2 /* Copyright (C) 1995-1997 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.]
62 #include <stdio.h> /* FILE */
70 #undef BN_LLONG /* experimental, so far... */
79 #if defined(SIZEOF_LONG_LONG) && SIZEOF_LONG_LONG == 8
81 # define THIRTY_TWO_BIT
83 # define SIXTY_FOUR_BIT_LONG
87 # define THIRTY_TWO_BIT
93 /* assuming long is 64bit - this is the DEC Alpha
94 * unsigned long long is only 64 bits :-(, don't define
95 * BN_LLONG for the DEC Alpha */
96 #ifdef SIXTY_FOUR_BIT_LONG
97 #define BN_ULLONG unsigned long long
98 #define BN_ULONG unsigned long
104 #define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
105 #define BN_MASK2 (0xffffffffffffffffL)
106 #define BN_MASK2l (0xffffffffL)
107 #define BN_MASK2h (0xffffffff00000000L)
108 #define BN_MASK2h1 (0xffffffff80000000L)
109 #define BN_TBIT (0x8000000000000000L)
110 #define BN_DEC_CONV (10000000000000000000UL)
111 #define BN_DEC_FMT1 "%lu"
112 #define BN_DEC_FMT2 "%019lu"
113 #define BN_DEC_NUM 19
116 /* This is where the long long data type is 64 bits, but long is 32.
117 * For machines where there are 64bit registers, this is the mode to use.
118 * IRIX, on R4000 and above should use this mode, along with the relevant
119 * assembler code :-). Do NOT define BN_LLONG.
121 #ifdef SIXTY_FOUR_BIT
124 #define BN_ULONG unsigned long long
125 #define BN_LONG long long
130 #define BN_MASK2 (0xffffffffffffffffLL)
131 #define BN_MASK2l (0xffffffffL)
132 #define BN_MASK2h (0xffffffff00000000LL)
133 #define BN_MASK2h1 (0xffffffff80000000LL)
134 #define BN_TBIT (0x8000000000000000LL)
135 #define BN_DEC_CONV (10000000000000000000LL)
136 #define BN_DEC_FMT1 "%llu"
137 #define BN_DEC_FMT2 "%019llu"
138 #define BN_DEC_NUM 19
141 #ifdef THIRTY_TWO_BIT
142 #if defined(WIN32) && !defined(__GNUC__)
143 #define BN_ULLONG unsigned _int64
145 #define BN_ULLONG unsigned long long
147 #define BN_ULONG unsigned long
154 /* VC++ doesn't like the LL suffix */
155 #define BN_MASK (0xffffffffffffffffL)
157 #define BN_MASK (0xffffffffffffffffLL)
159 #define BN_MASK2 (0xffffffffL)
160 #define BN_MASK2l (0xffff)
161 #define BN_MASK2h1 (0xffff8000L)
162 #define BN_MASK2h (0xffff0000L)
163 #define BN_TBIT (0x80000000L)
164 #define BN_DEC_CONV (1000000000L)
165 #define BN_DEC_FMT1 "%lu"
166 #define BN_DEC_FMT2 "%09lu"
174 #define BN_ULLONG unsigned long
175 #define BN_ULONG unsigned short
176 #define BN_LONG short
181 #define BN_MASK (0xffffffff)
182 #define BN_MASK2 (0xffff)
183 #define BN_MASK2l (0xff)
184 #define BN_MASK2h1 (0xff80)
185 #define BN_MASK2h (0xff00)
186 #define BN_TBIT (0x8000)
187 #define BN_DEC_CONV (100000)
188 #define BN_DEC_FMT1 "%u"
189 #define BN_DEC_FMT2 "%05u"
197 #define BN_ULLONG unsigned short
198 #define BN_ULONG unsigned char
204 #define BN_MASK (0xffff)
205 #define BN_MASK2 (0xff)
206 #define BN_MASK2l (0xf)
207 #define BN_MASK2h1 (0xf8)
208 #define BN_MASK2h (0xf0)
209 #define BN_TBIT (0x80)
210 #define BN_DEC_CONV (100)
211 #define BN_DEC_FMT1 "%u"
212 #define BN_DEC_FMT2 "%02u"
216 #define BN_DEFAULT_BITS 1280
