bn_mul.c revision 1.38
1/* $OpenBSD: bn_mul.c,v 1.38 2023/06/12 16:17:24 jsing 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#include <assert.h> 60#include <stdio.h> 61#include <string.h> 62 63#include <openssl/opensslconf.h> 64 65#include "bn_arch.h" 66#include "bn_internal.h" 67#include "bn_local.h" 68 69/* 70 * bn_mul_comba4() computes r[] = a[] * b[] using Comba multiplication 71 * (https://everything2.com/title/Comba+multiplication), where a and b are both 72 * four word arrays, producing an eight word array result. 73 */ 74#ifndef HAVE_BN_MUL_COMBA4 75void 76bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) 77{ 78 BN_ULONG c0, c1, c2; 79 80 bn_mulw_addtw(a[0], b[0], 0, 0, 0, &c2, &c1, &r[0]); 81 82 bn_mulw_addtw(a[0], b[1], 0, c2, c1, &c2, &c1, &c0); 83 bn_mulw_addtw(a[1], b[0], c2, c1, c0, &c2, &c1, &r[1]); 84 85 bn_mulw_addtw(a[2], b[0], 0, c2, c1, &c2, &c1, &c0); 86 bn_mulw_addtw(a[1], b[1], c2, c1, c0, &c2, &c1, &c0); 87 bn_mulw_addtw(a[0], b[2], c2, c1, c0, &c2, &c1, &r[2]); 88 89 bn_mulw_addtw(a[0], b[3], 0, c2, c1, &c2, &c1, &c0); 90 bn_mulw_addtw(a[1], b[2], c2, c1, c0, &c2, &c1, &c0); 91 bn_mulw_addtw(a[2], b[1], c2, c1, c0, &c2, &c1, &c0); 92 bn_mulw_addtw(a[3], b[0], c2, c1, c0, &c2, &c1, &r[3]); 93 94 bn_mulw_addtw(a[3], b[1], 0, c2, c1, &c2, &c1, &c0); 95 bn_mulw_addtw(a[2], b[2], c2, c1, c0, &c2, &c1, &c0); 96 bn_mulw_addtw(a[1], b[3], c2, c1, c0, &c2, &c1, &r[4]); 97 98 bn_mulw_addtw(a[2], b[3], 0, c2, c1, &c2, &c1, &c0); 99 bn_mulw_addtw(a[3], b[2], c2, c1, c0, &c2, &c1, &r[5]); 100 101 bn_mulw_addtw(a[3], b[3], 0, c2, c1, &c2, &r[7], &r[6]); 102} 103#endif 104 105/* 106 * bn_mul_comba8() computes r[] = a[] * b[] using Comba multiplication 107 * (https://everything2.com/title/Comba+multiplication), where a and b are both 108 * eight word arrays, producing a 16 word array result. 109 */ 110#ifndef HAVE_BN_MUL_COMBA8 111void 112bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) 113{ 114 BN_ULONG c0, c1, c2; 115 116 bn_mulw_addtw(a[0], b[0], 0, 0, 0, &c2, &c1, &r[0]); 117 118 bn_mulw_addtw(a[0], b[1], 0, c2, c1, &c2, &c1, &c0); 119 bn_mulw_addtw(a[1], b[0], c2, c1, c0, &c2, &c1, &r[1]); 120 121 bn_mulw_addtw(a[2], b[0], 0, c2, c1, &c2, &c1, &c0); 122 bn_mulw_addtw(a[1], b[1], c2, c1, c0, &c2, &c1, &c0); 123 bn_mulw_addtw(a[0], b[2], c2, c1, c0, &c2, &c1, &r[2]); 124 125 bn_mulw_addtw(a[0], b[3], 0, c2, c1, &c2, &c1, &c0); 126 bn_mulw_addtw(a[1], b[2], c2, c1, c0, &c2, &c1, &c0); 127 bn_mulw_addtw(a[2], b[1], c2, c1, c0, &c2, &c1, &c0); 128 bn_mulw_addtw(a[3], b[0], c2, c1, c0, &c2, &c1, &r[3]); 129 130 bn_mulw_addtw(a[4], b[0], 0, c2, c1, &c2, &c1, &c0); 131 bn_mulw_addtw(a[3], b[1], c2, c1, c0, &c2, &c1, &c0); 132 bn_mulw_addtw(a[2], b[2], c2, c1, c0, &c2, &c1, &c0); 133 bn_mulw_addtw(a[1], b[3], c2, c1, c0, &c2, &c1, &c0); 134 bn_mulw_addtw(a[0], b[4], c2, c1, c0, &c2, &c1, &r[4]); 135 136 bn_mulw_addtw(a[0], b[5], 0, c2, c1, &c2, &c1, &c0); 137 bn_mulw_addtw(a[1], b[4], c2, c1, c0, &c2, &c1, &c0); 138 bn_mulw_addtw(a[2], b[3], c2, c1, c0, &c2, &c1, &c0); 139 bn_mulw_addtw(a[3], b[2], c2, c1, c0, &c2, &c1, &c0); 140 