text: /**
   * \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
   *
   *  This file is provided under the Apache License 2.0, or the
   *  GNU General Public License v2.0 or later.
   *
   *  **********
   *  Apache License 2.0:
   *
   *  Licensed under the Apache License, Version 2.0 (the "License"); you may
   *  not use this file except in compliance with the License.
   *  You may obtain a copy of the License at
   *
   *  http://www.apache.org/licenses/LICENSE-2.0
   *
   *  Unless required by applicable law or agreed to in writing, software
   *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
   *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   *  See the License for the specific language governing permissions and
   *  limitations under the License.
   *
   *  **********
   *
   *  **********
   *  GNU General Public License v2.0 or later:
   *
   *  This program is free software; you can redistribute it and/or modify
   *  it under the terms of the GNU General Public License as published by
   *  the Free Software Foundation; either version 2 of the License, or
   *  (at your option) any later version.
   *
   *  This program is distributed in the hope that it will be useful,
   *  but WITHOUT ANY WARRANTY; without even the implied warranty of
   *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   *  GNU General Public License for more details.
   *
   *  You should have received a copy of the GNU General Public License along
   *  with this program; if not, write to the Free Software Foundation, Inc.,
   *  51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
   *
   *  **********
   */
  
  #ifndef BLCRYPTO_SUITE_ECP_H
  #define BLCRYPTO_SUITE_ECP_H
  
  #if !defined(BLCRYPTO_SUITE_CONFIG_FILE)
  #include "blcrypto_suite/blcrypto_suite_config.h"
  #else
  #include BLCRYPTO_SUITE_CONFIG_FILE
  #endif
  
  #include "blcrypto_suite/blcrypto_suite_bignum.h"
  
  /*
   * ECP error codes
   */
  #define BLCRYPTO_SUITE_ERR_ECP_BAD_INPUT_DATA                    -0x4F80  /**< Bad input parameters to function. */
  #define BLCRYPTO_SUITE_ERR_ECP_BUFFER_TOO_SMALL                  -0x4F00  /**< The buffer is too small to write to. */
  #define BLCRYPTO_SUITE_ERR_ECP_FEATURE_UNAVAILABLE               -0x4E80  /**< The requested feature is not available, for example, the requested curve is not supported. */
  #define BLCRYPTO_SUITE_ERR_ECP_VERIFY_FAILED                     -0x4E00  /**< The signature is not valid. */
  #define BLCRYPTO_SUITE_ERR_ECP_ALLOC_FAILED                      -0x4D80  /**< Memory allocation failed. */
  #define BLCRYPTO_SUITE_ERR_ECP_RANDOM_FAILED                     -0x4D00  /**< Generation of random value, such as ephemeral key, failed. */
  #define BLCRYPTO_SUITE_ERR_ECP_INVALID_KEY                       -0x4C80  /**< Invalid private or public key. */
  #define BLCRYPTO_SUITE_ERR_ECP_SIG_LEN_MISMATCH                  -0x4C00  /**< The buffer contains a valid signature followed by more data. */
  
  /* BLCRYPTO_SUITE_ERR_ECP_HW_ACCEL_FAILED is deprecated and should not be used. */
  #define BLCRYPTO_SUITE_ERR_ECP_HW_ACCEL_FAILED                   -0x4B80  /**< The ECP hardware accelerator failed. */
  
  #define BLCRYPTO_SUITE_ERR_ECP_IN_PROGRESS                       -0x4B00  /**< Operation in progress, call again with the same parameters to continue. */
  
