2 /* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
58 /* ====================================================================
59 * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved.
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
87 * 6. Redistributions of any form whatsoever must retain the following
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
111 /* ====================================================================
112 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
114 * Portions of the attached software ("Contribution") are developed by
115 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
117 * The Contribution is licensed pursuant to the Eric Young open source
118 * license provided above.
120 * The binary polynomial arithmetic software is originally written by
121 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
128 # include <openssl/e_os2.h>
129 # ifndef OPENSSL_NO_FP_API
130 # include <stdio.h> /* FILE */
132 # include <openssl/ossl_typ.h>
133 # include <openssl/crypto.h>
140 * These preprocessor symbols control various aspects of the bignum headers
141 * and library code. They're not defined by any "normal" configuration, as
142 * they are intended for development and testing purposes. NB: defining all
143 * three can be useful for debugging application code as well as openssl
144 * itself. BN_DEBUG - turn on various debugging alterations to the bignum
145 * code BN_DEBUG_RAND - uses random poisoning of unused words to trip up
146 * mismanagement of bignum internals. You must also define BN_DEBUG.
148 /* #define BN_DEBUG */
149 /* #define BN_DEBUG_RAND */
151 # ifndef OPENSSL_SMALL_FOOTPRINT
152 # define BN_MUL_COMBA
153 # define BN_SQR_COMBA
154 # define BN_RECURSION
158 * This next option uses the C libraries (2 word)/(1 word) function. If it is
159 * not defined, I use my C version (which is slower). The reason for this
160 * flag is that when the particular C compiler library routine is used, and
161 * the library is linked with a different compiler, the library is missing.
162 * This mostly happens when the library is built with gcc and then linked
163 * using normal cc. This would be a common occurrence because gcc normally
164 * produces code that is 2 times faster than system compilers for the big
165 * number stuff. For machines with only one compiler (or shared libraries),
166 * this should be on. Again this in only really a problem on machines using
167 * "long long's", are 32bit, and are not using my assembler code.
169 # if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
170 defined(OPENSSL_SYS_WIN32) || defined(linux)
177 * assuming long is 64bit - this is the DEC Alpha unsigned long long is only
178 * 64 bits :-(, don't define BN_LLONG for the DEC Alpha
180 # ifdef SIXTY_FOUR_BIT_LONG
181 # define BN_ULLONG unsigned long long
182 # define BN_ULONG unsigned long
183 # define BN_LONG long
188 # define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
189 # define BN_MASK2 (0xffffffffffffffffL)
190 # define BN_MASK2l (0xffffffffL)
191 # define BN_MASK2h (0xffffffff00000000L)
192 # define BN_MASK2h1 (0xffffffff80000000L)
193 # define BN_TBIT (0x8000000000000000L)
194 # define BN_DEC_CONV (10000000000000000000UL)
195 # define BN_DEC_FMT1 "%lu"
196 # define BN_DEC_FMT2 "%019lu"
197 # define BN_DEC_NUM 19
198 # define BN_HEX_FMT1 "%lX"
199 # define BN_HEX_FMT2 "%016lX"
203 * This is where the long long data type is 64 bits, but long is 32. For
204 * machines where there are 64bit registers, this is the mode to use. IRIX,
205 * on R4000 and above should use this mode, along with the relevant assembler
206 * code :-). Do NOT define BN_LLONG.