bn_mulw_addtw(a[4], b[1], c2, c1, c0, &c2, &c1, &c0); 141 bn_mulw_addtw(a[5], b[0], c2, c1, c0, &c2, &c1, &r[5]); 142 143 bn_mulw_addtw(a[6], b[0], 0, c2, c1, &c2, &c1, &c0); 144 bn_mulw_addtw(a[5], b[1], c2, c1, c0, &c2, &c1, &c0); 145 bn_mulw_addtw(a[4], b[2], c2, c1, c0, &c2, &c1, &c0); 146 bn_mulw_addtw(a[3], b[3], c2, c1, c0, &c2, &c1, &c0); 147 bn_mulw_addtw(a[2], b[4], c2, c1, c0, &c2, &c1, &c0); 148 bn_mulw_addtw(a[1], b[5], c2, c1, c0, &c2, &c1, &c0); 149 bn_mulw_addtw(a[0], b[6], c2, c1, c0, &c2, &c1, &r[6]); 150 151 bn_mulw_addtw(a[0], b[7], 0, c2, c1, &c2, &c1, &c0); 152 bn_mulw_addtw(a[1], b[6], c2, c1, c0, &c2, &c1, &c0); 153 bn_mulw_addtw(a[2], b[5], c2, c1, c0, &c2, &c1, &c0); 154 bn_mulw_addtw(a[3], b[4], c2, c1, c0, &c2, &c1, &c0); 155 bn_mulw_addtw(a[4], b[3], c2, c1, c0, &c2, &c1, &c0); 156 bn_mulw_addtw(a[5], b[2], c2, c1, c0, &c2, &c1, &c0); 157 bn_mulw_addtw(a[6], b[1], c2, c1, c0, &c2, &c1, &c0); 158 bn_mulw_addtw(a[7], b[0], c2, c1, c0, &c2, &c1, &r[7]); 159 160 bn_mulw_addtw(a[7], b[1], 0, c2, c1, &c2, &c1, &c0); 161 bn_mulw_addtw(a[6], b[2], c2, c1, c0, &c2, &c1, &c0); 162 bn_mulw_addtw(a[5], b[3], c2, c1, c0, &c2, &c1, &c0); 163 bn_mulw_addtw(a[4], b[4], c2, c1, c0, &c2, &c1, &c0); 164 bn_mulw_addtw(a[3], b[5], c2, c1, c0, &c2, &c1, &c0); 165 bn_mulw_addtw(a[2], b[6], c2, c1, c0, &c2, &c1, &c0); 166 bn_mulw_addtw(a[1], b[7], c2, c1, c0, &c2, &c1, &r[8]); 167 168 bn_mulw_addtw(a[2], b[7], 0, c2, c1, &c2, &c1, &c0); 169 bn_mulw_addtw(a[3], b[6], c2, c1, c0, &c2, &c1, &c0); 170 bn_mulw_addtw(a[4], b[5], c2, c1, c0, &c2, &c1, &c0); 171 bn_mulw_addtw(a[5], b[4], c2, c1, c0, &c2, &c1, &c0); 172 bn_mulw_addtw(a[6], b[3], c2, c1, c0, &c2, &c1, &c0); 173 bn_mulw_addtw(a[7], b[2], c2, c1, c0, &c2, &c1, &r[9]); 174 175 bn_mulw_addtw(a[7], b[3], 0, c2, c1, &c2, &c1, &c0); 176 bn_mulw_addtw(a[6], b[4], c2, c1, c0, &c2, &c1, &c0); 177 bn_mulw_addtw(a[5], b[5], c2, c1, c0, &c2, &c1, &c0); 178 bn_mulw_addtw(a[4], b[6], c2, c1, c0, &c2, &c1, &c0); 179 bn_mulw_addtw(a[3], b[7], c2, c1, c0, &c2, &c1, &r[10]); 180 181 bn_mulw_addtw(a[4], b[7], 0, c2, c1, &c2, &c1, &c0); 182 bn_mulw_addtw(a[5], b[6], c2, c1, c0, &c2, &c1, &c0); 183 bn_mulw_addtw(a[6], b[5], c2, c1, c0, &c2, &c1, &c0); 184 bn_mulw_addtw(a[7], b[4], c2, c1, c0, &c2, &c1, &r[11]); 185 186 bn_mulw_addtw(a[7], b[5], 0, c2, c1, &c2, &c1, &c0); 187 bn_mulw_addtw(a[6], b[6], c2, c1, c0, &c2, &c1, &c0); 188 bn_mulw_addtw(a[5], b[7], c2, c1, c0, &c2, &c1, &r[12]); 189 190 bn_mulw_addtw(a[6], b[7], 0, c2, c1, &c2, &c1, &c0); 191 bn_mulw_addtw(a[7], b[6], c2, c1, c0, &c2, &c1, &r[13]); 192 193 bn_mulw_addtw(a[7], b[7], 0, c2, c1, &c2, &r[15], &r[14]); 194} 195#endif 196 197/* 198 * bn_mul_words() computes (carry:r[i]) = a[i] * w + carry, where a is an array 199 * of words and w is a single word. This should really be called bn_mulw_words() 200 * since only one input is an array. This is used as a step in the multiplication 201 * of word arrays. 