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>
138 /* These preprocessor symbols control various aspects of the bignum headers and
139 * library code. They're not defined by any "normal" configuration, as they are
140 * intended for development and testing purposes. NB: defining all three can be
141 * useful for debugging application code as well as openssl itself.
143 * BN_DEBUG - turn on various debugging alterations to the bignum code
144 * BN_DEBUG_RAND - uses random poisoning of unused words to trip up
145 * mismanagement of bignum internals. You must also define BN_DEBUG.
147 /* #define BN_DEBUG */
148 /* #define BN_DEBUG_RAND */
150 #ifndef OPENSSL_SMALL_FOOTPRINT
156 /* This next option uses the C libraries (2 word)/(1 word) function.
157 * If it is not defined, I use my C version (which is slower).
158 * The reason for this flag is that when the particular C compiler
159 * library routine is used, and the library is linked with a different
160 * compiler, the library is missing. This mostly happens when the
161 * library is built with gcc and then linked using normal cc. This would
162 * be a common occurrence because gcc normally produces code that is
163 * 2 times faster than system compilers for the big number stuff.
164 * For machines with only one compiler (or shared libraries), this should
165 * be on. Again this in only really a problem on machines
166 * using "long long's", are 32bit, and are not using my assembler code. */
167 #if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
168 defined(OPENSSL_SYS_WIN32) || defined(linux)
174 /* assuming long is 64bit - this is the DEC Alpha
175 * unsigned long long is only 64 bits :-(, don't define
176 * BN_LLONG for the DEC Alpha */
177 #ifdef SIXTY_FOUR_BIT_LONG
178 #define BN_ULLONG unsigned long long
179 #define BN_ULONG unsigned long
185 #define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
186 #define BN_MASK2 (0xffffffffffffffffL)
187 #define BN_MASK2l (0xffffffffL)
188 #define BN_MASK2h (0xffffffff00000000L)
189 #define BN_MASK2h1 (0xffffffff80000000L)
190 #define BN_TBIT (0x8000000000000000L)
191 #define BN_DEC_CONV (10000000000000000000UL)
192 #define BN_DEC_FMT1 "%lu"
193 #define BN_DEC_FMT2 "%019lu"
194 #define BN_DEC_NUM 19
195 #define BN_HEX_FMT1 "%lX"
196 #define BN_HEX_FMT2 "%016lX"
199 /* This is where the long long data type is 64 bits, but long is 32.
200 * For machines where there are 64bit registers, this is the mode to use.
201 * IRIX, on R4000 and above should use this mode, along with the relevant
202 * assembler code :-). Do NOT define BN_LLONG.
204 #ifdef SIXTY_FOUR_BIT
207 #define BN_ULONG unsigned long long
208 #define BN_LONG long long
213 #define BN_MASK2 (0xffffffffffffffffLL)
214 #define BN_MASK2l (0xffffffffL)
215 #define BN_MASK2h (0xffffffff00000000LL)
216 #define BN_MASK2h1 (0xffffffff80000000LL)
217 #define BN_TBIT (0x8000000000000000LL)
218 #define BN_DEC_CONV (10000000000000000000ULL)
219 #define BN_DEC_FMT1 "%llu"
220 #define BN_DEC_FMT2 "%019llu"
221 #define BN_DEC_NUM 19
222 #define BN_HEX_FMT1 "%llX"
223 #define BN_HEX_FMT2 "%016llX"
226 #ifdef THIRTY_TWO_BIT
228 # if defined(_WIN32) && !defined(__GNUC__)
229 # define BN_ULLONG unsigned __int64
230 # define BN_MASK (0xffffffffffffffffI64)
232 # define BN_ULLONG unsigned long long
233 # define BN_MASK (0xffffffffffffffffLL)
236 #define BN_ULONG unsigned int
242 #define BN_MASK2 (0xffffffffL)
243 #define BN_MASK2l (0xffff)
244 #define BN_MASK2h1 (0xffff8000L)
245 #define BN_MASK2h (0xffff0000L)
246 #define BN_TBIT (0x80000000L)
247 #define BN_DEC_CONV (1000000000L)
248 #define BN_DEC_FMT1 "%u"
249 #define BN_DEC_FMT2 "%09u"
251 #define BN_HEX_FMT1 "%X"
252 #define BN_HEX_FMT2 "%08X"
255 #define BN_DEFAULT_BITS 1280
257 #define BN_FLG_MALLOCED 0x01
258 #define BN_FLG_STATIC_DATA 0x02
259 #define BN_FLG_EXP_CONSTTIME 0x04 /* avoid leaking exponent information through timings
260 * (BN_mod_exp_mont() will call BN_mod_exp_mont_consttime) */
261 #ifndef OPENSSL_NO_DEPRECATED
262 #define BN_FLG_FREE 0x8000 /* used for debuging */
264 #define BN_set_flags(b,n) ((b)->flags|=(n))
265 #define BN_get_flags(b,n) ((b)->flags&(n))
267 /* get a clone of a BIGNUM with changed flags, for *temporary* use only
268 * (the two BIGNUMs cannot not be used in parallel!) */
269 #define BN_with_flags(dest,b,n) ((dest)->d=(b)->d, \
270 (dest)->top=(b)->top, \
271 (dest)->dmax=(b)->dmax, \
272 (dest)->neg=(b)->neg, \
273 (dest)->flags=(((dest)->flags & BN_FLG_MALLOCED) \
