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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 The Mbed TLS Contributors
19  *  SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
20  *
21  *  This file is provided under the Apache License 2.0, or the
22  *  GNU General Public License v2.0 or later.
23  *
24  *  **********
25  *  Apache License 2.0:
26  *
27  *  Licensed under the Apache License, Version 2.0 (the "License"); you may
28  *  not use this file except in compliance with the License.
29  *  You may obtain a copy of the License at
30  *
31  *  http://www.apache.org/licenses/LICENSE-2.0
32  *
33  *  Unless required by applicable law or agreed to in writing, software
34  *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
35  *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
36  *  See the License for the specific language governing permissions and
37  *  limitations under the License.
38  *
39  *  **********
40  *
41  *  **********
42  *  GNU General Public License v2.0 or later:
43  *
44  *  This program is free software; you can redistribute it and/or modify
45  *  it under the terms of the GNU General Public License as published by
46  *  the Free Software Foundation; either version 2 of the License, or
47  *  (at your option) any later version.
48  *
49  *  This program is distributed in the hope that it will be useful,
50  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
51  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
52  *  GNU General Public License for more details.
53  *
54  *  You should have received a copy of the GNU General Public License along
55  *  with this program; if not, write to the Free Software Foundation, Inc.,
56  *  51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
57  *
58  *  **********
59  */
60 
61 #ifndef MBEDTLS_ECP_H
62 #define MBEDTLS_ECP_H
63 
64 #if !defined(MBEDTLS_CONFIG_FILE)
65 #include "config.h"
66 #else
67 #include MBEDTLS_CONFIG_FILE
68 #endif
69 
70 #include "bignum.h"
71 
72 /*
73  * ECP error codes
74  */
75 #define MBEDTLS_ERR_ECP_BAD_INPUT_DATA                    -0x4F80  /**< Bad input parameters to function. */
76 #define MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL                  -0x4F00  /**< The buffer is too small to write to. */
77 #define MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE               -0x4E80  /**< The requested feature is not available, for example, the requested curve is not supported. */
78 #define MBEDTLS_ERR_ECP_VERIFY_FAILED                     -0x4E00  /**< The signature is not valid. */
79 #define MBEDTLS_ERR_ECP_ALLOC_FAILED                      -0x4D80  /**< Memory allocation failed. */
80 #define MBEDTLS_ERR_ECP_RANDOM_FAILED                     -0x4D00  /**< Generation of random value, such as ephemeral key, failed. */
81 #define MBEDTLS_ERR_ECP_INVALID_KEY                       -0x4C80  /**< Invalid private or public key. */
82 #define MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH                  -0x4C00  /**< The buffer contains a valid signature followed by more data. */
83 
84 /* MBEDTLS_ERR_ECP_HW_ACCEL_FAILED is deprecated and should not be used. */
85 #define MBEDTLS_ERR_ECP_HW_ACCEL_FAILED                   -0x4B80  /**< The ECP hardware accelerator failed. */
86 
87 #define MBEDTLS_ERR_ECP_IN_PROGRESS                       -0x4B00  /**< Operation in progress, call again with the same parameters to continue. */
88 
89 #ifdef __cplusplus
90 extern "C" {
91 #endif
92 
93 /**
94  * Domain-parameter identifiers: curve, subgroup, and generator.
95  *
96  * \note Only curves over prime fields are supported.
97  *
98  * \warning This library does not support validation of arbitrary domain
99  * parameters. Therefore, only standardized domain parameters from trusted
100  * sources should be used. See mbedtls_ecp_group_load().
101  */
102 typedef enum
103 {
104     MBEDTLS_ECP_DP_NONE = 0,       /*!< Curve not defined. */
105     MBEDTLS_ECP_DP_SECP192R1,      /*!< Domain parameters for the 192-bit curve defined by FIPS 186-4 and SEC1. */
106     MBEDTLS_ECP_DP_SECP224R1,      /*!< Domain parameters for the 224-bit curve defined by FIPS 186-4 and SEC1. */
107     MBEDTLS_ECP_DP_SECP256R1,      /*!< Domain parameters for the 256-bit curve defined by FIPS 186-4 and SEC1. */
108     MBEDTLS_ECP_DP_SECP384R1,      /*!< Domain parameters for the 384-bit curve defined by FIPS 186-4 and SEC1. */
109     MBEDTLS_ECP_DP_SECP521R1,      /*!< Domain parameters for the 521-bit curve defined by FIPS 186-4 and SEC1. */
110     MBEDTLS_ECP_DP_BP256R1,        /*!< Domain parameters for 256-bit Brainpool curve. */
111     MBEDTLS_ECP_DP_BP384R1,        /*!< Domain parameters for 384-bit Brainpool curve. */
112     MBEDTLS_ECP_DP_BP512R1,        /*!< Domain parameters for 512-bit Brainpool curve. */
113     MBEDTLS_ECP_DP_CURVE25519,     /*!< Domain parameters for Curve25519. */
114     MBEDTLS_ECP_DP_SECP192K1,      /*!< Domain parameters for 192-bit "Koblitz" curve. */
115     MBEDTLS_ECP_DP_SECP224K1,      /*!< Domain parameters for 224-bit "Koblitz" curve. */
116     MBEDTLS_ECP_DP_SECP256K1,      /*!< Domain parameters for 256-bit "Koblitz" curve. */
117     MBEDTLS_ECP_DP_CURVE448,       /*!< Domain parameters for Curve448. */
118 } mbedtls_ecp_group_id;
119 
120 /**
121  * The number of supported curves, plus one for #MBEDTLS_ECP_DP_NONE.
122  *
123  * \note Montgomery curves are currently excluded.
124  */
125 #define MBEDTLS_ECP_DP_MAX     12
126 
127 /**
128  * Curve information, for use by other modules.
