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>
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.
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.
148 /* #define BN_DEBUG */
149 /* #define BN_DEBUG_RAND */
151 #ifndef OPENSSL_SMALL_FOOTPRINT
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)
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
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"
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.
205 #ifdef SIXTY_FOUR_BIT
208 #define BN_ULONG unsigned long long
209 #define BN_LONG long long
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"
227 #ifdef THIRTY_TWO_BIT
229 # if defined(_WIN32) && !defined(__GNUC__)
230 # define BN_ULLONG unsigned __int64
231 # define BN_MASK (0xffffffffffffffffI64)
233 # define BN_ULLONG unsigned long long
234 # define BN_MASK (0xffffffffffffffffLL)
237 #define BN_ULONG unsigned int
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"
252 #define BN_HEX_FMT1 "%X"
253 #define BN_HEX_FMT2 "%08X"
256 #define BN_DEFAULT_BITS 1280
258 #define BN_FLG_MALLOCED 0x01
259 #define BN_FLG_STATIC_DATA 0x02
260 #define BN_FLG_CONSTTIME 0x04 /* avoid leaking exponent information through timing,
261 * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime,
262 * BN_div() will call BN_div_no_branch,
263 * BN_mod_inverse() will call BN_mod_inverse_no_branch.
266 #ifndef OPENSSL_NO_DEPRECATED
267 #define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME /* deprecated name for the flag */
268 /* avoid leaking exponent information through timings
269 * (BN_mod_exp_mont() will call BN_mod_exp_mont_consttime) */
272 #ifndef OPENSSL_NO_DEPRECATED
273 #define BN_FLG_FREE 0x8000 /* used for debuging */
275 #define BN_set_flags(b,n) ((b)->flags|=(n))
276 #define BN_get_flags(b,n) ((b)->flags&(n))
278 /* get a clone of a BIGNUM with changed flags, for *temporary* use only
279 * (the two BIGNUMs cannot not be used in parallel!) */
280 #define BN_with_flags(dest,b,n) ((dest)->d=(b)->d, \
281 (dest)->top=(b)->top, \
282 (dest)->dmax=(b)->dmax, \
283 (dest)->neg=(b)->neg, \
284 (dest)->flags=(((dest)->flags & BN_FLG_MALLOCED) \
285 | ((b)->flags & ~BN_FLG_MALLOCED) \
286 | BN_FLG_STATIC_DATA \
289 /* Already declared in ossl_typ.h */
291 typedef struct bignum_st BIGNUM
;
292 /* Used for temp variables (declaration hidden in bn_lcl.h) */
293 typedef struct bignum_ctx BN_CTX
;
294 typedef struct bn_blinding_st BN_BLINDING
;
295 typedef struct bn_mont_ctx_st BN_MONT_CTX
;
296 typedef struct bn_recp_ctx_st BN_RECP_CTX
;
297 typedef struct bn_gencb_st BN_GENCB
;
302 BN_ULONG
*d
; /* Pointer to an array of 'BN_BITS2' bit chunks. */
303 int top
; /* Index of last used d +1. */
304 /* The next are internal book keeping for bn_expand. */
305 int dmax
; /* Size of the d array. */
306 int neg
; /* one if the number is negative */
310 /* Used for montgomery multiplication */
311 struct bn_mont_ctx_st
313 int ri
; /* number of bits in R */
314 BIGNUM RR
; /* used to convert to montgomery form */
315 BIGNUM N
; /* The modulus */
316 BIGNUM Ni
; /* R*(1/R mod N) - N*Ni = 1
317 * (Ni is only stored for bignum algorithm) */
