1/* crypto/bn/bn.h */
2/* Copyright (C) 1995-1997 Eric Young ([email protected])
3 * All rights reserved.
4 *
5 * This package is an SSL implementation written
6 * by Eric Young ([email protected]).
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 ([email protected]).
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 ([email protected])"
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 ([email protected])"
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 * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved.
60 *
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
63 * are met:
64 *
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
67 *
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
71 * distribution.
72 *
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
77 *
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * [email protected].
82 *
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
86 *
87 * 6. Redistributions of any form whatsoever must retain the following
88 * acknowledgment:
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91 *
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
105 *
106 * This product includes cryptographic software written by Eric Young
107 * ([email protected]). This product includes software written by Tim
108 * Hudson ([email protected]).
109 *
110 */
111/* ====================================================================
112 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
113 *
114 * Portions of the attached software ("Contribution") are developed by
115 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
116 *
117 * The Contribution is licensed pursuant to the Eric Young open source
118 * license provided above.
119 *
120 * The binary polynomial arithmetic software is originally written by
121 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
122 *
123 */
124
125#ifndef HEADER_BN_H
126# define HEADER_BN_H
127
128# include <limits.h>
129# include <openssl/e_os2.h>
130# ifndef OPENSSL_NO_FP_API
131# include <stdio.h> /* FILE */
132# endif
133# include <openssl/ossl_typ.h>
134# include <openssl/crypto.h>
135
136#ifdef __cplusplus
137extern "C" {
138#endif
139
140/*
141 * These preprocessor symbols control various aspects of the bignum headers
142 * and library code. They're not defined by any "normal" configuration, as
143 * they are intended for development and testing purposes. NB: defining all
144 * three can be useful for debugging application code as well as openssl
145 * itself. BN_DEBUG - turn on various debugging alterations to the bignum
146 * code BN_DEBUG_RAND - uses random poisoning of unused words to trip up
147 * mismanagement of bignum internals. You must also define BN_DEBUG.
148 */
149/* #define BN_DEBUG */
150/* #define BN_DEBUG_RAND */
151
152# ifndef OPENSSL_SMALL_FOOTPRINT
153# define BN_MUL_COMBA
154# define BN_SQR_COMBA
155# define BN_RECURSION
156# endif
157
158/*
159 * This next option uses the C libraries (2 word)/(1 word) function. If it is
160 * not defined, I use my C version (which is slower). The reason for this
161 * flag is that when the particular C compiler library routine is used, and
162 * the library is linked with a different compiler, the library is missing.
163 * This mostly happens when the library is built with gcc and then linked
164 * using normal cc. This would be a common occurrence because gcc normally
165 * produces code that is 2 times faster than system compilers for the big
166 * number stuff. For machines with only one compiler (or shared libraries),
167 * this should be on. Again this in only really a problem on machines using
168 * "long long's", are 32bit, and are not using my assembler code.
169 */
170# if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
171 defined(OPENSSL_SYS_WIN32) || defined(linux)
172# ifndef BN_DIV2W
173# define BN_DIV2W
174# endif
175# endif
176
177/*
178 * assuming long is 64bit - this is the DEC Alpha unsigned long long is only
179 * 64 bits :-(, don't define BN_LLONG for the DEC Alpha
180 */
181# ifdef SIXTY_FOUR_BIT_LONG
182# define BN_ULLONG unsigned long long
183# define BN_ULONG unsigned long
184# define BN_LONG long
185# define BN_BITS 128
186# define BN_BYTES 8
187# define BN_BITS2 64
188# define BN_BITS4 32
189# define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
190# define BN_MASK2 (0xffffffffffffffffL)
191# define BN_MASK2l (0xffffffffL)
192# define BN_MASK2h (0xffffffff00000000L)
193# define BN_MASK2h1 (0xffffffff80000000L)
194# define BN_TBIT (0x8000000000000000L)
195# define BN_DEC_CONV (10000000000000000000UL)
196# define BN_DEC_FMT1 "%lu"
197# define BN_DEC_FMT2 "%019lu"
198# define BN_DEC_NUM 19
199# define BN_HEX_FMT1 "%lX"
200# define BN_HEX_FMT2 "%016lX"
201# endif
202
203/*
204 * This is where the long long data type is 64 bits, but long is 32. For
205 * machines where there are 64bit registers, this is the mode to use. IRIX,
206 * on R4000 and above should use this mode, along with the relevant assembler
207 * code :-). Do NOT define BN_LLONG.
