lib/libcrypto/bn/bn_mul.c

   1 /* $OpenBSD: bn_mul.c,v 1.20 2015/02/09 15:49:22 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 #ifndef BN_DEBUG
  60 # undef NDEBUG /* avoid conflicting definitions */
  61 # define NDEBUG
  62 #endif
  63
  64 #include <assert.h>
  65 #include <stdio.h>
  66 #include <string.h>
  67
  68 #include <openssl/opensslconf.h>
  69
  70 #include "bn_lcl.h"
  71
  72 #if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
  73 /* Here follows specialised variants of bn_add_words() and
  74    bn_sub_words().  They have the property performing operations on
  75    arrays of different sizes.  The sizes of those arrays is expressed through
  76    cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
  77    which is the delta between the two lengths, calculated as len(a)-len(b).
  78    All lengths are the number of BN_ULONGs...  For the operations that require
  79    a result array as parameter, it must have the length cl+abs(dl).
  80    These functions should probably end up in bn_asm.c as soon as there are
  81    assembler counterparts for the systems that use assembler files.  */
  82
  83 BN_ULONG
  84 bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl,
  85     int dl)
  86 {
  87         BN_ULONG c, t;
  88
  89         assert(cl >= 0);
  90         c = bn_sub_words(r, a, b, cl);
  91
  92         if (dl == 0)
  93                 return c;
  94
  95         r += cl;
  96         a += cl;
  97         b += cl;
  98
  99         if (dl < 0) {
 100 #ifdef BN_COUNT
 101                 fprintf(stderr,
 102                     "  bn_sub_part_words %d + %d (dl < 0, c = %d)\n",
 103                     cl, dl, c);
 104 #endif
 105                 for (;;) {
 106                         t = b[0];
 107                         r[0] = (0 - t - c) & BN_MASK2;
 108                         if (t != 0)
 109                                 c = 1;
 110                         if (++dl >= 0)
 111                                 break;
 112
 113                         t = b[1];
 114                         r[1] = (0 - t - c) & BN_MASK2;
 115                         if (t != 0)
 116                                 c = 1;
 117                         if (++dl >= 0)
 118                                 break;
 119
 120                         t = b[2];
 121                         r[2] = (0 - t - c) & BN_MASK2;
 122                         if (t != 0)
 123                                 c = 1;
 124                         if (++dl >= 0)
 125                                 break;
 126
 127                         t = b[3];
 128                         r[3] = (0 - t - c) & BN_MASK2;
 129                         if (t != 0)
 130                                 c = 1;
 131                         if (++dl >= 0)
 132                                 break;
 133
 134                         b += 4;
 135                         r += 4;
 136                 }
 137         } else {
 138                 int save_dl = dl;
 139 #ifdef BN_COUNT
 140                 fprintf(stderr,
 141                     "  bn_sub_part_words %d + %d (dl > 0, c = %d)\n",
 142                     cl, dl, c);
 143 #endif
 144                 while (c) {
 145                         t = a[0];
 146                         r[0] = (t - c) & BN_MASK2;
 147                         if (t != 0)
 148                                 c = 0;
 149                         if (--dl <= 0)
 150                                 break;
 151
 152                         t = a[1];
 153                         r[1] = (t - c) & BN_MASK2;
 154                         if (t != 0)
 155                                 c = 0;
 156                         if (--dl <= 0)
 157                                 break;
 158
 159                         t = a[2];
 160                         r[2] = (t - c) & BN_MASK2;
 161                         if (t != 0)
 162                                 c = 0;
 163                         if (--dl <= 0)
 164                                 break;
 165
 166                         t = a[3];
 167                         r[3] = (t - c) & BN_MASK2;
 168                         if (t != 0)
 169                                 c = 0;
 170                         if (--dl <= 0)
 171                                 break;
 172
 173                         save_dl = dl;
 174                         a += 4;
 175                         r += 4;
 176                 }
 177                 if (dl > 0) {
 178 #ifdef BN_COUNT
 179                         fprintf(stderr,
 180                             "  bn_sub_part_words %d + %d (dl > 0, c == 0)\n",
 181                             cl, dl);
 182 #endif
 183                         if (save_dl > dl) {
 184                                 switch (save_dl - dl) {
 185                                 case 1:
 186                                         r[1] = a[1];
 187                                         if (--dl <= 0)
 188                                                 break;
 189                                 case 2:
 190                                         r[2] = a[2];
 191                                         if (--dl <= 0)
 192                                                 break;
 193                                 case 3:
 194                                         r[3] = a[3];
 195                                         if (--dl <= 0)
 196                                                 break;
 197                                 }
 198                                 a += 4;
 199                                 r += 4;
 200                         }
 201                 }
 202                 if (dl > 0) {
 203 #ifdef BN_COUNT
 204                         fprintf(stderr,
 205                             "  bn_sub_part_words %d + %d (dl > 0, copy)\n",
