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diff --git a/include/mbedtls/ecp.h b/include/mbedtls/ecp.h
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+/**
+ * \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 The Mbed TLS Contributors
+ *  SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
+ */
+
+#ifndef MBEDTLS_ECP_H
+#define MBEDTLS_ECP_H
+#include "mbedtls/private_access.h"
+
+#include "mbedtls/build_info.h"
+
+#include "mbedtls/bignum.h"
+
+/*
+ * ECP error codes
+ */
+/** Bad input parameters to function. */
+#define MBEDTLS_ERR_ECP_BAD_INPUT_DATA                    -0x4F80
+/** The buffer is too small to write to. */
+#define MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL                  -0x4F00
+/** The requested feature is not available, for example, the requested curve is not supported. */
+#define MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE               -0x4E80
+/** The signature is not valid. */
+#define MBEDTLS_ERR_ECP_VERIFY_FAILED                     -0x4E00
+/** Memory allocation failed. */
+#define MBEDTLS_ERR_ECP_ALLOC_FAILED                      -0x4D80
+/** Generation of random value, such as ephemeral key, failed. */
+#define MBEDTLS_ERR_ECP_RANDOM_FAILED                     -0x4D00
+/** Invalid private or public key. */
+#define MBEDTLS_ERR_ECP_INVALID_KEY                       -0x4C80
+/** The buffer contains a valid signature followed by more data. */
+#define MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH                  -0x4C00
+/** Operation in progress, call again with the same parameters to continue. */
+#define MBEDTLS_ERR_ECP_IN_PROGRESS                       -0x4B00
+
+/* Flags indicating whether to include code that is specific to certain
+ * types of curves. These flags are for internal library use only. */
+#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \
+    defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
+    defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
+    defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \
+    defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \
+    defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \
+    defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \
+    defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \
+    defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
+    defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
+    defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
+#define MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED
+#endif
+#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) || \
+    defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
+#define MBEDTLS_ECP_MONTGOMERY_ENABLED
+#endif
+
+#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().
+ */
+/* Note: when adding a new curve:
+ * - Add it at the end of this enum, otherwise you'll break the ABI by
+ *   changing the numerical value for existing curves.
+ * - Increment MBEDTLS_ECP_DP_MAX below if needed.
+ * - Update the calculation of MBEDTLS_ECP_MAX_BITS below.
+ * - Add the corresponding MBEDTLS_ECP_DP_xxx_ENABLED macro definition to
+ *   mbedtls_config.h.
+ * - List the curve as a dependency of MBEDTLS_ECP_C and
+ *   MBEDTLS_ECDSA_C if supported in check_config.h.
+ * - Add the curve to the appropriate curve type macro
+ *   MBEDTLS_ECP_yyy_ENABLED above.
+ * - Add the necessary definitions to ecp_curves.c.
+ * - Add the curve to the ecp_supported_curves array in ecp.c.
+ * - Add the curve to applicable profiles in x509_crt.c.
+ * - Add the curve to applicable presets in ssl_tls.c.
+ */
+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.
+ */
+#define MBEDTLS_ECP_DP_MAX     14
+
+/*
+ * Curve types
+ */
+typedef enum {
+    MBEDTLS_ECP_TYPE_NONE = 0,
+    MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS,    /* y^2 = x^3 + a x + b      */
+    MBEDTLS_ECP_TYPE_MONTGOMERY,           /* y^2 = x^3 + a x^2 + x    */
+} mbedtls_ecp_curve_type;
+
+/**
+ * Curve information, for use by other modules.
+ *
+ * The fields of this structure are part of the public API and can be
+ * accessed directly by applications. Future versions of the library may
+ * add extra fields or reorder existing fields.
+ */
+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 MBEDTLS_PRIVATE(X);          /*!< The X coordinate of the ECP point. */
+    mbedtls_mpi MBEDTLS_PRIVATE(Y);          /*!< The Y coordinate of the ECP point. */
+    mbedtls_mpi MBEDTLS_PRIVATE(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.