274 | ((b)->flags & ~BN_FLG_MALLOCED) \
275 | BN_FLG_STATIC_DATA \
278 /* Already declared in ossl_typ.h */
280 typedef struct bignum_st BIGNUM;
281 /* Used for temp variables (declaration hidden in bn_lcl.h) */
282 typedef struct bignum_ctx BN_CTX;
283 typedef struct bn_blinding_st BN_BLINDING;
284 typedef struct bn_mont_ctx_st BN_MONT_CTX;
285 typedef struct bn_recp_ctx_st BN_RECP_CTX;
286 typedef struct bn_gencb_st BN_GENCB;
291 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */
292 int top; /* Index of last used d +1. */
293 /* The next are internal book keeping for bn_expand. */
294 int dmax; /* Size of the d array. */
295 int neg; /* one if the number is negative */
299 /* Used for montgomery multiplication */
300 struct bn_mont_ctx_st
302 int ri; /* number of bits in R */
303 BIGNUM RR; /* used to convert to montgomery form */
304 BIGNUM N; /* The modulus */
305 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
306 * (Ni is only stored for bignum algorithm) */
307 BN_ULONG n0[2];/* least significant word(s) of Ni */
311 /* Used for reciprocal division/mod functions
312 * It cannot be shared between threads
314 struct bn_recp_ctx_st
316 BIGNUM N; /* the divisor */
317 BIGNUM Nr; /* the reciprocal */
323 /* Used for slow "generation" functions. */
326 unsigned int ver; /* To handle binary (in)compatibility */
327 void *arg; /* callback-specific data */
330 /* if(ver==1) - handles old style callbacks */
331 void (*cb_1)(int, int, void *);
332 /* if(ver==2) - new callback style */
333 int (*cb_2)(int, int, BN_GENCB *);
336 /* Wrapper function to make using BN_GENCB easier, */
337 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
338 /* Macro to populate a BN_GENCB structure with an "old"-style callback */
339 #define BN_GENCB_set_old(gencb, callback, cb_arg) { \
340 BN_GENCB *tmp_gencb = (gencb); \
341 tmp_gencb->ver = 1; \
342 tmp_gencb->arg = (cb_arg); \
343 tmp_gencb->cb.cb_1 = (callback); }
344 /* Macro to populate a BN_GENCB structure with a "new"-style callback */
345 #define BN_GENCB_set(gencb, callback, cb_arg) { \
346 BN_GENCB *tmp_gencb = (gencb); \
347 tmp_gencb->ver = 2; \
348 tmp_gencb->arg = (cb_arg); \
349 tmp_gencb->cb.cb_2 = (callback); }
351 #define BN_prime_checks 0 /* default: select number of iterations
352 based on the size of the number */
354 /* number of Miller-Rabin iterations for an error rate of less than 2^-80
355 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
356 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
357 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
358 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
359 #define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
372 #define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
374 /* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
375 #define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
376 (((w) == 0) && ((a)->top == 0)))
377 #define BN_is_zero(a) ((a)->top == 0)
378 #define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
379 #define BN_is_word(a,w) (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
380 #define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
382 #define BN_one(a) (BN_set_word((a),1))
383 #define BN_zero_ex(a) \
385 BIGNUM *_tmp_bn = (a); \
389 #ifdef OPENSSL_NO_DEPRECATED
390 #define BN_zero(a) BN_zero_ex(a)
392 #define BN_zero(a) (BN_set_word((a),0))
395 const BIGNUM *BN_value_one(void);
396 char * BN_options(void);
397 BN_CTX *BN_CTX_new(void);
398 #ifndef OPENSSL_NO_DEPRECATED
399 void BN_CTX_init(BN_CTX *c);
401 void BN_CTX_free(BN_CTX *c);
402 void BN_CTX_start(BN_CTX *ctx);
403 BIGNUM *BN_CTX_get(BN_CTX *ctx);
404 void BN_CTX_end(BN_CTX *ctx);
405 int BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
406 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top,int bottom);
407 int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
408 int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);
409 int BN_num_bits(const BIGNUM *a);
410 int BN_num_bits_word(BN_ULONG);
411 BIGNUM *BN_new(void);
412 void BN_init(BIGNUM *);
413 void BN_clear_free(BIGNUM *a);
414 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
415 void BN_swap(BIGNUM *a, BIGNUM *b);
416 BIGNUM *BN_bin2bn(const unsigned char *s,int len,BIGNUM *ret);
417 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
418 BIGNUM *BN_mpi2bn(const unsigned char *s,int len,BIGNUM *ret);
419 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