208 */
209# ifdef SIXTY_FOUR_BIT
210# undef BN_LLONG
211# undef BN_ULLONG
212# define BN_ULONG unsigned long long
213# define BN_LONG long long
214# define BN_BITS 128
215# define BN_BYTES 8
216# define BN_BITS2 64
217# define BN_BITS4 32
218# define BN_MASK2 (0xffffffffffffffffLL)
219# define BN_MASK2l (0xffffffffL)
220# define BN_MASK2h (0xffffffff00000000LL)
221# define BN_MASK2h1 (0xffffffff80000000LL)
222# define BN_TBIT (0x8000000000000000LL)
223# define BN_DEC_CONV (10000000000000000000ULL)
224# define BN_DEC_FMT1 "%llu"
225# define BN_DEC_FMT2 "%019llu"
226# define BN_DEC_NUM 19
227# define BN_HEX_FMT1 "%llX"
228# define BN_HEX_FMT2 "%016llX"
229# endif
230
231# ifdef THIRTY_TWO_BIT
232# ifdef BN_LLONG
233# if defined(_WIN32) && !defined(__GNUC__)
234# define BN_ULLONG unsigned __int64
235# define BN_MASK (0xffffffffffffffffI64)
236# else
237# define BN_ULLONG unsigned long long
238# define BN_MASK (0xffffffffffffffffLL)
239# endif
240# endif
241# define BN_ULONG unsigned int
242# define BN_LONG int
243# define BN_BITS 64
244# define BN_BYTES 4
245# define BN_BITS2 32
246# define BN_BITS4 16
247# define BN_MASK2 (0xffffffffL)
248# define BN_MASK2l (0xffff)
249# define BN_MASK2h1 (0xffff8000L)
250# define BN_MASK2h (0xffff0000L)
251# define BN_TBIT (0x80000000L)
252# define BN_DEC_CONV (1000000000L)
253# define BN_DEC_FMT1 "%u"
254# define BN_DEC_FMT2 "%09u"
255# define BN_DEC_NUM 9
256# define BN_HEX_FMT1 "%X"
257# define BN_HEX_FMT2 "%08X"
258# endif
259
260# define BN_DEFAULT_BITS 1280
261
262# define BN_FLG_MALLOCED 0x01
263# define BN_FLG_STATIC_DATA 0x02
264
265/*
266 * avoid leaking exponent information through timing,
267 * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime,
268 * BN_div() will call BN_div_no_branch,
269 * BN_mod_inverse() will call BN_mod_inverse_no_branch.
270 */
271# define BN_FLG_CONSTTIME 0x04
272
273# ifdef OPENSSL_NO_DEPRECATED
274/* deprecated name for the flag */
275# define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME
276/*
277 * avoid leaking exponent information through timings
278 * (BN_mod_exp_mont() will call BN_mod_exp_mont_consttime)
279 */
280# endif
281
282# ifndef OPENSSL_NO_DEPRECATED
283# define BN_FLG_FREE 0x8000
284 /* used for debuging */
285# endif
286# define BN_set_flags(b,n) ((b)->flags|=(n))
287# define BN_get_flags(b,n) ((b)->flags&(n))
288
289/*
290 * get a clone of a BIGNUM with changed flags, for *temporary* use only (the
291 * two BIGNUMs cannot not be used in parallel!)