318 BN_ULONG n0
[2];/* least significant word(s) of Ni;
319 (type changed with 0.9.9, was "BN_ULONG n0;" before) */
323 /* Used for reciprocal division/mod functions
324 * It cannot be shared between threads
326 struct bn_recp_ctx_st
328 BIGNUM N
; /* the divisor */
329 BIGNUM Nr
; /* the reciprocal */
335 /* Used for slow "generation" functions. */
338 unsigned int ver
; /* To handle binary (in)compatibility */
339 void *arg
; /* callback-specific data */
342 /* if(ver==1) - handles old style callbacks */
343 void (*cb_1
)(int, int, void *);
344 /* if(ver==2) - new callback style */
345 int (*cb_2
)(int, int, BN_GENCB
*);
348 /* Wrapper function to make using BN_GENCB easier, */
349 int BN_GENCB_call(BN_GENCB
*cb
, int a
, int b
);
350 /* Macro to populate a BN_GENCB structure with an "old"-style callback */
351 #define BN_GENCB_set_old(gencb, callback, cb_arg) { \
352 BN_GENCB *tmp_gencb = (gencb); \
353 tmp_gencb->ver = 1; \
354 tmp_gencb->arg = (cb_arg); \
355 tmp_gencb->cb.cb_1 = (callback); }
356 /* Macro to populate a BN_GENCB structure with a "new"-style callback */
357 #define BN_GENCB_set(gencb, callback, cb_arg) { \
358 BN_GENCB *tmp_gencb = (gencb); \
359 tmp_gencb->ver = 2; \
360 tmp_gencb->arg = (cb_arg); \
361 tmp_gencb->cb.cb_2 = (callback); }
363 #define BN_prime_checks 0 /* default: select number of iterations
364 based on the size of the number */
366 /* number of Miller-Rabin iterations for an error rate of less than 2^-80
367 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
368 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
369 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
370 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
371 #define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
384 #define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
386 /* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
387 #define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
388 (((w) == 0) && ((a)->top == 0)))
389 #define BN_is_zero(a) ((a)->top == 0)
390 #define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
391 #define BN_is_word(a,w) (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
392 #define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
394 #define BN_one(a) (BN_set_word((a),1))
395 #define BN_zero_ex(a) \
397 BIGNUM *_tmp_bn = (a); \
401 #ifdef OPENSSL_NO_DEPRECATED
402 #define BN_zero(a) BN_zero_ex(a)
404 #define BN_zero(a) (BN_set_word((a),0))
407 const BIGNUM
*BN_value_one(void);
408 char * BN_options(void);
409 BN_CTX
*BN_CTX_new(void);
410 #ifndef OPENSSL_NO_DEPRECATED
411 void BN_CTX_init(BN_CTX
*c
);
413 void BN_CTX_free(BN_CTX
*c
);
414 void BN_CTX_start(BN_CTX
*ctx
);
415 BIGNUM
*BN_CTX_get(BN_CTX
*ctx
);
416 void BN_CTX_end(BN_CTX
*ctx
);
417 int BN_rand(BIGNUM
*rnd
, int bits
, int top
,int bottom
);
418 int BN_pseudo_rand(BIGNUM
*rnd
, int bits
, int top
,int bottom
);
419 int BN_rand_range(BIGNUM
*rnd
, const BIGNUM
*range
);
420 int BN_pseudo_rand_range(BIGNUM
*rnd
, const BIGNUM
*range
);
421 int BN_num_bits(const BIGNUM
*a
);
422 int BN_num_bits_word(BN_ULONG
);
423 BIGNUM
*BN_new(void);
