/* | |
* Elliptic curves over GF(p): generic functions | |
* | |
* Copyright (C) 2006-2015, ARM Limited, All Rights Reserved | |
* SPDX-License-Identifier: Apache-2.0 | |
* | |
* Licensed under the Apache License, Version 2.0 (the "License"); you may | |
* not use this file except in compliance with the License. | |
* You may obtain a copy of the License at | |
* | |
* http://www.apache.org/licenses/LICENSE-2.0 | |
* | |
* Unless required by applicable law or agreed to in writing, software | |
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT | |
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
* See the License for the specific language governing permissions and | |
* limitations under the License. | |
* | |
* This file is part of mbed TLS (https://tls.mbed.org) | |
*/ | |
/* | |
* References: | |
* | |
* SEC1 http://www.secg.org/index.php?action=secg,docs_secg | |
* GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone | |
* FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf | |
* RFC 4492 for the related TLS structures and constants | |
* RFC 7748 for the Curve448 and Curve25519 curve definitions | |
* | |
* [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf | |
* | |
* [2] CORON, Jean-S'ebastien. Resistance against differential power analysis | |
* for elliptic curve cryptosystems. In : Cryptographic Hardware and | |
* Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302. | |
* <http://link.springer.com/chapter/10.1007/3-540-48059-5_25> | |
* | |
* [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to | |
* render ECC resistant against Side Channel Attacks. IACR Cryptology | |
* ePrint Archive, 2004, vol. 2004, p. 342. | |
* <http://eprint.iacr.org/2004/342.pdf> | |
*/ | |
#if !defined(MBEDTLS_CONFIG_FILE) | |
#include "mbedtls/config.h" | |
#else | |
#include MBEDTLS_CONFIG_FILE | |
#endif | |
/** | |
* \brief Function level alternative implementation. | |
* | |
* The MBEDTLS_ECP_INTERNAL_ALT macro enables alternative implementations to | |
* replace certain functions in this module. The alternative implementations are | |
* typically hardware accelerators and need to activate the hardware before the | |
* computation starts and deactivate it after it finishes. The | |
* mbedtls_internal_ecp_init() and mbedtls_internal_ecp_free() functions serve | |
* this purpose. | |
* | |
* To preserve the correct functionality the following conditions must hold: | |
* | |
* - The alternative implementation must be activated by | |
* mbedtls_internal_ecp_init() before any of the replaceable functions is | |
* called. | |
* - mbedtls_internal_ecp_free() must \b only be called when the alternative | |
* implementation is activated. | |
* - mbedtls_internal_ecp_init() must \b not be called when the alternative | |
* implementation is activated. | |
* - Public functions must not return while the alternative implementation is | |
* activated. | |
* - Replaceable functions are guarded by \c MBEDTLS_ECP_XXX_ALT macros and | |
* before calling them an \code if( mbedtls_internal_ecp_grp_capable( grp ) ) | |
* \endcode ensures that the alternative implementation supports the current | |
* group. | |
*/ | |
#if defined(MBEDTLS_ECP_INTERNAL_ALT) | |
#endif | |
#if defined(MBEDTLS_ECP_C) | |
#include "mbedtls/ecp.h" | |
#include "mbedtls/threading.h" | |
#include "mbedtls/platform_util.h" | |
#include <string.h> | |
#if !defined(MBEDTLS_ECP_ALT) | |
/* Parameter validation macros based on platform_util.h */ | |
#define ECP_VALIDATE_RET( cond ) \ | |
MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA ) | |
#define ECP_VALIDATE( cond ) \ | |
MBEDTLS_INTERNAL_VALIDATE( cond ) | |
#if defined(MBEDTLS_PLATFORM_C) | |
#include "mbedtls/platform.h" | |
#else | |
#include <stdlib.h> | |
#include <stdio.h> | |
#define mbedtls_printf printf | |
#define mbedtls_calloc calloc | |
