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     MBEDTLS_ECP_DP_NONE = 0,       /*!< Curve not defined. */
115     MBEDTLS_ECP_DP_SECP192R1,      /*!< Domain parameters for the 192-bit curve defined by FIPS 186-4 and SEC1. */
116     MBEDTLS_ECP_DP_SECP224R1,      /*!< Domain parameters for the 224-bit curve defined by FIPS 186-4 and SEC1. */
117     MBEDTLS_ECP_DP_SECP256R1,      /*!< Domain parameters for the 256-bit curve defined by FIPS 186-4 and SEC1. */
118     MBEDTLS_ECP_DP_SECP384R1,      /*!< Domain parameters for the 384-bit curve defined by FIPS 186-4 and SEC1. */
119     MBEDTLS_ECP_DP_SECP521R1,      /*!< Domain parameters for the 521-bit curve defined by FIPS 186-4 and SEC1. */
120     MBEDTLS_ECP_DP_BP256R1,        /*!< Domain parameters for 256-bit Brainpool curve. */
121     MBEDTLS_ECP_DP_BP384R1,        /*!< Domain parameters for 384-bit Brainpool curve. */
122     MBEDTLS_ECP_DP_BP512R1,        /*!< Domain parameters for 512-bit Brainpool curve. */
123     MBEDTLS_ECP_DP_CURVE25519,     /*!< Domain parameters for Curve25519. */
124     MBEDTLS_ECP_DP_SECP192K1,      /*!< Domain parameters for 192-bit "Koblitz" curve. */
125     MBEDTLS_ECP_DP_SECP224K1,      /*!< Domain parameters for 224-bit "Koblitz" curve. */
126     MBEDTLS_ECP_DP_SECP256K1,      /*!< Domain parameters for 256-bit "Koblitz" curve. */
127     MBEDTLS_ECP_DP_CURVE448,       /*!< Domain parameters for Curve448. */
128 } mbedtls_ecp_group_id;
129 
130 /**
131  * The number of supported curves, plus one for #MBEDTLS_ECP_DP_NONE.
132  */
133 #define MBEDTLS_ECP_DP_MAX     14
134 
135 /*
136  * Curve types
137  */
138 typedef enum {
139     MBEDTLS_ECP_TYPE_NONE = 0,
140     MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS,    /* y^2 = x^3 + a x + b      */
141     MBEDTLS_ECP_TYPE_MONTGOMERY,           /* y^2 = x^3 + a x^2 + x    */
142 } mbedtls_ecp_curve_type;
143 
144 /*
145  * Curve modulus types
146  */
147 typedef enum {
148     MBEDTLS_ECP_MOD_NONE = 0,
149     MBEDTLS_ECP_MOD_COORDINATE,
150     MBEDTLS_ECP_MOD_SCALAR
151 } mbedtls_ecp_modulus_type;
152 
153 /**
154  * Curve information, for use by other modules.
155  *
156  * The fields of this structure are part of the public API and can be
157  * accessed directly by applications. Future versions of the library may
158  * add extra fields or reorder existing fields.
159  */
160 typedef struct mbedtls_ecp_curve_info {
161     mbedtls_ecp_group_id grp_id;    /*!< An internal identifier. */
162     uint16_t tls_id;                /*!< The TLS NamedCurve identifier. */
163     uint16_t bit_size;              /*!< The curve size in bits. */
164     const char *name;               /*!< A human-friendly name. */
165 } mbedtls_ecp_curve_info;
166 
167 /**
168  * \brief           The ECP point structure, in Jacobian coordinates.
169  *
170  * \note            All functions expect and return points satisfying
171  *                  the following condition: <code>Z == 0</code> or
172  *                  <code>Z == 1</code>. Other values of \p Z are
173  *                  used only by internal functions.
174  *                  The point is zero, or "at infinity", if <code>Z == 0</code>.
175  *                  Otherwise, \p X and \p Y are its standard (affine)
176  *                  coordinates.
177  */
178 typedef struct mbedtls_ecp_point {
179     mbedtls_mpi MBEDTLS_PRIVATE(X);          /*!< The X coordinate of the ECP point. */
180     mbedtls_mpi MBEDTLS_PRIVATE(Y);          /*!< The Y coordinate of the ECP point. */
181     mbedtls_mpi MBEDTLS_PRIVATE(Z);          /*!< The Z coordinate of the ECP point. */
182 }
183 mbedtls_ecp_point;
184 
185 #if !defined(MBEDTLS_ECP_ALT)
186 /*
187  * default mbed TLS elliptic curve arithmetic implementation
188  *
189  * (in case MBEDTLS_ECP_ALT is defined then the developer has to provide an
190  * alternative implementation for the whole module and it will replace this
191  * one.)
192  */
193 
194 /**
195  * \brief           The ECP group structure.
196  *
197  * We consider two types of curve equations:
198  * <ul><li>Short Weierstrass: <code>y^2 = x^3 + A x + B mod P</code>
199  * (SEC1 + RFC-4492)</li>
200  * <li>Montgomery: <code>y^2 = x^3 + A x^2 + x mod P</code> (Curve25519,
201  * Curve448)</li></ul>
202  * In both cases, the generator (\p G) for a prime-order subgroup is fixed.
203  *
204  * For Short Weierstrass, this subgroup is the whole curve, and its
205  * cardinality is denoted by \p N. Our code requires that \p N is an
206  * odd prime as mbedtls_ecp_mul() requires an odd number, and
207  * mbedtls_ecdsa_sign() requires that it is prime for blinding purposes.
208  *
209  * For Montgomery curves, we do not store \p A, but <code>(A + 2) / 4</code>,
210  * which is the quantity used in the formulas. Additionally, \p nbits is
211  * not the size of \p N but the required size for private keys.
212  *
213  * If \p modp is NULL, reduction modulo \p P is done using a generic algorithm.
214  * Otherwise, \p modp must point to a function that takes an \p mbedtls_mpi in the
215  * range of <code>0..2^(2*pbits)-1</code>, and transforms it in-place to an integer
216  * which is congruent mod \p P to the given MPI, and is close enough to \p pbits
217  * in size, so that it may be efficiently brought in the 0..P-1 range by a few
218  * additions or subtractions. Therefore, it is only an approximative modular
219  * reduction. It must return 0 on success and non-zero on failure.
220  *
221  * \note        Alternative implementations of the ECP module must obey the
222  *              following constraints.
223  *              * Group IDs must be distinct: if two group structures have
224  *                the same ID, then they must be identical.
225  *              * The fields \c id, \c P, \c A, \c B, \c G, \c N,
226  *                \c pbits and \c nbits must have the same type and semantics
227  *                as in the built-in implementation.
228  *                They must be available for reading, but direct modification
229  *                of these fields does not need to be supported.