424 void BN_init(BIGNUM
*);
425 void BN_clear_free(BIGNUM
*a
);
426 BIGNUM
*BN_copy(BIGNUM
*a
, const BIGNUM
*b
);
427 void BN_swap(BIGNUM
*a
, BIGNUM
*b
);
428 BIGNUM
*BN_bin2bn(const unsigned char *s
,int len
,BIGNUM
*ret
);
429 int BN_bn2bin(const BIGNUM
*a
, unsigned char *to
);
430 BIGNUM
*BN_mpi2bn(const unsigned char *s
,int len
,BIGNUM
*ret
);
431 int BN_bn2mpi(const BIGNUM
*a
, unsigned char *to
);
432 int BN_sub(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
);
433 int BN_usub(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
);
434 int BN_uadd(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
);
435 int BN_add(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
);
436 int BN_mul(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
);
437 int BN_sqr(BIGNUM
*r
, const BIGNUM
*a
,BN_CTX
*ctx
);
438 /** BN_set_negative sets sign of a BIGNUM
439 * \param b pointer to the BIGNUM object
440 * \param n 0 if the BIGNUM b should be positive and a value != 0 otherwise
442 void BN_set_negative(BIGNUM
*b
, int n
);
443 /** BN_is_negative returns 1 if the BIGNUM is negative
444 * \param a pointer to the BIGNUM object
445 * \return 1 if a < 0 and 0 otherwise
447 #define BN_is_negative(a) ((a)->neg != 0)
449 int BN_div(BIGNUM
*dv
, BIGNUM
*rem
, const BIGNUM
*m
, const BIGNUM
*d
,
451 #define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
452 int BN_nnmod(BIGNUM
*r
, const BIGNUM
*m
, const BIGNUM
*d
, BN_CTX
*ctx
);
453 int BN_mod_add(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const BIGNUM
*m
, BN_CTX
*ctx
);
454 int BN_mod_add_quick(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const BIGNUM
*m
);
455 int BN_mod_sub(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const BIGNUM
*m
, BN_CTX
*ctx
);
456 int BN_mod_sub_quick(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const BIGNUM
*m
);
457 int BN_mod_mul(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
458 const BIGNUM
*m
, BN_CTX
*ctx
);
459 int BN_mod_sqr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*m
, BN_CTX
*ctx
);
460 int BN_mod_lshift1(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*m
, BN_CTX
*ctx
);
461 int BN_mod_lshift1_quick(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*m
);
462 int BN_mod_lshift(BIGNUM
*r
, const BIGNUM
*a
, int n
, const BIGNUM
*m
, BN_CTX
*ctx
);
463 int BN_mod_lshift_quick(BIGNUM
*r
, const BIGNUM
*a
, int n
, const BIGNUM
*m
);
465 BN_ULONG
BN_mod_word(const BIGNUM
*a
, BN_ULONG w
);
466 BN_ULONG
BN_div_word(BIGNUM
*a
, BN_ULONG w
);
467 int BN_mul_word(BIGNUM
*a
, BN_ULONG w
);
468 int BN_add_word(BIGNUM
*a
, BN_ULONG w
);
469 int BN_sub_word(BIGNUM
*a
, BN_ULONG w
);
470 int BN_set_word(BIGNUM
*a
, BN_ULONG w
);
471 BN_ULONG
BN_get_word(const BIGNUM
*a
);
473 int BN_cmp(const BIGNUM
*a
, const BIGNUM
*b
);
474 void BN_free(BIGNUM
*a
);
475 int BN_is_bit_set(const BIGNUM
*a
, int n
);
476 int BN_lshift(BIGNUM
*r
, const BIGNUM
*a
, int n
);
477 int BN_lshift1(BIGNUM
*r
, const BIGNUM
*a
);
478 int BN_exp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,BN_CTX
*ctx
);
480 int BN_mod_exp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
