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1 /**
2  * \file ecp.h
3  *
4  * \brief This file provides an API for Elliptic Curves over GF(P) (ECP).
5  *
6  * The use of ECP in cryptography and TLS is defined in
7  * <em>Standards for Efficient Cryptography Group (SECG): SEC1
8  * Elliptic Curve Cryptography</em> and
9  * <em>RFC-4492: Elliptic Curve Cryptography (ECC) Cipher Suites
10  * for Transport Layer Security (TLS)</em>.
11  *
12  * <em>RFC-2409: The Internet Key Exchange (IKE)</em> defines ECP
13  * group types.
14  *
15  */
16 
17 /*
18  *  Copyright (C) 2006-2018, Arm Limited (or its affiliates), All Rights Reserved
19  *  SPDX-License-Identifier: Apache-2.0
20  *
21  *  Licensed under the Apache License, Version 2.0 (the "License"); you may
22  *  not use this file except in compliance with the License.
23  *  You may obtain a copy of the License at
24  *
25  *  http://www.apache.org/licenses/LICENSE-2.0
26  *
27  *  Unless required by applicable law or agreed to in writing, software
28  *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
29  *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
30  *  See the License for the specific language governing permissions and
31  *  limitations under the License.
32  *
33  *  This file is part of Mbed TLS (https://tls.mbed.org)
34  */
35 
36 #ifndef MBEDTLS_ECP_H
37 #define MBEDTLS_ECP_H
38 
39 #if !defined(MBEDTLS_CONFIG_FILE)
40 #include "config.h"
41 #else
42 #include MBEDTLS_CONFIG_FILE
43 #endif
44 
45 #include "bignum.h"
46 
47 /*
48  * ECP error codes
49  */
50 #define MBEDTLS_ERR_ECP_BAD_INPUT_DATA                    -0x4F80  /**< Bad input parameters to function. */
51 #define MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL                  -0x4F00  /**< The buffer is too small to write to. */
52 #define MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE               -0x4E80  /**< The requested feature is not available, for example, the requested curve is not supported. */
53 #define MBEDTLS_ERR_ECP_VERIFY_FAILED                     -0x4E00  /**< The signature is not valid. */
54 #define MBEDTLS_ERR_ECP_ALLOC_FAILED                      -0x4D80  /**< Memory allocation failed. */
55 #define MBEDTLS_ERR_ECP_RANDOM_FAILED                     -0x4D00  /**< Generation of random value, such as ephemeral key, failed. */
56 #define MBEDTLS_ERR_ECP_INVALID_KEY                       -0x4C80  /**< Invalid private or public key. */
57 #define MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH                  -0x4C00  /**< The buffer contains a valid signature followed by more data. */
58 
59 /* MBEDTLS_ERR_ECP_HW_ACCEL_FAILED is deprecated and should not be used. */
60 #define MBEDTLS_ERR_ECP_HW_ACCEL_FAILED                   -0x4B80  /**< The ECP hardware accelerator failed. */
61 
62 #define MBEDTLS_ERR_ECP_IN_PROGRESS                       -0x4B00  /**< Operation in progress, call again with the same parameters to continue. */
63 
64 #ifdef __cplusplus
65 extern "C" {
66 #endif
67 
68 /**
69  * Domain-parameter identifiers: curve, subgroup, and generator.
70  *
71  * \note Only curves over prime fields are supported.
72  *
73  * \warning This library does not support validation of arbitrary domain
74  * parameters. Therefore, only standardized domain parameters from trusted
75  * sources should be used. See mbedtls_ecp_group_load().
76  */
77 typedef enum
78 {
79     MBEDTLS_ECP_DP_NONE = 0,       /*!< Curve not defined. */
80     MBEDTLS_ECP_DP_SECP192R1,      /*!< Domain parameters for the 192-bit curve defined by FIPS 186-4 and SEC1. */
81     MBEDTLS_ECP_DP_SECP224R1,      /*!< Domain parameters for the 224-bit curve defined by FIPS 186-4 and SEC1. */
82     MBEDTLS_ECP_DP_SECP256R1,      /*!< Domain parameters for the 256-bit curve defined by FIPS 186-4 and SEC1. */
83     MBEDTLS_ECP_DP_SECP384R1,      /*!< Domain parameters for the 384-bit curve defined by FIPS 186-4 and SEC1. */
84     MBEDTLS_ECP_DP_SECP521R1,      /*!< Domain parameters for the 521-bit curve defined by FIPS 186-4 and SEC1. */
85     MBEDTLS_ECP_DP_BP256R1,        /*!< Domain parameters for 256-bit Brainpool curve. */
86     MBEDTLS_ECP_DP_BP384R1,        /*!< Domain parameters for 384-bit Brainpool curve. */
87     MBEDTLS_ECP_DP_BP512R1,        /*!< Domain parameters for 512-bit Brainpool curve. */
88     MBEDTLS_ECP_DP_CURVE25519,     /*!< Domain parameters for Curve25519. */
89     MBEDTLS_ECP_DP_SECP192K1,      /*!< Domain parameters for 192-bit "Koblitz" curve. */
90     MBEDTLS_ECP_DP_SECP224K1,      /*!< Domain parameters for 224-bit "Koblitz" curve. */
91     MBEDTLS_ECP_DP_SECP256K1,      /*!< Domain parameters for 256-bit "Koblitz" curve. */
92     MBEDTLS_ECP_DP_CURVE448,       /*!< Domain parameters for Curve448. */
93 } mbedtls_ecp_group_id;
94 
95 /**
96  * The number of supported curves, plus one for #MBEDTLS_ECP_DP_NONE.
97  *
98  * \note Montgomery curves are currently excluded.
99  */
100 #define MBEDTLS_ECP_DP_MAX     12
101 
102 /**
103  * Curve information, for use by other modules.