208 # ifdef SIXTY_FOUR_BIT
211 # define BN_ULONG unsigned long long
212 # define BN_LONG long long
217 # define BN_MASK2 (0xffffffffffffffffLL)
218 # define BN_MASK2l (0xffffffffL)
219 # define BN_MASK2h (0xffffffff00000000LL)
220 # define BN_MASK2h1 (0xffffffff80000000LL)
221 # define BN_TBIT (0x8000000000000000LL)
222 # define BN_DEC_CONV (10000000000000000000ULL)
223 # define BN_DEC_FMT1 "%llu"
224 # define BN_DEC_FMT2 "%019llu"
225 # define BN_DEC_NUM 19
226 # define BN_HEX_FMT1 "%llX"
227 # define BN_HEX_FMT2 "%016llX"
230 # ifdef THIRTY_TWO_BIT
232 # if defined(_WIN32) && !defined(__GNUC__)
233 # define BN_ULLONG unsigned __int64
234 # define BN_MASK (0xffffffffffffffffI64)
236 # define BN_ULLONG unsigned long long
237 # define BN_MASK (0xffffffffffffffffLL)
240 # define BN_ULONG unsigned int
246 # define BN_MASK2 (0xffffffffL)
247 # define BN_MASK2l (0xffff)
248 # define BN_MASK2h1 (0xffff8000L)
249 # define BN_MASK2h (0xffff0000L)
250 # define BN_TBIT (0x80000000L)
251 # define BN_DEC_CONV (1000000000L)
252 # define BN_DEC_FMT1 "%u"
253 # define BN_DEC_FMT2 "%09u"
254 # define BN_DEC_NUM 9
255 # define BN_HEX_FMT1 "%X"
256 # define BN_HEX_FMT2 "%08X"
260 * 2011-02-22 SMS. In various places, a size_t variable or a type cast to
261 * size_t was used to perform integer-only operations on pointers. This
262 * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t
263 * is still only 32 bits. What's needed in these cases is an integer type
264 * with the same size as a pointer, which size_t is not certain to be. The
265 * only fix here is VMS-specific.
267 # if defined(OPENSSL_SYS_VMS)
268 # if __INITIAL_POINTER_SIZE == 64
269 # define PTR_SIZE_INT long long
270 # else /* __INITIAL_POINTER_SIZE == 64 */
271 # define PTR_SIZE_INT int
272 # endif /* __INITIAL_POINTER_SIZE == 64 [else] */
273 # else /* defined(OPENSSL_SYS_VMS) */
274 # define PTR_SIZE_INT size_t
275 # endif /* defined(OPENSSL_SYS_VMS) [else] */
277 # define BN_DEFAULT_BITS 1280
279 # define BN_FLG_MALLOCED 0x01
280 # define BN_FLG_STATIC_DATA 0x02
283 * avoid leaking exponent information through timing,
284 * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime,
285 * BN_div() will call BN_div_no_branch,
286 * BN_mod_inverse() will call BN_mod_inverse_no_branch.
288 # define BN_FLG_CONSTTIME 0x04
290 # ifdef OPENSSL_NO_DEPRECATED
291 /* deprecated name for the flag */
292 # define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME
294 * avoid leaking exponent information through timings
295 * (BN_mod_exp_mont() will call BN_mod_exp_mont_consttime)
299 # ifndef OPENSSL_NO_DEPRECATED
300 # define BN_FLG_FREE 0x8000
301 /* used for debuging */
303 # define BN_set_flags(b,n) ((b)->flags|=(n))
304 # define BN_get_flags(b,n) ((b)->flags&(n))
307 * get a clone of a BIGNUM with changed flags, for *temporary* use only (the
308 * two BIGNUMs cannot not be used in parallel!)
