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 /* r is 2*n2 words in size,
65 * a and b are both n2 words in size.
66 * n2 must be a power of 2.
67 * We multiply and return the result.
68 * t must be 2*n2 words in size
71 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
74 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
78 unsigned int neg,zero;
82 printf(" bn_mul_recursive %d * %d\n",n2,n2);
96 if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
98 /* This should not happen */
99 bn_mul_normal(r,a,n2,b,n2);
102 /* r=(a[0]-a[1])*(b[1]-b[0]) */
103 c1=bn_cmp_words(a,&(a[n]),n);
104 c2=bn_cmp_words(&(b[n]),b,n);
109 bn_sub_words(t, &(a[n]),a, n); /* - */
110 bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
116 bn_sub_words(t, &(a[n]),a, n); /* - */
117 bn_sub_words(&(t[n]),&(b[n]),b, n); /* + */
126 bn_sub_words(t, a, &(a[n]),n); /* + */
127 bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
134 bn_sub_words(t, a, &(a[n]),n);
135 bn_sub_words(&(t[n]),&(b[n]),b, n);
143 bn_mul_comba4(&(t[n2]),t,&(t[n]));
145 memset(&(t[n2]),0,8*sizeof(BN_ULONG));
147 bn_mul_comba4(r,a,b);
148 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
153 bn_mul_comba8(&(t[n2]),t,&(t[n]));
155 memset(&(t[n2]),0,16*sizeof(BN_ULONG));
157 bn_mul_comba8(r,a,b);
158 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
165 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
167 memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
168 bn_mul_recursive(r,a,b,n,p);
169 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,p);
172 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
173 * r[10] holds (a[0]*b[0])
174 * r[32] holds (b[1]*b[1])
177 c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
179 if (neg) /* if t[32] is negative */
181 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
185 /* Might have a carry */
186 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
189 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
190 * r[10] holds (a[0]*b[0])
191 * r[32] holds (b[1]*b[1])
192 * c1 holds the carry bits
194 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
202 /* The overflow will stop before we over write
203 * words we should not overwrite */
204 if (ln < (BN_ULONG)c1)
216 /* n+tn is the word length
217 * t needs to be n*4 is size, as does r */
218 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
226 printf(" bn_mul_part_recursive %d * %d\n",tn+n,tn+n);
231 bn_mul_normal(r,a,i,b,i);
235 /* r=(a[0]-a[1])*(b[1]-b[0]) */
236 bn_sub_words(t, a, &(a[n]),n); /* + */
237 bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
241 bn_mul_comba4(&(t[n2]),t,&(t[n]));
242 bn_mul_comba4(r,a,b);
243 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
244 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
248 bn_mul_comba8(&(t[n2]),t,&(t[n]));
249 bn_mul_comba8(r,a,b);
250 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
251 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
256 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
257 bn_mul_recursive(r,a,b,n,p);
259 /* If there is only a bottom half to the number,
264 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),i,p);
265 memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
267 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
269 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
271 memset(&(r[n2+tn*2]),0,
272 sizeof(BN_ULONG)*(n2-tn*2));
274 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
276 memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
277 if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
279 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
288 bn_mul_part_recursive(&(r[n2]),
295 bn_mul_recursive(&(r[n2]),
305 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
306 * r[10] holds (a[0]*b[0])
307 * r[32] holds (b[1]*b[1])
310 c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
311 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
313 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
314 * r[10] holds (a[0]*b[0])
315 * r[32] holds (b[1]*b[1])
316 * c1 holds the carry bits
318 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
326 /* The overflow will stop before we over write
327 * words we should not overwrite */
340 /* a and b must be the same size, which is n2.
341 * r needs to be n2 words and t needs to be n2*2
343 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
349 printf(" bn_mul_low_recursive %d * %d\n",n2,n2);
352 bn_mul_recursive(r,a,b,n,&(t[0]));
353 if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
355 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
356 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
357 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
358 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
362 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
363 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
364 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
365 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
369 /* a and b must be the same size, which is n2.
370 * r needs to be n2 words and t needs to be n2*2
371 * l is the low words of the output.