420 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
421 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
422 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
423 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
424 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
425 int BN_sqr(BIGNUM *r, const BIGNUM *a,BN_CTX *ctx);
426 /** BN_set_negative sets sign of a BIGNUM
427 * \param b pointer to the BIGNUM object
428 * \param n 0 if the BIGNUM b should be positive and a value != 0 otherwise
430 void BN_set_negative(BIGNUM *b, int n);
431 /** BN_is_negative returns 1 if the BIGNUM is negative
432 * \param a pointer to the BIGNUM object
433 * \return 1 if a < 0 and 0 otherwise
435 #define BN_is_negative(a) ((a)->neg != 0)
437 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
439 #define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
440 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
441 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
442 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
443 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
444 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
445 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
446 const BIGNUM *m, BN_CTX *ctx);
447 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
448 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
449 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
450 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx);
451 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
453 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
454 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
455 int BN_mul_word(BIGNUM *a, BN_ULONG w);
456 int BN_add_word(BIGNUM *a, BN_ULONG w);
457 int BN_sub_word(BIGNUM *a, BN_ULONG w);
458 int BN_set_word(BIGNUM *a, BN_ULONG w);
459 BN_ULONG BN_get_word(const BIGNUM *a);
461 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
462 void BN_free(BIGNUM *a);
463 int BN_is_bit_set(const BIGNUM *a, int n);
464 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
465 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
466 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,BN_CTX *ctx);
468 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
469 const BIGNUM *m,BN_CTX *ctx);
470 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
471 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
472 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
473 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont);
474 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
475 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
476 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
477 const BIGNUM *a2, const BIGNUM *p2,const BIGNUM *m,
478 BN_CTX *ctx,BN_MONT_CTX *m_ctx);
479 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
480 const BIGNUM *m,BN_CTX *ctx);
482 int BN_mask_bits(BIGNUM *a,int n);
483 #ifndef OPENSSL_NO_FP_API
484 int BN_print_fp(FILE *fp, const BIGNUM *a);
487 int BN_print(BIO *fp, const BIGNUM *a);
489 int BN_print(void *fp, const BIGNUM *a);
491 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
492 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
493 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
494 void BN_clear(BIGNUM *a);
495 BIGNUM *BN_dup(const BIGNUM *a);
496 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
497 int BN_set_bit(BIGNUM *a, int n);
498 int BN_clear_bit(BIGNUM *a, int n);
499 char * BN_bn2hex(const BIGNUM *a);
500 char * BN_bn2dec(const BIGNUM *a);
501 int BN_hex2bn(BIGNUM **a, const char *str);
502 int BN_dec2bn(BIGNUM **a, const char *str);
503 int BN_asc2bn(BIGNUM **a, const char *str);
504 int BN_gcd(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx);
505 int BN_kronecker(const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx); /* returns -2 for error */
506 BIGNUM *BN_mod_inverse(BIGNUM *ret,
507 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
508 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
509 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
511 /* Deprecated versions */
512 #ifndef OPENSSL_NO_DEPRECATED
513 BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,
514 const BIGNUM *add, const BIGNUM *rem,
515 void (*callback)(int,int,void *),void *cb_arg);
516 int BN_is_prime(const BIGNUM *p,int nchecks,
517 void (*callback)(int,int,void *),
518 BN_CTX *ctx,void *cb_arg);
519 int BN_is_prime_fasttest(const BIGNUM *p,int nchecks,
