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Diffstat (limited to 'thirdparty/mbedtls/library/ecp.c')
| -rw-r--r-- | thirdparty/mbedtls/library/ecp.c | 2195 |
1 files changed, 2195 insertions, 0 deletions
diff --git a/thirdparty/mbedtls/library/ecp.c b/thirdparty/mbedtls/library/ecp.c new file mode 100644 index 0000000000..b41baef27a --- /dev/null +++ b/thirdparty/mbedtls/library/ecp.c @@ -0,0 +1,2195 @@ +/* + * 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 + * + * [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 + +#if defined(MBEDTLS_ECP_C) + +#include "mbedtls/ecp.h" +#include "mbedtls/threading.h" + +#include <string.h> + +#if !defined(MBEDTLS_ECP_ALT) + +#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 + +/* Implementation that should never be optimized out by the compiler */ +static void mbedtls_zeroize( void *v, size_t n ) { + volatile unsigned char *p = v; while( n-- ) *p++ = 0; +} + +#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_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) +#define ECP_MONTGOMERY +#endif + +/* + * Curve types: internal for now, might be exposed later + */ +typedef enum +{ + ECP_TYPE_NONE = 0, + ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */ + ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */ +} ecp_curve_type; + +/* + * 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; + + for( curve_info = mbedtls_ecp_curve_list(); + curve_info->grp_id != MBEDTLS_ECP_DP_NONE; + curve_info++ ) + { + if( strcmp( curve_info->name, name ) == 0 ) + return( curve_info ); + } + + return( NULL ); +} + +/* + * Get the type of a curve + */ +static inline ecp_curve_type ecp_get_type( const mbedtls_ecp_group *grp ) +{ + if( grp->G.X.p == NULL ) + return( ECP_TYPE_NONE ); + + if( grp->G.Y.p == NULL ) + return( ECP_TYPE_MONTGOMERY ); + else + return( ECP_TYPE_SHORT_WEIERSTRASS ); +} + +/* + * Initialize (the components of) a point + */ +void mbedtls_ecp_point_init( mbedtls_ecp_point *pt ) +{ + if( pt == NULL ) + return; + + 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 ) +{ + if( grp == NULL ) + return; + + memset( grp, 0, sizeof( mbedtls_ecp_group ) ); +} + +/* + * Initialize (the components of) a key pair + */ +void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key ) +{ + if( key == NULL ) + return; + + 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_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; + + 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 ) +{ + return mbedtls_ecp_group_load( dst, src->id ); +} + +/* + * Set point to zero + */ +int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt ) +{ + int ret; + + 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 ) +{ + return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 ); +} + +/* + * Compare two points lazyly + */ +int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P, + const mbedtls_ecp_point *Q ) +{ + 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; + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) ); + +cleanup: + return( ret ); +} + +/* + * Export a point into unsigned binary data (SEC1 2.3.3) + */ +int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P, + int format, size_t *olen, + unsigned char *buf, size_t buflen ) +{ + int ret = 0; + size_t plen; + + if( format != MBEDTLS_ECP_PF_UNCOMPRESSED && + format != MBEDTLS_ECP_PF_COMPRESSED ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + /* + * Common case: P == 0 + */ + if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 ) + { + if( buflen < 1 ) + return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); + + buf[0] = 0x00; + *olen = 1; + + return( 0 ); + } + + plen = mbedtls_mpi_size( &grp->P ); + + if( format == MBEDTLS_ECP_PF_UNCOMPRESSED ) + { + *olen = 2 * plen + 1; + + if( buflen < *olen ) + return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); + + buf[0] = 0x04; + MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) ); + } + else if( format == MBEDTLS_ECP_PF_COMPRESSED ) + { + *olen = plen + 1; + + if( buflen < *olen ) + return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL ); + + buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 ); + MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) ); + } + +cleanup: + return( ret ); +} + +/* + * Import a point from unsigned binary data (SEC1 2.3.4) + */ +int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt, + const unsigned char *buf, size_t ilen ) +{ + int ret; + size_t plen; + + if( ilen < 1 ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + if( buf[0] == 0x00 ) + { + if( ilen == 1 ) + return( mbedtls_ecp_set_zero( pt ) ); + else + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + } + + plen = mbedtls_mpi_size( &grp->P ); + + if( buf[0] != 0x04 ) + return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); + + if( ilen != 2 * plen + 1 ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, buf + 1 + plen, plen ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) ); + +cleanup: + return( ret ); +} + +/* + * Import a point from a TLS ECPoint record (RFC 4492) + * struct { + * opaque point <1..2^8-1>; + * } ECPoint; + */ +int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt, + const unsigned char **buf, size_t buf_len ) +{ + unsigned char data_len; + const unsigned char *buf_start; + + /* + * 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; + + /* + * 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 ) +{ + uint16_t tls_id; + const mbedtls_ecp_curve_info *curve_info; + + /* + * 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 ); + + return mbedtls_ecp_group_load( grp, curve_info->grp_id ); +} + +/* + * 