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 */
64 #define OPENSSL_FIPSAPI
72 const char BN_version[]="Big Number" OPENSSL_VERSION_PTEXT;
74 /* This stuff appears to be completely unused, so is deprecated */
75 #ifndef OPENSSL_NO_DEPRECATED
76 /* For a 32 bit machine
85 static int bn_limit_bits=0;
86 static int bn_limit_num=8; /* (1<<bn_limit_bits) */
87 static int bn_limit_bits_low=0;
88 static int bn_limit_num_low=8; /* (1<<bn_limit_bits_low) */
89 static int bn_limit_bits_high=0;
90 static int bn_limit_num_high=8; /* (1<<bn_limit_bits_high) */
91 static int bn_limit_bits_mont=0;
92 static int bn_limit_num_mont=8; /* (1<<bn_limit_bits_mont) */
94 void BN_set_params(int mult, int high, int low, int mont)
98 if (mult > (int)(sizeof(int)*8)-1)
101 bn_limit_num=1<<mult;
105 if (high > (int)(sizeof(int)*8)-1)
106 high=sizeof(int)*8-1;
107 bn_limit_bits_high=high;
108 bn_limit_num_high=1<<high;
112 if (low > (int)(sizeof(int)*8)-1)
114 bn_limit_bits_low=low;
115 bn_limit_num_low=1<<low;
119 if (mont > (int)(sizeof(int)*8)-1)
120 mont=sizeof(int)*8-1;
121 bn_limit_bits_mont=mont;
122 bn_limit_num_mont=1<<mont;
126 int BN_get_params(int which)
128 if (which == 0) return(bn_limit_bits);
129 else if (which == 1) return(bn_limit_bits_high);
130 else if (which == 2) return(bn_limit_bits_low);
131 else if (which == 3) return(bn_limit_bits_mont);
136 const BIGNUM *BN_value_one(void)
138 static const BN_ULONG data_one=1L;
139 static const BIGNUM const_one={(BN_ULONG *)&data_one,1,1,0,BN_FLG_STATIC_DATA};
144 int BN_num_bits_word(BN_ULONG l)
147 static const unsigned char bits[256]={
148 0,1,2,2,3,3,3,3,4,4,4,4,4,4,4,4,
149 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
150 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
151 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
152 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
153 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
154 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
155 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
156 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
157 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
158 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
159 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
160 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
161 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
162 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
163 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
166 #if defined(SIXTY_FOUR_BIT_LONG)
167 if (l & 0xffffffff00000000L)
169 if (l & 0xffff000000000000L)
171 if (l & 0xff00000000000000L)
173 return(bits[(int)(l>>56)]+56);
175 else return(bits[(int)(l>>48)]+48);
179 if (l & 0x0000ff0000000000L)
181 return(bits[(int)(l>>40)]+40);
183 else return(bits[(int)(l>>32)]+32);
188 #ifdef SIXTY_FOUR_BIT
189 if (l & 0xffffffff00000000LL)
191 if (l & 0xffff000000000000LL)
193 if (l & 0xff00000000000000LL)
195 return(bits[(int)(l>>56)]+56);
197 else return(bits[(int)(l>>48)]+48);
201 if (l & 0x0000ff0000000000LL)
203 return(bits[(int)(l>>40)]+40);
205 else return(bits[(int)(l>>32)]+32);
212 #if defined(THIRTY_TWO_BIT) || defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
216 return(bits[(int)(l>>24L)]+24);
217 else return(bits[(int)(l>>16L)]+16);
222 #if defined(THIRTY_TWO_BIT) || defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
224 return(bits[(int)(l>>8)]+8);
227 return(bits[(int)(l )] );
232 int BN_num_bits(const BIGNUM *a)
237 if (BN_is_zero(a)) return 0;
238 return ((i*BN_BITS2) + BN_num_bits_word(a->d[i]));
241 void BN_clear_free(BIGNUM *a)
245 if (a == NULL) return;
249 OPENSSL_cleanse(a->d,a->dmax*sizeof(a->d[0]));
250 if (!(BN_get_flags(a,BN_FLG_STATIC_DATA)))
253 i=BN_get_flags(a,BN_FLG_MALLOCED);
254 OPENSSL_cleanse(a,sizeof(BIGNUM));
259 void BN_free(BIGNUM *a)
261 if (a == NULL) return;
263 if ((a->d != NULL) && !(BN_get_flags(a,BN_FLG_STATIC_DATA)))
265 if (a->flags & BN_FLG_MALLOCED)
269 #ifndef OPENSSL_NO_DEPRECATED
270 a->flags|=BN_FLG_FREE;
276 void BN_init(BIGNUM *a)
278 memset(a,0,sizeof(BIGNUM));
286 if ((ret=(BIGNUM *)OPENSSL_malloc(sizeof(BIGNUM))) == NULL)
288 BNerr(BN_F_BN_NEW,ERR_R_MALLOC_FAILURE);
291 ret->flags=BN_FLG_MALLOCED;
300 /* This is used both by bn_expand2() and bn_dup_expand() */
301 /* The caller MUST check that words > b->dmax before calling this */
302 static BN_ULONG *bn_expand_internal(const BIGNUM *b, int words)
304 BN_ULONG *A,*a = NULL;
310 if (words > (INT_MAX/(4*BN_BITS2)))
312 BNerr(BN_F_BN_EXPAND_INTERNAL,BN_R_BIGNUM_TOO_LONG);
315 if (BN_get_flags(b,BN_FLG_STATIC_DATA))
317 BNerr(BN_F_BN_EXPAND_INTERNAL,BN_R_EXPAND_ON_STATIC_BIGNUM_DATA);
320 a=A=(BN_ULONG *)OPENSSL_malloc(sizeof(BN_ULONG)*words);
323 BNerr(BN_F_BN_EXPAND_INTERNAL,ERR_R_MALLOC_FAILURE);
327 /* Valgrind complains in BN_consttime_swap because we process the whole
328 * array even if it's not initialised yet. This doesn't matter in that
329 * function - what's important is constant time operation (we're not
330 * actually going to use the data)
332 memset(a, 0, sizeof(BN_ULONG)*words);
337 /* Check if the previous number needs to be copied */
340 for (i=b->top>>2; i>0; i--,A+=4,B+=4)
343 * The fact that the loop is unrolled
344 * 4-wise is a tribute to Intel. It's
345 * the one that doesn't have enough
346 * registers to accomodate more data.