  #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 blcrypto_suite_ecp_group_load().
   */
  typedef enum
  {
      BLCRYPTO_SUITE_ECP_DP_NONE = 0,       /*!< Curve not defined. */
      BLCRYPTO_SUITE_ECP_DP_SECP192R1,      /*!< Domain parameters for the 192-bit curve defined by FIPS 186-4 and SEC1. */
      BLCRYPTO_SUITE_ECP_DP_SECP224R1,      /*!< Domain parameters for the 224-bit curve defined by FIPS 186-4 and SEC1. */
      BLCRYPTO_SUITE_ECP_DP_SECP256R1,      /*!< Domain parameters for the 256-bit curve defined by FIPS 186-4 and SEC1. */
      BLCRYPTO_SUITE_ECP_DP_SECP384R1,      /*!< Domain parameters for the 384-bit curve defined by FIPS 186-4 and SEC1. */
      BLCRYPTO_SUITE_ECP_DP_SECP521R1,      /*!< Domain parameters for the 521-bit curve defined by FIPS 186-4 and SEC1. */
      BLCRYPTO_SUITE_ECP_DP_BP256R1,        /*!< Domain parameters for 256-bit Brainpool curve. */
      BLCRYPTO_SUITE_ECP_DP_BP384R1,        /*!< Domain parameters for 384-bit Brainpool curve. */
      BLCRYPTO_SUITE_ECP_DP_BP512R1,        /*!< Domain parameters for 512-bit Brainpool curve. */
      BLCRYPTO_SUITE_ECP_DP_CURVE25519,     /*!< Domain parameters for Curve25519. */
      BLCRYPTO_SUITE_ECP_DP_SECP192K1,      /*!< Domain parameters for 192-bit "Koblitz" curve. */
      BLCRYPTO_SUITE_ECP_DP_SECP224K1,      /*!< Domain parameters for 224-bit "Koblitz" curve. */
      BLCRYPTO_SUITE_ECP_DP_SECP256K1,      /*!< Domain parameters for 256-bit "Koblitz" curve. */
      BLCRYPTO_SUITE_ECP_DP_CURVE448,       /*!< Domain parameters for Curve448. */
  } blcrypto_suite_ecp_group_id;
  
  /**
   * The number of supported curves, plus one for #BLCRYPTO_SUITE_ECP_DP_NONE.
   *
   * \note Montgomery curves are currently excluded.
   */
  #define BLCRYPTO_SUITE_ECP_DP_MAX     12
  
  /**
   * Curve information, for use by other modules.
   */
  typedef struct blcrypto_suite_ecp_curve_info
  {
      blcrypto_suite_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. */
  } blcrypto_suite_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 blcrypto_suite_ecp_point
  {
      blcrypto_suite_mpi X;          /*!< The X coordinate of the ECP point. */
      blcrypto_suite_mpi Y;          /*!< The Y coordinate of the ECP point. */
      blcrypto_suite_mpi Z;          /*!< The Z coordinate of the ECP point. */
  }
  blcrypto_suite_ecp_point;
  
  #if !defined(BLCRYPTO_SUITE_ECP_ALT)
  /*
   * default mbed TLS elliptic curve arithmetic implementation
   *
   * (in case BLCRYPTO_SUITE_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 blcrypto_suite_ecp_mul() requires an odd number, and
   * blcrypto_suite_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 blcrypto_suite_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 must keep the group IDs distinct. If
   *              two group structures have the same ID, then they must be
   *              identical.
   *
   */
  typedef struct blcrypto_suite_ecp_group
  {
      blcrypto_suite_ecp_group_id id;    /*!< An internal group identifier. */
      blcrypto_suite_mpi P;              /*!< The prime modulus of the base field. */
      blcrypto_suite_mpi A;              /*!< For Short Weierstrass: \p A in the equation. For
                                       Montgomery curves: <code>(A + 2) / 4</code>. */
      blcrypto_suite_mpi B;              /*!< For Short Weierstrass: \p B in the equation.
                                       For Montgomery curves: unused. */
      blcrypto_suite_ecp_point G;        /*!< The generator of the subgroup used. */
      blcrypto_suite_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)(blcrypto_suite_mpi *); /*!< The function for fast pseudo-reduction
                                       mod \p P (see above).*/
      int (*t_pre)(blcrypto_suite_ecp_point *, void *);  /*!< Unused. */
      int (*t_post)(blcrypto_suite_ecp_point *, void *); /*!< Unused. */
      void *t_data;               /*!< Unused. */
      blcrypto_suite_ecp_point *T;       /*!< Pre-computed points for ecp_mul_comb(). */
      size_t T_size;              /*!< The number of pre-computed points. */
  }
  blcrypto_suite_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(BLCRYPTO_SUITE_ECP_MAX_BITS)
  /**
   * The maximum size of the groups, that is, of \c N and \c P.
   */
  #define BLCRYPTO_SUITE_ECP_MAX_BITS     521   /**< The maximum size of groups, in bits. */
  #endif
  