#define mbedtls_free free | |
#endif | |
#include "mbedtls/ecp_internal.h" | |
#if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \ | |
!defined(inline) && !defined(__cplusplus) | |
#define inline __inline | |
#endif | |
#if defined(MBEDTLS_SELF_TEST) | |
/* | |
* Counts of point addition and doubling, and field multiplications. | |
* Used to test resistance of point multiplication to simple timing attacks. | |
*/ | |
static unsigned long add_count, dbl_count, mul_count; | |
#endif | |
#if defined(MBEDTLS_ECP_RESTARTABLE) | |
/* | |
* Maximum number of "basic operations" to be done in a row. | |
* | |
* Default value 0 means that ECC operations will not yield. | |
* Note that regardless of the value of ecp_max_ops, always at | |
* least one step is performed before yielding. | |
* | |
* Setting ecp_max_ops=1 can be suitable for testing purposes | |
* as it will interrupt computation at all possible points. | |
*/ | |
static unsigned ecp_max_ops = 0; | |
/* | |
* Set ecp_max_ops | |
*/ | |
void mbedtls_ecp_set_max_ops( unsigned max_ops ) | |
{ | |
ecp_max_ops = max_ops; | |
} | |
/* | |
* Check if restart is enabled | |
*/ | |
int mbedtls_ecp_restart_is_enabled( void ) | |
{ | |
return( ecp_max_ops != 0 ); | |
} | |
/* | |
* Restart sub-context for ecp_mul_comb() | |
*/ | |
struct mbedtls_ecp_restart_mul | |
{ | |
mbedtls_ecp_point R; /* current intermediate result */ | |
size_t i; /* current index in various loops, 0 outside */ | |
mbedtls_ecp_point *T; /* table for precomputed points */ | |
unsigned char T_size; /* number of points in table T */ | |
enum { /* what were we doing last time we returned? */ | |
ecp_rsm_init = 0, /* nothing so far, dummy initial state */ | |
ecp_rsm_pre_dbl, /* precompute 2^n multiples */ | |
ecp_rsm_pre_norm_dbl, /* normalize precomputed 2^n multiples */ | |
ecp_rsm_pre_add, /* precompute remaining points by adding */ | |
ecp_rsm_pre_norm_add, /* normalize all precomputed points */ | |
ecp_rsm_comb_core, /* ecp_mul_comb_core() */ | |
ecp_rsm_final_norm, /* do the final normalization */ | |
} state; | |
}; | |
/* | |
* Init restart_mul sub-context | |
*/ | |
static void ecp_restart_rsm_init( mbedtls_ecp_restart_mul_ctx *ctx ) | |
{ | |
mbedtls_ecp_point_init( &ctx->R ); | |
ctx->i = 0; | |
ctx->T = NULL; | |
ctx->T_size = 0; | |
ctx->state = ecp_rsm_init; | |
} | |
/* | |
* Free the components of a restart_mul sub-context | |
*/ | |
static void ecp_restart_rsm_free( mbedtls_ecp_restart_mul_ctx *ctx ) | |
{ | |
unsigned char i; | |
if( ctx == NULL ) | |
return; | |
mbedtls_ecp_point_free( &ctx->R ); | |
if( ctx->T != NULL ) | |
{ | |
for( i = 0; i < ctx->T_size; i++ ) | |
mbedtls_ecp_point_free( ctx->T + i ); | |
mbedtls_free( ctx->T ); | |
} | |
ecp_restart_rsm_init( ctx ); | |
} | |
/* | |
* Restart context for ecp_muladd() | |
*/ | |
struct mbedtls_ecp_restart_muladd | |
{ | |
mbedtls_ecp_point mP; /* mP value */ | |
mbedtls_ecp_point R; /* R intermediate result */ | |
enum { /* what should we do next? */ | |
ecp_rsma_mul1 = 0, /* first multiplication */ | |
ecp_rsma_mul2, /* second multiplication */ | |
ecp_rsma_add, /* addition */ | |
ecp_rsma_norm, /* normalization */ | |
} state; | |
}; | |
/* | |
* Init restart_muladd sub-context | |
*/ | |
static void ecp_restart_ma_init( mbedtls_ecp_restart_muladd_ctx *ctx ) | |
{ | |
mbedtls_ecp_point_init( &ctx->mP ); | |
mbedtls_ecp_point_init( &ctx->R ); | |
ctx->state = ecp_rsma_mul1; | |
} | |
/* | |
* Free the components of a restart_muladd sub-context | |
*/ | |
static void ecp_restart_ma_free( mbedtls_ecp_restart_muladd_ctx *ctx ) | |
{ | |
if( ctx == NULL ) | |
return; | |
mbedtls_ecp_point_free( &ctx->mP ); | |
mbedtls_ecp_point_free( &ctx->R ); | |
ecp_restart_ma_init( ctx ); | |
} | |
/* | |
* Initialize a restart context | |
*/ | |