292 */
293# define BN_with_flags(dest,b,n) ((dest)->d=(b)->d, \
294 (dest)->top=(b)->top, \
295 (dest)->dmax=(b)->dmax, \
296 (dest)->neg=(b)->neg, \
297 (dest)->flags=(((dest)->flags & BN_FLG_MALLOCED) \
298 | ((b)->flags & ~BN_FLG_MALLOCED) \
299 | BN_FLG_STATIC_DATA \
300 | (n)))
301
302/* Already declared in ossl_typ.h */
303# if 0
304typedef struct bignum_st BIGNUM;
305/* Used for temp variables (declaration hidden in bn_lcl.h) */
306typedef struct bignum_ctx BN_CTX;
307typedef struct bn_blinding_st BN_BLINDING;
308typedef struct bn_mont_ctx_st BN_MONT_CTX;
309typedef struct bn_recp_ctx_st BN_RECP_CTX;
310typedef struct bn_gencb_st BN_GENCB;
311# endif
312
313struct bignum_st {
314 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit
315 * chunks. */
316 int top; /* Index of last used d +1. */
317 /* The next are internal book keeping for bn_expand. */
318 int dmax; /* Size of the d array. */
319 int neg; /* one if the number is negative */
320 int flags;
321};
322
323/* Used for montgomery multiplication */
324struct bn_mont_ctx_st {
325 int ri; /* number of bits in R */
326 BIGNUM RR; /* used to convert to montgomery form */
327 BIGNUM N; /* The modulus */
328 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 (Ni is only
329 * stored for bignum algorithm) */
330 BN_ULONG n0[2]; /* least significant word(s) of Ni; (type
331 * changed with 0.9.9, was "BN_ULONG n0;"
332 * before) */
333 int flags;
334};
335
336/*
337 * Used for reciprocal division/mod functions It cannot be shared between
338 * threads
339 */
340struct bn_recp_ctx_st {
341 BIGNUM N; /* the divisor */
342 BIGNUM Nr; /* the reciprocal */
343 int num_bits;
344 int shift;
345 int flags;
346};
347
348/* Used for slow "generation" functions. */
349struct bn_gencb_st {
350 unsigned int ver; /* To handle binary (in)compatibility */
351 void *arg; /* callback-specific data */
352 union {
353 /* if(ver==1) - handles old style callbacks */
354 void (*cb_1) (int, int, void *);
355 /* if(ver==2) - new callback style */
356 int (*cb_2) (int, int, BN_GENCB *);
357 } cb;
358};
359/* Wrapper function to make using BN_GENCB easier, */
360int BN_GENCB_call(BN_GENCB *cb, int a, int b);
361/* Macro to populate a BN_GENCB structure with an "old"-style callback */
362# define BN_GENCB_set_old(gencb, callback, cb_arg) { \
363 BN_GENCB *tmp_gencb = (gencb); \
364 tmp_gencb->ver = 1; \
365 tmp_gencb->arg = (cb_arg); \
366 tmp_gencb->cb.cb_1 = (callback); }
367/* Macro to populate a BN_GENCB structure with a "new"-style callback */
368# define BN_GENCB_set(gencb, callback, cb_arg) { \
369 BN_GENCB *tmp_gencb = (gencb); \
370 tmp_gencb->ver = 2; \
371 tmp_gencb->arg = (cb_arg); \
372 tmp_gencb->cb.cb_2 = (callback); }
373
374# define BN_prime_checks 0 /* default: select number of iterations based
375 * on the size of the number */
376
377/*
378 * number of Miller-Rabin iterations for an error rate of less than 2^-80 for
379 * random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook of
380 * Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
381 * original paper: Damgaard, Landrock, Pomerance: Average case error
382 * estimates for the strong probable prime test. -- Math. Comp. 61 (1993)
383 * 177-194)
384 */
385# define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
386 (b) >= 850 ? 3 : \
387 (b) >= 650 ? 4 : \
388 (b) >= 550 ? 5 : \
389 (b) >= 450 ? 6 : \
390 (b) >= 400 ? 7 : \
391 (b) >= 350 ? 8 : \
392 (b) >= 300 ? 9 : \
393 (b) >= 250 ? 12 : \
394 (b) >= 200 ? 15 : \
395 (b) >= 150 ? 18 : \
396 /* b >= 100 */ 27)
397
398# define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
399
400/* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
401# define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
402 (((w) == 0) && ((a)->top == 0)))
403# define BN_is_zero(a) ((a)->top == 0)
404# define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
405# define BN_is_word(a,w) (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
406# define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
407
408# define BN_one(a) (BN_set_word((a),1))
409# define BN_zero_ex(a) \
410 do { \
411 BIGNUM *_tmp_bn = (a); \
412 _tmp_bn->top = 0; \
413 _tmp_bn->neg = 0; \
414 } while(0)
415# ifdef OPENSSL_NO_DEPRECATED
416# define BN_zero(a) BN_zero_ex(a)
417# else
418# define BN_zero(a) (BN_set_word((a),0))
419# endif
420
421const BIGNUM *BN_value_one(void);
422char *BN_options(void);
423BN_CTX *BN_CTX_new(void);
424# ifndef OPENSSL_NO_DEPRECATED
425void BN_CTX_init(BN_CTX *c);
426# endif