230  *                They do not need to be at the same offset in the structure.
231  */
232 typedef struct mbedtls_ecp_group {
233     mbedtls_ecp_group_id id;    /*!< An internal group identifier. */
234     mbedtls_mpi P;              /*!< The prime modulus of the base field. */
235     mbedtls_mpi A;              /*!< For Short Weierstrass: \p A in the equation. For
236                                      Montgomery curves: <code>(A + 2) / 4</code>. */
237     mbedtls_mpi B;              /*!< For Short Weierstrass: \p B in the equation.
238                                      For Montgomery curves: unused. */
239     mbedtls_ecp_point G;        /*!< The generator of the subgroup used. */
240     mbedtls_mpi N;              /*!< The order of \p G. */
241     size_t pbits;               /*!< The number of bits in \p P.*/
242     size_t nbits;               /*!< For Short Weierstrass: The number of bits in \p P.
243                                      For Montgomery curves: the number of bits in the
244                                      private keys. */
245     /* End of public fields */
246 
247     unsigned int MBEDTLS_PRIVATE(h);             /*!< \internal 1 if the constants are static. */
248     int(*MBEDTLS_PRIVATE(modp))(mbedtls_mpi *);  /*!< The function for fast pseudo-reduction
249                                                     mod \p P (see above).*/
250     int(*MBEDTLS_PRIVATE(t_pre))(mbedtls_ecp_point *, void *);   /*!< Unused. */
251     int(*MBEDTLS_PRIVATE(t_post))(mbedtls_ecp_point *, void *);  /*!< Unused. */
252     void *MBEDTLS_PRIVATE(t_data);               /*!< Unused. */
253     mbedtls_ecp_point *MBEDTLS_PRIVATE(T);       /*!< Pre-computed points for ecp_mul_comb(). */
254     size_t MBEDTLS_PRIVATE(T_size);              /*!< The number of dynamic allocated pre-computed points. */
255 }
256 mbedtls_ecp_group;
257 
258 /**
259  * \name SECTION: Module settings
260  *
261  * The configuration options you can set for this module are in this section.
262  * Either change them in mbedtls_config.h, or define them using the compiler command line.
263  * \{
264  */
265 
266 #if !defined(MBEDTLS_ECP_WINDOW_SIZE)
267 /*
268  * Maximum "window" size used for point multiplication.
269  * Default: a point where higher memory usage yields diminishing performance
270  *          returns.
271  * Minimum value: 2. Maximum value: 7.
272  *
273  * Result is an array of at most ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
274  * points used for point multiplication. This value is directly tied to EC
275  * peak memory usage, so decreasing it by one should roughly cut memory usage
276  * by two (if large curves are in use).
277  *
278  * Reduction in size may reduce speed, but larger curves are impacted first.
279  * Sample performances (in ECDHE handshakes/s, with FIXED_POINT_OPTIM = 1):
280  *      w-size:     6       5       4       3       2
281  *      521       145     141     135     120      97
282  *      384       214     209     198     177     146
283  *      256       320     320     303     262     226
284  *      224       475     475     453     398     342
285  *      192       640     640     633     587     476
286  */
287 #define MBEDTLS_ECP_WINDOW_SIZE    4   /**< The maximum window size used. */
288 #endif /* MBEDTLS_ECP_WINDOW_SIZE */
289 
290 #if !defined(MBEDTLS_ECP_FIXED_POINT_OPTIM)
291 /*
292  * Trade code size for speed on fixed-point multiplication.
293  *
294  * This speeds up repeated multiplication of the generator (that is, the
295  * multiplication in ECDSA signatures, and half of the multiplications in
296  * ECDSA verification and ECDHE) by a factor roughly 3 to 4.
297  *
298  * For each n-bit Short Weierstrass curve that is enabled, this adds 4n bytes
299  * of code size if n < 384 and 8n otherwise.
300  *
301  * Change this value to 0 to reduce code size.
302  */
303 #define MBEDTLS_ECP_FIXED_POINT_OPTIM  1   /**< Enable fixed-point speed-up. */
304 #endif /* MBEDTLS_ECP_FIXED_POINT_OPTIM */
305 
306 /** \} name SECTION: Module settings */
307 
308 #else  /* MBEDTLS_ECP_ALT */
309 #include "ecp_alt.h"
310 #endif /* MBEDTLS_ECP_ALT */
311 
312 /**
313  * The maximum size of the groups, that is, of \c N and \c P.
314  */
315 #if !defined(MBEDTLS_ECP_C)
316 /* Dummy definition to help code that has optional ECP support and
317  * defines an MBEDTLS_ECP_MAX_BYTES-sized array unconditionally. */
318 #define MBEDTLS_ECP_MAX_BITS 1
319 /* Note: the curves must be listed in DECREASING size! */
320 #elif defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
321 #define MBEDTLS_ECP_MAX_BITS 521
322 #elif defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
323 #define MBEDTLS_ECP_MAX_BITS 512
324 #elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
325 #define MBEDTLS_ECP_MAX_BITS 448
326 #elif defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
327 #define MBEDTLS_ECP_MAX_BITS 384
328 #elif defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
329 #define MBEDTLS_ECP_MAX_BITS 384
330 #elif defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
331 #define MBEDTLS_ECP_MAX_BITS 256
332 #elif defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
333 #define MBEDTLS_ECP_MAX_BITS 256
334 #elif defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
335 #define MBEDTLS_ECP_MAX_BITS 256
336 #elif defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
337 #define MBEDTLS_ECP_MAX_BITS 255
338 #elif defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
339 #define MBEDTLS_ECP_MAX_BITS 225 // n is slightly above 2^224
340 #elif defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
341 #define MBEDTLS_ECP_MAX_BITS 224
342 #elif defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
343 #define MBEDTLS_ECP_MAX_BITS 192
344 #elif defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
345 #define MBEDTLS_ECP_MAX_BITS 192
346 #else
347 #error "Missing definition of MBEDTLS_ECP_MAX_BITS"
348 #endif
349 
350 #define MBEDTLS_ECP_MAX_BYTES    ((MBEDTLS_ECP_MAX_BITS + 7) / 8)
351 #define MBEDTLS_ECP_MAX_PT_LEN   (2 * MBEDTLS_ECP_MAX_BYTES + 1)
352 
353 #if defined(MBEDTLS_ECP_RESTARTABLE)
354 
355 /**
356  * \brief           Internal restart context for multiplication
357  *
358  * \note            Opaque struct
359  */
360 typedef struct mbedtls_ecp_restart_mul mbedtls_ecp_restart_mul_ctx;
361 
362 /**
363  * \brief           Internal restart context for ecp_muladd()
364  *
365  * \note            Opaque struct
366  */
367 typedef struct mbedtls_ecp_restart_muladd mbedtls_ecp_restart_muladd_ctx;
368 
369 /**
370  * \brief           General context for resuming ECC operations
371  */
372 typedef struct {
373     unsigned MBEDTLS_PRIVATE(ops_done);                  /*!<  current ops count             */
374     unsigned MBEDTLS_PRIVATE(depth);                     /*!<  call depth (0 = top-level)    */
375     mbedtls_ecp_restart_mul_ctx *MBEDTLS_PRIVATE(rsm);   /*!<  ecp_mul_comb() sub-context    */
376     mbedtls_ecp_restart_muladd_ctx *MBEDTLS_PRIVATE(ma); /*!<  ecp_muladd() sub-context      */
377 } mbedtls_ecp_restart_ctx;
378 
379 /*
380  * Operation counts for restartable functions
381  */
382 #define MBEDTLS_ECP_OPS_CHK   3 /*!< basic ops count for ecp_check_pubkey()  */
383 #define MBEDTLS_ECP_OPS_DBL   8 /*!< basic ops count for ecp_double_jac()    */
384 #define MBEDTLS_ECP_OPS_ADD  11 /*!< basic ops count for see ecp_add_mixed() */
385 #define MBEDTLS_ECP_OPS_INV 120 /*!< empirical equivalent for mpi_mod_inv()  */
386 
387 /**
388  * \brief           Internal; for restartable functions in other modules.