374 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
380 BN_ULONG ll,lc,*lp,*mp;
383 printf(" bn_mul_high %d * %d\n",n2,n2);
387 /* Calculate (al-ah)*(bh-bl) */
389 c1=bn_cmp_words(&(a[0]),&(a[n]),n);
390 c2=bn_cmp_words(&(b[n]),&(b[0]),n);
394 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
395 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
401 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
402 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
411 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
412 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
419 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
420 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
425 /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
426 /* r[10] = (a[1]*b[1]) */
430 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
431 bn_mul_comba8(r,&(a[n]),&(b[n]));
436 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,&(t[n2]));
437 bn_mul_recursive(r,&(a[n]),&(b[n]),n,&(t[n2]));
441 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
442 * We know s0 and s1 so the only unknown is high(al*bl)
443 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
444 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
449 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
458 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
461 bn_add_words(&(t[n2]),lp,&(t[0]),n);
467 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
474 lp[i]=((~mp[i])+1)&BN_MASK2;
479 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
480 * r[10] = (a[1]*b[1])
483 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
486 /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
487 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
488 * R[3]=r[1]+(carry/borrow)
493 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
500 c1+=(int)(bn_add_words(&(t[n2]),lp, &(r[0]),n));
502 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
504 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
506 c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
507 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
509 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
511 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
513 if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
520 ll=(r[i]+lc)&BN_MASK2;
530 r[i++]=(ll-lc)&BN_MASK2;
535 if (c2 != 0) /* Add starting at r[1] */
542 ll=(r[i]+lc)&BN_MASK2;
552 r[i++]=(ll-lc)&BN_MASK2;
560 int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
570 printf("BN_mul %d * %d\n",a->top,b->top);
579 r->neg=a->neg^b->neg;
581 if ((al == 0) || (bl == 0))
589 if ((r == a) || (r == b))
591 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
596 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
602 if (bn_wexpand(rr,8) == NULL) goto err;
604 bn_mul_comba4(rr->d,a->d,b->d);
609 if (bn_wexpand(rr,16) == NULL) goto err;
611 bn_mul_comba8(rr->d,a->d,b->d);
617 if (al < BN_MULL_SIZE_NORMAL)
620 if (bn_wexpand(rr,top) == NULL) goto err;
622 bn_mul_normal(rr->d,a->d,al,b->d,bl);
631 else if ((al < BN_MULL_SIZE_NORMAL) || (bl < BN_MULL_SIZE_NORMAL))
633 if (bn_wexpand(rr,top) == NULL) goto err;
635 bn_mul_normal(rr->d,a->d,al,b->d,bl);
641 if ((i == 1) && !BN_get_flags(b,BN_FLG_STATIC_DATA))
648 else if ((i == -1) && !BN_get_flags(a,BN_FLG_STATIC_DATA))
658 /* asymmetric and >= 4 */
659 if (bn_wexpand(rr,top) == NULL) goto err;
661 bn_mul_normal(rr->d,a->d,al,b->d,bl);
667 /* symmetric and > 4 */
669 j=BN_num_bits_word((BN_ULONG)al);
673 if (al == j) /* exact multiple */
677 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
685 for (i=a->top; i<k; i++)
687 for (i=b->top; i<k; i++)
689 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
694 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
698 if (r != rr) BN_copy(r,rr);
706 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
711 printf(" bn_mul_normal %d * %d\n",na,nb);
719 itmp=na; na=nb; nb=itmp;
724 rr[0]=bn_mul_words(r,a,na,b[0]);
728 if (--nb <= 0) return;
729 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
730 if (--nb <= 0) return;
731 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
732 if (--nb <= 0) return;
733 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
734 if (--nb <= 0) return;
735 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
742 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
745 printf(" bn_mul_low_normal %d * %d\n",n,n);
747 bn_mul_words(r,a,n,b[0]);
751 if (--n <= 0) return;
752 bn_mul_add_words(&(r[1]),a,n,b[1]);
753 if (--n <= 0) return;
754 bn_mul_add_words(&(r[2]),a,n,b[2]);
755 if (--n <= 0) return;
756 bn_mul_add_words(&(r[3]),a,n,b[3]);
757 if (--n <= 0) return;
758 bn_mul_add_words(&(r[4]),a,n,b[4]);