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include/mbedtls/ecp.h
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@ -1,10 +1,20 @@
/** /**
* \file ecp.h * \file ecp.h
* *
* \brief Elliptic curves over GF(p) * \brief This file contains ECP definitions and functions.
*
* The Elliptic Curve over P (ECP) is defined in <em>Standards for Efficient
* Cryptography Group (SECG): SEC1 Elliptic Curve Cryptography</em> and
* <em>RFC-4492: Elliptic Curve Cryptography (ECC) Cipher Suites
* for Transport Layer Security (TLS)</em>.
*
* <em>RFC-2409: The Internet Key Exchange (IKE)</em> defines ECP
* group types.
*
*/ */
/* /*
* Copyright (C) 2006-2015, ARM Limited, All Rights Reserved * Copyright (C) 2006-2018, Arm Limited (or its affiliates), All Rights Reserved
* SPDX-License-Identifier: Apache-2.0 * SPDX-License-Identifier: Apache-2.0
* *
* Licensed under the Apache License, Version 2.0 (the "License"); you may * Licensed under the Apache License, Version 2.0 (the "License"); you may
@ -19,8 +29,9 @@
* See the License for the specific language governing permissions and * See the License for the specific language governing permissions and
* limitations under the License. * limitations under the License.
* *
* This file is part of mbed TLS (https://tls.mbed.org) * This file is part of Mbed TLS (https://tls.mbed.org)
*/ */
#ifndef MBEDTLS_ECP_H #ifndef MBEDTLS_ECP_H
#define MBEDTLS_ECP_H #define MBEDTLS_ECP_H
@ -31,13 +42,13 @@
*/ */
#define MBEDTLS_ERR_ECP_BAD_INPUT_DATA -0x4F80 /**< Bad input parameters to function. */ #define MBEDTLS_ERR_ECP_BAD_INPUT_DATA -0x4F80 /**< Bad input parameters to function. */
#define MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL -0x4F00 /**< The buffer is too small to write to. */ #define MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL -0x4F00 /**< The buffer is too small to write to. */
#define MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE -0x4E80 /**< Requested curve not available. */ #define MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE -0x4E80 /**< The requested curve not available. */
#define MBEDTLS_ERR_ECP_VERIFY_FAILED -0x4E00 /**< The signature is not valid. */ #define MBEDTLS_ERR_ECP_VERIFY_FAILED -0x4E00 /**< The signature is not valid. */
#define MBEDTLS_ERR_ECP_ALLOC_FAILED -0x4D80 /**< Memory allocation failed. */ #define MBEDTLS_ERR_ECP_ALLOC_FAILED -0x4D80 /**< Memory allocation failed. */
#define MBEDTLS_ERR_ECP_RANDOM_FAILED -0x4D00 /**< Generation of random value, such as (ephemeral) key, failed. */ #define MBEDTLS_ERR_ECP_RANDOM_FAILED -0x4D00 /**< Generation of random value, such as ephemeral key, failed. */
#define MBEDTLS_ERR_ECP_INVALID_KEY -0x4C80 /**< Invalid private or public key. */ #define MBEDTLS_ERR_ECP_INVALID_KEY -0x4C80 /**< Invalid private or public key. */
#define MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH -0x4C00 /**< The buffer contains a valid signature followed by more data. */ #define MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH -0x4C00 /**< The buffer contains a valid signature followed by more data. */
#define MBEDTLS_ERR_ECP_HW_ACCEL_FAILED -0x4B80 /**< ECP hardware accelerator failed. */ #define MBEDTLS_ERR_ECP_HW_ACCEL_FAILED -0x4B80 /**< The ECP hardware accelerator failed. */
#if !defined(MBEDTLS_ECP_ALT) #if !defined(MBEDTLS_ECP_ALT)
/* /*
@ -53,9 +64,9 @@ extern "C" {
#endif #endif
/** /**
* Domain parameters (curve, subgroup and generator) identifiers. * Definition of domain parameter identifiers: curve, subgroup and generator.
* *
* Only curves over prime fields are supported. * \note Only curves over prime fields are supported.
