ecp.h

00001 /**
00002  * \file ecp.h
00003  *
00004  * \brief Elliptic curves over GF(p)
00005  *
00006  *  Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
00007  *  SPDX-License-Identifier: Apache-2.0
00008  *
00009  *  Licensed under the Apache License, Version 2.0 (the "License"); you may
00010  *  not use this file except in compliance with the License.
00011  *  You may obtain a copy of the License at
00012  *
00013  *  http://www.apache.org/licenses/LICENSE-2.0
00014  *
00015  *  Unless required by applicable law or agreed to in writing, software
00016  *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
00017  *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
00018  *  See the License for the specific language governing permissions and
00019  *  limitations under the License.
00020  *
00021  *  This file is part of mbed TLS (https://tls.mbed.org)
00022  */
00023 #ifndef MBEDTLS_ECP_H
00024 #define MBEDTLS_ECP_H
00025 
00026 #include "bignum.h"
00027 
00028 /*
00029  * ECP error codes
00030  */
00031 #define MBEDTLS_ERR_ECP_BAD_INPUT_DATA                    -0x4F80  /**< Bad input parameters to function. */
00032 #define MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL                  -0x4F00  /**< The buffer is too small to write to. */
00033 #define MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE               -0x4E80  /**< Requested curve not available. */
00034 #define MBEDTLS_ERR_ECP_VERIFY_FAILED                     -0x4E00  /**< The signature is not valid. */
00035 #define MBEDTLS_ERR_ECP_ALLOC_FAILED                      -0x4D80  /**< Memory allocation failed. */
00036 #define MBEDTLS_ERR_ECP_RANDOM_FAILED                     -0x4D00  /**< Generation of random value, such as (ephemeral) key, failed. */
00037 #define MBEDTLS_ERR_ECP_INVALID_KEY                       -0x4C80  /**< Invalid private or public key. */
00038 #define MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH                  -0x4C00  /**< Signature is valid but shorter than the user-supplied length. */
00039 
00040 #if !defined(MBEDTLS_ECP_ALT)
00041 /*
00042  * default mbed TLS elliptic curve arithmetic implementation
00043  *
00044  * (in case MBEDTLS_ECP_ALT is defined then the developer has to provide an
00045  * alternative implementation for the whole module and it will replace this
00046  * one.)
00047  */
00048 
00049 #ifdef __cplusplus
00050 extern "C" {
00051 #endif
00052 
00053 /**
00054  * Domain parameters (curve, subgroup and generator) identifiers.
00055  *
00056  * Only curves over prime fields are supported.
00057  *
00058  * \warning This library does not support validation of arbitrary domain
00059  * parameters. Therefore, only well-known domain parameters from trusted
00060  * sources should be used. See mbedtls_ecp_group_load().
00061  */
00062 typedef enum
00063 {
00064     MBEDTLS_ECP_DP_NONE = 0,
00065     MBEDTLS_ECP_DP_SECP192R1,      /*!< 192-bits NIST curve  */
00066     MBEDTLS_ECP_DP_SECP224R1,      /*!< 224-bits NIST curve  */
00067     MBEDTLS_ECP_DP_SECP256R1,      /*!< 256-bits NIST curve  */
00068     MBEDTLS_ECP_DP_SECP384R1,      /*!< 384-bits NIST curve  */
00069     MBEDTLS_ECP_DP_SECP521R1,      /*!< 521-bits NIST curve  */
00070     MBEDTLS_ECP_DP_BP256R1,        /*!< 256-bits Brainpool curve */
00071     MBEDTLS_ECP_DP_BP384R1,        /*!< 384-bits Brainpool curve */
00072     MBEDTLS_ECP_DP_BP512R1,        /*!< 512-bits Brainpool curve */
00073     MBEDTLS_ECP_DP_CURVE25519,           /*!< Curve25519               */
00074     MBEDTLS_ECP_DP_SECP192K1,      /*!< 192-bits "Koblitz" curve */
00075     MBEDTLS_ECP_DP_SECP224K1,      /*!< 224-bits "Koblitz" curve */
00076     MBEDTLS_ECP_DP_SECP256K1,      /*!< 256-bits "Koblitz" curve */
00077 } mbedtls_ecp_group_id;
00078 
00079 /**
00080  * Number of supported curves (plus one for NONE).
