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1/* $OpenBSD: bn.h,v 1.26 2015/02/07 13:19:15 doug Exp $ */
2/* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
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.
8 *
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).
15 *
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.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
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)"
40 *
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
51 * SUCH DAMAGE.
52 *
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.]
57 */
58/* ====================================================================
59 * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved.
60 *
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
63 * are met:
64 *
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
67 *
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
71 * distribution.
72 *
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/)"
77 *
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.
82 *
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.
86 *
87 * 6. Redistributions of any form whatsoever must retain the following
88 * acknowledgment:
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91 *
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 * ====================================================================
105 *
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).
109 *
110 */
111/* ====================================================================
112 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
113 *
114 * Portions of the attached software ("Contribution") are developed by
115 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
116 *
117 * The Contribution is licensed pursuant to the Eric Young open source
118 * license provided above.
119 *
120 * The binary polynomial arithmetic software is originally written by
121 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
122 *
123 */
124
125#ifndef HEADER_BN_H
126#define HEADER_BN_H
127
128#include <stdio.h>
129#include <stdlib.h>
130
131#include <openssl/opensslconf.h>
132
133#include <openssl/ossl_typ.h>
134#include <openssl/crypto.h>
135
136#ifdef __cplusplus
137extern "C" {
138#endif
139
140/* These preprocessor symbols control various aspects of the bignum headers and
141 * library code. They're not defined by any "normal" configuration, as they are
142 * intended for development and testing purposes. NB: defining all three can be
143 * useful for debugging application code as well as openssl itself.
144 *
145 * BN_DEBUG - turn on various debugging alterations to the bignum code
146 * BN_DEBUG_RAND - uses random poisoning of unused words to trip up
147 * mismanagement of bignum internals. You must also define BN_DEBUG.
148 */
149/* #define BN_DEBUG */
150/* #define BN_DEBUG_RAND */
151
152#ifndef OPENSSL_SMALL_FOOTPRINT
153#define BN_MUL_COMBA
154#define BN_SQR_COMBA
155#define BN_RECURSION
156#endif
157
158/* This next option uses the C libraries (2 word)/(1 word) function.
159 * If it is not defined, I use my C version (which is slower).
160 * The reason for this flag is that when the particular C compiler
161 * library routine is used, and the library is linked with a different
162 * compiler, the library is missing. This mostly happens when the
163 * library is built with gcc and then linked using normal cc. This would
164 * be a common occurrence because gcc normally produces code that is
165 * 2 times faster than system compilers for the big number stuff.
166 * For machines with only one compiler (or shared libraries), this should
167 * be on. Again this in only really a problem on machines
168 * using "long long's", are 32bit, and are not using my assembler code. */
169/* #define BN_DIV2W */
170
171#ifdef _LP64
172#undef BN_LLONG
173#define BN_ULONG unsigned long
174#define BN_LONG long
175#define BN_BITS 128
176#define BN_BYTES 8
177#define BN_BITS2 64
178#define BN_BITS4 32
179#define BN_MASK2 (0xffffffffffffffffL)
180#define BN_MASK2l (0xffffffffL)
181#define BN_MASK2h (0xffffffff00000000L)
182#define BN_MASK2h1 (0xffffffff80000000L)
183#define BN_TBIT (0x8000000000000000L)
184#define BN_DEC_CONV (10000000000000000000UL)
185#define BN_DEC_FMT1 "%lu"
186#define BN_DEC_FMT2 "%019lu"
187#define BN_DEC_NUM 19
188#define BN_HEX_FMT1 "%lX"
189#define BN_HEX_FMT2 "%016lX"
190#else
191#define BN_ULLONG unsigned long long
192#define BN_LLONG
193#define BN_ULONG unsigned int
194#define BN_LONG int
195#define BN_BITS 64
196#define BN_BYTES 4
197#define BN_BITS2 32
198#define BN_BITS4 16
199#define BN_MASK (0xffffffffffffffffLL)
200#define BN_MASK2 (0xffffffffL)
201#define BN_MASK2l (0xffff)
202#define BN_MASK2h1 (0xffff8000L)
203#define BN_MASK2h (0xffff0000L)
204#define BN_TBIT (0x80000000L)
205#define BN_DEC_CONV (1000000000L)
206#define BN_DEC_FMT1 "%u"
207#define BN_DEC_FMT2 "%09u"
208#define BN_DEC_NUM 9
209#define BN_HEX_FMT1 "%X"
210#define BN_HEX_FMT2 "%08X"
211#endif
212
213#define BN_FLG_MALLOCED 0x01
214#define BN_FLG_STATIC_DATA 0x02
215#define BN_FLG_CONSTTIME 0x04 /* avoid leaking exponent information through timing,
216 * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime,
217 * BN_div() will call BN_div_no_branch,
218 * BN_mod_inverse() will call BN_mod_inverse_no_branch.
