5 BN_generate_prime_ex2, BN_generate_prime_ex, BN_is_prime_ex, BN_check_prime,
6 BN_is_prime_fasttest_ex, BN_GENCB_call, BN_GENCB_new, BN_GENCB_free,
7 BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg, BN_generate_prime,
8 BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality
12 #include <openssl/bn.h>
14 int BN_generate_prime_ex2(BIGNUM *ret, int bits, int safe,
15 const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb,
18 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
19 const BIGNUM *rem, BN_GENCB *cb);
21 int BN_check_prime(const BIGNUM *p, BN_CTX *ctx, BN_GENCB *cb);
23 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
25 BN_GENCB *BN_GENCB_new(void);
27 void BN_GENCB_free(BN_GENCB *cb);
29 void BN_GENCB_set_old(BN_GENCB *gencb,
30 void (*callback)(int, int, void *), void *cb_arg);
32 void BN_GENCB_set(BN_GENCB *gencb,
33 int (*callback)(int, int, BN_GENCB *), void *cb_arg);
35 void *BN_GENCB_get_arg(BN_GENCB *cb);
37 Deprecated since OpenSSL 0.9.8, can be hidden entirely by defining
38 B<OPENSSL_API_COMPAT> with a suitable version value, see
39 L<openssl_user_macros(7)>:
41 BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
42 BIGNUM *rem, void (*callback)(int, int, void *),
45 int BN_is_prime(const BIGNUM *p, int nchecks,
46 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
48 int BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
49 void (*callback)(int, int, void *), BN_CTX *ctx,
50 void *cb_arg, int do_trial_division);
52 Deprecated since OpenSSL 3.0:
54 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
56 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
57 int do_trial_division, BN_GENCB *cb);
61 BN_generate_prime_ex2() generates a pseudo-random prime number of
62 at least bit length B<bits> using the BN_CTX provided in B<ctx>. The value of
63 B<ctx> must not be NULL.
65 The returned number is probably prime with a negligible error.
66 The maximum error rate is 2^-128.
67 It's 2^-287 for a 512 bit prime, 2^-435 for a 1024 bit prime,
68 2^-648 for a 2048 bit prime, and lower than 2^-882 for primes larger
71 If B<add> is B<NULL> the returned prime number will have exact bit
72 length B<bits> with the top most two bits set.
74 If B<ret> is not B<NULL>, it will be used to store the number.
76 If B<cb> is not B<NULL>, it is used as follows:
82 B<BN_GENCB_call(cb, 0, i)> is called after generating the i-th
83 potential prime number.
87 While the number is being tested for primality,
88 B<BN_GENCB_call(cb, 1, j)> is called as described below.
92 When a prime has been found, B<BN_GENCB_call(cb, 2, i)> is called.
96 The callers of BN_generate_prime_ex() may call B<BN_GENCB_call(cb, i, j)> with
97 other values as described in their respective man pages; see L</SEE ALSO>.
101 The prime may have to fulfill additional requirements for use in
102 Diffie-Hellman key exchange:
104 If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add>
105 == B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given
108 If B<safe> is true, it will be a safe prime (i.e. a prime p so
109 that (p-1)/2 is also prime). If B<safe> is true, and B<rem> == B<NULL>
110 the condition will be p % B<add> == 3.
111 It is recommended that B<add> is a multiple of 4.
113 The random generator must be seeded prior to calling BN_generate_prime_ex().
114 If the automatic seeding or reseeding of the OpenSSL CSPRNG fails due to
115 external circumstances (see L<RAND(7)>), the operation will fail.
116 The random number generator configured for the OPENSSL_CTX associated with
119 BN_generate_prime_ex() is the same as BN_generate_prime_ex2() except that no
120 B<ctx> parameter is passed.
121 In this case the random number generator associated with the default OPENSSL_CTX
124 BN_check_prime(), BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime()
125 and BN_is_prime_fasttest() test if the number B<p> is prime.
126 The functions tests until one of the tests shows that B<p> is composite,
127 or all the tests passed.
128 If B<p> passes all these tests, it is considered a probable prime.
130 The test performed on B<p> are trial division by a number of small primes
131 and rounds of the of the Miller-Rabin probabilistic primality test.
