1/*
2 * Copyright 1995-2020 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
4 *
5 * Licensed under the OpenSSL license (the "License").  You may not use
6 * this file except in compliance with the License.  You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
9 */
10
11#ifndef HEADER_BN_H
12# define HEADER_BN_H
13
14# include <openssl/e_os2.h>
15# ifndef OPENSSL_NO_STDIO
16#  include <stdio.h>
17# endif
18# include <openssl/opensslconf.h>
19# include <openssl/ossl_typ.h>
20# include <openssl/crypto.h>
21# include <openssl/bnerr.h>
22
23#ifdef  __cplusplus
24extern "C" {
25#endif
26
27/*
28 * 64-bit processor with LP64 ABI
29 */
30# ifdef SIXTY_FOUR_BIT_LONG
31#  define BN_ULONG        unsigned long
32#  define BN_BYTES        8
33# endif
34
35/*
36 * 64-bit processor other than LP64 ABI
37 */
38# ifdef SIXTY_FOUR_BIT
39#  define BN_ULONG        unsigned long long
40#  define BN_BYTES        8
41# endif
42
43# ifdef THIRTY_TWO_BIT
44#  define BN_ULONG        unsigned int
45#  define BN_BYTES        4
46# endif
47
48# define BN_BITS2       (BN_BYTES * 8)
49# define BN_BITS        (BN_BITS2 * 2)
50# define BN_TBIT        ((BN_ULONG)1 << (BN_BITS2 - 1))
51
52# define BN_FLG_MALLOCED         0x01
53# define BN_FLG_STATIC_DATA      0x02
54
55/*
56 * avoid leaking exponent information through timing,
57 * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime,
58 * BN_div() will call BN_div_no_branch,
59 * BN_mod_inverse() will call bn_mod_inverse_no_branch.
60 */
61# define BN_FLG_CONSTTIME        0x04
62# define BN_FLG_SECURE           0x08
63
64# if OPENSSL_API_COMPAT < 0x00908000L
65/* deprecated name for the flag */
66#  define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME
67#  define BN_FLG_FREE            0x8000 /* used for debugging */
68# endif
69
70void BN_set_flags(BIGNUM *b, int n);
71int BN_get_flags(const BIGNUM *b, int n);
72
73/* Values for |top| in BN_rand() */
74#define BN_RAND_TOP_ANY    -1
75#define BN_RAND_TOP_ONE     0
76#define BN_RAND_TOP_TWO     1
77
78/* Values for |bottom| in BN_rand() */
79#define BN_RAND_BOTTOM_ANY  0
80#define BN_RAND_BOTTOM_ODD  1
81
82/*
83 * get a clone of a BIGNUM with changed flags, for *temporary* use only (the
84 * two BIGNUMs cannot be used in parallel!). Also only for *read only* use. The
85 * value |dest| should be a newly allocated BIGNUM obtained via BN_new() that
86 * has not been otherwise initialised or used.
87 */
88void BN_with_flags(BIGNUM *dest, const BIGNUM *b, int flags);
89
90/* Wrapper function to make using BN_GENCB easier */
91int BN_GENCB_call(BN_GENCB *cb, int a, int b);
92
93BN_GENCB *BN_GENCB_new(void);
94void BN_GENCB_free(BN_GENCB *cb);
95
96/* Populate a BN_GENCB structure with an "old"-style callback */
97void BN_GENCB_set_old(BN_GENCB *gencb, void (*callback) (int, int, void *),
98                      void *cb_arg);
99
100/* Populate a BN_GENCB structure with a "new"-style callback */
101void BN_GENCB_set(BN_GENCB *gencb, int (*callback) (int, int, BN_GENCB *),
102                  void *cb_arg);
103
104void *BN_GENCB_get_arg(BN_GENCB *cb);
105
106# define BN_prime_checks 0      /* default: select number of iterations based
107                                 * on the size of the number */
108
109/*
110 * BN_prime_checks_for_size() returns the number of Miller-Rabin iterations
111 * that will be done for checking that a random number is probably prime. The
112 * error rate for accepting a composite number as prime depends on the size of
113 * the prime |b|. The error rates used are for calculating an RSA key with 2 primes,
114 * and so the level is what you would expect for a key of double the size of the
115 * prime.