129  */
130 typedef struct mbedtls_ecp_curve_info
131 {
132     mbedtls_ecp_group_id grp_id;    /*!< An internal identifier. */
133     uint16_t tls_id;                /*!< The TLS NamedCurve identifier. */
134     uint16_t bit_size;              /*!< The curve size in bits. */
135     const char *name;               /*!< A human-friendly name. */
136 } mbedtls_ecp_curve_info;
137 
138 /**
139  * \brief           The ECP point structure, in Jacobian coordinates.
140  *
141  * \note            All functions expect and return points satisfying
142  *                  the following condition: <code>Z == 0</code> or
143  *                  <code>Z == 1</code>. Other values of \p Z are
144  *                  used only by internal functions.
145  *                  The point is zero, or "at infinity", if <code>Z == 0</code>.
146  *                  Otherwise, \p X and \p Y are its standard (affine)
147  *                  coordinates.
148  */
149 typedef struct mbedtls_ecp_point
150 {
151     mbedtls_mpi X;          /*!< The X coordinate of the ECP point. */
152     mbedtls_mpi Y;          /*!< The Y coordinate of the ECP point. */
153     mbedtls_mpi Z;          /*!< The Z coordinate of the ECP point. */
154 }
155 mbedtls_ecp_point;
156 
157 #if !defined(MBEDTLS_ECP_ALT)
158 /*
159  * default mbed TLS elliptic curve arithmetic implementation
160  *
161  * (in case MBEDTLS_ECP_ALT is defined then the developer has to provide an
162  * alternative implementation for the whole module and it will replace this
163  * one.)
164  */
165 
166 /**
167  * \brief           The ECP group structure.
168  *
169  * We consider two types of curve equations:
170  * <ul><li>Short Weierstrass: <code>y^2 = x^3 + A x + B mod P</code>
171  * (SEC1 + RFC-4492)</li>
172  * <li>Montgomery: <code>y^2 = x^3 + A x^2 + x mod P</code> (Curve25519,
173  * Curve448)</li></ul>
174  * In both cases, the generator (\p G) for a prime-order subgroup is fixed.
175  *
176  * For Short Weierstrass, this subgroup is the whole curve, and its
177  * cardinality is denoted by \p N. Our code requires that \p N is an
178  * odd prime as mbedtls_ecp_mul() requires an odd number, and
179  * mbedtls_ecdsa_sign() requires that it is prime for blinding purposes.
180  *
181  * For Montgomery curves, we do not store \p A, but <code>(A + 2) / 4</code>,
182  * which is the quantity used in the formulas. Additionally, \p nbits is
183  * not the size of \p N but the required size for private keys.
184  *
185  * If \p modp is NULL, reduction modulo \p P is done using a generic algorithm.
186  * Otherwise, \p modp must point to a function that takes an \p mbedtls_mpi in the
187  * range of <code>0..2^(2*pbits)-1</code>, and transforms it in-place to an integer
188  * which is congruent mod \p P to the given MPI, and is close enough to \p pbits
189  * in size, so that it may be efficiently brought in the 0..P-1 range by a few
190  * additions or subtractions. Therefore, it is only an approximative modular
191  * reduction. It must return 0 on success and non-zero on failure.
192  *
193  * \note        Alternative implementations must keep the group IDs distinct. If
194  *              two group structures have the same ID, then they must be
195  *              identical.
196  *
197  */
198 typedef struct mbedtls_ecp_group
199 {
200     mbedtls_ecp_group_id id;    /*!< An internal group identifier. */
201     mbedtls_mpi P;              /*!< The prime modulus of the base field. */
202     mbedtls_mpi A;              /*!< For Short Weierstrass: \p A in the equation. For
203                                      Montgomery curves: <code>(A + 2) / 4</code>. */
204     mbedtls_mpi B;              /*!< For Short Weierstrass: \p B in the equation.
205                                      For Montgomery curves: unused. */
206     mbedtls_ecp_point G;        /*!< The generator of the subgroup used. */
207     mbedtls_mpi N;              /*!< The order of \p G. */
208     size_t pbits;               /*!< The number of bits in \p P.*/
209     size_t nbits;               /*!< For Short Weierstrass: The number of bits in \p P.
210                                      For Montgomery curves: the number of bits in the
211                                      private keys. */
212     unsigned int h;             /*!< \internal 1 if the constants are static. */
213     int (*modp)(mbedtls_mpi *); /*!< The function for fast pseudo-reduction
214                                      mod \p P (see above).*/
215     int (*t_pre)(mbedtls_ecp_point *, void *);  /*!< Unused. */
216     int (*t_post)(mbedtls_ecp_point *, void *); /*!< Unused. */
217     void *t_data;               /*!< Unused. */
218     mbedtls_ecp_point *T;       /*!< Pre-computed points for ecp_mul_comb(). */
219     size_t T_size;              /*!< The number of pre-computed points. */
220 }
221 mbedtls_ecp_group;
222 
223 /**
224  * \name SECTION: Module settings
225  *
226  * The configuration options you can set for this module are in this section.
227  * Either change them in config.h, or define them using the compiler command line.
228  * \{
229  */
230 
231 #if !defined(MBEDTLS_ECP_MAX_BITS)
232 /**
233  * The maximum size of the groups, that is, of \c N and \c P.
234  */
235 #define MBEDTLS_ECP_MAX_BITS     521   /**< The maximum size of groups, in bits. */
236 #endif
237 
238 #define MBEDTLS_ECP_MAX_BYTES    ( ( MBEDTLS_ECP_MAX_BITS + 7 ) / 8 )
239 #define MBEDTLS_ECP_MAX_PT_LEN   ( 2 * MBEDTLS_ECP_MAX_BYTES + 1 )
240 
241 #if !defined(MBEDTLS_ECP_WINDOW_SIZE)
242 /*
243  * Maximum "window" size used for point multiplication.
244  * Default: 6.
245  * Minimum value: 2. Maximum value: 7.
