Kev Mann / mbed-dev-OS5_10_4

RTC auf true

features/mbedtls/src/ecp.c@0:38ceb79fef03, 2018-11-28 (annotated)

Committer:
kevman
Date:
Wed Nov 28 15:10:15 2018 +0000
Revision:
0:38ceb79fef03
RTC modified

Who changed what in which revision?

UserRevisionLine numberNew contents of line
kevman 0:38ceb79fef03 1 /*
kevman 0:38ceb79fef03 2 * Elliptic curves over GF(p): generic functions
kevman 0:38ceb79fef03 3 *
kevman 0:38ceb79fef03 4 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
kevman 0:38ceb79fef03 5 * SPDX-License-Identifier: Apache-2.0
kevman 0:38ceb79fef03 6 *
kevman 0:38ceb79fef03 7 * Licensed under the Apache License, Version 2.0 (the "License"); you may
kevman 0:38ceb79fef03 8 * not use this file except in compliance with the License.
kevman 0:38ceb79fef03 9 * You may obtain a copy of the License at
kevman 0:38ceb79fef03 10 *
kevman 0:38ceb79fef03 11 * http://www.apache.org/licenses/LICENSE-2.0
kevman 0:38ceb79fef03 12 *
kevman 0:38ceb79fef03 13 * Unless required by applicable law or agreed to in writing, software
kevman 0:38ceb79fef03 14 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
kevman 0:38ceb79fef03 15 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
kevman 0:38ceb79fef03 16 * See the License for the specific language governing permissions and
kevman 0:38ceb79fef03 17 * limitations under the License.
kevman 0:38ceb79fef03 18 *
kevman 0:38ceb79fef03 19 * This file is part of mbed TLS (https://tls.mbed.org)
kevman 0:38ceb79fef03 20 */
kevman 0:38ceb79fef03 21
kevman 0:38ceb79fef03 22 /*
kevman 0:38ceb79fef03 23 * References:
kevman 0:38ceb79fef03 24 *
kevman 0:38ceb79fef03 25 * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
kevman 0:38ceb79fef03 26 * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
kevman 0:38ceb79fef03 27 * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
kevman 0:38ceb79fef03 28 * RFC 4492 for the related TLS structures and constants
kevman 0:38ceb79fef03 29 * RFC 7748 for the Curve448 and Curve25519 curve definitions
kevman 0:38ceb79fef03 30 *
kevman 0:38ceb79fef03 31 * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf
kevman 0:38ceb79fef03 32 *
kevman 0:38ceb79fef03 33 * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
kevman 0:38ceb79fef03 34 * for elliptic curve cryptosystems. In : Cryptographic Hardware and
kevman 0:38ceb79fef03 35 * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
kevman 0:38ceb79fef03 36 * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
kevman 0:38ceb79fef03 37 *
kevman 0:38ceb79fef03 38 * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
kevman 0:38ceb79fef03 39 * render ECC resistant against Side Channel Attacks. IACR Cryptology
kevman 0:38ceb79fef03 40 * ePrint Archive, 2004, vol. 2004, p. 342.
kevman 0:38ceb79fef03 41 * <http://eprint.iacr.org/2004/342.pdf>
kevman 0:38ceb79fef03 42 */
kevman 0:38ceb79fef03 43
kevman 0:38ceb79fef03 44 #if !defined(MBEDTLS_CONFIG_FILE)
kevman 0:38ceb79fef03 45 #include "mbedtls/config.h"
kevman 0:38ceb79fef03 46 #else
kevman 0:38ceb79fef03 47 #include MBEDTLS_CONFIG_FILE
kevman 0:38ceb79fef03 48 #endif
kevman 0:38ceb79fef03 49
kevman 0:38ceb79fef03 50 #if defined(MBEDTLS_ECP_C)
kevman 0:38ceb79fef03 51
kevman 0:38ceb79fef03 52 #include "mbedtls/ecp.h"
kevman 0:38ceb79fef03 53 #include "mbedtls/threading.h"
kevman 0:38ceb79fef03 54 #include "mbedtls/platform_util.h"
kevman 0:38ceb79fef03 55
kevman 0:38ceb79fef03 56 #include <string.h>
kevman 0:38ceb79fef03 57
kevman 0:38ceb79fef03 58 #if !defined(MBEDTLS_ECP_ALT)
kevman 0:38ceb79fef03 59
kevman 0:38ceb79fef03 60 #if defined(MBEDTLS_PLATFORM_C)
kevman 0:38ceb79fef03 61 #include "mbedtls/platform.h"
kevman 0:38ceb79fef03 62 #else
kevman 0:38ceb79fef03 63 #include <stdlib.h>
kevman 0:38ceb79fef03 64 #include <stdio.h>
kevman 0:38ceb79fef03 65 #define mbedtls_printf printf
kevman 0:38ceb79fef03 66 #define mbedtls_calloc calloc
kevman 0:38ceb79fef03 67 #define mbedtls_free free
kevman 0:38ceb79fef03 68 #endif
kevman 0:38ceb79fef03 69
kevman 0:38ceb79fef03 70 #include "mbedtls/ecp_internal.h"
kevman 0:38ceb79fef03 71
kevman 0:38ceb79fef03 72 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
kevman 0:38ceb79fef03 73 !defined(inline) && !defined(__cplusplus)
kevman 0:38ceb79fef03 74 #define inline __inline
kevman 0:38ceb79fef03 75 #endif
kevman 0:38ceb79fef03 76
kevman 0:38ceb79fef03 77 #if defined(MBEDTLS_SELF_TEST)
kevman 0:38ceb79fef03 78 /*
kevman 0:38ceb79fef03 79 * Counts of point addition and doubling, and field multiplications.
kevman 0:38ceb79fef03 80 * Used to test resistance of point multiplication to simple timing attacks.
