Willie Solano
mbed TLS Build
Diff: library/ecp.c
- Revision:
- 0:cdf462088d13
diff -r 000000000000 -r cdf462088d13 library/ecp.c
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/library/ecp.c Thu Jan 05 00:18:44 2017 +0000
@@ -0,0 +1,2092 @@
+/*
+ * 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 <string.h>
+
+#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
+
+#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 );
+
+ 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( ( 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
+
+ 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
+
+ /*
+ * 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 = ( grp->pbits + 7 ) / 8;
+ int count = 0;
+
+ mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
+
+ /* Generate l such that 1 < l < p */
+ do
+ {
+ 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;
+
+ 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 = ( grp->pbits + 7 ) / 8;
+ int count = 0;
+
+ mbedtls_mpi_init( &l );
+
+ /* Generate l such that 1 < l < p */
+ do
+ {
+ 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;
+
+ 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;
+
+ /* 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(ECP_MONTGOMERY)
+ if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
+ return( 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 )
+ return( ecp_mul_comb( grp, R, m, P, f_rng, p_rng ) );
+#endif
+ return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+}
+
+#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( 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 ) );
+
+ MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, &mP, R ) );
+ MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
+
+cleanup:
+ 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;
+ unsigned char rnd[MBEDTLS_ECP_MAX_BYTES];
+
+ /*
+ * 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( f_rng( p_rng, rnd, n_size ) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( d, rnd, n_size ) );
+ 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_C */
