6b00357d53
Fixes https://tls.mbed.org/tech-updates/security-advisories/mbedtls-security-advisory-2020-04
3027 lines
94 KiB
C
3027 lines
94 KiB
C
/*
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* Elliptic curves over GF(p): generic functions
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*
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* Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
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* SPDX-License-Identifier: Apache-2.0
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*
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* Licensed under the Apache License, Version 2.0 (the "License"); you may
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* not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*
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* This file is part of mbed TLS (https://tls.mbed.org)
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*/
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/*
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* References:
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*
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* SEC1 http://www.secg.org/index.php?action=secg,docs_secg
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* GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
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* FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
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* RFC 4492 for the related TLS structures and constants
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* RFC 7748 for the Curve448 and Curve25519 curve definitions
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*
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* [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf
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*
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* [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
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* for elliptic curve cryptosystems. In : Cryptographic Hardware and
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* Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
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* <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
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*
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* [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
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* render ECC resistant against Side Channel Attacks. IACR Cryptology
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* ePrint Archive, 2004, vol. 2004, p. 342.
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* <http://eprint.iacr.org/2004/342.pdf>
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*/
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#if !defined(MBEDTLS_CONFIG_FILE)
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#include "mbedtls/config.h"
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#else
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#include MBEDTLS_CONFIG_FILE
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#endif
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/**
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* \brief Function level alternative implementation.
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*
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* The MBEDTLS_ECP_INTERNAL_ALT macro enables alternative implementations to
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* replace certain functions in this module. The alternative implementations are
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* typically hardware accelerators and need to activate the hardware before the
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* computation starts and deactivate it after it finishes. The
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* mbedtls_internal_ecp_init() and mbedtls_internal_ecp_free() functions serve
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* this purpose.
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*
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* To preserve the correct functionality the following conditions must hold:
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*
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* - The alternative implementation must be activated by
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* mbedtls_internal_ecp_init() before any of the replaceable functions is
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* called.
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* - mbedtls_internal_ecp_free() must \b only be called when the alternative
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* implementation is activated.
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* - mbedtls_internal_ecp_init() must \b not be called when the alternative
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* implementation is activated.
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* - Public functions must not return while the alternative implementation is
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* activated.
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* - Replaceable functions are guarded by \c MBEDTLS_ECP_XXX_ALT macros and
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* before calling them an \code if( mbedtls_internal_ecp_grp_capable( grp ) )
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* \endcode ensures that the alternative implementation supports the current
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* group.
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*/
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#if defined(MBEDTLS_ECP_INTERNAL_ALT)
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#endif
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#if defined(MBEDTLS_ECP_C)
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#include "mbedtls/ecp.h"
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#include "mbedtls/threading.h"
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#include "mbedtls/platform_util.h"
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#include <string.h>
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#if !defined(MBEDTLS_ECP_ALT)
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/* Parameter validation macros based on platform_util.h */
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#define ECP_VALIDATE_RET( cond ) \
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MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA )
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#define ECP_VALIDATE( cond ) \
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MBEDTLS_INTERNAL_VALIDATE( cond )
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#if defined(MBEDTLS_PLATFORM_C)
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#include "mbedtls/platform.h"
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#else
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#include <stdlib.h>
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#include <stdio.h>
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#define mbedtls_printf printf
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#define mbedtls_calloc calloc
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#define mbedtls_free free
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#endif
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#include "mbedtls/ecp_internal.h"
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#if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
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!defined(inline) && !defined(__cplusplus)
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#define inline __inline
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#endif
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#if defined(MBEDTLS_SELF_TEST)
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/*
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* Counts of point addition and doubling, and field multiplications.
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* Used to test resistance of point multiplication to simple timing attacks.
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*/
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static unsigned long add_count, dbl_count, mul_count;
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#endif
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#if defined(MBEDTLS_ECP_RESTARTABLE)
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/*
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* Maximum number of "basic operations" to be done in a row.
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*
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* Default value 0 means that ECC operations will not yield.
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* Note that regardless of the value of ecp_max_ops, always at
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* least one step is performed before yielding.
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*
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* Setting ecp_max_ops=1 can be suitable for testing purposes
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* as it will interrupt computation at all possible points.
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*/
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static unsigned ecp_max_ops = 0;
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/*
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* Set ecp_max_ops
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*/
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void mbedtls_ecp_set_max_ops( unsigned max_ops )
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{
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ecp_max_ops = max_ops;
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}
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/*
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* Check if restart is enabled
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*/
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int mbedtls_ecp_restart_is_enabled( void )
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{
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return( ecp_max_ops != 0 );
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}
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/*
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* Restart sub-context for ecp_mul_comb()
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*/
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struct mbedtls_ecp_restart_mul
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{
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mbedtls_ecp_point R; /* current intermediate result */
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size_t i; /* current index in various loops, 0 outside */
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mbedtls_ecp_point *T; /* table for precomputed points */
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unsigned char T_size; /* number of points in table T */
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enum { /* what were we doing last time we returned? */
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ecp_rsm_init = 0, /* nothing so far, dummy initial state */
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ecp_rsm_pre_dbl, /* precompute 2^n multiples */
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ecp_rsm_pre_norm_dbl, /* normalize precomputed 2^n multiples */
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ecp_rsm_pre_add, /* precompute remaining points by adding */
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ecp_rsm_pre_norm_add, /* normalize all precomputed points */
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ecp_rsm_comb_core, /* ecp_mul_comb_core() */
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ecp_rsm_final_norm, /* do the final normalization */
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} state;
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};
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/*
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* Init restart_mul sub-context
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*/
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static void ecp_restart_rsm_init( mbedtls_ecp_restart_mul_ctx *ctx )
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{
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mbedtls_ecp_point_init( &ctx->R );
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ctx->i = 0;
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ctx->T = NULL;
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ctx->T_size = 0;
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ctx->state = ecp_rsm_init;
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}
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/*
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* Free the components of a restart_mul sub-context
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*/
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static void ecp_restart_rsm_free( mbedtls_ecp_restart_mul_ctx *ctx )
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{
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unsigned char i;
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if( ctx == NULL )
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return;
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mbedtls_ecp_point_free( &ctx->R );
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if( ctx->T != NULL )
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{
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for( i = 0; i < ctx->T_size; i++ )
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mbedtls_ecp_point_free( ctx->T + i );
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mbedtls_free( ctx->T );
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}
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ecp_restart_rsm_init( ctx );
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}
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/*
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* Restart context for ecp_muladd()
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*/
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struct mbedtls_ecp_restart_muladd
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{
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mbedtls_ecp_point mP; /* mP value */
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mbedtls_ecp_point R; /* R intermediate result */
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enum { /* what should we do next? */
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ecp_rsma_mul1 = 0, /* first multiplication */
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ecp_rsma_mul2, /* second multiplication */
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ecp_rsma_add, /* addition */
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ecp_rsma_norm, /* normalization */
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} state;
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};
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/*
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* Init restart_muladd sub-context
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*/
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static void ecp_restart_ma_init( mbedtls_ecp_restart_muladd_ctx *ctx )
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{
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mbedtls_ecp_point_init( &ctx->mP );
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mbedtls_ecp_point_init( &ctx->R );
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ctx->state = ecp_rsma_mul1;
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}
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/*
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* Free the components of a restart_muladd sub-context
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*/
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static void ecp_restart_ma_free( mbedtls_ecp_restart_muladd_ctx *ctx )
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{
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if( ctx == NULL )
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return;
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mbedtls_ecp_point_free( &ctx->mP );
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mbedtls_ecp_point_free( &ctx->R );
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ecp_restart_ma_init( ctx );
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}
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/*
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* Initialize a restart context
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*/
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void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx )
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{
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ECP_VALIDATE( ctx != NULL );
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ctx->ops_done = 0;
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ctx->depth = 0;
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ctx->rsm = NULL;
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ctx->ma = NULL;
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}
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/*
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* Free the components of a restart context
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*/
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void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx )
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{
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if( ctx == NULL )
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return;
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ecp_restart_rsm_free( ctx->rsm );
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mbedtls_free( ctx->rsm );
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ecp_restart_ma_free( ctx->ma );
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mbedtls_free( ctx->ma );
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mbedtls_ecp_restart_init( ctx );
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}
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/*
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* Check if we can do the next step
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*/
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int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp,
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mbedtls_ecp_restart_ctx *rs_ctx,
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unsigned ops )
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{
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ECP_VALIDATE_RET( grp != NULL );
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if( rs_ctx != NULL && ecp_max_ops != 0 )
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{
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/* scale depending on curve size: the chosen reference is 256-bit,
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* and multiplication is quadratic. Round to the closest integer. */
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if( grp->pbits >= 512 )
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ops *= 4;
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else if( grp->pbits >= 384 )
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ops *= 2;
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/* Avoid infinite loops: always allow first step.