481 const BIGNUM
*m
,BN_CTX
*ctx
);
482 int BN_mod_exp_mont(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
483 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*m_ctx
);
484 int BN_mod_exp_mont_consttime(BIGNUM
*rr
, const BIGNUM
*a
, const BIGNUM
*p
,
485 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*in_mont
);
486 int BN_mod_exp_mont_word(BIGNUM
*r
, BN_ULONG a
, const BIGNUM
*p
,
487 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*m_ctx
);
488 int BN_mod_exp2_mont(BIGNUM
*r
, const BIGNUM
*a1
, const BIGNUM
*p1
,
489 const BIGNUM
*a2
, const BIGNUM
*p2
,const BIGNUM
*m
,
490 BN_CTX
*ctx
,BN_MONT_CTX
*m_ctx
);
491 int BN_mod_exp_simple(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
492 const BIGNUM
*m
,BN_CTX
*ctx
);
494 int BN_mask_bits(BIGNUM
*a
,int n
);
495 #ifndef OPENSSL_NO_FP_API
496 int BN_print_fp(FILE *fp
, const BIGNUM
*a
);
499 int BN_print(BIO
*fp
, const BIGNUM
*a
);
501 int BN_print(void *fp
, const BIGNUM
*a
);
503 int BN_reciprocal(BIGNUM
*r
, const BIGNUM
*m
, int len
, BN_CTX
*ctx
);
504 int BN_rshift(BIGNUM
*r
, const BIGNUM
*a
, int n
);
505 int BN_rshift1(BIGNUM
*r
, const BIGNUM
*a
);
506 void BN_clear(BIGNUM
*a
);
507 BIGNUM
*BN_dup(const BIGNUM
*a
);
508 int BN_ucmp(const BIGNUM
*a
, const BIGNUM
*b
);
509 int BN_set_bit(BIGNUM
*a
, int n
);
510 int BN_clear_bit(BIGNUM
*a
, int n
);
511 char * BN_bn2hex(const BIGNUM
*a
);
512 char * BN_bn2dec(const BIGNUM
*a
);
513 int BN_hex2bn(BIGNUM
**a
, const char *str
);
514 int BN_dec2bn(BIGNUM
**a
, const char *str
);
515 int BN_asc2bn(BIGNUM
**a
, const char *str
);
516 int BN_gcd(BIGNUM
*r
,const BIGNUM
*a
,const BIGNUM
*b
,BN_CTX
*ctx
);
517 int BN_kronecker(const BIGNUM
*a
,const BIGNUM
*b
,BN_CTX
*ctx
); /* returns -2 for error */
518 BIGNUM
*BN_mod_inverse(BIGNUM
*ret
,
519 const BIGNUM
*a
, const BIGNUM
*n
,BN_CTX
*ctx
);
520 BIGNUM
*BN_mod_sqrt(BIGNUM
*ret
,
521 const BIGNUM
*a
, const BIGNUM
*n
,BN_CTX
*ctx
);
523 void BN_consttime_swap(BN_ULONG swap
, BIGNUM
*a
, BIGNUM
*b
, int nwords
);
525 /* Deprecated versions */
526 #ifndef OPENSSL_NO_DEPRECATED
527 BIGNUM
*BN_generate_prime(BIGNUM
*ret
,int bits
,int safe
,
528 const BIGNUM
*add
, const BIGNUM
*rem
,
529 void (*callback
)(int,int,void *),void *cb_arg
);
530 int BN_is_prime(const BIGNUM
*p
,int nchecks
,
531 void (*callback
)(int,int,void *),
532 BN_CTX
*ctx
,void *cb_arg
);
533 int BN_is_prime_fasttest(const BIGNUM
*p
,int nchecks
,
534 void (*callback
)(int,int,void *),BN_CTX
*ctx
,void *cb_arg
,
535 int do_trial_division
);
536 #endif /* !defined(OPENSSL_NO_DEPRECATED) */
539 int BN_generate_prime_ex(BIGNUM
*ret
,int bits
,int safe
, const BIGNUM
*add
,
540 const BIGNUM
*rem
, BN_GENCB
*cb
);
541 int BN_is_prime_ex(const BIGNUM
*p
,int nchecks
, BN_CTX
*ctx
, BN_GENCB
*cb
);
542 int BN_is_prime_fasttest_ex(const BIGNUM
*p
,int nchecks
, BN_CTX
*ctx
,
543 int do_trial_division
, BN_GENCB
*cb
);
545 int BN_X931_generate_Xpq(BIGNUM
*Xp
, BIGNUM
*Xq
, int nbits
, BN_CTX
*ctx
);
547 int BN_X931_derive_prime_ex(BIGNUM
*p
, BIGNUM
*p1
, BIGNUM
*p2
,
548 const BIGNUM
*Xp
, const BIGNUM
*Xp1
, const BIGNUM
