bn_mul.c revision 1.34
1/* $OpenBSD: bn_mul.c,v 1.34 2023/02/22 05:57:19 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#ifndef OPENSSL_SMALL_FOOTPRINT 214 while (num & ~3) { 215 bn_mulw_addw(a[0], w, carry, &carry, &r[0]); 216 bn_mulw_addw(a[1], w, carry, &carry, &r[1]); 217 bn_mulw_addw(a[2], w, carry, &carry, &r[2]); 218 bn_mulw_addw(a[3], w, carry, &carry, &r[3]); 219 a += 4; 220 r += 4; 221 num -= 4; 222 } 223#endif 224 while (num) { 225 bn_mulw_addw(a[0], w, carry, &carry, &r[0]); 226 a++; 227 r++; 228 num--; 229 } 230 return carry; 231} 232#endif 233 234/* 235 * bn_mul_add_words() computes (carry:r[i]) = a[i] * w + r[i] + carry, where 236 * a is an array of words and w is a single word. This should really be called 237 * bn_mulw_add_words() since only one input is an array. This is used as a step 238 * in the multiplication of word arrays. 239 */ 240#ifndef HAVE_BN_MUL_ADD_WORDS 241BN_ULONG 242bn_mul_add_words(BN_ULONG *r, const BN_ULONG *a, int num, BN_ULONG w) 243{ 244 BN_ULONG carry = 0; 245 246 assert(num >= 0); 247 if (num <= 0) 248 return 0; 249 250#ifndef OPENSSL_SMALL_FOOTPRINT 251 while (num & ~3) { 252 bn_mulw_addw_addw(a[0], w, r[0], carry, &carry, &r[0]); 253 bn_mulw_addw_addw(a[1], w, r[1], carry, &carry, &r[1]); 254 bn_mulw_addw_addw(a[2], w, r[2], carry, &carry, &r[2]); 255 bn_mulw_addw_addw(a[3], w, r[3], carry, &carry, &r[3]); 256 a += 4; 257 r += 4; 258 num -= 4; 259 } 260#endif 261 while (num) { 262 bn_mulw_addw_addw(a[0], w, r[0], carry, &carry, &r[0]); 263 a++; 264 r++; 265 num--; 266 } 267 268 return carry; 269} 270#endif 271 272void 273bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb) 274{ 275 BN_ULONG *rr; 276 277 278 if (na < nb) { 279 int itmp; 280 BN_ULONG *ltmp; 281 282 itmp = na; 283 na = nb; 284 nb = itmp; 285 ltmp = a; 286 a = b; 287 b = ltmp; 288 289 } 290 rr = &(r[na]); 291 if (nb <= 0) { 292 (void)bn_mul_words(r, a, na, 0); 293 return; 294 } else 295 rr[0] = bn_mul_words(r, a, na, b[0]); 296 297 for (;;) { 298 if (--nb <= 0) 299 return; 300 rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]); 301 if (--nb <= 0) 302 return; 303 rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]); 304 if (--nb <= 0) 305 return; 306 rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]); 307 if (--nb <= 0) 308 return; 309 rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]); 310 rr += 4; 311 r += 4; 312 b += 4; 313 } 314} 315 316#ifdef BN_RECURSION 317/* Karatsuba recursive multiplication algorithm 318 * (cf. Knuth, The Art of Computer Programming, Vol. 2) */ 319 320/* r is 2*n2 words in size, 321 * a and b are both n2 words in size. 322 * n2 must be a power of 2. 323 * We multiply and return the result. 324 * t must be 2*n2 words in size 325 * We calculate 326 * a[0]*b[0] 327 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0]) 328 * a[1]*b[1] 329 */ 330/* dnX may not be positive, but n2/2+dnX has to be */ 331void 332bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, int dna, 333 int dnb, BN_ULONG *t) 334{ 335 int n = n2 / 2, c1, c2; 336 int tna = n + dna, tnb = n + dnb; 337 unsigned int neg, zero; 338 BN_ULONG ln, lo, *p; 339 340# ifdef BN_MUL_COMBA 341# if 0 342 if (n2 == 4) { 343 bn_mul_comba4(r, a, b); 344 return; 345 } 346# endif 347 /* Only call bn_mul_comba 8 if n2 == 8 and the 348 * two arrays are complete [steve] 349 */ 350 if (n2 == 8 && dna == 0 && dnb == 0) { 351 bn_mul_comba8(r, a, b); 352 return; 353 } 354# endif /* BN_MUL_COMBA */ 355 /* Else do normal multiply */ 356 if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) { 