00081  *
00082  * (Montgomery curves excluded for now.)
00083  */
00084 #define MBEDTLS_ECP_DP_MAX     12
00085 
00086 /**
00087  * Curve information for use by other modules
00088  */
00089 typedef struct
00090 {
00091     mbedtls_ecp_group_id grp_id ;    /*!< Internal identifier        */
00092     uint16_t tls_id ;                /*!< TLS NamedCurve identifier  */
00093     uint16_t bit_size ;              /*!< Curve size in bits         */
00094     const char *name ;               /*!< Human-friendly name        */
00095 } mbedtls_ecp_curve_info;
00096 
00097 /**
00098  * \brief           ECP point structure (jacobian coordinates)
00099  *
00100  * \note            All functions expect and return points satisfying
00101  *                  the following condition: Z == 0 or Z == 1. (Other
00102  *                  values of Z are used by internal functions only.)
00103  *                  The point is zero, or "at infinity", if Z == 0.
00104  *                  Otherwise, X and Y are its standard (affine) coordinates.
00105  */
00106 typedef struct
00107 {
00108     mbedtls_mpi X ;          /*!<  the point's X coordinate  */
00109     mbedtls_mpi Y ;          /*!<  the point's Y coordinate  */
00110     mbedtls_mpi Z ;          /*!<  the point's Z coordinate  */
00111 }
00112 mbedtls_ecp_point;
00113 
00114 /**
00115  * \brief           ECP group structure
00116  *
00117  * We consider two types of curves equations:
00118  * 1. Short Weierstrass y^2 = x^3 + A x + B     mod P   (SEC1 + RFC 4492)
00119  * 2. Montgomery,       y^2 = x^3 + A x^2 + x   mod P   (Curve25519 + draft)
00120  * In both cases, a generator G for a prime-order subgroup is fixed. In the
00121  * short weierstrass, this subgroup is actually the whole curve, and its
00122  * cardinal is denoted by N.
00123  *
00124  * In the case of Short Weierstrass curves, our code requires that N is an odd
00125  * prime. (Use odd in mbedtls_ecp_mul() and prime in mbedtls_ecdsa_sign() for blinding.)
00126  *
00127  * In the case of Montgomery curves, we don't store A but (A + 2) / 4 which is
00128  * the quantity actually used in the formulas. Also, nbits is not the size of N
00129  * but the required size for private keys.
00130  *
00131  * If modp is NULL, reduction modulo P is done using a generic algorithm.
00132  * Otherwise, it must point to a function that takes an mbedtls_mpi in the range
00133  * 0..2^(2*pbits)-1 and transforms it in-place in an integer of little more
00134  * than pbits, so that the integer may be efficiently brought in the 0..P-1
00135  * range by a few additions or substractions. It must return 0 on success and
00136  * non-zero on failure.