222 #define BN_FLG_MALLOCED 0x01
223 #define BN_FLG_STATIC_DATA 0x02
224 #define BN_FLG_FREE 0x8000 /* used for debuging */
225 #define BN_set_flags(b,n) ((b)->flags|=(n))
226 #define BN_get_flags(b,n) ((b)->flags&(n))
228 typedef struct bignum_st
230 BN_ULONG
*d
; /* Pointer to an array of 'BN_BITS2' bit chunks. */
231 int top
; /* Index of last used d +1. */
232 /* The next are internal book keeping for bn_expand. */
233 int dmax
; /* Size of the d array. */
234 int neg
; /* one if the number is negative */
238 /* Used for temp variables */
239 #define BN_CTX_NUM 12
240 #define BN_CTX_NUM_POS 12
241 typedef struct bignum_ctx
244 BIGNUM bn
[BN_CTX_NUM
];
247 int pos
[BN_CTX_NUM_POS
];
251 /* Used for montgomery multiplication */
252 typedef struct bn_mont_ctx_st
254 int ri
; /* number of bits in R */
255 BIGNUM RR
; /* used to convert to montgomery form */
256 BIGNUM N
; /* The modulus */
257 BIGNUM Ni
; /* R*(1/R mod N) - N*Ni = 1
258 * (Ni is only stored for bignum algorithm) */
259 BN_ULONG n0
; /* least significant word of Ni */
263 /* Used for reciprocal division/mod functions
264 * It cannot be shared between threads
266 typedef struct bn_recp_ctx_st
268 BIGNUM N
; /* the divisor */
269 BIGNUM Nr
; /* the reciprocal */
275 #define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
276 r,a,&((mont)->RR),(mont),ctx)
278 #define BN_prime_checks 0 /* default: select number of iterations
279 based on the size of the number */
281 /* number of Miller-Rabin iterations for an error rate of less than 2^-80
282 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
283 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
284 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
285 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
286 #define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
299 #define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
300 #define BN_is_word(a,w) (((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w)))
301 #define BN_is_zero(a) (((a)->top == 0) || BN_is_word(a,0))
302 #define BN_is_one(a) (BN_is_word((a),1))
303 #define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
304 #define BN_one(a) (BN_set_word((a),1))
305 #define BN_zero(a) (BN_set_word((a),0))
307 BIGNUM
*BN_value_one(void);
308 char * BN_options(void);
309 BN_CTX
*BN_CTX_new(void);
310 void BN_CTX_init(BN_CTX
*c
);
311 void BN_CTX_free(BN_CTX
*c
);
312 void BN_CTX_start(BN_CTX
*ctx
);
313 BIGNUM
*BN_CTX_get(BN_CTX
*ctx
);
314 void BN_CTX_end(BN_CTX
*ctx
);
315 int BN_rand(BIGNUM
*rnd
, int bits
, int top
,int bottom
);
316 int BN_pseudo_rand(BIGNUM
*rnd
, int bits
, int top
,int bottom
);
317 int BN_num_bits(const BIGNUM
*a
);
318 int BN_num_bits_word(BN_ULONG
);
319 BIGNUM
*BN_new(void);
320 void BN_init(BIGNUM
*);
321 void BN_clear_free(BIGNUM
*a
);
322 BIGNUM
*BN_copy(BIGNUM
*a
, const BIGNUM
*b
);
323 BIGNUM
*BN_bin2bn(const unsigned char *s
,int len
,BIGNUM
*ret
);
324 int BN_bn2bin(const BIGNUM
*a
, unsigned char *to
);
325 int BN_sub(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
