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-.\" $OpenBSD: BN_generate_prime.3,v 1.19 2020/06/24 18:15:00 jmc Exp $
-.\" full merge up to: OpenSSL f987a4dd Jun 27 10:12:08 2019 +0200
-.\"
-.\" This 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/)"
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-.\"
-.\" 5. Products derived from this software may not be called "OpenSSL"
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-.\"    permission of the OpenSSL Project.
-.\"
-.\" 6. Redistributions of any form whatsoever must retain the following
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-.\"    "This product includes software developed by the OpenSSL Project
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-.Dd $Mdocdate: June 24 2020 $
-.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_new ,
-.Nm BN_GENCB_free ,
-.Nm BN_GENCB_set_old ,
-.Nm BN_GENCB_set ,
-.Nm BN_GENCB_get_arg ,
-.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
-.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_old
-.Fa "BN_GENCB *gencb"
-.Fa "void (*callback)(int, int, void *)"
-.Fa "void *cb_arg"
-.Fc
-.Ft void
-.Fo BN_GENCB_set
-.Fa "BN_GENCB *gencb"
-.Fa "int (*callback)(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 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 at least bit length
-.Fa bits .
-The returned number is probably prime, but there is a very small
-probability of returning a non-prime number.
-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.
-.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
-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
-.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\(ha-64 for random input.
-The error rate depends on the size of the prime
-and goes down for bigger primes.
-The rate is 2\(ha-80 starting at 308 bits, 2\(ha-112 at 852 bits,
-2\(ha-128 at 1080 bits, 2\(ha-192 at 3747 bits
-and 2\(ha-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,
-.Fa nchecks
-should be set to 64.
-.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
-A
-.Vt BN_GENCB
-structure should be created through a call to
-.Fn BN_GENCB_new
-and freed through a call to
-.Fn BN_GENCB_free .
-.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
-It is possible to obtain the argument associated with a
-.Vt BN_GENCB
-structure (set via a call to
-.Fn BN_GENCB_set
-or
-.Fn BN_GENCB_set_old )
-using
-.Fn BN_GENCB_get_arg .
-.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
-.Fn BN_GENCB_new
-returns a pointer to a
-.Vt BN_GENCB
-structure on success, or
-.Dv NULL
-otherwise.
-.Pp
-.Fn BN_GENCB_get_arg
-returns the argument previously associated with a
-.Vt BN_GENCB
-structure.
-.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_new 3 ,
-.Xr DH_generate_parameters 3 ,
-.Xr DSA_generate_parameters 3 ,
-.Xr RSA_generate_key 3
-.Sh HISTORY
-.Fn BN_generate_prime
-and
-.Fn BN_is_prime
-first appeared in SSLeay 0.5.1 and had their
-.Fa cb_arg
-argument added in SSLeay 0.9.0.
-These two functions have been available since
-.Ox 2.4 .
-.Pp
-The
-.Fa ret
-argument to
-.Fn BN_generate_prime
-was added in SSLeay 0.9.1 and
-.Ox 2.6 .
-.Pp
-.Fn BN_is_prime_fasttest
-first appeared in OpenSSL 0.9.5 and has been available since
-.Ox 2.7 .
-.Pp
-.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 .