/**
* \file ecp.h
*
* \brief Elliptic curves over GF(p)
*
* Copyright (C) 2006-2013, 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 "polarssl/bignum.h"
/*
* ECP error codes
*/
#define POLARSSL_ERR_ECP_BAD_INPUT_DATA -0x4F80 /**< Bad input parameters to function. */
#define POLARSSL_ERR_ECP_BUFFER_TOO_SMALL -0x4F00 /**< The buffer is too small to write to. */
#define POLARSSL_ERR_ECP_GENERIC -0x4E80 /**< Generic ECP error */
#define POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE -0x4E00 /**< Requested curve not available. */
#ifdef __cplusplus
extern "C" {
#endif
/**
* \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;
/*
* RFC 4492 defines an enum NamedCurve with two-bytes values
*/
typedef uint16_t ecp_group_id;
/**
* \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
{
ecp_group_id id; /*!< RFC 4492 group ID */
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;
/**
* \brief ECP key pair structure
*
* A generic key pair that could be used for ECDSA, fixed ECDH, etc.
* Usage can be restricted to a particular algorithm by the 'alg' field,
* see POLARSSL_ECP_KEY_ALG_* constants (default: unrestricted).
*
* \sa ecdh_context
* \sa ecdsa_context
*/
typedef struct
{
ecp_group grp; /*!< Elliptic curve and base point */
mpi d; /*!< our secret value */
ecp_point Q; /*!< our public value */
int alg; /*!< algorithm to use this key with */
}
ecp_keypair;
/**
* 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().
*
* \note The values are taken from RFC 4492's enum NamedCurve.
*/
#define POLARSSL_ECP_DP_SECP192R1 19
#define POLARSSL_ECP_DP_SECP224R1 21
#define POLARSSL_ECP_DP_SECP256R1 23
#define POLARSSL_ECP_DP_SECP384R1 24
#define POLARSSL_ECP_DP_SECP521R1 25
/**
* 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. */
/*
* Point formats, from RFC 4492's enum ECPointFormat
*/
#define POLARSSL_ECP_PF_UNCOMPRESSED 0 /**< Uncompressed point format */
#define POLARSSL_ECP_PF_COMPRESSED 1 /**< Compressed point format */
/*
* Some other constants from RFC 4492
*/
#define POLARSSL_ECP_TLS_NAMED_CURVE 3 /**< ECCurveType's named_curve */
/*
* Algorithm identifiers from RFC 5480 for use with EC keys
*/
#define POLARSSL_ECP_KEY_ALG_UNRESTRICTED 0 /**< RFC 5480 2.1.1 */
#define POLARSSL_ECP_KEY_ALG_ECDH 1 /**< RFC 5480 2.1.2 */
#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 Initialize a key pair (as an invalid one)
*/
void ecp_keypair_init( ecp_keypair *key );
/**
* \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 Free the components of a key pair
*/
void ecp_keypair_free( ecp_keypair *key );
/**
* \brief Set a point to zero
*
* \param pt Destination point
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*/
int ecp_set_zero( ecp_point *pt );
/**
* \brief Tell if a point is zero
*
* \param pt Point to test
*
* \return 1 if point is zero, 0 otherwise
*/
int ecp_is_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
*
* \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 Export a point into unsigned binary data
*
* \param grp Group to which the point should belong
* \param P Point to export
* \param format Point format, should be a POLARSSL_ECP_PF_XXX macro
* \param olen Length of the actual output
* \param buf Output buffer
* \param buflen Length of the output buffer
*
* \return 0 if successful,
* or POLARSSL_ERR_ECP_BAD_INPUT_DATA
* or POLARSSL_ERR_ECP_BUFFER_TOO_SMALL
*/
int ecp_point_write_binary( const ecp_group *grp, const ecp_point *P,
int format, size_t *olen,
unsigned char *buf, size_t buflen );
/**
* \brief Import a point from unsigned binary data
*
* \param grp Group to which the point should belong
* \param P Point to import
* \param buf Input buffer
* \param ilen Actual length of input
*
* \return 0 if successful,
* POLARSSL_ERR_ECP_GENERIC if input is invalid
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*
* \note This function does NOT check that the point actually
* belongs to the given group, see ecp_check_pubkey() for
* that.
