--- /dev/null
+/**
+ * \file ecp.h
+ *
+ * \brief This file provides an API for Elliptic Curves over GF(P) (ECP).
+ *
+ * The use of ECP in cryptography and TLS 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) 2006-2018, Arm Limited (or its affiliates), All Rights Reserved
+ * SPDX-License-Identifier: GPL-2.0
+ *
+ * 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.
+ *
+ * This file is part of Mbed TLS (https://tls.mbed.org)
+ */
+
+#ifndef MBEDTLS_ECP_H
+#define MBEDTLS_ECP_H
+
+#include "bignum.h"
+
+/*
+ * ECP error codes
+ */
+#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_FEATURE_UNAVAILABLE -0x4E80 /**< The requested feature is not available, for example, the requested curve is not supported. */
+#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_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_SIG_LEN_MISMATCH -0x4C00 /**< The buffer contains a valid signature followed by more data. */
+#define MBEDTLS_ERR_ECP_HW_ACCEL_FAILED -0x4B80 /**< The ECP hardware accelerator failed. */
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/**
+ * Domain-parameter identifiers: curve, subgroup, and generator.
+ *
+ * \note Only curves over prime fields are supported.
+ *
+ * \warning This library does not support validation of arbitrary domain
+ * parameters. Therefore, only standardized domain parameters from trusted
+ * sources should be used. See mbedtls_ecp_group_load().
+ */
+typedef enum
+{
+ MBEDTLS_ECP_DP_NONE = 0, /*!< Curve not defined. */
+ MBEDTLS_ECP_DP_SECP192R1, /*!< Domain parameters for the 192-bit curve defined by FIPS 186-4 and SEC1. */
+ MBEDTLS_ECP_DP_SECP224R1, /*!< Domain parameters for the 224-bit curve defined by FIPS 186-4 and SEC1. */
+ MBEDTLS_ECP_DP_SECP256R1, /*!< Domain parameters for the 256-bit curve defined by FIPS 186-4 and SEC1. */
+ MBEDTLS_ECP_DP_SECP384R1, /*!< Domain parameters for the 384-bit curve defined by FIPS 186-4 and SEC1. */
+ MBEDTLS_ECP_DP_SECP521R1, /*!< Domain parameters for the 521-bit curve defined by FIPS 186-4 and SEC1. */
+ MBEDTLS_ECP_DP_BP256R1, /*!< Domain parameters for 256-bit Brainpool curve. */
+ MBEDTLS_ECP_DP_BP384R1, /*!< Domain parameters for 384-bit Brainpool curve. */
+ MBEDTLS_ECP_DP_BP512R1, /*!< Domain parameters for 512-bit Brainpool curve. */
+ MBEDTLS_ECP_DP_CURVE25519, /*!< Domain parameters for Curve25519. */
+ MBEDTLS_ECP_DP_SECP192K1, /*!< Domain parameters for 192-bit "Koblitz" curve. */
+ MBEDTLS_ECP_DP_SECP224K1, /*!< Domain parameters for 224-bit "Koblitz" curve. */
+ MBEDTLS_ECP_DP_SECP256K1, /*!< Domain parameters for 256-bit "Koblitz" curve. */
+ MBEDTLS_ECP_DP_CURVE448, /*!< Domain parameters for Curve448. */
+} mbedtls_ecp_group_id;
+
+/**
+ * The number of supported curves, plus one for #MBEDTLS_ECP_DP_NONE.
+ *
+ * \note Montgomery curves are currently excluded.
+ */
+#define MBEDTLS_ECP_DP_MAX 12
+
+/**
+ * Curve information, for use by other modules.
+ */
+typedef struct mbedtls_ecp_curve_info
+{
+ mbedtls_ecp_group_id grp_id; /*!< An internal identifier. */
+ uint16_t tls_id; /*!< The TLS NamedCurve identifier. */
+ uint16_t bit_size; /*!< The curve size in bits. */
+ const char *name; /*!< A human-friendly name. */
+} mbedtls_ecp_curve_info;
+
+/**
+ * \brief The ECP point structure, in Jacobian coordinates.