246  *
247  * Result is an array of at most ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
248  * points used for point multiplication. This value is directly tied to EC
249  * peak memory usage, so decreasing it by one should roughly cut memory usage
250  * by two (if large curves are in use).
251  *
252  * Reduction in size may reduce speed, but larger curves are impacted first.
253  * Sample performances (in ECDHE handshakes/s, with FIXED_POINT_OPTIM = 1):
254  *      w-size:     6       5       4       3       2
255  *      521       145     141     135     120      97
256  *      384       214     209     198     177     146
257  *      256       320     320     303     262     226
258  *      224       475     475     453     398     342
259  *      192       640     640     633     587     476
260  */
261 #define MBEDTLS_ECP_WINDOW_SIZE    6   /**< The maximum window size used. */
262 #endif /* MBEDTLS_ECP_WINDOW_SIZE */
263 
264 #if !defined(MBEDTLS_ECP_FIXED_POINT_OPTIM)
265 /*
266  * Trade memory for speed on fixed-point multiplication.
267  *
268  * This speeds up repeated multiplication of the generator (that is, the
269  * multiplication in ECDSA signatures, and half of the multiplications in
270  * ECDSA verification and ECDHE) by a factor roughly 3 to 4.
271  *
272  * The cost is increasing EC peak memory usage by a factor roughly 2.
273  *
274  * Change this value to 0 to reduce peak memory usage.
275  */
276 #define MBEDTLS_ECP_FIXED_POINT_OPTIM  1   /**< Enable fixed-point speed-up. */
277 #endif /* MBEDTLS_ECP_FIXED_POINT_OPTIM */
278 
279 /* \} name SECTION: Module settings */
280 
281 #else  /* MBEDTLS_ECP_ALT */
282 #include "ecp_alt.h"
283 #endif /* MBEDTLS_ECP_ALT */
284 
285 #if defined(MBEDTLS_ECP_RESTARTABLE)
286 
287 /**
288  * \brief           Internal restart context for multiplication
289  *
290  * \note            Opaque struct
291  */
292 typedef struct mbedtls_ecp_restart_mul mbedtls_ecp_restart_mul_ctx;
293 
294 /**
295  * \brief           Internal restart context for ecp_muladd()
296  *
297  * \note            Opaque struct
298  */
299 typedef struct mbedtls_ecp_restart_muladd mbedtls_ecp_restart_muladd_ctx;
300 
301 /**
302  * \brief           General context for resuming ECC operations
303  */
304 typedef struct
305 {
306     unsigned ops_done;                  /*!<  current ops count             */
307     unsigned depth;                     /*!<  call depth (0 = top-level)    */
308     mbedtls_ecp_restart_mul_ctx *rsm;   /*!<  ecp_mul_comb() sub-context    */
309     mbedtls_ecp_restart_muladd_ctx *ma; /*!<  ecp_muladd() sub-context      */
310 } mbedtls_ecp_restart_ctx;
311 
312 /*
313  * Operation counts for restartable functions
314  */
315 #define MBEDTLS_ECP_OPS_CHK   3 /*!< basic ops count for ecp_check_pubkey()  */
316 #define MBEDTLS_ECP_OPS_DBL   8 /*!< basic ops count for ecp_double_jac()    */
317 #define MBEDTLS_ECP_OPS_ADD  11 /*!< basic ops count for see ecp_add_mixed() */
318 #define MBEDTLS_ECP_OPS_INV 120 /*!< empirical equivalent for mpi_mod_inv()  */
319 
320 /**
321  * \brief           Internal; for restartable functions in other modules.
322  *                  Check and update basic ops budget.
323  *
324  * \param grp       Group structure
325  * \param rs_ctx    Restart context
326  * \param ops       Number of basic ops to do
327  *
328  * \return          \c 0 if doing \p ops basic ops is still allowed,
329  * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS otherwise.
330  */
331 int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp,
332                               mbedtls_ecp_restart_ctx *rs_ctx,
333                               unsigned ops );
334 
335 /* Utility macro for checking and updating ops budget */
336 #define MBEDTLS_ECP_BUDGET( ops )   \
337     MBEDTLS_MPI_CHK( mbedtls_ecp_check_budget( grp, rs_ctx, \
338                                                (unsigned) (ops) ) );
339 
340 #else /* MBEDTLS_ECP_RESTARTABLE */
341 
342 #define MBEDTLS_ECP_BUDGET( ops )   /* no-op; for compatibility */
343 
344 /* We want to declare restartable versions of existing functions anyway */
345 typedef void mbedtls_ecp_restart_ctx;
346 
347 #endif /* MBEDTLS_ECP_RESTARTABLE */
348 
349 /**
350  * \brief    The ECP key-pair structure.
351  *
352  * A generic key-pair that may be used for ECDSA and fixed ECDH, for example.
353  *
354  * \note    Members are deliberately in the same order as in the
355  *          ::mbedtls_ecdsa_context structure.
356  */
357 typedef struct mbedtls_ecp_keypair
358 {
359     mbedtls_ecp_group grp;      /*!<  Elliptic curve and base point     */
360     mbedtls_mpi d;              /*!<  our secret value                  */
361     mbedtls_ecp_point Q;        /*!<  our public value                  */
362 }
363 mbedtls_ecp_keypair;
364 
365 /*
366  * Point formats, from RFC 4492's enum ECPointFormat
367  */
368 #define MBEDTLS_ECP_PF_UNCOMPRESSED    0   /**< Uncompressed point format. */
369 #define MBEDTLS_ECP_PF_COMPRESSED      1   /**< Compressed point format. */
370 
371 /*
372  * Some other constants from RFC 4492
373  */
374 #define MBEDTLS_ECP_TLS_NAMED_CURVE    3   /**< The named_curve of ECCurveType. */
375 
376 #if defined(MBEDTLS_ECP_RESTARTABLE)
377 /**
378  * \brief           Set the maximum number of basic operations done in a row.
