2 /* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
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.
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).
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.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
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)"
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
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.]
58 /* ====================================================================
59 * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved.
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
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
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/)"
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.
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.
87 * 6. Redistributions of any form whatsoever must retain the following
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 * ====================================================================
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).
111 /* ====================================================================
112 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
114 * Portions of the attached software ("Contribution") are developed by
115 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
117 * The Contribution is licensed pursuant to the Eric Young open source
118 * license provided above.
120 * The binary polynomial arithmetic software is originally written by
121 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
128 # include <openssl/e_os2.h>
129 # ifndef OPENSSL_NO_STDIO
130 # include <stdio.h> /* FILE */
132 # include <openssl/opensslconf.h>
133 # include <openssl/ossl_typ.h>
134 # include <openssl/crypto.h>
141 * These preprocessor symbols control various aspects of the bignum headers
142 * and library code. They're not defined by any "normal" configuration, as
143 * they are intended for development and testing purposes. NB: defining all
144 * three can be useful for debugging application code as well as openssl
145 * itself. BN_DEBUG - turn on various debugging alterations to the bignum
146 * code BN_DEBUG_RAND - uses random poisoning of unused words to trip up
147 * mismanagement of bignum internals. You must also define BN_DEBUG.
149 /* #define BN_DEBUG */
150 /* #define BN_DEBUG_RAND */
152 # ifndef OPENSSL_SMALL_FOOTPRINT
153 # define BN_MUL_COMBA
154 # define BN_SQR_COMBA
155 # define BN_RECURSION
159 * This next option uses the C libraries (2 word)/(1 word) function. If it is
160 * not defined, I use my C version (which is slower). The reason for this
161 * flag is that when the particular C compiler library routine is used, and
162 * the library is linked with a different compiler, the library is missing.
163 * This mostly happens when the library is built with gcc and then linked
164 * using normal cc. This would be a common occurrence because gcc normally
165 * produces code that is 2 times faster than system compilers for the big
166 * number stuff. For machines with only one compiler (or shared libraries),
167 * this should be on. Again this in only really a problem on machines using
168 * "long long's", are 32bit, and are not using my assembler code.
170 # if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
171 defined(OPENSSL_SYS_WIN32) || defined(linux)
178 * assuming long is 64bit - this is the DEC Alpha unsigned long long is only
179 * 64 bits :-(, don't define BN_LLONG for the DEC Alpha
181 # ifdef SIXTY_FOUR_BIT_LONG
182 # define BN_ULLONG unsigned long long
183 # define BN_ULONG unsigned long
184 # define BN_LONG long
189 # define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
190 # define BN_MASK2 (0xffffffffffffffffL)
191 # define BN_MASK2l (0xffffffffL)
192 # define BN_MASK2h (0xffffffff00000000L)
193 # define BN_MASK2h1 (0xffffffff80000000L)
194 # define BN_TBIT (0x8000000000000000L)
195 # define BN_DEC_CONV (10000000000000000000UL)
196 # define BN_DEC_FMT1 "%lu"
197 # define BN_DEC_FMT2 "%019lu"
198 # define BN_DEC_NUM 19
199 # define BN_HEX_FMT1 "%lX"
200 # define BN_HEX_FMT2 "%016lX"
204 * This is where the long long data type is 64 bits, but long is 32. For
205 * machines where there are 64bit registers, this is the mode to use. IRIX,
206 * on R4000 and above should use this mode, along with the relevant assembler
207 * code :-). Do NOT define BN_LLONG.
