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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 /* These preprocessor symbols control various aspects of the bignum headers and
140  * library code. They're not defined by any "normal" configuration, as they are
141  * intended for development and testing purposes. NB: defining all three can be
142  * useful for debugging application code as well as openssl itself.
143  *
144  * BN_DEBUG - turn on various debugging alterations to the bignum code
145  * 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 /* This next option uses the C libraries (2 word)/(1 word) function.
158  * If it is not defined, I use my C version (which is slower).
159  * The reason for this flag is that when the particular C compiler
160  * library routine is used, and the library is linked with a different
161  * compiler, the library is missing.  This mostly happens when the
162  * library is built with gcc and then linked using normal cc.  This would
163  * be a common occurrence because gcc normally produces code that is
164  * 2 times faster than system compilers for the big number stuff.
165  * For machines with only one compiler (or shared libraries), this should
166  * be on.  Again this in only really a problem on machines
167  * using "long long's", are 32bit, and are not using my assembler code. */
168 #if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
169     defined(OPENSSL_SYS_WIN32) || defined(linux)
170 # ifndef BN_DIV2W
171 #  define BN_DIV2W
172 # endif
173 #endif
174 
175 /* assuming long is 64bit - this is the DEC Alpha
176  * unsigned long long is only 64 bits :-(, don't define
177  * BN_LLONG for the DEC Alpha */
178 #ifdef SIXTY_FOUR_BIT_LONG
179 #define BN_ULLONG	unsigned long long
180 #define BN_ULONG	unsigned long
181 #define BN_LONG		long
182 #define BN_BITS		128
183 #define BN_BYTES	8
184 #define BN_BITS2	64
185 #define BN_BITS4	32
186 #define BN_MASK		(0xffffffffffffffffffffffffffffffffLL)
187 #define BN_MASK2	(0xffffffffffffffffL)
188 #define BN_MASK2l	(0xffffffffL)
189 #define BN_MASK2h	(0xffffffff00000000L)
190 #define BN_MASK2h1	(0xffffffff80000000L)
191 #define BN_TBIT		(0x8000000000000000L)
192 #define BN_DEC_CONV	(10000000000000000000UL)
193 #define BN_DEC_FMT1	"%lu"
194 #define BN_DEC_FMT2	"%019lu"
195 #define BN_DEC_NUM	19
196 #define BN_HEX_FMT1	"%lX"
197 #define BN_HEX_FMT2	"%016lX"
198 #endif
199 
200 /* This is where the long long data type is 64 bits, but long is 32.
201  * For machines where there are 64bit registers, this is the mode to use.
202  * IRIX, on R4000 and above should use this mode, along with the relevant
203  * assembler 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 /* 2011-02-22 SMS.
257  * In various places, a size_t variable or a type cast to size_t was
258  * used to perform integer-only operations on pointers.  This failed on
259  * VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t is
260  * still only 32 bits.  What's needed in these cases is an integer type
261  * with the same size as a pointer, which size_t is not certain to be.
262  * The only fix here is VMS-specific.
263  */
264 #if defined(OPENSSL_SYS_VMS)
265 # if __INITIAL_POINTER_SIZE == 64
266 #  define PTR_SIZE_INT long long
267 # else /* __INITIAL_POINTER_SIZE == 64 */
268 #  define PTR_SIZE_INT int
269 # endif /* __INITIAL_POINTER_SIZE == 64 [else] */
270 #else /* defined(OPENSSL_SYS_VMS) */
271 # define PTR_SIZE_INT size_t
272 #endif /* defined(OPENSSL_SYS_VMS) [else] */
273 
274 #define BN_DEFAULT_BITS	1280
275 
276 #define BN_FLG_MALLOCED		0x01
277 #define BN_FLG_STATIC_DATA	0x02
278 #define BN_FLG_CONSTTIME	0x04 /* avoid leaking exponent information through timing,
279                                       * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime,
280                                       * BN_div() will call BN_div_no_branch,
281                                       * BN_mod_inverse() will call BN_mod_inverse_no_branch.