  #define BLCRYPTO_SUITE_ECP_MAX_BYTES    ( ( BLCRYPTO_SUITE_ECP_MAX_BITS + 7 ) / 8 )
  #define BLCRYPTO_SUITE_ECP_MAX_PT_LEN   ( 2 * BLCRYPTO_SUITE_ECP_MAX_BYTES + 1 )
  
  #if !defined(BLCRYPTO_SUITE_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 << ( BLCRYPTO_SUITE_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 BLCRYPTO_SUITE_ECP_WINDOW_SIZE    6   /**< The maximum window size used. */
  #endif /* BLCRYPTO_SUITE_ECP_WINDOW_SIZE */
  
  #if !defined(BLCRYPTO_SUITE_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 BLCRYPTO_SUITE_ECP_FIXED_POINT_OPTIM  1   /**< Enable fixed-point speed-up. */
  #endif /* BLCRYPTO_SUITE_ECP_FIXED_POINT_OPTIM */
  
  /* \} name SECTION: Module settings */
  
  #else  /* BLCRYPTO_SUITE_ECP_ALT */
  #include "ecp_alt.h"
  #endif /* BLCRYPTO_SUITE_ECP_ALT */
  
  #if defined(BLCRYPTO_SUITE_ECP_RESTARTABLE)
  
  /**
   * \brief           Internal restart context for multiplication
   *
   * \note            Opaque struct
   */
  typedef struct blcrypto_suite_ecp_restart_mul blcrypto_suite_ecp_restart_mul_ctx;
  
  /**
   * \brief           Internal restart context for ecp_muladd()
   *
   * \note            Opaque struct
   */
  typedef struct blcrypto_suite_ecp_restart_muladd blcrypto_suite_ecp_restart_muladd_ctx;
  
  /**
   * \brief           General context for resuming ECC operations
   */
  typedef struct
  {
      unsigned ops_done;                  /*!<  current ops count             */
      unsigned depth;                     /*!<  call depth (0 = top-level)    */
      blcrypto_suite_ecp_restart_mul_ctx *rsm;   /*!<  ecp_mul_comb() sub-context    */
      blcrypto_suite_ecp_restart_muladd_ctx *ma; /*!<  ecp_muladd() sub-context      */
  } blcrypto_suite_ecp_restart_ctx;
  
  /*
   * Operation counts for restartable functions
   */
  #define BLCRYPTO_SUITE_ECP_OPS_CHK   3 /*!< basic ops count for ecp_check_pubkey()  */
  #define BLCRYPTO_SUITE_ECP_OPS_DBL   8 /*!< basic ops count for ecp_double_jac()    */
  #define BLCRYPTO_SUITE_ECP_OPS_ADD  11 /*!< basic ops count for see ecp_add_mixed() */
  #define BLCRYPTO_SUITE_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          #BLCRYPTO_SUITE_ERR_ECP_IN_PROGRESS otherwise.
   */
  int blcrypto_suite_ecp_check_budget( const blcrypto_suite_ecp_group *grp,
                                blcrypto_suite_ecp_restart_ctx *rs_ctx,
                                unsigned ops );
  
  /* Utility macro for checking and updating ops budget */
  #define BLCRYPTO_SUITE_ECP_BUDGET( ops )   \
      BLCRYPTO_SUITE_MPI_CHK( blcrypto_suite_ecp_check_budget( grp, rs_ctx, \
                                                 (unsigned) (ops) ) );
  
  #else /* BLCRYPTO_SUITE_ECP_RESTARTABLE */
  
  #define BLCRYPTO_SUITE_ECP_BUDGET( ops )   /* no-op; for compatibility */
  
  /* We want to declare restartable versions of existing functions anyway */
  typedef void blcrypto_suite_ecp_restart_ctx;
  
  #endif /* BLCRYPTO_SUITE_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
   *          ::blcrypto_suite_ecdsa_context structure.
   */
  typedef struct blcrypto_suite_ecp_keypair
  {
      blcrypto_suite_ecp_group grp;      /*!<  Elliptic curve and base point     */
      blcrypto_suite_mpi d;              /*!<  our secret value                  */
      blcrypto_suite_ecp_point Q;        /*!<  our public value                  */
  }
  blcrypto_suite_ecp_keypair;
  
