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