* *
* \warning This library does not support validation of arbitrary domain * \warning This library does not support validation of arbitrary domain
* parameters. Therefore, only well-known domain parameters from trusted * parameters. Therefore, only well-known domain parameters from trusted
@ -63,113 +74,119 @@ extern "C" {
*/ */
typedef enum typedef enum
{ {
MBEDTLS_ECP_DP_NONE = 0, MBEDTLS_ECP_DP_NONE = 0, /*!< Curve not defined. */
MBEDTLS_ECP_DP_SECP192R1, /*!< 192-bits NIST curve */ MBEDTLS_ECP_DP_SECP192R1, /*!< Domain parameters for 192-bit NIST curve. */
MBEDTLS_ECP_DP_SECP224R1, /*!< 224-bits NIST curve */ MBEDTLS_ECP_DP_SECP224R1, /*!< Domain parameters for 224-bit NIST curve. */
MBEDTLS_ECP_DP_SECP256R1, /*!< 256-bits NIST curve */ MBEDTLS_ECP_DP_SECP256R1, /*!< Domain parameters for 256-bit NIST curve. */
MBEDTLS_ECP_DP_SECP384R1, /*!< 384-bits NIST curve */ MBEDTLS_ECP_DP_SECP384R1, /*!< Domain parameters for 384-bit NIST curve. */
MBEDTLS_ECP_DP_SECP521R1, /*!< 521-bits NIST curve */ MBEDTLS_ECP_DP_SECP521R1, /*!< Domain parameters for 521-bit NIST curve. */
MBEDTLS_ECP_DP_BP256R1, /*!< 256-bits Brainpool curve */ MBEDTLS_ECP_DP_BP256R1, /*!< Domain parameters for 256-bit Brainpool curve. */
MBEDTLS_ECP_DP_BP384R1, /*!< 384-bits Brainpool curve */ MBEDTLS_ECP_DP_BP384R1, /*!< Domain parameters for 384-bit Brainpool curve. */
MBEDTLS_ECP_DP_BP512R1, /*!< 512-bits Brainpool curve */ MBEDTLS_ECP_DP_BP512R1, /*!< Domain parameters for 512-bit Brainpool curve. */
MBEDTLS_ECP_DP_CURVE25519, /*!< Curve25519 */ MBEDTLS_ECP_DP_CURVE25519, /*!< Domain parameters for a Curve25519 curve. */
MBEDTLS_ECP_DP_CURVE448, /*!< Curve448 */ MBEDTLS_ECP_DP_CURVE448, /*!< Domain parameters for a Curve448 curve. */
MBEDTLS_ECP_DP_SECP192K1, /*!< 192-bits "Koblitz" curve */ MBEDTLS_ECP_DP_SECP192K1, /*!< Domain parameters for 192-bit "Koblitz" curve. */
MBEDTLS_ECP_DP_SECP224K1, /*!< 224-bits "Koblitz" curve */ MBEDTLS_ECP_DP_SECP224K1, /*!< Domain parameters for 224-bit "Koblitz" curve. */
MBEDTLS_ECP_DP_SECP256K1, /*!< 256-bits "Koblitz" curve */ MBEDTLS_ECP_DP_SECP256K1, /*!< Domain parameters for 256-bit "Koblitz" curve. */
} mbedtls_ecp_group_id; } mbedtls_ecp_group_id;
/** /**
* Number of supported curves (plus one for NONE). * The number of supported curves, plus one for none.
* *
* (Montgomery curves excluded for now.) * \note Montgomery curves are currently excluded.
*/ */
#define MBEDTLS_ECP_DP_MAX 12 #define MBEDTLS_ECP_DP_MAX 12
/** /**
* Curve information for use by other modules * Curve information, for use by other modules.
*/ */
typedef struct typedef struct
{ {
mbedtls_ecp_group_id grp_id; /*!< Internal identifier */ mbedtls_ecp_group_id grp_id; /*!< An internal identifier. */
uint16_t tls_id; /*!< TLS NamedCurve identifier */ uint16_t tls_id; /*!< The TLS NamedCurve identifier. */
uint16_t bit_size; /*!< Curve size in bits */ uint16_t bit_size; /*!< The size of the curve in bits. */
const char *name; /*!< Human-friendly name */ const char *name; /*!< A human-friendly name. */
} mbedtls_ecp_curve_info; } mbedtls_ecp_curve_info;
/** /**
* \brief ECP point structure (jacobian coordinates) * \brief The ECP point structure, in jacobian coordinates.
* *
* \note All functions expect and return points satisfying * \note All functions expect and return points satisfying
* the following condition: Z == 0 or Z == 1. (Other * the following condition: \p Z == 0 or \p Z == 1. Other
* values of Z are used by internal functions only.) * values of \p Z are used only by internal functions.
* The point is zero, or "at infinity", if Z == 0. * The point is zero, or "at infinity", if Z == 0.
* Otherwise, X and Y are its standard (affine) coordinates. * Otherwise, X and Y are its standard (affine) coordinates.
*/ */
typedef struct typedef struct
{ {
mbedtls_mpi X; /*!< the point's X coordinate */ mbedtls_mpi X; /*!< The X coordinate of the ECP point. */
mbedtls_mpi Y; /*!< the point's Y coordinate */ mbedtls_mpi Y; /*!< The Y coordinate of the ECP point. */
mbedtls_mpi Z; /*!< the point's Z coordinate */ mbedtls_mpi Z; /*!< The Z coordinate of the ECP point. */
} }
mbedtls_ecp_point; mbedtls_ecp_point;
/** /**
* \brief ECP group structure * \brief The ECP group structure.
