Commit #16325 fixed one thing but broke DH with certain moduli.
[openssl.git] / 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 #ifndef BN_DEBUG
60 # undef NDEBUG /* avoid conflicting definitions */
61 # define NDEBUG
62 #endif
63
64 #include <stdio.h>
65 #include <assert.h>
66 #include "cryptlib.h"
67 #include "bn_lcl.h"
68
69 #if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
70 /* Here follows specialised variants of bn_add_words() and
71    bn_sub_words().  They have the property performing operations on
72    arrays of different sizes.  The sizes of those arrays is expressed through
73    cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
74    which is the delta between the two lengths, calculated as len(a)-len(b).
75    All lengths are the number of BN_ULONGs...  For the operations that require
76    a result array as parameter, it must have the length cl+abs(dl).
77    These functions should probably end up in bn_asm.c as soon as there are
78    assembler counterparts for the systems that use assembler files.  */
79
80 BN_ULONG bn_sub_part_words(BN_ULONG *r,
81         const BN_ULONG *a, const BN_ULONG *b,
82         int cl, int dl)
83         {
84         BN_ULONG c, t;
85
86         assert(cl >= 0);
87         c = bn_sub_words(r, a, b, cl);
88
89         if (dl == 0)
90                 return c;
91
92         r += cl;
93         a += cl;
94         b += cl;
95
96         if (dl < 0)
97                 {
98 #ifdef BN_COUNT
99                 fprintf(stderr, "  bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
100 #endif
101                 for (;;)
102                         {
103                         t = b[0];
104                         r[0] = (0-t-c)&BN_MASK2;
105                         if (t != 0) c=1;
106                         if (++dl >= 0) break;
107
108                         t = b[1];
109                         r[1] = (0-t-c)&BN_MASK2;
110                         if (t != 0) c=1;
111                         if (++dl >= 0) break;
112
113                         t = b[2];
114                         r[2] = (0-t-c)&BN_MASK2;
115                         if (t != 0) c=1;
116                         if (++dl >= 0) break;
117
118                         t = b[3];
119                         r[3] = (0-t-c)&BN_MASK2;
120                         if (t != 0) c=1;
121                         if (++dl >= 0) break;
122
123                         b += 4;
124                         r += 4;
125                         }
126                 }
127         else
128                 {
129                 int save_dl = dl;
130 #ifdef BN_COUNT
131                 fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl, dl, c);
132 #endif
133                 while(c)
134                         {
135                         t = a[0];
136                         r[0] = (t-c)&BN_MASK2;
137                         if (t != 0) c=0;
138                         if (--dl <= 0) break;
139
140                         t = a[1];
141                         r[1] = (t-c)&BN_MASK2;
142                         if (t != 0) c=0;
143                         if (--dl <= 0) break;
144
145                         t = a[2];
146                         r[2] = (t-c)&BN_MASK2;
147                         if (t != 0) c=0;
148                         if (--dl <= 0) break;
149
150                         t = a[3];
151                         r[3] = (t-c)&BN_MASK2;
152                         if (t != 0) c=0;
153                         if (--dl <= 0) break;
154
155                         save_dl = dl;
156                         a += 4;
157                         r += 4;
158                         }
159                 if (dl > 0)
160                         {
161 #ifdef BN_COUNT
162                         fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
163 #endif
164                         if (save_dl > dl)
165                                 {
166                                 switch (save_dl - dl)
167                                         {
168                                 case 1:
169                                         r[1] = a[1];
170                                         if (--dl <= 0) break;
171                                 case 2:
172                                         r[2] = a[2];
173                                         if (--dl <= 0) break;
174                                 case 3:
175                                         r[3] = a[3];
176                                         if (--dl <= 0) break;
177                                         }
178                                 a += 4;
179                                 r += 4;
180                                 }
181                         }
182                 if (dl > 0)
183                         {
184 #ifdef BN_COUNT
185                         fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, copy)\n", cl, dl);
186 #endif
187                         for(;;)
188                                 {
189                                 r[0] = a[0];
190                                 if (--dl <= 0) break;
191                                 r[1] = a[1];
192                                 if (--dl <= 0) break;
193                                 r[2] = a[2];
194                                 if (--dl <= 0) break;
195                                 r[3] = a[3];
196                                 if (--dl <= 0) break;
197
198                                 a += 4;
199                                 r += 4;
200                                 }
201                         }
202                 }
203         return c;
204         }
205 #endif
206
207 BN_ULONG bn_add_part_words(BN_ULONG *r,
208         const BN_ULONG *a, const BN_ULONG *b,
209         int cl, int dl)
210         {
211         BN_ULONG c, l, t;
212
213         assert(cl >= 0);
214         c = bn_add_words(r, a, b, cl);
215
216         if (dl == 0)
217                 return c;
218
219         r += cl;
220         a += cl;
221         b += cl;
222
223         if (dl < 0)
224                 {
225                 int save_dl = dl;
226 #ifdef BN_COUNT
227                 fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
