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>. 55If B<ret> is not B<NULL>, it will be used to store the number. 56 57If B<cb> is not B<NULL>, it is used as follows: 58 59=over 2 60 61=item * 62 63B<BN_GENCB_call(cb, 0, i)> is called after generating the i-th 64potential prime number. 65 66=item * 67 68While the number is being tested for primality, 69B<BN_GENCB_call(cb, 1, j)> is called as described below. 70 71=item * 72 73When a prime has been found, B<BN_GENCB_call(cb, 2, i)> is called. 74 75=item * 76 77The callers of BN_generate_prime_ex() may call B<BN_GENCB_call(cb, i, j)> with 78other values as described in their respective man pages; see L</SEE ALSO>. 79 80=back 81 82The prime may have to fulfill additional requirements for use in 83Diffie-Hellman key exchange: 84 85If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add> 86== B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given 87generator. 88 89If B<safe> is true, it will be a safe prime (i.e. a prime p so 90that (p-1)/2 is also prime). 91 92The PRNG must be seeded prior to calling BN_generate_prime_ex(). 93The prime number generation has a negligible error probability. 94 95BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number B<p> is 96prime. The following tests are performed until one of them shows that 97B<p> is composite; if B<p> passes all these tests, it is considered 98prime. 99 100BN_is_prime_fasttest_ex(), when called with B<do_trial_division == 1>, 101first attempts trial division by a number of small primes; 102if no divisors are found by this test and B<cb> is not B<NULL>, 103B<BN_GENCB_call(cb, 1, -1)> is called. 104If B<do_trial_division == 0>, this test is skipped. 105 106Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin 107probabilistic primality test with B<nchecks> iterations. If 108B<nchecks == BN_prime_checks>, a number of iterations is used that 109yields a false positive rate of at most 2^-64 for random input. 110The error rate depends on the size of the prime and goes down for bigger primes. 111The rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits, 1122^-192 at 3747 bits and 2^-256 at 6394 bits. 113 114When the source of the prime is not random or not trusted, the number 115of checks needs to be much higher to reach the same level of assurance: 116It should equal half of the targeted security level in bits (rounded up to the 117next integer if necessary). 118For instance, to reach the 128 bit security level, B<nchecks> should be set to 11964. 120 121If B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called 122after the j-th iteration (j = 0, 1, ...). B<ctx> is a 123pre-allocated B<BN_CTX> (to save the overhead of allocating and 124freeing the structure in a loop), or B<NULL>. 125 126BN_GENCB_call() calls the callback function held in the B<BN_GENCB> structure 127and passes the ints B<a> and B<b> as arguments. There are two types of 128B<BN_GENCB> structure that are supported: "new" style and "old" style. New 129programs should prefer the "new" style, whilst the "old" style is provided 130for backwards compatibility purposes. 131 132A B<BN_GENCB> structure should be created through a call to BN_GENCB_new(), 133and freed through a call to BN_GENCB_free(). 134 135For "new" style callbacks a BN_GENCB structure should be initialised with a 136call to BN_GENCB_set(), where B<gencb> is a B<BN_GENCB *>, B<callback> is of 137type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>. 138"Old" style callbacks are the same except they are initialised with a call 139to BN_GENCB_set_old() and B<callback> is of type 140B<void (*callback)(int, int, void *)>. 141 142A callback is invoked through a call to B<BN_GENCB_call>. This will check 143the type of the callback and will invoke B<callback(a, b, gencb)> for new 144style callbacks or B<callback(a, b, cb_arg)> for old style. 145 146It is possible to obtain the argument associated with a BN_GENCB structure 147(set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg. 148 149BN_generate_prime() (deprecated) works in the same way as 150BN_generate_prime_ex() but expects an old-style callback function 151directly in the B<callback> parameter, and an argument to pass to it in 152the B<cb_arg>. BN_is_prime() and BN_is_prime_fasttest() 153can similarly be compared to BN_is_prime_ex() and 154BN_is_prime_fasttest_ex(), respectively. 155 156=head1 RETURN VALUES 157 158BN_generate_prime_ex() return 1 on success or 0 on error. 159 160BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and 161BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is 162prime with an error probability of less than 0.25^B<nchecks>, and 163-1 on error. 164 165BN_generate_prime() returns the prime number on success, B<NULL> otherwise. 166 167BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or B<NULL> 168otherwise. 169 170BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB 171structure. 172 173Callback functions should return 1 on success or 0 on error. 174 175The error codes can be obtained by L<ERR_get_error(3)>. 176 177=head1 REMOVED FUNCTIONALITY 178 179As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure 180directly, as in: 181 182 BN_GENCB callback; 183 184Instead applications should create a BN_GENCB structure using BN_GENCB_new: 185 186 BN_GENCB *callback; 187 callback = BN_GENCB_new(); 188 if (!callback) 189 /* error */ 190 ... 191 BN_GENCB_free(callback); 192 193=head1 SEE ALSO 194 195L<DH_generate_parameters(3)>, L<DSA_generate_parameters(3)>, 196L<RSA_generate_key(3)>, L<ERR_get_error(3)>, L<RAND_bytes(3)> 197 198=head1 HISTORY 199 200BN_GENCB_new(), BN_GENCB_free(), 201and BN_GENCB_get_arg() were added in OpenSSL 1.1.0 202 203=head1 COPYRIGHT 204 205Copyright 2000-2018 The OpenSSL Project Authors. All Rights Reserved. 206 207Licensed under the OpenSSL license (the "License"). You may not use 208this file except in compliance with the License. You can obtain a copy 209in the file LICENSE in the source distribution or at 210L<https://www.openssl.org/source/license.html>. 211 212=cut 213