1 /* crypto/bn/bn_lib.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.]
60 # undef NDEBUG /* avoid conflicting definitions */
70 const char *BN_version="Big Number" OPENSSL_VERSION_PTEXT;
72 /* For a 32 bit machine
81 static int bn_limit_bits=0;
82 static int bn_limit_num=8; /* (1<<bn_limit_bits) */
83 static int bn_limit_bits_low=0;
84 static int bn_limit_num_low=8; /* (1<<bn_limit_bits_low) */
85 static int bn_limit_bits_high=0;
86 static int bn_limit_num_high=8; /* (1<<bn_limit_bits_high) */
87 static int bn_limit_bits_mont=0;
88 static int bn_limit_num_mont=8; /* (1<<bn_limit_bits_mont) */
90 void BN_set_params(int mult, int high, int low, int mont)
94 if (mult > (sizeof(int)*8)-1)
101 if (high > (sizeof(int)*8)-1)
102 high=sizeof(int)*8-1;
103 bn_limit_bits_high=high;
104 bn_limit_num_high=1<<high;
108 if (low > (sizeof(int)*8)-1)
110 bn_limit_bits_low=low;
111 bn_limit_num_low=1<<low;
115 if (mont > (sizeof(int)*8)-1)
116 mont=sizeof(int)*8-1;
117 bn_limit_bits_mont=mont;
118 bn_limit_num_mont=1<<mont;
122 int BN_get_params(int which)
124 if (which == 0) return(bn_limit_bits);
125 else if (which == 1) return(bn_limit_bits_high);
126 else if (which == 2) return(bn_limit_bits_low);
127 else if (which == 3) return(bn_limit_bits_mont);
131 BIGNUM *BN_value_one(void)
133 static BN_ULONG data_one=1L;
134 static BIGNUM const_one={&data_one,1,1,0};
139 char *BN_options(void)
142 static char data[16];
148 sprintf(data,"bn(%d,%d)",(int)sizeof(BN_ULLONG)*8,
149 (int)sizeof(BN_ULONG)*8);
151 sprintf(data,"bn(%d,%d)",(int)sizeof(BN_ULONG)*8,
152 (int)sizeof(BN_ULONG)*8);
158 int BN_num_bits_word(BN_ULONG l)
160 static const char bits[256]={
161 0,1,2,2,3,3,3,3,4,4,4,4,4,4,4,4,
162 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
163 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
164 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
165 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
166 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
167 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
168 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
169 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
170 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
171 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
172 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
173 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
174 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
175 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
176 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
179 #if defined(SIXTY_FOUR_BIT_LONG)
180 if (l & 0xffffffff00000000L)
182 if (l & 0xffff000000000000L)
184 if (l & 0xff00000000000000L)
186 return(bits[(int)(l>>56)]+56);
188 else return(bits[(int)(l>>48)]+48);
192 if (l & 0x0000ff0000000000L)
194 return(bits[(int)(l>>40)]+40);
196 else return(bits[(int)(l>>32)]+32);
201 #ifdef SIXTY_FOUR_BIT
202 if (l & 0xffffffff00000000LL)
204 if (l & 0xffff000000000000LL)
206 if (l & 0xff00000000000000LL)
208 return(bits[(int)(l>>56)]+56);
210 else return(bits[(int)(l>>48)]+48);
214 if (l & 0x0000ff0000000000LL)
216 return(bits[(int)(l>>40)]+40);
218 else return(bits[(int)(l>>32)]+32);
225 #if defined(THIRTY_TWO_BIT) || defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
229 return(bits[(int)(l>>24L)]+24);
230 else return(bits[(int)(l>>16L)]+16);
235 #if defined(SIXTEEN_BIT) || defined(THIRTY_TWO_BIT) || defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
237 return(bits[(int)(l>>8)]+8);
240 return(bits[(int)(l )] );
245 int BN_num_bits(const BIGNUM *a)
252 if (a->top == 0) return(0);
255 i=(a->top-1)*BN_BITS2;
256 return(i+BN_num_bits_word(l));
259 void BN_clear_free(BIGNUM *a)
263 if (a == NULL) return;
266 memset(a->d,0,a->dmax*sizeof(a->d[0]));
267 if (!(BN_get_flags(a,BN_FLG_STATIC_DATA)))
270 i=BN_get_flags(a,BN_FLG_MALLOCED);
271 memset(a,0,sizeof(BIGNUM));
276 void BN_free(BIGNUM *a)
278 if (a == NULL) return;
279 if ((a->d != NULL) && !(BN_get_flags(a,BN_FLG_STATIC_DATA)))
281 a->flags|=BN_FLG_FREE; /* REMOVE? */
282 if (a->flags & BN_FLG_MALLOCED)
286 void BN_init(BIGNUM *a)
288 memset(a,0,sizeof(BIGNUM));
295 if ((ret=(BIGNUM *)OPENSSL_malloc(sizeof(BIGNUM))) == NULL)
297 BNerr(BN_F_BN_NEW,ERR_R_MALLOC_FAILURE);
300 ret->flags=BN_FLG_MALLOCED;
308 /* This is an internal function that should not be used in applications.