520 void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg,
521 int do_trial_division);
522 #endif /* !defined(OPENSSL_NO_DEPRECATED) */
525 int BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add,
526 const BIGNUM *rem, BN_GENCB *cb);
527 int BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb);
528 int BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx,
529 int do_trial_division, BN_GENCB *cb);
531 BN_MONT_CTX *BN_MONT_CTX_new(void );
532 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
533 int BN_mod_mul_montgomery(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,
534 BN_MONT_CTX *mont, BN_CTX *ctx);
535 #define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
536 (r),(a),&((mont)->RR),(mont),(ctx))
537 int BN_from_montgomery(BIGNUM *r,const BIGNUM *a,
538 BN_MONT_CTX *mont, BN_CTX *ctx);
539 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
540 int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *mod,BN_CTX *ctx);
541 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,BN_MONT_CTX *from);
542 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
543 const BIGNUM *mod, BN_CTX *ctx);
545 /* BN_BLINDING flags */
546 #define BN_BLINDING_NO_UPDATE 0x00000001
547 #define BN_BLINDING_NO_RECREATE 0x00000002
549 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
550 void BN_BLINDING_free(BN_BLINDING *b);
551 int BN_BLINDING_update(BN_BLINDING *b,BN_CTX *ctx);
552 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
553 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
554 int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
555 int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b, BN_CTX *);
556 unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
557 void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
558 void *BN_BLINDING_get_thread_idptr(const BN_BLINDING *);
559 void BN_BLINDING_set_thread_idptr(BN_BLINDING *, void *);
560 unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
561 void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
562 BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
563 const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
564 int (*bn_mod_exp)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
565 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx),
568 #ifndef OPENSSL_NO_DEPRECATED
569 void BN_set_params(int mul,int high,int low,int mont);
570 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
573 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
574 BN_RECP_CTX *BN_RECP_CTX_new(void);
575 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
576 int BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx);
577 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
578 BN_RECP_CTX *recp,BN_CTX *ctx);
579 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
580 const BIGNUM *m, BN_CTX *ctx);
581 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
582 BN_RECP_CTX *recp, BN_CTX *ctx);
584 /* Functions for arithmetic over binary polynomials represented by BIGNUMs.
586 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
589 * Note that input arguments are not const so that their bit arrays can
590 * be expanded to the appropriate size if needed.
593 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /*r = a + b*/
594 #define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
595 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /*r=a mod p*/
596 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
597 const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
598 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
599 BN_CTX *ctx); /* r = (a * a) mod p */
600 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p,
601 BN_CTX *ctx); /* r = (1 / b) mod p */
602 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
603 const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
604 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
605 const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */
606 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
607 BN_CTX *ctx); /* r = sqrt(a) mod p */
608 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
609 BN_CTX *ctx); /* r^2 + r = a mod p */
610 #define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
611 /* Some functions allow for representation of the irreducible polynomials
612 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
613 * t^p[0] + t^p[1] + ... + t^p[k]
614 * where m = p[0] > p[1] > ... > p[k] = 0.