310 # define BN_with_flags(dest,b,n) ((dest)->d=(b)->d, \
311 (dest)->top=(b)->top, \
312 (dest)->dmax=(b)->dmax, \
313 (dest)->neg=(b)->neg, \
314 (dest)->flags=(((dest)->flags & BN_FLG_MALLOCED) \
315 | ((b)->flags & ~BN_FLG_MALLOCED) \
316 | BN_FLG_STATIC_DATA \
319 /* Already declared in ossl_typ.h */
321 typedef struct bignum_st BIGNUM;
322 /* Used for temp variables (declaration hidden in bn_lcl.h) */
323 typedef struct bignum_ctx BN_CTX;
324 typedef struct bn_blinding_st BN_BLINDING;
325 typedef struct bn_mont_ctx_st BN_MONT_CTX;
326 typedef struct bn_recp_ctx_st BN_RECP_CTX;
327 typedef struct bn_gencb_st BN_GENCB;
331 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit
333 int top; /* Index of last used d +1. */
334 /* The next are internal book keeping for bn_expand. */
335 int dmax; /* Size of the d array. */
336 int neg; /* one if the number is negative */
340 /* Used for montgomery multiplication */
341 struct bn_mont_ctx_st {
342 int ri; /* number of bits in R */
343 BIGNUM RR; /* used to convert to montgomery form */
344 BIGNUM N; /* The modulus */
345 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 (Ni is only
346 * stored for bignum algorithm) */
347 BN_ULONG n0[2]; /* least significant word(s) of Ni; (type
348 * changed with 0.9.9, was "BN_ULONG n0;"
354 * Used for reciprocal division/mod functions It cannot be shared between
357 struct bn_recp_ctx_st {
358 BIGNUM N; /* the divisor */
359 BIGNUM Nr; /* the reciprocal */
365 /* Used for slow "generation" functions. */
367 unsigned int ver; /* To handle binary (in)compatibility */
368 void *arg; /* callback-specific data */
370 /* if(ver==1) - handles old style callbacks */
371 void (*cb_1) (int, int, void *);
372 /* if(ver==2) - new callback style */
373 int (*cb_2) (int, int, BN_GENCB *);
376 /* Wrapper function to make using BN_GENCB easier, */
377 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
378 /* Macro to populate a BN_GENCB structure with an "old"-style callback */
379 # define BN_GENCB_set_old(gencb, callback, cb_arg) { \
380 BN_GENCB *tmp_gencb = (gencb); \
381 tmp_gencb->ver = 1; \
382 tmp_gencb->arg = (cb_arg); \
383 tmp_gencb->cb.cb_1 = (callback); }
384 /* Macro to populate a BN_GENCB structure with a "new"-style callback */
385 # define BN_GENCB_set(gencb, callback, cb_arg) { \
386 BN_GENCB *tmp_gencb = (gencb); \
387 tmp_gencb->ver = 2; \
388 tmp_gencb->arg = (cb_arg); \
389 tmp_gencb->cb.cb_2 = (callback); }
391 # define BN_prime_checks 0 /* default: select number of iterations based
392 * on the size of the number */
395 * number of Miller-Rabin iterations for an error rate of less than 2^-80 for
396 * random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook of
397 * Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
398 * original paper: Damgaard, Landrock, Pomerance: Average case error
399 * estimates for the strong probable prime test. -- Math. Comp. 61 (1993)
402 # define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
415 # define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
417 /* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
418 # define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
419 (((w) == 0) && ((a)->top == 0)))
420 # define BN_is_zero(a) ((a)->top == 0)
421 # define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
422 # define BN_is_word(a,w) (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
423 # define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
425 # define BN_one(a) (BN_set_word((a),1))
426 # define BN_zero_ex(a) \
428 BIGNUM *_tmp_bn = (a); \
432 # ifdef OPENSSL_NO_DEPRECATED
433 # define BN_zero(a) BN_zero_ex(a)
435 # define BN_zero(a) (BN_set_word((a),0))
438 const BIGNUM *BN_value_one(void);
439 char *BN_options(void);
440 BN_CTX *BN_CTX_new(void);
441 # ifndef OPENSSL_NO_DEPRECATED
442 void BN_CTX_init(BN_CTX *c);
444 void BN_CTX_free(BN_CTX *c);
445 void BN_CTX_start(BN_CTX *ctx);
446 BIGNUM *BN_CTX_get(BN_CTX *ctx);
447 void BN_CTX_end(BN_CTX *ctx);
448 int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
449 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
450 int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
451 int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
452 int BN_num_bits(const BIGNUM *a);
453 int BN_num_bits_word(BN_ULONG);
454 BIGNUM *BN_new(void);
455 void BN_init(BIGNUM *);
456 void BN_clear_free(BIGNUM *a);
457 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
458 void BN_swap(BIGNUM *a, BIGNUM *b);
459 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
460 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
461 BIGNUM *BN_mpi2bn(const unsigned char *s, int len, BIGNUM *ret);
462 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
463 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
464 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
465 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
466 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
467 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
468 int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
469 /** BN_set_negative sets sign of a BIGNUM
470 * \param b pointer to the BIGNUM object
471 * \param n 0 if the BIGNUM b should be positive and a value != 0 otherwise
473 void BN_set_negative(BIGNUM *b, int n);
474 /** BN_is_negative returns 1 if the BIGNUM is negative
475 * \param a pointer to the BIGNUM object
476 * \return 1 if a < 0 and 0 otherwise
478 # define BN_is_negative(a) ((a)->neg != 0)