+ *
+ * \note All functions expect and return points satisfying
+ * the following condition: <code>Z == 0</code> or
+ * <code>Z == 1</code>. Other values of \p Z are
+ * used only by internal functions.
+ * The point is zero, or "at infinity", if <code>Z == 0</code>.
+ * Otherwise, \p X and \p Y are its standard (affine)
+ * coordinates.
+ */
+typedef struct mbedtls_ecp_point
+{
+ mbedtls_mpi X; /*!< The X coordinate of the ECP point. */
+ mbedtls_mpi Y; /*!< The Y coordinate of the ECP point. */
+ mbedtls_mpi Z; /*!< The Z coordinate of the ECP point. */
+}
+mbedtls_ecp_point;
+
+#if !defined(MBEDTLS_ECP_ALT)
+/*
+ * default mbed TLS elliptic curve arithmetic implementation
+ *
+ * (in case MBEDTLS_ECP_ALT is defined then the developer has to provide an
+ * alternative implementation for the whole module and it will replace this
+ * one.)
+ */
+
+/**
+ * \brief The ECP group structure.
+ *
+ * We consider two types of curve equations:
+ * <ul><li>Short Weierstrass: <code>y^2 = x^3 + A x + B mod P</code>
+ * (SEC1 + RFC-4492)</li>
+ * <li>Montgomery: <code>y^2 = x^3 + A x^2 + x mod P</code> (Curve25519,
+ * Curve448)</li></ul>
+ * In both cases, the generator (\p G) for a prime-order subgroup is fixed.
+ *
+ * For Short Weierstrass, this subgroup is the whole curve, and its
+ * cardinality is denoted by \p N. Our code requires that \p N is an
+ * odd prime as mbedtls_ecp_mul() requires an odd number, and
+ * mbedtls_ecdsa_sign() requires that it is prime for blinding purposes.
+ *
+ * For Montgomery curves, we do not store \p A, but <code>(A + 2) / 4</code>,
+ * which is the quantity used in the formulas. Additionally, \p nbits is
+ * not the size of \p N but the required size for private keys.
+ *
+ * If \p modp is NULL, reduction modulo \p P is done using a generic algorithm.
+ * Otherwise, \p modp must point to a function that takes an \p mbedtls_mpi in the
+ * range of <code>0..2^(2*pbits)-1</code>, and transforms it in-place to an integer
+ * which is congruent mod \p P to the given MPI, and is close enough to \p pbits
+ * in size, so that it may be efficiently brought in the 0..P-1 range by a few
+ * additions or subtractions. Therefore, it is only an approximative modular
+ * reduction. It must return 0 on success and non-zero on failure.
+ *
+ */
+typedef struct mbedtls_ecp_group
+{
+ mbedtls_ecp_group_id id; /*!< An internal group identifier. */
+ mbedtls_mpi P; /*!< The prime modulus of the base field. */
+ mbedtls_mpi A; /*!< For Short Weierstrass: \p A in the equation. For
+ Montgomery curves: <code>(A + 2) / 4</code>. */
+ mbedtls_mpi B; /*!< For Short Weierstrass: \p B in the equation.
+ For Montgomery curves: unused. */
+ mbedtls_ecp_point G; /*!< The generator of the subgroup used. */
+ mbedtls_mpi N; /*!< The order of \p G. */
+ size_t pbits; /*!< The number of bits in \p P.*/
+ size_t nbits; /*!< For Short Weierstrass: The number of bits in \p P.