00137  */
00138 typedef struct
00139 {
00140     mbedtls_ecp_group_id id ;    /*!<  internal group identifier                     */
00141     mbedtls_mpi P ;              /*!<  prime modulus of the base field               */
00142     mbedtls_mpi A ;              /*!<  1. A in the equation, or 2. (A + 2) / 4       */
00143     mbedtls_mpi B ;              /*!<  1. B in the equation, or 2. unused            */
00144     mbedtls_ecp_point G ;        /*!<  generator of the (sub)group used              */
00145     mbedtls_mpi N ;              /*!<  1. the order of G, or 2. unused               */
00146     size_t pbits ;       /*!<  number of bits in P                           */
00147     size_t nbits ;       /*!<  number of bits in 1. P, or 2. private keys    */
00148     unsigned int h ;     /*!<  internal: 1 if the constants are static       */
00149     int (*modp)(mbedtls_mpi *); /*!<  function for fast reduction mod P             */
00150     int (*t_pre)(mbedtls_ecp_point *, void *);  /*!< unused                         */
00151     int (*t_post)(mbedtls_ecp_point *, void *); /*!< unused                         */
00152     void *t_data ;                       /*!< unused                         */
00153     mbedtls_ecp_point *T ;       /*!<  pre-computed points for ecp_mul_comb()        */
00154     size_t T_size ;      /*!<  number for pre-computed points                */
00155 }
00156 mbedtls_ecp_group;
00157 
00158 /**
00159  * \brief           ECP key pair structure
00160  *
00161  * A generic key pair that could be used for ECDSA, fixed ECDH, etc.
00162  *
00163  * \note Members purposefully in the same order as struc mbedtls_ecdsa_context.
00164  */
00165 typedef struct
00166 {
00167     mbedtls_ecp_group grp ;      /*!<  Elliptic curve and base point     */
00168     mbedtls_mpi d ;              /*!<  our secret value                  */
00169     mbedtls_ecp_point Q ;        /*!<  our public value                  */
00170 }
00171 mbedtls_ecp_keypair;
00172 
00173 /**
00174  * \name SECTION: Module settings
00175  *
00176  * The configuration options you can set for this module are in this section.
00177  * Either change them in config.h or define them on the compiler command line.
00178  * \{
00179  */
00180 
00181 #if !defined(MBEDTLS_ECP_MAX_BITS)
00182 /**
00183  * Maximum size of the groups (that is, of N and P)
00184  */
00185 #define MBEDTLS_ECP_MAX_BITS     521   /**< Maximum bit size of groups */
00186 #endif
00187 
00188 #define MBEDTLS_ECP_MAX_BYTES    ( ( MBEDTLS_ECP_MAX_BITS + 7 ) / 8 )
00189 #define MBEDTLS_ECP_MAX_PT_LEN   ( 2 * MBEDTLS_ECP_MAX_BYTES + 1 )
00190 
00191 #if !defined(MBEDTLS_ECP_WINDOW_SIZE)
00192 /*
00193  * Maximum "window" size used for point multiplication.
00194  * Default: 6.
00195  * Minimum value: 2. Maximum value: 7.
00196  *
00197  * Result is an array of at most ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
00198  * points used for point multiplication. This value is directly tied to EC
00199  * peak memory usage, so decreasing it by one should roughly cut memory usage
00200  * by two (if large curves are in use).
00201  *
00202  * Reduction in size may reduce speed, but larger curves are impacted first.
00203  * Sample performances (in ECDHE handshakes/s, with FIXED_POINT_OPTIM = 1):
00204  *      w-size:     6       5       4       3       2
00205  *      521       145     141     135     120      97
00206  *      384       214     209     198     177     146
00207  *      256       320     320     303     262     226
00208 
00209  *      224       475     475     453     398     342
00210  *      192       640     640     633     587     476
00211  */
00212 #define MBEDTLS_ECP_WINDOW_SIZE    6   /**< Maximum window size used */
00213 #endif /* MBEDTLS_ECP_WINDOW_SIZE */
00214 
00215 #if !defined(MBEDTLS_ECP_FIXED_POINT_OPTIM)
00216 /*
00217  * Trade memory for speed on fixed-point multiplication.
00218  *
00219  * This speeds up repeated multiplication of the generator (that is, the
00220  * multiplication in ECDSA signatures, and half of the multiplications in
00221  * ECDSA verification and ECDHE) by a factor roughly 3 to 4.
00222  *
00223  * The cost is increasing EC peak memory usage by a factor roughly 2.
00224  *
00225  * Change this value to 0 to reduce peak memory usage.
