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
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 
34 #ifndef MBEDTLS_ECP_H
35 #define MBEDTLS_ECP_H
36 #include "mbedtls/private_access.h"
37 
38 #include "mbedtls/build_info.h"
39 
40 #include "mbedtls/bignum.h"
41 
42 /*
43  * ECP error codes
44  */
45 /** Bad input parameters to function. */
46 #define MBEDTLS_ERR_ECP_BAD_INPUT_DATA                    -0x4F80
47 /** The buffer is too small to write to. */
48 #define MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL                  -0x4F00
49 /** The requested feature is not available, for example, the requested curve is not supported. */
50 #define MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE               -0x4E80
51 /** The signature is not valid. */
52 #define MBEDTLS_ERR_ECP_VERIFY_FAILED                     -0x4E00
53 /** Memory allocation failed. */
54 #define MBEDTLS_ERR_ECP_ALLOC_FAILED                      -0x4D80
55 /** Generation of random value, such as ephemeral key, failed. */
56 #define MBEDTLS_ERR_ECP_RANDOM_FAILED                     -0x4D00
57 /** Invalid private or public key. */
58 #define MBEDTLS_ERR_ECP_INVALID_KEY                       -0x4C80
59 /** The buffer contains a valid signature followed by more data. */
60 #define MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH                  -0x4C00
61 /** Operation in progress, call again with the same parameters to continue. */
62 #define MBEDTLS_ERR_ECP_IN_PROGRESS                       -0x4B00
63 
64 /* Flags indicating whether to include code that is specific to certain
65  * types of curves. These flags are for internal library use only. */
66 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \
67     defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
68     defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
69     defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \
70     defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \
71     defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \
72     defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \
73     defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \
74     defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
75     defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
76     defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
77 #define MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED
78 #endif
79 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) || \
80     defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
81 #define MBEDTLS_ECP_MONTGOMERY_ENABLED
82 #endif
83 
84 #ifdef __cplusplus
85 extern "C" {
86 #endif
87 
88 /**
89  * Domain-parameter identifiers: curve, subgroup, and generator.
90  *
91  * \note Only curves over prime fields are supported.
92  *
93  * \warning This library does not support validation of arbitrary domain
94  * parameters. Therefore, only standardized domain parameters from trusted
95  * sources should be used. See mbedtls_ecp_group_load().
96  */
97 /* Note: when adding a new curve:
98  * - Add it at the end of this enum, otherwise you'll break the ABI by
99  *   changing the numerical value for existing curves.
100  * - Increment MBEDTLS_ECP_DP_MAX below if needed.
101  * - Update the calculation of MBEDTLS_ECP_MAX_BITS below.
102  * - Add the corresponding MBEDTLS_ECP_DP_xxx_ENABLED macro definition to
103  *   mbedtls_config.h.
104  * - List the curve as a dependency of MBEDTLS_ECP_C and
105  *   MBEDTLS_ECDSA_C if supported in check_config.h.
106  * - Add the curve to the appropriate curve type macro
107  *   MBEDTLS_ECP_yyy_ENABLED above.
108  * - Add the necessary definitions to ecp_curves.c.
109  * - Add the curve to the ecp_supported_curves array in ecp.c.
110  * - Add the curve to applicable profiles in x509_crt.c.
111  * - Add the curve to applicable presets in ssl_tls.c.
112  */
113 typedef enum
114 {
115     MBEDTLS_ECP_DP_NONE = 0,       /*!< Curve not defined. */
116     MBEDTLS_ECP_DP_SECP192R1,      /*!< Domain parameters for the 192-bit curve defined by FIPS 186-4 and SEC1. */
117     MBEDTLS_ECP_DP_SECP224R1,      /*!< Domain parameters for the 224-bit curve defined by FIPS 186-4 and SEC1. */
118     MBEDTLS_ECP_DP_SECP256R1,      /*!< Domain parameters for the 256-bit curve defined by FIPS 186-4 and SEC1. */
119     MBEDTLS_ECP_DP_SECP384R1,      /*!< Domain parameters for the 384-bit curve defined by FIPS 186-4 and SEC1. */
120     MBEDTLS_ECP_DP_SECP521R1,      /*!< Domain parameters for the 521-bit curve defined by FIPS 186-4 and SEC1. */
121     MBEDTLS_ECP_DP_BP256R1,        /*!< Domain parameters for 256-bit Brainpool curve. */
122     MBEDTLS_ECP_DP_BP384R1,        /*!< Domain parameters for 384-bit Brainpool curve. */
123     MBEDTLS_ECP_DP_BP512R1,        /*!< Domain parameters for 512-bit Brainpool curve. */
124     MBEDTLS_ECP_DP_CURVE25519,     /*!< Domain parameters for Curve25519. */
125     MBEDTLS_ECP_DP_SECP192K1,      /*!< Domain parameters for 192-bit "Koblitz" curve. */
126     MBEDTLS_ECP_DP_SECP224K1,      /*!< Domain parameters for 224-bit "Koblitz" curve. */
127     MBEDTLS_ECP_DP_SECP256K1,      /*!< Domain parameters for 256-bit "Koblitz" curve. */
128     MBEDTLS_ECP_DP_CURVE448,       /*!< Domain parameters for Curve448. */
129 } mbedtls_ecp_group_id;
130 
131 /**
132  * The number of supported curves, plus one for #MBEDTLS_ECP_DP_NONE.
133  */
134 #define MBEDTLS_ECP_DP_MAX     14
135 
136 /*
137  * Curve types
138  */
139 typedef enum
140 {
141     MBEDTLS_ECP_TYPE_NONE = 0,
142     MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS,    /* y^2 = x^3 + a x + b      */
143     MBEDTLS_ECP_TYPE_MONTGOMERY,           /* y^2 = x^3 + a x^2 + x    */
144 } mbedtls_ecp_curve_type;
145 
146 /**
147  * Curve information, for use by other modules.
148  *
149  * The fields of this structure are part of the public API and can be
150  * accessed directly by applications. Future versions of the library may
151  * add extra fields or reorder existing fields.
152  */
153 typedef struct mbedtls_ecp_curve_info
154 {
155     mbedtls_ecp_group_id grp_id;    /*!< An internal identifier. */
156     uint16_t tls_id;                /*!< The TLS NamedCurve identifier. */
157     uint16_t bit_size;              /*!< The curve size in bits. */
158     const char *name;               /*!< A human-friendly name. */
159 } mbedtls_ecp_curve_info;
160 
161 /**
162  * \brief           The ECP point structure, in Jacobian coordinates.