357 bn_mul_normal(r, a, n2 + dna, b, n2 + dnb); 358 if ((dna + dnb) < 0) 359 memset(&r[2*n2 + dna + dnb], 0, 360 sizeof(BN_ULONG) * -(dna + dnb)); 361 return; 362 } 363 /* r=(a[0]-a[1])*(b[1]-b[0]) */ 364 c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna); 365 c2 = bn_cmp_part_words(&(b[n]), b,tnb, tnb - n); 366 zero = neg = 0; 367 switch (c1 * 3 + c2) { 368 case -4: 369 bn_sub(t, n, &a[n], tna, a, n); /* - */ 370 bn_sub(&t[n], n, b, n, &b[n], tnb); /* - */ 371 break; 372 case -3: 373 zero = 1; 374 break; 375 case -2: 376 bn_sub(t, n, &a[n], tna, a, n); /* - */ 377 bn_sub(&t[n], n, &b[n], tnb, b, n); /* + */ 378 neg = 1; 379 break; 380 case -1: 381 case 0: 382 case 1: 383 zero = 1; 384 break; 385 case 2: 386 bn_sub(t, n, a, n, &a[n], tna); /* + */ 387 bn_sub(&t[n], n, b, n, &b[n], tnb); /* - */ 388 neg = 1; 389 break; 390 case 3: 391 zero = 1; 392 break; 393 case 4: 394 bn_sub(t, n, a, n, &a[n], tna); 395 bn_sub(&t[n], n, &b[n], tnb, b, n); 396 break; 397 } 398 399# ifdef BN_MUL_COMBA 400 if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take 401 extra args to do this well */ 402 { 403 if (!zero) 404 bn_mul_comba4(&(t[n2]), t, &(t[n])); 405 else 406 memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG)); 407 408 bn_mul_comba4(r, a, b); 409 bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n])); 410 } else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could 411 take extra args to do this 412 well */ 413 { 414 if (!zero) 415 bn_mul_comba8(&(t[n2]), t, &(t[n])); 416 else 417 memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG)); 418 419 bn_mul_comba8(r, a, b); 420 bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n])); 421 } else 422# endif /* BN_MUL_COMBA */ 423 { 424 p = &(t[n2 * 2]); 425 if (!zero) 426 bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p); 427 else 428 memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG)); 429 bn_mul_recursive(r, a, b, n, 0, 0, p); 430 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p); 431 } 432 433 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign 434 * r[10] holds (a[0]*b[0]) 435 * r[32] holds (b[1]*b[1]) 436 */ 437 438 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2)); 439 440 if (neg) /* if t[32] is negative */ 441 { 442 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2)); 443 } else { 444 /* Might have a carry */ 445 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2)); 446 } 447 448 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1]) 449 * r[10] holds (a[0]*b[0]) 450 * r[32] holds (b[1]*b[1]) 451 * c1 holds the carry bits 452 */ 453 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2)); 454 if (c1) { 455 p = &(r[n + n2]); 456 lo= *p; 457 ln = (lo + c1) & BN_MASK2; 458 *p = ln; 459 460 /* The overflow will stop before we over write 461 * words we should not overwrite */ 462 if (ln < (BN_ULONG)c1) { 463 do { 464 p++; 465 lo= *p; 466 ln = (lo + 1) & BN_MASK2; 467 *p = ln; 468 } while (ln == 0); 469 } 470 } 471} 472 473/* n+tn is the word length 474 * t needs to be n*4 is size, as does r */ 475/* tnX may not be negative but less than n */ 476void 477bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n, int tna, 478 int tnb, BN_ULONG *t) 479{ 480 int i, j, n2 = n * 2; 481 int c1, c2, neg; 482 BN_ULONG ln, lo, *p; 483 484 if (n < 8) { 485 bn_mul_normal(r, a, n + tna, b, n + tnb); 486 return; 487 } 488 489 /* r=(a[0]-a[1])*(b[1]-b[0]) */ 490 c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna); 491 c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n); 