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-.\" $OpenBSD: BN_generate_prime.3,v 1.25 2023/12/29 19:12:46 tb Exp $
-.\" full merge up to: OpenSSL f987a4dd Jun 27 10:12:08 2019 +0200
-.\"
-.\" This file is a derived work.
-.\" The changes are covered by the following Copyright and license:
-.\"
-.\" Copyright (c) 2022 Ingo Schwarze <schwarze@openbsd.org>
-.\"
-.\" Permission to use, copy, modify, and distribute this software for any
-.\" purpose with or without fee is hereby granted, provided that the above
-.\" copyright notice and this permission notice appear in all copies.
-.\"
-.\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
-.\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
-.\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
-.\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
-.\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
-.\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
-.\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
-.\"
-.\" The original file was written by Ulf Moeller <ulf@openssl.org>
-.\" Bodo Moeller <bodo@openssl.org>, and Matt Caswell <matt@openssl.org>.
-.\" Copyright (c) 2000, 2003, 2013, 2014, 2018 The OpenSSL Project.
-.\" All rights reserved.
-.\"
-.\" Redistribution and use in source and binary forms, with or without
-.\" modification, are permitted provided that the following conditions
-.\" are met:
-.\"
-.\" 1. Redistributions of source code must retain the above copyright
-.\"    notice, this list of conditions and the following disclaimer.
-.\"
-.\" 2. Redistributions in binary form must reproduce the above copyright
-.\"    notice, this list of conditions and the following disclaimer in
-.\"    the documentation and/or other materials provided with the
-.\"    distribution.
-.\"
-.\" 3. All advertising materials mentioning features or use of this
-.\"    software must display the following acknowledgment:
-.\"    "This product includes software developed by the OpenSSL Project
-.\"    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
-.\"
-.\" 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
-.\"    endorse or promote products derived from this software without
-.\"    prior written permission. For written permission, please contact
-.\"    openssl-core@openssl.org.
-.\"
-.\" 5. Products derived from this software may not be called "OpenSSL"
-.\"    nor may "OpenSSL" appear in their names without prior written
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-.\" 6. Redistributions of any form whatsoever must retain the following
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-.\" ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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-.\" LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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-.\"
-.Dd $Mdocdate: December 29 2023 $
-.Dt BN_GENERATE_PRIME 3
-.Os
-.Sh NAME
-.Nm BN_is_prime_ex ,
-.Nm BN_is_prime_fasttest_ex ,
-.Nm BN_generate_prime_ex ,
-.Nm BN_GENCB_call ,
-.Nm BN_GENCB_new ,
-.Nm BN_GENCB_free ,
-.Nm BN_GENCB_set ,
-.Nm BN_GENCB_get_arg ,
-.Nm BN_GENCB_set_old
-.\" Nm BN_prime_checks_for_size is intentionally undocumented
-.\" because it should not be used outside of libcrypto.
-.Nd generate primes and test for primality
-.Sh SYNOPSIS
-.In openssl/bn.h
-.Ft int
-.Fo BN_is_prime_ex
-.Fa "const BIGNUM *a"
-.Fa "int nchecks"
-.Fa "BN_CTX *ctx"
-.Fa "BN_GENCB *cb"
-.Fc
-.Ft int
-.Fo BN_is_prime_fasttest_ex
-.Fa "const BIGNUM *a"
-.Fa "int nchecks"
-.Fa "BN_CTX *ctx"
-.Fa "int do_trial_division"
-.Fa "BN_GENCB *cb"
-.Fc
-.Ft int
-.Fo BN_generate_prime_ex
-.Fa "BIGNUM *ret"
-.Fa "int bits"
-.Fa "int safe"
-.Fa "const BIGNUM *modulus"
-.Fa "const BIGNUM *remainder"
-.Fa "BN_GENCB *cb"
-.Fc
-.Ft int
-.Fo BN_GENCB_call
-.Fa "BN_GENCB *cb"
-.Fa "int state_code"
-.Fa "int serial_number"
-.Fc
-.Ft BN_GENCB *
-.Fn BN_GENCB_new void
-.Ft void
-.Fo BN_GENCB_free
-.Fa "BN_GENCB *cb"
-.Fc
-.Ft void
-.Fo BN_GENCB_set
-.Fa "BN_GENCB *cb"
-.Fa "int (*cb_fp)(int, int, BN_GENCB *)"
-.Fa "void *cb_arg"
-.Fc
-.Ft void *
-.Fo BN_GENCB_get_arg
-.Fa "BN_GENCB *cb"
-.Fc
-.Pp
-Deprecated:
-.Pp
-.Ft void
-.Fo BN_GENCB_set_old
-.Fa "BN_GENCB *cb"
-.Fa "void (*cb_fp)(int, int, void *)"
-.Fa "void *cb_arg"
-.Fc
-.Sh DESCRIPTION
-.Fn BN_is_prime_ex
-and
-.Fn BN_is_prime_fasttest_ex
-test whether the number
-.Fa a
-is prime.
-In LibreSSL, both functions behave identically
-and use the Baillie-Pomerance-Selfridge-Wagstaff algorithm
-combined with
-.Fa checks
-Miller-Rabin rounds.
-The
-.Fa do_trial_division
-argument is ignored.
-.Pp
-It is unknown whether any composite number exists that the
-Baillie-PSW algorithm misclassifies as a prime.
-Some suspect that there may be infinitely many such numbers,
-but not a single one is currently known.
-It is known that no such number exists below 2\(ha64.
-.Pp
-In order to reduce the likelihood of a composite number
-passing the primality tests
-.Fn BN_is_prime_fasttest_ex
-and
-.Fn BN_is_prime_ex ,
-a number of rounds of the probabilistic Miller-Rabin test is performed.