163  *
164  * \note            All functions expect and return points satisfying
165  *                  the following condition: <code>Z == 0</code> or
166  *                  <code>Z == 1</code>. Other values of \p Z are
167  *                  used only by internal functions.
168  *                  The point is zero, or "at infinity", if <code>Z == 0</code>.
169  *                  Otherwise, \p X and \p Y are its standard (affine)
170  *                  coordinates.
171  */
172 typedef struct mbedtls_ecp_point
173 {
174     mbedtls_mpi MBEDTLS_PRIVATE(X);          /*!< The X coordinate of the ECP point. */
175     mbedtls_mpi MBEDTLS_PRIVATE(Y);          /*!< The Y coordinate of the ECP point. */
176     mbedtls_mpi MBEDTLS_PRIVATE(Z);          /*!< The Z coordinate of the ECP point. */
177 }
178 mbedtls_ecp_point;
179 
180 #if !defined(MBEDTLS_ECP_ALT)
181 /*
182  * default mbed TLS elliptic curve arithmetic implementation
183  *
184  * (in case MBEDTLS_ECP_ALT is defined then the developer has to provide an
185  * alternative implementation for the whole module and it will replace this
186  * one.)
187  */
188 
189 /**
190  * \brief           The ECP group structure.
191  *
192  * We consider two types of curve equations:
193  * <ul><li>Short Weierstrass: <code>y^2 = x^3 + A x + B mod P</code>
194  * (SEC1 + RFC-4492)</li>
195  * <li>Montgomery: <code>y^2 = x^3 + A x^2 + x mod P</code> (Curve25519,
196  * Curve448)</li></ul>
197  * In both cases, the generator (\p G) for a prime-order subgroup is fixed.
198  *
199  * For Short Weierstrass, this subgroup is the whole curve, and its
200  * cardinality is denoted by \p N. Our code requires that \p N is an
201  * odd prime as mbedtls_ecp_mul() requires an odd number, and
202  * mbedtls_ecdsa_sign() requires that it is prime for blinding purposes.
203  *
204  * For Montgomery curves, we do not store \p A, but <code>(A + 2) / 4</code>,
205  * which is the quantity used in the formulas. Additionally, \p nbits is
206  * not the size of \p N but the required size for private keys.
207  *
208  * If \p modp is NULL, reduction modulo \p P is done using a generic algorithm.
209  * Otherwise, \p modp must point to a function that takes an \p mbedtls_mpi in the
210  * range of <code>0..2^(2*pbits)-1</code>, and transforms it in-place to an integer
211  * which is congruent mod \p P to the given MPI, and is close enough to \p pbits
212  * in size, so that it may be efficiently brought in the 0..P-1 range by a few
213  * additions or subtractions. Therefore, it is only an approximative modular
214  * reduction. It must return 0 on success and non-zero on failure.
215  *
216  * \note        Alternative implementations of the ECP module must obey the
217  *              following constraints.
218  *              * Group IDs must be distinct: if two group structures have
219  *                the same ID, then they must be identical.
220  *              * The fields \c id, \c P, \c A, \c B, \c G, \c N,
221  *                \c pbits and \c nbits must have the same type and semantics
222  *                as in the built-in implementation.
223  *                They must be available for reading, but direct modification
224  *                of these fields does not need to be supported.
225  *                They do not need to be at the same offset in the structure.
226  */
227 typedef struct mbedtls_ecp_group
228 {
229     mbedtls_ecp_group_id id;    /*!< An internal group identifier. */
230     mbedtls_mpi P;              /*!< The prime modulus of the base field. */
231     mbedtls_mpi A;              /*!< For Short Weierstrass: \p A in the equation. For
232                                      Montgomery curves: <code>(A + 2) / 4</code>. */
233     mbedtls_mpi B;              /*!< For Short Weierstrass: \p B in the equation.
234                                      For Montgomery curves: unused. */
235     mbedtls_ecp_point G;        /*!< The generator of the subgroup used. */
236     mbedtls_mpi N;              /*!< The order of \p G. */
237     size_t pbits;               /*!< The number of bits in \p P.*/
238     size_t nbits;               /*!< For Short Weierstrass: The number of bits in \p P.
239                                      For Montgomery curves: the number of bits in the
240                                      private keys. */
241     /* End of public fields */
242 
243     unsigned int MBEDTLS_PRIVATE(h);             /*!< \internal 1 if the constants are static. */
244     int (*MBEDTLS_PRIVATE(modp))(mbedtls_mpi *); /*!< The function for fast pseudo-reduction
245                                      mod \p P (see above).*/
246     int (*MBEDTLS_PRIVATE(t_pre))(mbedtls_ecp_point *, void *);  /*!< Unused. */
247     int (*MBEDTLS_PRIVATE(t_post))(mbedtls_ecp_point *, void *); /*!< Unused. */
248     void *MBEDTLS_PRIVATE(t_data);               /*!< Unused. */
249     mbedtls_ecp_point *MBEDTLS_PRIVATE(T);       /*!< Pre-computed points for ecp_mul_comb(). */
250     size_t MBEDTLS_PRIVATE(T_size);              /*!< The number of dynamic allocated pre-computed points. */
251 }
252 mbedtls_ecp_group;
253 
254 /**
255  * \name SECTION: Module settings
256  *
257  * The configuration options you can set for this module are in this section.
258  * Either change them in mbedtls_config.h, or define them using the compiler command line.
259  * \{
260  */
261 
262 #if !defined(MBEDTLS_ECP_WINDOW_SIZE)
263 /*
264  * Maximum "window" size used for point multiplication.
265  * Default: a point where higher memory usage yields disminishing performance
266  *          returns.
267  * Minimum value: 2. Maximum value: 7.
268  *
269  * Result is an array of at most ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
270  * points used for point multiplication. This value is directly tied to EC
271  * peak memory usage, so decreasing it by one should roughly cut memory usage
272  * by two (if large curves are in use).
273  *
274  * Reduction in size may reduce speed, but larger curves are impacted first.
275  * Sample performances (in ECDHE handshakes/s, with FIXED_POINT_OPTIM = 1):
276  *      w-size:     6       5       4       3       2
277  *      521       145     141     135     120      97
278  *      384       214     209     198     177     146
279  *      256       320     320     303     262     226
280  *      224       475     475     453     398     342
281  *      192       640     640     633     587     476
282  */
283 #define MBEDTLS_ECP_WINDOW_SIZE    4   /**< The maximum window size used. */
284 #endif /* MBEDTLS_ECP_WINDOW_SIZE */
285 
286 #if !defined(MBEDTLS_ECP_FIXED_POINT_OPTIM)
287 /*
288  * Trade code size for speed on fixed-point multiplication.