480 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
482 # define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
483 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
484 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
486 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
488 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
490 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
492 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
494 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
495 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
496 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
497 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
499 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
501 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
502 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
503 int BN_mul_word(BIGNUM *a, BN_ULONG w);
504 int BN_add_word(BIGNUM *a, BN_ULONG w);
505 int BN_sub_word(BIGNUM *a, BN_ULONG w);
506 int BN_set_word(BIGNUM *a, BN_ULONG w);
507 BN_ULONG BN_get_word(const BIGNUM *a);
509 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
510 void BN_free(BIGNUM *a);
511 int BN_is_bit_set(const BIGNUM *a, int n);
512 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
513 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
514 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
516 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
517 const BIGNUM *m, BN_CTX *ctx);
518 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
519 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
520 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
521 const BIGNUM *m, BN_CTX *ctx,
522 BN_MONT_CTX *in_mont);
523 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
524 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
525 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
526 const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
527 BN_CTX *ctx, BN_MONT_CTX *m_ctx);
528 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
529 const BIGNUM *m, BN_CTX *ctx);
531 int BN_mask_bits(BIGNUM *a, int n);
532 # ifndef OPENSSL_NO_FP_API
533 int BN_print_fp(FILE *fp, const BIGNUM *a);
536 int BN_print(BIO *fp, const BIGNUM *a);
538 int BN_print(void *fp, const BIGNUM *a);
540 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
541 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
542 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
543 void BN_clear(BIGNUM *a);
544 BIGNUM *BN_dup(const BIGNUM *a);
545 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
546 int BN_set_bit(BIGNUM *a, int n);
547 int BN_clear_bit(BIGNUM *a, int n);
548 char *BN_bn2hex(const BIGNUM *a);
549 char *BN_bn2dec(const BIGNUM *a);
550 int BN_hex2bn(BIGNUM **a, const char *str);
551 int BN_dec2bn(BIGNUM **a, const char *str);
552 int BN_asc2bn(BIGNUM **a, const char *str);
553 int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
554 int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); /* returns
557 BIGNUM *BN_mod_inverse(BIGNUM *ret,
558 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
559 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
560 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
562 void BN_consttime_swap(BN_ULONG swap, BIGNUM *a, BIGNUM *b, int nwords);
564 /* Deprecated versions */
565 # ifndef OPENSSL_NO_DEPRECATED
566 BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
567 const BIGNUM *add, const BIGNUM *rem,
568 void (*callback) (int, int, void *), void *cb_arg);
569 int BN_is_prime(const BIGNUM *p, int nchecks,
570 void (*callback) (int, int, void *),
571 BN_CTX *ctx, void *cb_arg);
572 int BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
573 void (*callback) (int, int, void *), BN_CTX *ctx,
574 void *cb_arg, int do_trial_division);
575 # endif /* !defined(OPENSSL_NO_DEPRECATED) */
578 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
579 const BIGNUM *rem, BN_GENCB *cb);
580 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
581 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
582 int do_trial_division, BN_GENCB *cb);
584 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx);
586 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
587 const BIGNUM *Xp, const BIGNUM *Xp1,
588 const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
590 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, BIGNUM *Xp1,
591 BIGNUM *Xp2, const BIGNUM *Xp, const BIGNUM *e,
592 BN_CTX *ctx, BN_GENCB *cb);
594 BN_MONT_CTX *BN_MONT_CTX_new(void);
595 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
596 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
597 BN_MONT_CTX *mont, BN_CTX *ctx);
598 # define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
599 (r),(a),&((mont)->RR),(mont),(ctx))
600 int BN_from_montgomery(BIGNUM *r, const BIGNUM *a,
601 BN_MONT_CTX *mont, BN_CTX *ctx);
602 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
603 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx);
604 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
605 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
606 const BIGNUM *mod, BN_CTX *ctx);
608 /* BN_BLINDING flags */
609 # define BN_BLINDING_NO_UPDATE 0x00000001
610 # define BN_BLINDING_NO_RECREATE 0x00000002
612 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
613 void BN_BLINDING_free(BN_BLINDING *b);
614 int BN_BLINDING_update(BN_BLINDING *b, BN_CTX *ctx);