void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx ) | |
{ | |
ECP_VALIDATE( ctx != NULL ); | |
ctx->ops_done = 0; | |
ctx->depth = 0; | |
ctx->rsm = NULL; | |
ctx->ma = NULL; | |
} | |
/* | |
* Free the components of a restart context | |
*/ | |
void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx ) | |
{ | |
if( ctx == NULL ) | |
return; | |
ecp_restart_rsm_free( ctx->rsm ); | |
mbedtls_free( ctx->rsm ); | |
ecp_restart_ma_free( ctx->ma ); | |
mbedtls_free( ctx->ma ); | |
mbedtls_ecp_restart_init( ctx ); | |
} | |
/* | |
* Check if we can do the next step | |
*/ | |
int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp, | |
mbedtls_ecp_restart_ctx *rs_ctx, | |
unsigned ops ) | |
{ | |
ECP_VALIDATE_RET( grp != NULL ); | |
if( rs_ctx != NULL && ecp_max_ops != 0 ) | |
{ | |
/* scale depending on curve size: the chosen reference is 256-bit, | |
* and multiplication is quadratic. Round to the closest integer. */ | |
if( grp->pbits >= 512 ) | |
ops *= 4; | |
else if( grp->pbits >= 384 ) | |
ops *= 2; | |
/* Avoid infinite loops: always allow first step. | |
* Because of that, however, it's not generally true | |
* that ops_done <= ecp_max_ops, so the check | |
* ops_done > ecp_max_ops below is mandatory. */ | |
if( ( rs_ctx->ops_done != 0 ) && | |
( rs_ctx->ops_done > ecp_max_ops || | |
ops > ecp_max_ops - rs_ctx->ops_done ) ) | |
{ | |
return( MBEDTLS_ERR_ECP_IN_PROGRESS ); | |
} | |
/* update running count */ | |
rs_ctx->ops_done += ops; | |
} | |
return( 0 ); | |
} | |
/* Call this when entering a function that needs its own sub-context */ | |
#define ECP_RS_ENTER( SUB ) do { \ | |
/* reset ops count for this call if top-level */ \ | |
if( rs_ctx != NULL && rs_ctx->depth++ == 0 ) \ | |
rs_ctx->ops_done = 0; \ | |
\ | |
/* set up our own sub-context if needed */ \ | |
if( mbedtls_ecp_restart_is_enabled() && \ | |
rs_ctx != NULL && rs_ctx->SUB == NULL ) \ | |
{ \ | |
rs_ctx->SUB = mbedtls_calloc( 1, sizeof( *rs_ctx->SUB ) ); \ | |
if( rs_ctx->SUB == NULL ) \ | |
return( MBEDTLS_ERR_ECP_ALLOC_FAILED ); \ | |
\ | |
ecp_restart_## SUB ##_init( rs_ctx->SUB ); \ | |
} \ | |
} while( 0 ) | |
/* Call this when leaving a function that needs its own sub-context */ | |
#define ECP_RS_LEAVE( SUB ) do { \ | |
/* clear our sub-context when not in progress (done or error) */ \ | |
if( rs_ctx != NULL && rs_ctx->SUB != NULL && \ | |
ret != MBEDTLS_ERR_ECP_IN_PROGRESS ) \ | |
{ \ | |
ecp_restart_## SUB ##_free( rs_ctx->SUB ); \ | |
mbedtls_free( rs_ctx->SUB ); \ | |
rs_ctx->SUB = NULL; \ | |
} \ | |
\ | |
if( rs_ctx != NULL ) \ | |
rs_ctx->depth--; \ | |
} while( 0 ) | |
#else /* MBEDTLS_ECP_RESTARTABLE */ | |
#define ECP_RS_ENTER( sub ) (void) rs_ctx; | |
#define ECP_RS_LEAVE( sub ) (void) rs_ctx; | |
#endif /* MBEDTLS_ECP_RESTARTABLE */ | |
#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \ | |
defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ | |
defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \ | |
defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \ | |
defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \ | |
defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \ | |
defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \ | |
defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \ | |
defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \ | |
defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ | |
defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) | |
#define ECP_SHORTWEIERSTRASS | |
#endif | |
#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) || \ | |
defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) | |
#define ECP_MONTGOMERY | |
#endif | |
/* | |
* List of supported curves: | |
* - internal ID | |
* - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2) | |
* - size in bits | |
* - readable name | |
* | |
