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.\" ========================================================================
.\"
.IX Title "BN_generate_prime 3"
.TH BN_generate_prime 3 "2006-10-01" "0.9.8d" "OpenSSL"
.SH "NAME"
BN_generate_prime, BN_is_prime, BN_is_prime_fasttest \- generate primes and test for primality
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\& #include <openssl/bn.h>
.Ve
.PP
.Vb 2
\& BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
\& BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
.Ve
.PP
.Vb 2
\& int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int,
\& void *), BN_CTX *ctx, void *cb_arg);
.Ve
.PP
.Vb 3
\& int BN_is_prime_fasttest(const BIGNUM *a, int checks,
\& void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg,
\& int do_trial_division);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
\&\fIBN_generate_prime()\fR generates a pseudo-random prime number of \fBnum\fR
bits.
If \fBret\fR is not \fB\s-1NULL\s0\fR, it will be used to store the number.
.PP
If \fBcallback\fR is not \fB\s-1NULL\s0\fR, it is called as follows:
.IP "\(bu" 4
\&\fBcallback(0, i, cb_arg)\fR is called after generating the i\-th
potential prime number.
.IP "\(bu" 4
While the number is being tested for primality, \fBcallback(1, j,
cb_arg)\fR is called as described below.
.IP "\(bu" 4
When a prime has been found, \fBcallback(2, i, cb_arg)\fR is called.
.PP
The prime may have to fulfill additional requirements for use in
Diffie-Hellman key exchange:
.PP
If \fBadd\fR is not \fB\s-1NULL\s0\fR, the prime will fulfill the condition p % \fBadd\fR
== \fBrem\fR (p % \fBadd\fR == 1 if \fBrem\fR == \fB\s-1NULL\s0\fR) in order to suit a given
generator.
.PP
If \fBsafe\fR is true, it will be a safe prime (i.e. a prime p so
that (p\-1)/2 is also prime).
.PP
The \s-1PRNG\s0 must be seeded prior to calling \fIBN_generate_prime()\fR.
The prime number generation has a negligible error probability.
.PP
\&\fIBN_is_prime()\fR and \fIBN_is_prime_fasttest()\fR test if the number \fBa\fR is
prime. The following tests are performed until one of them shows that
\&\fBa\fR is composite; if \fBa\fR passes all these tests, it is considered
prime.
.PP
\&\fIBN_is_prime_fasttest()\fR, when called with \fBdo_trial_division == 1\fR,
first attempts trial division by a number of small primes;
if no divisors are found by this test and \fBcallback\fR is not \fB\s-1NULL\s0\fR,
\&\fBcallback(1, \-1, cb_arg)\fR is called.
If \fBdo_trial_division == 0\fR, this test is skipped.
.PP
Both \fIBN_is_prime()\fR and \fIBN_is_prime_fasttest()\fR perform a Miller-Rabin
probabilistic primality test with \fBchecks\fR iterations. If
\&\fBchecks == BN_prime_checks\fR, a number of iterations is used that
yields a false positive rate of at most 2^\-80 for random input.
.PP
If \fBcallback\fR is not \fB\s-1NULL\s0\fR, \fBcallback(1, j, cb_arg)\fR is called
after the j\-th iteration (j = 0, 1, ...). \fBctx\fR is a
pre-allocated \fB\s-1BN_CTX\s0\fR (to save the overhead of allocating and
freeing the structure in a loop), or \fB\s-1NULL\s0\fR.
.SH "RETURN VALUES"
.IX Header "RETURN VALUES"
\&\fIBN_generate_prime()\fR returns the prime number on success, \fB\s-1NULL\s0\fR otherwise.
.PP
\&\fIBN_is_prime()\fR returns 0 if the number is composite, 1 if it is
prime with an error probability of less than 0.25^\fBchecks\fR, and
\&\-1 on error.
.PP
The error codes can be obtained by \fIERR_get_error\fR\|(3).
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\fIbn\fR\|(3), \fIERR_get_error\fR\|(3), \fIrand\fR\|(3)
.SH "HISTORY"
.IX Header "HISTORY"
The \fBcb_arg\fR arguments to \fIBN_generate_prime()\fR and to \fIBN_is_prime()\fR
were added in SSLeay 0.9.0. The \fBret\fR argument to \fIBN_generate_prime()\fR
was added in SSLeay 0.9.1.
\&\fIBN_is_prime_fasttest()\fR was added in OpenSSL 0.9.5.
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