);
326 int BN_usub(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
);
327 int BN_uadd(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
);
328 int BN_add(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
);
329 int BN_mod(BIGNUM
*rem
, const BIGNUM
*m
, const BIGNUM
*d
, BN_CTX
*ctx
);
330 int BN_div(BIGNUM
*dv
, BIGNUM
*rem
, const BIGNUM
*m
, const BIGNUM
*d
,
332 int BN_mul(BIGNUM
*r
, BIGNUM
*a
, BIGNUM
*b
, BN_CTX
*ctx
);
333 int BN_sqr(BIGNUM
*r
, BIGNUM
*a
,BN_CTX
*ctx
);
334 BN_ULONG
BN_mod_word(const BIGNUM
*a
, BN_ULONG w
);
335 BN_ULONG
BN_div_word(BIGNUM
*a
, BN_ULONG w
);
336 int BN_mul_word(BIGNUM
*a
, BN_ULONG w
);
337 int BN_add_word(BIGNUM
*a
, BN_ULONG w
);
338 int BN_sub_word(BIGNUM
*a
, BN_ULONG w
);
339 int BN_set_word(BIGNUM
*a
, BN_ULONG w
);
340 BN_ULONG
BN_get_word(BIGNUM
*a
);
341 int BN_cmp(const BIGNUM
*a
, const BIGNUM
*b
);
342 void BN_free(BIGNUM
*a
);
343 int BN_is_bit_set(const BIGNUM
*a
, int n
);
344 int BN_lshift(BIGNUM
*r
, const BIGNUM
*a
, int n
);
345 int BN_lshift1(BIGNUM
*r
, BIGNUM
*a
);
346 int BN_exp(BIGNUM
*r
, BIGNUM
*a
, BIGNUM
*p
,BN_CTX
*ctx
);
347 int BN_mod_exp(BIGNUM
*r
, BIGNUM
*a
, const BIGNUM
*p
,
348 const BIGNUM
*m
,BN_CTX
*ctx
);
349 int BN_mod_exp_mont(BIGNUM
*r
, BIGNUM
*a
, const BIGNUM
*p
,
350 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*m_ctx
);
351 int BN_mod_exp_mont_word(BIGNUM
*r
, BN_ULONG a
, const BIGNUM
*p
,
352 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*m_ctx
);
353 int BN_mod_exp_simple(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
354 const BIGNUM
*m
,BN_CTX
*ctx
);
355 int BN_mask_bits(BIGNUM
*a
,int n
);
356 int BN_mod_mul(BIGNUM
*ret
, BIGNUM
*a
, BIGNUM
*b
, const BIGNUM
*m
, BN_CTX
*ctx
);
357 int BN_reciprocal(BIGNUM
*r
, BIGNUM
*m
, int len
, BN_CTX
*ctx
);
358 int BN_rshift(BIGNUM
*r
, BIGNUM
*a
, int n
);
359 int BN_rshift1(BIGNUM
*r
, BIGNUM
*a
);
360 void BN_clear(BIGNUM
*a
);
361 BIGNUM
*BN_dup(const BIGNUM
*a
);
362 int BN_ucmp(const BIGNUM
*a
, const BIGNUM
*b
);
363 int BN_set_bit(BIGNUM
*a
, int n
);
364 int BN_clear_bit(BIGNUM
*a
, int n
);
365 int BN_gcd(BIGNUM
*r
,BIGNUM
*in_a
,BIGNUM
*in_b
,BN_CTX
*ctx
);
366 BIGNUM
*BN_mod_inverse(BIGNUM
*ret
,BIGNUM
*a
, const BIGNUM
*n
,BN_CTX
*ctx
);
367 BIGNUM
*BN_generate_prime(BIGNUM
*ret
,int bits
,int safe
,BIGNUM
*add
,
368 BIGNUM
*rem
,void (*callback
)(int,int,void *),void *cb_arg
);
369 int BN_is_prime(const BIGNUM
*p
,int nchecks
,
370 void (*callback
)(int,int,void *),
371 BN_CTX
*ctx
,void *cb_arg
);
372 int BN_is_prime_fasttest(const BIGNUM
*p
,int nchecks
,
373 void (*callback
)(int,int,void *),BN_CTX
*ctx
,void *cb_arg
,
374 int do_trial_division
);
376 BN_MONT_CTX
*BN_MONT_CTX_new(void );
377 void BN_MONT_CTX_init(BN_MONT_CTX
*ctx
);
378 int BN_mod_mul_montgomery(BIGNUM
*r
,BIGNUM
*a
,BIGNUM
*b
,BN_MONT_CTX
*mont
,
380 int BN_from_montgomery(BIGNUM
*r
,BIGNUM
*a
,BN_MONT_CTX
*mont
,BN_CTX
*ctx
);
381 void BN_MONT_CTX_free(BN_MONT_CTX
*mont
);
