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_set_old, BN_GENCB_set, BN_generate_prime, BN_is_prime, 7BN_is_prime_fasttest - generate primes and test for primality 8 9=head1 SYNOPSIS 10 11 #include <openssl/bn.h> 12 13 int BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add, 14 const BIGNUM *rem, BN_GENCB *cb); 15 16 int BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb); 17 18 int BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, 19 int do_trial_division, BN_GENCB *cb); 20 21 int BN_GENCB_call(BN_GENCB *cb, int a, int b); 22 23 #define BN_GENCB_set_old(gencb, callback, cb_arg) ... 24 25 #define BN_GENCB_set(gencb, callback, cb_arg) ... 26 27 28Deprecated: 29 30 BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add, 31 BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg); 32 33 int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int, 34 void *), BN_CTX *ctx, void *cb_arg); 35 36 int BN_is_prime_fasttest(const BIGNUM *a, int checks, 37 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg, 38 int do_trial_division); 39 40=head1 DESCRIPTION 41 42BN_generate_prime_ex() generates a pseudo-random prime number of 43bit length B<bits>. 44If B<ret> is not B<NULL>, it will be used to store the number. 45 46If B<cb> is not B<NULL>, it is used as follows: 47 48=over 4 49 50=item * 51 52B<BN_GENCB_call(cb, 0, i)> is called after generating the i-th 53potential prime number. 54 55=item * 56 57While the number is being tested for primality, 58B<BN_GENCB_call(cb, 1, j)> is called as described below. 59 60=item * 61 62When a prime has been found, B<BN_GENCB_call(cb, 2, i)> is called. 63 64=back 65 66The prime may have to fulfill additional requirements for use in 67Diffie-Hellman key exchange: 68 69If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add> 70== B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given 71generator. 72 73If B<safe> is true, it will be a safe prime (i.e. a prime p so 74that (p-1)/2 is also prime). 75 76The PRNG must be seeded prior to calling BN_generate_prime_ex(). 77The prime number generation has a negligible error probability. 78 79BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number B<p> is 80prime. The following tests are performed until one of them shows that 81B<p> is composite; if B<p> passes all these tests, it is considered 82prime. 83 84BN_is_prime_fasttest_ex(), when called with B<do_trial_division == 1>, 85first attempts trial division by a number of small primes; 86if no divisors are found by this test and B<cb> is not B<NULL>, 87B<BN_GENCB_call(cb, 1, -1)> is called. 88If B<do_trial_division == 0>, this test is skipped. 89 90Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin 91probabilistic primality test with B<nchecks> iterations. If 92B<nchecks == BN_prime_checks>, a number of iterations is used that 93yields a false positive rate of at most 2^-80 for random input. 94 95If B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called 96after the j-th iteration (j = 0, 1, ...). B<ctx> is a 97pre-allocated B<BN_CTX> (to save the overhead of allocating and 98freeing the structure in a loop), or B<NULL>. 99 100BN_GENCB_call calls the callback function held in the B<BN_GENCB> structure 101and passes the ints B<a> and B<b> as arguments. There are two types of 102B<BN_GENCB> structure that are supported: "new" style and "old" style. New 103programs should prefer the "new" style, whilst the "old" style is provided 104for backwards compatibility purposes. 105 106For "new" style callbacks a BN_GENCB structure should be initialised with a 107call to BN_GENCB_set, where B<gencb> is a B<BN_GENCB *>, B<callback> is of 108type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>. 109"Old" style callbacks are the same except they are initialised with a call 110to BN_GENCB_set_old and B<callback> is of type 111B<void (*callback)(int, int, void *)>. 112 113A callback is invoked through a call to B<BN_GENCB_call>. This will check 114the type of the callback and will invoke B<callback(a, b, gencb)> for new 115style callbacks or B<callback(a, b, cb_arg)> for old style. 116 117BN_generate_prime (deprecated) works in the same way as 118BN_generate_prime_ex but expects an old style callback function 119directly in the B<callback> parameter, and an argument to pass to it in 120the B<cb_arg>. Similarly BN_is_prime and BN_is_prime_fasttest are 121deprecated and can be compared to BN_is_prime_ex and 122BN_is_prime_fasttest_ex respectively. 123 124=head1 RETURN VALUES 125 126BN_generate_prime_ex() return 1 on success or 0 on error. 127 128BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and 129BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is 130prime with an error probability of less than 0.25^B<nchecks>, and 131-1 on error. 132 133BN_generate_prime() returns the prime number on success, B<NULL> otherwise. 134 135Callback functions should return 1 on success or 0 on error. 136 137The error codes can be obtained by L<ERR_get_error(3)|ERR_get_error(3)>. 138 139=head1 SEE ALSO 140 141L<bn(3)|bn(3)>, L<ERR_get_error(3)|ERR_get_error(3)>, L<rand(3)|rand(3)> 142 143=head1 HISTORY 144 145The B<cb_arg> arguments to BN_generate_prime() and to BN_is_prime() 146were added in SSLeay 0.9.0. The B<ret> argument to BN_generate_prime() 147was added in SSLeay 0.9.1. 148BN_is_prime_fasttest() was added in OpenSSL 0.9.5. 149 150=cut 151