389  *                  Check and update basic ops budget.
390  *
391  * \param grp       Group structure
392  * \param rs_ctx    Restart context
393  * \param ops       Number of basic ops to do
394  *
395  * \return          \c 0 if doing \p ops basic ops is still allowed,
396  * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS otherwise.
397  */
398 int mbedtls_ecp_check_budget(const mbedtls_ecp_group *grp,
399                              mbedtls_ecp_restart_ctx *rs_ctx,
400                              unsigned ops);
401 
402 /* Utility macro for checking and updating ops budget */
403 #define MBEDTLS_ECP_BUDGET(ops)   \
404     MBEDTLS_MPI_CHK(mbedtls_ecp_check_budget(grp, rs_ctx, \
405                                              (unsigned) (ops)));
406 
407 #else /* MBEDTLS_ECP_RESTARTABLE */
408 
409 #define MBEDTLS_ECP_BUDGET(ops)     /* no-op; for compatibility */
410 
411 /* We want to declare restartable versions of existing functions anyway */
412 typedef void mbedtls_ecp_restart_ctx;
413 
414 #endif /* MBEDTLS_ECP_RESTARTABLE */
415 
416 /**
417  * \brief    The ECP key-pair structure.
418  *
419  * A generic key-pair that may be used for ECDSA and fixed ECDH, for example.
420  *
421  * \note    Members are deliberately in the same order as in the
422  *          ::mbedtls_ecdsa_context structure.
423  */
424 typedef struct mbedtls_ecp_keypair {
425     mbedtls_ecp_group MBEDTLS_PRIVATE(grp);      /*!<  Elliptic curve and base point     */
426     mbedtls_mpi MBEDTLS_PRIVATE(d);              /*!<  our secret value                  */
427     mbedtls_ecp_point MBEDTLS_PRIVATE(Q);        /*!<  our public value                  */
428 }
429 mbedtls_ecp_keypair;
430 
431 /**
432  * The uncompressed point format for Short Weierstrass curves
433  * (MBEDTLS_ECP_DP_SECP_XXX and MBEDTLS_ECP_DP_BP_XXX).
434  */
435 #define MBEDTLS_ECP_PF_UNCOMPRESSED    0
436 /**
437  * The compressed point format for Short Weierstrass curves
438  * (MBEDTLS_ECP_DP_SECP_XXX and MBEDTLS_ECP_DP_BP_XXX).
439  *
440  * \warning     While this format is supported for all concerned curves for
441  *              writing, when it comes to parsing, it is not supported for all
442  *              curves. Specifically, parsing compressed points on
443  *              MBEDTLS_ECP_DP_SECP224R1 and MBEDTLS_ECP_DP_SECP224K1 is not
444  *              supported.
445  */
446 #define MBEDTLS_ECP_PF_COMPRESSED      1
447 
448 /*
449  * Some other constants from RFC 4492
450  */
451 #define MBEDTLS_ECP_TLS_NAMED_CURVE    3   /**< The named_curve of ECCurveType. */
452 
453 #if defined(MBEDTLS_ECP_RESTARTABLE)
454 /**
455  * \brief           Set the maximum number of basic operations done in a row.
456  *
457  *                  If more operations are needed to complete a computation,
458  *                  #MBEDTLS_ERR_ECP_IN_PROGRESS will be returned by the
459  *                  function performing the computation. It is then the
460  *                  caller's responsibility to either call again with the same
461  *                  parameters until it returns 0 or an error code; or to free
462  *                  the restart context if the operation is to be aborted.
463  *
464  *                  It is strictly required that all input parameters and the
465  *                  restart context be the same on successive calls for the
466  *                  same operation, but output parameters need not be the
467  *                  same; they must not be used until the function finally
468  *                  returns 0.
469  *
470  *                  This only applies to functions whose documentation
471  *                  mentions they may return #MBEDTLS_ERR_ECP_IN_PROGRESS (or
472  *                  #MBEDTLS_ERR_SSL_CRYPTO_IN_PROGRESS for functions in the
473  *                  SSL module). For functions that accept a "restart context"
474  *                  argument, passing NULL disables restart and makes the
475  *                  function equivalent to the function with the same name
476  *                  with \c _restartable removed. For functions in the ECDH
477  *                  module, restart is disabled unless the function accepts
478  *                  an "ECDH context" argument and
479  *                  mbedtls_ecdh_enable_restart() was previously called on
480  *                  that context. For function in the SSL module, restart is
481  *                  only enabled for specific sides and key exchanges
482  *                  (currently only for clients and ECDHE-ECDSA).
483  *
484  * \warning         Using the PSA interruptible interfaces with keys in local
485  *                  storage and no accelerator driver will also call this
486  *                  function to set the values specified via those interfaces,
487  *                  overwriting values previously set. Care should be taken if
488  *                  mixing these two interfaces.
489  *
490  * \param max_ops   Maximum number of basic operations done in a row.
491  *                  Default: 0 (unlimited).
492  *                  Lower (non-zero) values mean ECC functions will block for
493  *                  a lesser maximum amount of time.
494  *
495  * \note            A "basic operation" is defined as a rough equivalent of a
496  *                  multiplication in GF(p) for the NIST P-256 curve.