* Curves are listed in order: largest curves first, and for a given size, | |
* fastest curves first. This provides the default order for the SSL module. | |
* | |
* Reminder: update profiles in x509_crt.c when adding a new curves! | |
*/ | |
static const mbedtls_ecp_curve_info ecp_supported_curves[] = | |
{ | |
#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) | |
{ MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" }, | |
#endif | |
#if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) | |
{ MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" }, | |
#endif | |
#if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) | |
{ MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" }, | |
#endif | |
#if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) | |
{ MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" }, | |
#endif | |
#if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) | |
{ MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" }, | |
#endif | |
#if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) | |
{ MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" }, | |
#endif | |
#if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) | |
{ MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" }, | |
#endif | |
#if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) | |
{ MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" }, | |
#endif | |
#if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) | |
{ MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" }, | |
#endif | |
#if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) | |
{ MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" }, | |
#endif | |
#if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) | |
{ MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" }, | |
#endif | |
{ MBEDTLS_ECP_DP_NONE, 0, 0, NULL }, | |
}; | |
#define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \ | |
sizeof( ecp_supported_curves[0] ) | |
static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES]; | |
/* | |
* List of supported curves and associated info | |
*/ | |
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void ) | |
{ | |
return( ecp_supported_curves ); | |
} | |
/* | |
* List of supported curves, group ID only | |
*/ | |
const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void ) | |
{ | |
static int init_done = 0; | |
if( ! init_done ) | |
{ | |
size_t i = 0; | |
const mbedtls_ecp_curve_info *curve_info; | |
for( curve_info = mbedtls_ecp_curve_list(); | |
curve_info->grp_id != MBEDTLS_ECP_DP_NONE; | |
curve_info++ ) | |
{ | |
ecp_supported_grp_id[i++] = curve_info->grp_id; | |
} | |
ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE; | |
init_done = 1; | |
} | |
return( ecp_supported_grp_id ); | |
} | |
/* | |
* Get the curve info for the internal identifier | |
*/ | |
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id ) | |
{ | |
const mbedtls_ecp_curve_info *curve_info; | |
for( curve_info = mbedtls_ecp_curve_list(); | |
curve_info->grp_id != MBEDTLS_ECP_DP_NONE; | |
curve_info++ ) | |
{ | |
if( curve_info->grp_id == grp_id ) | |
return( curve_info ); | |
} | |
return( NULL ); | |
} | |
/* | |
* Get the curve info from the TLS identifier | |
*/ | |
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id ) | |
{ | |
const mbedtls_ecp_curve_info *curve_info; | |
for( curve_info = mbedtls_ecp_curve_list(); | |
curve_info->grp_id != MBEDTLS_ECP_DP_NONE; | |
curve_info++ ) | |
{ | |
if( curve_info->tls_id == tls_id ) | |
return( curve_info ); | |
} | |
return( NULL ); | |
} | |
/* | |
* Get the curve info from the name | |
*/ | |
const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name ) | |
{ | |
const mbedtls_ecp_curve_info *curve_info; | |
if( name == NULL ) | |
return( NULL ); | |
for( curve_info = mbedtls_ecp_curve_list(); | |