  /*
   * Point formats, from RFC 4492's enum ECPointFormat
   */
  #define BLCRYPTO_SUITE_ECP_PF_UNCOMPRESSED    0   /**< Uncompressed point format. */
  #define BLCRYPTO_SUITE_ECP_PF_COMPRESSED      1   /**< Compressed point format. */
  
  /*
   * Some other constants from RFC 4492
   */
  #define BLCRYPTO_SUITE_ECP_TLS_NAMED_CURVE    3   /**< The named_curve of ECCurveType. */
  
  #if defined(BLCRYPTO_SUITE_ECP_RESTARTABLE)
  /**
   * \brief           Set the maximum number of basic operations done in a row.
   *
   *                  If more operations are needed to complete a computation,
   *                  #BLCRYPTO_SUITE_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 #BLCRYPTO_SUITE_ERR_ECP_IN_PROGRESS (or
   *                  #BLCRYPTO_SUITE_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
   *                  blcrypto_suite_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).
   *
   * \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 blcrypto_suite_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 BLCRYPTO_SUITE_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 blcrypto_suite_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 blcrypto_suite_ecp_restart_is_enabled( void );
  #endif /* BLCRYPTO_SUITE_ECP_RESTARTABLE */
  
  /**
   * \brief           This function retrieves the information defined in
   *                  blcrypto_suite_ecp_curve_info() for all supported curves in order
   *                  of preference.
   *
   * \return          A statically allocated array. The last entry is 0.
   */
  const blcrypto_suite_ecp_curve_info *blcrypto_suite_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 BLCRYPTO_SUITE_ECP_DP_NONE.
   */
  const blcrypto_suite_ecp_group_id *blcrypto_suite_ecp_grp_id_list( void );
  
  /**
   * \brief           This function retrieves curve information from an internal
   *                  group identifier.
   *
   * \param grp_id    An \c BLCRYPTO_SUITE_ECP_DP_XXX value.
   *
   * \return          The associated curve information on success.
   * \return          NULL on failure.
   */
  const blcrypto_suite_ecp_curve_info *blcrypto_suite_ecp_curve_info_from_grp_id( blcrypto_suite_ecp_group_id grp_id );
  
  /**
   * \brief           This function retrieves curve information from a TLS
   *                  NamedCurve value.
   *
   * \param tls_id    An \c BLCRYPTO_SUITE_ECP_DP_XXX value.
   *
   * \return          The associated curve information on success.
   * \return          NULL on failure.
   */
  const blcrypto_suite_ecp_curve_info *blcrypto_suite_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 blcrypto_suite_ecp_curve_info *blcrypto_suite_ecp_curve_info_from_name( const char *name );
  
  /**
   * \brief           This function initializes a point as zero.
   *
   * \param pt        The point to initialize.
   */
  void blcrypto_suite_ecp_point_init( blcrypto_suite_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
   *                  blcrypto_suite_ecp_group_load() or blcrypto_suite_ecp_tls_read_group()
   *                  functions.
   */
  void blcrypto_suite_ecp_group_init( blcrypto_suite_ecp_group *grp );
  
  /**
   * \brief           This function initializes a key pair as an invalid one.
   *
   * \param key       The key pair to initialize.
   */
  void blcrypto_suite_ecp_keypair_init( blcrypto_suite_ecp_keypair *key );
  
  /**
   * \brief           This function frees the components of a point.
   *
   * \param pt        The point to free.
   */
  void blcrypto_suite_ecp_point_free( blcrypto_suite_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 blcrypto_suite_ecp_group_free( blcrypto_suite_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 blcrypto_suite_ecp_keypair_free( blcrypto_suite_ecp_keypair *key );
  
