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.\"
.IX Title "BN_generate_prime 3"
.TH BN_generate_prime 3 "2014-07-11" "LibreSSL" "LibreSSL"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
BN_generate_prime, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call,
BN_GENCB_set_old, BN_GENCB_set, 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>
\&
\& int BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add,
\&     const BIGNUM *rem, BN_GENCB *cb);
\&
\& int BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb);
\&
\& int BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx,
\&     int do_trial_division, BN_GENCB *cb);
\&
\& int BN_GENCB_call(BN_GENCB *cb, int a, int b);
\&
\& #define BN_GENCB_set_old(gencb, callback, cb_arg) ...
\&
\& #define BN_GENCB_set(gencb, callback, cb_arg) ...
.Ve
.PP
Deprecated:
.PP
\&\s-1BIGNUM\s0 *BN_generate_prime(\s-1BIGNUM\s0 *ret, int num, int safe, \s-1BIGNUM\s0 *add,
     \s-1BIGNUM\s0 *rem, void (*callback)(int, int, void *), void *cb_arg);
.PP
.Vb 2
\& int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int,
\&     void *), BN_CTX *ctx, void *cb_arg);
\&
\& 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_ex()\fR generates a pseudo-random prime number of
bit length \fBbits\fR.
If \fBret\fR is not \fB\s-1NULL\s0\fR, it will be used to store the number.
.PP
If \fBcb\fR is not \fB\s-1NULL\s0\fR, it is used as follows:
.IP "\(bu" 4
\&\fBBN_GENCB_call(cb, 0, i)\fR is called after generating the i\-th
potential prime number.
.IP "\(bu" 4
While the number is being tested for primality,
\&\fBBN_GENCB_call(cb, 1, j)\fR is called as described below.
.IP "\(bu" 4
When a prime has been found, \fBBN_GENCB_call(cb, 2, i)\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 prime number generation has a negligible error probability.
.PP
\&\fIBN_is_prime_ex()\fR and \fIBN_is_prime_fasttest_ex()\fR test if the number \fBp\fR is
prime.  The following tests are performed until one of them shows that
\&\fBp\fR is composite; if \fBp\fR passes all these tests, it is considered
prime.
.PP
\&\fIBN_is_prime_fasttest_ex()\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 \fBcb\fR is not \fB\s-1NULL\s0\fR,
\&\fBBN_GENCB_call(cb, 1, \-1)\fR is called.
If \fBdo_trial_division == 0\fR, this test is skipped.
.PP
Both \fIBN_is_prime_ex()\fR and \fIBN_is_prime_fasttest_ex()\fR perform a Miller-Rabin
probabilistic primality test with \fBnchecks\fR iterations. If
\&\fBnchecks == 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 \fBcb\fR is not \fB\s-1NULL\s0\fR, \fBBN_GENCB_call(cb, 1, j)\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.
.PP
BN_GENCB_call calls the callback function held in the \fB\s-1BN_GENCB\s0\fR structure
and passes the ints \fBa\fR and \fBb\fR as arguments. There are two types of
\&\fB\s-1BN_GENCB\s0\fR structure that are supported: \*(L"new\*(R" style and \*(L"old\*(R" style. New
programs should prefer the \*(L"new\*(R" style, whilst the \*(L"old\*(R" style is provided
for backwards compatibility purposes.
.PP
For \*(L"new\*(R" style callbacks a \s-1BN_GENCB\s0 structure should be initialised with a
call to BN_GENCB_set, where \fBgencb\fR is a \fB\s-1BN_GENCB\s0 *\fR, \fBcallback\fR is of
type \fBint (*callback)(int, int, \s-1BN_GENCB\s0 *)\fR and \fBcb_arg\fR is a \fBvoid *\fR.
\&\*(L"Old\*(R" style callbacks are the same except they are initialised with a call
to BN_GENCB_set_old and \fBcallback\fR is of type
\&\fBvoid (*callback)(int, int, void *)\fR.
.PP
A callback is invoked through a call to \fBBN_GENCB_call\fR. This will check
the type of the callback and will invoke \fBcallback(a, b, gencb)\fR for new
style callbacks or \fBcallback(a, b, cb_arg)\fR for old style.
.PP
BN_generate_prime (deprecated) works in the same way as
BN_generate_prime_ex but expects an old style callback function
directly in the \fBcallback\fR parameter, and an argument to pass to it in
the \fBcb_arg\fR. Similarly BN_is_prime and BN_is_prime_fasttest are
deprecated and can be compared to BN_is_prime_ex and
BN_is_prime_fasttest_ex respectively.
.SH "RETURN VALUES"
.IX Header "RETURN VALUES"
\&\fIBN_generate_prime_ex()\fR returns 1 on success or 0 on error.
.PP
\&\fIBN_is_prime_ex()\fR, \fIBN_is_prime_fasttest_ex()\fR, \fIBN_is_prime()\fR and
\&\fIBN_is_prime_fasttest()\fR return 0 if the number is composite, 1 if it is
prime with an error probability of less than 0.25^\fBnchecks\fR, and
\&\-1 on error.
.PP
\&\fIBN_generate_prime()\fR returns the prime number on success, \fB\s-1NULL\s0\fR otherwise.
.PP
Callback functions should return 1 on success or 0 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.