289  *
290  * This speeds up repeated multiplication of the generator (that is, the
291  * multiplication in ECDSA signatures, and half of the multiplications in
292  * ECDSA verification and ECDHE) by a factor roughly 3 to 4.
293  *
294  * For each n-bit Short Weierstrass curve that is enabled, this adds 4n bytes
295  * of code size if n < 384 and 8n otherwise.
296  *
297  * Change this value to 0 to reduce code size.
298  */
299 #define MBEDTLS_ECP_FIXED_POINT_OPTIM  1   /**< Enable fixed-point speed-up. */
300 #endif /* MBEDTLS_ECP_FIXED_POINT_OPTIM */
301 
302 /* \} name SECTION: Module settings */
303 
304 #else  /* MBEDTLS_ECP_ALT */
305 #include "ecp_alt.h"
306 #endif /* MBEDTLS_ECP_ALT */
307 
308 /**
309  * The maximum size of the groups, that is, of \c N and \c P.
310  */
311 #if !defined(MBEDTLS_ECP_C)
312 /* Dummy definition to help code that has optional ECP support and
313  * defines an MBEDTLS_ECP_MAX_BYTES-sized array unconditionally. */
314 #define MBEDTLS_ECP_MAX_BITS 1
315 /* Note: the curves must be listed in DECREASING size! */
316 #elif defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
317 #define MBEDTLS_ECP_MAX_BITS 521
318 #elif defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
319 #define MBEDTLS_ECP_MAX_BITS 512
320 #elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
321 #define MBEDTLS_ECP_MAX_BITS 448
322 #elif defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
323 #define MBEDTLS_ECP_MAX_BITS 384
324 #elif defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
325 #define MBEDTLS_ECP_MAX_BITS 384
326 #elif defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
327 #define MBEDTLS_ECP_MAX_BITS 256
328 #elif defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
329 #define MBEDTLS_ECP_MAX_BITS 256
330 #elif defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
331 #define MBEDTLS_ECP_MAX_BITS 256
332 #elif defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
333 #define MBEDTLS_ECP_MAX_BITS 255
334 #elif defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
335 #define MBEDTLS_ECP_MAX_BITS 225 // n is slightly above 2^224
336 #elif defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
337 #define MBEDTLS_ECP_MAX_BITS 224
338 #elif defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
339 #define MBEDTLS_ECP_MAX_BITS 192
340 #elif defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
341 #define MBEDTLS_ECP_MAX_BITS 192
342 #else
343 #error "Missing definition of MBEDTLS_ECP_MAX_BITS"
344 #endif
345 
346 #define MBEDTLS_ECP_MAX_BYTES    ( ( MBEDTLS_ECP_MAX_BITS + 7 ) / 8 )
347 #define MBEDTLS_ECP_MAX_PT_LEN   ( 2 * MBEDTLS_ECP_MAX_BYTES + 1 )
348 
349 #if defined(MBEDTLS_ECP_RESTARTABLE)
350 
351 /**
352  * \brief           Internal restart context for multiplication
353  *
354  * \note            Opaque struct
355  */
356 typedef struct mbedtls_ecp_restart_mul mbedtls_ecp_restart_mul_ctx;
357 
358 /**
359  * \brief           Internal restart context for ecp_muladd()
360  *
361  * \note            Opaque struct
362  */
363 typedef struct mbedtls_ecp_restart_muladd mbedtls_ecp_restart_muladd_ctx;
364 
365 /**
366  * \brief           General context for resuming ECC operations
367  */
368 typedef struct
369 {
370     unsigned MBEDTLS_PRIVATE(ops_done);                  /*!<  current ops count             */
371     unsigned MBEDTLS_PRIVATE(depth);                     /*!<  call depth (0 = top-level)    */
372     mbedtls_ecp_restart_mul_ctx *MBEDTLS_PRIVATE(rsm);   /*!<  ecp_mul_comb() sub-context    */
373     mbedtls_ecp_restart_muladd_ctx *MBEDTLS_PRIVATE(ma); /*!<  ecp_muladd() sub-context      */
374 } mbedtls_ecp_restart_ctx;
375 
376 /*
377  * Operation counts for restartable functions
378  */
379 #define MBEDTLS_ECP_OPS_CHK   3 /*!< basic ops count for ecp_check_pubkey()  */
380 #define MBEDTLS_ECP_OPS_DBL   8 /*!< basic ops count for ecp_double_jac()    */
381 #define MBEDTLS_ECP_OPS_ADD  11 /*!< basic ops count for see ecp_add_mixed() */
382 #define MBEDTLS_ECP_OPS_INV 120 /*!< empirical equivalent for mpi_mod_inv()  */
383 
384 /**
385  * \brief           Internal; for restartable functions in other modules.
386  *                  Check and update basic ops budget.
387  *
388  * \param grp       Group structure
389  * \param rs_ctx    Restart context
390  * \param ops       Number of basic ops to do
391  *
392  * \return          \c 0 if doing \p ops basic ops is still allowed,
393  * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS otherwise.
394  */
395 int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp,
396                               mbedtls_ecp_restart_ctx *rs_ctx,
397                               unsigned ops );
398 
399 /* Utility macro for checking and updating ops budget */
400 #define MBEDTLS_ECP_BUDGET( ops )   \
401     MBEDTLS_MPI_CHK( mbedtls_ecp_check_budget( grp, rs_ctx, \
402                                                (unsigned) (ops) ) );
403 
404 #else /* MBEDTLS_ECP_RESTARTABLE */
405 
406 #define MBEDTLS_ECP_BUDGET( ops )   /* no-op; for compatibility */
407 
408 /* We want to declare restartable versions of existing functions anyway */
409 typedef void mbedtls_ecp_restart_ctx;
410 
411 #endif /* MBEDTLS_ECP_RESTARTABLE */
412 
413 /**
414  * \brief    The ECP key-pair structure.
415  *
416  * A generic key-pair that may be used for ECDSA and fixed ECDH, for example.
417  *
418  * \note    Members are deliberately in the same order as in the
419  *          ::mbedtls_ecdsa_context structure.
