/* * Entropy accumulator implementation * * Copyright The Mbed TLS Contributors * SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later * * This file is provided under the Apache License 2.0, or the * GNU General Public License v2.0 or later. * * ********** * Apache License 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. * * ********** * * ********** * GNU General Public License v2.0 or later: * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License along * with this program; if not, write to the Free Software Foundation, Inc., * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. * * ********** */ #if !defined(MBEDTLS_CONFIG_FILE) #include "mbedtls/config.h" #else #include MBEDTLS_CONFIG_FILE #endif #if defined(MBEDTLS_ENTROPY_C) #if defined(MBEDTLS_TEST_NULL_ENTROPY) #warning "**** WARNING! MBEDTLS_TEST_NULL_ENTROPY defined! " #warning "**** THIS BUILD HAS NO DEFINED ENTROPY SOURCES " #warning "**** THIS BUILD IS *NOT* SUITABLE FOR PRODUCTION USE " #endif #include "mbedtls/entropy.h" #include "mbedtls/entropy_poll.h" #include "mbedtls/platform_util.h" #include <string.h> #if defined(MBEDTLS_FS_IO) #include <stdio.h> #endif #if defined(MBEDTLS_ENTROPY_NV_SEED) #include "mbedtls/platform.h" #endif #if defined(MBEDTLS_SELF_TEST) #if defined(MBEDTLS_PLATFORM_C) #include "mbedtls/platform.h" #else #include <stdio.h> #define mbedtls_printf printf #endif /* MBEDTLS_PLATFORM_C */ #endif /* MBEDTLS_SELF_TEST */ #if defined(MBEDTLS_HAVEGE_C) #include "mbedtls/havege.h" #endif #define ENTROPY_MAX_LOOP 256 /**< Maximum amount to loop before error */ void mbedtls_entropy_init( mbedtls_entropy_context *ctx ) { ctx->source_count = 0; memset( ctx->source, 0, sizeof( ctx->source ) ); #if defined(MBEDTLS_THREADING_C) mbedtls_mutex_init( &ctx->mutex ); #endif ctx->accumulator_started = 0; #if defined(MBEDTLS_ENTROPY_SHA512_ACCUMULATOR) mbedtls_sha512_init( &ctx->accumulator ); #else mbedtls_sha256_init( &ctx->accumulator ); #endif #if defined(MBEDTLS_HAVEGE_C) mbedtls_havege_init( &ctx->havege_data ); #endif /* Reminder: Update ENTROPY_HAVE_STRONG in the test files * when adding more strong entropy sources here. */ #if defined(MBEDTLS_TEST_NULL_ENTROPY) mbedtls_entropy_add_source( ctx, mbedtls_null_entropy_poll, NULL, 1, MBEDTLS_ENTROPY_SOURCE_STRONG ); #endif #if !defined(MBEDTLS_NO_DEFAULT_ENTROPY_SOURCES) #if !defined(MBEDTLS_NO_PLATFORM_ENTROPY) mbedtls_entropy_add_source( ctx, mbedtls_platform_entropy_poll, NULL, MBEDTLS_ENTROPY_MIN_PLATFORM, MBEDTLS_ENTROPY_SOURCE_STRONG ); #endif #if defined(MBEDTLS_TIMING_C) mbedtls_entropy_add_source( ctx, mbedtls_hardclock_poll, NULL, MBEDTLS_ENTROPY_MIN_HARDCLOCK, MBEDTLS_ENTROPY_SOURCE_WEAK ); #endif #if defined(MBEDTLS_HAVEGE_C) mbedtls_entropy_add_source( ctx, mbedtls_havege_poll, &ctx->havege_data, MBEDTLS_ENTROPY_MIN_HAVEGE, MBEDTLS_ENTROPY_SOURCE_STRONG ); #endif #if defined(MBEDTLS_ENTROPY_HARDWARE_ALT) mbedtls_entropy_add_source( ctx, mbedtls_hardware_poll, NULL, MBEDTLS_ENTROPY_MIN_HARDWARE, MBEDTLS_ENTROPY_SOURCE_STRONG ); #endif #if defined(MBEDTLS_ENTROPY_NV_SEED) mbedtls_entropy_add_source( ctx, mbedtls_nv_seed_poll, NULL, MBEDTLS_ENTROPY_BLOCK_SIZE, MBEDTLS_ENTROPY_SOURCE_STRONG ); ctx->initial_entropy_run = 0; #endif #endif /* MBEDTLS_NO_DEFAULT_ENTROPY_SOURCES */ } void mbedtls_entropy_free( mbedtls_entropy_context *ctx ) { /* If the context was already free, don't call free() again. * This is important for mutexes which don't allow double-free. */ if( ctx->accumulator_started == -1 ) return; #if defined(MBEDTLS_HAVEGE_C) mbedtls_havege_free( &ctx->havege_data ); #endif #if defined(MBEDTLS_THREADING_C) mbedtls_mutex_free( &ctx->mutex ); #endif #if defined(MBEDTLS_ENTROPY_SHA512_ACCUMULATOR) mbedtls_sha512_free( &ctx->accumulator ); #else mbedtls_sha256_free( &ctx->accumulator ); #endif #if defined(MBEDTLS_ENTROPY_NV_SEED) ctx->initial_entropy_run = 0; #endif ctx->source_count = 0; mbedtls_platform_zeroize( ctx->source, sizeof( ctx->source ) ); ctx->accumulator_started = -1; } int mbedtls_entropy_add_source( mbedtls_entropy_context *ctx, mbedtls_entropy_f_source_ptr f_source, void *p_source, size_t threshold, int strong ) { int idx, ret = 0; #if defined(MBEDTLS_THREADING_C) if( ( ret = mbedtls_mutex_lock( &ctx->mutex ) ) != 0 ) return( ret ); #endif idx = ctx->source_count; if( idx >= MBEDTLS_ENTROPY_MAX_SOURCES ) { ret = MBEDTLS_ERR_ENTROPY_MAX_SOURCES; goto exit; } ctx->source[idx].f_source = f_source; ctx->source[idx].p_source = p_source; ctx->source[idx].threshold = threshold; ctx->source[idx].strong = strong; ctx->source_count++; exit: #if defined(MBEDTLS_THREADING_C) if( mbedtls_mutex_unlock( &ctx->mutex ) != 0 ) return( MBEDTLS_ERR_THREADING_MUTEX_ERROR ); #endif return( ret ); } /* * Entropy accumulator update */ static int entropy_update( mbedtls_entropy_context *ctx, unsigned char source_id, const unsigned char *data, size_t len ) { unsigned char header[2]; unsigned char tmp[MBEDTLS_ENTROPY_BLOCK_SIZE]; size_t use_len = len; const unsigned char *p = data; int ret = 0; if( use_len > MBEDTLS_ENTROPY_BLOCK_SIZE ) { #if defined(MBEDTLS_ENTROPY_SHA512_ACCUMULATOR) if( ( ret = mbedtls_sha512_ret( data, len, tmp, 0 ) ) != 0 ) goto cleanup; #else if( ( ret = mbedtls_sha256_ret( data, len, tmp, 0 ) ) != 0 ) goto cleanup; #endif p = tmp; use_len = MBEDTLS_ENTROPY_BLOCK_SIZE; } header[0] = source_id; header[1] = use_len & 0xFF; /* * Start the accumulator if this has not already happened. Note that * it is sufficient to start the accumulator here only because all calls to * gather entropy eventually execute this code. */ #if defined(MBEDTLS_ENTROPY_SHA512_ACCUMULATOR) if( ctx->accumulator_started == 0 && ( ret = mbedtls_sha512_starts_ret( &ctx->accumulator, 0 ) ) != 0 ) goto cleanup; else ctx->accumulator_started = 1; if( ( ret = mbedtls_sha512_update_ret( &ctx->accumulator, header, 2 ) ) != 0 ) goto cleanup; ret = mbedtls_sha512_update_ret( &ctx->accumulator, p, use_len ); #else if( ctx->accumulator_started == 0 && ( ret = mbedtls_sha256_starts_ret( &ctx->accumulator, 0 ) ) != 0 ) goto cleanup; else ctx->accumulator_started = 1; if( ( ret = mbedtls_sha256_update_ret( &ctx->accumulator, header, 2 ) ) != 0 ) goto cleanup; ret = mbedtls_sha256_update_ret( &ctx->accumulator, p, use_len ); #endif cleanup: mbedtls_platform_zeroize( tmp, sizeof( tmp ) ); return( ret ); } int mbedtls_entropy_update_manual( mbedtls_entropy_context *ctx, const unsigned char *data, size_t len ) { int ret; #if defined(MBEDTLS_THREADING_C) if( ( ret = mbedtls_mutex_lock( &ctx->mutex ) ) != 0 ) return( ret ); #endif ret = entropy_update( ctx, MBEDTLS_ENTROPY_SOURCE_MANUAL, data, len ); #if defined(MBEDTLS_THREADING_C) if( mbedtls_mutex_unlock( &ctx->mutex ) != 0 ) return( MBEDTLS_ERR_THREADING_MUTEX_ERROR ); #endif return( ret ); } /* * Run through the different sources to add entropy to our accumulator */ static int entropy_gather_internal( mbedtls_entropy_context *ctx ) { int ret, i, have_one_strong = 0; unsigned char buf[MBEDTLS_ENTROPY_MAX_GATHER]; size_t olen; if( ctx->source_count == 0 ) return( MBEDTLS_ERR_ENTROPY_NO_SOURCES_DEFINED ); /* * Run through our entropy sources */ for( i = 0; i < ctx->source_count; i++ ) { if( ctx->source[i].strong == MBEDTLS_ENTROPY_SOURCE_STRONG ) have_one_strong = 1; olen = 0; if( ( ret = ctx->source[i].f_source( ctx->source[i].p_source, buf, MBEDTLS_ENTROPY_MAX_GATHER, &olen ) ) != 0 ) { goto cleanup; } /* * Add if we actually gathered something */ if( olen > 0 ) { if( ( ret = entropy_update( ctx, (unsigned char) i, buf, olen ) ) != 0 ) return( ret ); ctx->source[i].size += olen; } } if( have_one_strong == 0 ) ret = MBEDTLS_ERR_ENTROPY_NO_STRONG_SOURCE; cleanup: mbedtls_platform_zeroize( buf, sizeof( buf ) ); return( ret ); } /* * Thread-safe wrapper for entropy_gather_internal() */ int mbedtls_entropy_gather( mbedtls_entropy_context *ctx ) { int ret; #if defined(MBEDTLS_THREADING_C) if( ( ret = mbedtls_mutex_lock( &ctx->mutex ) ) != 0 ) return( ret ); #endif ret = entropy_gather_internal( ctx ); #if defined(MBEDTLS_THREADING_C) if( mbedtls_mutex_unlock( &ctx->mutex ) != 0 ) return( MBEDTLS_ERR_THREADING_MUTEX_ERROR ); #endif return( ret ); } int mbedtls_entropy_func( void *data, unsigned char *output, size_t len ) { int ret, count = 0, i, done; mbedtls_entropy_context *ctx = (mbedtls_entropy_context *) data; unsigned char buf[MBEDTLS_ENTROPY_BLOCK_SIZE]; if( len > MBEDTLS_ENTROPY_BLOCK_SIZE ) return( MBEDTLS_ERR_ENTROPY_SOURCE_FAILED ); #if defined(MBEDTLS_ENTROPY_NV_SEED) /* Update the NV entropy seed before generating any entropy for outside * use. */ if( ctx->initial_entropy_run == 0 ) { ctx->initial_entropy_run = 1; if( ( ret = mbedtls_entropy_update_nv_seed( ctx ) ) != 0 ) return( ret ); } #endif #if defined(MBEDTLS_THREADING_C) if( ( ret = mbedtls_mutex_lock( &ctx->mutex ) ) != 0 ) return( ret ); #endif /* * Always gather extra entropy before a call */ do { if( count++ > ENTROPY_MAX_LOOP ) { ret = MBEDTLS_ERR_ENTROPY_SOURCE_FAILED; goto exit; } if( ( ret = entropy_gather_internal( ctx ) ) != 0 ) goto exit; done = 1; for( i = 0; i < ctx->source_count; i++ ) if( ctx->source[i].size < ctx->source[i].threshold ) done = 0; } while( ! done ); memset( buf, 0, MBEDTLS_ENTROPY_BLOCK_SIZE ); #if defined(MBEDTLS_ENTROPY_SHA512_ACCUMULATOR) /* * Note that at this stage it is assumed that the accumulator was started * in a previous call to entropy_update(). If this is not guaranteed, the * code below will fail. */ if( ( ret = mbedtls_sha512_finish_ret( &ctx->accumulator, buf ) ) != 0 ) goto exit; /* * Reset accumulator and counters and recycle existing entropy */ mbedtls_sha512_free( &ctx->accumulator ); mbedtls_sha512_init( &ctx->accumulator ); if( ( ret = mbedtls_sha512_starts_ret( &ctx->accumulator, 0 ) ) != 0 ) goto exit; if( ( ret = mbedtls_sha512_update_ret( &ctx->accumulator, buf, MBEDTLS_ENTROPY_BLOCK_SIZE ) ) != 0 ) goto exit; /* * Perform second SHA-512 on entropy */ if( ( ret = mbedtls_sha512_ret( buf, MBEDTLS_ENTROPY_BLOCK_SIZE, buf, 0 ) ) != 0 ) goto exit; #else /* MBEDTLS_ENTROPY_SHA512_ACCUMULATOR */ if( ( ret = mbedtls_sha256_finish_ret( &ctx->accumulator, buf ) ) != 0 ) goto exit; /* * Reset accumulator and counters and recycle existing entropy */ mbedtls_sha256_free( &ctx->accumulator ); mbedtls_sha256_init( &ctx->accumulator ); if( ( ret = mbedtls_sha256_starts_ret( &ctx->accumulator, 0 ) ) != 0 ) goto exit; if( ( ret = mbedtls_sha256_update_ret( &ctx->accumulator, buf, MBEDTLS_ENTROPY_BLOCK_SIZE ) ) != 0 ) goto exit; /* * Perform second SHA-256 on entropy */ if( ( ret = mbedtls_sha256_ret( buf, MBEDTLS_ENTROPY_BLOCK_SIZE, buf, 0 ) ) != 0 ) goto exit; #endif /* MBEDTLS_ENTROPY_SHA512_ACCUMULATOR */ for( i = 0; i < ctx->source_count; i++ ) ctx->source[i].size = 0; memcpy( output, buf, len ); ret = 0; exit: mbedtls_platform_zeroize( buf, sizeof( buf ) ); #if defined(MBEDTLS_THREADING_C) if( mbedtls_mutex_unlock( &ctx->mutex ) != 0 ) return( MBEDTLS_ERR_THREADING_MUTEX_ERROR ); #endif return( ret ); } #if defined(MBEDTLS_ENTROPY_NV_SEED) int mbedtls_entropy_update_nv_seed( mbedtls_entropy_context *ctx ) { int ret = MBEDTLS_ERR_ENTROPY_FILE_IO_ERROR; unsigned char buf[MBEDTLS_ENTROPY_BLOCK_SIZE]; /* Read new seed and write it to NV */ if( ( ret = mbedtls_entropy_func( ctx, buf, MBEDTLS_ENTROPY_BLOCK_SIZE ) ) != 0 ) return( ret ); if( mbedtls_nv_seed_write( buf, MBEDTLS_ENTROPY_BLOCK_SIZE ) < 0 ) return( MBEDTLS_ERR_ENTROPY_FILE_IO_ERROR ); /* Manually update the remaining stream with a separator value to diverge */ memset( buf, 0, MBEDTLS_ENTROPY_BLOCK_SIZE ); ret = mbedtls_entropy_update_manual( ctx, buf, MBEDTLS_ENTROPY_BLOCK_SIZE ); return( ret ); } #endif /* MBEDTLS_ENTROPY_NV_SEED */ #if defined(MBEDTLS_FS_IO) int mbedtls_entropy_write_seed_file( mbedtls_entropy_context *ctx, const char *path ) { int ret = MBEDTLS_ERR_ENTROPY_FILE_IO_ERROR; FILE *f = NULL; unsigned