1/* crypto/bn/bn_exp2.c */ 2/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) 3 * All rights reserved. 4 * 5 * This package is an SSL implementation written 6 * by Eric Young (eay@cryptsoft.com). 7 * The implementation was written so as to conform with Netscapes SSL. 8 * 9 * This library is free for commercial and non-commercial use as long as 10 * the following conditions are aheared to. The following conditions 11 * apply to all code found in this distribution, be it the RC4, RSA, 12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation 13 * included with this distribution is covered by the same copyright terms 14 * except that the holder is Tim Hudson (tjh@cryptsoft.com). 15 * 16 * Copyright remains Eric Young's, and as such any Copyright notices in 17 * the code are not to be removed. 18 * If this package is used in a product, Eric Young should be given attribution 19 * as the author of the parts of the library used. 20 * This can be in the form of a textual message at program startup or 21 * in documentation (online or textual) provided with the package. 22 * 23 * Redistribution and use in source and binary forms, with or without 24 * modification, are permitted provided that the following conditions 25 * are met: 26 * 1. Redistributions of source code must retain the copyright 27 * notice, this list of conditions and the following disclaimer. 28 * 2. Redistributions in binary form must reproduce the above copyright 29 * notice, this list of conditions and the following disclaimer in the 30 * documentation and/or other materials provided with the distribution. 31 * 3. All advertising materials mentioning features or use of this software 32 * must display the following acknowledgement: 33 * "This product includes cryptographic software written by 34 * Eric Young (eay@cryptsoft.com)" 35 * The word 'cryptographic' can be left out if the rouines from the library 36 * being used are not cryptographic related :-). 37 * 4. If you include any Windows specific code (or a derivative thereof) from 38 * the apps directory (application code) you must include an acknowledgement: 39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" 40 * 41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND 42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 51 * SUCH DAMAGE. 52 * 53 * The licence and distribution terms for any publically available version or 54 * derivative of this code cannot be changed. i.e. this code cannot simply be 55 * copied and put under another distribution licence 56 * [including the GNU Public Licence.] 57 */ 58/* ==================================================================== 59 * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved. 60 * 61 * Redistribution and use in source and binary forms, with or without 62 * modification, are permitted provided that the following conditions 63 * are met: 64 * 65 * 1. Redistributions of source code must retain the above copyright 66 * notice, this list of conditions and the following disclaimer. 67 * 68 * 2. Redistributions in binary form must reproduce the above copyright 69 * notice, this list of conditions and the following disclaimer in 70 * the documentation and/or other materials provided with the 71 * distribution. 72 * 73 * 3. All advertising materials mentioning features or use of this 74 * software must display the following acknowledgment: 75 * "This product includes software developed by the OpenSSL Project 76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 77 * 78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 79 * endorse or promote products derived from this software without 80 * prior written permission. For written permission, please contact 81 * openssl-core@openssl.org. 82 * 83 * 5. Products derived from this software may not be called "OpenSSL" 84 * nor may "OpenSSL" appear in their names without prior written 85 * permission of the OpenSSL Project. 86 * 87 * 6. Redistributions of any form whatsoever must retain the following 88 * acknowledgment: 89 * "This product includes software developed by the OpenSSL Project 90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 91 * 92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 103 * OF THE POSSIBILITY OF SUCH DAMAGE. 104 * ==================================================================== 105 * 106 * This product includes cryptographic software written by Eric Young 107 * (eay@cryptsoft.com). This product includes software written by Tim 108 * Hudson (tjh@cryptsoft.com). 