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 /* Karatsuba recursive multiplication algorithm
65 * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
67 /* r is 2*n2 words in size,
68 * a and b are both n2 words in size.
69 * n2 must be a power of 2.
70 * We multiply and return the result.
71 * t must be 2*n2 words in size
74 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
77 void bn_mul_recursive(BN_ULONG
*r
, BN_ULONG
*a
, BN_ULONG
*b
, int n2
,
81 unsigned int neg
,zero
;
85 printf(" bn_mul_recursive %d * %d\n",n2
,n2
);
100 # endif /* BN_MUL_COMBA */
101 if (n2
< BN_MUL_RECURSIVE_SIZE_NORMAL
)
103 /* This should not happen */
104 bn_mul_normal(r
,a
,n2
,b
,n2
);
107 /* r=(a[0]-a[1])*(b[1]-b[0]) */
108 c1
=bn_cmp_words(a
,&(a
[n
]),n
);
109 c2
=bn_cmp_words(&(b
[n
]),b
,n
);
114 bn_sub_words(t
, &(a
[n
]),a
, n
); /* - */
115 bn_sub_words(&(t
[n
]),b
, &(b
[n
]),n
); /* - */
121 bn_sub_words(t
, &(a
[n
]),a
, n
); /* - */
122 bn_sub_words(&(t
[n
]),&(b
[n
]),b
, n
); /* + */
131 bn_sub_words(t
, a
, &(a
[n
]),n
); /* + */
132 bn_sub_words(&(t
[n
]),b
, &(b
[n
]),n
); /* - */
139 bn_sub_words(t
, a
, &(a
[n
]),n
);
140 bn_sub_words(&(t
[n
]),&(b
[n
]),b
, n
);
148 bn_mul_comba4(&(t
[n2
]),t
,&(t
[n
]));
150 memset(&(t
[n2
]),0,8*sizeof(BN_ULONG
));
152 bn_mul_comba4(r
,a
,b
);
153 bn_mul_comba4(&(r
[n2
]),&(a
[n
]),&(b
[n
]));
158 bn_mul_comba8(&(t
[n2
]),t
,&(t
[n
]));
160 memset(&(t
[n2
]),0,16*sizeof(BN_ULONG
));
162 bn_mul_comba8(r
,a
,b
);
163 bn_mul_comba8(&(r
[n2
]),&(a
[n
]),&(b
[n
]));
166 # endif /* BN_MUL_COMBA */
170 bn_mul_recursive(&(t
[n2
]),t
,&(t
[n
]),n
,p
);
172 memset(&(t
[n2
]),0,n2
*sizeof(BN_ULONG
));
173 bn_mul_recursive(r
,a
,b
,n
,p
);
174 bn_mul_recursive(&(r
[n2
]),&(a
[n
]),&(b
[n
]),n
,p
);
177 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
178 * r[10] holds (a[0]*b[0])
179 * r[32] holds (b[1]*b[1])
182 c1
=(int)(bn_add_words(t
,r
,&(r
[n2
]),n2
));
184 if (neg
) /* if t[32] is negative */
186 c1
-=(int)(bn_sub_words(&(t
[n2
]),t
,&(t
[n2
]),n2
));
190 /* Might have a carry */
191 c1
+=(int)(bn_add_words(&(t
[n2
]),&(t
[n2
]),t
,n2
));
194 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
195 * r[10] holds (a[0]*b[0])
196 * r[32] holds (b[1]*b[1])
197 * c1 holds the carry bits
199 c1
+=(int)(bn_add_words(&(r
[n
]),&(r
[n
]),&(t
[n2
]),n2
));
207 /* The overflow will stop before we over write
208 * words we should not overwrite */
209 if (ln
< (BN_ULONG
)c1
)
221 /* n+tn is the word length
222 * t needs to be n*4 is size, as does r */
223 void bn_mul_part_recursive(BN_ULONG
*r
, BN_ULONG
*a
, BN_ULONG
*b
, int tn
,
227 unsigned int c1
,c2
,neg
,zero
;
231 printf(" bn_mul_part_recursive %d * %d\n",tn
+n
,tn
+n
);
236 bn_mul_normal(r
,a
,i
,b
,i
);
240 /* r=(a[0]-a[1])*(b[1]-b[0]) */
241 c1
=bn_cmp_words(a
,&(a
[n
]),n
);
242 c2
=bn_cmp_words(&(b
[n
]),b
,n
);
247 bn_sub_words(t
, &(a
[n
]),a
, n
); /* - */
248 bn_sub_words(&(t
[n
]),b
, &(b
[n
]),n
); /* - */
254 bn_sub_words(t
, &(a
[n
