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 if (a
->flags
& BN_FLG_MALLOCED
)
285 #ifndef OPENSSL_NO_DEPRECATED
286 a
->flags
|=BN_FLG_FREE
;
292 void BN_init(BIGNUM
*a
)
294 memset(a
,0,sizeof(BIGNUM
));
302 if ((ret
=(BIGNUM
*)OPENSSL_malloc(sizeof(BIGNUM
))) == NULL
)
304 BNerr(BN_F_BN_NEW
,ERR_R_MALLOC_FAILURE
);
307 ret
->flags
=BN_FLG_MALLOCED
;
316 /* This is used both by bn_expand2() and bn_dup_expand() */
317 /* The caller MUST check that words > b->dmax before calling this */
318 static BN_ULONG
*bn_expand_internal(const BIGNUM
*b
, int words
)
320 BN_ULONG
*A
,*a
= NULL
;
324 if (words
> (INT_MAX
/(4*BN_BITS2
)))
326 BNerr(BN_F_BN_EXPAND_INTERNAL
,BN_R_BIGNUM_TOO_LONG
);
331 if (BN_get_flags(b
,BN_FLG_STATIC_DATA
))
333 BNerr(BN_F_BN_EXPAND_INTERNAL
,BN_R_EXPAND_ON_STATIC_BIGNUM_DATA
);
336 a
=A
=(BN_ULONG
*)OPENSSL_malloc(sizeof(BN_ULONG
)*(words
+1));
339 BNerr(BN_F_BN_EXPAND_INTERNAL
,ERR_R_MALLOC_FAILURE
);
344 /* Check if the previous number needs to be copied */
347 for (i
=b
->top
>>2; i
>0; i
--,A
+=4,B
+=4)
350 * The fact that the loop is unrolled
351 * 4-wise is a tribute to Intel. It's
352 * the one that doesn't have enough
353 * registers to accomodate more data.
354 * I'd unroll it 8-wise otherwise:-)
356 * <appro@fy.chalmers.se>
358 BN_ULONG a0
,a1
,a2
,a3
;
359 a0
=B
[0]; a1
=B
[1]; a2
=B
[2]; a3
=B
[3];
360 A
[0]=a0
; A
[1]=a1
; A
[2]=a2
; A
[3]=a3
;
367 case 0: /* workaround for ultrix cc: without 'case 0', the optimizer does
368 * the switch table by doing a=top&3; a--; goto jump_table[a];
369 * which fails for top== 0 */
375 memset(A
,0,sizeof(BN_ULONG
)*(words
+1));
376 memcpy(A
,b
->d
,sizeof(b
->d
[0])*b
->top
);
382 /* This is an internal function that can be used instead of bn_expand2()
383 * when there is a need to copy BIGNUMs instead of only expanding the
384 * data part, while still expanding them.
385 * Especially useful when needing to expand BIGNUMs that are declared
386 * 'const' and should therefore not be changed.
387 * The reason to use this instead of a BN_dup() followed by a bn_expand2()
388 * is memory allocation overhead. A BN_dup() followed by a bn_expand2()
389 * will allocate new memory for the BIGNUM data twice, and free it once,
390 * while bn_dup_expand() makes sure allocation is made only once.
393 BIGNUM
*bn_dup_expand(const BIGNUM
*b
, int words
)
397 /* This function does not work if
398 * words <= b->dmax && top < words
399 * because BN_dup() does not preserve 'dmax'!
400 * (But bn_dup_expand() is not used anywhere yet.)
405 BN_ULONG
*a
= bn_expand_internal(b
, words
);
419 /* r == NULL, BN_new failure */
423 /* If a == NULL, there was an error in allocation in
424 bn_expand_internal(), and NULL should be returned */
435 /* This is an internal function that should not be used in applications.
436 * It ensures that 'b' has enough room for a 'words' word number
437 * and initialises any unused part of b->d with leading zeros.