kevman 0:38ceb79fef03 81 */
kevman 0:38ceb79fef03 82 static unsigned long add_count, dbl_count, mul_count;
kevman 0:38ceb79fef03 83 #endif
kevman 0:38ceb79fef03 84
kevman 0:38ceb79fef03 85 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \
kevman 0:38ceb79fef03 86 defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
kevman 0:38ceb79fef03 87 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
kevman 0:38ceb79fef03 88 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \
kevman 0:38ceb79fef03 89 defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \
kevman 0:38ceb79fef03 90 defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \
kevman 0:38ceb79fef03 91 defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \
kevman 0:38ceb79fef03 92 defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \
kevman 0:38ceb79fef03 93 defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
kevman 0:38ceb79fef03 94 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
kevman 0:38ceb79fef03 95 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
kevman 0:38ceb79fef03 96 #define ECP_SHORTWEIERSTRASS
kevman 0:38ceb79fef03 97 #endif
kevman 0:38ceb79fef03 98
kevman 0:38ceb79fef03 99 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) || \
kevman 0:38ceb79fef03 100 defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
kevman 0:38ceb79fef03 101 #define ECP_MONTGOMERY
kevman 0:38ceb79fef03 102 #endif
kevman 0:38ceb79fef03 103
kevman 0:38ceb79fef03 104 /*
kevman 0:38ceb79fef03 105 * Curve types: internal for now, might be exposed later
kevman 0:38ceb79fef03 106 */
kevman 0:38ceb79fef03 107 typedef enum
kevman 0:38ceb79fef03 108 {
kevman 0:38ceb79fef03 109 ECP_TYPE_NONE = 0,
kevman 0:38ceb79fef03 110 ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */
kevman 0:38ceb79fef03 111 ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */
kevman 0:38ceb79fef03 112 } ecp_curve_type;
kevman 0:38ceb79fef03 113
kevman 0:38ceb79fef03 114 /*
kevman 0:38ceb79fef03 115 * List of supported curves:
kevman 0:38ceb79fef03 116 * - internal ID
kevman 0:38ceb79fef03 117 * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2)
kevman 0:38ceb79fef03 118 * - size in bits
kevman 0:38ceb79fef03 119 * - readable name
kevman 0:38ceb79fef03 120 *
kevman 0:38ceb79fef03 121 * Curves are listed in order: largest curves first, and for a given size,
kevman 0:38ceb79fef03 122 * fastest curves first. This provides the default order for the SSL module.
kevman 0:38ceb79fef03 123 *
kevman 0:38ceb79fef03 124 * Reminder: update profiles in x509_crt.c when adding a new curves!
kevman 0:38ceb79fef03 125 */
kevman 0:38ceb79fef03 126 static const mbedtls_ecp_curve_info ecp_supported_curves[] =
kevman 0:38ceb79fef03 127 {
kevman 0:38ceb79fef03 128 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
kevman 0:38ceb79fef03 129 { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" },
kevman 0:38ceb79fef03 130 #endif
kevman 0:38ceb79fef03 131 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
kevman 0:38ceb79fef03 132 { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
kevman 0:38ceb79fef03 133 #endif
kevman 0:38ceb79fef03 134 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
kevman 0:38ceb79fef03 135 { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
kevman 0:38ceb79fef03 136 #endif
kevman 0:38ceb79fef03 137 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
kevman 0:38ceb79fef03 138 { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
kevman 0:38ceb79fef03 139 #endif
kevman 0:38ceb79fef03 140 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
kevman 0:38ceb79fef03 141 { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
kevman 0:38ceb79fef03 142 #endif
kevman 0:38ceb79fef03 143 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
kevman 0:38ceb79fef03 144 { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
kevman 0:38ceb79fef03 145 #endif
kevman 0:38ceb79fef03 146 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
kevman 0:38ceb79fef03 147 { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" },
kevman 0:38ceb79fef03 148 #endif
kevman 0:38ceb79fef03 149 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
kevman 0:38ceb79fef03 150 { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" },
kevman 0:38ceb79fef03 151 #endif
kevman 0:38ceb79fef03 152 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
kevman 0:38ceb79fef03 153 { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" },
kevman 0:38ceb79fef03 154 #endif
kevman 0:38ceb79fef03 155 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
kevman 0:38ceb79fef03 156 { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" },
kevman 0:38ceb79fef03 157 #endif
kevman 0:38ceb79fef03 158 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
kevman 0:38ceb79fef03 159 { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" },
kevman 0:38ceb79fef03 160 #endif
kevman 0:38ceb79fef03 161 { MBEDTLS_ECP_DP_NONE, 0, 0, NULL },
kevman 0:38ceb79fef03 162 };
kevman 0:38ceb79fef03 163
kevman 0:38ceb79fef03 164 #define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \
kevman 0:38ceb79fef03 165 sizeof( ecp_supported_curves[0] )
kevman 0:38ceb79fef03 166
