2 * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
5 * Licensed under the Apache License 2.0 (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
15 # include <openssl/macros.h>
20 # include <openssl/e_os2.h>
21 # ifndef OPENSSL_NO_STDIO
24 # include <openssl/opensslconf.h>
25 # include <openssl/types.h>
26 # include <openssl/crypto.h>
27 # include <openssl/bnerr.h>
34 * 64-bit processor with LP64 ABI
36 # ifdef SIXTY_FOUR_BIT_LONG
37 # define BN_ULONG unsigned long
42 * 64-bit processor other than LP64 ABI
44 # ifdef SIXTY_FOUR_BIT
45 # define BN_ULONG unsigned long long
49 # ifdef THIRTY_TWO_BIT
50 # define BN_ULONG unsigned int
54 # define BN_BITS2 (BN_BYTES * 8)
55 # define BN_BITS (BN_BITS2 * 2)
56 # define BN_TBIT ((BN_ULONG)1 << (BN_BITS2 - 1))
58 # define BN_FLG_MALLOCED 0x01
59 # define BN_FLG_STATIC_DATA 0x02
62 * avoid leaking exponent information through timing,
63 * BN_mod_exp_mont() will call BN_mod_exp_mont_consttime,
64 * BN_div() will call BN_div_no_branch,
65 * BN_mod_inverse() will call BN_mod_inverse_no_branch.
67 # define BN_FLG_CONSTTIME 0x04
68 # define BN_FLG_SECURE 0x08
70 # if !OPENSSL_API_0_9_8
71 /* deprecated name for the flag */
72 # define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME
73 # define BN_FLG_FREE 0x8000 /* used for debugging */
76 void BN_set_flags(BIGNUM *b, int n);
77 int BN_get_flags(const BIGNUM *b, int n);
79 /* Values for |top| in BN_rand() */
80 #define BN_RAND_TOP_ANY -1
81 #define BN_RAND_TOP_ONE 0
82 #define BN_RAND_TOP_TWO 1
84 /* Values for |bottom| in BN_rand() */
85 #define BN_RAND_BOTTOM_ANY 0
86 #define BN_RAND_BOTTOM_ODD 1
89 * get a clone of a BIGNUM with changed flags, for *temporary* use only (the
90 * two BIGNUMs cannot be used in parallel!). Also only for *read only* use. The
91 * value |dest| should be a newly allocated BIGNUM obtained via BN_new() that
92 * has not been otherwise initialised or used.
94 void BN_with_flags(BIGNUM *dest, const BIGNUM *b, int flags);
96 /* Wrapper function to make using BN_GENCB easier */
97 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
99 BN_GENCB *BN_GENCB_new(void);
100 void BN_GENCB_free(BN_GENCB *cb);
102 /* Populate a BN_GENCB structure with an "old"-style callback */
103 void BN_GENCB_set_old(BN_GENCB *gencb, void (*callback) (int, int, void *),
106 /* Populate a BN_GENCB structure with a "new"-style callback */
107 void BN_GENCB_set(BN_GENCB *gencb, int (*callback) (int, int, BN_GENCB *),
110 void *BN_GENCB_get_arg(BN_GENCB *cb);
112 # define BN_prime_checks 0 /* default: select number of iterations based
113 * on the size of the number */
116 * BN_prime_checks_for_size() returns the number of Miller-Rabin iterations
117 * that will be done for checking that a random number is probably prime. The
118 * error rate for accepting a composite number as prime depends on the size of
119 * the prime |b|. The error rates used are for calculating an RSA key with 2 primes,
120 * and so the level is what you would expect for a key of double the size of the
123 * This table is generated using the algorithm of FIPS PUB 186-4
124 * Digital Signature Standard (DSS), section F.1, page 117.
