include/polarssl/ecp.h - security/mbedtls - Rivoreo Source Code Repositories

 /**
  * \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 <polarssl_maintainer at polarssl.org>
  *
  *  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 (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_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

 #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           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
  */
 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 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
  */
 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 successul,
  *                  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           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,
  */
 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
	/**
	* \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 <polarssl_maintainer at polarssl.org>
	*
	* 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 (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_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

	#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 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
	*/
	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 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
	*/
	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 successul,
	* 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 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,
	*/
	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