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.]
63 #include <stdio.h> /* FILE */
65 #include <openssl/opensslconf.h>
72 #undef BN_LLONG /* experimental, so far... */
79 /* This next option uses the C libraries (2 word)/(1 word) function.
80 * If it is not defined, I use my C version (which is slower).
81 * The reason for this flag is that when the particular C compiler
82 * library routine is used, and the library is linked with a different
83 * compiler, the library is missing. This mostly happens when the
84 * library is built with gcc and then linked using normal cc. This would
85 * be a common occurrence because gcc normally produces code that is
86 * 2 times faster than system compilers for the big number stuff.
87 * For machines with only one compiler (or shared libraries), this should
88 * be on. Again this in only really a problem on machines
89 * using "long long's", are 32bit, and are not using my assembler code. */
90 #if defined(MSDOS) || defined(WINDOWS) || defined(WIN32) || defined(linux)
95 /* assuming long is 64bit - this is the DEC Alpha
96 * unsigned long long is only 64 bits :-(, don't define
97 * BN_LLONG for the DEC Alpha */
98 #ifdef SIXTY_FOUR_BIT_LONG
99 #define BN_ULLONG unsigned long long
100 #define BN_ULONG unsigned long
106 #define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
107 #define BN_MASK2 (0xffffffffffffffffL)
108 #define BN_MASK2l (0xffffffffL)
109 #define BN_MASK2h (0xffffffff00000000L)
110 #define BN_MASK2h1 (0xffffffff80000000L)
111 #define BN_TBIT (0x8000000000000000L)
112 #define BN_DEC_CONV (10000000000000000000UL)
113 #define BN_DEC_FMT1 "%lu"
114 #define BN_DEC_FMT2 "%019lu"
115 #define BN_DEC_NUM 19
118 /* This is where the long long data type is 64 bits, but long is 32.
119 * For machines where there are 64bit registers, this is the mode to use.
120 * IRIX, on R4000 and above should use this mode, along with the relevant
121 * assembler code :-). Do NOT define BN_LLONG.
123 #ifdef SIXTY_FOUR_BIT
126 #define BN_ULONG unsigned long long
127 #define BN_LONG long long
132 #define BN_MASK2 (0xffffffffffffffffLL)
133 #define BN_MASK2l (0xffffffffL)
134 #define BN_MASK2h (0xffffffff00000000LL)
135 #define BN_MASK2h1 (0xffffffff80000000LL)
136 #define BN_TBIT (0x8000000000000000LL)
137 #define BN_DEC_CONV (10000000000000000000LL)
138 #define BN_DEC_FMT1 "%llu"
139 #define BN_DEC_FMT2 "%019llu"
140 #define BN_DEC_NUM 19
143 #ifdef THIRTY_TWO_BIT
144 #if defined(WIN32) && !defined(__GNUC__)
145 #define BN_ULLONG unsigned _int64
147 #define BN_ULLONG unsigned long long
149 #define BN_ULONG unsigned long
156 /* VC++ doesn't like the LL suffix */
157 #define BN_MASK (0xffffffffffffffffL)
159 #define BN_MASK (0xffffffffffffffffLL)
161 #define BN_MASK2 (0xffffffffL)
162 #define BN_MASK2l (0xffff)
163 #define BN_MASK2h1 (0xffff8000L)
164 #define BN_MASK2h (0xffff0000L)
165 #define BN_TBIT (0x80000000L)
166 #define BN_DEC_CONV (1000000000L)
167 #define BN_DEC_FMT1 "%lu"
168 #define BN_DEC_FMT2 "%09lu"
176 #define BN_ULLONG unsigned long
177 #define BN_ULONG unsigned short
178 #define BN_LONG short
183 #define BN_MASK (0xffffffff)
184 #define BN_MASK2 (0xffff)
185 #define BN_MASK2l (0xff)
186 #define BN_MASK2h1 (0xff80)
187 #define BN_MASK2h (0xff00)
188 #define BN_TBIT (0x8000)
189 #define BN_DEC_CONV (100000)
190 #define BN_DEC_FMT1 "%u"
191 #define BN_DEC_FMT2 "%05u"
199 #define BN_ULLONG unsigned short
200 #define BN_ULONG unsigned char
206 #define BN_MASK (0xffff)
207 #define BN_MASK2 (0xff)
208 #define BN_MASK2l (0xf)
209 #define BN_MASK2h1 (0xf8)
210 #define BN_MASK2h (0xf0)
211 #define BN_TBIT (0x80)
212 #define BN_DEC_CONV (100)
213 #define BN_DEC_FMT1 "%u"
214 #define BN_DEC_FMT2 "%02u"
218 #define BN_DEFAULT_BITS 1280
224 #define BN_FLG_MALLOCED 0x01
225 #define BN_FLG_STATIC_DATA 0x02
226 #define BN_FLG_FREE 0x8000 /* used for debuging */
227 #define BN_set_flags(b,n) ((b)->flags|=(n))
228 #define BN_get_flags(b,n) ((b)->flags&(n))
230 typedef struct bignum_st
232 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */
233 int top; /* Index of last used d +1. */
234 /* The next are internal book keeping for bn_expand. */
235 int dmax; /* Size of the d array. */
236 int neg; /* one if the number is negative */
240 /* Used for temp variables */
241 #define BN_CTX_NUM 16
242 #define BN_CTX_NUM_POS 12
243 typedef struct bignum_ctx
246 BIGNUM bn[BN_CTX_NUM];
249 int pos[BN_CTX_NUM_POS];
253 typedef struct bn_blinding_st
258 BIGNUM *mod; /* just a reference */
261 /* Used for montgomery multiplication */
262 typedef struct bn_mont_ctx_st
264 int ri; /* number of bits in R */
265 BIGNUM RR; /* used to convert to montgomery form */
266 BIGNUM N; /* The modulus */
267 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
268 * (Ni is only stored for bignum algorithm) */
269 BN_ULONG n0; /* least significant word of Ni */
