123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512513514515516517518519520521522523524525526527528529530531532533534535536537538539540541542543544545546547548549550551552553554555556557558559560561562563564565566567568569570571572573574575576577578579580581582583584585586587588589590591592593594595596597598599600601602603604605606607608609610611612613614615616617618619620621622623624625626627628629630631632633634635636637638639640641642643644645646647648649650651652653654655656657658659660661662663664665666667668669670671672673674675676677678679680681682683684685686687688689690691692693694695696697698699700701702703704705706707708709710711712713714715716717718719720721722723724725726727728729730731732733734735736737738739740741742743744745746747748749750751752753754755756757758759760761762763764765766767768769770771772773774775776777778779780781782783784785786787788789790791792793794795796797798799800801802803804805806807808809810811812813814815816817818819820821822823824825826827828829830831832833834835836837838839840841842843844845846847848849850851852853854855856857858859860861862863864865866867868869870871872873874875876877878879880881882883884885886887888889890891892893894895896897898899900901902903904905906907908909910911912913914915916917918919920921922923924925926927928929930931932933934935936937938939940941942943944945946947948949950951952953954955956957958959960961962963964965966967968969970971972973974975976977978979980981982983984985986987988989990991992993994995996997998999100010011002100310041005100610071008100910101011101210131014101510161017101810191020102110221023102410251026102710281029103010311032103310341035103610371038103910401041104210431044104510461047104810491050105110521053105410551056105710581059106010611062106310641065106610671068106910701071107210731074107510761077107810791080108110821083108410851086108710881089109010911092109310941095109610971098109911001101110211031104110511061107110811091110111111121113111411151116111711181119112011211122112311241125112611271128112911301131113211331134113511361137113811391140114111421143114411451146114711481149115011511152115311541155115611571158115911601161116211631164116511661167116811691170117111721173117411751176117711781179118011811182118311841185118611871188118911901191119211931194119511961197119811991200120112021203120412051206120712081209121012111212121312141215121612171218121912201221122212231224122512261227122812291230123112321233123412351236123712381239124012411242124312441245124612471248124912501251125212531254125512561257125812591260126112621263126412651266126712681269127012711272127312741275127612771278127912801281128212831284128512861287128812891290129112921293129412951296129712981299130013011302130313041305 |
- /**
- * \file ecp.h
- *
- * \brief This file provides an API for Elliptic Curves over GF(P) (ECP).
- *
- * The use of ECP in cryptography and TLS is defined in
- * <em>Standards for Efficient Cryptography Group (SECG): SEC1
- * Elliptic Curve Cryptography</em> and
- * <em>RFC-4492: Elliptic Curve Cryptography (ECC) Cipher Suites
- * for Transport Layer Security (TLS)</em>.
- *
- * <em>RFC-2409: The Internet Key Exchange (IKE)</em> defines ECP
- * group types.
- *
- */
- /*
- * Copyright The Mbed TLS Contributors
- * SPDX-License-Identifier: Apache-2.0
- *
- * Licensed under the Apache License, Version 2.0 (the "License"); you may
- * not use this file except in compliance with the License.
- * You may obtain a copy of the License at
- *
- * http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
- * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
- #ifndef MBEDTLS_ECP_H
- #define MBEDTLS_ECP_H
- #if !defined(MBEDTLS_CONFIG_FILE)
- #include "mbedtls/config.h"
- #else
- #include MBEDTLS_CONFIG_FILE
- #endif
- #include "mbedtls/bignum.h"
- /*
- * ECP error codes
- */
- #define MBEDTLS_ERR_ECP_BAD_INPUT_DATA -0x4F80 /**< Bad input parameters to function. */
- #define MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL -0x4F00 /**< The buffer is too small to write to. */
- #define MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE -0x4E80 /**< The requested feature is not available, for example, the requested curve is not supported. */
- #define MBEDTLS_ERR_ECP_VERIFY_FAILED -0x4E00 /**< The signature is not valid. */
- #define MBEDTLS_ERR_ECP_ALLOC_FAILED -0x4D80 /**< Memory allocation failed. */
- #define MBEDTLS_ERR_ECP_RANDOM_FAILED -0x4D00 /**< Generation of random value, such as ephemeral key, failed. */
- #define MBEDTLS_ERR_ECP_INVALID_KEY -0x4C80 /**< Invalid private or public key. */
- #define MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH -0x4C00 /**< The buffer contains a valid signature followed by more data. */
- /* MBEDTLS_ERR_ECP_HW_ACCEL_FAILED is deprecated and should not be used. */
- #define MBEDTLS_ERR_ECP_HW_ACCEL_FAILED -0x4B80 /**< The ECP hardware accelerator failed. */
- #define MBEDTLS_ERR_ECP_IN_PROGRESS -0x4B00 /**< Operation in progress, call again with the same parameters to continue. */
- /* Flags indicating whether to include code that is specific to certain
- * types of curves. These flags are for internal library use only. */
- #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \
- defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
- defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
- defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \
- defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \
- defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \
- defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \
- defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \
- defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
- defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
- defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) || \
- defined(MBEDTLS_ECP_DP_SM2_ENABLED)
- #define MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED
- #endif
- #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) || \
- defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
- #define MBEDTLS_ECP_MONTGOMERY_ENABLED
- #endif
- #ifdef __cplusplus
- extern "C" {
- #endif
- /**
- * Domain-parameter identifiers: curve, subgroup, and generator.
- *
- * \note Only curves over prime fields are supported.
- *
- * \warning This library does not support validation of arbitrary domain
- * parameters. Therefore, only standardized domain parameters from trusted
- * sources should be used. See mbedtls_ecp_group_load().
- */
- /* Note: when adding a new curve:
- * - Add it at the end of this enum, otherwise you'll break the ABI by
- * changing the numerical value for existing curves.
- * - Increment MBEDTLS_ECP_DP_MAX below if needed.
- * - Update the calculation of MBEDTLS_ECP_MAX_BITS_MIN below.
- * - Add the corresponding MBEDTLS_ECP_DP_xxx_ENABLED macro definition to
- * config.h.
- * - List the curve as a dependency of MBEDTLS_ECP_C and
- * MBEDTLS_ECDSA_C if supported in check_config.h.