282                                       */
283 
284 #ifndef OPENSSL_NO_DEPRECATED
285 #define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME /* deprecated name for the flag */
286                                       /* avoid leaking exponent information through timings
287                                       * (BN_mod_exp_mont() will call BN_mod_exp_mont_consttime) */
288 #endif
289 
290 #ifndef OPENSSL_NO_DEPRECATED
291 #define BN_FLG_FREE		0x8000	/* used for debuging */
292 #endif
293 #define BN_set_flags(b,n)	((b)->flags|=(n))
294 #define BN_get_flags(b,n)	((b)->flags&(n))
295 
296 /* get a clone of a BIGNUM with changed flags, for *temporary* use only
297  * (the two BIGNUMs cannot not be used in parallel!) */
298 #define BN_with_flags(dest,b,n)  ((dest)->d=(b)->d, \
299                                   (dest)->top=(b)->top, \
300                                   (dest)->dmax=(b)->dmax, \
301                                   (dest)->neg=(b)->neg, \
302                                   (dest)->flags=(((dest)->flags & BN_FLG_MALLOCED) \
303                                                  |  ((b)->flags & ~BN_FLG_MALLOCED) \
304                                                  |  BN_FLG_STATIC_DATA \
305                                                  |  (n)))
306 
307 /* Already declared in ossl_typ.h */
308 #if 0
309 typedef struct bignum_st BIGNUM;
310 /* Used for temp variables (declaration hidden in bn_lcl.h) */
311 typedef struct bignum_ctx BN_CTX;
312 typedef struct bn_blinding_st BN_BLINDING;
313 typedef struct bn_mont_ctx_st BN_MONT_CTX;
314 typedef struct bn_recp_ctx_st BN_RECP_CTX;
315 typedef struct bn_gencb_st BN_GENCB;
316 #endif
317 
318 struct bignum_st
319 	{
320 	BN_ULONG *d;	/* Pointer to an array of 'BN_BITS2' bit chunks. */
321 	int top;	/* Index of last used d +1. */
322 	/* The next are internal book keeping for bn_expand. */
323 	int dmax;	/* Size of the d array. */
324 	int neg;	/* one if the number is negative */
325 	int flags;
326 	};
327 
328 /* Used for montgomery multiplication */
329 struct bn_mont_ctx_st
330 	{
331 	int ri;        /* number of bits in R */
332 	BIGNUM RR;     /* used to convert to montgomery form */
333 	BIGNUM N;      /* The modulus */
334 	BIGNUM Ni;     /* R*(1/R mod N) - N*Ni = 1
335 	                * (Ni is only stored for bignum algorithm) */
336 	BN_ULONG n0[2];/* least significant word(s) of Ni;
337 	                  (type changed with 0.9.9, was "BN_ULONG n0;" before) */
338 	int flags;
339 	};
340 
341 /* Used for reciprocal division/mod functions
342  * It cannot be shared between threads
343  */
344 struct bn_recp_ctx_st
345 	{
346 	BIGNUM N;	/* the divisor */
347 	BIGNUM Nr;	/* the reciprocal */
348 	int num_bits;
349 	int shift;
350 	int flags;
351 	};
352 
353 /* Used for slow "generation" functions. */
354 struct bn_gencb_st
355 	{
356 	unsigned int ver;	/* To handle binary (in)compatibility */
357 	void *arg;		/* callback-specific data */
358 	union
359 		{
360 		/* if(ver==1) - handles old style callbacks */
361 		void (*cb_1)(int, int, void *);
362 		/* if(ver==2) - new callback style */
363 		int (*cb_2)(int, int, BN_GENCB *);
364 		} cb;
365 	};
366 /* Wrapper function to make using BN_GENCB easier,  */
367 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
368 /* Macro to populate a BN_GENCB structure with an "old"-style callback */
369 #define BN_GENCB_set_old(gencb, callback, cb_arg) { \
370 		BN_GENCB *tmp_gencb = (gencb); \
371 		tmp_gencb->ver = 1; \
372 		tmp_gencb->arg = (cb_arg); \
373 		tmp_gencb->cb.cb_1 = (callback); }
374 /* Macro to populate a BN_GENCB structure with a "new"-style callback */
375 #define BN_GENCB_set(gencb, callback, cb_arg) { \
376 		BN_GENCB *tmp_gencb = (gencb); \
377 		tmp_gencb->ver = 2; \
378 		tmp_gencb->arg = (cb_arg); \
379 		tmp_gencb->cb.cb_2 = (callback); }
380 
381 #define BN_prime_checks 0 /* default: select number of iterations
382 			     based on the size of the number */
383 
384 /* number of Miller-Rabin iterations for an error rate  of less than 2^-80
385  * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
386  * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
387  * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
388  * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
389 #define BN_prime_checks_for_size(b) ((b) >= 1300 ?  2 : \
390                                 (b) >=  850 ?  3 : \
391                                 (b) >=  650 ?  4 : \
392                                 (b) >=  550 ?  5 : \
