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/**
* \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 "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_FEATURE_UNAVAILABLE -0x4E80 /**< Requested curve not available. */
#define POLARSSL_ERR_ECP_VERIFY_FAILED -0x4E00 /**< The signature is not valid. */
#define POLARSSL_ERR_ECP_MALLOC_FAILED -0x4D80 /**< Memory allocation failed. */
#define POLARSSL_ERR_ECP_RANDOM_FAILED -0x4D00 /**< Generation of random value, such as (ephemeral) key, failed. */
#define POLARSSL_ERR_ECP_INVALID_KEY -0x4C80 /**< Invalid private or public key. */
#define POLARSSL_ERR_ECP_SIG_LEN_MISMATCH -0x4C00 /**< Signature is valid but shorter than the user-supplied length. */
#ifdef __cplusplus
extern "C" {
#endif
/**
* Domain parameters (curve, subgroup and generator) identifiers.
*
* Only curves over prime fields are supported.
*
* \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().
*/
typedef enum
{
POLARSSL_ECP_DP_NONE = 0,
POLARSSL_ECP_DP_SECP192R1, /*!< 192-bits NIST curve */
POLARSSL_ECP_DP_SECP224R1, /*!< 224-bits NIST curve */
POLARSSL_ECP_DP_SECP256R1, /*!< 256-bits NIST curve */
POLARSSL_ECP_DP_SECP384R1, /*!< 384-bits NIST curve */
POLARSSL_ECP_DP_SECP521R1, /*!< 521-bits NIST curve */
POLARSSL_ECP_DP_BP256R1, /*!< 256-bits Brainpool curve */
POLARSSL_ECP_DP_BP384R1, /*!< 384-bits Brainpool curve */
POLARSSL_ECP_DP_BP512R1, /*!< 512-bits Brainpool curve */
POLARSSL_ECP_DP_M221, /*!< (not implemented yet) */
POLARSSL_ECP_DP_M255, /*!< Curve25519 */
POLARSSL_ECP_DP_M383, /*!< (not implemented yet) */
POLARSSL_ECP_DP_M511, /*!< (not implemented yet) */
POLARSSL_ECP_DP_SECP192K1, /*!< 192-bits "Koblitz" curve */
POLARSSL_ECP_DP_SECP224K1, /*!< 224-bits "Koblitz" curve */
POLARSSL_ECP_DP_SECP256K1, /*!< 256-bits "Koblitz" curve */
} ecp_group_id;
/**
* Number of supported curves (plus one for NONE).
*
* (Montgomery curves excluded for now.)
*/
#define POLARSSL_ECP_DP_MAX 12
/**
* Curve information for use by other modules
*/
typedef struct
{
ecp_group_id grp_id; /*!< Internal identifier */
uint16_t tls_id; /*!< TLS NamedCurve identifier */
uint16_t size; /*!< Curve size in bits */
const char *name; /*!< Human-friendly name */
} ecp_curve_info;
/**
* \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
*
* We consider two types of curves equations:
* 1. Short Weierstrass y^2 = x^3 + A x + B mod P (SEC1 + RFC 4492)
* 2. Montgomery, y^2 = x^3 + A x^2 + x mod P (M255 + draft)
* In both cases, a generator G for a prime-order subgroup is fixed. In the
* short weierstrass, this subgroup is actually the whole curve, and its
* cardinal is denoted by N.
*
* In the case of Short Weierstrass curves, our code requires that N is an odd
* prime. (Use odd in ecp_mul() and prime in ecdsa_sign() for blinding.)
*
* In the case of Montgomery curves, we don't store A but (A + 2) / 4 which is
* the quantity actually used in the formulas. Also, nbits is not the size of N
* but the required size for private keys.
*
* 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)-1 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-1
* range by a few additions or substractions. It must return 0 on success and
* non-zero on failure.
*/
typedef struct
{
ecp_group_id id; /*!< internal group identifier */
mpi P; /*!< prime modulus of the base field */
mpi A; /*!< 1. A in the equation, or 2. (A + 2) / 4 */
mpi B; /*!< 1. B in the equation, or 2. unused */
ecp_point G; /*!< generator of the (sub)group used */
mpi N; /*!< 1. the order of G, or 2. unused */
size_t pbits; /*!< number of bits in P */
size_t nbits; /*!< number of bits in 1. P, or 2. private keys */
unsigned int h; /*!< internal: 1 if the constants are static */
int (*modp)(mpi *); /*!< function for fast reduction mod P */
int (*t_pre)(ecp_point *, void *); /*!< unused */
int (*t_post)(ecp_point *, void *); /*!< unused */
void *t_data; /*!< unused */
ecp_point *T; /*!< pre-computed points for ecp_mul_comb() */
size_t T_size; /*!< number for pre-computed points */
}
ecp_group;
/**
* \brief ECP key pair structure
*
* A generic key pair that could be used for ECDSA, fixed ECDH, etc.
*
* \note Members purposefully in the same order as struc ecdsa_context.
*/
typedef struct
{
ecp_group grp; /*!< Elliptic curve and base point */
mpi d; /*!< our secret value */
ecp_point Q; /*!< our public value */
}
ecp_keypair;
/**
* \name SECTION: Module settings
*
* The configuration options you can set for this module are in this section.
* Either change them in config.h or define them on the compiler command line.