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* Because of that, however, it's not generally true
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* that ops_done <= ecp_max_ops, so the check
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* ops_done > ecp_max_ops below is mandatory. */
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if( ( rs_ctx->ops_done != 0 ) &&
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( rs_ctx->ops_done > ecp_max_ops ||
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ops > ecp_max_ops - rs_ctx->ops_done ) )
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{
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return( MBEDTLS_ERR_ECP_IN_PROGRESS );
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}
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/* update running count */
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rs_ctx->ops_done += ops;
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}
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return( 0 );
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}
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/* Call this when entering a function that needs its own sub-context */
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#define ECP_RS_ENTER( SUB ) do { \
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/* reset ops count for this call if top-level */ \
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if( rs_ctx != NULL && rs_ctx->depth++ == 0 ) \
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rs_ctx->ops_done = 0; \
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\
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/* set up our own sub-context if needed */ \
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if( mbedtls_ecp_restart_is_enabled() && \
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rs_ctx != NULL && rs_ctx->SUB == NULL ) \
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{ \
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rs_ctx->SUB = mbedtls_calloc( 1, sizeof( *rs_ctx->SUB ) ); \
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if( rs_ctx->SUB == NULL ) \
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return( MBEDTLS_ERR_ECP_ALLOC_FAILED ); \
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\
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ecp_restart_## SUB ##_init( rs_ctx->SUB ); \
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} \
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} while( 0 )
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/* Call this when leaving a function that needs its own sub-context */
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#define ECP_RS_LEAVE( SUB ) do { \
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/* clear our sub-context when not in progress (done or error) */ \
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if( rs_ctx != NULL && rs_ctx->SUB != NULL && \
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ret != MBEDTLS_ERR_ECP_IN_PROGRESS ) \
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{ \
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ecp_restart_## SUB ##_free( rs_ctx->SUB ); \
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mbedtls_free( rs_ctx->SUB ); \
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rs_ctx->SUB = NULL; \
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} \
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\
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if( rs_ctx != NULL ) \
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rs_ctx->depth--; \
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} while( 0 )
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#else /* MBEDTLS_ECP_RESTARTABLE */
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#define ECP_RS_ENTER( sub ) (void) rs_ctx;
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#define ECP_RS_LEAVE( sub ) (void) rs_ctx;
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#endif /* MBEDTLS_ECP_RESTARTABLE */
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#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \
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defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
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defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
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defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \
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defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \
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defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \
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defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \
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defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \
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defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
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defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
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defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
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#define ECP_SHORTWEIERSTRASS
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#endif
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#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) || \
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defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
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#define ECP_MONTGOMERY
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#endif
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/*
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* Curve types: internal for now, might be exposed later
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*/
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typedef enum
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{
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ECP_TYPE_NONE = 0,
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ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */
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ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */
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} ecp_curve_type;
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/*
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* List of supported curves:
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* - internal ID
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* - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2)
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* - size in bits
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* - readable name
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*
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* Curves are listed in order: largest curves first, and for a given size,
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* fastest curves first. This provides the default order for the SSL module.
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*
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* Reminder: update profiles in x509_crt.c when adding a new curves!
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*/
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static const mbedtls_ecp_curve_info ecp_supported_curves[] =
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{
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#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
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{ MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" },
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#endif
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#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
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{ MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
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#endif
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#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
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{ MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
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#endif
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#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
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{ MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
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#endif
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#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
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{ MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
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#endif
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#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
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{ MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
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#endif
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#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
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{ MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" },
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#endif
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#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
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{ MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" },
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#endif
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#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
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{ MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" },
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#endif
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#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
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{ MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" },
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#endif
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#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
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{ MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" },
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#endif
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{ MBEDTLS_ECP_DP_NONE, 0, 0, NULL },
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};
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#define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \
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sizeof( ecp_supported_curves[0] )
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static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
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/*
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* List of supported curves and associated info
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*/
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const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
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{
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return( ecp_supported_curves );
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}
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/*
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* List of supported curves, group ID only
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*/
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const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
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{
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static int init_done = 0;
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if( ! init_done )
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{
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size_t i = 0;