393                                 (b) >=  450 ?  6 : \
394                                 (b) >=  400 ?  7 : \
395                                 (b) >=  350 ?  8 : \
396                                 (b) >=  300 ?  9 : \
397                                 (b) >=  250 ? 12 : \
398                                 (b) >=  200 ? 15 : \
399                                 (b) >=  150 ? 18 : \
400                                 /* b >= 100 */ 27)
401 
402 #define BN_num_bytes(a)	((BN_num_bits(a)+7)/8)
403 
404 /* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
405 #define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
406 				(((w) == 0) && ((a)->top == 0)))
407 #define BN_is_zero(a)       ((a)->top == 0)
408 #define BN_is_one(a)        (BN_abs_is_word((a),1) && !(a)->neg)
409 #define BN_is_word(a,w)     (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
410 #define BN_is_odd(a)	    (((a)->top > 0) && ((a)->d[0] & 1))
411 
412 #define BN_one(a)	(BN_set_word((a),1))
413 #define BN_zero_ex(a) \
414 	do { \
415 		BIGNUM *_tmp_bn = (a); \
416 		_tmp_bn->top = 0; \
417 		_tmp_bn->neg = 0; \
418 	} while(0)
419 #ifdef OPENSSL_NO_DEPRECATED
420 #define BN_zero(a)	BN_zero_ex(a)
421 #else
422 #define BN_zero(a)	(BN_set_word((a),0))
423 #endif
424 
425 const BIGNUM *BN_value_one(void);
426 char *	BN_options(void);
427 BN_CTX *BN_CTX_new(void);
428 #ifndef OPENSSL_NO_DEPRECATED
429 void	BN_CTX_init(BN_CTX *c);
430 #endif
431 void	BN_CTX_free(BN_CTX *c);
432 void	BN_CTX_start(BN_CTX *ctx);
433 BIGNUM *BN_CTX_get(BN_CTX *ctx);
434 void	BN_CTX_end(BN_CTX *ctx);
435 int     BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
436 int     BN_pseudo_rand(BIGNUM *rnd, int bits, int top,int bottom);
437 int	BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
438 int	BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
439 int	BN_num_bits(const BIGNUM *a);
440 int	BN_num_bits_word(BN_ULONG);
441 BIGNUM *BN_new(void);
442 void	BN_init(BIGNUM *);
443 void	BN_clear_free(BIGNUM *a);
444 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
445 void	BN_swap(BIGNUM *a, BIGNUM *b);
446 BIGNUM *BN_bin2bn(const unsigned char *s,int len,BIGNUM *ret);
447 int	BN_bn2bin(const BIGNUM *a, unsigned char *to);
448 BIGNUM *BN_mpi2bn(const unsigned char *s,int len,BIGNUM *ret);
449 int	BN_bn2mpi(const BIGNUM *a, unsigned char *to);
450 int	BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
451 int	BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
452 int	BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
453 int	BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
454 int	BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
455 int	BN_sqr(BIGNUM *r, const BIGNUM *a,BN_CTX *ctx);
456 /** BN_set_negative sets sign of a BIGNUM
457  * \param  b  pointer to the BIGNUM object
458  * \param  n  0 if the BIGNUM b should be positive and a value != 0 otherwise
459  */
460 void	BN_set_negative(BIGNUM *b, int n);
461 /** BN_is_negative returns 1 if the BIGNUM is negative
462  * \param  a  pointer to the BIGNUM object
463  * \return 1 if a < 0 and 0 otherwise
464  */
465 #define BN_is_negative(a) ((a)->neg != 0)
466 
467 int	BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
468 	BN_CTX *ctx);
469 #define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
470 int	BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
471 int	BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
472 int	BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
473 int	BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
474 int	BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
475 int	BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
476 	const BIGNUM *m, BN_CTX *ctx);
477 int	BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
478 int	BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
479 int	BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
480 int	BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, 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, BN_MONT_CTX *in_mont);
504 int	BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
505 	const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
506 int	BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
507 	const BIGNUM *a2, const BIGNUM *p2,const BIGNUM *m,
508 	BN_CTX *ctx,BN_MONT_CTX *m_ctx);
509 int	BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
510 	const BIGNUM *m,BN_CTX *ctx);
511 
512 int	BN_mask_bits(BIGNUM *a,int n);
513 #ifndef OPENSSL_NO_FP_API