379  *
380  *                  If more operations are needed to complete a computation,
381  *                  #MBEDTLS_ERR_ECP_IN_PROGRESS will be returned by the
382  *                  function performing the computation. It is then the
383  *                  caller's responsibility to either call again with the same
384  *                  parameters until it returns 0 or an error code; or to free
385  *                  the restart context if the operation is to be aborted.
386  *
387  *                  It is strictly required that all input parameters and the
388  *                  restart context be the same on successive calls for the
389  *                  same operation, but output parameters need not be the
390  *                  same; they must not be used until the function finally
391  *                  returns 0.
392  *
393  *                  This only applies to functions whose documentation
394  *                  mentions they may return #MBEDTLS_ERR_ECP_IN_PROGRESS (or
395  *                  #MBEDTLS_ERR_SSL_CRYPTO_IN_PROGRESS for functions in the
396  *                  SSL module). For functions that accept a "restart context"
397  *                  argument, passing NULL disables restart and makes the
398  *                  function equivalent to the function with the same name
399  *                  with \c _restartable removed. For functions in the ECDH
400  *                  module, restart is disabled unless the function accepts
401  *                  an "ECDH context" argument and
402  *                  mbedtls_ecdh_enable_restart() was previously called on
403  *                  that context. For function in the SSL module, restart is
404  *                  only enabled for specific sides and key exchanges
405  *                  (currently only for clients and ECDHE-ECDSA).
406  *
407  * \param max_ops   Maximum number of basic operations done in a row.
408  *                  Default: 0 (unlimited).
409  *                  Lower (non-zero) values mean ECC functions will block for
410  *                  a lesser maximum amount of time.
411  *
412  * \note            A "basic operation" is defined as a rough equivalent of a
413  *                  multiplication in GF(p) for the NIST P-256 curve.
414  *                  As an indication, with default settings, a scalar
415  *                  multiplication (full run of \c mbedtls_ecp_mul()) is:
416  *                  - about 3300 basic operations for P-256
417  *                  - about 9400 basic operations for P-384
418  *
419  * \note            Very low values are not always respected: sometimes
420  *                  functions need to block for a minimum number of
421  *                  operations, and will do so even if max_ops is set to a
422  *                  lower value.  That minimum depends on the curve size, and
423  *                  can be made lower by decreasing the value of
424  *                  \c MBEDTLS_ECP_WINDOW_SIZE.  As an indication, here is the
425  *                  lowest effective value for various curves and values of
426  *                  that parameter (w for short):
427  *                          w=6     w=5     w=4     w=3     w=2
428  *                  P-256   208     208     160     136     124
429  *                  P-384   682     416     320     272     248
430  *                  P-521  1364     832     640     544     496
431  *
432  * \note            This setting is currently ignored by Curve25519.
433  */
434 void mbedtls_ecp_set_max_ops( unsigned max_ops );
435 
436 /**
437  * \brief           Check if restart is enabled (max_ops != 0)
438  *
439  * \return          \c 0 if \c max_ops == 0 (restart disabled)
440  * \return          \c 1 otherwise (restart enabled)
441  */
442 int mbedtls_ecp_restart_is_enabled( void );
443 #endif /* MBEDTLS_ECP_RESTARTABLE */
444 
445 /**
446  * \brief           This function retrieves the information defined in
447  *                  mbedtls_ecp_curve_info() for all supported curves in order
448  *                  of preference.
449  *
450  * \return          A statically allocated array. The last entry is 0.
451  */
452 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void );
453 
454 /**
455  * \brief           This function retrieves the list of internal group
456  *                  identifiers of all supported curves in the order of
457  *                  preference.
458  *
459  * \return          A statically allocated array,
460  *                  terminated with MBEDTLS_ECP_DP_NONE.
461  */
462 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void );
463 
464 /**
465  * \brief           This function retrieves curve information from an internal
466  *                  group identifier.
467  *
468  * \param grp_id    An \c MBEDTLS_ECP_DP_XXX value.
469  *
470  * \return          The associated curve information on success.
471  * \return          NULL on failure.
472  */
473 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id );
474 
475 /**
476  * \brief           This function retrieves curve information from a TLS
477  *                  NamedCurve value.
478  *
479  * \param tls_id    An \c MBEDTLS_ECP_DP_XXX value.
480  *
481  * \return          The associated curve information on success.
482  * \return          NULL on failure.
483  */
484 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id );
485 
486 /**
487  * \brief           This function retrieves curve information from a
488  *                  human-readable name.
489  *
490  * \param name      The human-readable name.
491  *
492  * \return          The associated curve information on success.
493  * \return          NULL on failure.
494  */
495 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name );
496 
497 /**
498  * \brief           This function initializes a point as zero.
499  *
500  * \param pt        The point to initialize.
501  */
502 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt );
503 
504 /**
505  * \brief           This function initializes an ECP group context
506  *                  without loading any domain parameters.
507  *
508  * \note            After this function is called, domain parameters
509  *                  for various ECP groups can be loaded through the
510  *                  mbedtls_ecp_group_load() or mbedtls_ecp_tls_read_group()
511  *                  functions.
512  */
513 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp );
514 
515 /**
516  * \brief           This function initializes a key pair as an invalid one.
517  *
518  * \param key       The key pair to initialize.
519  */
520 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key );
521 
522 /**
523  * \brief           This function frees the components of a point.
524  *
525  * \param pt        The point to free.
526  */
527 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt );
528 
529 /**
530  * \brief           This function frees the components of an ECP group.
531  *
532  * \param grp       The group to free. This may be \c NULL, in which
533  *                  case this function returns immediately. If it is not
534  *                  \c NULL, it must point to an initialized ECP group.
535  */
536 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp );
537 
538 /**
539  * \brief           This function frees the components of a key pair.