438 * It is mostly used by the various BIGNUM routines. If there is an error,
439 * NULL is returned. If not, 'b' is returned. */
441 BIGNUM
*bn_expand2(BIGNUM
*b
, int words
)
448 BN_ULONG
*a
= bn_expand_internal(b
, words
);
461 /* NB: bn_wexpand() calls this only if the BIGNUM really has to grow */
462 if ((b
!= NULL
) && (b
->top
< b
->dmax
))
465 for (i
=(b
->dmax
- b
->top
)>>3; i
>0; i
--,A
+=8)
467 A
[0]=0; A
[1]=0; A
[2]=0; A
[3]=0;
468 A
[4]=0; A
[5]=0; A
[6]=0; A
[7]=0;
470 for (i
=(b
->dmax
- b
->top
)&7; i
>0; i
--,A
++)
472 assert(A
== &(b
->d
[b
->dmax
]));
474 else if(b
) bn_check_top(b
);
478 BIGNUM
*BN_dup(const BIGNUM
*a
)
482 if (a
== NULL
) return NULL
;
487 if (t
== NULL
) return(NULL
);
489 /* now r == t || r == NULL */
496 BIGNUM
*BN_copy(BIGNUM
*a
, const BIGNUM
*b
)
504 if (a
== b
) return(a
);
505 if (bn_wexpand(a
,b
->top
) == NULL
) return(NULL
);
510 for (i
=b
->top
>>2; i
>0; i
--,A
+=4,B
+=4)
512 BN_ULONG a0
,a1
,a2
,a3
;
513 a0
=B
[0]; a1
=B
[1]; a2
=B
[2]; a3
=B
[3];
514 A
[0]=a0
; A
[1]=a1
; A
[2]=a2
; A
[3]=a3
;
521 case 0: ; /* ultrix cc workaround, see comments in bn_expand_internal */
524 memcpy(a
->d
,b
->d
,sizeof(b
->d
[0])*b
->top
);
527 /* memset(&(a->d[b->top]),0,sizeof(a->d[0])*(a->max-b->top));*/
529 if ((a
->top
== 0) && (a
->d
!= NULL
))
536 BIGNUM
*BN_ncopy(BIGNUM
*a
, const BIGNUM
*b
, size_t n
)
547 min
= (b
->top
< (int)n
)? b
->top
: (int)n
;
555 if (bn_wexpand(a
, min
) == NULL
)
560 for (i
=min
>>2; i
>0; i
--, A
+=4, B
+=4)
562 BN_ULONG a0
,a1
,a2
,a3
;
563 a0
=B
[0]; a1
=B
[1]; a2
=B
[2]; a3
=B
[3];
564 A
[0]=a0
; A
[1]=a1
; A
[2]=a2
; A
[3]=a3
;
582 void BN_swap(BIGNUM
*a
, BIGNUM
*b
)
584 int flags_old_a
, flags_old_b
;
586 int tmp_top
, tmp_dmax
, tmp_neg
;
591 flags_old_a
= a
->flags
;
592 flags_old_b
= b
->flags
;
609 a
->flags
= (flags_old_a
& BN_FLG_MALLOCED
) | (flags_old_b
& BN_FLG_STATIC_DATA
);
610 b
->flags
= (flags_old_b
& BN_FLG_MALLOCED
) | (flags_old_a
& BN_FLG_STATIC_DATA
);
616 void BN_clear(BIGNUM
*a
)
620 memset(a
->d
,0,a
->dmax
*sizeof(a
->d
[0]));
625 BN_ULONG
BN_get_word(const BIGNUM
*a
)
631 if (n
> (int)sizeof(BN_ULONG
))
633 for (i
=a
->top
-1; i
>=0; i
--)
635 #ifndef SIXTY_FOUR_BIT /* the data item > unsigned long */
636 ret
<<=BN_BITS4
; /* stops the compiler complaining */
646 int BN_set_word(BIGNUM
*a
, BN_ULONG w
)
650 if (bn_expand(a
,(int)sizeof(BN_ULONG
)*8) == NULL
) return(0);
652 n
=sizeof(BN_ULONG
)/BN_BYTES
;
655 a
->d
[0]=(BN_ULONG
)w
&BN_MASK2
;
656 if (a
->d
[0] != 0) a
->top
=1;
659 /* the following is done instead of