125 * (https://dx.doi.org/10.6028/NIST.FIPS.186-4)
127 * The following magma script was used to generate the output:
131 * for M:=3 to Floor(2*Sqrt(k-1)-1) do
138 * s+:=(RealField(32)!2)^-(j+(k-1)/j);
140 * S+:=2^(m-(m-1)*t)*s;
143 * B:=8*(Pi(RealField(32))^2-6)/3*2^(k-2)*S;
144 * pkt:=2.00743*Log(2)*k*2^-k*(A+B);
145 * seclevel:=Floor(-Log(2,pkt));
146 * if seclevel ge securitybits then
147 * printf "k: %5o, security: %o bits (t: %o, M: %o)\n",k,seclevel,t,M;
151 * if seclevel ge securitybits then break; end if;
154 * It can be run online at:
155 * http://magma.maths.usyd.edu.au/calc
158 * k: 1024, security: 129 bits (t: 6, M: 23)
160 * k is the number of bits of the prime, securitybits is the level we want to
163 * prime length | RSA key size | # MR tests | security level
164 * -------------+--------------|------------+---------------
165 * (b) >= 6394 | >= 12788 | 3 | 256 bit
166 * (b) >= 3747 | >= 7494 | 3 | 192 bit
167 * (b) >= 1345 | >= 2690 | 4 | 128 bit
168 * (b) >= 1080 | >= 2160 | 5 | 128 bit
169 * (b) >= 852 | >= 1704 | 5 | 112 bit
170 * (b) >= 476 | >= 952 | 5 | 80 bit
171 * (b) >= 400 | >= 800 | 6 | 80 bit
172 * (b) >= 347 | >= 694 | 7 | 80 bit
173 * (b) >= 308 | >= 616 | 8 | 80 bit
174 * (b) >= 55 | >= 110 | 27 | 64 bit
175 * (b) >= 6 | >= 12 | 34 | 64 bit
178 # define BN_prime_checks_for_size(b) ((b) >= 3747 ? 3 : \
187 # define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
189 int BN_abs_is_word(const BIGNUM *a, const BN_ULONG w);
190 int BN_is_zero(const BIGNUM *a);
191 int BN_is_one(const BIGNUM *a);
192 int BN_is_word(const BIGNUM *a, const BN_ULONG w);
193 int BN_is_odd(const BIGNUM *a);
195 # define BN_one(a) (BN_set_word((a),1))
197 void BN_zero_ex(BIGNUM *a);
199 # if OPENSSL_API_0_9_8
200 # define BN_zero(a) BN_zero_ex(a)
202 # define BN_zero(a) (BN_set_word((a),0))
205 const BIGNUM *BN_value_one(void);
206 char *BN_options(void);
207 BN_CTX *BN_CTX_new_ex(OPENSSL_CTX *ctx);
208 BN_CTX *BN_CTX_new(void);
209 BN_CTX *BN_CTX_secure_new_ex(OPENSSL_CTX *ctx);
210 BN_CTX *BN_CTX_secure_new(void);
211 void BN_CTX_free(BN_CTX *c);
212 void BN_CTX_start(BN_CTX *ctx);
213 BIGNUM *BN_CTX_get(BN_CTX *ctx);
214 void BN_CTX_end(BN_CTX *ctx);
215 int BN_rand_ex(BIGNUM *rnd, int bits, int top, int bottom, BN_CTX *ctx);
216 int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
217 int BN_priv_rand_ex(BIGNUM *rnd, int bits, int top, int bottom, BN_CTX *ctx);
218 int BN_priv_rand(BIGNUM *rnd, int bits, int top, int bottom);
219 int BN_rand_range_ex(BIGNUM *r, const BIGNUM *range, BN_CTX *ctx);
220 int BN_rand_range(BIGNUM *rnd, const BIGNUM *range);
221 int BN_priv_rand_range_ex(BIGNUM *r, const BIGNUM *range, BN_CTX *ctx);
222 int BN_priv_rand_range(BIGNUM *rnd, const BIGNUM *range);
223 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
224 int BN_pseudo_rand_range(BIGNUM *rnd, const BIGNUM *range);
225 int BN_num_bits(const BIGNUM *a);
226 int BN_num_bits_word(BN_ULONG l);
227 int BN_security_bits(int L, int N);
228 BIGNUM *BN_new(void);
229 BIGNUM *BN_secure_new(void);
230 void BN_clear_free(BIGNUM *a);
231 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
232 void BN_swap(BIGNUM *a, BIGNUM *b);
233 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
234 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
235 int BN_bn2binpad(const BIGNUM *a, unsigned char *to, int tolen);
236 BIGNUM *BN_lebin2bn(const unsigned char *s, int len, BIGNUM *ret);
237 int BN_bn2lebinpad(const BIGNUM *a, unsigned char *to, int tolen);
238 BIGNUM *BN_native2bn(const unsigned char *s, int len, BIGNUM *ret);
239 int BN_bn2nativepad(const BIGNUM *a, unsigned char *to, int tolen);
240 BIGNUM *BN_mpi2bn(const unsigned char *s, int len, BIGNUM *ret);
241 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
242 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
243 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
244 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
245 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
246 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
247 int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
248 /** BN_set_negative sets sign of a BIGNUM
249 * \param b pointer to the BIGNUM object
250 * \param n 0 if the BIGNUM b should be positive and a value != 0 otherwise
252 void BN_set_negative(BIGNUM *b, int n);
253 /** BN_is_negative returns 1 if the BIGNUM is negative
254 * \param b pointer to the BIGNUM object
255 * \return 1 if a < 0 and 0 otherwise
257 int BN_is_negative(const BIGNUM *b);
259 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
261 # define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
262 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
263 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
265 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
267 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
269 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
271 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
273 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
274 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
275 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
276 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
278 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
280 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
281 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
282 int BN_mul_word(BIGNUM *a, BN_ULONG w);
283 int BN_add_word(BIGNUM *a, BN_ULONG w);
284 int BN_sub_word(BIGNUM *a, BN_ULONG w);
285 int BN_set_word(BIGNUM *a, BN_ULONG w);
286 BN_ULONG BN_get_word(const BIGNUM *a);
288 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