00226  */
00227 #define MBEDTLS_ECP_FIXED_POINT_OPTIM  1   /**< Enable fixed-point speed-up */
00228 #endif /* MBEDTLS_ECP_FIXED_POINT_OPTIM */
00229 
00230 /* \} name SECTION: Module settings */
00231 
00232 /*
00233  * Point formats, from RFC 4492's enum ECPointFormat
00234  */
00235 #define MBEDTLS_ECP_PF_UNCOMPRESSED    0   /**< Uncompressed point format */
00236 #define MBEDTLS_ECP_PF_COMPRESSED      1   /**< Compressed point format */
00237 
00238 /*
00239  * Some other constants from RFC 4492
00240  */
00241 #define MBEDTLS_ECP_TLS_NAMED_CURVE    3   /**< ECCurveType's named_curve */
00242 
00243 /**
00244  * \brief           Get the list of supported curves in order of preferrence
00245  *                  (full information)
00246  *
00247  * \return          A statically allocated array, the last entry is 0.
00248  */
00249 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void );
00250 
00251 /**
00252  * \brief           Get the list of supported curves in order of preferrence
00253  *                  (grp_id only)
00254  *
00255  * \return          A statically allocated array,
00256  *                  terminated with MBEDTLS_ECP_DP_NONE.
00257  */
00258 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void );
00259 
00260 /**
00261  * \brief           Get curve information from an internal group identifier
00262  *
00263  * \param grp_id    A MBEDTLS_ECP_DP_XXX value
00264  *
00265  * \return          The associated curve information or NULL
00266  */
00267 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id );
00268 
00269 /**
00270  * \brief           Get curve information from a TLS NamedCurve value
00271  *
00272  * \param tls_id    A MBEDTLS_ECP_DP_XXX value
00273  *
00274  * \return          The associated curve information or NULL
00275  */
00276 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id );
00277 
00278 /**
00279  * \brief           Get curve information from a human-readable name
00280  *
00281  * \param name      The name
00282  *
00283  * \return          The associated curve information or NULL
00284  */
00285 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name );
00286 
00287 /**
00288  * \brief           Initialize a point (as zero)
00289  */
00290 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt );
00291 
00292 /**
00293  * \brief           Initialize a group (to something meaningless)
00294  */
00295 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp );
00296 
00297 /**
00298  * \brief           Initialize a key pair (as an invalid one)
00299  */
00300 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key );
00301 
00302 /**
00303  * \brief           Free the components of a point
00304  */
00305 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt );
00306 
00307 /**
00308  * \brief           Free the components of an ECP group
00309  */
00310 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp );
00311 
00312 /**
00313  * \brief           Free the components of a key pair
00314  */
00315 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key );
00316 
00317 /**
00318  * \brief           Copy the contents of point Q into P
00319  *
00320  * \param P         Destination point
00321  * \param Q         Source point
00322  *
00323  * \return          0 if successful,
00324  *                  MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00325  */
00326 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q );
00327 
00328 /**
00329  * \brief           Copy the contents of a group object
00330  *
00331  * \param dst       Destination group
00332  * \param src       Source group
00333  *
00334  * \return          0 if successful,
00335  *                  MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00336  */
00337 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src );
00338 
00339 /**
00340  * \brief           Set a point to zero
00341  *
00342  * \param pt        Destination point
00343  *
00344  * \return          0 if successful,
00345  *                  MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00346  */
00347 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt );
00348 
00349 /**
00350  * \brief           Tell if a point is zero
00351  *
00352  * \param pt        Point to test
00353  *
00354  * \return          1 if point is zero, 0 otherwise
00355  */
00356 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt );
00357 
00358 /**
00359  * \brief           Compare two points
00360  *
00361  * \note            This assumes the points are normalized. Otherwise,
00362  *                  they may compare as "not equal" even if they are.