660 * w>>=BN_BITS2 so compilers don't complain
661 * on builds where sizeof(long) == BN_TYPES */
662 #ifndef SIXTY_FOUR_BIT /* the data item > unsigned long */
668 a
->d
[i
]=(BN_ULONG
)w
&BN_MASK2
;
669 if (a
->d
[i
] != 0) a
->top
=i
+1;
675 BIGNUM
*BN_bin2bn(const unsigned char *s
, int len
, BIGNUM
*ret
)
681 if (ret
== NULL
) ret
=BN_new();
682 if (ret
== NULL
) return(NULL
);
691 if (bn_expand(ret
,(int)(n
+2)*8) == NULL
)
693 i
=((n
-1)/BN_BYTES
)+1;
694 m
=((n
-1)%(BN_BYTES
));
707 /* need to call this due to clear byte at top if avoiding
708 * having the top bit set (-ve number) */
713 /* ignore negative */
714 int BN_bn2bin(const BIGNUM
*a
, unsigned char *to
)
724 *(to
++)=(unsigned char)(l
>>(8*(i
%BN_BYTES
)))&0xff;
729 int BN_ucmp(const BIGNUM
*a
, const BIGNUM
*b
)
732 BN_ULONG t1
,t2
,*ap
,*bp
;
738 if (i
!= 0) return(i
);
741 for (i
=a
->top
-1; i
>=0; i
--)
746 return(t1
> t2
?1:-1);
751 int BN_cmp(const BIGNUM
*a
, const BIGNUM
*b
)
757 if ((a
== NULL
) || (b
== NULL
))
770 if (a
->neg
!= b
->neg
)
778 else { gt
= -1; lt
=1; }
780 if (a
->top
> b
->top
) return(gt
);
781 if (a
->top
< b
->top
) return(lt
);
782 for (i
=a
->top
-1; i
>=0; i
--)
786 if (t1
> t2
) return(gt
);
787 if (t1
< t2
) return(lt
);
792 int BN_set_bit(BIGNUM
*a
, int n
)
803 if (bn_wexpand(a
,i
+1) == NULL
) return(0);
804 for(k
=a
->top
; k
<i
+1; k
++)
809 a
->d
[i
]|=(((BN_ULONG
)1)<<j
);
814 int BN_clear_bit(BIGNUM
*a
, int n
)
823 if (a
->top
<= i
) return(0);
825 a
->d
[i
]&=(~(((BN_ULONG
)1)<<j
));
830 int BN_is_bit_set(const BIGNUM
*a
, int n
)
834 if (n
< 0) return(0);
837 if (a
->top
<= i
) return(0);
838 return((a
->d
[i
]&(((BN_ULONG
)1)<<j
))?1:0);
841 int BN_mask_bits(BIGNUM
*a
, int n
)
850 if (w
>= a
->top
) return(0);
856 a
->d
[w
]&= ~(BN_MASK2
<<b
);
862 int bn_cmp_words(const BN_ULONG
*a
, const BN_ULONG
*b
, int n
)
869 if (aa
!= bb
) return((aa
> bb
)?1:-1);
870 for (i
=n
-2; i
>=0; i
--)
874 if (aa
!= bb
) return((aa
> bb
)?1:-1);
879 /* Here follows a specialised variants of bn_cmp_words(). It has the
880 property of performing the operation on arrays of different sizes.
881 The sizes of those arrays is expressed through cl, which is the
882 common length ( basicall, min(len(a),len(b)) ), and dl, which is the
883 delta between the two lengths, calculated as len(a)-len(b).
884 All lengths are the number of BN_ULONGs... */
886 int bn_cmp_part_words(const BN_ULONG
*a
, const BN_ULONG
*b
,
897 return -1; /* a < b */
905 return 1; /* a > b */
908 return bn_cmp_words(a
,b
,cl
);