616 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
618 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
619 const int p[], BN_CTX *ctx); /* r = (a * b) mod p */
620 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
621 BN_CTX *ctx); /* r = (a * a) mod p */
622 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
623 BN_CTX *ctx); /* r = (1 / b) mod p */
624 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
625 const int p[], BN_CTX *ctx); /* r = (a / b) mod p */
626 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
627 const int p[], BN_CTX *ctx); /* r = (a ^ b) mod p */
628 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
629 const int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
630 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
631 const int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
632 int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max);
633 int BN_GF2m_arr2poly(const int p[], BIGNUM *a);
635 /* faster mod functions for the 'NIST primes'
637 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
638 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
639 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
640 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
641 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
643 const BIGNUM *BN_get0_nist_prime_192(void);
644 const BIGNUM *BN_get0_nist_prime_224(void);
645 const BIGNUM *BN_get0_nist_prime_256(void);
646 const BIGNUM *BN_get0_nist_prime_384(void);
647 const BIGNUM *BN_get0_nist_prime_521(void);
649 /* library internal functions */
651 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
652 (a):bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2))
653 #define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
654 BIGNUM *bn_expand2(BIGNUM *a, int words);
655 #ifndef OPENSSL_NO_DEPRECATED
656 BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
659 /* Bignum consistency macros
660 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
661 * bignum data after direct manipulations on the data. There is also an
662 * "internal" macro, bn_check_top(), for verifying that there are no leading
663 * zeroes. Unfortunately, some auditing is required due to the fact that
664 * bn_fix_top() has become an overabused duct-tape because bignum data is
665 * occasionally passed around in an inconsistent state. So the following
666 * changes have been made to sort this out;
667 * - bn_fix_top()s implementation has been moved to bn_correct_top()
668 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
669 * bn_check_top() is as before.
670 * - if BN_DEBUG *is* defined;
671 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
672 * consistent. (ed: only if BN_DEBUG_RAND is defined)
673 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
674 * The idea is to have debug builds flag up inconsistent bignums when they
675 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
676 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
677 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
678 * was not appropriate, we convert it permanently to bn_check_top() and track
679 * down the cause of the bug. Eventually, no internal code should be using the
680 * bn_fix_top() macro. External applications and libraries should try this with
681 * their own code too, both in terms of building against the openssl headers
682 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
683 * defined. This not only improves external code, it provides more test
684 * coverage for openssl's own code.
689 /* We only need assert() when debugging */
693 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
694 #ifndef RAND_pseudo_bytes
695 int RAND_pseudo_bytes(unsigned char *buf,int num);
696 #define BN_DEBUG_TRIX
698 #define bn_pollute(a) \
700 const BIGNUM *_bnum1 = (a); \
701 if(_bnum1->top < _bnum1->dmax) { \
702 unsigned char _tmp_char; \
703 /* We cast away const without the compiler knowing, any \
704 * *genuinely* constant variables that aren't mutable \
705 * wouldn't be constructed with top!=dmax. */ \
706 BN_ULONG *_not_const; \
707 memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
708 RAND_pseudo_bytes(&_tmp_char, 1); \
709 memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
710 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
714 #undef RAND_pseudo_bytes
717 #define bn_pollute(a)
719 #define bn_check_top(a) \
721 const BIGNUM *_bnum2 = (a); \
722 if (_bnum2 != NULL) { \
723 assert((_bnum2->top == 0) || \
724 (_bnum2->d[_bnum2->top - 1] != 0)); \
725 bn_pollute(_bnum2); \
729 #define bn_fix_top(a) bn_check_top(a)
731 #else /* !BN_DEBUG */
733 #define bn_pollute(a)
734 #define bn_check_top(a)
735 #define bn_fix_top(a) bn_correct_top(a)
739 #define bn_correct_top(a) \
744 for (ftl= &((a)->d[(a)->top-1]); (a)->top > 0; (a)->top--) \
745 if (*(ftl--)) break; \
750 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
751 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
752 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
753 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
754 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
755 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
757 /* Primes from RFC 2409 */
758 BIGNUM *get_rfc2409_prime_768(BIGNUM *bn);
759 BIGNUM *get_rfc2409_prime_1024(BIGNUM *bn);
761 /* Primes from RFC 3526 */
762 BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn);
763 BIGNUM *get_rfc3526_prime_2048(BIGNUM *bn);
764 BIGNUM *get_rfc3526_prime_3072(BIGNUM *bn);
765 BIGNUM *get_rfc3526_prime_4096(BIGNUM *bn);
766 BIGNUM *get_rfc3526_prime_6144(BIGNUM *bn);
767 BIGNUM *get_rfc3526_prime_8192(BIGNUM *bn);
769 int BN_bntest_rand(BIGNUM *rnd, int bits, int top,int bottom);
771 /* BEGIN ERROR CODES */
772 /* The following lines are auto generated by the script mkerr.pl. Any changes
773 * made after this point may be overwritten when the script is next run.
