]>
git.ipfire.org Git - thirdparty/openssl.git/blob - include/openssl/bn.h
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
14 # include <openssl/e_os2.h>
15 # ifndef OPENSSL_NO_STDIO
18 # include <openssl/opensslconf.h>
19 # include <openssl/ossl_typ.h>
20 # include <openssl/crypto.h>
21 # include <openssl/bnerr.h>
28 * 64-bit processor with LP64 ABI
30 # ifdef SIXTY_FOUR_BIT_LONG
31 # define BN_ULONG unsigned long
36 * 64-bit processor other than LP64 ABI
38 # ifdef SIXTY_FOUR_BIT
39 # define BN_ULONG unsigned long long
43 # ifdef THIRTY_TWO_BIT
44 # define BN_ULONG unsigned int
48 # define BN_BITS2 (BN_BYTES * 8)
49 # define BN_BITS (BN_BITS2 * 2)
50 # define BN_TBIT ((BN_ULONG)1 << (BN_BITS2 - 1))
52 # define BN_FLG_MALLOCED 0x01
53 # define BN_FLG_STATIC_DATA 0x02
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.
61 # define BN_FLG_CONSTTIME 0x04
62 # define BN_FLG_SECURE 0x08
64 # if !OPENSSL_API_0_9_8
65 /* deprecated name for the flag */
66 # define BN_FLG_EXP_CONSTTIME BN_FLG_CONSTTIME
67 # define BN_FLG_FREE 0x8000 /* used for debugging */
70 void BN_set_flags(BIGNUM
*b
, int n
);
71 int BN_get_flags(const BIGNUM
*b
, int n
);
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
78 /* Values for |bottom| in BN_rand() */
79 #define BN_RAND_BOTTOM_ANY 0
80 #define BN_RAND_BOTTOM_ODD 1
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.
88 void BN_with_flags(BIGNUM
*dest
, const BIGNUM
*b
, int flags
);
90 /* Wrapper function to make using BN_GENCB easier */
91 int BN_GENCB_call(BN_GENCB
*cb
, int a
, int b
);
93 BN_GENCB
*BN_GENCB_new(void);
94 void BN_GENCB_free(BN_GENCB
*cb
);
96 /* Populate a BN_GENCB structure with an "old"-style callback */
97 void BN_GENCB_set_old(BN_GENCB
*gencb
, void (*callback
) (int, int, void *),
100 /* Populate a BN_GENCB structure with a "new"-style callback */
101 void BN_GENCB_set(BN_GENCB
*gencb
, int (*callback
) (int, int, BN_GENCB
*),
104 void *BN_GENCB_get_arg(BN_GENCB
*cb
);
106 # define BN_prime_checks 0 /* default: select number of iterations based
107 * on the size of the number */
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
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)
121 * The following magma script was used to generate the output:
125 * for M:=3 to Floor(2*Sqrt(k-1)-1) do
132 * s+:=(RealField(32)!2)^-(j+(k-1)/j);
134 * S+:=2^(m-(m-1)*t)*s;
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;
145 * if seclevel ge securitybits then break; end if;
148 * It can be run online at:
149 * http://magma.maths.usyd.edu.au/calc
152 * k: 1024, security: 129 bits (t: 6, M: 23)
154 * k is the number of bits of the prime, securitybits is the level we want to
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
172 # define BN_prime_checks_for_size(b) ((b) >= 3747 ? 3 : \
181 # define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
183 int BN_abs_is_word(const BIGNUM
*a
, const BN_ULONG w
);
184 int BN_is_zero(const BIGNUM
*a
);
185 int BN_is_one(const BIGNUM