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; + + 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_len ) +{ + int ret; + size_t i; + mbedtls_mpi *c, u, Zi, ZZi; + + if( t_len < 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_len); + } +#endif + + if( ( c = mbedtls_calloc( t_len, sizeof( mbedtls_mpi ) ) ) == NULL ) + return( MBEDTLS_ERR_ECP_ALLOC_FAILED ); + + 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_len; 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_len-1], &grp->P ) ); + + for( i = t_len - 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_len; 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. + * + * Also, for the sake of compactness, only the seven low-order bits of x[i] + * are used to represent K_i, and the msb of x[i] encodes the 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_fixed( 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 comb method + * + * If i = i_{w-1} ... i_1 is the binary representation of i, then + * T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P + * + * T must be able to hold 2^{w - 1} elements + * + * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1) + */ +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 ) +{ + int ret; + unsigned char i, k; + size_t j; + mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1]; + + /* + * 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 ) ); + + k = 0; + for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 ) + { + cur = T + i; + MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) ); + for( j = 0; j < d; j++ ) + MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) ); + + TT[k++] = cur; + } + + MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) ); + + /* + * Compute the remaining ones using the minimal number of additions + * Be careful to update T[2^l] only after using it! + */ + k = 0; + for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 ) + { + j = i; + while( j-- ) + { + MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) ); + TT[k++] = &T[i + j]; + } + } + + MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) ); + +cleanup: + + return( ret ); +} + +/* + * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ] + */ +static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, + const mbedtls_ecp_point T[], unsigned char t_len, + 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_len; 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_len, + const unsigned char x[], size_t d, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng ) +{ + int ret; + mbedtls_ecp_point Txi; + size_t i; + + mbedtls_ecp_point_init( &Txi ); + + /* Start with a non-zero point and randomize its coordinates */ + i = d; + MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, t_len, 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_MPI_CHK( ecp_double_jac( grp, R, R ) ); + MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, t_len, x[i] ) ); + MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) ); + } + +cleanup: + + mbedtls_ecp_point_free( &Txi ); + + return( ret ); +} + +/* + * Multiplication using the comb method, + * for curves in short Weierstrass form + */ +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 ) +{ + int ret; + unsigned char w, m_is_odd, p_eq_g, pre_len, i; + size_t d; + unsigned char k[COMB_MAX_D + 1]; + mbedtls_ecp_point *T; + mbedtls_mpi M, mm; + + mbedtls_mpi_init( &M ); + mbedtls_mpi_init( &mm ); + + /* we need N to be odd to trnaform m in an odd number, check now */ + if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + /* + * 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 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 ); + if( p_eq_g ) + w++; +#else + p_eq_g = 0; +#endif + + /* + * 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; + + /* Other sizes that depend on w */ + pre_len = 1U << ( w - 1 ); + d = ( grp->nbits + w - 1 ) / w; + + /* + * Prepare precomputed points: if P == G we want to + * use grp->T if already initialized, or initialize it. + */ + T = p_eq_g ? grp->T : NULL; + + if( T == NULL ) + { + T = mbedtls_calloc( pre_len, sizeof( mbedtls_ecp_point ) ); + if( T == NULL ) + { + ret = MBEDTLS_ERR_ECP_ALLOC_FAILED; + goto cleanup; + } + + MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d ) ); + + if( p_eq_g ) + { + grp->T = T; + grp->T_size = pre_len; + } + } + + /* + * Make sure M is odd (M = m or M = N - m, since N is odd) + * using the fact that m * P = - (N - m) * P + */ + m_is_odd = ( mbedtls_mpi_get_bit( m, 0 ) == 1 ); + 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, ! m_is_odd ) ); + + /* + * Go for comb multiplication, R = M * P + */ + ecp_comb_fixed( k, d, w, &M ); + MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, R, T, pre_len, k, d, f_rng, p_rng ) ); + + /* + * Now get m * P from M * P and normalize it + */ + MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, ! m_is_odd ) ); + MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) ); + +cleanup: + + if( T != NULL && ! p_eq_g ) + { + for( i = 0; i < pre_len; i++ ) + mbedtls_ecp_point_free( &T[i] ); + mbedtls_free( T ); + } + + mbedtls_mpi_free( &M ); + mbedtls_mpi_free( &mm ); + + if( ret != 0 ) + mbedtls_ecp_point_free( R ); + + 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 */ + +/* + * 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 ) +{ + int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA; +#if defined(MBEDTLS_ECP_INTERNAL_ALT) + char is_grp_capable = 0; +#endif + + /* Common sanity checks */ + if( mbedtls_mpi_cmp_int( &P->Z, 1 ) != 0 ) + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + + if( ( ret = mbedtls_ecp_check_privkey( grp, m ) ) != 0 || + ( ret = mbedtls_ecp_check_pubkey( grp, P ) ) != 0 ) + return( ret ); + +#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(ECP_MONTGOMERY) + if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY ) + ret = ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ); + +#endif +#if defined(ECP_SHORTWEIERSTRASS) + if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS ) + ret = ecp_mul_comb( grp, R, m, P, f_rng, p_rng ); + +#endif +#if defined(MBEDTLS_ECP_INTERNAL_ALT) +cleanup: + + if ( is_grp_capable ) + { + mbedtls_internal_ecp_free( grp ); + } + +#endif /* MBEDTLS_ECP_INTERNAL_ALT */ + return( ret ); +} + +#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 ) +{ + 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( grp, R, m, P, NULL, NULL ) ); + } + +cleanup: + 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 ) +{ + int ret; + mbedtls_ecp_point mP; +#if defined(MBEDTLS_ECP_INTERNAL_ALT) + char is_grp_capable = 0; +#endif + + if( ecp_get_type( grp ) != ECP_TYPE_SHORT_WEIERSTRASS ) + return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); + + mbedtls_ecp_point_init( &mP ); + + MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, &mP, m, P ) ); + MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, R, n, Q ) ); + +#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 */ + MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, &mP, R ) ); + MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) ); + +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 ); + + return( ret ); +} + + +#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 */ + 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 ) +{ + /* Must use affine coordinates */ + if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 ) + return( MBEDTLS_ERR_ECP_INVALID_KEY ); + +#if defined(ECP_MONTGOMERY) + if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY ) + return( ecp_check_pubkey_mx( grp, pt ) ); +#endif +#if defined(ECP_SHORTWEIERSTRASS) + if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS ) + return( ecp_check_pubkey_sw( grp, pt ) ); +#endif + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); +} + +/* + * Check that an mbedtls_mpi is valid as a private key + */ +int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d ) +{ +#if defined(ECP_MONTGOMERY) + if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY ) + { + /* see [Curve25519] page 5 */ + if( mbedtls_mpi_get_bit( d, 0 ) != 0 || + mbedtls_mpi_get_bit( d, 1 ) != 0 || + mbedtls_mpi_get_bit( d, 2 ) != 0 || + mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */ + return( MBEDTLS_ERR_ECP_INVALID_KEY ); + else + return( 0 ); + } +#endif /* ECP_MONTGOMERY */ +#if defined(ECP_SHORTWEIERSTRASS) + if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS ) + { + /* see SEC1 3.2 */ + if( mbedtls_mpi_cmp_int( d, 1 ) < 0 || + mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 ) + return( MBEDTLS_ERR_ECP_INVALID_KEY ); + else + return( 0 ); + } +#endif /* ECP_SHORTWEIERSTRASS */ + + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); +} + +/* + * Generate a 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; + size_t n_size = ( grp->nbits + 7 ) / 8; + +#if defined(ECP_MONTGOMERY) + if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY ) + { + /* [M225] page 5 */ + size_t b; + + do { + MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) ); + } while( mbedtls_mpi_bitlen( d ) == 0); + + /* Make sure the most significant bit is nbits */ + b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */ + if( b > grp->nbits ) + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) ); + else + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) ); + + /* Make sure the last three bits are unset */ + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) ); + } + else +#endif /* ECP_MONTGOMERY */ +#if defined(ECP_SHORTWEIERSTRASS) + if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS ) + { + /* SEC1 3.2.1: Generate d such that 1 <= n < N */ + int count = 0; + + /* + * Match the procedure given in RFC 6979 (deterministic ECDSA): + * - use the same byte ordering; + * - keep the leftmost nbits bits of the generated octet string; + * - try until result is in the desired range. + * This also avoids any biais, which is especially important for ECDSA. + */ + do + { + MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) ); + + /* + * Each try has at worst a probability 1/2 of failing (the msb has + * a probability 1/2 of being 0, and then the result will be < N), + * so after 30 tries failure probability is a most 2**(-30). + * + * For most curves, 1 try is enough with overwhelming probability, + * since N starts with a lot of 1s in binary, but some curves + * such as secp224k1 are actually very close to the worst case. + */ + if( ++count > 30 ) + return( MBEDTLS_ERR_ECP_RANDOM_FAILED ); + } + while( mbedtls_mpi_cmp_int( d, 1 ) < 0 || + mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 ); + } + else +#endif /* ECP_SHORTWEIERSTRASS */ + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + +cleanup: + if( ret != 0 ) + return( ret ); + + return( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) ); +} + +/* + * 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 ) +{ + 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; + + if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 ) + return( ret ); + + return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) ); +} + +/* + * Check a public-private key pair + */ +int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv ) +{ + int ret; + mbedtls_ecp_point Q; + mbedtls_ecp_group grp; + + 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 */ |