1BN_generate_prime(3)                OpenSSL               BN_generate_prime(3)
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NAME

6       BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes
7       and test for primality
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SYNOPSIS

10        #include <openssl/bn.h>
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12        BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
13            BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
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15        int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int,
16            void *), BN_CTX *ctx, void *cb_arg);
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18        int BN_is_prime_fasttest(const BIGNUM *a, int checks,
19            void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg,
20            int do_trial_division);
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DESCRIPTION

23       BN_generate_prime() generates a pseudo-random prime number of num bits.
24       If ret is not NULL, it will be used to store the number.
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26       If callback is not NULL, it is called as follows:
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28       ·   callback(0, i, cb_arg) is called after generating the i-th poten‐
29           tial prime number.
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31       ·   While the number is being tested for primality, callback(1, j,
32           cb_arg) is called as described below.
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34       ·   When a prime has been found, callback(2, i, cb_arg) is called.
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36       The prime may have to fulfill additional requirements for use in
37       Diffie-Hellman key exchange:
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39       If add is not NULL, the prime will fulfill the condition p % add == rem
40       (p % add == 1 if rem == NULL) in order to suit a given generator.
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42       If safe is true, it will be a safe prime (i.e. a prime p so that
43       (p-1)/2 is also prime).
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45       The PRNG must be seeded prior to calling BN_generate_prime().  The
46       prime number generation has a negligible error probability.
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48       BN_is_prime() and BN_is_prime_fasttest() test if the number a is prime.
49       The following tests are performed until one of them shows that a is
50       composite; if a passes all these tests, it is considered prime.
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52       BN_is_prime_fasttest(), when called with do_trial_division == 1, first
53       attempts trial division by a number of small primes; if no divisors are
54       found by this test and callback is not NULL, callback(1, -1, cb_arg) is
55       called.  If do_trial_division == 0, this test is skipped.
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57       Both BN_is_prime() and BN_is_prime_fasttest() perform a Miller-Rabin
58       probabilistic primality test with checks iterations. If checks ==
59       BN_prime_checks, a number of iterations is used that yields a false
60       positive rate of at most 2^-80 for random input.
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62       If callback is not NULL, callback(1, j, cb_arg) is called after the
63       j-th iteration (j = 0, 1, ...). ctx is a pre-allocated BN_CTX (to save
64       the overhead of allocating and freeing the structure in a loop), or
65       NULL.
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RETURN VALUES

68       BN_generate_prime() returns the prime number on success, NULL other‐
69       wise.
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71       BN_is_prime() returns 0 if the number is composite, 1 if it is prime
72       with an error probability of less than 0.25^checks, and -1 on error.
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74       The error codes can be obtained by ERR_get_error(3).
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SEE ALSO

77       bn(3), ERR_get_error(3), rand(3)
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HISTORY

80       The cb_arg arguments to BN_generate_prime() and to BN_is_prime() were
81       added in SSLeay 0.9.0. The ret argument to BN_generate_prime() was
82       added in SSLeay 0.9.1.  BN_is_prime_fasttest() was added in OpenSSL
83       0.9.5.
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870.9.8b                            2003-01-13              BN_generate_prime(3)