109 * 110 */ 111 112#include <stdio.h> 113#include "cryptlib.h" 114#include "bn_lcl.h" 115 116#define TABLE_SIZE 32 117 118int BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1, 119 const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m, 120 BN_CTX *ctx, BN_MONT_CTX *in_mont) 121{ 122 int i, j, bits, b, bits1, bits2, ret = 123 0, wpos1, wpos2, window1, window2, wvalue1, wvalue2; 124 int r_is_one = 1; 125 BIGNUM *d, *r; 126 const BIGNUM *a_mod_m; 127 /* Tables of variables obtained from 'ctx' */ 128 BIGNUM *val1[TABLE_SIZE], *val2[TABLE_SIZE]; 129 BN_MONT_CTX *mont = NULL; 130 131 bn_check_top(a1); 132 bn_check_top(p1); 133 bn_check_top(a2); 134 bn_check_top(p2); 135 bn_check_top(m); 136 137 if (!(m->d[0] & 1)) { 138 BNerr(BN_F_BN_MOD_EXP2_MONT, BN_R_CALLED_WITH_EVEN_MODULUS); 139 return (0); 140 } 141 bits1 = BN_num_bits(p1); 142 bits2 = BN_num_bits(p2); 143 if ((bits1 == 0) && (bits2 == 0)) { 144 ret = BN_one(rr); 145 return ret; 146 } 147 148 bits = (bits1 > bits2) ? bits1 : bits2; 149 150 BN_CTX_start(ctx); 151 d = BN_CTX_get(ctx); 152 r = BN_CTX_get(ctx); 153 val1[0] = BN_CTX_get(ctx); 154 val2[0] = BN_CTX_get(ctx); 155 if (!d || !r || !val1[0] || !val2[0]) 156 goto err; 157 158 if (in_mont != NULL) 159 mont = in_mont; 160 else { 161 if ((mont = BN_MONT_CTX_new()) == NULL) 162 goto err; 163 if (!BN_MONT_CTX_set(mont, m, ctx)) 164 goto err; 165 } 166 167 window1 = BN_window_bits_for_exponent_size(bits1); 168 window2 = BN_window_bits_for_exponent_size(bits2); 169 170 /* 171 * Build table for a1: val1[i] := a1^(2*i + 1) mod m for i = 0 .. 2^(window1-1) 172 */ 173 if (a1->neg || BN_ucmp(a1, m) >= 0) { 174 if (!BN_mod(val1[0], a1, m, ctx)) 175 goto err; 176 a_mod_m = val1[0]; 177 } else 178 a_mod_m = a1; 179 if (BN_is_zero(a_mod_m)) { 180 BN_zero(rr); 181 ret = 1; 182 goto err; 183 } 184 185 if (!BN_to_montgomery(val1[0], a_mod_m, mont, ctx)) 186 goto err; 187 if (window1 > 1) { 188 if (!BN_mod_mul_montgomery(d, val1[0], val1[0], mont, ctx)) 189 goto err; 190 191 j = 1 << (window1 - 1); 192 for (i = 1; i < j; i++) { 193 if (((val1[i] = BN_CTX_get(ctx)) == NULL) || 194 !BN_mod_mul_montgomery(val1[i], val1[i - 1], d, mont, ctx)) 195 goto err; 196 } 197 } 198 199 /* 200 * Build table for a2: val2[i] := a2^(2*i + 1) mod m for i = 0 .. 2^(window2-1) 201 */ 202 if (a2->neg || BN_ucmp(a2, m) >= 0) { 203 if (!BN_mod(val2[0], a2, m, ctx)) 204 goto err; 205 a_mod_m = val2[0]; 206 } else 207 a_mod_m = a2; 208 if (BN_is_zero(a_mod_m)) { 209 BN_zero(rr); 210 ret = 1; 211 goto err; 212 } 213 if (!BN_to_montgomery(val2[0], a_mod_m, mont, ctx)) 214 goto err; 215 if (window2 > 1) { 216 if (!BN_mod_mul_montgomery(d, val2[0], val2[0], mont, ctx)) 217 goto err; 218 219 j = 1 << (window2 - 1); 220 for (i = 1; i < j; i++) { 221 if (((val2[i] = BN_CTX_get(ctx)) == NULL) || 222 !BN_mod_mul_montgomery(val2[i], val2[i - 1], d, mont, ctx)) 223 goto err; 224 } 225 } 226 227 /* Now compute the power product, using independent windows. */ 228 r_is_one = 1; 229 wvalue1 = 0; /* The 'value' of the first window */ 230 wvalue2 = 0; /* The 'value' of the second window */ 231 wpos1 = 0; /* If wvalue1 > 0, the bottom bit of the 232 * first window */ 233 wpos2 = 0; /* If wvalue2 > 0, the bottom bit of the 234 * second window */ 235 236 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx)) 237 goto err; 238 for (b = bits - 1; b >= 0; b--) { 239 if (!r_is_one) { 240 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) 241 goto err; 242 } 243 244 if (!wvalue1) 245 if (BN_is_bit_set(p1, b)) { 246 /* 247 * consider bits b-window1+1 .. b for this window 248 */ 249 i = b - window1 + 1; 250 while (!BN_is_bit_set(p1, i)) /* works for i<0 */ 251 i++; 252 wpos1 = i; 253 wvalue1 = 1; 254 for (i = b - 1; i >= wpos1; i--) { 255 wvalue1 <<= 1; 256 if (BN_is_bit_set(p1, i)) 257 wvalue1++; 258 } 259 } 260 261 if (!wvalue2) 262 if (BN_is_bit_set(p2, b)) { 263 /* 264 * consider bits b-window2+1 .. b for this window 265 */ 266 i = b - window2 + 1; 267 while (!BN_is_bit_set(p2, i)) 268 i++; 269 wpos2 = i; 270 wvalue2 = 1; 271 for (i = b - 1; i >= wpos2; i--) { 272 wvalue2 <<= 1; 273 if (BN_is_bit_set(p2, i)) 274 wvalue2++; 275 } 276 } 277 278 if (wvalue1 && b == wpos1) { 279 /* wvalue1 is odd and < 2^window1 */ 280 if (!BN_mod_mul_montgomery(r, r, val1[wvalue1 >> 1], mont, ctx)) 281 goto err; 282 wvalue1 = 0; 283 r_is_one = 0; 284 } 285 286 if (wvalue2 && b == wpos2) { 287 /* wvalue2 is odd and < 2^window2 */ 288 if (!BN_mod_mul_montgomery(r, r, val2[wvalue2 >> 1], mont, ctx)) 289 goto err; 290 wvalue2 = 0; 291 r_is_one = 0; 292 } 293 } 294 if (!BN_from_montgomery(rr, r, mont, ctx)) 295 goto err; 296 ret = 1; 297 err: 298 if ((in_mont == NULL) && (mont != NULL)) 299 BN_MONT_CTX_free(mont); 300 BN_CTX_end(ctx); 301 bn_check_top(rr); 302 return (ret); 303} 304