kevman 0:38ceb79fef03 167 static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
kevman 0:38ceb79fef03 168
kevman 0:38ceb79fef03 169 /*
kevman 0:38ceb79fef03 170 * List of supported curves and associated info
kevman 0:38ceb79fef03 171 */
kevman 0:38ceb79fef03 172 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
kevman 0:38ceb79fef03 173 {
kevman 0:38ceb79fef03 174 return( ecp_supported_curves );
kevman 0:38ceb79fef03 175 }
kevman 0:38ceb79fef03 176
kevman 0:38ceb79fef03 177 /*
kevman 0:38ceb79fef03 178 * List of supported curves, group ID only
kevman 0:38ceb79fef03 179 */
kevman 0:38ceb79fef03 180 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
kevman 0:38ceb79fef03 181 {
kevman 0:38ceb79fef03 182 static int init_done = 0;
kevman 0:38ceb79fef03 183
kevman 0:38ceb79fef03 184 if( ! init_done )
kevman 0:38ceb79fef03 185 {
kevman 0:38ceb79fef03 186 size_t i = 0;
kevman 0:38ceb79fef03 187 const mbedtls_ecp_curve_info *curve_info;
kevman 0:38ceb79fef03 188
kevman 0:38ceb79fef03 189 for( curve_info = mbedtls_ecp_curve_list();
kevman 0:38ceb79fef03 190 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
kevman 0:38ceb79fef03 191 curve_info++ )
kevman 0:38ceb79fef03 192 {
kevman 0:38ceb79fef03 193 ecp_supported_grp_id[i++] = curve_info->grp_id;
kevman 0:38ceb79fef03 194 }
kevman 0:38ceb79fef03 195 ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
kevman 0:38ceb79fef03 196
kevman 0:38ceb79fef03 197 init_done = 1;
kevman 0:38ceb79fef03 198 }
kevman 0:38ceb79fef03 199
kevman 0:38ceb79fef03 200 return( ecp_supported_grp_id );
kevman 0:38ceb79fef03 201 }
kevman 0:38ceb79fef03 202
kevman 0:38ceb79fef03 203 /*
kevman 0:38ceb79fef03 204 * Get the curve info for the internal identifier
kevman 0:38ceb79fef03 205 */
kevman 0:38ceb79fef03 206 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id )
kevman 0:38ceb79fef03 207 {
kevman 0:38ceb79fef03 208 const mbedtls_ecp_curve_info *curve_info;
kevman 0:38ceb79fef03 209
kevman 0:38ceb79fef03 210 for( curve_info = mbedtls_ecp_curve_list();
kevman 0:38ceb79fef03 211 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
kevman 0:38ceb79fef03 212 curve_info++ )
kevman 0:38ceb79fef03 213 {
kevman 0:38ceb79fef03 214 if( curve_info->grp_id == grp_id )
kevman 0:38ceb79fef03 215 return( curve_info );
kevman 0:38ceb79fef03 216 }
kevman 0:38ceb79fef03 217
kevman 0:38ceb79fef03 218 return( NULL );
kevman 0:38ceb79fef03 219 }
kevman 0:38ceb79fef03 220
kevman 0:38ceb79fef03 221 /*
kevman 0:38ceb79fef03 222 * Get the curve info from the TLS identifier
kevman 0:38ceb79fef03 223 */
kevman 0:38ceb79fef03 224 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id )
kevman 0:38ceb79fef03 225 {
kevman 0:38ceb79fef03 226 const mbedtls_ecp_curve_info *curve_info;
kevman 0:38ceb79fef03 227
kevman 0:38ceb79fef03 228 for( curve_info = mbedtls_ecp_curve_list();
kevman 0:38ceb79fef03 229 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
kevman 0:38ceb79fef03 230 curve_info++ )
kevman 0:38ceb79fef03 231 {
kevman 0:38ceb79fef03 232 if( curve_info->tls_id == tls_id )
kevman 0:38ceb79fef03 233 return( curve_info );
kevman 0:38ceb79fef03 234 }
kevman 0:38ceb79fef03 235
kevman 0:38ceb79fef03 236 return( NULL );
kevman 0:38ceb79fef03 237 }
kevman 0:38ceb79fef03 238
kevman 0:38ceb79fef03 239 /*
kevman 0:38ceb79fef03 240 * Get the curve info from the name
kevman 0:38ceb79fef03 241 */
kevman 0:38ceb79fef03 242 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name )
kevman 0:38ceb79fef03 243 {
kevman 0:38ceb79fef03 244 const mbedtls_ecp_curve_info *curve_info;
kevman 0:38ceb79fef03 245
kevman 0:38ceb79fef03 246 for( curve_info = mbedtls_ecp_curve_list();
kevman 0:38ceb79fef03 247 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
kevman 0:38ceb79fef03 248 curve_info++ )
kevman 0:38ceb79fef03 249 {
kevman 0:38ceb79fef03 250 if( strcmp( curve_info->name, name ) == 0 )
kevman 0:38ceb79fef03 251 return( curve_info );
kevman 0:38ceb79fef03 252 }
kevman 0:38ceb79fef03 253
kevman 0:38ceb79fef03 254 return( NULL );
kevman 0:38ceb79fef03 255 }
kevman 0:38ceb79fef03 256
kevman 0:38ceb79fef03 257 /*
kevman 0:38ceb79fef03 258 * Get the type of a curve
kevman 0:38ceb79fef03 259 */
kevman 0:38ceb79fef03 260 static inline ecp_curve_type ecp_get_type( const mbedtls_ecp_group *grp )
kevman 0:38ceb79fef03 261 {
kevman 0:38ceb79fef03 262 if( grp->G.X.p == NULL )
kevman 0:38ceb79fef03 263 return( ECP_TYPE_NONE );
kevman 0:38ceb79fef03 264
kevman 0:38ceb79fef03 265 if( grp->G.Y.p == NULL )
kevman 0:38ceb79fef03 266 return( ECP_TYPE_MONTGOMERY );
kevman 0:38ceb79fef03 267 else
kevman 0:38ceb79fef03 268 return( ECP_TYPE_SHORT_WEIERSTRASS );
kevman 0:38ceb79fef03 269 }
kevman 0:38ceb79fef03 270
kevman 0:38ceb79fef03 271 /*
kevman 0:38ceb79fef03 272 * Initialize (the components of) a point
kevman 0:38ceb79fef03 273 */
kevman 0:38ceb79fef03 274 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
kevman 0:38ceb79fef03 275 {
kevman 0:38ceb79fef03 276 if( pt == NULL )
kevman 0:38ceb79fef03 277 return;
kevman 0:38ceb79fef03 278
kevman 0:38ceb79fef03 279 mbedtls_mpi_init( &pt->X );
kevman 0:38ceb79fef03 280 mbedtls_mpi_init( &pt->Y );
kevman 0:38ceb79fef03 281 mbedtls_mpi_init( &pt->Z );
kevman 0:38ceb79fef03 282 }
kevman 0:38ceb79fef03 283
kevman 0:38ceb79fef03 284 /*
