1=pod 2 3=head1 NAME 4 5BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call, 6BN_GENCB_new, BN_GENCB_free, BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg, 7BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test 8for primality 9 10=head1 SYNOPSIS 11 12 #include <openssl/bn.h> 13 14 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add, 15 const BIGNUM *rem, BN_GENCB *cb); 16 17 int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb); 18 19 int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, 20 int do_trial_division, BN_GENCB *cb); 21 22 int BN_GENCB_call(BN_GENCB *cb, int a, int b); 23 24 BN_GENCB *BN_GENCB_new(void); 25 26 void BN_GENCB_free(BN_GENCB *cb); 27 28 void BN_GENCB_set_old(BN_GENCB *gencb, 29 void (*callback)(int, int, void *), void *cb_arg); 30 31 void BN_GENCB_set(BN_GENCB *gencb, 32 int (*callback)(int, int, BN_GENCB *), void *cb_arg); 33 34 void *BN_GENCB_get_arg(BN_GENCB *cb); 35 36Deprecated: 37 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 *), 41 void *cb_arg); 42 43 int BN_is_prime(const BIGNUM *a, int checks, 44 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg); 45 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); 49 #endif 50 51=head1 DESCRIPTION 52 53BN_generate_prime_ex() generates a pseudo-random prime number of 54at least bit length B<bits>. The returned number is probably prime 55with a negligible error. 56 57If B<ret> is not B<NULL>, it will be used to store the number. 58 59If B<cb> is not B<NULL>, it is used as follows: 60 61=over 2 62 63=item * 64 65B<BN_GENCB_call(cb, 0, i)> is called after generating the i-th 66potential prime number. 67 68=item * 69 70While the number is being tested for primality, 71B<BN_GENCB_call(cb, 1, j)> is called as described below. 72 73=item * 74 75When a prime has been found, B<BN_GENCB_call(cb, 2, i)> is called. 76 77=item * 78 79The callers of BN_generate_prime_ex() may call B<BN_GENCB_call(cb, i, j)> with 80other values as described in their respective man pages; see L</SEE ALSO>. 81 82=back 83 84The prime may have to fulfill additional requirements for use in 85Diffie-Hellman key exchange: 86 87If 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 89generator. 90 91If B<safe> is true, it will be a safe prime (i.e. a prime p so 92that (p-1)/2 is also prime). 93 94The random generator must be seeded prior to calling BN_generate_prime_ex(). 95If the automatic seeding or reseeding of the OpenSSL CSPRNG fails due to 96external circumstances (see L<RAND(7)>), the operation will fail. 97 98BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number B<p> is 99prime. The following tests are performed until one of them shows that 100B<p> is composite; if B<p> passes all these tests, it is considered 101prime. 102 103BN_is_prime_fasttest_ex(), when called with B<do_trial_division == 1>, 104first attempts trial division by a number of small primes; 105if no divisors are found by this test and B<cb> is not B<NULL>, 106B<BN_GENCB_call(cb, 1, -1)> is called. 107If B<do_trial_division == 0>, this test is skipped. 108 109Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin 110probabilistic primality test with B<nchecks> iterations. If 111B<nchecks == BN_prime_checks>, a number of iterations is used that 112yields a false positive rate of at most 2^-64 for random input. 113The error rate depends on the size of the prime and goes down for bigger primes. 114The rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits, 1152^-192 at 3747 bits and 2^-256 at 6394 bits. 116 117When the source of the prime is not random or not trusted, the number 118of checks needs to be much higher to reach the same level of assurance: 119It should equal half of the targeted security level in bits (rounded up to the 120next integer if necessary). 121For instance, to reach the 128 bit security level, B<nchecks> should be set to 12264. 123 124If B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called 125after the j-th iteration (j = 0, 1, ...). B<ctx> is a 126pre-allocated B<BN_CTX> (to save the overhead of allocating and 127freeing the structure in a loop), or B<NULL>. 128 129BN_GENCB_call() calls the callback function held in the B<BN_GENCB> structure 130and passes the ints B<a> and B<b> as arguments. There are two types of 131B<BN_GENCB> structure that are supported: "new" style and "old" style. New 132programs should prefer the "new" style, whilst the "old" style is provided 133for backwards compatibility purposes. 134 135A B<BN_GENCB> structure should be created through a call to BN_GENCB_new(), 136and freed through a call to BN_GENCB_free(). 137 138For "new" style callbacks a BN_GENCB structure should be initialised with a 139call to BN_GENCB_set(), where B<gencb> is a B<BN_GENCB *>, B<callback> is of 140type 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 142to BN_GENCB_set_old() and B<callback> is of type 143B<void (*callback)(int, int, void *)>. 144 145A callback is invoked through a call to B<BN_GENCB_call>. This will check 146the type of the callback and will invoke B<callback(a, b, gencb)> for new 147style callbacks or B<callback(a, b, cb_arg)> for old style. 148 149It 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. 151 152BN_generate_prime() (deprecated) works in the same way as 153BN_generate_prime_ex() but expects an old-style callback function 154directly in the B<callback> parameter, and an argument to pass to it in 155the B<cb_arg>. BN_is_prime() and BN_is_prime_fasttest() 156can similarly be compared to BN_is_prime_ex() and 157BN_is_prime_fasttest_ex(), respectively. 158 159=head1 RETURN VALUES 160 161BN_generate_prime_ex() return 1 on success or 0 on error. 162 163BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and 164BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is 165prime with an error probability of less than 0.25^B<nchecks>, and 166-1 on error. 167 168BN_generate_prime() returns the prime number on success, B<NULL> otherwise. 169 170BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or B<NULL> 171otherwise. 172 173BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB 174structure. 175 176Callback functions should return 1 on success or 0 on error. 177 178The error codes can be obtained by L<ERR_get_error(3)>. 179 180=head1 REMOVED FUNCTIONALITY 181 182As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure 183directly, as in: 184 185 BN_GENCB callback; 186 187Instead applications should create a BN_GENCB structure using BN_GENCB_new: 188 189 BN_GENCB *callback; 190 callback = BN_GENCB_new(); 191 if (!callback) 192 /* error */ 193 ... 194 BN_GENCB_free(callback); 195 196=head1 SEE ALSO 197 198L<DH_generate_parameters(3)>, L<DSA_generate_parameters(3)>, 199L<RSA_generate_key(3)>, L<ERR_get_error(3)>, L<RAND_bytes(3)>, 200L<RAND(7)> 201 202=head1 HISTORY 203 204The BN_GENCB_new(), BN_GENCB_free(), 205and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0. 206 207=head1 COPYRIGHT 208 209Copyright 2000-2019 The OpenSSL Project Authors. All Rights Reserved. 210 211Licensed under the OpenSSL license (the "License"). You may not use 212this file except in compliance with the License. You can obtain a copy 213in the file LICENSE in the source distribution or at 214L<https://www.openssl.org/source/license.html>. 215 216=cut 217