273 /* Used for reciprocal division/mod functions
274 * It cannot be shared between threads
276 typedef struct bn_recp_ctx_st
278 BIGNUM N; /* the divisor */
279 BIGNUM Nr; /* the reciprocal */
285 #define BN_prime_checks 0 /* default: select number of iterations
286 based on the size of the number */
288 /* number of Miller-Rabin iterations for an error rate of less than 2^-80
289 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
290 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
291 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
292 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
293 #define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
306 #define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
307 #define BN_is_word(a,w) (((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w)))
308 #define BN_is_zero(a) (((a)->top == 0) || BN_is_word(a,0))
309 #define BN_is_one(a) (BN_is_word((a),1))
310 #define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
311 #define BN_one(a) (BN_set_word((a),1))
312 #define BN_zero(a) (BN_set_word((a),0))
314 /*#define BN_ascii2bn(a) BN_hex2bn(a) */
315 /*#define BN_bn2ascii(a) BN_bn2hex(a) */
317 BIGNUM *BN_value_one(void);
318 char * BN_options(void);
319 BN_CTX *BN_CTX_new(void);
320 void BN_CTX_init(BN_CTX *c);
321 void BN_CTX_free(BN_CTX *c);
322 void BN_CTX_start(BN_CTX *ctx);
323 BIGNUM *BN_CTX_get(BN_CTX *ctx);
324 void BN_CTX_end(BN_CTX *ctx);
325 int BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
326 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top,int bottom);
327 int BN_num_bits(const BIGNUM *a);
328 int BN_num_bits_word(BN_ULONG);
329 BIGNUM *BN_new(void);
330 void BN_init(BIGNUM *);
331 void BN_clear_free(BIGNUM *a);
332 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
333 void BN_swap(BIGNUM *a, BIGNUM *b);
334 BIGNUM *BN_bin2bn(const unsigned char *s,int len,BIGNUM *ret);
335 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
336 BIGNUM *BN_mpi2bn(const unsigned char *s,int len,BIGNUM *ret);
337 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
338 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
339 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
340 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
341 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
342 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
343 int BN_sqr(BIGNUM *r, const BIGNUM *a,BN_CTX *ctx);
345 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
347 #define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
348 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
349 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
350 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
351 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
352 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
353 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
354 const BIGNUM *m, BN_CTX *ctx);
355 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
356 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
357 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx);
358 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
360 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
361 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
362 int BN_mul_word(BIGNUM *a, BN_ULONG w);
363 int BN_add_word(BIGNUM *a, BN_ULONG w);
364 int BN_sub_word(BIGNUM *a, BN_ULONG w);
365 int BN_set_word(BIGNUM *a, BN_ULONG w);
366 BN_ULONG BN_get_word(const BIGNUM *a);
368 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
369 void BN_free(BIGNUM *a);
370 int BN_is_bit_set(const BIGNUM *a, int n);
371 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
372 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
373 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,BN_CTX *ctx);
375 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
376 const BIGNUM *m,BN_CTX *ctx);
377 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
378 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
379 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
380 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
381 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
382 const BIGNUM *a2, const BIGNUM *p2,const BIGNUM *m,
383 BN_CTX *ctx,BN_MONT_CTX *m_ctx);
384 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
385 const BIGNUM *m,BN_CTX *ctx);
387 int BN_mask_bits(BIGNUM *a,int n);
389 int BN_print_fp(FILE *fp, const BIGNUM *a);
392 int BN_print(BIO *fp, const BIGNUM *a);
394 int BN_print(void *fp, const BIGNUM *a);
396 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
397 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
398 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
399 void BN_clear(BIGNUM *a);
400 BIGNUM *BN_dup(const BIGNUM *a);
401 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
