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(r
,a
,b
,n2
,t
)
80 unsigned int neg
,zero
;
84 printf(" bn_mul_recursive %d * %d\n",n2
,n2
);
98 if (n2
< BN_MUL_RECURSIVE_SIZE_NORMAL
)
100 /* This should not happen */
101 bn_mul_normal(r
,a
,n2
,b
,n2
);
104 /* r=(a[0]-a[1])*(b[1]-b[0]) */
105 c1
=bn_cmp_words(a
,&(a
[n
]),n
);
106 c2
=bn_cmp_words(&(b
[n
]),b
,n
);
111 bn_sub_words(t
, &(a
[n
]),a
, n
); /* - */
112 bn_sub_words(&(t
[n
]),b
, &(b
[n
]),n
); /* - */
118 bn_sub_words(t
, &(a
[n
]),a
, n
); /* - */
119 bn_sub_words(&(t
[n
]),&(b
[n
]),b
, n
); /* + */
128 bn_sub_words(t
, a
, &(a
[n
]),n
); /* + */
129 bn_sub_words(&(t
[n
]),b
, &(b
[n
]),n
); /* - */
136 bn_sub_words(t
, a
, &(a
[n
]),n
);
137 bn_sub_words(&(t
[n
]),&(b
[n
]),b
, n
);
145 bn_mul_comba4(&(t
[n2
]),t
,&(t
[n
]));
147 memset(&(t
[n2
]),0,8*sizeof(BN_ULONG
));
149 bn_mul_comba4(r
,a
,b
);
150 bn_mul_comba4(&(r
[n2
]),&(a
[n
]),&(b
[n
]));
155 bn_mul_comba8(&(t
[n2
]),t
,&(t
[n
]));
157 memset(&(t
[n2
]),0,16*sizeof(BN_ULONG
));
159 bn_mul_comba8(r
,a
,b
);
160 bn_mul_comba8(&(r
[n2
]),&(a
[n
]),&(b
[n
]));
167 bn_mul_recursive(&(t
[n2
]),t
,&(t
[n
]),n
,p
);
169 memset(&(t
[n2
]),0,n2
*sizeof(BN_ULONG
));
170 bn_mul_recursive(r
,a
,b
,n
,p
);
171 bn_mul_recursive(&(r
[n2
]),&(a
[n
]),&(b
[n
]),n
,p
);
174 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
175 * r[10] holds (a[0]*b[0])
176 * r[32] holds (b[1]*b[1])
179 c1
=bn_add_words(t
,r
,&(r
[n2
]),n2
);
181 if (neg
) /* if t[32] is negative */
183 c1
-=bn_sub_words(&(t
[n2
]),t
,&(t
[n2
]),n2
);
187 /* Might have a carry */
188 c1
+=bn_add_words(&(t
[n2
]),&(t
[n2
]),t
,n2
);
191 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
192 * r[10] holds (a[0]*b[0])
193 * r[32] holds (b[1]*b[1])
194 * c1 holds the carry bits
196 c1
+=bn_add_words(&(r
[n
]),&(r
[n
]),&(t
[n2
]),n2
);
204 /* The overflow will stop before we over write
205 * words we should not overwrite */
206 if (ln
< (BN_ULONG
)c1
)
218 /* n+tn is the word length
219 * t needs to be n*4 is size, as does r */
220 void bn_mul_part_recursive(r
,a
,b
,tn
,n
,t
)
230 printf(" bn_mul_part_recursive %d * %d\n",tn
+n
,tn
+n
);
235 bn_mul_normal(r
,a
,i
,b
,i
);
239 /* r=(a[0]-a[1])*(b[1]-b[0]) */
240 bn_sub_words(t
, a
, &(a
[n
]),n
); /* + */
241 bn_sub_words(&(t
[n
]),b
, &(b
[n
]),n
); /* - */
245 bn_mul_comba4(&(t[n2]),t,&(t[n]));
246 bn_mul_comba4(r,a,b);
247 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
248 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
252 bn_mul_comba8(&(t
[n2
]),t
,&(t
[n
]));
253 bn_mul_comba8(r
,a
,b
);
254 bn_mul_normal(&(r
[n2
]),&(a
[n
]),tn
,&(b
[n
]),tn
);
255 memset(&(r
[n2
+tn
*2]),0,sizeof(BN_ULONG
)*(n2
-tn
*2));
260 bn_mul_recursive(&(t
[n2
]),t
,&(t
[n
]),n
,p
);
261 bn_mul_recursive(r
,a
,b
,n
,p
);
263 /* If there is only a bottom half to the number,
268 bn_mul_recursive(&(r
[n2
]),&(a
[n
]),&(b
[n
]),i
,p
);
269 memset(&(r
[n2
+i
*2]),0,sizeof(BN_ULONG
)*(n2
-i
*2));
271 else if (j
> 0) /* eg, n == 16, i == 8 and tn == 11 */
273 bn_mul_part_recursive(&(r
[n2
]),&(a
[n
]),&(b
[n
]),
275 memset(&(r
[n2
+tn
*2]),0,
276 sizeof(BN_ULONG
)*(n2
-tn
*2));
278 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
280 memset(&(r
[n2
]),0,sizeof(BN_ULONG
)*n2
);
281 if (tn
< BN_MUL_RECURSIVE_SIZE_NORMAL
)
283 bn_mul_normal(&(r
[n2
]),&(a
[n
]),tn
,&(b
[n
]),tn
);
292 bn_mul_part_recursive(&(r
[n2
]),
299 bn_mul_recursive(&(r
[n2
]),
309 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
310 * r[10] holds (a[0]*b[0])
311 * r[32] holds (b[1]*b[1])
314 c1
=bn_add_words(t
,r
,&(r
[n2
]),n2
);
315 c1
-=bn_sub_words(&(t
[n2
]),t
,&(t
[n2
]),n2
);
317 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
318 * r[10] holds (a[0]*b[0])
319 * r[32] holds (b[1]*b[1])
320 * c1 holds the carry bits
322 c1
+=bn_add_words(&(r
[n
]),&(r
[n
]),&(t
[n2
]),n2
);
330 /* The overflow will stop before we over write
331 * words we should not overwrite */
344 /* a and b must be the same size, which is n2.
