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