bn_mod.c revision 337982
1/* crypto/bn/bn_mod.c */ 2/* 3 * Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de> 4 * for the OpenSSL project. 5 */ 6/* ==================================================================== 7 * Copyright (c) 1998-2018 The OpenSSL Project. All rights reserved. 8 * 9 * Redistribution and use in source and binary forms, with or without 10 * modification, are permitted provided that the following conditions 11 * are met: 12 * 13 * 1. Redistributions of source code must retain the above copyright 14 * notice, this list of conditions and the following disclaimer. 15 * 16 * 2. Redistributions in binary form must reproduce the above copyright 17 * notice, this list of conditions and the following disclaimer in 18 * the documentation and/or other materials provided with the 19 * distribution. 20 * 21 * 3. All advertising materials mentioning features or use of this 22 * software must display the following acknowledgment: 23 * "This product includes software developed by the OpenSSL Project 24 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 25 * 26 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 27 * endorse or promote products derived from this software without 28 * prior written permission. For written permission, please contact 29 * openssl-core@openssl.org. 30 * 31 * 5. Products derived from this software may not be called "OpenSSL" 32 * nor may "OpenSSL" appear in their names without prior written 33 * permission of the OpenSSL Project. 34 * 35 * 6. Redistributions of any form whatsoever must retain the following 36 * acknowledgment: 37 * "This product includes software developed by the OpenSSL Project 38 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 39 * 40 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 41 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 43 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 44 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 45 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 46 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 47 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 49 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 50 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 51 * OF THE POSSIBILITY OF SUCH DAMAGE. 52 * ==================================================================== 53 * 54 * This product includes cryptographic software written by Eric Young 55 * (eay@cryptsoft.com). This product includes software written by Tim 56 * Hudson (tjh@cryptsoft.com). 57 * 58 */ 59/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) 60 * All rights reserved. 61 * 62 * This package is an SSL implementation written 63 * by Eric Young (eay@cryptsoft.com). 64 * The implementation was written so as to conform with Netscapes SSL. 65 * 66 * This library is free for commercial and non-commercial use as long as 67 * the following conditions are aheared to. The following conditions 68 * apply to all code found in this distribution, be it the RC4, RSA, 69 * lhash, DES, etc., code; not just the SSL code. The SSL documentation 70 * included with this distribution is covered by the same copyright terms 71 * except that the holder is Tim Hudson (tjh@cryptsoft.com). 72 * 73 * Copyright remains Eric Young's, and as such any Copyright notices in 74 * the code are not to be removed. 75 * If this package is used in a product, Eric Young should be given attribution 76 * as the author of the parts of the library used. 77 * This can be in the form of a textual message at program startup or 78 * in documentation (online or textual) provided with the package. 79 * 80 * Redistribution and use in source and binary forms, with or without 81 * modification, are permitted provided that the following conditions 82 * are met: 83 * 1. Redistributions of source code must retain the copyright 84 * notice, this list of conditions and the following disclaimer. 85 * 2. Redistributions in binary form must reproduce the above copyright 86 * notice, this list of conditions and the following disclaimer in the 87 * documentation and/or other materials provided with the distribution. 88 * 3. All advertising materials mentioning features or use of this software 89 * must display the following acknowledgement: 90 * "This product includes cryptographic software written by 91 * Eric Young (eay@cryptsoft.com)" 92 * The word 'cryptographic' can be left out if the rouines from the library 93 * being used are not cryptographic related :-). 94 * 4. If you include any Windows specific code (or a derivative thereof) from 95 * the apps directory (application code) you must include an acknowledgement: 96 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" 97 * 98 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND 99 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 100 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 101 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 102 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 103 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 104 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 105 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 106 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 107 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 108 * SUCH DAMAGE. 109 * 110 * The licence and distribution terms for any publically available version or 111 * derivative of this code cannot be changed. i.e. this code cannot simply be 112 * copied and put under another distribution licence 113 * [including the GNU Public Licence.] 