/* * 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. * * * [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. * */ #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 "bn_mul.h" #include "ecp_invasive.h" #include #if !defined(MBEDTLS_ECP_ALT) #include "mbedtls/platform.h" #include "ecp_internal_alt.h" #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_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; }; /* * 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; } /* * 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 ); } 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 ) { 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 ) { 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 */ static void mpi_init_many( mbedtls_mpi *arr, size_t size ) { while( size-- ) mbedtls_mpi_init( arr++ ); } static void mpi_free_many( mbedtls_mpi *arr, size_t size ) { while( size-- ) mbedtls_mpi_free( arr++ ); } /* * 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. * * Reminder: update profiles in x509_crt.c and ssl_tls.c when adding a new curve! */ 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 ) { 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 ) { 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 ) { 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 ) ); } /* * Check that the comb table (grp->T) is static initialized. */ static int ecp_group_is_static_comb_table( const mbedtls_ecp_group *grp ) { #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1 return grp->T != NULL && grp->T_size == 0; #else (void) grp; return 0; #endif } /* * 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( !ecp_group_is_static_comb_table(grp) && 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; 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 ) { 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; 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 ) { 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 ) { 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; 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; if( format != MBEDTLS_ECP_PF_UNCOMPRESSED && format != MBEDTLS_ECP_PF_COMPRESSED ) return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); 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; if( ilen < 1 ) return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); plen = mbedtls_mpi_size( &grp->P ); #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) { if( plen != ilen ) return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &pt->X, buf, plen ) ); mbedtls_mpi_free( &pt->Y ); if( grp->id == MBEDTLS_ECP_DP_CURVE25519 ) /* Set most significant bit to 0 as prescribed in RFC7748 ยง5 */ MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &pt->X, plen * 8 - 1, 0 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) ); } #endif #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) { if( buf[0] == 0x00 ) { if( ilen == 1 ) return( mbedtls_ecp_set_zero( pt ) ); else return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); } if( buf[0] != 0x04 ) return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); if( ilen != 2 * plen + 1 ) return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, buf + 1 + plen, plen ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) ); } #endif cleanup: return( ret ); } /* * Import a point from a TLS ECPoint record (RFC 4492) * struct { * opaque point <1..2^8-1>; * } ECPoint; */ int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt, const unsigned char **buf, size_t buf_len ) { unsigned char data_len; const unsigned char *buf_start; /* * 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; if( format != MBEDTLS_ECP_PF_UNCOMPRESSED && format != MBEDTLS_ECP_PF_COMPRESSED ) return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); /* * 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; 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; /* * 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; 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 */ MBEDTLS_PUT_UINT16_BE( curve_info->tls_id, buf, 0 ); 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 ) \ do { \ while( (N)->s < 0 && mbedtls_mpi_cmp_int( (N), 0 ) != 0 ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( (N), (N), &grp->P ) ); \ } while( 0 ) #if ( defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \ !( defined(MBEDTLS_ECP_NO_FALLBACK) && \ defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \ defined(MBEDTLS_ECP_ADD_MIXED_ALT) ) ) || \ ( defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) && \ !( defined(MBEDTLS_ECP_NO_FALLBACK) && \ defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) ) ) static inline int mbedtls_mpi_sub_mod( const mbedtls_ecp_group *grp, mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ) { int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( X, A, B ) ); MOD_SUB( X ); cleanup: return( ret ); } #endif /* All functions referencing mbedtls_mpi_sub_mod() are alt-implemented without fallback */ /* * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int. * We known P, N and the result are positive, so sub_abs is correct, and * a bit faster. */ #define MOD_ADD( N ) \ while( mbedtls_mpi_cmp_mpi( (N), &grp->P ) >= 0 ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( (N), (N), &grp->P ) ) static inline int mbedtls_mpi_add_mod( const mbedtls_ecp_group *grp, mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ) { int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, A, B ) ); MOD_ADD( X ); cleanup: return( ret ); } static inline int mbedtls_mpi_mul_int_mod( const mbedtls_ecp_group *grp, mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint c ) { int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( X, A, c ) ); MOD_ADD( X ); cleanup: return( ret ); } static inline int mbedtls_mpi_sub_int_mod( const mbedtls_ecp_group *grp, mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint c ) { int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( X, A, c ) ); MOD_SUB( X ); cleanup: return( ret ); } #define MPI_ECP_SUB_INT( X, A, c ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int_mod( grp, X, A, c ) ) #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \ !( defined(MBEDTLS_ECP_NO_FALLBACK) && \ defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \ defined(MBEDTLS_ECP_ADD_MIXED_ALT) ) static inline int mbedtls_mpi_shift_l_mod( const mbedtls_ecp_group *grp, mbedtls_mpi *X, size_t count ) { int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( X, count ) ); MOD_ADD( X ); cleanup: return( ret ); } #endif /* All functions referencing mbedtls_mpi_shift_l_mod() are alt-implemented without fallback */ /* * Macro wrappers around ECP modular arithmetic * * Currently, these wrappers are defined via the bignum module. */ #define MPI_ECP_ADD( X, A, B ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, X, A, B ) ) #define MPI_ECP_SUB( X, A, B ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, X, A, B ) ) #define MPI_ECP_MUL( X, A, B ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, X, A, B ) ) #define MPI_ECP_SQR( X, A ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, X, A, A ) ) #define MPI_ECP_MUL_INT( X, A, c ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int_mod( grp, X, A, c ) ) #define MPI_ECP_INV( dst, src ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( (dst), (src), &grp->P ) ) #define MPI_ECP_MOV( X, A ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) ) #define MPI_ECP_SHIFT_L( X, count ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, X, count ) ) #define MPI_ECP_LSET( X, c ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, c ) ) #define MPI_ECP_CMP_INT( X, c ) \ mbedtls_mpi_cmp_int( X, c ) #define MPI_ECP_CMP( X, Y ) \ mbedtls_mpi_cmp_mpi( X, Y ) /* Needs f_rng, p_rng to be defined. */ #define MPI_ECP_RAND( X ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_random( (X), 2, &grp->P, f_rng, p_rng ) ) /* Conditional negation * Needs grp and a temporary MPI tmp to be defined. */ #define MPI_ECP_COND_NEG( X, cond ) \ do \ { \ unsigned char nonzero = mbedtls_mpi_cmp_int( (X), 0 ) != 0; \ MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &tmp, &grp->P, (X) ) ); \ MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( (X), &tmp, \ nonzero & cond ) ); \ } while( 0 ) #define MPI_ECP_NEG( X ) MPI_ECP_COND_NEG( (X), 1 ) #define MPI_ECP_VALID( X ) \ ( (X)->p != NULL ) #define MPI_ECP_COND_ASSIGN( X, Y, cond ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( (X), (Y), (cond) ) ) #define MPI_ECP_COND_SWAP( X, Y, cond ) \ MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( (X), (Y), (cond) ) ) #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 countermeasures 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( MPI_ECP_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 T; mbedtls_mpi_init( &T ); MPI_ECP_INV( &T, &pt->Z ); /* T <- 1 / Z */ MPI_ECP_MUL( &pt->Y, &pt->Y, &T ); /* Y' <- Y*T = Y / Z */ MPI_ECP_SQR( &T, &T ); /* T <- T^2 = 1 / Z^2 */ MPI_ECP_MUL( &pt->X, &pt->X, &T ); /* X <- X * T = X / Z^2 */ MPI_ECP_MUL( &pt->Y, &pt->Y, &T ); /* Y'' <- Y' * T = Y / Z^3 */ MPI_ECP_LSET( &pt->Z, 1 ); cleanup: mbedtls_mpi_free( &T ); 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, t; if( ( c = mbedtls_calloc( T_size, sizeof( mbedtls_mpi ) ) ) == NULL ) return( MBEDTLS_ERR_ECP_ALLOC_FAILED ); mbedtls_mpi_init( &t ); mpi_init_many( c, T_size ); /* * c[i] = Z_0 * ... * Z_i, i = 0,..,n := T_size-1 */ MPI_ECP_MOV( &c[0], &T[0]->Z ); for( i = 1; i < T_size; i++ ) { MPI_ECP_MUL( &c[i], &c[i-1], &T[i]->Z ); } /* * c[n] = 1 / (Z_0 * ... * Z_n) mod P */ MPI_ECP_INV( &c[T_size-1], &c[T_size-1] ); for( i = T_size - 1; ; i-- ) { /* At the start of iteration i (note that i decrements), we have * - c[j] = Z_0 * .... * Z_j for j < i, * - c[j] = 1 / (Z_0 * .... * Z_j) for j == i, * * This is maintained via * - c[i-1] <- c[i] * Z_i * * We also derive 1/Z_i = c[i] * c[i-1] for i>0 and use that * to do the actual normalization. For i==0, we already have * c[0] = 1 / Z_0. */ if( i > 0 ) { /* Compute 1/Z_i and establish invariant for the next iteration. */ MPI_ECP_MUL( &t, &c[i], &c[i-1] ); MPI_ECP_MUL( &c[i-1], &c[i], &T[i]->Z ); } else { MPI_ECP_MOV( &t, &c[0] ); } /* Now t holds 1 / Z_i; normalize as in ecp_normalize_jac() */ MPI_ECP_MUL( &T[i]->Y, &T[i]->Y, &t ); MPI_ECP_SQR( &t, &t ); MPI_ECP_MUL( &T[i]->X, &T[i]->X, &t ); MPI_ECP_MUL( &T[i]->Y, &T[i]->Y, &t ); /* * 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 ) ); MPI_ECP_LSET( &T[i]->Z, 1 ); if( i == 0 ) break; } cleanup: mbedtls_mpi_free( &t ); mpi_free_many( c, T_size ); 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; mbedtls_mpi tmp; mbedtls_mpi_init( &tmp ); MPI_ECP_COND_NEG( &Q->Y, inv ); cleanup: mbedtls_mpi_free( &tmp ); 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, mbedtls_mpi tmp[4] ) { #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; /* Special case for A = -3 */ if( grp->A.p == NULL ) { /* tmp[0] <- M = 3(X + Z^2)(X - Z^2) */ MPI_ECP_SQR( &tmp[1], &P->Z ); MPI_ECP_ADD( &tmp[2], &P->X, &tmp[1] ); MPI_ECP_SUB( &tmp[3], &P->X, &tmp[1] ); MPI_ECP_MUL( &tmp[1], &tmp[2], &tmp[3] ); MPI_ECP_MUL_INT( &tmp[0], &tmp[1], 3 ); } else { /* tmp[0] <- M = 3.X^2 + A.Z^4 */ MPI_ECP_SQR( &tmp[1], &P->X ); MPI_ECP_MUL_INT( &tmp[0], &tmp[1], 3 ); /* Optimize away for "koblitz" curves with A = 0 */ if( MPI_ECP_CMP_INT( &grp->A, 0 ) != 0 ) { /* M += A.Z^4 */ MPI_ECP_SQR( &tmp[1], &P->Z ); MPI_ECP_SQR( &tmp[2], &tmp[1] ); MPI_ECP_MUL( &tmp[1], &tmp[2], &grp->A ); MPI_ECP_ADD( &tmp[0], &tmp[0], &tmp[1] ); } } /* tmp[1] <- S = 4.X.Y^2 */ MPI_ECP_SQR( &tmp[2], &P->Y ); MPI_ECP_SHIFT_L( &tmp[2], 1 ); MPI_ECP_MUL( &tmp[1], &P->X, &tmp[2] ); MPI_ECP_SHIFT_L( &tmp[1], 1 ); /* tmp[3] <- U = 8.Y^4 */ MPI_ECP_SQR( &tmp[3], &tmp[2] ); MPI_ECP_SHIFT_L( &tmp[3], 1 ); /* tmp[2] <- T = M^2 - 2.S */ MPI_ECP_SQR( &tmp[2], &tmp[0] ); MPI_ECP_SUB( &tmp[2], &tmp[2], &tmp[1] ); MPI_ECP_SUB( &tmp[2], &tmp[2], &tmp[1] ); /* tmp[1] <- S = M(S - T) - U */ MPI_ECP_SUB( &tmp[1], &tmp[1], &tmp[2] ); MPI_ECP_MUL( &tmp[1], &tmp[1], &tmp[0] ); MPI_ECP_SUB( &tmp[1], &tmp[1], &tmp[3] ); /* tmp[3] <- U = 2.Y.Z */ MPI_ECP_MUL( &tmp[3], &P->Y, &P->Z ); MPI_ECP_SHIFT_L( &tmp[3], 1 ); /* Store results */ MPI_ECP_MOV( &R->X, &tmp[2] ); MPI_ECP_MOV( &R->Y, &tmp[1] ); MPI_ECP_MOV( &R->Z, &tmp[3] ); cleanup: 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. * * P,Q,R may alias, but only at the level of EC points: they must be either * equal as pointers, or disjoint (including the coordinate data buffers). * Fine-grained aliasing at the level of coordinates is not supported. * * 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. * * 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, mbedtls_mpi tmp[4] ) { #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; /* NOTE: Aliasing between input and output is allowed, so one has to make * sure that at the point X,Y,Z are written, {P,Q}->{X,Y,Z} are no * longer read from. */ mbedtls_mpi * const X = &R->X; mbedtls_mpi * const Y = &R->Y; mbedtls_mpi * const Z = &R->Z; if( !MPI_ECP_VALID( &Q->Z ) ) return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); /* * Trivial cases: P == 0 or Q == 0 (case 1) */ if( MPI_ECP_CMP_INT( &P->Z, 0 ) == 0 ) return( mbedtls_ecp_copy( R, Q ) ); if( MPI_ECP_CMP_INT( &Q->Z, 0 ) == 0 ) return( mbedtls_ecp_copy( R, P ) ); /* * Make sure Q coordinates are normalized */ if( MPI_ECP_CMP_INT( &Q->Z, 1 ) != 0 ) return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); MPI_ECP_SQR( &tmp[0], &P->Z ); MPI_ECP_MUL( &tmp[1], &tmp[0], &P->Z ); MPI_ECP_MUL( &tmp[0], &tmp[0], &Q->X ); MPI_ECP_MUL( &tmp[1], &tmp[1], &Q->Y ); MPI_ECP_SUB( &tmp[0], &tmp[0], &P->X ); MPI_ECP_SUB( &tmp[1], &tmp[1], &P->Y ); /* Special cases (2) and (3) */ if( MPI_ECP_CMP_INT( &tmp[0], 0 ) == 0 ) { if( MPI_ECP_CMP_INT( &tmp[1], 0 ) == 0 ) { ret = ecp_double_jac( grp, R, P, tmp ); goto cleanup; } else { ret = mbedtls_ecp_set_zero( R ); goto cleanup; } } /* {P,Q}->Z no longer used, so OK to write to Z even if there's aliasing. */ MPI_ECP_MUL( Z, &P->Z, &tmp[0] ); MPI_ECP_SQR( &tmp[2], &tmp[0] ); MPI_ECP_MUL( &tmp[3], &tmp[2], &tmp[0] ); MPI_ECP_MUL( &tmp[2], &tmp[2], &P->X ); MPI_ECP_MOV( &tmp[0], &tmp[2] ); MPI_ECP_SHIFT_L( &tmp[0], 1 ); /* {P,Q}->X no longer used, so OK to write to X even if there's aliasing. */ MPI_ECP_SQR( X, &tmp[1] ); MPI_ECP_SUB( X, X, &tmp[0] ); MPI_ECP_SUB( X, X, &tmp[3] ); MPI_ECP_SUB( &tmp[2], &tmp[2], X ); MPI_ECP_MUL( &tmp[2], &tmp[2], &tmp[1] ); MPI_ECP_MUL( &tmp[3], &tmp[3], &P->Y ); /* {P,Q}->Y no longer used, so OK to write to Y even if there's aliasing. */ MPI_ECP_SUB( Y, &tmp[2], &tmp[3] ); cleanup: 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; mbedtls_mpi_init( &l ); /* Generate l such that 1 < l < p */ MPI_ECP_RAND( &l ); /* Z' = l * Z */ MPI_ECP_MUL( &pt->Z, &pt->Z, &l ); /* Y' = l * Y */ MPI_ECP_MUL( &pt->Y, &pt->Y, &l ); /* X' = l^2 * X */ MPI_ECP_SQR( &l, &l ); MPI_ECP_MUL( &pt->X, &pt->X, &l ); /* Y'' = l^2 * Y' = l^3 * Y */ MPI_ECP_MUL( &pt->Y, &pt->Y, &l ); cleanup: mbedtls_mpi_free( &l ); if( ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE ) ret = MBEDTLS_ERR_ECP_RANDOM_FAILED; return( ret ); #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_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] = {NULL}; mbedtls_mpi tmp[4]; mpi_init_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) ); #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, tmp ) ); } #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 to allow them to be used in * ecp_add_mixed() below, which requires one normalized input. * * 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], tmp ) ); } #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 ) ); /* Free Z coordinate (=1 after normalization) to save RAM. * This makes T[i] invalid as mbedtls_ecp_points, but this is OK * since from this point onwards, they are only accessed indirectly * via the getter function ecp_select_comb() which does set the * target's Z coordinate to 1. */ for( i = 0; i < T_size; i++ ) mbedtls_mpi_free( &T[i].Z ); cleanup: mpi_free_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) ); #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++ ) { MPI_ECP_COND_ASSIGN( &R->X, &T[j].X, j == ii ); MPI_ECP_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 ) ); MPI_ECP_LSET( &R->Z, 1 ); 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; mbedtls_mpi tmp[4]; size_t i; mbedtls_ecp_point_init( &Txi ); mpi_init_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) ); #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] ) ); if( f_rng != 0 ) 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, tmp ) ); MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, T_size, x[i] ) ); MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi, tmp ) ); } cleanup: mbedtls_ecp_point_free( &Txi ); mpi_free_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) ); #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( f_rng != 0 ) 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++; /* * If static comb table may not be used (!p_eq_g) or static comb table does * not exists, make sure w is within bounds. * (The last test is useful only for very small curves in the test suite.) * * The user reduces MBEDTLS_ECP_WINDOW_SIZE does not changes the size of * static comb table, because the size of static comb table is fixed when * it is generated. */ #if( MBEDTLS_ECP_WINDOW_SIZE < 6 ) if( (!p_eq_g || !ecp_group_is_static_comb_table(grp)) && 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 transfer, 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; ECP_RS_ENTER( rsm ); /* Is P the base point ? */ #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1 p_eq_g = ( MPI_ECP_CMP( &P->Y, &grp->G.Y ) == 0 && MPI_ECP_CMP( &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: /* 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 ); } /* prevent caller from using invalid value */ int should_free_R = ( ret != 0 ); #if defined(MBEDTLS_ECP_RESTARTABLE) /* don't free R while in progress in case R == P */ if( ret == MBEDTLS_ERR_ECP_IN_PROGRESS ) should_free_R = 0; #endif if( should_free_R ) 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 * internally 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; MPI_ECP_INV( &P->Z, &P->Z ); MPI_ECP_MUL( &P->X, &P->X, &P->Z ); MPI_ECP_LSET( &P->Z, 1 ); cleanup: return( ret ); #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) */ } /* * Randomize projective x/z coordinates: * (X, Z) -> (l X, l Z) for random l * This is sort of the reverse operation of ecp_normalize_mxz(). * * This countermeasure was first suggested in [2]. * Cost: 2M */ static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) { #if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) if( mbedtls_internal_ecp_grp_capable( grp ) ) return( mbedtls_internal_ecp_randomize_mxz( grp, P, f_rng, p_rng ) ); #endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */ #if defined(MBEDTLS_ECP_NO_FALLBACK) && defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); #else int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; mbedtls_mpi l; mbedtls_mpi_init( &l ); /* Generate l such that 1 < l < p */ MPI_ECP_RAND( &l ); MPI_ECP_MUL( &P->X, &P->X, &l ); MPI_ECP_MUL( &P->Z, &P->Z, &l ); cleanup: mbedtls_mpi_free( &l ); if( ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE ) ret = MBEDTLS_ERR_ECP_RANDOM_FAILED; return( ret ); #endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) */ } /* * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q), * for Montgomery curves in x/z coordinates. * * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3 * with * d = X1 * P = (X2, Z2) * Q = (X3, Z3) * R = (X4, Z4) * S = (X5, Z5) * and eliminating temporary variables tO, ..., t4. * * Cost: 5M + 4S */ static int ecp_double_add_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, mbedtls_ecp_point *S, const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q, const mbedtls_mpi *d, mbedtls_mpi T[4] ) { #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; MPI_ECP_ADD( &T[0], &P->X, &P->Z ); /* Pp := PX + PZ */ MPI_ECP_SUB( &T[1], &P->X, &P->Z ); /* Pm := PX - PZ */ MPI_ECP_ADD( &T[2], &Q->X, &Q->Z ); /* Qp := QX + XZ */ MPI_ECP_SUB( &T[3], &Q->X, &Q->Z ); /* Qm := QX - QZ */ MPI_ECP_MUL( &T[3], &T[3], &T[0] ); /* Qm * Pp */ MPI_ECP_MUL( &T[2], &T[2], &T[1] ); /* Qp * Pm */ MPI_ECP_SQR( &T[0], &T[0] ); /* Pp^2 */ MPI_ECP_SQR( &T[1], &T[1] ); /* Pm^2 */ MPI_ECP_MUL( &R->X, &T[0], &T[1] ); /* Pp^2 * Pm^2 */ MPI_ECP_SUB( &T[0], &T[0], &T[1] ); /* Pp^2 - Pm^2 */ MPI_ECP_MUL( &R->Z, &grp->A, &T[0] ); /* A * (Pp^2 - Pm^2) */ MPI_ECP_ADD( &R->Z, &T[1], &R->Z ); /* [ A * (Pp^2-Pm^2) ] + Pm^2 */ MPI_ECP_ADD( &S->X, &T[3], &T[2] ); /* Qm*Pp + Qp*Pm */ MPI_ECP_SQR( &S->X, &S->X ); /* (Qm*Pp + Qp*Pm)^2 */ MPI_ECP_SUB( &S->Z, &T[3], &T[2] ); /* Qm*Pp - Qp*Pm */ MPI_ECP_SQR( &S->Z, &S->Z ); /* (Qm*Pp - Qp*Pm)^2 */ MPI_ECP_MUL( &S->Z, d, &S->Z ); /* d * ( Qm*Pp - Qp*Pm )^2 */ MPI_ECP_MUL( &R->Z, &T[0], &R->Z ); /* [A*(Pp^2-Pm^2)+Pm^2]*(Pp^2-Pm^2) */ cleanup: 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; mbedtls_mpi tmp[4]; mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX ); mpi_init_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) ); if( f_rng == NULL ) return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); /* Save PX and read from P before writing to R, in case P == R */ MPI_ECP_MOV( &PX, &P->X ); MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) ); /* Set R to zero in modified x/z coordinates */ MPI_ECP_LSET( &R->X, 1 ); MPI_ECP_LSET( &R->Z, 0 ); mbedtls_mpi_free( &R->Y ); /* RP.X might be slightly larger than P, so reduce it */ MOD_ADD( &RP.X ); /* Randomize coordinates of the starting point */ MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) ); /* Loop invariant: R = result so far, RP = R + P */ i = grp->nbits + 1; /* one past the (zero-based) required msb for private keys */ 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 */ MPI_ECP_COND_SWAP( &R->X, &RP.X, b ); MPI_ECP_COND_SWAP( &R->Z, &RP.Z, b ); MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX, tmp ) ); MPI_ECP_COND_SWAP( &R->X, &RP.X, b ); MPI_ECP_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. */ MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, R, f_rng, p_rng ) ); MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) ); cleanup: mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX ); mpi_free_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) ); return( ret ); } #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ /* * Restartable multiplication R = m * P * * This internal function can be called without an RNG in case where we know * the inputs are not sensitive. */ static int ecp_mul_restartable_internal( 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 #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 */ int restarting = 0; #if defined(MBEDTLS_ECP_RESTARTABLE) restarting = ( rs_ctx != NULL && rs_ctx->rsm != NULL ); #endif /* skip argument check when restarting */ if( !restarting ) { /* 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 ); } /* * 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 ) { if( f_rng == NULL ) return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); return( ecp_mul_restartable_internal( grp, R, m, P, f_rng, p_rng, rs_ctx ) ); } /* * 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 ) { 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 */ MPI_ECP_SQR( &YY, &pt->Y ); MPI_ECP_SQR( &RHS, &pt->X ); /* Special case for A = -3 */ if( grp->A.p == NULL ) { MPI_ECP_SUB_INT( &RHS, &RHS, 3 ); } else { MPI_ECP_ADD( &RHS, &RHS, &grp->A ); } MPI_ECP_MUL( &RHS, &RHS, &pt->X ); MPI_ECP_ADD( &RHS, &RHS, &grp->B ); if( MPI_ECP_CMP( &YY, &RHS ) != 0 ) ret = MBEDTLS_ERR_ECP_INVALID_KEY; cleanup: mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS ); return( ret ); } #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) /* * R = m * P with shortcuts for m == 0, m == 1 and m == -1 * NOT constant-time - ONLY for short Weierstrass! */ static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, const mbedtls_mpi *m, const mbedtls_ecp_point *P, mbedtls_ecp_restart_ctx *rs_ctx ) { int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; mbedtls_mpi tmp; mbedtls_mpi_init( &tmp ); if( mbedtls_mpi_cmp_int( m, 0 ) == 0 ) { MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, P ) ); MBEDTLS_MPI_CHK( mbedtls_ecp_set_zero( R ) ); } else if( mbedtls_mpi_cmp_int( m, 1 ) == 0 ) { MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, P ) ); MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) ); } else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 ) { MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, P ) ); MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) ); MPI_ECP_NEG( &R->Y ); } else { MBEDTLS_MPI_CHK( ecp_mul_restartable_internal( grp, R, m, P, NULL, NULL, rs_ctx ) ); } cleanup: mbedtls_mpi_free( &tmp ); 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; mbedtls_mpi tmp[4]; #if defined(MBEDTLS_ECP_INTERNAL_ALT) char is_grp_capable = 0; #endif if( mbedtls_ecp_get_type( grp ) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); mbedtls_ecp_point_init( &mP ); mpi_init_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) ); 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, tmp ) ); #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: mpi_free_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) ); #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 ) { return( mbedtls_ecp_muladd_restartable( grp, R, m, P, n, Q, NULL ) ); } #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) #define ECP_MPI_INIT(s, n, p) {s, (n), (mbedtls_mpi_uint *)(p)} #define ECP_MPI_INIT_ARRAY(x) \ ECP_MPI_INIT(1, sizeof(x) / sizeof(mbedtls_mpi_uint), x) /* * Constants for the two points other than 0, 1, -1 (mod p) in * https://cr.yp.to/ecdh.html#validate * See ecp_check_pubkey_x25519(). */ static const mbedtls_mpi_uint x25519_bad_point_1[] = { MBEDTLS_BYTES_TO_T_UINT_8( 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae ), MBEDTLS_BYTES_TO_T_UINT_8( 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a ), MBEDTLS_BYTES_TO_T_UINT_8( 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd ), MBEDTLS_BYTES_TO_T_UINT_8( 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00 ), }; static const mbedtls_mpi_uint x25519_bad_point_2[] = { MBEDTLS_BYTES_TO_T_UINT_8( 0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24 ), MBEDTLS_BYTES_TO_T_UINT_8( 0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b ), MBEDTLS_BYTES_TO_T_UINT_8( 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86 ), MBEDTLS_BYTES_TO_T_UINT_8( 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57 ), }; static const mbedtls_mpi ecp_x25519_bad_point_1 = ECP_MPI_INIT_ARRAY( x25519_bad_point_1 ); static const mbedtls_mpi ecp_x25519_bad_point_2 = ECP_MPI_INIT_ARRAY( x25519_bad_point_2 ); #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ /* * Check that the input point is not one of the low-order points. * This is recommended by the "May the Fourth" paper: * https://eprint.iacr.org/2017/806.pdf * Those points are never sent by an honest peer. */ static int ecp_check_bad_points_mx( const mbedtls_mpi *X, const mbedtls_mpi *P, const mbedtls_ecp_group_id grp_id ) { int ret; mbedtls_mpi XmP; mbedtls_mpi_init( &XmP ); /* Reduce X mod P so that we only need to check values less than P. * We know X < 2^256 so we can proceed by subtraction. */ MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &XmP, X ) ); while( mbedtls_mpi_cmp_mpi( &XmP, P ) >= 0 ) MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &XmP, &XmP, P ) ); /* Check against the known bad values that are less than P. For Curve448 * these are 0, 1 and -1. For Curve25519 we check the values less than P * from the following list: https://cr.yp.to/ecdh.html#validate */ if( mbedtls_mpi_cmp_int( &XmP, 1 ) <= 0 ) /* takes care of 0 and 1 */ { ret = MBEDTLS_ERR_ECP_INVALID_KEY; goto cleanup; } #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) if( grp_id == MBEDTLS_ECP_DP_CURVE25519 ) { if( mbedtls_mpi_cmp_mpi( &XmP, &ecp_x25519_bad_point_1 ) == 0 ) { ret = MBEDTLS_ERR_ECP_INVALID_KEY; goto cleanup; } if( mbedtls_mpi_cmp_mpi( &XmP, &ecp_x25519_bad_point_2 ) == 0 ) { ret = MBEDTLS_ERR_ECP_INVALID_KEY; goto cleanup; } } #else (void) grp_id; #endif /* Final check: check if XmP + 1 is P (final because it changes XmP!) */ MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &XmP, &XmP, 1 ) ); if( mbedtls_mpi_cmp_mpi( &XmP, P ) == 0 ) { ret = MBEDTLS_ERR_ECP_INVALID_KEY; goto cleanup; } ret = 0; cleanup: mbedtls_mpi_free( &XmP ); return( ret ); } /* * Check validity of a public key for Montgomery curves with x-only schemes */ static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt ) { /* [Curve25519 p. 5] Just check X is the correct number of bytes */ /* Allow any public value, if it's too big then we'll just reduce it mod p * (RFC 7748 sec. 5 para. 3). */ if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 ) return( MBEDTLS_ERR_ECP_INVALID_KEY ); /* Implicit in all standards (as they don't consider negative numbers): * X must be non-negative. This is normally ensured by the way it's * encoded for transmission, but let's be extra sure. */ if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ) return( MBEDTLS_ERR_ECP_INVALID_KEY ); return( ecp_check_bad_points_mx( &pt->X, &grp->P, grp->id ) ); } #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ /* * Check that a point is valid as a public key */ int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt ) { /* 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 ) { #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) { /* see RFC 7748 sec. 5 para. 5 */ if( mbedtls_mpi_get_bit( d, 0 ) != 0 || mbedtls_mpi_get_bit( d, 1 ) != 0 || mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */ return( MBEDTLS_ERR_ECP_INVALID_KEY ); /* see [Curve25519] page 5 */ if( grp->nbits == 254 && mbedtls_mpi_get_bit( d, 2 ) != 0 ) return( MBEDTLS_ERR_ECP_INVALID_KEY ); return( 0 ); } #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) { /* see SEC1 3.2 */ if( mbedtls_mpi_cmp_int( d, 1 ) < 0 || mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 ) return( MBEDTLS_ERR_ECP_INVALID_KEY ); else return( 0 ); } #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); } #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) MBEDTLS_STATIC_TESTABLE int mbedtls_ecp_gen_privkey_mx( size_t high_bit, mbedtls_mpi *d, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) { int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; size_t n_random_bytes = high_bit / 8 + 1; /* [Curve25519] page 5 */ /* Generate a (high_bit+1)-bit random number by generating just enough * random bytes, then shifting out extra bits from the top (necessary * when (high_bit+1) is not a multiple of 8). */ MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_random_bytes, f_rng, p_rng ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_random_bytes - high_bit - 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, high_bit, 1 ) ); /* Make sure the last two bits are unset for Curve448, three bits for Curve25519 */ MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) ); if( high_bit == 254 ) { MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) ); } cleanup: return( ret ); } #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) static int mbedtls_ecp_gen_privkey_sw( const mbedtls_mpi *N, mbedtls_mpi *d, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) { int ret = mbedtls_mpi_random( d, 1, N, f_rng, p_rng ); switch( ret ) { case MBEDTLS_ERR_MPI_NOT_ACCEPTABLE: return( MBEDTLS_ERR_ECP_RANDOM_FAILED ); default: return( ret ); } } #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ /* * Generate a private key */ int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp, mbedtls_mpi *d, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) { #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) return( mbedtls_ecp_gen_privkey_mx( grp->nbits, d, f_rng, p_rng ) ); #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) return( mbedtls_ecp_gen_privkey_sw( &grp->N, d, f_rng, p_rng ) ); #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); } /* * Generate a keypair with configurable base point */ int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp, const mbedtls_ecp_point *G, mbedtls_mpi *d, mbedtls_ecp_point *Q, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) { int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; MBEDTLS_MPI_CHK( mbedtls_ecp_gen_privkey( grp, d, f_rng, p_rng ) ); MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) ); cleanup: return( ret ); } /* * Generate key pair, wrapper for conventional base point */ int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, mbedtls_mpi *d, mbedtls_ecp_point *Q, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) { return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) ); } /* * Generate a keypair, prettier wrapper */ int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) { int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 ) return( ret ); return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) ); } #define ECP_CURVE25519_KEY_SIZE 32 #define ECP_CURVE448_KEY_SIZE 56 /* * Read a private key. */ int mbedtls_ecp_read_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, const unsigned char *buf, size_t buflen ) { int ret = 0; if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 ) return( ret ); ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) { /* * Mask the key as mandated by RFC7748 for Curve25519 and Curve448. */ if( grp_id == MBEDTLS_ECP_DP_CURVE25519 ) { if( buflen != ECP_CURVE25519_KEY_SIZE ) return( MBEDTLS_ERR_ECP_INVALID_KEY ); MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &key->d, buf, buflen ) ); /* Set the three least significant bits to 0 */ MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 0, 0 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 1, 0 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 2, 0 ) ); /* Set the most significant bit to 0 */ MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, ECP_CURVE25519_KEY_SIZE * 8 - 1, 0 ) ); /* Set the second most significant bit to 1 */ MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, ECP_CURVE25519_KEY_SIZE * 8 - 2, 1 ) ); } else if( grp_id == MBEDTLS_ECP_DP_CURVE448 ) { if( buflen != ECP_CURVE448_KEY_SIZE ) return( MBEDTLS_ERR_ECP_INVALID_KEY ); MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &key->d, buf, buflen ) ); /* Set the two least significant bits to 0 */ MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 0, 0 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 1, 0 ) ); /* Set the most significant bit to 1 */ MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, ECP_CURVE448_KEY_SIZE * 8 - 1, 1 ) ); } } #endif #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) { MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &key->d, buf, buflen ) ); MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( &key->grp, &key->d ) ); } #endif cleanup: if( ret != 0 ) mbedtls_mpi_free( &key->d ); return( ret ); } /* * Write a private key. */ int mbedtls_ecp_write_key( mbedtls_ecp_keypair *key, unsigned char *buf, size_t buflen ) { int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) { if( key->grp.id == MBEDTLS_ECP_DP_CURVE25519 ) { if( buflen < ECP_CURVE25519_KEY_SIZE ) return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); } else if( key->grp.id == MBEDTLS_ECP_DP_CURVE448 ) { if( buflen < ECP_CURVE448_KEY_SIZE ) return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); } MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary_le( &key->d, buf, buflen ) ); } #endif #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) { MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &key->d, buf, buflen ) ); } #endif cleanup: return( ret ); } /* * Check a public-private key pair */ int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) { int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; mbedtls_ecp_point Q; mbedtls_ecp_group grp; if( pub->grp.id == MBEDTLS_ECP_DP_NONE || pub->grp.id != prv->grp.id || mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) || mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) || mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) ) { return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); } mbedtls_ecp_point_init( &Q ); mbedtls_ecp_group_init( &grp ); /* mbedtls_ecp_mul() needs a non-const group... */ mbedtls_ecp_group_copy( &grp, &prv->grp ); /* Also checks d is valid */ MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, f_rng, p_rng ) ); if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) || mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) || mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) ) { ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; goto cleanup; } cleanup: mbedtls_ecp_point_free( &Q ); mbedtls_ecp_group_free( &grp ); return( ret ); } /* * Export generic key-pair parameters. */ int mbedtls_ecp_export(const mbedtls_ecp_keypair *key, mbedtls_ecp_group *grp, mbedtls_mpi *d, mbedtls_ecp_point *Q) { int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; if( ( ret = mbedtls_ecp_group_copy( grp, &key->grp ) ) != 0 ) return ret; if( ( ret = mbedtls_mpi_copy( d, &key->d ) ) != 0 ) return ret; if( ( ret = mbedtls_ecp_copy( Q, &key->Q ) ) != 0 ) return ret; return 0; } #if defined(MBEDTLS_SELF_TEST) /* * PRNG for test - !!!INSECURE NEVER USE IN PRODUCTION!!! * * This is the linear congruential generator from numerical recipes, * except we only use the low byte as the output. See * https://en.wikipedia.org/wiki/Linear_congruential_generator#Parameters_in_common_use */ static int self_test_rng( void *ctx, unsigned char *out, size_t len ) { static uint32_t state = 42; (void) ctx; for( size_t i = 0; i < len; i++ ) { state = state * 1664525u + 1013904223u; out[i] = (unsigned char) state; } return( 0 ); } /* Adjust the exponent to be a valid private point for the specified curve. * This is sometimes necessary because we use a single set of exponents * for all curves but the validity of values depends on the curve. */ static int self_test_adjust_exponent( const mbedtls_ecp_group *grp, mbedtls_mpi *m ) { int ret = 0; switch( grp->id ) { /* If Curve25519 is available, then that's what we use for the * Montgomery test, so we don't need the adjustment code. */ #if ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) case MBEDTLS_ECP_DP_CURVE448: /* Move highest bit from 254 to N-1. Setting bit N-1 is * necessary to enforce the highest-bit-set