*a
);
186 int BN_is_word(const BIGNUM
*a
, const BN_ULONG w
);
187 int BN_is_odd(const BIGNUM
*a
);
189 # define BN_one(a) (BN_set_word((a),1))
191 void BN_zero_ex(BIGNUM
*a
);
193 # if OPENSSL_API_0_9_8
194 # define BN_zero(a) BN_zero_ex(a)
196 # define BN_zero(a) (BN_set_word((a),0))
199 const BIGNUM
*BN_value_one(void);
200 char *BN_options(void);
201 BN_CTX
*BN_CTX_new_ex(OPENSSL_CTX
*ctx
);
202 BN_CTX
*BN_CTX_new(void);
203 BN_CTX
*BN_CTX_secure_new_ex(OPENSSL_CTX
*ctx
);
204 BN_CTX
*BN_CTX_secure_new(void);
205 void BN_CTX_free(BN_CTX
*c
);
206 void BN_CTX_start(BN_CTX
*ctx
);
207 BIGNUM
*BN_CTX_get(BN_CTX
*ctx
);
208 void BN_CTX_end(BN_CTX
*ctx
);
209 int BN_rand(BIGNUM
*rnd
, int bits
, int top
, int bottom
);
210 int BN_priv_rand(BIGNUM
*rnd
, int bits
, int top
, int bottom
);
211 int BN_rand_range(BIGNUM
*rnd
, const BIGNUM
*range
);
212 int BN_priv_rand_range(BIGNUM
*rnd
, const BIGNUM
*range
);
213 int BN_pseudo_rand(BIGNUM
*rnd
, int bits
, int top
, int bottom
);
214 int BN_pseudo_rand_range(BIGNUM
*rnd
, const BIGNUM
*range
);
215 int BN_num_bits(const BIGNUM
*a
);
216 int BN_num_bits_word(BN_ULONG l
);
217 int BN_security_bits(int L
, int N
);
218 BIGNUM
*BN_new(void);
219 BIGNUM
*BN_secure_new(void);
220 void BN_clear_free(BIGNUM
*a
);
221 BIGNUM
*BN_copy(BIGNUM
*a
, const BIGNUM
*b
);
222 void BN_swap(BIGNUM
*a
, BIGNUM
*b
);
223 BIGNUM
*BN_bin2bn(const unsigned char *s
, int len
, BIGNUM
*ret
);
224 int BN_bn2bin(const BIGNUM
*a
, unsigned char *to
);
225 int BN_bn2binpad(const BIGNUM
*a
, unsigned char *to
, int tolen
);
226 BIGNUM
*BN_lebin2bn(const unsigned char *s
, int len
, BIGNUM
*ret
);
227 int BN_bn2lebinpad(const BIGNUM
*a
, unsigned char *to
, int tolen
);
228 BIGNUM
*BN_native2bn(const unsigned char *s
, int len
, BIGNUM
*ret
);
229 int BN_bn2nativepad(const BIGNUM
*a
, unsigned char *to
, int tolen
);
230 BIGNUM
*BN_mpi2bn(const unsigned char *s
, int len
, BIGNUM
*ret
);
231 int BN_bn2mpi(const BIGNUM
*a
, unsigned char *to
);
232 int BN_sub(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
);
233 int BN_usub(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
);
234 int BN_uadd(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
);
235 int BN_add(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
);
236 int BN_mul(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
);
237 int BN_sqr(BIGNUM
*r
, const BIGNUM
*a
, BN_CTX
*ctx
);
238 /** BN_set_negative sets sign of a BIGNUM
239 * \param b pointer to the BIGNUM object
240 * \param n 0 if the BIGNUM b should be positive and a value != 0 otherwise
242 void BN_set_negative(BIGNUM
*b
, int n
);
243 /** BN_is_negative returns 1 if the BIGNUM is negative
244 * \param b pointer to the BIGNUM object
245 * \return 1 if a < 0 and 0 otherwise
247 int BN_is_negative(const BIGNUM
*b
);
249 int BN_div(BIGNUM
*dv
, BIGNUM
*rem
, const BIGNUM
*m
, const BIGNUM
*d
,
251 # define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
