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102 lines
3.1 KiB
102 lines
3.1 KiB
=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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