curve_info->grp_id != MBEDTLS_ECP_DP_NONE; | |
curve_info++ ) | |
{ | |
if( strcmp( curve_info->name, name ) == 0 ) | |
return( curve_info ); | |
} | |
return( NULL ); | |
} | |
/* | |
* Get the type of a curve | |
*/ | |
mbedtls_ecp_curve_type mbedtls_ecp_get_type( const mbedtls_ecp_group *grp ) | |
{ | |
if( grp->G.X.p == NULL ) | |
return( MBEDTLS_ECP_TYPE_NONE ); | |
if( grp->G.Y.p == NULL ) | |
return( MBEDTLS_ECP_TYPE_MONTGOMERY ); | |
else | |
return( MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ); | |
} | |
/* | |
* Initialize (the components of) a point | |
*/ | |
void mbedtls_ecp_point_init( mbedtls_ecp_point *pt ) | |
{ | |
ECP_VALIDATE( pt != NULL ); | |
mbedtls_mpi_init( &pt->X ); | |
mbedtls_mpi_init( &pt->Y ); | |
mbedtls_mpi_init( &pt->Z ); | |
} | |
/* | |
* Initialize (the components of) a group | |
*/ | |
void mbedtls_ecp_group_init( mbedtls_ecp_group *grp ) | |
{ | |
ECP_VALIDATE( grp != NULL ); | |
grp->id = MBEDTLS_ECP_DP_NONE; | |
mbedtls_mpi_init( &grp->P ); | |
mbedtls_mpi_init( &grp->A ); | |
mbedtls_mpi_init( &grp->B ); | |
mbedtls_ecp_point_init( &grp->G ); | |
mbedtls_mpi_init( &grp->N ); | |
grp->pbits = 0; | |
grp->nbits = 0; | |
grp->h = 0; | |
grp->modp = NULL; | |
grp->t_pre = NULL; | |
grp->t_post = NULL; | |
grp->t_data = NULL; | |
grp->T = NULL; | |
grp->T_size = 0; | |
} | |
/* | |
* Initialize (the components of) a key pair | |
*/ | |
void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key ) | |
{ | |
ECP_VALIDATE( key != NULL ); | |
mbedtls_ecp_group_init( &key->grp ); | |
mbedtls_mpi_init( &key->d ); | |
mbedtls_ecp_point_init( &key->Q ); | |
} | |
/* | |
* Unallocate (the components of) a point | |
*/ | |
void mbedtls_ecp_point_free( mbedtls_ecp_point *pt ) | |
{ | |
if( pt == NULL ) | |
return; | |
mbedtls_mpi_free( &( pt->X ) ); | |
mbedtls_mpi_free( &( pt->Y ) ); | |
mbedtls_mpi_free( &( pt->Z ) ); | |
} | |
/* | |
* Unallocate (the components of) a group | |
*/ | |
void mbedtls_ecp_group_free( mbedtls_ecp_group *grp ) | |
{ | |
size_t i; | |
if( grp == NULL ) | |
return; | |
if( grp->h != 1 ) | |
{ | |
mbedtls_mpi_free( &grp->P ); | |
mbedtls_mpi_free( &grp->A ); | |
mbedtls_mpi_free( &grp->B ); | |
mbedtls_ecp_point_free( &grp->G ); | |
mbedtls_mpi_free( &grp->N ); | |
} | |
if( grp->T != NULL ) | |
{ | |
for( i = 0; i < grp->T_size; i++ ) | |
mbedtls_ecp_point_free( &grp->T[i] ); | |
mbedtls_free( grp->T ); | |
} | |
mbedtls_platform_zeroize( grp, sizeof( mbedtls_ecp_group ) ); | |
} | |
/* | |
* Unallocate (the components of) a key pair | |
*/ | |
void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key ) | |
{ | |
if( key == NULL ) | |
return; | |
mbedtls_ecp_group_free( &key->grp ); | |
mbedtls_mpi_free( &key->d ); | |
mbedtls_ecp_point_free( &key->Q ); | |
} | |
/* | |
* Copy the contents of a point | |
*/ | |
int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q ) | |
{ | |
int ret; | |
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 and RFC7748) | |
*/ | |
int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, | |
const mbedtls_ecp_point *P, | |
int format, size_t *olen, | |
unsigned char *buf, size_t buflen ) | |
{ | |
int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; | |
size_t plen; | |
ECP_VALIDATE_RET( grp != NULL ); | |
ECP_VALIDATE_RET( P != NULL ); | |
ECP_VALIDATE_RET( olen != NULL ); | |
ECP_VALIDATE_RET( buf != NULL ); | |
ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED || | |
format == MBEDTLS_ECP_PF_COMPRESSED ); | |
plen = mbedtls_mpi_size( &grp->P ); | |
#if defined(ECP_MONTGOMERY) | |
if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) | |
{ | |
*olen = plen; | |
if( buflen < *olen ) | |
return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary_le( &P->X, buf, plen ) ); | |
} | |
#endif | |
#if defined(ECP_SHORTWEIERSTRASS) | |
