171a7efd02
The private keys used in ECDH differ in the case of Weierstrass and Montgomery curves. They have different constraints, the former is based on big endian, the latter little endian byte order. The fundamental approach is different too: - Weierstrass keys have to be in the right interval, otherwise they are rejected. - Any byte array of the right size is a valid Montgomery key and it needs to be masked before interpreting it as a number. Historically it was sufficient to use mbedtls_mpi_read_binary() to read private keys, but as a preparation to improve support for Montgomery curves we add mbedtls_ecp_read_key() to enable uniform treatment of EC keys. For the masking the `mbedtls_mpi_set_bit()` function is used. This is suboptimal but seems to provide the best trade-off at this time. Alternatives considered: - Making a copy of the input buffer (less efficient) - removing the `const` constraint from the input buffer (breaks the api and makes it less user friendly) - applying the mask directly to the limbs (violates the api between the modules and creates and unwanted dependency)
3067 lines
95 KiB
C
3067 lines
95 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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/*
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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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|
|
/*
|
|
* 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
|
|
* - readable name
|
|
*
|
|
* Curves are listed in order: largest curves first, and for a given size,
|
|
* fastest curves first. This provides the default order for the SSL module.
|
|
*
|
|
* Reminder: update profiles in x509_crt.c when adding a new curves!
|
|
*/
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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
|
|
#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" },
|
|
#endif
|
|
#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
|
|
{ MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" },
|
|
#endif
|
|
{ MBEDTLS_ECP_DP_NONE, 0, 0, NULL },
|
|
};
|
|
|
|
#define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \
|
|
sizeof( ecp_supported_curves[0] )
|
|
|
|
static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
|
|
|
|
/*
|
|
* List of supported curves and associated info
|
|
*/
|
|
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
|
|
{
|
|
return( ecp_supported_curves );
|
|
}
|
|
|
|
/*
|
|
* List of supported curves, group ID only
|
|
*/
|
|
const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
|
|
{
|
|
static int init_done = 0;
|
|
|
|
if( ! init_done )
|
|
{
|
|
size_t i = 0;
|
|
const mbedtls_ecp_curve_info *curve_info;
|
|
|
|
for( curve_info = mbedtls_ecp_curve_list();
|
|
curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
|
|
curve_info++ )
|
|
{
|
|
ecp_supported_grp_id[i++] = curve_info->grp_id;
|
|
}
|
|
ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
|
|
|
|
init_done = 1;
|
|
}
|
|
|
|
return( ecp_supported_grp_id );
|
|
}
|
|
|
|
/*
|
|
* Get the curve info for the internal identifier
|
|
*/
|
|
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id )
|
|
{
|
|
const mbedtls_ecp_curve_info *curve_info;
|
|
|
|
for( curve_info = mbedtls_ecp_curve_list();
|
|
curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
|
|
curve_info++ )
|
|
{
|
|
if( curve_info->grp_id == grp_id )
|
|
return( curve_info );
|
|
}
|
|
|
|
return( NULL );
|
|
}
|
|
|
|
/*
|
|
* Get the curve info from the TLS identifier
|
|
*/
|
|
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id )
|
|
{
|
|
const mbedtls_ecp_curve_info *curve_info;
|
|
|
|
for( curve_info = mbedtls_ecp_curve_list();
|
|
curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
|
|
curve_info++ )
|
|
{
|
|
if( curve_info->tls_id == tls_id )
|
|
return( curve_info );
|
|
}
|
|
|
|
return( NULL );
|
|
}
|
|
|
|
/*
|
|
* Get the curve info from the name
|
|
*/
|
|
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name )