497  *                  As an indication, with default settings, a scalar
498  *                  multiplication (full run of \c mbedtls_ecp_mul()) is:
499  *                  - about 3300 basic operations for P-256
500  *                  - about 9400 basic operations for P-384
501  *
502  * \note            Very low values are not always respected: sometimes
503  *                  functions need to block for a minimum number of
504  *                  operations, and will do so even if max_ops is set to a
505  *                  lower value.  That minimum depends on the curve size, and
506  *                  can be made lower by decreasing the value of
507  *                  \c MBEDTLS_ECP_WINDOW_SIZE.  As an indication, here is the
508  *                  lowest effective value for various curves and values of
509  *                  that parameter (w for short):
510  *                          w=6     w=5     w=4     w=3     w=2
511  *                  P-256   208     208     160     136     124
512  *                  P-384   682     416     320     272     248
513  *                  P-521  1364     832     640     544     496
514  *
515  * \note            This setting is currently ignored by Curve25519.
516  */
517 void mbedtls_ecp_set_max_ops(unsigned max_ops);
518 
519 /**
520  * \brief           Check if restart is enabled (max_ops != 0)
521  *
522  * \return          \c 0 if \c max_ops == 0 (restart disabled)
523  * \return          \c 1 otherwise (restart enabled)
524  */
525 int mbedtls_ecp_restart_is_enabled(void);
526 #endif /* MBEDTLS_ECP_RESTARTABLE */
527 
528 /*
529  * Get the type of a curve
530  */
531 mbedtls_ecp_curve_type mbedtls_ecp_get_type(const mbedtls_ecp_group *grp);
532 
533 /**
534  * \brief           This function retrieves the information defined in
535  *                  mbedtls_ecp_curve_info() for all supported curves.
536  *
537  * \note            This function returns information about all curves
538  *                  supported by the library. Some curves may not be
539  *                  supported for all algorithms. Call mbedtls_ecdh_can_do()
540  *                  or mbedtls_ecdsa_can_do() to check if a curve is
541  *                  supported for ECDH or ECDSA.
542  *
543  * \return          A statically allocated array. The last entry is 0.
544  */
545 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list(void);
546 
547 /**
548  * \brief           This function retrieves the list of internal group
549  *                  identifiers of all supported curves in the order of
550  *                  preference.
551  *
552  * \note            This function returns information about all curves
553  *                  supported by the library. Some curves may not be
554  *                  supported for all algorithms. Call mbedtls_ecdh_can_do()
555  *                  or mbedtls_ecdsa_can_do() to check if a curve is
556  *                  supported for ECDH or ECDSA.
557  *
558  * \return          A statically allocated array,
559  *                  terminated with MBEDTLS_ECP_DP_NONE.
560  */
561 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list(void);
562 
563 /**
564  * \brief           This function retrieves curve information from an internal
565  *                  group identifier.
566  *
567  * \param grp_id    An \c MBEDTLS_ECP_DP_XXX value.
568  *
569  * \return          The associated curve information on success.
570  * \return          NULL on failure.
571  */
572 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id(mbedtls_ecp_group_id grp_id);
573 
574 /**
575  * \brief           This function retrieves curve information from a TLS
576  *                  NamedCurve value.
577  *
578  * \param tls_id    An \c MBEDTLS_ECP_DP_XXX value.
579  *
580  * \return          The associated curve information on success.
581  * \return          NULL on failure.
582  */
583 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id(uint16_t tls_id);
584 
585 /**
586  * \brief           This function retrieves curve information from a
587  *                  human-readable name.
588  *
589  * \param name      The human-readable name.
590  *
591  * \return          The associated curve information on success.
592  * \return          NULL on failure.
593  */
594 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name(const char *name);
595 
596 /**
597  * \brief           This function initializes a point as zero.
598  *
599  * \param pt        The point to initialize.
600  */
601 void mbedtls_ecp_point_init(mbedtls_ecp_point *pt);
602 
603 /**
604  * \brief           This function initializes an ECP group context
605  *                  without loading any domain parameters.
606  *
607  * \note            After this function is called, domain parameters
608  *                  for various ECP groups can be loaded through the
609  *                  mbedtls_ecp_group_load() or mbedtls_ecp_tls_read_group()
610  *                  functions.
611  */
612 void mbedtls_ecp_group_init(mbedtls_ecp_group *grp);
613 
614 /**
615  * \brief           This function initializes a key pair as an invalid one.
616  *
617  * \param key       The key pair to initialize.
618  */
619 void mbedtls_ecp_keypair_init(mbedtls_ecp_keypair *key);
620 
621 /**
622  * \brief           This function frees the components of a point.
623  *
624  * \param pt        The point to free.
625  */
626 void mbedtls_ecp_point_free(mbedtls_ecp_point *pt);
627 
628 /**
629  * \brief           This function frees the components of an ECP group.
630  *
631  * \param grp       The group to free. This may be \c NULL, in which
632  *                  case this function returns immediately. If it is not
633  *                  \c NULL, it must point to an initialized ECP group.
634  */
635 void mbedtls_ecp_group_free(mbedtls_ecp_group *grp);
636 
637 /**
638  * \brief           This function frees the components of a key pair.
639  *
640  * \param key       The key pair to free. This may be \c NULL, in which
641  *                  case this function returns immediately. If it is not
642  *                  \c NULL, it must point to an initialized ECP key pair.
643  */
644 void mbedtls_ecp_keypair_free(mbedtls_ecp_keypair *key);
645 
646 #if defined(MBEDTLS_ECP_RESTARTABLE)
647 /**
648  * \brief           Initialize a restart context.
649  *
650  * \param ctx       The restart context to initialize. This must
651  *                  not be \c NULL.
652  */
653 void mbedtls_ecp_restart_init(mbedtls_ecp_restart_ctx *ctx);
654 
655 /**
656  * \brief           Free the components of a restart context.
657  *
658  * \param ctx       The restart context to free. This may be \c NULL, in which
659  *                  case this function returns immediately. If it is not
660  *                  \c NULL, it must point to an initialized restart context.
661  */
662 void mbedtls_ecp_restart_free(mbedtls_ecp_restart_ctx *ctx);
663 #endif /* MBEDTLS_ECP_RESTARTABLE */
664 
665 /**
666  * \brief           This function copies the contents of point \p Q into
667  *                  point \p P.
668  *
669  * \param P         The destination point. This must be initialized.
670  * \param Q         The source point. This must be initialized.
671  *
672  * \return          \c 0 on success.
673  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
674  * \return          Another negative error code for other kinds of failure.
675  */
676 int mbedtls_ecp_copy(mbedtls_ecp_point *P, const mbedtls_ecp_point *Q);
677 
678 /**
679  * \brief           This function copies the contents of group \p src into
680  *                  group \p dst.
681  *
682  * \param dst       The destination group. This must be initialized.
683  * \param src       The source group. This must be initialized.