- * - Add the curve to the appropriate curve type macro
- * MBEDTLS_ECP_yyy_ENABLED above.
- * - Add the necessary definitions to ecp_curves.c.
- * - Add the curve to the ecp_supported_curves array in ecp.c.
- * - Add the curve to applicable profiles in x509_crt.c if applicable.
- */
- typedef enum
- {
- MBEDTLS_ECP_DP_NONE = 0, /*!< Curve not defined. */
- MBEDTLS_ECP_DP_SECP192R1, /*!< Domain parameters for the 192-bit curve defined by FIPS 186-4 and SEC1. */
- MBEDTLS_ECP_DP_SECP224R1, /*!< Domain parameters for the 224-bit curve defined by FIPS 186-4 and SEC1. */
- MBEDTLS_ECP_DP_SECP256R1, /*!< Domain parameters for the 256-bit curve defined by FIPS 186-4 and SEC1. */
- MBEDTLS_ECP_DP_SECP384R1, /*!< Domain parameters for the 384-bit curve defined by FIPS 186-4 and SEC1. */
- MBEDTLS_ECP_DP_SECP521R1, /*!< Domain parameters for the 521-bit curve defined by FIPS 186-4 and SEC1. */
- MBEDTLS_ECP_DP_BP256R1, /*!< Domain parameters for 256-bit Brainpool curve. */
- MBEDTLS_ECP_DP_BP384R1, /*!< Domain parameters for 384-bit Brainpool curve. */
- MBEDTLS_ECP_DP_BP512R1, /*!< Domain parameters for 512-bit Brainpool curve. */
- MBEDTLS_ECP_DP_CURVE25519, /*!< Domain parameters for Curve25519. */
- MBEDTLS_ECP_DP_SECP192K1, /*!< Domain parameters for 192-bit "Koblitz" curve. */
- MBEDTLS_ECP_DP_SECP224K1, /*!< Domain parameters for 224-bit "Koblitz" curve. */
- MBEDTLS_ECP_DP_SECP256K1, /*!< Domain parameters for 256-bit "Koblitz" curve. */
- MBEDTLS_ECP_DP_CURVE448, /*!< Domain parameters for Curve448. */
- MBEDTLS_ECP_DP_SM2, /*!< Domain parameters for SM2. */
- } mbedtls_ecp_group_id;
- /**
- * The number of supported curves, plus one for #MBEDTLS_ECP_DP_NONE.
- *
- * \note Montgomery curves are currently excluded.
- */
- #define MBEDTLS_ECP_DP_MAX 12
- /*
- * Curve types
- */
- typedef enum
- {
- MBEDTLS_ECP_TYPE_NONE = 0,
- MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */
- MBEDTLS_ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */
- } mbedtls_ecp_curve_type;
- /**
- * Curve information, for use by other modules.
- */
- typedef struct mbedtls_ecp_curve_info
- {
- mbedtls_ecp_group_id grp_id; /*!< An internal identifier. */
- uint16_t tls_id; /*!< The TLS NamedCurve identifier. */
- uint16_t bit_size; /*!< The curve size in bits. */
- const char *name; /*!< A human-friendly name. */
- } mbedtls_ecp_curve_info;
- /**
- * \brief The ECP point structure, in Jacobian coordinates.
- *
- * \note All functions expect and return points satisfying
- * the following condition: <code>Z == 0</code> or
- * <code>Z == 1</code>. Other values of \p Z are
- * used only by internal functions.
- * The point is zero, or "at infinity", if <code>Z == 0</code>.
- * Otherwise, \p X and \p Y are its standard (affine)
- * coordinates.
- */
- typedef struct mbedtls_ecp_point
- {
- mbedtls_mpi X; /*!< The X coordinate of the ECP point. */
- mbedtls_mpi Y; /*!< The Y coordinate of the ECP point. */
- mbedtls_mpi Z; /*!< The Z coordinate of the ECP point. */
- }
- mbedtls_ecp_point;
- /* Determine the minimum safe value of MBEDTLS_ECP_MAX_BITS. */
- #if !defined(MBEDTLS_ECP_C)
- #define MBEDTLS_ECP_MAX_BITS_MIN 0
- /* Note: the curves must be listed in DECREASING size! */
- #elif defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
- #define MBEDTLS_ECP_MAX_BITS_MIN 521
- #elif defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
- #define MBEDTLS_ECP_MAX_BITS_MIN 512
- #elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
- #define MBEDTLS_ECP_MAX_BITS_MIN 448
- #elif defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
- #define MBEDTLS_ECP_MAX_BITS_MIN 384
- #elif defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
- #define MBEDTLS_ECP_MAX_BITS_MIN 384
- #elif defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
- #define MBEDTLS_ECP_MAX_BITS_MIN 256
- #elif defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
- #define MBEDTLS_ECP_MAX_BITS_MIN 256
- #elif defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
- #define MBEDTLS_ECP_MAX_BITS_MIN 256
- #elif defined(MBEDTLS_ECP_DP_SM2_ENABLED)
- #define MBEDTLS_ECP_MAX_BITS_MIN 256
- #elif defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
- #define MBEDTLS_ECP_MAX_BITS_MIN 255
- #elif defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
- #define MBEDTLS_ECP_MAX_BITS_MIN 225 // n is slightly above 2^224
- #elif defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
- #define MBEDTLS_ECP_MAX_BITS_MIN 224
- #elif defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
- #define MBEDTLS_ECP_MAX_BITS_MIN 192
- #elif defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
- #define MBEDTLS_ECP_MAX_BITS_MIN 192
- #else
- #error "MBEDTLS_ECP_C enabled, but no curve?"
- #endif
- #if !defined(MBEDTLS_ECP_ALT)
- /*
- * default mbed TLS elliptic curve arithmetic implementation
- *
- * (in case MBEDTLS_ECP_ALT is defined then the developer has to provide an
- * alternative implementation for the whole module and it will replace this
- * one.)
- */
- /**
- * \brief The ECP group structure.
- *
- * We consider two types of curve equations:
- * <ul><li>Short Weierstrass: <code>y^2 = x^3 + A x + B mod P</code>
- * (SEC1 + RFC-4492)</li>
- * <li>Montgomery: <code>y^2 = x^3 + A x^2 + x mod P</code> (Curve25519,
- * Curve448)</li></ul>
- * In both cases, the generator (\p G) for a prime-order subgroup is fixed.