252 int BN_nnmod(BIGNUM
*r
, const BIGNUM
*m
, const BIGNUM
*d
, BN_CTX
*ctx
);
253 int BN_mod_add(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const BIGNUM
*m
,
255 int BN_mod_add_quick(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
257 int BN_mod_sub(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const BIGNUM
*m
,
259 int BN_mod_sub_quick(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
261 int BN_mod_mul(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, const BIGNUM
*m
,
263 int BN_mod_sqr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*m
, BN_CTX
*ctx
);
264 int BN_mod_lshift1(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*m
, BN_CTX
*ctx
);
265 int BN_mod_lshift1_quick(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*m
);
266 int BN_mod_lshift(BIGNUM
*r
, const BIGNUM
*a
, int n
, const BIGNUM
*m
,
268 int BN_mod_lshift_quick(BIGNUM
*r
, const BIGNUM
*a
, int n
, const BIGNUM
*m
);
270 BN_ULONG
BN_mod_word(const BIGNUM
*a
, BN_ULONG w
);
271 BN_ULONG
BN_div_word(BIGNUM
*a
, BN_ULONG w
);
272 int BN_mul_word(BIGNUM
*a
, BN_ULONG w
);
273 int BN_add_word(BIGNUM
*a
, BN_ULONG w
);
274 int BN_sub_word(BIGNUM
*a
, BN_ULONG w
);
275 int BN_set_word(BIGNUM
*a
, BN_ULONG w
);
276 BN_ULONG
BN_get_word(const BIGNUM
*a
);
278 int BN_cmp(const BIGNUM
*a
, const BIGNUM
*b
);
279 void BN_free(BIGNUM
*a
);
280 int BN_is_bit_set(const BIGNUM
*a
, int n
);
281 int BN_lshift(BIGNUM
*r
, const BIGNUM
*a
, int n
);
282 int BN_lshift1(BIGNUM
*r
, const BIGNUM
*a
);
283 int BN_exp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
);
285 int BN_mod_exp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
286 const BIGNUM
*m
, BN_CTX
*ctx
);
287 int BN_mod_exp_mont(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
288 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*m_ctx
);
289 int BN_mod_exp_mont_consttime(BIGNUM
*rr
, const BIGNUM
*a
, const BIGNUM
*p
,
290 const BIGNUM
*m
, BN_CTX
*ctx
,
291 BN_MONT_CTX
*in_mont
);
292 int BN_mod_exp_mont_word(BIGNUM
*r
, BN_ULONG a
, const BIGNUM
*p
,
293 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*m_ctx
);
294 int BN_mod_exp2_mont(BIGNUM
*r
, const BIGNUM
*a1
, const BIGNUM
*p1
,
295 const BIGNUM
*a2
, const BIGNUM
*p2
, const BIGNUM
*m
,
296 BN_CTX
*ctx
, BN_MONT_CTX
*m_ctx
);
297 int BN_mod_exp_simple(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
298 const BIGNUM
*m
, BN_CTX
*ctx
);
300 int BN_mask_bits(BIGNUM
*a
, int n
);
301 # ifndef OPENSSL_NO_STDIO
302 int BN_print_fp(FILE *fp
, const BIGNUM
*a
);
304 int BN_print(BIO
*bio
, const BIGNUM
*a
);
305 int BN_reciprocal(BIGNUM
*r
, const BIGNUM
*m
, int len
, BN_CTX
*ctx
);
306 int BN_rshift(BIGNUM
*r
, const BIGNUM
*a
, int n
);
307 int BN_rshift1(BIGNUM
*r
, const BIGNUM
*a
);
308 void BN_clear(BIGNUM
*a
);
309 BIGNUM
*BN_dup(const BIGNUM
*a
);
310 int BN_ucmp(const BIGNUM
*a
, const BIGNUM
*b
);
311 int BN_set_bit(BIGNUM
*a
, int n
);
312 int BN_clear_bit(BIGNUM
*a
, int n
);