420  */
421 typedef struct mbedtls_ecp_keypair
422 {
423     mbedtls_ecp_group MBEDTLS_PRIVATE(grp);      /*!<  Elliptic curve and base point     */
424     mbedtls_mpi MBEDTLS_PRIVATE(d);              /*!<  our secret value                  */
425     mbedtls_ecp_point MBEDTLS_PRIVATE(Q);        /*!<  our public value                  */
426 }
427 mbedtls_ecp_keypair;
428 
429 /*
430  * Point formats, from RFC 4492's enum ECPointFormat
431  */
432 #define MBEDTLS_ECP_PF_UNCOMPRESSED    0   /**< Uncompressed point format. */
433 #define MBEDTLS_ECP_PF_COMPRESSED      1   /**< Compressed point format. */
434 
435 /*
436  * Some other constants from RFC 4492
437  */
438 #define MBEDTLS_ECP_TLS_NAMED_CURVE    3   /**< The named_curve of ECCurveType. */
439 
440 #if defined(MBEDTLS_ECP_RESTARTABLE)
441 /**
442  * \brief           Set the maximum number of basic operations done in a row.
443  *
444  *                  If more operations are needed to complete a computation,
445  *                  #MBEDTLS_ERR_ECP_IN_PROGRESS will be returned by the
446  *                  function performing the computation. It is then the
447  *                  caller's responsibility to either call again with the same
448  *                  parameters until it returns 0 or an error code; or to free
449  *                  the restart context if the operation is to be aborted.
450  *
451  *                  It is strictly required that all input parameters and the
452  *                  restart context be the same on successive calls for the
453  *                  same operation, but output parameters need not be the
454  *                  same; they must not be used until the function finally
455  *                  returns 0.
456  *
457  *                  This only applies to functions whose documentation
458  *                  mentions they may return #MBEDTLS_ERR_ECP_IN_PROGRESS (or
459  *                  #MBEDTLS_ERR_SSL_CRYPTO_IN_PROGRESS for functions in the
460  *                  SSL module). For functions that accept a "restart context"
461  *                  argument, passing NULL disables restart and makes the
462  *                  function equivalent to the function with the same name
463  *                  with \c _restartable removed. For functions in the ECDH
464  *                  module, restart is disabled unless the function accepts
465  *                  an "ECDH context" argument and
466  *                  mbedtls_ecdh_enable_restart() was previously called on
467  *                  that context. For function in the SSL module, restart is
468  *                  only enabled for specific sides and key exchanges
469  *                  (currently only for clients and ECDHE-ECDSA).
470  *
471  * \param max_ops   Maximum number of basic operations done in a row.
472  *                  Default: 0 (unlimited).
473  *                  Lower (non-zero) values mean ECC functions will block for
474  *                  a lesser maximum amount of time.
475  *
476  * \note            A "basic operation" is defined as a rough equivalent of a
477  *                  multiplication in GF(p) for the NIST P-256 curve.
478  *                  As an indication, with default settings, a scalar
479  *                  multiplication (full run of \c mbedtls_ecp_mul()) is:
480  *                  - about 3300 basic operations for P-256
481  *                  - about 9400 basic operations for P-384
482  *
483  * \note            Very low values are not always respected: sometimes
484  *                  functions need to block for a minimum number of
485  *                  operations, and will do so even if max_ops is set to a
486  *                  lower value.  That minimum depends on the curve size, and
487  *                  can be made lower by decreasing the value of
488  *                  \c MBEDTLS_ECP_WINDOW_SIZE.  As an indication, here is the
489  *                  lowest effective value for various curves and values of
490  *                  that parameter (w for short):
491  *                          w=6     w=5     w=4     w=3     w=2
492  *                  P-256   208     208     160     136     124
493  *                  P-384   682     416     320     272     248
494  *                  P-521  1364     832     640     544     496
495  *
496  * \note            This setting is currently ignored by Curve25519.
497  */
498 void mbedtls_ecp_set_max_ops( unsigned max_ops );
499 
500 /**
501  * \brief           Check if restart is enabled (max_ops != 0)
502  *
503  * \return          \c 0 if \c max_ops == 0 (restart disabled)
504  * \return          \c 1 otherwise (restart enabled)
505  */
506 int mbedtls_ecp_restart_is_enabled( void );
507 #endif /* MBEDTLS_ECP_RESTARTABLE */
508 
509 /*
510  * Get the type of a curve
511  */
512 mbedtls_ecp_curve_type mbedtls_ecp_get_type( const mbedtls_ecp_group *grp );
513 
514 /**
515  * \brief           This function retrieves the information defined in
516  *                  mbedtls_ecp_curve_info() for all supported curves.
517  *
518  * \note            This function returns information about all curves
519  *                  supported by the library. Some curves may not be
520  *                  supported for all algorithms. Call mbedtls_ecdh_can_do()
521  *                  or mbedtls_ecdsa_can_do() to check if a curve is
522  *                  supported for ECDH or ECDSA.
523  *
524  * \return          A statically allocated array. The last entry is 0.
525  */
526 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void );
527 
528 /**
529  * \brief           This function retrieves the list of internal group
530  *                  identifiers of all supported curves in the order of
531  *                  preference.
532  *
533  * \note            This function returns information about all curves
534  *                  supported by the library. Some curves may not be
535  *                  supported for all algorithms. Call mbedtls_ecdh_can_do()
536  *                  or mbedtls_ecdsa_can_do() to check if a curve is
537  *                  supported for ECDH or ECDSA.
538  *
539  * \return          A statically allocated array,
540  *                  terminated with MBEDTLS_ECP_DP_NONE.
541  */
542 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void );
543 
544 /**
545  * \brief           This function retrieves curve information from an internal
546  *                  group identifier.
547  *
548  * \param grp_id    An \c MBEDTLS_ECP_DP_XXX value.
549  *
550  * \return          The associated curve information on success.
551  * \return          NULL on failure.
552  */
553 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id );
554 
555 /**
556  * \brief           This function retrieves curve information from a TLS
557  *                  NamedCurve value.
558  *
559  * \param tls_id    An \c MBEDTLS_ECP_DP_XXX value.
560  *
561  * \return          The associated curve information on success.
562  * \return          NULL on failure.
563  */
564 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id );
565 
566 /**
567  * \brief           This function retrieves curve information from a
568  *                  human-readable name.
569  *
570  * \param name      The human-readable name.
571  *
572  * \return          The associated curve information on success.
573  * \return          NULL on failure.
574  */
575 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name );
576 
577 /**
578  * \brief           This function initializes a point as zero.
579  *
580  * \param pt        The point to initialize.
581  */
582 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt );
583 
584 /**
585  * \brief           This function initializes an ECP group context
586  *                  without loading any domain parameters.
587  *
588  * \note            After this function is called, domain parameters
589  *                  for various ECP groups can be loaded through the
590  *                  mbedtls_ecp_group_load() or mbedtls_ecp_tls_read_group()
591  *                  functions.
592  */
593 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp );
594 
595 /**
596  * \brief           This function initializes a key pair as an invalid one.