if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) | |
{ | |
/* | |
* Common case: P == 0 | |
*/ | |
if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 ) | |
{ | |
if( buflen < 1 ) | |
return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); | |
buf[0] = 0x00; | |
*olen = 1; | |
return( 0 ); | |
} | |
if( format == MBEDTLS_ECP_PF_UNCOMPRESSED ) | |
{ | |
*olen = 2 * plen + 1; | |
if( buflen < *olen ) | |
return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); | |
buf[0] = 0x04; | |
MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) ); | |
} | |
else if( format == MBEDTLS_ECP_PF_COMPRESSED ) | |
{ | |
*olen = plen + 1; | |
if( buflen < *olen ) | |
return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); | |
buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) ); | |
} | |
} | |
#endif | |
cleanup: | |
return( ret ); | |
} | |
/* | |
* Import a point from unsigned binary data (SEC1 2.3.4 and RFC7748) | |
*/ | |
int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, | |
mbedtls_ecp_point *pt, | |
const unsigned char *buf, size_t ilen ) | |
{ | |
int ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; | |
size_t plen; | |
ECP_VALIDATE_RET( grp != NULL ); | |
ECP_VALIDATE_RET( pt != NULL ); | |
ECP_VALIDATE_RET( buf != NULL ); | |
if( ilen < 1 ) | |
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); | |
plen = mbedtls_mpi_size( &grp->P ); | |
#if defined(ECP_MONTGOMERY) | |
if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) | |
{ | |
if( plen != ilen ) | |
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &pt->X, buf, plen ) ); | |
mbedtls_mpi_free( &pt->Y ); | |
if( grp->id == MBEDTLS_ECP_DP_CURVE25519 ) | |
/* Set most significant bit to 0 as prescribed in RFC7748 §5 */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &pt->X, plen * 8 - 1, 0 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) ); | |
} | |
#endif | |
#if defined(ECP_SHORTWEIERSTRASS) | |
if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) | |
{ | |
if( buf[0] == 0x00 ) | |
{ | |
if( ilen == 1 ) | |
return( mbedtls_ecp_set_zero( pt ) ); | |
else | |
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); | |
} | |
if( buf[0] != 0x04 ) | |
return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); | |
if( ilen != 2 * plen + 1 ) | |
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, | |
buf + 1 + plen, plen ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) ); | |
} | |
#endif | |
cleanup: | |
return( ret ); | |
} | |
/* | |
* Import a point from a TLS ECPoint record (RFC 4492) | |
* struct { | |
* opaque point <1..2^8-1>; | |
* } ECPoint; | |
*/ | |
int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, | |
mbedtls_ecp_point *pt, | |
const unsigned char **buf, size_t buf_len ) | |
{ | |
unsigned char data_len; | |
const unsigned char *buf_start; | |
ECP_VALIDATE_RET( grp != NULL ); | |
ECP_VALIDATE_RET( pt != NULL ); | |
ECP_VALIDATE_RET( buf != NULL ); | |
ECP_VALIDATE_RET( *buf != NULL ); | |
/* | |
* We must have at least two bytes (1 for length, at least one for data) | |
*/ | |
if( buf_len < 2 ) | |
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); | |
data_len = *(*buf)++; | |
if( data_len < 1 || data_len > buf_len - 1 ) | |
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); | |
/* | |
* Save buffer start for read_binary and update buf | |
*/ | |
buf_start = *buf; | |
*buf += data_len; | |
return( mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len ) ); | |
} | |
/* | |
* Export a point as a TLS ECPoint record (RFC 4492) | |
* struct { | |
* opaque point <1..2^8-1>; | |
* } ECPoint; | |
*/ | |
int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt, | |
int format, size_t *olen, | |
unsigned char *buf, size_t blen ) | |
{ | |
int ret; | |
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( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) | |