313 char *BN_bn2hex(const BIGNUM
*a
);
314 char *BN_bn2dec(const BIGNUM
*a
);
315 int BN_hex2bn(BIGNUM
**a
, const char *str
);
316 int BN_dec2bn(BIGNUM
**a
, const char *str
);
317 int BN_asc2bn(BIGNUM
**a
, const char *str
);
318 int BN_gcd(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
);
319 int BN_kronecker(const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
); /* returns
322 BIGNUM
*BN_mod_inverse(BIGNUM
*ret
,
323 const BIGNUM
*a
, const BIGNUM
*n
, BN_CTX
*ctx
);
324 BIGNUM
*BN_mod_sqrt(BIGNUM
*ret
,
325 const BIGNUM
*a
, const BIGNUM
*n
, BN_CTX
*ctx
);
327 void BN_consttime_swap(BN_ULONG swap
, BIGNUM
*a
, BIGNUM
*b
, int nwords
);
329 /* Deprecated versions */
330 DEPRECATEDIN_0_9_8(BIGNUM
*BN_generate_prime(BIGNUM
*ret
, int bits
, int safe
,
333 void (*callback
) (int, int,
336 DEPRECATEDIN_0_9_8(int
337 BN_is_prime(const BIGNUM
*p
, int nchecks
,
338 void (*callback
) (int, int, void *),
339 BN_CTX
*ctx
, void *cb_arg
))
340 DEPRECATEDIN_0_9_8(int
341 BN_is_prime_fasttest(const BIGNUM
*p
, int nchecks
,
342 void (*callback
) (int, int, void *),
343 BN_CTX
*ctx
, void *cb_arg
,
344 int do_trial_division
))
347 int BN_generate_prime_ex(BIGNUM
*ret
, int bits
, int safe
, const BIGNUM
*add
,
348 const BIGNUM
*rem
, BN_GENCB
*cb
);
349 int BN_is_prime_ex(const BIGNUM
*p
, int nchecks
, BN_CTX
*ctx
, BN_GENCB
*cb
);
350 int BN_is_prime_fasttest_ex(const BIGNUM
*p
, int nchecks
, BN_CTX
*ctx
,
351 int do_trial_division
, BN_GENCB
*cb
);
353 int BN_X931_generate_Xpq(BIGNUM
*Xp
, BIGNUM
*Xq
, int nbits
, BN_CTX
*ctx
);
355 int BN_X931_derive_prime_ex(BIGNUM
*p
, BIGNUM
*p1
, BIGNUM
*p2
,
356 const BIGNUM
*Xp
, const BIGNUM
*Xp1
,
357 const BIGNUM
*Xp2
, const BIGNUM
*e
, BN_CTX
*ctx
,
359 int BN_X931_generate_prime_ex(BIGNUM
*p
, BIGNUM
*p1
, BIGNUM
*p2
, BIGNUM
*Xp1
,
360 BIGNUM
*Xp2
, const BIGNUM
*Xp
, const BIGNUM
*e
,
361 BN_CTX
*ctx
, BN_GENCB
*cb
);
363 BN_MONT_CTX
*BN_MONT_CTX_new(void);
364 int BN_mod_mul_montgomery(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
365 BN_MONT_CTX
*mont
, BN_CTX
*ctx
);
366 int BN_to_montgomery(BIGNUM
*r
, const BIGNUM
*a
, BN_MONT_CTX
*mont
,
368 int BN_from_montgomery(BIGNUM
*r
, const BIGNUM
*a
, BN_MONT_CTX
*mont
,
370 void BN_MONT_CTX_free(BN_MONT_CTX
*mont
);
371 int BN_MONT_CTX_set(BN_MONT_CTX
*mont
, const BIGNUM
*mod
, BN_CTX
*ctx
);
372 BN_MONT_CTX
*BN_MONT_CTX_copy(BN_MONT_CTX
*to
, BN_MONT_CTX
*from
);
373 BN_MONT_CTX
*BN_MONT_CTX_set_locked(BN_MONT_CTX
**pmont
, CRYPTO_RWLOCK
*lock
,
374 const BIGNUM
*mod
, BN_CTX
*ctx
);
376 /* BN_BLINDING flags */
377 # define BN_BLINDING_NO_UPDATE 0x00000001
378 # define BN_BLINDING_NO_RECREATE 0x00000002
380 BN_BLINDING
*BN_BLINDING_new(const BIGNUM
*A
, const BIGNUM
*Ai
, BIGNUM
*mod
);
381 void BN_BLINDING_free(BN_BLINDING
*b
);
382 int BN_BLINDING_update(BN_BLINDING
*b
, BN_CTX
*ctx
);
383 int BN_BLINDING_convert(BIGNUM
*n
, BN_BLINDING
*b
, BN_CTX
*ctx
);
384 int BN_BLINDING_invert(BIGNUM
*n
, BN_BLINDING
*b
, BN_CTX