* *
* We consider two types of curves equations: * We consider two types of curve equations:
* 1. Short Weierstrass y^2 = x^3 + A x + B mod P (SEC1 + RFC 4492) * <ul><li>Short Weierstrass: y^2 = x^3 + \p A x + \p B mod P
* 2. Montgomery, y^2 = x^3 + A x^2 + x mod P (Curve25519 + draft) * (SEC1 + RFC-4492)</li>
* In both cases, a generator G for a prime-order subgroup is fixed. In the * <li>Montgomery: y^2 = x^3 + A x^2 + x mod P (Curve25519 + draft)</li></ul>
* short weierstrass, this subgroup is actually the whole curve, and its * In both cases, the generator (G) for a prime-order subgroup is fixed.
* cardinal is denoted by N.
* *
* In the case of Short Weierstrass curves, our code requires that N is an odd * For Short Weierstrass, this subgroup is the whole curve, and its
* prime. (Use odd in mbedtls_ecp_mul() and prime in mbedtls_ecdsa_sign() for blinding.) * cardinal is denoted by \p N. Our code requires that \p N is an odd prime.
* *
* In the case of Montgomery curves, we don't store A but (A + 2) / 4 which is * \note For blinding, use odd in mbedtls_ecp_mul() and prime in
* the quantity actually used in the formulas. Also, nbits is not the size of N * mbedtls_ecdsa_sign().
* but the required size for private keys.
* *
* If modp is NULL, reduction modulo P is done using a generic algorithm. * For Montgomery curves, we do not store \p A, but (A + 2) / 4, which is
* Otherwise, it must point to a function that takes an mbedtls_mpi in the range * the quantity used in the formulas. Additionally, \p nbits is not the
* 0..2^(2*pbits)-1 and transforms it in-place in an integer of little more * size of \p N but the required size for private keys.
* 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 * If \p modp is NULL, reduction modulo \p P is done using a generic algorithm.
* non-zero on failure. * Otherwise, it must point to a function that takes an \p mbedtls_mpi in the
* range of 0..2^(2*pbits)-1, and transforms it in-place in an integer of
* little more than \p pbits, so that the integer may be efficiently brought
* in the 0..P-1 range by a few additions or substractions.
*
* \return \c 0 on success
* \return Non-zero on failure.
*/ */
typedef struct typedef struct
{ {
mbedtls_ecp_group_id id; /*!< internal group identifier */ mbedtls_ecp_group_id id; /*!< An internal group identifier. */
mbedtls_mpi P; /*!< prime modulus of the base field */ mbedtls_mpi P; /*!< A prime modulus of the base field. */
mbedtls_mpi A; /*!< 1. A in the equation, or 2. (A + 2) / 4 */ mbedtls_mpi A; /*!< \p A in the equation or <code>(A + 2) / 4</code>. */
mbedtls_mpi B; /*!< 1. B in the equation, or 2. unused */ mbedtls_mpi B; /*!< \p B in the equation or unused. */
mbedtls_ecp_point G; /*!< generator of the (sub)group used */ mbedtls_ecp_point G; /*!< The generator of the (sub)group used. */
mbedtls_mpi N; /*!< the order of G */ mbedtls_mpi N; /*!< The order of \p G. */
size_t pbits; /*!< number of bits in P */ size_t pbits; /*!< The number of bits in \p P.*/
size_t nbits; /*!< number of bits in 1. P, or 2. private keys */ size_t nbits; /*!< The number of bits in \p P, or the private
unsigned int h; /*!< internal: 1 if the constants are static */ keys. */
int (*modp)(mbedtls_mpi *); /*!< function for fast reduction mod P */ unsigned int h; /*!< \internal 1 if the constants are static. */
int (*t_pre)(mbedtls_ecp_point *, void *); /*!< unused */ int (*modp)(mbedtls_mpi *); /*!< The function for fast reduction mod P.*/
int (*t_post)(mbedtls_ecp_point *, void *); /*!< unused */ int (*t_pre)(mbedtls_ecp_point *, void *); /*!< Unused. */
void *t_data; /*!< unused */ int (*t_post)(mbedtls_ecp_point *, void *); /*!< Unused. */
mbedtls_ecp_point *T; /*!< pre-computed points for ecp_mul_comb() */ void *t_data; /*!< Unused. */
size_t T_size; /*!< number for pre-computed points */ mbedtls_ecp_point *T; /*!< Pre-computed points for ecp_mul_comb(). */
size_t T_size; /*!< The number for pre-computed points. */
} }
mbedtls_ecp_group; mbedtls_ecp_group;
/** /**
* \brief ECP key pair structure * \brief The ECP key-pair structure.
* *
* A generic key pair that could be used for ECDSA, fixed ECDH, etc. * A generic key-pair that may be used for ECDSA and fixed ECDH, for example.
* *
* \note Members purposefully in the same order as struc mbedtls_ecdsa_context. * \note Members are deliberately in the same order as in the
* #mbedtls_ecdsa_context structure.
*/ */
typedef struct typedef struct
{ {
mbedtls_ecp_group grp; /*!< Elliptic curve and base point */ mbedtls_ecp_group grp; /*!< The elliptic curve and base point. */
mbedtls_mpi d; /*!< our secret value */ mbedtls_mpi d; /*!< Our secret value. */
mbedtls_ecp_point Q; /*!< our public value */ mbedtls_ecp_point Q; /*!< Our public value. */
} }
mbedtls_ecp_keypair; mbedtls_ecp_keypair;
@ -177,15 +194,15 @@ mbedtls_ecp_keypair;
* \name SECTION: Module settings * \name SECTION: Module settings
* *
* The configuration options you can set for this module are in this section. * 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. * Either change them in config.h, or define them using the compiler command line.