  #if defined(BLCRYPTO_SUITE_ECP_RESTARTABLE)
  /**
   * \brief           Initialize a restart context.
   *
   * \param ctx       The restart context to initialize. This must
   *                  not be \c NULL.
   */
  void blcrypto_suite_ecp_restart_init( blcrypto_suite_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 blcrypto_suite_ecp_restart_free( blcrypto_suite_ecp_restart_ctx *ctx );
  #endif /* BLCRYPTO_SUITE_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          #BLCRYPTO_SUITE_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
   * \return          Another negative error code for other kinds of failure.
   */
  int blcrypto_suite_ecp_copy( blcrypto_suite_ecp_point *P, const blcrypto_suite_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          #BLCRYPTO_SUITE_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
   * \return          Another negative error code on other kinds of failure.
   */
  int blcrypto_suite_ecp_group_copy( blcrypto_suite_ecp_group *dst,
                              const blcrypto_suite_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          #BLCRYPTO_SUITE_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
   * \return          Another negative error code on other kinds of failure.
   */
  int blcrypto_suite_ecp_set_zero( blcrypto_suite_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 blcrypto_suite_ecp_is_zero( blcrypto_suite_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          #BLCRYPTO_SUITE_ERR_ECP_BAD_INPUT_DATA if the points are not equal.
   */
  int blcrypto_suite_ecp_point_cmp( const blcrypto_suite_ecp_point *P,
                             const blcrypto_suite_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 BLCRYPTO_SUITE_ERR_MPI_XXX error code on failure.
   */
  int blcrypto_suite_ecp_point_read_string( blcrypto_suite_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 blcrypto_suite_ecp_group_load().
   * \param P         The point to export. This must be initialized.
   * \param format    The point format. This must be either
   *                  #BLCRYPTO_SUITE_ECP_PF_COMPRESSED or #BLCRYPTO_SUITE_ECP_PF_UNCOMPRESSED.
   * \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          #BLCRYPTO_SUITE_ERR_ECP_BUFFER_TOO_SMALL if the output buffer
   *                  is too small to hold the point.
   * \return          Another negative error code on other kinds of failure.
   */
  int blcrypto_suite_ecp_point_write_binary( const blcrypto_suite_ecp_group *grp, const blcrypto_suite_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 blcrypto_suite_ecp_check_pubkey()
   *                  for that.
   *
   * \param grp       The group to which the point should belong.
   *                  This must be initialized and have group parameters
   *                  set, for example through blcrypto_suite_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          #BLCRYPTO_SUITE_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
   * \return          #BLCRYPTO_SUITE_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
   * \return          #BLCRYPTO_SUITE_ERR_ECP_FEATURE_UNAVAILABLE if the point format
   *                  is not implemented.
   */
  int blcrypto_suite_ecp_point_read_binary( const blcrypto_suite_ecp_group *grp,
                                     blcrypto_suite_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 blcrypto_suite_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 BLCRYPTO_SUITE_ERR_MPI_XXX error code on initialization
   *                  failure.
   * \return          #BLCRYPTO_SUITE_ERR_ECP_BAD_INPUT_DATA if input is invalid.
   */
  int blcrypto_suite_ecp_tls_read_point( const blcrypto_suite_ecp_group *grp,
                                  blcrypto_suite_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 blcrypto_suite_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
   *                  #BLCRYPTO_SUITE_ECP_PF_COMPRESSED or #BLCRYPTO_SUITE_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          #BLCRYPTO_SUITE_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
   * \return          #BLCRYPTO_SUITE_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 blcrypto_suite_ecp_tls_write_point( const blcrypto_suite_ecp_group *grp,
                                   const blcrypto_suite_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 BLCRYPTO_SUITE_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          #BLCRYPTO_SUITE_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 blcrypto_suite_ecp_group_load( blcrypto_suite_ecp_group *grp, blcrypto_suite_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          #BLCRYPTO_SUITE_ERR_ECP_BAD_INPUT_DATA if input is invalid.
   * \return          #BLCRYPTO_SUITE_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
   *                  recognized.
   * \return          Another negative error code on other kinds of failure.
   */
  int blcrypto_suite_ecp_tls_read_group( blcrypto_suite_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          #BLCRYPTO_SUITE_ERR_ECP_BAD_INPUT_DATA if input is invalid.
   * \return          #BLCRYPTO_SUITE_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
   *                  recognized.
   * \return          Another negative error code on other kinds of failure.
   */
  int blcrypto_suite_ecp_tls_read_group_id( blcrypto_suite_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 blcrypto_suite_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          #BLCRYPTO_SUITE_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 blcrypto_suite_ecp_tls_write_group( const blcrypto_suite_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.
   *
   * \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.
   *                  Note: unless #BLCRYPTO_SUITE_ECP_NO_INTERNAL_RNG is defined, when
   *                  \p f_rng is NULL, an internal RNG (seeded from the value
   *                  of \p m) will be used instead.
   *
   * \param grp       The ECP group to use.
   *                  This must be initialized and have group parameters
   *                  set, for example through blcrypto_suite_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 may be \c NULL if randomization
   *                  of intermediate results isn't desired (discouraged).
   * \param p_rng     The RNG context to be passed to \p p_rng.
   *
   * \return          \c 0 on success.
   * \return          #BLCRYPTO_SUITE_ERR_ECP_INVALID_KEY if \p m is not a valid private
   *                  key, or \p P is not a valid public key.
   * \return          #BLCRYPTO_SUITE_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
   * \return          Another negative error code on other kinds of failure.
   */
  int blcrypto_suite_ecp_mul( blcrypto_suite_ecp_group *grp, blcrypto_suite_ecp_point *R,
               const blcrypto_suite_mpi *m, const blcrypto_suite_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             blcrypto_suite_ecp_mul()
   *
   * \note            This function does the same as \c blcrypto_suite_ecp_mul(), but
   *                  it can return early and restart according to the limit set
   *                  with \c blcrypto_suite_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 blcrypto_suite_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 may be \c NULL if randomization
   *                  of intermediate results isn't desired (discouraged).
   * \param p_rng     The RNG context to be passed to \p p_rng.
   * \param rs_ctx    The restart context (NULL disables restart).
   *
   * \return          \c 0 on success.
   * \return          #BLCRYPTO_SUITE_ERR_ECP_INVALID_KEY if \p m is not a valid private
   *                  key, or \p P is not a valid public key.
   * \return          #BLCRYPTO_SUITE_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
   * \return          #BLCRYPTO_SUITE_ERR_ECP_IN_PROGRESS if maximum number of
   *                  operations was reached: see \c blcrypto_suite_ecp_set_max_ops().
   * \return          Another negative error code on other kinds of failure.
   */
  int blcrypto_suite_ecp_mul_restartable( blcrypto_suite_ecp_group *grp, blcrypto_suite_ecp_point *R,
               const blcrypto_suite_mpi *m, const blcrypto_suite_ecp_point *P,
               int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
               blcrypto_suite_ecp_restart_ctx *rs_ctx );
  