615 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
616 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
617 int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
618 int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b,
620 # ifndef OPENSSL_NO_DEPRECATED
621 unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
622 void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
624 CRYPTO_THREADID *BN_BLINDING_thread_id(BN_BLINDING *);
625 unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
626 void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
627 BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
628 const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
629 int (*bn_mod_exp) (BIGNUM *r,
637 # ifndef OPENSSL_NO_DEPRECATED
638 void BN_set_params(int mul, int high, int low, int mont);
639 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
642 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
643 BN_RECP_CTX *BN_RECP_CTX_new(void);
644 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
645 int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *rdiv, BN_CTX *ctx);
646 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
647 BN_RECP_CTX *recp, BN_CTX *ctx);
648 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
649 const BIGNUM *m, BN_CTX *ctx);
650 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
651 BN_RECP_CTX *recp, BN_CTX *ctx);
653 # ifndef OPENSSL_NO_EC2M
656 * Functions for arithmetic over binary polynomials represented by BIGNUMs.
657 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
658 * ignored. Note that input arguments are not const so that their bit arrays
659 * can be expanded to the appropriate size if needed.
665 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
666 # define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
670 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p);
671 /* r = (a * b) mod p */
672 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
673 const BIGNUM *p, BN_CTX *ctx);
674 /* r = (a * a) mod p */
675 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
676 /* r = (1 / b) mod p */
677 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx);
678 /* r = (a / b) mod p */
679 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
680 const BIGNUM *p, BN_CTX *ctx);
681 /* r = (a ^ b) mod p */
682 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
683 const BIGNUM *p, BN_CTX *ctx);
684 /* r = sqrt(a) mod p */
685 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
687 /* r^2 + r = a mod p */
688 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
690 # define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
692 * Some functions allow for representation of the irreducible polynomials
693 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
694 * t^p[0] + t^p[1] + ... + t^p[k]
695 * where m = p[0] > p[1] > ... > p[k] = 0.
698 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
699 /* r = (a * b) mod p */
700 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
701 const int p[], BN_CTX *ctx);
702 /* r = (a * a) mod p */
703 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
705 /* r = (1 / b) mod p */
706 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
708 /* r = (a / b) mod p */
709 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
710 const int p[], BN_CTX *ctx);
711 /* r = (a ^ b) mod p */
712 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
713 const int p[], BN_CTX *ctx);
714 /* r = sqrt(a) mod p */
715 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
716 const int p[], BN_CTX *ctx);
717 /* r^2 + r = a mod p */
718 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
719 const int p[], BN_CTX *ctx);
720 int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max);
721 int BN_GF2m_arr2poly(const int p[], BIGNUM *a);
726 * faster mod functions for the 'NIST primes' 0 <= a < p^2
728 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
729 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
730 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
731 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
732 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
734 const BIGNUM *BN_get0_nist_prime_192(void);
735 const BIGNUM *BN_get0_nist_prime_224(void);
736 const BIGNUM *BN_get0_nist_prime_256(void);
737 const BIGNUM *BN_get0_nist_prime_384(void);
738 const BIGNUM *BN_get0_nist_prime_521(void);
740 /* library internal functions */
742 # define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
743 (a):bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2))
744 # define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
745 BIGNUM *bn_expand2(BIGNUM *a, int words);
746 # ifndef OPENSSL_NO_DEPRECATED
747 BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
751 * Bignum consistency macros
752 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
753 * bignum data after direct manipulations on the data. There is also an
754 * "internal" macro, bn_check_top(), for verifying that there are no leading
755 * zeroes. Unfortunately, some auditing is required due to the fact that
756 * bn_fix_top() has become an overabused duct-tape because bignum data is
757 * occasionally passed around in an inconsistent state. So the following
758 * changes have been made to sort this out;
759 * - bn_fix_top()s implementation has been moved to bn_correct_top()
760 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
761 * bn_check_top() is as before.