104  */
105 typedef struct mbedtls_ecp_curve_info
106 {
107     mbedtls_ecp_group_id grp_id;    /*!< An internal identifier. */
108     uint16_t tls_id;                /*!< The TLS NamedCurve identifier. */
109     uint16_t bit_size;              /*!< The curve size in bits. */
110     const char *name;               /*!< A human-friendly name. */
111 } mbedtls_ecp_curve_info;
112 
113 /**
114  * \brief           The ECP point structure, in Jacobian coordinates.
115  *
116  * \note            All functions expect and return points satisfying
117  *                  the following condition: <code>Z == 0</code> or
118  *                  <code>Z == 1</code>. Other values of \p Z are
119  *                  used only by internal functions.
120  *                  The point is zero, or "at infinity", if <code>Z == 0</code>.
121  *                  Otherwise, \p X and \p Y are its standard (affine)
122  *                  coordinates.
123  */
124 typedef struct mbedtls_ecp_point
125 {
126     mbedtls_mpi X;          /*!< The X coordinate of the ECP point. */
127     mbedtls_mpi Y;          /*!< The Y coordinate of the ECP point. */
128     mbedtls_mpi Z;          /*!< The Z coordinate of the ECP point. */
129 }
130 mbedtls_ecp_point;
131 
132 #if !defined(MBEDTLS_ECP_ALT)
133 /*
134  * default mbed TLS elliptic curve arithmetic implementation
135  *
136  * (in case MBEDTLS_ECP_ALT is defined then the developer has to provide an
137  * alternative implementation for the whole module and it will replace this
138  * one.)
139  */
140 
141 /**
142  * \brief           The ECP group structure.
143  *
144  * We consider two types of curve equations:
145  * <ul><li>Short Weierstrass: <code>y^2 = x^3 + A x + B mod P</code>
146  * (SEC1 + RFC-4492)</li>
147  * <li>Montgomery: <code>y^2 = x^3 + A x^2 + x mod P</code> (Curve25519,
148  * Curve448)</li></ul>
149  * In both cases, the generator (\p G) for a prime-order subgroup is fixed.
150  *
151  * For Short Weierstrass, this subgroup is the whole curve, and its
152  * cardinality is denoted by \p N. Our code requires that \p N is an
153  * odd prime as mbedtls_ecp_mul() requires an odd number, and
154  * mbedtls_ecdsa_sign() requires that it is prime for blinding purposes.
155  *
156  * For Montgomery curves, we do not store \p A, but <code>(A + 2) / 4</code>,
157  * which is the quantity used in the formulas. Additionally, \p nbits is
158  * not the size of \p N but the required size for private keys.
159  *
160  * If \p modp is NULL, reduction modulo \p P is done using a generic algorithm.
161  * Otherwise, \p modp must point to a function that takes an \p mbedtls_mpi in the
162  * range of <code>0..2^(2*pbits)-1</code>, and transforms it in-place to an integer
163  * which is congruent mod \p P to the given MPI, and is close enough to \p pbits
164  * in size, so that it may be efficiently brought in the 0..P-1 range by a few
165  * additions or subtractions. Therefore, it is only an approximative modular
166  * reduction. It must return 0 on success and non-zero on failure.
167  *
168  * \note        Alternative implementations must keep the group IDs distinct. If
169  *              two group structures have the same ID, then they must be
170  *              identical.
171  *
172  */
173 typedef struct mbedtls_ecp_group
174 {
175     mbedtls_ecp_group_id id;    /*!< An internal group identifier. */
176     mbedtls_mpi P;              /*!< The prime modulus of the base field. */
177     mbedtls_mpi A;              /*!< For Short Weierstrass: \p A in the equation. For
178                                      Montgomery curves: <code>(A + 2) / 4</code>. */
179     mbedtls_mpi B;              /*!< For Short Weierstrass: \p B in the equation.
180                                      For Montgomery curves: unused. */
181     mbedtls_ecp_point G;        /*!< The generator of the subgroup used. */
182     mbedtls_mpi N;              /*!< The order of \p G. */
183     size_t pbits;               /*!< The number of bits in \p P.*/
184     size_t nbits;               /*!< For Short Weierstrass: The number of bits in \p P.
185                                      For Montgomery curves: the number of bits in the
186                                      private keys. */
187     unsigned int h;             /*!< \internal 1 if the constants are static. */
188     int (*modp)(mbedtls_mpi *); /*!< The function for fast pseudo-reduction
189                                      mod \p P (see above).*/
190     int (*t_pre)(mbedtls_ecp_point *, void *);  /*!< Unused. */
191     int (*t_post)(mbedtls_ecp_point *, void *); /*!< Unused. */
192     void *t_data;               /*!< Unused. */
193     mbedtls_ecp_point *T;       /*!< Pre-computed points for ecp_mul_comb(). */
194     size_t T_size;              /*!< The number of pre-computed points. */
195 }
196 mbedtls_ecp_group;
197 
198 /**
199  * \name SECTION: Module settings
200  *
201  * The configuration options you can set for this module are in this section.
202  * Either change them in config.h, or define them using the compiler command line.
203  * \{
204  */
205 
206 #if !defined(MBEDTLS_ECP_MAX_BITS)
207 /**
208  * The maximum size of the groups, that is, of \c N and \c P.
209  */
210 #define MBEDTLS_ECP_MAX_BITS     521   /**< The maximum size of groups, in bits. */
211 #endif
212 
213 #define MBEDTLS_ECP_MAX_BYTES    ( ( MBEDTLS_ECP_MAX_BITS + 7 ) / 8 )
214 #define MBEDTLS_ECP_MAX_PT_LEN   ( 2 * MBEDTLS_ECP_MAX_BYTES + 1 )
215 
216 #if !defined(MBEDTLS_ECP_WINDOW_SIZE)
217 /*
218  * Maximum "window" size used for point multiplication.
219  * Default: 6.
220  * Minimum value: 2. Maximum value: 7.