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const mbedtls_ecp_curve_info *curve_info;
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for( curve_info = mbedtls_ecp_curve_list();
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curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
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curve_info++ )
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{
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ecp_supported_grp_id[i++] = curve_info->grp_id;
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}
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ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
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init_done = 1;
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}
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return( ecp_supported_grp_id );
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}
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/*
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* Get the curve info for the internal identifier
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*/
|
|
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
|
|
*/
|
|
static inline ecp_curve_type ecp_get_type( const mbedtls_ecp_group *grp )
|
|
{
|
|
if( grp->G.X.p == NULL )
|
|
return( ECP_TYPE_NONE );
|
|
|
|
if( grp->G.Y.p == NULL )
|
|
return( ECP_TYPE_MONTGOMERY );
|
|
else
|
|
return( ECP_TYPE_SHORT_WEIERSTRASS );
|
|
}
|
|
|
|
/*
|
|
* Initialize (the components of) a point
|
|
*/
|
|
void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
|
|
{
|
|
ECP_VALIDATE( pt != NULL );
|
|
|
|
mbedtls_mpi_init( &pt->X );
|
|
mbedtls_mpi_init( &pt->Y );
|
|
mbedtls_mpi_init( &pt->Z );
|
|
}
|
|
|
|
/*
|
|
* Initialize (the components of) a group
|
|
*/
|
|
void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
|
|
{
|
|
ECP_VALIDATE( grp != NULL );
|
|
|
|
grp->id = MBEDTLS_ECP_DP_NONE;
|
|
mbedtls_mpi_init( &grp->P );
|
|
mbedtls_mpi_init( &grp->A );
|
|
mbedtls_mpi_init( &grp->B );
|
|
mbedtls_ecp_point_init( &grp->G );
|
|
mbedtls_mpi_init( &grp->N );
|
|
grp->pbits = 0;
|
|
grp->nbits = 0;
|
|
grp->h = 0;
|
|
grp->modp = NULL;
|
|
grp->t_pre = NULL;
|
|
grp->t_post = NULL;
|
|
grp->t_data = NULL;
|
|
grp->T = NULL;
|
|
grp->T_size = 0;
|
|
}
|
|
|
|
/*
|
|
* Initialize (the components of) a key pair
|
|
*/
|
|
void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
|
|
{
|
|
ECP_VALIDATE( key != NULL );
|
|
|
|
mbedtls_ecp_group_init( &key->grp );
|
|
mbedtls_mpi_init( &key->d );
|
|
mbedtls_ecp_point_init( &key->Q );
|
|
}
|
|
|
|
/*
|
|
* Unallocate (the components of) a point
|
|
*/
|
|
void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
|
|
{
|
|
if( pt == NULL )
|
|
return;
|
|
|
|
mbedtls_mpi_free( &( pt->X ) );
|
|
mbedtls_mpi_free( &( pt->Y ) );
|
|
mbedtls_mpi_free( &( pt->Z ) );
|
|
}
|
|
|
|
/*
|
|
* Unallocate (the components of) a group
|
|
*/
|
|
void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
|
|
{
|
|
size_t i;
|
|
|
|
if( grp == NULL )
|
|
return;
|
|
|
|
if( grp->h != 1 )
|
|
{
|
|
mbedtls_mpi_free( &grp->P );
|
|
mbedtls_mpi_free( &grp->A );
|
|
mbedtls_mpi_free( &grp->B );
|
|
mbedtls_ecp_point_free( &grp->G );
|
|
mbedtls_mpi_free( &grp->N );
|
|
}
|
|
|
|
if( grp->T != NULL )
|
|
{
|
|
for( i = 0; i < grp->T_size; i++ )
|
|
mbedtls_ecp_point_free( &grp->T[i] );
|
|
mbedtls_free( grp->T );
|
|
}
|
|
|
|
mbedtls_platform_zeroize( grp, sizeof( mbedtls_ecp_group ) );
|
|
}
|
|
|
|
/*
|
|
* Unallocate (the components of) a key pair
|
|
*/
|
|
void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
|
|
{
|
|
if( key == NULL )
|
|
return;
|
|
|
|
mbedtls_ecp_group_free( &key->grp );
|
|
mbedtls_mpi_free( &key->d );
|
|
mbedtls_ecp_point_free( &key->Q );
|
|
}
|
|
|
|
/*
|
|
* Copy the contents of a point
|
|
*/
|
|
int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
|
|
{
|
|
int ret;
|
|
ECP_VALIDATE_RET( P != NULL );
|
|
ECP_VALIDATE_RET( Q != NULL );
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) );
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Copy the contents of a group object
|
|
*/
|
|
int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
|
|
{
|
|
ECP_VALIDATE_RET( dst != NULL );
|
|
ECP_VALIDATE_RET( src != NULL );
|
|
|
|
return( mbedtls_ecp_group_load( dst, src->id ) );
|
|
}
|
|
|
|
/*
|
|
* Set point to zero
|
|
*/
|
|
int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
|
|
{
|
|
int ret;
|
|
ECP_VALIDATE_RET( pt != NULL );
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) );
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Tell if a point is zero
|
|
*/
|
|
int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
|
|
{
|
|
ECP_VALIDATE_RET( pt != NULL );
|
|
|
|
return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 );
|
|
}
|
|
|
|
/*
|
|
* Compare two points lazily
|
|
*/
|
|
int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
|
|
const mbedtls_ecp_point *Q )
|
|
{
|
|
ECP_VALIDATE_RET( P != NULL );
|
|
ECP_VALIDATE_RET( Q != NULL );
|
|
|
|
if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
|
|
mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 &&
|
|
mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 )
|
|
{
|
|
return( 0 );
|
|
}
|
|
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
}
|
|
|
|
/*
|
|
* Import a non-zero point from ASCII strings
|
|
*/
|
|
int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
|
|
const char *x, const char *y )
|
|
{
|
|
int ret;
|
|
ECP_VALIDATE_RET( P != NULL );
|
|
ECP_VALIDATE_RET( x != NULL );
|
|
ECP_VALIDATE_RET( y != NULL );
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Export a point into unsigned binary data (SEC1 2.3.3)
|
|
*/
|
|
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 = 0;
|
|
size_t plen;
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( P != NULL );
|
|
ECP_VALIDATE_RET( olen != NULL );
|
|
ECP_VALIDATE_RET( buf != NULL );
|
|
ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
|
|
format == MBEDTLS_ECP_PF_COMPRESSED );
|
|
|
|
/*
|
|
* 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 );
|
|
}
|
|
|
|
plen = mbedtls_mpi_size( &grp->P );
|
|
|
|
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 ) );
|
|
}
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Import a point from unsigned binary data (SEC1 2.3.4)
|
|
*/
|
|
int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp,
|
|
mbedtls_ecp_point *pt,
|
|
const unsigned char *buf, size_t ilen )
|
|
{
|
|
int ret;
|
|
size_t plen;
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( pt != NULL );
|
|
ECP_VALIDATE_RET( buf != NULL );
|
|
|
|
if( ilen < 1 )
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
|
|
if( buf[0] == 0x00 )
|
|
{
|
|
if( ilen == 1 )
|
|
return( mbedtls_ecp_set_zero( pt ) );
|
|
else
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
}
|
|
|
|
plen = mbedtls_mpi_size( &grp->P );
|
|
|
|
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 ) );
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Import a point from a TLS ECPoint record (RFC 4492)
|
|
* struct {
|
|
* opaque point <1..2^8-1>;
|
|
* } ECPoint;
|
|
*/
|
|
int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp,
|
|
mbedtls_ecp_point *pt,
|
|
const unsigned char **buf, size_t buf_len )
|
|
{
|
|
unsigned char data_len;
|
|
const unsigned char *buf_start;
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( pt != NULL );
|
|
ECP_VALIDATE_RET( buf != NULL );
|
|
ECP_VALIDATE_RET( *buf != NULL );
|
|
|
|
/*
|
|
* We must have at least two bytes (1 for length, at least one for data)
|
|
*/
|
|
if( buf_len < 2 )
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
|
|
data_len = *(*buf)++;
|
|
if( data_len < 1 || data_len > buf_len - 1 )
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
|
|
/*
|
|
* Save buffer start for read_binary and update buf
|
|
*/
|
|
buf_start = *buf;
|
|
*buf += data_len;
|
|
|
|
return( mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len ) );
|
|
}
|
|
|
|
/*
|
|
* Export a point as a TLS ECPoint record (RFC 4492)
|
|
* struct {
|
|
* opaque point <1..2^8-1>;
|
|
* } ECPoint;
|
|
*/
|
|
int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
|
|
int format, size_t *olen,
|
|
unsigned char *buf, size_t blen )
|
|
{
|
|
int ret;
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( pt != NULL );
|
|
ECP_VALIDATE_RET( olen != NULL );
|
|
ECP_VALIDATE_RET( buf != NULL );
|
|
ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
|
|
format == MBEDTLS_ECP_PF_COMPRESSED );
|
|
|
|
/*
|
|
* buffer length must be at least one, for our length byte
|
|
*/
|
|
if( blen < 1 )
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
|
|
if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
|
|
olen, buf + 1, blen - 1) ) != 0 )
|
|
return( ret );
|
|
|
|
/*
|
|
* write length to the first byte and update total length
|
|
*/
|
|
buf[0] = (unsigned char) *olen;
|
|
++*olen;
|
|
|
|
return( 0 );
|
|
}
|
|
|
|
/*
|
|
* Set a group from an ECParameters record (RFC 4492)
|
|
*/
|
|
int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp,
|
|
const unsigned char **buf, size_t len )
|
|
{
|
|
int ret;
|
|
mbedtls_ecp_group_id grp_id;
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( buf != NULL );
|
|
ECP_VALIDATE_RET( *buf != NULL );
|
|
|
|
if( ( ret = mbedtls_ecp_tls_read_group_id( &grp_id, buf, len ) ) != 0 )
|
|
return( ret );
|
|
|
|
return( mbedtls_ecp_group_load( grp, grp_id ) );
|
|
}
|
|
|
|
/*
|
|
* Read a group id from an ECParameters record (RFC 4492) and convert it to
|
|
* mbedtls_ecp_group_id.
|
|
*/
|
|
int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp,
|
|
const unsigned char **buf, size_t len )
|
|
{
|
|
uint16_t tls_id;
|
|
const mbedtls_ecp_curve_info *curve_info;
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( buf != NULL );
|
|
ECP_VALIDATE_RET( *buf != NULL );
|
|
|
|
/*
|
|
* We expect at least three bytes (see below)
|
|
*/
|
|
if( len < 3 )
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
|
|
/*
|
|
* First byte is curve_type; only named_curve is handled
|
|
*/
|
|
if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
|
|
/*
|
|
* Next two bytes are the namedcurve value
|
|
*/
|
|
tls_id = *(*buf)++;
|
|
tls_id <<= 8;
|
|
tls_id |= *(*buf)++;
|
|
|
|
if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
|
|
return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
|
|
|
|
*grp = curve_info->grp_id;
|
|
|
|
return( 0 );
|
|
}
|
|
|
|
/*
|
|
* Write the ECParameters record corresponding to a group (RFC 4492)
|
|
*/
|
|
int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
|
|
unsigned char *buf, size_t blen )
|
|
{
|
|
const mbedtls_ecp_curve_info *curve_info;
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( buf != NULL );
|
|
ECP_VALIDATE_RET( olen != NULL );
|
|
|
|
if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
|
|
/*
|
|
* We are going to write 3 bytes (see below)
|
|
*/
|
|
*olen = 3;
|
|
if( blen < *olen )
|
|
return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
|
|
|
|
/*
|
|
* First byte is curve_type, always named_curve
|
|
*/
|
|
*buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
|
|
|
|
/*
|
|
* Next two bytes are the namedcurve value
|
|
*/
|
|
buf[0] = curve_info->tls_id >> 8;
|
|
buf[1] = curve_info->tls_id & 0xFF;
|
|
|
|
return( 0 );
|
|
}
|
|
|
|
/*
|
|
* Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
|
|
* See the documentation of struct mbedtls_ecp_group.
|
|
*
|
|
* This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
|
|
*/
|
|
static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
|
|
{
|
|
int ret;
|
|
|
|
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 )
|
|
|
|
/*
|
|
* Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
|
|
* N->s < 0 is a very fast test, which fails only if N is 0
|
|
*/
|
|
#define MOD_SUB( N ) \
|
|
while( (N).s < 0 && mbedtls_mpi_cmp_int( &(N), 0 ) != 0 ) \
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &(N), &(N), &grp->P ) )
|
|
|
|
/*
|
|
* 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 ) )
|
|
|
|
#if defined(ECP_SHORTWEIERSTRASS)
|
|
/*
|
|
* For curves in short Weierstrass form, we do all the internal operations in
|
|
* Jacobian coordinates.
|
|
*
|
|
* For multiplication, we'll use a comb method with coutermeasueres against
|
|
* SPA, hence timing attacks.