 206                             cl, dl);
 207 #endif
 208                         for (;;) {
 209                                 r[0] = a[0];
 210                                 if (--dl <= 0)
 211                                         break;
 212                                 r[1] = a[1];
 213                                 if (--dl <= 0)
 214                                         break;
 215                                 r[2] = a[2];
 216                                 if (--dl <= 0)
 217                                         break;
 218                                 r[3] = a[3];
 219                                 if (--dl <= 0)
 220                                         break;
 221
 222                                 a += 4;
 223                                 r += 4;
 224                         }
 225                 }
 226         }
 227         return c;
 228 }
 229 #endif
 230
 231 BN_ULONG
 232 bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl,
 233     int dl)
 234 {
 235         BN_ULONG c, l, t;
 236
 237         assert(cl >= 0);
 238         c = bn_add_words(r, a, b, cl);
 239
 240         if (dl == 0)
 241                 return c;
 242
 243         r += cl;
 244         a += cl;
 245         b += cl;
 246
 247         if (dl < 0) {
 248                 int save_dl = dl;
 249 #ifdef BN_COUNT
 250                 fprintf(stderr,
 251                     "  bn_add_part_words %d + %d (dl < 0, c = %d)\n",
 252                     cl, dl, c);
 253 #endif
 254                 while (c) {
 255                         l = (c + b[0]) & BN_MASK2;
 256                         c = (l < c);
 257                         r[0] = l;
 258                         if (++dl >= 0)
 259                                 break;
 260
 261                         l = (c + b[1]) & BN_MASK2;
 262                         c = (l < c);
 263                         r[1] = l;
 264                         if (++dl >= 0)
 265                                 break;
 266
 267                         l = (c + b[2]) & BN_MASK2;
 268                         c = (l < c);
 269                         r[2] = l;
 270                         if (++dl >= 0)
 271                                 break;
 272
 273                         l = (c + b[3]) & BN_MASK2;
 274                         c = (l < c);
 275                         r[3] = l;
 276                         if (++dl >= 0)
 277                                 break;
 278
 279                         save_dl = dl;
 280                         b += 4;
 281                         r += 4;
 282                 }
 283                 if (dl < 0) {
 284 #ifdef BN_COUNT
 285                         fprintf(stderr,
 286                             "  bn_add_part_words %d + %d (dl < 0, c == 0)\n",
 287                             cl, dl);
 288 #endif
 289                         if (save_dl < dl) {
 290                                 switch (dl - save_dl) {
 291                                 case 1:
 292                                         r[1] = b[1];
 293                                         if (++dl >= 0)
 294                                                 break;
 295                                 case 2:
 296                                         r[2] = b[2];
 297                                         if (++dl >= 0)
 298                                                 break;
 299                                 case 3:
 300                                         r[3] = b[3];
 301                                         if (++dl >= 0)
 302                                                 break;
 303                                 }
 304                                 b += 4;
 305                                 r += 4;
 306                         }
 307                 }
 308                 if (dl < 0) {
 309 #ifdef BN_COUNT
 310                         fprintf(stderr,
 311                             "  bn_add_part_words %d + %d (dl < 0, copy)\n",
 312                             cl, dl);
 313 #endif
 314                         for (;;) {
 315                                 r[0] = b[0];
 316                                 if (++dl >= 0)
 317                                         break;
 318                                 r[1] = b[1];
 319                                 if (++dl >= 0)
 320                                         break;
 321                                 r[2] = b[2];
 322                                 if (++dl >= 0)
 323                                         break;
 324                                 r[3] = b[3];
 325                                 if (++dl >= 0)
 326                                         break;
 327
 328                                 b += 4;
 329                                 r += 4;
 330                         }
 331                 }
 332         } else {
 333                 int save_dl = dl;
 334 #ifdef BN_COUNT
 335                 fprintf(stderr,
 336                     "  bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
 337 #endif
 338                 while (c) {
 339                         t = (a[0] + c) & BN_MASK2;
 340                         c = (t < c);
 341                         r[0] = t;
 342                         if (--dl <= 0)
 343                                 break;
 344
 345                         t = (a[1] + c) & BN_MASK2;
 346                         c = (t < c);
 347                         r[1] = t;
 348                         if (--dl <= 0)
 349                                 break;
 350
 351                         t = (a[2] + c) & BN_MASK2;
 352                         c = (t < c);
 353                         r[2] = t;
 354                         if (--dl <= 0)
 355                                 break;
 356
