1 /* crypto/bn/bn_mul.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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.
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).
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.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
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)"
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
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.]
64 /* Here follows specialised variants of bn_add_words() and
65 bn_sub_words(). They 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. */
74 BN_ULONG bn_sub_part_words(BN_ULONG *r,
75 const BN_ULONG *a, const BN_ULONG *b,
81 c = bn_sub_words(r, a, b, cl);
93 fprintf(stderr, " bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
98 r[0] = (0-t-c)&BN_MASK2;
100 if (++dl >= 0) break;
103 r[1] = (0-t-c)&BN_MASK2;
105 if (++dl >= 0) break;
108 r[2] = (0-t-c)&BN_MASK2;
110 if (++dl >= 0) break;
113 r[3] = (0-t-c)&BN_MASK2;
115 if (++dl >= 0) break;
125 fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl, dl, c);
130 r[0] = (t-c)&BN_MASK2;
132 if (--dl <= 0) break;
135 r[1] = (t-c)&BN_MASK2;
137 if (--dl <= 0) break;
140 r[2] = (t-c)&BN_MASK2;
142 if (--dl <= 0) break;
145 r[3] = (t-c)&BN_MASK2;
147 if (--dl <= 0) break;
156 fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
160 switch (save_dl - dl)
164 if (--dl <= 0) break;
167 if (--dl <= 0) break;
170 if (--dl <= 0) break;
179 fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, copy)\n", cl, dl);
184 if (--dl <= 0) break;
186 if (--dl <= 0) break;
188 if (--dl <= 0) break;
190 if (--dl <= 0) break;
200 BN_ULONG bn_add_part_words(BN_ULONG *r,
201 const BN_ULONG *a, const BN_ULONG *b,
207 c = bn_add_words(r, a, b, cl);
220 fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
227 if (++dl >= 0) break;
232 if (++dl >= 0) break;
237 if (++dl >= 0) break;
242 if (++dl >= 0) break;
251 fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c == 0)\n", cl, dl);
255 switch (dl - save_dl)
259 if (++dl >= 0) break;
262 if (++dl >= 0) break;
265 if (++dl >= 0) break;
274 fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, copy)\n", cl, dl);
279 if (++dl >= 0) break;
281 if (++dl >= 0) break;
283 if (++dl >= 0) break;
285 if (++dl >= 0) break;
296 fprintf(stderr, " bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
303 if (--dl <= 0) break;
308 if (--dl <= 0) break;
313 if (--dl <= 0) break;
318 if (--dl <= 0) break;
325 fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
331 switch (save_dl - dl)
335 if (--dl <= 0) break;
338 if (--dl <= 0) break;
341 if (--dl <= 0) break;
350 fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, copy)\n", cl, dl);
355 if (--dl <= 0) break;
357 if (--dl <= 0) break;
359 if (--dl <= 0) break;
361 if (--dl <= 0) break;
372 /* Karatsuba recursive multiplication algorithm
373 * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
375 /* r is 2*n2 words in size,
376 * a and b are both n2 words in size.
377 * n2 must be a power of 2.
378 * We multiply and return the result.