|
|
*/
|
|
|
|
/*
|
|
* Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
|
|
* Cost: 1N := 1I + 3M + 1S
|
|
*/
|
|
static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
|
|
{
|
|
int ret;
|
|
mbedtls_mpi Zi, ZZi;
|
|
|
|
if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
|
|
return( 0 );
|
|
|
|
#if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
|
|
if( mbedtls_internal_ecp_grp_capable( grp ) )
|
|
return( mbedtls_internal_ecp_normalize_jac( grp, pt ) );
|
|
#endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */
|
|
|
|
mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
|
|
|
|
/*
|
|
* X = X / Z^2 mod p
|
|
*/
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ZZi ) ); MOD_MUL( pt->X );
|
|
|
|
/*
|
|
* Y = Y / Z^3 mod p
|
|
*/
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ZZi ) ); MOD_MUL( pt->Y );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &Zi ) ); MOD_MUL( pt->Y );
|
|
|
|
/*
|
|
* Z = 1
|
|
*/
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
|
|
|
|
cleanup:
|
|
|
|
mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
|
|
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* 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 )
|
|
{
|
|
int ret;
|
|
size_t i;
|
|
mbedtls_mpi *c, u, Zi, ZZi;
|
|
|
|
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( ( c = mbedtls_calloc( T_size, sizeof( mbedtls_mpi ) ) ) == NULL )
|
|
return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
|
|
|
|
for( i = 0; i < T_size; i++ )
|
|
mbedtls_mpi_init( &c[i] );
|
|
|
|
mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
|
|
|
|
/*
|
|
* c[i] = Z_0 * ... * Z_i
|
|
*/
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
|
|
for( i = 1; i < T_size; i++ )
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &c[i], &c[i-1], &T[i]->Z ) );
|
|
MOD_MUL( c[i] );
|
|
}
|
|
|
|
/*
|
|
* u = 1 / (Z_0 * ... * Z_n) mod P
|
|
*/
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[T_size-1], &grp->P ) );
|
|
|
|
for( i = T_size - 1; ; i-- )
|
|
{
|
|
/*
|
|
* Zi = 1 / Z_i mod p
|
|
* u = 1 / (Z_0 * ... * Z_i) mod P
|
|
*/
|
|
if( i == 0 ) {
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
|
|
}
|
|
else
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Zi, &u, &c[i-1] ) ); MOD_MUL( Zi );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u, &u, &T[i]->Z ) ); MOD_MUL( u );
|
|
}
|
|
|
|
/*
|
|
* proceed as in normalize()
|
|
*/
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->X, &T[i]->X, &ZZi ) ); MOD_MUL( T[i]->X );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &ZZi ) ); MOD_MUL( T[i]->Y );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &Zi ) ); MOD_MUL( T[i]->Y );
|
|
|
|
/*
|
|
* Post-precessing: reclaim some memory by shrinking coordinates
|
|
* - not storing Z (always 1)
|
|
* - shrinking other coordinates, but still keeping the same number of
|
|
* limbs as P, as otherwise it will too likely be regrown too fast.
|
|
*/
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
|
|
mbedtls_mpi_free( &T[i]->Z );
|
|
|
|
if( i == 0 )
|
|
break;
|
|
}
|
|
|
|
cleanup:
|
|
|
|
mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
|
|
for( i = 0; i < T_size; i++ )
|
|
mbedtls_mpi_free( &c[i] );
|
|
mbedtls_free( c );
|
|
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* 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;
|
|
unsigned char nonzero;
|
|
mbedtls_mpi mQY;
|
|
|
|
mbedtls_mpi_init( &mQY );
|
|
|
|
/* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
|
|
nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
|
|
|
|
cleanup:
|
|
mbedtls_mpi_free( &mQY );
|
|
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Point doubling R = 2 P, Jacobian coordinates
|
|
*
|
|
* Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
|
|
*
|
|
* We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
|
|
* (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
|
|
*
|
|
* Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
|
|
*
|
|
* Cost: 1D := 3M + 4S (A == 0)
|
|
* 4M + 4S (A == -3)
|
|
* 3M + 6S + 1a otherwise
|
|
*/
|
|
static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
|
const mbedtls_ecp_point *P )
|
|
{
|
|
int ret;
|
|
mbedtls_mpi M, S, T, U;
|
|
|
|
#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 */
|
|
|
|
mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
|
|
|
|
/* Special case for A = -3 */
|
|
if( grp->A.p == NULL )
|
|
{
|
|
/* M = 3(X + Z^2)(X - Z^2) */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &P->X, &S ) ); MOD_ADD( T );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U, &P->X, &S ) ); MOD_SUB( U );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &U ) ); MOD_MUL( S );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
|
|
}
|
|
else
|
|
{
|
|
/* M = 3.X^2 */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &P->X ) ); MOD_MUL( S );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
|
|
|
|
/* Optimize away for "koblitz" curves with A = 0 */
|
|
if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
|
|
{
|
|
/* M += A.Z^4 */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &S, &S ) ); MOD_MUL( T );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &grp->A ) ); MOD_MUL( S );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &S ) ); MOD_ADD( M );
|
|
}
|
|
}
|
|
|
|
/* S = 4.X.Y^2 */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &P->Y, &P->Y ) ); MOD_MUL( T );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T, 1 ) ); MOD_ADD( T );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &T ) ); MOD_MUL( S );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &S, 1 ) ); MOD_ADD( S );
|
|
|
|
/* U = 8.Y^4 */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &T, &T ) ); MOD_MUL( U );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
|
|
|
|
/* T = M^2 - 2.S */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &M, &M ) ); MOD_MUL( T );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
|
|
|
|
/* S = M(S - T) - U */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &T ) ); MOD_SUB( S );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &S, &M ) ); MOD_MUL( S );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &U ) ); MOD_SUB( S );
|
|
|
|
/* U = 2.Y.Z */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &P->Y, &P->Z ) ); MOD_MUL( U );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
|
|
|
|
cleanup:
|
|
mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
|
|
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
|
|
*
|
|
* The coordinates of Q must be normalized (= affine),
|
|
* but those of P don't need to. R is not normalized.
|
|
*
|
|
* Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
|
|
* None of these cases can happen as intermediate step in ecp_mul_comb():
|
|
* - at each step, P, Q and R are multiples of the base point, the factor
|
|
* being less than its order, so none of them is zero;
|
|
* - Q is an odd multiple of the base point, P an even multiple,
|
|
* due to the choice of precomputed points in the modified comb method.
|
|
* So branches for these cases do not leak secret information.
|
|
*
|
|
* We accept Q->Z being unset (saving memory in tables) as meaning 1.
|
|
*
|
|
* Cost: 1A := 8M + 3S
|
|
*/
|
|
static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
|
const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
|
|
{
|
|
int ret;
|
|
mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
|
|
|
|
#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 */
|
|
|
|
/*
|
|
* Trivial cases: P == 0 or Q == 0 (case 1)
|
|
*/
|
|
if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
|
|
return( mbedtls_ecp_copy( R, Q ) );
|
|
|
|
if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
|
|
return( mbedtls_ecp_copy( R, P ) );
|
|
|
|
/*
|
|
* Make sure Q coordinates are normalized
|
|
*/
|
|
if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
|
|
mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
|
|
mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &P->Z, &P->Z ) ); MOD_MUL( T1 );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T1, &P->Z ) ); MOD_MUL( T2 );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T1, &Q->X ) ); MOD_MUL( T1 );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T2, &Q->Y ) ); MOD_MUL( T2 );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T1, &T1, &P->X ) ); MOD_SUB( T1 );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T2, &T2, &P->Y ) ); MOD_SUB( T2 );
|
|
|
|
/* Special cases (2) and (3) */
|
|
if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
|
|
{
|
|
if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
|
|
{
|
|
ret = ecp_double_jac( grp, R, P );
|
|
goto cleanup;
|
|
}
|
|
else
|
|
{
|
|
ret = mbedtls_ecp_set_zero( R );
|
|
goto cleanup;
|
|
}
|
|
}
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Z, &P->Z, &T1 ) ); MOD_MUL( Z );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T1, &T1 ) ); MOD_MUL( T3 );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T3, &T1 ) ); MOD_MUL( T4 );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &P->X ) ); MOD_MUL( T3 );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T3, 2 ) ); MOD_ADD( T1 );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &T2, &T2 ) ); MOD_MUL( X );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) ); MOD_SUB( X );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T4 ) ); MOD_SUB( X );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T3, &T3, &X ) ); MOD_SUB( T3 );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &T2 ) ); MOD_MUL( T3 );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T4, &P->Y ) ); MOD_MUL( T4 );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &Y, &T3, &T4 ) ); MOD_SUB( Y );
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
|
|
|
|
cleanup:
|
|
|
|
mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
|
|
mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
|
|
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* 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 )
|
|
{
|
|
int ret;
|
|
mbedtls_mpi l, ll;
|
|
size_t p_size;
|
|
int count = 0;
|
|
|
|
#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 */
|
|
|
|
p_size = ( grp->pbits + 7 ) / 8;
|
|
mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
|
|
|
|
/* Generate l such that 1 < l < p */
|
|
do
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
|
|
|
|
while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
|
|
|
|
if( count++ > 10 )
|
|
return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
|
|
}
|
|
while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
|
|
|
|
/* Z = l * Z */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Z, &pt->Z, &l ) ); MOD_MUL( pt->Z );
|
|
|
|
/* X = l^2 * X */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &l, &l ) ); MOD_MUL( ll );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ll ) ); MOD_MUL( pt->X );
|
|
|
|
/* Y = l^3 * Y */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &ll, &l ) ); MOD_MUL( ll );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ll ) ); MOD_MUL( pt->Y );
|
|
|
|
cleanup:
|
|
mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
|
|
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* 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;
|
|
unsigned char i;
|
|
size_t j = 0;
|
|
const unsigned char T_size = 1U << ( w - 1 );
|
|
mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->rsm != NULL )
|
|
{
|
|
if( rs_ctx->rsm->state == ecp_rsm_pre_dbl )
|
|
goto dbl;
|
|
if( rs_ctx->rsm->state == ecp_rsm_pre_norm_dbl )
|
|
goto norm_dbl;
|
|
if( rs_ctx->rsm->state == ecp_rsm_pre_add )
|
|
goto add;
|
|
if( rs_ctx->rsm->state == ecp_rsm_pre_norm_add )
|
|
goto norm_add;
|
|
}
|
|
#else
|
|
(void) rs_ctx;
|
|
#endif
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->rsm != NULL )
|
|
{
|
|
rs_ctx->rsm->state = ecp_rsm_pre_dbl;
|
|
|
|
/* initial state for the loop */
|
|
rs_ctx->rsm->i = 0;
|
|
}
|
|
|
|
dbl:
|
|
#endif
|
|
/*
|
|
* Set T[0] = P and
|
|
* T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
|
|
*/
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0 )
|
|
j = rs_ctx->rsm->i;
|
|
else
|
|
#endif
|
|
j = 0;
|
|
|
|
for( ; j < d * ( w - 1 ); j++ )
|
|
{
|
|
MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_DBL );
|
|
|
|
i = 1U << ( j / d );
|
|
cur = T + i;
|
|
|
|
if( j % d == 0 )
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
|
|
|
|
MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
|
|
}
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->rsm != NULL )
|
|
rs_ctx->rsm->state = ecp_rsm_pre_norm_dbl;
|
|
|
|
norm_dbl:
|
|
#endif
|
|
/*
|
|
* Normalize current elements in T. As T has holes,
|
|
* use an auxiliary array of pointers to elements in T.