+ *
+ * The default implementation only initializes \p A without setting it to the
+ * authentic value for curves with <code>A = -3</code>(SECP256R1, etc), in which
+ * case you need to load \p A by yourself when using domain parameters directly,
+ * for example:
+ * \code
+ * mbedtls_mpi_init(&A);
+ * mbedtls_ecp_group_init(&grp);
+ * CHECK_RETURN(mbedtls_ecp_group_load(&grp, grp_id));
+ * if (mbedtls_ecp_group_a_is_minus_3(&grp)) {
+ *     CHECK_RETURN(mbedtls_mpi_sub_int(&A, &grp.P, 3));
+ * } else {
+ *     CHECK_RETURN(mbedtls_mpi_copy(&A, &grp.A));
+ * }
+ *
+ * do_something_with_a(&A);
+ *
+ * cleanup:
+ * mbedtls_mpi_free(&A);
+ * mbedtls_ecp_group_free(&grp);
+ * \endcode
+ *
+ * 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.
+ *
+ * \note        Alternative implementations of the ECP module must obey the
+ *              following constraints.
+ *              * Group IDs must be distinct: if two group structures have
+ *                the same ID, then they must be identical.
+ *              * The fields \c id, \c P, \c A, \c B, \c G, \c N,
+ *                \c pbits and \c nbits must have the same type and semantics
+ *                as in the built-in implementation.
+ *                They must be available for reading, but direct modification
+ *                of these fields does not need to be supported.
+ *                They do not need to be at the same offset in the structure.
+ */
+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. Note that
+                                     \p A is not set to the authentic value in some cases.
+                                     Refer to detailed description of ::mbedtls_ecp_group if
+                                     using domain parameters in the structure.
+                                     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. */
+    /* End of public fields */
+
+    unsigned int MBEDTLS_PRIVATE(h);             /*!< \internal 1 if the constants are static. */
+    int(*MBEDTLS_PRIVATE(modp))(mbedtls_mpi *);  /*!< The function for fast pseudo-reduction
+                                                    mod \p P (see above).*/
+    int(*MBEDTLS_PRIVATE(t_pre))(mbedtls_ecp_point *, void *);   /*!< Unused. */
+    int(*MBEDTLS_PRIVATE(t_post))(mbedtls_ecp_point *, void *);  /*!< Unused. */
+    void *MBEDTLS_PRIVATE(t_data);               /*!< Unused. */
+    mbedtls_ecp_point *MBEDTLS_PRIVATE(T);       /*!< Pre-computed points for ecp_mul_comb(). */
+    size_t MBEDTLS_PRIVATE(T_size);              /*!< The number of dynamic allocated 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 mbedtls_config.h, or define them using the compiler command line.
+ * \{
+ */
+
+#if !defined(MBEDTLS_ECP_WINDOW_SIZE)
+/*
+ * Maximum "window" size used for point multiplication.
+ * Default: a point where higher memory usage yields diminishing performance
+ *          returns.
+ * 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    4   /**< The maximum window size used. */
+#endif /* MBEDTLS_ECP_WINDOW_SIZE */
+
+#if !defined(MBEDTLS_ECP_FIXED_POINT_OPTIM)
+/*
+ * Trade code size 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.
+ *
+ * For each n-bit Short Weierstrass curve that is enabled, this adds 4n bytes
+ * of code size if n < 384 and 8n otherwise.
+ *
+ * Change this value to 0 to reduce code size.
+ */
+#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 */
+
+/**
+ * The maximum size of the groups, that is, of \c N and \c P.