]),a
, n
); /* - */
255 bn_sub_words(&(t
[n
]),&(b
[n
]),b
, n
); /* + */
264 bn_sub_words(t
, a
, &(a
[n
]),n
); /* + */
265 bn_sub_words(&(t
[n
]),b
, &(b
[n
]),n
); /* - */
272 bn_sub_words(t
, a
, &(a
[n
]),n
);
273 bn_sub_words(&(t
[n
]),&(b
[n
]),b
, n
);
276 /* The zero case isn't yet implemented here. The speedup
277 would probably be negligible. */
281 bn_mul_comba4(&(t
[n2
]),t
,&(t
[n
]));
282 bn_mul_comba4(r
,a
,b
);
283 bn_mul_normal(&(r
[n2
]),&(a
[n
]),tn
,&(b
[n
]),tn
);
284 memset(&(r
[n2
+tn
*2]),0,sizeof(BN_ULONG
)*(n2
-tn
*2));
290 bn_mul_comba8(&(t
[n2
]),t
,&(t
[n
]));
291 bn_mul_comba8(r
,a
,b
);
292 bn_mul_normal(&(r
[n2
]),&(a
[n
]),tn
,&(b
[n
]),tn
);
293 memset(&(r
[n2
+tn
*2]),0,sizeof(BN_ULONG
)*(n2
-tn
*2));
298 bn_mul_recursive(&(t
[n2
]),t
,&(t
[n
]),n
,p
);
299 bn_mul_recursive(r
,a
,b
,n
,p
);
301 /* If there is only a bottom half to the number,
306 bn_mul_recursive(&(r
[n2
]),&(a
[n
]),&(b
[n
]),i
,p
);
307 memset(&(r
[n2
+i
*2]),0,sizeof(BN_ULONG
)*(n2
-i
*2));
309 else if (j
> 0) /* eg, n == 16, i == 8 and tn == 11 */
311 bn_mul_part_recursive(&(r
[n2
]),&(a
[n
]),&(b
[n
]),
313 memset(&(r
[n2
+tn
*2]),0,
314 sizeof(BN_ULONG
)*(n2
-tn
*2));
316 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
318 memset(&(r
[n2
]),0,sizeof(BN_ULONG
)*n2
);
319 if (tn
< BN_MUL_RECURSIVE_SIZE_NORMAL
)
321 bn_mul_normal(&(r
[n2
]),&(a
[n
]),tn
,&(b
[n
]),tn
);
330 bn_mul_part_recursive(&(r
[n2
]),
337 bn_mul_recursive(&(r
[n2
]),
347 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
348 * r[10] holds (a[0]*b[0])
349 * r[32] holds (b[1]*b[1])
352 c1
=(int)(bn_add_words(t
,r
,&(r
[n2
]),n2
));
354 if (neg
) /* if t[32] is negative */
356 c1
-=(int)(bn_sub_words(&(t
[n2
]),t
,&(t
[n2
]),n2
));
360 /* Might have a carry */
361 c1
+=(int)(bn_add_words(&(t
[n2
]),&(t
[n2
]),t
,n2
));
364 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
365 * r[10] holds (a[0]*b[0])
366 * r[32] holds (b[1]*b[1])
367 * c1 holds the carry bits
369 c1
+=(int)(bn_add_words(&(r
[n
]),&(r
[n
]),&(t
[n2
]),n2
));
377 /* The overflow will stop before we over write
378 * words we should not overwrite */
391 /* a and b must be the same size, which is n2.
392 * r needs to be n2 words and t needs to be n2*2
394 void bn_mul_low_recursive(BN_ULONG
*r
, BN_ULONG
*a
, BN_ULONG
*b
, int n2
,
400 printf(" bn_mul_low_recursive %d * %d\n",n2
,n2
);
403 bn_mul_recursive(r
,a
,b
,n
,&(t
[0]));
404 if (n
>= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL
)
406 bn_mul_low_recursive(&(t
[0]),&(a
[0]),&(b
[n
]),n
,&(t
[n2
]));
407 bn_add_words(&(r
[n
]),&(r
[n
]),&(t
[0]),n
);
408 bn_mul_low_recursive(&(t
[0]),&(a
[n
]),&(b
[0]),n
,&(t
[n2
]));
409 bn_add_words(&(r
[n
]),&(r
[n
]),&(t
[0]),n
);
413 bn_mul_low_normal(&(t
[0]),&(a
[0]),&(b
[n
]),n
);
414 bn_mul_low_normal(&(t
[n
]),&(a
[n
]),&(b
[0]),n
);
415 bn_add_words(&(r
[n
]),&(r
[n
]),&(t
[0]),n
);
416 bn_add_words(&(r
[n
]),&(r
[n
]),&(t
[n
]),n
);
420 /* a and b must be the same size, which is n2.