116 *
117 * This table is generated using the algorithm of FIPS PUB 186-4
118 * Digital Signature Standard (DSS), section F.1, page 117.
119 * (https://dx.doi.org/10.6028/NIST.FIPS.186-4)
120 *
121 * The following magma script was used to generate the output:
122 * securitybits:=125;
123 * k:=1024;
124 * for t:=1 to 65 do
125 *   for M:=3 to Floor(2*Sqrt(k-1)-1) do
126 *     S:=0;
127 *     // Sum over m
128 *     for m:=3 to M do
129 *       s:=0;
130 *       // Sum over j
131 *       for j:=2 to m do
132 *         s+:=(RealField(32)!2)^-(j+(k-1)/j);
133 *       end for;
134 *       S+:=2^(m-(m-1)*t)*s;
135 *     end for;
136 *     A:=2^(k-2-M*t);
137 *     B:=8*(Pi(RealField(32))^2-6)/3*2^(k-2)*S;
138 *     pkt:=2.00743*Log(2)*k*2^-k*(A+B);
139 *     seclevel:=Floor(-Log(2,pkt));
140 *     if seclevel ge securitybits then
141 *       printf "k: %5o, security: %o bits  (t: %o, M: %o)\n",k,seclevel,t,M;
142 *       break;
143 *     end if;
144 *   end for;
145 *   if seclevel ge securitybits then break; end if;
146 * end for;
147 *
148 * It can be run online at:
149 * http://magma.maths.usyd.edu.au/calc
150 *
151 * And will output:
152 * k:  1024, security: 129 bits  (t: 6, M: 23)
153 *
154 * k is the number of bits of the prime, securitybits is the level we want to
155 * reach.
156 *
157 * prime length | RSA key size | # MR tests | security level
158 * -------------+--------------|------------+---------------
159 *  (b) >= 6394 |     >= 12788 |          3 |        256 bit
160 *  (b) >= 3747 |     >=  7494 |          3 |        192 bit
161 *  (b) >= 1345 |     >=  2690 |          4 |        128 bit
162 *  (b) >= 1080 |     >=  2160 |          5 |        128 bit
163 *  (b) >=  852 |     >=  1704 |          5 |        112 bit
164 *  (b) >=  476 |     >=   952 |          5 |         80 bit
165 *  (b) >=  400 |     >=   800 |          6 |         80 bit
166 *  (b) >=  347 |     >=   694 |          7 |         80 bit
167 *  (b) >=  308 |     >=   616 |          8 |         80 bit
168 *  (b) >=   55 |     >=   110 |         27 |         64 bit
169 *  (b) >=    6 |     >=    12 |         34 |         64 bit
170 */
171
172# define BN_prime_checks_for_size(b) ((b) >= 3747 ?  3 : \
173                                (b) >=  1345 ?  4 : \
174                                (b) >=  476 ?  5 : \
175                                (b) >=  400 ?  6 : \
176                                (b) >=  347 ?  7 : \
177                                (b) >=  308 ?  8 : \
178                                (b) >=  55  ? 27 : \
179                                /* b >= 6 */ 34)
180
181# define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
182
183int BN_abs_is_word(const BIGNUM *a, const BN_ULONG w);
184int BN_is_zero(const BIGNUM *a);
185int BN_is_one(const BIGNUM *a);
186int BN_is_word(const BIGNUM *a, const BN_ULONG w);
187int BN_is_odd(const BIGNUM *a);
188
189# define BN_one(a)       (BN_set_word((a),1))
190
191void BN_zero_ex(BIGNUM *a);
192
193# if OPENSSL_API_COMPAT >= 0x00908000L
194#  define BN_zero(a)      BN_zero_ex(a)
195# else
196#  define BN_zero(a)      (BN_set_word((a),0))
197# endif
198
199const BIGNUM *BN_value_one(void);
200char *BN_options(void);
201BN_CTX *BN_CTX_new(void);
202BN_CTX *BN_CTX_secure_new(void);
203void BN_CTX_free(BN_CTX *c);
204void BN_CTX_start(BN_CTX *ctx);
205BIGNUM *BN_CTX_get(BN_CTX *ctx);
206void BN_CTX_end(BN_CTX *ctx);
207int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
208int BN_priv_rand(BIGNUM *rnd, int bits, int top, int bottom);
209int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
210int BN_priv_rand_range(BIGNUM *rnd, const BIGNUM *range);
211int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
212int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
213int BN_num_bits(const BIGNUM *a);
214int BN_num_bits_word(BN_ULONG l);
215int BN_security_bits(int L, int N);
216BIGNUM *BN_new(void);
217BIGNUM *BN_secure_new(void);
218void BN_clear_free(BIGNUM *a);
219BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
220void BN_swap(BIGNUM *a, BIGNUM *b);
221BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
222int BN_bn2bin(const BIGNUM *a, unsigned char *to);
223int BN_bn2binpad(const BIGNUM *a, unsigned char *to, int tolen);
224BIGNUM *BN_lebin2bn(const unsigned char *s, int len, BIGNUM *ret);
225int BN_bn2lebinpad(const BIGNUM *a, unsigned char *to, int tolen);
226BIGNUM *BN_mpi2bn(const unsigned char *s, int len, BIGNUM *ret);
227int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
228int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
229int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
230int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
231int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
232int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
