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, 0 insertions, 3605 deletions
diff --git a/lib/mbedtls-2.27.0/library/ecp.c b/lib/mbedtls-2.27.0/library/ecp.c deleted file mode 100644 index ca49f99..0000000 --- a/lib/mbedtls-2.27.0/library/ecp.c +++ /dev/null @@ -1,3605 +0,0 @@ -/* - * 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 */ |