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-.\" $OpenBSD: get_rfc3526_prime_8192.3,v 1.4 2018/03/23 23:18:17 schwarze Exp $
-.\" checked up to: OpenSSL DH_get_1024_160 99d63d46 Oct 26 13:56:48 2016 -0400
-.\"
-.\" Copyright (c) 2017 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.
-.\"
-.Dd $Mdocdate: March 23 2018 $
-.Dt GET_RFC3526_PRIME_8192 3
-.Os
-.Sh NAME
-.Nm get_rfc2409_prime_768 ,
-.Nm get_rfc2409_prime_1024 ,
-.Nm get_rfc3526_prime_1536 ,
-.Nm get_rfc3526_prime_2048 ,
-.Nm get_rfc3526_prime_3072 ,
-.Nm get_rfc3526_prime_4096 ,
-.Nm get_rfc3526_prime_6144 ,
-.Nm get_rfc3526_prime_8192 ,
-.Nm BN_get_rfc2409_prime_768 ,
-.Nm BN_get_rfc2409_prime_1024 ,
-.Nm BN_get_rfc3526_prime_2048 ,
-.Nm BN_get_rfc3526_prime_3072 ,
-.Nm BN_get_rfc3526_prime_4096 ,
-.Nm BN_get_rfc3526_prime_6144 ,
-.Nm BN_get_rfc3526_prime_8192
-.Nd standard moduli for Diffie-Hellmann key exchange
-.Sh SYNOPSIS
-.In openssl/bn.h
-.Ft BIGNUM *
-.Fn get_rfc2409_prime_768 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn get_rfc2409_prime_1024 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn get_rfc3526_prime_1536 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn get_rfc3526_prime_2048 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn get_rfc3526_prime_3072 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn get_rfc3526_prime_4096 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn get_rfc3526_prime_6144 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn get_rfc3526_prime_8192 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn BN_get_rfc2409_prime_768 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn BN_get_rfc2409_prime_1024 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn BN_get_rfc3526_prime_1536 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn BN_get_rfc3526_prime_2048 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn BN_get_rfc3526_prime_3072 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn BN_get_rfc3526_prime_4096 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn BN_get_rfc3526_prime_6144 "BIGNUM *bn"
-.Ft BIGNUM *
-.Fn BN_get_rfc3526_prime_8192 "BIGNUM *bn"
-.Sh DESCRIPTION
-Each of these functions returns one specific constant Sophie Germain
-prime number
-.Fa p .
-The names with the prefix
-.Sq BN_
-are aliases for the names without that prefix.
-.Pp
-If
-.Fa bn
-is
-.Dv NULL ,
-a new
-.Vt BIGNUM
-object is created and returned.
-Otherwise, the number is stored in
-.Pf * Fa bn
-and
-.Fa bn
-is returned.
-.Pp
-All these numbers are of the form
-.Pp
-.EQ
-p = 2 sup s - 2 sup left ( s - 64 right ) - 1 + 2 sup 64 *
-left { left [ 2 sup left ( s - 130 right ) pi right ] + offset right }
-delim $$
-.EN
-.Pp
-where
-.Ar s
-is the size of the binary representation of the number in bits
-and appears at the end of the function names.
-As long as the offset is sufficiently small, the above form assures
-that the top and bottom 64 bits of each number are all 1.
-.Pp
-The offsets are defined in the standards as follows:
-.Bl -column 16n 8n -offset indent
-.It size Ar s Ta Ar offset
-.It Ta
-.It \ 768 = 3 * 2^8  Ta  149686
-.It 1024 = 2 * 2^9  Ta  129093
-.It 1536 = 3 * 2^9  Ta  741804
-.It 2048 = 2 * 2^10 Ta  124476
-.It 3072 = 3 * 2^10 Ta 1690314
-.It 4096 = 2 * 2^11 Ta  240904
-.It 6144 = 3 * 2^11 Ta  929484
-.It 8192 = 2 * 2^12 Ta 4743158
-.El
-.Pp
-For each of these prime numbers, the finite group of natural numbers
-smaller than
-.Fa p ,
-where the group operation is defined as multiplication modulo
-.Fa p ,
-is used for Diffie-Hellmann key exchange.
-The first two of these groups are called the First Oakley Group and
-the Second Oakley Group.
-Obiviously, all these groups are cyclic groups of order
-.Fa p ,
-respectively, and the numbers returned by these functions are not
-secrets.
-.Sh RETURN VALUES
-If memory allocation fails, these functions return
-.Dv NULL .
-That can happen even if
-.Fa bn
-is not
-.Dv NULL .
-.Sh SEE ALSO
-.Xr BN_mod_exp 3 ,
-.Xr BN_new 3 ,
-.Xr BN_set_flags 3 ,
-.Xr DH_new 3
-.Sh STANDARDS
-RFC 2409, "The Internet Key Exchange (IKE)", defines the Oakley Groups.
-.Pp
-RFC 2412, "The OAKLEY Key Determination Protocol", contains additional
-information about these numbers.
-.Pp
-RFC 3526, "More Modular Exponential (MODP) Diffie-Hellman groups
-for Internet Key Exchange (IKE)", defines the other six numbers.
-.Sh HISTORY
-.Fn get_rfc2409_prime_768 ,
-.Fn get_rfc2409_prime_1024 ,
-.Fn get_rfc3526_prime_1536 ,
-.Fn get_rfc3526_prime_2048 ,
-.Fn get_rfc3526_prime_3072 ,
-.Fn get_rfc3526_prime_4096 ,
-.Fn get_rfc3526_prime_6144 ,
-and
-.Fn get_rfc3526_prime_8192
-first appeared in OpenSSL 0.9.8a and have been available since
-.Ox 4.5 .
-.Pp
-The
-.Sy BN_
-aliases first appeared in OpenSSL 1.1.0 and have been available since
-.Ox 6.3 .
-.Sh CAVEATS
-As all the memory needed for storing the numbers is dynamically
-allocated, the
-.Dv BN_FLG_STATIC_DATA
-flag is not set on the returned
-.Vt BIGNUM
-objects.
-So be careful to not change the returned numbers.