597  *
598  * \param key       The key pair to initialize.
599  */
600 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key );
601 
602 /**
603  * \brief           This function frees the components of a point.
604  *
605  * \param pt        The point to free.
606  */
607 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt );
608 
609 /**
610  * \brief           This function frees the components of an ECP group.
611  *
612  * \param grp       The group to free. This may be \c NULL, in which
613  *                  case this function returns immediately. If it is not
614  *                  \c NULL, it must point to an initialized ECP group.
615  */
616 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp );
617 
618 /**
619  * \brief           This function frees the components of a key pair.
620  *
621  * \param key       The key pair to free. This may be \c NULL, in which
622  *                  case this function returns immediately. If it is not
623  *                  \c NULL, it must point to an initialized ECP key pair.
624  */
625 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key );
626 
627 #if defined(MBEDTLS_ECP_RESTARTABLE)
628 /**
629  * \brief           Initialize a restart context.
630  *
631  * \param ctx       The restart context to initialize. This must
632  *                  not be \c NULL.
633  */
634 void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx );
635 
636 /**
637  * \brief           Free the components of a restart context.
638  *
639  * \param ctx       The restart context to free. This may be \c NULL, in which
640  *                  case this function returns immediately. If it is not
641  *                  \c NULL, it must point to an initialized restart context.
642  */
643 void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx );
644 #endif /* MBEDTLS_ECP_RESTARTABLE */
645 
646 /**
647  * \brief           This function copies the contents of point \p Q into
648  *                  point \p P.
649  *
650  * \param P         The destination point. This must be initialized.
651  * \param Q         The source point. This must be initialized.
652  *
653  * \return          \c 0 on success.
654  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
655  * \return          Another negative error code for other kinds of failure.
656  */
657 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q );
658 
659 /**
660  * \brief           This function copies the contents of group \p src into
661  *                  group \p dst.
662  *
663  * \param dst       The destination group. This must be initialized.
664  * \param src       The source group. This must be initialized.
665  *
666  * \return          \c 0 on success.
667  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
668  * \return          Another negative error code on other kinds of failure.
669  */
670 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst,
671                             const mbedtls_ecp_group *src );
672 
673 /**
674  * \brief           This function sets a point to the point at infinity.
675  *
676  * \param pt        The point to set. This must be initialized.
677  *
678  * \return          \c 0 on success.
679  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
680  * \return          Another negative error code on other kinds of failure.
681  */
682 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt );
683 
684 /**
685  * \brief           This function checks if a point is the point at infinity.
686  *
687  * \param pt        The point to test. This must be initialized.
688  *
689  * \return          \c 1 if the point is zero.
690  * \return          \c 0 if the point is non-zero.
691  * \return          A negative error code on failure.
692  */
693 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt );
694 
695 /**
696  * \brief           This function compares two points.
697  *
698  * \note            This assumes that the points are normalized. Otherwise,
699  *                  they may compare as "not equal" even if they are.
700  *
701  * \param P         The first point to compare. This must be initialized.
702  * \param Q         The second point to compare. This must be initialized.
703  *
704  * \return          \c 0 if the points are equal.
705  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the points are not equal.
706  */
707 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
708                            const mbedtls_ecp_point *Q );
709 
710 /**
711  * \brief           This function imports a non-zero point from two ASCII
712  *                  strings.
713  *
714  * \param P         The destination point. This must be initialized.
715  * \param radix     The numeric base of the input.
716  * \param x         The first affine coordinate, as a null-terminated string.
717  * \param y         The second affine coordinate, as a null-terminated string.
718  *
719  * \return          \c 0 on success.
720  * \return          An \c MBEDTLS_ERR_MPI_XXX error code on failure.
721  */
722 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
723                            const char *x, const char *y );
724 
725 /**
726  * \brief           This function exports a point into unsigned binary data.
727  *
728  * \param grp       The group to which the point should belong.
729  *                  This must be initialized and have group parameters
730  *                  set, for example through mbedtls_ecp_group_load().
731  * \param P         The point to export. This must be initialized.
732  * \param format    The point format. This must be either
733  *                  #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED.
734  *                  (For groups without these formats, this parameter is
735  *                  ignored. But it still has to be either of the above
736  *                  values.)
737  * \param olen      The address at which to store the length of
738  *                  the output in Bytes. This must not be \c NULL.
739  * \param buf       The output buffer. This must be a writable buffer
740  *                  of length \p buflen Bytes.
741  * \param buflen    The length of the output buffer \p buf in Bytes.
742  *
743  * \return          \c 0 on success.
744  * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output buffer
745  *                  is too small to hold the point.
746  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format
747  *                  or the export for the given group is not implemented.
748  * \return          Another negative error code on other kinds of failure.
749  */
750 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp,
751                                     const mbedtls_ecp_point *P,
752                                     int format, size_t *olen,
753                                     unsigned char *buf, size_t buflen );
754 
755 /**
756  * \brief           This function imports a point from unsigned binary data.
757  *
758  * \note            This function does not check that the point actually
759  *                  belongs to the given group, see mbedtls_ecp_check_pubkey()
760  *                  for that.
761  *
762  * \param grp       The group to which the point should belong.
763  *                  This must be initialized and have group parameters
764  *                  set, for example through mbedtls_ecp_group_load().
765  * \param P         The destination context to import the point to.
766  *                  This must be initialized.
767  * \param buf       The input buffer. This must be a readable buffer
768  *                  of length \p ilen Bytes.
769  * \param ilen      The length of the input buffer \p buf in Bytes.
770  *
771  * \return          \c 0 on success.
772  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
773  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
774  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the import for the
775  *                  given group is not implemented.
776  */
777 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp,
778                                    mbedtls_ecp_point *P,
779                                    const unsigned char *buf, size_t ilen );
780 
781 /**
782  * \brief           This function imports a point from a TLS ECPoint record.
783  *
784  * \note            On function return, \p *buf is updated to point immediately
785  *                  after the ECPoint record.
786  *
787  * \param grp       The ECP group to use.
788  *                  This must be initialized and have group parameters
789  *                  set, for example through mbedtls_ecp_group_load().
790  * \param pt        The destination point.
791  * \param buf       The address of the pointer to the start of the input buffer.
792  * \param len       The length of the buffer.
793  *
794  * \return          \c 0 on success.
795  * \return          An \c MBEDTLS_ERR_MPI_XXX error code on initialization
796  *                  failure.
797  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
798  */
799 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp,
800                                 mbedtls_ecp_point *pt,
801                                 const unsigned char **buf, size_t len );
802 
803 /**
804  * \brief           This function exports a point as a TLS ECPoint record
805  *                  defined in RFC 4492, Section 5.4.