427void BN_CTX_free(BN_CTX *c);
428void BN_CTX_start(BN_CTX *ctx);
429BIGNUM *BN_CTX_get(BN_CTX *ctx);
430void BN_CTX_end(BN_CTX *ctx);
431int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
432int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
433int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
434int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
435int BN_num_bits(const BIGNUM *a);
436int BN_num_bits_word(BN_ULONG);
437BIGNUM *BN_new(void);
438void BN_init(BIGNUM *);
439void BN_clear_free(BIGNUM *a);
440BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
441void BN_swap(BIGNUM *a, BIGNUM *b);
442BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
443int BN_bn2bin(const BIGNUM *a, unsigned char *to);
444BIGNUM *BN_mpi2bn(const unsigned char *s, int len, BIGNUM *ret);
445int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
446int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
447int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
448int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
449int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
450int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
451int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
452/** BN_set_negative sets sign of a BIGNUM
453 * \param b pointer to the BIGNUM object
454 * \param n 0 if the BIGNUM b should be positive and a value != 0 otherwise
455 */
456void BN_set_negative(BIGNUM *b, int n);
457/** BN_is_negative returns 1 if the BIGNUM is negative
458 * \param a pointer to the BIGNUM object
459 * \return 1 if a < 0 and 0 otherwise
460 */
461# define BN_is_negative(a) ((a)->neg != 0)
462
463int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
464 BN_CTX *ctx);
465# define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
466int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
467int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
468 BN_CTX *ctx);
469int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
470 const BIGNUM *m);
471int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
472 BN_CTX *ctx);
473int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
474 const BIGNUM *m);
475int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
476 BN_CTX *ctx);
477int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
478int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
479int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
480int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
481 BN_CTX *ctx);
482int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
483
484BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
485BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
486int BN_mul_word(BIGNUM *a, BN_ULONG w);
487int BN_add_word(BIGNUM *a, BN_ULONG w);
488int BN_sub_word(BIGNUM *a, BN_ULONG w);
489int BN_set_word(BIGNUM *a, BN_ULONG w);
490BN_ULONG BN_get_word(const BIGNUM *a);
491
492int BN_cmp(const BIGNUM *a, const BIGNUM *b);
493void BN_free(BIGNUM *a);
494int BN_is_bit_set(const BIGNUM *a, int n);
495int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
496int BN_lshift1(BIGNUM *r, const BIGNUM *a);
497int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
498
499int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
500 const BIGNUM *m, BN_CTX *ctx);
501int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
502 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
503int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
504 const BIGNUM *m, BN_CTX *ctx,
505 BN_MONT_CTX *in_mont);
506int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
507 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
508int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
509 const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
510 BN_CTX *ctx, BN_MONT_CTX *m_ctx);
511int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
512 const BIGNUM *m, BN_CTX *ctx);
513
514int BN_mask_bits(BIGNUM *a, int n);
515# ifndef OPENSSL_NO_FP_API
516int BN_print_fp(FILE *fp, const BIGNUM *a);
517# endif
518# ifdef HEADER_BIO_H
519int BN_print(BIO *fp, const BIGNUM *a);
520# else
521int BN_print(void *fp, const BIGNUM *a);
522# endif
523int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
524int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
525int BN_rshift1(BIGNUM *r, const BIGNUM *a);
526void BN_clear(BIGNUM *a);
527BIGNUM *BN_dup(const BIGNUM *a);
528int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
529int BN_set_bit(BIGNUM *a, int n);
530int BN_clear_bit(BIGNUM *a, int n);