221  *
222  * Result is an array of at most ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
223  * points used for point multiplication. This value is directly tied to EC
224  * peak memory usage, so decreasing it by one should roughly cut memory usage
225  * by two (if large curves are in use).
226  *
227  * Reduction in size may reduce speed, but larger curves are impacted first.
228  * Sample performances (in ECDHE handshakes/s, with FIXED_POINT_OPTIM = 1):
229  *      w-size:     6       5       4       3       2
230  *      521       145     141     135     120      97
231  *      384       214     209     198     177     146
232  *      256       320     320     303     262     226
233  *      224       475     475     453     398     342
234  *      192       640     640     633     587     476
235  */
236 #define MBEDTLS_ECP_WINDOW_SIZE    6   /**< The maximum window size used. */
237 #endif /* MBEDTLS_ECP_WINDOW_SIZE */
238 
239 #if !defined(MBEDTLS_ECP_FIXED_POINT_OPTIM)
240 /*
241  * Trade memory for speed on fixed-point multiplication.
242  *
243  * This speeds up repeated multiplication of the generator (that is, the
244  * multiplication in ECDSA signatures, and half of the multiplications in
245  * ECDSA verification and ECDHE) by a factor roughly 3 to 4.
246  *
247  * The cost is increasing EC peak memory usage by a factor roughly 2.
248  *
249  * Change this value to 0 to reduce peak memory usage.
250  */
251 #define MBEDTLS_ECP_FIXED_POINT_OPTIM  1   /**< Enable fixed-point speed-up. */
252 #endif /* MBEDTLS_ECP_FIXED_POINT_OPTIM */
253 
254 /* \} name SECTION: Module settings */
255 
256 #else  /* MBEDTLS_ECP_ALT */
257 #include "ecp_alt.h"
258 #endif /* MBEDTLS_ECP_ALT */
259 
260 #if defined(MBEDTLS_ECP_RESTARTABLE)
261 
262 /**
263  * \brief           Internal restart context for multiplication
264  *
265  * \note            Opaque struct
266  */
267 typedef struct mbedtls_ecp_restart_mul mbedtls_ecp_restart_mul_ctx;
268 
269 /**
270  * \brief           Internal restart context for ecp_muladd()
271  *
272  * \note            Opaque struct
273  */
274 typedef struct mbedtls_ecp_restart_muladd mbedtls_ecp_restart_muladd_ctx;
275 
276 /**
277  * \brief           General context for resuming ECC operations
278  */
279 typedef struct
280 {
281     unsigned ops_done;                  /*!<  current ops count             */
282     unsigned depth;                     /*!<  call depth (0 = top-level)    */
283     mbedtls_ecp_restart_mul_ctx *rsm;   /*!<  ecp_mul_comb() sub-context    */
284     mbedtls_ecp_restart_muladd_ctx *ma; /*!<  ecp_muladd() sub-context      */
285 } mbedtls_ecp_restart_ctx;
286 
287 /*
288  * Operation counts for restartable functions
289  */
290 #define MBEDTLS_ECP_OPS_CHK   3 /*!< basic ops count for ecp_check_pubkey()  */
291 #define MBEDTLS_ECP_OPS_DBL   8 /*!< basic ops count for ecp_double_jac()    */
292 #define MBEDTLS_ECP_OPS_ADD  11 /*!< basic ops count for see ecp_add_mixed() */
293 #define MBEDTLS_ECP_OPS_INV 120 /*!< empirical equivalent for mpi_mod_inv()  */
294 
295 /**
296  * \brief           Internal; for restartable functions in other modules.
297  *                  Check and update basic ops budget.
298  *
299  * \param grp       Group structure
300  * \param rs_ctx    Restart context
301  * \param ops       Number of basic ops to do
302  *
303  * \return          \c 0 if doing \p ops basic ops is still allowed,
304  * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS otherwise.
305  */
306 int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp,
307                               mbedtls_ecp_restart_ctx *rs_ctx,
308                               unsigned ops );
309 
310 /* Utility macro for checking and updating ops budget */
311 #define MBEDTLS_ECP_BUDGET( ops )   \
312     MBEDTLS_MPI_CHK( mbedtls_ecp_check_budget( grp, rs_ctx, \
313                                                (unsigned) (ops) ) );
314 
315 #else /* MBEDTLS_ECP_RESTARTABLE */
316 
317 #define MBEDTLS_ECP_BUDGET( ops )   /* no-op; for compatibility */
318 
319 /* We want to declare restartable versions of existing functions anyway */
320 typedef void mbedtls_ecp_restart_ctx;
321 
322 #endif /* MBEDTLS_ECP_RESTARTABLE */
323 
324 /**
325  * \brief    The ECP key-pair structure.
326  *
327  * A generic key-pair that may be used for ECDSA and fixed ECDH, for example.
328  *
329  * \note    Members are deliberately in the same order as in the
330  *          ::mbedtls_ecdsa_context structure.
331  */
332 typedef struct mbedtls_ecp_keypair
333 {
334     mbedtls_ecp_group grp;      /*!<  Elliptic curve and base point     */
335     mbedtls_mpi d;              /*!<  our secret value                  */
336     mbedtls_ecp_point Q;        /*!<  our public value                  */
337 }
338 mbedtls_ecp_keypair;
339 
340 /*
341  * Point formats, from RFC 4492's enum ECPointFormat
342  */
343 #define MBEDTLS_ECP_PF_UNCOMPRESSED    0   /**< Uncompressed point format. */
344 #define MBEDTLS_ECP_PF_COMPRESSED      1   /**< Compressed point format. */
345 
346 /*
347  * Some other constants from RFC 4492
348  */
349 #define MBEDTLS_ECP_TLS_NAMED_CURVE    3   /**< The named_curve of ECCurveType. */
350 
351 #if defined(MBEDTLS_ECP_RESTARTABLE)
352 /**
353  * \brief           Set the maximum number of basic operations done in a row.