|
|
{
|
|
const mbedtls_ecp_curve_info *curve_info;
|
|
|
|
if( name == NULL )
|
|
return( NULL );
|
|
|
|
for( curve_info = mbedtls_ecp_curve_list();
|
|
curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
|
|
curve_info++ )
|
|
{
|
|
if( strcmp( curve_info->name, name ) == 0 )
|
|
return( curve_info );
|
|
}
|
|
|
|
return( NULL );
|
|
}
|
|
|
|
/*
|
|
* Get the type of a curve
|
|
*/
|
|
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 and RFC7748)
|
|
*/
|
|
int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp,
|
|
mbedtls_ecp_point *pt,
|
|
const unsigned char *buf, size_t ilen )
|
|
{
|
|
int ret;
|
|
size_t plen;
|
|
ECP_VALIDATE_RET( grp != NULL );
|
|
ECP_VALIDATE_RET( pt != NULL );
|
|
ECP_VALIDATE_RET( buf != NULL );
|
|
|
|
if( ilen < 1 )
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
|
|
plen = mbedtls_mpi_size( &grp->P );
|
|
|
|
#if defined(ECP_MONTGOMERY)
|
|
if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
|
|
{
|
|
if( plen != ilen )
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &pt->X, buf, plen ) );
|
|
mbedtls_mpi_free( &pt->Y );
|
|
|
|
if( grp->id == MBEDTLS_ECP_DP_CURVE25519 )
|
|
/* Set most significant bit to 0 */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &pt->X, plen * 8 - 1, 0 ) );
|
|
}
|
|
#endif
|
|
#if defined(ECP_SHORTWEIERSTRASS)
|
|
if( ecp_get_type( grp ) != ECP_TYPE_MONTGOMERY )
|
|
{
|
|
if( buf[0] == 0x00 )
|
|
{
|
|
if( ilen == 1 )
|
|
return( mbedtls_ecp_set_zero( pt ) );
|
|
else
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
}
|
|
|
|
if( buf[0] != 0x04 )
|
|
return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
|
|
|
|
if( ilen != 2 * plen + 1 )
|
|
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y,
|
|
buf + 1 + plen, plen ) );
|
|
}
|
|
#endif
|
|
|
|
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
|
|
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 ) );
|
|
}
|
|
|
|
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;
|
|
|
|
/*
|
|
* 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 );
|
|
}
|
|
while( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
|
|
mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 );
|
|
}
|
|
#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 ) );
|
|
}
|
|
|
|
#define ECP_CURVE255_KEY_SIZE 32
|
|
/*
|
|
* Read a private key.
|
|
*/
|
|
int mbedtls_ecp_read_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
|
|
const unsigned char *buf, size_t buflen )
|
|
{
|
|
int ret = 0;
|
|
|
|
if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
|
|
return( ret );
|
|
|
|
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
|
|
/*
|
|
* If it is Curve25519 curve then mask the key as mandated by RFC7748
|
|
*/
|
|
if( grp_id == MBEDTLS_ECP_DP_CURVE25519 )
|
|
{
|
|
if( buflen != ECP_CURVE255_KEY_SIZE )
|
|
return MBEDTLS_ERR_ECP_INVALID_KEY;
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &key->d, buf, buflen ) );
|
|
|
|
/* Set the three least significant bits to 0 */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 0, 0 ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 1, 0 ) );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 2, 0 ) );
|
|
|
|
/* Set the most significant bit to 0 */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d,
|
|
ECP_CURVE255_KEY_SIZE * 8 - 1,
|
|
0 ) );
|
|
|
|
/* Set the second most significant bit to 1 */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d,
|
|
ECP_CURVE255_KEY_SIZE * 8 - 2,
|
|
1 ) );
|
|
}
|
|
|
|
#endif
|
|
#if defined(ECP_SHORTWEIERSTRASS)
|
|
if( ecp_get_type( &key->grp ) != ECP_TYPE_MONTGOMERY )
|
|
{
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &key->d, buf, buflen ) );
|
|
|
|
MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( &key->grp, &key->d ) );
|
|
}
|
|
|
|
#endif
|
|
cleanup:
|
|
|
|
if( ret != 0 )
|
|
mbedtls_mpi_free( &key->d );
|
|
|
|
return( ret );
|
|
}
|
|
|
|
/*
|
|
* 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 */
|