*ctx
);
385 int BN_BLINDING_convert_ex(BIGNUM
*n
, BIGNUM
*r
, BN_BLINDING
*b
, BN_CTX
*);
386 int BN_BLINDING_invert_ex(BIGNUM
*n
, const BIGNUM
*r
, BN_BLINDING
*b
,
389 int BN_BLINDING_is_current_thread(BN_BLINDING
*b
);
390 void BN_BLINDING_set_current_thread(BN_BLINDING
*b
);
391 int BN_BLINDING_lock(BN_BLINDING
*b
);
392 int BN_BLINDING_unlock(BN_BLINDING
*b
);
394 unsigned long BN_BLINDING_get_flags(const BN_BLINDING
*);
395 void BN_BLINDING_set_flags(BN_BLINDING
*, unsigned long);
396 BN_BLINDING
*BN_BLINDING_create_param(BN_BLINDING
*b
,
397 const BIGNUM
*e
, BIGNUM
*m
, BN_CTX
*ctx
,
398 int (*bn_mod_exp
) (BIGNUM
*r
,
406 DEPRECATEDIN_0_9_8(void BN_set_params(int mul
, int high
, int low
, int mont
))
407 DEPRECATEDIN_0_9_8(int BN_get_params(int which
)) /* 0, mul, 1 high, 2 low, 3
410 BN_RECP_CTX
*BN_RECP_CTX_new(void);
411 void BN_RECP_CTX_free(BN_RECP_CTX
*recp
);
412 int BN_RECP_CTX_set(BN_RECP_CTX
*recp
, const BIGNUM
*rdiv
, BN_CTX
*ctx
);
413 int BN_mod_mul_reciprocal(BIGNUM
*r
, const BIGNUM
*x
, const BIGNUM
*y
,
414 BN_RECP_CTX
*recp
, BN_CTX
*ctx
);
415 int BN_mod_exp_recp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
416 const BIGNUM
*m
, BN_CTX
*ctx
);
417 int BN_div_recp(BIGNUM
*dv
, BIGNUM
*rem
, const BIGNUM
*m
,
418 BN_RECP_CTX
*recp
, BN_CTX
*ctx
);
420 # ifndef OPENSSL_NO_EC2M
423 * Functions for arithmetic over binary polynomials represented by BIGNUMs.
424 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
425 * ignored. Note that input arguments are not const so that their bit arrays
426 * can be expanded to the appropriate size if needed.
432 int BN_GF2m_add(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
);
433 # define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
437 int BN_GF2m_mod(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
);
438 /* r = (a * b) mod p */
439 int BN_GF2m_mod_mul(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
440 const BIGNUM
*p
, BN_CTX
*ctx
);
441 /* r = (a * a) mod p */
442 int BN_GF2m_mod_sqr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
);
443 /* r = (1 / b) mod p */
444 int BN_GF2m_mod_inv(BIGNUM
*r
, const BIGNUM
*b
, const BIGNUM
*p
, BN_CTX
*ctx
);
445 /* r = (a / b) mod p */
446 int BN_GF2m_mod_div(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
447 const BIGNUM
*p
, BN_CTX
*ctx
);
448 /* r = (a ^ b) mod p */
449 int BN_GF2m_mod_exp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
450 const BIGNUM
*p
, BN_CTX
*ctx
);
451 /* r = sqrt(a) mod p */
452 int BN_GF2m_mod_sqrt(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
454 /* r^2 + r = a mod p */
455 int BN_GF2m_mod_solve_quad(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
457 # define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
459 * Some functions allow for representation of the irreducible polynomials
460 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
461 * t^p[0] + t^p[1] + ... + t^p[k]
462 * where m = p[0] > p[1] > ... > p[k] = 0.