*Xp2
,
549 const BIGNUM
*e
, BN_CTX
*ctx
, BN_GENCB
*cb
);
550 int BN_X931_generate_prime_ex(BIGNUM
*p
, BIGNUM
*p1
, BIGNUM
*p2
,
551 BIGNUM
*Xp1
, BIGNUM
*Xp2
,
553 const BIGNUM
*e
, BN_CTX
*ctx
,
556 BN_MONT_CTX
*BN_MONT_CTX_new(void );
557 void BN_MONT_CTX_init(BN_MONT_CTX
*ctx
);
558 int BN_mod_mul_montgomery(BIGNUM
*r
,const BIGNUM
*a
,const BIGNUM
*b
,
559 BN_MONT_CTX
*mont
, BN_CTX
*ctx
);
560 #define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
561 (r),(a),&((mont)->RR),(mont),(ctx))
562 int BN_from_montgomery(BIGNUM
*r
,const BIGNUM
*a
,
563 BN_MONT_CTX
*mont
, BN_CTX
*ctx
);
564 void BN_MONT_CTX_free(BN_MONT_CTX
*mont
);
565 int BN_MONT_CTX_set(BN_MONT_CTX
*mont
,const BIGNUM
*mod
,BN_CTX
*ctx
);
566 BN_MONT_CTX
*BN_MONT_CTX_copy(BN_MONT_CTX
*to
,BN_MONT_CTX
*from
);
567 BN_MONT_CTX
*BN_MONT_CTX_set_locked(BN_MONT_CTX
**pmont
, int lock
,
568 const BIGNUM
*mod
, BN_CTX
*ctx
);
570 /* BN_BLINDING flags */
571 #define BN_BLINDING_NO_UPDATE 0x00000001
572 #define BN_BLINDING_NO_RECREATE 0x00000002
574 BN_BLINDING
*BN_BLINDING_new(const BIGNUM
*A
, const BIGNUM
*Ai
, BIGNUM
*mod
);
575 void BN_BLINDING_free(BN_BLINDING
*b
);
576 int BN_BLINDING_update(BN_BLINDING
*b
,BN_CTX
*ctx
);
577 int BN_BLINDING_convert(BIGNUM
*n
, BN_BLINDING
*b
, BN_CTX
*ctx
);
578 int BN_BLINDING_invert(BIGNUM
*n
, BN_BLINDING
*b
, BN_CTX
*ctx
);
579 int BN_BLINDING_convert_ex(BIGNUM
*n
, BIGNUM
*r
, BN_BLINDING
*b
, BN_CTX
*);
580 int BN_BLINDING_invert_ex(BIGNUM
*n
, const BIGNUM
*r
, BN_BLINDING
*b
, BN_CTX
*);
581 #ifndef OPENSSL_NO_DEPRECATED
582 unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING
*);
583 void BN_BLINDING_set_thread_id(BN_BLINDING
*, unsigned long);
585 CRYPTO_THREADID
*BN_BLINDING_thread_id(BN_BLINDING
*);
586 unsigned long BN_BLINDING_get_flags(const BN_BLINDING
*);
587 void BN_BLINDING_set_flags(BN_BLINDING
*, unsigned long);
588 BN_BLINDING
*BN_BLINDING_create_param(BN_BLINDING
*b
,
589 const BIGNUM
*e
, BIGNUM
*m
, BN_CTX
*ctx
,
590 int (*bn_mod_exp
)(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
591 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*m_ctx
),
594 #ifndef OPENSSL_NO_DEPRECATED
595 void BN_set_params(int mul
,int high
,int low
,int mont
);
596 int BN_get_params(int which
); /* 0, mul, 1 high, 2 low, 3 mont */
599 void BN_RECP_CTX_init(BN_RECP_CTX
*recp
);
600 BN_RECP_CTX
*BN_RECP_CTX_new(void);
601 void BN_RECP_CTX_free(BN_RECP_CTX
*recp
);
602 int BN_RECP_CTX_set(BN_RECP_CTX
*recp
,const BIGNUM
*rdiv
,BN_CTX
*ctx
);
603 int BN_mod_mul_reciprocal(BIGNUM
*r
, const BIGNUM
*x
, const BIGNUM
*y
,
604 BN_RECP_CTX
*recp
,BN_CTX
*ctx
);
605 int BN_mod_exp_recp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
606 const BIGNUM
*m
, BN_CTX
*ctx
);
607 int BN_div_recp(BIGNUM
*dv
, BIGNUM
*rem
, const BIGNUM
*m
,
608 BN_RECP_CTX
*recp
, BN_CTX
*ctx
);
610 #ifndef OPENSSL_NO_EC2M
612 /* Functions for arithmetic over binary polynomials represented by BIGNUMs.
614 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
617 * Note that input arguments are not const so that their bit arrays can
618 * be expanded to the appropriate size if needed.