514 int	BN_print_fp(FILE *fp, const BIGNUM *a);
515 #endif
516 #ifdef HEADER_BIO_H
517 int	BN_print(BIO *fp, const BIGNUM *a);
518 #else
519 int	BN_print(void *fp, const BIGNUM *a);
520 #endif
521 int	BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
522 int	BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
523 int	BN_rshift1(BIGNUM *r, const BIGNUM *a);
524 void	BN_clear(BIGNUM *a);
525 BIGNUM *BN_dup(const BIGNUM *a);
526 int	BN_ucmp(const BIGNUM *a, const BIGNUM *b);
527 int	BN_set_bit(BIGNUM *a, int n);
528 int	BN_clear_bit(BIGNUM *a, int n);
529 char *	BN_bn2hex(const BIGNUM *a);
530 char *	BN_bn2dec(const BIGNUM *a);
531 int 	BN_hex2bn(BIGNUM **a, const char *str);
532 int 	BN_dec2bn(BIGNUM **a, const char *str);
533 int	BN_asc2bn(BIGNUM **a, const char *str);
534 int	BN_gcd(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx);
535 int	BN_kronecker(const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx); /* returns -2 for error */
536 BIGNUM *BN_mod_inverse(BIGNUM *ret,
537 	const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
538 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
539 	const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
540 
541 /* Deprecated versions */
542 #ifndef OPENSSL_NO_DEPRECATED
543 BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,
544 	const BIGNUM *add, const BIGNUM *rem,
545 	void (*callback)(int,int,void *),void *cb_arg);
546 int	BN_is_prime(const BIGNUM *p,int nchecks,
547 	void (*callback)(int,int,void *),
548 	BN_CTX *ctx,void *cb_arg);
549 int	BN_is_prime_fasttest(const BIGNUM *p,int nchecks,
550 	void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg,
551 	int do_trial_division);
552 #endif /* !defined(OPENSSL_NO_DEPRECATED) */
553 
554 /* Newer versions */
555 int	BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add,
556 		const BIGNUM *rem, BN_GENCB *cb);
557 int	BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb);
558 int	BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx,
559 		int do_trial_division, BN_GENCB *cb);
560 
561 BN_MONT_CTX *BN_MONT_CTX_new(void );
562 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
563 int BN_mod_mul_montgomery(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,
564 	BN_MONT_CTX *mont, BN_CTX *ctx);
565 #define BN_to_montgomery(r,a,mont,ctx)	BN_mod_mul_montgomery(\
566 	(r),(a),&((mont)->RR),(mont),(ctx))
567 int BN_from_montgomery(BIGNUM *r,const BIGNUM *a,
568 	BN_MONT_CTX *mont, BN_CTX *ctx);
569 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
570 int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *mod,BN_CTX *ctx);
571 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,BN_MONT_CTX *from);
572 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
573 					const BIGNUM *mod, BN_CTX *ctx);
574 
575 /* BN_BLINDING flags */
576 #define	BN_BLINDING_NO_UPDATE	0x00000001
577 #define	BN_BLINDING_NO_RECREATE	0x00000002
578 
579 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
580 void BN_BLINDING_free(BN_BLINDING *b);
581 int BN_BLINDING_update(BN_BLINDING *b,BN_CTX *ctx);
582 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
583 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
584 int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
585 int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b, BN_CTX *);
586 #ifndef OPENSSL_NO_DEPRECATED
587 unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
588 void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
589 #endif
590 CRYPTO_THREADID *BN_BLINDING_thread_id(BN_BLINDING *);
591 unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
592 void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
593 BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
594 	const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
595 	int (*bn_mod_exp)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
596 			  const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx),
597 	BN_MONT_CTX *m_ctx);
598 
599 #ifndef OPENSSL_NO_DEPRECATED
600 void BN_set_params(int mul,int high,int low,int mont);
601 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
602 #endif
603 
604 void	BN_RECP_CTX_init(BN_RECP_CTX *recp);
605 BN_RECP_CTX *BN_RECP_CTX_new(void);
606 void	BN_RECP_CTX_free(BN_RECP_CTX *recp);
607 int	BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx);
608 int	BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
609 	BN_RECP_CTX *recp,BN_CTX *ctx);
610 int	BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
611 	const BIGNUM *m, BN_CTX *ctx);