421 * r needs to be n2 words and t needs to be n2*2
422 * l is the low words of the output.
425 void bn_mul_high(BN_ULONG
*r
, BN_ULONG
*a
, BN_ULONG
*b
, BN_ULONG
*l
, int n2
,
431 BN_ULONG ll
,lc
,*lp
,*mp
;
434 printf(" bn_mul_high %d * %d\n",n2
,n2
);
438 /* Calculate (al-ah)*(bh-bl) */
440 c1
=bn_cmp_words(&(a
[0]),&(a
[n
]),n
);
441 c2
=bn_cmp_words(&(b
[n
]),&(b
[0]),n
);
445 bn_sub_words(&(r
[0]),&(a
[n
]),&(a
[0]),n
);
446 bn_sub_words(&(r
[n
]),&(b
[0]),&(b
[n
]),n
);
452 bn_sub_words(&(r
[0]),&(a
[n
]),&(a
[0]),n
);
453 bn_sub_words(&(r
[n
]),&(b
[n
]),&(b
[0]),n
);
462 bn_sub_words(&(r
[0]),&(a
[0]),&(a
[n
]),n
);
463 bn_sub_words(&(r
[n
]),&(b
[0]),&(b
[n
]),n
);
470 bn_sub_words(&(r
[0]),&(a
[0]),&(a
[n
]),n
);
471 bn_sub_words(&(r
[n
]),&(b
[n
]),&(b
[0]),n
);
476 /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
477 /* r[10] = (a[1]*b[1]) */
481 bn_mul_comba8(&(t
[0]),&(r
[0]),&(r
[n
]));
482 bn_mul_comba8(r
,&(a
[n
]),&(b
[n
]));
487 bn_mul_recursive(&(t
[0]),&(r
[0]),&(r
[n
]),n
,&(t
[n2
]));
488 bn_mul_recursive(r
,&(a
[n
]),&(b
[n
]),n
,&(t
[n2
]));
492 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
493 * We know s0 and s1 so the only unknown is high(al*bl)
494 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
495 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
500 c1
=(int)(bn_add_words(lp
,&(r
[0]),&(l
[0]),n
));
509 neg
=(int)(bn_sub_words(&(t
[n2
]),lp
,&(t
[0]),n
));
512 bn_add_words(&(t
[n2
]),lp
,&(t
[0]),n
);
518 bn_sub_words(&(t
[n2
+n
]),&(l
[n
]),&(t
[n2
]),n
);
525 lp
[i
]=((~mp
[i
])+1)&BN_MASK2
;
530 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
531 * r[10] = (a[1]*b[1])
534 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
537 /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
538 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
539 * R[3]=r[1]+(carry/borrow)
544 c1
= (int)(bn_add_words(lp
,&(t
[n2
+n
]),&(l
[0]),n
));
551 c1
+=(int)(bn_add_words(&(t
[n2
]),lp
, &(r
[0]),n
));
553 c1
-=(int)(bn_sub_words(&(t
[n2
]),&(t
[n2
]),&(t
[0]),n
));
555 c1
+=(int)(bn_add_words(&(t
[n2
]),&(t
[n2
]),&(t
[0]),n
));
557 c2
=(int)(bn_add_words(&(r
[0]),&(r
[0]),&(t
[n2
+n
]),n
));
558 c2
+=(int)(bn_add_words(&(r
[0]),&(r
[0]),&(r
[n
]),n
));
560 c2
-=(int)(bn_sub_words(&(r
[0]),&(r
[0]),&(t
[n
]),n
));
562 c2
+=(int)(bn_add_words(&(r
[0]),&(r
[0]),&(t
[n
]),n
));
564 if (c1
!= 0) /* Add starting at r[0], could be +ve or -ve */
571 ll
=(r
[i
]+lc
)&BN_MASK2
;
581 r
[i
++]=(ll
-lc
)&BN_MASK2
;
586 if (c2
!= 0) /* Add starting at r[1] */
593 ll
=(r
[i
]+lc
)&BN_MASK2
;
603 r
[i
++]=(ll
-lc
)&BN_MASK2
;
609 #endif /* BN_RECURSION */
611 int BN_mul(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