- *
- * For Short Weierstrass, this subgroup is the whole curve, and its
- * cardinality is denoted by \p N. Our code requires that \p N is an
- * odd prime as mbedtls_ecp_mul() requires an odd number, and
- * mbedtls_ecdsa_sign() requires that it is prime for blinding purposes.
- *
- * For Montgomery curves, we do not store \p A, but <code>(A + 2) / 4</code>,
- * which is the quantity used in the formulas. Additionally, \p nbits is
- * not the size of \p N but the required size for private keys.
- *
- * If \p modp is NULL, reduction modulo \p P is done using a generic algorithm.
- * Otherwise, \p modp must point to a function that takes an \p mbedtls_mpi in the
- * range of <code>0..2^(2*pbits)-1</code>, and transforms it in-place to an integer
- * which is congruent mod \p P to the given MPI, and is close enough to \p pbits
- * in size, so that it may be efficiently brought in the 0..P-1 range by a few
- * additions or subtractions. Therefore, it is only an approximative modular
- * reduction. It must return 0 on success and non-zero on failure.
- *
- * \note Alternative implementations must keep the group IDs distinct. If
- * two group structures have the same ID, then they must be
- * identical.
- *
- */
- typedef struct mbedtls_ecp_group
- {
- mbedtls_ecp_group_id id; /*!< An internal group identifier. */
- mbedtls_mpi P; /*!< The prime modulus of the base field. */
- mbedtls_mpi A; /*!< For Short Weierstrass: \p A in the equation. For
- Montgomery curves: <code>(A + 2) / 4</code>. */
- mbedtls_mpi B; /*!< For Short Weierstrass: \p B in the equation.
- For Montgomery curves: unused. */
- mbedtls_ecp_point G; /*!< The generator of the subgroup used. */
- mbedtls_mpi N; /*!< The order of \p G. */
- size_t pbits; /*!< The number of bits in \p P.*/
- size_t nbits; /*!< For Short Weierstrass: The number of bits in \p P.
- For Montgomery curves: the number of bits in the
- private keys. */
- unsigned int h; /*!< \internal 1 if the constants are static. */
- int (*modp)(mbedtls_mpi *); /*!< The function for fast pseudo-reduction
- mod \p P (see above).*/
- int (*t_pre)(mbedtls_ecp_point *, void *); /*!< Unused. */
- int (*t_post)(mbedtls_ecp_point *, void *); /*!< Unused. */
- void *t_data; /*!< Unused. */
- mbedtls_ecp_point *T; /*!< Pre-computed points for ecp_mul_comb(). */
- size_t T_size; /*!< The number of pre-computed points. */
- }
- mbedtls_ecp_group;
- /**
- * \name SECTION: Module settings
- *
- * The configuration options you can set for this module are in this section.
- * Either change them in config.h, or define them using the compiler command line.
- * \{
- */
- #if defined(MBEDTLS_ECP_MAX_BITS)
- #if MBEDTLS_ECP_MAX_BITS < MBEDTLS_ECP_MAX_BITS_MIN
- #error "MBEDTLS_ECP_MAX_BITS is smaller than the largest supported curve"
- #endif
- #elif defined(MBEDTLS_ECP_C)
- /**
- * The maximum size of the groups, that is, of \c N and \c P.
- */
- #define MBEDTLS_ECP_MAX_BITS MBEDTLS_ECP_MAX_BITS_MIN
- #else
- /* MBEDTLS_ECP_MAX_BITS is not relevant without MBEDTLS_ECP_C, but set it
- * to a nonzero value so that code that unconditionally allocates an array
- * of a size based on it keeps working if built without ECC support. */
- #define MBEDTLS_ECP_MAX_BITS 1
- #endif
- #define MBEDTLS_ECP_MAX_BYTES ( ( MBEDTLS_ECP_MAX_BITS + 7 ) / 8 )
- #define MBEDTLS_ECP_MAX_PT_LEN ( 2 * MBEDTLS_ECP_MAX_BYTES + 1 )
- #if !defined(MBEDTLS_ECP_WINDOW_SIZE)
- /*
- * Maximum "window" size used for point multiplication.
- * Default: a point where higher memory usage yields disminishing performance
- * returns.
- * Minimum value: 2. Maximum value: 7.
- *
- * Result is an array of at most ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
- * points used for point multiplication. This value is directly tied to EC
- * peak memory usage, so decreasing it by one should roughly cut memory usage
- * by two (if large curves are in use).
- *
- * Reduction in size may reduce speed, but larger curves are impacted first.
- * Sample performances (in ECDHE handshakes/s, with FIXED_POINT_OPTIM = 1):
- * w-size: 6 5 4 3 2
- * 521 145 141 135 120 97
- * 384 214 209 198 177 146
- * 256 320 320 303 262 226
- * 224 475 475 453 398 342
- * 192 640 640 633 587 476
- */
- #define MBEDTLS_ECP_WINDOW_SIZE 4 /**< The maximum window size used. */
- #endif /* MBEDTLS_ECP_WINDOW_SIZE */
- #if !defined(MBEDTLS_ECP_FIXED_POINT_OPTIM)
- /*
- * Trade memory for speed on fixed-point multiplication.
- *
- * This speeds up repeated multiplication of the generator (that is, the
- * multiplication in ECDSA signatures, and half of the multiplications in
- * ECDSA verification and ECDHE) by a factor roughly 3 to 4.
- *
- * The cost is increasing EC peak memory usage by a factor roughly 2.
- *
- * Change this value to 0 to reduce peak memory usage.
