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