kevman 0:38ceb79fef03 285 * Initialize (the components of) a group
kevman 0:38ceb79fef03 286 */
kevman 0:38ceb79fef03 287 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
kevman 0:38ceb79fef03 288 {
kevman 0:38ceb79fef03 289 if( grp == NULL )
kevman 0:38ceb79fef03 290 return;
kevman 0:38ceb79fef03 291
kevman 0:38ceb79fef03 292 memset( grp, 0, sizeof( mbedtls_ecp_group ) );
kevman 0:38ceb79fef03 293 }
kevman 0:38ceb79fef03 294
kevman 0:38ceb79fef03 295 /*
kevman 0:38ceb79fef03 296 * Initialize (the components of) a key pair
kevman 0:38ceb79fef03 297 */
kevman 0:38ceb79fef03 298 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
kevman 0:38ceb79fef03 299 {
kevman 0:38ceb79fef03 300 if( key == NULL )
kevman 0:38ceb79fef03 301 return;
kevman 0:38ceb79fef03 302
kevman 0:38ceb79fef03 303 mbedtls_ecp_group_init( &key->grp );
kevman 0:38ceb79fef03 304 mbedtls_mpi_init( &key->d );
kevman 0:38ceb79fef03 305 mbedtls_ecp_point_init( &key->Q );
kevman 0:38ceb79fef03 306 }
kevman 0:38ceb79fef03 307
kevman 0:38ceb79fef03 308 /*
kevman 0:38ceb79fef03 309 * Unallocate (the components of) a point
kevman 0:38ceb79fef03 310 */
kevman 0:38ceb79fef03 311 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
kevman 0:38ceb79fef03 312 {
kevman 0:38ceb79fef03 313 if( pt == NULL )
kevman 0:38ceb79fef03 314 return;
kevman 0:38ceb79fef03 315
kevman 0:38ceb79fef03 316 mbedtls_mpi_free( &( pt->X ) );
kevman 0:38ceb79fef03 317 mbedtls_mpi_free( &( pt->Y ) );
kevman 0:38ceb79fef03 318 mbedtls_mpi_free( &( pt->Z ) );
kevman 0:38ceb79fef03 319 }
kevman 0:38ceb79fef03 320
kevman 0:38ceb79fef03 321 /*
kevman 0:38ceb79fef03 322 * Unallocate (the components of) a group
kevman 0:38ceb79fef03 323 */
kevman 0:38ceb79fef03 324 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
kevman 0:38ceb79fef03 325 {
kevman 0:38ceb79fef03 326 size_t i;
kevman 0:38ceb79fef03 327
kevman 0:38ceb79fef03 328 if( grp == NULL )
kevman 0:38ceb79fef03 329 return;
kevman 0:38ceb79fef03 330
kevman 0:38ceb79fef03 331 if( grp->h != 1 )
kevman 0:38ceb79fef03 332 {
kevman 0:38ceb79fef03 333 mbedtls_mpi_free( &grp->P );
kevman 0:38ceb79fef03 334 mbedtls_mpi_free( &grp->A );
kevman 0:38ceb79fef03 335 mbedtls_mpi_free( &grp->B );
kevman 0:38ceb79fef03 336 mbedtls_ecp_point_free( &grp->G );
kevman 0:38ceb79fef03 337 mbedtls_mpi_free( &grp->N );
kevman 0:38ceb79fef03 338 }
kevman 0:38ceb79fef03 339
kevman 0:38ceb79fef03 340 if( grp->T != NULL )
kevman 0:38ceb79fef03 341 {
kevman 0:38ceb79fef03 342 for( i = 0; i < grp->T_size; i++ )
kevman 0:38ceb79fef03 343 mbedtls_ecp_point_free( &grp->T[i] );
kevman 0:38ceb79fef03 344 mbedtls_free( grp->T );
kevman 0:38ceb79fef03 345 }
kevman 0:38ceb79fef03 346
kevman 0:38ceb79fef03 347 mbedtls_platform_zeroize( grp, sizeof( mbedtls_ecp_group ) );
kevman 0:38ceb79fef03 348 }
kevman 0:38ceb79fef03 349
kevman 0:38ceb79fef03 350 /*
kevman 0:38ceb79fef03 351 * Unallocate (the components of) a key pair
kevman 0:38ceb79fef03 352 */
kevman 0:38ceb79fef03 353 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
kevman 0:38ceb79fef03 354 {
kevman 0:38ceb79fef03 355 if( key == NULL )
kevman 0:38ceb79fef03 356 return;
kevman 0:38ceb79fef03 357
kevman 0:38ceb79fef03 358 mbedtls_ecp_group_free( &key->grp );
kevman 0:38ceb79fef03 359 mbedtls_mpi_free( &key->d );
kevman 0:38ceb79fef03 360 mbedtls_ecp_point_free( &key->Q );
kevman 0:38ceb79fef03 361 }
kevman 0:38ceb79fef03 362
kevman 0:38ceb79fef03 363 /*
kevman 0:38ceb79fef03 364 * Copy the contents of a point
kevman 0:38ceb79fef03 365 */
kevman 0:38ceb79fef03 366 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
kevman 0:38ceb79fef03 367 {
kevman 0:38ceb79fef03 368 int ret;
kevman 0:38ceb79fef03 369
kevman 0:38ceb79fef03 370 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) );
kevman 0:38ceb79fef03 371 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) );
kevman 0:38ceb79fef03 372 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) );
kevman 0:38ceb79fef03 373
kevman 0:38ceb79fef03 374 cleanup:
kevman 0:38ceb79fef03 375 return( ret );
kevman 0:38ceb79fef03 376 }
kevman 0:38ceb79fef03 377
kevman 0:38ceb79fef03 378 /*
kevman 0:38ceb79fef03 379 * Copy the contents of a group object
kevman 0:38ceb79fef03 380 */
kevman 0:38ceb79fef03 381 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
kevman 0:38ceb79fef03 382 {
kevman 0:38ceb79fef03 383 return mbedtls_ecp_group_load( dst, src->id );
kevman 0:38ceb79fef03 384 }
kevman 0:38ceb79fef03 385
kevman 0:38ceb79fef03 386 /*
kevman 0:38ceb79fef03 387 * Set point to zero
kevman 0:38ceb79fef03 388 */
kevman 0:38ceb79fef03 389 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
kevman 0:38ceb79fef03 390 {
kevman 0:38ceb79fef03 391 int ret;
kevman 0:38ceb79fef03 392
kevman 0:38ceb79fef03 393 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) );
kevman 0:38ceb79fef03 394 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) );
kevman 0:38ceb79fef03 395 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) );
kevman 0:38ceb79fef03 396
kevman 0:38ceb79fef03 397 cleanup:
kevman 0:38ceb79fef03 398 return( ret );
kevman 0:38ceb79fef03 399 }
kevman 0:38ceb79fef03 400
kevman 0:38ceb79fef03 401 /*
kevman 0:38ceb79fef03 402 * Tell if a point is zero
