diff options
Diffstat (limited to 'lib/mbedtls-2.27.0/library/ecp.c')
| -rw-r--r-- | lib/mbedtls-2.27.0/library/ecp.c | 3605 |
1 files changed, 3605 insertions, 0 deletions
diff --git a/lib/mbedtls-2.27.0/library/ecp.c b/lib/mbedtls-2.27.0/library/ecp.c new file mode 100644 index 0000000..ca49f99 --- /dev/null +++ b/lib/mbedtls-2.27.0/library/ecp.c @@ -0,0 +1,3605 @@ +/* + * Elliptic curves over GF(p): generic functions + * + * 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. + */ + +/* + * References: + * + * SEC1 http://www.secg.org/index.php?action=secg,docs_secg + * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone + * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf + * RFC 4492 for the related TLS structures and constants + * RFC 7748 for the Curve448 and Curve25519 curve definitions + * + * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf + * + * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis + * for elliptic curve cryptosystems. In : Cryptographic Hardware and + * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302. + * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25> + * + * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to + * render ECC resistant against Side Channel Attacks. IACR Cryptology + * ePrint Archive, 2004, vol. 2004, p. 342. + * <http://eprint.iacr.org/2004/342.pdf> + */ + +#include "common.h" + +/** + * \brief Function level alternative implementation. + * + * The MBEDTLS_ECP_INTERNAL_ALT macro enables alternative implementations to + * replace certain functions in this module. The alternative implementations are + * typically hardware accelerators and need to activate the hardware before the + * computation starts and deactivate it after it finishes. The + * mbedtls_internal_ecp_init() and mbedtls_internal_ecp_free() functions serve + * this purpose. + * + * To preserve the correct functionality the following conditions must hold: + * + * - The alternative implementation must be activated by + * mbedtls_internal_ecp_init() before any of the replaceable functions is + * called. + * - mbedtls_internal_ecp_free() must \b only be called when the alternative + * implementation is activated. + * - mbedtls_internal_ecp_init() must \b not be called when the alternative + * implementation is activated. + * - Public functions must not return while the alternative implementation is + * activated. + * - Replaceable functions are guarded by \c MBEDTLS_ECP_XXX_ALT macros and + * before calling them an \code if( mbedtls_internal_ecp_grp_capable( grp ) ) + * \endcode ensures that the alternative implementation supports the current + * group. + */ +#if defined(MBEDTLS_ECP_INTERNAL_ALT) +#endif + +#if defined(MBEDTLS_ECP_C) + +#include "mbedtls/ecp.h" +#include "mbedtls/threading.h" +#include "mbedtls/platform_util.h" +#include "mbedtls/error.h" +#include "mbedtls/bn_mul.h" + +#include "ecp_invasive.h" + +#include <string.h> + +#if !defined(MBEDTLS_ECP_ALT) + +/* Parameter validation macros based on platform_util.h */ +#define ECP_VALIDATE_RET( cond ) \ + MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA ) +#define ECP_VALIDATE( cond ) \ + MBEDTLS_INTERNAL_VALIDATE( cond ) + +#if defined(MBEDTLS_PLATFORM_C) +#include "mbedtls/platform.h" +#else +#include <stdlib.h> +#include <stdio.h> +#define mbedtls_printf printf +#define mbedtls_calloc calloc +#define mbedtls_free free +#endif + +#include "mbedtls/ecp_internal.h" + +#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG) +#if defined(MBEDTLS_HMAC_DRBG_C) +#include "mbedtls/hmac_drbg.h" +#elif defined(MBEDTLS_CTR_DRBG_C) +#include "mbedtls/ctr_drbg.h" +#else +#error "Invalid configuration detected. Include check_config.h to ensure that the configuration is valid." +#endif +#endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */ + +#if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \ + !defined(inline) && !defined(__cplusplus) +#define inline __inline +#endif + +#if defined(MBEDTLS_SELF_TEST) +/* + * Counts of point addition and doubling, and field multiplications. + * Used to test resistance of point multiplication to simple timing attacks. + */ +static unsigned long add_count, dbl_count, mul_count; +#endif + +#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG) +/* + * Currently ecp_mul() takes a RNG function as an argument, used for + * side-channel protection, but it can be NULL. The initial reasoning was + * that people will pass non-NULL RNG when they care about side-channels, but + * unfortunately we have some APIs that call ecp_mul() with a NULL RNG, with + * no opportunity for the user to do anything about it. + * + * The obvious strategies for addressing that include: + * - change those APIs so that they take RNG arguments; + * - require a global RNG to be available to all crypto modules. + * + * Unfortunately those would break compatibility. So what we do instead is + * have our own internal DRBG instance, seeded from the secret scalar. + * + * The following is a light-weight abstraction layer for doing that with + * HMAC_DRBG (first choice) or CTR_DRBG. + */ + +#if defined(MBEDTLS_HMAC_DRBG_C) + +/* DRBG context type */ +typedef mbedtls_hmac_drbg_context ecp_drbg_context; + +/* DRBG context init */ +static inline void ecp_drbg_init( ecp_drbg_context *ctx ) +{ + mbedtls_hmac_drbg_init( ctx ); +} + +/* DRBG context free */ +static inline void ecp_drbg_free( ecp_drbg_context *ctx ) +{ + mbedtls_hmac_drbg_free( ctx ); +} + +/* DRBG function */ +static inline int ecp_drbg_random( void *p_rng, + unsigned char *output, size_t output_len ) +{ + return( mbedtls_hmac_drbg_random( p_rng, output, output_len ) ); +} + +/* DRBG context seeding */ +static int ecp_drbg_seed( ecp_drbg_context *ctx, + const mbedtls_mpi *secret, size_t secret_len ) +{ + int ret; + unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES]; + /* The list starts with strong hashes */ + const mbedtls_md_type_t md_type = mbedtls_md_list()[0]; + const mbedtls_md_info_t *md_info = mbedtls_md_info_from_type( md_type ); + + if( secret_len > MBEDTLS_ECP_MAX_BYTES ) + { + ret = MBEDTLS_ERR_ECP_RANDOM_FAILED; + goto cleanup; + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( secret, + secret_bytes, secret_len ) ); + + ret = mbedtls_hmac_drbg_seed_buf( ctx, md_info, secret_bytes, secret_len ); + +cleanup: + mbedtls_platform_zeroize( secret_bytes, secret_len ); + + return( ret ); +} + +#elif defined(MBEDTLS_CTR_DRBG_C) + +/* DRBG context type */ +typedef mbedtls_ctr_drbg_context ecp_drbg_context; + +/* DRBG context init */ +static inline void ecp_drbg_init( ecp_drbg_context *ctx ) +{ + mbedtls_ctr_drbg_init( ctx ); +} + +/* DRBG context free */ +static inline void ecp_drbg_free( ecp_drbg_context *ctx ) +{ + mbedtls_ctr_drbg_free( ctx ); +} + +/* DRBG function */ +static inline int ecp_drbg_random( void *p_rng, + unsigned char *output, size_t output_len ) +{ + return( mbedtls_ctr_drbg_random( p_rng, output, output_len ) ); +} + +/* + * Since CTR_DRBG doesn't have a seed_buf() function the way HMAC_DRBG does, + * we need to pass an entropy function when seeding. So we use a dummy + * function for that, and pass the actual entropy as customisation string. + * (During seeding of CTR_DRBG the entropy input and customisation string are + * concatenated before being used to update the secret state.) + */ +static int ecp_ctr_drbg_null_entropy(void *ctx, unsigned char *out, size_t len) +{ + (void) ctx; + memset( out, 0, len ); + return( 0 ); +} + +/* DRBG context seeding */ +static int ecp_drbg_seed( ecp_drbg_context *ctx, + const mbedtls_mpi *secret, size_t secret_len ) +{ + int ret; + unsigned char secret_bytes[MBEDTLS_ECP_MAX_BYTES]; + + if( secret_len > MBEDTLS_ECP_MAX_BYTES ) + { + ret = MBEDTLS_ERR_ECP_RANDOM_FAILED; + goto cleanup; + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( secret, + secret_bytes, secret_len ) ); + + ret = mbedtls_ctr_drbg_seed( ctx, ecp_ctr_drbg_null_entropy, NULL, + secret_bytes, secret_len ); + +cleanup: + mbedtls_platform_zeroize( secret_bytes, secret_len ); + + return( ret ); +} + +#else +#error "Invalid configuration detected. Include check_config.h to ensure that the configuration is valid." +#endif /* DRBG modules */ +#endif /* MBEDTLS_ECP_NO_INTERNAL_RNG */ + +#if defined(MBEDTLS_ECP_RESTARTABLE) +/* + * Maximum number of "basic operations" to be done in a row. + * + * Default value 0 means that ECC operations will not yield. + * Note that regardless of the value of ecp_max_ops, always at + * least one step is performed before yielding. + * + * Setting ecp_max_ops=1 can be suitable for testing purposes + * as it will interrupt computation at all possible points. + */ +static unsigned ecp_max_ops = 0; + +/* + * Set ecp_max_ops + */ +void mbedtls_ecp_set_max_ops( unsigned max_ops ) +{ + ecp_max_ops = max_ops; +} + +/* + * Check if restart is enabled + */ +int mbedtls_ecp_restart_is_enabled( void ) +{ + return( ecp_max_ops != 0 ); +} + +/* + * Restart sub-context for ecp_mul_comb() + */ +struct mbedtls_ecp_restart_mul +{ + mbedtls_ecp_point R; /* current intermediate result */ + size_t i; /* current index in various loops, 0 outside */ + mbedtls_ecp_point *T; /* table for precomputed points */ + unsigned char T_size; /* number of points in table T */ + enum { /* what were we doing last time we returned? */ + ecp_rsm_init = 0, /* nothing so far, dummy initial state */ + ecp_rsm_pre_dbl, /* precompute 2^n multiples */ + ecp_rsm_pre_norm_dbl, /* normalize precomputed 2^n multiples */ + ecp_rsm_pre_add, /* precompute remaining points by adding */ + ecp_rsm_pre_norm_add, /* normalize all precomputed points */ + ecp_rsm_comb_core, /* ecp_mul_comb_core() */ + ecp_rsm_final_norm, /* do the final normalization */ + } state; +#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG) + ecp_drbg_context drbg_ctx; + unsigned char drbg_seeded; +#endif +}; + +/* + * Init restart_mul sub-context + */ +static void ecp_restart_rsm_init( mbedtls_ecp_restart_mul_ctx *ctx ) +{ + mbedtls_ecp_point_init( &ctx->R ); + ctx->i = 0; + ctx->T = NULL; + ctx->T_size = 0; + ctx->state = ecp_rsm_init; +#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG) + ecp_drbg_init( &ctx->drbg_ctx ); + ctx->drbg_seeded = 0; +#endif +} + +/* + * Free the components of a restart_mul sub-context + */ +static void ecp_restart_rsm_free( mbedtls_ecp_restart_mul_ctx *ctx ) +{ + unsigned char i; + + if( ctx == NULL ) + return; + + mbedtls_ecp_point_free( &ctx->R ); + + if( ctx->T != NULL ) + { + for( i = 0; i < ctx->T_size; i++ ) + mbedtls_ecp_point_free( ctx->T + i ); + mbedtls_free( ctx->T ); + } + +#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG) + ecp_drbg_free( &ctx->drbg_ctx ); +#endif + + ecp_restart_rsm_init( ctx ); +} + +/* + * Restart context for ecp_muladd() + */ +struct mbedtls_ecp_restart_muladd +{ + mbedtls_ecp_point mP; /* mP value */ + mbedtls_ecp_point R; /* R intermediate result */ + enum { /* what should we do next? */ + ecp_rsma_mul1 = 0, /* first multiplication */ + ecp_rsma_mul2, /* second multiplication */ + ecp_rsma_add, /* addition */ + ecp_rsma_norm, /* normalization */ + } state; +}; + +/* + * Init restart_muladd sub-context + */ +static void ecp_restart_ma_init( mbedtls_ecp_restart_muladd_ctx *ctx ) +{ + mbedtls_ecp_point_init( &ctx->mP ); + mbedtls_ecp_point_init( &ctx->R ); + ctx->state = ecp_rsma_mul1; +} + +/* + * Free the components of a restart_muladd sub-context + */ +static void ecp_restart_ma_free( mbedtls_ecp_restart_muladd_ctx *ctx ) +{ + if( ctx == NULL ) + return; + + mbedtls_ecp_point_free( &ctx->mP ); + mbedtls_ecp_point_free( &ctx->R ); + + ecp_restart_ma_init( ctx ); +} + +/* + * Initialize a restart context + */ +void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx ) +{ + ECP_VALIDATE( ctx != NULL ); + ctx->ops_done = 0; + ctx->depth = 0; + ctx->rsm = NULL; + ctx->ma = NULL; +} + +/* + * Free the components of a restart context + */ +void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx ) +{ + if( ctx == NULL ) + return; + + ecp_restart_rsm_free( ctx->rsm ); + mbedtls_free( ctx->rsm ); + + ecp_restart_ma_free( ctx->ma ); + mbedtls_free( ctx->ma ); + + mbedtls_ecp_restart_init( ctx ); +} + +/* + * Check if we can do the next step + */ +int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp, + mbedtls_ecp_restart_ctx *rs_ctx, + unsigned ops ) +{ + ECP_VALIDATE_RET( grp != NULL ); + + if( rs_ctx != NULL && ecp_max_ops != 0 ) + { + /* scale depending on curve size: the chosen reference is 256-bit, + * and multiplication is quadratic. Round to the closest integer. */ + if( grp->pbits >= 512 ) + ops *= 4; + else if( grp->pbits >= 384 ) + ops *= 2; + + /* Avoid infinite loops: always allow first step. + * Because of that, however, it's not generally true + * that ops_done <= ecp_max_ops, so the check + * ops_done > ecp_max_ops below is mandatory. */ + if( ( rs_ctx->ops_done != 0 ) && + ( rs_ctx->ops_done > ecp_max_ops || + ops > ecp_max_ops - rs_ctx->ops_done ) ) + { + return( MBEDTLS_ERR_ECP_IN_PROGRESS ); + } + + /* update running count */ + rs_ctx->ops_done += ops; + } + + return( 0 ); +} + +/* Call this when entering a function that needs its own sub-context */ +#define ECP_RS_ENTER( SUB ) do { \ + /* reset ops count for this call if top-level */ \ + if( rs_ctx != NULL && rs_ctx->depth++ == 0 ) \ + rs_ctx->ops_done = 0; \ + \ + /* set up our own sub-context if needed */ \ + if( mbedtls_ecp_restart_is_enabled() && \ + rs_ctx != NULL && rs_ctx->SUB == NULL ) \ + { \ + rs_ctx->SUB = mbedtls_calloc( 1, sizeof( *rs_ctx->SUB ) ); \ + if( rs_ctx->SUB == NULL ) \ + return( MBEDTLS_ERR_ECP_ALLOC_FAILED ); \ + \ + ecp_restart_## SUB ##_init( rs_ctx->SUB ); \ + } \ +} while( 0 ) + +/* Call this when leaving a function that needs its own sub-context */ +#define ECP_RS_LEAVE( SUB ) do { \ + /* clear our sub-context when not in progress (done or error) */ \ + if( rs_ctx != NULL && rs_ctx->SUB != NULL && \ + ret != MBEDTLS_ERR_ECP_IN_PROGRESS ) \ + { \ + ecp_restart_## SUB ##_free( rs_ctx->SUB ); \ + mbedtls_free( rs_ctx->SUB ); \ + rs_ctx->SUB = NULL; \ + } \ + \ + if( rs_ctx != NULL ) \ + rs_ctx->depth--; \ +} while( 0 ) + +#else /* MBEDTLS_ECP_RESTARTABLE */ + +#define ECP_RS_ENTER( sub ) (void) rs_ctx; +#define ECP_RS_LEAVE( sub ) (void) rs_ctx; + +#endif /* MBEDTLS_ECP_RESTARTABLE */ + +/* + * List of supported curves: + * - internal ID + * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2, RFC 8446 sec. 4.2.7) + * - size in bits + * - readable name + * + * Curves are listed in order: largest curves first, and for a given size, + * fastest curves first. This provides the default order for the SSL module. + * + * Reminder: update profiles in x509_crt.c when adding a new curves! + */ +static const mbedtls_ecp_curve_info ecp_supported_curves[] = +{ +#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) + { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" }, +#endif +#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) + { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" }, +#endif +#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) + { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" }, +#endif +#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) + { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" }, +#endif +#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) + { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" }, +#endif +#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) + { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" }, +#endif +#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) + { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" }, +#endif +#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) + { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" }, +#endif +#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) + { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" }, +#endif +#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) + { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" }, +#endif +#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) + { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" }, +#endif +#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) + { MBEDTLS_ECP_DP_CURVE25519, 29, 256, "x25519" }, +#endif +#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) + { MBEDTLS_ECP_DP_CURVE448, 30, 448, "x448" }, +#endif + { MBEDTLS_ECP_DP_NONE, 0, 0, NULL }, +}; + +#define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \ + sizeof( ecp_supported_curves[0] ) + +static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES]; + +/* + * List of supported curves and associated info + */ +const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void ) +{ + return( ecp_supported_curves ); +} + +/* + * List of supported curves, group ID only + */ +const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void ) +{ + static int init_done = 0; + + if( ! init_done ) + { + size_t i = 0; + const mbedtls_ecp_curve_info *curve_info; + + for( curve_info = mbedtls_ecp_curve_list(); + curve_info->grp_id != MBEDTLS_ECP_DP_NONE; + curve_info++ ) + { + ecp_supported_grp_id[i++] = curve_info->grp_id; + } + ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE; + + init_done = 1; + } + + return( ecp_supported_grp_id ); +} + +/* + * Get the curve info for the internal identifier + */ +const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id ) +{ + const mbedtls_ecp_curve_info *curve_info; + + for( curve_info = mbedtls_ecp_curve_list(); + curve_info->grp_id != MBEDTLS_ECP_DP_NONE; + curve_info++ ) + { + if( curve_info->grp_id == grp_id ) + return( curve_info ); + } + + return( NULL ); +} + +/* + * Get the curve info from the TLS identifier + */ +const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id ) +{ + const mbedtls_ecp_curve_info *curve_info; + + for( curve_info = mbedtls_ecp_curve_list(); + curve_info->grp_id != MBEDTLS_ECP_DP_NONE; + curve_info++ ) + { + if( curve_info->tls_id == tls_id ) + return( curve_info ); + } + + return( NULL ); +} + +/* + * Get the curve info from the name + */ +const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name ) +{ + const mbedtls_ecp_curve_info *curve_info; + + if( name == NULL ) + return( NULL ); + + for( curve_info = mbedtls_ecp_curve_list(); + curve_info->grp_id != MBEDTLS_ECP_DP_NONE; + curve_info++ ) + { + if( strcmp( curve_info->name, name ) == 0 ) + return( curve_info ); + } + + return( NULL ); +} + +/* + * Get the type of a curve + */ +mbedtls_ecp_curve_type mbedtls_ecp_get_type( const mbedtls_ecp_group *grp ) +{ + if( grp->G.X.p == NULL ) + return( MBEDTLS_ECP_TYPE_NONE ); + + if( grp->G.Y.p == NULL ) + return( MBEDTLS_ECP_TYPE_MONTGOMERY ); + else + return( MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ); +} + +/* + * Initialize (the components of) a point + */ +void mbedtls_ecp_point_init( mbedtls_ecp_point *pt ) +{ + ECP_VALIDATE( pt != NULL ); + + mbedtls_mpi_init( &pt->X ); + mbedtls_mpi_init( &pt->Y ); + mbedtls_mpi_init( &pt->Z ); +} + +/* + * Initialize (the components of) a group + */ +void mbedtls_ecp_group_init( mbedtls_ecp_group *grp ) +{ + ECP_VALIDATE( grp != NULL ); + + grp->id = MBEDTLS_ECP_DP_NONE; + mbedtls_mpi_init( &grp->P ); + mbedtls_mpi_init( &grp->A ); + mbedtls_mpi_init( &grp->B ); + mbedtls_ecp_point_init( &grp->G ); + mbedtls_mpi_init( &grp->N ); + grp->pbits = 0; + grp->nbits = 0; + grp->h = 0; + grp->modp = NULL; + grp->t_pre = NULL; + grp->t_post = NULL; + grp->t_data = NULL; + grp->T = NULL; + grp->T_size = 0; +} + +/* + * Initialize (the components of) a key pair + */ +void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key ) +{ + ECP_VALIDATE( key != NULL ); + + mbedtls_ecp_group_init( &key->grp ); + mbedtls_mpi_init( &key->d ); + mbedtls_ecp_point_init( &key->Q ); +} + +/* + * Unallocate (the components of) a point + */ +void mbedtls_ecp_point_free( mbedtls_ecp_point *pt ) +{ + if( pt == NULL ) + return; + + mbedtls_mpi_free( &( pt->X ) ); + mbedtls_mpi_free( &( pt->Y ) ); + mbedtls_mpi_free( &( pt->Z ) ); +} + +/* + * Unallocate (the components of) a group + */ +void mbedtls_ecp_group_free( mbedtls_ecp_group *grp ) +{ + size_t i; + + if( grp == NULL ) + return; + + if( grp->h != 1 ) + { + mbedtls_mpi_free( &grp->P ); + mbedtls_mpi_free( &grp->A ); + mbedtls_mpi_free( &grp->B ); + mbedtls_ecp_point_free( &grp->G ); + mbedtls_mpi_free( &grp->N ); + } + + if( grp->T != NULL ) + { + for( i = 0; i < grp->T_size; i++ ) + mbedtls_ecp_point_free( &grp->T[i] ); + mbedtls_free( grp->T ); + } + + mbedtls_platform_zeroize( grp, sizeof( mbedtls_ecp_group ) ); +} + +/* + * Unallocate (the components of) a key pair + */ +void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key ) +{ + if( key == NULL ) + return; + + mbedtls_ecp_group_free( &key->grp ); + mbedtls_mpi_free( &key->d ); + mbedtls_ecp_point_free( &key->Q ); +} + +/* + * Copy the contents of a point + */ +int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + ECP_VALIDATE_RET( P != NULL ); + ECP_VALIDATE_RET( Q != NULL ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) ); + +cleanup: + return( ret ); +} + +/* + * Copy the contents of a group object + */ +int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src ) +{ + ECP_VALIDATE_RET( dst != NULL ); + ECP_VALIDATE_RET( src != NULL ); + + return( mbedtls_ecp_group_load( dst, src->id ) ); +} + +/* + * Set point to zero + */ +int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + ECP_VALIDATE_RET( pt != NULL ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) ); + +cleanup: + return( ret ); +} + +/* + * Tell if a point is zero + */ +int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt ) +{ + ECP_VALIDATE_RET( pt != NULL ); + + return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 ); +} + +/* + * Compare two points lazily + */ +int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P, + const mbedtls_ecp_point *Q ) +{ + ECP_VALIDATE_RET( P != NULL ); + ECP_VALIDATE_RET( Q != NULL ); + + if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 && + mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 && + mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 ) + { + return( 0 ); + } + + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); +} + +/* + * Import a non-zero point from ASCII strings + */ +int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix, + const char *x, const char *y ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + ECP_VALIDATE_RET( P != NULL ); + ECP_VALIDATE_RET( x != NULL ); + ECP_VALIDATE_RET( y != NULL ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) ); + +cleanup: + return( ret ); +} + +/* + * Export a point into unsigned binary data (SEC1 2.3.3 and RFC7748) + */ +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 ) +{ + int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; + size_t plen; + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( P != NULL ); + ECP_VALIDATE_RET( olen != NULL ); + ECP_VALIDATE_RET( buf != NULL ); + ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED || + format == MBEDTLS_ECP_PF_COMPRESSED ); + + plen = mbedtls_mpi_size( &grp->P ); + +#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) + (void) format; /* Montgomery curves always use the same point format */ + if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) + { + *olen = plen; + if( buflen < *olen ) + return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary_le( &P->X, buf, plen ) ); + } +#endif +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) + if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) + { + /* + * Common case: P == 0 + */ + if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 ) + { + if( buflen < 1 ) + return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); + + buf[0] = 0x00; + *olen = 1; + + return( 0 ); + } + + if( format == MBEDTLS_ECP_PF_UNCOMPRESSED ) + { + *olen = 2 * plen + 1; + + if( buflen < *olen ) + return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); + + buf[0] = 0x04; + MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) ); + } + else if( format == MBEDTLS_ECP_PF_COMPRESSED ) + { + *olen = plen + 1; + + if( buflen < *olen ) + return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); + + buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 ); + MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) ); + } + } +#endif + +cleanup: + return( ret ); +} + +/* + * Import a point from unsigned binary data (SEC1 2.3.4 and RFC7748) + */ +int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, + mbedtls_ecp_point *pt, + const unsigned char *buf, size_t ilen ) +{ + int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; + size_t plen; + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( pt != NULL ); + ECP_VALIDATE_RET( buf != NULL ); + + if( ilen < 1 ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + plen = mbedtls_mpi_size( &grp->P ); + +#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) + if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) + { + if( plen != ilen ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &pt->X, buf, plen ) ); + mbedtls_mpi_free( &pt->Y ); + + if( grp->id == MBEDTLS_ECP_DP_CURVE25519 ) + /* Set most significant bit to 0 as prescribed in RFC7748 ยง5 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &pt->X, plen * 8 - 1, 0 ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) ); + } +#endif +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) + if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) + { + if( buf[0] == 0x00 ) + { + if( ilen == 1 ) + return( mbedtls_ecp_set_zero( pt ) ); + else + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + } + + if( buf[0] != 0x04 ) + return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); + + if( ilen != 2 * plen + 1 ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, + buf + 1 + plen, plen ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) ); + } +#endif + +cleanup: + return( ret ); +} + +/* + * Import a point from a TLS ECPoint record (RFC 4492) + * struct { + * opaque point <1..2^8-1>; + * } ECPoint; + */ +int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, + mbedtls_ecp_point *pt, + const unsigned char **buf, size_t buf_len ) +{ + unsigned char data_len; + const unsigned char *buf_start; + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( pt != NULL ); + ECP_VALIDATE_RET( buf != NULL ); + ECP_VALIDATE_RET( *buf != NULL ); + + /* + * We must have at least two bytes (1 for length, at least one for data) + */ + if( buf_len < 2 ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + data_len = *(*buf)++; + if( data_len < 1 || data_len > buf_len - 1 ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + /* + * Save buffer start for read_binary and update buf + */ + buf_start = *buf; + *buf += data_len; + + return( mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len ) ); +} + +/* + * Export a point as a TLS ECPoint record (RFC 4492) + * struct { + * opaque point <1..2^8-1>; + * } ECPoint; + */ +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 ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( pt != NULL ); + ECP_VALIDATE_RET( olen != NULL ); + ECP_VALIDATE_RET( buf != NULL ); + ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED || + format == MBEDTLS_ECP_PF_COMPRESSED ); + + /* + * buffer length must be at least one, for our length byte + */ + if( blen < 1 ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format, + olen, buf + 1, blen - 1) ) != 0 ) + return( ret ); + + /* + * write length to the first byte and update total length + */ + buf[0] = (unsigned char) *olen; + ++*olen; + + return( 0 ); +} + +/* + * Set a group from an ECParameters record (RFC 4492) + */ +int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, + const unsigned char **buf, size_t len ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_ecp_group_id grp_id; + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( buf != NULL ); + ECP_VALIDATE_RET( *buf != NULL ); + + if( ( ret = mbedtls_ecp_tls_read_group_id( &grp_id, buf, len ) ) != 0 ) + return( ret ); + + return( mbedtls_ecp_group_load( grp, grp_id ) ); +} + +/* + * Read a group id from an ECParameters record (RFC 4492) and convert it to + * mbedtls_ecp_group_id. + */ +int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp, + const unsigned char **buf, size_t len ) +{ + uint16_t tls_id; + const mbedtls_ecp_curve_info *curve_info; + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( buf != NULL ); + ECP_VALIDATE_RET( *buf != NULL ); + + /* + * We expect at least three bytes (see below) + */ + if( len < 3 ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + /* + * First byte is curve_type; only named_curve is handled + */ + if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + /* + * Next two bytes are the namedcurve value + */ + tls_id = *(*buf)++; + tls_id <<= 8; + tls_id |= *(*buf)++; + + if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL ) + return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); + + *grp = curve_info->grp_id; + + return( 0 ); +} + +/* + * Write the ECParameters record corresponding to a group (RFC 4492) + */ +int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen, + unsigned char *buf, size_t blen ) +{ + const mbedtls_ecp_curve_info *curve_info; + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( buf != NULL ); + ECP_VALIDATE_RET( olen != NULL ); + + if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + /* + * We are going to write 3 bytes (see below) + */ + *olen = 3; + if( blen < *olen ) + return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); + + /* + * First byte is curve_type, always named_curve + */ + *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE; + + /* + * Next two bytes are the namedcurve value + */ + buf[0] = curve_info->tls_id >> 8; + buf[1] = curve_info->tls_id & 0xFF; + + return( 0 ); +} + +/* + * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi. + * See the documentation of struct mbedtls_ecp_group. + * + * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf. + */ +static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + + if( grp->modp == NULL ) + return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) ); + + /* N->s < 0 is a much faster test, which fails only if N is 0 */ + if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) || + mbedtls_mpi_bitlen( N ) > 2 * grp->pbits ) + { + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + } + + MBEDTLS_MPI_CHK( grp->modp( N ) ); + + /* N->s < 0 is a much faster test, which fails only if N is 0 */ + while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) ); + + while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 ) + /* we known P, N and the result are positive */ + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) ); + +cleanup: + return( ret ); +} + +/* + * Fast mod-p functions expect their argument to be in the 0..p^2 range. + * + * In order to guarantee that, we need to ensure that operands of + * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will + * bring the result back to this range. + * + * The following macros are shortcuts for doing that. + */ + +/* + * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi + */ +#if defined(MBEDTLS_SELF_TEST) +#define INC_MUL_COUNT mul_count++; +#else +#define INC_MUL_COUNT +#endif + +#define MOD_MUL( N ) \ + do \ + { \ + MBEDTLS_MPI_CHK( ecp_modp( &(N), grp ) ); \ + INC_MUL_COUNT \ + } while( 0 ) + +static inline int mbedtls_mpi_mul_mod( const mbedtls_ecp_group *grp, + mbedtls_mpi *X, + const mbedtls_mpi *A, + const mbedtls_mpi *B ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( X, A, B ) ); + MOD_MUL( *X ); +cleanup: + return( ret ); +} + +/* + * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi + * N->s < 0 is a very fast test, which fails only if N is 0 + */ +#define MOD_SUB( N ) \ + while( (N).s < 0 && mbedtls_mpi_cmp_int( &(N), 0 ) != 0 ) \ + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &(N), &(N), &grp->P ) ) + +#if ( defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \ + !( defined(MBEDTLS_ECP_NO_FALLBACK) && \ + defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \ + defined(MBEDTLS_ECP_ADD_MIXED_ALT) ) ) || \ + ( defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) && \ + !( defined(MBEDTLS_ECP_NO_FALLBACK) && \ + defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) ) ) +static inline int mbedtls_mpi_sub_mod( const mbedtls_ecp_group *grp, + mbedtls_mpi *X, + const mbedtls_mpi *A, + const mbedtls_mpi *B ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( X, A, B ) ); + MOD_SUB( *X ); +cleanup: + return( ret ); +} +#endif /* All functions referencing mbedtls_mpi_sub_mod() are alt-implemented without fallback */ + +/* + * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int. + * We known P, N and the result are positive, so sub_abs is correct, and + * a bit faster. + */ +#define MOD_ADD( N ) \ + while( mbedtls_mpi_cmp_mpi( &(N), &grp->P ) >= 0 ) \ + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &(N), &(N), &grp->P ) ) + +static inline int mbedtls_mpi_add_mod( const mbedtls_ecp_group *grp, + mbedtls_mpi *X, + const mbedtls_mpi *A, + const mbedtls_mpi *B ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, A, B ) ); + MOD_ADD( *X ); +cleanup: + return( ret ); +} + +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \ + !( defined(MBEDTLS_ECP_NO_FALLBACK) && \ + defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \ + defined(MBEDTLS_ECP_ADD_MIXED_ALT) ) +static inline int mbedtls_mpi_shift_l_mod( const mbedtls_ecp_group *grp, + mbedtls_mpi *X, + size_t count ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( X, count ) ); + MOD_ADD( *X ); +cleanup: + return( ret ); +} +#endif /* All functions referencing mbedtls_mpi_shift_l_mod() are alt-implemented without fallback */ + +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) +/* + * For curves in short Weierstrass form, we do all the internal operations in + * Jacobian coordinates. + * + * For multiplication, we'll use a comb method with coutermeasueres against + * SPA, hence timing attacks. + */ + +/* + * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1) + * Cost: 1N := 1I + 3M + 1S + */ +static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt ) +{ + if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 ) + return( 0 ); + +#if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) + if( mbedtls_internal_ecp_grp_capable( grp ) ) + return( mbedtls_internal_ecp_normalize_jac( grp, pt ) ); +#endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */ + +#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) + return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); +#else + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_mpi Zi, ZZi; + mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi ); + + /* + * X = X / Z^2 mod p + */ + MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ZZi, &Zi, &Zi ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->X, &pt->X, &ZZi ) ); + + /* + * Y = Y / Z^3 mod p + */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &ZZi ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &Zi ) ); + + /* + * Z = 1 + */ + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) ); + +cleanup: + + mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi ); + + return( ret ); +#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) */ +} + +/* + * Normalize jacobian coordinates of an array of (pointers to) points, + * using Montgomery's trick to perform only one inversion mod P. + * (See for example Cohen's "A Course in Computational Algebraic Number + * Theory", Algorithm 10.3.4.) + * + * Warning: fails (returning an error) if one of the points is zero! + * This should never happen, see choice of w in ecp_mul_comb(). + * + * Cost: 1N(t) := 1I + (6t - 3)M + 1S + */ +static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp, + mbedtls_ecp_point *T[], size_t T_size ) +{ + if( T_size < 2 ) + return( ecp_normalize_jac( grp, *T ) ); + +#if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) + if( mbedtls_internal_ecp_grp_capable( grp ) ) + return( mbedtls_internal_ecp_normalize_jac_many( grp, T, T_size ) ); +#endif + +#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) + return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); +#else + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t i; + mbedtls_mpi *c, u, Zi, ZZi; + + if( ( c = mbedtls_calloc( T_size, sizeof( mbedtls_mpi ) ) ) == NULL ) + return( MBEDTLS_ERR_ECP_ALLOC_FAILED ); + + for( i = 0; i < T_size; i++ ) + mbedtls_mpi_init( &c[i] ); + + mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi ); + + /* + * c[i] = Z_0 * ... * Z_i + */ + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) ); + for( i = 1; i < T_size; i++ ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &c[i], &c[i-1], &T[i]->Z ) ); + } + + /* + * u = 1 / (Z_0 * ... * Z_n) mod P + */ + MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[T_size-1], &grp->P ) ); + + for( i = T_size - 1; ; i-- ) + { + /* + * Zi = 1 / Z_i mod p + * u = 1 / (Z_0 * ... * Z_i) mod P + */ + if( i == 0 ) { + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) ); + } + else + { + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &Zi, &u, &c[i-1] ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &u, &u, &T[i]->Z ) ); + } + + /* + * proceed as in normalize() + */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ZZi, &Zi, &Zi ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->X, &T[i]->X, &ZZi ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->Y, &T[i]->Y, &ZZi ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->Y, &T[i]->Y, &Zi ) ); + + /* + * Post-precessing: reclaim some memory by shrinking coordinates + * - not storing Z (always 1) + * - shrinking other coordinates, but still keeping the same number of + * limbs as P, as otherwise it will too likely be regrown too fast. + */ + MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) ); + mbedtls_mpi_free( &T[i]->Z ); + + if( i == 0 ) + break; + } + +cleanup: + + mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi ); + for( i = 0; i < T_size; i++ ) + mbedtls_mpi_free( &c[i] ); + mbedtls_free( c ); + + return( ret ); +#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) */ +} + +/* + * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak. + * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid + */ +static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp, + mbedtls_ecp_point *Q, + unsigned char inv ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + unsigned char nonzero; + mbedtls_mpi mQY; + + mbedtls_mpi_init( &mQY ); + + /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) ); + nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0; + MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) ); + +cleanup: + mbedtls_mpi_free( &mQY ); + + return( ret ); +} + +/* + * Point doubling R = 2 P, Jacobian coordinates + * + * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 . + * + * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR + * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring. + * + * Standard optimizations are applied when curve parameter A is one of { 0, -3 }. + * + * Cost: 1D := 3M + 4S (A == 0) + * 4M + 4S (A == -3) + * 3M + 6S + 1a otherwise + */ +static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, + const mbedtls_ecp_point *P ) +{ +#if defined(MBEDTLS_SELF_TEST) + dbl_count++; +#endif + +#if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) + if( mbedtls_internal_ecp_grp_capable( grp ) ) + return( mbedtls_internal_ecp_double_jac( grp, R, P ) ); +#endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */ + +#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) + return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); +#else + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_mpi M, S, T, U; + + mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U ); + + /* Special case for A = -3 */ + if( grp->A.p == NULL ) + { + /* M = 3(X + Z^2)(X - Z^2) */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->Z, &P->Z ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &T, &P->X, &S ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &U, &P->X, &S ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &T, &U ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M ); + } + else + { + /* M = 3.X^2 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->X, &P->X ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M ); + + /* Optimize away for "koblitz" curves with A = 0 */ + if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 ) + { + /* M += A.Z^4 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->Z, &P->Z ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &S, &S ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &T, &grp->A ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &M, &M, &S ) ); + } + } + + /* S = 4.X.Y^2 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &P->Y, &P->Y ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &T, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->X, &T ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &S, 1 ) ); + + /* U = 8.Y^4 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &U, &T, &T ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &U, 1 ) ); + + /* T = M^2 - 2.S */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &M, &M ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T, &T, &S ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T, &T, &S ) ); + + /* S = M(S - T) - U */ + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S, &S, &T ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &S, &M ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S, &S, &U ) ); + + /* U = 2.Y.Z */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &U, &P->Y, &P->Z ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &U, 1 ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) ); + +cleanup: + mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U ); + + return( ret ); +#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) */ +} + +/* + * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22) + * + * The coordinates of Q must be normalized (= affine), + * but those of P don't need to. R is not normalized. + * + * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q. + * None of these cases can happen as intermediate step in ecp_mul_comb(): + * - at each step, P, Q and R are multiples of the base point, the factor + * being less than its order, so none of them is zero; + * - Q is an odd multiple of the base point, P an even multiple, + * due to the choice of precomputed points in the modified comb method. + * So branches for these cases do not leak secret information. + * + * We accept Q->Z being unset (saving memory in tables) as meaning 1. + * + * Cost: 1A := 8M + 3S + */ +static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, + const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q ) +{ +#if defined(MBEDTLS_SELF_TEST) + add_count++; +#endif + +#if defined(MBEDTLS_ECP_ADD_MIXED_ALT) + if( mbedtls_internal_ecp_grp_capable( grp ) ) + return( mbedtls_internal_ecp_add_mixed( grp, R, P, Q ) ); +#endif /* MBEDTLS_ECP_ADD_MIXED_ALT */ + +#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_ADD_MIXED_ALT) + return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); +#else + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_mpi T1, T2, T3, T4, X, Y, Z; + + /* + * Trivial cases: P == 0 or Q == 0 (case 1) + */ + if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 ) + return( mbedtls_ecp_copy( R, Q ) ); + + if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 ) + return( mbedtls_ecp_copy( R, P ) ); + + /* + * Make sure Q coordinates are normalized + */ + if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 ); + mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T1, &P->Z, &P->Z ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T2, &T1, &P->Z ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T1, &T1, &Q->X ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T2, &T2, &Q->Y ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T1, &T1, &P->X ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T2, &T2, &P->Y ) ); + + /* Special cases (2) and (3) */ + if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 ) + { + if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 ) + { + ret = ecp_double_jac( grp, R, P ); + goto cleanup; + } + else + { + ret = mbedtls_ecp_set_zero( R ); + goto cleanup; + } + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &Z, &P->Z, &T1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T1, &T1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T4, &T3, &T1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T3, &P->X ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T1, &T3 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &T1, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &X, &T2, &T2 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &X, &X, &T1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &X, &X, &T4 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T3, &T3, &X ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T3, &T2 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T4, &T4, &P->Y ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &Y, &T3, &T4 ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) ); + +cleanup: + + mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 ); + mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z ); + + return( ret ); +#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_ADD_MIXED_ALT) */ +} + +/* + * Randomize jacobian coordinates: + * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l + * This is sort of the reverse operation of ecp_normalize_jac(). + * + * This countermeasure was first suggested in [2]. + */ +static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt, + int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) +{ +#if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) + if( mbedtls_internal_ecp_grp_capable( grp ) ) + return( mbedtls_internal_ecp_randomize_jac( grp, pt, f_rng, p_rng ) ); +#endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */ + +#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) + return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); +#else + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_mpi l, ll; + + mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll ); + + /* Generate l such that 1 < l < p */ + MBEDTLS_MPI_CHK( mbedtls_mpi_random( &l, 2, &grp->P, f_rng, p_rng ) ); + + /* Z = l * Z */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Z, &pt->Z, &l ) ); + + /* X = l^2 * X */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ll, &l, &l ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->X, &pt->X, &ll ) ); + + /* Y = l^3 * Y */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ll, &ll, &l ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &ll ) ); + +cleanup: + mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll ); + + if( ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE ) + ret = MBEDTLS_ERR_ECP_RANDOM_FAILED; + return( ret ); +#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) */ +} + +/* + * Check and define parameters used by the comb method (see below for details) + */ +#if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7 +#error "MBEDTLS_ECP_WINDOW_SIZE out of bounds" +#endif + +/* d = ceil( n / w ) */ +#define COMB_MAX_D ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2 + +/* number of precomputed points */ +#define COMB_MAX_PRE ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) ) + +/* + * Compute the representation of m that will be used with our comb method. + * + * The basic comb method is described in GECC 3.44 for example. We use a + * modified version that provides resistance to SPA by avoiding zero + * digits in the representation as in [3]. We modify the method further by + * requiring that all K_i be odd, which has the small cost that our + * representation uses one more K_i, due to carries, but saves on the size of + * the precomputed table. + * + * Summary of the comb method and its modifications: + * + * - The goal is to compute m*P for some w*d-bit integer m. + * + * - The basic comb method splits m into the w-bit integers + * x[0] .. x[d-1] where x[i] consists of the bits in m whose + * index has residue i modulo d, and computes m * P as + * S[x[0]] + 2 * S[x[1]] + .. + 2^(d-1) S[x[d-1]], where + * S[i_{w-1} .. i_0] := i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + i_0 P. + * + * - If it happens that, say, x[i+1]=0 (=> S[x[i+1]]=0), one can replace the sum by + * .. + 2^{i-1} S[x[i-1]] - 2^i S[x[i]] + 2^{i+1} S[x[i]] + 2^{i+2} S[x[i+2]] .., + * thereby successively converting it into a form where all summands + * are nonzero, at the cost of negative summands. This is the basic idea of [3]. + * + * - More generally, even if x[i+1] != 0, we can first transform the sum as + * .. - 2^i S[x[i]] + 2^{i+1} ( S[x[i]] + S[x[i+1]] ) + 2^{i+2} S[x[i+2]] .., + * and then replace S[x[i]] + S[x[i+1]] = S[x[i] ^ x[i+1]] + 2 S[x[i] & x[i+1]]. + * Performing and iterating this procedure for those x[i] that are even + * (keeping track of carry), we can transform the original sum into one of the form + * S[x'[0]] +- 2 S[x'[1]] +- .. +- 2^{d-1} S[x'[d-1]] + 2^d S[x'[d]] + * with all x'[i] odd. It is therefore only necessary to know S at odd indices, + * which is why we are only computing half of it in the first place in + * ecp_precompute_comb and accessing it with index abs(i) / 2 in ecp_select_comb. + * + * - For the sake of compactness, only the seven low-order bits of x[i] + * are used to represent its absolute value (K_i in the paper), and the msb + * of x[i] encodes the sign (s_i in the paper): it is set if and only if + * if s_i == -1; + * + * Calling conventions: + * - x is an array of size d + 1 + * - w is the size, ie number of teeth, of the comb, and must be between + * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE) + * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d + * (the result will be incorrect if these assumptions are not satisfied) + */ +static void ecp_comb_recode_core( unsigned char x[], size_t d, + unsigned char w, const mbedtls_mpi *m ) +{ + size_t i, j; + unsigned char c, cc, adjust; + + memset( x, 0, d+1 ); + + /* First get the classical comb values (except for x_d = 0) */ + for( i = 0; i < d; i++ ) + for( j = 0; j < w; j++ ) + x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j; + + /* Now make sure x_1 .. x_d are odd */ + c = 0; + for( i = 1; i <= d; i++ ) + { + /* Add carry and update it */ + cc = x[i] & c; + x[i] = x[i] ^ c; + c = cc; + + /* Adjust if needed, avoiding branches */ + adjust = 1 - ( x[i] & 0x01 ); + c |= x[i] & ( x[i-1] * adjust ); + x[i] = x[i] ^ ( x[i-1] * adjust ); + x[i-1] |= adjust << 7; + } +} + +/* + * Precompute points for the adapted comb method + * + * Assumption: T must be able to hold 2^{w - 1} elements. + * + * Operation: If i = i_{w-1} ... i_1 is the binary representation of i, + * sets T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P. + * + * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1) + * + * Note: Even comb values (those where P would be omitted from the + * sum defining T[i] above) are not needed in our adaption + * the comb method. See ecp_comb_recode_core(). + * + * This function currently works in four steps: + * (1) [dbl] Computation of intermediate T[i] for 2-power values of i + * (2) [norm_dbl] Normalization of coordinates of these T[i] + * (3) [add] Computation of all T[i] + * (4) [norm_add] Normalization of all T[i] + * + * Step 1 can be interrupted but not the others; together with the final + * coordinate normalization they are the largest steps done at once, depending + * on the window size. Here are operation counts for P-256: + * + * step (2) (3) (4) + * w = 5 142 165 208 + * w = 4 136 77 160 + * w = 3 130 33 136 + * w = 2 124 11 124 + * + * So if ECC operations are blocking for too long even with a low max_ops + * value, it's useful to set MBEDTLS_ECP_WINDOW_SIZE to a lower value in order + * to minimize maximum blocking time. + */ +static int ecp_precompute_comb( const mbedtls_ecp_group *grp, + mbedtls_ecp_point T[], const mbedtls_ecp_point *P, + unsigned char w, size_t d, + mbedtls_ecp_restart_ctx *rs_ctx ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + unsigned char i; + size_t j = 0; + const unsigned char T_size = 1U << ( w - 1 ); + mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1]; + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL ) + { + if( rs_ctx->rsm->state == ecp_rsm_pre_dbl ) + goto dbl; + if( rs_ctx->rsm->state == ecp_rsm_pre_norm_dbl ) + goto norm_dbl; + if( rs_ctx->rsm->state == ecp_rsm_pre_add ) + goto add; + if( rs_ctx->rsm->state == ecp_rsm_pre_norm_add ) + goto norm_add; + } +#else + (void) rs_ctx; +#endif + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL ) + { + rs_ctx->rsm->state = ecp_rsm_pre_dbl; + + /* initial state for the loop */ + rs_ctx->rsm->i = 0; + } + +dbl: +#endif + /* + * Set T[0] = P and + * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value) + */ + MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) ); + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0 ) + j = rs_ctx->rsm->i; + else +#endif + j = 0; + + for( ; j < d * ( w - 1 ); j++ ) + { + MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_DBL ); + + i = 1U << ( j / d ); + cur = T + i; + + if( j % d == 0 ) + MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) ); + + MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) ); + } + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL ) + rs_ctx->rsm->state = ecp_rsm_pre_norm_dbl; + +norm_dbl: +#endif + /* + * Normalize current elements in T. As T has holes, + * use an auxiliary array of pointers to elements in T. + */ + j = 0; + for( i = 1; i < T_size; i <<= 1 ) + TT[j++] = T + i; + + MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV + 6 * j - 2 ); + + MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) ); + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL ) + rs_ctx->rsm->state = ecp_rsm_pre_add; + +add: +#endif + /* + * Compute the remaining ones using the minimal number of additions + * Be careful to update T[2^l] only after using it! + */ + MBEDTLS_ECP_BUDGET( ( T_size - 1 ) * MBEDTLS_ECP_OPS_ADD ); + + for( i = 1; i < T_size; i <<= 1 ) + { + j = i; + while( j-- ) + MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) ); + } + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL ) + rs_ctx->rsm->state = ecp_rsm_pre_norm_add; + +norm_add: +#endif + /* + * Normalize final elements in T. Even though there are no holes now, we + * still need the auxiliary array for homogeneity with the previous + * call. Also, skip T[0] which is already normalised, being a copy of P. + */ + for( j = 0; j + 1 < T_size; j++ ) + TT[j] = T + j + 1; + + MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV + 6 * j - 2 ); + + MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) ); + +cleanup: +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL && + ret == MBEDTLS_ERR_ECP_IN_PROGRESS ) + { + if( rs_ctx->rsm->state == ecp_rsm_pre_dbl ) + rs_ctx->rsm->i = j; + } +#endif + + return( ret ); +} + +/* + * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ] + * + * See ecp_comb_recode_core() for background + */ +static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, + const mbedtls_ecp_point T[], unsigned char T_size, + unsigned char i ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + unsigned char ii, j; + + /* Ignore the "sign" bit and scale down */ + ii = ( i & 0x7Fu ) >> 1; + + /* Read the whole table to thwart cache-based timing attacks */ + for( j = 0; j < T_size; j++ ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) ); + } + + /* Safely invert result if i is "negative" */ + MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) ); + +cleanup: + return( ret ); +} + +/* + * Core multiplication algorithm for the (modified) comb method. + * This part is actually common with the basic comb method (GECC 3.44) + * + * Cost: d A + d D + 1 R + */ +static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, + const mbedtls_ecp_point T[], unsigned char T_size, + const unsigned char x[], size_t d, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng, + mbedtls_ecp_restart_ctx *rs_ctx ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_ecp_point Txi; + size_t i; + + mbedtls_ecp_point_init( &Txi ); + +#if !defined(MBEDTLS_ECP_RESTARTABLE) + (void) rs_ctx; +#endif + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL && + rs_ctx->rsm->state != ecp_rsm_comb_core ) + { + rs_ctx->rsm->i = 0; + rs_ctx->rsm->state = ecp_rsm_comb_core; + } + + /* new 'if' instead of nested for the sake of the 'else' branch */ + if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0 ) + { + /* restore current index (R already pointing to rs_ctx->rsm->R) */ + i = rs_ctx->rsm->i; + } + else +#endif + { + /* Start with a non-zero point and randomize its coordinates */ + i = d; + MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, T_size, x[i] ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) ); +#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG) + if( f_rng != 0 ) +#endif + MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) ); + } + + while( i != 0 ) + { + MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_DBL + MBEDTLS_ECP_OPS_ADD ); + --i; + + MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) ); + MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, T_size, x[i] ) ); + MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) ); + } + +cleanup: + + mbedtls_ecp_point_free( &Txi ); + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL && + ret == MBEDTLS_ERR_ECP_IN_PROGRESS ) + { + rs_ctx->rsm->i = i; + /* no need to save R, already pointing to rs_ctx->rsm->R */ + } +#endif + + return( ret ); +} + +/* + * Recode the scalar to get constant-time comb multiplication + * + * As the actual scalar recoding needs an odd scalar as a starting point, + * this wrapper ensures that by replacing m by N - m if necessary, and + * informs the caller that the result of multiplication will be negated. + * + * This works because we only support large prime order for Short Weierstrass + * curves, so N is always odd hence either m or N - m is. + * + * See ecp_comb_recode_core() for background. + */ +static int ecp_comb_recode_scalar( const mbedtls_ecp_group *grp, + const mbedtls_mpi *m, + unsigned char k[COMB_MAX_D + 1], + size_t d, + unsigned char w, + unsigned char *parity_trick ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_mpi M, mm; + + mbedtls_mpi_init( &M ); + mbedtls_mpi_init( &mm ); + + /* N is always odd (see above), just make extra sure */ + if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + /* do we need the parity trick? */ + *parity_trick = ( mbedtls_mpi_get_bit( m, 0 ) == 0 ); + + /* execute parity fix in constant time */ + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, *parity_trick ) ); + + /* actual scalar recoding */ + ecp_comb_recode_core( k, d, w, &M ); + +cleanup: + mbedtls_mpi_free( &mm ); + mbedtls_mpi_free( &M ); + + return( ret ); +} + +/* + * Perform comb multiplication (for short Weierstrass curves) + * once the auxiliary table has been pre-computed. + * + * Scalar recoding may use a parity trick that makes us compute -m * P, + * if that is the case we'll need to recover m * P at the end. + */ +static int ecp_mul_comb_after_precomp( const mbedtls_ecp_group *grp, + mbedtls_ecp_point *R, + const mbedtls_mpi *m, + const mbedtls_ecp_point *T, + unsigned char T_size, + unsigned char w, + size_t d, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng, + mbedtls_ecp_restart_ctx *rs_ctx ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + unsigned char parity_trick; + unsigned char k[COMB_MAX_D + 1]; + mbedtls_ecp_point *RR = R; + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL ) + { + RR = &rs_ctx->rsm->R; + + if( rs_ctx->rsm->state == ecp_rsm_final_norm ) + goto final_norm; + } +#endif + + MBEDTLS_MPI_CHK( ecp_comb_recode_scalar( grp, m, k, d, w, + &parity_trick ) ); + MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, RR, T, T_size, k, d, + f_rng, p_rng, rs_ctx ) ); + MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, RR, parity_trick ) ); + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL ) + rs_ctx->rsm->state = ecp_rsm_final_norm; + +final_norm: + MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV ); +#endif + /* + * Knowledge of the jacobian coordinates may leak the last few bits of the + * scalar [1], and since our MPI implementation isn't constant-flow, + * inversion (used for coordinate normalization) may leak the full value + * of its input via side-channels [2]. + * + * [1] https://eprint.iacr.org/2003/191 + * [2] https://eprint.iacr.org/2020/055 + * + * Avoid the leak by randomizing coordinates before we normalize them. + */ +#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG) + if( f_rng != 0 ) +#endif + MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, RR, f_rng, p_rng ) ); + + MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, RR ) ); + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL ) + MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, RR ) ); +#endif + +cleanup: + return( ret ); +} + +/* + * Pick window size based on curve size and whether we optimize for base point + */ +static unsigned char ecp_pick_window_size( const mbedtls_ecp_group *grp, + unsigned char p_eq_g ) +{ + unsigned char w; + + /* + * Minimize the number of multiplications, that is minimize + * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w ) + * (see costs of the various parts, with 1S = 1M) + */ + w = grp->nbits >= 384 ? 5 : 4; + + /* + * If P == G, pre-compute a bit more, since this may be re-used later. + * Just adding one avoids upping the cost of the first mul too much, + * and the memory cost too. + */ + if( p_eq_g ) + w++; + + /* + * Make sure w is within bounds. + * (The last test is useful only for very small curves in the test suite.) + */ +#if( MBEDTLS_ECP_WINDOW_SIZE < 6 ) + if( w > MBEDTLS_ECP_WINDOW_SIZE ) + w = MBEDTLS_ECP_WINDOW_SIZE; +#endif + if( w >= grp->nbits ) + w = 2; + + return( w ); +} + +/* + * Multiplication using the comb method - for curves in short Weierstrass form + * + * This function is mainly responsible for administrative work: + * - managing the restart context if enabled + * - managing the table of precomputed points (passed between the below two + * functions): allocation, computation, ownership tranfer, freeing. + * + * It delegates the actual arithmetic work to: + * ecp_precompute_comb() and ecp_mul_comb_with_precomp() + * + * See comments on ecp_comb_recode_core() regarding the computation strategy. + */ +static int ecp_mul_comb( 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 ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + unsigned char w, p_eq_g, i; + size_t d; + unsigned char T_size = 0, T_ok = 0; + mbedtls_ecp_point *T = NULL; +#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG) + ecp_drbg_context drbg_ctx; + + ecp_drbg_init( &drbg_ctx ); +#endif + + ECP_RS_ENTER( rsm ); + +#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG) + if( f_rng == NULL ) + { + /* Adjust pointers */ + f_rng = &ecp_drbg_random; +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL ) + p_rng = &rs_ctx->rsm->drbg_ctx; + else +#endif + p_rng = &drbg_ctx; + + /* Initialize internal DRBG if necessary */ +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx == NULL || rs_ctx->rsm == NULL || + rs_ctx->rsm->drbg_seeded == 0 ) +#endif + { + const size_t m_len = ( grp->nbits + 7 ) / 8; + MBEDTLS_MPI_CHK( ecp_drbg_seed( p_rng, m, m_len ) ); + } +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL ) + rs_ctx->rsm->drbg_seeded = 1; +#endif + } +#endif /* !MBEDTLS_ECP_NO_INTERNAL_RNG */ + + /* Is P the base point ? */ +#if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1 + p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 && + mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 ); +#else + p_eq_g = 0; +#endif + + /* Pick window size and deduce related sizes */ + w = ecp_pick_window_size( grp, p_eq_g ); + T_size = 1U << ( w - 1 ); + d = ( grp->nbits + w - 1 ) / w; + + /* Pre-computed table: do we have it already for the base point? */ + if( p_eq_g && grp->T != NULL ) + { + /* second pointer to the same table, will be deleted on exit */ + T = grp->T; + T_ok = 1; + } + else +#if defined(MBEDTLS_ECP_RESTARTABLE) + /* Pre-computed table: do we have one in progress? complete? */ + if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->T != NULL ) + { + /* transfer ownership of T from rsm to local function */ + T = rs_ctx->rsm->T; + rs_ctx->rsm->T = NULL; + rs_ctx->rsm->T_size = 0; + + /* This effectively jumps to the call to mul_comb_after_precomp() */ + T_ok = rs_ctx->rsm->state >= ecp_rsm_comb_core; + } + else +#endif + /* Allocate table if we didn't have any */ + { + T = mbedtls_calloc( T_size, sizeof( mbedtls_ecp_point ) ); + if( T == NULL ) + { + ret = MBEDTLS_ERR_ECP_ALLOC_FAILED; + goto cleanup; + } + + for( i = 0; i < T_size; i++ ) + mbedtls_ecp_point_init( &T[i] ); + + T_ok = 0; + } + + /* Compute table (or finish computing it) if not done already */ + if( !T_ok ) + { + MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d, rs_ctx ) ); + + if( p_eq_g ) + { + /* almost transfer ownership of T to the group, but keep a copy of + * the pointer to use for calling the next function more easily */ + grp->T = T; + grp->T_size = T_size; + } + } + + /* Actual comb multiplication using precomputed points */ + MBEDTLS_MPI_CHK( ecp_mul_comb_after_precomp( grp, R, m, + T, T_size, w, d, + f_rng, p_rng, rs_ctx ) ); + +cleanup: + +#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG) + ecp_drbg_free( &drbg_ctx ); +#endif + + /* does T belong to the group? */ + if( T == grp->T ) + T = NULL; + + /* does T belong to the restart context? */ +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->rsm != NULL && ret == MBEDTLS_ERR_ECP_IN_PROGRESS && T != NULL ) + { + /* transfer ownership of T from local function to rsm */ + rs_ctx->rsm->T_size = T_size; + rs_ctx->rsm->T = T; + T = NULL; + } +#endif + + /* did T belong to us? then let's destroy it! */ + if( T != NULL ) + { + for( i = 0; i < T_size; i++ ) + mbedtls_ecp_point_free( &T[i] ); + mbedtls_free( T ); + } + + /* don't free R while in progress in case R == P */ +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( ret != MBEDTLS_ERR_ECP_IN_PROGRESS ) +#endif + /* prevent caller from using invalid value */ + if( ret != 0 ) + mbedtls_ecp_point_free( R ); + + ECP_RS_LEAVE( rsm ); + + return( ret ); +} + +#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ + +#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) +/* + * For Montgomery curves, we do all the internal arithmetic in projective + * coordinates. Import/export of points uses only the x coordinates, which is + * internaly represented as X / Z. + * + * For scalar multiplication, we'll use a Montgomery ladder. + */ + +/* + * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1 + * Cost: 1M + 1I + */ +static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P ) +{ +#if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) + if( mbedtls_internal_ecp_grp_capable( grp ) ) + return( mbedtls_internal_ecp_normalize_mxz( grp, P ) ); +#endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */ + +#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) + return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); +#else + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->X, &P->X, &P->Z ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) ); + +cleanup: + return( ret ); +#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) */ +} + +/* + * Randomize projective x/z coordinates: + * (X, Z) -> (l X, l Z) for random l + * This is sort of the reverse operation of ecp_normalize_mxz(). + * + * This countermeasure was first suggested in [2]. + * Cost: 2M + */ +static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P, + int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) +{ +#if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) + if( mbedtls_internal_ecp_grp_capable( grp ) ) + return( mbedtls_internal_ecp_randomize_mxz( grp, P, f_rng, p_rng ) ); +#endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */ + +#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) + return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); +#else + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_mpi l; + mbedtls_mpi_init( &l ); + + /* Generate l such that 1 < l < p */ + MBEDTLS_MPI_CHK( mbedtls_mpi_random( &l, 2, &grp->P, f_rng, p_rng ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->X, &P->X, &l ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->Z, &P->Z, &l ) ); + +cleanup: + mbedtls_mpi_free( &l ); + + if( ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE ) + ret = MBEDTLS_ERR_ECP_RANDOM_FAILED; + return( ret ); +#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) */ +} + +/* + * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q), + * for Montgomery curves in x/z coordinates. + * + * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3 + * with + * d = X1 + * P = (X2, Z2) + * Q = (X3, Z3) + * R = (X4, Z4) + * S = (X5, Z5) + * and eliminating temporary variables tO, ..., t4. + * + * Cost: 5M + 4S + */ +static int ecp_double_add_mxz( const mbedtls_ecp_group *grp, + mbedtls_ecp_point *R, mbedtls_ecp_point *S, + const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q, + const mbedtls_mpi *d ) +{ +#if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) + if( mbedtls_internal_ecp_grp_capable( grp ) ) + return( mbedtls_internal_ecp_double_add_mxz( grp, R, S, P, Q, d ) ); +#endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */ + +#if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) + return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); +#else + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB; + + mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B ); + mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C ); + mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &A, &P->X, &P->Z ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &AA, &A, &A ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &B, &P->X, &P->Z ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &BB, &B, &B ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &E, &AA, &BB ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &C, &Q->X, &Q->Z ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &D, &Q->X, &Q->Z ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &DA, &D, &A ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &CB, &C, &B ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &S->X, &DA, &CB ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->X, &S->X, &S->X ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S->Z, &DA, &CB ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->Z, &S->Z, &S->Z ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->Z, d, &S->Z ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->X, &AA, &BB ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->Z, &grp->A, &E ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &R->Z, &BB, &R->Z ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->Z, &E, &R->Z ) ); + +cleanup: + mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B ); + mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C ); + mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB ); + + return( ret ); +#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) */ +} + +/* + * Multiplication with Montgomery ladder in x/z coordinates, + * for curves in Montgomery form + */ +static int ecp_mul_mxz( 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 ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t i; + unsigned char b; + mbedtls_ecp_point RP; + mbedtls_mpi PX; +#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG) + ecp_drbg_context drbg_ctx; + + ecp_drbg_init( &drbg_ctx ); +#endif + mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX ); + +#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG) + if( f_rng == NULL ) + { + const size_t m_len = ( grp->nbits + 7 ) / 8; + MBEDTLS_MPI_CHK( ecp_drbg_seed( &drbg_ctx, m, m_len ) ); + f_rng = &ecp_drbg_random; + p_rng = &drbg_ctx; + } +#endif /* !MBEDTLS_ECP_NO_INTERNAL_RNG */ + + /* Save PX and read from P before writing to R, in case P == R */ + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) ); + MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) ); + + /* Set R to zero in modified x/z coordinates */ + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) ); + mbedtls_mpi_free( &R->Y ); + + /* RP.X might be sligtly larger than P, so reduce it */ + MOD_ADD( RP.X ); + + /* Randomize coordinates of the starting point */ +#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG) + if( f_rng != NULL ) +#endif + MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) ); + + /* Loop invariant: R = result so far, RP = R + P */ + i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */ + while( i-- > 0 ) + { + b = mbedtls_mpi_get_bit( m, i ); + /* + * if (b) R = 2R + P else R = 2R, + * which is: + * if (b) double_add( RP, R, RP, R ) + * else double_add( R, RP, R, RP ) + * but using safe conditional swaps to avoid leaks + */ + MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) ); + MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) ); + } + + /* + * Knowledge of the projective coordinates may leak the last few bits of the + * scalar [1], and since our MPI implementation isn't constant-flow, + * inversion (used for coordinate normalization) may leak the full value + * of its input via side-channels [2]. + * + * [1] https://eprint.iacr.org/2003/191 + * [2] https://eprint.iacr.org/2020/055 + * + * Avoid the leak by randomizing coordinates before we normalize them. + */ +#if defined(MBEDTLS_ECP_NO_INTERNAL_RNG) + if( f_rng != NULL ) +#endif + MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, R, f_rng, p_rng ) ); + + MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) ); + +cleanup: +#if !defined(MBEDTLS_ECP_NO_INTERNAL_RNG) + ecp_drbg_free( &drbg_ctx ); +#endif + + mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX ); + + return( ret ); +} + +#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ + +/* + * Restartable multiplication R = m * P + */ +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 ) +{ + int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; +#if defined(MBEDTLS_ECP_INTERNAL_ALT) + char is_grp_capable = 0; +#endif + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( R != NULL ); + ECP_VALIDATE_RET( m != NULL ); + ECP_VALIDATE_RET( P != NULL ); + +#if defined(MBEDTLS_ECP_RESTARTABLE) + /* reset ops count for this call if top-level */ + if( rs_ctx != NULL && rs_ctx->depth++ == 0 ) + rs_ctx->ops_done = 0; +#else + (void) rs_ctx; +#endif + +#if defined(MBEDTLS_ECP_INTERNAL_ALT) + if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) ) + MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) ); +#endif /* MBEDTLS_ECP_INTERNAL_ALT */ + +#if defined(MBEDTLS_ECP_RESTARTABLE) + /* skip argument check when restarting */ + if( rs_ctx == NULL || rs_ctx->rsm == NULL ) +#endif + { + /* check_privkey is free */ + MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_CHK ); + + /* Common sanity checks */ + MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( grp, m ) ); + MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, P ) ); + } + + ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; +#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) + if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) + MBEDTLS_MPI_CHK( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) ); +#endif +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) + if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) + MBEDTLS_MPI_CHK( ecp_mul_comb( grp, R, m, P, f_rng, p_rng, rs_ctx ) ); +#endif + +cleanup: + +#if defined(MBEDTLS_ECP_INTERNAL_ALT) + if( is_grp_capable ) + mbedtls_internal_ecp_free( grp ); +#endif /* MBEDTLS_ECP_INTERNAL_ALT */ + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL ) + rs_ctx->depth--; +#endif + + return( ret ); +} + +/* + * Multiplication R = m * P + */ +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 ) +{ + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( R != NULL ); + ECP_VALIDATE_RET( m != NULL ); + ECP_VALIDATE_RET( P != NULL ); + return( mbedtls_ecp_mul_restartable( grp, R, m, P, f_rng, p_rng, NULL ) ); +} + +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) +/* + * Check