219 */
220
221#ifndef OPENSSL_NO_DEPRECATED
222#define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME /* deprecated name for the flag */
223 /* avoid leaking exponent information through timings
224 * (BN_mod_exp_mont() will call BN_mod_exp_mont_consttime) */
225#endif
226
227#ifndef OPENSSL_NO_DEPRECATED
228#define BN_FLG_FREE 0x8000 /* used for debuging */
229#endif
230#define BN_set_flags(b,n) ((b)->flags|=(n))
231#define BN_get_flags(b,n) ((b)->flags&(n))
232
233/* get a clone of a BIGNUM with changed flags, for *temporary* use only
234 * (the two BIGNUMs cannot not be used in parallel!) */
235#define BN_with_flags(dest,b,n) ((dest)->d=(b)->d, \
236 (dest)->top=(b)->top, \
237 (dest)->dmax=(b)->dmax, \
238 (dest)->neg=(b)->neg, \
239 (dest)->flags=(((dest)->flags & BN_FLG_MALLOCED) \
240 | ((b)->flags & ~BN_FLG_MALLOCED) \
241 | BN_FLG_STATIC_DATA \
242 | (n)))
243
244struct bignum_st {
245 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */
246 int top; /* Index of last used d +1. */
247 /* The next are internal book keeping for bn_expand. */
248 int dmax; /* Size of the d array. */
249 int neg; /* one if the number is negative */
250 int flags;
251};
252
253/* Used for montgomery multiplication */
254struct bn_mont_ctx_st {
255 int ri; /* number of bits in R */
256 BIGNUM RR; /* used to convert to montgomery form */
257 BIGNUM N; /* The modulus */
258 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
259 * (Ni is only stored for bignum algorithm) */
260 BN_ULONG n0[2];/* least significant word(s) of Ni;
261 (type changed with 0.9.9, was "BN_ULONG n0;" before) */
262 int flags;
263};
264
265/* Used for reciprocal division/mod functions
266 * It cannot be shared between threads
267 */
268struct bn_recp_ctx_st {
269 BIGNUM N; /* the divisor */
270 BIGNUM Nr; /* the reciprocal */
271 int num_bits;
272 int shift;
273 int flags;
274};
275
276/* Used for slow "generation" functions. */
277struct bn_gencb_st {
278 unsigned int ver; /* To handle binary (in)compatibility */
279 void *arg; /* callback-specific data */
280 union {
281 /* if(ver==1) - handles old style callbacks */
282 void (*cb_1)(int, int, void *);
283 /* if(ver==2) - new callback style */
284 int (*cb_2)(int, int, BN_GENCB *);
285 } cb;
286};
287/* Wrapper function to make using BN_GENCB easier, */
288int BN_GENCB_call(BN_GENCB *cb, int a, int b);
289/* Macro to populate a BN_GENCB structure with an "old"-style callback */
290#define BN_GENCB_set_old(gencb, callback, cb_arg) { \
291 BN_GENCB *tmp_gencb = (gencb); \
292 tmp_gencb->ver = 1; \
293 tmp_gencb->arg = (cb_arg); \
294 tmp_gencb->cb.cb_1 = (callback); }
295/* Macro to populate a BN_GENCB structure with a "new"-style callback */
296#define BN_GENCB_set(gencb, callback, cb_arg) { \
297 BN_GENCB *tmp_gencb = (gencb); \
298 tmp_gencb->ver = 2; \
299 tmp_gencb->arg = (cb_arg); \
300 tmp_gencb->cb.cb_2 = (callback); }
301
302#define BN_prime_checks 0 /* default: select number of iterations
303 based on the size of the number */
304
305/* number of Miller-Rabin iterations for an error rate of less than 2^-80
306 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
307 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
308 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
309 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
310#define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
311 (b) >= 850 ? 3 : \
312 (b) >= 650 ? 4 : \
313 (b) >= 550 ? 5 : \
314 (b) >= 450 ? 6 : \
315 (b) >= 400 ? 7 : \
316 (b) >= 350 ? 8 : \
317 (b) >= 300 ? 9 : \
318 (b) >= 250 ? 12 : \
319 (b) >= 200 ? 15 : \
320 (b) >= 150 ? 18 : \
321 /* b >= 100 */ 27)
322
323#define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
324
325/* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
326#define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
327 (((w) == 0) && ((a)->top == 0)))
328#define BN_is_zero(a) ((a)->top == 0)
329#define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
330#define BN_is_word(a,w) (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
331#define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
332
333#define BN_one(a) (BN_set_word((a),1))
334#define BN_zero_ex(a) \
335 do { \
336 BIGNUM *_tmp_bn = (a); \
337 _tmp_bn->top = 0; \
338 _tmp_bn->neg = 0; \
339 } while(0)
340
341#ifdef OPENSSL_NO_DEPRECATED
342#define BN_zero(a) BN_zero_ex(a)
343#else
344#define BN_zero(a) (BN_set_word((a),0))
345#endif
346