kevman 0:38ceb79fef03 403 */
kevman 0:38ceb79fef03 404 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
kevman 0:38ceb79fef03 405 {
kevman 0:38ceb79fef03 406 return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 );
kevman 0:38ceb79fef03 407 }
kevman 0:38ceb79fef03 408
kevman 0:38ceb79fef03 409 /*
kevman 0:38ceb79fef03 410 * Compare two points lazyly
kevman 0:38ceb79fef03 411 */
kevman 0:38ceb79fef03 412 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
kevman 0:38ceb79fef03 413 const mbedtls_ecp_point *Q )
kevman 0:38ceb79fef03 414 {
kevman 0:38ceb79fef03 415 if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
kevman 0:38ceb79fef03 416 mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 &&
kevman 0:38ceb79fef03 417 mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 )
kevman 0:38ceb79fef03 418 {
kevman 0:38ceb79fef03 419 return( 0 );
kevman 0:38ceb79fef03 420 }
kevman 0:38ceb79fef03 421
kevman 0:38ceb79fef03 422 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 423 }
kevman 0:38ceb79fef03 424
kevman 0:38ceb79fef03 425 /*
kevman 0:38ceb79fef03 426 * Import a non-zero point from ASCII strings
kevman 0:38ceb79fef03 427 */
kevman 0:38ceb79fef03 428 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
kevman 0:38ceb79fef03 429 const char *x, const char *y )
kevman 0:38ceb79fef03 430 {
kevman 0:38ceb79fef03 431 int ret;
kevman 0:38ceb79fef03 432
kevman 0:38ceb79fef03 433 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) );
kevman 0:38ceb79fef03 434 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) );
kevman 0:38ceb79fef03 435 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
kevman 0:38ceb79fef03 436
kevman 0:38ceb79fef03 437 cleanup:
kevman 0:38ceb79fef03 438 return( ret );
kevman 0:38ceb79fef03 439 }
kevman 0:38ceb79fef03 440
kevman 0:38ceb79fef03 441 /*
kevman 0:38ceb79fef03 442 * Export a point into unsigned binary data (SEC1 2.3.3)
kevman 0:38ceb79fef03 443 */
kevman 0:38ceb79fef03 444 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P,
kevman 0:38ceb79fef03 445 int format, size_t *olen,
kevman 0:38ceb79fef03 446 unsigned char *buf, size_t buflen )
kevman 0:38ceb79fef03 447 {
kevman 0:38ceb79fef03 448 int ret = 0;
kevman 0:38ceb79fef03 449 size_t plen;
kevman 0:38ceb79fef03 450
kevman 0:38ceb79fef03 451 if( format != MBEDTLS_ECP_PF_UNCOMPRESSED &&
kevman 0:38ceb79fef03 452 format != MBEDTLS_ECP_PF_COMPRESSED )
kevman 0:38ceb79fef03 453 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 454
kevman 0:38ceb79fef03 455 /*
kevman 0:38ceb79fef03 456 * Common case: P == 0
kevman 0:38ceb79fef03 457 */
kevman 0:38ceb79fef03 458 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
kevman 0:38ceb79fef03 459 {
kevman 0:38ceb79fef03 460 if( buflen < 1 )
kevman 0:38ceb79fef03 461 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
kevman 0:38ceb79fef03 462
kevman 0:38ceb79fef03 463 buf[0] = 0x00;
kevman 0:38ceb79fef03 464 *olen = 1;
kevman 0:38ceb79fef03 465
kevman 0:38ceb79fef03 466 return( 0 );
kevman 0:38ceb79fef03 467 }
kevman 0:38ceb79fef03 468
kevman 0:38ceb79fef03 469 plen = mbedtls_mpi_size( &grp->P );
kevman 0:38ceb79fef03 470
kevman 0:38ceb79fef03 471 if( format == MBEDTLS_ECP_PF_UNCOMPRESSED )
kevman 0:38ceb79fef03 472 {
kevman 0:38ceb79fef03 473 *olen = 2 * plen + 1;
kevman 0:38ceb79fef03 474
kevman 0:38ceb79fef03 475 if( buflen < *olen )
kevman 0:38ceb79fef03 476 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
kevman 0:38ceb79fef03 477
kevman 0:38ceb79fef03 478 buf[0] = 0x04;
kevman 0:38ceb79fef03 479 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
kevman 0:38ceb79fef03 480 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) );
kevman 0:38ceb79fef03 481 }
kevman 0:38ceb79fef03 482 else if( format == MBEDTLS_ECP_PF_COMPRESSED )
kevman 0:38ceb79fef03 483 {
kevman 0:38ceb79fef03 484 *olen = plen + 1;
kevman 0:38ceb79fef03 485
kevman 0:38ceb79fef03 486 if( buflen < *olen )
kevman 0:38ceb79fef03 487 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
kevman 0:38ceb79fef03 488
kevman 0:38ceb79fef03 489 buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 );
kevman 0:38ceb79fef03 490 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
kevman 0:38ceb79fef03 491 }
kevman 0:38ceb79fef03 492
kevman 0:38ceb79fef03 493 cleanup:
kevman 0:38ceb79fef03 494 return( ret );
kevman 0:38ceb79fef03 495 }
kevman 0:38ceb79fef03 496
kevman 0:38ceb79fef03 497 /*
kevman 0:38ceb79fef03 498 * Import a point from unsigned binary data (SEC1 2.3.4)
kevman 0:38ceb79fef03 499 */
kevman 0:38ceb79fef03 500 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
kevman 0:38ceb79fef03 501 const unsigned char *buf, size_t ilen )
kevman 0:38ceb79fef03 502 {
kevman 0:38ceb79fef03 503 int ret;
kevman 0:38ceb79fef03 504 size_t plen;
kevman 0:38ceb79fef03 505
kevman 0:38ceb79fef03 506 if( ilen < 1 )
kevman 0:38ceb79fef03 507 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 508
kevman 0:38ceb79fef03 509 if( buf[0] == 0x00 )
kevman 0:38ceb79fef03 510 {
kevman 0:38ceb79fef03 511 if( ilen == 1 )
kevman 0:38ceb79fef03 512 return( mbedtls_ecp_set_zero( pt ) );
kevman 0:38ceb79fef03 513 else
kevman 0:38ceb79fef03 514 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 515 }
