1 /* $OpenBSD: bn_exp2.c,v 1.12 2017/01/29 17:49:22 beck Exp $ */ 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> 113 114 #include <openssl/err.h> 115 116 #include "bn_lcl.h" 117 118 #define TABLE_SIZE 32 119 120 int 121 BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1, 122 const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m, BN_CTX *ctx, 123 BN_MONT_CTX *in_mont) 124 { 125 int i, j, bits, b, bits1, bits2, ret = 0, wpos1, wpos2, window1, window2, wvalue1, wvalue2; 126 int r_is_one = 1; 127 BIGNUM *d, *r; 128 const BIGNUM *a_mod_m; 129 /* Tables of variables obtained from 'ctx' */ 130 BIGNUM *val1[TABLE_SIZE], *val2[TABLE_SIZE]; 131 BN_MONT_CTX *mont = NULL; 132 133 bn_check_top(a1); 134 bn_check_top(p1); 135 bn_check_top(a2); 136 bn_check_top(p2); 137 bn_check_top(m); 138 139 if (!(m->d[0] & 1)) { 140 BNerror(BN_R_CALLED_WITH_EVEN_MODULUS); 141 return (0); 142 } 143 bits1 = BN_num_bits(p1); 144 bits2 = BN_num_bits(p2); 145 if ((bits1 == 0) && (bits2 == 0)) { 146 ret = BN_one(rr); 147 return ret; 148 } 149 150 bits = (bits1 > bits2) ? bits1 : bits2; 151 152 BN_CTX_start(ctx); 153 if ((d = BN_CTX_get(ctx)) == NULL) 154 goto err; 155 if ((r = BN_CTX_get(ctx)) == NULL) 156 goto err; 157 if ((val1[0] = BN_CTX_get(ctx)) == NULL) 158 goto err; 159 if ((val2[0] = BN_CTX_get(ctx)) == NULL) 160 goto err; 161 162 if (in_mont != NULL) 163 mont = in_mont; 164 else { 165 if ((mont = BN_MONT_CTX_new()) == NULL) 166 goto err; 167 if (!BN_MONT_CTX_set(mont, m, ctx)) 168 goto err; 169 } 170 171 window1 = BN_window_bits_for_exponent_size(bits1); 172 window2 = BN_window_bits_for_exponent_size(bits2); 173 174 /* 175 * Build table for a1: val1[i] := a1^(2*i + 1) mod m for i = 0 .. 2^(window1-1) 176 */ 177 if (a1->neg || BN_ucmp(a1, m) >= 0) { 178 if (!BN_mod_ct(val1[0], a1, m, ctx)) 179 goto err; 180 a_mod_m = val1[0]; 181 } else 182 a_mod_m = a1; 183 if (BN_is_zero(a_mod_m)) { 184 BN_zero(rr); 185 ret = 1; 186 goto err; 187 } 188 189 if (!BN_to_montgomery(val1[0], a_mod_m, mont, ctx)) 190 goto err; 191 if (window1 > 1) { 192 if (!BN_mod_mul_montgomery(d, val1[0], val1[0], mont, ctx)) 193 goto err; 194 195 j = 1 << (window1 - 1); 196 for (i = 1; i < j; i++) { 197 if (((val1[i] = BN_CTX_get(ctx)) == NULL) || 198 !BN_mod_mul_montgomery(val1[i], val1[i - 1], 199 d, mont, ctx)) 200 goto err; 201 } 202 } 203 204 205 /* 206 * Build table for a2: val2[i] := a2^(2*i + 1) mod m for i = 0 .. 2^(window2-1) 207 */ 208 if (a2->neg || BN_ucmp(a2, m) >= 0) { 209 if (!BN_mod_ct(val2[0], a2, m, ctx)) 210 goto err; 211 a_mod_m = val2[0]; 212 } else 213 a_mod_m = a2; 214 if (BN_is_zero(a_mod_m)) { 215 BN_zero(rr); 216 ret = 1; 217 goto err; 218 } 219 if (!BN_to_montgomery(val2[0], a_mod_m, mont, ctx)) 220 goto err; 221 if (window2 > 1) { 222 if (!BN_mod_mul_montgomery(d, val2[0], val2[0], mont, ctx)) 223 goto err; 224 225 j = 1 << (window2 - 1); 226 for (i = 1; i < j; i++) { 227 if (((val2[i] = BN_CTX_get(ctx)) == NULL) || 228 !BN_mod_mul_montgomery(val2[i], val2[i - 1], 229 d, mont, ctx)) 230 goto err; 231 } 232 } 233 234 235 /* Now compute the power product, using independent windows. */ 236 r_is_one = 1; 237 wvalue1 = 0; /* The 'value' of the first window */ 238 wvalue2 = 0; /* The 'value' of the second window */ 239 wpos1 = 0; /* If wvalue1 > 0, the bottom bit of the first window */ 240 wpos2 = 0; /* If wvalue2 > 0, the bottom bit of the second window */ 241 242 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx)) 243 goto err; 244 for (b = bits - 1; b >= 0; b--) { 245 if (!r_is_one) { 246 if (!BN_mod_mul_montgomery(r, r,r, mont, ctx)) 247 goto err; 248 } 249 250 if (!wvalue1) 251 if (BN_is_bit_set(p1, b)) { 252 /* consider bits b-window1+1 .. b for this window */ 253 i = b - window1 + 1; 254 while (!BN_is_bit_set(p1, i)) /* works for i<0 */ 255 i++; 256 wpos1 = i; 257 wvalue1 = 1; 258 for (i = b - 1; i >= wpos1; i--) { 259 wvalue1 <<= 1; 260 if (BN_is_bit_set(p1, i)) 261 wvalue1++; 262 } 263 } 264 265 if (!wvalue2) 266 if (BN_is_bit_set(p2, b)) { 267 /* consider bits b-window2+1 .. b for this window */ 268 i = b - window2 + 1; 269 while (!BN_is_bit_set(p2, i)) 270 i++; 271 wpos2 = i; 272 wvalue2 = 1; 273 for (i = b - 1; i >= wpos2; i--) { 274 wvalue2 <<= 1; 275 if (BN_is_bit_set(p2, i)) 276 wvalue2++; 277 } 278 } 279 280 if (wvalue1 && b == wpos1) { 281 /* wvalue1 is odd and < 2^window1 */ 282 if (!BN_mod_mul_montgomery(r, r, val1[wvalue1 >> 1], 283 mont, ctx)) 284 goto err; 285 wvalue1 = 0; 286 r_is_one = 0; 287 } 288 289 if (wvalue2 && b == wpos2) { 290 /* wvalue2 is odd and < 2^window2 */ 291 if (!BN_mod_mul_montgomery(r, r, val2[wvalue2 >> 1], 292 mont, ctx)) 293 goto err; 294 wvalue2 = 0; 295 r_is_one = 0; 296 } 297 } 298 if (!BN_from_montgomery(rr, r,mont, ctx)) 299 goto err; 300 ret = 1; 301 302 err: 303 if ((in_mont == NULL) && (mont != NULL)) 304 BN_MONT_CTX_free(mont); 305 BN_CTX_end(ctx); 306 bn_check_top(rr); 307 return (ret); 308 } 309