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1 office 1 /* crypto/bn/bn.h */
2 /* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
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.
8 *
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).
15 *
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.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
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)"
40 *
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
51 * SUCH DAMAGE.
52 *
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.]
57 */
58  
59 #ifndef HEADER_BN_H
60 #define HEADER_BN_H
61  
62 #include <stdio.h> /* FILE */
63 #include "config.h"
64  
65 #ifdef __cplusplus
66 extern "C" {
67 #endif
68  
69 #ifdef VMS
70 #undef BN_LLONG /* experimental, so far... */
71 #endif
72  
73 #undef BN_MUL_COMBA
74 #undef BN_SQR_COMBA
75 #undef BN_RECURSION
76 #undef RECP_MUL_MOD
77 #undef MONT_MUL_MOD
78  
79 #if defined(SIZEOF_LONG_LONG) && SIZEOF_LONG_LONG == 8
80 # if SIZEOF_LONG == 4
81 # define THIRTY_TWO_BIT
82 # else
83 # define SIXTY_FOUR_BIT_LONG
84 # endif
85 #else
86 # if SIZEOF_LONG == 4
87 # define THIRTY_TWO_BIT
88 # endif
89 #endif
90  
91 #undef BN_LLONG
92  
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
99 #define BN_LONG long
100 #define BN_BITS 128
101 #define BN_BYTES 8
102 #define BN_BITS2 64
103 #define BN_BITS4 32
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
114 #endif
115  
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.
120 */
121 #ifdef SIXTY_FOUR_BIT
122 #undef BN_LLONG
123 #undef BN_ULLONG
124 #define BN_ULONG unsigned long long
125 #define BN_LONG long long
126 #define BN_BITS 128
127 #define BN_BYTES 8
128 #define BN_BITS2 64
129 #define BN_BITS4 32
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
139 #endif
140  
141 #ifdef THIRTY_TWO_BIT
142 #if defined(WIN32) && !defined(__GNUC__)
143 #define BN_ULLONG unsigned _int64
144 #else
145 #define BN_ULLONG unsigned long long
146 #endif
147 #define BN_ULONG unsigned long
148 #define BN_LONG long
149 #define BN_BITS 64
150 #define BN_BYTES 4
151 #define BN_BITS2 32
152 #define BN_BITS4 16
153 #ifdef WIN32
154 /* VC++ doesn't like the LL suffix */
155 #define BN_MASK (0xffffffffffffffffL)
156 #else
157 #define BN_MASK (0xffffffffffffffffLL)
158 #endif
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"
167 #define BN_DEC_NUM 9
168 #endif
169  
170 #ifdef SIXTEEN_BIT
171 #ifndef BN_DIV2W
172 #define BN_DIV2W
173 #endif
174 #define BN_ULLONG unsigned long
175 #define BN_ULONG unsigned short
176 #define BN_LONG short
177 #define BN_BITS 32
178 #define BN_BYTES 2
179 #define BN_BITS2 16
180 #define BN_BITS4 8
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"
190 #define BN_DEC_NUM 5
191 #endif
192  
193 #ifdef EIGHT_BIT
194 #ifndef BN_DIV2W
195 #define BN_DIV2W
196 #endif
197 #define BN_ULLONG unsigned short
198 #define BN_ULONG unsigned char
199 #define BN_LONG char
200 #define BN_BITS 16
201 #define BN_BYTES 1
202 #define BN_BITS2 8
203 #define BN_BITS4 4
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"
213 #define BN_DEC_NUM 2
214 #endif
215  
216 #define BN_DEFAULT_BITS 1280
217  
218 #ifdef BIGNUM
219 #undef BIGNUM
220 #endif
221  
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))
227  
228 typedef struct bignum_st
229 {
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 */
235 int flags;
236 } BIGNUM;
237  
238 /* Used for temp variables */
239 #define BN_CTX_NUM 12
240 #define BN_CTX_NUM_POS 12
241 typedef struct bignum_ctx
242 {
243 int tos;
244 BIGNUM bn[BN_CTX_NUM];
245 int flags;
246 int depth;
247 int pos[BN_CTX_NUM_POS];
248 int too_many;
249 } BN_CTX;
250  
251 /* Used for montgomery multiplication */
252 typedef struct bn_mont_ctx_st
253 {
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 */
260 int flags;
261 } BN_MONT_CTX;
262  
263 /* Used for reciprocal division/mod functions
264 * It cannot be shared between threads
265 */
266 typedef struct bn_recp_ctx_st
267 {
268 BIGNUM N; /* the divisor */
269 BIGNUM Nr; /* the reciprocal */
270 int num_bits;
271 int shift;
272 int flags;
273 } BN_RECP_CTX;
274  
275 #define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
276 r,a,&((mont)->RR),(mont),ctx)
277  
278 #define BN_prime_checks 0 /* default: select number of iterations
279 based on the size of the number */
280  
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 : \
287 (b) >= 850 ? 3 : \
288 (b) >= 650 ? 4 : \
289 (b) >= 550 ? 5 : \
290 (b) >= 450 ? 6 : \
291 (b) >= 400 ? 7 : \
292 (b) >= 350 ? 8 : \
293 (b) >= 300 ? 9 : \
294 (b) >= 250 ? 12 : \
295 (b) >= 200 ? 15 : \
296 (b) >= 150 ? 18 : \
297 /* b >= 100 */ 27)
298  
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))
306  
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,
331 BN_CTX *ctx);
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);
375  
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,
379 BN_CTX *ctx);
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);
384  
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 */
387  
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);
398  
399 /* library internal functions */
400  
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);
405  
406 #define bn_fix_top(a) \
407 { \
408 BN_ULONG *ftl; \
409 if ((a)->top > 0) \
410 { \
411 for (ftl= &((a)->d[(a)->top-1]); (a)->top > 0; (a)->top--) \
412 if (*(ftl--)) break; \
413 } \
414 }
415  
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);
422  
423 #ifdef BN_DEBUG
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);
428 #else
429 # define bn_print(a)
430 # define bn_dump(a,b)
431 #endif
432  
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.
436 */
437  
438 /* Error codes for the BN functions. */
439  
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
454  
455 /* Reason codes. */
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
466  
467 #ifdef __cplusplus
468 }
469 #endif
470 #endif
471