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. If B<add> is B<NULL> the returned prime
56 number will have exact bit length B<bits> with the top most two
59 If B<ret> is not B<NULL>, it will be used to store the number.
61 If B<cb> is not B<NULL>, it is used as follows:
67 B<BN_GENCB_call(cb, 0, i)> is called after generating the i-th
68 potential prime number.
72 While the number is being tested for primality,
73 B<BN_GENCB_call(cb, 1, j)> is called as described below.
77 When a prime has been found, B<BN_GENCB_call(cb, 2, i)> is called.
81 The callers of BN_generate_prime_ex() may call B<BN_GENCB_call(cb, i, j)> with
82 other values as described in their respective man pages; see L</SEE ALSO>.
86 The prime may have to fulfill additional requirements for use in
87 Diffie-Hellman key exchange:
89 If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add>
90 == B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given
93 If B<safe> is true, it will be a safe prime (i.e. a prime p so
94 that (p-1)/2 is also prime). If B<safe> is true, and B<rem> == B<NULL>
95 the condition will be p % B<add> == 3.
96 It is recommended that B<add> is a multiple of 4.
98 The random generator must be seeded prior to calling BN_generate_prime_ex().
99 If the automatic seeding or reseeding of the OpenSSL CSPRNG fails due to
100 external circumstances (see L<RAND(7)>), the operation will fail.
102 BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number B<p> is
103 prime. The following tests are performed until one of them shows that
104 B<p> is composite; if B<p> passes all these tests, it is considered
107 BN_is_prime_fasttest_ex(), when called with B<do_trial_division == 1>,
108 first attempts trial division by a number of small primes;
109 if no divisors are found by this test and B<cb> is not B<NULL>,
110 B<BN_GENCB_call(cb, 1, -1)> is called.
111 If B<do_trial_division == 0>, this test is skipped.
113 Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin
114 probabilistic primality test with B<nchecks> iterations. If
115 B<nchecks == BN_prime_checks>, a number of iterations is used that
116 yields a false positive rate of at most 2^-64 for random input.
117 The error rate depends on the size of the prime and goes down for bigger primes.
118 The rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits,
119 2^-192 at 3747 bits and 2^-256 at 6394 bits.
121 When the source of the prime is not random or not trusted, the number
122 of checks needs to be much higher to reach the same level of assurance:
123 It should equal half of the targeted security level in bits (rounded up to the
124 next integer if necessary).
125 For instance, to reach the 128 bit security level, B<nchecks> should be set to
128 If B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called
129 after the j-th iteration (j = 0, 1, ...). B<ctx> is a
130 pre-allocated B<BN_CTX> (to save the overhead of allocating and
131 freeing the structure in a loop), or B<NULL>.
133 BN_GENCB_call() calls the callback function held in the B<BN_GENCB> structure
134 and passes the ints B<a> and B<b> as arguments. There are two types of
135 B<BN_GENCB> structure that are supported: "new" style and "old" style. New
136 programs should prefer the "new" style, whilst the "old" style is provided
137 for backwards compatibility purposes.
139 A B<BN_GENCB> structure should be created through a call to BN_GENCB_new(),
140 and freed through a call to BN_GENCB_free().
142 For "new" style callbacks a BN_GENCB structure should be initialised with a
143 call to BN_GENCB_set(), where B<gencb> is a B<BN_GENCB *>, B<callback> is of
144 type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>.
145 "Old" style callbacks are the same except they are initialised with a call
146 to BN_GENCB_set_old() and B<callback> is of type
147 B<void (*callback)(int, int, void *)>.
149 A callback is invoked through a call to B<BN_GENCB_call>. This will check
150 the type of the callback and will invoke B<callback(a, b, gencb)> for new
151 style callbacks or B<callback(a, b, cb_arg)> for old style.
153 It is possible to obtain the argument associated with a BN_GENCB structure
154 (set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg.
156 BN_generate_prime() (deprecated) works in the same way as
157 BN_generate_prime_ex() but expects an old-style callback function
158 directly in the B<callback> parameter, and an argument to pass to it in
159 the B<cb_arg>. BN_is_prime() and BN_is_prime_fasttest()
160 can similarly be compared to BN_is_prime_ex() and
161 BN_is_prime_fasttest_ex(), respectively.
165 BN_generate_prime_ex() return 1 on success or 0 on error.
167 BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and
168 BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is
169 prime with an error probability of less than 0.25^B<nchecks>, and
172 BN_generate_prime() returns the prime number on success, B<NULL> otherwise.
174 BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or B<NULL>
177 BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB
180 Callback functions should return 1 on success or 0 on error.
182 The error codes can be obtained by L<ERR_get_error(3)>.
184 =head1 REMOVED FUNCTIONALITY
186 As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure
191 Instead applications should create a BN_GENCB structure using BN_GENCB_new:
194 callback = BN_GENCB_new();
198 BN_GENCB_free(callback);
202 L<DH_generate_parameters(3)>, L<DSA_generate_parameters(3)>,
203 L<RSA_generate_key(3)>, L<ERR_get_error(3)>, L<RAND_bytes(3)>,
208 The BN_GENCB_new(), BN_GENCB_free(),
209 and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0.
213 Copyright 2000-2020 The OpenSSL Project Authors. All Rights Reserved.
215 Licensed under the OpenSSL license (the "License"). You may not use
216 this file except in compliance with the License. You can obtain a copy
217 in the file LICENSE in the source distribution or at
218 L<https://www.openssl.org/source/license.html>.