347const BIGNUM *BN_value_one(void);
348char * BN_options(void);
349BN_CTX *BN_CTX_new(void);
350#ifndef OPENSSL_NO_DEPRECATED
351void BN_CTX_init(BN_CTX *c);
352#endif
353void BN_CTX_free(BN_CTX *c);
354void BN_CTX_start(BN_CTX *ctx);
355BIGNUM *BN_CTX_get(BN_CTX *ctx);
356void BN_CTX_end(BN_CTX *ctx);
357int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
358int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
359int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
360int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
361int BN_num_bits(const BIGNUM *a);
362int BN_num_bits_word(BN_ULONG);
363BIGNUM *BN_new(void);
364void BN_init(BIGNUM *);
365void BN_clear_free(BIGNUM *a);
366BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
367void BN_swap(BIGNUM *a, BIGNUM *b);
368BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
369int BN_bn2bin(const BIGNUM *a, unsigned char *to);
370BIGNUM *BN_mpi2bn(const unsigned char *s, int len, BIGNUM *ret);
371int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
372int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
373int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
374int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
375int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
376int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
377int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
378/** BN_set_negative sets sign of a BIGNUM
379 * \param b pointer to the BIGNUM object
380 * \param n 0 if the BIGNUM b should be positive and a value != 0 otherwise
381 */
382void BN_set_negative(BIGNUM *b, int n);
383/** BN_is_negative returns 1 if the BIGNUM is negative
384 * \param a pointer to the BIGNUM object
385 * \return 1 if a < 0 and 0 otherwise
386 */
387#define BN_is_negative(a) ((a)->neg != 0)
388
389int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
390 BN_CTX *ctx);
391#define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
392int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
393int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
394int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
395int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
396int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
397int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
398 const BIGNUM *m, BN_CTX *ctx);
399int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
400int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
401int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
402int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx);
403int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
404
405BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
406BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
407int BN_mul_word(BIGNUM *a, BN_ULONG w);
408int BN_add_word(BIGNUM *a, BN_ULONG w);
409int BN_sub_word(BIGNUM *a, BN_ULONG w);
410int BN_set_word(BIGNUM *a, BN_ULONG w);
411BN_ULONG BN_get_word(const BIGNUM *a);
412
413int BN_cmp(const BIGNUM *a, const BIGNUM *b);
414void BN_free(BIGNUM *a);
415int BN_is_bit_set(const BIGNUM *a, int n);
416int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
417int BN_lshift1(BIGNUM *r, const BIGNUM *a);
418int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
419
420int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
421 const BIGNUM *m, BN_CTX *ctx);
422int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
423 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
424int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
425 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont);
426int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
427 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
428int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
429 const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
430 BN_CTX *ctx, BN_MONT_CTX *m_ctx);
431int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
432 const BIGNUM *m, BN_CTX *ctx);
433
434int BN_mask_bits(BIGNUM *a, int n);
435int BN_print_fp(FILE *fp, const BIGNUM *a);
436#ifdef HEADER_BIO_H
437int BN_print(BIO *fp, const BIGNUM *a);
438#else
439int BN_print(void *fp, const BIGNUM *a);
440#endif
441int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
442int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
443int BN_rshift1(BIGNUM *r, const BIGNUM *a);
444void BN_clear(BIGNUM *a);
445BIGNUM *BN_dup(const BIGNUM *a);
