */ |
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460 |
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461 void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb); |
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462 IMPORT_C void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); |
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463 IMPORT_C void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); |
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464 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp); |
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465 IMPORT_C void bn_sqr_comba8(BN_ULONG *r,const BN_ULONG *a); |
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466 IMPORT_C void bn_sqr_comba4(BN_ULONG *r,const BN_ULONG *a); |
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467 IMPORT_C int bn_cmp_words(const BN_ULONG *a,const BN_ULONG *b,int n); |
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468 IMPORT_C int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, |
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469 int cl, int dl); |
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470 void bn_mul_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2, |
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471 int dna,int dnb,BN_ULONG *t); |
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472 void bn_mul_part_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, |
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473 int n,int tna,int tnb,BN_ULONG *t); |
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474 void bn_sqr_recursive(BN_ULONG *r,const BN_ULONG *a, int n2, BN_ULONG *t); |
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475 void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n); |
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476 void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2, |
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477 BN_ULONG *t); |
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478 void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2, |
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479 BN_ULONG *t); |
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480 BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, |
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481 int cl, int dl); |
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482 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, |
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483 int cl, int dl); |
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484 |
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485 #ifdef __cplusplus |
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486 } |
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487 #endif |
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488 |
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489 #endif |