+ */
+#if !defined(MBEDTLS_ECP_LIGHT)
+/* Dummy definition to help code that has optional ECP support and
+ * defines an MBEDTLS_ECP_MAX_BYTES-sized array unconditionally. */
+#define MBEDTLS_ECP_MAX_BITS 1
+/* Note: the curves must be listed in DECREASING size! */
+#elif defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS 521
+#elif defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS 512
+#elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS 448
+#elif defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS 384
+#elif defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS 384
+#elif defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS 256
+#elif defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS 256
+#elif defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS 256
+#elif defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS 255
+#elif defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS 225 // n is slightly above 2^224
+#elif defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS 224
+#elif defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS 192
+#elif defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
+#define MBEDTLS_ECP_MAX_BITS 192
+#else /* !MBEDTLS_ECP_LIGHT */
+#error "Missing definition of MBEDTLS_ECP_MAX_BITS"
+#endif /* !MBEDTLS_ECP_LIGHT */
+
+#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_RESTARTABLE)
+
+/**
+ * \brief           Internal restart context for multiplication
+ *
+ * \note            Opaque struct
+ */
+typedef struct mbedtls_ecp_restart_mul mbedtls_ecp_restart_mul_ctx;
+
+/**
+ * \brief           Internal restart context for ecp_muladd()
+ *
+ * \note            Opaque struct
+ */
+typedef struct mbedtls_ecp_restart_muladd mbedtls_ecp_restart_muladd_ctx;
+
+/**
+ * \brief           General context for resuming ECC operations
+ */
+typedef struct {
+    unsigned MBEDTLS_PRIVATE(ops_done);                  /*!<  current ops count             */
+    unsigned MBEDTLS_PRIVATE(depth);                     /*!<  call depth (0 = top-level)    */
+    mbedtls_ecp_restart_mul_ctx *MBEDTLS_PRIVATE(rsm);   /*!<  ecp_mul_comb() sub-context    */
+    mbedtls_ecp_restart_muladd_ctx *MBEDTLS_PRIVATE(ma); /*!<  ecp_muladd() sub-context      */
+} mbedtls_ecp_restart_ctx;
+
+/*
+ * Operation counts for restartable functions
+ */
+#define MBEDTLS_ECP_OPS_CHK   3 /*!< basic ops count for ecp_check_pubkey()  */
+#define MBEDTLS_ECP_OPS_DBL   8 /*!< basic ops count for ecp_double_jac()    */
+#define MBEDTLS_ECP_OPS_ADD  11 /*!< basic ops count for see ecp_add_mixed() */
+#define MBEDTLS_ECP_OPS_INV 120 /*!< empirical equivalent for mpi_mod_inv()  */
+
+/**
+ * \brief           Internal; for restartable functions in other modules.
+ *                  Check and update basic ops budget.
+ *
+ * \param grp       Group structure
+ * \param rs_ctx    Restart context
+ * \param ops       Number of basic ops to do
+ *
+ * \return          \c 0 if doing \p ops basic ops is still allowed,
+ * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS otherwise.
+ */
+int mbedtls_ecp_check_budget(const mbedtls_ecp_group *grp,
+                             mbedtls_ecp_restart_ctx *rs_ctx,
+                             unsigned ops);
+
+/* Utility macro for checking and updating ops budget */
+#define MBEDTLS_ECP_BUDGET(ops)   \
+    MBEDTLS_MPI_CHK(mbedtls_ecp_check_budget(grp, rs_ctx, \
+                                             (unsigned) (ops)));
+
+#else /* MBEDTLS_ECP_RESTARTABLE */
+
+#define MBEDTLS_ECP_BUDGET(ops)     /* no-op; for compatibility */
+
+/* We want to declare restartable versions of existing functions anyway */
+typedef void mbedtls_ecp_restart_ctx;
+
+#endif /* MBEDTLS_ECP_RESTARTABLE */
+
+/**
+ * \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 MBEDTLS_PRIVATE(grp);      /*!<  Elliptic curve and base point     */
+    mbedtls_mpi MBEDTLS_PRIVATE(d);              /*!<  our secret value                  */
+    mbedtls_ecp_point MBEDTLS_PRIVATE(Q);        /*!<  our public value                  */
+}
+mbedtls_ecp_keypair;
+
+/**
+ * The uncompressed point format for Short Weierstrass curves
+ * (MBEDTLS_ECP_DP_SECP_XXX and MBEDTLS_ECP_DP_BP_XXX).
+ */
+#define MBEDTLS_ECP_PF_UNCOMPRESSED    0
+/**
+ * The compressed point format for Short Weierstrass curves
+ * (MBEDTLS_ECP_DP_SECP_XXX and MBEDTLS_ECP_DP_BP_XXX).
+ *
+ * \warning     While this format is supported for all concerned curves for
+ *              writing, when it comes to parsing, it is not supported for all
+ *              curves. Specifically, parsing compressed points on
+ *              MBEDTLS_ECP_DP_SECP224R1 and MBEDTLS_ECP_DP_SECP224K1 is not
+ *              supported.
+ */
+#define MBEDTLS_ECP_PF_COMPRESSED      1
+
+/*
+ * Some other constants from RFC 4492
+ */
+#define MBEDTLS_ECP_TLS_NAMED_CURVE    3   /**< The named_curve of ECCurveType. */
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+/**
+ * \brief           Set the maximum number of basic operations done in a row.