531char *BN_bn2hex(const BIGNUM *a);
532char *BN_bn2dec(const BIGNUM *a);
533int BN_hex2bn(BIGNUM **a, const char *str);
534int BN_dec2bn(BIGNUM **a, const char *str);
535int BN_asc2bn(BIGNUM **a, const char *str);
536int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
537int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); /* returns
538 * -2 for
539 * error */
540BIGNUM *BN_mod_inverse(BIGNUM *ret,
541 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
542BIGNUM *BN_mod_sqrt(BIGNUM *ret,
543 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
544
545void BN_consttime_swap(BN_ULONG swap, BIGNUM *a, BIGNUM *b, int nwords);
546
547/* Deprecated versions */
548# ifndef OPENSSL_NO_DEPRECATED
549BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
550 const BIGNUM *add, const BIGNUM *rem,
551 void (*callback) (int, int, void *), void *cb_arg);
552int BN_is_prime(const BIGNUM *p, int nchecks,
553 void (*callback) (int, int, void *),
554 BN_CTX *ctx, void *cb_arg);
555int BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
556 void (*callback) (int, int, void *), BN_CTX *ctx,
557 void *cb_arg, int do_trial_division);
558# endif /* !defined(OPENSSL_NO_DEPRECATED) */
559
560/* Newer versions */
561int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
562 const BIGNUM *rem, BN_GENCB *cb);
563int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
564int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
565 int do_trial_division, BN_GENCB *cb);
566
567int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx);
568
569int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
570 const BIGNUM *Xp, const BIGNUM *Xp1,
571 const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
572 BN_GENCB *cb);
573int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, BIGNUM *Xp1,
574 BIGNUM *Xp2, const BIGNUM *Xp, const BIGNUM *e,
575 BN_CTX *ctx, BN_GENCB *cb);
576
577BN_MONT_CTX *BN_MONT_CTX_new(void);
578void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
579int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
580 BN_MONT_CTX *mont, BN_CTX *ctx);
581# define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
582 (r),(a),&((mont)->RR),(mont),(ctx))
583int BN_from_montgomery(BIGNUM *r, const BIGNUM *a,
584 BN_MONT_CTX *mont, BN_CTX *ctx);
585void BN_MONT_CTX_free(BN_MONT_CTX *mont);
586int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx);
587BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
588BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
589 const BIGNUM *mod, BN_CTX *ctx);
590
591/* BN_BLINDING flags */
592# define BN_BLINDING_NO_UPDATE 0x00000001
593# define BN_BLINDING_NO_RECREATE 0x00000002
594
595BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
596void BN_BLINDING_free(BN_BLINDING *b);
597int BN_BLINDING_update(BN_BLINDING *b, BN_CTX *ctx);
598int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
599int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
600int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
601int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b,
602 BN_CTX *);
603# ifndef OPENSSL_NO_DEPRECATED
604unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
605void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
606# endif
607CRYPTO_THREADID *BN_BLINDING_thread_id(BN_BLINDING *);
608unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
609void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
610BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
611 const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
612 int (*bn_mod_exp) (BIGNUM *r,
613 const BIGNUM *a,
614 const BIGNUM *p,
615 const BIGNUM *m,
616 BN_CTX *ctx,
617 BN_MONT_CTX *m_ctx),
618 BN_MONT_CTX *m_ctx);
619
620# ifndef OPENSSL_NO_DEPRECATED
621void BN_set_params(int mul, int high, int low, int mont);
622int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
623# endif
624
625void BN_RECP_CTX_init(BN_RECP_CTX *recp);
626BN_RECP_CTX *BN_RECP_CTX_new(void);
627void BN_RECP_CTX_free(BN_RECP_CTX *recp);
628int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *rdiv, BN_CTX *ctx);
629int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
630 BN_RECP_CTX *recp, BN_CTX *ctx);
631int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
632 const BIGNUM *m, BN_CTX *ctx);
633int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
634 BN_RECP_CTX *recp, BN_CTX *ctx);
635
636# ifndef OPENSSL_NO_EC2M
637
638/*
639 * Functions for arithmetic over binary polynomials represented by BIGNUMs.