-If
-.Fa checks
-is positive, it is used as the number of rounds;
-if it is zero or the special value
-.Dv BN_prime_checks ,
-a suitable number of rounds is calculated from the bit length of
-.Fa a .
-.Pp
-If
-.Dv NULL
-is passed for the
-.Fa ctx
-argument, these function allocate a
-.Vt BN_CTX
-object internally when they need one and free it before returning.
-Alternatively, to save the overhead of allocating and freeing
-that object for each call, the caller can pre-allocate a
-.Vt BN_CTX
-object and pass it in the
-.Fa ctx
-argument.
-.Pp
-.Fn BN_generate_prime_ex
-generates a pseudo-random prime number of at least bit length
-.Fa bits
-and places it in
-.Fa ret .
-Primality of
-.Fa ret
-is tested internally using
-.Fn BN_is_prime_ex .
-Consequently, for
-.Fa bits
-larger than 64, it is theoretically possible
-that this function might place a composite number into
-.Fa ret ;
-the probability of such an event is unknown but very small.
-.Pp
-The prime may have to fulfill additional requirements for use in
-Diffie-Hellman key exchange:
-.Bl -bullet
-.It
-If
-.Fa modulus
-is not
-.Dv NULL ,
-a prime is generated that fulfills the condition
-.Fa ret No % Fa modulus No = Fa remainder .
-If the
-.Fa remainder
-argument is
-.Dv NULL ,
-1 is used as the desired remainder.
-.It
-If the
-.Fa safe
-argument is non-zero, a safe prime is generated, that is,
-.Po Fa ret No \- 1 Pc Ns /2
-is also prime.
-.El
-.Pp
-If
-.Fa cb
-is not
-.Dv NULL ,
-it is used as follows:
-.Bl -bullet
-.It
-.Fn BN_GENCB_call cb 0 serial_number
-is called after generating a potential prime number.
-.It
-The
-.Fa state_code
-of 1 is reserved for callbacks during primality testing,
-but LibreSSL performs no such callbacks.
-.It
-When
-.Fa safe
-is non-zero and a safe prime has been found,
-.Fn BN_GENCB_call cb 2 serial_number
-is called.
-.It
-The callers of
-.Fn BN_generate_prime_ex
-may call
-.Fn BN_GENCB_call
-with other values as described in their respective manual pages; see
-.Sx SEE ALSO .
-.El
-.Pp
-In all cases, the
-.Fa serial_number
-is the number of candidates that have already been discarded
-for not being prime; that is,
-.Fa serial_number
-is 0 for the first candidate
-and then incremented whenever a new candidate is generated.
-.Pp
-.Fn BN_GENCB_call
-calls the callback function held in
-.Fa cb
-and passes the
-.Fa state_code
-and the
-.Fa serial_number
-as arguments.
-If
-.Fa cb
-is
-.Dv NULL
-or does not contain a callback function, no action occurs.
-.Pp
-.Fn BN_GENCB_new
-allocates a new
-.Vt BN_GENCB
-object.
-.Pp
-.Fn BN_GENCB_free
-frees
-.Fa cb .
-If
-.Fa cb
-is
-.Dv NULL ,
-no action occurs.
-.Pp
-.Fn BN_GENCB_set
-initialises
-.Fa cb
-to use the callback function pointer
-.Fa cb_fp
-and the additional callback argument
-.Fa cb_arg .
-.Pp
-The deprecated function
-.Fn BN_GENCB_set_old
-initialises
-.Fa cb
-to use the old-style callback function pointer
-.Fa cb_fp
-and the additional callback argument
-.Fa cb_arg .
-.Sh RETURN VALUES
-.Fn BN_is_prime_ex
-and
-.Fn BN_is_prime_fasttest_ex
-return 0 if the number is composite, 1 if it is prime with a very small
-error probability, or \-1 on error.
-.Pp
-.Fn BN_generate_prime_ex
-returns 1 on success or 0 on error.
-.Pp
-.Fn BN_GENCB_call
-returns 1 on success, including when
-.Fa cb
-is
-.Dv NULL
-or does not contain a callback function,
-or 0 on error.
-.Pp
-.Fn BN_GENCB_new
-returns a pointer to the newly allocated
-.Vt BN_GENCB
-object or
-.Dv NULL
-if memory allocation fails.
-.Pp
-The callback functions pointed to by the
-.Fa cb_fp
-arguments are supposed to return 1 on success or 0 on error.
-.Pp
-.Fn BN_GENCB_get_arg
-returns the
-.Fa cb_arg
-pointer that was previously stored in
-.Fa cb
-using
-.Fn BN_GENCB_set
-or
-.Fn BN_GENCB_set_old .
-.Pp
-In some cases, error codes can be obtained by
-.Xr ERR_get_error 3 .
-.Sh SEE ALSO
-.Xr BN_new 3 ,
-.Xr DH_generate_parameters 3 ,
-.Xr DSA_generate_parameters_ex 3 ,
-.Xr RSA_generate_key 3
-.Sh HISTORY
-.Fn BN_generate_prime_ex ,
-.Fn BN_is_prime_ex ,
-.Fn BN_is_prime_fasttest_ex ,
-.Fn BN_GENCB_call ,
-.Fn BN_GENCB_set_old ,
-and
-.Fn BN_GENCB_set
-first appeared in OpenSSL 0.9.8 and have been available since
-.Ox 4.5 .
-.Pp
-.Fn BN_GENCB_new ,
-.Fn BN_GENCB_free ,
-and
-.Fn BN_GENCB_get_arg
-first appeared in OpenSSL 1.1.0 and have been available since
-.Ox 6.3 .