+ *
+ *                  If more operations are needed to complete a computation,
+ *                  #MBEDTLS_ERR_ECP_IN_PROGRESS will be returned by the
+ *                  function performing the computation. It is then the
+ *                  caller's responsibility to either call again with the same
+ *                  parameters until it returns 0 or an error code; or to free
+ *                  the restart context if the operation is to be aborted.
+ *
+ *                  It is strictly required that all input parameters and the
+ *                  restart context be the same on successive calls for the
+ *                  same operation, but output parameters need not be the
+ *                  same; they must not be used until the function finally
+ *                  returns 0.
+ *
+ *                  This only applies to functions whose documentation
+ *                  mentions they may return #MBEDTLS_ERR_ECP_IN_PROGRESS (or
+ *                  #MBEDTLS_ERR_SSL_CRYPTO_IN_PROGRESS for functions in the
+ *                  SSL module). For functions that accept a "restart context"
+ *                  argument, passing NULL disables restart and makes the
+ *                  function equivalent to the function with the same name
+ *                  with \c _restartable removed. For functions in the ECDH
+ *                  module, restart is disabled unless the function accepts
+ *                  an "ECDH context" argument and
+ *                  mbedtls_ecdh_enable_restart() was previously called on
+ *                  that context. For function in the SSL module, restart is
+ *                  only enabled for specific sides and key exchanges
+ *                  (currently only for clients and ECDHE-ECDSA).
+ *
+ * \warning         Using the PSA interruptible interfaces with keys in local
+ *                  storage and no accelerator driver will also call this
+ *                  function to set the values specified via those interfaces,
+ *                  overwriting values previously set. Care should be taken if
+ *                  mixing these two interfaces.
+ *
+ * \param max_ops   Maximum number of basic operations done in a row.
+ *                  Default: 0 (unlimited).
+ *                  Lower (non-zero) values mean ECC functions will block for
+ *                  a lesser maximum amount of time.
+ *
+ * \note            A "basic operation" is defined as a rough equivalent of a
+ *                  multiplication in GF(p) for the NIST P-256 curve.
+ *                  As an indication, with default settings, a scalar
+ *                  multiplication (full run of \c mbedtls_ecp_mul()) is:
+ *                  - about 3300 basic operations for P-256
+ *                  - about 9400 basic operations for P-384
+ *
+ * \note            Very low values are not always respected: sometimes
+ *                  functions need to block for a minimum number of
+ *                  operations, and will do so even if max_ops is set to a
+ *                  lower value.  That minimum depends on the curve size, and
+ *                  can be made lower by decreasing the value of
+ *                  \c MBEDTLS_ECP_WINDOW_SIZE.  As an indication, here is the
+ *                  lowest effective value for various curves and values of
+ *                  that parameter (w for short):
+ *                          w=6     w=5     w=4     w=3     w=2
+ *                  P-256   208     208     160     136     124
+ *                  P-384   682     416     320     272     248
+ *                  P-521  1364     832     640     544     496
+ *
+ * \note            This setting is currently ignored by Curve25519.
+ */
+void mbedtls_ecp_set_max_ops(unsigned max_ops);
+
+/**
+ * \brief           Check if restart is enabled (max_ops != 0)
+ *
+ * \return          \c 0 if \c max_ops == 0 (restart disabled)
+ * \return          \c 1 otherwise (restart enabled)
+ */
+int mbedtls_ecp_restart_is_enabled(void);
+#endif /* MBEDTLS_ECP_RESTARTABLE */
+
+/*
+ * Get the type of a curve
+ */
+mbedtls_ecp_curve_type mbedtls_ecp_get_type(const mbedtls_ecp_group *grp);
+
+/**
+ * \brief           This function retrieves the information defined in
+ *                  mbedtls_ecp_curve_info() for all supported curves.
+ *
+ * \note            This function returns information about all curves
+ *                  supported by the library. Some curves may not be
+ *                  supported for all algorithms. Call mbedtls_ecdh_can_do()
+ *                  or mbedtls_ecdsa_can_do() to check if a curve is
+ *                  supported for ECDH or ECDSA.
+ *
+ * \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.