|
|
*/
|
|
j = 0;
|
|
for( i = 1; i < T_size; i <<= 1 )
|
|
TT[j++] = T + i;
|
|
|
|
MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV + 6 * j - 2 );
|
|
|
|
MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) );
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->rsm != NULL )
|
|
rs_ctx->rsm->state = ecp_rsm_pre_add;
|
|
|
|
add:
|
|
#endif
|
|
/*
|
|
* Compute the remaining ones using the minimal number of additions
|
|
* Be careful to update T[2^l] only after using it!
|
|
*/
|
|
MBEDTLS_ECP_BUDGET( ( T_size - 1 ) * MBEDTLS_ECP_OPS_ADD );
|
|
|
|
for( i = 1; i < T_size; i <<= 1 )
|
|
{
|
|
j = i;
|
|
while( j-- )
|
|
MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
|
|
}
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->rsm != NULL )
|
|
rs_ctx->rsm->state = ecp_rsm_pre_norm_add;
|
|
|
|
norm_add:
|
|
#endif
|
|
/*
|
|
* Normalize final elements in T. Even though there are no holes now, we
|
|
* still need the auxiliary array for homogeneity with the previous
|
|
* call. Also, skip T[0] which is already normalised, being a copy of P.
|
|
*/
|
|
for( j = 0; j + 1 < T_size; j++ )
|
|
TT[j] = T + j + 1;
|
|
|
|
MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV + 6 * j - 2 );
|
|
|
|
MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) );
|
|
|
|
cleanup:
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
|
|
ret == MBEDTLS_ERR_ECP_IN_PROGRESS )
|
|
{
|
|
if( rs_ctx->rsm->state == ecp_rsm_pre_dbl )
|
|
rs_ctx->rsm->i = j;
|
|
}
|
|
#endif
|
|
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
|
|
*
|
|
* See ecp_comb_recode_core() for background
|
|
*/
|
|
static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
|
const mbedtls_ecp_point T[], unsigned char T_size,
|
|
unsigned char i )
|
|
{
|
|
int ret;
|
|
unsigned char ii, j;
|
|
|
|
/* Ignore the "sign" bit and scale down */
|
|
ii = ( i & 0x7Fu ) >> 1;
|
|
|
|
/* Read the whole table to thwart cache-based timing attacks */
|
|
for( j = 0; j < T_size; j++ )
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
|
|
}
|
|
|
|
/* Safely invert result if i is "negative" */
|
|
MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Core multiplication algorithm for the (modified) comb method.
|
|
* This part is actually common with the basic comb method (GECC 3.44)
|
|
*
|
|
* Cost: d A + d D + 1 R
|
|
*/
|
|
static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
|
const mbedtls_ecp_point T[], unsigned char T_size,
|
|
const unsigned char x[], size_t d,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng,
|
|
mbedtls_ecp_restart_ctx *rs_ctx )
|
|
{
|
|
int ret;
|
|
mbedtls_ecp_point Txi;
|
|
size_t i;
|
|
|
|
mbedtls_ecp_point_init( &Txi );
|
|
|
|
#if !defined(MBEDTLS_ECP_RESTARTABLE)
|
|
(void) rs_ctx;
|
|
#endif
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
|
|
rs_ctx->rsm->state != ecp_rsm_comb_core )
|
|
{
|
|
rs_ctx->rsm->i = 0;
|
|
rs_ctx->rsm->state = ecp_rsm_comb_core;
|
|
}
|
|
|
|
/* new 'if' instead of nested for the sake of the 'else' branch */
|
|
if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0 )
|
|
{
|
|
/* restore current index (R already pointing to rs_ctx->rsm->R) */
|
|
i = rs_ctx->rsm->i;
|
|
}
|
|
else
|
|
#endif
|
|
{
|
|
/* Start with a non-zero point and randomize its coordinates */
|
|
i = d;
|
|
MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, T_size, x[i] ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
|
|
if( 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 ) );
|
|
MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, T_size, x[i] ) );
|
|
MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
|
|
}
|
|
|
|
cleanup:
|
|
|
|
mbedtls_ecp_point_free( &Txi );
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
|
|
ret == MBEDTLS_ERR_ECP_IN_PROGRESS )
|
|
{
|
|
rs_ctx->rsm->i = i;
|
|
/* no need to save R, already pointing to rs_ctx->rsm->R */
|
|
}
|
|
#endif
|
|
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Recode the scalar to get constant-time comb multiplication
|
|
*
|
|
* As the actual scalar recoding needs an odd scalar as a starting point,
|
|
* this wrapper ensures that by replacing m by N - m if necessary, and
|
|
* informs the caller that the result of multiplication will be negated.
|
|
*
|
|
* This works because we only support large prime order for Short Weierstrass
|
|
* curves, so N is always odd hence either m or N - m is.
|
|
*
|
|
* See ecp_comb_recode_core() for background.
|
|
*/
|
|
static int ecp_comb_recode_scalar( const mbedtls_ecp_group *grp,
|
|
const mbedtls_mpi *m,
|
|
unsigned char k[COMB_MAX_D + 1],
|
|
size_t d,
|
|
unsigned char w,
|
|
unsigned char *parity_trick )
|
|
{
|
|
int ret;
|
|
mbedtls_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;
|
|
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:
|
|
#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_ECP_BUDGET( MBEDTLS_ECP_OPS_INV );
|
|
MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, RR ) );
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->rsm != NULL )
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, RR ) );
|
|
#endif
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Pick window size based on curve size and whether we optimize for base point
|
|
*/
|
|
static unsigned char ecp_pick_window_size( const mbedtls_ecp_group *grp,
|
|
unsigned char p_eq_g )
|
|
{
|
|
unsigned char w;
|
|
|
|
/*
|
|
* Minimize the number of multiplications, that is minimize
|
|
* 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
|
|
* (see costs of the various parts, with 1S = 1M)
|
|
*/
|
|
w = grp->nbits >= 384 ? 5 : 4;
|
|
|
|
/*
|
|
* If P == G, pre-compute a bit more, since this may be re-used later.
|
|
* Just adding one avoids upping the cost of the first mul too much,
|
|
* and the memory cost too.
|
|
*/
|
|
if( p_eq_g )
|
|
w++;
|
|
|
|
/*
|
|
* Make sure w is within bounds.
|
|
* (The last test is useful only for very small curves in the test suite.)
|
|
*/
|
|
if( w > MBEDTLS_ECP_WINDOW_SIZE )
|
|
w = MBEDTLS_ECP_WINDOW_SIZE;
|
|
if( w >= grp->nbits )
|
|
w = 2;
|
|
|
|
return( w );
|
|
}
|
|
|
|
/*
|
|
* Multiplication using the comb method - for curves in short Weierstrass form
|
|
*
|
|
* This function is mainly responsible for administrative work:
|
|
* - managing the restart context if enabled
|
|
* - managing the table of precomputed points (passed between the below two
|
|
* functions): allocation, computation, ownership tranfer, freeing.
|
|
*
|
|
* It delegates the actual arithmetic work to:
|
|
* ecp_precompute_comb() and ecp_mul_comb_with_precomp()
|
|
*
|
|
* See comments on ecp_comb_recode_core() regarding the computation strategy.