621 int BN_GF2m_add(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
); /*r = a + b*/
622 #define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
623 int BN_GF2m_mod(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
); /*r=a mod p*/
624 int BN_GF2m_mod_mul(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
625 const BIGNUM
*p
, BN_CTX
*ctx
); /* r = (a * b) mod p */
626 int BN_GF2m_mod_sqr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
627 BN_CTX
*ctx
); /* r = (a * a) mod p */
628 int BN_GF2m_mod_inv(BIGNUM
*r
, const BIGNUM
*b
, const BIGNUM
*p
,
629 BN_CTX
*ctx
); /* r = (1 / b) mod p */
630 int BN_GF2m_mod_div(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
631 const BIGNUM
*p
, BN_CTX
*ctx
); /* r = (a / b) mod p */
632 int BN_GF2m_mod_exp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
633 const BIGNUM
*p
, BN_CTX
*ctx
); /* r = (a ^ b) mod p */
634 int BN_GF2m_mod_sqrt(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
635 BN_CTX
*ctx
); /* r = sqrt(a) mod p */
636 int BN_GF2m_mod_solve_quad(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
637 BN_CTX
*ctx
); /* r^2 + r = a mod p */
638 #define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
639 /* Some functions allow for representation of the irreducible polynomials
640 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
641 * t^p[0] + t^p[1] + ... + t^p[k]
642 * where m = p[0] > p[1] > ... > p[k] = 0.
644 int BN_GF2m_mod_arr(BIGNUM
*r
, const BIGNUM
*a
, const int p
[]);
646 int BN_GF2m_mod_mul_arr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
647 const int p
[], BN_CTX
*ctx
); /* r = (a * b) mod p */
648 int BN_GF2m_mod_sqr_arr(BIGNUM
*r
, const BIGNUM
*a
, const int p
[],
649 BN_CTX
*ctx
); /* r = (a * a) mod p */
650 int BN_GF2m_mod_inv_arr(BIGNUM
*r
, const BIGNUM
*b
, const int p
[],
651 BN_CTX
*ctx
); /* r = (1 / b) mod p */
652 int BN_GF2m_mod_div_arr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
653 const int p
[], BN_CTX
*ctx
); /* r = (a / b) mod p */
654 int BN_GF2m_mod_exp_arr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
655 const int p
[], BN_CTX
*ctx
); /* r = (a ^ b) mod p */
656 int BN_GF2m_mod_sqrt_arr(BIGNUM
*r
, const BIGNUM
*a
,
657 const int p
[], BN_CTX
*ctx
); /* r = sqrt(a) mod p */
658 int BN_GF2m_mod_solve_quad_arr(BIGNUM
*r
, const BIGNUM
*a
,
659 const int p
[], BN_CTX
*ctx
); /* r^2 + r = a mod p */
660 int BN_GF2m_poly2arr(const BIGNUM
*a
, int p
[], int max
);
661 int BN_GF2m_arr2poly(const int p
[], BIGNUM
*a
);
665 /* faster mod functions for the 'NIST primes'
667 int BN_nist_mod_192(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
);
668 int BN_nist_mod_224(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
);
669 int BN_nist_mod_256(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
);
670 int BN_nist_mod_384(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
);
671 int BN_nist_mod_521(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
);
673 const BIGNUM
*BN_get0_nist_prime_192(void);
674 const BIGNUM
*BN_get0_nist_prime_224(void);
675 const BIGNUM
*BN_get0_nist_prime_256(void);
676 const BIGNUM
*BN_get0_nist_prime_384(void);
677 const BIGNUM
*BN_get0_nist_prime_521(void);
679 /* library internal functions */
681 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
682 (a):bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2))
683 #define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
684 BIGNUM
*bn_expand2(BIGNUM
*a
, int words
);
685 #ifndef OPENSSL_NO_DEPRECATED
686 BIGNUM
*bn_dup_expand(const BIGNUM
*a
, int words
); /* unused */
689 /* Bignum consistency macros
690 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
691 * bignum data after direct manipulations on the data. There is also an
692 * "internal" macro, bn_check_top(), for verifying that there are no leading
693 * zeroes. Unfortunately, some auditing is required due to the fact that
694 * bn_fix_top() has become an overabused duct-tape because bignum data is
695 * occasionally passed around in an inconsistent state. So the following
696 * changes have been made to sort this out;
697 * - bn_fix_top()s implementation has been moved to bn_correct_top()
698 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
699 * bn_check_top() is as before.