+ *
+ * \note            This function returns information about all curves
+ *                  supported by the library. Some curves may not be
+ *                  supported for all algorithms. Call mbedtls_ecdh_can_do()
+ *                  or mbedtls_ecdsa_can_do() to check if a curve is
+ *                  supported for ECDH or ECDSA.
+ *
+ * \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_group_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. This may be \c NULL, in which
+ *                  case this function returns immediately. If it is not
+ *                  \c NULL, it must point to an initialized ECP group.
+ */
+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. This may be \c NULL, in which
+ *                  case this function returns immediately. If it is not
+ *                  \c NULL, it must point to an initialized ECP key pair.
+ */
+void mbedtls_ecp_keypair_free(mbedtls_ecp_keypair *key);
+
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+/**
+ * \brief           Initialize a restart context.
+ *
+ * \param ctx       The restart context to initialize. This must
+ *                  not be \c NULL.
+ */
+void mbedtls_ecp_restart_init(mbedtls_ecp_restart_ctx *ctx);
+
+/**
+ * \brief           Free the components of a restart context.
+ *
+ * \param ctx       The restart context to free. This may be \c NULL, in which
+ *                  case this function returns immediately. If it is not
+ *                  \c NULL, it must point to an initialized restart context.
+ */
+void mbedtls_ecp_restart_free(mbedtls_ecp_restart_ctx *ctx);
+#endif /* MBEDTLS_ECP_RESTARTABLE */
+
+/**
+ * \brief           This function copies the contents of point \p Q into
+ *                  point \p P.
+ *
+ * \param P         The destination point. This must be initialized.
+ * \param Q         The source point. This must be initialized.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
+ * \return          Another negative error code for other kinds of 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. This must be initialized.
+ * \param src       The source group. This must be initialized.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
+ * \return          Another negative error code on other kinds of failure.
+ */
+int mbedtls_ecp_group_copy(mbedtls_ecp_group *dst,
+                           const mbedtls_ecp_group *src);
+
+/**
+ * \brief           This function sets a point to the point at infinity.
+ *
+ * \param pt        The point to set. This must be initialized.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
+ * \return          Another negative error code on other kinds of failure.
+ */
+int mbedtls_ecp_set_zero(mbedtls_ecp_point *pt);
+
+/**
+ * \brief           This function checks if a point is the point at infinity.
+ *
+ * \param pt        The point to test. This must be initialized.
+ *
+ * \return          \c 1 if the point is zero.
+ * \return          \c 0 if the point is non-zero.
+ * \return          A negative error code on failure.
+ */
+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. This must be initialized.
+ * \param Q         The second point to compare. This must be initialized.
+ *
+ * \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. This must be initialized.
+ * \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.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param P         The point to export. This must be initialized.
+ * \param format    The point format. This must be either
+ *                  #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED.
+ *                  (For groups without these formats, this parameter is
+ *                  ignored. But it still has to be either of the above
+ *                  values.)
+ * \param olen      The address at which to store the length of
+ *                  the output in Bytes. This must not be \c NULL.
+ * \param buf       The output buffer. This must be a writable buffer
+ *                  of length \p buflen Bytes.
+ * \param buflen    The length of the output buffer \p buf in Bytes.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output buffer
+ *                  is too small to hold the point.
+ * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format
+ *                  or the export for the given group is not implemented.
+ * \return          Another negative error code on other kinds of 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.
+ *
+ * \note            For compressed points, see #MBEDTLS_ECP_PF_COMPRESSED for
+ *                  limitations.
+ *
+ * \param grp       The group to which the point should belong.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param P         The destination context to import the point to.
+ *                  This must be initialized.
+ * \param buf       The input buffer. This must be a readable buffer
+ *                  of length \p ilen Bytes.
+ * \param ilen      The length of the input buffer \p buf in Bytes.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
+ * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
+ * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the import for the
+ *                  given group 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 immediately
+ *                  after the ECPoint record.
+ *
+ * \param grp       The ECP group to use.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \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
+ *                  defined in RFC 4492, Section 5.4.
+ *
+ * \param grp       The ECP group to use.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param pt        The point to be exported. This must be initialized.
+ * \param format    The point format to use. This must be either
+ *                  #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED.
+ * \param olen      The address at which to store the length in Bytes
+ *                  of the data written.
+ * \param buf       The target buffer. This must be a writable buffer of
+ *                  length \p blen Bytes.