209 # ifdef SIXTY_FOUR_BIT
212 # define BN_ULONG unsigned long long
213 # define BN_LONG long long
218 # define BN_MASK2 (0xffffffffffffffffLL)
219 # define BN_MASK2l (0xffffffffL)
220 # define BN_MASK2h (0xffffffff00000000LL)
221 # define BN_MASK2h1 (0xffffffff80000000LL)
222 # define BN_TBIT (0x8000000000000000LL)
223 # define BN_DEC_CONV (10000000000000000000ULL)
224 # define BN_DEC_FMT1 "%llu"
225 # define BN_DEC_FMT2 "%019llu"
226 # define BN_DEC_NUM 19
227 # define BN_HEX_FMT1 "%llX"
228 # define BN_HEX_FMT2 "%016llX"
231 # ifdef THIRTY_TWO_BIT
233 # if defined(_WIN32) && !defined(__GNUC__)
234 # define BN_ULLONG unsigned __int64
235 # define BN_MASK (0xffffffffffffffffI64)
237 # define BN_ULLONG unsigned long long
238 # define BN_MASK (0xffffffffffffffffLL)
241 # define BN_ULONG unsigned int
247 # define BN_MASK2 (0xffffffffL)
248 # define BN_MASK2l (0xffff)
249 # define BN_MASK2h1 (0xffff8000L)
250 # define BN_MASK2h (0xffff0000L)
251 # define BN_TBIT (0x80000000L)
252 # define BN_DEC_CONV (1000000000L)
253 # define BN_DEC_FMT1 "%u"
254 # define BN_DEC_FMT2 "%09u"
255 # define BN_DEC_NUM 9
256 # define BN_HEX_FMT1 "%X"
257 # define BN_HEX_FMT2 "%08X"
260 # define BN_DEFAULT_BITS 1280
262 # define BN_FLG_MALLOCED 0x01
263 # define BN_FLG_STATIC_DATA 0x02
266 * avoid leaking exponent information through timing,
267 * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime,
268 * BN_div() will call BN_div_no_branch,
269 * BN_mod_inverse() will call BN_mod_inverse_no_branch.
271 # define BN_FLG_CONSTTIME 0x04
272 # define BN_FLG_SECURE 0x08
274 # if OPENSSL_API_COMPAT < 0x00908000L
275 /* deprecated name for the flag */
276 # define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME
277 # define BN_FLG_FREE 0x8000 /* used for debuging */
280 void BN_set_flags(BIGNUM *b, int n);
281 int BN_get_flags(const BIGNUM *b, int n);
284 * get a clone of a BIGNUM with changed flags, for *temporary* use only (the
285 * two BIGNUMs cannot be used in parallel!). Also only for *read only* use. The
286 * value |dest| should be a newly allocated BIGNUM obtained via BN_new() that
287 * has not been otherwise initialised or used.
289 void BN_with_flags(BIGNUM *dest, const BIGNUM *b, int flags);
291 /* Wrapper function to make using BN_GENCB easier, */
292 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
294 BN_GENCB *BN_GENCB_new(void);
295 void BN_GENCB_free(BN_GENCB *cb);
297 /* Populate a BN_GENCB structure with an "old"-style callback */
298 void BN_GENCB_set_old(BN_GENCB *gencb, void (*callback) (int, int, void *),
301 /* Populate a BN_GENCB structure with a "new"-style callback */
302 void BN_GENCB_set(BN_GENCB *gencb, int (*callback) (int, int, BN_GENCB *),
305 void *BN_GENCB_get_arg(BN_GENCB *cb);
307 # define BN_prime_checks 0 /* default: select number of iterations based
308 * on the size of the number */
311 * number of Miller-Rabin iterations for an error rate of less than 2^-80 for
312 * random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook of
313 * Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
314 * original paper: Damgaard, Landrock, Pomerance: Average case error
315 * estimates for the strong probable prime test. -- Math. Comp. 61 (1993)
318 # define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
331 # define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
333 int BN_abs_is_word(const BIGNUM *a, const BN_ULONG w);
334 int BN_is_zero(const BIGNUM *a);
335 int BN_is_one(const BIGNUM *a);
336 int BN_is_word(const BIGNUM *a, const BN_ULONG w);
337 int BN_is_odd(const BIGNUM *a);
339 # define BN_one(a) (BN_set_word((a),1))
341 void BN_zero_ex(BIGNUM *a);
343 # if OPENSSL_API_COMPAT >= 0x00908000L
344 # define BN_zero(a) BN_zero_ex(a)
346 # define BN_zero(a) (BN_set_word((a),0))
349 const BIGNUM *BN_value_one(void);
350 char *BN_options(void);
351 BN_CTX *BN_CTX_new(void);
352 BN_CTX *BN_CTX_secure_new(void);
353 void BN_CTX_free(BN_CTX *c);
354 void BN_CTX_start(BN_CTX *ctx);
355 BIGNUM *BN_CTX_get(BN_CTX *ctx);
356 void BN_CTX_end(BN_CTX *ctx);
357 int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
358 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
359 int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
360 int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
361 int BN_num_bits(const BIGNUM *a);
362 int BN_num_bits_word(BN_ULONG l);
363 int BN_security_bits(int L, int N);
364 BIGNUM *BN_new(void);
365 BIGNUM *BN_secure_new(void);
366 void BN_clear_free(BIGNUM *a);
367 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
368 void BN_swap(BIGNUM *a, BIGNUM *b);
369 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
370 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
371 BIGNUM *BN_mpi2bn(const unsigned char *s, int len, BIGNUM *ret);
372 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
373 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
374 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
375 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
376 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
377 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
378 int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
379 /** BN_set_negative sets sign of a BIGNUM
380 * \param b pointer to the BIGNUM object
381 * \param n 0 if the BIGNUM b should be positive and a value != 0 otherwise
383 void BN_set_negative(BIGNUM *b, int n);