446int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
447int BN_set_bit(BIGNUM *a, int n);
448int BN_clear_bit(BIGNUM *a, int n);
449char * BN_bn2hex(const BIGNUM *a);
450char * BN_bn2dec(const BIGNUM *a);
451int BN_hex2bn(BIGNUM **a, const char *str);
452int BN_dec2bn(BIGNUM **a, const char *str);
453int BN_asc2bn(BIGNUM **a, const char *str);
454int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
455int BN_kronecker(const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx); /* returns -2 for error */
456BIGNUM *BN_mod_inverse(BIGNUM *ret,
457 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
458BIGNUM *BN_mod_sqrt(BIGNUM *ret,
459 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
460
461void BN_consttime_swap(BN_ULONG swap, BIGNUM *a, BIGNUM *b, int nwords);
462
463/* Deprecated versions */
464#ifndef OPENSSL_NO_DEPRECATED
465BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
466 const BIGNUM *add, const BIGNUM *rem,
467 void (*callback)(int, int, void *), void *cb_arg);
468int BN_is_prime(const BIGNUM *p, int nchecks,
469 void (*callback)(int, int, void *),
470 BN_CTX *ctx, void *cb_arg);
471int BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
472 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg,
473 int do_trial_division);
474#endif /* !defined(OPENSSL_NO_DEPRECATED) */
475
476/* Newer versions */
477int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
478 const BIGNUM *rem, BN_GENCB *cb);
479int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
480int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
481 int do_trial_division, BN_GENCB *cb);
482
483int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx);
484
485int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
486 const BIGNUM *Xp, const BIGNUM *Xp1, const BIGNUM *Xp2,
487 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb);
488int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
489 BIGNUM *Xp1, BIGNUM *Xp2,
490 const BIGNUM *Xp,
491 const BIGNUM *e, BN_CTX *ctx,
492 BN_GENCB *cb);
493
494BN_MONT_CTX *BN_MONT_CTX_new(void );
495void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
496int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
497 BN_MONT_CTX *mont, BN_CTX *ctx);
498#define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
499 (r),(a),&((mont)->RR),(mont),(ctx))
500int BN_from_montgomery(BIGNUM *r, const BIGNUM *a,
501 BN_MONT_CTX *mont, BN_CTX *ctx);
502void BN_MONT_CTX_free(BN_MONT_CTX *mont);
503int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx);
504BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
505BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
506 const BIGNUM *mod, BN_CTX *ctx);
507
508/* BN_BLINDING flags */
509#define BN_BLINDING_NO_UPDATE 0x00000001
510#define BN_BLINDING_NO_RECREATE 0x00000002
511
512BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
513void BN_BLINDING_free(BN_BLINDING *b);
514int BN_BLINDING_update(BN_BLINDING *b, BN_CTX *ctx);
515int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
516int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
517int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
518int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b, BN_CTX *);
519#ifndef OPENSSL_NO_DEPRECATED
520unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
521void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
522#endif
523CRYPTO_THREADID *BN_BLINDING_thread_id(BN_BLINDING *);
524unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
525void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
526BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
527 const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
528 int (*bn_mod_exp)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
529 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx),
530 BN_MONT_CTX *m_ctx);
531
532#ifndef OPENSSL_NO_DEPRECATED
533void BN_set_params(int mul, int high, int low, int mont);
534int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
535#endif
536
537void BN_RECP_CTX_init(BN_RECP_CTX *recp);
538BN_RECP_CTX *BN_RECP_CTX_new(void);
539void BN_RECP_CTX_free(BN_RECP_CTX *recp);
540int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *rdiv, BN_CTX *ctx);
541int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
542 BN_RECP_CTX *recp, BN_CTX *ctx);
543int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
544 const BIGNUM *m, BN_CTX *ctx);