640 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
641 * ignored. Note that input arguments are not const so that their bit arrays
642 * can be expanded to the appropriate size if needed.
643 */
644
645/*
646 * r = a + b
647 */
648int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
649# define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
650/*
651 * r=a mod p
652 */
653int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p);
654/* r = (a * b) mod p */
655int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
656 const BIGNUM *p, BN_CTX *ctx);
657/* r = (a * a) mod p */
658int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
659/* r = (1 / b) mod p */
660int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx);
661/* r = (a / b) mod p */
662int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
663 const BIGNUM *p, BN_CTX *ctx);
664/* r = (a ^ b) mod p */
665int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
666 const BIGNUM *p, BN_CTX *ctx);
667/* r = sqrt(a) mod p */
668int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
669 BN_CTX *ctx);
670/* r^2 + r = a mod p */
671int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
672 BN_CTX *ctx);
673# define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
674/*-
675 * Some functions allow for representation of the irreducible polynomials
676 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
677 * t^p[0] + t^p[1] + ... + t^p[k]
678 * where m = p[0] > p[1] > ... > p[k] = 0.
679 */
680/* r = a mod p */
681int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
682/* r = (a * b) mod p */
683int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
684 const int p[], BN_CTX *ctx);
685/* r = (a * a) mod p */
686int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
687 BN_CTX *ctx);
688/* r = (1 / b) mod p */
689int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
690 BN_CTX *ctx);
691/* r = (a / b) mod p */
692int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
693 const int p[], BN_CTX *ctx);
694/* r = (a ^ b) mod p */
695int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
696 const int p[], BN_CTX *ctx);
697/* r = sqrt(a) mod p */
698int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
699 const int p[], BN_CTX *ctx);
700/* r^2 + r = a mod p */
701int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
702 const int p[], BN_CTX *ctx);
703int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max);
704int BN_GF2m_arr2poly(const int p[], BIGNUM *a);
705
706# endif
707
708/*
709 * faster mod functions for the 'NIST primes' 0 <= a < p^2
710 */
711int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
712int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
713int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
714int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
715int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
716
717const BIGNUM *BN_get0_nist_prime_192(void);
718const BIGNUM *BN_get0_nist_prime_224(void);
719const BIGNUM *BN_get0_nist_prime_256(void);
720const BIGNUM *BN_get0_nist_prime_384(void);
721const BIGNUM *BN_get0_nist_prime_521(void);
722
723/* library internal functions */
724
725# define bn_expand(a,bits) \
726 ( \
727 bits > (INT_MAX - BN_BITS2 + 1) ? \
728 NULL \
729 : \
730 (((bits+BN_BITS2-1)/BN_BITS2) <= (a)->dmax) ? \
731 (a) \
732 : \
733 bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2) \
734 )
735
736# define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
737BIGNUM *bn_expand2(BIGNUM *a, int words);
738# ifndef OPENSSL_NO_DEPRECATED
739BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
740# endif
741
742/*-
743 * Bignum consistency macros
744 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
745 * bignum data after direct manipulations on the data. There is also an
746 * "internal" macro, bn_check_top(), for verifying that there are no leading
747 * zeroes. Unfortunately, some auditing is required due to the fact that
748 * bn_fix_top() has become an overabused duct-tape because bignum data is
749 * occasionally passed around in an inconsistent state. So the following
750 * changes have been made to sort this out;
751 * - bn_fix_top()s implementation has been moved to bn_correct_top()
752 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
753 * bn_check_top() is as before.