309 * It ensures that 'b' has enough room for a 'words' word number number.
310 * It is mostly used by the various BIGNUM routines. If there is an error,
311 * NULL is returned. If not, 'b' is returned. */
313 BIGNUM *bn_expand2(BIGNUM *b, int words)
323 if (words > (INT_MAX/(4*BN_BITS2)))
325 BNerr(BN_F_BN_EXPAND2,BN_R_TOO_LARGE);
330 if (BN_get_flags(b,BN_FLG_STATIC_DATA))
332 BNerr(BN_F_BN_EXPAND2,BN_R_EXPAND_ON_STATIC_BIGNUM_DATA);
335 a=A=(BN_ULONG *)OPENSSL_malloc(sizeof(BN_ULONG)*(words+1));
338 BNerr(BN_F_BN_EXPAND2,ERR_R_MALLOC_FAILURE);
343 /* Check if the previous number needs to be copied */
347 /* This lot is an unrolled loop to copy b->top
348 * BN_ULONGs from B to A
351 * I have nothing against unrolling but it's usually done for
352 * several reasons, namely:
353 * - minimize percentage of decision making code, i.e. branches;
354 * - avoid cache trashing;
355 * - make it possible to schedule loads earlier;
356 * Now let's examine the code below. The cornerstone of C is
357 * "programmer is always right" and that's what we love it for:-)
358 * For this very reason C compilers have to be paranoid when it
359 * comes to data aliasing and assume the worst. Yeah, but what
360 * does it mean in real life? This means that loop body below will
361 * be compiled to sequence of loads immediately followed by stores
362 * as compiler assumes the worst, something in A==B+1 style. As a
363 * result CPU pipeline is going to starve for incoming data. Secondly
364 * if A and B happen to share same cache line such code is going to
365 * cause severe cache trashing. Both factors have severe impact on
366 * performance of modern CPUs and this is the reason why this
367 * particular piece of code is #ifdefed away and replaced by more
368 * "friendly" version found in #else section below. This comment
369 * also applies to BN_copy function.
371 * <appro@fy.chalmers.se>
373 for (i=b->top&(~7); i>0; i-=8)
375 A[0]=B[0]; A[1]=B[1]; A[2]=B[2]; A[3]=B[3];
376 A[4]=B[4]; A[5]=B[5]; A[6]=B[6]; A[7]=B[7];
397 /* I need the 'case 0' entry for utrix cc.
398 * If the optimizer is turned on, it does the
399 * switch table by doing
402 * goto jump_table[a];
403 * If top is 0, this makes us jump to 0xffffffc
404 * which is rather bad :-(.
410 for (i=b->top>>2; i>0; i--,A+=4,B+=4)
413 * The fact that the loop is unrolled
414 * 4-wise is a tribute to Intel. It's
415 * the one that doesn't have enough
416 * registers to accomodate more data.