612 int	BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
613 	BN_RECP_CTX *recp, BN_CTX *ctx);
614 
615 /* Functions for arithmetic over binary polynomials represented by BIGNUMs.
616  *
617  * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
618  * ignored.
619  *
620  * Note that input arguments are not const so that their bit arrays can
621  * be expanded to the appropriate size if needed.
622  */
623 
624 int	BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /*r = a + b*/
625 #define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
626 int	BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /*r=a mod p*/
627 int	BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
628 	const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
629 int	BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
630 	BN_CTX *ctx); /* r = (a * a) mod p */
631 int	BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p,
632 	BN_CTX *ctx); /* r = (1 / b) mod p */
633 int	BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
634 	const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
635 int	BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
636 	const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */
637 int	BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
638 	BN_CTX *ctx); /* r = sqrt(a) mod p */
639 int	BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
640 	BN_CTX *ctx); /* r^2 + r = a mod p */
641 #define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
642 /* Some functions allow for representation of the irreducible polynomials
643  * as an unsigned int[], say p.  The irreducible f(t) is then of the form:
644  *     t^p[0] + t^p[1] + ... + t^p[k]
645  * where m = p[0] > p[1] > ... > p[k] = 0.
646  */
647 int	BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
648 	/* r = a mod p */
649 int	BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
650 	const int p[], BN_CTX *ctx); /* r = (a * b) mod p */
651 int	BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
652 	BN_CTX *ctx); /* r = (a * a) mod p */
653 int	BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
654 	BN_CTX *ctx); /* r = (1 / b) mod p */
655 int	BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
656 	const int p[], BN_CTX *ctx); /* r = (a / b) mod p */
657 int	BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
658 	const int p[], BN_CTX *ctx); /* r = (a ^ b) mod p */
659 int	BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
660 	const int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
661 int	BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
662 	const int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
663 int	BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max);
664 int	BN_GF2m_arr2poly(const int p[], BIGNUM *a);
665 
666 /* faster mod functions for the 'NIST primes'
667  * 0 <= a < p^2 */
668 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
669 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
670 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
671 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
672 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
673 
674 const BIGNUM *BN_get0_nist_prime_192(void);
675 const BIGNUM *BN_get0_nist_prime_224(void);
676 const BIGNUM *BN_get0_nist_prime_256(void);
677 const BIGNUM *BN_get0_nist_prime_384(void);
678 const BIGNUM *BN_get0_nist_prime_521(void);
679 
680 /* library internal functions */
681 
682 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
683 	(a):bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2))
684 #define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
685 BIGNUM *bn_expand2(BIGNUM *a, int words);
686 #ifndef OPENSSL_NO_DEPRECATED
687 BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
688 #endif
689 
690 /* Bignum consistency macros
691  * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
692  * bignum data after direct manipulations on the data. There is also an
693  * "internal" macro, bn_check_top(), for verifying that there are no leading
694  * zeroes. Unfortunately, some auditing is required due to the fact that
695  * bn_fix_top() has become an overabused duct-tape because bignum data is
696  * occasionally passed around in an inconsistent state. So the following
697  * changes have been made to sort this out;
698  * - bn_fix_top()s implementation has been moved to bn_correct_top()
699  * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
700  *   bn_check_top() is as before.