228 #endif
229                 while (c)
230                         {
231                         l=(c+b[0])&BN_MASK2;
232                         c=(l < c);
233                         r[0]=l;
234                         if (++dl >= 0) break;
235
236                         l=(c+b[1])&BN_MASK2;
237                         c=(l < c);
238                         r[1]=l;
239                         if (++dl >= 0) break;
240
241                         l=(c+b[2])&BN_MASK2;
242                         c=(l < c);
243                         r[2]=l;
244                         if (++dl >= 0) break;
245
246                         l=(c+b[3])&BN_MASK2;
247                         c=(l < c);
248                         r[3]=l;
249                         if (++dl >= 0) break;
250
251                         save_dl = dl;
252                         b+=4;
253                         r+=4;
254                         }
255                 if (dl < 0)
256                         {
257 #ifdef BN_COUNT
258                         fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, c == 0)\n", cl, dl);
259 #endif
260                         if (save_dl < dl)
261                                 {
262                                 switch (dl - save_dl)
263                                         {
264                                 case 1:
265                                         r[1] = b[1];
266                                         if (++dl >= 0) break;
267                                 case 2:
268                                         r[2] = b[2];
269                                         if (++dl >= 0) break;
270                                 case 3:
271                                         r[3] = b[3];
272                                         if (++dl >= 0) break;
273                                         }
274                                 b += 4;
275                                 r += 4;
276                                 }
277                         }
278                 if (dl < 0)
279                         {
280 #ifdef BN_COUNT
281                         fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, copy)\n", cl, dl);
282 #endif
283                         for(;;)
284                                 {
285                                 r[0] = b[0];
286                                 if (++dl >= 0) break;
287                                 r[1] = b[1];
288                                 if (++dl >= 0) break;
289                                 r[2] = b[2];
290                                 if (++dl >= 0) break;
291                                 r[3] = b[3];
292                                 if (++dl >= 0) break;
293
294                                 b += 4;
295                                 r += 4;
296                                 }
297                         }
298                 }
299         else
300                 {
301                 int save_dl = dl;
302 #ifdef BN_COUNT
303                 fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
304 #endif
305                 while (c)
306                         {
307                         t=(a[0]+c)&BN_MASK2;
308                         c=(t < c);
309                         r[0]=t;
310                         if (--dl <= 0) break;
311
312                         t=(a[1]+c)&BN_MASK2;
313                         c=(t < c);
314                         r[1]=t;
315                         if (--dl <= 0) break;
316
317                         t=(a[2]+c)&BN_MASK2;
318                         c=(t < c);
319                         r[2]=t;
320                         if (--dl <= 0) break;
321
322                         t=(a[3]+c)&BN_MASK2;
323                         c=(t < c);
324                         r[3]=t;
325                         if (--dl <= 0) break;
326
327                         save_dl = dl;
328                         a+=4;
329                         r+=4;
330                         }
331 #ifdef BN_COUNT
332                 fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
333 #endif
334                 if (dl > 0)
335                         {
336                         if (save_dl > dl)
337                                 {
338                                 switch (save_dl - dl)
339                                         {
340                                 case 1:
341                                         r[1] = a[1];
342                                         if (--dl <= 0) break;
343                                 case 2:
344                                         r[2] = a[2];
345                                         if (--dl <= 0) break;
346                                 case 3:
347                                         r[3] = a[3];
348                                         if (--dl <= 0) break;
349                                         }
350                                 a += 4;
351                                 r += 4;
352                                 }
353                         }
354                 if (dl > 0)
355                         {
356 #ifdef BN_COUNT
357                         fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0, copy)\n", cl, dl);
358 #endif
359                         for(;;)
360                                 {
361                                 r[0] = a[0];
362                                 if (--dl <= 0) break;
363                                 r[1] = a[1];
364                                 if (--dl <= 0) break;
365                                 r[2] = a[2];
366                                 if (--dl <= 0) break;
367                                 r[3] = a[3];
368                                 if (--dl <= 0) break;
369
370                                 a += 4;
371                                 r += 4;
372                                 }
373                         }
374                 }
375         return c;
376         }
377
378 #ifdef BN_RECURSION
379 /* Karatsuba recursive multiplication algorithm
380  * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
381
382 /* r is 2*n2 words in size,
383  * a and b are both n2 words in size.