492 neg = 0; 493 switch (c1 * 3 + c2) { 494 case -4: 495 bn_sub(t, n, &a[n], tna, a, n); /* - */ 496 bn_sub(&t[n], n, b, n, &b[n], tnb); /* - */ 497 break; 498 case -3: 499 /* break; */ 500 case -2: 501 bn_sub(t, n, &a[n], tna, a, n); /* - */ 502 bn_sub(&t[n], n, &b[n], tnb, b, n); /* + */ 503 neg = 1; 504 break; 505 case -1: 506 case 0: 507 case 1: 508 /* break; */ 509 case 2: 510 bn_sub(t, n, a, n, &a[n], tna); /* + */ 511 bn_sub(&t[n], n, b, n, &b[n], tnb); /* - */ 512 neg = 1; 513 break; 514 case 3: 515 /* break; */ 516 case 4: 517 bn_sub(t, n, a, n, &a[n], tna); 518 bn_sub(&t[n], n, &b[n], tnb, b, n); 519 break; 520 } 521 /* The zero case isn't yet implemented here. The speedup 522 would probably be negligible. */ 523# if 0 524 if (n == 4) { 525 bn_mul_comba4(&(t[n2]), t, &(t[n])); 526 bn_mul_comba4(r, a, b); 527 bn_mul_normal(&(r[n2]), &(a[n]), tn, &(b[n]), tn); 528 memset(&(r[n2 + tn * 2]), 0, sizeof(BN_ULONG) * (n2 - tn * 2)); 529 } else 530# endif 531 if (n == 8) { 532 bn_mul_comba8(&(t[n2]), t, &(t[n])); 533 bn_mul_comba8(r, a, b); 534 bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb); 535 memset(&(r[n2 + tna + tnb]), 0, 536 sizeof(BN_ULONG) * (n2 - tna - tnb)); 537 } else { 538 p = &(t[n2*2]); 539 bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p); 540 bn_mul_recursive(r, a, b, n, 0, 0, p); 541 i = n / 2; 542 /* If there is only a bottom half to the number, 543 * just do it */ 544 if (tna > tnb) 545 j = tna - i; 546 else 547 j = tnb - i; 548 if (j == 0) { 549 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), 550 i, tna - i, tnb - i, p); 551 memset(&(r[n2 + i * 2]), 0, 552 sizeof(BN_ULONG) * (n2 - i * 2)); 553 } 554 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */ 555 { 556 bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]), 557 i, tna - i, tnb - i, p); 558 memset(&(r[n2 + tna + tnb]), 0, 559 sizeof(BN_ULONG) * (n2 - tna - tnb)); 560 } 561 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */ 562 { 563 memset(&(r[n2]), 0, sizeof(BN_ULONG) * n2); 564 if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL && 565 tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) { 566 bn_mul_normal(&(r[n2]), &(a[n]), tna, 567 &(b[n]), tnb); 568 } else { 569 for (;;) { 570 i /= 2; 571 /* these simplified conditions work 572 * exclusively because difference 573 * between tna and tnb is 1 or 0 */ 574 if (i < tna || i < tnb) { 575 bn_mul_part_recursive(&(r[n2]), 576 &(a[n]), &(b[n]), i, 577 tna - i, tnb - i, p); 578 break; 579 } else if (i == tna || i == tnb) { 580 bn_mul_recursive(&(r[n2]), 581 &(a[n]), &(b[n]), i, 582 tna - i, tnb - i, p); 583 break; 584 } 585 } 586 } 587 } 588 } 589 590 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign 591 * r[10] holds (a[0]*b[0]) 592 * r[32] holds (b[1]*b[1]) 593 */ 594 595 c1 = (int)(bn_add_words(t, r,&(r[n2]), n2)); 596 597 if (neg) /* if t[32] is negative */ 598 { 599 c1 -= (int)(bn_sub_words(&(t[n2]), t,&(t[n2]), n2)); 600 } else { 601 /* Might have a carry */ 602 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2)); 603 } 604 605 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1]) 606 * r[10] holds (a[0]*b[0]) 607 * r[32] holds (b[1]*b[1]) 608 * c1 holds the carry bits 609 */ 610 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2)); 611 if (c1) { 612 p = &(r[n + n2]); 613 lo= *p; 614 ln = (lo + c1)&BN_MASK2; 615 *p = ln; 616 617 /* The overflow will stop before we over write 618 * words we should not overwrite */ 619 if (ln < (BN_ULONG)c1) { 620 do { 621 p++; 622 lo= *p; 623 ln = (lo + 