133 The functions do at least 64 rounds of the Miller-Rabin test giving a maximum
134 false positive rate of 2^-128.
135 If the size of B<p> is more than 2048 bits, they do at least 128 rounds
136 giving a maximum false positive rate of 2^-256.
138 If B<nchecks> is larger than the minimum above (64 or 128), B<nchecks>
139 rounds of the Miller-Rabin test will be done.
141 If B<do_trial_division> set to B<0>, the trial division will be skipped.
142 BN_is_prime_ex() and BN_is_prime() always skip the trial division.
144 BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime()
145 and BN_is_prime_fasttest() are deprecated.
147 BN_is_prime_fasttest() and BN_is_prime() behave just like
148 BN_is_prime_fasttest_ex() and BN_is_prime_ex() respectively, but with the old
151 B<ctx> is a pre-allocated B<BN_CTX> (to save the overhead of allocating and
152 freeing the structure in a loop), or B<NULL>.
154 If the trial division is done, and no divisors are found and B<cb>
155 is not B<NULL>, B<BN_GENCB_call(cb, 1, -1)> is called.
157 After each round of the Miller-Rabin probabilistic primality test,
158 if B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called
159 with B<j> the iteration (j = 0, 1, ...).
161 BN_GENCB_call() calls the callback function held in the B<BN_GENCB> structure
162 and passes the ints B<a> and B<b> as arguments. There are two types of
163 B<BN_GENCB> structure that are supported: "new" style and "old" style. New
164 programs should prefer the "new" style, whilst the "old" style is provided
165 for backwards compatibility purposes.
167 A B<BN_GENCB> structure should be created through a call to BN_GENCB_new(),
168 and freed through a call to BN_GENCB_free().
170 For "new" style callbacks a BN_GENCB structure should be initialised with a
171 call to BN_GENCB_set(), where B<gencb> is a B<BN_GENCB *>, B<callback> is of
172 type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>.
173 "Old" style callbacks are the same except they are initialised with a call
174 to BN_GENCB_set_old() and B<callback> is of type
175 B<void (*callback)(int, int, void *)>.
177 A callback is invoked through a call to B<BN_GENCB_call>. This will check
178 the type of the callback and will invoke B<callback(a, b, gencb)> for new
179 style callbacks or B<callback(a, b, cb_arg)> for old style.
181 It is possible to obtain the argument associated with a BN_GENCB structure
182 (set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg.
184 BN_generate_prime() (deprecated) works in the same way as
185 BN_generate_prime_ex() but expects an old-style callback function
186 directly in the B<callback> parameter, and an argument to pass to it in
187 the B<cb_arg>. BN_is_prime() and BN_is_prime_fasttest()
188 can similarly be compared to BN_is_prime_ex() and
189 BN_is_prime_fasttest_ex(), respectively.
193 BN_generate_prime_ex() return 1 on success or 0 on error.
195 BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime(),
196 BN_is_prime_fasttest() and BN_check_prime return 0 if the number is composite,
197 1 if it is prime with an error probability of less than 0.25^B<nchecks>, and
200 BN_generate_prime() returns the prime number on success, B<NULL> otherwise.
202 BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or B<NULL>
205 BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB
208 Callback functions should return 1 on success or 0 on error.
210 The error codes can be obtained by L<ERR_get_error(3)>.
212 =head1 REMOVED FUNCTIONALITY
214 As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure
219 Instead applications should create a BN_GENCB structure using BN_GENCB_new:
222 callback = BN_GENCB_new();
226 BN_GENCB_free(callback);
230 L<DH_generate_parameters(3)>, L<DSA_generate_parameters(3)>,
231 L<RSA_generate_key(3)>, L<ERR_get_error(3)>, L<RAND_bytes(3)>,
236 The BN_GENCB_new(), BN_GENCB_free(),
237 and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0.
239 BN_check_prime() was added in OpenSSL 3.0.
243 Copyright 2000-2019 The OpenSSL Project Authors. All Rights Reserved.
245 Licensed under the Apache License 2.0 (the "License"). You may not use
246 this file except in compliance with the License. You can obtain a copy
247 in the file LICENSE in the source distribution or at
248 L<https://www.openssl.org/source/license.html>.