347 * I'd unroll it 8-wise otherwise:-)
349 * <appro@fy.chalmers.se>
351 BN_ULONG a0,a1,a2,a3;
352 a0=B[0]; a1=B[1]; a2=B[2]; a3=B[3];
353 A[0]=a0; A[1]=a1; A[2]=a2; A[3]=a3;
360 case 0: /* workaround for ultrix cc: without 'case 0', the optimizer does
361 * the switch table by doing a=top&3; a--; goto jump_table[a];
362 * which fails for top== 0 */
368 memset(A,0,sizeof(BN_ULONG)*words);
369 memcpy(A,b->d,sizeof(b->d[0])*b->top);
375 /* This is an internal function that can be used instead of bn_expand2()
376 * when there is a need to copy BIGNUMs instead of only expanding the
377 * data part, while still expanding them.
378 * Especially useful when needing to expand BIGNUMs that are declared
379 * 'const' and should therefore not be changed.
380 * The reason to use this instead of a BN_dup() followed by a bn_expand2()
381 * is memory allocation overhead. A BN_dup() followed by a bn_expand2()
382 * will allocate new memory for the BIGNUM data twice, and free it once,
383 * while bn_dup_expand() makes sure allocation is made only once.
386 #ifndef OPENSSL_NO_DEPRECATED
387 BIGNUM *bn_dup_expand(const BIGNUM *b, int words)
393 /* This function does not work if
394 * words <= b->dmax && top < words
395 * because BN_dup() does not preserve 'dmax'!
396 * (But bn_dup_expand() is not used anywhere yet.)
401 BN_ULONG *a = bn_expand_internal(b, words);
415 /* r == NULL, BN_new failure */
419 /* If a == NULL, there was an error in allocation in
420 bn_expand_internal(), and NULL should be returned */
432 /* This is an internal function that should not be used in applications.
433 * It ensures that 'b' has enough room for a 'words' word number
434 * and initialises any unused part of b->d with leading zeros.
435 * It is mostly used by the various BIGNUM routines. If there is an error,
436 * NULL is returned. If not, 'b' is returned. */
438 BIGNUM *bn_expand2(BIGNUM *b, int words)
444 BN_ULONG *a = bn_expand_internal(b, words);
446 if(b->d) OPENSSL_free(b->d);
451 /* None of this should be necessary because of what b->top means! */
453 /* NB: bn_wexpand() calls this only if the BIGNUM really has to grow */
454 if (b->top < b->dmax)
457 BN_ULONG *A = &(b->d[b->top]);
458 for (i=(b->dmax - b->top)>>3; i>0; i--,A+=8)
460 A[0]=0; A[1]=0; A[2]=0; A[3]=0;
461 A[4]=0; A[5]=0; A[6]=0; A[7]=0;
463 for (i=(b->dmax - b->top)&7; i>0; i--,A++)
465 assert(A == &(b->d[b->dmax]));
472 BIGNUM *BN_dup(const BIGNUM *a)
476 if (a == NULL) return NULL;
480 if (t == NULL) return 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);
527 void BN_swap(BIGNUM *a, BIGNUM *b)
529 int flags_old_a, flags_old_b;
531 int tmp_top, tmp_dmax, tmp_neg;
536 flags_old_a = a->flags;
537 flags_old_b = b->flags;
554 a->flags = (flags_old_a & BN_FLG_MALLOCED) | (flags_old_b & BN_FLG_STATIC_DATA);
555 b->flags = (flags_old_b & BN_FLG_MALLOCED) | (flags_old_a & BN_FLG_STATIC_DATA);
560 void BN_clear(BIGNUM *a)
564 memset(a->d,0,a->dmax*sizeof(a->d[0]));
569 BN_ULONG BN_get_word(const BIGNUM *a)
573 else if (a->top == 1)
579 int BN_set_word(BIGNUM *a, BN_ULONG w)
582 if (bn_expand(a,(int)sizeof(BN_ULONG)*8) == NULL) return(0);
585 a->top = (w ? 1 : 0);
590 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret)
599 if (ret == NULL) return(NULL);
608 i=((n-1)/BN_BYTES)+1;
609 m=((n-1)%(BN_BYTES));
610 if (bn_wexpand(ret, (int)i) == NULL)
627 /* need to call this due to clear byte at top if avoiding