+ For Montgomery curves: the number of bits in the
+ private keys. */
+ unsigned int h; /*!< \internal 1 if the constants are static. */
+ int (*modp)(mbedtls_mpi *); /*!< The function for fast pseudo-reduction
+ mod \p P (see above).*/
+ int (*t_pre)(mbedtls_ecp_point *, void *); /*!< Unused. */
+ int (*t_post)(mbedtls_ecp_point *, void *); /*!< Unused. */
+ void *t_data; /*!< Unused. */
+ mbedtls_ecp_point *T; /*!< Pre-computed points for ecp_mul_comb(). */
+ size_t T_size; /*!< The number of pre-computed points. */
+}
+mbedtls_ecp_group;
+
+/**
+ * \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 using the compiler command line.
+ * \{
+ */
+
+#if !defined(MBEDTLS_ECP_MAX_BITS)
+/**
+ * The maximum size of the groups, that is, of \c N and \c P.
+ */
+#define MBEDTLS_ECP_MAX_BITS 521 /**< The maximum size of groups, in bits. */
+#endif
+
+#define MBEDTLS_ECP_MAX_BYTES ( ( MBEDTLS_ECP_MAX_BITS + 7 ) / 8 )
+#define MBEDTLS_ECP_MAX_PT_LEN ( 2 * MBEDTLS_ECP_MAX_BYTES + 1 )
+
+#if !defined(MBEDTLS_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 << ( MBEDTLS_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 MBEDTLS_ECP_WINDOW_SIZE 6 /**< The maximum window size used. */
+#endif /* MBEDTLS_ECP_WINDOW_SIZE */
+
+#if !defined(MBEDTLS_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 MBEDTLS_ECP_FIXED_POINT_OPTIM 1 /**< Enable fixed-point speed-up. */
+#endif /* MBEDTLS_ECP_FIXED_POINT_OPTIM */
+
+/* \} name SECTION: Module settings */
+
+#else /* MBEDTLS_ECP_ALT */
+#include "ecp_alt.h"
+#endif /* MBEDTLS_ECP_ALT */
+
+/**
+ * \brief The ECP key-pair structure.
+ *
+ * A generic key-pair that may be used for ECDSA and fixed ECDH, for example.
+ *
+ * \note Members are deliberately in the same order as in the
+ * ::mbedtls_ecdsa_context structure.
+ */
+typedef struct mbedtls_ecp_keypair
+{
+ mbedtls_ecp_group grp; /*!< Elliptic curve and base point */
+ mbedtls_mpi d; /*!< our secret value */
+ mbedtls_ecp_point Q; /*!< our public value */
+}
+mbedtls_ecp_keypair;
+
+/*
+ * Point formats, from RFC 4492's enum ECPointFormat
+ */
+#define MBEDTLS_ECP_PF_UNCOMPRESSED 0 /**< Uncompressed point format. */
+#define MBEDTLS_ECP_PF_COMPRESSED 1 /**< Compressed point format. */
+
+/*
+ * Some other constants from RFC 4492
+ */
+#define MBEDTLS_ECP_TLS_NAMED_CURVE 3 /**< The named_curve of ECCurveType. */
+
+/**
+ * \brief This function retrieves the information defined in
+ * mbedtls_ecp_curve_info() for all supported curves in order
+ * of preference.
+ *
+ * \return A statically allocated array. The last entry is 0.
+ */
+const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void );
+
+/**
+ * \brief This function retrieves the list of internal group
+ * identifiers of all supported curves in the order of
+ * preference.
+ *
+ * \return A statically allocated array,
+ * terminated with MBEDTLS_ECP_DP_NONE.
+ */
+const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void );
+
+/**
+ * \brief This function retrieves curve information from an internal
+ * group identifier.
+ *
+ * \param grp_id An \c MBEDTLS_ECP_DP_XXX value.
+ *
+ * \return The associated curve information on success.
+ * \return NULL on failure.
+ */
+const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id );
+
+/**
+ * \brief This function retrieves curve information from a TLS
+ * NamedCurve value.
+ *
+ * \param tls_id An \c MBEDTLS_ECP_DP_XXX value.
+ *
+ * \return The associated curve information on success.
+ * \return NULL on failure.
+ */
+const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id );
+
+/**
+ * \brief This function retrieves curve information from a
+ * human-readable name.