* \{ * \{
*/ */
#if !defined(MBEDTLS_ECP_MAX_BITS) #if !defined(MBEDTLS_ECP_MAX_BITS)
/** /**
* Maximum size of the groups (that is, of N and P) * The maximum size of the groups, that is, of N and P.
*/ */
#define MBEDTLS_ECP_MAX_BITS 521 /**< Maximum bit size of groups */ #define MBEDTLS_ECP_MAX_BITS 521 /**< The maximum size of groups, in bits. */
#endif #endif
#define MBEDTLS_ECP_MAX_BYTES ( ( MBEDTLS_ECP_MAX_BITS + 7 ) / 8 ) #define MBEDTLS_ECP_MAX_BYTES ( ( MBEDTLS_ECP_MAX_BITS + 7 ) / 8 )
@ -212,7 +229,7 @@ mbedtls_ecp_keypair;
* 224 475 475 453 398 342 * 224 475 475 453 398 342
* 192 640 640 633 587 476 * 192 640 640 633 587 476
*/ */
#define MBEDTLS_ECP_WINDOW_SIZE 6 /**< Maximum window size used */ #define MBEDTLS_ECP_WINDOW_SIZE 6 /**< The maximum window size used. */
#endif /* MBEDTLS_ECP_WINDOW_SIZE */ #endif /* MBEDTLS_ECP_WINDOW_SIZE */
#if !defined(MBEDTLS_ECP_FIXED_POINT_OPTIM) #if !defined(MBEDTLS_ECP_FIXED_POINT_OPTIM)
@ -227,7 +244,7 @@ mbedtls_ecp_keypair;
* *
* Change this value to 0 to reduce peak memory usage. * Change this value to 0 to reduce peak memory usage.
*/ */
#define MBEDTLS_ECP_FIXED_POINT_OPTIM 1 /**< Enable fixed-point speed-up */ #define MBEDTLS_ECP_FIXED_POINT_OPTIM 1 /**< Enable fixed-point speed-up. */
#endif /* MBEDTLS_ECP_FIXED_POINT_OPTIM */ #endif /* MBEDTLS_ECP_FIXED_POINT_OPTIM */
/* \} name SECTION: Module settings */ /* \} name SECTION: Module settings */
@ -235,25 +252,26 @@ mbedtls_ecp_keypair;
/* /*
* Point formats, from RFC 4492's enum ECPointFormat * Point formats, from RFC 4492's enum ECPointFormat
*/ */
#define MBEDTLS_ECP_PF_UNCOMPRESSED 0 /**< Uncompressed point format */ #define MBEDTLS_ECP_PF_UNCOMPRESSED 0 /**< Uncompressed point format. */
#define MBEDTLS_ECP_PF_COMPRESSED 1 /**< Compressed point format */ #define MBEDTLS_ECP_PF_COMPRESSED 1 /**< Compressed point format. */
/* /*
* Some other constants from RFC 4492 * Some other constants from RFC 4492
*/ */
#define MBEDTLS_ECP_TLS_NAMED_CURVE 3 /**< ECCurveType's named_curve */ #define MBEDTLS_ECP_TLS_NAMED_CURVE 3 /**< The named_curve of ECCurveType. */
/** /**
* \brief Get the list of supported curves in order of preferrence * \brief This function retrieves the information defined in
* (full information) * mbedtls_ecp_curve_info()for all supported curves in order
* of preference.
* *
* \return A statically allocated array, the last entry is 0. * \return A statically allocated array. The last entry is 0.
*/ */
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void ); const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void );
/** /**
* \brief Get the list of supported curves in order of preferrence * \brief This function retrieves the grp_id of all supported curves
* (grp_id only) * in order of preference.
* *
* \return A statically allocated array, * \return A statically allocated array,
* terminated with MBEDTLS_ECP_DP_NONE. * terminated with MBEDTLS_ECP_DP_NONE.
@ -261,358 +279,390 @@ const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void );
const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void ); const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void );
/** /**
* \brief Get curve information from an internal group identifier * \brief This function retrieves curve information from an internal
* group identifier.
* *
* \param grp_id A MBEDTLS_ECP_DP_XXX value * \param grp_id An \c MBEDTLS_ECP_DP_XXX value.
* *
* \return The associated curve information or NULL * \return The associated curve information, or NULL.
*/ */
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id ); const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id );
/** /**
* \brief Get curve information from a TLS NamedCurve value * \brief This function retrieves curve information from a TLS
* NamedCurve value.
* *
* \param tls_id A MBEDTLS_ECP_DP_XXX value * \param tls_id An \c MBEDTLS_ECP_DP_XXX value.
* *
* \return The associated curve information or NULL * \return The associated curve information, or NULL.