540  *
541  * \param key       The key pair to free. This may be \c NULL, in which
542  *                  case this function returns immediately. If it is not
543  *                  \c NULL, it must point to an initialized ECP key pair.
544  */
545 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key );
546 
547 #if defined(MBEDTLS_ECP_RESTARTABLE)
548 /**
549  * \brief           Initialize a restart context.
550  *
551  * \param ctx       The restart context to initialize. This must
552  *                  not be \c NULL.
553  */
554 void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx );
555 
556 /**
557  * \brief           Free the components of a restart context.
558  *
559  * \param ctx       The restart context to free. This may be \c NULL, in which
560  *                  case this function returns immediately. If it is not
561  *                  \c NULL, it must point to an initialized restart context.
562  */
563 void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx );
564 #endif /* MBEDTLS_ECP_RESTARTABLE */
565 
566 /**
567  * \brief           This function copies the contents of point \p Q into
568  *                  point \p P.
569  *
570  * \param P         The destination point. This must be initialized.
571  * \param Q         The source point. 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 for other kinds of failure.
576  */
577 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q );
578 
579 /**
580  * \brief           This function copies the contents of group \p src into
581  *                  group \p dst.
582  *
583  * \param dst       The destination group. This must be initialized.
584  * \param src       The source group. This must be initialized.
585  *
586  * \return          \c 0 on success.
587  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
588  * \return          Another negative error code on other kinds of failure.
589  */
590 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst,
591                             const mbedtls_ecp_group *src );
592 
593 /**
594  * \brief           This function sets a point to the point at infinity.
595  *
596  * \param pt        The point to set. This must be initialized.
597  *
598  * \return          \c 0 on success.
599  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
600  * \return          Another negative error code on other kinds of failure.
601  */
602 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt );
603 
604 /**
605  * \brief           This function checks if a point is the point at infinity.
606  *
607  * \param pt        The point to test. This must be initialized.
608  *
609  * \return          \c 1 if the point is zero.
610  * \return          \c 0 if the point is non-zero.
611  * \return          A negative error code on failure.
612  */
613 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt );
614 
615 /**
616  * \brief           This function compares two points.
617  *
618  * \note            This assumes that the points are normalized. Otherwise,
619  *                  they may compare as "not equal" even if they are.
620  *
621  * \param P         The first point to compare. This must be initialized.
622  * \param Q         The second point to compare. This must be initialized.
623  *
624  * \return          \c 0 if the points are equal.
625  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the points are not equal.
626  */
627 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
628                            const mbedtls_ecp_point *Q );
629 
630 /**
631  * \brief           This function imports a non-zero point from two ASCII
632  *                  strings.
633  *
634  * \param P         The destination point. This must be initialized.
635  * \param radix     The numeric base of the input.
636  * \param x         The first affine coordinate, as a null-terminated string.
637  * \param y         The second affine coordinate, as a null-terminated string.
638  *
639  * \return          \c 0 on success.
640  * \return          An \c MBEDTLS_ERR_MPI_XXX error code on failure.
641  */
642 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
643                            const char *x, const char *y );
644 
645 /**
646  * \brief           This function exports a point into unsigned binary data.
647  *
648  * \param grp       The group to which the point should belong.
649  *                  This must be initialized and have group parameters
650  *                  set, for example through mbedtls_ecp_group_load().
651  * \param P         The point to export. This must be initialized.
652  * \param format    The point format. This must be either
653  *                  #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED.
654  * \param olen      The address at which to store the length of
655  *                  the output in Bytes. This must not be \c NULL.
656  * \param buf       The output buffer. This must be a writable buffer
657  *                  of length \p buflen Bytes.
658  * \param buflen    The length of the output buffer \p buf in Bytes.
659  *
660  * \return          \c 0 on success.
661  * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output buffer
662  *                  is too small to hold the point.
663  * \return          Another negative error code on other kinds of failure.
664  */
665 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P,
666                             int format, size_t *olen,
667                             unsigned char *buf, size_t buflen );
668 
669 /**
670  * \brief           This function imports a point from unsigned binary data.
671  *
672  * \note            This function does not check that the point actually
673  *                  belongs to the given group, see mbedtls_ecp_check_pubkey()
674  *                  for that.
675  *
676  * \param grp       The group to which the point should belong.
677  *                  This must be initialized and have group parameters
678  *                  set, for example through mbedtls_ecp_group_load().
679  * \param P         The destination context to import the point to.
680  *                  This must be initialized.
681  * \param buf       The input buffer. This must be a readable buffer
682  *                  of length \p ilen Bytes.
683  * \param ilen      The length of the input buffer \p buf in Bytes.
684  *
685  * \return          \c 0 on success.
686  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
687  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
688  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format
689  *                  is not implemented.
690  */
691 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp,
692                                    mbedtls_ecp_point *P,
693                                    const unsigned char *buf, size_t ilen );
694 
695 /**
696  * \brief           This function imports a point from a TLS ECPoint record.
697  *
698  * \note            On function return, \p *buf is updated to point immediately
699  *                  after the ECPoint record.
700  *
701  * \param grp       The ECP group to use.
702  *                  This must be initialized and have group parameters
703  *                  set, for example through mbedtls_ecp_group_load().
704  * \param pt        The destination point.
705  * \param buf       The address of the pointer to the start of the input buffer.
706  * \param len       The length of the buffer.
707  *
708  * \return          \c 0 on success.
709  * \return          An \c MBEDTLS_ERR_MPI_XXX error code on initialization
710  *                  failure.
711  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
712  */
713 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp,
714                                 mbedtls_ecp_point *pt,
715                                 const unsigned char **buf, size_t len );
716 
717 /**
718  * \brief           This function exports a point as a TLS ECPoint record
719  *                  defined in RFC 4492, Section 5.4.
720  *
721  * \param grp       The ECP group to use.
722  *                  This must be initialized and have group parameters
723  *                  set, for example through mbedtls_ecp_group_load().