  /**
   * \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 blcrypto_suite_ecp_mul(), this function does not
   *                  guarantee a constant execution flow and timing.
   *
   * \param grp       The ECP group to use.
   *                  This must be initialized and have group parameters
   *                  set, for example through blcrypto_suite_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          #BLCRYPTO_SUITE_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          #BLCRYPTO_SUITE_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
   * \return          Another negative error code on other kinds of failure.
   */
  int blcrypto_suite_ecp_muladd( blcrypto_suite_ecp_group *grp, blcrypto_suite_ecp_point *R,
               const blcrypto_suite_mpi *m, const blcrypto_suite_ecp_point *P,
               const blcrypto_suite_mpi *n, const blcrypto_suite_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 blcrypto_suite_ecp_muladd()
   *
   * \note            This function works the same as \c blcrypto_suite_ecp_muladd(),
   *                  but it can return early and restart according to the limit
   *                  set with \c blcrypto_suite_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 blcrypto_suite_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          #BLCRYPTO_SUITE_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          #BLCRYPTO_SUITE_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
   * \return          #BLCRYPTO_SUITE_ERR_ECP_IN_PROGRESS if maximum number of
   *                  operations was reached: see \c blcrypto_suite_ecp_set_max_ops().
   * \return          Another negative error code on other kinds of failure.
   */
  int blcrypto_suite_ecp_muladd_restartable(
               blcrypto_suite_ecp_group *grp, blcrypto_suite_ecp_point *R,
               const blcrypto_suite_mpi *m, const blcrypto_suite_ecp_point *P,
               const blcrypto_suite_mpi *n, const blcrypto_suite_ecp_point *Q,
               blcrypto_suite_ecp_restart_ctx *rs_ctx );
  