384  * n2 must be a power of 2.
385  * We multiply and return the result.
386  * t must be 2*n2 words in size
387  * We calculate
388  * a[0]*b[0]
389  * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
390  * a[1]*b[1]
391  */
392 /* dnX may not be positive, but n2/2+dnX has to be */
393 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
394         int dna, int dnb, BN_ULONG *t)
395         {
396         int n=n2/2,c1,c2;
397         int tna=n+dna, tnb=n+dnb;
398         unsigned int neg,zero;
399         BN_ULONG ln,lo,*p;
400
401 # ifdef BN_COUNT
402         fprintf(stderr," bn_mul_recursive %d%+d * %d%+d\n",n2,dna,n2,dnb);
403 # endif
404 # ifdef BN_MUL_COMBA
405 #  if 0
406         if (n2 == 4)
407                 {
408                 bn_mul_comba4(r,a,b);
409                 return;
410                 }
411 #  endif
412         /* Only call bn_mul_comba 8 if n2 == 8 and the
413          * two arrays are complete [steve]
414          */
415         if (n2 == 8 && dna == 0 && dnb == 0)
416                 {
417                 bn_mul_comba8(r,a,b);
418                 return; 
419                 }
420 # endif /* BN_MUL_COMBA */
421         /* Else do normal multiply */
422         if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
423                 {
424                 bn_mul_normal(r,a,n2+dna,b,n2+dnb);
425                 if ((dna + dnb) < 0)
426                         memset(&r[2*n2 + dna + dnb], 0,
427                                 sizeof(BN_ULONG) * -(dna + dnb));
428                 return;
429                 }
430         /* r=(a[0]-a[1])*(b[1]-b[0]) */
431         c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
432         c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
433         zero=neg=0;
434         switch (c1*3+c2)
435                 {
436         case -4:
437                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
438                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
439                 break;
440         case -3:
441                 zero=1;
442                 break;
443         case -2:
444                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
445                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
446                 neg=1;
447                 break;
448         case -1:
449         case 0:
450         case 1:
451                 zero=1;
452                 break;
453         case 2:
454                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
455                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
456                 neg=1;
457                 break;
458         case 3:
459                 zero=1;
460                 break;
461         case 4:
462                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
463                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
464                 break;
465                 }
466
467 # ifdef BN_MUL_COMBA
468         if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
469                                                extra args to do this well */
470                 {
471                 if (!zero)
472                         bn_mul_comba4(&(t[n2]),t,&(t[n]));
473                 else
474                         memset(&(t[n2]),0,8*sizeof(BN_ULONG));
475                 
476                 bn_mul_comba4(r,a,b);
477                 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
478                 }
479         else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
480                                                     take extra args to do this
481                                                     well */
482                 {
483                 if (!zero)
484                         bn_mul_comba8(&(t[n2]),t,&(t[n]));
485                 else
486                         memset(&(t[n2]),0,16*sizeof(BN_ULONG));
487                 
488                 bn_mul_comba8(r,a,b);
489                 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
490                 }
491         else
492 # endif /* BN_MUL_COMBA */
493                 {
494                 p= &(t[n2*2]);
495                 if (!zero)
496                         bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
497                 else
498                         memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
499                 bn_mul_recursive(r,a,b,n,0,0,p);
500                 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p);
501                 }
502
503         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
504          * r[10] holds (a[0]*b[0])
505          * r[32] holds (b[1]*b[1])
506          */
507
508         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
509
510         if (neg) /* if t[32] is negative */
511                 {
512                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
513                 }
514         else
515                 {
516                 /* Might have a carry */
517                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
518                 }
519
520         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
521          * r[10] holds (a[0]*b[0])
522          * r[32] holds (b[1]*b[1])
523          * c1 holds the carry bits
524          */
525         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
526         if (c1)
527                 {
528                 p= &(r[n+n2]);
529                 lo= *p;
530                 ln=(lo+c1)&BN_MASK2;
531                 *p=ln;
532
533                 /* The overflow will stop before we over write
534                  * words we should not overwrite */
535                 if (ln < (BN_ULONG)c1)
536                         {
537                         do      {
538                                 p++;
539                                 lo= *p;
540                                 ln=(lo+1)&BN_MASK2;
541                                 *p=ln;
542                                 } while (ln == 0);
543                         }
544                 }
545         }
546
547 /* n+tn is the word length
548  * t needs to be n*4 is size, as does r */
549 /* tnX may not be negative but less than n */
550 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
551              int tna, int tnb, BN_ULONG *t)
552         {
553         int i,j,n2=n*2;
554         int c1,c2,neg,zero;
555         BN_ULONG ln,lo,*p;
556
557 # ifdef BN_COUNT
558         fprintf(stderr," bn_mul_part_recursive (%d%+d) * (%d%+d)\n",
559                 n, tna, n, tnb);
560 # endif
561         if (n < 8)
562                 {
563                 bn_mul_normal(r,a,n+tna,b,n+tnb);
564                 return;
565                 }
566
567         /* r=(a[0]-a[1])*(b[1]-b[0]) */
568         c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
569         c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