*/ */
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id ); const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id );
/** /**
* \brief Get curve information from a human-readable name * \brief This function retrieves curve information from a
* human-readable name.
* *
* \param name The name * \param name The human-readable name.
* *
* \return The associated curve information or NULL * \return The associated curve information, or NULL.
*/ */
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name ); const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name );
/** /**
* \brief Initialize a point (as zero) * \brief This function initializes a point as zero.
*
* \param pt The point to initialize.
*/ */
void mbedtls_ecp_point_init( mbedtls_ecp_point *pt ); void mbedtls_ecp_point_init( mbedtls_ecp_point *pt );
/** /**
* \brief Initialize a group (to something meaningless) * \brief This function initializes a group to something meaningless.
*/ */
void mbedtls_ecp_group_init( mbedtls_ecp_group *grp ); void mbedtls_ecp_group_init( mbedtls_ecp_group *grp );
/** /**
* \brief Initialize a key pair (as an invalid one) * \brief This function initializes a key pair as an invalid one.
*
* \param key The key pair to initialize.
*/ */
void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key ); void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key );
/** /**
* \brief Free the components of a point * \brief This function frees the components of a point.
*
* \param pt The point to free.
*/ */
void mbedtls_ecp_point_free( mbedtls_ecp_point *pt ); void mbedtls_ecp_point_free( mbedtls_ecp_point *pt );
/** /**
* \brief Free the components of an ECP group * \brief This function frees the components of an ECP group.
* \param grp The group to free.
*/ */
void mbedtls_ecp_group_free( mbedtls_ecp_group *grp ); void mbedtls_ecp_group_free( mbedtls_ecp_group *grp );
/** /**
* \brief Free the components of a key pair * \brief This function frees the components of a key pair.
* \param key The key pair to free.
*/ */
void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key ); void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key );
/** /**
* \brief Copy the contents of point Q into P * \brief This function copies the contents of point \p Q into
* point \p P.
* *
* \param P Destination point * \param P The destination point.
* \param Q Source point * \param Q The source point.
* *
* \return 0 if successful, * \return \c 0 on success.
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation fails.
*/ */
int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q ); int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q );
/** /**
* \brief Copy the contents of a group object * \brief This function copies the contents of group \p src into
* group \p dst.
* *
* \param dst Destination group * \param dst The destination group.
* \param src Source group * \param src The source group.
* *
* \return 0 if successful, * \return \c 0 on success.
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation fails.
*/ */
int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src ); int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src );
/** /**
* \brief Set a point to zero * \brief This function sets a point to zero.
* *
* \param pt Destination point * \param pt The point to set.
* *
* \return 0 if successful, * \return \c 0 on success.
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation fails.
*/ */
int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt ); int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt );
/** /**
* \brief Tell if a point is zero * \brief This function checks if a point is zero.
* *
* \param pt Point to test * \param pt The point to test.
* *
* \return 1 if point is zero, 0 otherwise * \return \c 1 if point is zero.
* \return \c 0 if point is non-zero.
*/ */
int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt ); int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt );
/** /**
* \brief Compare two points * \brief This function compares two points.
* *
* \note This assumes the points are normalized. Otherwise, * \note This assumes that the points are normalized. Otherwise,
* they may compare as "not equal" even if they are. * they may compare as "not equal" even if they are.
* *
* \param P First point to compare * \param P The first point to compare.
* \param Q Second point to compare * \param Q The second point to compare.
* *
* \return 0 if the points are equal, * \return \c 0 if the points are equal.
* MBEDTLS_ERR_ECP_BAD_INPUT_DATA otherwise * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the points are not equal.
*/ */
int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P, int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
const mbedtls_ecp_point *Q ); const mbedtls_ecp_point *Q );
/** /**
* \brief Import a non-zero point from two ASCII strings * \brief This function imports a non-zero point from two ASCII
* strings.
* *
* \param P Destination point * \param P The destination point.
* \param radix Input numeric base * \param radix The numeric base of the input.
* \param x First affine coordinate as a null-terminated string * \param x The first affine coordinate, as a null-terminated string.
* \param y Second affine coordinate as a null-terminated string * \param y The second affine coordinate, as a null-terminated string.
* *
* \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code * \return \c 0 on success.
* \return An \c MBEDTLS_ERR_MPI_XXX error code on failure.
*/ */
int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix, int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
const char *x, const char *y ); const char *x, const char *y );
/** /**
* \brief Export a point into unsigned binary data * \brief This function exports a point into unsigned binary data.
* *
* \param grp Group to which the point should belong * \param grp The group to which the point should belong.
* \param P Point to export * \param P The point to export.
* \param format Point format, should be a MBEDTLS_ECP_PF_XXX macro * \param format The point format. Should be an \c MBEDTLS_ECP_PF_XXX macro.
* \param olen Length of the actual output * \param olen The length of the output.
* \param buf Output buffer * \param buf The output buffer.
* \param buflen Length of the output buffer * \param buflen The length of the output buffer.