384 /** BN_is_negative returns 1 if the BIGNUM is negative
385 * \param a pointer to the BIGNUM object
386 * \return 1 if a < 0 and 0 otherwise
388 int BN_is_negative(const BIGNUM *b);
390 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
392 # define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
393 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
394 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
396 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
398 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
400 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
402 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
404 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
405 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
406 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
407 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
409 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
411 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
412 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
413 int BN_mul_word(BIGNUM *a, BN_ULONG w);
414 int BN_add_word(BIGNUM *a, BN_ULONG w);
415 int BN_sub_word(BIGNUM *a, BN_ULONG w);
416 int BN_set_word(BIGNUM *a, BN_ULONG w);
417 BN_ULONG BN_get_word(const BIGNUM *a);
419 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
420 void BN_free(BIGNUM *a);
421 int BN_is_bit_set(const BIGNUM *a, int n);
422 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
423 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
424 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
426 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
427 const BIGNUM *m, BN_CTX *ctx);
428 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
429 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
430 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
431 const BIGNUM *m, BN_CTX *ctx,
432 BN_MONT_CTX *in_mont);
433 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
434 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
435 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
436 const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
437 BN_CTX *ctx, BN_MONT_CTX *m_ctx);
438 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
439 const BIGNUM *m, BN_CTX *ctx);
441 int BN_mask_bits(BIGNUM *a, int n);
442 # ifndef OPENSSL_NO_STDIO
443 int BN_print_fp(FILE *fp, const BIGNUM *a);
446 int BN_print(BIO *fp, const BIGNUM *a);
448 int BN_print(void *fp, const BIGNUM *a);
450 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
451 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
452 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
453 void BN_clear(BIGNUM *a);
454 BIGNUM *BN_dup(const BIGNUM *a);
455 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
456 int BN_set_bit(BIGNUM *a, int n);
457 int BN_clear_bit(BIGNUM *a, int n);
458 char *BN_bn2hex(const BIGNUM *a);
459 char *BN_bn2dec(const BIGNUM *a);
460 int BN_hex2bn(BIGNUM **a, const char *str);
461 int BN_dec2bn(BIGNUM **a, const char *str);
462 int BN_asc2bn(BIGNUM **a, const char *str);
463 int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
464 int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); /* returns
467 BIGNUM *BN_mod_inverse(BIGNUM *ret,
468 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
469 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
470 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
472 void BN_consttime_swap(BN_ULONG swap, BIGNUM *a, BIGNUM *b, int nwords);
474 /* Deprecated versions */
475 DEPRECATEDIN_0_9_8(BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
478 void (*callback) (int, int,
481 DEPRECATEDIN_0_9_8(int
482 BN_is_prime(const BIGNUM *p, int nchecks,
483 void (*callback) (int, int, void *),
484 BN_CTX *ctx, void *cb_arg))
485 DEPRECATEDIN_0_9_8(int
486 BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
487 void (*callback) (int, int, void *),
488 BN_CTX *ctx, void *cb_arg,
489 int do_trial_division))
492 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
493 const BIGNUM *rem, BN_GENCB *cb);
494 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
495 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
496 int do_trial_division, BN_GENCB *cb);
498 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx);
500 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
501 const BIGNUM *Xp, const BIGNUM *Xp1,
502 const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
504 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, BIGNUM *Xp1,
505 BIGNUM *Xp2, const BIGNUM *Xp, const BIGNUM *e,
506 BN_CTX *ctx, BN_GENCB *cb);
508 BN_MONT_CTX *BN_MONT_CTX_new(void);
509 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
510 BN_MONT_CTX *mont, BN_CTX *ctx);
511 int BN_to_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
513 int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
515 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
516 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx);
517 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
518 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
519 const BIGNUM *mod, BN_CTX *ctx);
521 /* BN_BLINDING flags */
522 # define BN_BLINDING_NO_UPDATE 0x00000001
523 # define BN_BLINDING_NO_RECREATE 0x00000002
525 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
526 void BN_BLINDING_free(BN_BLINDING *b);