570         zero=neg=0;
571         switch (c1*3+c2)
572                 {
573         case -4:
574                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
575                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
576                 break;
577         case -3:
578                 zero=1;
579                 /* break; */
580         case -2:
581                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
582                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
583                 neg=1;
584                 break;
585         case -1:
586         case 0:
587         case 1:
588                 zero=1;
589                 /* break; */
590         case 2:
591                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
592                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
593                 neg=1;
594                 break;
595         case 3:
596                 zero=1;
597                 /* break; */
598         case 4:
599                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
600                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
601                 break;
602                 }
603                 /* The zero case isn't yet implemented here. The speedup
604                    would probably be negligible. */
605 # if 0
606         if (n == 4)
607                 {
608                 bn_mul_comba4(&(t[n2]),t,&(t[n]));
609                 bn_mul_comba4(r,a,b);
610                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
611                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
612                 }
613         else
614 # endif
615         if (n == 8)
616                 {
617                 bn_mul_comba8(&(t[n2]),t,&(t[n]));
618                 bn_mul_comba8(r,a,b);
619                 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
620                 memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb));
621                 }
622         else
623                 {
624                 p= &(t[n2*2]);
625                 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
626                 bn_mul_recursive(r,a,b,n,0,0,p);
627                 i=n/2;
628                 /* If there is only a bottom half to the number,
629                  * just do it */
630                 if (tna > tnb)
631                         j = tna - i;
632                 else
633                         j = tnb - i;
634                 if (j == 0)
635                         {
636                         bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),
637                                 i,tna-i,tnb-i,p);
638                         memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
639                         }
640                 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
641                                 {
642                                 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
643                                         i,tna-i,tnb-i,p);
644                                 memset(&(r[n2+tna+tnb]),0,
645                                         sizeof(BN_ULONG)*(n2-tna-tnb));
646                                 }
647                 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
648                         {
649                         memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
650                         if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
651                                 && tnb < BN_MUL_RECURSIVE_SIZE_NORMAL)
652                                 {
653                                 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
654                                 }
655                         else
656                                 {
657                                 for (;;)
658                                         {
659                                         i/=2;
660                                         /* these simplified conditions work
661                                          * exclusively because difference
662                                          * between tna and tnb is 1 or 0 */
663                                         if (i < tna || i < tnb)
664                                                 {
665                                                 bn_mul_part_recursive(&(r[n2]),
666                                                         &(a[n]),&(b[n]),
667                                                         i,tna-i,tnb-i,p);
668                                                 break;
669                                                 }
670                                         else if (i == tna || i == tnb)
671                                                 {
672                                                 bn_mul_recursive(&(r[n2]),
673                                                         &(a[n]),&(b[n]),
674                                                         i,tna-i,tnb-i,p);
675                                                 break;
676                                                 }
677                                         }
678                                 }
679                         }
680                 }
681
682         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
683          * r[10] holds (a[0]*b[0])
684          * r[32] holds (b[1]*b[1])
685          */
686
687         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
688
689         if (neg) /* if t[32] is negative */
690                 {
691                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
692                 }
693         else
694                 {
695                 /* Might have a carry */
696                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
697                 }
698
699         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
700          * r[10] holds (a[0]*b[0])
701          * r[32] holds (b[1]*b[1])
702          * c1 holds the carry bits
703          */
704         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
705         if (c1)
706                 {
707                 p= &(r[n+n2]);
708                 lo= *p;
709                 ln=(lo+c1)&BN_MASK2;
710                 *p=ln;
711
712                 /* The overflow will stop before we over write
713                  * words we should not overwrite */
714                 if (ln < (BN_ULONG)c1)
715                         {
716                         do      {
717                                 p++;
718                                 lo= *p;
719                                 ln=(lo+1)&BN_MASK2;
720                                 *p=ln;
721                                 } while (ln == 0);
722                         }
723                 }
724         }
725
726 /* a and b must be the same size, which is n2.
