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+.Dd $Mdocdate: February 23 2015 $
+.Dt BN_GENERATE_PRIME 3
+.Os
+.Sh NAME
+.Nm BN_generate_prime_ex ,
+.Nm BN_is_prime_ex ,
+.Nm BN_is_prime_fasttest_ex ,
+.Nm BN_GENCB_call ,
+.Nm BN_GENCB_set_old ,
+.Nm BN_GENCB_set ,
+.Nm BN_generate_prime ,
+.Nm BN_is_prime ,
+.Nm BN_is_prime_fasttest
+.Nd generate primes and test for primality
+.Sh SYNOPSIS
+.In openssl/bn.h
+.Ft int
+.Fo BN_generate_prime_ex
+.Fa "BIGNUM *ret"
+.Fa "int bits"
+.Fa "int safe"
+.Fa "const BIGNUM *add"
+.Fa "const BIGNUM *rem"
+.Fa "BN_GENCB *cb"
+.Fc
+.Ft int
+.Fo BN_is_prime_ex
+.Fa "const BIGNUM *p"
+.Fa "int nchecks"
+.Fa "BN_CTX *ctx"
+.Fa "BN_GENCB *cb"
+.Fc
+.Ft int
+.Fo BN_is_prime_fasttest_ex
+.Fa "const BIGNUM *p"
+.Fa "int nchecks"
+.Fa "BN_CTX *ctx"
+.Fa "int do_trial_division"
+.Fa "BN_GENCB *cb"
+.Fc
+.Ft int
+.Fo BN_GENCB_call
+.Fa "BN_GENCB *cb"
+.Fa "int a"
+.Fa "int b"
+.Fc
+.Fd #define BN_GENCB_set_old(gencb, callback, cb_arg) ...
+.Fd #define BN_GENCB_set(gencb, callback, cb_arg) ...
+.Pp
+Deprecated:
+.Pp
+.Ft BIGNUM *
+.Fo BN_generate_prime
+.Fa "BIGNUM *ret"
+.Fa "int num"
+.Fa "int safe"
+.Fa "BIGNUM *add"
+.Fa "BIGNUM *rem"
+.Fa "void (*callback)(int, int, void *)"
+.Fa "void *cb_arg"
+.Fc
+.Ft int
+.Fo BN_is_prime
+.Fa "const BIGNUM *a"
+.Fa "int checks"
+.Fa "void (*callback)(int, int, void *)"
+.Fa "BN_CTX *ctx"
+.Fa "void *cb_arg"
+.Fc
+.Ft int
+.Fo BN_is_prime_fasttest
+.Fa "const BIGNUM *a"
+.Fa "int checks"
+.Fa "void (*callback)(int, int, void *)"
+.Fa "BN_CTX *ctx"
+.Fa "void *cb_arg"
+.Fa "int do_trial_division"
+.Fc
+.Sh DESCRIPTION
+.Fn BN_generate_prime_ex
+generates a pseudo-random prime number of bit length
+.Fa bits .
+If
+.Fa ret
+is not
+.Dv NULL ,
+it will be used to store the number.
+.Pp
+If
+.Fa cb
+is not
+.Dv NULL ,
+it is used as follows:
+.Bl -bullet
+.It
+.Fn BN_GENCB_call cb 0 i
+is called after generating the i-th potential prime number.
+.It
+While the number is being tested for primality,
+.Fn BN_GENCB_call cb 1 j
+is called as described below.
+.It
+When a prime has been found,
+.Fn BN_GENCB_call cb 2 i
+is called.
+.El
+.Pp
+The prime may have to fulfill additional requirements for use in
+Diffie-Hellman key exchange:
+.Pp
+If
+.Fa add
+is not
+.Dv NULL ,
+the prime will fulfill the condition p %
+.Fa add
+==
+.Fa rem
+(p %
+.Fa add
+== 1 if
+.Fa rem
+==
+.Dv NULL )
+in order to suit a given generator.
+.Pp
+If
+.Fa safe
+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
+.Fn BN_is_prime_ex
+and
+.Fn BN_is_prime_fasttest_ex
+test if the number
+.Fa p
+is prime.
+The following tests are performed until one of them shows that
+.Fa p
+is composite; if
+.Fa p
+passes all these tests, it is considered prime.