724  * \param pt        The point to be exported. This must be initialized.
725  * \param format    The point format to use. This must be either
726  *                  #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED.
727  * \param olen      The address at which to store the length in Bytes
728  *                  of the data written.
729  * \param buf       The target buffer. This must be a writable buffer of
730  *                  length \p blen Bytes.
731  * \param blen      The length of the target buffer \p buf in Bytes.
732  *
733  * \return          \c 0 on success.
734  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
735  * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the target buffer
736  *                  is too small to hold the exported point.
737  * \return          Another negative error code on other kinds of failure.
738  */
739 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp,
740                                  const mbedtls_ecp_point *pt,
741                                  int format, size_t *olen,
742                                  unsigned char *buf, size_t blen );
743 
744 /**
745  * \brief           This function sets up an ECP group context
746  *                  from a standardized set of domain parameters.
747  *
748  * \note            The index should be a value of the NamedCurve enum,
749  *                  as defined in <em>RFC-4492: Elliptic Curve Cryptography
750  *                  (ECC) Cipher Suites for Transport Layer Security (TLS)</em>,
751  *                  usually in the form of an \c MBEDTLS_ECP_DP_XXX macro.
752  *
753  * \param grp       The group context to setup. This must be initialized.
754  * \param id        The identifier of the domain parameter set to load.
755  *
756  * \return          \c 0 on success.
757  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p id doesn't
758  *                  correspond to a known group.
759  * \return          Another negative error code on other kinds of failure.
760  */
761 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id );
762 
763 /**
764  * \brief           This function sets up an ECP group context from a TLS
765  *                  ECParameters record as defined in RFC 4492, Section 5.4.
766  *
767  * \note            The read pointer \p buf is updated to point right after
768  *                  the ECParameters record on exit.
769  *
770  * \param grp       The group context to setup. This must be initialized.
771  * \param buf       The address of the pointer to the start of the input buffer.
772  * \param len       The length of the input buffer \c *buf in Bytes.
773  *
774  * \return          \c 0 on success.
775  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
776  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
777  *                  recognized.
778  * \return          Another negative error code on other kinds of failure.
779  */
780 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp,
781                                 const unsigned char **buf, size_t len );
782 
783 /**
784  * \brief           This function extracts an elliptic curve group ID from a
785  *                  TLS ECParameters record as defined in RFC 4492, Section 5.4.
786  *
787  * \note            The read pointer \p buf is updated to point right after
788  *                  the ECParameters record on exit.
789  *
790  * \param grp       The address at which to store the group id.
791  *                  This must not be \c NULL.
792  * \param buf       The address of the pointer to the start of the input buffer.
793  * \param len       The length of the input buffer \c *buf in Bytes.
794  *
795  * \return          \c 0 on success.
796  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
797  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
798  *                  recognized.
799  * \return          Another negative error code on other kinds of failure.
800  */
801 int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp,
802                                    const unsigned char **buf,
803                                    size_t len );
804 /**
805  * \brief           This function exports an elliptic curve as a TLS
806  *                  ECParameters record as defined in RFC 4492, Section 5.4.
807  *
808  * \param grp       The ECP group to be exported.
809  *                  This must be initialized and have group parameters
810  *                  set, for example through mbedtls_ecp_group_load().
811  * \param olen      The address at which to store the number of Bytes written.
812  *                  This must not be \c NULL.
813  * \param buf       The buffer to write to. This must be a writable buffer
814  *                  of length \p blen Bytes.
815  * \param blen      The length of the output buffer \p buf in Bytes.
816  *
817  * \return          \c 0 on success.
818  * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output
819  *                  buffer is too small to hold the exported group.
820  * \return          Another negative error code on other kinds of failure.
821  */
822 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp,
823                                  size_t *olen,
824                                  unsigned char *buf, size_t blen );
825 
826 /**
827  * \brief           This function performs a scalar multiplication of a point
828  *                  by an integer: \p R = \p m * \p P.
829  *
830  *                  It is not thread-safe to use same group in multiple threads.
831  *
832  * \note            To prevent timing attacks, this function
833  *                  executes the exact same sequence of base-field
834  *                  operations for any valid \p m. It avoids any if-branch or
835  *                  array index depending on the value of \p m.
836  *
837  * \note            If \p f_rng is not NULL, it is used to randomize
838  *                  intermediate results to prevent potential timing attacks
839  *                  targeting these results. We recommend always providing
840  *                  a non-NULL \p f_rng. The overhead is negligible.
841  *                  Note: unless #MBEDTLS_ECP_NO_INTERNAL_RNG is defined, when
842  *                  \p f_rng is NULL, an internal RNG (seeded from the value
843  *                  of \p m) will be used instead.
844  *
845  * \param grp       The ECP group to use.
846  *                  This must be initialized and have group parameters
847  *                  set, for example through mbedtls_ecp_group_load().
848  * \param R         The point in which to store the result of the calculation.
849  *                  This must be initialized.
850  * \param m         The integer by which to multiply. This must be initialized.
851  * \param P         The point to multiply. This must be initialized.
852  * \param f_rng     The RNG function. This may be \c NULL if randomization
853  *                  of intermediate results isn't desired (discouraged).
854  * \param p_rng     The RNG context to be passed to \p p_rng.
855  *
856  * \return          \c 0 on success.
857  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private
858  *                  key, or \p P is not a valid public key.
859  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
860  * \return          Another negative error code on other kinds of failure.
861  */
862 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
863              const mbedtls_mpi *m, const mbedtls_ecp_point *P,
864              int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
865 
866 /**
867  * \brief           This function performs multiplication of a point by
868  *                  an integer: \p R = \p m * \p P in a restartable way.
869  *
870  * \see             mbedtls_ecp_mul()
871  *
872  * \note            This function does the same as \c mbedtls_ecp_mul(), but
873  *                  it can return early and restart according to the limit set
874  *                  with \c mbedtls_ecp_set_max_ops() to reduce blocking.