345 * r needs to be n2 words and t needs to be n2*2
347 void bn_mul_low_recursive(r
,a
,b
,n2
,t
)
355 printf(" bn_mul_low_recursive %d * %d\n",n2
,n2
);
358 bn_mul_recursive(r
,a
,b
,n
,&(t
[0]));
359 if (n
>= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL
)
361 bn_mul_low_recursive(&(t
[0]),&(a
[0]),&(b
[n
]),n
,&(t
[n2
]));
362 bn_add_words(&(r
[n
]),&(r
[n
]),&(t
[0]),n
);
363 bn_mul_low_recursive(&(t
[0]),&(a
[n
]),&(b
[0]),n
,&(t
[n2
]));
364 bn_add_words(&(r
[n
]),&(r
[n
]),&(t
[0]),n
);
368 bn_mul_low_normal(&(t
[0]),&(a
[0]),&(b
[n
]),n
);
369 bn_mul_low_normal(&(t
[n
]),&(a
[n
]),&(b
[0]),n
);
370 bn_add_words(&(r
[n
]),&(r
[n
]),&(t
[0]),n
);
371 bn_add_words(&(r
[n
]),&(r
[n
]),&(t
[n
]),n
);
375 /* a and b must be the same size, which is n2.
376 * r needs to be n2 words and t needs to be n2*2
377 * l is the low words of the output.
380 void bn_mul_high(r
,a
,b
,l
,n2
,t
)
381 BN_ULONG
*r
,*a
,*b
,*l
;
388 BN_ULONG ll
,lc
,*lp
,*mp
;
391 printf(" bn_mul_high %d * %d\n",n2
,n2
);
395 /* Calculate (al-ah)*(bh-bl) */
397 c1
=bn_cmp_words(&(a
[0]),&(a
[n
]),n
);
398 c2
=bn_cmp_words(&(b
[n
]),&(b
[0]),n
);
402 bn_sub_words(&(r
[0]),&(a
[n
]),&(a
[0]),n
);
403 bn_sub_words(&(r
[n
]),&(b
[0]),&(b
[n
]),n
);
409 bn_sub_words(&(r
[0]),&(a
[n
]),&(a
[0]),n
);
410 bn_sub_words(&(r
[n
]),&(b
[n
]),&(b
[0]),n
);
419 bn_sub_words(&(r
[0]),&(a
[0]),&(a
[n
]),n
);
420 bn_sub_words(&(r
[n
]),&(b
[0]),&(b
[n
]),n
);
427 bn_sub_words(&(r
[0]),&(a
[0]),&(a
[n
]),n
);
428 bn_sub_words(&(r
[n
]),&(b
[n
]),&(b
[0]),n
);
433 /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
434 /* r[10] = (a[1]*b[1]) */
438 bn_mul_comba8(&(t
[0]),&(r
[0]),&(r
[n
]));
439 bn_mul_comba8(r
,&(a
[n
]),&(b
[n
]));
444 bn_mul_recursive(&(t
[0]),&(r
[0]),&(r
[n
]),n
,&(t
[n2
]));
445 bn_mul_recursive(r
,&(a
[n
]),&(b
[n
]),n
,&(t
[n2
]));
449 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
450 * We know s0 and s1 so the only unknown is high(al*bl)
451 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
452 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
457 c1
=bn_add_words(lp
,&(r
[0]),&(l
[0]),n
);
466 neg
=bn_sub_words(&(t
[n2
]),lp
,&(t
[0]),n
);
469 bn_add_words(&(t
[n2
]),lp
,&(t
[0]),n
);
475 bn_sub_words(&(t
[n2
+n
]),&(l
[n
]),&(t
[n2
]),n
);
482 lp
[i
]=((~mp
[i
])+1)&BN_MASK2
;
487 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
488 * r[10] = (a[1]*b[1])
491 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
494 /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
495 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
496 * R[3]=r[1]+(carry/borrow)
501 c1
= bn_add_words(lp