354  *
355  *                  If more operations are needed to complete a computation,
356  *                  #MBEDTLS_ERR_ECP_IN_PROGRESS will be returned by the
357  *                  function performing the computation. It is then the
358  *                  caller's responsibility to either call again with the same
359  *                  parameters until it returns 0 or an error code; or to free
360  *                  the restart context if the operation is to be aborted.
361  *
362  *                  It is strictly required that all input parameters and the
363  *                  restart context be the same on successive calls for the
364  *                  same operation, but output parameters need not be the
365  *                  same; they must not be used until the function finally
366  *                  returns 0.
367  *
368  *                  This only applies to functions whose documentation
369  *                  mentions they may return #MBEDTLS_ERR_ECP_IN_PROGRESS (or
370  *                  #MBEDTLS_ERR_SSL_CRYPTO_IN_PROGRESS for functions in the
371  *                  SSL module). For functions that accept a "restart context"
372  *                  argument, passing NULL disables restart and makes the
373  *                  function equivalent to the function with the same name
374  *                  with \c _restartable removed. For functions in the ECDH
375  *                  module, restart is disabled unless the function accepts
376  *                  an "ECDH context" argument and
377  *                  mbedtls_ecdh_enable_restart() was previously called on
378  *                  that context. For function in the SSL module, restart is
379  *                  only enabled for specific sides and key exchanges
380  *                  (currently only for clients and ECDHE-ECDSA).
381  *
382  * \param max_ops   Maximum number of basic operations done in a row.
383  *                  Default: 0 (unlimited).
384  *                  Lower (non-zero) values mean ECC functions will block for
385  *                  a lesser maximum amount of time.
386  *
387  * \note            A "basic operation" is defined as a rough equivalent of a
388  *                  multiplication in GF(p) for the NIST P-256 curve.
389  *                  As an indication, with default settings, a scalar
390  *                  multiplication (full run of \c mbedtls_ecp_mul()) is:
391  *                  - about 3300 basic operations for P-256
392  *                  - about 9400 basic operations for P-384
393  *
394  * \note            Very low values are not always respected: sometimes
395  *                  functions need to block for a minimum number of
396  *                  operations, and will do so even if max_ops is set to a
397  *                  lower value.  That minimum depends on the curve size, and
398  *                  can be made lower by decreasing the value of
399  *                  \c MBEDTLS_ECP_WINDOW_SIZE.  As an indication, here is the
400  *                  lowest effective value for various curves and values of
401  *                  that parameter (w for short):
402  *                          w=6     w=5     w=4     w=3     w=2
403  *                  P-256   208     208     160     136     124
404  *                  P-384   682     416     320     272     248
405  *                  P-521  1364     832     640     544     496
406  *
407  * \note            This setting is currently ignored by Curve25519.
408  */
409 void mbedtls_ecp_set_max_ops( unsigned max_ops );
410 
411 /**
412  * \brief           Check if restart is enabled (max_ops != 0)
413  *
414  * \return          \c 0 if \c max_ops == 0 (restart disabled)
415  * \return          \c 1 otherwise (restart enabled)
416  */
417 int mbedtls_ecp_restart_is_enabled( void );
418 #endif /* MBEDTLS_ECP_RESTARTABLE */
419 
420 /**
421  * \brief           This function retrieves the information defined in
422  *                  mbedtls_ecp_curve_info() for all supported curves in order
423  *                  of preference.
424  *
425  * \return          A statically allocated array. The last entry is 0.
426  */
427 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void );
428 
429 /**
430  * \brief           This function retrieves the list of internal group
431  *                  identifiers of all supported curves in the order of
432  *                  preference.
433  *
434  * \return          A statically allocated array,
435  *                  terminated with MBEDTLS_ECP_DP_NONE.
436  */
437 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void );
438 
439 /**
440  * \brief           This function retrieves curve information from an internal
441  *                  group identifier.
442  *
443  * \param grp_id    An \c MBEDTLS_ECP_DP_XXX value.
444  *
445  * \return          The associated curve information on success.
446  * \return          NULL on failure.
447  */
448 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id );
449 
450 /**
451  * \brief           This function retrieves curve information from a TLS
452  *                  NamedCurve value.
453  *
454  * \param tls_id    An \c MBEDTLS_ECP_DP_XXX value.
455  *
456  * \return          The associated curve information on success.
457  * \return          NULL on failure.
458  */
459 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id );
460 
461 /**
462  * \brief           This function retrieves curve information from a
463  *                  human-readable name.
464  *
465  * \param name      The human-readable name.
466  *
467  * \return          The associated curve information on success.
468  * \return          NULL on failure.
469  */
470 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name );
471 
472 /**
473  * \brief           This function initializes a point as zero.
474  *
475  * \param pt        The point to initialize.
476  */
477 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt );
478 
479 /**
480  * \brief           This function initializes an ECP group context
481  *                  without loading any domain parameters.
482  *
483  * \note            After this function is called, domain parameters
484  *                  for various ECP groups can be loaded through the
485  *                  mbedtls_ecp_group_load() or mbedtls_ecp_tls_read_group()
486  *                  functions.
487  */
488 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp );
489 
490 /**
491  * \brief           This function initializes a key pair as an invalid one.
492  *
493  * \param key       The key pair to initialize.
494  */
495 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key );
496 
497 /**
498  * \brief           This function frees the components of a point.
499  *
500  * \param pt        The point to free.
501  */
502 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt );
503 
504 /**
505  * \brief           This function frees the components of an ECP group.
506  *
507  * \param grp       The group to free. This may be \c NULL, in which
508  *                  case this function returns immediately. If it is not
509  *                  \c NULL, it must point to an initialized ECP group.
510  */
511 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp );
512 
513 /**
514  * \brief           This function frees the components of a key pair.