+ * \param blen      The length of the target buffer \p buf in Bytes.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
+ * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the target buffer
+ *                  is too small to hold the exported point.
+ * \return          Another negative error code on other kinds of 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 up an ECP group context
+ *                  from a standardized set of 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 group context to setup. This must be initialized.
+ * \param id        The identifier of the domain parameter set to load.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p id doesn't
+ *                  correspond to a known group.
+ * \return          Another negative error code on other kinds of failure.
+ */
+int mbedtls_ecp_group_load(mbedtls_ecp_group *grp, mbedtls_ecp_group_id id);
+
+/**
+ * \brief           This function sets up an ECP group context from a TLS
+ *                  ECParameters record as defined in RFC 4492, Section 5.4.
+ *
+ * \note            The read pointer \p buf is updated to point right after
+ *                  the ECParameters record on exit.
+ *
+ * \param grp       The group context to setup. This must be initialized.
+ * \param buf       The address of the pointer to the start of the input buffer.
+ * \param len       The length of the input buffer \c *buf in Bytes.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
+ * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
+ *                  recognized.
+ * \return          Another negative error code on other kinds of failure.
+ */
+int mbedtls_ecp_tls_read_group(mbedtls_ecp_group *grp,
+                               const unsigned char **buf, size_t len);
+
+/**
+ * \brief           This function extracts an elliptic curve group ID from a
+ *                  TLS ECParameters record as defined in RFC 4492, Section 5.4.
+ *
+ * \note            The read pointer \p buf is updated to point right after
+ *                  the ECParameters record on exit.
+ *
+ * \param grp       The address at which to store the group id.
+ *                  This must not be \c NULL.
+ * \param buf       The address of the pointer to the start of the input buffer.
+ * \param len       The length of the input buffer \c *buf in Bytes.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
+ * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
+ *                  recognized.
+ * \return          Another negative error code on other kinds of failure.
+ */
+int mbedtls_ecp_tls_read_group_id(mbedtls_ecp_group_id *grp,
+                                  const unsigned char **buf,
+                                  size_t len);
+/**
+ * \brief           This function exports an elliptic curve as a TLS
+ *                  ECParameters record as defined in RFC 4492, Section 5.4.
+ *
+ * \param grp       The ECP group to be exported.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param olen      The address at which to store the number of Bytes written.
+ *                  This must not be \c NULL.
+ * \param buf       The buffer to write to. This must be a writable buffer
+ *                  of length \p blen Bytes.
+ * \param blen      The length of the output buffer \p buf in Bytes.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output
+ *                  buffer is too small to hold the exported group.
+ * \return          Another negative error code on other kinds of 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 a scalar 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. It also uses
+ *                  \p f_rng to randomize some intermediate results.
+ *
+ * \param grp       The ECP group to use.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param R         The point in which to store the result of the calculation.
+ *                  This must be initialized.
+ * \param m         The integer by which to multiply. This must be initialized.
+ * \param P         The point to multiply. This must be initialized.
+ * \param f_rng     The RNG function. This must not be \c NULL.
+ * \param p_rng     The RNG context to be passed to \p f_rng. This may be \c
+ *                  NULL if \p f_rng doesn't need a 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.
+ * \return          Another negative error code on other kinds of 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 of a point by
+ *                  an integer: \p R = \p m * \p P in a restartable way.
+ *
+ * \see             mbedtls_ecp_mul()
+ *
+ * \note            This function does the same as \c mbedtls_ecp_mul(), but
+ *                  it can return early and restart according to the limit set
+ *                  with \c mbedtls_ecp_set_max_ops() to reduce blocking.
+ *
+ * \param grp       The ECP group to use.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param R         The point in which to store the result of the calculation.
+ *                  This must be initialized.
+ * \param m         The integer by which to multiply. This must be initialized.
+ * \param P         The point to multiply. This must be initialized.
+ * \param f_rng     The RNG function. This must not be \c NULL.
+ * \param p_rng     The RNG context to be passed to \p f_rng. This may be \c
+ *                  NULL if \p f_rng doesn't need a context.
+ * \param rs_ctx    The restart context (NULL disables restart).
+ *
+ * \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.
+ * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
+ *                  operations was reached: see \c mbedtls_ecp_set_max_ops().