684  *
685  * \return          \c 0 on success.
686  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
687  * \return          Another negative error code on other kinds of failure.
688  */
689 int mbedtls_ecp_group_copy(mbedtls_ecp_group *dst,
690                            const mbedtls_ecp_group *src);
691 
692 /**
693  * \brief           This function sets a point to the point at infinity.
694  *
695  * \param pt        The point to set. This must be initialized.
696  *
697  * \return          \c 0 on success.
698  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
699  * \return          Another negative error code on other kinds of failure.
700  */
701 int mbedtls_ecp_set_zero(mbedtls_ecp_point *pt);
702 
703 /**
704  * \brief           This function checks if a point is the point at infinity.
705  *
706  * \param pt        The point to test. This must be initialized.
707  *
708  * \return          \c 1 if the point is zero.
709  * \return          \c 0 if the point is non-zero.
710  * \return          A negative error code on failure.
711  */
712 int mbedtls_ecp_is_zero(mbedtls_ecp_point *pt);
713 
714 /**
715  * \brief           This function compares two points.
716  *
717  * \note            This assumes that the points are normalized. Otherwise,
718  *                  they may compare as "not equal" even if they are.
719  *
720  * \param P         The first point to compare. This must be initialized.
721  * \param Q         The second point to compare. This must be initialized.
722  *
723  * \return          \c 0 if the points are equal.
724  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the points are not equal.
725  */
726 int mbedtls_ecp_point_cmp(const mbedtls_ecp_point *P,
727                           const mbedtls_ecp_point *Q);
728 
729 /**
730  * \brief           This function imports a non-zero point from two ASCII
731  *                  strings.
732  *
733  * \param P         The destination point. This must be initialized.
734  * \param radix     The numeric base of the input.
735  * \param x         The first affine coordinate, as a null-terminated string.
736  * \param y         The second affine coordinate, as a null-terminated string.
737  *
738  * \return          \c 0 on success.
739  * \return          An \c MBEDTLS_ERR_MPI_XXX error code on failure.
740  */
741 int mbedtls_ecp_point_read_string(mbedtls_ecp_point *P, int radix,
742                                   const char *x, const char *y);
743 
744 /**
745  * \brief           This function exports a point into unsigned binary data.
746  *
747  * \param grp       The group to which the point should belong.
748  *                  This must be initialized and have group parameters
749  *                  set, for example through mbedtls_ecp_group_load().
750  * \param P         The point to export. This must be initialized.
751  * \param format    The point format. This must be either
752  *                  #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED.
753  *                  (For groups without these formats, this parameter is
754  *                  ignored. But it still has to be either of the above
755  *                  values.)
756  * \param olen      The address at which to store the length of
757  *                  the output in Bytes. This must not be \c NULL.
758  * \param buf       The output buffer. This must be a writable buffer
759  *                  of length \p buflen Bytes.
760  * \param buflen    The length of the output buffer \p buf in Bytes.
761  *
762  * \return          \c 0 on success.
763  * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output buffer
764  *                  is too small to hold the point.
765  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format
766  *                  or the export for the given group is not implemented.
767  * \return          Another negative error code on other kinds of failure.
768  */
769 int mbedtls_ecp_point_write_binary(const mbedtls_ecp_group *grp,
770                                    const mbedtls_ecp_point *P,
771                                    int format, size_t *olen,
772                                    unsigned char *buf, size_t buflen);
773 
774 /**
775  * \brief           This function imports a point from unsigned binary data.
776  *
777  * \note            This function does not check that the point actually
778  *                  belongs to the given group, see mbedtls_ecp_check_pubkey()
779  *                  for that.
780  *
781  * \note            For compressed points, see #MBEDTLS_ECP_PF_COMPRESSED for
782  *                  limitations.
783  *
784  * \param grp       The group to which the point should belong.
785  *                  This must be initialized and have group parameters
786  *                  set, for example through mbedtls_ecp_group_load().
787  * \param P         The destination context to import the point to.
788  *                  This must be initialized.
789  * \param buf       The input buffer. This must be a readable buffer
790  *                  of length \p ilen Bytes.
791  * \param ilen      The length of the input buffer \p buf in Bytes.
792  *
793  * \return          \c 0 on success.
794  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
795  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
796  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the import for the
797  *                  given group is not implemented.
798  */
799 int mbedtls_ecp_point_read_binary(const mbedtls_ecp_group *grp,
800                                   mbedtls_ecp_point *P,
801                                   const unsigned char *buf, size_t ilen);
802 
803 /**
804  * \brief           This function imports a point from a TLS ECPoint record.
805  *
806  * \note            On function return, \p *buf is updated to point immediately
807  *                  after the ECPoint record.
808  *
809  * \param grp       The ECP group to use.
810  *                  This must be initialized and have group parameters
811  *                  set, for example through mbedtls_ecp_group_load().
812  * \param pt        The destination point.
813  * \param buf       The address of the pointer to the start of the input buffer.
814  * \param len       The length of the buffer.
815  *
816  * \return          \c 0 on success.
817  * \return          An \c MBEDTLS_ERR_MPI_XXX error code on initialization
818  *                  failure.
819  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
820  */
821 int mbedtls_ecp_tls_read_point(const mbedtls_ecp_group *grp,
822                                mbedtls_ecp_point *pt,
823                                const unsigned char **buf, size_t len);
824 
825 /**
826  * \brief           This function exports a point as a TLS ECPoint record
827  *                  defined in RFC 4492, Section 5.4.
828  *
829  * \param grp       The ECP group to use.
830  *                  This must be initialized and have group parameters
831  *                  set, for example through mbedtls_ecp_group_load().
832  * \param pt        The point to be exported. This must be initialized.
833  * \param format    The point format to use. This must be either
834  *                  #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED.
835  * \param olen      The address at which to store the length in Bytes
836  *                  of the data written.
837  * \param buf       The target buffer. This must be a writable buffer of
838  *                  length \p blen Bytes.
839  * \param blen      The length of the target buffer \p buf in Bytes.
840  *
841  * \return          \c 0 on success.
842  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
843  * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the target buffer
844  *                  is too small to hold the exported point.
845  * \return          Another negative error code on other kinds of failure.
846  */
847 int mbedtls_ecp_tls_write_point(const mbedtls_ecp_group *grp,
848                                 const mbedtls_ecp_point *pt,
849                                 int format, size_t *olen,
850                                 unsigned char *buf, size_t blen);
851 
852 /**
853  * \brief           This function sets up an ECP group context
854  *                  from a standardized set of domain parameters.
855  *
856  * \note            The index should be a value of the NamedCurve enum,
857  *                  as defined in <em>RFC-4492: Elliptic Curve Cryptography
858  *                  (ECC) Cipher Suites for Transport Layer Security (TLS)</em>,
859  *                  usually in the form of an \c MBEDTLS_ECP_DP_XXX macro.