* *
* \return 0 if successful, * \return \c 0 on success.
* or MBEDTLS_ERR_ECP_BAD_INPUT_DATA * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA
* or MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL * or #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL on failure.
*/ */
int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P, int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P,
int format, size_t *olen, int format, size_t *olen,
unsigned char *buf, size_t buflen ); unsigned char *buf, size_t buflen );
/** /**
* \brief Import a point from unsigned binary data * \brief This function imports a point from unsigned binary data.
* *
* \param grp Group to which the point should belong * \note This function does not check that the point actually
* \param P Point to import * belongs to the given group, see mbedtls_ecp_check_pubkey()
* \param buf Input buffer * for that.
* \param ilen Actual length of input
* *
* \return 0 if successful, * \param grp The group to which the point should belong.
* MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid, * \param P The point to import.
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, * \param buf The input buffer.
* MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format * \param ilen The length of the input.
*
* \return \c 0 on success.
* \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format
* is not implemented. * is not implemented.
* *
* \note This function does NOT check that the point actually
* belongs to the given group, see mbedtls_ecp_check_pubkey() for
* that.
*/ */
int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P, int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
const unsigned char *buf, size_t ilen ); const unsigned char *buf, size_t ilen );
/** /**
* \brief Import a point from a TLS ECPoint record * \brief This function imports a point from a TLS ECPoint record.
* *
* \param grp ECP group used * \note On function return, \p buf is updated to point to immediately
* \param pt Destination point * after the ECPoint.
* \param buf $(Start of input buffer)
* \param len Buffer length
* *
* \note buf is updated to point right after the ECPoint on exit * \param grp The ECP group used.
* \param pt The destination point.
* \param buf The address of the pointer to the start of input buffer.
* \param len The length of the buffer.
* *
* \return 0 if successful, * \return \c 0 on success.
* MBEDTLS_ERR_MPI_XXX if initialization failed * \return An \c MBEDTLS_ERR_MPI_XXX error code if initialization failed.
* MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
*/ */
int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt, int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
const unsigned char **buf, size_t len ); const unsigned char **buf, size_t len );
/** /**
* \brief Export a point as a TLS ECPoint record * \brief This function exports a point as a TLS ECPoint record.
* *
* \param grp ECP group used * \param grp The ECP group used.
* \param pt Point to export * \param pt The point to export.
* \param format Export format * \param format The export format.
* \param olen length of data written * \param olen The length of data written.
* \param buf Buffer to write to * \param buf The Buffer to write to.
* \param blen Buffer length * \param blen The length of the Buffer.
* *
* \return 0 if successful, * \return \c 0 on success.
* or MBEDTLS_ERR_ECP_BAD_INPUT_DATA * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA or
* or MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL * #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL on failure.
*/ */
int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt, int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
int format, size_t *olen, int format, size_t *olen,
unsigned char *buf, size_t blen ); unsigned char *buf, size_t blen );
/** /**
* \brief Set a group using well-known domain parameters * \brief This function sets a group using well-known domain parameters.
* *
* \param grp Destination group * \note The index should be a value of the NamedCurve enum,
* \param id Index in the list of well-known domain parameters * as defined in <em>RFC-4492: Elliptic Curve Cryptography
* (ECC) Cipher Suites for Transport Layer Security (TLS)</em>,
* usually in the form of an \c MBEDTLS_ECP_DP_XXX macro.
* *
* \return 0 if successful, * \param grp The destination group.
* MBEDTLS_ERR_MPI_XXX if initialization failed * \param id The index in the list of well-known domain parameters.
* MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE for unkownn groups
* *
* \note Index should be a value of RFC 4492's enum NamedCurve, * \return \c 0 on success,
* usually in the form of a MBEDTLS_ECP_DP_XXX macro. * \return An \c MBEDTLS_ERR_MPI_XXX error code if initialization fails.
* \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE for unkownn groups.
*/ */
int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id ); int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id );
/** /**
* \brief Set a group from a TLS ECParameters record * \brief This function sets a group from a TLS ECParameters record.
* *
* \param grp Destination group * \note \p buf is updated to point right after ECParameters on exit.
* \param buf &(Start of input buffer)
* \param len Buffer length
* *
* \note buf is updated to point right after ECParameters on exit * \param grp The destination group.
* \param buf The address of the pointer to the start of input buffer.
* \param len The length of the buffer.
* *
* \return 0 if successful, * \return \c 0 on success.
* MBEDTLS_ERR_MPI_XXX if initialization failed * \return An \c MBEDTLS_ERR_MPI_XXX error code if initialization fails.
* MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
*/ */
int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, const unsigned char **buf, size_t len ); int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, const unsigned char **buf, size_t len );
/** /**
* \brief Write the TLS ECParameters record for a group * \brief This function writes the TLS ECParameters record for a group.
* *
* \param grp ECP group used * \param grp The ECP group used.
* \param olen Number of bytes actually written * \param olen The number of Bytes written.
* \param buf Buffer to write to * \param buf The buffer to write to.
* \param blen Buffer length * \param blen The length of the buffer.