 357                         t = (a[3] + c) & BN_MASK2;
 358                         c = (t < c);
 359                         r[3] = t;
 360                         if (--dl <= 0)
 361                                 break;
 362
 363                         save_dl = dl;
 364                         a += 4;
 365                         r += 4;
 366                 }
 367 #ifdef BN_COUNT
 368                 fprintf(stderr,
 369                     "  bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
 370 #endif
 371                 if (dl > 0) {
 372                         if (save_dl > dl) {
 373                                 switch (save_dl - dl) {
 374                                 case 1:
 375                                         r[1] = a[1];
 376                                         if (--dl <= 0)
 377                                                 break;
 378                                 case 2:
 379                                         r[2] = a[2];
 380                                         if (--dl <= 0)
 381                                                 break;
 382                                 case 3:
 383                                         r[3] = a[3];
 384                                         if (--dl <= 0)
 385                                                 break;
 386                                 }
 387                                 a += 4;
 388                                 r += 4;
 389                         }
 390                 }
 391                 if (dl > 0) {
 392 #ifdef BN_COUNT
 393                         fprintf(stderr,
 394                             "  bn_add_part_words %d + %d (dl > 0, copy)\n",
 395                             cl, dl);
 396 #endif
 397                         for (;;) {
 398                                 r[0] = a[0];
 399                                 if (--dl <= 0)
 400                                         break;
 401                                 r[1] = a[1];
 402                                 if (--dl <= 0)
 403                                         break;
 404                                 r[2] = a[2];
 405                                 if (--dl <= 0)
 406                                         break;
 407                                 r[3] = a[3];
 408                                 if (--dl <= 0)
 409                                         break;
 410
 411                                 a += 4;
 412                                 r += 4;
 413                         }
 414                 }
 415         }
 416         return c;
 417 }
 418
 419 #ifdef BN_RECURSION
 420 /* Karatsuba recursive multiplication algorithm
 421  * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
 422
 423 /* r is 2*n2 words in size,
 424  * a and b are both n2 words in size.
 425  * n2 must be a power of 2.
 426  * We multiply and return the result.
 427  * t must be 2*n2 words in size
 428  * We calculate
 429  * a[0]*b[0]
 430  * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
 431  * a[1]*b[1]
 432  */
 433 /* dnX may not be positive, but n2/2+dnX has to be */
 434 void
 435 bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, int dna,
 436     int dnb, BN_ULONG *t)
 437 {
 438         int n = n2 / 2, c1, c2;
 439         int tna = n + dna, tnb = n + dnb;
 440         unsigned int neg, zero;
 441         BN_ULONG ln, lo, *p;
 442
 443 # ifdef BN_COUNT
 444         fprintf(stderr, " bn_mul_recursive %d%+d * %d%+d\n",n2,dna,n2,dnb);
 445 # endif
 446 # ifdef BN_MUL_COMBA
 447 #  if 0
 448         if (n2 == 4) {
 449                 bn_mul_comba4(r, a, b);
 450                 return;
 451         }
 452 #  endif
 453         /* Only call bn_mul_comba 8 if n2 == 8 and the
 454          * two arrays are complete [steve]
 455          */
 456         if (n2 == 8 && dna == 0 && dnb == 0) {
 457                 bn_mul_comba8(r, a, b);
 458                 return;
 459         }
 460 # endif /* BN_MUL_COMBA */
 461         /* Else do normal multiply */
 462         if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
 463                 bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
 464                 if ((dna + dnb) < 0)
 465                         memset(&r[2*n2 + dna + dnb], 0,
 466                             sizeof(BN_ULONG) * -(dna + dnb));
 467                 return;
 468         }
 469         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 470         c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
 471         c2 = bn_cmp_part_words(&(b[n]), b,tnb, tnb - n);
 472         zero = neg = 0;
 473         switch (c1 * 3 + c2) {
 474         case -4:
 475                 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
 476                 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
 477                 break;
 478         case -3:
 479                 zero = 1;
 480                 break;
 481         case -2:
 482                 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
 483                 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
 484                 neg = 1;
 485                 break;
 486         case -1:
 487         case 0:
 488         case 1:
 489                 zero = 1;
 490                 break;
 491         case 2:
 492                 bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
 493                 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
 494                 neg = 1;
 495                 break;
 496         case 3:
 497                 zero = 1;
 498                 break;
 499         case 4:
 500                 bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
 501                 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
 502                 break;