|
|
*/
|
|
static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
|
const mbedtls_mpi *m, const mbedtls_ecp_point *P,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng,
|
|
mbedtls_ecp_restart_ctx *rs_ctx )
|
|
{
|
|
int ret;
|
|
unsigned char w, p_eq_g, i;
|
|
size_t d;
|
|
unsigned char T_size, T_ok;
|
|
mbedtls_ecp_point *T;
|
|
|
|
ECP_RS_ENTER( rsm );
|
|
|
|
/* Is P the base point ? */
|
|
#if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
|
|
p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
|
|
mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
|
|
#else
|
|
p_eq_g = 0;
|
|
#endif
|
|
|
|
/* Pick window size and deduce related sizes */
|
|
w = ecp_pick_window_size( grp, p_eq_g );
|
|
T_size = 1U << ( w - 1 );
|
|
d = ( grp->nbits + w - 1 ) / w;
|
|
|
|
/* Pre-computed table: do we have it already for the base point? */
|
|
if( p_eq_g && grp->T != NULL )
|
|
{
|
|
/* second pointer to the same table, will be deleted on exit */
|
|
T = grp->T;
|
|
T_ok = 1;
|
|
}
|
|
else
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
/* Pre-computed table: do we have one in progress? complete? */
|
|
if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->T != NULL )
|
|
{
|
|
/* transfer ownership of T from rsm to local function */
|
|
T = rs_ctx->rsm->T;
|
|
rs_ctx->rsm->T = NULL;
|
|
rs_ctx->rsm->T_size = 0;
|
|
|
|
/* This effectively jumps to the call to mul_comb_after_precomp() */
|
|
T_ok = rs_ctx->rsm->state >= ecp_rsm_comb_core;
|
|
}
|
|
else
|
|
#endif
|
|
/* Allocate table if we didn't have any */
|
|
{
|
|
T = mbedtls_calloc( T_size, sizeof( mbedtls_ecp_point ) );
|
|
if( T == NULL )
|
|
{
|
|
ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
|
|
goto cleanup;
|
|
}
|
|
|
|
for( i = 0; i < T_size; i++ )
|
|
mbedtls_ecp_point_init( &T[i] );
|
|
|
|
T_ok = 0;
|
|
}
|
|
|
|
/* Compute table (or finish computing it) if not done already */
|
|
if( !T_ok )
|
|
{
|
|
MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d, rs_ctx ) );
|
|
|
|
if( p_eq_g )
|
|
{
|
|
/* almost transfer ownership of T to the group, but keep a copy of
|
|
* the pointer to use for calling the next function more easily */
|
|
grp->T = T;
|
|
grp->T_size = T_size;
|
|
}
|
|
}
|
|
|
|
/* Actual comb multiplication using precomputed points */
|
|
MBEDTLS_MPI_CHK( ecp_mul_comb_after_precomp( grp, R, m,
|
|
T, T_size, w, d,
|
|
f_rng, p_rng, rs_ctx ) );
|
|
|
|
cleanup:
|
|
|
|
/* does T belong to the group? */
|
|
if( T == grp->T )
|
|
T = NULL;
|
|
|
|
/* does T belong to the restart context? */
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->rsm != NULL && ret == MBEDTLS_ERR_ECP_IN_PROGRESS && T != NULL )
|
|
{
|
|
/* transfer ownership of T from local function to rsm */
|
|
rs_ctx->rsm->T_size = T_size;
|
|
rs_ctx->rsm->T = T;
|
|
T = NULL;
|
|
}
|
|
#endif
|
|
|
|
/* did T belong to us? then let's destroy it! */
|
|
if( T != NULL )
|
|
{
|
|
for( i = 0; i < T_size; i++ )
|
|
mbedtls_ecp_point_free( &T[i] );
|
|
mbedtls_free( T );
|
|
}
|
|
|
|
/* don't free R while in progress in case R == P */
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( ret != MBEDTLS_ERR_ECP_IN_PROGRESS )
|
|
#endif
|
|
/* prevent caller from using invalid value */
|
|
if( ret != 0 )
|
|
mbedtls_ecp_point_free( R );
|
|
|
|
ECP_RS_LEAVE( rsm );
|
|
|
|
return( ret );
|
|
}
|
|
|
|
#endif /* ECP_SHORTWEIERSTRASS */
|
|
|
|
#if defined(ECP_MONTGOMERY)
|
|
/*
|
|
* For Montgomery curves, we do all the internal arithmetic in projective
|
|
* coordinates. Import/export of points uses only the x coordinates, which is
|
|
* internaly represented as X / Z.
|
|
*
|
|
* For scalar multiplication, we'll use a Montgomery ladder.
|
|
*/
|
|
|
|
/*
|
|
* Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
|
|
* Cost: 1M + 1I
|
|
*/
|
|
static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
|
|
{
|
|
int ret;
|
|
|
|
#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 */
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* 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 )
|
|
{
|
|
int ret;
|
|
mbedtls_mpi l;
|
|
size_t p_size;
|
|
int count = 0;
|
|
|
|
#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 */
|
|
|
|
p_size = ( grp->pbits + 7 ) / 8;
|
|
mbedtls_mpi_init( &l );
|
|
|
|
/* Generate l such that 1 < l < p */
|
|
do
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
|
|
|
|
while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
|
|
|
|
if( count++ > 10 )
|
|
return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
|
|
}
|
|
while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z );
|
|
|
|
cleanup:
|
|
mbedtls_mpi_free( &l );
|
|
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* 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 )
|
|
{
|
|
int ret;
|
|
mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
|
|
|
|
#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 */
|
|
|
|
mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
|
|
mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
|
|
mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &A, &P->X, &P->Z ) ); MOD_ADD( A );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &AA, &A, &A ) ); MOD_MUL( AA );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &B, &P->X, &P->Z ) ); MOD_SUB( B );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &BB, &B, &B ) ); MOD_MUL( BB );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &E, &AA, &BB ) ); MOD_SUB( E );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &C, &Q->X, &Q->Z ) ); MOD_ADD( C );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &D, &Q->X, &Q->Z ) ); MOD_SUB( D );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DA, &D, &A ) ); MOD_MUL( DA );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &CB, &C, &B ) ); MOD_MUL( CB );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &S->X, &DA, &CB ) ); MOD_MUL( S->X );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->X, &S->X, &S->X ) ); MOD_MUL( S->X );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S->Z, &DA, &CB ) ); MOD_SUB( S->Z );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, &S->Z, &S->Z ) ); MOD_MUL( S->Z );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, d, &S->Z ) ); MOD_MUL( S->Z );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->X, &AA, &BB ) ); MOD_MUL( R->X );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &grp->A, &E ) ); MOD_MUL( R->Z );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &R->Z, &BB, &R->Z ) ); MOD_ADD( R->Z );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &E, &R->Z ) ); MOD_MUL( R->Z );
|
|
|
|
cleanup:
|
|
mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
|
|
mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
|
|
mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
|
|
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* 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;
|
|
size_t i;
|
|
unsigned char b;
|
|
mbedtls_ecp_point RP;
|
|
mbedtls_mpi PX;
|
|
|
|
mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
|
|
|
|
/* Save PX and read from P before writing to R, in case P == R */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
|
|
|
|
/* Set R to zero in modified x/z coordinates */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
|
|
mbedtls_mpi_free( &R->Y );
|
|
|
|
/* RP.X might be sligtly larger than P, so reduce it */
|
|
MOD_ADD( RP.X );
|
|
|
|
/* Randomize coordinates of the starting point */
|
|
if( f_rng != NULL )
|
|
MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
|
|
|
|
/* Loop invariant: R = result so far, RP = R + P */
|
|
i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
|
|
while( i-- > 0 )
|
|
{
|
|
b = mbedtls_mpi_get_bit( m, i );
|
|
/*
|
|
* if (b) R = 2R + P else R = 2R,
|
|
* which is:
|
|
* if (b) double_add( RP, R, RP, R )
|
|
* else double_add( R, RP, R, RP )
|
|
* but using safe conditional swaps to avoid leaks
|
|
*/
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
|
|
MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
|
|
}
|
|
|
|
/*
|
|
* Knowledge of the projective coordinates may leak the last few bits of the
|
|
* scalar [1], and since our MPI implementation isn't constant-flow,
|
|
* inversion (used for coordinate normalization) may leak the full value
|
|
* of its input via side-channels [2].
|
|
*
|
|
* [1] https://eprint.iacr.org/2003/191
|
|
* [2] https://eprint.iacr.org/2020/055
|
|
*
|
|
* Avoid the leak by randomizing coordinates before we normalize them.