515  *
516  * \param key       The key pair to free. This may be \c NULL, in which
517  *                  case this function returns immediately. If it is not
518  *                  \c NULL, it must point to an initialized ECP key pair.
519  */
520 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key );
521 
522 #if defined(MBEDTLS_ECP_RESTARTABLE)
523 /**
524  * \brief           Initialize a restart context.
525  *
526  * \param ctx       The restart context to initialize. This must
527  *                  not be \c NULL.
528  */
529 void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx );
530 
531 /**
532  * \brief           Free the components of a restart context.
533  *
534  * \param ctx       The restart context to free. This may be \c NULL, in which
535  *                  case this function returns immediately. If it is not
536  *                  \c NULL, it must point to an initialized restart context.
537  */
538 void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx );
539 #endif /* MBEDTLS_ECP_RESTARTABLE */
540 
541 /**
542  * \brief           This function copies the contents of point \p Q into
543  *                  point \p P.
544  *
545  * \param P         The destination point. This must be initialized.
546  * \param Q         The source point. This must be initialized.
547  *
548  * \return          \c 0 on success.
549  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
550  * \return          Another negative error code for other kinds of failure.
551  */
552 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q );
553 
554 /**
555  * \brief           This function copies the contents of group \p src into
556  *                  group \p dst.
557  *
558  * \param dst       The destination group. This must be initialized.
559  * \param src       The source group. This must be initialized.
560  *
561  * \return          \c 0 on success.
562  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
563  * \return          Another negative error code on other kinds of failure.
564  */
565 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst,
566                             const mbedtls_ecp_group *src );
567 
568 /**
569  * \brief           This function sets a point to the point at infinity.
570  *
571  * \param pt        The point to set. This must be initialized.
572  *
573  * \return          \c 0 on success.
574  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
575  * \return          Another negative error code on other kinds of failure.
576  */
577 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt );
578 
579 /**
580  * \brief           This function checks if a point is the point at infinity.
581  *
582  * \param pt        The point to test. This must be initialized.
583  *
584  * \return          \c 1 if the point is zero.
585  * \return          \c 0 if the point is non-zero.
586  * \return          A negative error code on failure.
587  */
588 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt );
589 
590 /**
591  * \brief           This function compares two points.
592  *
593  * \note            This assumes that the points are normalized. Otherwise,
594  *                  they may compare as "not equal" even if they are.
595  *
596  * \param P         The first point to compare. This must be initialized.
597  * \param Q         The second point to compare. This must be initialized.
598  *
599  * \return          \c 0 if the points are equal.
600  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the points are not equal.
601  */
602 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
603                            const mbedtls_ecp_point *Q );
604 
605 /**
606  * \brief           This function imports a non-zero point from two ASCII
607  *                  strings.
608  *
609  * \param P         The destination point. This must be initialized.
610  * \param radix     The numeric base of the input.
611  * \param x         The first affine coordinate, as a null-terminated string.
612  * \param y         The second affine coordinate, as a null-terminated string.
613  *
614  * \return          \c 0 on success.
615  * \return          An \c MBEDTLS_ERR_MPI_XXX error code on failure.
616  */
617 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
618                            const char *x, const char *y );
619 
620 /**
621  * \brief           This function exports a point into unsigned binary data.
622  *
623  * \param grp       The group to which the point should belong.
624  *                  This must be initialized and have group parameters
625  *                  set, for example through mbedtls_ecp_group_load().
626  * \param P         The point to export. This must be initialized.
627  * \param format    The point format. This must be either
628  *                  #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED.
629  * \param olen      The address at which to store the length of
630  *                  the output in Bytes. This must not be \c NULL.
631  * \param buf       The output buffer. This must be a writable buffer
632  *                  of length \p buflen Bytes.
633  * \param buflen    The length of the output buffer \p buf in Bytes.
634  *
635  * \return          \c 0 on success.
636  * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output buffer
637  *                  is too small to hold the point.
638  * \return          Another negative error code on other kinds of failure.
639  */
640 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P,
641                             int format, size_t *olen,
642                             unsigned char *buf, size_t buflen );
643 
644 /**
645  * \brief           This function imports a point from unsigned binary data.
646  *
647  * \note            This function does not check that the point actually
648  *                  belongs to the given group, see mbedtls_ecp_check_pubkey()
649  *                  for that.
650  *
651  * \param grp       The group to which the point should belong.
652  *                  This must be initialized and have group parameters
653  *                  set, for example through mbedtls_ecp_group_load().
654  * \param P         The destination context to import the point to.
655  *                  This must be initialized.
656  * \param buf       The input buffer. This must be a readable buffer
657  *                  of length \p ilen Bytes.
658  * \param ilen      The length of the input buffer \p buf in Bytes.
659  *
660  * \return          \c 0 on success.
661  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
662  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
663  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format
664  *                  is not implemented.
665  */
666 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp,
667                                    mbedtls_ecp_point *P,
668                                    const unsigned char *buf, size_t ilen );
669 
670 /**
671  * \brief           This function imports a point from a TLS ECPoint record.
672  *
673  * \note            On function return, \p *buf is updated to point immediately
674  *                  after the ECPoint record.
675  *
676  * \param grp       The ECP group to use.
677  *                  This must be initialized and have group parameters
678  *                  set, for example through mbedtls_ecp_group_load().
679  * \param pt        The destination point.
680  * \param buf       The address of the pointer to the start of the input buffer.
681  * \param len       The length of the buffer.
682  *
683  * \return          \c 0 on success.
684  * \return          An \c MBEDTLS_ERR_MPI_XXX error code on initialization
685  *                  failure.
686  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
687  */
688 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp,
689                                 mbedtls_ecp_point *pt,
690                                 const unsigned char **buf, size_t len );
691 
692 /**
693  * \brief           This function exports a point as a TLS ECPoint record
694  *                  defined in RFC 4492, Section 5.4.