+ *
+ * \param name The human-readable name.
+ *
+ * \return The associated curve information on success.
+ * \return NULL on failure.
+ */
+const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name );
+
+/**
+ * \brief This function initializes a point as zero.
+ *
+ * \param pt The point to initialize.
+ */
+void mbedtls_ecp_point_init( mbedtls_ecp_point *pt );
+
+/**
+ * \brief This function initializes an ECP group context
+ * without loading any domain parameters.
+ *
+ * \note After this function is called, domain parameters
+ * for various ECP groups can be loaded through the
+ * mbedtls_ecp_load() or mbedtls_ecp_tls_read_group()
+ * functions.
+ */
+void mbedtls_ecp_group_init( mbedtls_ecp_group *grp );
+
+/**
+ * \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 );
+
+/**
+ * \brief This function frees the components of a point.
+ *
+ * \param pt The point to free.
+ */
+void mbedtls_ecp_point_free( mbedtls_ecp_point *pt );
+
+/**
+ * \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 );
+
+/**
+ * \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 );
+
+/**
+ * \brief This function copies the contents of point \p Q into
+ * point \p P.
+ *
+ * \param P The destination point.
+ * \param Q The source point.
+ *
+ * \return \c 0 on success.
+ * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
+ */
+int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q );
+
+/**
+ * \brief This function copies the contents of group \p src into
+ * group \p dst.
+ *
+ * \param dst The destination group.
+ * \param src The source group.
+ *
+ * \return \c 0 on success.
+ * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
+ */
+int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src );
+
+/**
+ * \brief This function sets a point to zero.
+ *
+ * \param pt The point to set.
+ *
+ * \return \c 0 on success.
+ * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
+ */
+int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt );
+
+/**
+ * \brief This function checks if a point is zero.
+ *
+ * \param pt The point to test.
+ *
+ * \return \c 1 if the point is zero.
+ * \return \c 0 if the point is non-zero.
+ */
+int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt );
+
+/**
+ * \brief This function compares two points.
+ *
+ * \note This assumes that the points are normalized. Otherwise,
+ * they may compare as "not equal" even if they are.
+ *
+ * \param P The first point to compare.
+ * \param Q The second point to compare.
+ *
+ * \return \c 0 if the points are equal.
+ * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the points are not equal.
+ */
+int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
+ const mbedtls_ecp_point *Q );
+
+/**
+ * \brief This function imports a non-zero point from two ASCII
+ * strings.
+ *
+ * \param P The destination point.
+ * \param radix The numeric base of the input.
+ * \param x The first affine coordinate, as a null-terminated string.
+ * \param y The second affine coordinate, as a null-terminated string.
+ *
+ * \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,
+ const char *x, const char *y );
+
+/**
+ * \brief This function exports a point into unsigned binary data.
+ *
+ * \param grp The group to which the point should belong.
+ * \param P The point to export.
+ * \param format The point format. Should be an \c MBEDTLS_ECP_PF_XXX macro.
+ * \param olen The length of the output.
+ * \param buf The output buffer.
+ * \param buflen The length of the output buffer.
+ *
+ * \return \c 0 on success.
+ * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA
+ * 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 format, size_t *olen,
+ unsigned char *buf, size_t buflen );
+
+/**
+ * \brief This function imports a point from unsigned binary data.
+ *
+ * \note This function does not check that the point actually
+ * belongs to the given group, see mbedtls_ecp_check_pubkey()
+ * for that.
+ *
+ * \param grp The group to which the point should belong.
+ * \param P The point to import.
+ * \param buf The input buffer.
+ * \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 on memory-allocation failure.
+ * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format
+ * is not implemented.
+ *
+ */
+int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
+ const unsigned char *buf, size_t ilen );
+
+/**
+ * \brief This function imports a point from a TLS ECPoint record.
+ *
+ * \note On function return, \p buf is updated to point to immediately
+ * after the ECPoint record.
+ *
+ * \param grp The ECP group used.