701  * - if BN_DEBUG *is* defined;
702  *   - bn_check_top() tries to pollute unused words even if the bignum 'top' is
703  *     consistent. (ed: only if BN_DEBUG_RAND is defined)
704  *   - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
705  * The idea is to have debug builds flag up inconsistent bignums when they
706  * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
707  * the use of bn_fix_top() was appropriate (ie. it follows directly after code
708  * that manipulates the bignum) it is converted to bn_correct_top(), and if it
709  * was not appropriate, we convert it permanently to bn_check_top() and track
710  * down the cause of the bug. Eventually, no internal code should be using the
711  * bn_fix_top() macro. External applications and libraries should try this with
712  * their own code too, both in terms of building against the openssl headers
713  * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
714  * defined. This not only improves external code, it provides more test
715  * coverage for openssl's own code.
716  */
717 
718 #ifdef BN_DEBUG
719 
720 /* We only need assert() when debugging */
721 #include <assert.h>
722 
723 #ifdef BN_DEBUG_RAND
724 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
725 #ifndef RAND_pseudo_bytes
726 int RAND_pseudo_bytes(unsigned char *buf,int num);
727 #define BN_DEBUG_TRIX
728 #endif
729 #define bn_pollute(a) \
730 	do { \
731 		const BIGNUM *_bnum1 = (a); \
732 		if(_bnum1->top < _bnum1->dmax) { \
733 			unsigned char _tmp_char; \
734 			/* We cast away const without the compiler knowing, any \
735 			 * *genuinely* constant variables that aren't mutable \
736 			 * wouldn't be constructed with top!=dmax. */ \
737 			BN_ULONG *_not_const; \
738 			memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
739 			RAND_pseudo_bytes(&_tmp_char, 1); \
740 			memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
741 				(_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
742 		} \
743 	} while(0)
744 #ifdef BN_DEBUG_TRIX
745 #undef RAND_pseudo_bytes
746 #endif
747 #else
748 #define bn_pollute(a)
749 #endif
750 #define bn_check_top(a) \
751 	do { \
752 		const BIGNUM *_bnum2 = (a); \
753 		if (_bnum2 != NULL) { \
754 			assert((_bnum2->top == 0) || \
755 				(_bnum2->d[_bnum2->top - 1] != 0)); \
756 			bn_pollute(_bnum2); \
757 		} \
758 	} while(0)
759 
760 #define bn_fix_top(a)		bn_check_top(a)
761 
762 #else /* !BN_DEBUG */
763 
764 #define bn_pollute(a)
765 #define bn_check_top(a)
766 #define bn_fix_top(a)		bn_correct_top(a)
767 
768 #endif
769 
770 #define bn_correct_top(a) \
771         { \
772         BN_ULONG *ftl; \
773 	int tmp_top = (a)->top; \
774 	if (tmp_top > 0) \
775 		{ \
776 		for (ftl= &((a)->d[tmp_top-1]); tmp_top > 0; tmp_top--) \
777 			if (*(ftl--)) break; \
778 		(a)->top = tmp_top; \
779 		} \
780 	bn_pollute(a); \
781 	}
782 
783 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
784 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
785 void     bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
786 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
787 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
788 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
789 
790 /* Primes from RFC 2409 */
791 BIGNUM *get_rfc2409_prime_768(BIGNUM *bn);
792 BIGNUM *get_rfc2409_prime_1024(BIGNUM *bn);
793 
794 /* Primes from RFC 3526 */
795 BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn);
796 BIGNUM *get_rfc3526_prime_2048(BIGNUM *bn);
797 BIGNUM *get_rfc3526_prime_3072(BIGNUM *bn);
798 BIGNUM *get_rfc3526_prime_4096(BIGNUM *bn);
799 BIGNUM *get_rfc3526_prime_6144(BIGNUM *bn);
800 BIGNUM *get_rfc3526_prime_8192(BIGNUM *bn);
801 
802 int BN_bntest_rand(BIGNUM *rnd, int bits, int top,int bottom);
803 
804 /* BEGIN ERROR CODES */
805 /* The following lines are auto generated by the script mkerr.pl. Any changes
806  * made after this point may be overwritten when the script is next run.