727  * r needs to be n2 words and t needs to be n2*2
728  */
729 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
730              BN_ULONG *t)
731         {
732         int n=n2/2;
733
734 # ifdef BN_COUNT
735         fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);
736 # endif
737
738         bn_mul_recursive(r,a,b,n,0,0,&(t[0]));
739         if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
740                 {
741                 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
742                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
743                 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
744                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
745                 }
746         else
747                 {
748                 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
749                 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
750                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
751                 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
752                 }
753         }
754
755 /* a and b must be the same size, which is n2.
756  * r needs to be n2 words and t needs to be n2*2
757  * l is the low words of the output.
758  * t needs to be n2*3
759  */
760 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
761              BN_ULONG *t)
762         {
763         int i,n;
764         int c1,c2;
765         int neg,oneg,zero;
766         BN_ULONG ll,lc,*lp,*mp;
767
768 # ifdef BN_COUNT
769         fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);
770 # endif
771         n=n2/2;
772
773         /* Calculate (al-ah)*(bh-bl) */
774         neg=zero=0;
775         c1=bn_cmp_words(&(a[0]),&(a[n]),n);
776         c2=bn_cmp_words(&(b[n]),&(b[0]),n);
777         switch (c1*3+c2)
778                 {
779         case -4:
780                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
781                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
782                 break;
783         case -3:
784                 zero=1;
785                 break;
786         case -2:
787                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
788                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
789                 neg=1;
790                 break;
791         case -1:
792         case 0:
793         case 1:
794                 zero=1;
795                 break;
796         case 2:
797                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
798                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
799                 neg=1;
800                 break;
801         case 3:
802                 zero=1;
803                 break;
804         case 4:
805                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
806                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
807                 break;
808                 }
809                 
810         oneg=neg;
811         /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
812         /* r[10] = (a[1]*b[1]) */
813 # ifdef BN_MUL_COMBA
814         if (n == 8)
815                 {
816                 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
817                 bn_mul_comba8(r,&(a[n]),&(b[n]));
818                 }
819         else
820 # endif
821                 {
822                 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2]));
823                 bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2]));
824                 }
825
826         /* s0 == low(al*bl)
827          * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
828          * We know s0 and s1 so the only unknown is high(al*bl)
829          * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
830          * high(al*bl) == s1 - (r[0]+l[0]+t[0])
831          */
832         if (l != NULL)
833                 {
834                 lp= &(t[n2+n]);
835                 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
836                 }
837         else
838                 {
839                 c1=0;
840                 lp= &(r[0]);
841                 }
842
843         if (neg)
844                 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
845         else
846                 {
847                 bn_add_words(&(t[n2]),lp,&(t[0]),n);
848                 neg=0;
849                 }
850
851         if (l != NULL)
852                 {
853                 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
854                 }
855         else
856                 {
857                 lp= &(t[n2+n]);
858                 mp= &(t[n2]);
859                 for (i=0; i<n; i++)
860                         lp[i]=((~mp[i])+1)&BN_MASK2;
861                 }
862
863         /* s[0] = low(al*bl)
864          * t[3] = high(al*bl)
865          * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
866          * r[10] = (a[1]*b[1])
867          */
868         /* R[10] = al*bl
869          * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
870          * R[32] = ah*bh
871          */
872         /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
873          * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
874          * R[3]=r[1]+(carry/borrow)
875          */
876         if (l != NULL)
877                 {
878                 lp= &(t[n2]);