860  *
861  * \param grp       The group context to setup. This must be initialized.
862  * \param id        The identifier of the domain parameter set to load.
863  *
864  * \return          \c 0 on success.
865  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p id doesn't
866  *                  correspond to a known group.
867  * \return          Another negative error code on other kinds of failure.
868  */
869 int mbedtls_ecp_group_load(mbedtls_ecp_group *grp, mbedtls_ecp_group_id id);
870 
871 /**
872  * \brief           This function sets up an ECP group context from a TLS
873  *                  ECParameters record as defined in RFC 4492, Section 5.4.
874  *
875  * \note            The read pointer \p buf is updated to point right after
876  *                  the ECParameters record on exit.
877  *
878  * \param grp       The group context to setup. This must be initialized.
879  * \param buf       The address of the pointer to the start of the input buffer.
880  * \param len       The length of the input buffer \c *buf in Bytes.
881  *
882  * \return          \c 0 on success.
883  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
884  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
885  *                  recognized.
886  * \return          Another negative error code on other kinds of failure.
887  */
888 int mbedtls_ecp_tls_read_group(mbedtls_ecp_group *grp,
889                                const unsigned char **buf, size_t len);
890 
891 /**
892  * \brief           This function extracts an elliptic curve group ID from a
893  *                  TLS ECParameters record as defined in RFC 4492, Section 5.4.
894  *
895  * \note            The read pointer \p buf is updated to point right after
896  *                  the ECParameters record on exit.
897  *
898  * \param grp       The address at which to store the group id.
899  *                  This must not be \c NULL.
900  * \param buf       The address of the pointer to the start of the input buffer.
901  * \param len       The length of the input buffer \c *buf in Bytes.
902  *
903  * \return          \c 0 on success.
904  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
905  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
906  *                  recognized.
907  * \return          Another negative error code on other kinds of failure.
908  */
909 int mbedtls_ecp_tls_read_group_id(mbedtls_ecp_group_id *grp,
910                                   const unsigned char **buf,
911                                   size_t len);
912 /**
913  * \brief           This function exports an elliptic curve as a TLS
914  *                  ECParameters record as defined in RFC 4492, Section 5.4.
915  *
916  * \param grp       The ECP group to be exported.
917  *                  This must be initialized and have group parameters
918  *                  set, for example through mbedtls_ecp_group_load().
919  * \param olen      The address at which to store the number of Bytes written.
920  *                  This must not be \c NULL.
921  * \param buf       The buffer to write to. This must be a writable buffer
922  *                  of length \p blen Bytes.
923  * \param blen      The length of the output buffer \p buf in Bytes.
924  *
925  * \return          \c 0 on success.
926  * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output
927  *                  buffer is too small to hold the exported group.
928  * \return          Another negative error code on other kinds of failure.
929  */
930 int mbedtls_ecp_tls_write_group(const mbedtls_ecp_group *grp,
931                                 size_t *olen,
932                                 unsigned char *buf, size_t blen);
933 
934 /**
935  * \brief           This function performs a scalar multiplication of a point
936  *                  by an integer: \p R = \p m * \p P.
937  *
938  *                  It is not thread-safe to use same group in multiple threads.
939  *
940  * \note            To prevent timing attacks, this function
941  *                  executes the exact same sequence of base-field
942  *                  operations for any valid \p m. It avoids any if-branch or
943  *                  array index depending on the value of \p m. It also uses
944  *                  \p f_rng to randomize some intermediate results.
945  *
946  * \param grp       The ECP group to use.
947  *                  This must be initialized and have group parameters
948  *                  set, for example through mbedtls_ecp_group_load().
949  * \param R         The point in which to store the result of the calculation.
950  *                  This must be initialized.
951  * \param m         The integer by which to multiply. This must be initialized.
952  * \param P         The point to multiply. This must be initialized.
953  * \param f_rng     The RNG function. This must not be \c NULL.
954  * \param p_rng     The RNG context to be passed to \p f_rng. This may be \c
955  *                  NULL if \p f_rng doesn't need a context.
956  *
957  * \return          \c 0 on success.
958  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private
959  *                  key, or \p P is not a valid public key.
960  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
961  * \return          Another negative error code on other kinds of failure.
962  */
963 int mbedtls_ecp_mul(mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
964                     const mbedtls_mpi *m, const mbedtls_ecp_point *P,
965                     int (*f_rng)(void *, unsigned char *, size_t), void *p_rng);
966 
967 /**
968  * \brief           This function performs multiplication of a point by
969  *                  an integer: \p R = \p m * \p P in a restartable way.
970  *
971  * \see             mbedtls_ecp_mul()
972  *
973  * \note            This function does the same as \c mbedtls_ecp_mul(), but
974  *                  it can return early and restart according to the limit set
975  *                  with \c mbedtls_ecp_set_max_ops() to reduce blocking.
976  *
977  * \param grp       The ECP group to use.
978  *                  This must be initialized and have group parameters
979  *                  set, for example through mbedtls_ecp_group_load().
980  * \param R         The point in which to store the result of the calculation.
981  *                  This must be initialized.
982  * \param m         The integer by which to multiply. This must be initialized.
983  * \param P         The point to multiply. This must be initialized.
984  * \param f_rng     The RNG function. This must not be \c NULL.
985  * \param p_rng     The RNG context to be passed to \p f_rng. This may be \c
986  *                  NULL if \p f_rng doesn't need a context.
987  * \param rs_ctx    The restart context (NULL disables restart).
988  *
989  * \return          \c 0 on success.
990  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private
991  *                  key, or \p P is not a valid public key.
992  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
993  * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
994  *                  operations was reached: see \c mbedtls_ecp_set_max_ops().
995  * \return          Another negative error code on other kinds of failure.
996  */
997 int mbedtls_ecp_mul_restartable(mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
998                                 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
999                                 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
1000                                 mbedtls_ecp_restart_ctx *rs_ctx);
1001 
1002 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
1003 /**
1004  * \brief           This function performs multiplication and addition of two
1005  *                  points by integers: \p R = \p m * \p P + \p n * \p Q
1006  *
1007  *                  It is not thread-safe to use same group in multiple threads.
1008  *
1009  * \note            In contrast to mbedtls_ecp_mul(), this function does not
1010  *                  guarantee a constant execution flow and timing.
1011  *
1012  * \note            This function is only defined for short Weierstrass curves.
1013  *                  It may not be included in builds without any short
1014  *                  Weierstrass curve.
1015  *
1016  * \param grp       The ECP group to use.
1017  *                  This must be initialized and have group parameters
1018  *                  set, for example through mbedtls_ecp_group_load().
1019  * \param R         The point in which to store the result of the calculation.