754 * - if BN_DEBUG *is* defined;
755 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
756 * consistent. (ed: only if BN_DEBUG_RAND is defined)
757 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
758 * The idea is to have debug builds flag up inconsistent bignums when they
759 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
760 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
761 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
762 * was not appropriate, we convert it permanently to bn_check_top() and track
763 * down the cause of the bug. Eventually, no internal code should be using the
764 * bn_fix_top() macro. External applications and libraries should try this with
765 * their own code too, both in terms of building against the openssl headers
766 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
767 * defined. This not only improves external code, it provides more test
768 * coverage for openssl's own code.
769 */
770
771# ifdef BN_DEBUG
772
773/* We only need assert() when debugging */
774# include <assert.h>
775
776# ifdef BN_DEBUG_RAND
777/* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
778# ifndef RAND_pseudo_bytes
779int RAND_pseudo_bytes(unsigned char *buf, int num);
780# define BN_DEBUG_TRIX
781# endif
782# define bn_pollute(a) \
783 do { \
784 const BIGNUM *_bnum1 = (a); \
785 if(_bnum1->top < _bnum1->dmax) { \
786 unsigned char _tmp_char; \
787 /* We cast away const without the compiler knowing, any \
788 * *genuinely* constant variables that aren't mutable \
789 * wouldn't be constructed with top!=dmax. */ \
790 BN_ULONG *_not_const; \
791 memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
792 /* Debug only - safe to ignore error return */ \
793 RAND_pseudo_bytes(&_tmp_char, 1); \
794 memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
795 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
796 } \
797 } while(0)
798# ifdef BN_DEBUG_TRIX
799# undef RAND_pseudo_bytes
800# endif
801# else
802# define bn_pollute(a)
803# endif
804# define bn_check_top(a) \
805 do { \
806 const BIGNUM *_bnum2 = (a); \
807 if (_bnum2 != NULL) { \
808 assert((_bnum2->top == 0) || \
809 (_bnum2->d[_bnum2->top - 1] != 0)); \
810 bn_pollute(_bnum2); \
811 } \
812 } while(0)
813
814# define bn_fix_top(a) bn_check_top(a)
815
816# define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
817# define bn_wcheck_size(bn, words) \
818 do { \
819 const BIGNUM *_bnum2 = (bn); \
820 assert((words) <= (_bnum2)->dmax && (words) >= (_bnum2)->top); \
821 /* avoid unused variable warning with NDEBUG */ \
822 (void)(_bnum2); \
823 } while(0)
824
825# else /* !BN_DEBUG */
826
827# define bn_pollute(a)
828# define bn_check_top(a)
829# define bn_fix_top(a) bn_correct_top(a)
830# define bn_check_size(bn, bits)
831# define bn_wcheck_size(bn, words)
832
833# endif
834
835# define bn_correct_top(a) \
836 { \
837 BN_ULONG *ftl; \
838 int tmp_top = (a)->top; \
839 if (tmp_top > 0) \
840 { \
841 for (ftl= &((a)->d[tmp_top-1]); tmp_top > 0; tmp_top--) \
842 if (*(ftl--)) break; \
843 (a)->top = tmp_top; \
844 } \
845 bn_pollute(a); \
846 }
847
848BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
849 BN_ULONG w);
850BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
851void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
852BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
853BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
854 int num);
855BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
856 int num);
857
858/* Primes from RFC 2409 */
859BIGNUM *get_rfc2409_prime_768(BIGNUM *bn);
860BIGNUM *get_rfc2409_prime_1024(BIGNUM *bn);
861
862/* Primes from RFC 3526 */
863BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn);
864BIGNUM *get_rfc3526_prime_2048(BIGNUM *bn);
865BIGNUM *get_rfc3526_prime_3072(BIGNUM *bn);
866BIGNUM *get_rfc3526_prime_4096(BIGNUM *bn);
867BIGNUM *get_rfc3526_prime_6144(BIGNUM *bn);
868BIGNUM *get_rfc3526_prime_8192(BIGNUM *bn);
869
870int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom);
871
872/* BEGIN ERROR CODES */
873/*
874 * The following lines are auto generated by the script mkerr.pl. Any changes
875 * made after this point may be overwritten when the script is next run.
876 */
877void ERR_load_BN_strings(void);
878
879/* Error codes for the BN functions. */
880
881/* Function codes. */
882# define BN_F_BNRAND 127
883# define BN_F_BN_BLINDING_CONVERT_EX 100
884# define BN_F_BN_BLINDING_CREATE_PARAM 128
885# define BN_F_BN_BLINDING_INVERT_EX 101
886# define BN_F_BN_BLINDING_NEW 102
887# define BN_F_BN_BLINDING_UPDATE 103
888# define BN_F_BN_BN2DEC 104
889# define BN_F_BN_BN2HEX 105
890# define BN_F_BN_CTX_GET 116
891# define BN_F_BN_CTX_NEW 106
892# define BN_F_BN_CTX_START 129
893# define BN_F_BN_DIV 107
894# define BN_F_BN_DIV_NO_BRANCH 138
895# define BN_F_BN_DIV_RECP 130
896# define BN_F_BN_EXP 123
897# define BN_F_BN_EXPAND2 108
898# define BN_F_BN_EXPAND_INTERNAL 120
899# define BN_F_BN_GF2M_MOD 131
900# define BN_F_BN_GF2M_MOD_EXP 132
901# define BN_F_BN_GF2M_MOD_MUL 133
902# define BN_F_BN_GF2M_MOD_SOLVE_QUAD 134
903# define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 135
904# define BN_F_BN_GF2M_MOD_SQR 136
905# define BN_F_BN_GF2M_MOD_SQRT 137
906# define BN_F_BN_LSHIFT 145
907# define BN_F_BN_MOD_EXP2_MONT 118
908# define BN_F_BN_MOD_EXP_MONT 109
909# define BN_F_BN_MOD_EXP_MONT_CONSTTIME 124
910# define BN_F_BN_MOD_EXP_MONT_WORD 117
911# define BN_F_BN_MOD_EXP_RECP 125
912# define BN_F_BN_MOD_EXP_SIMPLE 126
913# define BN_F_BN_MOD_INVERSE 110
914# define BN_F_BN_MOD_INVERSE_NO_BRANCH 139
915# define BN_F_BN_MOD_LSHIFT_QUICK 119
916# define BN_F_BN_MOD_MUL_RECIPROCAL 111
917# define BN_F_BN_MOD_SQRT 121
918# define BN_F_BN_MPI2BN 112
919# define BN_F_BN_NEW 113
920# define BN_F_BN_RAND 114
921# define BN_F_BN_RAND_RANGE 122
922# define BN_F_BN_RSHIFT 146
923# define BN_F_BN_USUB 115
924
925/* Reason codes. */
926# define BN_R_ARG2_LT_ARG3 100
927# define BN_R_BAD_RECIPROCAL 101
928# define BN_R_BIGNUM_TOO_LONG 114
929# define BN_R_BITS_TOO_SMALL 118
930# define BN_R_CALLED_WITH_EVEN_MODULUS 102
931# define BN_R_DIV_BY_ZERO 103
932# define BN_R_ENCODING_ERROR 104
933# define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
934# define BN_R_INPUT_NOT_REDUCED 110
935# define BN_R_INVALID_LENGTH 106
936# define BN_R_INVALID_RANGE 115
937# define BN_R_INVALID_SHIFT 119
938# define BN_R_NOT_A_SQUARE 111
939# define BN_R_NOT_INITIALIZED 107
940# define BN_R_NO_INVERSE 108
941# define BN_R_NO_SOLUTION 116
942# define BN_R_P_IS_NOT_PRIME 112
943# define BN_R_TOO_MANY_ITERATIONS 113
944# define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109
945
946#ifdef __cplusplus
947}
948#endif
949#endif
950