00363  *
00364  * \param P         First point to compare
00365  * \param Q         Second point to compare
00366  *
00367  * \return          0 if the points are equal,
00368  *                  MBEDTLS_ERR_ECP_BAD_INPUT_DATA otherwise
00369  */
00370 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
00371                            const mbedtls_ecp_point *Q );
00372 
00373 /**
00374  * \brief           Import a non-zero point from two ASCII strings
00375  *
00376  * \param P         Destination point
00377  * \param radix     Input numeric base
00378  * \param x         First affine coordinate as a null-terminated string
00379  * \param y         Second affine coordinate as a null-terminated string
00380  *
00381  * \return          0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
00382  */
00383 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
00384                            const char *x, const char *y );
00385 
00386 /**
00387  * \brief           Export a point into unsigned binary data
00388  *
00389  * \param grp       Group to which the point should belong
00390  * \param P         Point to export
00391  * \param format    Point format, should be a MBEDTLS_ECP_PF_XXX macro
00392  * \param olen      Length of the actual output
00393  * \param buf       Output buffer
00394  * \param buflen    Length of the output buffer
00395  *
00396  * \return          0 if successful,
00397  *                  or MBEDTLS_ERR_ECP_BAD_INPUT_DATA
00398  *                  or MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL
00399  */
00400 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P,
00401                             int format, size_t *olen,
00402                             unsigned char *buf, size_t buflen );
00403 
00404 /**
00405  * \brief           Import a point from unsigned binary data
00406  *
00407  * \param grp       Group to which the point should belong
00408  * \param P         Point to import
00409  * \param buf       Input buffer
00410  * \param ilen      Actual length of input
00411  *
00412  * \return          0 if successful,
00413  *                  MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid,
00414  *                  MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00415  *                  MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format
00416  *                  is not implemented.
00417  *
00418  * \note            This function does NOT check that the point actually
00419  *                  belongs to the given group, see mbedtls_ecp_check_pubkey() for
00420  *                  that.
00421  */
00422 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
00423                            const unsigned char *buf, size_t ilen );
00424 
00425 /**
00426  * \brief           Import a point from a TLS ECPoint record
00427  *
00428  * \param grp       ECP group used
00429  * \param pt        Destination point
00430  * \param buf       $(Start of input buffer)
00431  * \param len       Buffer length
00432  *
00433  * \note            buf is updated to point right after the ECPoint on exit
00434  *
00435  * \return          0 if successful,
00436  *                  MBEDTLS_ERR_MPI_XXX if initialization failed
00437  *                  MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid
00438  */
00439 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
00440                         const unsigned char **buf, size_t len );
00441 
00442 /**
00443  * \brief           Export a point as a TLS ECPoint record
00444  *
00445  * \param grp       ECP group used
00446  * \param pt        Point to export
00447  * \param format    Export format
00448  * \param olen      length of data written
00449  * \param buf       Buffer to write to
00450  * \param blen      Buffer length
00451  *
00452  * \return          0 if successful,
00453  *                  or MBEDTLS_ERR_ECP_BAD_INPUT_DATA
00454  *                  or MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL
00455  */
00456 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
00457                          int format, size_t *olen,
00458                          unsigned char *buf, size_t blen );
00459 
00460 /**
00461  * \brief           Set a group using well-known domain parameters
00462  *
00463  * \param grp       Destination group
00464  * \param id        Index in the list of well-known domain parameters
00465  *
00466  * \return          0 if successful,
00467  *                  MBEDTLS_ERR_MPI_XXX if initialization failed
00468  *                  MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE for unkownn groups
00469  *
00470  * \note            Index should be a value of RFC 4492's enum NamedCurve,
00471  *                  usually in the form of a MBEDTLS_ECP_DP_XXX macro.