- */
- #define MBEDTLS_ECP_FIXED_POINT_OPTIM 1 /**< Enable fixed-point speed-up. */
- #endif /* MBEDTLS_ECP_FIXED_POINT_OPTIM */
- /* \} name SECTION: Module settings */
- #else /* MBEDTLS_ECP_ALT */
- #include "ecp_alt.h"
- #endif /* MBEDTLS_ECP_ALT */
- #if defined(MBEDTLS_ECP_RESTARTABLE)
- /**
- * \brief Internal restart context for multiplication
- *
- * \note Opaque struct
- */
- typedef struct mbedtls_ecp_restart_mul mbedtls_ecp_restart_mul_ctx;
- /**
- * \brief Internal restart context for ecp_muladd()
- *
- * \note Opaque struct
- */
- typedef struct mbedtls_ecp_restart_muladd mbedtls_ecp_restart_muladd_ctx;
- /**
- * \brief General context for resuming ECC operations
- */
- typedef struct
- {
- unsigned ops_done; /*!< current ops count */
- unsigned depth; /*!< call depth (0 = top-level) */
- mbedtls_ecp_restart_mul_ctx *rsm; /*!< ecp_mul_comb() sub-context */
- mbedtls_ecp_restart_muladd_ctx *ma; /*!< ecp_muladd() sub-context */
- } mbedtls_ecp_restart_ctx;
- /*
- * Operation counts for restartable functions
- */
- #define MBEDTLS_ECP_OPS_CHK 3 /*!< basic ops count for ecp_check_pubkey() */
- #define MBEDTLS_ECP_OPS_DBL 8 /*!< basic ops count for ecp_double_jac() */
- #define MBEDTLS_ECP_OPS_ADD 11 /*!< basic ops count for see ecp_add_mixed() */
- #define MBEDTLS_ECP_OPS_INV 120 /*!< empirical equivalent for mpi_mod_inv() */
- /**
- * \brief Internal; for restartable functions in other modules.
- * Check and update basic ops budget.
- *
- * \param grp Group structure
- * \param rs_ctx Restart context
- * \param ops Number of basic ops to do
- *
- * \return \c 0 if doing \p ops basic ops is still allowed,
- * \return #MBEDTLS_ERR_ECP_IN_PROGRESS otherwise.
- */
- int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp,
- mbedtls_ecp_restart_ctx *rs_ctx,
- unsigned ops );
- /* Utility macro for checking and updating ops budget */
- #define MBEDTLS_ECP_BUDGET( ops ) \
- MBEDTLS_MPI_CHK( mbedtls_ecp_check_budget( grp, rs_ctx, \
- (unsigned) (ops) ) );
- #else /* MBEDTLS_ECP_RESTARTABLE */
- #define MBEDTLS_ECP_BUDGET( ops ) /* no-op; for compatibility */
- /* We want to declare restartable versions of existing functions anyway */
- typedef void mbedtls_ecp_restart_ctx;
- #endif /* MBEDTLS_ECP_RESTARTABLE */
- /**
- * \brief The ECP key-pair structure.
- *
- * A generic key-pair that may be used for ECDSA and fixed ECDH, for example.
- *
- * \note Members are deliberately in the same order as in the
- * ::mbedtls_ecdsa_context structure.
- */
- typedef struct mbedtls_ecp_keypair
- {
- mbedtls_ecp_group grp; /*!< Elliptic curve and base point */
- mbedtls_mpi d; /*!< our secret value */
- mbedtls_ecp_point Q; /*!< our public value */
- }
- mbedtls_ecp_keypair;
- /*
- * Point formats, from RFC 4492's enum ECPointFormat
- */
- #define MBEDTLS_ECP_PF_UNCOMPRESSED 0 /**< Uncompressed point format. */
- #define MBEDTLS_ECP_PF_COMPRESSED 1 /**< Compressed point format. */
- /*
- * Some other constants from RFC 4492
- */
- #define MBEDTLS_ECP_TLS_NAMED_CURVE 3 /**< The named_curve of ECCurveType. */
- #if defined(MBEDTLS_ECP_RESTARTABLE)
- /**
- * \brief Set the maximum number of basic operations done in a row.
- *
- * If more operations are needed to complete a computation,
- * #MBEDTLS_ERR_ECP_IN_PROGRESS will be returned by the
- * function performing the computation. It is then the
- * caller's responsibility to either call again with the same
- * parameters until it returns 0 or an error code; or to free
- * the restart context if the operation is to be aborted.
- *
- * It is strictly required that all input parameters and the
- * restart context be the same on successive calls for the
- * same operation, but output parameters need not be the
- * same; they must not be used until the function finally
- * returns 0.
- *
- * This only applies to functions whose documentation
- * mentions they may return #MBEDTLS_ERR_ECP_IN_PROGRESS (or
- * #MBEDTLS_ERR_SSL_CRYPTO_IN_PROGRESS for functions in the
- * SSL module). For functions that accept a "restart context"
- * argument, passing NULL disables restart and makes the
- * function equivalent to the function with the same name
- * with \c _restartable removed. For functions in the ECDH
- * module, restart is disabled unless the function accepts
- * an "ECDH context" argument and
- * mbedtls_ecdh_enable_restart() was previously called on
- * that context. For function in the SSL module, restart is
- * only enabled for specific sides and key exchanges
- * (currently only for clients and ECDHE-ECDSA).
- *
- * \param max_ops Maximum number of basic operations done in a row.
- * Default: 0 (unlimited).
- * Lower (non-zero) values mean ECC functions will block for
- * a lesser maximum amount of time.
- *
- * \note A "basic operation" is defined as a rough equivalent of a
- * multiplication in GF(p) for the NIST P-256 curve.
- * As an indication, with default settings, a scalar
- * multiplication (full run of \c mbedtls_ecp_mul()) is:
- * - about 3300 basic operations for P-256
- * - about 9400 basic operations for P-384
- *
- * \note Very low values are not always respected: sometimes
- * functions need to block for a minimum number of
- * operations, and will do so even if max_ops is set to a
- * lower value. That minimum depends on the curve size, and
- * can be made lower by decreasing the value of
- * \c MBEDTLS_ECP_WINDOW_SIZE. As an indication, here is the
- * lowest effective value for various curves and values of
- * that parameter (w for short):
- * w=6 w=5 w=4 w=3 w=2
- * P-256 208 208 160 136 124
- * P-384 682 416 320 272 248
- * P-521 1364 832 640 544 496
- *
- * \note This setting is currently ignored by Curve25519.