1020  *                  This must be initialized.
1021  * \param m         The integer by which to multiply \p P.
1022  *                  This must be initialized.
1023  * \param P         The point to multiply by \p m. This must be initialized.
1024  * \param n         The integer by which to multiply \p Q.
1025  *                  This must be initialized.
1026  * \param Q         The point to be multiplied by \p n.
1027  *                  This must be initialized.
1028  *
1029  * \return          \c 0 on success.
1030  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not
1031  *                  valid private keys, or \p P or \p Q are not valid public
1032  *                  keys.
1033  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
1034  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not
1035  *                  designate a short Weierstrass curve.
1036  * \return          Another negative error code on other kinds of failure.
1037  */
1038 int mbedtls_ecp_muladd(mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1039                        const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1040                        const mbedtls_mpi *n, const mbedtls_ecp_point *Q);
1041 
1042 /**
1043  * \brief           This function performs multiplication and addition of two
1044  *                  points by integers: \p R = \p m * \p P + \p n * \p Q in a
1045  *                  restartable way.
1046  *
1047  * \see             \c mbedtls_ecp_muladd()
1048  *
1049  * \note            This function works the same as \c mbedtls_ecp_muladd(),
1050  *                  but it can return early and restart according to the limit
1051  *                  set with \c mbedtls_ecp_set_max_ops() to reduce blocking.
1052  *
1053  * \note            This function is only defined for short Weierstrass curves.
1054  *                  It may not be included in builds without any short
1055  *                  Weierstrass curve.
1056  *
1057  * \param grp       The ECP group to use.
1058  *                  This must be initialized and have group parameters
1059  *                  set, for example through mbedtls_ecp_group_load().
1060  * \param R         The point in which to store the result of the calculation.
1061  *                  This must be initialized.
1062  * \param m         The integer by which to multiply \p P.
1063  *                  This must be initialized.
1064  * \param P         The point to multiply by \p m. This must be initialized.
1065  * \param n         The integer by which to multiply \p Q.
1066  *                  This must be initialized.
1067  * \param Q         The point to be multiplied by \p n.
1068  *                  This must be initialized.
1069  * \param rs_ctx    The restart context (NULL disables restart).
1070  *
1071  * \return          \c 0 on success.
1072  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not
1073  *                  valid private keys, or \p P or \p Q are not valid public
1074  *                  keys.
1075  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
1076  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not
1077  *                  designate a short Weierstrass curve.
1078  * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
1079  *                  operations was reached: see \c mbedtls_ecp_set_max_ops().
1080  * \return          Another negative error code on other kinds of failure.
1081  */
1082 int mbedtls_ecp_muladd_restartable(
1083     mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
1084     const mbedtls_mpi *m, const mbedtls_ecp_point *P,
1085     const mbedtls_mpi *n, const mbedtls_ecp_point *Q,
1086     mbedtls_ecp_restart_ctx *rs_ctx);
1087 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
1088 
1089 /**
1090  * \brief           This function checks that a point is a valid public key
1091  *                  on this curve.
1092  *
1093  *                  It only checks that the point is non-zero, has
1094  *                  valid coordinates and lies on the curve. It does not verify
1095  *                  that it is indeed a multiple of \p G. This additional
1096  *                  check is computationally more expensive, is not required
1097  *                  by standards, and should not be necessary if the group
1098  *                  used has a small cofactor. In particular, it is useless for
1099  *                  the NIST groups which all have a cofactor of 1.
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 point should belong to.
1107  *                  This must be initialized and have group parameters
1108  *                  set, for example through mbedtls_ecp_group_load().
1109  * \param pt        The point to check. This must be initialized.
1110  *
1111  * \return          \c 0 if the point is a valid public key.
1112  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not
1113  *                  a valid public key for the given curve.
1114  * \return          Another negative error code on other kinds of failure.
1115  */
1116 int mbedtls_ecp_check_pubkey(const mbedtls_ecp_group *grp,
1117                              const mbedtls_ecp_point *pt);
1118 
1119 /**
1120  * \brief           This function checks that an \p mbedtls_mpi is a
1121  *                  valid private key for this curve.
1122  *
1123  * \note            This function uses bare components rather than an
1124  *                  ::mbedtls_ecp_keypair structure to ease use with other
1125  *                  structures, such as ::mbedtls_ecdh_context or
1126  *                  ::mbedtls_ecdsa_context.
1127  *
1128  * \param grp       The ECP group the private key should belong to.
1129  *                  This must be initialized and have group parameters
1130  *                  set, for example through mbedtls_ecp_group_load().
1131  * \param d         The integer to check. This must be initialized.
1132  *
1133  * \return          \c 0 if the point is a valid private key.
1134  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not a valid
1135  *                  private key for the given curve.
1136  * \return          Another negative error code on other kinds of failure.
1137  */
1138 int mbedtls_ecp_check_privkey(const mbedtls_ecp_group *grp,
1139                               const mbedtls_mpi *d);
1140 
1141 /**
1142  * \brief           This function generates a private key.
1143  *
1144  * \param grp       The ECP group to generate a private key for.
1145  *                  This must be initialized and have group parameters
1146  *                  set, for example through mbedtls_ecp_group_load().
1147  * \param d         The destination MPI (secret part). This must be initialized.
1148  * \param f_rng     The RNG function. This must not be \c NULL.
1149  * \param p_rng     The RNG parameter to be passed to \p f_rng. This may be
1150  *                  \c NULL if \p f_rng doesn't need a context argument.
1151  *
1152  * \return          \c 0 on success.
1153  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1154  *                  on failure.
1155  */
1156 int mbedtls_ecp_gen_privkey(const mbedtls_ecp_group *grp,
1157                             mbedtls_mpi *d,
1158                             int (*f_rng)(void *, unsigned char *, size_t),
1159                             void *p_rng);
1160 
1161 /**
1162  * \brief           This function generates a keypair with a configurable base
1163  *                  point.
1164  *
1165  * \note            This function uses bare components rather than an
1166  *                  ::mbedtls_ecp_keypair structure to ease use with other
1167  *                  structures, such as ::mbedtls_ecdh_context or
1168  *                  ::mbedtls_ecdsa_context.
1169  *
1170  * \param grp       The ECP group to generate a key pair for.
1171  *                  This must be initialized and have group parameters
1172  *                  set, for example through mbedtls_ecp_group_load().
1173  * \param G         The base point to use. This must be initialized
1174  *                  and belong to \p grp. It replaces the default base
1175  *                  point \c grp->G used by mbedtls_ecp_gen_keypair().
1176  * \param d         The destination MPI (secret part).
1177  *                  This must be initialized.
1178  * \param Q         The destination point (public part).
1179  *                  This must be initialized.
