crypto/bn/bn_mul.c

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