| /* |
| * 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 <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 §5 */ |
| 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 ) ) |
| |
| 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 ); |
| } |
| |
| /* |
| * 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 ); |
| } |
| |
| 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 ); |
| } |
| |
| #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; |
| int count = 0; |
| size_t p_size = ( grp->pbits + 7 ) / 8; |
| |
| mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll ); |
| |
| /* Generate l such that 1 < l < p */ |
| do |
| { |
| MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) ); |
| |
| while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 ) |
| MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) ); |
| |
| if( count++ > 10 ) |
| { |
| ret = MBEDTLS_ERR_ECP_RANDOM_FAILED; |
| goto cleanup; |
| } |
| } |
| while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 ); |
| |
| /* 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 ); |
| |
| 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; |
| int count = 0; |
| size_t p_size = ( grp->pbits + 7 ) / 8; |
| mbedtls_mpi_init( &l ); |
| |
| /* Generate l such that 1 < l < p */ |
| do |
| { |
| MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) ); |
| |
| while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 ) |
| MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) ); |
| |
| if( count++ > 10 ) |
| { |
| ret = MBEDTLS_ERR_ECP_RANDOM_FAILED; |
| goto cleanup; |
| } |
| } |
| while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 ); |
| |
| 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 ); |
| |
| 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 == 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, 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) |
| /* |
| * 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 ); |
| |
| return( 0 ); |
| } |
| #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 ); |
| } |
| |
| /* |
| * 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 ) |
| { |
| int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; |
| size_t n_size; |
| |
| ECP_VALIDATE_RET( grp != NULL ); |
| ECP_VALIDATE_RET( d != NULL ); |
| ECP_VALIDATE_RET( f_rng != NULL ); |
| |
| n_size = ( grp->nbits + 7 ) / 8; |
| |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) |
| { |
| /* [M225] page 5 */ |
| size_t b; |
| |
| do { |
| MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) ); |
| } while( mbedtls_mpi_bitlen( d ) == 0); |
| |
| /* Make sure the most significant bit is nbits */ |
| b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */ |
| if( b > grp->nbits ) |
| |