382 int BN_MONT_CTX_set(BN_MONT_CTX
*mont
,const BIGNUM
*modulus
,BN_CTX
*ctx
);
383 BN_MONT_CTX
*BN_MONT_CTX_copy(BN_MONT_CTX
*to
,BN_MONT_CTX
*from
);
385 void BN_set_params(int mul
,int high
,int low
,int mont
);
386 int BN_get_params(int which
); /* 0, mul, 1 high, 2 low, 3 mont */
388 void BN_RECP_CTX_init(BN_RECP_CTX
*recp
);
389 BN_RECP_CTX
*BN_RECP_CTX_new(void);
390 void BN_RECP_CTX_free(BN_RECP_CTX
*recp
);
391 int BN_RECP_CTX_set(BN_RECP_CTX
*recp
,const BIGNUM
*rdiv
,BN_CTX
*ctx
);
392 int BN_mod_mul_reciprocal(BIGNUM
*r
, BIGNUM
*x
, BIGNUM
*y
,
393 BN_RECP_CTX
*recp
,BN_CTX
*ctx
);
394 int BN_mod_exp_recp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
395 const BIGNUM
*m
, BN_CTX
*ctx
);
396 int BN_div_recp(BIGNUM
*dv
, BIGNUM
*rem
, BIGNUM
*m
,
397 BN_RECP_CTX
*recp
, BN_CTX
*ctx
);
399 /* library internal functions */
401 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
402 (a):bn_expand2((a),(bits)/BN_BITS2+1))
403 #define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
404 BIGNUM
*bn_expand2(BIGNUM
*a
, int words
);
406 #define bn_fix_top(a) \
411 for (ftl= &((a)->d[(a)->top-1]); (a)->top > 0; (a)->top--) \
412 if (*(ftl--)) break; \
416 BN_ULONG
bn_mul_add_words(BN_ULONG
*rp
, BN_ULONG
*ap
, int num
, BN_ULONG w
);
417 BN_ULONG
bn_mul_words(BN_ULONG
*rp
, BN_ULONG
*ap
, int num
, BN_ULONG w
);
418 void bn_sqr_words(BN_ULONG
*rp
, BN_ULONG
*ap
, int num
);
419 BN_ULONG
bn_div_words(BN_ULONG h
, BN_ULONG l
, BN_ULONG d
);
420 BN_ULONG
bn_add_words(BN_ULONG
*rp
, BN_ULONG
*ap
, BN_ULONG
*bp
,int num
);
421 BN_ULONG
bn_sub_words(BN_ULONG
*rp
, BN_ULONG
*ap
, BN_ULONG
*bp
,int num
);
424 void bn_dump1(FILE *o
, const char *a
, BN_ULONG
*b
,int n
);
425 # define bn_print(a) {fprintf(stderr, #a "="); BN_print_fp(stderr,a); \
426 fprintf(stderr,"\n");}
427 # define bn_dump(a,n) bn_dump1(stderr,#a,a,n);
430 # define bn_dump(a,b)
433 /* BEGIN ERROR CODES */
434 /* The following lines are auto generated by the script mkerr.pl. Any changes
435 * made after this point may be overwritten when the script is next run.
438 /* Error codes for the BN functions. */
440 /* Function codes. */
441 #define BN_F_BN_CTX_GET 116
442 #define BN_F_BN_CTX_NEW 106
443 #define BN_F_BN_DIV 107
444 #define BN_F_BN_EXPAND2 108
445 #define BN_F_BN_MOD_EXP2_MONT 118
446 #define BN_F_BN_MOD_EXP_MONT 109
447 #define BN_F_BN_MOD_EXP_MONT_WORD 117
448 #define BN_F_BN_MOD_INVERSE 110
449 #define BN_F_BN_MOD_MUL_RECIPROCAL 111
450 #define BN_F_BN_MPI2BN 112
451 #define BN_F_BN_NEW 113
452 #define BN_F_BN_RAND 114
453 #define BN_F_BN_USUB 115
456 #define BN_R_ARG2_LT_ARG3 100
457 #define BN_R_BAD_RECIPROCAL 101
458 #define BN_R_CALLED_WITH_EVEN_MODULUS 102
459 #define BN_R_DIV_BY_ZERO 103
460 #define BN_R_ENCODING_ERROR 104
461 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
462 #define BN_R_INVALID_LENGTH 106
463 #define BN_R_NOT_INITIALIZED 107
464 #define BN_R_NO_INVERSE 108
465 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109
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