545int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
546 BN_RECP_CTX *recp, BN_CTX *ctx);
547
548#ifndef OPENSSL_NO_EC2M
549
550/* Functions for arithmetic over binary polynomials represented by BIGNUMs.
551 *
552 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
553 * ignored.
554 *
555 * Note that input arguments are not const so that their bit arrays can
556 * be expanded to the appropriate size if needed.
557 */
558
559int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /*r = a + b*/
560#define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
561int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /*r=a mod p*/
562int
563BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
564 const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
565int
566BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
567 BN_CTX *ctx); /* r = (a * a) mod p */
568int
569BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p,
570 BN_CTX *ctx); /* r = (1 / b) mod p */
571int
572BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
573 const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
574int
575BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
576 const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */
577int
578BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
579 BN_CTX *ctx); /* r = sqrt(a) mod p */
580int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
581 BN_CTX *ctx); /* r^2 + r = a mod p */
582#define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
583/* Some functions allow for representation of the irreducible polynomials
584 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
585 * t^p[0] + t^p[1] + ... + t^p[k]
586 * where m = p[0] > p[1] > ... > p[k] = 0.
587 */
588int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
589/* r = a mod p */
590int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
591 const int p[], BN_CTX *ctx); /* r = (a * b) mod p */
592int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
593 BN_CTX *ctx); /* r = (a * a) mod p */
594int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
595 BN_CTX *ctx); /* r = (1 / b) mod p */
596int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
597 const int p[], BN_CTX *ctx); /* r = (a / b) mod p */
598int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
599 const int p[], BN_CTX *ctx); /* r = (a ^ b) mod p */
600int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
601 const int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
602int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
603 const int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
604int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max);
605int BN_GF2m_arr2poly(const int p[], BIGNUM *a);
606
607#endif
608
609/* faster mod functions for the 'NIST primes'
610 * 0 <= a < p^2 */
611int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
612int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
613int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
614int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
615int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
616
617const BIGNUM *BN_get0_nist_prime_192(void);
618const BIGNUM *BN_get0_nist_prime_224(void);
619const BIGNUM *BN_get0_nist_prime_256(void);
620const BIGNUM *BN_get0_nist_prime_384(void);
621const BIGNUM *BN_get0_nist_prime_521(void);
622
623/* library internal functions */
624
625#define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
626 (a):bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2))
627#define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
628BIGNUM *bn_expand2(BIGNUM *a, int words);
629#ifndef OPENSSL_NO_DEPRECATED
630BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
631#endif
632
633/* Bignum consistency macros
634 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
635 * bignum data after direct manipulations on the data. There is also an
636 * "internal" macro, bn_check_top(), for verifying that there are no leading
637 * zeroes. Unfortunately, some auditing is required due to the fact that
638 * bn_fix_top() has become an overabused duct-tape because bignum data is
639 * occasionally passed around in an inconsistent state. So the following
640 * changes have been made to sort this out;
641 * - bn_fix_top()s implementation has been moved to bn_correct_top()
642 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
643 * bn_check_top() is as before.