233int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
234/** BN_set_negative sets sign of a BIGNUM
235 * \param  b  pointer to the BIGNUM object
236 * \param  n  0 if the BIGNUM b should be positive and a value != 0 otherwise
237 */
238void BN_set_negative(BIGNUM *b, int n);
239/** BN_is_negative returns 1 if the BIGNUM is negative
240 * \param  b  pointer to the BIGNUM object
241 * \return 1 if a < 0 and 0 otherwise
242 */
243int BN_is_negative(const BIGNUM *b);
244
245int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
246           BN_CTX *ctx);
247# define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
248int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
249int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
250               BN_CTX *ctx);
251int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
252                     const BIGNUM *m);
253int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
254               BN_CTX *ctx);
255int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
256                     const BIGNUM *m);
257int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
258               BN_CTX *ctx);
259int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
260int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
261int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
262int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
263                  BN_CTX *ctx);
264int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
265
266BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
267BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
268int BN_mul_word(BIGNUM *a, BN_ULONG w);
269int BN_add_word(BIGNUM *a, BN_ULONG w);
270int BN_sub_word(BIGNUM *a, BN_ULONG w);
271int BN_set_word(BIGNUM *a, BN_ULONG w);
272BN_ULONG BN_get_word(const BIGNUM *a);
273
274int BN_cmp(const BIGNUM *a, const BIGNUM *b);
275void BN_free(BIGNUM *a);
276int BN_is_bit_set(const BIGNUM *a, int n);
277int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
278int BN_lshift1(BIGNUM *r, const BIGNUM *a);
279int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
280
281int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
282               const BIGNUM *m, BN_CTX *ctx);
283int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
284                    const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
285int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
286                              const BIGNUM *m, BN_CTX *ctx,
287                              BN_MONT_CTX *in_mont);
288int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
289                         const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
290int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
291                     const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
292                     BN_CTX *ctx, BN_MONT_CTX *m_ctx);
293int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
294                      const BIGNUM *m, BN_CTX *ctx);
295
296int BN_mask_bits(BIGNUM *a, int n);
297# ifndef OPENSSL_NO_STDIO
298int BN_print_fp(FILE *fp, const BIGNUM *a);
299# endif
300int BN_print(BIO *bio, const BIGNUM *a);
301int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
302int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
303int BN_rshift1(BIGNUM *r, const BIGNUM *a);
304void BN_clear(BIGNUM *a);
305BIGNUM *BN_dup(const BIGNUM *a);
306int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
307int BN_set_bit(BIGNUM *a, int n);
308int BN_clear_bit(BIGNUM *a, int n);
309char *BN_bn2hex(const BIGNUM *a);
310char *BN_bn2dec(const BIGNUM *a);
311int BN_hex2bn(BIGNUM **a, const char *str);
312int BN_dec2bn(BIGNUM **a, const char *str);
313int BN_asc2bn(BIGNUM **a, const char *str);
314int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
315int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); /* returns
316                                                                  * -2 for
317                                                                  * error */
318BIGNUM *BN_mod_inverse(BIGNUM *ret,
319                       const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
320BIGNUM *BN_mod_sqrt(BIGNUM *ret,
321                    const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
322
323void BN_consttime_swap(BN_ULONG swap, BIGNUM *a, BIGNUM *b, int nwords);
324
325/* Deprecated versions */
326DEPRECATEDIN_0_9_8(BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
327                                             const BIGNUM *add,
328                                             const BIGNUM *rem,
329                                             void (*callback) (int, int,
330                                                               void *),
