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103 lines
3.1 KiB
Plaintext
103 lines
3.1 KiB
Plaintext
=pod
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=head1 NAME
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BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality
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=head1 SYNOPSIS
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#include <openssl/bn.h>
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BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
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BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
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int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int,
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void *), BN_CTX *ctx, void *cb_arg);
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int BN_is_prime_fasttest(const BIGNUM *a, int checks,
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void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg,
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int do_trial_division);
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=head1 DESCRIPTION
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BN_generate_prime() generates a pseudo-random prime number of B<num>
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bits.
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If B<ret> is not B<NULL>, it will be used to store the number.
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If B<callback> is not B<NULL>, it is called as follows:
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=over 4
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=item *
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B<callback(0, i, cb_arg)> is called after generating the i-th
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potential prime number.
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=item *
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While the number is being tested for primality, B<callback(1, j,
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cb_arg)> is called as described below.
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=item *
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When a prime has been found, B<callback(2, i, cb_arg)> is called.
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=back
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The prime may have to fulfill additional requirements for use in
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Diffie-Hellman key exchange:
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If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add>
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== B<rem> (p % B<add> == 1 if B<rem> == B<NULL>) in order to suit a given
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generator.
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If B<safe> is true, it will be a safe prime (i.e. a prime p so
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that (p-1)/2 is also prime).
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The PRNG must be seeded prior to calling BN_generate_prime().
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The prime number generation has a negligible error probability.
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BN_is_prime() and BN_is_prime_fasttest() test if the number B<a> is
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prime. The following tests are performed until one of them shows that
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B<a> is composite; if B<a> passes all these tests, it is considered
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prime.
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BN_is_prime_fasttest(), when called with B<do_trial_division == 1>,
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first attempts trial division by a number of small primes;
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if no divisors are found by this test and B<callback> is not B<NULL>,
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B<callback(1, -1, cb_arg)> is called.
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If B<do_trial_division == 0>, this test is skipped.
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Both BN_is_prime() and BN_is_prime_fasttest() perform a Miller-Rabin
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probabilistic primality test with B<checks> iterations. If
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B<checks == BN_prime_checks>, a number of iterations is used that
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yields a false positive rate of at most 2^-80 for random input.
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If B<callback> is not B<NULL>, B<callback(1, j, cb_arg)> is called
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after the j-th iteration (j = 0, 1, ...). B<ctx> is a
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pre-allocated B<BN_CTX> (to save the overhead of allocating and
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freeing the structure in a loop), or B<NULL>.
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=head1 RETURN VALUES
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BN_generate_prime() returns the prime number on success, B<NULL> otherwise.
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BN_is_prime() returns 0 if the number is composite, 1 if it is
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prime with an error probability of less than 0.25^B<checks>, and
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-1 on error.
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The error codes can be obtained by L<ERR_get_error(3)|ERR_get_error(3)>.
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=head1 SEE ALSO
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L<bn(3)|bn(3)>, L<ERR_get_error(3)|ERR_get_error(3)>, L<rand(3)|rand(3)>
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=head1 HISTORY
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The B<cb_arg> arguments to BN_generate_prime() and to BN_is_prime()
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were added in SSLeay 0.9.0. The B<ret> argument to BN_generate_prime()
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was added in SSLeay 0.9.1.
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BN_is_prime_fasttest() was added in OpenSSL 0.9.5.
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=cut
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