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 > (int)(sizeof(int)*8)-1)
101 if (high > (int)(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 > (int)(sizeof(int)*8)-1)
110 bn_limit_bits_low=low;
111 bn_limit_num_low=1<<low;
115 if (mont > (int)(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 const BIGNUM *BN_value_one(void)
133 static BN_ULONG data_one=1L;
134 static BIGNUM const_one={&data_one,1,1,0,BN_FLG_STATIC_DATA};
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 OPENSSL_cleanse(a->d,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 OPENSSL_cleanse(a,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));
296 if ((ret=(BIGNUM *)OPENSSL_malloc(sizeof(BIGNUM))) == NULL)
298 BNerr(BN_F_BN_NEW,ERR_R_MALLOC_FAILURE);
301 ret->flags=BN_FLG_MALLOCED;
310 /* This is used both by bn_expand2() and bn_dup_expand() */
311 /* The caller MUST check that words > b->dmax before calling this */
312 static BN_ULONG *bn_expand_internal(const BIGNUM *b, int words)
314 BN_ULONG *A,*a = NULL;
318 if (words > (INT_MAX/(4*BN_BITS2)))
320 BNerr(BN_F_BN_EXPAND_INTERNAL,BN_R_BIGNUM_TOO_LONG);
325 if (BN_get_flags(b,BN_FLG_STATIC_DATA))
327 BNerr(BN_F_BN_EXPAND_INTERNAL,BN_R_EXPAND_ON_STATIC_BIGNUM_DATA);
330 a=A=(BN_ULONG *)OPENSSL_malloc(sizeof(BN_ULONG)*(words+1));
333 BNerr(BN_F_BN_EXPAND_INTERNAL,ERR_R_MALLOC_FAILURE);
338 /* Check if the previous number needs to be copied */
341 for (i=b->top>>2; i>0; i--,A+=4,B+=4)
344 * The fact that the loop is unrolled
345 * 4-wise is a tribute to Intel. It's
346 * the one that doesn't have enough
347 * registers to accomodate more data.
348 * I'd unroll it 8-wise otherwise:-)
350 * <appro@fy.chalmers.se>
352 BN_ULONG a0,a1,a2,a3;
353 a0=B[0]; a1=B[1]; a2=B[2]; a3=B[3];
354 A[0]=a0; A[1]=a1; A[2]=a2; A[3]=a3;
361 case 0: /* workaround for ultrix cc: without 'case 0', the optimizer does
362 * the switch table by doing a=top&3; a--; goto jump_table[a];
363 * which fails for top== 0 */
369 memset(A,0,sizeof(BN_ULONG)*(words+1));
370 memcpy(A,b->d,sizeof(b->d[0])*b->top);
376 /* This is an internal function that can be used instead of bn_expand2()
377 * when there is a need to copy BIGNUMs instead of only expanding the
378 * data part, while still expanding them.
379 * Especially useful when needing to expand BIGNUMs that are declared
380 * 'const' and should therefore not be changed.
381 * The reason to use this instead of a BN_dup() followed by a bn_expand2()
382 * is memory allocation overhead. A BN_dup() followed by a bn_expand2()
383 * will allocate new memory for the BIGNUM data twice, and free it once,
384 * while bn_dup_expand() makes sure allocation is made only once.
387 BIGNUM *bn_dup_expand(const BIGNUM *b, int words)
391 /* This function does not work if
392 * words <= b->dmax && top < words
393 * because BN_dup() does not preserve 'dmax'!
394 * (But bn_dup_expand() is not used anywhere yet.)
399 BN_ULONG *a = bn_expand_internal(b, words);
413 /* r == NULL, BN_new failure */
417 /* If a == NULL, there was an error in allocation in
418 bn_expand_internal(), and NULL should be returned */
429 /* This is an internal function that should not be used in applications.
430 * It ensures that 'b' has enough room for a 'words' word number
431 * and initialises any unused part of b->d with leading zeros.