695  *
696  * \param grp       The ECP group to use.
697  *                  This must be initialized and have group parameters
698  *                  set, for example through mbedtls_ecp_group_load().
699  * \param pt        The point to be exported. This must be initialized.
700  * \param format    The point format to use. This must be either
701  *                  #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED.
702  * \param olen      The address at which to store the length in Bytes
703  *                  of the data written.
704  * \param buf       The target buffer. This must be a writable buffer of
705  *                  length \p blen Bytes.
706  * \param blen      The length of the target buffer \p buf in Bytes.
707  *
708  * \return          \c 0 on success.
709  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
710  * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the target buffer
711  *                  is too small to hold the exported point.
712  * \return          Another negative error code on other kinds of failure.
713  */
714 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp,
715                                  const mbedtls_ecp_point *pt,
716                                  int format, size_t *olen,
717                                  unsigned char *buf, size_t blen );
718 
719 /**
720  * \brief           This function sets up an ECP group context
721  *                  from a standardized set of domain parameters.
722  *
723  * \note            The index should be a value of the NamedCurve enum,
724  *                  as defined in <em>RFC-4492: Elliptic Curve Cryptography
725  *                  (ECC) Cipher Suites for Transport Layer Security (TLS)</em>,
726  *                  usually in the form of an \c MBEDTLS_ECP_DP_XXX macro.
727  *
728  * \param grp       The group context to setup. This must be initialized.
729  * \param id        The identifier of the domain parameter set to load.
730  *
731  * \return          \c 0 on success.
732  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p id doesn't
733  *                  correspond to a known group.
734  * \return          Another negative error code on other kinds of failure.
735  */
736 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id );
737 
738 /**
739  * \brief           This function sets up an ECP group context from a TLS
740  *                  ECParameters record as defined in RFC 4492, Section 5.4.
741  *
742  * \note            The read pointer \p buf is updated to point right after
743  *                  the ECParameters record on exit.
744  *
745  * \param grp       The group context to setup. This must be initialized.
746  * \param buf       The address of the pointer to the start of the input buffer.
747  * \param len       The length of the input buffer \c *buf in Bytes.
748  *
749  * \return          \c 0 on success.
750  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
751  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
752  *                  recognized.
753  * \return          Another negative error code on other kinds of failure.
754  */
755 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp,
756                                 const unsigned char **buf, size_t len );
757 
758 /**
759  * \brief           This function extracts an elliptic curve group ID from a
760  *                  TLS ECParameters record as defined in RFC 4492, Section 5.4.
761  *
762  * \note            The read pointer \p buf is updated to point right after
763  *                  the ECParameters record on exit.
764  *
765  * \param grp       The address at which to store the group id.
766  *                  This must not be \c NULL.
767  * \param buf       The address of the pointer to the start of the input buffer.
768  * \param len       The length of the input buffer \c *buf in Bytes.
769  *
770  * \return          \c 0 on success.
771  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
772  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
773  *                  recognized.
774  * \return          Another negative error code on other kinds of failure.
775  */
776 int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp,
777                                    const unsigned char **buf,
778                                    size_t len );
779 /**
780  * \brief           This function exports an elliptic curve as a TLS
781  *                  ECParameters record as defined in RFC 4492, Section 5.4.
782  *
783  * \param grp       The ECP group to be exported.
784  *                  This must be initialized and have group parameters
785  *                  set, for example through mbedtls_ecp_group_load().
786  * \param olen      The address at which to store the number of Bytes written.
787  *                  This must not be \c NULL.
788  * \param buf       The buffer to write to. This must be a writable buffer
789  *                  of length \p blen Bytes.
790  * \param blen      The length of the output buffer \p buf in Bytes.
791  *
792  * \return          \c 0 on success.
793  * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output
794  *                  buffer is too small to hold the exported group.
795  * \return          Another negative error code on other kinds of failure.
796  */
797 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp,
798                                  size_t *olen,
799                                  unsigned char *buf, size_t blen );
800 
801 /**
802  * \brief           This function performs a scalar multiplication of a point
803  *                  by an integer: \p R = \p m * \p P.
804  *
805  *                  It is not thread-safe to use same group in multiple threads.
806  *
807  * \note            To prevent timing attacks, this function
808  *                  executes the exact same sequence of base-field
809  *                  operations for any valid \p m. It avoids any if-branch or
810  *                  array index depending on the value of \p m.
811  *
812  * \note            If \p f_rng is not NULL, it is used to randomize
813  *                  intermediate results to prevent potential timing attacks
814  *                  targeting these results. We recommend always providing
815  *                  a non-NULL \p f_rng. The overhead is negligible.
816  *
817  * \param grp       The ECP group to use.
818  *                  This must be initialized and have group parameters
819  *                  set, for example through mbedtls_ecp_group_load().
820  * \param R         The point in which to store the result of the calculation.
821  *                  This must be initialized.
822  * \param m         The integer by which to multiply. This must be initialized.
823  * \param P         The point to multiply. This must be initialized.
824  * \param f_rng     The RNG function. This may be \c NULL if randomization
825  *                  of intermediate results isn't desired (discouraged).
826  * \param p_rng     The RNG context to be passed to \p p_rng.
827  *
828  * \return          \c 0 on success.
829  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private
830  *                  key, or \p P is not a valid public key.
831  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
832  * \return          Another negative error code on other kinds of failure.
833  */
834 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
835              const mbedtls_mpi *m, const mbedtls_ecp_point *P,
836              int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
837 
838 /**
839  * \brief           This function performs multiplication of a point by
840  *                  an integer: \p R = \p m * \p P in a restartable way.
841  *
842  * \see             mbedtls_ecp_mul()
843  *
844  * \note            This function does the same as \c mbedtls_ecp_mul(), but
845  *                  it can return early and restart according to the limit set
846  *                  with \c mbedtls_ecp_set_max_ops() to reduce blocking.