  /**
   * \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
   *                  ::blcrypto_suite_ecp_keypair structure, to ease use with other
   *                  structures, such as ::blcrypto_suite_ecdh_context or
   *                  ::blcrypto_suite_ecdsa_context.
   *
   * \param grp       The ECP group the point should belong to.
   *                  This must be initialized and have group parameters
   *                  set, for example through blcrypto_suite_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          #BLCRYPTO_SUITE_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 blcrypto_suite_ecp_check_pubkey( const blcrypto_suite_ecp_group *grp,
                                const blcrypto_suite_ecp_point *pt );
  
  /**
   * \brief           This function checks that an \p blcrypto_suite_mpi is a
   *                  valid private key for this curve.
   *
   * \note            This function uses bare components rather than an
   *                  ::blcrypto_suite_ecp_keypair structure to ease use with other
   *                  structures, such as ::blcrypto_suite_ecdh_context or
   *                  ::blcrypto_suite_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 blcrypto_suite_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          #BLCRYPTO_SUITE_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 blcrypto_suite_ecp_check_privkey( const blcrypto_suite_ecp_group *grp,
                                 const blcrypto_suite_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 blcrypto_suite_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 BLCRYPTO_SUITE_ERR_ECP_XXX or \c BLCRYPTO_SUITE_MPI_XXX error code
   *                  on failure.
   */
  int blcrypto_suite_ecp_gen_privkey( const blcrypto_suite_ecp_group *grp,
                       blcrypto_suite_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
   *                  ::blcrypto_suite_ecp_keypair structure to ease use with other
   *                  structures, such as ::blcrypto_suite_ecdh_context or
   *                  ::blcrypto_suite_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 blcrypto_suite_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 blcrypto_suite_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 BLCRYPTO_SUITE_ERR_ECP_XXX or \c BLCRYPTO_SUITE_MPI_XXX error code
   *                  on failure.
   */
  int blcrypto_suite_ecp_gen_keypair_base( blcrypto_suite_ecp_group *grp,
                                    const blcrypto_suite_ecp_point *G,
                                    blcrypto_suite_mpi *d, blcrypto_suite_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
   *                  ::blcrypto_suite_ecp_keypair structure to ease use with other
   *                  structures, such as ::blcrypto_suite_ecdh_context or
   *                  ::blcrypto_suite_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 blcrypto_suite_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 BLCRYPTO_SUITE_ERR_ECP_XXX or \c BLCRYPTO_SUITE_MPI_XXX error code
   *                  on failure.
   */
  int blcrypto_suite_ecp_gen_keypair( blcrypto_suite_ecp_group *grp, blcrypto_suite_mpi *d,
                               blcrypto_suite_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 BLCRYPTO_SUITE_ERR_ECP_XXX or \c BLCRYPTO_SUITE_MPI_XXX error code
   *                  on failure.
   */
  int blcrypto_suite_ecp_gen_key( blcrypto_suite_ecp_group_id grp_id, blcrypto_suite_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. 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.
   *
   * \return          \c 0 on success, meaning that the keys are valid and match.
   * \return          #BLCRYPTO_SUITE_ERR_ECP_BAD_INPUT_DATA if the keys are invalid or do not match.
   * \return          An \c BLCRYPTO_SUITE_ERR_ECP_XXX or an \c BLCRYPTO_SUITE_ERR_MPI_XXX
   *                  error code on calculation failure.
   */
  int blcrypto_suite_ecp_check_pub_priv( const blcrypto_suite_ecp_keypair *pub,
                                  const blcrypto_suite_ecp_keypair *prv );
  
  #if defined(BLCRYPTO_SUITE_SELF_TEST)
  
  /**
   * \brief          The ECP checkup routine.
   *
   * \return         \c 0 on success.
   * \return         \c 1 on failure.
   */
  int blcrypto_suite_ecp_self_test( int verbose );
  
  #endif /* BLCRYPTO_SUITE_SELF_TEST */
  
  #ifdef __cplusplus
  }
  #endif
  
  #endif /* ecp.h */
  