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