875  *
876  * \param grp       The ECP group to use.
877  *                  This must be initialized and have group parameters
878  *                  set, for example through mbedtls_ecp_group_load().
879  * \param R         The point in which to store the result of the calculation.
880  *                  This must be initialized.
881  * \param m         The integer by which to multiply. This must be initialized.
882  * \param P         The point to multiply. This must be initialized.
883  * \param f_rng     The RNG function. This may be \c NULL if randomization
884  *                  of intermediate results isn't desired (discouraged).
885  * \param p_rng     The RNG context to be passed to \p p_rng.
886  * \param rs_ctx    The restart context (NULL disables restart).
887  *
888  * \return          \c 0 on success.
889  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private
890  *                  key, or \p P is not a valid public key.
891  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
892  * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
893  *                  operations was reached: see \c mbedtls_ecp_set_max_ops().
894  * \return          Another negative error code on other kinds of failure.
895  */
896 int mbedtls_ecp_mul_restartable( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
897              const mbedtls_mpi *m, const mbedtls_ecp_point *P,
898              int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
899              mbedtls_ecp_restart_ctx *rs_ctx );
900 
901 /**
902  * \brief           This function performs multiplication and addition of two
903  *                  points by integers: \p R = \p m * \p P + \p n * \p Q
904  *
905  *                  It is not thread-safe to use same group in multiple threads.
906  *
907  * \note            In contrast to mbedtls_ecp_mul(), this function does not
908  *                  guarantee a constant execution flow and timing.
909  *
910  * \param grp       The ECP group to use.
911  *                  This must be initialized and have group parameters
912  *                  set, for example through mbedtls_ecp_group_load().
913  * \param R         The point in which to store the result of the calculation.
914  *                  This must be initialized.
915  * \param m         The integer by which to multiply \p P.
916  *                  This must be initialized.
917  * \param P         The point to multiply by \p m. This must be initialized.
918  * \param n         The integer by which to multiply \p Q.
919  *                  This must be initialized.
920  * \param Q         The point to be multiplied by \p n.
921  *                  This must be initialized.
922  *
923  * \return          \c 0 on success.
924  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not
925  *                  valid private keys, or \p P or \p Q are not valid public
926  *                  keys.
927  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
928  * \return          Another negative error code on other kinds of failure.
929  */
930 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
931              const mbedtls_mpi *m, const mbedtls_ecp_point *P,
932              const mbedtls_mpi *n, const mbedtls_ecp_point *Q );
933 
934 /**
935  * \brief           This function performs multiplication and addition of two
936  *                  points by integers: \p R = \p m * \p P + \p n * \p Q in a
937  *                  restartable way.
938  *
939  * \see             \c mbedtls_ecp_muladd()
940  *
941  * \note            This function works the same as \c mbedtls_ecp_muladd(),
942  *                  but it can return early and restart according to the limit
943  *                  set with \c mbedtls_ecp_set_max_ops() to reduce blocking.
944  *
945  * \param grp       The ECP group to use.
946  *                  This must be initialized and have group parameters
947  *                  set, for example through mbedtls_ecp_group_load().
948  * \param R         The point in which to store the result of the calculation.
949  *                  This must be initialized.
950  * \param m         The integer by which to multiply \p P.
951  *                  This must be initialized.
952  * \param P         The point to multiply by \p m. This must be initialized.
953  * \param n         The integer by which to multiply \p Q.
954  *                  This must be initialized.
955  * \param Q         The point to be multiplied by \p n.
956  *                  This must be initialized.
957  * \param rs_ctx    The restart context (NULL disables restart).
958  *
959  * \return          \c 0 on success.
960  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not
961  *                  valid private keys, or \p P or \p Q are not valid public
962  *                  keys.
963  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
964  * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
965  *                  operations was reached: see \c mbedtls_ecp_set_max_ops().
966  * \return          Another negative error code on other kinds of failure.
967  */
968 int mbedtls_ecp_muladd_restartable(
969              mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
970              const mbedtls_mpi *m, const mbedtls_ecp_point *P,
971              const mbedtls_mpi *n, const mbedtls_ecp_point *Q,
972              mbedtls_ecp_restart_ctx *rs_ctx );
973 
974 /**
975  * \brief           This function checks that a point is a valid public key
976  *                  on this curve.
977  *
978  *                  It only checks that the point is non-zero, has
979  *                  valid coordinates and lies on the curve. It does not verify
980  *                  that it is indeed a multiple of \p G. This additional
981  *                  check is computationally more expensive, is not required
982  *                  by standards, and should not be necessary if the group
983  *                  used has a small cofactor. In particular, it is useless for
984  *                  the NIST groups which all have a cofactor of 1.
985  *
986  * \note            This function uses bare components rather than an
987  *                  ::mbedtls_ecp_keypair structure, to ease use with other
988  *                  structures, such as ::mbedtls_ecdh_context or
989  *                  ::mbedtls_ecdsa_context.
990  *
991  * \param grp       The ECP group the point should belong to.
992  *                  This must be initialized and have group parameters
993  *                  set, for example through mbedtls_ecp_group_load().
994  * \param pt        The point to check. This must be initialized.
995  *
996  * \return          \c 0 if the point is a valid public key.
997  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not
998  *                  a valid public key for the given curve.
999  * \return          Another negative error code on other kinds of failure.
1000  */
1001 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp,
1002                               const mbedtls_ecp_point *pt );
1003 
1004 /**
1005  * \brief           This function checks that an \p mbedtls_mpi is a
1006  *                  valid private key for this curve.
1007  *
1008  * \note            This function uses bare components rather than an
1009  *                  ::mbedtls_ecp_keypair structure to ease use with other
1010  *                  structures, such as ::mbedtls_ecdh_context or
1011  *                  ::mbedtls_ecdsa_context.