+ * \return          Another negative error code on other kinds of failure.
+ */
+int mbedtls_ecp_mul_restartable(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,
+                                mbedtls_ecp_restart_ctx *rs_ctx);
+
+#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
+/**
+ * \brief           This function checks if domain parameter A of the curve is
+ *                  \c -3.
+ *
+ * \note            This function is only defined for short Weierstrass curves.
+ *                  It may not be included in builds without any short
+ *                  Weierstrass curve.
+ *
+ * \param grp       The ECP group to use.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ *
+ * \return          \c 1 if <code>A = -3</code>.
+ * \return          \c 0 Otherwise.
+ */
+static inline int mbedtls_ecp_group_a_is_minus_3(const mbedtls_ecp_group *grp)
+{
+    return grp->A.MBEDTLS_PRIVATE(p) == NULL;
+}
+
+/**
+ * \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.
+ *
+ * \note            This function is only defined for short Weierstrass curves.
+ *                  It may not be included in builds without any short
+ *                  Weierstrass curve.
+ *
+ * \param grp       The ECP group to use.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param R         The point in which to store the result of the calculation.
+ *                  This must be initialized.
+ * \param m         The integer by which to multiply \p P.
+ *                  This must be initialized.
+ * \param P         The point to multiply by \p m. This must be initialized.
+ * \param n         The integer by which to multiply \p Q.
+ *                  This must be initialized.
+ * \param Q         The point to be multiplied by \p n.
+ *                  This must be initialized.
+ *
+ * \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.
+ * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not
+ *                  designate a short Weierstrass curve.
+ * \return          Another negative error code on other kinds of 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 performs multiplication and addition of two
+ *                  points by integers: \p R = \p m * \p P + \p n * \p Q in a
+ *                  restartable way.
+ *
+ * \see             \c mbedtls_ecp_muladd()
+ *
+ * \note            This function works the same as \c mbedtls_ecp_muladd(),
+ *                  but it can return early and restart according to the limit
+ *                  set with \c mbedtls_ecp_set_max_ops() to reduce blocking.
+ *
+ * \note            This function is only defined for short Weierstrass curves.
+ *                  It may not be included in builds without any short
+ *                  Weierstrass curve.
+ *
+ * \param grp       The ECP group to use.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param R         The point in which to store the result of the calculation.
+ *                  This must be initialized.
+ * \param m         The integer by which to multiply \p P.
+ *                  This must be initialized.
+ * \param P         The point to multiply by \p m. This must be initialized.
+ * \param n         The integer by which to multiply \p Q.
+ *                  This must be initialized.
+ * \param Q         The point to be multiplied by \p n.
+ *                  This must be initialized.
+ * \param rs_ctx    The restart context (NULL disables restart).
+ *
+ * \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.
+ * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not
+ *                  designate a short Weierstrass curve.
+ * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
+ *                  operations was reached: see \c mbedtls_ecp_set_max_ops().
+ * \return          Another negative error code on other kinds of failure.
+ */
+int mbedtls_ecp_muladd_restartable(
+    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,
+    mbedtls_ecp_restart_ctx *rs_ctx);
+#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
+
+/**
+ * \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 \c 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 ECP group the point should belong to.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param pt        The point to check. This must be initialized.
+ *
+ * \return          \c 0 if the point is a valid public key.
+ * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not
+ *                  a valid public key for the given curve.
+ * \return          Another negative error code on other kinds of failure.
+ */
+int mbedtls_ecp_check_pubkey(const mbedtls_ecp_group *grp,
+                             const mbedtls_ecp_point *pt);
+
+/**
+ * \brief           This function checks that an \c 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 ECP group the private key should belong to.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param d         The integer to check. This must be initialized.
+ *
+ * \return          \c 0 if the point is a valid private key.
+ * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not a valid
+ *                  private key for the given curve.
+ * \return          Another negative error code on other kinds of failure.
+ */
+int mbedtls_ecp_check_privkey(const mbedtls_ecp_group *grp,
+                              const mbedtls_mpi *d);
+
+/**
+ * \brief           This function generates a private key.
+ *
+ * \param grp       The ECP group to generate a private key for.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param d         The destination MPI (secret part). This must be initialized.
+ * \param f_rng     The RNG function. This must not be \c NULL.
