5 BN_generate_prime_ex2, BN_generate_prime_ex, BN_is_prime_ex,
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_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
23 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
24 int do_trial_division, BN_GENCB *cb);
26 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
28 BN_GENCB *BN_GENCB_new(void);
30 void BN_GENCB_free(BN_GENCB *cb);
32 void BN_GENCB_set_old(BN_GENCB *gencb,
33 void (*callback)(int, int, void *), void *cb_arg);
35 void BN_GENCB_set(BN_GENCB *gencb,
36 int (*callback)(int, int, BN_GENCB *), void *cb_arg);
38 void *BN_GENCB_get_arg(BN_GENCB *cb);
40 Deprecated since OpenSSL 0.9.8, can be hidden entirely by defining
41 B<OPENSSL_API_COMPAT> with a suitable version value, see
42 L<openssl_user_macros(7)>:
44 BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
45 BIGNUM *rem, void (*callback)(int, int, void *),
48 int BN_is_prime(const BIGNUM *a, int checks,
49 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
51 int BN_is_prime_fasttest(const BIGNUM *a, int checks,
52 void (*callback)(int, int, void *), BN_CTX *ctx,
53 void *cb_arg, int do_trial_division);
57 BN_generate_prime_ex2() generates a pseudo-random prime number of
58 at least bit length B<bits> using the BN_CTX provided in B<ctx>. The value of
59 B<ctx> must not be NULL.
60 The returned number is probably prime with a negligible error.
62 If B<ret> is not B<NULL>, it will be used to store the number.
64 If B<cb> is not B<NULL>, it is used as follows:
70 B<BN_GENCB_call(cb, 0, i)> is called after generating the i-th
71 potential prime number.
75 While the number is being tested for primality,
76 B<BN_GENCB_call(cb, 1, j)> is called as described below.
80 When a prime has been found, B<BN_GENCB_call(cb, 2, i)> is called.
84 The callers of BN_generate_prime_ex() may call B<BN_GENCB_call(cb, i, j)> with
85 other values as described in their respective man pages; see L</SEE ALSO>.
89 The prime may have to fulfill additional requirements for use in
90 Diffie-Hellman key exchange:
92 If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add>
93 == B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given
96 If B<safe> is true, it will be a safe prime (i.e. a prime p so
97 that (p-1)/2 is also prime).
99 The random generator must be seeded prior to calling BN_generate_prime_ex().
100 If the automatic seeding or reseeding of the OpenSSL CSPRNG fails due to
101 external circumstances (see L<RAND(7)>), the operation will fail.
102 The random number generator configured for the OPENSSL_CTX associated with
105 BN_generate_prime_ex() is the same as BN_generate_prime_ex2() except that no
106 B<ctx> parameter is passed.
107 In this case the random number generator associated with the default OPENSSL_CTX
110 BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number B<p> is
111 prime. The following tests are performed until one of them shows that
112 B<p> is composite; if B<p> passes all these tests, it is considered
115 BN_is_prime_fasttest_ex(), when called with B<do_trial_division == 1>,
116 first attempts trial division by a number of small primes;
117 if no divisors are found by this test and B<cb> is not B<NULL>,
118 B<BN_GENCB_call(cb, 1, -1)> is called.
119 If B<do_trial_division == 0>, this test is skipped.
121 Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin
122 probabilistic primality test with B<nchecks> iterations. If
123 B<nchecks == BN_prime_checks>, a number of iterations is used that
124 yields a false positive rate of at most 2^-64 for random input.
125 The error rate depends on the size of the prime and goes down for bigger primes.
126 The rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits,
127 2^-192 at 3747 bits and 2^-256 at 6394 bits.
129 When the source of the prime is not random or not trusted, the number
130 of checks needs to be much higher to reach the same level of assurance:
131 It should equal half of the targeted security level in bits (rounded up to the
132 next integer if necessary).
133 For instance, to reach the 128 bit security level, B<nchecks> should be set to
136 If B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called
137 after the j-th iteration (j = 0, 1, ...). B<ctx> is a
138 pre-allocated B<BN_CTX> (to save the overhead of allocating and
139 freeing the structure in a loop), or B<NULL>.
141 BN_GENCB_call() calls the callback function held in the B<BN_GENCB> structure
142 and passes the ints B<a> and B<b> as arguments. There are two types of
143 B<BN_GENCB> structure that are supported: "new" style and "old" style. New
144 programs should prefer the "new" style, whilst the "old" style is provided
145 for backwards compatibility purposes.
147 A B<BN_GENCB> structure should be created through a call to BN_GENCB_new(),
148 and freed through a call to BN_GENCB_free().
150 For "new" style callbacks a BN_GENCB structure should be initialised with a
151 call to BN_GENCB_set(), where B<gencb> is a B<BN_GENCB *>, B<callback> is of
152 type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>.
153 "Old" style callbacks are the same except they are initialised with a call
154 to BN_GENCB_set_old() and B<callback> is of type
155 B<void (*callback)(int, int, void *)>.
157 A callback is invoked through a call to B<BN_GENCB_call>. This will check
158 the type of the callback and will invoke B<callback(a, b, gencb)> for new
159 style callbacks or B<callback(a, b, cb_arg)> for old style.
161 It is possible to obtain the argument associated with a BN_GENCB structure
162 (set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg.
164 BN_generate_prime() (deprecated) works in the same way as
165 BN_generate_prime_ex() but expects an old-style callback function
166 directly in the B<callback> parameter, and an argument to pass to it in
167 the B<cb_arg>. BN_is_prime() and BN_is_prime_fasttest()
168 can similarly be compared to BN_is_prime_ex() and
169 BN_is_prime_fasttest_ex(), respectively.
173 BN_generate_prime_ex() return 1 on success or 0 on error.
175 BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and
176 BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is
177 prime with an error probability of less than 0.25^B<nchecks>, and
180 BN_generate_prime() returns the prime number on success, B<NULL> otherwise.
182 BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or B<NULL>
185 BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB
188 Callback functions should return 1 on success or 0 on error.
190 The error codes can be obtained by L<ERR_get_error(3)>.
192 =head1 REMOVED FUNCTIONALITY
194 As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure
199 Instead applications should create a BN_GENCB structure using BN_GENCB_new:
202 callback = BN_GENCB_new();
206 BN_GENCB_free(callback);
210 L<DH_generate_parameters(3)>, L<DSA_generate_parameters(3)>,
211 L<RSA_generate_key(3)>, L<ERR_get_error(3)>, L<RAND_bytes(3)>,
216 The BN_GENCB_new(), BN_GENCB_free(),
217 and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0.
221 Copyright 2000-2018 The OpenSSL Project Authors. All Rights Reserved.
223 Licensed under the Apache License 2.0 (the "License"). You may not use
224 this file except in compliance with the License. You can obtain a copy
225 in the file LICENSE in the source distribution or at
226 L<https://www.openssl.org/source/license.html>.