879                 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
880                 }
881         else
882                 {
883                 lp= &(t[n2+n]);
884                 c1=0;
885                 }
886         c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
887         if (oneg)
888                 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
889         else
890                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
891
892         c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
893         c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
894         if (oneg)
895                 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
896         else
897                 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
898         
899         if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
900                 {
901                 i=0;
902                 if (c1 > 0)
903                         {
904                         lc=c1;
905                         do      {
906                                 ll=(r[i]+lc)&BN_MASK2;
907                                 r[i++]=ll;
908                                 lc=(lc > ll);
909                                 } while (lc);
910                         }
911                 else
912                         {
913                         lc= -c1;
914                         do      {
915                                 ll=r[i];
916                                 r[i++]=(ll-lc)&BN_MASK2;
917                                 lc=(lc > ll);
918                                 } while (lc);
919                         }
920                 }
921         if (c2 != 0) /* Add starting at r[1] */
922                 {
923                 i=n;
924                 if (c2 > 0)
925                         {
926                         lc=c2;
927                         do      {
928                                 ll=(r[i]+lc)&BN_MASK2;
929                                 r[i++]=ll;
930                                 lc=(lc > ll);
931                                 } while (lc);
932                         }
933                 else
934                         {
935                         lc= -c2;
936                         do      {
937                                 ll=r[i];
938                                 r[i++]=(ll-lc)&BN_MASK2;
939                                 lc=(lc > ll);
940                                 } while (lc);
941                         }
942                 }
943         }
944 #endif /* BN_RECURSION */
945
946 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
947         {
948         int ret=0;
949         int top,al,bl;
950         BIGNUM *rr;
951 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
952         int i;
953 #endif
954 #ifdef BN_RECURSION
955         BIGNUM *t=NULL;
956         int j=0,k;
957 #endif
958
959 #ifdef BN_COUNT
960         fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);
961 #endif
962
963         bn_check_top(a);
964         bn_check_top(b);
965         bn_check_top(r);
966
967         al=a->top;
968         bl=b->top;
969
970         if ((al == 0) || (bl == 0))
971                 {
972                 BN_zero(r);
973                 return(1);
974                 }
975         top=al+bl;
976
977         BN_CTX_start(ctx);
978         if ((r == a) || (r == b))
979                 {
980                 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
981                 }
982         else
983                 rr = r;
984         rr->neg=a->neg^b->neg;
985
986 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
987         i = al-bl;
988 #endif
989 #ifdef BN_MUL_COMBA
990         if (i == 0)
991                 {
992 # if 0
993                 if (al == 4)
994                         {
995                         if (bn_wexpand(rr,8) == NULL) goto err;
996                         rr->top=8;
997                         bn_mul_comba4(rr->d,a->d,b->d);
998                         goto end;
999                         }
1000 # endif
1001                 if (al == 8)
1002                         {
1003                         if (bn_wexpand(rr,16) == NULL) goto err;
1004                         rr->top=16;
1005                         bn_mul_comba8(rr->d,a->d,b->d);
1006                         goto end;
1007                         }
1008                 }
1009 #endif /* BN_MUL_COMBA */
1010 #ifdef BN_RECURSION
1011         if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
1012                 {
1013                 if (i >= -1 && i <= 1)
1014                         {
1015                         int sav_j =0;
1016                         /* Find out the power of two lower or equal
1017                            to the longest of the two numbers */
1018                         if (i >= 0)
1019                                 {
1020                                 j = BN_num_bits_word((BN_ULONG)al);
1021                                 }
1022                         if (i == -1)
1023                                 {
1024                                 j = BN_num_bits_word((BN_ULONG)bl);
1025                                 }
1026                         sav_j = j;
1027                         j = 1<<(j-1);
1028                         assert(j <= al || j <= bl);
1029                         k = j+j;
1030                         t = BN_CTX_get(ctx);
1031                         if (al > j || bl > j)