+.Pp
+.Fn BN_is_prime_fasttest_ex ,
+when called with
+.Fa do_trial_division
+== 1, first attempts trial division by a number of small primes;
+if no divisors are found by this test and
+.Fa cb
+is not
+.Dv NULL ,
+.Sy BN_GENCB_call(cb, 1, -1)
+is called.
+If
+.Fa do_trial_division
+== 0, this test is skipped.
+.Pp
+Both
+.Fn BN_is_prime_ex
+and
+.Fn BN_is_prime_fasttest_ex
+perform a Miller-Rabin probabilistic primality test with
+.Fa nchecks
+iterations.
+If
+.Fa nchecks
+==
+.Dv BN_prime_checks ,
+a number of iterations is used that yields a false positive rate of at
+most 2^-80 for random input.
+.Pp
+If
+.Fa cb
+is not
+.Dv NULL ,
+.Fa BN_GENCB_call cb 1 j
+is called after the j-th iteration (j = 0, 1, ...).
+.Fa ctx
+is a pre-allocated
+.Vt BN_CTX
+(to save the overhead of allocating and freeing the structure in a
+loop), or
+.Dv NULL .
+.Pp
+.Fn BN_GENCB_call
+calls the callback function held in the
+.Vt BN_GENCB
+structure and passes the ints
+.Fa a
+and
+.Fa b
+as arguments.
+There are two types of
+.Vt BN_GENCB
+structures that are supported: "new" style and "old" style.
+New programs should prefer the "new" style, whilst the "old" style is
+provided for backwards compatibility purposes.
+.Pp
+For "new" style callbacks a
+.Vt BN_GENCB
+structure should be initialised with a call to
+.Fn BN_GENCB_set ,
+where
+.Fa gencb
+is a
+.Vt BN_GENCB * ,
+.Fa callback
+is of type
+.Vt int (*callback)(int, int, BN_GENCB *)
+and
+.Fa cb_arg
+is a
+.Vt void * .
+"Old" style callbacks are the same except they are initialised with a
+call to
+.Fn BN_GENCB_set_old
+and
+.Fa callback
+is of type
+.Vt void (*callback)(int, int, void *) .
+.Pp
+A callback is invoked through a call to
+.Fn BN_GENCB_call .
+This will check the type of the callback and will invoke
+.Fn callback a b gencb
+for new style callbacks or
+.Fn callback a b cb_arg
+for old style.
+.Pp
+.Fn BN_generate_prime
+(deprecated) works in the same way as
+.Fn BN_generate_prime_ex
+but expects an old style callback function directly in the
+.Fa callback
+parameter, and an argument to pass to it in the
+.Fa cb_arg .
+Similarly
+.Fn BN_is_prime
+and
+.Fn BN_is_prime_fasttest
+are deprecated and can be compared to
+.Fn BN_is_prime_ex
+and
+.Fn BN_is_prime_fasttest_ex
+respectively.
+.Sh RETURN VALUES
+.Fn BN_generate_prime_ex
+returns 1 on success or 0 on error.
+.Pp
+.Fn BN_is_prime_ex ,
+.Fn BN_is_prime_fasttest_ex ,
+.Fn BN_is_prime ,
+and
+.Fn BN_is_prime_fasttest
+return 0 if the number is composite, 1 if it is prime with an error
+probability of less than
+.Pf 0.25^ Fa nchecks ,
+and -1 on error.
+.Pp
+.Fn BN_generate_prime
+returns the prime number on success,
+.Dv NULL
+otherwise.
+.Pp
+Callback functions should return 1 on success or 0 on error.
+.Pp
+The error codes can be obtained by
+.Xr ERR_get_error 3 .
+.Sh SEE ALSO
+.Xr bn 3 ,
+.Xr ERR_get_error 3 ,
+.Xr rand 3
+.Sh HISTORY
+The
+.Fa cb_arg
+arguments to
+.Fn BN_generate_prime
+and to
+.Fn BN_is_prime
+were added in SSLeay 0.9.0.
+The
+.Fa ret
+argument to
+.Fn BN_generate_prime
+was added in SSLeay 0.9.1.
+.Fn BN_is_prime_fasttest
+was added in OpenSSL 0.9.5.