465 int BN_GF2m_mod_arr(BIGNUM
*r
, const BIGNUM
*a
, const int p
[]);
466 /* r = (a * b) mod p */
467 int BN_GF2m_mod_mul_arr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
468 const int p
[], BN_CTX
*ctx
);
469 /* r = (a * a) mod p */
470 int BN_GF2m_mod_sqr_arr(BIGNUM
*r
, const BIGNUM
*a
, const int p
[],
472 /* r = (1 / b) mod p */
473 int BN_GF2m_mod_inv_arr(BIGNUM
*r
, const BIGNUM
*b
, const int p
[],
475 /* r = (a / b) mod p */
476 int BN_GF2m_mod_div_arr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
477 const int p
[], BN_CTX
*ctx
);
478 /* r = (a ^ b) mod p */
479 int BN_GF2m_mod_exp_arr(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
480 const int p
[], BN_CTX
*ctx
);
481 /* r = sqrt(a) mod p */
482 int BN_GF2m_mod_sqrt_arr(BIGNUM
*r
, const BIGNUM
*a
,
483 const int p
[], BN_CTX
*ctx
);
484 /* r^2 + r = a mod p */
485 int BN_GF2m_mod_solve_quad_arr(BIGNUM
*r
, const BIGNUM
*a
,
486 const int p
[], BN_CTX
*ctx
);
487 int BN_GF2m_poly2arr(const BIGNUM
*a
, int p
[], int max
);
488 int BN_GF2m_arr2poly(const int p
[], BIGNUM
*a
);
493 * faster mod functions for the 'NIST primes' 0 <= a < p^2
495 int BN_nist_mod_192(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
);
496 int BN_nist_mod_224(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
);
497 int BN_nist_mod_256(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
);
498 int BN_nist_mod_384(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
);
499 int BN_nist_mod_521(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
);
501 const BIGNUM
*BN_get0_nist_prime_192(void);
502 const BIGNUM
*BN_get0_nist_prime_224(void);
503 const BIGNUM
*BN_get0_nist_prime_256(void);
504 const BIGNUM
*BN_get0_nist_prime_384(void);
505 const BIGNUM
*BN_get0_nist_prime_521(void);
507 int (*BN_nist_mod_func(const BIGNUM
*p
)) (BIGNUM
*r
, const BIGNUM
*a
,
508 const BIGNUM
*field
, BN_CTX
*ctx
);
510 int BN_generate_dsa_nonce(BIGNUM
*out
, const BIGNUM
*range
,
511 const BIGNUM
*priv
, const unsigned char *message
,
512 size_t message_len
, BN_CTX
*ctx
);
514 /* Primes from RFC 2409 */
515 BIGNUM
*BN_get_rfc2409_prime_768(BIGNUM
*bn
);
516 BIGNUM
*BN_get_rfc2409_prime_1024(BIGNUM
*bn
);
518 /* Primes from RFC 3526 */
519 BIGNUM
*BN_get_rfc3526_prime_1536(BIGNUM
*bn
);
520 BIGNUM
*BN_get_rfc3526_prime_2048(BIGNUM
*bn
);
521 BIGNUM
*BN_get_rfc3526_prime_3072(BIGNUM
*bn
);
522 BIGNUM
*BN_get_rfc3526_prime_4096(BIGNUM
*bn
);
523 BIGNUM
*BN_get_rfc3526_prime_6144(BIGNUM
*bn
);
524 BIGNUM
*BN_get_rfc3526_prime_8192(BIGNUM
*bn
);
526 # if !OPENSSL_API_1_1_0
527 # define get_rfc2409_prime_768 BN_get_rfc2409_prime_768
528 # define get_rfc2409_prime_1024 BN_get_rfc2409_prime_1024
529 # define get_rfc3526_prime_1536 BN_get_rfc3526_prime_1536
530 # define get_rfc3526_prime_2048 BN_get_rfc3526_prime_2048
531 # define get_rfc3526_prime_3072 BN_get_rfc3526_prime_3072
532 # define get_rfc3526_prime_4096 BN_get_rfc3526_prime_4096
533 # define get_rfc3526_prime_6144 BN_get_rfc3526_prime_6144
534 # define get_rfc3526_prime_8192 BN_get_rfc3526_prime_8192
537 int BN_bntest_rand(BIGNUM
*rnd
, int bits
, int top
, int bottom
);