527 int BN_BLINDING_update(BN_BLINDING *b, BN_CTX *ctx);
528 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
529 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
530 int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
531 int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b,
533 DEPRECATEDIN_1_0_0(unsigned long
534 BN_BLINDING_get_thread_id(const BN_BLINDING *))
535 DEPRECATEDIN_1_0_0(void
536 BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long))
537 CRYPTO_THREADID *BN_BLINDING_thread_id(BN_BLINDING *);
538 unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
539 void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
540 BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
541 const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
542 int (*bn_mod_exp) (BIGNUM *r,
550 DEPRECATEDIN_0_9_8(void BN_set_params(int mul, int high, int low, int mont))
551 DEPRECATEDIN_0_9_8(int BN_get_params(int which)) /* 0, mul, 1 high, 2 low, 3
554 BN_RECP_CTX *BN_RECP_CTX_new(void);
555 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
556 int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *rdiv, BN_CTX *ctx);
557 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
558 BN_RECP_CTX *recp, BN_CTX *ctx);
559 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
560 const BIGNUM *m, BN_CTX *ctx);
561 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
562 BN_RECP_CTX *recp, BN_CTX *ctx);
564 # ifndef OPENSSL_NO_EC2M
567 * Functions for arithmetic over binary polynomials represented by BIGNUMs.
568 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
569 * ignored. Note that input arguments are not const so that their bit arrays
570 * can be expanded to the appropriate size if needed.
576 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
577 # define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
581 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p);
582 /* r = (a * b) mod p */
583 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
584 const BIGNUM *p, BN_CTX *ctx);
585 /* r = (a * a) mod p */
586 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
587 /* r = (1 / b) mod p */
588 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx);
589 /* r = (a / b) mod p */
590 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
591 const BIGNUM *p, BN_CTX *ctx);
592 /* r = (a ^ b) mod p */
593 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
594 const BIGNUM *p, BN_CTX *ctx);
595 /* r = sqrt(a) mod p */
596 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
598 /* r^2 + r = a mod p */
599 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
601 # define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
603 * Some functions allow for representation of the irreducible polynomials
604 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
605 * t^p[0] + t^p[1] + ... + t^p[k]
606 * where m = p[0] > p[1] > ... > p[k] = 0.
609 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
610 /* r = (a * b) mod p */
611 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
612 const int p[], BN_CTX *ctx);
613 /* r = (a * a) mod p */
614 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
616 /* r = (1 / b) mod p */
617 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
619 /* r = (a / b) mod p */
620 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
621 const int p[], BN_CTX *ctx);
622 /* r = (a ^ b) mod p */
623 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
624 const int p[], BN_CTX *ctx);
625 /* r = sqrt(a) mod p */
626 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
627 const int p[], BN_CTX *ctx);
628 /* r^2 + r = a mod p */
629 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
630 const int p[], BN_CTX *ctx);
631 int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max);
632 int BN_GF2m_arr2poly(const int p[], BIGNUM *a);
637 * faster mod functions for the 'NIST primes' 0 <= a < p^2
639 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
640 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
641 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
642 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
643 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
645 const BIGNUM *BN_get0_nist_prime_192(void);
646 const BIGNUM *BN_get0_nist_prime_224(void);
647 const BIGNUM *BN_get0_nist_prime_256(void);
648 const BIGNUM *BN_get0_nist_prime_384(void);
649 const BIGNUM *BN_get0_nist_prime_521(void);
651 int (*BN_nist_mod_func(const BIGNUM *p)) (BIGNUM *r, const BIGNUM *a,
652 const BIGNUM *field, BN_CTX *ctx);
654 int BN_generate_dsa_nonce(BIGNUM *out, const BIGNUM *range,
655 const BIGNUM *priv, const unsigned char *message,
656 size_t message_len, BN_CTX *ctx);
658 /* Primes from RFC 2409 */
659 BIGNUM *get_rfc2409_prime_768(BIGNUM *bn);
660 BIGNUM *get_rfc2409_prime_1024(BIGNUM *bn);
662 /* Primes from RFC 3526 */
663 BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn);
664 BIGNUM *get_rfc3526_prime_2048(BIGNUM *bn);
665 BIGNUM *get_rfc3526_prime_3072(BIGNUM *bn);
666 BIGNUM *get_rfc3526_prime_4096(BIGNUM *bn);
667 BIGNUM *get_rfc3526_prime_6144(BIGNUM *bn);
668 BIGNUM *get_rfc3526_prime_8192(BIGNUM *bn);
670 int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom);
672 /* BEGIN ERROR CODES */
674 * The following lines are auto generated by the script mkerr.pl. Any changes
675 * made after this point may be overwritten when the script is next run.