kevman 0:38ceb79fef03 516
kevman 0:38ceb79fef03 517 plen = mbedtls_mpi_size( &grp->P );
kevman 0:38ceb79fef03 518
kevman 0:38ceb79fef03 519 if( buf[0] != 0x04 )
kevman 0:38ceb79fef03 520 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
kevman 0:38ceb79fef03 521
kevman 0:38ceb79fef03 522 if( ilen != 2 * plen + 1 )
kevman 0:38ceb79fef03 523 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 524
kevman 0:38ceb79fef03 525 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
kevman 0:38ceb79fef03 526 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, buf + 1 + plen, plen ) );
kevman 0:38ceb79fef03 527 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
kevman 0:38ceb79fef03 528
kevman 0:38ceb79fef03 529 cleanup:
kevman 0:38ceb79fef03 530 return( ret );
kevman 0:38ceb79fef03 531 }
kevman 0:38ceb79fef03 532
kevman 0:38ceb79fef03 533 /*
kevman 0:38ceb79fef03 534 * Import a point from a TLS ECPoint record (RFC 4492)
kevman 0:38ceb79fef03 535 * struct {
kevman 0:38ceb79fef03 536 * opaque point <1..2^8-1>;
kevman 0:38ceb79fef03 537 * } ECPoint;
kevman 0:38ceb79fef03 538 */
kevman 0:38ceb79fef03 539 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
kevman 0:38ceb79fef03 540 const unsigned char **buf, size_t buf_len )
kevman 0:38ceb79fef03 541 {
kevman 0:38ceb79fef03 542 unsigned char data_len;
kevman 0:38ceb79fef03 543 const unsigned char *buf_start;
kevman 0:38ceb79fef03 544
kevman 0:38ceb79fef03 545 /*
kevman 0:38ceb79fef03 546 * We must have at least two bytes (1 for length, at least one for data)
kevman 0:38ceb79fef03 547 */
kevman 0:38ceb79fef03 548 if( buf_len < 2 )
kevman 0:38ceb79fef03 549 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 550
kevman 0:38ceb79fef03 551 data_len = *(*buf)++;
kevman 0:38ceb79fef03 552 if( data_len < 1 || data_len > buf_len - 1 )
kevman 0:38ceb79fef03 553 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 554
kevman 0:38ceb79fef03 555 /*
kevman 0:38ceb79fef03 556 * Save buffer start for read_binary and update buf
kevman 0:38ceb79fef03 557 */
kevman 0:38ceb79fef03 558 buf_start = *buf;
kevman 0:38ceb79fef03 559 *buf += data_len;
kevman 0:38ceb79fef03 560
kevman 0:38ceb79fef03 561 return mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len );
kevman 0:38ceb79fef03 562 }
kevman 0:38ceb79fef03 563
kevman 0:38ceb79fef03 564 /*
kevman 0:38ceb79fef03 565 * Export a point as a TLS ECPoint record (RFC 4492)
kevman 0:38ceb79fef03 566 * struct {
kevman 0:38ceb79fef03 567 * opaque point <1..2^8-1>;
kevman 0:38ceb79fef03 568 * } ECPoint;
kevman 0:38ceb79fef03 569 */
kevman 0:38ceb79fef03 570 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
kevman 0:38ceb79fef03 571 int format, size_t *olen,
kevman 0:38ceb79fef03 572 unsigned char *buf, size_t blen )
kevman 0:38ceb79fef03 573 {
kevman 0:38ceb79fef03 574 int ret;
kevman 0:38ceb79fef03 575
kevman 0:38ceb79fef03 576 /*
kevman 0:38ceb79fef03 577 * buffer length must be at least one, for our length byte
kevman 0:38ceb79fef03 578 */
kevman 0:38ceb79fef03 579 if( blen < 1 )
kevman 0:38ceb79fef03 580 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 581
kevman 0:38ceb79fef03 582 if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
kevman 0:38ceb79fef03 583 olen, buf + 1, blen - 1) ) != 0 )
kevman 0:38ceb79fef03 584 return( ret );
kevman 0:38ceb79fef03 585
kevman 0:38ceb79fef03 586 /*
kevman 0:38ceb79fef03 587 * write length to the first byte and update total length
kevman 0:38ceb79fef03 588 */
kevman 0:38ceb79fef03 589 buf[0] = (unsigned char) *olen;
kevman 0:38ceb79fef03 590 ++*olen;
kevman 0:38ceb79fef03 591
kevman 0:38ceb79fef03 592 return( 0 );
kevman 0:38ceb79fef03 593 }
kevman 0:38ceb79fef03 594
kevman 0:38ceb79fef03 595 /*
kevman 0:38ceb79fef03 596 * Set a group from an ECParameters record (RFC 4492)
kevman 0:38ceb79fef03 597 */
kevman 0:38ceb79fef03 598 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, const unsigned char **buf, size_t len )
kevman 0:38ceb79fef03 599 {
kevman 0:38ceb79fef03 600 uint16_t tls_id;
kevman 0:38ceb79fef03 601 const mbedtls_ecp_curve_info *curve_info;
kevman 0:38ceb79fef03 602
kevman 0:38ceb79fef03 603 /*
kevman 0:38ceb79fef03 604 * We expect at least three bytes (see below)
kevman 0:38ceb79fef03 605 */
kevman 0:38ceb79fef03 606 if( len < 3 )
kevman 0:38ceb79fef03 607 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 608
kevman 0:38ceb79fef03 609 /*
kevman 0:38ceb79fef03 610 * First byte is curve_type; only named_curve is handled
kevman 0:38ceb79fef03 611 */
kevman 0:38ceb79fef03 612 if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
kevman 0:38ceb79fef03 613 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 614
kevman 0:38ceb79fef03 615 /*
kevman 0:38ceb79fef03 616 * Next two bytes are the namedcurve value
kevman 0:38ceb79fef03 617 */
kevman 0:38ceb79fef03 618 tls_id = *(*buf)++;
kevman 0:38ceb79fef03 619 tls_id <<= 8;
kevman 0:38ceb79fef03 620 tls_id |= *(*buf)++;
kevman 0:38ceb79fef03 621
kevman 0:38ceb79fef03 622 if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
kevman 0:38ceb79fef03 623 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
kevman 0:38ceb79fef03 624
kevman 0:38ceb79fef03 625 return mbedtls_ecp_group_load( grp, curve_info->grp_id );
kevman 0:38ceb79fef03 626 }