289 void BN_free(BIGNUM *a);
290 int BN_is_bit_set(const BIGNUM *a, int n);
291 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
292 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
293 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
295 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
296 const BIGNUM *m, BN_CTX *ctx);
297 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
298 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
299 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
300 const BIGNUM *m, BN_CTX *ctx,
301 BN_MONT_CTX *in_mont);
302 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
303 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
304 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
305 const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
306 BN_CTX *ctx, BN_MONT_CTX *m_ctx);
307 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
308 const BIGNUM *m, BN_CTX *ctx);
310 int BN_mask_bits(BIGNUM *a, int n);
311 # ifndef OPENSSL_NO_STDIO
312 int BN_print_fp(FILE *fp, const BIGNUM *a);
314 int BN_print(BIO *bio, const BIGNUM *a);
315 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
316 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
317 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
318 void BN_clear(BIGNUM *a);
319 BIGNUM *BN_dup(const BIGNUM *a);
320 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
321 int BN_set_bit(BIGNUM *a, int n);
322 int BN_clear_bit(BIGNUM *a, int n);
323 char *BN_bn2hex(const BIGNUM *a);
324 char *BN_bn2dec(const BIGNUM *a);
325 int BN_hex2bn(BIGNUM **a, const char *str);
326 int BN_dec2bn(BIGNUM **a, const char *str);
327 int BN_asc2bn(BIGNUM **a, const char *str);
328 int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
329 int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); /* returns
332 BIGNUM *BN_mod_inverse(BIGNUM *ret,
333 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
334 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
335 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
337 void BN_consttime_swap(BN_ULONG swap, BIGNUM *a, BIGNUM *b, int nwords);
339 /* Deprecated versions */
340 DEPRECATEDIN_0_9_8(BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
343 void (*callback) (int, int,
346 DEPRECATEDIN_0_9_8(int
347 BN_is_prime(const BIGNUM *p, int nchecks,
348 void (*callback) (int, int, void *),
349 BN_CTX *ctx, void *cb_arg))
350 DEPRECATEDIN_0_9_8(int
351 BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
352 void (*callback) (int, int, void *),
353 BN_CTX *ctx, void *cb_arg,
354 int do_trial_division))
357 int BN_generate_prime_ex2(BIGNUM *ret, int bits, int safe,
358 const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb,
360 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
361 const BIGNUM *rem, BN_GENCB *cb);
362 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
363 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
364 int do_trial_division, BN_GENCB *cb);
366 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx);
368 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
369 const BIGNUM *Xp, const BIGNUM *Xp1,
370 const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
372 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, BIGNUM *Xp1,
373 BIGNUM *Xp2, const BIGNUM *Xp, const BIGNUM *e,
374 BN_CTX *ctx, BN_GENCB *cb);
376 BN_MONT_CTX *BN_MONT_CTX_new(void);
377 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
378 BN_MONT_CTX *mont, BN_CTX *ctx);
379 int BN_to_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
381 int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
383 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
384 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx);
385 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
386 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_RWLOCK *lock,
387 const BIGNUM *mod, BN_CTX *ctx);
389 /* BN_BLINDING flags */
390 # define BN_BLINDING_NO_UPDATE 0x00000001
391 # define BN_BLINDING_NO_RECREATE 0x00000002
393 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
394 void BN_BLINDING_free(BN_BLINDING *b);
395 int BN_BLINDING_update(BN_BLINDING *b, BN_CTX *ctx);
396 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
397 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
398 int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
399 int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b,
402 int BN_BLINDING_is_current_thread(BN_BLINDING *b);
403 void BN_BLINDING_set_current_thread(BN_BLINDING *b);
404 int BN_BLINDING_lock(BN_BLINDING *b);
405 int BN_BLINDING_unlock(BN_BLINDING *b);
407 unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
408 void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
409 BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
410 const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
411 int (*bn_mod_exp) (BIGNUM *r,
419 DEPRECATEDIN_0_9_8(void BN_set_params(int mul, int high, int low, int mont))
420 DEPRECATEDIN_0_9_8(int BN_get_params(int which)) /* 0, mul, 1 high, 2 low, 3
423 BN_RECP_CTX *BN_RECP_CTX_new(void);
424 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
425 int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *rdiv, BN_CTX *ctx);
426 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
427 BN_RECP_CTX *recp, BN_CTX *ctx);
428 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
429 const BIGNUM *m, BN_CTX *ctx);
430 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
431 BN_RECP_CTX *recp, BN_CTX *ctx);
433 # ifndef OPENSSL_NO_EC2M
436 * Functions for arithmetic over binary polynomials represented by BIGNUMs.
