/** * \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 * * (Only one error code available...) */ #define POLARSSL_ERR_ECP_GENERIC -0x007E /**< Generic ECP error */ /** * \brief ECP point structure (jacobian coordinates) * * \note All functions expect and return points satisfying * the following condition: Z == 0 or Z == 1. (Other * values of Z are used by internal functions only.) * The point is zero, or "at infinity", if Z == 0. * Otherwise, X and Y are its standard (affine) coordinates. */ typedef struct { mpi X; /*!< the point's X coordinate */ mpi Y; /*!< the point's Y coordinate */ mpi Z; /*!< the point's Z 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 of order N is fixed. * * pbits and nbits must be the size of P and N in bits. * * If modp is NULL, reduction modulo P is done using a generic * algorithm. Otherwise, it must point to a function that takes an mpi * in the range 0..2^(2*pbits) and transforms it in-place in an integer * of little more than pbits, so that the integer may be efficiently * brought in the 0..P range by a few additions or substractions. It * must return 0 on success and a POLARSSL_ERR_ECP_XXX error on failure. */ 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 */ size_t pbits; /*!< number of bits in P */ size_t nbits; /*!< number of bits in N */ int (*modp)(mpi *); /*!< function for fast reduction mod P */ } 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 should be used. See ecp_use_known_dp(). */ #define POLARSSL_ECP_DP_SECP192R1 0 #define POLARSSL_ECP_DP_SECP224R1 1 #define POLARSSL_ECP_DP_SECP256R1 2 #define POLARSSL_ECP_DP_SECP384R1 3 #define POLARSSL_ECP_DP_SECP521R1 4 /** * Maximum bit size of the groups (that is, of N) */ #define POLARSSL_ECP_MAX_N_BITS 521 /* * Maximum window size (actually, NAF width) used for point multipliation. * Default: 7. * Minimum value: 2. Maximum value: 8. * * Result is an array of at most ( 1 << ( POLARSSL_ECP_WINDOW_SIZE - 1 ) ) * points used for point multiplication, so at most 64 by default. * In practice, most curves will use less precomputed points. * * Reduction in size may reduce speed for big curves. */ #define POLARSSL_ECP_WINDOW_SIZE 7 /**< Maximum NAF width used. */ #ifdef __cplusplus extern "C" { #endif /** * \brief Initialize a point (as zero) */ void ecp_point_init( ecp_point *pt ); /** * \brief Initialize a group (to something meaningless) */ void ecp_group_init( ecp_group *grp ); /** * \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 * * \return 0 if successful, * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed */ int 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 Check that a point is a valid public key on this curve * * \param grp Curve/group the point should belong to * \param pt Point to check * * \return 0 if point is a valid public key, * POLARSSL_ERR_ECP_GENERIC otherwise. * * \note This function only checks the point is non-zero, has valid * coordinates and lies on the curve, but not that it is * indeed a multiple of G. This is additional check is more * expensive, isn't required by standards, and shouldn't be * necessary if the group used has a small cofactor. In * particular, it is useless for the NIST groups which all * have a cofactor of 1. */ int ecp_check_pubkey( const ecp_group *grp, const ecp_point *pt ); /** * \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 numeric 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 * * \note Sets all fields except modp. */ 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 Set a group using well-known domain parameters * * \param grp Destination group * \param index Index in the list of well-known domain parameters * * \return O if successful, * POLARSSL_ERR_MPI_XXX if initialization failed * POLARSSL_ERR_ECP_GENERIC if index is out of range * * \note Index should be a POLARSSL_ECP_DP_XXX macro. */ int ecp_use_known_dp( ecp_group *grp, size_t index ); /** * \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 */ int ecp_add( const ecp_group *grp, ecp_point *R, const ecp_point *P, const ecp_point *Q ); /** * \brief Subtraction: 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 */ int ecp_sub( 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_ECP_GENERIC if m < 0 of m has greater bit * length than N, the number of points in the group. * * \note This function executes a constant number of operations * for random m in the allowed range. */ 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