1) & BN_MASK2; 624 *p = ln; 625 } while (ln == 0); 626 } 627 } 628} 629#endif /* BN_RECURSION */ 630 631#ifndef HAVE_BN_MUL 632#ifndef BN_RECURSION 633int 634bn_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, int rn, BN_CTX *ctx) 635{ 636 bn_mul_normal(r->d, a->d, a->top, b->d, b->top); 637 638 return 1; 639} 640 641#else /* BN_RECURSION */ 642int 643bn_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, int rn, BN_CTX *ctx) 644{ 645 BIGNUM *t = NULL; 646 int al, bl, i, k; 647 int j = 0; 648 int ret = 0; 649 650 BN_CTX_start(ctx); 651 652 al = a->top; 653 bl = b->top; 654 655 i = al - bl; 656 657 if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) { 658 if (i >= -1 && i <= 1) { 659 /* Find out the power of two lower or equal 660 to the longest of the two numbers */ 661 if (i >= 0) { 662 j = BN_num_bits_word((BN_ULONG)al); 663 } 664 if (i == -1) { 665 j = BN_num_bits_word((BN_ULONG)bl); 666 } 667 j = 1 << (j - 1); 668 assert(j <= al || j <= bl); 669 k = j + j; 670 if ((t = BN_CTX_get(ctx)) == NULL) 671 goto err; 672 if (al > j || bl > j) { 673 if (!bn_wexpand(t, k * 4)) 674 goto err; 675 if (!bn_wexpand(r, k * 4)) 676 goto err; 677 bn_mul_part_recursive(r->d, a->d, b->d, 678 j, al - j, bl - j, t->d); 679 } 680 else /* al <= j || bl <= j */ 681 { 682 if (!bn_wexpand(t, k * 2)) 683 goto err; 684 if (!bn_wexpand(r, k * 2)) 685 goto err; 686 bn_mul_recursive(r->d, a->d, b->d, 687 j, al - j, bl - j, t->d); 688 } 689 r->top = rn; 690 goto end; 691 } 692#if 0 693 if (i == 1 && !BN_get_flags(b, BN_FLG_STATIC_DATA)) { 694 BIGNUM *tmp_bn = (BIGNUM *)b; 695 if (!bn_wexpand(tmp_bn, al)) 696 goto err; 697 tmp_bn->d[bl] = 0; 698 bl++; 699 i--; 700 } else if (i == -1 && !BN_get_flags(a, BN_FLG_STATIC_DATA)) { 701 BIGNUM *tmp_bn = (BIGNUM *)a; 702 if (!bn_wexpand(tmp_bn, bl)) 703 goto err; 704 tmp_bn->d[al] = 0; 705 al++; 706 i++; 707 } 708 if (i == 0) { 709 /* symmetric and > 4 */ 710 /* 16 or larger */ 711 j = BN_num_bits_word((BN_ULONG)al); 712 j = 1 << (j - 1); 713 k = j + j; 714 if ((t = BN_CTX_get(ctx)) == NULL) 715 goto err; 716 if (al == j) /* exact multiple */ 717 { 718 if (!bn_wexpand(t, k * 2)) 719 goto err; 720 if (!bn_wexpand(r, k * 2)) 721 goto err; 722 bn_mul_recursive(r->d, a->d, b->d, al, t->d); 723 } else { 724 if (!bn_wexpand(t, k * 4)) 725 goto err; 726 if (!bn_wexpand(r, k * 4)) 727 goto err; 728 bn_mul_part_recursive(r->d, a->d, b->d, 729 al - j, j, t->d); 730 } 731 r->top = top; 732 goto end; 733 } 734#endif 735 } 736 737 bn_mul_normal(r->d, a->d, al, b->d, bl); 738 739 end: 740 ret = 1; 741 err: 742 BN_CTX_end(ctx); 743 744 return ret; 745} 746#endif /* BN_RECURSION */ 747#endif /* HAVE_BN_MUL */ 748 749int 750BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 751{ 752 BIGNUM *rr; 753 int rn; 754 int ret = 0; 755 756 BN_CTX_start(ctx); 757 758 if (BN_is_zero(a) || BN_is_zero(b)) { 759 BN_zero(r); 760 goto done; 761 } 762 763 rr = r; 764 if (rr == a || rr == b) 765 rr = BN_CTX_get(ctx); 766 if (rr == NULL) 767 goto err; 768 769 rn = a->top + b->top; 770 if (rn < a->top) 771 goto err; 772 if (!bn_wexpand(rr, rn)) 773 goto err; 774 775 if (a->top == 4 && b->top == 4) { 776 bn_mul_comba4(rr->d, a->d, b->d); 777 } else if (a->top == 8 && b->top == 8) { 778 bn_mul_comba8(rr->d, a->d, b->d); 779 } else { 780 if (!bn_mul(rr, a, b, rn, ctx)) 781 goto err; 782 } 783 784 rr->top = rn; 785 bn_correct_top(rr); 786 787 BN_set_negative(rr, a->neg ^ b->neg); 788 789 if (r != rr) 790 BN_copy(r, rr); 791 done: 792 ret = 1; 793 err: 794 BN_CTX_end(ctx); 795 796 return ret; 797} 798