644 * - if BN_DEBUG *is* defined;
645 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
646 * consistent. (ed: only if BN_DEBUG_RAND is defined)
647 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
648 * The idea is to have debug builds flag up inconsistent bignums when they
649 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
650 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
651 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
652 * was not appropriate, we convert it permanently to bn_check_top() and track
653 * down the cause of the bug. Eventually, no internal code should be using the
654 * bn_fix_top() macro. External applications and libraries should try this with
655 * their own code too, both in terms of building against the openssl headers
656 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
657 * defined. This not only improves external code, it provides more test
658 * coverage for openssl's own code.
659 */
660
661#ifdef BN_DEBUG
662
663/* We only need assert() when debugging */
664#include <assert.h>
665
666#ifdef BN_DEBUG_RAND
667#define bn_pollute(a) \
668 do { \
669 const BIGNUM *_bnum1 = (a); \
670 if(_bnum1->top < _bnum1->dmax) { \
671 unsigned char _tmp_char; \
672 /* We cast away const without the compiler knowing, any \
673 * *genuinely* constant variables that aren't mutable \
674 * wouldn't be constructed with top!=dmax. */ \
675 BN_ULONG *_not_const; \
676 memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
677 arc4random_buf(&_tmp_char, 1); \
678 memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
679 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
680 } \
681 } while(0)
682#else
683#define bn_pollute(a)
684#endif
685
686#define bn_check_top(a) \
687 do { \
688 const BIGNUM *_bnum2 = (a); \
689 if (_bnum2 != NULL) { \
690 assert((_bnum2->top == 0) || \
691 (_bnum2->d[_bnum2->top - 1] != 0)); \
692 bn_pollute(_bnum2); \
693 } \
694 } while(0)
695
696#define bn_fix_top(a) bn_check_top(a)
697
698#define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
699#define bn_wcheck_size(bn, words) \
700 do { \
701 const BIGNUM *_bnum2 = (bn); \
702 assert(words <= (_bnum2)->dmax && words >= (_bnum2)->top); \
703 } while(0)
704
705#else /* !BN_DEBUG */
706
707#define bn_pollute(a)
708#define bn_check_top(a)
709#define bn_fix_top(a) bn_correct_top(a)
710#define bn_check_size(bn, bits)
711#define bn_wcheck_size(bn, words)
712
713#endif
714
715#define bn_correct_top(a) \
716 { \
717 BN_ULONG *ftl; \
718 int tmp_top = (a)->top; \
719 if (tmp_top > 0) \
720 { \
721 for (ftl= &((a)->d[tmp_top-1]); tmp_top > 0; tmp_top--) \
722 if (*(ftl--)) break; \
723 (a)->top = tmp_top; \
724 } \
725 bn_pollute(a); \
726 }
727
728 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
729BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
730void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
731BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
732BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, int num);
733BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, int num);
734
735/* Primes from RFC 2409 */
736BIGNUM *get_rfc2409_prime_768(BIGNUM *bn);
737BIGNUM *get_rfc2409_prime_1024(BIGNUM *bn);
738
739/* Primes from RFC 3526 */
740BIGNUM *get_rfc3526_prime_1536(BIGNUM *bn);
741BIGNUM *get_rfc3526_prime_2048(BIGNUM *bn);
742BIGNUM *get_rfc3526_prime_3072(BIGNUM *bn);
743BIGNUM *get_rfc3526_prime_4096(BIGNUM *bn);
744BIGNUM *get_rfc3526_prime_6144(BIGNUM *bn);
745BIGNUM *get_rfc3526_prime_8192(BIGNUM *bn);
746
747int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom);
748
749/* BEGIN ERROR CODES */
750/* The following lines are auto generated by the script mkerr.pl. Any changes
751 * made after this point may be overwritten when the script is next run.