417 * I'd unroll it 8-wise otherwise:-)
419 * <appro@fy.chalmers.se>
421 BN_ULONG a0,a1,a2,a3;
422 a0=B[0]; a1=B[1]; a2=B[2]; a3=B[3];
423 A[0]=a0; A[1]=a1; A[2]=a2; A[3]=a3;
430 case 0: ; /* ultrix cc workaround, see above */
439 /* Now need to zero any data between b->top and b->max */
442 for (i=(b->dmax - b->top)>>3; i>0; i--,A+=8)
444 A[0]=0; A[1]=0; A[2]=0; A[3]=0;
445 A[4]=0; A[5]=0; A[6]=0; A[7]=0;
447 for (i=(b->dmax - b->top)&7; i>0; i--,A++)
450 memset(A,0,sizeof(BN_ULONG)*(words+1));
451 memcpy(A,b->d,sizeof(b->d[0])*b->top);
456 /* memset(&(p[b->max]),0,((words+1)-b->max)*sizeof(BN_ULONG)); */
457 /* { int i; for (i=b->max; i<words+1; i++) p[i]=i;} */
463 BIGNUM *BN_dup(const BIGNUM *a)
467 if (a == NULL) return NULL;
472 if (r == NULL) return(NULL);
473 return((BIGNUM *)BN_copy(r,a));
476 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b)
484 if (a == b) return(a);
485 if (bn_wexpand(a,b->top) == NULL) return(NULL);
490 for (i=b->top>>2; i>0; i--,A+=4,B+=4)
492 BN_ULONG a0,a1,a2,a3;
493 a0=B[0]; a1=B[1]; a2=B[2]; a3=B[3];
494 A[0]=a0; A[1]=a1; A[2]=a2; A[3]=a3;
501 case 0: ; /* ultrix cc workaround, see comments in bn_expand2 */
504 memcpy(a->d,b->d,sizeof(b->d[0])*b->top);
507 /* memset(&(a->d[b->top]),0,sizeof(a->d[0])*(a->max-b->top));*/
509 if ((a->top == 0) && (a->d != NULL))
515 void BN_clear(BIGNUM *a)
518 memset(a->d,0,a->dmax*sizeof(a->d[0]));
523 BN_ULONG BN_get_word(BIGNUM *a)
529 if (n > sizeof(BN_ULONG))
531 for (i=a->top-1; i>=0; i--)
533 #ifndef SIXTY_FOUR_BIT /* the data item > unsigned long */
534 ret<<=BN_BITS4; /* stops the compiler complaining */
544 int BN_set_word(BIGNUM *a, BN_ULONG w)
547 if (bn_expand(a,sizeof(BN_ULONG)*8) == NULL) return(0);
549 n=sizeof(BN_ULONG)/BN_BYTES;
552 a->d[0]=(BN_ULONG)w&BN_MASK2;
553 if (a->d[0] != 0) a->top=1;
556 /* the following is done instead of
557 * w>>=BN_BITS2 so compilers don't complain
558 * on builds where sizeof(long) == BN_TYPES */
559 #ifndef SIXTY_FOUR_BIT /* the data item > unsigned long */
565 a->d[i]=(BN_ULONG)w&BN_MASK2;
566 if (a->d[i] != 0) a->top=i+1;
571 /* ignore negative */
572 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret)
578 if (ret == NULL) ret=BN_new();
579 if (ret == NULL) return(NULL);
587 if (bn_expand(ret,(int)(n+2)*8) == NULL)
589 i=((n-1)/BN_BYTES)+1;
590 m=((n-1)%(BN_BYTES));
602 /* need to call this due to clear byte at top if avoiding
603 * having the top bit set (-ve number) */
608 /* ignore negative */
609 int BN_bn2bin(const BIGNUM *a, unsigned char *to)
618 *(to++)=(unsigned char)(l>>(8*(i%BN_BYTES)))&0xff;
623 int BN_ucmp(const BIGNUM *a, const BIGNUM *b)
626 BN_ULONG t1,t2,*ap,*bp;
632 if (i != 0) return(i);
635 for (i=a->top-1; i>=0; i--)
640 return(t1 > t2?1:-1);
645 int BN_cmp(const BIGNUM *a, const BIGNUM *b)
651 if ((a == NULL) || (b == NULL))
664 if (a->neg != b->neg)
672 else { gt= -1; lt=1; }
674 if (a->top > b->top) return(gt);
675 if (a->top < b->top) return(lt);
676 for (i=a->top-1; i>=0; i--)
680 if (t1 > t2) return(gt);
681 if (t1 < t2) return(lt);
686 int BN_set_bit(BIGNUM *a, int n)
694 if (bn_wexpand(a,i+1) == NULL) return(0);
695 for(k=a->top; k<i+1; k++)
700 a->d[i]|=(((BN_ULONG)1)<<j);
704 int BN_clear_bit(BIGNUM *a, int n)
710 if (a->top <= i) return(0);
712 a->d[i]&=(~(((BN_ULONG)1)<<j));
717 int BN_is_bit_set(const BIGNUM *a, int n)
721 if (n < 0) return(0);
724 if (a->top <= i) return(0);
725 return((a->d[i]&(((BN_ULONG)1)<<j))?1:0);
728 int BN_mask_bits(BIGNUM *a, int n)
734 if (w >= a->top) return(0);
740 a->d[w]&= ~(BN_MASK2<<b);
746 int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n)
753 if (aa != bb) return((aa > bb)?1:-1);
754 for (i=n-2; i>=0; i--)
758 if (aa != bb) return((aa > bb)?1:-1);