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bn.h
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1 /* crypto/bn/bn.h */
2 /* Copyright (C) 1995-1997 Eric Young ([email protected])
3  * All rights reserved.
4  *
5  * This package is an SSL implementation written
6  * by Eric Young ([email protected]).
7  * The implementation was written so as to conform with Netscapes SSL.
8  *
9  * This library is free for commercial and non-commercial use as long as
10  * the following conditions are aheared to. The following conditions
11  * apply to all code found in this distribution, be it the RC4, RSA,
12  * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13  * included with this distribution is covered by the same copyright terms
14  * except that the holder is Tim Hudson ([email protected]).
15  *
16  * Copyright remains Eric Young's, and as such any Copyright notices in
17  * the code are not to be removed.
18  * If this package is used in a product, Eric Young should be given attribution
19  * as the author of the parts of the library used.
20  * This can be in the form of a textual message at program startup or
21  * in documentation (online or textual) provided with the package.
22  *
23  * Redistribution and use in source and binary forms, with or without
24  * modification, are permitted provided that the following conditions
25  * are met:
26  * 1. Redistributions of source code must retain the copyright
27  * notice, this list of conditions and the following disclaimer.
28  * 2. Redistributions in binary form must reproduce the above copyright
29  * notice, this list of conditions and the following disclaimer in the
30  * documentation and/or other materials provided with the distribution.
31  * 3. All advertising materials mentioning features or use of this software
32  * must display the following acknowledgement:
33  * "This product includes cryptographic software written by
34  * Eric Young ([email protected])"
35  * The word 'cryptographic' can be left out if the rouines from the library
36  * being used are not cryptographic related :-).
37  * 4. If you include any Windows specific code (or a derivative thereof) from
38  * the apps directory (application code) you must include an acknowledgement:
39  * "This product includes software written by Tim Hudson ([email protected])"
40  *
41  * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44  * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
51  * SUCH DAMAGE.
52  *
53  * The licence and distribution terms for any publically available version or
54  * derivative of this code cannot be changed. i.e. this code cannot simply be
55  * copied and put under another distribution licence
56  * [including the GNU Public Licence.]
57  */
58 /* ====================================================================
59  * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved.
60  *
61  * Redistribution and use in source and binary forms, with or without
62  * modification, are permitted provided that the following conditions
63  * are met:
64  *
65  * 1. Redistributions of source code must retain the above copyright
66  * notice, this list of conditions and the following disclaimer.
67  *
68  * 2. Redistributions in binary form must reproduce the above copyright
69  * notice, this list of conditions and the following disclaimer in
70  * the documentation and/or other materials provided with the
71  * distribution.
72  *
73  * 3. All advertising materials mentioning features or use of this
74  * software must display the following acknowledgment:
75  * "This product includes software developed by the OpenSSL Project
76  * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
77  *
78  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79  * endorse or promote products derived from this software without
80  * prior written permission. For written permission, please contact
82  *
83  * 5. Products derived from this software may not be called "OpenSSL"
84  * nor may "OpenSSL" appear in their names without prior written
85  * permission of the OpenSSL Project.
86  *
87  * 6. Redistributions of any form whatsoever must retain the following
88  * acknowledgment:
89  * "This product includes software developed by the OpenSSL Project
90  * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91  *
92  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95  * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103  * OF THE POSSIBILITY OF SUCH DAMAGE.
104  * ====================================================================
105  *
106  * This product includes cryptographic software written by Eric Young
107  * ([email protected]). This product includes software written by Tim
108  * Hudson ([email protected]).
109  *
110  */
111 /* ====================================================================
112  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
113  *
114  * Portions of the attached software ("Contribution") are developed by
115  * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
116  *
117  * The Contribution is licensed pursuant to the Eric Young open source
118  * license provided above.
119  *
120  * The binary polynomial arithmetic software is originally written by
121  * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
122  *
123  */
124 
125 #ifndef HEADER_BN_H
126 #define HEADER_BN_H
127 
128 #include <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
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;
315 typedef struct bn_gencb_st BN_GENCB;
316 #endif
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  };
328 /* Used for montgomery multiplication */
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  };
341 /* Used for reciprocal division/mod functions
342  * It cannot be shared between threads
343  */
345  {
346  BIGNUM N; /* the divisor */
347  BIGNUM Nr; /* the reciprocal */
348  int num_bits;
349  int shift;
350  int flags;
351  };
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)
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);
460 void BN_set_negative(BIGNUM *b, int n);
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 */
537  const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
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 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx);
562 
564  const BIGNUM *Xp, const BIGNUM *Xp1, const BIGNUM *Xp2,
565  const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb);
567  BIGNUM *Xp1, BIGNUM *Xp2,
568  const BIGNUM *Xp,
569  const BIGNUM *e, BN_CTX *ctx,
570  BN_GENCB *cb);
573 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
574 int BN_mod_mul_montgomery(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,
575  BN_MONT_CTX *mont, BN_CTX *ctx);
576 #define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
577  (r),(a),&((mont)->RR),(mont),(ctx))
578 int BN_from_montgomery(BIGNUM *r,const BIGNUM *a,
579  BN_MONT_CTX *mont, BN_CTX *ctx);
580 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
581 int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *mod,BN_CTX *ctx);
584  const BIGNUM *mod, BN_CTX *ctx);
585 
586 /* BN_BLINDING flags */
587 #define BN_BLINDING_NO_UPDATE 0x00000001
588 #define BN_BLINDING_NO_RECREATE 0x00000002
589 
590 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
596 int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b, BN_CTX *);
597 #ifndef OPENSSL_NO_DEPRECATED
598 unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
599 void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
600 #endif
602 unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
603 void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
605  const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
606  int (*bn_mod_exp)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
607  const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx),
608  BN_MONT_CTX *m_ctx);
609 
610 #ifndef OPENSSL_NO_DEPRECATED
611 void BN_set_params(int mul,int high,int low,int mont);
612 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
613 #endif
614 
615 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
617 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
618 int BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx);
619 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
620  BN_RECP_CTX *recp,BN_CTX *ctx);
621 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
622  const BIGNUM *m, BN_CTX *ctx);
623 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
624  BN_RECP_CTX *recp, BN_CTX *ctx);
625 
626 #ifndef OPENSSL_NO_EC2M
627 
628 /* Functions for arithmetic over binary polynomials represented by BIGNUMs.
629  *
630  * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
631  * ignored.
632  *
633  * Note that input arguments are not const so that their bit arrays can
634  * be expanded to the appropriate size if needed.
635  */
636 
637 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /*r = a + b*/
638 #define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
639 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /*r=a mod p*/
640 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
641  const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
642 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
643  BN_CTX *ctx); /* r = (a * a) mod p */
644 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p,
645  BN_CTX *ctx); /* r = (1 / b) mod p */
646 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
647  const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
648 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
649  const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */
650 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
651  BN_CTX *ctx); /* r = sqrt(a) mod p */
652 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
653  BN_CTX *ctx); /* r^2 + r = a mod p */
654 #define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
655 /* Some functions allow for representation of the irreducible polynomials
656  * as an unsigned int[], say p. The irreducible f(t) is then of the form:
657  * t^p[0] + t^p[1] + ... + t^p[k]
658  * where m = p[0] > p[1] > ... > p[k] = 0.
659  */
660 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
661  /* r = a mod p */
662 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
663  const int p[], BN_CTX *ctx); /* r = (a * b) mod p */
664 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
665  BN_CTX *ctx); /* r = (a * a) mod p */
666 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
667  BN_CTX *ctx); /* r = (1 / b) mod p */
668 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
669  const int p[], BN_CTX *ctx); /* r = (a / b) mod p */
670 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
671  const int p[], BN_CTX *ctx); /* r = (a ^ b) mod p */
672 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
673  const int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
675  const int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
676 int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max);
677 int BN_GF2m_arr2poly(const int p[], BIGNUM *a);
678 
679 #endif
680 
681 /* faster mod functions for the 'NIST primes'
682  * 0 <= a < p^2 */
683 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
684 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
685 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
686 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
687 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
688 
689 const BIGNUM *BN_get0_nist_prime_192(void);
690 const BIGNUM *BN_get0_nist_prime_224(void);
691 const BIGNUM *BN_get0_nist_prime_256(void);
693 const BIGNUM *BN_get0_nist_prime_521(void);
695 /* library internal functions */
696 
697 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
698  (a):bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2))
699 #define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
700 BIGNUM *bn_expand2(BIGNUM *a, int words);
701 #ifndef OPENSSL_NO_DEPRECATED
702 BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
703 #endif
704 
705 /* Bignum consistency macros
706  * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
707  * bignum data after direct manipulations on the data. There is also an
708  * "internal" macro, bn_check_top(), for verifying that there are no leading
709  * zeroes. Unfortunately, some auditing is required due to the fact that
710  * bn_fix_top() has become an overabused duct-tape because bignum data is
711  * occasionally passed around in an inconsistent state. So the following
712  * changes have been made to sort this out;
713  * - bn_fix_top()s implementation has been moved to bn_correct_top()
714  * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
715  * bn_check_top() is as before.
716  * - if BN_DEBUG *is* defined;
717  * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
718  * consistent. (ed: only if BN_DEBUG_RAND is defined)
719  * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
720  * The idea is to have debug builds flag up inconsistent bignums when they
721  * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
722  * the use of bn_fix_top() was appropriate (ie. it follows directly after code
723  * that manipulates the bignum) it is converted to bn_correct_top(), and if it
724  * was not appropriate, we convert it permanently to bn_check_top() and track
725  * down the cause of the bug. Eventually, no internal code should be using the
726  * bn_fix_top() macro. External applications and libraries should try this with
727  * their own code too, both in terms of building against the openssl headers
728  * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
729  * defined. This not only improves external code, it provides more test
730  * coverage for openssl's own code.
731  */
732 
733 #ifdef BN_DEBUG
734 
735 /* We only need assert() when debugging */
736 #include <assert.h>
737 
738 #ifdef BN_DEBUG_RAND
739 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
740 #ifndef RAND_pseudo_bytes
741 int RAND_pseudo_bytes(unsigned char *buf,int num);
742 #define BN_DEBUG_TRIX
743 #endif
744 #define bn_pollute(a) \
745  do { \
746  const BIGNUM *_bnum1 = (a); \
747  if(_bnum1->top < _bnum1->dmax) { \
748  unsigned char _tmp_char; \
749  /* We cast away const without the compiler knowing, any \
750  * *genuinely* constant variables that aren't mutable \
751  * wouldn't be constructed with top!=dmax. */ \
752  BN_ULONG *_not_const; \
753  memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
754  RAND_pseudo_bytes(&_tmp_char, 1); \
755  memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
756  (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
757  } \
758  } while(0)
759 #ifdef BN_DEBUG_TRIX
760 #undef RAND_pseudo_bytes
761 #endif
762 #else
763 #define bn_pollute(a)
764 #endif
765 #define bn_check_top(a) \
766  do { \
767  const BIGNUM *_bnum2 = (a); \
768  if (_bnum2 != NULL) { \
769  assert((_bnum2->top == 0) || \
770  (_bnum2->d[_bnum2->top - 1] != 0)); \
771  bn_pollute(_bnum2); \
772  } \
773  } while(0)
775 #define bn_fix_top(a) bn_check_top(a)
777 #else /* !BN_DEBUG */
778 
779 #define bn_pollute(a)
780 #define bn_check_top(a)
781 #define bn_fix_top(a) bn_correct_top(a)
782 
783 #endif
784 
785 #define bn_correct_top(a) \
786  { \
787  BN_ULONG *ftl; \
788  int tmp_top = (a)->top; \
789  if (tmp_top > 0) \
790  { \
791  for (ftl= &((a)->d[tmp_top-1]); tmp_top > 0; tmp_top--) \
792  if (*(ftl--)) break; \
793  (a)->top = tmp_top; \
794  } \
795  bn_pollute(a); \
796  }
797 
798 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
799 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
800 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
801 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
802 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
803 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
804 
805 /* Primes from RFC 2409 */
808 
809 /* Primes from RFC 3526 */
816 
817 int BN_bntest_rand(BIGNUM *rnd, int bits, int top,int bottom);
818 
819 /* BEGIN ERROR CODES */
820 /* The following lines are auto generated by the script mkerr.pl. Any changes
821  * made after this point may be overwritten when the script is next run.
822  */
825 /* Error codes for the BN functions. */
827 /* Function codes. */
828 #define BN_F_BNRAND 127
829 #define BN_F_BN_BLINDING_CONVERT_EX 100
830 #define BN_F_BN_BLINDING_CREATE_PARAM 128
831 #define BN_F_BN_BLINDING_INVERT_EX 101
832 #define BN_F_BN_BLINDING_NEW 102
833 #define BN_F_BN_BLINDING_UPDATE 103
834 #define BN_F_BN_BN2DEC 104
835 #define BN_F_BN_BN2HEX 105
836 #define BN_F_BN_CTX_GET 116
837 #define BN_F_BN_CTX_NEW 106
838 #define BN_F_BN_CTX_START 129
839 #define BN_F_BN_DIV 107
840 #define BN_F_BN_DIV_NO_BRANCH 138
841 #define BN_F_BN_DIV_RECP 130
842 #define BN_F_BN_EXP 123
843 #define BN_F_BN_EXPAND2 108
844 #define BN_F_BN_EXPAND_INTERNAL 120
845 #define BN_F_BN_GF2M_MOD 131
846 #define BN_F_BN_GF2M_MOD_EXP 132
847 #define BN_F_BN_GF2M_MOD_MUL 133
848 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD 134
849 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 135
850 #define BN_F_BN_GF2M_MOD_SQR 136
851 #define BN_F_BN_GF2M_MOD_SQRT 137
852 #define BN_F_BN_MOD_EXP2_MONT 118
853 #define BN_F_BN_MOD_EXP_MONT 109
854 #define BN_F_BN_MOD_EXP_MONT_CONSTTIME 124
855 #define BN_F_BN_MOD_EXP_MONT_WORD 117
856 #define BN_F_BN_MOD_EXP_RECP 125
857 #define BN_F_BN_MOD_EXP_SIMPLE 126
858 #define BN_F_BN_MOD_INVERSE 110
859 #define BN_F_BN_MOD_INVERSE_NO_BRANCH 139
860 #define BN_F_BN_MOD_LSHIFT_QUICK 119
861 #define BN_F_BN_MOD_MUL_RECIPROCAL 111
862 #define BN_F_BN_MOD_SQRT 121
863 #define BN_F_BN_MPI2BN 112
864 #define BN_F_BN_NEW 113
865 #define BN_F_BN_RAND 114
866 #define BN_F_BN_RAND_RANGE 122
867 #define BN_F_BN_USUB 115
869 /* Reason codes. */
870 #define BN_R_ARG2_LT_ARG3 100
871 #define BN_R_BAD_RECIPROCAL 101
872 #define BN_R_BIGNUM_TOO_LONG 114
873 #define BN_R_CALLED_WITH_EVEN_MODULUS 102
874 #define BN_R_DIV_BY_ZERO 103
875 #define BN_R_ENCODING_ERROR 104
876 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
877 #define BN_R_INPUT_NOT_REDUCED 110
878 #define BN_R_INVALID_LENGTH 106
879 #define BN_R_INVALID_RANGE 115
880 #define BN_R_NOT_A_SQUARE 111
881 #define BN_R_NOT_INITIALIZED 107
882 #define BN_R_NO_INVERSE 108
883 #define BN_R_NO_SOLUTION 116
884 #define BN_R_P_IS_NOT_PRIME 112
885 #define BN_R_TOO_MANY_ITERATIONS 113
886 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109
887 
888 #ifdef __cplusplus
889 }
890 #endif
891 #endif