628 * having the top bit set (-ve number) */
633 /* ignore negative */
634 int BN_bn2bin(const BIGNUM *a, unsigned char *to)
644 *(to++)=(unsigned char)(l>>(8*(i%BN_BYTES)))&0xff;
649 int BN_ucmp(const BIGNUM *a, const BIGNUM *b)
652 BN_ULONG t1,t2,*ap,*bp;
658 if (i != 0) return(i);
661 for (i=a->top-1; i>=0; i--)
666 return((t1 > t2) ? 1 : -1);
671 int BN_cmp(const BIGNUM *a, const BIGNUM *b)
677 if ((a == NULL) || (b == NULL))
690 if (a->neg != b->neg)
698 else { gt= -1; lt=1; }
700 if (a->top > b->top) return(gt);
701 if (a->top < b->top) return(lt);
702 for (i=a->top-1; i>=0; i--)
706 if (t1 > t2) return(gt);
707 if (t1 < t2) return(lt);
712 int BN_set_bit(BIGNUM *a, int n)
723 if (bn_wexpand(a,i+1) == NULL) return(0);
724 for(k=a->top; k<i+1; k++)
729 a->d[i]|=(((BN_ULONG)1)<<j);
734 int BN_clear_bit(BIGNUM *a, int n)
743 if (a->top <= i) return(0);
745 a->d[i]&=(~(((BN_ULONG)1)<<j));
750 int BN_is_bit_set(const BIGNUM *a, int n)
758 if (a->top <= i) return 0;
759 return (int)(((a->d[i])>>j)&((BN_ULONG)1));
762 int BN_mask_bits(BIGNUM *a, int n)
771 if (w >= a->top) return 0;
777 a->d[w]&= ~(BN_MASK2<<b);
783 void BN_set_negative(BIGNUM *a, int b)
785 if (b && !BN_is_zero(a))
791 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n)
798 if (aa != bb) return((aa > bb)?1:-1);
799 for (i=n-2; i>=0; i--)
803 if (aa != bb) return((aa > bb)?1:-1);
808 /* Here follows a specialised variants of bn_cmp_words(). It has the
809 property of performing the operation on arrays of different sizes.
810 The sizes of those arrays is expressed through cl, which is the
811 common length ( basicall, min(len(a),len(b)) ), and dl, which is the
812 delta between the two lengths, calculated as len(a)-len(b).
813 All lengths are the number of BN_ULONGs... */
815 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b,
826 return -1; /* a < b */
834 return 1; /* a > b */
837 return bn_cmp_words(a,b,cl);
841 * Constant-time conditional swap of a and b.
842 * a and b are swapped if condition is not 0. The code assumes that at most one bit of condition is set.
843 * nwords is the number of words to swap. The code assumes that at least nwords are allocated in both a and b,
844 * and that no more than nwords are used by either a or b.
845 * a and b cannot be the same number
847 void BN_consttime_swap(BN_ULONG condition, BIGNUM *a, BIGNUM *b, int nwords)
852 bn_wcheck_size(a, nwords);
853 bn_wcheck_size(b, nwords);
856 assert((condition & (condition - 1)) == 0);
857 assert(sizeof(BN_ULONG) >= sizeof(int));
859 condition = ((condition - 1) >> (BN_BITS2 - 1)) - 1;
861 t = (a->top^b->top) & condition;
865 #define BN_CONSTTIME_SWAP(ind) \
867 t = (a->d[ind] ^ b->d[ind]) & condition; \
875 for (i = 10; i < nwords; i++)
876 BN_CONSTTIME_SWAP(i);
878 case 10: BN_CONSTTIME_SWAP(9); /* Fallthrough */
879 case 9: BN_CONSTTIME_SWAP(8); /* Fallthrough */
880 case 8: BN_CONSTTIME_SWAP(7); /* Fallthrough */
881 case 7: BN_CONSTTIME_SWAP(6); /* Fallthrough */
882 case 6: BN_CONSTTIME_SWAP(5); /* Fallthrough */
883 case 5: BN_CONSTTIME_SWAP(4); /* Fallthrough */
884 case 4: BN_CONSTTIME_SWAP(3); /* Fallthrough */
885 case 3: BN_CONSTTIME_SWAP(2); /* Fallthrough */
886 case 2: BN_CONSTTIME_SWAP(1); /* Fallthrough */
887 case 1: BN_CONSTTIME_SWAP(0);
889 #undef BN_CONSTTIME_SWAP
892 /* Bits of security, see SP800-57 */
894 int BN_security_bits(int L, int N)
914 return bits >= secbits ? secbits : bits;