202 */ 203#ifndef HAVE_BN_MUL_WORDS 204BN_ULONG 205bn_mul_words(BN_ULONG *r, const BN_ULONG *a, int num, BN_ULONG w) 206{ 207 BN_ULONG carry = 0; 208 209 assert(num >= 0); 210 if (num <= 0) 211 return 0; 212 213 while (num & ~3) { 214 bn_qwmulw_addw(a[3], a[2], a[1], a[0], w, carry, &carry, 215 &r[3], &r[2], &r[1], &r[0]); 216 a += 4; 217 r += 4; 218 num -= 4; 219 } 220 while (num) { 221 bn_mulw_addw(a[0], w, carry, &carry, &r[0]); 222 a++; 223 r++; 224 num--; 225 } 226 return carry; 227} 228#endif 229 230/* 231 * bn_mul_add_words() computes (carry:r[i]) = a[i] * w + r[i] + carry, where 232 * a is an array of words and w is a single word. This should really be called 233 * bn_mulw_add_words() since only one input is an array. This is used as a step 234 * in the multiplication of word arrays. 235 */ 236#ifndef HAVE_BN_MUL_ADD_WORDS 237BN_ULONG 238bn_mul_add_words(BN_ULONG *r, const BN_ULONG *a, int num, BN_ULONG w) 239{ 240 BN_ULONG carry = 0; 241 242 assert(num >= 0); 243 if (num <= 0) 244 return 0; 245 246 while (num & ~3) { 247 bn_qwmulw_addqw_addw(a[3], a[2], a[1], a[0], w, 248 r[3], r[2], r[1], r[0], carry, &carry, 249 &r[3], &r[2], &r[1], &r[0]); 250 a += 4; 251 r += 4; 252 num -= 4; 253 } 254 while (num) { 255 bn_mulw_addw_addw(a[0], w, r[0], carry, &carry, &r[0]); 256 a++; 257 r++; 258 num--; 259 } 260 261 return carry; 262} 263#endif 264 265void 266bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb) 267{ 268 BN_ULONG *rr; 269 270 271 if (na < nb) { 272 int itmp; 273 BN_ULONG *ltmp; 274 275 itmp = na; 276 na = nb; 277 nb = itmp; 278 ltmp = a; 279 a = b; 280 b = ltmp; 281 282 } 283 rr = &(r[na]); 284 if (nb <= 0) { 285 (void)bn_mul_words(r, a, na, 0); 286 return; 287 } else 288 rr[0] = bn_mul_words(r, a, na, b[0]); 289 290 for (;;) { 291 if (--nb <= 0) 292 return; 293 rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]); 294 if (--nb <= 0) 295 return; 296 rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]); 297 if (--nb <= 0) 298 return; 299 rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]); 300 if (--nb <= 0) 301 return; 302 rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]); 303 rr += 4; 304 r += 4; 305 b += 4; 306 } 307} 308 309 310#ifndef HAVE_BN_MUL 311int 312bn_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, int rn, BN_CTX *ctx) 313{ 314 bn_mul_normal(r->d, a->d, a->top, b->d, b->top); 315 316 return 1; 317} 318 319#endif /* HAVE_BN_MUL */ 320 321int 322BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 323{ 324 BIGNUM *rr; 325 int rn; 326 int ret = 0; 327 328 BN_CTX_start(ctx); 329 330 if (BN_is_zero(a) || BN_is_zero(b)) { 331 BN_zero(r); 332 goto done; 333 } 334 335 rr = r; 336 if (rr == a || rr == b) 337 rr = BN_CTX_get(ctx); 338 if (rr == NULL) 339 goto err; 340 341 rn = a->top + b->top; 342 if (rn < a->top) 343 goto err; 344 if (!bn_wexpand(rr, rn)) 345 goto err; 346 347 if (a->top == 4 && b->top == 4) { 348 bn_mul_comba4(rr->d, a->d, b->d); 349 } else if (a->top == 8 && b->top == 8) { 350 bn_mul_comba8(rr->d, a->d, b->d); 351 } else { 352 if (!bn_mul(rr, a, b, rn, ctx)) 353 goto err; 354 } 355 356 rr->top = rn; 357 bn_correct_top(rr); 358 359 BN_set_negative(rr, a->neg ^ b->neg); 360 361 if (!bn_copy(r, rr)) 362 goto err; 363 done: 364 ret = 1; 365 err: 366 BN_CTX_end(ctx); 367 368 return ret; 369} 370