1.\" $OpenBSD: EC_GFp_simple_method.3,v 1.10 2022/07/02 17:09:09 jsing Exp $ 2.\" OpenSSL b97fdb57 Nov 11 09:33:09 2016 +0100 3.\" 4.\" This file was written by Matt Caswell <matt@openssl.org>. 5.\" Copyright (c) 2013 The OpenSSL Project. All rights reserved. 6.\" 7.\" Redistribution and use in source and binary forms, with or without 8.\" modification, are permitted provided that the following conditions 9.\" are met: 10.\" 11.\" 1. Redistributions of source code must retain the above copyright 12.\" notice, this list of conditions and the following disclaimer. 13.\" 14.\" 2. Redistributions in binary form must reproduce the above copyright 15.\" notice, this list of conditions and the following disclaimer in 16.\" the documentation and/or other materials provided with the 17.\" distribution. 18.\" 19.\" 3. 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Redistributions of any form whatsoever must retain the following 34.\" acknowledgment: 35.\" "This product includes software developed by the OpenSSL Project 36.\" for use in the OpenSSL Toolkit (http://www.openssl.org/)" 37.\" 38.\" THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 39.\" EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 40.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 41.\" PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 42.\" ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 43.\" SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 44.\" NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 45.\" LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 46.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 47.\" STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 48.\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 49.\" OF THE POSSIBILITY OF SUCH DAMAGE. 50.\" 51.Dd $Mdocdate: July 2 2022 $ 52.Dt EC_GFP_SIMPLE_METHOD 3 53.Os 54.Sh NAME 55.Nm EC_GFp_simple_method , 56.Nm EC_GFp_mont_method , 57.Nm EC_GFp_nist_method , 58.Nm EC_GFp_nistp224_method , 59.Nm EC_GFp_nistp256_method , 60.Nm EC_GFp_nistp521_method , 61.Nm EC_GF2m_simple_method , 62.Nm EC_METHOD_get_field_type 63.Nd obtain EC_METHOD objects 64.Sh SYNOPSIS 65.In openssl/ec.h 66.Ft const EC_METHOD * 67.Fn EC_GFp_simple_method void 68.Ft const EC_METHOD * 69.Fn EC_GFp_mont_method void 70.Ft const EC_METHOD * 71.Fn EC_GFp_nist_method void 72.Ft const EC_METHOD * 73.Fn EC_GFp_nistp224_method void 74.Ft const EC_METHOD * 75.Fn EC_GFp_nistp256_method void 76.Ft const EC_METHOD * 77.Fn EC_GFp_nistp521_method void 78.Ft const EC_METHOD * 79.Fn EC_GF2m_simple_method void 80.Ft int 81.Fo EC_METHOD_get_field_type 82.Fa "const EC_METHOD *meth" 83.Fc 84.Sh DESCRIPTION 85The elliptic curve library provides a number of different 86implementations through a single common interface. 87Each implementation is optimised for different scenarios. 88An implementation is represented by an 89.Vt EC_METHOD 90structure. 91.Pp 92When constructing a curve using 93.Xr EC_GROUP_new 3 , 94an implementation method must be provided. 95The functions described here all return a const pointer to an 96.Sy EC_METHOD 97structure that can be passed to 98.Xr EC_GROUP_new 3 . 99It is important that the correct implementation type for the form 100of curve selected is used. 101.Pp 102For F2^m curves there is only one implementation choice, 103.Fn EC_GF2_simple_method . 104.Pp 105For Fp curves the lowest common denominator implementation is the 106.Fn EC_GFp_simple_method 107implementation. 108All other implementations are based on this one. 109.Fn EC_GFp_mont_method 110adds the use of Montgomery multiplication (see 111.Xr BN_mod_mul_montgomery 3 ) . 112.Fn EC_GFp_nist_method 113offers an implementation optimised for use with NIST recommended 114curves. 115NIST curves are available through 116.Xr EC_GROUP_new_by_curve_name 3 . 117.Pp 118The functions 119.Fn EC_GFp_nistp224_method , 120.Fn EC_GFp_nistp256_method , 121and 122.Fn EC_GFp_nistp521_method 123offer 64-bit optimised implementations for the NIST P224, P256 and 124P521 curves respectively. 125Note, however, that these implementations are not available on all 126platforms. 127.Pp 128.Fn EC_METHOD_get_field_type 129identifies what type of field the 130.Vt EC_METHOD 131structure supports, which will be either F2^m or Fp. 132If the field type is Fp, then the value 133.Dv NID_X9_62_prime_field 134is returned. 135If the field type is F2^m, then the value 136.Dv NID_X9_62_characteristic_two_field 137is returned. 138These values are defined in the 139.In openssl/objects.h 140header file. 141.Sh RETURN VALUES 142All 143.Fn EC_GFp* 144functions and 145.Fn EC_GF2m_simple_method 146always return a const pointer to an 147.Vt EC_METHOD 148structure. 149.Pp 150.Fn EC_METHOD_get_field_type 151returns an integer that identifies the type of field the 152.Vt EC_METHOD 153structure supports. 154.Sh SEE ALSO 155.Xr BN_mod_mul_montgomery 3 , 156.Xr d2i_ECPKParameters 3 , 157.Xr EC_GROUP_copy 3 , 158.Xr EC_GROUP_new 3 , 159.Xr EC_KEY_new 3 , 160.Xr EC_POINT_add 3 , 161.Xr EC_POINT_new 3 162.Sh HISTORY 163.Fn EC_GFp_simple_method 164and 165.Fn EC_GFp_mont_method 166first appeared in OpenSSL 0.9.7 and have been available since 167.Ox 3.2 . 168.Pp 169.Fn EC_GFp_nist_method , 170.Fn EC_GF2m_simple_method , 171and 172.Fn EC_METHOD_get_field_type 173first appeared in OpenSSL 0.9.8 and have been available since 174.Ox 4.5 . 175.Pp 176.Fn EC_GFp_nistp224_method , 177.Fn EC_GFp_nistp256_method , 178and 179.Fn EC_GFp_nistp521_method 180first appeared in OpenSSL 1.0.1 and have been available since 181.Ox 5.3 . 182