that an affine point is valid as a public key, + * short weierstrass curves (SEC1 3.2.3.1) + */ +static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_mpi YY, RHS; + + /* pt coordinates must be normalized for our checks */ + if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 || + mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 || + mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 || + mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 ) + return( MBEDTLS_ERR_ECP_INVALID_KEY ); + + mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS ); + + /* + * YY = Y^2 + * RHS = X (X^2 + A) + B = X^3 + A X + B + */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &YY, &pt->Y, &pt->Y ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &RHS, &pt->X, &pt->X ) ); + + /* Special case for A = -3 */ + if( grp->A.p == NULL ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS ); + } + else + { + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &RHS, &RHS, &grp->A ) ); + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &RHS, &RHS, &pt->X ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &RHS, &RHS, &grp->B ) ); + + if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 ) + ret = MBEDTLS_ERR_ECP_INVALID_KEY; + +cleanup: + + mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS ); + + return( ret ); +} +#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ + +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) +/* + * R = m * P with shortcuts for m == 0, m == 1 and m == -1 + * NOT constant-time - ONLY for short Weierstrass! + */ +static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp, + mbedtls_ecp_point *R, + const mbedtls_mpi *m, + const mbedtls_ecp_point *P, + mbedtls_ecp_restart_ctx *rs_ctx ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + + if( mbedtls_mpi_cmp_int( m, 0 ) == 0 ) + { + MBEDTLS_MPI_CHK( mbedtls_ecp_set_zero( R ) ); + } + else if( mbedtls_mpi_cmp_int( m, 1 ) == 0 ) + { + MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) ); + } + else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 ) + { + MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) ); + if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 ) + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) ); + } + else + { + MBEDTLS_MPI_CHK( mbedtls_ecp_mul_restartable( grp, R, m, P, + NULL, NULL, rs_ctx ) ); + } + +cleanup: + return( ret ); +} + +/* + * Restartable linear combination + * NOT constant-time + */ +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 ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_ecp_point mP; + mbedtls_ecp_point *pmP = &mP; + mbedtls_ecp_point *pR = R; +#if defined(MBEDTLS_ECP_INTERNAL_ALT) + char is_grp_capable = 0; +#endif + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( R != NULL ); + ECP_VALIDATE_RET( m != NULL ); + ECP_VALIDATE_RET( P != NULL ); + ECP_VALIDATE_RET( n != NULL ); + ECP_VALIDATE_RET( Q != NULL ); + + if( mbedtls_ecp_get_type( grp ) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) + return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); + + mbedtls_ecp_point_init( &mP ); + + ECP_RS_ENTER( ma ); + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->ma != NULL ) + { + /* redirect intermediate results to restart context */ + pmP = &rs_ctx->ma->mP; + pR = &rs_ctx->ma->R; + + /* jump to next operation */ + if( rs_ctx->ma->state == ecp_rsma_mul2 ) + goto mul2; + if( rs_ctx->ma->state == ecp_rsma_add ) + goto add; + if( rs_ctx->ma->state == ecp_rsma_norm ) + goto norm; + } +#endif /* MBEDTLS_ECP_RESTARTABLE */ + + MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pmP, m, P, rs_ctx ) ); +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->ma != NULL ) + rs_ctx->ma->state = ecp_rsma_mul2; + +mul2: +#endif + MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pR, n, Q, rs_ctx ) ); + +#if defined(MBEDTLS_ECP_INTERNAL_ALT) + if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) ) + MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) ); +#endif /* MBEDTLS_ECP_INTERNAL_ALT */ + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->ma != NULL ) + rs_ctx->ma->state = ecp_rsma_add; + +add: +#endif + MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_ADD ); + MBEDTLS_MPI_CHK( ecp_add_mixed( grp, pR, pmP, pR ) ); +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->ma != NULL ) + rs_ctx->ma->state = ecp_rsma_norm; + +norm: +#endif + MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV ); + MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, pR ) ); + +#if defined(MBEDTLS_ECP_RESTARTABLE) + if( rs_ctx != NULL && rs_ctx->ma != NULL ) + MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, pR ) ); +#endif + +cleanup: +#if defined(MBEDTLS_ECP_INTERNAL_ALT) + if( is_grp_capable ) + mbedtls_internal_ecp_free( grp ); +#endif /* MBEDTLS_ECP_INTERNAL_ALT */ + + mbedtls_ecp_point_free( &mP ); + + ECP_RS_LEAVE( ma ); + + return( ret ); +} + +/* + * Linear combination + * NOT constant-time + */ +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 ) +{ + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( R != NULL ); + ECP_VALIDATE_RET( m != NULL ); + ECP_VALIDATE_RET( P != NULL ); + ECP_VALIDATE_RET( n != NULL ); + ECP_VALIDATE_RET( Q != NULL ); + return( mbedtls_ecp_muladd_restartable( grp, R, m, P, n, Q, NULL ) ); +} +#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ + +#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) +#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) +#define ECP_MPI_INIT(s, n, p) {s, (n), (mbedtls_mpi_uint *)(p)} +#define ECP_MPI_INIT_ARRAY(x) \ + ECP_MPI_INIT(1, sizeof(x) / sizeof(mbedtls_mpi_uint), x) +/* + * Constants for the two points other than 0, 1, -1 (mod p) in + * https://cr.yp.to/ecdh.html#validate + * See ecp_check_pubkey_x25519(). + */ +static const mbedtls_mpi_uint x25519_bad_point_1[] = { + MBEDTLS_BYTES_TO_T_UINT_8( 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae ), + MBEDTLS_BYTES_TO_T_UINT_8( 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a ), + MBEDTLS_BYTES_TO_T_UINT_8( 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd ), + MBEDTLS_BYTES_TO_T_UINT_8( 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00 ), +}; +static const mbedtls_mpi_uint x25519_bad_point_2[] = { + MBEDTLS_BYTES_TO_T_UINT_8( 0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24 ), + MBEDTLS_BYTES_TO_T_UINT_8( 0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b ), + MBEDTLS_BYTES_TO_T_UINT_8( 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86 ), + MBEDTLS_BYTES_TO_T_UINT_8( 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57 ), +}; +static const mbedtls_mpi ecp_x25519_bad_point_1 = ECP_MPI_INIT_ARRAY( + x25519_bad_point_1 ); +static const mbedtls_mpi ecp_x25519_bad_point_2 = ECP_MPI_INIT_ARRAY( + x25519_bad_point_2 ); +#endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ + +/* + * Check that the input point is not one of the low-order points. + * This is recommended by the "May the Fourth" paper: + * https://eprint.iacr.org/2017/806.pdf + * Those points are never sent by an honest peer. + */ +static int ecp_check_bad_points_mx( const mbedtls_mpi *X, const mbedtls_mpi *P, + const mbedtls_ecp_group_id grp_id ) +{ + int ret; + mbedtls_mpi XmP; + + mbedtls_mpi_init( &XmP ); + + /* Reduce X mod P so that we only need to check values less than P. + * We know X < 2^256 so we can proceed by subtraction. */ + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &XmP, X ) ); + while( mbedtls_mpi_cmp_mpi( &XmP, P ) >= 0 ) + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &XmP, &XmP, P ) ); + + /* Check against the known bad values that are less than P. For Curve448 + * these are 0, 1 and -1. For Curve25519 we check the values less than P + * from the following list: https://cr.yp.to/ecdh.html#validate */ + if( mbedtls_mpi_cmp_int( &XmP, 1 ) <= 0 ) /* takes care of 0 and 1 */ + { + ret = MBEDTLS_ERR_ECP_INVALID_KEY; + goto cleanup; + } + +#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) + if( grp_id == MBEDTLS_ECP_DP_CURVE25519 ) + { + if( mbedtls_mpi_cmp_mpi( &XmP, &ecp_x25519_bad_point_1 ) == 0 ) + { + ret = MBEDTLS_ERR_ECP_INVALID_KEY; + goto cleanup; + } + + if( mbedtls_mpi_cmp_mpi( &XmP, &ecp_x25519_bad_point_2 ) == 0 ) + { + ret = MBEDTLS_ERR_ECP_INVALID_KEY; + goto cleanup; + } + } +#else + (void) grp_id; +#endif + + /* Final check: check if XmP + 1 is P (final because it changes XmP!) */ + MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &XmP, &XmP, 1 ) ); + if( mbedtls_mpi_cmp_mpi( &XmP, P ) == 0 ) + { + ret = MBEDTLS_ERR_ECP_INVALID_KEY; + goto cleanup; + } + + ret = 0; + +cleanup: + mbedtls_mpi_free( &XmP ); + + return( ret ); +} + +/* + * Check validity of a public key for Montgomery curves with x-only schemes + */ +static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt ) +{ + /* [Curve25519 p. 5] Just check X is the correct number of bytes */ + /* Allow any public value, if it's too big then we'll just reduce it mod p + * (RFC 7748 sec. 5 para. 3). */ + if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 ) + return( MBEDTLS_ERR_ECP_INVALID_KEY ); + + /* Implicit in all standards (as they don't consider negative numbers): + * X must be non-negative. This is normally ensured by the way it's + * encoded for transmission, but let's be extra sure. */ + if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ) + return( MBEDTLS_ERR_ECP_INVALID_KEY ); + + return( ecp_check_bad_points_mx( &pt->X, &grp->P, grp->id ) ); +} +#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ + +/* + * Check that a point is valid as a public key + */ +int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, + const mbedtls_ecp_point *pt ) +{ + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( pt != NULL ); + + /* Must use affine coordinates */ + if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 ) + return( MBEDTLS_ERR_ECP_INVALID_KEY ); + +#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) + if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) + return( ecp_check_pubkey_mx( grp, pt ) ); +#endif +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) + if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) + return( ecp_check_pubkey_sw( grp, pt ) ); +#endif + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); +} + +/* + * Check that an mbedtls_mpi is valid as a private key + */ +int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, + const mbedtls_mpi *d ) +{ + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( d != NULL ); + +#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) + if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) + { + /* see RFC 7748 sec. 5 para. 5 */ + if( mbedtls_mpi_get_bit( d, 0 ) != 0 || + mbedtls_mpi_get_bit( d, 1 ) != 0 || + mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */ + return( MBEDTLS_ERR_ECP_INVALID_KEY ); + + /* see [Curve25519] page 5 */ + if( grp->nbits == 254 && mbedtls_mpi_get_bit( d, 2 ) != 0 ) + return( MBEDTLS_ERR_ECP_INVALID_KEY ); + + return( 0 ); + } +#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) + if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) + { + /* see SEC1 3.2 */ + if( mbedtls_mpi_cmp_int( d, 1 ) < 0 || + mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 ) + return( MBEDTLS_ERR_ECP_INVALID_KEY ); + else + return( 0 ); + } +#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ + + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); +} + +#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) +MBEDTLS_STATIC_TESTABLE +int mbedtls_ecp_gen_privkey_mx( size_t high_bit, + mbedtls_mpi *d, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng ) +{ + int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; + size_t n_random_bytes = high_bit / 8 + 1; + + /* [Curve25519] page 5 */ + /* Generate a (high_bit+1)-bit random number by generating just enough + * random bytes, then shifting out extra bits from the top (necessary + * when (high_bit+1) is not a multiple of 8). */ + MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_random_bytes, + f_rng, p_rng ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_random_bytes - high_bit - 1 ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, high_bit, 1 ) ); + + /* Make sure the last two bits are unset for Curve448, three bits for + Curve25519 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) ); + if( high_bit == 254 ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) ); + } + +cleanup: + return( ret ); +} +#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ + +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) +static int mbedtls_ecp_gen_privkey_sw( + const mbedtls_mpi *N, mbedtls_mpi *d, + int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) +{ + int ret = mbedtls_mpi_random( d, 1, N, f_rng, p_rng ); + switch( ret ) + { + case MBEDTLS_ERR_MPI_NOT_ACCEPTABLE: + return( MBEDTLS_ERR_ECP_RANDOM_FAILED ); + default: + return( ret ); + } +} +#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ + +/* + * Generate a private key + */ +int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp, + mbedtls_mpi *d, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng ) +{ + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( d != NULL ); + ECP_VALIDATE_RET( f_rng != NULL ); + +#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) + if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) + return( mbedtls_ecp_gen_privkey_mx( grp->nbits, d, f_rng, p_rng ) ); +#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ + +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) + if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) + return( mbedtls_ecp_gen_privkey_sw( &grp->N, d, f_rng, p_rng ) ); +#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ + + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); +} + +/* + * Generate a keypair with configurable base point + */ +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 ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( d != NULL ); + ECP_VALIDATE_RET( G != NULL ); + ECP_VALIDATE_RET( Q != NULL ); + ECP_VALIDATE_RET( f_rng != NULL ); + + MBEDTLS_MPI_CHK( mbedtls_ecp_gen_privkey( grp, d, f_rng, p_rng ) ); + MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) ); + +cleanup: + return( ret ); +} + +/* + * Generate key pair, wrapper for conventional base point + */ +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 ) +{ + ECP_VALIDATE_RET( grp != NULL ); + ECP_VALIDATE_RET( d != NULL ); + ECP_VALIDATE_RET( Q != NULL ); + ECP_VALIDATE_RET( f_rng != NULL ); + + return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) ); +} + +/* + * Generate a keypair, prettier wrapper + */ +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 ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + ECP_VALIDATE_RET( key != NULL ); + ECP_VALIDATE_RET( f_rng != NULL ); + + if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 ) + return( ret ); + + return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) ); +} + +#define ECP_CURVE25519_KEY_SIZE 32 +/* + * Read a private key. + */ +int mbedtls_ecp_read_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, + const unsigned char *buf, size_t buflen ) +{ + int ret = 0; + + ECP_VALIDATE_RET( key != NULL ); + ECP_VALIDATE_RET( buf != NULL ); + + if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 ) + return( ret ); + + ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; + +#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) + if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) + { + /* + * If it is Curve25519 curve then mask the key as mandated by RFC7748 + */ + if( grp_id == MBEDTLS_ECP_DP_CURVE25519 ) + { + if( buflen != ECP_CURVE25519_KEY_SIZE ) + return MBEDTLS_ERR_ECP_INVALID_KEY; + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &key->d, buf, buflen ) ); + + /* Set the three least significant bits to 0 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 0, 0 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 1, 0 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 2, 0 ) ); + + /* Set the most significant bit to 0 */ + MBEDTLS_MPI_CHK( + mbedtls_mpi_set_bit( &key->d, + ECP_CURVE25519_KEY_SIZE * 8 - 1, 0 ) + ); + + /* Set the second most significant bit to 1 */ + MBEDTLS_MPI_CHK( + mbedtls_mpi_set_bit( &key->d, + ECP_CURVE25519_KEY_SIZE * 8 - 2, 1 ) + ); + } + else + ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; + } + +#endif +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) + if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &key->d, buf, buflen ) ); + + MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( &key->grp, &key->d ) ); + } + +#endif +cleanup: + + if( ret != 0 ) + mbedtls_mpi_free( &key->d ); + + return( ret ); +} + +/* + * Write a private key. + */ +int mbedtls_ecp_write_key( mbedtls_ecp_keypair *key, + unsigned char *buf, size_t buflen ) +{ + int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; + + ECP_VALIDATE_RET( key != NULL ); + ECP_VALIDATE_RET( buf != NULL ); + +#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) + if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) + { + if( key->grp.id == MBEDTLS_ECP_DP_CURVE25519 ) + { + if( buflen < ECP_CURVE25519_KEY_SIZE ) + return MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL; + + MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary_le( &key->d, buf, buflen ) ); + } + else + ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; + } + +#endif +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) + if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &key->d, buf, buflen ) ); + } + +#endif +cleanup: + + return( ret ); +} + + +/* + * Check a public-private key pair + */ +int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_ecp_point Q; + mbedtls_ecp_group grp; + ECP_VALIDATE_RET( pub != NULL ); + ECP_VALIDATE_RET( prv != NULL ); + + if( pub->grp.id == MBEDTLS_ECP_DP_NONE || + pub->grp.id != prv->grp.id || + mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) || + mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) || + mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) ) + { + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + } + + mbedtls_ecp_point_init( &Q ); + mbedtls_ecp_group_init( &grp ); + + /* mbedtls_ecp_mul() needs a non-const group... */ + mbedtls_ecp_group_copy( &grp, &prv->grp ); + + /* Also checks d is valid */ + MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) ); + + if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) || + mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) || + mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) ) + { + ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; + goto cleanup; + } + +cleanup: + mbedtls_ecp_point_free( &Q ); + mbedtls_ecp_group_free( &grp ); + + return( ret ); +} + +#if defined(MBEDTLS_SELF_TEST) + +/* Adjust the exponent to be a valid private point for the specified curve. + * This is sometimes necessary because we use a single set of exponents + * for all curves but the validity of values depends on the curve. */ +static int self_test_adjust_exponent( const mbedtls_ecp_group *grp, + mbedtls_mpi *m ) +{ + int ret = 0; + switch( grp->id ) + { + /* If Curve25519 is available, then that's what we use for the + * Montgomery test, so we don't need the adjustment code. */ +#if ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) +#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) + case MBEDTLS_ECP_DP_CURVE448: + /* Move highest bit from 254 to N-1. Setting bit N-1 is + * necessary to enforce the highest-bit-set constraint. */ + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( m, 254, 0 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( m, grp->nbits, 1 ) ); + /* Copy second-highest bit from 253 to N-2. This is not + * necessary but improves the test variety a bit. */ + MBEDTLS_MPI_CHK( + mbedtls_mpi_set_bit( m, grp->nbits - 1, + mbedtls_mpi_get_bit( m, 253 ) ) ); + break; +#endif +#endif /* ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) */ + default: + /* Non-Montgomery curves and Curve25519 need no adjustment. */ + (void) grp; + (void) m; + goto cleanup; + } +cleanup: + return( ret ); +} + +/* Calculate R = m.P for each m in exponents. Check that the number of + * basic operations doesn't depend on the value of m. */ +static int self_test_point( int verbose, + mbedtls_ecp_group *grp, + mbedtls_ecp_point *R, + mbedtls_mpi *m, + const mbedtls_ecp_point *P, + const char *const *exponents, + size_t n_exponents ) +{ + int ret = 0; + size_t i = 0; + unsigned long add_c_prev, dbl_c_prev, mul_c_prev; + add_count = 0; + dbl_count = 0; + mul_count = 0; + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( m, 16, exponents[0] ) ); + MBEDTLS_MPI_CHK( self_test_adjust_exponent( grp, m ) ); + MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) ); + + for( i = 1; i < n_exponents; i++ ) + { + add_c_prev = add_count; + dbl_c_prev = dbl_count; + mul_c_prev = mul_count; + add_count = 0; + dbl_count = 0; + mul_count = 0; + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( m, 16, exponents[i] ) ); + MBEDTLS_MPI_CHK( self_test_adjust_exponent( grp, m ) ); + MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) ); + + if( add_count != add_c_prev || + dbl_count != dbl_c_prev || + mul_count != mul_c_prev ) + { + ret = 1; + break; + } + } + +cleanup: + if( verbose != 0 ) + { + if( ret != 0 ) + mbedtls_printf( "failed (%u)\n", (unsigned int) i ); + else + mbedtls_printf( "passed\n" ); + } + return( ret ); +} + +/* + * Checkup routine + */ +int mbedtls_ecp_self_test( int verbose ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_ecp_group grp; + mbedtls_ecp_point R, P; + mbedtls_mpi m; + +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) + /* Exponents especially adapted for secp192k1, which has the lowest + * order n of all supported curves (secp192r1 is in a slightly larger + * field but the order of its base point is slightly smaller). */ + const char *sw_exponents[] = + { + "000000000000000000000000000000000000000000000001", /* one */ + "FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8C", /* n - 1 */ + "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */ + "400000000000000000000000000000000000000000000000", /* one and zeros */ + "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */ + "555555555555555555555555555555555555555555555555", /* 101010... */ + }; +#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ +#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) + const char *m_exponents[] = + { + /* Valid private values for Curve25519. In a build with Curve448 + * but not Curve25519, they will be adjusted in + * self_test_adjust_exponent(). */ + "4000000000000000000000000000000000000000000000000000000000000000", + "5C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C30", + "5715ECCE24583F7A7023C24164390586842E816D7280A49EF6DF4EAE6B280BF8", + "41A2B017516F6D254E1F002BCCBADD54BE30F8CEC737A0E912B4963B6BA74460", + "5555555555555555555555555555555555555555555555555555555555555550", + "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF8", + }; +#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ + + mbedtls_ecp_group_init( &grp ); + mbedtls_ecp_point_init( &R ); + mbedtls_ecp_point_init( &P ); + mbedtls_mpi_init( &m ); + +#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) + /* Use secp192r1 if available, or any available curve */ +#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) + MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) ); +#else + MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) ); +#endif + + if( verbose != 0 ) + mbedtls_printf( " ECP SW test #1 (constant op_count, base point G): " ); + /* Do a dummy multiplication first to trigger precomputation */ + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) ); + MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) ); + ret = self_test_point( verbose, + &grp, &R, &m, &grp.G, + sw_exponents, + sizeof( sw_exponents ) / sizeof( sw_exponents[0] )); + if( ret != 0 ) + goto cleanup; + + if( verbose != 0 ) + mbedtls_printf( " ECP SW test #2 (constant op_count, other point): " ); + /* We computed P = 2G last time, use it */ + ret = self_test_point( verbose, + &grp, &R, &m, &P, + sw_exponents, + sizeof( sw_exponents ) / sizeof( sw_exponents[0] )); + if( ret != 0 ) + goto cleanup; + + mbedtls_ecp_group_free( &grp ); + mbedtls_ecp_point_free( &R ); +#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ + +#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) + if( verbose != 0 ) + mbedtls_printf( " ECP Montgomery test (constant op_count): " ); +#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) + MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_CURVE25519 ) ); +#elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) + MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_CURVE448 ) ); +#else +#error "MBEDTLS_ECP_MONTGOMERY_ENABLED is defined, but no curve is supported for self-test" +#endif + ret = self_test_point( verbose, + &grp, &R, &m, &grp.G, + m_exponents, + sizeof( m_exponents ) / sizeof( m_exponents[0] )); + if( ret != 0 ) + goto cleanup; +#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ + +cleanup: + + if( ret < 0 && verbose != 0 ) + mbedtls_printf( "Unexpected error, return code = %08X\n", (unsigned int) ret ); + + mbedtls_ecp_group_free( &grp ); + mbedtls_ecp_point_free( &R ); + mbedtls_ecp_point_free( &P ); + mbedtls_mpi_free( &m ); + + if( verbose != 0 ) + mbedtls_printf( "\n" ); + + return( ret ); +} + +#endif /* MBEDTLS_SELF_TEST */ + +#endif /* !MBEDTLS_ECP_ALT */ + +#endif /* MBEDTLS_ECP_C */ |