+ * \param pt The destination point.
+ * \param buf The address of the pointer to the start of the input buffer.
+ * \param len The length of the buffer.
+ *
+ * \return \c 0 on success.
+ * \return An \c MBEDTLS_ERR_MPI_XXX error code on initialization failure.
+ * \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,
+ const unsigned char **buf, size_t len );
+
+/**
+ * \brief This function exports a point as a TLS ECPoint record.
+ *
+ * \param grp The ECP group used.
+ * \param pt The point format to export to. The point format is an
+ * \c MBEDTLS_ECP_PF_XXX constant.
+ * \param format The export format.
+ * \param olen The length of the data written.
+ * \param buf The buffer to write to.
+ * \param blen The length of the buffer.
+ *
+ * \return \c 0 on success.
+ * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA or
+ * #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 format, size_t *olen,
+ unsigned char *buf, size_t blen );
+
+/**
+ * \brief This function sets a group using standardized domain parameters.
+ *
+ * \note The index should be a value of the NamedCurve enum,
+ * 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.
+ *
+ * \param grp The destination group.
+ * \param id The identifier of the domain parameter set to load.
+ *
+ * \return \c 0 on success,
+ * \return An \c MBEDTLS_ERR_MPI_XXX error code on initialization failure.
+ * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE for unkownn groups.
+
+ */
+int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id );
+
+/**
+ * \brief This function sets a group from a TLS ECParameters record.
+ *
+ * \note \p buf is updated to point right after the ECParameters record
+ * on exit.
+ *
+ * \param grp The destination group.
+ * \param buf The address of the pointer to the start of the input buffer.
+ * \param len The length of the buffer.
+ *
+ * \return \c 0 on success.
+ * \return An \c MBEDTLS_ERR_MPI_XXX error code on initialization failure.
+ * \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 );
+
+/**
+ * \brief This function writes the TLS ECParameters record for a group.
+ *
+ * \param grp The ECP group used.
+ * \param olen The number of Bytes written.
+ * \param buf The buffer to write to.
+ * \param blen The length of the buffer.
+ *
+ * \return \c 0 on success.
+ * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL on failure.
+ */
+int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
+ unsigned char *buf, size_t blen );
+
+/**
+ * \brief This function performs multiplication of a point by
+ * an integer: \p R = \p m * \p P.
+ *
+ * It is not thread-safe to use same group in multiple threads.
+ *
+ * \note To prevent timing attacks, this function
+ * executes the exact same sequence of base-field
+ * operations for any valid \p m. It avoids any if-branch or
+ * array index depending on the value of \p m.
+ *
+ * \note If \p f_rng is not NULL, it is used to randomize
+ * intermediate results to prevent potential timing attacks
+ * targeting these results. We recommend always providing
+ * a non-NULL \p f_rng. The overhead is negligible.
+ *
+ * \param grp The ECP group.
+ * \param R The destination point.
+ * \param m The integer by which to multiply.
+ * \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 private
+ * key, or \p P is not a valid public key.
+ * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
+ */
+int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+ const mbedtls_mpi *m, const mbedtls_ecp_point *P,
+ int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
+
+/**
+ * \brief This function performs multiplication and addition of two
+ * points by integers: \p R = \p m * \p P + \p n * \p Q
+ *
+ * It is not thread-safe to use same group in multiple threads.
+ *
+ * \note In contrast to mbedtls_ecp_mul(), this function does not
+ * guarantee a constant execution flow and timing.
+ *
+ * \param grp The ECP group.
+ * \param R The destination point.
+ * \param m The integer by which to multiply \p P.
+ * \param P The point to multiply by \p m.
+ * \param n The integer by which to multiply \p Q.
+ * \param Q The point to be multiplied by \p n.
+ *
+ * \return \c 0 on success.
+ * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not
+ * valid private keys, or \p P or \p Q are not valid public
+ * keys.
+ * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
+ */
+int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
+ const mbedtls_mpi *m, const mbedtls_ecp_point *P,
+ const mbedtls_mpi *n, const mbedtls_ecp_point *Q );
+
+/**
+ * \brief This function checks that a point is a valid public key
+ * on this curve.
+ *
+ * It only checks that the point is non-zero, has
+ * 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.
+ *
+ * \note This function uses bare components rather than an
+ * ::mbedtls_ecp_keypair structure, to ease use with other
+ * structures, such as ::mbedtls_ecdh_context or
+ * ::mbedtls_ecdsa_context.
+ *
+ * \param grp The curve the point should lie on.
+ * \param pt The point to check.
+ *
+ * \return \c 0 if the point is a valid public key.
+ * \return #MBEDTLS_ERR_ECP_INVALID_KEY on failure.
+ */
+int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt );
+
+/**
+ * \brief This function checks that an \p mbedtls_mpi is a valid private
+ * key for this curve.
+ *
+ * \note This function uses bare components rather than an
+ * ::mbedtls_ecp_keypair structure to ease use with other
+ * structures, such as ::mbedtls_ecdh_context or
+ * ::mbedtls_ecdsa_context.
+ *
+ * \param grp The group used.
+ * \param d The integer to check.
+ *
+ * \return \c 0 if the point is a valid private key.
+ * \return #MBEDTLS_ERR_ECP_INVALID_KEY on failure.
+ */
+int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d );
+
+/**
+ * \brief This function generates a keypair with a configurable base
+ * point.
+ *
+ * \note This function uses bare components rather than an
+ * ::mbedtls_ecp_keypair structure to ease use with other
+ * structures, such as ::mbedtls_ecdh_context or
+ * ::mbedtls_ecdsa_context.
+ *
+ * \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 \c 0 on success.
+ * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
+ * on failure.
+ */
+int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
+ const mbedtls_ecp_point *G,
+ mbedtls_mpi *d, mbedtls_ecp_point *Q,
+ int (*f_rng)(void *, unsigned char *, size_t),
+ void *p_rng );
+
+/**
+ * \brief This function generates an ECP keypair.
+ *
+ * \note This function uses bare components rather than an
+ * ::mbedtls_ecp_keypair structure to ease use with other
+ * structures, such as ::mbedtls_ecdh_context or
+ * ::mbedtls_ecdsa_context.
+ *
+ * \param grp The ECP group.
+ * \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 \c 0 on success.
+ * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
+ * on failure.
+ */
+int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, mbedtls_mpi *d, mbedtls_ecp_point *Q,
+ int (*f_rng)(void *, unsigned char *, size_t),
+ void *p_rng );
+
+/**
+ * \brief This function generates an ECP key.
+ *
+ * \param grp_id The ECP group identifier.
+ * \param key The destination key.
+ * \param f_rng The RNG function.
+ * \param p_rng The RNG context.
+ *
+ * \return \c 0 on success.
+ * \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 (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
+
+/**
+ * \brief This function checks that the keypair objects
+ * \p pub and \p prv have the same group and the
+ * same public point, and that the private key in
+ * \p prv is consistent with the public key.
+ *
+ * \param pub The keypair structure holding the public key.
+ * If it contains a private key, that part is ignored.
+ * \param prv The keypair structure holding the full keypair.
+ *
+ * \return \c 0 on success, meaning that the keys are valid and match.
+ * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the keys are invalid or do not match.
+ * \return An \c MBEDTLS_ERR_ECP_XXX or an \c MBEDTLS_ERR_MPI_XXX
+ * error code on calculation failure.
+ */
+int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv );
+
+#if defined(MBEDTLS_SELF_TEST)
+
+/**
+ * \brief The ECP checkup routine.
+ *
+ * \return \c 0 on success.
+ * \return \c 1 on failure.
+ */
+int mbedtls_ecp_self_test( int verbose );
+
+#endif /* MBEDTLS_SELF_TEST */
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* ecp.h */
projects / proxmark3-svn / blobdiff