1012  *
1013  * \param grp       The ECP group the private key should belong to.
1014  *                  This must be initialized and have group parameters
1015  *                  set, for example through mbedtls_ecp_group_load().
1016  * \param d         The integer to check. This must be initialized.
1017  *
1018  * \return          \c 0 if the point is a valid private key.
1019  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not a valid
1020  *                  private key for the given curve.
1021  * \return          Another negative error code on other kinds of failure.
1022  */
1023 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp,
1024                                const mbedtls_mpi *d );
1025 
1026 /**
1027  * \brief           This function generates a private key.
1028  *
1029  * \param grp       The ECP group to generate a private key for.
1030  *                  This must be initialized and have group parameters
1031  *                  set, for example through mbedtls_ecp_group_load().
1032  * \param d         The destination MPI (secret part). This must be initialized.
1033  * \param f_rng     The RNG function. This must not be \c NULL.
1034  * \param p_rng     The RNG parameter to be passed to \p f_rng. This may be
1035  *                  \c NULL if \p f_rng doesn't need a context argument.
1036  *
1037  * \return          \c 0 on success.
1038  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1039  *                  on failure.
1040  */
1041 int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp,
1042                      mbedtls_mpi *d,
1043                      int (*f_rng)(void *, unsigned char *, size_t),
1044                      void *p_rng );
1045 
1046 /**
1047  * \brief           This function generates a keypair with a configurable base
1048  *                  point.
1049  *
1050  * \note            This function uses bare components rather than an
1051  *                  ::mbedtls_ecp_keypair structure to ease use with other
1052  *                  structures, such as ::mbedtls_ecdh_context or
1053  *                  ::mbedtls_ecdsa_context.
1054  *
1055  * \param grp       The ECP group to generate a key pair for.
1056  *                  This must be initialized and have group parameters
1057  *                  set, for example through mbedtls_ecp_group_load().
1058  * \param G         The base point to use. This must be initialized
1059  *                  and belong to \p grp. It replaces the default base
1060  *                  point \c grp->G used by mbedtls_ecp_gen_keypair().
1061  * \param d         The destination MPI (secret part).
1062  *                  This must be initialized.
1063  * \param Q         The destination point (public part).
1064  *                  This must be initialized.
1065  * \param f_rng     The RNG function. This must not be \c NULL.
1066  * \param p_rng     The RNG context to be passed to \p f_rng. This may
1067  *                  be \c NULL if \p f_rng doesn't need a context argument.
1068  *
1069  * \return          \c 0 on success.
1070  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1071  *                  on failure.
1072  */
1073 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
1074                                   const mbedtls_ecp_point *G,
1075                                   mbedtls_mpi *d, 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 keypair.
1081  *
1082  * \note            This function uses bare components rather than an
1083  *                  ::mbedtls_ecp_keypair structure to ease use with other
1084  *                  structures, such as ::mbedtls_ecdh_context or
1085  *                  ::mbedtls_ecdsa_context.
1086  *
1087  * \param grp       The ECP group to generate a key pair for.
1088  *                  This must be initialized and have group parameters
1089  *                  set, for example through mbedtls_ecp_group_load().
1090  * \param d         The destination MPI (secret part).
1091  *                  This must be initialized.
1092  * \param Q         The destination point (public part).
1093  *                  This must be initialized.
1094  * \param f_rng     The RNG function. This must not be \c NULL.
1095  * \param p_rng     The RNG context to be passed to \p f_rng. This may
1096  *                  be \c NULL if \p f_rng doesn't need a context argument.
1097  *
1098  * \return          \c 0 on success.
1099  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1100  *                  on failure.
1101  */
1102 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, mbedtls_mpi *d,
1103                              mbedtls_ecp_point *Q,
1104                              int (*f_rng)(void *, unsigned char *, size_t),
1105                              void *p_rng );
1106 
1107 /**
1108  * \brief           This function generates an ECP key.
1109  *
1110  * \param grp_id    The ECP group identifier.
1111  * \param key       The destination key. This must be initialized.
1112  * \param f_rng     The RNG function to use. This must not be \c NULL.
1113  * \param p_rng     The RNG context to be passed to \p f_rng. This may
1114  *                  be \c NULL if \p f_rng doesn't need a context argument.
1115  *
1116  * \return          \c 0 on success.
1117  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1118  *                  on failure.
1119  */
1120 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
1121                          int (*f_rng)(void *, unsigned char *, size_t),
1122                          void *p_rng );
1123 
1124 /**
1125  * \brief           This function checks that the keypair objects
1126  *                  \p pub and \p prv have the same group and the
1127  *                  same public point, and that the private key in
1128  *                  \p prv is consistent with the public key.
1129  *
1130  * \param pub       The keypair structure holding the public key. This
1131  *                  must be initialized. If it contains a private key, that
1132  *                  part is ignored.
1133  * \param prv       The keypair structure holding the full keypair.
1134  *                  This must be initialized.
1135  *
1136  * \return          \c 0 on success, meaning that the keys are valid and match.
1137  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the keys are invalid or do not match.
1138  * \return          An \c MBEDTLS_ERR_ECP_XXX or an \c MBEDTLS_ERR_MPI_XXX
1139  *                  error code on calculation failure.
1140  */
1141 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub,
1142                                 const mbedtls_ecp_keypair *prv );
1143 
1144 #if defined(MBEDTLS_SELF_TEST)
1145 
1146 /**
1147  * \brief          The ECP checkup routine.
1148  *
1149  * \return         \c 0 on success.
1150  * \return         \c 1 on failure.
1151  */
1152 int mbedtls_ecp_self_test( int verbose );
1153 
1154 #endif /* MBEDTLS_SELF_TEST */
1155 
1156 #ifdef __cplusplus
1157 }
1158 #endif
1159 
1160 #endif /* ecp.h */
1161