807  */
808 void ERR_load_BN_strings(void);
809 
810 /* Error codes for the BN functions. */
811 
812 /* Function codes. */
813 #define BN_F_BNRAND					 127
814 #define BN_F_BN_BLINDING_CONVERT_EX			 100
815 #define BN_F_BN_BLINDING_CREATE_PARAM			 128
816 #define BN_F_BN_BLINDING_INVERT_EX			 101
817 #define BN_F_BN_BLINDING_NEW				 102
818 #define BN_F_BN_BLINDING_UPDATE				 103
819 #define BN_F_BN_BN2DEC					 104
820 #define BN_F_BN_BN2HEX					 105
821 #define BN_F_BN_CTX_GET					 116
822 #define BN_F_BN_CTX_NEW					 106
823 #define BN_F_BN_CTX_START				 129
824 #define BN_F_BN_DIV					 107
825 #define BN_F_BN_DIV_NO_BRANCH				 138
826 #define BN_F_BN_DIV_RECP				 130
827 #define BN_F_BN_EXP					 123
828 #define BN_F_BN_EXPAND2					 108
829 #define BN_F_BN_EXPAND_INTERNAL				 120
830 #define BN_F_BN_GF2M_MOD				 131
831 #define BN_F_BN_GF2M_MOD_EXP				 132
832 #define BN_F_BN_GF2M_MOD_MUL				 133
833 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD			 134
834 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR			 135
835 #define BN_F_BN_GF2M_MOD_SQR				 136
836 #define BN_F_BN_GF2M_MOD_SQRT				 137
837 #define BN_F_BN_MOD_EXP2_MONT				 118
838 #define BN_F_BN_MOD_EXP_MONT				 109
839 #define BN_F_BN_MOD_EXP_MONT_CONSTTIME			 124
840 #define BN_F_BN_MOD_EXP_MONT_WORD			 117
841 #define BN_F_BN_MOD_EXP_RECP				 125
842 #define BN_F_BN_MOD_EXP_SIMPLE				 126
843 #define BN_F_BN_MOD_INVERSE				 110
844 #define BN_F_BN_MOD_INVERSE_NO_BRANCH			 139
845 #define BN_F_BN_MOD_LSHIFT_QUICK			 119
846 #define BN_F_BN_MOD_MUL_RECIPROCAL			 111
847 #define BN_F_BN_MOD_SQRT				 121
848 #define BN_F_BN_MPI2BN					 112
849 #define BN_F_BN_NEW					 113
850 #define BN_F_BN_RAND					 114
851 #define BN_F_BN_RAND_RANGE				 122
852 #define BN_F_BN_USUB					 115
853 
854 /* Reason codes. */
855 #define BN_R_ARG2_LT_ARG3				 100
856 #define BN_R_BAD_RECIPROCAL				 101
857 #define BN_R_BIGNUM_TOO_LONG				 114
858 #define BN_R_CALLED_WITH_EVEN_MODULUS			 102
859 #define BN_R_DIV_BY_ZERO				 103
860 #define BN_R_ENCODING_ERROR				 104
861 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA		 105
862 #define BN_R_INPUT_NOT_REDUCED				 110
863 #define BN_R_INVALID_LENGTH				 106
864 #define BN_R_INVALID_RANGE				 115
865 #define BN_R_NOT_A_SQUARE				 111
866 #define BN_R_NOT_INITIALIZED				 107
867 #define BN_R_NO_INVERSE					 108
868 #define BN_R_NO_SOLUTION				 116
869 #define BN_R_P_IS_NOT_PRIME				 112
870 #define BN_R_TOO_MANY_ITERATIONS			 113
871 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES		 109
872 
873 #ifdef  __cplusplus
874 }
875 #endif
876 #endif
877