- */
- void mbedtls_ecp_set_max_ops( unsigned max_ops );
- /**
- * \brief Check if restart is enabled (max_ops != 0)
- *
- * \return \c 0 if \c max_ops == 0 (restart disabled)
- * \return \c 1 otherwise (restart enabled)
- */
- int mbedtls_ecp_restart_is_enabled( void );
- #endif /* MBEDTLS_ECP_RESTARTABLE */
- /*
- * Get the type of a curve
- */
- mbedtls_ecp_curve_type mbedtls_ecp_get_type( const mbedtls_ecp_group *grp );
- /**
- * \brief This function retrieves the information defined in
- * mbedtls_ecp_curve_info() for all supported curves.
- *
- * \note This function returns information about all curves
- * supported by the library. Some curves may not be
- * supported for all algorithms. Call mbedtls_ecdh_can_do()
- * or mbedtls_ecdsa_can_do() to check if a curve is
- * supported for ECDH or ECDSA.
- *
- * \return A statically allocated array. The last entry is 0.
- */
- const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void );
- /**
- * \brief This function retrieves the list of internal group
- * identifiers of all supported curves in the order of
- * preference.
- *
- * \note This function returns information about all curves
- * supported by the library. Some curves may not be
- * supported for all algorithms. Call mbedtls_ecdh_can_do()
- * or mbedtls_ecdsa_can_do() to check if a curve is
- * supported for ECDH or ECDSA.
- *
- * \return A statically allocated array,
- * terminated with MBEDTLS_ECP_DP_NONE.
- */
- const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void );
- /**
- * \brief This function retrieves curve information from an internal
- * group identifier.
- *
- * \param grp_id An \c MBEDTLS_ECP_DP_XXX value.
- *
- * \return The associated curve information on success.
- * \return NULL on failure.
- */
- const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id );
- /**
- * \brief This function retrieves curve information from a TLS
- * NamedCurve value.
- *
- * \param tls_id An \c MBEDTLS_ECP_DP_XXX value.
- *
- * \return The associated curve information on success.
- * \return NULL on failure.
- */
- const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id );
- /**
- * \brief This function retrieves curve information from a
- * human-readable name.
- *
- * \param name The human-readable name.
- *
- * \return The associated curve information on success.
- * \return NULL on failure.
- */
- const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name );
- /**
- * \brief This function initializes a point as zero.
- *
- * \param pt The point to initialize.
- */
- void mbedtls_ecp_point_init( mbedtls_ecp_point *pt );
- /**
- * \brief This function initializes an ECP group context
- * without loading any domain parameters.
- *
- * \note After this function is called, domain parameters
- * for various ECP groups can be loaded through the
- * mbedtls_ecp_group_load() or mbedtls_ecp_tls_read_group()
- * functions.
- */
- void mbedtls_ecp_group_init( mbedtls_ecp_group *grp );
- /**
- * \brief This function initializes a key pair as an invalid one.
- *
- * \param key The key pair to initialize.
- */
- void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key );
- /**
- * \brief This function frees the components of a point.
- *
- * \param pt The point to free.
- */
- void mbedtls_ecp_point_free( mbedtls_ecp_point *pt );
- /**
- * \brief This function frees the components of an ECP group.
- *
- * \param grp The group to free. This may be \c NULL, in which
- * case this function returns immediately. If it is not
- * \c NULL, it must point to an initialized ECP group.
- */
- void mbedtls_ecp_group_free( mbedtls_ecp_group *grp );
- /**
- * \brief This function frees the components of a key pair.
- *
- * \param key The key pair to free. This may be \c NULL, in which
- * case this function returns immediately. If it is not
- * \c NULL, it must point to an initialized ECP key pair.
- */
- void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key );
- #if defined(MBEDTLS_ECP_RESTARTABLE)
- /**
- * \brief Initialize a restart context.
- *
- * \param ctx The restart context to initialize. This must
- * not be \c NULL.
- */
- void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx );
- /**
- * \brief Free the components of a restart context.
- *
- * \param ctx The restart context to free. This may be \c NULL, in which
- * case this function returns immediately. If it is not
- * \c NULL, it must point to an initialized restart context.
- */
- void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx );
- #endif /* MBEDTLS_ECP_RESTARTABLE */
- /**
- * \brief This function copies the contents of point \p Q into
- * point \p P.
- *
- * \param P The destination point. This must be initialized.
- * \param Q The source point. This must be initialized.
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
- * \return Another negative error code for other kinds of failure.
- */
- int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q );
- /**
- * \brief This function copies the contents of group \p src into
- * group \p dst.
- *
- * \param dst The destination group. This must be initialized.
- * \param src The source group. This must be initialized.
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
- * \return Another negative error code on other kinds of failure.
- */
- int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst,
- const mbedtls_ecp_group *src );
- /**
- * \brief This function sets a point to the point at infinity.
- *
- * \param pt The point to set. This must be initialized.
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
- * \return Another negative error code on other kinds of failure.
- */
- int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt );
- /**
- * \brief This function checks if a point is the point at infinity.
- *
- * \param pt The point to test. This must be initialized.
- *
- * \return \c 1 if the point is zero.
- * \return \c 0 if the point is non-zero.
- * \return A negative error code on failure.
- */
- int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt );
- /**
- * \brief This function compares two points.
- *
- * \note This assumes that the points are normalized. Otherwise,
- * they may compare as "not equal" even if they are.
- *
- * \param P The first point to compare. This must be initialized.
- * \param Q The second point to compare. This must be initialized.
- *
- * \return \c 0 if the points are equal.
- * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the points are not equal.
- */
- int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
- const mbedtls_ecp_point *Q );
- /**
- * \brief This function imports a non-zero point from two ASCII
- * strings.
- *
- * \param P The destination point. This must be initialized.
- * \param radix The numeric base of the input.
- * \param x The first affine coordinate, as a null-terminated string.
- * \param y The second affine coordinate, as a null-terminated string.
- *
- * \return \c 0 on success.
- * \return An \c MBEDTLS_ERR_MPI_XXX error code on failure.
- */
- int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
- const char *x, const char *y );
- /**
- * \brief This function exports a point into unsigned binary data.
- *
- * \param grp The group to which the point should belong.
- * This must be initialized and have group parameters
- * set, for example through mbedtls_ecp_group_load().
- * \param P The point to export. This must be initialized.
- * \param format The point format. This must be either
- * #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED.
- * (For groups without these formats, this parameter is
- * ignored. But it still has to be either of the above
- * values.)