432 * It is mostly used by the various BIGNUM routines. If there is an error,
433 * NULL is returned. If not, 'b' is returned. */
435 BIGNUM *bn_expand2(BIGNUM *b, int words)
442 BN_ULONG *a = bn_expand_internal(b, words);
455 /* NB: bn_wexpand() calls this only if the BIGNUM really has to grow */
456 if ((b != NULL) && (b->top < b->dmax))
459 for (i=(b->dmax - b->top)>>3; i>0; i--,A+=8)
461 A[0]=0; A[1]=0; A[2]=0; A[3]=0;
462 A[4]=0; A[5]=0; A[6]=0; A[7]=0;
464 for (i=(b->dmax - b->top)&7; i>0; i--,A++)
466 assert(A == &(b->d[b->dmax]));
468 else if(b) bn_check_top(b);
472 BIGNUM *BN_dup(const BIGNUM *a)
476 if (a == NULL) return NULL;
481 if (t == NULL) return(NULL);
483 /* now r == t || r == NULL */
490 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b)
498 if (a == b) return(a);
499 if (bn_wexpand(a,b->top) == NULL) return(NULL);
504 for (i=b->top>>2; i>0; i--,A+=4,B+=4)
506 BN_ULONG a0,a1,a2,a3;
507 a0=B[0]; a1=B[1]; a2=B[2]; a3=B[3];
508 A[0]=a0; A[1]=a1; A[2]=a2; A[3]=a3;
515 case 0: ; /* ultrix cc workaround, see comments in bn_expand_internal */
518 memcpy(a->d,b->d,sizeof(b->d[0])*b->top);
521 /* memset(&(a->d[b->top]),0,sizeof(a->d[0])*(a->max-b->top));*/
523 if ((a->top == 0) && (a->d != NULL))
530 BIGNUM *BN_ncopy(BIGNUM *a, const BIGNUM *b, size_t n)
541 min = (b->top < (int)n)? b->top: (int)n;
549 if (bn_wexpand(a, min) == NULL)
554 for (i=min>>2; i>0; i--, A+=4, B+=4)
556 BN_ULONG a0,a1,a2,a3;
557 a0=B[0]; a1=B[1]; a2=B[2]; a3=B[3];
558 A[0]=a0; A[1]=a1; A[2]=a2; A[3]=a3;
576 void BN_swap(BIGNUM *a, BIGNUM *b)
578 int flags_old_a, flags_old_b;
580 int tmp_top, tmp_dmax, tmp_neg;
585 flags_old_a = a->flags;
586 flags_old_b = b->flags;
603 a->flags = (flags_old_a & BN_FLG_MALLOCED) | (flags_old_b & BN_FLG_STATIC_DATA);
604 b->flags = (flags_old_b & BN_FLG_MALLOCED) | (flags_old_a & BN_FLG_STATIC_DATA);
610 void BN_clear(BIGNUM *a)
614 memset(a->d,0,a->dmax*sizeof(a->d[0]));
619 BN_ULONG BN_get_word(const BIGNUM *a)
625 if (n > (int)sizeof(BN_ULONG))
627 for (i=a->top-1; i>=0; i--)
629 #ifndef SIXTY_FOUR_BIT /* the data item > unsigned long */
630 ret<<=BN_BITS4; /* stops the compiler complaining */
640 int BN_set_word(BIGNUM *a, BN_ULONG w)
644 if (bn_expand(a,(int)sizeof(BN_ULONG)*8) == NULL) return(0);
646 n=sizeof(BN_ULONG)/BN_BYTES;
649 a->d[0]=(BN_ULONG)w&BN_MASK2;
650 if (a->d[0] != 0) a->top=1;
653 /* the following is done instead of
654 * w>>=BN_BITS2 so compilers don't complain
655 * on builds where sizeof(long) == BN_TYPES */
656 #ifndef SIXTY_FOUR_BIT /* the data item > unsigned long */
662 a->d[i]=(BN_ULONG)w&BN_MASK2;
663 if (a->d[i] != 0) a->top=i+1;
669 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret)
675 if (ret == NULL) ret=BN_new();
676 if (ret == NULL) return(NULL);
685 if (bn_expand(ret,(int)(n+2)*8) == NULL)
687 i=((n-1)/BN_BYTES)+1;
688 m=((n-1)%(BN_BYTES));
701 /* need to call this due to clear byte at top if avoiding
702 * having the top bit set (-ve number) */
707 /* ignore negative */
708 int BN_bn2bin(const BIGNUM *a, unsigned char *to)
718 *(to++)=(unsigned char)(l>>(8*(i%BN_BYTES)))&0xff;
723 int BN_ucmp(const BIGNUM *a, const BIGNUM *b)
726 BN_ULONG t1,t2,*ap,*bp;
732 if (i != 0) return(i);
735 for (i=a->top-1; i>=0; i--)
740 return(t1 > t2?1:-1);
745 int BN_cmp(const BIGNUM *a, const BIGNUM *b)
751 if ((a == NULL) || (b == NULL))
764 if (a->neg != b->neg)
772 else { gt= -1; lt=1; }
774 if (a->top > b->top) return(gt);
775 if (a->top < b->top) return(lt);
776 for (i=a->top-1; i>=0; i--)
780 if (t1 > t2) return(gt);
781 if (t1 < t2) return(lt);
786 int BN_set_bit(BIGNUM *a, int n)
797 if (bn_wexpand(a,i+1) == NULL) return(0);
798 for(k=a->top; k<i+1; k++)
803 a->d[i]|=(((BN_ULONG)1)<<j);
808 int BN_clear_bit(BIGNUM *a, int n)
817 if (a->top <= i) return(0);
819 a->d[i]&=(~(((BN_ULONG)1)<<j));
824 int BN_is_bit_set(const BIGNUM *a, int n)
828 if (n < 0) return(0);
831 if (a->top <= i) return(0);
832 return((a->d[i]&(((BN_ULONG)1)<<j))?1:0);
835 int BN_mask_bits(BIGNUM *a, int n)
844 if (w >= a->top) return(0);
850 a->d[w]&= ~(BN_MASK2<<b);
856 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n)
863 if (aa != bb) return((aa > bb)?1:-1);
864 for (i=n-2; i>=0; i--)
868 if (aa != bb) return((aa > bb)?1:-1);
873 /* Here follows a specialised variants of bn_cmp_words(). It has the
874 property of performing the operation on arrays of different sizes.
875 The sizes of those arrays is expressed through cl, which is the
876 common length ( basicall, min(len(a),len(b)) ), and dl, which is the
877 delta between the two lengths, calculated as len(a)-len(b).
878 All lengths are the number of BN_ULONGs... */
880 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b,
891 return -1; /* a < b */
899 return 1; /* a > b */
902 return bn_cmp_words(a,b,cl);