* *
* \return 0 if successful, * \return \c 0 on success.
* or MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL on failure.
*/ */
int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen, int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
unsigned char *buf, size_t blen ); unsigned char *buf, size_t blen );
/** /**
* \brief Multiplication by an integer: R = m * P * \brief This function performs multiplication of a point by
* (Not thread-safe to use same group in multiple threads) * an integer: \p R = \p m * \p P.
* *
* \note In order to prevent timing attacks, this function * It is not thread-safe to use same group in multiple threads.
* 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 * \note To prevent timing attacks, this function
* results in order to prevent potential timing attacks * executes the exact same sequence of base-field
* targeting these results. It is recommended to always * operations for any valid \p m. It avoids any if-branch or
* provide a non-NULL f_rng (the overhead is negligible). * array index depending on the value of \p m.
* *
* \param grp ECP group * \note If \p f_rng is not NULL, it is used to randomize
* \param R Destination point * intermediate results to prevent potential timing attacks
* \param m Integer by which to multiply * targeting these results. We recommend always providing
* \param P Point to multiply * a non-NULL \p f_rng. The overhead is negligible.
* \param f_rng RNG function (see notes)
* \param p_rng RNG parameter
* *
* \return 0 if successful, * \param grp The ECP group.
* MBEDTLS_ERR_ECP_INVALID_KEY if m is not a valid privkey * \param R The destination point.
* or P is not a valid pubkey, * \param m The integer by which to multiply.
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed * \param P The point to multiply.
* \param f_rng The RNG function.
* \param p_rng The RNG context.
*
* \return \c 0 on success.
* \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid privkey,
* or \p P is not a valid pubkey.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory allocation failure.
*/ */
int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
const mbedtls_mpi *m, const mbedtls_ecp_point *P, const mbedtls_mpi *m, const mbedtls_ecp_point *P,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ); int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
/** /**
* \brief Multiplication and addition of two points by integers: * \brief This function performs multiplication and addition of two
* R = m * P + n * Q * points by integers: \p R = \p m * \p P + \p n * \p Q
* (Not thread-safe to use same group in multiple threads)
* It is not thread-safe to use same group in multiple threads.
* *
* \note In contrast to mbedtls_ecp_mul(), this function does not guarantee * \note In contrast to mbedtls_ecp_mul(), this function does not
* a constant execution flow and timing. * guarantee a constant execution flow and timing.
* *
* \param grp ECP group * \param grp The ECP group.
* \param R Destination point * \param R The destination point.
* \param m Integer by which to multiply P * \param m The integer by which to multiply \p P.
* \param P Point to multiply by m * \param P The point to multiply by \p m.
* \param n Integer by which to multiply Q * \param n The integer by which to multiply \p Q.
* \param Q Point to be multiplied by n * \param Q The point to be multiplied by \p n.
* *
* \return 0 if successful, * \return \c 0 on success.
* MBEDTLS_ERR_ECP_INVALID_KEY if m or n is not a valid privkey * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not
* or P or Q is not a valid pubkey, * valid private keys, or \p P or \p Q are not valid public
* MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed * keys.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory allocation failure.
*/ */
int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
const mbedtls_mpi *m, const mbedtls_ecp_point *P, const mbedtls_mpi *m, const mbedtls_ecp_point *P,
const mbedtls_mpi *n, const mbedtls_ecp_point *Q ); const mbedtls_mpi *n, const mbedtls_ecp_point *Q );
/** /**
* \brief Check that a point is a valid public key on this curve * \brief This function checks that a point is a valid public key
* on this curve.
* *
* \param grp Curve/group the point should belong to * It only checks that the point is non-zero, has
* \param pt Point to check * valid coordinates and lies on the curve. It does not verify
* that it is indeed a multiple of \p G. This additional
* check is computationally more expensive, is not required
* by standards, and should not 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.
* *
* \return 0 if point is a valid public key, * \note This function uses bare components rather than an
* MBEDTLS_ERR_ECP_INVALID_KEY otherwise. * mbedtls_ecp_keypair() structure, to ease use with other
* structures. For example, mbedtls_ecdh_context() or
* mbedtls_ecdsa_context().
* *
* \note This function only checks the point is non-zero, has valid * \param grp The curve or group the point should belong to.
* coordinates and lies on the curve, but not that it is * \param pt The point to check.
* 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 mbedtls_ecp_keypair structure * \return \c 0 if the point is a valid public key.
* in order to ease use with other structures such as * \return #MBEDTLS_ERR_ECP_INVALID_KEY otherwise.
* mbedtls_ecdh_context of mbedtls_ecdsa_context.
*/ */
int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt ); int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt );
/** /**
* \brief Check that an mbedtls_mpi is a valid private key for this curve * \brief This function checks that an \p mbedtls_mpi is a valid private
* key for this curve.
* *
* \param grp Group used * \note This function uses bare components rather than an
* \param d Integer to check * mbedtls_ecp_keypair() structure to ease use with other
* structures such as mbedtls_ecdh_context() or
* mbedtls_ecdsa_context().