+ * \param p_rng     The RNG parameter to be passed to \p f_rng. This may be
+ *                  \c NULL if \p f_rng doesn't need a context argument.
+ *
+ * \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_privkey(const mbedtls_ecp_group *grp,
+                            mbedtls_mpi *d,
+                            int (*f_rng)(void *, unsigned char *, size_t),
+                            void *p_rng);
+
+/**
+ * \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 to generate a key pair for.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param G         The base point to use. This must be initialized
+ *                  and belong to \p grp. It replaces the default base
+ *                  point \c grp->G used by mbedtls_ecp_gen_keypair().
+ * \param d         The destination MPI (secret part).
+ *                  This must be initialized.
+ * \param Q         The destination point (public part).
+ *                  This must be initialized.
+ * \param f_rng     The RNG function. This must not be \c NULL.
+ * \param p_rng     The RNG context to be passed to \p f_rng. This may
+ *                  be \c NULL if \p f_rng doesn't need a context argument.
+ *
+ * \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 to generate a key pair for.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param d         The destination MPI (secret part).
+ *                  This must be initialized.
+ * \param Q         The destination point (public part).
+ *                  This must be initialized.
+ * \param f_rng     The RNG function. This must not be \c NULL.
+ * \param p_rng     The RNG context to be passed to \p f_rng. This may
+ *                  be \c NULL if \p f_rng doesn't need a context argument.
+ *
+ * \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. This must be initialized.
+ * \param f_rng     The RNG function to use. This must not be \c NULL.
+ * \param p_rng     The RNG context to be passed to \p f_rng. This may
+ *                  be \c NULL if \p f_rng doesn't need a context argument.
+ *
+ * \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 reads an elliptic curve private key.
+ *
+ * \param grp_id    The ECP group identifier.
+ * \param key       The destination key.
+ * \param buf       The buffer containing the binary representation of the
+ *                  key. (Big endian integer for Weierstrass curves, byte
+ *                  string for Montgomery curves.)
+ * \param buflen    The length of the buffer in bytes.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_ECP_INVALID_KEY error if the key is
+ *                  invalid.
+ * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
+ * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for
+ *                  the group is not implemented.
+ * \return          Another negative error code on different kinds of failure.
+ */
+int mbedtls_ecp_read_key(mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
+                         const unsigned char *buf, size_t buflen);
+
+/**
+ * \brief           This function exports an elliptic curve private key.
+ *
+ * \param key       The private key.
+ * \param buf       The output buffer for containing the binary representation
+ *                  of the key. (Big endian integer for Weierstrass curves, byte
+ *                  string for Montgomery curves.)
+ * \param buflen    The total length of the buffer in bytes.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the \p key
+                    representation is larger than the available space in \p buf.
+ * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for
+ *                  the group is not implemented.
+ * \return          Another negative error code on different kinds of failure.
+ */
+int mbedtls_ecp_write_key(mbedtls_ecp_keypair *key,
+                          unsigned char *buf, size_t buflen);
+
+/**
+ * \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. This
+ *                  must be initialized. If it contains a private key, that
+ *                  part is ignored.
+ * \param prv       The keypair structure holding the full keypair.
+ *                  This must be initialized.
+ * \param f_rng     The RNG function. This must not be \c NULL.
+ * \param p_rng     The RNG context to be passed to \p f_rng. This may be \c
+ *                  NULL if \p f_rng doesn't need a context.
+ *
+ * \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,
+    int (*f_rng)(void *, unsigned char *, size_t), void *p_rng);
+
+/**
+ * \brief           This function exports generic key-pair parameters.
+ *
+ * \param key       The key pair to export from.
+ * \param grp       Slot for exported ECP group.
+ *                  It must point to an initialized ECP group.
+ * \param d         Slot for the exported secret value.
+ *                  It must point to an initialized mpi.
+ * \param Q         Slot for the exported public value.
+ *                  It must point to an initialized ECP point.
+ *
+ * \return          \c 0 on success,
+ * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
+ * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if key id doesn't
+ *                  correspond to a known group.
+ * \return          Another negative error code on other kinds of failure.
+ */
+int mbedtls_ecp_export(const mbedtls_ecp_keypair *key, mbedtls_ecp_group *grp,
+                       mbedtls_mpi *d, mbedtls_ecp_point *Q);
+
+#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 */