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.\" ========================================================================
.\"
.IX Title "BN_generate_prime 3"
.TH BN_generate_prime 3 "2019-12-20" "1.0.2u" "OpenSSL"
.\" 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_ex, 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
.Vb 2
\& BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
\&     BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
\&
\& 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"
\&\fBBN_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 \s-1PRNG\s0 must be seeded prior to calling \fBBN_generate_prime_ex()\fR.
The prime number generation has a negligible error probability.
.PP
\&\fBBN_is_prime_ex()\fR and \fBBN_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
\&\fBBN_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 \fBBN_is_prime_ex()\fR and \fBBN_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^\-64 for random input.
The error rate depends on the size of the prime and goes down for bigger primes.
The rate is 2^\-80 starting at 308 bits, 2^\-112 at 852 bits, 2^\-128 at 1080 bits,
2^\-192 at 3747 bits and 2^\-256 at 6394 bits.
.PP
When the source of the prime is not random or not trusted, the number
of checks needs to be much higher to reach the same level of assurance:
It should equal half of the targeted security level in bits (rounded up to the
next integer if necessary).
For instance, to reach the 128 bit security level, \fBnchecks\fR should be set to
64.
.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"
\&\fBBN_generate_prime_ex()\fR return 1 on success or 0 on error.
.PP
\&\fBBN_is_prime_ex()\fR, \fBBN_is_prime_fasttest_ex()\fR, \fBBN_is_prime()\fR and
\&\fBBN_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
\&\fBBN_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 \fBERR_get_error\fR\|(3).
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\fBbn\fR\|(3), \fBERR_get_error\fR\|(3), \fBrand\fR\|(3)
.SH "HISTORY"
.IX Header "HISTORY"
The \fBcb_arg\fR arguments to \fBBN_generate_prime()\fR and to \fBBN_is_prime()\fR
were added in SSLeay 0.9.0. The \fBret\fR argument to \fBBN_generate_prime()\fR
was added in SSLeay 0.9.1.
\&\fBBN_is_prime_fasttest()\fR was added in OpenSSL 0.9.5.

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✏️ BN_is_prime.3ssl