752 */
753void ERR_load_BN_strings(void);
754
755/* Error codes for the BN functions. */
756
757/* Function codes. */
758#define BN_F_BNRAND 127
759#define BN_F_BN_BLINDING_CONVERT_EX 100
760#define BN_F_BN_BLINDING_CREATE_PARAM 128
761#define BN_F_BN_BLINDING_INVERT_EX 101
762#define BN_F_BN_BLINDING_NEW 102
763#define BN_F_BN_BLINDING_UPDATE 103
764#define BN_F_BN_BN2DEC 104
765#define BN_F_BN_BN2HEX 105
766#define BN_F_BN_CTX_GET 116
767#define BN_F_BN_CTX_NEW 106
768#define BN_F_BN_CTX_START 129
769#define BN_F_BN_DIV 107
770#define BN_F_BN_DIV_NO_BRANCH 138
771#define BN_F_BN_DIV_RECP 130
772#define BN_F_BN_EXP 123
773#define BN_F_BN_EXPAND2 108
774#define BN_F_BN_EXPAND_INTERNAL 120
775#define BN_F_BN_GF2M_MOD 131
776#define BN_F_BN_GF2M_MOD_EXP 132
777#define BN_F_BN_GF2M_MOD_MUL 133
778#define BN_F_BN_GF2M_MOD_SOLVE_QUAD 134
779#define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 135
780#define BN_F_BN_GF2M_MOD_SQR 136
781#define BN_F_BN_GF2M_MOD_SQRT 137
782#define BN_F_BN_MOD_EXP2_MONT 118
783#define BN_F_BN_MOD_EXP_MONT 109
784#define BN_F_BN_MOD_EXP_MONT_CONSTTIME 124
785#define BN_F_BN_MOD_EXP_MONT_WORD 117
786#define BN_F_BN_MOD_EXP_RECP 125
787#define BN_F_BN_MOD_EXP_SIMPLE 126
788#define BN_F_BN_MOD_INVERSE 110
789#define BN_F_BN_MOD_INVERSE_NO_BRANCH 139
790#define BN_F_BN_MOD_LSHIFT_QUICK 119
791#define BN_F_BN_MOD_MUL_RECIPROCAL 111
792#define BN_F_BN_MOD_SQRT 121
793#define BN_F_BN_MPI2BN 112
794#define BN_F_BN_NEW 113
795#define BN_F_BN_RAND 114
796#define BN_F_BN_RAND_RANGE 122
797#define BN_F_BN_USUB 115
798
799/* Reason codes. */
800#define BN_R_ARG2_LT_ARG3 100
801#define BN_R_BAD_RECIPROCAL 101
802#define BN_R_BIGNUM_TOO_LONG 114
803#define BN_R_CALLED_WITH_EVEN_MODULUS 102
804#define BN_R_DIV_BY_ZERO 103
805#define BN_R_ENCODING_ERROR 104
806#define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
807#define BN_R_INPUT_NOT_REDUCED 110
808#define BN_R_INVALID_LENGTH 106
809#define BN_R_INVALID_RANGE 115
810#define BN_R_NOT_A_SQUARE 111
811#define BN_R_NOT_INITIALIZED 107
812#define BN_R_NO_INVERSE 108
813#define BN_R_NO_SOLUTION 116
814#define BN_R_P_IS_NOT_PRIME 112
815#define BN_R_TOO_MANY_ITERATIONS 113
816#define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109
817
818#ifdef __cplusplus
819}
820#endif
821#endif
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-04-02 16:55:06 +0000