437 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
438 * ignored. Note that input arguments are not const so that their bit arrays
439 * can be expanded to the appropriate size if needed.
445 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
446 # define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
450 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p);
451 /* r = (a * b) mod p */
452 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
453 const BIGNUM *p, BN_CTX *ctx);
454 /* r = (a * a) mod p */
455 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
456 /* r = (1 / b) mod p */
457 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx);
458 /* r = (a / b) mod p */
459 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
460 const BIGNUM *p, BN_CTX *ctx);
461 /* r = (a ^ b) mod p */
462 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
463 const BIGNUM *p, BN_CTX *ctx);
464 /* r = sqrt(a) mod p */
465 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
467 /* r^2 + r = a mod p */
468 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
470 # define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
472 * Some functions allow for representation of the irreducible polynomials
473 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
474 * t^p[0] + t^p[1] + ... + t^p[k]
475 * where m = p[0] > p[1] > ... > p[k] = 0.
478 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]);
479 /* r = (a * b) mod p */
480 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
481 const int p[], BN_CTX *ctx);
482 /* r = (a * a) mod p */
483 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
485 /* r = (1 / b) mod p */
486 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const int p[],
488 /* r = (a / b) mod p */
489 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
490 const int p[], BN_CTX *ctx);
491 /* r = (a ^ b) mod p */
492 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
493 const int p[], BN_CTX *ctx);
494 /* r = sqrt(a) mod p */
495 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
496 const int p[], BN_CTX *ctx);
497 /* r^2 + r = a mod p */
498 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
499 const int p[], BN_CTX *ctx);
500 int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max);
501 int BN_GF2m_arr2poly(const int p[], BIGNUM *a);
506 * faster mod functions for the 'NIST primes' 0 <= a < p^2
508 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
509 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
510 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
511 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
512 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
514 const BIGNUM *BN_get0_nist_prime_192(void);
515 const BIGNUM *BN_get0_nist_prime_224(void);
516 const BIGNUM *BN_get0_nist_prime_256(void);
517 const BIGNUM *BN_get0_nist_prime_384(void);
518 const BIGNUM *BN_get0_nist_prime_521(void);
520 int (*BN_nist_mod_func(const BIGNUM *p)) (BIGNUM *r, const BIGNUM *a,
521 const BIGNUM *field, BN_CTX *ctx);
523 int BN_generate_dsa_nonce(BIGNUM *out, const BIGNUM *range,
524 const BIGNUM *priv, const unsigned char *message,
525 size_t message_len, BN_CTX *ctx);
527 /* Primes from RFC 2409 */
528 BIGNUM *BN_get_rfc2409_prime_768(BIGNUM *bn);
529 BIGNUM *BN_get_rfc2409_prime_1024(BIGNUM *bn);
531 /* Primes from RFC 3526 */
532 BIGNUM *BN_get_rfc3526_prime_1536(BIGNUM *bn);
533 BIGNUM *BN_get_rfc3526_prime_2048(BIGNUM *bn);
534 BIGNUM *BN_get_rfc3526_prime_3072(BIGNUM *bn);
535 BIGNUM *BN_get_rfc3526_prime_4096(BIGNUM *bn);
536 BIGNUM *BN_get_rfc3526_prime_6144(BIGNUM *bn);
537 BIGNUM *BN_get_rfc3526_prime_8192(BIGNUM *bn);
539 # if !OPENSSL_API_1_1_0
540 # define get_rfc2409_prime_768 BN_get_rfc2409_prime_768
541 # define get_rfc2409_prime_1024 BN_get_rfc2409_prime_1024
542 # define get_rfc3526_prime_1536 BN_get_rfc3526_prime_1536
543 # define get_rfc3526_prime_2048 BN_get_rfc3526_prime_2048
544 # define get_rfc3526_prime_3072 BN_get_rfc3526_prime_3072
545 # define get_rfc3526_prime_4096 BN_get_rfc3526_prime_4096
546 # define get_rfc3526_prime_6144 BN_get_rfc3526_prime_6144
547 # define get_rfc3526_prime_8192 BN_get_rfc3526_prime_8192
550 int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom);