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