 503         }
 504
 505 # ifdef BN_MUL_COMBA
 506         if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
 507                                                extra args to do this well */
 508         {
 509                 if (!zero)
 510                         bn_mul_comba4(&(t[n2]), t, &(t[n]));
 511                 else
 512                         memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG));
 513
 514                 bn_mul_comba4(r, a, b);
 515                 bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n]));
 516         } else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
 517                                                     take extra args to do this
 518                                                     well */
 519         {
 520                 if (!zero)
 521                         bn_mul_comba8(&(t[n2]), t, &(t[n]));
 522                 else
 523                         memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG));
 524
 525                 bn_mul_comba8(r, a, b);
 526                 bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
 527         } else
 528 # endif /* BN_MUL_COMBA */
 529         {
 530                 p = &(t[n2 * 2]);
 531                 if (!zero)
 532                         bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
 533                 else
 534                         memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
 535                 bn_mul_recursive(r, a, b, n, 0, 0, p);
 536                 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p);
 537         }
 538
 539         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 540          * r[10] holds (a[0]*b[0])
 541          * r[32] holds (b[1]*b[1])
 542          */
 543
 544         c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
 545
 546         if (neg) /* if t[32] is negative */
 547         {
 548                 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
 549         } else {
 550                 /* Might have a carry */
 551                 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
 552         }
 553
 554         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 555          * r[10] holds (a[0]*b[0])
 556          * r[32] holds (b[1]*b[1])
 557          * c1 holds the carry bits
 558          */
 559         c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
 560         if (c1) {
 561                 p = &(r[n + n2]);
 562                 lo= *p;
 563                 ln = (lo + c1) & BN_MASK2;
 564                 *p = ln;
 565
 566                 /* The overflow will stop before we over write
 567                  * words we should not overwrite */
 568                 if (ln < (BN_ULONG)c1) {
 569                         do {
 570                                 p++;
 571                                 lo= *p;
 572                                 ln = (lo + 1) & BN_MASK2;
 573                                 *p = ln;
 574                         } while (ln == 0);
 575                 }
 576         }
 577 }
 578
 579 /* n+tn is the word length
 580  * t needs to be n*4 is size, as does r */
 581 /* tnX may not be negative but less than n */
 582 void
 583 bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n, int tna,
 584     int tnb, BN_ULONG *t)
 585 {
 586         int i, j, n2 = n * 2;
 587         int c1, c2, neg;
 588         BN_ULONG ln, lo, *p;
 589
 590 # ifdef BN_COUNT
 591         fprintf(stderr, " bn_mul_part_recursive (%d%+d) * (%d%+d)\n",
 592             n, tna, n, tnb);
 593 # endif
 594         if (n < 8) {
 595                 bn_mul_normal(r, a, n + tna, b, n + tnb);
 596                 return;
 597         }
 598
 599         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 600         c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
 601         c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
 602         neg = 0;
 603         switch (c1 * 3 + c2) {
 604         case -4:
 605                 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
 606                 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
 607                 break;
 608         case -3:
 609                 /* break; */
 610         case -2:
 611                 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
 612                 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
 613                 neg = 1;
 614                 break;
 615         case -1:
 616         case 0:
 617         case 1:
 618                 /* break; */
 619         case 2:
 620                 bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
 621                 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
 622                 neg = 1;
 623                 break;
 624         case 3:
 625                 /* break; */
 626         case 4:
 627                 bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
 628                 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
 629                 break;
 630         }
 631                 /* The zero case isn't yet implemented here. The speedup
 632                    would probably be negligible. */
 633 # if 0
 634         if (n == 4) {
 635                 bn_mul_comba4(&(t[n2]), t, &(t[n]));
 636                 bn_mul_comba4(r, a, b);
 637                 bn_mul_normal(&(r[n2]), &(a[n]), tn, &(b[n]), tn);
 638                 memset(&(r[n2 + tn * 2]), 0, sizeof(BN_ULONG) * (n2 - tn * 2));
 639         } else
 640 # endif
 641                 if (n == 8) {
 642                 bn_mul_comba8(&(t[n2]), t, &(t[n]));
 643                 bn_mul_comba8(r, a, b);
 644                 bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
 645                 memset(&(r[n2 + tna + tnb]), 0,