677 void ERR_load_BN_strings(void);
679 /* Error codes for the BN functions. */
681 /* Function codes. */
682 # define BN_F_BNRAND 127
683 # define BN_F_BN_BLINDING_CONVERT_EX 100
684 # define BN_F_BN_BLINDING_CREATE_PARAM 128
685 # define BN_F_BN_BLINDING_INVERT_EX 101
686 # define BN_F_BN_BLINDING_NEW 102
687 # define BN_F_BN_BLINDING_UPDATE 103
688 # define BN_F_BN_BN2DEC 104
689 # define BN_F_BN_BN2HEX 105
690 # define BN_F_BN_COMPUTE_WNAF 142
691 # define BN_F_BN_CTX_GET 116
692 # define BN_F_BN_CTX_NEW 106
693 # define BN_F_BN_CTX_START 129
694 # define BN_F_BN_DIV 107
695 # define BN_F_BN_DIV_NO_BRANCH 138
696 # define BN_F_BN_DIV_RECP 130
697 # define BN_F_BN_EXP 123
698 # define BN_F_BN_EXPAND2 108
699 # define BN_F_BN_EXPAND_INTERNAL 120
700 # define BN_F_BN_GENCB_NEW 143
701 # define BN_F_BN_GENERATE_DSA_NONCE 140
702 # define BN_F_BN_GENERATE_PRIME_EX 141
703 # define BN_F_BN_GF2M_MOD 131
704 # define BN_F_BN_GF2M_MOD_EXP 132
705 # define BN_F_BN_GF2M_MOD_MUL 133
706 # define BN_F_BN_GF2M_MOD_SOLVE_QUAD 134
707 # define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 135
708 # define BN_F_BN_GF2M_MOD_SQR 136
709 # define BN_F_BN_GF2M_MOD_SQRT 137
710 # define BN_F_BN_LSHIFT 145
711 # define BN_F_BN_MOD_EXP2_MONT 118
712 # define BN_F_BN_MOD_EXP_MONT 109
713 # define BN_F_BN_MOD_EXP_MONT_CONSTTIME 124
714 # define BN_F_BN_MOD_EXP_MONT_WORD 117
715 # define BN_F_BN_MOD_EXP_RECP 125
716 # define BN_F_BN_MOD_EXP_SIMPLE 126
717 # define BN_F_BN_MOD_INVERSE 110
718 # define BN_F_BN_MOD_INVERSE_NO_BRANCH 139
719 # define BN_F_BN_MOD_LSHIFT_QUICK 119
720 # define BN_F_BN_MOD_MUL_RECIPROCAL 111
721 # define BN_F_BN_MOD_SQRT 121
722 # define BN_F_BN_MPI2BN 112
723 # define BN_F_BN_NEW 113
724 # define BN_F_BN_RAND 114
725 # define BN_F_BN_RAND_RANGE 122
726 # define BN_F_BN_RSHIFT 146
727 # define BN_F_BN_SET_WORDS 144
728 # define BN_F_BN_USUB 115
731 # define BN_R_ARG2_LT_ARG3 100
732 # define BN_R_BAD_RECIPROCAL 101
733 # define BN_R_BIGNUM_TOO_LONG 114
734 # define BN_R_BITS_TOO_SMALL 118
735 # define BN_R_CALLED_WITH_EVEN_MODULUS 102
736 # define BN_R_DIV_BY_ZERO 103
737 # define BN_R_ENCODING_ERROR 104
738 # define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
739 # define BN_R_INPUT_NOT_REDUCED 110
740 # define BN_R_INVALID_LENGTH 106
741 # define BN_R_INVALID_RANGE 115
742 # define BN_R_INVALID_SHIFT 119
743 # define BN_R_NOT_A_SQUARE 111
744 # define BN_R_NOT_INITIALIZED 107
745 # define BN_R_NO_INVERSE 108
746 # define BN_R_NO_SOLUTION 116
747 # define BN_R_PRIVATE_KEY_TOO_LARGE 117
748 # define BN_R_P_IS_NOT_PRIME 112
749 # define BN_R_TOO_MANY_ITERATIONS 113
750 # define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109