402 int BN_set_bit(BIGNUM *a, int n);
403 int BN_clear_bit(BIGNUM *a, int n);
404 char * BN_bn2hex(const BIGNUM *a);
405 char * BN_bn2dec(const BIGNUM *a);
406 int BN_hex2bn(BIGNUM **a, const char *str);
407 int BN_dec2bn(BIGNUM **a, const char *str);
408 int BN_gcd(BIGNUM *r,const BIGNUM *in_a,const BIGNUM *in_b,BN_CTX *ctx);
409 BIGNUM *BN_mod_inverse(BIGNUM *ret,
410 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
411 BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,
412 const BIGNUM *add, const BIGNUM *rem,
413 void (*callback)(int,int,void *),void *cb_arg);
414 int BN_is_prime(const BIGNUM *p,int nchecks,
415 void (*callback)(int,int,void *),
416 BN_CTX *ctx,void *cb_arg);
417 int BN_is_prime_fasttest(const BIGNUM *p,int nchecks,
418 void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg,
419 int do_trial_division);
420 void ERR_load_BN_strings(void );
422 BN_MONT_CTX *BN_MONT_CTX_new(void );
423 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
424 int BN_mod_mul_montgomery(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,
425 BN_MONT_CTX *mont, BN_CTX *ctx);
426 #define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
427 (r),(a),&((mont)->RR),(mont),(ctx))
428 int BN_from_montgomery(BIGNUM *r,const BIGNUM *a,
429 BN_MONT_CTX *mont, BN_CTX *ctx);
430 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
431 int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *modulus,BN_CTX *ctx);
432 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,BN_MONT_CTX *from);
434 BN_BLINDING *BN_BLINDING_new(BIGNUM *A,BIGNUM *Ai,BIGNUM *mod);
435 void BN_BLINDING_free(BN_BLINDING *b);
436 int BN_BLINDING_update(BN_BLINDING *b,BN_CTX *ctx);
437 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *r, BN_CTX *ctx);
438 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
440 void BN_set_params(int mul,int high,int low,int mont);
441 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
443 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
444 BN_RECP_CTX *BN_RECP_CTX_new(void);
445 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
446 int BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx);
447 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
448 BN_RECP_CTX *recp,BN_CTX *ctx);
449 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
450 const BIGNUM *m, BN_CTX *ctx);
451 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
452 BN_RECP_CTX *recp, BN_CTX *ctx);
454 /* library internal functions */
456 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
457 (a):bn_expand2((a),(bits)/BN_BITS2+1))
458 #define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
459 BIGNUM *bn_expand2(BIGNUM *a, int words);
460 BIGNUM *bn_dup_expand(const BIGNUM *a, int words);
462 #define bn_fix_top(a) \
467 for (ftl= &((a)->d[(a)->top-1]); (a)->top > 0; (a)->top--) \
468 if (*(ftl--)) break; \
472 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
473 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
474 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
475 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
476 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
477 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
480 void bn_dump1(FILE *o, const char *a, const BN_ULONG *b,int n);
481 # define bn_print(a) {fprintf(stderr, #a "="); BN_print_fp(stderr,a); \
482 fprintf(stderr,"\n");}
483 # define bn_dump(a,n) bn_dump1(stderr,#a,a,n);
486 # define bn_dump(a,b)
489 /* BEGIN ERROR CODES */
490 /* The following lines are auto generated by the script mkerr.pl. Any changes
491 * made after this point may be overwritten when the script is next run.
494 /* Error codes for the BN functions. */
496 /* Function codes. */
497 #define BN_F_BN_BLINDING_CONVERT 100
498 #define BN_F_BN_BLINDING_INVERT 101
499 #define BN_F_BN_BLINDING_NEW 102
500 #define BN_F_BN_BLINDING_UPDATE 103
501 #define BN_F_BN_BN2DEC 104
502 #define BN_F_BN_BN2HEX 105
503 #define BN_F_BN_CTX_GET 116
504 #define BN_F_BN_CTX_NEW 106
505 #define BN_F_BN_DIV 107
506 #define BN_F_BN_EXPAND2 108
507 #define BN_F_BN_MOD_EXP2_MONT 118
508 #define BN_F_BN_MOD_EXP_MONT 109
509 #define BN_F_BN_MOD_EXP_MONT_WORD 117
510 #define BN_F_BN_MOD_INVERSE 110
511 #define BN_F_BN_MOD_LSHIFT_QUICK 119
512 #define BN_F_BN_MOD_MUL_RECIPROCAL 111
513 #define BN_F_BN_MPI2BN 112
514 #define BN_F_BN_NEW 113
515 #define BN_F_BN_RAND 114
516 #define BN_F_BN_USUB 115
519 #define BN_R_ARG2_LT_ARG3 100
520 #define BN_R_BAD_RECIPROCAL 101
521 #define BN_R_CALLED_WITH_EVEN_MODULUS 102
522 #define BN_R_DIV_BY_ZERO 103
523 #define BN_R_ENCODING_ERROR 104
524 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
525 #define BN_R_INPUT_NOT_REDUCED 110
526 #define BN_R_INVALID_LENGTH 106
527 #define BN_R_NOT_INITIALIZED 107
528 #define BN_R_NO_INVERSE 108
529 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109