char buf[MBEDTLS_ENTROPY_BLOCK_SIZE]; if( ( ret = mbedtls_entropy_func( ctx, buf, MBEDTLS_ENTROPY_BLOCK_SIZE ) ) != 0 ) { ret = MBEDTLS_ERR_ENTROPY_SOURCE_FAILED; goto exit; } if( ( f = fopen( path, "wb" ) ) == NULL ) { ret = MBEDTLS_ERR_ENTROPY_FILE_IO_ERROR; goto exit; } if( fwrite( buf, 1, MBEDTLS_ENTROPY_BLOCK_SIZE, f ) != MBEDTLS_ENTROPY_BLOCK_SIZE ) { ret = MBEDTLS_ERR_ENTROPY_FILE_IO_ERROR; goto exit; } ret = 0; exit: mbedtls_platform_zeroize( buf, sizeof( buf ) ); if( f != NULL ) fclose( f ); return( ret ); } int mbedtls_entropy_update_seed_file( mbedtls_entropy_context *ctx, const char *path ) { int ret = 0; FILE *f; size_t n; unsigned char buf[ MBEDTLS_ENTROPY_MAX_SEED_SIZE ]; if( ( f = fopen( path, "rb" ) ) == NULL ) return( MBEDTLS_ERR_ENTROPY_FILE_IO_ERROR ); fseek( f, 0, SEEK_END ); n = (size_t) ftell( f ); fseek( f, 0, SEEK_SET ); if( n > MBEDTLS_ENTROPY_MAX_SEED_SIZE ) n = MBEDTLS_ENTROPY_MAX_SEED_SIZE; if( fread( buf, 1, n, f ) != n ) ret = MBEDTLS_ERR_ENTROPY_FILE_IO_ERROR; else ret = mbedtls_entropy_update_manual( ctx, buf, n ); fclose( f ); mbedtls_platform_zeroize( buf, sizeof( buf ) ); if( ret != 0 ) return( ret ); return( mbedtls_entropy_write_seed_file( ctx, path ) ); } #endif /* MBEDTLS_FS_IO */ #if defined(MBEDTLS_SELF_TEST) #if !defined(MBEDTLS_TEST_NULL_ENTROPY) /* * Dummy source function */ static int entropy_dummy_source( void *data, unsigned char *output, size_t len, size_t *olen ) { ((void) data); memset( output, 0x2a, len ); *olen = len; return( 0 ); } #endif /* !MBEDTLS_TEST_NULL_ENTROPY */ #if defined(MBEDTLS_ENTROPY_HARDWARE_ALT) static int mbedtls_entropy_source_self_test_gather( unsigned char *buf, size_t buf_len ) { int ret = 0; size_t entropy_len = 0; size_t olen = 0; size_t attempts = buf_len; while( attempts > 0 && entropy_len < buf_len ) { if( ( ret = mbedtls_hardware_poll( NULL, buf + entropy_len, buf_len - entropy_len, &olen ) ) != 0 ) return( ret ); entropy_len += olen; attempts--; } if( entropy_len < buf_len ) { ret = 1; } return( ret ); } static int mbedtls_entropy_source_self_test_check_bits( const unsigned char *buf, size_t buf_len ) { unsigned char set= 0xFF; unsigned char unset = 0x00; size_t i; for( i = 0; i < buf_len; i++ ) { set &= buf[i]; unset |= buf[i]; } return( set == 0xFF || unset == 0x00 ); } /* * A test to ensure hat the entropy sources are functioning correctly * and there is no obvious failure. The test performs the following checks: * - The entropy source is not providing only 0s (all bits unset) or 1s (all * bits set). * - The entropy source is not providing values in a pattern. Because the * hardware could be providing data in an arbitrary length, this check polls * the hardware entropy source twice and compares the result to ensure they * are not equal. * - The error code returned by the entropy source is not an error. */ int mbedtls_entropy_source_self_test( int verbose ) { int ret = 0; unsigned char buf0[2 * sizeof( unsigned long long int )]; unsigned char buf1[2 * sizeof( unsigned long long int )]; if( verbose != 0 ) mbedtls_printf( " ENTROPY_BIAS test: " ); memset( buf0, 0x00, sizeof( buf0 ) ); memset( buf1, 0x00, sizeof( buf1 ) ); if( ( ret = mbedtls_entropy_source_self_test_gather( buf0, sizeof( buf0 ) ) ) != 0 ) goto cleanup; if( ( ret = mbedtls_entropy_source_self_test_gather( buf1, sizeof( buf1 ) ) ) != 0 ) goto cleanup; /* Make sure that the returned values are not all 0 or 1 */ if( ( ret = mbedtls_entropy_source_self_test_check_bits( buf0, sizeof( buf0 ) ) ) != 0 ) goto cleanup; if( ( ret = mbedtls_entropy_source_self_test_check_bits( buf1, sizeof( buf1 ) ) ) != 0 ) goto cleanup; /* Make sure that the entropy source is not returning values in a * pattern */ ret = memcmp( buf0, buf1, sizeof( buf0 ) ) == 0; cleanup: if( verbose != 0 ) { if( ret != 0 ) mbedtls_printf( "failed\n" ); else mbedtls_printf( "passed\n" ); mbedtls_printf( "\n" ); } return( ret != 0 ); } #endif /* MBEDTLS_ENTROPY_HARDWARE_ALT */ /* * The actual entropy quality is hard to test, but we can at least * test that the functions don't cause errors and write the correct * amount of data to buffers. */ int mbedtls_entropy_self_test( int verbose ) { int ret = 1; #if !defined(MBEDTLS_TEST_NULL_ENTROPY) mbedtls_entropy_context ctx; unsigned char buf[MBEDTLS_ENTROPY_BLOCK_SIZE] = { 0 }; unsigned char acc[MBEDTLS_ENTROPY_BLOCK_SIZE] = { 0 }; size_t i, j; #endif /* !MBEDTLS_TEST_NULL_ENTROPY */ if( verbose != 0 ) mbedtls_printf( " ENTROPY test: " ); #if !defined(MBEDTLS_TEST_NULL_ENTROPY) mbedtls_entropy_init( &ctx ); /* First do a gather to make sure we have default sources */ if( ( ret = mbedtls_entropy_gather( &ctx ) ) != 0 ) goto cleanup; ret = mbedtls_entropy_add_source( &ctx, entropy_dummy_source, NULL, 16, MBEDTLS_ENTROPY_SOURCE_WEAK ); if( ret != 0 ) goto cleanup; if( ( ret = mbedtls_entropy_update_manual( &ctx, buf, sizeof buf ) ) != 0 ) goto cleanup; /* * To test that mbedtls_entropy_func writes correct number of bytes: * - use the whole buffer and rely on ASan to detect overruns * - collect entropy 8 times and OR the result in an accumulator: * any byte should then be 0 with probably 2^(-64), so requiring * each of the 32 or 64 bytes to be non-zero has a false failure rate * of at most 2^(-58) which is acceptable. */ for( i = 0; i < 8; i++ ) { if( ( ret = mbedtls_entropy_func( &ctx, buf, sizeof( buf ) ) ) != 0 ) goto cleanup; for( j = 0; j < sizeof( buf ); j++ ) acc[j] |= buf[j]; } for( j = 0; j < sizeof( buf ); j++ ) { if( acc[j] == 0 ) { ret = 1; goto cleanup; } } #if defined(MBEDTLS_ENTROPY_HARDWARE_ALT) if( ( ret = mbedtls_entropy_source_self_test( 0 ) ) != 0 ) goto cleanup; #endif cleanup: mbedtls_entropy_free( &ctx ); #endif /* !MBEDTLS_TEST_NULL_ENTROPY */ if( verbose != 0 ) { if( ret != 0 ) mbedtls_printf( "failed\n" ); else mbedtls_printf( "passed\n" ); mbedtls_printf( "\n" ); } return( ret != 0 ); } #endif /* MBEDTLS_SELF_TEST */ #endif /* MBEDTLS_ENTROPY_C */