5 BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call,
6 BN_GENCB_new, BN_GENCB_free, BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg,
7 BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test
12 #include <openssl/bn.h>
14 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
15 const BIGNUM *rem, BN_GENCB *cb);
17 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
19 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
20 int do_trial_division, BN_GENCB *cb);
22 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
24 BN_GENCB *BN_GENCB_new(void);
26 void BN_GENCB_free(BN_GENCB *cb);
28 void BN_GENCB_set_old(BN_GENCB *gencb,
29 void (*callback)(int, int, void *), void *cb_arg);
31 void BN_GENCB_set(BN_GENCB *gencb,
32 int (*callback)(int, int, BN_GENCB *), void *cb_arg);
34 void *BN_GENCB_get_arg(BN_GENCB *cb);
38 #if OPENSSL_API_COMPAT < 0x00908000L
39 BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
40 BIGNUM *rem, void (*callback)(int, int, void *),
43 int BN_is_prime(const BIGNUM *a, int checks,
44 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
46 int BN_is_prime_fasttest(const BIGNUM *a, int checks,
47 void (*callback)(int, int, void *), BN_CTX *ctx,
48 void *cb_arg, int do_trial_division);
53 BN_generate_prime_ex() generates a pseudo-random prime number of
54 at least bit length B<bits>. The returned number is probably prime
55 with a negligible error.
57 If B<ret> is not B<NULL>, it will be used to store the number.
59 If B<cb> is not B<NULL>, it is used as follows:
65 B<BN_GENCB_call(cb, 0, i)> is called after generating the i-th
66 potential prime number.
70 While the number is being tested for primality,
71 B<BN_GENCB_call(cb, 1, j)> is called as described below.
75 When a prime has been found, B<BN_GENCB_call(cb, 2, i)> is called.
79 The callers of BN_generate_prime_ex() may call B<BN_GENCB_call(cb, i, j)> with
80 other values as described in their respective man pages; see L</SEE ALSO>.
84 The prime may have to fulfill additional requirements for use in
85 Diffie-Hellman key exchange:
87 If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add>
88 == B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given
91 If B<safe> is true, it will be a safe prime (i.e. a prime p so
92 that (p-1)/2 is also prime).
94 The random generator must be seeded prior to calling BN_generate_prime_ex().
95 If the automatic seeding or reseeding of the OpenSSL CSPRNG fails due to
96 external circumstances (see L<RAND(7)>), the operation will fail.
98 BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number B<p> is
99 prime. The following tests are performed until one of them shows that
100 B<p> is composite; if B<p> passes all these tests, it is considered
103 BN_is_prime_fasttest_ex(), when called with B<do_trial_division == 1>,
104 first attempts trial division by a number of small primes;
105 if no divisors are found by this test and B<cb> is not B<NULL>,
106 B<BN_GENCB_call(cb, 1, -1)> is called.
107 If B<do_trial_division == 0>, this test is skipped.
109 Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin
110 probabilistic primality test with B<nchecks> iterations. If
111 B<nchecks == BN_prime_checks>, a number of iterations is used that
112 yields a false positive rate of at most 2^-64 for random input.
113 The error rate depends on the size of the prime and goes down for bigger primes.
114 The rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits,
115 2^-192 at 3747 bits and 2^-256 at 6394 bits.
117 When the source of the prime is not random or not trusted, the number
118 of checks needs to be much higher to reach the same level of assurance:
119 It should equal half of the targeted security level in bits (rounded up to the
120 next integer if necessary).
121 For instance, to reach the 128 bit security level, B<nchecks> should be set to
124 If B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called
125 after the j-th iteration (j = 0, 1, ...). B<ctx> is a
126 pre-allocated B<BN_CTX> (to save the overhead of allocating and
127 freeing the structure in a loop), or B<NULL>.
129 BN_GENCB_call() calls the callback function held in the B<BN_GENCB> structure
130 and passes the ints B<a> and B<b> as arguments. There are two types of
131 B<BN_GENCB> structure that are supported: "new" style and "old" style. New
132 programs should prefer the "new" style, whilst the "old" style is provided
133 for backwards compatibility purposes.
135 A B<BN_GENCB> structure should be created through a call to BN_GENCB_new(),
136 and freed through a call to BN_GENCB_free().
138 For "new" style callbacks a BN_GENCB structure should be initialised with a
139 call to BN_GENCB_set(), where B<gencb> is a B<BN_GENCB *>, B<callback> is of
140 type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>.
141 "Old" style callbacks are the same except they are initialised with a call
142 to BN_GENCB_set_old() and B<callback> is of type
143 B<void (*callback)(int, int, void *)>.
145 A callback is invoked through a call to B<BN_GENCB_call>. This will check
146 the type of the callback and will invoke B<callback(a, b, gencb)> for new
147 style callbacks or B<callback(a, b, cb_arg)> for old style.
149 It is possible to obtain the argument associated with a BN_GENCB structure
150 (set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg.
152 BN_generate_prime() (deprecated) works in the same way as
153 BN_generate_prime_ex() but expects an old-style callback function
154 directly in the B<callback> parameter, and an argument to pass to it in
155 the B<cb_arg>. BN_is_prime() and BN_is_prime_fasttest()
156 can similarly be compared to BN_is_prime_ex() and
157 BN_is_prime_fasttest_ex(), respectively.
161 BN_generate_prime_ex() return 1 on success or 0 on error.
163 BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and
164 BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is
165 prime with an error probability of less than 0.25^B<nchecks>, and
168 BN_generate_prime() returns the prime number on success, B<NULL> otherwise.
170 BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or B<NULL>
173 BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB
176 Callback functions should return 1 on success or 0 on error.
178 The error codes can be obtained by L<ERR_get_error(3)>.
180 =head1 REMOVED FUNCTIONALITY
182 As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure
187 Instead applications should create a BN_GENCB structure using BN_GENCB_new:
190 callback = BN_GENCB_new();
194 BN_GENCB_free(callback);
198 L<DH_generate_parameters(3)>, L<DSA_generate_parameters(3)>,
199 L<RSA_generate_key(3)>, L<ERR_get_error(3)>, L<RAND_bytes(3)>,
204 The BN_GENCB_new(), BN_GENCB_free(),
205 and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0.
209 Copyright 2000-2018 The OpenSSL Project Authors. All Rights Reserved.
211 Licensed under the OpenSSL license (the "License"). You may not use
212 this file except in compliance with the License. You can obtain a copy
213 in the file LICENSE in the source distribution or at
214 L<https://www.openssl.org/source/license.html>.