331                                             void *cb_arg))
332DEPRECATEDIN_0_9_8(int
333                   BN_is_prime(const BIGNUM *p, int nchecks,
334                               void (*callback) (int, int, void *),
335                               BN_CTX *ctx, void *cb_arg))
336DEPRECATEDIN_0_9_8(int
337                   BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
338                                        void (*callback) (int, int, void *),
339                                        BN_CTX *ctx, void *cb_arg,
340                                        int do_trial_division))
341
342/* Newer versions */
343int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
344                         const BIGNUM *rem, BN_GENCB *cb);
345int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
346int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
347                            int do_trial_division, BN_GENCB *cb);
348
349int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx);
350
351int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
352                            const BIGNUM *Xp, const BIGNUM *Xp1,
353                            const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
354                            BN_GENCB *cb);
355int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, BIGNUM *Xp1,
356                              BIGNUM *Xp2, const BIGNUM *Xp, const BIGNUM *e,
357                              BN_CTX *ctx, BN_GENCB *cb);
358
359BN_MONT_CTX *BN_MONT_CTX_new(void);
360int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
361                          BN_MONT_CTX *mont, BN_CTX *ctx);
362int BN_to_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
363                     BN_CTX *ctx);
364int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
365                       BN_CTX *ctx);
366void BN_MONT_CTX_free(BN_MONT_CTX *mont);
367int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx);
368BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
369BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock,
370                                    const BIGNUM *mod, BN_CTX *ctx);
371
372/* BN_BLINDING flags */
373# define BN_BLINDING_NO_UPDATE   0x00000001
374# define BN_BLINDING_NO_RECREATE 0x00000002
375
376BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
377void BN_BLINDING_free(BN_BLINDING *b);
378int BN_BLINDING_update(BN_BLINDING *b, BN_CTX *ctx);
379int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
380int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
381int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
382int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b,
383                          BN_CTX *);
384
385int BN_BLINDING_is_current_thread(BN_BLINDING *b);
386void BN_BLINDING_set_current_thread(BN_BLINDING *b);
387int BN_BLINDING_lock(BN_BLINDING *b);
388int BN_BLINDING_unlock(BN_BLINDING *b);
389
390unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
391void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
392BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
393                                      const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
394                                      int (*bn_mod_exp) (BIGNUM *r,
395                                                         const BIGNUM *a,
396                                                         const BIGNUM *p,
397                                                         const BIGNUM *m,
398                                                         BN_CTX *ctx,
399                                                         BN_MONT_CTX *m_ctx),
400                                      BN_MONT_CTX *m_ctx);
401
402DEPRECATEDIN_0_9_8(void BN_set_params(int mul, int high, int low, int mont))
403DEPRECATEDIN_0_9_8(int BN_get_params(int which)) /* 0, mul, 1 high, 2 low, 3
404                                                  * mont */
405
406BN_RECP_CTX *BN_RECP_CTX_new(void);
407void BN_RECP_CTX_free(BN_RECP_CTX *recp);
408int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *rdiv, BN_CTX *ctx);
409int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
410                          BN_RECP_CTX *recp, BN_CTX *ctx);
411int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
412                    const BIGNUM *m, BN_CTX *ctx);
413int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
414                BN_RECP_CTX *recp, BN_CTX *ctx);
415
416# ifndef OPENSSL_NO_EC2M
417
418/*
419 * Functions for arithmetic over binary polynomials represented by BIGNUMs.
420 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
421 * ignored. Note that input arguments are not const so that their bit arrays
422 * can be expanded to the appropriate size if needed.