114 */ 115 116#include "cryptlib.h" 117#include "bn_lcl.h" 118 119#if 0 /* now just a #define */ 120int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx) 121{ 122 return (BN_div(NULL, rem, m, d, ctx)); 123 /* note that rem->neg == m->neg (unless the remainder is zero) */ 124} 125#endif 126 127int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx) 128{ 129 /* 130 * like BN_mod, but returns non-negative remainder (i.e., 0 <= r < |d| 131 * always holds) 132 */ 133 134 if (!(BN_mod(r, m, d, ctx))) 135 return 0; 136 if (!r->neg) 137 return 1; 138 /* now -|d| < r < 0, so we have to set r := r + |d| */ 139 return (d->neg ? BN_sub : BN_add) (r, r, d); 140} 141 142int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, 143 BN_CTX *ctx) 144{ 145 if (!BN_add(r, a, b)) 146 return 0; 147 return BN_nnmod(r, r, m, ctx); 148} 149 150/* 151 * BN_mod_add variant that may be used if both a and b are non-negative and 152 * less than m. The original algorithm was 153 * 154 * if (!BN_uadd(r, a, b)) 155 * return 0; 156 * if (BN_ucmp(r, m) >= 0) 157 * return BN_usub(r, r, m); 158 * 159 * which is replaced with addition, subtracting modulus, and conditional 160 * move depending on whether or not subtraction borrowed. 161 */ 162int bn_mod_add_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 163 const BIGNUM *m) 164{ 165 size_t i, ai, bi, mtop = m->top; 166 BN_ULONG storage[1024 / BN_BITS2]; 167 BN_ULONG carry, temp, mask, *rp, *tp = storage; 168 const BN_ULONG *ap, *bp; 169 170 if (bn_wexpand(r, m->top) == NULL) 171 return 0; 172 173 if (mtop > sizeof(storage) / sizeof(storage[0]) 174 && (tp = OPENSSL_malloc(mtop * sizeof(BN_ULONG))) == NULL) 175 return 0; 176 177 ap = a->d != NULL ? a->d : tp; 178 bp = b->d != NULL ? b->d : tp; 179 180 for (i = 0, ai = 0, bi = 0, carry = 0; i < mtop;) { 181 mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1)); 182 temp = ((ap[ai] & mask) + carry) & BN_MASK2; 183 carry = (temp < carry); 184 185 mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1)); 186 tp[i] = ((bp[bi] & mask) + temp) & BN_MASK2; 187 carry += (tp[i] < temp); 188 189 i++; 190 ai += (i - a->dmax) >> (8 * sizeof(i) - 1); 191 bi += (i - b->dmax) >> (8 * sizeof(i) - 1); 192 } 193 rp = r->d; 194 carry -= bn_sub_words(rp, tp, m->d, mtop); 195 for (i = 0; i < mtop; i++) { 196 rp[i] = (carry & tp[i]) | (~carry & rp[i]); 197 ((volatile BN_ULONG *)tp)[i] = 0; 198 } 199 r->top = mtop; 200 r->neg = 0; 201 202 if (tp != storage) 203 OPENSSL_free(tp); 204 205 return 1; 206} 207 208int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 209 const BIGNUM *m) 210{ 211 int ret = bn_mod_add_fixed_top(r, a, b, m); 212 213 if (ret) 214 bn_correct_top(r); 215 216 return ret; 217} 218 219int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, 220 BN_CTX *ctx) 221{ 222 if (!BN_sub(r, a, b)) 223 return 0; 224 return BN_nnmod(r, r, m, ctx); 225} 226 227/* 228 * BN_mod_sub variant that may be used if both a and b are non-negative and 229 * less than m 230 */ 231int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 232 const BIGNUM *m) 233{ 234 if (!BN_sub(r, a, b)) 235 return 0; 236 if (r->neg) 237 return BN_add(r, r, m); 238 return 1; 239} 240 241/* slow but works */ 242int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, 243 BN_CTX *ctx) 244{ 245 BIGNUM *t; 246 int ret = 0; 247 248 bn_check_top(a); 249 bn_check_top(b); 250 bn_check_top(m); 251 252 BN_CTX_start(ctx); 253 if ((t = BN_CTX_get(ctx)) == NULL) 254 goto err; 255 if (a == b) { 256 if (!BN_sqr(t, a, ctx)) 257 goto err; 258 } else { 259 if (!BN_mul(t, a, b, ctx)) 260 goto err; 261 } 262 if (!BN_nnmod(r, t, m, ctx)) 263 goto err; 264 bn_check_top(r); 265 ret = 1; 266 err: 267 BN_CTX_end(ctx); 268 return (ret); 269} 270 271int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx) 272{ 273 if (!BN_sqr(r, a, ctx)) 274 return 0; 275 /* r->neg == 0, thus we don't need BN_nnmod */ 276 return BN_mod(r, r, m, ctx); 277} 278 279int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx) 280{ 281 if (!BN_lshift1(r, a)) 282 return 0; 283 bn_check_top(r); 284 return BN_nnmod(r, r, m, ctx); 285} 286 287/* 288 * BN_mod_lshift1 variant that may be used if a is non-negative and less than 289 * m 290 */ 291int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m) 292{ 293 if (!BN_lshift1(r, a)) 294 return 0; 295 bn_check_top(r); 296 if (BN_cmp(r, m) >= 0) 297 return BN_sub(r, r, m); 298 return 1; 299} 300 301int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, 302 BN_CTX *ctx) 303{ 304 BIGNUM *abs_m = NULL; 305 int ret; 306 307 if (!BN_nnmod(r, a, m, ctx)) 308 return 0; 309 310 if (m->neg) { 311 abs_m = BN_dup(m); 312 if (abs_m == NULL) 313 return 0; 314 abs_m->neg = 0; 315 } 316 317 ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m)); 318 bn_check_top(r); 319 320 if (abs_m) 321 BN_free(abs_m); 322 return ret; 323} 324 325/* 326 * BN_mod_lshift variant that may be used if a is non-negative and less than 327 * m 328 */ 329int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m) 330{ 331 if (r != a) { 332 if (BN_copy(r, a) == NULL) 333 return 0; 334 } 335 336 while (n > 0) { 337 int max_shift; 338 339 /* 0 < r < m */ 340 max_shift = BN_num_bits(m) - BN_num_bits(r); 341 /* max_shift >= 0 */ 342 343 if (max_shift < 0) { 344 BNerr(BN_F_BN_MOD_LSHIFT_QUICK, BN_R_INPUT_NOT_REDUCED); 345 return 0; 346 } 347 348 if (max_shift > n) 349 max_shift = n; 350 351 if (max_shift) { 352 if (!BN_lshift(r, r, max_shift)) 353 return 0; 354 n -= max_shift; 355 } else { 356 if (!BN_lshift1(r, r)) 357 return 0; 358 --n; 359 } 360 361 /* BN_num_bits(r) <= BN_num_bits(m) */ 362 363 if (BN_cmp(r, m) >= 0) { 364 if (!BN_sub(r, r, m)) 365 return 0; 366 } 367 } 368 bn_check_top(r); 369 370 return 1; 371} 372