1032                                 {
1033                                 bn_wexpand(t,k*4);
1034                                 bn_wexpand(rr,k*4);
1035                                 bn_mul_part_recursive(rr->d,a->d,b->d,
1036                                         j,al-j,bl-j,t->d);
1037                                 }
1038                         else    /* al <= j || bl <= j */
1039                                 {
1040                                 bn_wexpand(t,k*2);
1041                                 bn_wexpand(rr,k*2);
1042                                 bn_mul_recursive(rr->d,a->d,b->d,
1043                                         j,al-j,bl-j,t->d);
1044                                 }
1045                         rr->top=top;
1046                         goto end;
1047                         }
1048 #if 0
1049                 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
1050                         {
1051                         BIGNUM *tmp_bn = (BIGNUM *)b;
1052                         if (bn_wexpand(tmp_bn,al) == NULL) goto err;
1053                         tmp_bn->d[bl]=0;
1054                         bl++;
1055                         i--;
1056                         }
1057                 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
1058                         {
1059                         BIGNUM *tmp_bn = (BIGNUM *)a;
1060                         if (bn_wexpand(tmp_bn,bl) == NULL) goto err;
1061                         tmp_bn->d[al]=0;
1062                         al++;
1063                         i++;
1064                         }
1065                 if (i == 0)
1066                         {
1067                         /* symmetric and > 4 */
1068                         /* 16 or larger */
1069                         j=BN_num_bits_word((BN_ULONG)al);
1070                         j=1<<(j-1);
1071                         k=j+j;
1072                         t = BN_CTX_get(ctx);
1073                         if (al == j) /* exact multiple */
1074                                 {
1075                                 if (bn_wexpand(t,k*2) == NULL) goto err;
1076                                 if (bn_wexpand(rr,k*2) == NULL) goto err;
1077                                 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
1078                                 }
1079                         else
1080                                 {
1081                                 if (bn_wexpand(t,k*4) == NULL) goto err;
1082                                 if (bn_wexpand(rr,k*4) == NULL) goto err;
1083                                 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
1084                                 }
1085                         rr->top=top;
1086                         goto end;
1087                         }
1088 #endif
1089                 }
1090 #endif /* BN_RECURSION */
1091         if (bn_wexpand(rr,top) == NULL) goto err;
1092         rr->top=top;
1093         bn_mul_normal(rr->d,a->d,al,b->d,bl);
1094
1095 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1096 end:
1097 #endif
1098         bn_correct_top(rr);
1099         if (r != rr) BN_copy(r,rr);
1100         ret=1;
1101 err:
1102         bn_check_top(r);
1103         BN_CTX_end(ctx);
1104         return(ret);
1105         }
1106
1107 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1108         {
1109         BN_ULONG *rr;
1110
1111 #ifdef BN_COUNT
1112         fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
1113 #endif
1114
1115         if (na < nb)
1116                 {
1117                 int itmp;
1118                 BN_ULONG *ltmp;
1119
1120                 itmp=na; na=nb; nb=itmp;
1121                 ltmp=a;   a=b;   b=ltmp;
1122
1123                 }
1124         rr= &(r[na]);
1125         if (nb <= 0)
1126                 {
1127                 (void)bn_mul_words(r,a,na,0);
1128                 return;
1129                 }
1130         else
1131                 rr[0]=bn_mul_words(r,a,na,b[0]);
1132
1133         for (;;)
1134                 {
1135                 if (--nb <= 0) return;
1136                 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
1137                 if (--nb <= 0) return;
1138                 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
1139                 if (--nb <= 0) return;
1140                 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
1141                 if (--nb <= 0) return;
1142                 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
1143                 rr+=4;
1144                 r+=4;
1145                 b+=4;
1146                 }
1147         }
1148
1149 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1150         {
1151 #ifdef BN_COUNT
1152         fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
1153 #endif
1154         bn_mul_words(r,a,n,b[0]);
1155
1156         for (;;)
1157                 {
1158                 if (--n <= 0) return;
1159                 bn_mul_add_words(&(r[1]),a,n,b[1]);
1160                 if (--n <= 0) return;
1161                 bn_mul_add_words(&(r[2]),a,n,b[2]);
1162                 if (--n <= 0) return;
1163                 bn_mul_add_words(&(r[3]),a,n,b[3]);
1164                 if (--n <= 0) return;
1165                 bn_mul_add_words(&(r[4]),a,n,b[4]);
1166                 r+=4;
1167                 b+=4;
1168                 }
1169         }