constraint. */ MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( m, 254, 0 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( m, grp->nbits, 1 ) ); /* Copy second-highest bit from 253 to N-2. This is not * necessary but improves the test variety a bit. */ MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( m, grp->nbits - 1, mbedtls_mpi_get_bit( m, 253 ) ) ); break; #endif #endif /* ! defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) */ default: /* Non-Montgomery curves and Curve25519 need no adjustment. */ (void) grp; (void) m; goto cleanup; } cleanup: return( ret ); } /* Calculate R = m.P for each m in exponents. Check that the number of * basic operations doesn't depend on the value of m. */ static int self_test_point( int verbose, mbedtls_ecp_group *grp, mbedtls_ecp_point *R, mbedtls_mpi *m, const mbedtls_ecp_point *P, const char *const *exponents, size_t n_exponents ) { int ret = 0; size_t i = 0; unsigned long add_c_prev, dbl_c_prev, mul_c_prev; add_count = 0; dbl_count = 0; mul_count = 0; MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( m, 16, exponents[0] ) ); MBEDTLS_MPI_CHK( self_test_adjust_exponent( grp, m ) ); MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, self_test_rng, NULL ) ); for( i = 1; i < n_exponents; i++ ) { add_c_prev = add_count; dbl_c_prev = dbl_count; mul_c_prev = mul_count; add_count = 0; dbl_count = 0; mul_count = 0; MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( m, 16, exponents[i] ) ); MBEDTLS_MPI_CHK( self_test_adjust_exponent( grp, m ) ); MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, self_test_rng, NULL ) ); if( add_count != add_c_prev || dbl_count != dbl_c_prev || mul_count != mul_c_prev ) { ret = 1; break; } } cleanup: if( verbose != 0 ) { if( ret != 0 ) mbedtls_printf( "failed (%u)\n", (unsigned int) i ); else mbedtls_printf( "passed\n" ); } return( ret ); } /* * Checkup routine */ int mbedtls_ecp_self_test( int verbose ) { int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; mbedtls_ecp_group grp; mbedtls_ecp_point R, P; mbedtls_mpi m; #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) /* Exponents especially adapted for secp192k1, which has the lowest * order n of all supported curves (secp192r1 is in a slightly larger * field but the order of its base point is slightly smaller). */ const char *sw_exponents[] = { "000000000000000000000000000000000000000000000001", /* one */ "FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8C", /* n - 1 */ "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */ "400000000000000000000000000000000000000000000000", /* one and zeros */ "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */ "555555555555555555555555555555555555555555555555", /* 101010... */ }; #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) const char *m_exponents[] = { /* Valid private values for Curve25519. In a build with Curve448 * but not Curve25519, they will be adjusted in * self_test_adjust_exponent(). */ "4000000000000000000000000000000000000000000000000000000000000000", "5C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C30", "5715ECCE24583F7A7023C24164390586842E816D7280A49EF6DF4EAE6B280BF8", "41A2B017516F6D254E1F002BCCBADD54BE30F8CEC737A0E912B4963B6BA74460", "5555555555555555555555555555555555555555555555555555555555555550", "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF8", }; #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ mbedtls_ecp_group_init( &grp ); mbedtls_ecp_point_init( &R ); mbedtls_ecp_point_init( &P ); mbedtls_mpi_init( &m ); #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) /* Use secp192r1 if available, or any available curve */ #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) ); #else MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) ); #endif if( verbose != 0 ) mbedtls_printf( " ECP SW test #1 (constant op_count, base point G): " ); /* Do a dummy multiplication first to trigger precomputation */ MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) ); MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, self_test_rng, NULL ) ); ret = self_test_point( verbose, &grp, &R, &m, &grp.G, sw_exponents, sizeof( sw_exponents ) / sizeof( sw_exponents[0] )); if( ret != 0 ) goto cleanup; if( verbose != 0 ) mbedtls_printf( " ECP SW test #2 (constant op_count, other point): " ); /* We computed P = 2G last time, use it */ ret = self_test_point( verbose, &grp, &R, &m, &P, sw_exponents, sizeof( sw_exponents ) / sizeof( sw_exponents[0] )); if( ret != 0 ) goto cleanup; mbedtls_ecp_group_free( &grp ); mbedtls_ecp_point_free( &R ); #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) if( verbose != 0 ) mbedtls_printf( " ECP Montgomery test (constant op_count): " ); #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_CURVE25519 ) ); #elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_CURVE448 ) ); #else #error "MBEDTLS_ECP_MONTGOMERY_ENABLED is defined, but no curve is supported for self-test" #endif ret = self_test_point( verbose, &grp, &R, &m, &grp.G, m_exponents, sizeof( m_exponents ) / sizeof( m_exponents[0] )); if( ret != 0 ) goto cleanup; #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ cleanup: if( ret < 0 && verbose != 0 ) mbedtls_printf( "Unexpected error, return code = %08X\n", (unsigned int) ret ); mbedtls_ecp_group_free( &grp ); mbedtls_ecp_point_free( &R ); mbedtls_ecp_point_free( &P ); mbedtls_mpi_free( &m ); if( verbose != 0 ) mbedtls_printf( "\n" ); return( ret ); } #endif /* MBEDTLS_SELF_TEST */ #endif /* !MBEDTLS_ECP_ALT */ #endif /* MBEDTLS_ECP_C */