806  *
807  * \param grp       The ECP group to use.
808  *                  This must be initialized and have group parameters
809  *                  set, for example through mbedtls_ecp_group_load().
810  * \param pt        The point to be exported. This must be initialized.
811  * \param format    The point format to use. This must be either
812  *                  #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED.
813  * \param olen      The address at which to store the length in Bytes
814  *                  of the data written.
815  * \param buf       The target buffer. This must be a writable buffer of
816  *                  length \p blen Bytes.
817  * \param blen      The length of the target buffer \p buf in Bytes.
818  *
819  * \return          \c 0 on success.
820  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
821  * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the target buffer
822  *                  is too small to hold the exported point.
823  * \return          Another negative error code on other kinds of failure.
824  */
825 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp,
826                                  const mbedtls_ecp_point *pt,
827                                  int format, size_t *olen,
828                                  unsigned char *buf, size_t blen );
829 
830 /**
831  * \brief           This function sets up an ECP group context
832  *                  from a standardized set of domain parameters.
833  *
834  * \note            The index should be a value of the NamedCurve enum,
835  *                  as defined in <em>RFC-4492: Elliptic Curve Cryptography
836  *                  (ECC) Cipher Suites for Transport Layer Security (TLS)</em>,
837  *                  usually in the form of an \c MBEDTLS_ECP_DP_XXX macro.
838  *
839  * \param grp       The group context to setup. This must be initialized.
840  * \param id        The identifier of the domain parameter set to load.
841  *
842  * \return          \c 0 on success.
843  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p id doesn't
844  *                  correspond to a known group.
845  * \return          Another negative error code on other kinds of failure.
846  */
847 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id );
848 
849 /**
850  * \brief           This function sets up an ECP group context from a TLS
851  *                  ECParameters record as defined in RFC 4492, Section 5.4.
852  *
853  * \note            The read pointer \p buf is updated to point right after
854  *                  the ECParameters record on exit.
855  *
856  * \param grp       The group context to setup. This must be initialized.
857  * \param buf       The address of the pointer to the start of the input buffer.
858  * \param len       The length of the input buffer \c *buf in Bytes.
859  *
860  * \return          \c 0 on success.
861  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
862  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
863  *                  recognized.
864  * \return          Another negative error code on other kinds of failure.
865  */
866 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp,
867                                 const unsigned char **buf, size_t len );
868 
869 /**
870  * \brief           This function extracts an elliptic curve group ID from a
871  *                  TLS ECParameters record as defined in RFC 4492, Section 5.4.
872  *
873  * \note            The read pointer \p buf is updated to point right after
874  *                  the ECParameters record on exit.
875  *
876  * \param grp       The address at which to store the group id.
877  *                  This must not be \c NULL.
878  * \param buf       The address of the pointer to the start of the input buffer.
879  * \param len       The length of the input buffer \c *buf in Bytes.
880  *
881  * \return          \c 0 on success.
882  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
883  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
884  *                  recognized.
885  * \return          Another negative error code on other kinds of failure.
886  */
887 int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp,
888                                    const unsigned char **buf,
889                                    size_t len );
890 /**
891  * \brief           This function exports an elliptic curve as a TLS
892  *                  ECParameters record as defined in RFC 4492, Section 5.4.
893  *
894  * \param grp       The ECP group to be exported.
895  *                  This must be initialized and have group parameters
896  *                  set, for example through mbedtls_ecp_group_load().
897  * \param olen      The address at which to store the number of Bytes written.
898  *                  This must not be \c NULL.
899  * \param buf       The buffer to write to. This must be a writable buffer
900  *                  of length \p blen Bytes.
901  * \param blen      The length of the output buffer \p buf in Bytes.
902  *
903  * \return          \c 0 on success.
904  * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output
905  *                  buffer is too small to hold the exported group.
906  * \return          Another negative error code on other kinds of failure.
907  */
908 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp,
909                                  size_t *olen,
910                                  unsigned char *buf, size_t blen );
911 
912 /**
913  * \brief           This function performs a scalar multiplication of a point
914  *                  by an integer: \p R = \p m * \p P.
915  *
916  *                  It is not thread-safe to use same group in multiple threads.
917  *
918  * \note            To prevent timing attacks, this function
919  *                  executes the exact same sequence of base-field
920  *                  operations for any valid \p m. It avoids any if-branch or
921  *                  array index depending on the value of \p m. If also uses
922  *                  \p f_rng to randomize some intermediate results.
923  *
924  * \param grp       The ECP group to use.
925  *                  This must be initialized and have group parameters
926  *                  set, for example through mbedtls_ecp_group_load().
927  * \param R         The point in which to store the result of the calculation.
928  *                  This must be initialized.
929  * \param m         The integer by which to multiply. This must be initialized.
930  * \param P         The point to multiply. This must be initialized.
931  * \param f_rng     The RNG function. This must not be \c NULL.
932  * \param p_rng     The RNG context to be passed to \p f_rng. This may be \c
933  *                  NULL if \p f_rng doesn't need a context.
934  *
935  * \return          \c 0 on success.
936  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private
937  *                  key, or \p P is not a valid public key.
938  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
939  * \return          Another negative error code on other kinds of failure.
940  */
941 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
942              const mbedtls_mpi *m, const mbedtls_ecp_point *P,
943              int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
944 
945 /**
946  * \brief           This function performs multiplication of a point by
947  *                  an integer: \p R = \p m * \p P in a restartable way.
948  *
949  * \see             mbedtls_ecp_mul()
950  *
951  * \note            This function does the same as \c mbedtls_ecp_mul(), but
952  *                  it can return early and restart according to the limit set
953  *                  with \c mbedtls_ecp_set_max_ops() to reduce blocking.
954  *
955  * \param grp       The ECP group to use.
956  *                  This must be initialized and have group parameters
957  *                  set, for example through mbedtls_ecp_group_load().
958  * \param R         The point in which to store the result of the calculation.
959  *                  This must be initialized.
960  * \param m         The integer by which to multiply. This must be initialized.
961  * \param P         The point to multiply. This must be initialized.
962  * \param f_rng     The RNG function. This must not be \c NULL.
963  * \param p_rng     The RNG context to be passed to \p f_rng. This may be \c
964  *                  NULL if \p f_rng doesn't need a context.
965  * \param rs_ctx    The restart context (NULL disables restart).
966  *
967  * \return          \c 0 on success.
968  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private
969  *                  key, or \p P is not a valid public key.
970  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
971  * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
972  *                  operations was reached: see \c mbedtls_ecp_set_max_ops().