775 void ERR_load_BN_strings(void);
777 /* Error codes for the BN functions. */
779 /* Function codes. */
780 #define BN_F_BNRAND 127
781 #define BN_F_BN_BLINDING_CONVERT_EX 100
782 #define BN_F_BN_BLINDING_CREATE_PARAM 128
783 #define BN_F_BN_BLINDING_INVERT_EX 101
784 #define BN_F_BN_BLINDING_NEW 102
785 #define BN_F_BN_BLINDING_UPDATE 103
786 #define BN_F_BN_BN2DEC 104
787 #define BN_F_BN_BN2HEX 105
788 #define BN_F_BN_CTX_GET 116
789 #define BN_F_BN_CTX_NEW 106
790 #define BN_F_BN_CTX_START 129
791 #define BN_F_BN_DIV 107
792 #define BN_F_BN_DIV_RECP 130
793 #define BN_F_BN_EXP 123
794 #define BN_F_BN_EXPAND2 108
795 #define BN_F_BN_EXPAND_INTERNAL 120
796 #define BN_F_BN_GF2M_MOD 131
797 #define BN_F_BN_GF2M_MOD_EXP 132
798 #define BN_F_BN_GF2M_MOD_MUL 133
799 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD 134
800 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 135
801 #define BN_F_BN_GF2M_MOD_SQR 136
802 #define BN_F_BN_GF2M_MOD_SQRT 137
803 #define BN_F_BN_MOD_EXP2_MONT 118
804 #define BN_F_BN_MOD_EXP_MONT 109
805 #define BN_F_BN_MOD_EXP_MONT_CONSTTIME 124
806 #define BN_F_BN_MOD_EXP_MONT_WORD 117
807 #define BN_F_BN_MOD_EXP_RECP 125
808 #define BN_F_BN_MOD_EXP_SIMPLE 126
809 #define BN_F_BN_MOD_INVERSE 110
810 #define BN_F_BN_MOD_LSHIFT_QUICK 119
811 #define BN_F_BN_MOD_MUL_RECIPROCAL 111
812 #define BN_F_BN_MOD_SQRT 121
813 #define BN_F_BN_MPI2BN 112
814 #define BN_F_BN_NEW 113
815 #define BN_F_BN_RAND 114
816 #define BN_F_BN_RAND_RANGE 122
817 #define BN_F_BN_USUB 115
820 #define BN_R_ARG2_LT_ARG3 100
821 #define BN_R_BAD_RECIPROCAL 101
822 #define BN_R_BIGNUM_TOO_LONG 114
823 #define BN_R_CALLED_WITH_EVEN_MODULUS 102
824 #define BN_R_DIV_BY_ZERO 103
825 #define BN_R_ENCODING_ERROR 104
826 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
827 #define BN_R_INPUT_NOT_REDUCED 110
828 #define BN_R_INVALID_LENGTH 106
829 #define BN_R_INVALID_RANGE 115
830 #define BN_R_NOT_A_SQUARE 111
831 #define BN_R_NOT_INITIALIZED 107
832 #define BN_R_NO_INVERSE 108
833 #define BN_R_NO_SOLUTION 116
834 #define BN_R_P_IS_NOT_PRIME 112
835 #define BN_R_TOO_MANY_ITERATIONS 113
836 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109