847  *
848  * \param grp       The ECP group to use.
849  *                  This must be initialized and have group parameters
850  *                  set, for example through mbedtls_ecp_group_load().
851  * \param R         The point in which to store the result of the calculation.
852  *                  This must be initialized.
853  * \param m         The integer by which to multiply. This must be initialized.
854  * \param P         The point to multiply. This must be initialized.
855  * \param f_rng     The RNG function. This may be \c NULL if randomization
856  *                  of intermediate results isn't desired (discouraged).
857  * \param p_rng     The RNG context to be passed to \p p_rng.
858  * \param rs_ctx    The restart context (NULL disables restart).
859  *
860  * \return          \c 0 on success.
861  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private
862  *                  key, or \p P is not a valid public key.
863  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
864  * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
865  *                  operations was reached: see \c mbedtls_ecp_set_max_ops().
866  * \return          Another negative error code on other kinds of failure.
867  */
868 int mbedtls_ecp_mul_restartable( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
869              const mbedtls_mpi *m, const mbedtls_ecp_point *P,
870              int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
871              mbedtls_ecp_restart_ctx *rs_ctx );
872 
873 /**
874  * \brief           This function performs multiplication and addition of two
875  *                  points by integers: \p R = \p m * \p P + \p n * \p Q
876  *
877  *                  It is not thread-safe to use same group in multiple threads.
878  *
879  * \note            In contrast to mbedtls_ecp_mul(), this function does not
880  *                  guarantee a constant execution flow and timing.
881  *
882  * \param grp       The ECP group to use.
883  *                  This must be initialized and have group parameters
884  *                  set, for example through mbedtls_ecp_group_load().
885  * \param R         The point in which to store the result of the calculation.
886  *                  This must be initialized.
887  * \param m         The integer by which to multiply \p P.
888  *                  This must be initialized.
889  * \param P         The point to multiply by \p m. This must be initialized.
890  * \param n         The integer by which to multiply \p Q.
891  *                  This must be initialized.
892  * \param Q         The point to be multiplied by \p n.
893  *                  This must be initialized.
894  *
895  * \return          \c 0 on success.
896  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not
897  *                  valid private keys, or \p P or \p Q are not valid public
898  *                  keys.
899  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
900  * \return          Another negative error code on other kinds of failure.
901  */
902 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
903              const mbedtls_mpi *m, const mbedtls_ecp_point *P,
904              const mbedtls_mpi *n, const mbedtls_ecp_point *Q );
905 
906 /**
907  * \brief           This function performs multiplication and addition of two
908  *                  points by integers: \p R = \p m * \p P + \p n * \p Q in a
909  *                  restartable way.
910  *
911  * \see             \c mbedtls_ecp_muladd()
912  *
913  * \note            This function works the same as \c mbedtls_ecp_muladd(),
914  *                  but it can return early and restart according to the limit
915  *                  set with \c mbedtls_ecp_set_max_ops() to reduce blocking.
916  *
917  * \param grp       The ECP group to use.
918  *                  This must be initialized and have group parameters
919  *                  set, for example through mbedtls_ecp_group_load().
920  * \param R         The point in which to store the result of the calculation.
921  *                  This must be initialized.
922  * \param m         The integer by which to multiply \p P.
923  *                  This must be initialized.
924  * \param P         The point to multiply by \p m. This must be initialized.
925  * \param n         The integer by which to multiply \p Q.
926  *                  This must be initialized.
927  * \param Q         The point to be multiplied by \p n.
928  *                  This must be initialized.
929  * \param rs_ctx    The restart context (NULL disables restart).
930  *
931  * \return          \c 0 on success.
932  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not
933  *                  valid private keys, or \p P or \p Q are not valid public
934  *                  keys.
935  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
936  * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
937  *                  operations was reached: see \c mbedtls_ecp_set_max_ops().
938  * \return          Another negative error code on other kinds of failure.
939  */
940 int mbedtls_ecp_muladd_restartable(
941              mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
942              const mbedtls_mpi *m, const mbedtls_ecp_point *P,
943              const mbedtls_mpi *n, const mbedtls_ecp_point *Q,
944              mbedtls_ecp_restart_ctx *rs_ctx );
945 
946 /**
947  * \brief           This function checks that a point is a valid public key
948  *                  on this curve.
949  *
950  *                  It only checks that the point is non-zero, has
951  *                  valid coordinates and lies on the curve. It does not verify
952  *                  that it is indeed a multiple of \p G. This additional
953  *                  check is computationally more expensive, is not required
954  *                  by standards, and should not be necessary if the group
955  *                  used has a small cofactor. In particular, it is useless for
956  *                  the NIST groups which all have a cofactor of 1.
957  *
958  * \note            This function uses bare components rather than an
959  *                  ::mbedtls_ecp_keypair structure, to ease use with other
960  *                  structures, such as ::mbedtls_ecdh_context or
961  *                  ::mbedtls_ecdsa_context.
962  *
963  * \param grp       The ECP group the point should belong to.
964  *                  This must be initialized and have group parameters
965  *                  set, for example through mbedtls_ecp_group_load().
966  * \param pt        The point to check. This must be initialized.
967  *
968  * \return          \c 0 if the point is a valid public key.
969  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not
970  *                  a valid public key for the given curve.
971  * \return          Another negative error code on other kinds of failure.
972  */
973 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp,
974                               const mbedtls_ecp_point *pt );
975 
976 /**
977  * \brief           This function checks that an \p mbedtls_mpi is a
978  *                  valid private key for this curve.
979  *
980  * \note            This function uses bare components rather than an
981  *                  ::mbedtls_ecp_keypair structure to ease use with other
982  *                  structures, such as ::mbedtls_ecdh_context or
983  *                  ::mbedtls_ecdsa_context.
984  *
985  * \param grp       The ECP group the private key should belong to.
