diff options
Diffstat (limited to 'FreeRTOS-Labs/Source/mbedtls/library/ecp.c')
| -rw-r--r-- | FreeRTOS-Labs/Source/mbedtls/library/ecp.c | 3089 |
1 files changed, 3089 insertions, 0 deletions
diff --git a/FreeRTOS-Labs/Source/mbedtls/library/ecp.c b/FreeRTOS-Labs/Source/mbedtls/library/ecp.c new file mode 100644 index 000000000..4b8442ea0 --- /dev/null +++ b/FreeRTOS-Labs/Source/mbedtls/library/ecp.c @@ -0,0 +1,3089 @@ +/*
+ * 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 ยง5 */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &pt->X, plen * 8 - 1, 0 ) );
+
+ MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
+ }
+#endif
+#if defined(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 */
|