*/
int ecp_point_read_binary( const ecp_group *grp, ecp_point *P,
const unsigned char *buf, size_t ilen );
/**
* \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 value of RFC 4492's enum NamdeCurve,
* possibly in the form of a POLARSSL_ECP_DP_XXX macro.
*/
int ecp_use_known_dp( ecp_group *grp, ecp_group_id id );
/**
* \brief Set a group from a TLS ECParameters record
*
* \param grp Destination group
* \param buf &(Start of input buffer)
* \param len Buffer length
*
* \return O if successful,
* POLARSSL_ERR_MPI_XXX if initialization failed
* POLARSSL_ERR_ECP_BAD_INPUT_DATA if input is invalid
*/
int ecp_tls_read_group( ecp_group *grp, const unsigned char **buf, size_t len );
/**
* \brief Write the TLS ECParameters record for a group
*
* \param grp ECP group used
* \param olen Number of bytes actually written
* \param buf Buffer to write to
* \param blen Buffer length
*
* \return 0 if successful,
* or POLARSSL_ERR_ECP_BUFFER_TOO_SMALL
*/
int ecp_tls_write_group( const ecp_group *grp, size_t *olen,
unsigned char *buf, size_t blen );
/**
* \brief Import a point from a TLS ECPoint record
*
* \param grp ECP group used
* \param pt Destination point
* \param buf $(Start of input buffer)
* \param len Buffer length
*
* \return O if successful,
* POLARSSL_ERR_MPI_XXX if initialization failed
* POLARSSL_ERR_ECP_BAD_INPUT_DATA if input is invalid
*/
int ecp_tls_read_point( const ecp_group *grp, ecp_point *pt,
const unsigned char **buf, size_t len );
/**
* \brief Export a point as a TLS ECPoint record
*
* \param grp ECP group used
* \param pt Point to export
* \param format Export format
* \param buf Buffer to write to
* \param len Buffer length
*
* \return 0 if successful,
* or POLARSSL_ERR_ECP_BAD_INPUT_DATA
* or POLARSSL_ERR_ECP_BUFFER_TOO_SMALL
*/
int ecp_tls_write_point( const ecp_group *grp, const ecp_point *pt,
int format, size_t *olen,
unsigned char *buf, size_t blen );
/**
* \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 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.
*
* \note Uses bare components rather than an ecp_keypair structure
* in order to ease use with other structures such as
* ecdh_context of ecdsa_context.
*/
int ecp_check_pubkey( const ecp_group *grp, const ecp_point *pt );
/**
* \brief Check that an mpi is a valid private key for this curve
*
* \param grp Group used
* \param d Integer to check
*
* \return 0 if point is a valid private key,
* POLARSSL_ERR_ECP_GENERIC otherwise.
*
* \note Uses bare components rather than an ecp_keypair structure
* in order to ease use with other structures such as
* ecdh_context of ecdsa_context.
*/
int ecp_check_prvkey( const ecp_group *grp, const mpi *d );
/**
* \brief Generate a keypair
*
* \param grp ECP group
* \param d Destination MPI (secret part)
* \param Q Destination point (public part)
* \param f_rng RNG function
* \param p_rng RNG parameter
*
* \return 0 if successful,
* or a POLARSSL_ERR_ECP_XXX or POLARSSL_MPI_XXX error code
*
* \note Uses bare components rather than an ecp_keypair structure
* in order to ease use with other structures such as
* ecdh_context of ecdsa_context.
*/
int ecp_gen_keypair( const ecp_group *grp, mpi *d, ecp_point *Q,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng );
/**
* \brief Checkup routine
*
* \return 0 if successful, or 1 if the test failed
*/
int ecp_self_test( int verbose );
#ifdef __cplusplus
}
#endif
#endif