 646                     sizeof(BN_ULONG) * (n2 - tna - tnb));
 647         } else {
 648                 p = &(t[n2*2]);
 649                 bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
 650                 bn_mul_recursive(r, a, b, n, 0, 0, p);
 651                 i = n / 2;
 652                 /* If there is only a bottom half to the number,
 653                  * just do it */
 654                 if (tna > tnb)
 655                         j = tna - i;
 656                 else
 657                         j = tnb - i;
 658                 if (j == 0) {
 659                         bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]),
 660                             i, tna - i, tnb - i, p);
 661                         memset(&(r[n2 + i * 2]), 0,
 662                             sizeof(BN_ULONG) * (n2 - i * 2));
 663                 }
 664                 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
 665                 {
 666                         bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]),
 667                             i, tna - i, tnb - i, p);
 668                         memset(&(r[n2 + tna + tnb]), 0,
 669                             sizeof(BN_ULONG) * (n2 - tna - tnb));
 670                 }
 671                 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
 672                 {
 673                         memset(&(r[n2]), 0, sizeof(BN_ULONG) * n2);
 674                         if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL &&
 675                             tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {
 676                                 bn_mul_normal(&(r[n2]), &(a[n]), tna,
 677                                     &(b[n]), tnb);
 678                         } else {
 679                                 for (;;) {
 680                                         i /= 2;
 681                                         /* these simplified conditions work
 682                                          * exclusively because difference
 683                                          * between tna and tnb is 1 or 0 */
 684                                         if (i < tna || i < tnb) {
 685                                                 bn_mul_part_recursive(&(r[n2]),
 686                                                     &(a[n]), &(b[n]), i,
 687                                                     tna - i, tnb - i, p);
 688                                                 break;
 689                                         } else if (i == tna || i == tnb) {
 690                                                 bn_mul_recursive(&(r[n2]),
 691                                                     &(a[n]), &(b[n]), i,
 692                                                     tna - i, tnb - i, p);
 693                                                 break;
 694                                         }
 695                                 }
 696                         }
 697                 }
 698         }
 699
 700         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 701          * r[10] holds (a[0]*b[0])
 702          * r[32] holds (b[1]*b[1])
 703          */
 704
 705         c1 = (int)(bn_add_words(t, r,&(r[n2]), n2));
 706
 707         if (neg) /* if t[32] is negative */
 708         {
 709                 c1 -= (int)(bn_sub_words(&(t[n2]), t,&(t[n2]), n2));
 710         } else {
 711                 /* Might have a carry */
 712                 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
 713         }
 714
 715         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 716          * r[10] holds (a[0]*b[0])
 717          * r[32] holds (b[1]*b[1])
 718          * c1 holds the carry bits
 719          */
 720         c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
 721         if (c1) {
 722                 p = &(r[n + n2]);
 723                 lo= *p;
 724                 ln = (lo + c1)&BN_MASK2;
 725                 *p = ln;
 726
 727                 /* The overflow will stop before we over write
 728                  * words we should not overwrite */
 729                 if (ln < (BN_ULONG)c1) {
 730                         do {
 731                                 p++;
 732                                 lo= *p;
 733                                 ln = (lo + 1) & BN_MASK2;
 734                                 *p = ln;
 735                         } while (ln == 0);
 736                 }
 737         }
 738 }
 739
 740 /* a and b must be the same size, which is n2.
 741  * r needs to be n2 words and t needs to be n2*2
 742  */
 743 void
 744 bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, BN_ULONG *t)
 745 {
 746         int n = n2 / 2;
 747
 748 # ifdef BN_COUNT
 749         fprintf(stderr, " bn_mul_low_recursive %d * %d\n",n2,n2);
 750 # endif
 751
 752         bn_mul_recursive(r, a, b, n, 0, 0, &(t[0]));
 753         if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL) {
 754                 bn_mul_low_recursive(&(t[0]), &(a[0]), &(b[n]), n, &(t[n2]));
 755                 bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
 756                 bn_mul_low_recursive(&(t[0]), &(a[n]), &(b[0]), n, &(t[n2]));
 757                 bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
 758         } else {
 759                 bn_mul_low_normal(&(t[0]), &(a[0]), &(b[n]), n);
 760                 bn_mul_low_normal(&(t[n]), &(a[n]), &(b[0]), n);
 761                 bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
 762                 bn_add_words(&(r[n]), &(r[n]), &(t[n]), n);
 763         }
 764 }
 765
 766 /* a and b must be the same size, which is n2.
 767  * r needs to be n2 words and t needs to be n2*2
 768  * l is the low words of the output.
