BN_generate_prime.pod revision 337982
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^-64 for random input. 94The error rate depends on the size of the prime and goes down for bigger primes. 95The rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits, 962^-192 at 3747 bits and 2^-256 at 6394 bits. 97 98When the source of the prime is not random or not trusted, the number 99of checks needs to be much higher to reach the same level of assurance: 100It should equal half of the targeted security level in bits (rounded up to the 101next integer if necessary). 102For instance, to reach the 128 bit security level, B<nchecks> should be set to 10364. 104 105If B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called 106after the j-th iteration (j = 0, 1, ...). B<ctx> is a 107pre-allocated B<BN_CTX> (to save the overhead of allocating and 108freeing the structure in a loop), or B<NULL>. 109 110BN_GENCB_call calls the callback function held in the B<BN_GENCB> structure 111and passes the ints B<a> and B<b> as arguments. There are two types of 112B<BN_GENCB> structure that are supported: "new" style and "old" style. New 113programs should prefer the "new" style, whilst the "old" style is provided 114for backwards compatibility purposes. 115 116For "new" style callbacks a BN_GENCB structure should be initialised with a 117call to BN_GENCB_set, where B<gencb> is a B<BN_GENCB *>, B<callback> is of 118type B<int (*callback)(int, int, BN_GENCB *)> and B<cb_arg> is a B<void *>. 119"Old" style callbacks are the same except they are initialised with a call 120to BN_GENCB_set_old and B<callback> is of type 121B<void (*callback)(int, int, void *)>. 122 123A callback is invoked through a call to B<BN_GENCB_call>. This will check 124the type of the callback and will invoke B<callback(a, b, gencb)> for new 125style callbacks or B<callback(a, b, cb_arg)> for old style. 126 127BN_generate_prime (deprecated) works in the same way as 128BN_generate_prime_ex but expects an old style callback function 129directly in the B<callback> parameter, and an argument to pass to it in 130the B<cb_arg>. Similarly BN_is_prime and BN_is_prime_fasttest are 131deprecated and can be compared to BN_is_prime_ex and 132BN_is_prime_fasttest_ex respectively. 133 134=head1 RETURN VALUES 135 136BN_generate_prime_ex() return 1 on success or 0 on error. 137 138BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and 139BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is 140prime with an error probability of less than 0.25^B<nchecks>, and 141-1 on error. 142 143BN_generate_prime() returns the prime number on success, B<NULL> otherwise. 144 145Callback functions should return 1 on success or 0 on error. 146 147The error codes can be obtained by L<ERR_get_error(3)|ERR_get_error(3)>. 148 149=head1 SEE ALSO 150 151L<bn(3)|bn(3)>, L<ERR_get_error(3)|ERR_get_error(3)>, L<rand(3)|rand(3)> 152 153=head1 HISTORY 154 155The B<cb_arg> arguments to BN_generate_prime() and to BN_is_prime() 156were added in SSLeay 0.9.0. The B<ret> argument to BN_generate_prime() 157was added in SSLeay 0.9.1. 158BN_is_prime_fasttest() was added in OpenSSL 0.9.5. 159 160=cut 161