700 * - if BN_DEBUG *is* defined;
701 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
702 * consistent. (ed: only if BN_DEBUG_RAND is defined)
703 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
704 * The idea is to have debug builds flag up inconsistent bignums when they
705 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
706 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
707 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
708 * was not appropriate, we convert it permanently to bn_check_top() and track
709 * down the cause of the bug. Eventually, no internal code should be using the
710 * bn_fix_top() macro. External applications and libraries should try this with
711 * their own code too, both in terms of building against the openssl headers
712 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
713 * defined. This not only improves external code, it provides more test
714 * coverage for openssl's own code.
719 /* We only need assert() when debugging */
723 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
724 #ifndef RAND_pseudo_bytes
725 int RAND_pseudo_bytes(unsigned char *buf
,int num
);
726 #define BN_DEBUG_TRIX
728 #define bn_pollute(a) \
730 const BIGNUM *_bnum1 = (a); \
731 if(_bnum1->top < _bnum1->dmax) { \
732 unsigned char _tmp_char; \
733 /* We cast away const without the compiler knowing, any \
734 * *genuinely* constant variables that aren't mutable \
735 * wouldn't be constructed with top!=dmax. */ \
736 BN_ULONG *_not_const; \
737 memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
738 RAND_pseudo_bytes(&_tmp_char, 1); \
739 memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
740 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
744 #undef RAND_pseudo_bytes
747 #define bn_pollute(a)
749 #define bn_check_top(a) \
751 const BIGNUM *_bnum2 = (a); \
752 if (_bnum2 != NULL) { \
753 assert((_bnum2->top == 0) || \
754 (_bnum2->d[_bnum2->top - 1] != 0)); \
755 bn_pollute(_bnum2); \
759 #define bn_fix_top(a) bn_check_top(a)
761 #define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
762 #define bn_wcheck_size(bn, words) \
764 const BIGNUM *_bnum2 = (bn); \
765 assert((words) <= (_bnum2)->dmax && (words) >= (_bnum2)->top); \
766 /* avoid unused variable warning with NDEBUG */ \
770 #else /* !BN_DEBUG */
772 #define bn_pollute(a)
773 #define bn_check_top(a)
774 #define bn_fix_top(a) bn_correct_top(a)
775 #define bn_check_size(bn, bits)
776 #define bn_wcheck_size(bn, words)
780 #define bn_correct_top(a) \
783 int tmp_top = (a)->top; \
786 for (ftl= &((a)->d[tmp_top-1]); tmp_top > 0; tmp_top--) \
787 if (*(ftl--)) break; \
788 (a)->top = tmp_top; \
793 BN_ULONG
bn_mul_add_words(BN_ULONG
*rp
, const BN_ULONG
*ap
, int num
, BN_ULONG w
);
794 BN_ULONG
bn_mul_words(BN_ULONG
*rp
, const BN_ULONG
*ap
, int num
, BN_ULONG w
);
795 void bn_sqr_words(BN_ULONG
*rp
, const BN_ULONG
*ap
, int num
);
796 BN_ULONG
bn_div_words(BN_ULONG h
, BN_ULONG l
, BN_ULONG d
);
797 BN_ULONG
bn_add_words(BN_ULONG
*rp
, const BN_ULONG
*ap
, const BN_ULONG
*bp
,int num
);
798 BN_ULONG
bn_sub_words(BN_ULONG
*rp
, const BN_ULONG
*ap
, const BN_ULONG
*bp
,int num
);
800 /* Primes from RFC 2409 */
801 BIGNUM
*get_rfc2409_prime_768(BIGNUM
*bn
);
802 BIGNUM
*get_rfc2409_prime_1024(BIGNUM
*bn
);
804 /* Primes from RFC 3526 */
805 BIGNUM
*get_rfc3526_prime_1536(BIGNUM
*bn
);
806 BIGNUM
*get_rfc3526_prime_2048(BIGNUM
*bn
);
807 BIGNUM
*get_rfc3526_prime_3072(BIGNUM
*bn
);
808 BIGNUM
*get_rfc3526_prime_4096(BIGNUM
*bn
);
809 BIGNUM
*get_rfc3526_prime_6144(BIGNUM
*bn
);
810 BIGNUM
*get_rfc3526_prime_8192(BIGNUM
*bn
);
812 int BN_bntest_rand(BIGNUM
*rnd
, int bits
, int top
,int bottom
);
814 /* BEGIN ERROR CODES */
815 /* The following lines are auto generated by the script mkerr.pl. Any changes
816 * made after this point may be overwritten when the script is next run.