762 * - if BN_DEBUG *is* defined;
763 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
764 * consistent. (ed: only if BN_DEBUG_RAND is defined)
765 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
766 * The idea is to have debug builds flag up inconsistent bignums when they
767 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
768 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
769 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
770 * was not appropriate, we convert it permanently to bn_check_top() and track
771 * down the cause of the bug. Eventually, no internal code should be using the
772 * bn_fix_top() macro. External applications and libraries should try this with
773 * their own code too, both in terms of building against the openssl headers
774 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
775 * defined. This not only improves external code, it provides more test
776 * coverage for openssl's own code.
781 /* We only need assert() when debugging */
784 # ifdef BN_DEBUG_RAND
785 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
786 # ifndef RAND_pseudo_bytes
787 int RAND_pseudo_bytes(unsigned char *buf, int num);
788 # define BN_DEBUG_TRIX
790 # define bn_pollute(a) \
792 const BIGNUM *_bnum1 = (a); \
793 if(_bnum1->top < _bnum1->dmax) { \
794 unsigned char _tmp_char; \
795 /* We cast away const without the compiler knowing, any \
796 * *genuinely* constant variables that aren't mutable \
797 * wouldn't be constructed with top!=dmax. */ \
798 BN_ULONG *_not_const; \
799 memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
800 RAND_pseudo_bytes(&_tmp_char, 1); \
801 memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
802 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
805 # ifdef BN_DEBUG_TRIX
806 # undef RAND_pseudo_bytes
809 # define bn_pollute(a)
811 # define bn_check_top(a) \
813 const BIGNUM *_bnum2 = (a); \
814 if (_bnum2 != NULL) { \
815 assert((_bnum2->top == 0) || \
816 (_bnum2->d[_bnum2->top - 1] != 0)); \
817 bn_pollute(_bnum2); \
821 # define bn_fix_top(a) bn_check_top(a)
823 # define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
824 # define bn_wcheck_size(bn, words) \
826 const BIGNUM *_bnum2 = (bn); \
827 assert((words) <= (_bnum2)->dmax && (words) >= (_bnum2)->top); \
828 /* avoid unused variable warning with NDEBUG */ \
832 # else /* !BN_DEBUG */
834 # define bn_pollute(a)
835 # define bn_check_top(a)
836 # define bn_fix_top(a) bn_correct_top(a)
837 # define bn_check_size(bn, bits)
838 # define bn_wcheck_size(bn, words)
842 # define bn_correct_top(a) \
845 int tmp_top = (a)->top; \
848 for (ftl= &((a)->d[tmp_top-1]); tmp_top > 0; tmp_top--) \
849 if (*(ftl--)) break; \
850 (a)->top = tmp_top; \
855 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
857 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
858 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
859 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
860 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
862 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
865 /* Primes from RFC 2409 */
866 BIGNUM *get_rfc2409_prime_768(BIGNUM *bn);
867 BIGNUM *get_rfc2409_prime_1024(BIGNUM *bn);
869 /* Primes from RFC 3526 */
870 BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn);
871 BIGNUM *get_rfc3526_prime_2048(BIGNUM *bn);
872 BIGNUM *get_rfc3526_prime_3072(BIGNUM *bn);
873 BIGNUM *get_rfc3526_prime_4096(BIGNUM *bn);
874 BIGNUM *get_rfc3526_prime_6144(BIGNUM *bn);
875 BIGNUM *get_rfc3526_prime_8192(BIGNUM *bn);
877 int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom);
879 /* BEGIN ERROR CODES */
881 * The following lines are auto generated by the script mkerr.pl. Any changes
882 * made after this point may be overwritten when the script is next run.