986  *                  This must be initialized and have group parameters
987  *                  set, for example through mbedtls_ecp_group_load().
988  * \param d         The integer to check. This must be initialized.
989  *
990  * \return          \c 0 if the point is a valid private key.
991  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not a valid
992  *                  private key for the given curve.
993  * \return          Another negative error code on other kinds of failure.
994  */
995 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp,
996                                const mbedtls_mpi *d );
997 
998 /**
999  * \brief           This function generates a private key.
1000  *
1001  * \param grp       The ECP group to generate a private key for.
1002  *                  This must be initialized and have group parameters
1003  *                  set, for example through mbedtls_ecp_group_load().
1004  * \param d         The destination MPI (secret part). This must be initialized.
1005  * \param f_rng     The RNG function. This must not be \c NULL.
1006  * \param p_rng     The RNG parameter to be passed to \p f_rng. This may be
1007  *                  \c NULL if \p f_rng doesn't need a context argument.
1008  *
1009  * \return          \c 0 on success.
1010  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1011  *                  on failure.
1012  */
1013 int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp,
1014                      mbedtls_mpi *d,
1015                      int (*f_rng)(void *, unsigned char *, size_t),
1016                      void *p_rng );
1017 
1018 /**
1019  * \brief           This function generates a keypair with a configurable base
1020  *                  point.
1021  *
1022  * \note            This function uses bare components rather than an
1023  *                  ::mbedtls_ecp_keypair structure to ease use with other
1024  *                  structures, such as ::mbedtls_ecdh_context or
1025  *                  ::mbedtls_ecdsa_context.
1026  *
1027  * \param grp       The ECP group to generate a key pair for.
1028  *                  This must be initialized and have group parameters
1029  *                  set, for example through mbedtls_ecp_group_load().
1030  * \param G         The base point to use. This must be initialized
1031  *                  and belong to \p grp. It replaces the default base
1032  *                  point \c grp->G used by mbedtls_ecp_gen_keypair().
1033  * \param d         The destination MPI (secret part).
1034  *                  This must be initialized.
1035  * \param Q         The destination point (public part).
1036  *                  This must be initialized.
1037  * \param f_rng     The RNG function. This must not be \c NULL.
1038  * \param p_rng     The RNG context to be passed to \p f_rng. This may
1039  *                  be \c NULL if \p f_rng doesn't need a context argument.
1040  *
1041  * \return          \c 0 on success.
1042  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1043  *                  on failure.
1044  */
1045 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
1046                                   const mbedtls_ecp_point *G,
1047                                   mbedtls_mpi *d, mbedtls_ecp_point *Q,
1048                                   int (*f_rng)(void *, unsigned char *, size_t),
1049                                   void *p_rng );
1050 
1051 /**
1052  * \brief           This function generates an ECP keypair.
1053  *
1054  * \note            This function uses bare components rather than an
1055  *                  ::mbedtls_ecp_keypair structure to ease use with other
1056  *                  structures, such as ::mbedtls_ecdh_context or
1057  *                  ::mbedtls_ecdsa_context.
1058  *
1059  * \param grp       The ECP group to generate a key pair for.
1060  *                  This must be initialized and have group parameters
1061  *                  set, for example through mbedtls_ecp_group_load().
1062  * \param d         The destination MPI (secret part).
1063  *                  This must be initialized.
1064  * \param Q         The destination point (public part).
1065  *                  This must be initialized.
1066  * \param f_rng     The RNG function. This must not be \c NULL.
1067  * \param p_rng     The RNG context to be passed to \p f_rng. This may
1068  *                  be \c NULL if \p f_rng doesn't need a context argument.
1069  *
1070  * \return          \c 0 on success.
1071  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1072  *                  on failure.
1073  */
1074 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, mbedtls_mpi *d,
1075                              mbedtls_ecp_point *Q,
1076                              int (*f_rng)(void *, unsigned char *, size_t),
1077                              void *p_rng );
1078 
1079 /**
1080  * \brief           This function generates an ECP key.
1081  *
1082  * \param grp_id    The ECP group identifier.
1083  * \param key       The destination key. This must be initialized.
1084  * \param f_rng     The RNG function to use. This must not be \c NULL.
1085  * \param p_rng     The RNG context to be passed to \p f_rng. This may
1086  *                  be \c NULL if \p f_rng doesn't need a context argument.
1087  *
1088  * \return          \c 0 on success.
1089  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1090  *                  on failure.
1091  */
1092 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
1093                          int (*f_rng)(void *, unsigned char *, size_t),
1094                          void *p_rng );
1095 
1096 /**
1097  * \brief           This function checks that the keypair objects
1098  *                  \p pub and \p prv have the same group and the
1099  *                  same public point, and that the private key in
1100  *                  \p prv is consistent with the public key.
1101  *
1102  * \param pub       The keypair structure holding the public key. This
1103  *                  must be initialized. If it contains a private key, that
1104  *                  part is ignored.
1105  * \param prv       The keypair structure holding the full keypair.
1106  *                  This must be initialized.
1107  *
1108  * \return          \c 0 on success, meaning that the keys are valid and match.
1109  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the keys are invalid or do not match.
1110  * \return          An \c MBEDTLS_ERR_ECP_XXX or an \c MBEDTLS_ERR_MPI_XXX
1111  *                  error code on calculation failure.
1112  */
1113 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub,
1114                                 const mbedtls_ecp_keypair *prv );
1115 
1116 #if defined(MBEDTLS_SELF_TEST)
1117 
1118 /**
1119  * \brief          The ECP checkup routine.
1120  *
1121  * \return         \c 0 on success.
1122  * \return         \c 1 on failure.
1123  */
1124 int mbedtls_ecp_self_test( int verbose );
1125 
1126 #endif /* MBEDTLS_SELF_TEST */
1127 
1128 #ifdef __cplusplus
1129 }
1130 #endif
1131 
1132 #endif /* ecp.h */
1133