818 void ERR_load_BN_strings(void);
820 /* Error codes for the BN functions. */
822 /* Function codes. */
823 #define BN_F_BNRAND 127
824 #define BN_F_BN_BLINDING_CONVERT_EX 100
825 #define BN_F_BN_BLINDING_CREATE_PARAM 128
826 #define BN_F_BN_BLINDING_INVERT_EX 101
827 #define BN_F_BN_BLINDING_NEW 102
828 #define BN_F_BN_BLINDING_UPDATE 103
829 #define BN_F_BN_BN2DEC 104
830 #define BN_F_BN_BN2HEX 105
831 #define BN_F_BN_CTX_GET 116
832 #define BN_F_BN_CTX_NEW 106
833 #define BN_F_BN_CTX_START 129
834 #define BN_F_BN_DIV 107
835 #define BN_F_BN_DIV_NO_BRANCH 138
836 #define BN_F_BN_DIV_RECP 130
837 #define BN_F_BN_EXP 123
838 #define BN_F_BN_EXPAND2 108
839 #define BN_F_BN_EXPAND_INTERNAL 120
840 #define BN_F_BN_GF2M_MOD 131
841 #define BN_F_BN_GF2M_MOD_EXP 132
842 #define BN_F_BN_GF2M_MOD_MUL 133
843 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD 134
844 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 135
845 #define BN_F_BN_GF2M_MOD_SQR 136
846 #define BN_F_BN_GF2M_MOD_SQRT 137
847 #define BN_F_BN_MOD_EXP2_MONT 118
848 #define BN_F_BN_MOD_EXP_MONT 109
849 #define BN_F_BN_MOD_EXP_MONT_CONSTTIME 124
850 #define BN_F_BN_MOD_EXP_MONT_WORD 117
851 #define BN_F_BN_MOD_EXP_RECP 125
852 #define BN_F_BN_MOD_EXP_SIMPLE 126
853 #define BN_F_BN_MOD_INVERSE 110
854 #define BN_F_BN_MOD_INVERSE_NO_BRANCH 139
855 #define BN_F_BN_MOD_LSHIFT_QUICK 119
856 #define BN_F_BN_MOD_MUL_RECIPROCAL 111
857 #define BN_F_BN_MOD_SQRT 121
858 #define BN_F_BN_MPI2BN 112
859 #define BN_F_BN_NEW 113
860 #define BN_F_BN_RAND 114
861 #define BN_F_BN_RAND_RANGE 122
862 #define BN_F_BN_USUB 115
865 #define BN_R_ARG2_LT_ARG3 100
866 #define BN_R_BAD_RECIPROCAL 101
867 #define BN_R_BIGNUM_TOO_LONG 114
868 #define BN_R_CALLED_WITH_EVEN_MODULUS 102
869 #define BN_R_DIV_BY_ZERO 103
870 #define BN_R_ENCODING_ERROR 104
871 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
872 #define BN_R_INPUT_NOT_REDUCED 110
873 #define BN_R_INVALID_LENGTH 106
874 #define BN_R_INVALID_RANGE 115
875 #define BN_R_NOT_A_SQUARE 111
876 #define BN_R_NOT_INITIALIZED 107
877 #define BN_R_NO_INVERSE 108
878 #define BN_R_NO_SOLUTION 116
879 #define BN_R_P_IS_NOT_PRIME 112
880 #define BN_R_TOO_MANY_ITERATIONS 113
881 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109