* \{
*/
#if !defined(POLARSSL_ECP_MAX_BITS)
/**
* Maximum size of the groups (that is, of N and P)
*/
#define POLARSSL_ECP_MAX_BITS 521 /**< Maximum bit size of groups */
#endif
#define POLARSSL_ECP_MAX_BYTES ( ( POLARSSL_ECP_MAX_BITS + 7 ) / 8 )
#define POLARSSL_ECP_MAX_PT_LEN ( 2 * POLARSSL_ECP_MAX_BYTES + 1 )
#if !defined(POLARSSL_ECP_WINDOW_SIZE)
/*
* Maximum "window" size used for point multiplication.
* Default: 6.
* Minimum value: 2. Maximum value: 7.
*
* Result is an array of at most ( 1 << ( POLARSSL_ECP_WINDOW_SIZE - 1 ) )
* points used for point multiplication. This value is directly tied to EC
* peak memory usage, so decreasing it by one should roughly cut memory usage
* by two (if large curves are in use).
*
* Reduction in size may reduce speed, but larger curves are impacted first.
* Sample performances (in ECDHE handshakes/s, with FIXED_POINT_OPTIM = 1):
* w-size: 6 5 4 3 2
* 521 145 141 135 120 97
* 384 214 209 198 177 146
* 256 320 320 303 262 226
* 224 475 475 453 398 342
* 192 640 640 633 587 476
*/
#define POLARSSL_ECP_WINDOW_SIZE 6 /**< Maximum window size used */
#endif
#if !defined(POLARSSL_ECP_FIXED_POINT_OPTIM)
/*
* Trade memory for speed on fixed-point multiplication.
*
* This speeds up repeated multiplication of the generator (that is, the
* multiplication in ECDSA signatures, and half of the multiplications in
* ECDSA verification and ECDHE) by a factor roughly 3 to 4.
*
* The cost is increasing EC peak memory usage by a factor roughly 2.
*
* Change this value to 0 to reduce peak memory usage.
*/
#define POLARSSL_ECP_FIXED_POINT_OPTIM 1 /**< Enable fixed-point speed-up */
#endif
/* \} name SECTION: Module settings */
/*
* 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 */
/**
* \brief Get the list of supported curves in order of preferrence
* (full information)
*
* \return A statically allocated array, the last entry is 0.
*/
const ecp_curve_info *ecp_curve_list( void );
/**
* \brief Get the list of supported curves in order of preferrence
* (grp_id only)
*
* \return A statically allocated array,
* terminated with POLARSSL_ECP_DP_NONE.
*/
const ecp_group_id *ecp_grp_id_list( void );
/**
* \brief Get curve information from an internal group identifier
*
* \param grp_id A POLARSSL_ECP_DP_XXX value
*
* \return The associated curve information or NULL
*/
const ecp_curve_info *ecp_curve_info_from_grp_id( ecp_group_id grp_id );
/**
* \brief Get curve information from a TLS NamedCurve value
*
* \param tls_id A POLARSSL_ECP_DP_XXX value
*
* \return The associated curve information or NULL
*/
const ecp_curve_info *ecp_curve_info_from_tls_id( uint16_t tls_id );
/**
* \brief Get curve information from a human-readable name
*
* \param name The name
*
* \return The associated curve information or NULL
*/
const ecp_curve_info *ecp_curve_info_from_name( const char *name );
/**
* \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 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 Copy the contents of a group object
*
* \param dst Destination group
* \param src Source group
*
* \return 0 if successful,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*/
int ecp_group_copy( ecp_group *dst, const ecp_group *src );
/**
* \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 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 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_BAD_INPUT_DATA if input is invalid,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,
* POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE if the point format
* is not implemented.
*
* \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 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 olen length of data written
* \param buf Buffer to write to
* \param blen 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 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_FEATURE_UNAVAILABLE for unkownn groups
*
* \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 index );
/**
* \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 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
*
* \note This function does not support Montgomery curves, such as
* Curve25519.
*/
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
*
* \note This function does not support Montgomery curves, such as
* Curve25519.
*/
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
* (Not thread-safe to use same group in multiple threads)
*
* \param grp ECP group
* \param R Destination point
* \param m Integer by which to multiply
* \param P Point to multiply
* \param f_rng RNG function (see notes)
* \param p_rng RNG parameter
*
* \return 0 if successful,
* POLARSSL_ERR_ECP_INVALID_KEY if m is not a valid privkey
* or P is not a valid pubkey,
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
*
* \note In order to prevent timing attacks, this function
* executes the exact same sequence of (base field)
* operations for any valid m. It avoids any if-branch or
* array index depending on the value of m.
*
* \note If f_rng is not NULL, it is used to randomize intermediate
* results in order to prevent potential timing attacks
* targeting these results. It is recommended to always
* provide a non-NULL f_rng (the overhead is negligible).
*/
int ecp_mul( ecp_group *grp, ecp_point *R,
const mpi *m, const ecp_point *P,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
/**
* \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_INVALID_KEY 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_INVALID_KEY 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_privkey( 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( ecp_group *grp, mpi *d, ecp_point *Q,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng );
/**
* \brief Generate a keypair
*
* \param grp_id ECP group identifier
* \param key Destination keypair
* \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
*/
int ecp_gen_key( ecp_group_id grp_id, ecp_keypair *key,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
#if defined(POLARSSL_SELF_TEST)
/**
* \brief Checkup routine
*
* \return 0 if successful, or 1 if a test failed
*/
int ecp_self_test( int verbose );
#endif
#ifdef __cplusplus
}
#endif
#endif /* ecp.h */
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