 769  * t needs to be n2*3
 770  */
 771 void
 772 bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
 773     BN_ULONG *t)
 774 {
 775         int i, n;
 776         int c1, c2;
 777         int neg, oneg, zero;
 778         BN_ULONG ll, lc, *lp, *mp;
 779
 780 # ifdef BN_COUNT
 781         fprintf(stderr, " bn_mul_high %d * %d\n",n2,n2);
 782 # endif
 783         n = n2 / 2;
 784
 785         /* Calculate (al-ah)*(bh-bl) */
 786         neg = zero = 0;
 787         c1 = bn_cmp_words(&(a[0]), &(a[n]), n);
 788         c2 = bn_cmp_words(&(b[n]), &(b[0]), n);
 789         switch (c1 * 3 + c2) {
 790         case -4:
 791                 bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
 792                 bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
 793                 break;
 794         case -3:
 795                 zero = 1;
 796                 break;
 797         case -2:
 798                 bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
 799                 bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
 800                 neg = 1;
 801                 break;
 802         case -1:
 803         case 0:
 804         case 1:
 805                 zero = 1;
 806                 break;
 807         case 2:
 808                 bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
 809                 bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
 810                 neg = 1;
 811                 break;
 812         case 3:
 813                 zero = 1;
 814                 break;
 815         case 4:
 816                 bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
 817                 bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
 818                 break;
 819         }
 820
 821         oneg = neg;
 822         /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
 823         /* r[10] = (a[1]*b[1]) */
 824 # ifdef BN_MUL_COMBA
 825         if (n == 8) {
 826                 bn_mul_comba8(&(t[0]), &(r[0]), &(r[n]));
 827                 bn_mul_comba8(r, &(a[n]), &(b[n]));
 828         } else
 829 # endif
 830         {
 831                 bn_mul_recursive(&(t[0]), &(r[0]), &(r[n]), n, 0, 0, &(t[n2]));
 832                 bn_mul_recursive(r, &(a[n]), &(b[n]), n, 0, 0, &(t[n2]));
 833         }
 834
 835         /* s0 == low(al*bl)
 836          * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
 837          * We know s0 and s1 so the only unknown is high(al*bl)
 838          * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
 839          * high(al*bl) == s1 - (r[0]+l[0]+t[0])
 840          */
 841         if (l != NULL) {
 842                 lp = &(t[n2 + n]);
 843                 c1 = (int)(bn_add_words(lp, &(r[0]), &(l[0]), n));
 844         } else {
 845                 c1 = 0;
 846                 lp = &(r[0]);
 847         }
 848
 849         if (neg)
 850                 neg = (int)(bn_sub_words(&(t[n2]), lp, &(t[0]), n));
 851         else {
 852                 bn_add_words(&(t[n2]), lp, &(t[0]), n);
 853                 neg = 0;
 854         }
 855
 856         if (l != NULL) {
 857                 bn_sub_words(&(t[n2 + n]), &(l[n]), &(t[n2]), n);
 858         } else {
 859                 lp = &(t[n2 + n]);
 860                 mp = &(t[n2]);
 861                 for (i = 0; i < n; i++)
 862                         lp[i] = ((~mp[i]) + 1) & BN_MASK2;
 863         }
 864
 865         /* s[0] = low(al*bl)
 866          * t[3] = high(al*bl)
 867          * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
 868          * r[10] = (a[1]*b[1])
 869          */
 870         /* R[10] = al*bl
 871          * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
 872          * R[32] = ah*bh
 873          */
 874         /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
 875          * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
 876          * R[3]=r[1]+(carry/borrow)
 877          */
 878         if (l != NULL) {
 879                 lp = &(t[n2]);
 880                 c1 = (int)(bn_add_words(lp, &(t[n2 + n]), &(l[0]), n));
 881         } else {
 882                 lp = &(t[n2 + n]);
 883                 c1 = 0;
 884         }
 885         c1 += (int)(bn_add_words(&(t[n2]), lp, &(r[0]), n));
 886         if (oneg)
 887                 c1 -= (int)(bn_sub_words(&(t[n2]), &(t[n2]), &(t[0]), n));
 888         else
 889                 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), &(t[0]), n));
 890
 891         c2 = (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n2 + n]), n));
 892         c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(r[n]), n));
 893         if (oneg)
 894                 c2 -= (int)(bn_sub_words(&(r[0]), &(r[0]), &(t[n]), n));
 895         else
 896                 c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n]), n));
 897
 898         if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
 899         {
 900                 i = 0;
 901                 if (c1 > 0) {
 902                         lc = c1;
 903                         do {