kevman 0:38ceb79fef03 627
kevman 0:38ceb79fef03 628 /*
kevman 0:38ceb79fef03 629 * Write the ECParameters record corresponding to a group (RFC 4492)
kevman 0:38ceb79fef03 630 */
kevman 0:38ceb79fef03 631 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
kevman 0:38ceb79fef03 632 unsigned char *buf, size_t blen )
kevman 0:38ceb79fef03 633 {
kevman 0:38ceb79fef03 634 const mbedtls_ecp_curve_info *curve_info;
kevman 0:38ceb79fef03 635
kevman 0:38ceb79fef03 636 if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
kevman 0:38ceb79fef03 637 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 638
kevman 0:38ceb79fef03 639 /*
kevman 0:38ceb79fef03 640 * We are going to write 3 bytes (see below)
kevman 0:38ceb79fef03 641 */
kevman 0:38ceb79fef03 642 *olen = 3;
kevman 0:38ceb79fef03 643 if( blen < *olen )
kevman 0:38ceb79fef03 644 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
kevman 0:38ceb79fef03 645
kevman 0:38ceb79fef03 646 /*
kevman 0:38ceb79fef03 647 * First byte is curve_type, always named_curve
kevman 0:38ceb79fef03 648 */
kevman 0:38ceb79fef03 649 *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
kevman 0:38ceb79fef03 650
kevman 0:38ceb79fef03 651 /*
kevman 0:38ceb79fef03 652 * Next two bytes are the namedcurve value
kevman 0:38ceb79fef03 653 */
kevman 0:38ceb79fef03 654 buf[0] = curve_info->tls_id >> 8;
kevman 0:38ceb79fef03 655 buf[1] = curve_info->tls_id & 0xFF;
kevman 0:38ceb79fef03 656
kevman 0:38ceb79fef03 657 return( 0 );
kevman 0:38ceb79fef03 658 }
kevman 0:38ceb79fef03 659
kevman 0:38ceb79fef03 660 /*
kevman 0:38ceb79fef03 661 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
kevman 0:38ceb79fef03 662 * See the documentation of struct mbedtls_ecp_group.
kevman 0:38ceb79fef03 663 *
kevman 0:38ceb79fef03 664 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
kevman 0:38ceb79fef03 665 */
kevman 0:38ceb79fef03 666 static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
kevman 0:38ceb79fef03 667 {
kevman 0:38ceb79fef03 668 int ret;
kevman 0:38ceb79fef03 669
kevman 0:38ceb79fef03 670 if( grp->modp == NULL )
kevman 0:38ceb79fef03 671 return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) );
kevman 0:38ceb79fef03 672
kevman 0:38ceb79fef03 673 /* N->s < 0 is a much faster test, which fails only if N is 0 */
kevman 0:38ceb79fef03 674 if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) ||
kevman 0:38ceb79fef03 675 mbedtls_mpi_bitlen( N ) > 2 * grp->pbits )
kevman 0:38ceb79fef03 676 {
kevman 0:38ceb79fef03 677 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 678 }
kevman 0:38ceb79fef03 679
kevman 0:38ceb79fef03 680 MBEDTLS_MPI_CHK( grp->modp( N ) );
kevman 0:38ceb79fef03 681
kevman 0:38ceb79fef03 682 /* N->s < 0 is a much faster test, which fails only if N is 0 */
kevman 0:38ceb79fef03 683 while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 )
kevman 0:38ceb79fef03 684 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) );
kevman 0:38ceb79fef03 685
kevman 0:38ceb79fef03 686 while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 )
kevman 0:38ceb79fef03 687 /* we known P, N and the result are positive */
kevman 0:38ceb79fef03 688 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) );
kevman 0:38ceb79fef03 689
kevman 0:38ceb79fef03 690 cleanup:
kevman 0:38ceb79fef03 691 return( ret );
kevman 0:38ceb79fef03 692 }
kevman 0:38ceb79fef03 693
kevman 0:38ceb79fef03 694 /*
kevman 0:38ceb79fef03 695 * Fast mod-p functions expect their argument to be in the 0..p^2 range.
kevman 0:38ceb79fef03 696 *
kevman 0:38ceb79fef03 697 * In order to guarantee that, we need to ensure that operands of
kevman 0:38ceb79fef03 698 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will
kevman 0:38ceb79fef03 699 * bring the result back to this range.
kevman 0:38ceb79fef03 700 *
kevman 0:38ceb79fef03 701 * The following macros are shortcuts for doing that.
kevman 0:38ceb79fef03 702 */
kevman 0:38ceb79fef03 703
kevman 0:38ceb79fef03 704 /*
kevman 0:38ceb79fef03 705 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
kevman 0:38ceb79fef03 706 */
kevman 0:38ceb79fef03 707 #if defined(MBEDTLS_SELF_TEST)
kevman 0:38ceb79fef03 708 #define INC_MUL_COUNT mul_count++;
kevman 0:38ceb79fef03 709 #else
kevman 0:38ceb79fef03 710 #define INC_MUL_COUNT
kevman 0:38ceb79fef03 711 #endif
kevman 0:38ceb79fef03 712
kevman 0:38ceb79fef03 713 #define MOD_MUL( N ) do { MBEDTLS_MPI_CHK( ecp_modp( &N, grp ) ); INC_MUL_COUNT } \
kevman 0:38ceb79fef03 714 while( 0 )
kevman 0:38ceb79fef03 715
kevman 0:38ceb79fef03 716 /*
kevman 0:38ceb79fef03 717 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
kevman 0:38ceb79fef03 718 * N->s < 0 is a very fast test, which fails only if N is 0
kevman 0:38ceb79fef03 719 */
kevman 0:38ceb79fef03 720 #define MOD_SUB( N ) \
kevman 0:38ceb79fef03 721 while( N.s < 0 && mbedtls_mpi_cmp_int( &N, 0 ) != 0 ) \
kevman 0:38ceb79fef03 722 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &N, &N, &grp->P ) )
kevman 0:38ceb79fef03 723
kevman 0:38ceb79fef03 724 /*
kevman 0:38ceb79fef03 725 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
kevman 0:38ceb79fef03 726 * We known P, N and the result are positive, so sub_abs is correct, and
kevman 0:38ceb79fef03 727 * a bit faster.