- * \param olen The address at which to store the length of
- * the output in Bytes. This must not be \c NULL.
- * \param buf The output buffer. This must be a writable buffer
- * of length \p buflen Bytes.
- * \param buflen The length of the output buffer \p buf in Bytes.
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output buffer
- * is too small to hold the point.
- * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format
- * or the export for the given group is not implemented.
- * \return Another negative error code on other kinds of failure.
- */
- int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp,
- const mbedtls_ecp_point *P,
- int format, size_t *olen,
- unsigned char *buf, size_t buflen );
- /**
- * \brief This function imports a point from unsigned binary data.
- *
- * \note This function does not check that the point actually
- * belongs to the given group, see mbedtls_ecp_check_pubkey()
- * for that.
- *
- * \param grp The group to which the point should belong.
- * This must be initialized and have group parameters
- * set, for example through mbedtls_ecp_group_load().
- * \param P The destination context to import the point to.
- * This must be initialized.
- * \param buf The input buffer. This must be a readable buffer
- * of length \p ilen Bytes.
- * \param ilen The length of the input buffer \p buf in Bytes.
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
- * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
- * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the import for the
- * given group is not implemented.
- */
- int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp,
- mbedtls_ecp_point *P,
- const unsigned char *buf, size_t ilen );
- /**
- * \brief This function imports a point from a TLS ECPoint record.
- *
- * \note On function return, \p *buf is updated to point immediately
- * after the ECPoint record.
- *
- * \param grp The ECP group to use.
- * This must be initialized and have group parameters
- * set, for example through mbedtls_ecp_group_load().
- * \param pt The destination point.
- * \param buf The address of the pointer to the start of the input buffer.
- * \param len The length of the buffer.
- *
- * \return \c 0 on success.
- * \return An \c MBEDTLS_ERR_MPI_XXX error code on initialization
- * failure.
- * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
- */
- int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp,
- mbedtls_ecp_point *pt,
- const unsigned char **buf, size_t len );
- /**
- * \brief This function exports a point as a TLS ECPoint record
- * defined in RFC 4492, Section 5.4.
- *
- * \param grp The ECP group to use.
- * This must be initialized and have group parameters
- * set, for example through mbedtls_ecp_group_load().
- * \param pt The point to be exported. This must be initialized.
- * \param format The point format to use. This must be either
- * #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED.
- * \param olen The address at which to store the length in Bytes
- * of the data written.
- * \param buf The target buffer. This must be a writable buffer of
- * length \p blen Bytes.
- * \param blen The length of the target buffer \p buf in Bytes.
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid.
- * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the target buffer
- * is too small to hold the exported point.
- * \return Another negative error code on other kinds of failure.
- */
- int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp,
- const mbedtls_ecp_point *pt,
- int format, size_t *olen,
- unsigned char *buf, size_t blen );
- /**
- * \brief This function sets up an ECP group context
- * from a standardized set of domain parameters.
- *
- * \note The index should be a value of the NamedCurve enum,
- * as defined in <em>RFC-4492: Elliptic Curve Cryptography
- * (ECC) Cipher Suites for Transport Layer Security (TLS)</em>,
- * usually in the form of an \c MBEDTLS_ECP_DP_XXX macro.
- *
- * \param grp The group context to setup. This must be initialized.
- * \param id The identifier of the domain parameter set to load.
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p id doesn't
- * correspond to a known group.
- * \return Another negative error code on other kinds of failure.
- */
- int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id );
- /**
- * \brief This function sets up an ECP group context from a TLS
- * ECParameters record as defined in RFC 4492, Section 5.4.
- *
- * \note The read pointer \p buf is updated to point right after
- * the ECParameters record on exit.
- *
- * \param grp The group context to setup. This must be initialized.
- * \param buf The address of the pointer to the start of the input buffer.
- * \param len The length of the input buffer \c *buf in Bytes.
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
- * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
- * recognized.
- * \return Another negative error code on other kinds of failure.
- */
- int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp,
- const unsigned char **buf, size_t len );
- /**
- * \brief This function extracts an elliptic curve group ID from a
- * TLS ECParameters record as defined in RFC 4492, Section 5.4.
- *
- * \note The read pointer \p buf is updated to point right after
- * the ECParameters record on exit.
- *
- * \param grp The address at which to store the group id.
- * This must not be \c NULL.
- * \param buf The address of the pointer to the start of the input buffer.
- * \param len The length of the input buffer \c *buf in Bytes.
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid.
- * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not
- * recognized.
- * \return Another negative error code on other kinds of failure.
- */
- int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp,
- const unsigned char **buf,
- size_t len );
- /**
- * \brief This function exports an elliptic curve as a TLS
- * ECParameters record as defined in RFC 4492, Section 5.4.
- *
- * \param grp The ECP group to be exported.
- * This must be initialized and have group parameters
- * set, for example through mbedtls_ecp_group_load().
- * \param olen The address at which to store the number of Bytes written.
- * This must not be \c NULL.
- * \param buf The buffer to write to. This must be a writable buffer
- * of length \p blen Bytes.
- * \param blen The length of the output buffer \p buf in Bytes.
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output
- * buffer is too small to hold the exported group.
- * \return Another negative error code on other kinds of failure.
- */
- int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp,
- size_t *olen,
- unsigned char *buf, size_t blen );
- /**
- * \brief This function performs a scalar multiplication of a point
- * by an integer: \p R = \p m * \p P.
- *
- * It is not thread-safe to use same group in multiple threads.
- *
- * \note To prevent timing attacks, this function
- * executes the exact same sequence of base-field
- * operations for any valid \p m. It avoids any if-branch or
- * array index depending on the value of \p m.
- *
- * \note If \p f_rng is not NULL, it is used to randomize
- * intermediate results to prevent potential timing attacks
- * targeting these results. We recommend always providing
- * a non-NULL \p f_rng. The overhead is negligible.
- * Note: unless #MBEDTLS_ECP_NO_INTERNAL_RNG is defined, when
- * \p f_rng is NULL, an internal RNG (seeded from the value
- * of \p m) will be used instead.
- *
- * \param grp The ECP group to use.
- * This must be initialized and have group parameters
- * set, for example through mbedtls_ecp_group_load().