379 * t must be 2*n2 words in size
382 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
385 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
389 unsigned int neg,zero;
393 fprintf(stderr," bn_mul_recursive %d * %d\n",n2,n2);
399 bn_mul_comba4(r,a,b);
405 bn_mul_comba8(r,a,b);
408 # endif /* BN_MUL_COMBA */
409 if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
411 /* This should not happen */
412 bn_mul_normal(r,a,n2,b,n2);
415 /* r=(a[0]-a[1])*(b[1]-b[0]) */
416 c1=bn_cmp_words(a,&(a[n]),n);
417 c2=bn_cmp_words(&(b[n]),b,n);
422 bn_sub_words(t, &(a[n]),a, n); /* - */
423 bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
429 bn_sub_words(t, &(a[n]),a, n); /* - */
430 bn_sub_words(&(t[n]),&(b[n]),b, n); /* + */
439 bn_sub_words(t, a, &(a[n]),n); /* + */
440 bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
447 bn_sub_words(t, a, &(a[n]),n);
448 bn_sub_words(&(t[n]),&(b[n]),b, n);
456 bn_mul_comba4(&(t[n2]),t,&(t[n]));
458 memset(&(t[n2]),0,8*sizeof(BN_ULONG));
460 bn_mul_comba4(r,a,b);
461 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
466 bn_mul_comba8(&(t[n2]),t,&(t[n]));
468 memset(&(t[n2]),0,16*sizeof(BN_ULONG));
470 bn_mul_comba8(r,a,b);
471 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
474 # endif /* BN_MUL_COMBA */
478 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
480 memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
481 bn_mul_recursive(r,a,b,n,p);
482 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,p);
485 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
486 * r[10] holds (a[0]*b[0])
487 * r[32] holds (b[1]*b[1])
490 c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
492 if (neg) /* if t[32] is negative */
494 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
498 /* Might have a carry */
499 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
502 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
503 * r[10] holds (a[0]*b[0])
504 * r[32] holds (b[1]*b[1])
505 * c1 holds the carry bits
507 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
515 /* The overflow will stop before we over write
516 * words we should not overwrite */
517 if (ln < (BN_ULONG)c1)
529 /* n+tn is the word length
530 * t needs to be n*4 is size, as does r */
531 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
535 unsigned int c1,c2,neg,zero;
539 fprintf(stderr," bn_mul_part_recursive (%d+%d) * (%d+%d)\n",
545 bn_mul_normal(r,a,i,b,i);
549 /* r=(a[0]-a[1])*(b[1]-b[0]) */
550 c1=bn_cmp_part_words(a,&(a[n]),tn,n-tn);
551 c2=bn_cmp_part_words(&(b[n]),b,tn,tn-n);
556 bn_sub_part_words(t, &(a[n]),a, tn,tn-n); /* - */
557 bn_sub_part_words(&(t[n]),b, &(b[n]),tn,n-tn); /* - */
563 bn_sub_part_words(t, &(a[n]),a, tn,tn-n); /* - */
564 bn_sub_part_words(&(t[n]),&(b[n]),b, tn,tn-n); /* + */
573 bn_sub_part_words(t, a, &(a[n]),tn,n-tn); /* + */
574 bn_sub_part_words(&(t[n]),b, &(b[n]),tn,n-tn); /* - */
581 bn_sub_part_words(t, a, &(a[n]),tn,n-tn);
582 bn_sub_part_words(&(t[n]),&(b[n]),b, tn,tn-n);
585 /* The zero case isn't yet implemented here. The speedup
586 would probably be negligible. */
590 bn_mul_comba4(&(t[n2]),t,&(t[n]));
591 bn_mul_comba4(r,a,b);
592 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
593 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
599 bn_mul_comba8(&(t[n2]),t,&(t[n]));
600 bn_mul_comba8(r,a,b);
601 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
602 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
607 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
608 bn_mul_recursive(r,a,b,n,p);
610 /* If there is only a bottom half to the number,
615 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),i,p);
616 memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
618 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
620 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
622 memset(&(r[n2+tn*2]),0,
623 sizeof(BN_ULONG)*(n2-tn*2));
625 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
627 memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
628 if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
630 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
639 bn_mul_part_recursive(&(r[n2]),
646 bn_mul_recursive(&(r[n2]),
656 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
657 * r[10] holds (a[0]*b[0])
658 * r[32] holds (b[1]*b[1])
661 c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
663 if (neg) /* if t[32] is negative */
665 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
669 /* Might have a carry */
670 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
673 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
674 * r[10] holds (a[0]*b[0])
675 * r[32] holds (b[1]*b[1])
676 * c1 holds the carry bits
678 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
686 /* The overflow will stop before we over write
687 * words we should not overwrite */
700 /* a and b must be the same size, which is n2.
701 * r needs to be n2 words and t needs to be n2*2
703 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
709 fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);
712 bn_mul_recursive(r,a,b,n,&(t[0]));
713 if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
715 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
716 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
717 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
718 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
722 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
723 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
724 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
725 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
729 /* a and b must be the same size, which is n2.
730 * r needs to be n2 words and t needs to be n2*2
731 * l is the low words of the output.