* *
* \return 0 if point is a valid private key, * \param grp The group used.
* MBEDTLS_ERR_ECP_INVALID_KEY otherwise. * \param d The integer to check.
* *
* \note Uses bare components rather than an mbedtls_ecp_keypair structure * \return \c 0 if the point is a valid private key.
* in order to ease use with other structures such as * \return #MBEDTLS_ERR_ECP_INVALID_KEY otherwise.
* mbedtls_ecdh_context of mbedtls_ecdsa_context.
*/ */
int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d ); int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d );
/** /**
* \brief Generate a keypair with configurable base point * \brief This function generates a keypair with a configurable base
* point.
* *
* \param grp ECP group * \note This function uses bare components rather than an
* \param G Chosen base point * mbedtls_ecp_keypair() structure to ease use with other
* \param d Destination MPI (secret part) * structures such as mbedtls_ecdh_context() or
* \param Q Destination point (public part) * mbedtls_ecdsa_context().
* \param f_rng RNG function *
* \param p_rng RNG parameter * \param grp The ECP group.
* \param G The chosen base point.
* \param d The destination MPI (secret part).
* \param Q The destination point (public part).
* \param f_rng The RNG function.
* \param p_rng The RNG context.
* *
* \return 0 if successful, * \return \c 0 on success.
* or a MBEDTLS_ERR_ECP_XXX or MBEDTLS_MPI_XXX error code * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
* * on failure.
* \note Uses bare components rather than an mbedtls_ecp_keypair structure */
* in order to ease use with other structures such as
* mbedtls_ecdh_context of mbedtls_ecdsa_context.
*/
int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp, int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
const mbedtls_ecp_point *G, const mbedtls_ecp_point *G,
mbedtls_mpi *d, mbedtls_ecp_point *Q, mbedtls_mpi *d, mbedtls_ecp_point *Q,
@ -620,57 +670,64 @@ int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
void *p_rng ); void *p_rng );
/** /**
* \brief Generate a keypair * \brief This function generates a keypair.
* *
* \param grp ECP group * \note This function uses bare components rather than an
* \param d Destination MPI (secret part) * mbedtls_ecp_keypair() structure to ease use with other
* \param Q Destination point (public part) * structures such as mbedtls_ecdh_context() or
* \param f_rng RNG function * mbedtls_ecdsa_context().
* \param p_rng RNG parameter
* *
* \return 0 if successful, * \param grp The ECP group.
* or a MBEDTLS_ERR_ECP_XXX or MBEDTLS_MPI_XXX error code * \param d The destination MPI (secret part).
* \param Q The destination point (public part).
* \param f_rng The RNG function.
* \param p_rng The RNG context.
* *
* \note Uses bare components rather than an mbedtls_ecp_keypair structure * \return \c 0 on success.
* in order to ease use with other structures such as * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
* mbedtls_ecdh_context of mbedtls_ecdsa_context. * on failure.
*/ */
int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, mbedtls_mpi *d, mbedtls_ecp_point *Q, int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, mbedtls_mpi *d, mbedtls_ecp_point *Q,
int (*f_rng)(void *, unsigned char *, size_t), int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng ); void *p_rng );
/** /**
* \brief Generate a keypair * \brief This function generates a key.
* *
* \param grp_id ECP group identifier * \param grp_id The ECP group identifier.
* \param key Destination keypair * \param key The destination key.
* \param f_rng RNG function * \param f_rng The RNG function.
* \param p_rng RNG parameter * \param p_rng The RNG context.
* *
* \return 0 if successful, * \return \c 0 on success.
* or a MBEDTLS_ERR_ECP_XXX or MBEDTLS_MPI_XXX error code * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
* on failure.
*/ */
int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ); int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
/** /**
* \brief Check a public-private key pair * \brief This function checks a public-private key pair.
* *
* \param pub Keypair structure holding a public key * \param pub The keypair structure holding the public key.
* \param prv Keypair structure holding a private (plus public) key * \param prv The keypair structure holding the private key.
* *
* \return 0 if successful (keys are valid and match), or * \note The both are keypairs, and may optionally hold the corresponding other key, but the public key passed in thee pub is checked against the private key passed in prv.
* MBEDTLS_ERR_ECP_BAD_INPUT_DATA, or *
* a MBEDTLS_ERR_ECP_XXX or MBEDTLS_ERR_MPI_XXX code. * \return \c 0 on success - the keys are valid and match.
* \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA, or an \c
* MBEDTLS_ERR_ECP_XXX or an \c MBEDTLS_ERR_MPI_XXX
* error code on failure.
*/ */
int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv ); int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv );
#if defined(MBEDTLS_SELF_TEST) #if defined(MBEDTLS_SELF_TEST)
/** /**
* \brief Checkup routine * \brief The ECP checkup routine.
* *
* \return 0 if successful, or 1 if a test failed * \return \c 0 on success.
* \return \c 1 on failure.
*/ */
int mbedtls_ecp_self_test( int verbose ); int mbedtls_ecp_self_test( int verbose );