MBEDTLS_MPI_CHK( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) ); | |
#endif | |
#if defined(ECP_SHORTWEIERSTRASS) | |
if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) | |
MBEDTLS_MPI_CHK( ecp_mul_comb( grp, R, m, P, f_rng, p_rng, rs_ctx ) ); | |
#endif | |
cleanup: | |
#if defined(MBEDTLS_ECP_INTERNAL_ALT) | |
if( is_grp_capable ) | |
mbedtls_internal_ecp_free( grp ); | |
#endif /* MBEDTLS_ECP_INTERNAL_ALT */ | |
#if defined(MBEDTLS_ECP_RESTARTABLE) | |
if( rs_ctx != NULL ) | |
rs_ctx->depth--; | |
#endif | |
return( ret ); | |
} | |
/* | |
* Multiplication R = m * P | |
*/ | |
int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, | |
const mbedtls_mpi *m, const mbedtls_ecp_point *P, | |
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) | |
{ | |
ECP_VALIDATE_RET( grp != NULL ); | |
ECP_VALIDATE_RET( R != NULL ); | |
ECP_VALIDATE_RET( m != NULL ); | |
ECP_VALIDATE_RET( P != NULL ); | |
return( mbedtls_ecp_mul_restartable( grp, R, m, P, f_rng, p_rng, NULL ) ); | |
} | |
#if defined(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( mbedtls_ecp_get_type( grp ) != MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) | |
return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); | |
mbedtls_ecp_point_init( &mP ); | |
ECP_RS_ENTER( ma ); | |
#if defined(MBEDTLS_ECP_RESTARTABLE) | |
if( rs_ctx != NULL && rs_ctx->ma != NULL ) | |
{ | |
/* redirect intermediate results to restart context */ | |
pmP = &rs_ctx->ma->mP; | |
pR = &rs_ctx->ma->R; | |
/* jump to next operation */ | |
if( rs_ctx->ma->state == ecp_rsma_mul2 ) | |
goto mul2; | |
if( rs_ctx->ma->state == ecp_rsma_add ) | |
goto add; | |
if( rs_ctx->ma->state == ecp_rsma_norm ) | |
goto norm; | |
} | |
#endif /* MBEDTLS_ECP_RESTARTABLE */ | |
MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pmP, m, P, rs_ctx ) ); | |
#if defined(MBEDTLS_ECP_RESTARTABLE) | |
if( rs_ctx != NULL && rs_ctx->ma != NULL ) | |
rs_ctx->ma->state = ecp_rsma_mul2; | |
mul2: | |
#endif | |
MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pR, n, Q, rs_ctx ) ); | |
#if defined(MBEDTLS_ECP_INTERNAL_ALT) | |
if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) ) | |
MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) ); | |
#endif /* MBEDTLS_ECP_INTERNAL_ALT */ | |
#if defined(MBEDTLS_ECP_RESTARTABLE) | |
if( rs_ctx != NULL && rs_ctx->ma != NULL ) | |
rs_ctx->ma->state = ecp_rsma_add; | |
add: | |
#endif | |
MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_ADD ); | |
MBEDTLS_MPI_CHK( ecp_add_mixed( grp, pR, pmP, pR ) ); | |
#if defined(MBEDTLS_ECP_RESTARTABLE) | |
if( rs_ctx != NULL && rs_ctx->ma != NULL ) | |
rs_ctx->ma->state = ecp_rsma_norm; | |
norm: | |
#endif | |
MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV ); | |
MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, pR ) ); | |
#if defined(MBEDTLS_ECP_RESTARTABLE) | |
if( rs_ctx != NULL && rs_ctx->ma != NULL ) | |
MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, pR ) ); | |
#endif | |
cleanup: | |
#if defined(MBEDTLS_ECP_INTERNAL_ALT) | |
if( is_grp_capable ) | |
mbedtls_internal_ecp_free( grp ); | |
#endif /* MBEDTLS_ECP_INTERNAL_ALT */ | |
mbedtls_ecp_point_free( &mP ); | |
ECP_RS_LEAVE( ma ); | |
return( ret ); | |
} | |
/* | |
* Linear combination | |
* NOT constant-time | |
*/ | |
int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, | |
const mbedtls_mpi *m, const mbedtls_ecp_point *P, | |
const mbedtls_mpi *n, const mbedtls_ecp_point *Q ) | |
{ | |
ECP_VALIDATE_RET( grp != NULL ); | |
ECP_VALIDATE_RET( R != NULL ); | |
ECP_VALIDATE_RET( m != NULL ); | |
ECP_VALIDATE_RET( P != NULL ); | |
ECP_VALIDATE_RET( n != NULL ); | |
ECP_VALIDATE_RET( Q != NULL ); | |
return( mbedtls_ecp_muladd_restartable( grp, R, m, P, n, Q, NULL ) ); | |
} | |