- * \param R The point in which to store the result of the calculation.
- * This must be initialized.
- * \param m The integer by which to multiply. This must be initialized.
- * \param P The point to multiply. This must be initialized.
- * \param f_rng The RNG function. This may be \c NULL if randomization
- * of intermediate results isn't desired (discouraged).
- * \param p_rng The RNG context to be passed to \p p_rng.
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private
- * key, or \p P is not a valid public key.
- * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
- * \return Another negative error code on other kinds of failure.
- */
- int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
- const mbedtls_mpi *m, const mbedtls_ecp_point *P,
- int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
- /**
- * \brief This function performs multiplication of a point by
- * an integer: \p R = \p m * \p P in a restartable way.
- *
- * \see mbedtls_ecp_mul()
- *
- * \note This function does the same as \c mbedtls_ecp_mul(), but
- * it can return early and restart according to the limit set
- * with \c mbedtls_ecp_set_max_ops() to reduce blocking.
- *
- * \param grp The ECP group to use.
- * This must be initialized and have group parameters
- * set, for example through mbedtls_ecp_group_load().
- * \param R The point in which to store the result of the calculation.
- * This must be initialized.
- * \param m The integer by which to multiply. This must be initialized.
- * \param P The point to multiply. This must be initialized.
- * \param f_rng The RNG function. This may be \c NULL if randomization
- * of intermediate results isn't desired (discouraged).
- * \param p_rng The RNG context to be passed to \p p_rng.
- * \param rs_ctx The restart context (NULL disables restart).
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private
- * key, or \p P is not a valid public key.
- * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
- * \return #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
- * operations was reached: see \c mbedtls_ecp_set_max_ops().
- * \return Another negative error code on other kinds of failure.
- */
- int mbedtls_ecp_mul_restartable( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
- const mbedtls_mpi *m, const mbedtls_ecp_point *P,
- int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
- mbedtls_ecp_restart_ctx *rs_ctx );
- #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
- /**
- * \brief This function performs multiplication and addition of two
- * points by integers: \p R = \p m * \p P + \p n * \p Q
- *
- * It is not thread-safe to use same group in multiple threads.
- *
- * \note In contrast to mbedtls_ecp_mul(), this function does not
- * guarantee a constant execution flow and timing.
- *
- * \note This function is only defined for short Weierstrass curves.
- * It may not be included in builds without any short
- * Weierstrass curve.
- *
- * \param grp The ECP group to use.
- * This must be initialized and have group parameters
- * set, for example through mbedtls_ecp_group_load().
- * \param R The point in which to store the result of the calculation.
- * This must be initialized.
- * \param m The integer by which to multiply \p P.
- * This must be initialized.
- * \param P The point to multiply by \p m. This must be initialized.
- * \param n The integer by which to multiply \p Q.
- * This must be initialized.
- * \param Q The point to be multiplied by \p n.
- * This must be initialized.
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not
- * valid private keys, or \p P or \p Q are not valid public
- * keys.
- * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
- * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not
- * designate a short Weierstrass curve.
- * \return Another negative error code on other kinds of failure.
- */
- int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
- const mbedtls_mpi *m, const mbedtls_ecp_point *P,
- const mbedtls_mpi *n, const mbedtls_ecp_point *Q );
- /**
- * \brief This function performs multiplication and addition of two
- * points by integers: \p R = \p m * \p P + \p n * \p Q in a
- * restartable way.
- *
- * \see \c mbedtls_ecp_muladd()
- *
- * \note This function works the same as \c mbedtls_ecp_muladd(),
- * but it can return early and restart according to the limit
- * set with \c mbedtls_ecp_set_max_ops() to reduce blocking.
- *
- * \note This function is only defined for short Weierstrass curves.
- * It may not be included in builds without any short
- * Weierstrass curve.
- *
- * \param grp The ECP group to use.
- * This must be initialized and have group parameters
- * set, for example through mbedtls_ecp_group_load().
- * \param R The point in which to store the result of the calculation.
- * This must be initialized.
- * \param m The integer by which to multiply \p P.
- * This must be initialized.
- * \param P The point to multiply by \p m. This must be initialized.
- * \param n The integer by which to multiply \p Q.
- * This must be initialized.
- * \param Q The point to be multiplied by \p n.
- * This must be initialized.
- * \param rs_ctx The restart context (NULL disables restart).
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not
- * valid private keys, or \p P or \p Q are not valid public
- * keys.
- * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
- * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not
- * designate a short Weierstrass curve.
- * \return #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
- * operations was reached: see \c mbedtls_ecp_set_max_ops().
- * \return Another negative error code on other kinds of failure.
- */
- int mbedtls_ecp_muladd_restartable(
- mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
- const mbedtls_mpi *m, const mbedtls_ecp_point *P,
- const mbedtls_mpi *n, const mbedtls_ecp_point *Q,
- mbedtls_ecp_restart_ctx *rs_ctx );
- #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
- /**
- * \brief This function checks that a point is a valid public key
- * on this curve.
- *
- * It only checks that the point is non-zero, has
- * valid coordinates and lies on the curve. It does not verify
- * that it is indeed a multiple of \p G. This additional
- * check is computationally more expensive, is not required
- * by standards, and should not be necessary if the group
- * used has a small cofactor. In particular, it is useless for
- * the NIST groups which all have a cofactor of 1.
- *
- * \note This function uses bare components rather than an
- * ::mbedtls_ecp_keypair structure, to ease use with other
- * structures, such as ::mbedtls_ecdh_context or
- * ::mbedtls_ecdsa_context.
- *
- * \param grp The ECP group the point should belong to.
- * This must be initialized and have group parameters
- * set, for example through mbedtls_ecp_group_load().
- * \param pt The point to check. This must be initialized.
- *
- * \return \c 0 if the point is a valid public key.
- * \return #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not
- * a valid public key for the given curve.
- * \return Another negative error code on other kinds of failure.
- */
- int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp,
- const mbedtls_ecp_point *pt );
- /**
- * \brief This function checks that an \p mbedtls_mpi is a
- * valid private key for this curve.
- *
- * \note This function uses bare components rather than an
- * ::mbedtls_ecp_keypair structure to ease use with other
- * structures, such as ::mbedtls_ecdh_context or
- * ::mbedtls_ecdsa_context.