00472  */
00473 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id );
00474 
00475 /**
00476  * \brief           Set a group from a TLS ECParameters record
00477  *
00478  * \param grp       Destination group
00479  * \param buf       &(Start of input buffer)
00480  * \param len       Buffer length
00481  *
00482  * \note            buf is updated to point right after ECParameters on exit
00483  *
00484  * \return          0 if successful,
00485  *                  MBEDTLS_ERR_MPI_XXX if initialization failed
00486  *                  MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid
00487  */
00488 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, const unsigned char **buf, size_t len );
00489 
00490 /**
00491  * \brief           Write the TLS ECParameters record for a group
00492  *
00493  * \param grp       ECP group used
00494  * \param olen      Number of bytes actually written
00495  * \param buf       Buffer to write to
00496  * \param blen      Buffer length
00497  *
00498  * \return          0 if successful,
00499  *                  or MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL
00500  */
00501 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
00502                          unsigned char *buf, size_t blen );
00503 
00504 /**
00505  * \brief           Multiplication by an integer: R = m * P
00506  *                  (Not thread-safe to use same group in multiple threads)
00507  *
00508  * \note            In order to prevent timing attacks, this function
00509  *                  executes the exact same sequence of (base field)
00510  *                  operations for any valid m. It avoids any if-branch or
00511  *                  array index depending on the value of m.
00512  *
00513  * \note            If f_rng is not NULL, it is used to randomize intermediate
00514  *                  results in order to prevent potential timing attacks
00515  *                  targeting these results. It is recommended to always
00516  *                  provide a non-NULL f_rng (the overhead is negligible).
00517  *
00518  * \param grp       ECP group
00519  * \param R         Destination point
00520  * \param m         Integer by which to multiply
00521  * \param P         Point to multiply
00522  * \param f_rng     RNG function (see notes)
00523  * \param p_rng     RNG parameter
00524  *
00525  * \return          0 if successful,
00526  *                  MBEDTLS_ERR_ECP_INVALID_KEY if m is not a valid privkey
00527  *                  or P is not a valid pubkey,
00528  *                  MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00529  */
00530 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
00531              const mbedtls_mpi *m, const mbedtls_ecp_point *P,
00532              int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
00533 
00534 /**
00535  * \brief           Multiplication and addition of two points by integers:
00536  *                  R = m * P + n * Q
00537  *                  (Not thread-safe to use same group in multiple threads)
00538  *
00539  * \note            In contrast to mbedtls_ecp_mul(), this function does not guarantee
00540  *                  a constant execution flow and timing.
00541  *
00542  * \param grp       ECP group
00543  * \param R         Destination point
00544  * \param m         Integer by which to multiply P
00545  * \param P         Point to multiply by m
00546  * \param n         Integer by which to multiply Q
00547  * \param Q         Point to be multiplied by n
00548  *
00549  * \return          0 if successful,
00550  *                  MBEDTLS_ERR_ECP_INVALID_KEY if m or n is not a valid privkey
00551  *                  or P or Q is not a valid pubkey,
00552  *                  MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00553  */
00554 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
00555              const mbedtls_mpi *m, const mbedtls_ecp_point *P,
00556              const mbedtls_mpi *n, const mbedtls_ecp_point *Q );
00557 
00558 /**
00559  * \brief           Check that a point is a valid public key on this curve
00560  *
00561  * \param grp       Curve/group the point should belong to
00562  * \param pt        Point to check
00563  *
00564  * \return          0 if point is a valid public key,
00565  *                  MBEDTLS_ERR_ECP_INVALID_KEY otherwise.
00566  *
00567  * \note            This function only checks the point is non-zero, has valid
00568  *                  coordinates and lies on the curve, but not that it is
00569  *                  indeed a multiple of G. This is additional check is more
00570  *                  expensive, isn't required by standards, and shouldn't be
00571  *                  necessary if the group used has a small cofactor. In
00572  *                  particular, it is useless for the NIST groups which all
00573  *                  have a cofactor of 1.
00574  *
00575  * \note            Uses bare components rather than an mbedtls_ecp_keypair structure
00576  *                  in order to ease use with other structures such as
00577  *                  mbedtls_ecdh_context of mbedtls_ecdsa_context.
00578  */
00579 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt );
00580 
00581 /**
00582  * \brief           Check that an mbedtls_mpi is a valid private key for this curve
00583  *
00584  * \param grp       Group used
00585  * \param d         Integer to check
00586  *
00587  * \return          0 if point is a valid private key,
00588  *                  MBEDTLS_ERR_ECP_INVALID_KEY otherwise.