|
|
*/
|
|
if( f_rng != NULL )
|
|
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 );
|
|
|
|
return( ret );
|
|
}
|
|
|
|
#endif /* ECP_MONTGOMERY */
|
|
|
|
/*
|
|
* Restartable multiplication R = m * P
|
|
*/
|
|
int mbedtls_ecp_mul_restartable( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
|
const mbedtls_mpi *m, const mbedtls_ecp_point *P,
|
|
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
|
|
mbedtls_ecp_restart_ctx *rs_ctx )
|
|
{
|
|
int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
|
|
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
|
|
char is_grp_capable = 0;
|
|
#endif
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( R != NULL );
|
|
ECP_VALIDATE_RET( m != NULL );
|
|
ECP_VALIDATE_RET( P != NULL );
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
/* reset ops count for this call if top-level */
|
|
if( rs_ctx != NULL && rs_ctx->depth++ == 0 )
|
|
rs_ctx->ops_done = 0;
|
|
#endif
|
|
|
|
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
|
|
if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) )
|
|
MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
|
|
#endif /* MBEDTLS_ECP_INTERNAL_ALT */
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
/* skip argument check when restarting */
|
|
if( rs_ctx == NULL || rs_ctx->rsm == NULL )
|
|
#endif
|
|
{
|
|
/* check_privkey is free */
|
|
MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_CHK );
|
|
|
|
/* Common sanity checks */
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( grp, m ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, P ) );
|
|
}
|
|
|
|
ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
|
|
#if defined(ECP_MONTGOMERY)
|
|
if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
|
|
MBEDTLS_MPI_CHK( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) );
|
|
#endif
|
|
#if defined(ECP_SHORTWEIERSTRASS)
|
|
if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
|
|
MBEDTLS_MPI_CHK( ecp_mul_comb( grp, R, m, P, f_rng, p_rng, rs_ctx ) );
|
|
#endif
|
|
|
|
cleanup:
|
|
|
|
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
|
|
if( is_grp_capable )
|
|
mbedtls_internal_ecp_free( grp );
|
|
#endif /* MBEDTLS_ECP_INTERNAL_ALT */
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL )
|
|
rs_ctx->depth--;
|
|
#endif
|
|
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Multiplication R = m * P
|
|
*/
|
|
int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
|
const mbedtls_mpi *m, const mbedtls_ecp_point *P,
|
|
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
|
|
{
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( R != NULL );
|
|
ECP_VALIDATE_RET( m != NULL );
|
|
ECP_VALIDATE_RET( P != NULL );
|
|
return( mbedtls_ecp_mul_restartable( grp, R, m, P, f_rng, p_rng, NULL ) );
|
|
}
|
|
|
|
#if defined(ECP_SHORTWEIERSTRASS)
|
|
/*
|
|
* 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_mpi YY, RHS;
|
|
|
|
/* pt coordinates must be normalized for our checks */
|
|
if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ||
|
|
mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 ||
|
|
mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
|
|
mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
|
|
return( MBEDTLS_ERR_ECP_INVALID_KEY );
|
|
|
|
mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
|
|
|
|
/*
|
|
* YY = Y^2
|
|
* RHS = X (X^2 + A) + B = X^3 + A X + B
|
|
*/
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &YY, &pt->Y, &pt->Y ) ); MOD_MUL( YY );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &pt->X, &pt->X ) ); MOD_MUL( RHS );
|
|
|
|
/* Special case for A = -3 */
|
|
if( grp->A.p == NULL )
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS );
|
|
}
|
|
else
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->A ) ); MOD_ADD( RHS );
|
|
}
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &RHS, &pt->X ) ); MOD_MUL( RHS );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->B ) ); MOD_ADD( RHS );
|
|
|
|
if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
|
|
ret = MBEDTLS_ERR_ECP_INVALID_KEY;
|
|
|
|
cleanup:
|
|
|
|
mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
|
|
|
|
return( ret );
|
|
}
|
|
#endif /* ECP_SHORTWEIERSTRASS */
|
|
|
|
/*
|
|
* R = m * P with shortcuts for m == 1 and m == -1
|
|
* NOT constant-time - ONLY for short Weierstrass!
|
|
*/
|
|
static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
|
|
mbedtls_ecp_point *R,
|
|
const mbedtls_mpi *m,
|
|
const mbedtls_ecp_point *P,
|
|
mbedtls_ecp_restart_ctx *rs_ctx )
|
|
{
|
|
int ret;
|
|
|
|
if( mbedtls_mpi_cmp_int( m, 1 ) == 0 )
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
|
|
}
|
|
else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
|
|
if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 )
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
|
|
}
|
|
else
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_mul_restartable( grp, R, m, P,
|
|
NULL, NULL, rs_ctx ) );
|
|
}
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Restartable linear combination
|
|
* NOT constant-time
|
|
*/
|
|
int mbedtls_ecp_muladd_restartable(
|
|
mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
|
const mbedtls_mpi *m, const mbedtls_ecp_point *P,
|
|
const mbedtls_mpi *n, const mbedtls_ecp_point *Q,
|
|
mbedtls_ecp_restart_ctx *rs_ctx )
|
|
{
|
|
int ret;
|
|
mbedtls_ecp_point mP;
|
|
mbedtls_ecp_point *pmP = &mP;
|
|
mbedtls_ecp_point *pR = R;
|
|
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
|
|
char is_grp_capable = 0;
|
|
#endif
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( R != NULL );
|
|
ECP_VALIDATE_RET( m != NULL );
|
|
ECP_VALIDATE_RET( P != NULL );
|
|
ECP_VALIDATE_RET( n != NULL );
|
|
ECP_VALIDATE_RET( Q != NULL );
|
|
|
|
if( ecp_get_type( grp ) != ECP_TYPE_SHORT_WEIERSTRASS )
|
|
return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
|
|
|
|
mbedtls_ecp_point_init( &mP );
|
|
|
|
ECP_RS_ENTER( ma );
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->ma != NULL )
|
|
{
|
|
/* redirect intermediate results to restart context */
|
|
pmP = &rs_ctx->ma->mP;
|
|
pR = &rs_ctx->ma->R;
|
|
|
|
/* jump to next operation */
|
|
if( rs_ctx->ma->state == ecp_rsma_mul2 )
|
|
goto mul2;
|
|
if( rs_ctx->ma->state == ecp_rsma_add )
|
|
goto add;
|
|
if( rs_ctx->ma->state == ecp_rsma_norm )
|
|
goto norm;
|
|
}
|
|
#endif /* MBEDTLS_ECP_RESTARTABLE */
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pmP, m, P, rs_ctx ) );
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->ma != NULL )
|
|
rs_ctx->ma->state = ecp_rsma_mul2;
|
|
|
|
mul2:
|
|
#endif
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pR, n, Q, rs_ctx ) );
|
|
|
|
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
|
|
if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) )
|
|
MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
|
|
#endif /* MBEDTLS_ECP_INTERNAL_ALT */
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->ma != NULL )
|
|
rs_ctx->ma->state = ecp_rsma_add;
|
|
|
|
add:
|
|
#endif
|
|
MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_ADD );
|
|
MBEDTLS_MPI_CHK( ecp_add_mixed( grp, pR, pmP, pR ) );
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->ma != NULL )
|
|
rs_ctx->ma->state = ecp_rsma_norm;
|
|
|
|
norm:
|
|
#endif
|
|
MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV );
|
|
MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, pR ) );
|
|
|
|
#if defined(MBEDTLS_ECP_RESTARTABLE)
|
|
if( rs_ctx != NULL && rs_ctx->ma != NULL )
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, pR ) );
|
|
#endif
|
|
|
|
cleanup:
|
|
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
|
|
if( is_grp_capable )
|
|
mbedtls_internal_ecp_free( grp );
|
|
#endif /* MBEDTLS_ECP_INTERNAL_ALT */
|
|
|
|
mbedtls_ecp_point_free( &mP );
|
|
|
|
ECP_RS_LEAVE( ma );
|
|
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Linear combination
|
|
* NOT constant-time
|
|
*/
|
|
int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
|
const mbedtls_mpi *m, const mbedtls_ecp_point *P,
|
|
const mbedtls_mpi *n, const mbedtls_ecp_point *Q )
|
|
{
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( R != NULL );
|
|
ECP_VALIDATE_RET( m != NULL );
|
|
ECP_VALIDATE_RET( P != NULL );
|
|
ECP_VALIDATE_RET( n != NULL );
|
|
ECP_VALIDATE_RET( Q != NULL );
|
|
return( mbedtls_ecp_muladd_restartable( grp, R, m, P, n, Q, NULL ) );
|
|
}
|
|
|
|
#if defined(ECP_MONTGOMERY)
|
|
/*
|
|
* Check validity of a public key for Montgomery curves with x-only schemes
|
|
*/
|
|
static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
|
|
{
|
|
/* [Curve25519 p. 5] Just check X is the correct number of bytes */
|
|
/* Allow any public value, if it's too big then we'll just reduce it mod p
|
|
* (RFC 7748 sec. 5 para. 3). */
|
|
if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
|
|
return( MBEDTLS_ERR_ECP_INVALID_KEY );
|
|
|
|
return( 0 );
|
|
}
|
|
#endif /* ECP_MONTGOMERY */
|
|
|
|
/*
|
|
* Check that a point is valid as a public key
|
|
*/
|