,&(t
[n2
+n
]),&(l
[0]),n
);
508 c1
+=bn_add_words(&(t
[n2
]),lp
, &(r
[0]),n
);
510 c1
-=bn_sub_words(&(t
[n2
]),&(t
[n2
]),&(t
[0]),n
);
512 c1
+=bn_add_words(&(t
[n2
]),&(t
[n2
]),&(t
[0]),n
);
514 c2
=bn_add_words(&(r
[0]),&(r
[0]),&(t
[n2
+n
]),n
);
515 c2
+=bn_add_words(&(r
[0]),&(r
[0]),&(r
[n
]),n
);
517 c2
-=bn_sub_words(&(r
[0]),&(r
[0]),&(t
[n
]),n
);
519 c2
+=bn_add_words(&(r
[0]),&(r
[0]),&(t
[n
]),n
);
521 if (c1
!= 0) /* Add starting at r[0], could be +ve or -ve */
528 ll
=(r
[i
]+lc
)&BN_MASK2
;
538 r
[i
++]=(ll
-lc
)&BN_MASK2
;
543 if (c2
!= 0) /* Add starting at r[1] */
550 ll
=(r
[i
]+lc
)&BN_MASK2
;
560 r
[i
++]=(ll
-lc
)&BN_MASK2
;
568 int BN_mul(r
,a
,b
,ctx
)
579 printf("BN_mul %d * %d\n",a
->top
,b
->top
);
588 r
->neg
=a
->neg
^b
->neg
;
590 if ((al
== 0) || (bl
== 0))
596 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
602 if (bn_wexpand(r,8) == NULL) return(0);
604 bn_mul_comba4(r->d,a->d,b->d);
609 if (bn_wexpand(r
,16) == NULL
) return(0);
611 bn_mul_comba8(r
->d
,a
->d
,b
->d
);
617 if (al
< BN_MULL_SIZE_NORMAL
)
620 if (bn_wexpand(r
,top
) == NULL
) return(0);
622 bn_mul_normal(r
->d
,a
->d
,al
,b
->d
,bl
);
631 else if ((al
< BN_MULL_SIZE_NORMAL
) || (bl
< BN_MULL_SIZE_NORMAL
))
633 if (bn_wexpand(r
,top
) == NULL
) return(0);
635 bn_mul_normal(r
->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 /* asymetric and >= 4 */
659 if (bn_wexpand(r
,top
) == NULL
) return(0);
661 bn_mul_normal(r
->d
,a
->d
,al
,b
->d
,bl
);
667 /* symetric and > 4 */
669 j
=BN_num_bits_word((BN_ULONG
)al
);
672 t
= &(ctx
->bn
[ctx
->tos
]);
673 if (al
== j
) /* exact multiple */
677 bn_mul_recursive(r
->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(r
->d
,a
->d
,b
->d
,al
-j
,j
,t
->d
);
699 void bn_mul_normal(r
,a
,na
,b
,nb
)
708 printf(" bn_mul_normal %d * %d\n",na
,nb
);
716 itmp
=na
; na
=nb
; nb
=itmp
;
721 rr
[0]=bn_mul_words(r
,a
,na
,b
[0]);
725 if (--nb
<= 0) return;
726 rr
[1]=bn_mul_add_words(&(r
[1]),a
,na
,b
[1]);
727 if (--nb
<= 0) return;
728 rr
[2]=bn_mul_add_words(&(r
[2]),a
,na
,b
[2]);
729 if (--nb
<= 0) return;
730 rr
[3]=bn_mul_add_words(&(r
[3]),a
,na
,b
[3]);
731 if (--nb
<= 0) return;
732 rr
[4]=bn_mul_add_words(&(r
[4]),a
,na
,b
[4]);
739 void bn_mul_low_normal(r
,a
,b
,n
)
744 printf(" bn_mul_low_normal %d * %d\n",n
,n
);
746 bn_mul_words(r
,a
,n
,b
[0]);
750 if (--n
<= 0) return;
751 bn_mul_add_words(&(r
[1]),a
,n
,b
[1]);
752 if (--n
<= 0) return;
753 bn_mul_add_words(&(r
[2]),a
,n
,b
[2]);
754 if (--n
<= 0) return;
755 bn_mul_add_words(&(r
[3]),a
,n
,b
[3]);
756 if (--n
<= 0) return;
757 bn_mul_add_words(&(r
[4]),a
,n
,b
[4]);