734 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
740 BN_ULONG ll,lc,*lp,*mp;
743 fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);
747 /* Calculate (al-ah)*(bh-bl) */
749 c1=bn_cmp_words(&(a[0]),&(a[n]),n);
750 c2=bn_cmp_words(&(b[n]),&(b[0]),n);
754 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
755 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
761 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
762 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
771 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
772 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
779 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
780 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
785 /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
786 /* r[10] = (a[1]*b[1]) */
790 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
791 bn_mul_comba8(r,&(a[n]),&(b[n]));
796 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,&(t[n2]));
797 bn_mul_recursive(r,&(a[n]),&(b[n]),n,&(t[n2]));
801 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
802 * We know s0 and s1 so the only unknown is high(al*bl)
803 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
804 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
809 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
818 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
821 bn_add_words(&(t[n2]),lp,&(t[0]),n);
827 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
834 lp[i]=((~mp[i])+1)&BN_MASK2;
839 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
840 * r[10] = (a[1]*b[1])
843 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
846 /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
847 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
848 * R[3]=r[1]+(carry/borrow)
853 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
860 c1+=(int)(bn_add_words(&(t[n2]),lp, &(r[0]),n));
862 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
864 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
866 c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
867 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
869 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
871 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
873 if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
880 ll=(r[i]+lc)&BN_MASK2;
890 r[i++]=(ll-lc)&BN_MASK2;
895 if (c2 != 0) /* Add starting at r[1] */
902 ll=(r[i]+lc)&BN_MASK2;
912 r[i++]=(ll-lc)&BN_MASK2;
918 #endif /* BN_RECURSION */
920 int BN_mul(BIGNUM *r, /* almost const */ const BIGNUM *a, /* almost const */ const BIGNUM *b, BN_CTX *ctx)
925 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
932 BIGNUM *free_a = NULL, *free_b = NULL;
935 fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);
945 if ((al == 0) || (bl == 0))
953 if ((r == a) || (r == b))
955 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
959 rr->neg=a->neg^b->neg;
961 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
970 if (bn_wexpand(rr,8) == NULL) goto err;
972 bn_mul_comba4(rr->d,a->d,b->d);
978 if (bn_wexpand(rr,16) == NULL) goto err;
980 bn_mul_comba8(rr->d,a->d,b->d);
984 #endif /* BN_MUL_COMBA */
986 if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
988 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
990 BIGNUM *tmp_bn = (BIGNUM *)b;
991 bn_wexpand(tmp_bn,al);
996 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
998 BIGNUM *tmp_bn = (BIGNUM *)a;
999 bn_wexpand(tmp_bn,bl);
1006 /* symmetric and > 4 */
1008 j=BN_num_bits_word((BN_ULONG)al);
1011 t = BN_CTX_get(ctx);
1012 if (al == j) /* exact multiple */
1016 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
1022 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
1028 #endif /* BN_RECURSION */
1029 if (bn_wexpand(rr,top) == NULL) goto err;
1031 bn_mul_normal(rr->d,a->d,al,b->d,bl);
1033 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1037 if (r != rr) BN_copy(r,rr);
1040 if (free_a) BN_free(free_a);
1041 if (free_b) BN_free(free_b);
1046 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1051 fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
1059 itmp=na; na=nb; nb=itmp;
1060 ltmp=a; a=b; b=ltmp;
1064 rr[0]=bn_mul_words(r,a,na,b[0]);
1068 if (--nb <= 0) return;
1069 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
1070 if (--nb <= 0) return;
1071 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
1072 if (--nb <= 0) return;
1073 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
1074 if (--nb <= 0) return;
1075 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
1082 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1085 fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
1087 bn_mul_words(r,a,n,b[0]);
1091 if (--n <= 0) return;
1092 bn_mul_add_words(&(r[1]),a,n,b[1]);
1093 if (--n <= 0) return;
1094 bn_mul_add_words(&(r[2]),a,n,b[2]);
1095 if (--n <= 0) return;
1096 bn_mul_add_words(&(r[3]),a,n,b[3]);
1097 if (--n <= 0) return;
1098 bn_mul_add_words(&(r[4]),a,n,b[4]);