|
int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp,
|
|
const mbedtls_ecp_point *pt )
|
|
{
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( pt != NULL );
|
|
|
|
/* Must use affine coordinates */
|
|
if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
|
|
return( MBEDTLS_ERR_ECP_INVALID_KEY );
|
|
|
|
#if defined(ECP_MONTGOMERY)
|
|
if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
|
|
return( ecp_check_pubkey_mx( grp, pt ) );
|
|
#endif
|
|
#if defined(ECP_SHORTWEIERSTRASS)
|
|
if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
|
|
return( ecp_check_pubkey_sw( grp, pt ) );
|
|
#endif
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
}
|
|
|
|
/*
|
|
* Check that an mbedtls_mpi is valid as a private key
|
|
*/
|
|
int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp,
|
|
const mbedtls_mpi *d )
|
|
{
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( d != NULL );
|
|
|
|
#if defined(ECP_MONTGOMERY)
|
|
if( ecp_get_type( grp ) == 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 /* ECP_MONTGOMERY */
|
|
#if defined(ECP_SHORTWEIERSTRASS)
|
|
if( ecp_get_type( grp ) == 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 /* ECP_SHORTWEIERSTRASS */
|
|
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
}
|
|
|
|
/*
|
|
* Generate a private key
|
|
*/
|
|
int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp,
|
|
mbedtls_mpi *d,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng )
|
|
{
|
|
int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
|
|
size_t n_size;
|
|
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( d != NULL );
|
|
ECP_VALIDATE_RET( f_rng != NULL );
|
|
|
|
n_size = ( grp->nbits + 7 ) / 8;
|
|
|
|
#if defined(ECP_MONTGOMERY)
|
|
if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
|
|
{
|
|
/* [M225] page 5 */
|
|
size_t b;
|
|
|
|
do {
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
|
|
} while( mbedtls_mpi_bitlen( d ) == 0);
|
|
|
|
/* Make sure the most significant bit is nbits */
|
|
b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */
|
|
if( b > grp->nbits )
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) );
|
|
else
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 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( grp->nbits == 254 )
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
|
|
}
|
|
}
|
|
#endif /* ECP_MONTGOMERY */
|
|
|
|
#if defined(ECP_SHORTWEIERSTRASS)
|
|
if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
|
|
{
|
|
/* SEC1 3.2.1: Generate d such that 1 <= n < N */
|
|
int count = 0;
|
|
unsigned cmp = 0;
|
|
|
|
/*
|
|
* Match the procedure given in RFC 6979 (deterministic ECDSA):
|
|
* - use the same byte ordering;
|
|
* - keep the leftmost nbits bits of the generated octet string;
|
|
* - try until result is in the desired range.
|
|
* This also avoids any biais, which is especially important for ECDSA.
|
|
*/
|
|
do
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) );
|
|
|
|
/*
|
|
* Each try has at worst a probability 1/2 of failing (the msb has
|
|
* a probability 1/2 of being 0, and then the result will be < N),
|
|
* so after 30 tries failure probability is a most 2**(-30).
|
|
*
|
|
* For most curves, 1 try is enough with overwhelming probability,
|
|
* since N starts with a lot of 1s in binary, but some curves
|
|
* such as secp224k1 are actually very close to the worst case.
|
|
*/
|
|
if( ++count > 30 )
|
|
return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
|
|
|
|
ret = mbedtls_mpi_lt_mpi_ct( d, &grp->N, &cmp );
|
|
if( ret != 0 )
|
|
{
|
|
goto cleanup;
|
|
}
|
|
}
|
|
while( mbedtls_mpi_cmp_int( d, 1 ) < 0 || cmp != 1 );
|
|
}
|
|
#endif /* ECP_SHORTWEIERSTRASS */
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* 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;
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( d != NULL );
|
|
ECP_VALIDATE_RET( G != NULL );
|
|
ECP_VALIDATE_RET( Q != NULL );
|
|
ECP_VALIDATE_RET( f_rng != NULL );
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_gen_privkey( grp, d, f_rng, p_rng ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) );
|
|
|
|
cleanup:
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* Generate key pair, wrapper for conventional base point
|
|
*/
|
|
int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp,
|
|
mbedtls_mpi *d, mbedtls_ecp_point *Q,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng )
|
|
{
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( d != NULL );
|
|
ECP_VALIDATE_RET( Q != NULL );
|
|
ECP_VALIDATE_RET( f_rng != NULL );
|
|
|
|
return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) );
|
|
}
|
|
|
|
/*
|
|
* Generate a keypair, prettier wrapper
|
|
*/
|
|
int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
|
|
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
|
|
{
|
|
int ret;
|
|
ECP_VALIDATE_RET( key != NULL );
|
|
ECP_VALIDATE_RET( f_rng != NULL );
|
|
|
|
if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
|
|
return( ret );
|
|
|
|
return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
|
|
}
|
|
|
|
/*
|
|
* Check a public-private key pair
|
|
*/
|
|
int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
|
|
{
|
|
int ret;
|
|
mbedtls_ecp_point Q;
|
|
mbedtls_ecp_group grp;
|
|
ECP_VALIDATE_RET( pub != NULL );
|
|
ECP_VALIDATE_RET( prv != NULL );
|
|
|
|
if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
|
|
pub->grp.id != prv->grp.id ||
|
|
mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
|
|
mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
|
|
mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
|
|
{
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
}
|
|
|
|
mbedtls_ecp_point_init( &Q );
|
|
mbedtls_ecp_group_init( &grp );
|
|
|
|
/* mbedtls_ecp_mul() needs a non-const group... */
|
|
mbedtls_ecp_group_copy( &grp, &prv->grp );
|
|
|
|
/* Also checks d is valid */
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
|
|
|
|
if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
|
|
mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
|
|
mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
|
|
{
|
|
ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
|
|
goto cleanup;
|
|
}
|
|
|
|
cleanup:
|
|
mbedtls_ecp_point_free( &Q );
|
|
mbedtls_ecp_group_free( &grp );
|
|
|
|
return( ret );
|
|
}
|
|
|
|
#if defined(MBEDTLS_SELF_TEST)
|
|
|
|
/*
|
|
* Checkup routine
|
|
*/
|
|
int mbedtls_ecp_self_test( int verbose )
|
|
{
|
|
int ret;
|
|
size_t i;
|
|
mbedtls_ecp_group grp;
|
|
mbedtls_ecp_point R, P;
|
|
mbedtls_mpi m;
|
|
unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
|
|
/* exponents especially adapted for secp192r1 */
|
|
const char *exponents[] =
|
|
{
|
|
"000000000000000000000000000000000000000000000001", /* one */
|
|
"FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22830", /* N - 1 */
|
|
"5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
|
|
"400000000000000000000000000000000000000000000000", /* one and zeros */
|
|
"7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
|
|
"555555555555555555555555555555555555555555555555", /* 101010... */
|
|
};
|
|
|
|
mbedtls_ecp_group_init( &grp );
|
|
mbedtls_ecp_point_init( &R );
|
|
mbedtls_ecp_point_init( &P );
|
|
mbedtls_mpi_init( &m );
|
|
|
|
/* 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 test #1 (constant op_count, base point G): " );
|
|
|
|
/* Do a dummy multiplication first to trigger precomputation */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
|
|
|
|
add_count = 0;
|
|
dbl_count = 0;
|
|
mul_count = 0;
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
|
|
|
|
for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); 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( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
|
|
|
|
if( add_count != add_c_prev ||
|
|
dbl_count != dbl_c_prev ||
|
|
mul_count != mul_c_prev )
|
|
{
|
|
if( verbose != 0 )
|
|
mbedtls_printf( "failed (%u)\n", (unsigned int) i );
|
|
|
|
ret = 1;
|
|
goto cleanup;
|
|
}
|
|
}
|
|
|
|
if( verbose != 0 )
|
|
mbedtls_printf( "passed\n" );
|
|
|
|
if( verbose != 0 )
|
|
mbedtls_printf( " ECP test #2 (constant op_count, other point): " );
|
|
/* We computed P = 2G last time, use it */
|
|
|
|
add_count = 0;
|
|
dbl_count = 0;
|
|
mul_count = 0;
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
|
|
|
|
for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); 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( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
|
|
|
|
if( add_count != add_c_prev ||
|
|
dbl_count != dbl_c_prev ||
|
|
mul_count != mul_c_prev )
|
|
{
|
|
if( verbose != 0 )
|
|
mbedtls_printf( "failed (%u)\n", (unsigned int) i );
|
|
|
|
ret = 1;
|
|
goto cleanup;
|
|
}
|
|
}
|
|
|
|
if( verbose != 0 )
|
|
mbedtls_printf( "passed\n" );
|
|
|
|
cleanup:
|
|
|
|
if( ret < 0 && verbose != 0 )
|
|
mbedtls_printf( "Unexpected error, return code = %08X\n", 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 */
|