973  * \return          Another negative error code on other kinds of failure.
974  */
975 int mbedtls_ecp_mul_restartable( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
976              const mbedtls_mpi *m, const mbedtls_ecp_point *P,
977              int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
978              mbedtls_ecp_restart_ctx *rs_ctx );
979 
980 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
981 /**
982  * \brief           This function performs multiplication and addition of two
983  *                  points by integers: \p R = \p m * \p P + \p n * \p Q
984  *
985  *                  It is not thread-safe to use same group in multiple threads.
986  *
987  * \note            In contrast to mbedtls_ecp_mul(), this function does not
988  *                  guarantee a constant execution flow and timing.
989  *
990  * \note            This function is only defined for short Weierstrass curves.
991  *                  It may not be included in builds without any short
992  *                  Weierstrass curve.
993  *
994  * \param grp       The ECP group to use.
995  *                  This must be initialized and have group parameters
996  *                  set, for example through mbedtls_ecp_group_load().
997  * \param R         The point in which to store the result of the calculation.
998  *                  This must be initialized.
999  * \param m         The integer by which to multiply \p P.
1000  *                  This must be initialized.
1001  * \param P         The point to multiply by \p m. This must be initialized.
1002  * \param n         The integer by which to multiply \p Q.
1003  *                  This must be initialized.
1004  * \param Q         The point to be multiplied by \p n.
1005  *                  This must be initialized.
1006  *
1007  * \return          \c 0 on success.
1008  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not
1009  *                  valid private keys, or \p P or \p Q are not valid public
1010  *                  keys.
1011  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
1012  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not
1013  *                  designate a short Weierstrass curve.
1014  * \return          Another negative error code on other kinds of failure.
1015  */
1016 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1017              const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1018              const mbedtls_mpi *n, const mbedtls_ecp_point *Q );
1019 
1020 /**
1021  * \brief           This function performs multiplication and addition of two
1022  *                  points by integers: \p R = \p m * \p P + \p n * \p Q in a
1023  *                  restartable way.
1024  *
1025  * \see             \c mbedtls_ecp_muladd()
1026  *
1027  * \note            This function works the same as \c mbedtls_ecp_muladd(),
1028  *                  but it can return early and restart according to the limit
1029  *                  set with \c mbedtls_ecp_set_max_ops() to reduce blocking.
1030  *
1031  * \note            This function is only defined for short Weierstrass curves.
1032  *                  It may not be included in builds without any short
1033  *                  Weierstrass curve.
1034  *
1035  * \param grp       The ECP group to use.
1036  *                  This must be initialized and have group parameters
1037  *                  set, for example through mbedtls_ecp_group_load().
1038  * \param R         The point in which to store the result of the calculation.
1039  *                  This must be initialized.
1040  * \param m         The integer by which to multiply \p P.
1041  *                  This must be initialized.
1042  * \param P         The point to multiply by \p m. This must be initialized.
1043  * \param n         The integer by which to multiply \p Q.
1044  *                  This must be initialized.
1045  * \param Q         The point to be multiplied by \p n.
1046  *                  This must be initialized.
1047  * \param rs_ctx    The restart context (NULL disables restart).
1048  *
1049  * \return          \c 0 on success.
1050  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not
1051  *                  valid private keys, or \p P or \p Q are not valid public
1052  *                  keys.
1053  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
1054  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not
1055  *                  designate a short Weierstrass curve.
1056  * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
1057  *                  operations was reached: see \c mbedtls_ecp_set_max_ops().
1058  * \return          Another negative error code on other kinds of failure.
1059  */
1060 int mbedtls_ecp_muladd_restartable(
1061              mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1062              const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1063              const mbedtls_mpi *n, const mbedtls_ecp_point *Q,
1064              mbedtls_ecp_restart_ctx *rs_ctx );
1065 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
1066 
1067 /**
1068  * \brief           This function checks that a point is a valid public key
1069  *                  on this curve.
1070  *
1071  *                  It only checks that the point is non-zero, has
1072  *                  valid coordinates and lies on the curve. It does not verify
1073  *                  that it is indeed a multiple of \p G. This additional
1074  *                  check is computationally more expensive, is not required
1075  *                  by standards, and should not be necessary if the group
1076  *                  used has a small cofactor. In particular, it is useless for
1077  *                  the NIST groups which all have a cofactor of 1.
1078  *
1079  * \note            This function uses bare components rather than an
1080  *                  ::mbedtls_ecp_keypair structure, to ease use with other
1081  *                  structures, such as ::mbedtls_ecdh_context or
1082  *                  ::mbedtls_ecdsa_context.
1083  *
1084  * \param grp       The ECP group the point should belong to.
1085  *                  This must be initialized and have group parameters
1086  *                  set, for example through mbedtls_ecp_group_load().
1087  * \param pt        The point to check. This must be initialized.
1088  *
1089  * \return          \c 0 if the point is a valid public key.
1090  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not
1091  *                  a valid public key for the given curve.
1092  * \return          Another negative error code on other kinds of failure.
1093  */
1094 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp,
1095                               const mbedtls_ecp_point *pt );
1096 
1097 /**
1098  * \brief           This function checks that an \p mbedtls_mpi is a
1099  *                  valid private key for this curve.
1100  *
1101  * \note            This function uses bare components rather than an
1102  *                  ::mbedtls_ecp_keypair structure to ease use with other
1103  *                  structures, such as ::mbedtls_ecdh_context or
1104  *                  ::mbedtls_ecdsa_context.
1105  *
1106  * \param grp       The ECP group the private key should belong to.
1107  *                  This must be initialized and have group parameters
1108  *                  set, for example through mbedtls_ecp_group_load().
1109  * \param d         The integer to check. This must be initialized.
1110  *
1111  * \return          \c 0 if the point is a valid private key.
1112  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not a valid
1113  *                  private key for the given curve.
1114  * \return          Another negative error code on other kinds of failure.
1115  */
1116 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp,
1117                                const mbedtls_mpi *d );
1118 
1119 /**
1120  * \brief           This function generates a private key.
1121  *
1122  * \param grp       The ECP group to generate a private key for.
1123  *                  This must be initialized and have group parameters
1124  *                  set, for example through mbedtls_ecp_group_load().
1125  * \param d         The destination MPI (secret part). This must be initialized.
1126  * \param f_rng     The RNG function. This must not be \c NULL.
1127  * \param p_rng     The RNG parameter to be passed to \p f_rng. This may be
1128  *                  \c NULL if \p f_rng doesn't need a context argument.
1129  *
1130  * \return          \c 0 on success.
1131  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1132  *                  on failure.