- *
- * \param grp The ECP group the private key should belong to.
- * This must be initialized and have group parameters
- * set, for example through mbedtls_ecp_group_load().
- * \param d The integer to check. This must be initialized.
- *
- * \return \c 0 if the point is a valid private key.
- * \return #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not a valid
- * private key for the given curve.
- * \return Another negative error code on other kinds of failure.
- */
- int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp,
- const mbedtls_mpi *d );
- /**
- * \brief This function generates a private key.
- *
- * \param grp The ECP group to generate a private key for.
- * This must be initialized and have group parameters
- * set, for example through mbedtls_ecp_group_load().
- * \param d The destination MPI (secret part). This must be initialized.
- * \param f_rng The RNG function. This must not be \c NULL.
- * \param p_rng The RNG parameter to be passed to \p f_rng. This may be
- * \c NULL if \p f_rng doesn't need a context argument.
- *
- * \return \c 0 on success.
- * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
- * on failure.
- */
- int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp,
- mbedtls_mpi *d,
- int (*f_rng)(void *, unsigned char *, size_t),
- void *p_rng );
- /**
- * \brief This function generates a keypair with a configurable base
- * point.
- *
- * \note This function uses bare components rather than an
- * ::mbedtls_ecp_keypair structure to ease use with other
- * structures, such as ::mbedtls_ecdh_context or
- * ::mbedtls_ecdsa_context.
- *
- * \param grp The ECP group to generate a key pair for.
- * This must be initialized and have group parameters
- * set, for example through mbedtls_ecp_group_load().
- * \param G The base point to use. This must be initialized
- * and belong to \p grp. It replaces the default base
- * point \c grp->G used by mbedtls_ecp_gen_keypair().
- * \param d The destination MPI (secret part).
- * This must be initialized.
- * \param Q The destination point (public part).
- * This must be initialized.
- * \param f_rng The RNG function. This must not be \c NULL.
- * \param p_rng The RNG context to be passed to \p f_rng. This may
- * be \c NULL if \p f_rng doesn't need a context argument.
- *
- * \return \c 0 on success.
- * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
- * on failure.
- */
- int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
- const mbedtls_ecp_point *G,
- mbedtls_mpi *d, mbedtls_ecp_point *Q,
- int (*f_rng)(void *, unsigned char *, size_t),
- void *p_rng );
- /**
- * \brief This function generates an ECP keypair.
- *
- * \note This function uses bare components rather than an
- * ::mbedtls_ecp_keypair structure to ease use with other
- * structures, such as ::mbedtls_ecdh_context or
- * ::mbedtls_ecdsa_context.
- *
- * \param grp The ECP group to generate a key pair for.
- * This must be initialized and have group parameters
- * set, for example through mbedtls_ecp_group_load().
- * \param d The destination MPI (secret part).
- * This must be initialized.
- * \param Q The destination point (public part).
- * This must be initialized.
- * \param f_rng The RNG function. This must not be \c NULL.
- * \param p_rng The RNG context to be passed to \p f_rng. This may
- * be \c NULL if \p f_rng doesn't need a context argument.
- *
- * \return \c 0 on success.
- * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
- * on failure.
- */
- int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, mbedtls_mpi *d,
- mbedtls_ecp_point *Q,
- int (*f_rng)(void *, unsigned char *, size_t),
- void *p_rng );
- /**
- * \brief This function generates an ECP key.
- *
- * \param grp_id The ECP group identifier.
- * \param key The destination key. This must be initialized.
- * \param f_rng The RNG function to use. This must not be \c NULL.
- * \param p_rng The RNG context to be passed to \p f_rng. This may
- * be \c NULL if \p f_rng doesn't need a context argument.
- *
- * \return \c 0 on success.
- * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code
- * on failure.
- */
- int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
- int (*f_rng)(void *, unsigned char *, size_t),
- void *p_rng );
- /**
- * \brief This function reads an elliptic curve private key.
- *
- * \param grp_id The ECP group identifier.
- * \param key The destination key.
- * \param buf The buffer containing the binary representation of the
- * key. (Big endian integer for Weierstrass curves, byte
- * string for Montgomery curves.)
- * \param buflen The length of the buffer in bytes.
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_ECP_INVALID_KEY error if the key is
- * invalid.
- * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
- * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for
- * the group is not implemented.
- * \return Another negative error code on different kinds of failure.
- */
- int mbedtls_ecp_read_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
- const unsigned char *buf, size_t buflen );
- /**
- * \brief This function exports an elliptic curve private key.
- *
- * \param key The private key.
- * \param buf The output buffer for containing the binary representation
- * of the key. (Big endian integer for Weierstrass curves, byte
- * string for Montgomery curves.)
- * \param buflen The total length of the buffer in bytes.
- *
- * \return \c 0 on success.
- * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the \p key
- representation is larger than the available space in \p buf.
- * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for
- * the group is not implemented.
- * \return Another negative error code on different kinds of failure.
- */
- int mbedtls_ecp_write_key( mbedtls_ecp_keypair *key,
- unsigned char *buf, size_t buflen );
- /**
- * \brief This function checks that the keypair objects
- * \p pub and \p prv have the same group and the
- * same public point, and that the private key in
- * \p prv is consistent with the public key.
- *
- * \param pub The keypair structure holding the public key. This
- * must be initialized. If it contains a private key, that
- * part is ignored.
- * \param prv The keypair structure holding the full keypair.
- * This must be initialized.
- *
- * \return \c 0 on success, meaning that the keys are valid and match.
- * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the keys are invalid or do not match.
- * \return An \c MBEDTLS_ERR_ECP_XXX or an \c MBEDTLS_ERR_MPI_XXX
- * error code on calculation failure.
- */
- int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub,
- const mbedtls_ecp_keypair *prv );
- #if defined(MBEDTLS_SELF_TEST)
- /**
- * \brief The ECP checkup routine.
- *
- * \return \c 0 on success.
- * \return \c 1 on failure.
- */
- int mbedtls_ecp_self_test( int verbose );
- #endif /* MBEDTLS_SELF_TEST */
- #ifdef __cplusplus
- }
- #endif
- #endif /* ecp.h */
|