884 void ERR_load_BN_strings(void);
886 /* Error codes for the BN functions. */
888 /* Function codes. */
889 # define BN_F_BNRAND 127
890 # define BN_F_BN_BLINDING_CONVERT_EX 100
891 # define BN_F_BN_BLINDING_CREATE_PARAM 128
892 # define BN_F_BN_BLINDING_INVERT_EX 101
893 # define BN_F_BN_BLINDING_NEW 102
894 # define BN_F_BN_BLINDING_UPDATE 103
895 # define BN_F_BN_BN2DEC 104
896 # define BN_F_BN_BN2HEX 105
897 # define BN_F_BN_CTX_GET 116
898 # define BN_F_BN_CTX_NEW 106
899 # define BN_F_BN_CTX_START 129
900 # define BN_F_BN_DIV 107
901 # define BN_F_BN_DIV_NO_BRANCH 138
902 # define BN_F_BN_DIV_RECP 130
903 # define BN_F_BN_EXP 123
904 # define BN_F_BN_EXPAND2 108
905 # define BN_F_BN_EXPAND_INTERNAL 120
906 # define BN_F_BN_GF2M_MOD 131
907 # define BN_F_BN_GF2M_MOD_EXP 132
908 # define BN_F_BN_GF2M_MOD_MUL 133
909 # define BN_F_BN_GF2M_MOD_SOLVE_QUAD 134
910 # define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 135
911 # define BN_F_BN_GF2M_MOD_SQR 136
912 # define BN_F_BN_GF2M_MOD_SQRT 137
913 # define BN_F_BN_MOD_EXP2_MONT 118
914 # define BN_F_BN_MOD_EXP_MONT 109
915 # define BN_F_BN_MOD_EXP_MONT_CONSTTIME 124
916 # define BN_F_BN_MOD_EXP_MONT_WORD 117
917 # define BN_F_BN_MOD_EXP_RECP 125
918 # define BN_F_BN_MOD_EXP_SIMPLE 126
919 # define BN_F_BN_MOD_INVERSE 110
920 # define BN_F_BN_MOD_INVERSE_NO_BRANCH 139
921 # define BN_F_BN_MOD_LSHIFT_QUICK 119
922 # define BN_F_BN_MOD_MUL_RECIPROCAL 111
923 # define BN_F_BN_MOD_SQRT 121
924 # define BN_F_BN_MPI2BN 112
925 # define BN_F_BN_NEW 113
926 # define BN_F_BN_RAND 114
927 # define BN_F_BN_RAND_RANGE 122
928 # define BN_F_BN_USUB 115
931 # define BN_R_ARG2_LT_ARG3 100
932 # define BN_R_BAD_RECIPROCAL 101
933 # define BN_R_BIGNUM_TOO_LONG 114
934 # define BN_R_CALLED_WITH_EVEN_MODULUS 102
935 # define BN_R_DIV_BY_ZERO 103
936 # define BN_R_ENCODING_ERROR 104
937 # define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
938 # define BN_R_INPUT_NOT_REDUCED 110
939 # define BN_R_INVALID_LENGTH 106
940 # define BN_R_INVALID_RANGE 115
941 # define BN_R_NOT_A_SQUARE 111
942 # define BN_R_NOT_INITIALIZED 107
943 # define BN_R_NO_INVERSE 108
944 # define BN_R_NO_SOLUTION 116
945 # define BN_R_P_IS_NOT_PRIME 112
946 # define BN_R_TOO_MANY_ITERATIONS 113
947 # define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109