 904                                 ll = (r[i] + lc) & BN_MASK2;
 905                                 r[i++] = ll;
 906                                 lc = (lc > ll);
 907                         } while (lc);
 908                 } else {
 909                         lc = -c1;
 910                         do {
 911                                 ll = r[i];
 912                                 r[i++] = (ll - lc) & BN_MASK2;
 913                                 lc = (lc > ll);
 914                         } while (lc);
 915                 }
 916         }
 917         if (c2 != 0) /* Add starting at r[1] */
 918         {
 919                 i = n;
 920                 if (c2 > 0) {
 921                         lc = c2;
 922                         do {
 923                                 ll = (r[i] + lc) & BN_MASK2;
 924                                 r[i++] = ll;
 925                                 lc = (lc > ll);
 926                         } while (lc);
 927                 } else {
 928                         lc = -c2;
 929                         do {
 930                                 ll = r[i];
 931                                 r[i++] = (ll - lc) & BN_MASK2;
 932                                 lc = (lc > ll);
 933                         } while (lc);
 934                 }
 935         }
 936 }
 937 #endif /* BN_RECURSION */
 938
 939 int
 940 BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
 941 {
 942         int ret = 0;
 943         int top, al, bl;
 944         BIGNUM *rr;
 945 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 946         int i;
 947 #endif
 948 #ifdef BN_RECURSION
 949         BIGNUM *t = NULL;
 950         int j = 0, k;
 951 #endif
 952
 953 #ifdef BN_COUNT
 954         fprintf(stderr, "BN_mul %d * %d\n",a->top,b->top);
 955 #endif
 956
 957         bn_check_top(a);
 958         bn_check_top(b);
 959         bn_check_top(r);
 960
 961         al = a->top;
 962         bl = b->top;
 963
 964         if ((al == 0) || (bl == 0)) {
 965                 BN_zero(r);
 966                 return (1);
 967         }
 968         top = al + bl;
 969
 970         BN_CTX_start(ctx);
 971         if ((r == a) || (r == b)) {
 972                 if ((rr = BN_CTX_get(ctx)) == NULL)
 973                         goto err;
 974         } else
 975                 rr = r;
 976         rr->neg = a->neg ^ b->neg;
 977
 978 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 979         i = al - bl;
 980 #endif
 981 #ifdef BN_MUL_COMBA
 982         if (i == 0) {
 983 # if 0
 984                 if (al == 4) {
 985                         if (bn_wexpand(rr, 8) == NULL)
 986                                 goto err;
 987                         rr->top = 8;
 988                         bn_mul_comba4(rr->d, a->d, b->d);
 989                         goto end;
 990                 }
 991 # endif
 992                 if (al == 8) {
 993                         if (bn_wexpand(rr, 16) == NULL)
 994                                 goto err;
 995                         rr->top = 16;
 996                         bn_mul_comba8(rr->d, a->d, b->d);
 997                         goto end;
 998                 }
 999         }
1000 #endif /* BN_MUL_COMBA */
1001 #ifdef BN_RECURSION
1002         if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) {
1003                 if (i >= -1 && i <= 1) {
1004                         /* Find out the power of two lower or equal
1005                            to the longest of the two numbers */
1006                         if (i >= 0) {
1007                                 j = BN_num_bits_word((BN_ULONG)al);
1008                         }
1009                         if (i == -1) {
1010                                 j = BN_num_bits_word((BN_ULONG)bl);
1011                         }
1012                         j = 1 << (j - 1);
1013                         assert(j <= al || j <= bl);
1014                         k = j + j;
1015                         if ((t = BN_CTX_get(ctx)) == NULL)
1016                                 goto err;
1017                         if (al > j || bl > j) {
1018                                 if (bn_wexpand(t, k * 4) == NULL)
1019                                         goto err;
1020                                 if (bn_wexpand(rr, k * 4) == NULL)
1021                                         goto err;
1022                                 bn_mul_part_recursive(rr->d, a->d, b->d,
1023                                     j, al - j, bl - j, t->d);
1024                         }
1025                         else    /* al <= j || bl <= j */
1026                         {
1027                                 if (bn_wexpand(t, k * 2) == NULL)
1028                                         goto err;
1029                                 if (bn_wexpand(rr, k * 2) == NULL)
1030                                         goto err;
1031                                 bn_mul_recursive(rr->d, a->d, b->d,
1032                                     j, al - j, bl - j, t->d);
1033                         }
1034                         rr->top = top;