616 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
623 BIGNUM
*free_a
= NULL
, *free_b
= NULL
;
626 printf("BN_mul %d * %d\n",a
->top
,b
->top
);
636 if ((al
== 0) || (bl
== 0))
644 if ((r
== a
) || (r
== b
))
646 if ((rr
= BN_CTX_get(ctx
)) == NULL
) goto err
;
650 rr
->neg
=a
->neg
^b
->neg
;
652 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
661 if (bn_wexpand(rr
,8) == NULL
) goto err
;
663 bn_mul_comba4(rr
->d
,a
->d
,b
->d
);
669 if (bn_wexpand(rr
,16) == NULL
) goto err
;
671 bn_mul_comba8(rr
->d
,a
->d
,b
->d
);
675 #endif /* BN_MUL_COMBA */
677 if ((al
>= BN_MULL_SIZE_NORMAL
) && (bl
>= BN_MULL_SIZE_NORMAL
))
679 if (i
== 1 && !BN_get_flags(b
,BN_FLG_STATIC_DATA
))
681 BIGNUM
*tmp_bn
= free_b
;
682 b
= free_b
= bn_dup_expand(b
,al
);
686 if (tmp_bn
) BN_free(tmp_bn
);
688 else if (i
== -1 && !BN_get_flags(a
,BN_FLG_STATIC_DATA
))
690 BIGNUM
*tmp_bn
= free_a
;
691 a
= free_a
= bn_dup_expand(a
,bl
);
695 if (tmp_bn
) BN_free(tmp_bn
);
699 /* symmetric and > 4 */
701 j
=BN_num_bits_word((BN_ULONG
)al
);
705 if (al
== j
) /* exact multiple */
709 bn_mul_recursive(rr
->d
,a
->d
,b
->d
,al
,t
->d
);
713 BIGNUM
*tmp_a
= free_a
,*tmp_b
= free_b
;
714 a
= free_a
= bn_dup_expand(a
,k
);
715 b
= free_b
= bn_dup_expand(b
,k
);
716 if (tmp_a
) BN_free(tmp_a
);
717 if (tmp_b
) BN_free(tmp_b
);
720 for (i
=free_a
->top
; i
<k
; i
++)
722 for (i
=free_b
->top
; i
<k
; i
++)
724 bn_mul_part_recursive(rr
->d
,a
->d
,b
->d
,al
-j
,j
,t
->d
);
730 #endif /* BN_RECURSION */
731 if (bn_wexpand(rr
,top
) == NULL
) goto err
;
733 bn_mul_normal(rr
->d
,a
->d
,al
,b
->d
,bl
);
735 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
739 if (r
!= rr
) BN_copy(r
,rr
);
742 if (free_a
) BN_free(free_a
);
743 if (free_b
) BN_free(free_b
);
748 void bn_mul_normal(BN_ULONG
*r
, BN_ULONG
*a
, int na
, BN_ULONG
*b
, int nb
)
753 printf(" bn_mul_normal %d * %d\n",na
,nb
);
761 itmp
=na
; na
=nb
; nb
=itmp
;
766 rr
[0]=bn_mul_words(r
,a
,na
,b
[0]);
770 if (--nb
<= 0) return;
771 rr
[1]=bn_mul_add_words(&(r
[1]),a
,na
,b
[1]);
772 if (--nb
<= 0) return;
773 rr
[2]=bn_mul_add_words(&(r
[2]),a
,na
,b
[2]);
774 if (--nb
<= 0) return;
775 rr
[3]=bn_mul_add_words(&(r
[3]),a
,na
,b
[3]);
776 if (--nb
<= 0) return;
777 rr
[4]=bn_mul_add_words(&(r
[4]),a
,na
,b
[4]);
784 void bn_mul_low_normal(BN_ULONG
*r
, BN_ULONG
*a
, BN_ULONG
*b
, int n
)
787 printf(" bn_mul_low_normal %d * %d\n",n
,n
);
789 bn_mul_words(r
,a
,n
,b
[0]);
793 if (--n
<= 0) return;
794 bn_mul_add_words(&(r
[1]),a
,n
,b
[1]);
795 if (--n
<= 0) return;
796 bn_mul_add_words(&(r
[2]),a
,n
,b
[2]);
797 if (--n
<= 0) return;
798 bn_mul_add_words(&(r
[3]),a
,n
,b
[3]);
799 if (--n
<= 0) return;
800 bn_mul_add_words(&(r
[4]),a
,n
,b
[4]);