00589  *
00590  * \note            Uses bare components rather than an mbedtls_ecp_keypair structure
00591  *                  in order to ease use with other structures such as
00592  *                  mbedtls_ecdh_context of mbedtls_ecdsa_context.
00593  */
00594 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d );
00595 
00596 /**
00597  * \brief           Generate a keypair with configurable base point
00598  *
00599  * \param grp       ECP group
00600  * \param G         Chosen base point
00601  * \param d         Destination MPI (secret part)
00602  * \param Q         Destination point (public part)
00603  * \param f_rng     RNG function
00604  * \param p_rng     RNG parameter
00605  *
00606  * \return          0 if successful,
00607  *                  or a MBEDTLS_ERR_ECP_XXX or MBEDTLS_MPI_XXX error code
00608  *
00609  * \note            Uses bare components rather than an mbedtls_ecp_keypair structure
00610  *                  in order to ease use with other structures such as
00611  *                  mbedtls_ecdh_context of mbedtls_ecdsa_context.
00612  */
00613 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
00614                      const mbedtls_ecp_point *G,
00615                      mbedtls_mpi *d, mbedtls_ecp_point *Q,
00616                      int (*f_rng)(void *, unsigned char *, size_t),
00617                      void *p_rng );
00618 
00619 /**
00620  * \brief           Generate a keypair
00621  *
00622  * \param grp       ECP group
00623  * \param d         Destination MPI (secret part)
00624  * \param Q         Destination point (public part)
00625  * \param f_rng     RNG function
00626  * \param p_rng     RNG parameter
00627  *
00628  * \return          0 if successful,
00629  *                  or a MBEDTLS_ERR_ECP_XXX or MBEDTLS_MPI_XXX error code
00630  *
00631  * \note            Uses bare components rather than an mbedtls_ecp_keypair structure
00632  *                  in order to ease use with other structures such as
00633  *                  mbedtls_ecdh_context of mbedtls_ecdsa_context.
00634  */
00635 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, mbedtls_mpi *d, mbedtls_ecp_point *Q,
00636                      int (*f_rng)(void *, unsigned char *, size_t),
00637                      void *p_rng );
00638 
00639 /**
00640  * \brief           Generate a keypair
00641  *
00642  * \param grp_id    ECP group identifier
00643  * \param key       Destination keypair
00644  * \param f_rng     RNG function
00645  * \param p_rng     RNG parameter
00646  *
00647  * \return          0 if successful,
00648  *                  or a MBEDTLS_ERR_ECP_XXX or MBEDTLS_MPI_XXX error code
00649  */
00650 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
00651                 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
00652 
00653 /**
00654  * \brief           Check a public-private key pair
00655  *
00656  * \param pub       Keypair structure holding a public key
00657  * \param prv       Keypair structure holding a private (plus public) key
00658  *
00659  * \return          0 if successful (keys are valid and match), or
00660  *                  MBEDTLS_ERR_ECP_BAD_INPUT_DATA, or
00661  *                  a MBEDTLS_ERR_ECP_XXX or MBEDTLS_ERR_MPI_XXX code.
00662  */
00663 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv );
00664 
00665 #if defined(MBEDTLS_SELF_TEST)
00666 
00667 /**
00668  * \brief          Checkup routine
00669  *
00670  * \return         0 if successful, or 1 if a test failed
00671  */
00672 int mbedtls_ecp_self_test( int verbose );
00673 
00674 #endif /* MBEDTLS_SELF_TEST */
00675 
00676 #ifdef __cplusplus
00677 }
00678 #endif
00679 
00680 #else  /* MBEDTLS_ECP_ALT */
00681 #include "ecp_alt.h"
00682 #endif /* MBEDTLS_ECP_ALT */
00683 
00684 #endif /* ecp.h */