1035                         goto end;
1036                 }
1037 #if 0
1038                 if (i == 1 && !BN_get_flags(b, BN_FLG_STATIC_DATA)) {
1039                         BIGNUM *tmp_bn = (BIGNUM *)b;
1040                         if (bn_wexpand(tmp_bn, al) == NULL)
1041                                 goto err;
1042                         tmp_bn->d[bl] = 0;
1043                         bl++;
1044                         i--;
1045                 } else if (i == -1 && !BN_get_flags(a, BN_FLG_STATIC_DATA)) {
1046                         BIGNUM *tmp_bn = (BIGNUM *)a;
1047                         if (bn_wexpand(tmp_bn, bl) == NULL)
1048                                 goto err;
1049                         tmp_bn->d[al] = 0;
1050                         al++;
1051                         i++;
1052                 }
1053                 if (i == 0) {
1054                         /* symmetric and > 4 */
1055                         /* 16 or larger */
1056                         j = BN_num_bits_word((BN_ULONG)al);
1057                         j = 1 << (j - 1);
1058                         k = j + j;
1059                         if ((t = BN_CTX_get(ctx)) == NULL)
1060                                 goto err;
1061                         if (al == j) /* exact multiple */
1062                         {
1063                                 if (bn_wexpand(t, k * 2) == NULL)
1064                                         goto err;
1065                                 if (bn_wexpand(rr, k * 2) == NULL)
1066                                         goto err;
1067                                 bn_mul_recursive(rr->d, a->d, b->d, al, t->d);
1068                         } else {
1069                                 if (bn_wexpand(t, k * 4) == NULL)
1070                                         goto err;
1071                                 if (bn_wexpand(rr, k * 4) == NULL)
1072                                         goto err;
1073                                 bn_mul_part_recursive(rr->d, a->d, b->d,
1074                                     al - j, j, t->d);
1075                         }
1076                         rr->top = top;
1077                         goto end;
1078                 }
1079 #endif
1080         }
1081 #endif /* BN_RECURSION */
1082         if (bn_wexpand(rr, top) == NULL)
1083                 goto err;
1084         rr->top = top;
1085         bn_mul_normal(rr->d, a->d, al, b->d, bl);
1086
1087 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1088 end:
1089 #endif
1090         bn_correct_top(rr);
1091         if (r != rr)
1092                 BN_copy(r, rr);
1093         ret = 1;
1094 err:
1095         bn_check_top(r);
1096         BN_CTX_end(ctx);
1097         return (ret);
1098 }
1099
1100 void
1101 bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1102 {
1103         BN_ULONG *rr;
1104
1105 #ifdef BN_COUNT
1106         fprintf(stderr, " bn_mul_normal %d * %d\n", na, nb);
1107 #endif
1108
1109         if (na < nb) {
1110                 int itmp;
1111                 BN_ULONG *ltmp;
1112
1113                 itmp = na;
1114                 na = nb;
1115                 nb = itmp;
1116                 ltmp = a;
1117                 a = b;
1118                 b = ltmp;
1119
1120         }
1121         rr = &(r[na]);
1122         if (nb <= 0) {
1123                 (void)bn_mul_words(r, a, na, 0);
1124                 return;
1125         } else
1126                 rr[0] = bn_mul_words(r, a, na, b[0]);
1127
1128         for (;;) {
1129                 if (--nb <= 0)
1130                         return;
1131                 rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
1132                 if (--nb <= 0)
1133                         return;
1134                 rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
1135                 if (--nb <= 0)
1136                         return;
1137                 rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
1138                 if (--nb <= 0)
1139                         return;
1140                 rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
1141                 rr += 4;
1142                 r += 4;
1143                 b += 4;
1144         }
1145 }
1146
1147 void
1148 bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1149 {
1150 #ifdef BN_COUNT
1151         fprintf(stderr, " bn_mul_low_normal %d * %d\n", n, n);
1152 #endif
1153         bn_mul_words(r, a, n, b[0]);
1154
1155         for (;;) {
1156                 if (--n <= 0)
1157                         return;
1158                 bn_mul_add_words(&(r[1]), a, n, b[1]);
1159                 if (--n <= 0)
1160                         return;
1161                 bn_mul_add_words(&(r[2]), a, n, b[2]);
1162                 if (--n <= 0)
1163                         return;
1164                 bn_mul_add_words(&(r[3]), a, n, b[3]);
1165                 if (--n <= 0)
1166                         return;
1167                 bn_mul_add_words(&(r[4]), a, n, b[4]);
1168                 r += 4;
1169                 b += 4;
1170         }
1171 }