1180  * \param f_rng     The RNG function. This must not be \c NULL.
1181  * \param p_rng     The RNG context to be passed to \p f_rng. This may
1182  *                  be \c NULL if \p f_rng doesn't need a context argument.
1183  *
1184  * \return          \c 0 on success.
1185  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1186  *                  on failure.
1187  */
1188 int mbedtls_ecp_gen_keypair_base(mbedtls_ecp_group *grp,
1189                                  const mbedtls_ecp_point *G,
1190                                  mbedtls_mpi *d, mbedtls_ecp_point *Q,
1191                                  int (*f_rng)(void *, unsigned char *, size_t),
1192                                  void *p_rng);
1193 
1194 /**
1195  * \brief           This function generates an ECP keypair.
1196  *
1197  * \note            This function uses bare components rather than an
1198  *                  ::mbedtls_ecp_keypair structure to ease use with other
1199  *                  structures, such as ::mbedtls_ecdh_context or
1200  *                  ::mbedtls_ecdsa_context.
1201  *
1202  * \param grp       The ECP group to generate a key pair for.
1203  *                  This must be initialized and have group parameters
1204  *                  set, for example through mbedtls_ecp_group_load().
1205  * \param d         The destination MPI (secret part).
1206  *                  This must be initialized.
1207  * \param Q         The destination point (public part).
1208  *                  This must be initialized.
1209  * \param f_rng     The RNG function. This must not be \c NULL.
1210  * \param p_rng     The RNG context to be passed to \p f_rng. This may
1211  *                  be \c NULL if \p f_rng doesn't need a context argument.
1212  *
1213  * \return          \c 0 on success.
1214  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1215  *                  on failure.
1216  */
1217 int mbedtls_ecp_gen_keypair(mbedtls_ecp_group *grp, mbedtls_mpi *d,
1218                             mbedtls_ecp_point *Q,
1219                             int (*f_rng)(void *, unsigned char *, size_t),
1220                             void *p_rng);
1221 
1222 /**
1223  * \brief           This function generates an ECP key.
1224  *
1225  * \param grp_id    The ECP group identifier.
1226  * \param key       The destination key. This must be initialized.
1227  * \param f_rng     The RNG function to use. This must not be \c NULL.
1228  * \param p_rng     The RNG context to be passed to \p f_rng. This may
1229  *                  be \c NULL if \p f_rng doesn't need a context argument.
1230  *
1231  * \return          \c 0 on success.
1232  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
1233  *                  on failure.
1234  */
1235 int mbedtls_ecp_gen_key(mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
1236                         int (*f_rng)(void *, unsigned char *, size_t),
1237                         void *p_rng);
1238 
1239 /**
1240  * \brief           This function reads an elliptic curve private key.
1241  *
1242  * \param grp_id    The ECP group identifier.
1243  * \param key       The destination key.
1244  * \param buf       The buffer containing the binary representation of the
1245  *                  key. (Big endian integer for Weierstrass curves, byte
1246  *                  string for Montgomery curves.)
1247  * \param buflen    The length of the buffer in bytes.
1248  *
1249  * \return          \c 0 on success.
1250  * \return          #MBEDTLS_ERR_ECP_INVALID_KEY error if the key is
1251  *                  invalid.
1252  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
1253  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for
1254  *                  the group is not implemented.
1255  * \return          Another negative error code on different kinds of failure.
1256  */
1257 int mbedtls_ecp_read_key(mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
1258                          const unsigned char *buf, size_t buflen);
1259 
1260 /**
1261  * \brief           This function exports an elliptic curve private key.
1262  *
1263  * \param key       The private key.
1264  * \param buf       The output buffer for containing the binary representation
1265  *                  of the key. (Big endian integer for Weierstrass curves, byte
1266  *                  string for Montgomery curves.)
1267  * \param buflen    The total length of the buffer in bytes.
1268  *
1269  * \return          \c 0 on success.
1270  * \return          #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the \p key
1271                     representation is larger than the available space in \p buf.
1272  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for
1273  *                  the group is not implemented.
1274  * \return          Another negative error code on different kinds of failure.
1275  */
1276 int mbedtls_ecp_write_key(mbedtls_ecp_keypair *key,
1277                           unsigned char *buf, size_t buflen);
1278 
1279 /**
1280  * \brief           This function checks that the keypair objects
1281  *                  \p pub and \p prv have the same group and the
1282  *                  same public point, and that the private key in
1283  *                  \p prv is consistent with the public key.
1284  *
1285  * \param pub       The keypair structure holding the public key. This
1286  *                  must be initialized. If it contains a private key, that
1287  *                  part is ignored.
1288  * \param prv       The keypair structure holding the full keypair.
1289  *                  This must be initialized.
1290  * \param f_rng     The RNG function. This must not be \c NULL.
1291  * \param p_rng     The RNG context to be passed to \p f_rng. This may be \c
1292  *                  NULL if \p f_rng doesn't need a context.
1293  *
1294  * \return          \c 0 on success, meaning that the keys are valid and match.
1295  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the keys are invalid or do not match.
1296  * \return          An \c MBEDTLS_ERR_ECP_XXX or an \c MBEDTLS_ERR_MPI_XXX
1297  *                  error code on calculation failure.
1298  */
1299 int mbedtls_ecp_check_pub_priv(
1300     const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv,
1301     int (*f_rng)(void *, unsigned char *, size_t), void *p_rng);
1302 
1303 /**
1304  * \brief           This function exports generic key-pair parameters.
1305  *
1306  * \param key       The key pair to export from.
1307  * \param grp       Slot for exported ECP group.
1308  *                  It must point to an initialized ECP group.
1309  * \param d         Slot for the exported secret value.
1310  *                  It must point to an initialized mpi.
1311  * \param Q         Slot for the exported public value.
1312  *                  It must point to an initialized ECP point.
1313  *
1314  * \return          \c 0 on success,
1315  * \return          #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
1316  * \return          #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if key id doesn't
1317  *                  correspond to a known group.
1318  * \return          Another negative error code on other kinds of failure.
1319  */
1320 int mbedtls_ecp_export(const mbedtls_ecp_keypair *key, mbedtls_ecp_group *grp,
1321                        mbedtls_mpi *d, mbedtls_ecp_point *Q);
1322 
1323 #if defined(MBEDTLS_SELF_TEST)
1324 
1325 /**
1326  * \brief          The ECP checkup routine.
1327  *
1328  * \return         \c 0 on success.
1329  * \return         \c 1 on failure.
1330  */
1331 int mbedtls_ecp_self_test(int verbose);
1332 
1333 #endif /* MBEDTLS_SELF_TEST */
1334 
1335 #ifdef __cplusplus
1336 }
1337 #endif
1338 
1339 #endif /* ecp.h */
1340