423 */
424
425/*
426 * r = a + b
427 */
428int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
429#  define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
430/*
431 * r=a mod p
432 */
433int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p);
434/* r = (a * b) mod p */
435int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
436                    const BIGNUM *p, BN_CTX *ctx);
437/* r = (a * a) mod p */
438int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
439/* r = (1 / b) mod p */
440int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx);
441/* r = (a / b) mod p */
442int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
443                    const BIGNUM *p, BN_CTX *ctx);
444/* r = (a ^ b) mod p */
445int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
446                    const BIGNUM *p, BN_CTX *ctx);
447/* r = sqrt(a) mod p */
448int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
449                     BN_CTX *ctx);
450/* r^2 + r = a mod p */
451int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
452                           BN_CTX *ctx);
453#  define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
454/*-
455 * Some functions allow for representation of the irreducible polynomials
456 * as an unsigned int[], say p.  The irreducible f(t) is then of the form:
457 *     t^p[0] + t^p[1] + ... + t^p[k]
458 * where m = p[0] > p[1] > ... > p[k] = 0.
459 */
460/* r = a mod p */
461int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
462/* r = (a * b) mod p */
463int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
464                        const int p[], BN_CTX *ctx);
465/* r = (a * a) mod p */
466int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
467                        BN_CTX *ctx);
468/* r = (1 / b) mod p */
469int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
470                        BN_CTX *ctx);
471/* r = (a / b) mod p */
472int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
473                        const int p[], BN_CTX *ctx);
474/* r = (a ^ b) mod p */
475int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
476                        const int p[], BN_CTX *ctx);
477/* r = sqrt(a) mod p */
478int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
479                         const int p[], BN_CTX *ctx);
480/* r^2 + r = a mod p */
481int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
482                               const int p[], BN_CTX *ctx);
483int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max);
484int BN_GF2m_arr2poly(const int p[], BIGNUM *a);
485
486# endif
487
488/*
489 * faster mod functions for the 'NIST primes' 0 <= a < p^2
490 */
491int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
492int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
493int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
494int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
495int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
496
497const BIGNUM *BN_get0_nist_prime_192(void);
498const BIGNUM *BN_get0_nist_prime_224(void);
499const BIGNUM *BN_get0_nist_prime_256(void);
500const BIGNUM *BN_get0_nist_prime_384(void);
501const BIGNUM *BN_get0_nist_prime_521(void);
502
503int (*BN_nist_mod_func(const BIGNUM *p)) (BIGNUM *r, const BIGNUM *a,
504                                          const BIGNUM *field, BN_CTX *ctx);
505
506int BN_generate_dsa_nonce(BIGNUM *out, const BIGNUM *range,
507                          const BIGNUM *priv, const unsigned char *message,
508                          size_t message_len, BN_CTX *ctx);
509
510/* Primes from RFC 2409 */
511BIGNUM *BN_get_rfc2409_prime_768(BIGNUM *bn);
512BIGNUM *BN_get_rfc2409_prime_1024(BIGNUM *bn);
513
514/* Primes from RFC 3526 */
515BIGNUM *BN_get_rfc3526_prime_1536(BIGNUM *bn);
516BIGNUM *BN_get_rfc3526_prime_2048(BIGNUM *bn);
517BIGNUM *BN_get_rfc3526_prime_3072(BIGNUM *bn);
518BIGNUM *BN_get_rfc3526_prime_4096(BIGNUM *bn);
519BIGNUM *BN_get_rfc3526_prime_6144(BIGNUM *bn);
520BIGNUM *BN_get_rfc3526_prime_8192(BIGNUM *bn);
521
522# if OPENSSL_API_COMPAT < 0x10100000L
523#  define get_rfc2409_prime_768 BN_get_rfc2409_prime_768
524#  define get_rfc2409_prime_1024 BN_get_rfc2409_prime_1024
525#  define get_rfc3526_prime_1536 BN_get_rfc3526_prime_1536
526#  define get_rfc3526_prime_2048 BN_get_rfc3526_prime_2048
527#  define get_rfc3526_prime_3072 BN_get_rfc3526_prime_3072
528#  define get_rfc3526_prime_4096 BN_get_rfc3526_prime_4096
529#  define get_rfc3526_prime_6144 BN_get_rfc3526_prime_6144
530#  define get_rfc3526_prime_8192 BN_get_rfc3526_prime_8192
531# endif
532
533int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom);
534
535
536# ifdef  __cplusplus
537}
538# endif
539#endif
540