1133  */
1134 int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp,
1135                      mbedtls_mpi *d,
1136                      int (*f_rng)(void *, unsigned char *, size_t),
1137                      void *p_rng );
1138 
1139 /**
1140  * \brief           This function generates a keypair with a configurable base
1141  *                  point.
1142  *
1143  * \note            This function uses bare components rather than an
1144  *                  ::mbedtls_ecp_keypair structure to ease use with other
1145  *                  structures, such as ::mbedtls_ecdh_context or
1146  *                  ::mbedtls_ecdsa_context.
1147  *
1148  * \param grp       The ECP group to generate a key pair for.
1149  *                  This must be initialized and have group parameters
1150  *                  set, for example through mbedtls_ecp_group_load().
1151  * \param G         The base point to use. This must be initialized
1152  *                  and belong to \p grp. It replaces the default base
1153  *                  point \c grp->G used by mbedtls_ecp_gen_keypair().
1154  * \param d         The destination MPI (secret part).
1155  *                  This must be initialized.
1156  * \param Q         The destination point (public part).
1157  *                  This must be initialized.
1158  * \param f_rng     The RNG function. This must not be \c NULL.
1159  * \param p_rng     The RNG context to be passed to \p f_rng. This may
1160  *                  be \c NULL if \p f_rng doesn't need a context argument.
1161  *
1162  * \return          \c 0 on success.
1163  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1164  *                  on failure.
1165  */
1166 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
1167                                   const mbedtls_ecp_point *G,
1168                                   mbedtls_mpi *d, mbedtls_ecp_point *Q,
1169                                   int (*f_rng)(void *, unsigned char *, size_t),
1170                                   void *p_rng );
1171 
1172 /**
1173  * \brief           This function generates an ECP keypair.
1174  *
1175  * \note            This function uses bare components rather than an
1176  *                  ::mbedtls_ecp_keypair structure to ease use with other
1177  *                  structures, such as ::mbedtls_ecdh_context or
1178  *                  ::mbedtls_ecdsa_context.
1179  *
1180  * \param grp       The ECP group to generate a key pair for.
1181  *                  This must be initialized and have group parameters
1182  *                  set, for example through mbedtls_ecp_group_load().
1183  * \param d         The destination MPI (secret part).
1184  *                  This must be initialized.
1185  * \param Q         The destination point (public part).
1186  *                  This must be initialized.
1187  * \param f_rng     The RNG function. This must not be \c NULL.
1188  * \param p_rng     The RNG context to be passed to \p f_rng. This may
1189  *                  be \c NULL if \p f_rng doesn't need a context argument.
1190  *
1191  * \return          \c 0 on success.
1192  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1193  *                  on failure.
1194  */
1195 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, mbedtls_mpi *d,
1196                              mbedtls_ecp_point *Q,
1197                              int (*f_rng)(void *, unsigned char *, size_t),
1198                              void *p_rng );
1199 
1200 /**
1201  * \brief           This function generates an ECP key.
1202  *
1203  * \param grp_id    The ECP group identifier.
1204  * \param key       The destination key. This must be initialized.
1205  * \param f_rng     The RNG function to use. This must not be \c NULL.
1206  * \param p_rng     The RNG context to be passed to \p f_rng. This may
1207  *                  be \c NULL if \p f_rng doesn't need a context argument.
1208  *
1209  * \return          \c 0 on success.
1210  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1211  *                  on failure.
1212  */
1213 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
1214                          int (*f_rng)(void *, unsigned char *, size_t),
1215                          void *p_rng );
1216 
1217 /**
1218  * \brief           This function reads an elliptic curve private key.
1219  *
1220  * \param grp_id    The ECP group identifier.
1221  * \param key       The destination key.
1222  * \param buf       The buffer containing the binary representation of the
1223  *                  key. (Big endian integer for Weierstrass curves, byte
1224  *                  string for Montgomery curves.)
1225  * \param buflen    The length of the buffer in bytes.
1226  *
1227  * \return          \c 0 on success.
1228  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY error if the key is
1229  *                  invalid.
1230  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
1231  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for
1232  *                  the group is not implemented.
1233  * \return          Another negative error code on different kinds of failure.
1234  */
1235 int mbedtls_ecp_read_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
1236                           const unsigned char *buf, size_t buflen );
1237 
1238 /**
1239  * \brief           This function exports an elliptic curve private key.
1240  *
1241  * \param key       The private key.
1242  * \param buf       The output buffer for containing the binary representation
1243  *                  of the key. (Big endian integer for Weierstrass curves, byte
1244  *                  string for Montgomery curves.)
1245  * \param buflen    The total length of the buffer in bytes.
1246  *
1247  * \return          \c 0 on success.
1248  * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the \p key
1249                     representation is larger than the available space in \p buf.
1250  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for
1251  *                  the group is not implemented.
1252  * \return          Another negative error code on different kinds of failure.
1253  */
1254 int mbedtls_ecp_write_key( mbedtls_ecp_keypair *key,
1255                            unsigned char *buf, size_t buflen );
1256 
1257 /**
1258  * \brief           This function checks that the keypair objects
1259  *                  \p pub and \p prv have the same group and the
1260  *                  same public point, and that the private key in
1261  *                  \p prv is consistent with the public key.
1262  *
1263  * \param pub       The keypair structure holding the public key. This
1264  *                  must be initialized. If it contains a private key, that
1265  *                  part is ignored.
1266  * \param prv       The keypair structure holding the full keypair.
1267  *                  This must be initialized.
1268  * \param f_rng     The RNG function. This must not be \c NULL.
1269  * \param p_rng     The RNG context to be passed to \p f_rng. This may be \c
1270  *                  NULL if \p f_rng doesn't need a context.
1271  *
1272  * \return          \c 0 on success, meaning that the keys are valid and match.
1273  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the keys are invalid or do not match.
1274  * \return          An \c MBEDTLS_ERR_ECP_XXX or an \c MBEDTLS_ERR_MPI_XXX
1275  *                  error code on calculation failure.
1276  */
1277 int mbedtls_ecp_check_pub_priv(
1278         const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv,
1279         int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
1280 
1281 #if defined(MBEDTLS_SELF_TEST)
1282 
1283 /**
1284  * \brief          The ECP checkup routine.
1285  *
1286  * \return         \c 0 on success.
1287  * \return         \c 1 on failure.
1288  */
1289 int mbedtls_ecp_self_test( int verbose );
1290 
1291 #endif /* MBEDTLS_SELF_TEST */
1292 
1293 #ifdef __cplusplus
1294 }
1295 #endif
1296 
1297 #endif /* ecp.h */
1298