264 lines
8.9 KiB
C
264 lines
8.9 KiB
C
/**
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* \file ecp.h
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*
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* \brief Elliptic curves over GF(p)
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*
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* Copyright (C) 2012, Brainspark B.V.
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*
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* This file is part of PolarSSL (http://www.polarssl.org)
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* Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org>
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*
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* All rights reserved.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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*/
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#ifndef POLARSSL_ECP_H
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#define POLARSSL_ECP_H
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#include "bignum.h"
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/*
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* ECP error codes
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*
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* (The functions written up to now return MPI error codes only.)
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*/
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/**
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* \brief ECP point structure (affine coordinates)
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*
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* Note: if the point is zero, X and Y are irrelevant and should be freed.
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*/
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typedef struct
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{
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char is_zero; /*!< true if point at infinity */
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mpi X; /*!< the point's X coordinate */
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mpi Y; /*!< the point's Y coordinate */
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}
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ecp_point;
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/**
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* \brief ECP group structure
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*
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* The curves we consider are defined by y^2 = x^3 - 3x + b mod p,
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* and a generator for a large subgroup is fixed.
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*/
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typedef struct
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{
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mpi P; /*!< prime modulus of the base field */
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mpi B; /*!< constant term in the equation */
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ecp_point G; /*!< generator of the subgroup used */
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mpi N; /*!< the order of G */
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}
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ecp_group;
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/**
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* RFC 5114 defines a number of standardized ECP groups for use with TLS.
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*
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* These also are the NIST-recommended ECP groups, are the random ECP groups
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* recommended by SECG, and include the two groups used by NSA Suite B.
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* There are known as secpLLLr1 with LLL = 192, 224, 256, 384, 521.
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*
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* \warning This library does not support validation of arbitrary domain
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* parameters. Therefore, only well-known domain parameters from trusted
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* sources (such as the ones below) should be used.
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*/
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#define POLARSSL_ECP_SECP192R1_P \
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"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"
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#define POLARSSL_ECP_SECP192R1_B \
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"64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1"
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#define POLARSSL_ECP_SECP192R1_GX \
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"188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012"
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#define POLARSSL_ECP_SECP192R1_GY \
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"07192B95FFC8DA78631011ED6B24CDD573F977A11E794811"
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#define POLARSSL_ECP_SECP192R1_N \
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"FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831"
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#define POLARSSL_ECP_SECP224R1_P \
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"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001"
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#define POLARSSL_ECP_SECP224R1_B \
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"B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4"
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#define POLARSSL_ECP_SECP224R1_GX \
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"B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21"
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#define POLARSSL_ECP_SECP224R1_GY \
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"BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34"
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#define POLARSSL_ECP_SECP224R1_N \
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"FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D"
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#define POLARSSL_ECP_SECP256R1_P \
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"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"
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#define POLARSSL_ECP_SECP256R1_B \
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"5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B"
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#define POLARSSL_ECP_SECP256R1_GX \
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"6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"
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#define POLARSSL_ECP_SECP256R1_GY \
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"4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5"
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#define POLARSSL_ECP_SECP256R1_N \
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"FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551"
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#define POLARSSL_ECP_SECP384R1_P \
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"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
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"FFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF"
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#define POLARSSL_ECP_SECP384R1_B \
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"B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE814112" \
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"0314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF"
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#define POLARSSL_ECP_SECP384R1_GX \
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"AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B98" \
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"59F741E082542A385502F25DBF55296C3A545E3872760AB7"
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#define POLARSSL_ECP_SECP384R1_GY \
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"3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147C" \
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"E9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F"
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#define POLARSSL_ECP_SECP384R1_N \
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"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
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"C7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973"
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#define POLARSSL_ECP_SECP521R1_P \
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"000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
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"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
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"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
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#define POLARSSL_ECP_SECP521R1_B \
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"00000051953EB9618E1C9A1F929A21A0B68540EEA2DA725B" \
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"99B315F3B8B489918EF109E156193951EC7E937B1652C0BD" \
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"3BB1BF073573DF883D2C34F1EF451FD46B503F00"
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#define POLARSSL_ECP_SECP521R1_GX \
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"000000C6858E06B70404E9CD9E3ECB662395B4429C648139" \
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"053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127" \
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"A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66"
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#define POLARSSL_ECP_SECP521R1_GY \
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"0000011839296A789A3BC0045C8A5FB42C7D1BD998F54449" \
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"579B446817AFBD17273E662C97EE72995EF42640C550B901" \
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"3FAD0761353C7086A272C24088BE94769FD16650"
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#define POLARSSL_ECP_SECP521R1_N \
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"000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
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"FFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148" \
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"F709A5D03BB5C9B8899C47AEBB6FB71E91386409"
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#ifdef __cplusplus
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extern "C" {
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#endif
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/**
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* \brief Initialize a point (as zero)
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*/
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void ecp_point_init( ecp_point *pt );
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/**
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* \brief Initialize a group (to something meaningless)
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*/
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void ecp_group_init( ecp_group *grp );
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/**
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* \brief Free the components of a point
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*/
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void ecp_point_free( ecp_point *pt );
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/**
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* \brief Free the components of an ECP group
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*/
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void ecp_group_free( ecp_group *grp );
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/**
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* \brief Set a point to zero
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*/
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void ecp_set_zero( ecp_point *pt );
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/**
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* \brief Copy the contents of point Q into P
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*
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* \param P Destination point
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* \param Q Source point
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*
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* \return 0 if successful,
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* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
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*/
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int ecp_copy( ecp_point *P, const ecp_point *Q );
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/**
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* \brief Import a non-zero point from two ASCII strings
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*
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* \param P Destination point
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* \param radix Input numeric base
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* \param x First affine coordinate as a null-terminated string
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* \param y Second affine coordinate as a null-terminated string
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*
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* \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code
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*/
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int ecp_point_read_string( ecp_point *P, int radix,
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const char *x, const char *y );
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/**
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* \brief Import an ECP group from null-terminated ASCII strings
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*
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* \param grp Destination group
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* \param radix Input numeric base
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* \param p Prime modulus of the base field
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* \param b Constant term in the equation
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* \param gx The generator's X coordinate
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* \param gy The generator's Y coordinate
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* \param n The generator's order
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*
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* \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code
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*/
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int ecp_group_read_string( ecp_group *grp, int radix,
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const char *p, const char *b,
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const char *gx, const char *gy, const char *n);
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/**
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* \brief Addition: R = P + Q
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*
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* \param grp ECP group
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* \param R Destination point
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* \param P Left-hand point
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* \param Q Right-hand point
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*
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* \return 0 if successful,
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* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
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* POLARSSL_ERR_MPI_DIVISION_BY_ZERO (shouldn't happen)
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* (temporary, a faster version not using division will be
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* used in the future)
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*/
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int ecp_add( const ecp_group *grp, ecp_point *R,
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const ecp_point *P, const ecp_point *Q );
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/**
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* \brief Multiplication by an integer: R = m * P
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*
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* \param grp ECP group
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* \param R Destination point
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* \param m Integer by which to multiply
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* \param P Point to multiply
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*
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* \return 0 if successful,
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* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
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* POLARSSL_ERR_MPI_DIVISION_BY_ZERO (shouldn't happen)
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* (temporary, a faster version not using division will be
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* used in the future)
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*/
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int ecp_mul( const ecp_group *grp, ecp_point *R,
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const mpi *m, const ecp_point *P );
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/**
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* \brief Checkup routine
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*
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* \return 0 if successful, or 1 if the test failed
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*/
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int ecp_self_test( int verbose );
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#ifdef __cplusplus
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}
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#endif
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#endif
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