#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( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) | |
return( ecp_check_pubkey_mx( grp, pt ) ); | |
#endif | |
#if defined(ECP_SHORTWEIERSTRASS) | |
if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) | |
return( ecp_check_pubkey_sw( grp, pt ) ); | |
#endif | |
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); | |
} | |
/* | |
* Check that an mbedtls_mpi is valid as a private key | |
*/ | |
int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, | |
const mbedtls_mpi *d ) | |
{ | |
ECP_VALIDATE_RET( grp != NULL ); | |
ECP_VALIDATE_RET( d != NULL ); | |
#if defined(ECP_MONTGOMERY) | |
if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) | |
{ | |
/* see RFC 7748 sec. 5 para. 5 */ | |
if( mbedtls_mpi_get_bit( d, 0 ) != 0 || | |
mbedtls_mpi_get_bit( d, 1 ) != 0 || | |
mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */ | |
return( MBEDTLS_ERR_ECP_INVALID_KEY ); | |
/* see [Curve25519] page 5 */ | |
if( grp->nbits == 254 && mbedtls_mpi_get_bit( d, 2 ) != 0 ) | |
return( MBEDTLS_ERR_ECP_INVALID_KEY ); | |
return( 0 ); | |
} | |
#endif /* ECP_MONTGOMERY */ | |
#if defined(ECP_SHORTWEIERSTRASS) | |
if( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) | |
{ | |
/* see SEC1 3.2 */ | |
if( mbedtls_mpi_cmp_int( d, 1 ) < 0 || | |
mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 ) | |
return( MBEDTLS_ERR_ECP_INVALID_KEY ); | |
else | |
return( 0 ); | |
} | |
#endif /* 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( mbedtls_ecp_get_type( grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) | |
{ | |
/* [M225] page 5 */ | |
size_t b; | |
do { | |
MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) ); | |
} while( mbedtls_mpi_bitlen( d ) == 0); | |
/* Make sure the most significant bit is nbits */ | |
b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */ | |
if( b > grp->nbits ) | |
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( mbedtls_ecp_get_type( grp ) == MBEDTLS_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_CURVE25519_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; | |
ECP_VALIDATE_RET( key != NULL ); | |
ECP_VALIDATE_RET( buf != NULL ); | |
if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 ) | |
return( ret ); | |
ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; | |
#if defined(ECP_MONTGOMERY) | |
if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_MONTGOMERY ) | |
{ | |
/* | |
* If it is Curve25519 curve then mask the key as mandated by RFC7748 | |
*/ | |
if( grp_id == MBEDTLS_ECP_DP_CURVE25519 ) | |
{ | |
if( buflen != ECP_CURVE25519_KEY_SIZE ) | |
return MBEDTLS_ERR_ECP_INVALID_KEY; | |
MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &key->d, buf, buflen ) ); | |
/* Set the three least significant bits to 0 */ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 0, 0 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 1, 0 ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &key->d, 2, 0 ) ); | |
/* Set the most significant bit to 0 */ | |
MBEDTLS_MPI_CHK( | |
mbedtls_mpi_set_bit( &key->d, | |
ECP_CURVE25519_KEY_SIZE * 8 - 1, 0 ) | |
); | |
/* Set the second most significant bit to 1 */ | |
MBEDTLS_MPI_CHK( | |
mbedtls_mpi_set_bit( &key->d, | |
ECP_CURVE25519_KEY_SIZE * 8 - 2, 1 ) | |
); | |
} | |
else | |
ret = MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE; | |
} | |
#endif | |
#if defined(ECP_SHORTWEIERSTRASS) | |
if( mbedtls_ecp_get_type( &key->grp ) == MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS ) | |
{ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &key->d, buf, buflen ) ); | |
MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( &key->grp, &key->d ) ); | |
} | |
#endif | |
cleanup: | |
if( ret != 0 ) | |
mbedtls_mpi_free( &key->d ); | |
return( ret ); | |
} | |
/* | |
* 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 */ |