kevman 0:38ceb79fef03 728 */
kevman 0:38ceb79fef03 729 #define MOD_ADD( N ) \
kevman 0:38ceb79fef03 730 while( mbedtls_mpi_cmp_mpi( &N, &grp->P ) >= 0 ) \
kevman 0:38ceb79fef03 731 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &N, &N, &grp->P ) )
kevman 0:38ceb79fef03 732
kevman 0:38ceb79fef03 733 #if defined(ECP_SHORTWEIERSTRASS)
kevman 0:38ceb79fef03 734 /*
kevman 0:38ceb79fef03 735 * For curves in short Weierstrass form, we do all the internal operations in
kevman 0:38ceb79fef03 736 * Jacobian coordinates.
kevman 0:38ceb79fef03 737 *
kevman 0:38ceb79fef03 738 * For multiplication, we'll use a comb method with coutermeasueres against
kevman 0:38ceb79fef03 739 * SPA, hence timing attacks.
kevman 0:38ceb79fef03 740 */
kevman 0:38ceb79fef03 741
kevman 0:38ceb79fef03 742 /*
kevman 0:38ceb79fef03 743 * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
kevman 0:38ceb79fef03 744 * Cost: 1N := 1I + 3M + 1S
kevman 0:38ceb79fef03 745 */
kevman 0:38ceb79fef03 746 static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
kevman 0:38ceb79fef03 747 {
kevman 0:38ceb79fef03 748 int ret;
kevman 0:38ceb79fef03 749 mbedtls_mpi Zi, ZZi;
kevman 0:38ceb79fef03 750
kevman 0:38ceb79fef03 751 if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
kevman 0:38ceb79fef03 752 return( 0 );
kevman 0:38ceb79fef03 753
kevman 0:38ceb79fef03 754 #if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
kevman 0:38ceb79fef03 755 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kevman 0:38ceb79fef03 756 {
kevman 0:38ceb79fef03 757 return mbedtls_internal_ecp_normalize_jac( grp, pt );
kevman 0:38ceb79fef03 758 }
kevman 0:38ceb79fef03 759 #endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */
kevman 0:38ceb79fef03 760 mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
kevman 0:38ceb79fef03 761
kevman 0:38ceb79fef03 762 /*
kevman 0:38ceb79fef03 763 * X = X / Z^2 mod p
kevman 0:38ceb79fef03 764 */
kevman 0:38ceb79fef03 765 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
kevman 0:38ceb79fef03 766 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
kevman 0:38ceb79fef03 767 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ZZi ) ); MOD_MUL( pt->X );
kevman 0:38ceb79fef03 768
kevman 0:38ceb79fef03 769 /*
kevman 0:38ceb79fef03 770 * Y = Y / Z^3 mod p
kevman 0:38ceb79fef03 771 */
kevman 0:38ceb79fef03 772 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ZZi ) ); MOD_MUL( pt->Y );
kevman 0:38ceb79fef03 773 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &Zi ) ); MOD_MUL( pt->Y );
kevman 0:38ceb79fef03 774
kevman 0:38ceb79fef03 775 /*
kevman 0:38ceb79fef03 776 * Z = 1
kevman 0:38ceb79fef03 777 */
kevman 0:38ceb79fef03 778 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
kevman 0:38ceb79fef03 779
kevman 0:38ceb79fef03 780 cleanup:
kevman 0:38ceb79fef03 781
kevman 0:38ceb79fef03 782 mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
kevman 0:38ceb79fef03 783
kevman 0:38ceb79fef03 784 return( ret );
kevman 0:38ceb79fef03 785 }
kevman 0:38ceb79fef03 786
kevman 0:38ceb79fef03 787 /*
kevman 0:38ceb79fef03 788 * Normalize jacobian coordinates of an array of (pointers to) points,
kevman 0:38ceb79fef03 789 * using Montgomery's trick to perform only one inversion mod P.
kevman 0:38ceb79fef03 790 * (See for example Cohen's "A Course in Computational Algebraic Number
kevman 0:38ceb79fef03 791 * Theory", Algorithm 10.3.4.)
kevman 0:38ceb79fef03 792 *
kevman 0:38ceb79fef03 793 * Warning: fails (returning an error) if one of the points is zero!
kevman 0:38ceb79fef03 794 * This should never happen, see choice of w in ecp_mul_comb().
kevman 0:38ceb79fef03 795 *
kevman 0:38ceb79fef03 796 * Cost: 1N(t) := 1I + (6t - 3)M + 1S
kevman 0:38ceb79fef03 797 */
kevman 0:38ceb79fef03 798 static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
kevman 0:38ceb79fef03 799 mbedtls_ecp_point *T[], size_t t_len )
kevman 0:38ceb79fef03 800 {
kevman 0:38ceb79fef03 801 int ret;
kevman 0:38ceb79fef03 802 size_t i;
kevman 0:38ceb79fef03 803 mbedtls_mpi *c, u, Zi, ZZi;
kevman 0:38ceb79fef03 804
kevman 0:38ceb79fef03 805 if( t_len < 2 )
kevman 0:38ceb79fef03 806 return( ecp_normalize_jac( grp, *T ) );
kevman 0:38ceb79fef03 807
kevman 0:38ceb79fef03 808 #if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
kevman 0:38ceb79fef03 809 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kevman 0:38ceb79fef03 810 {
kevman 0:38ceb79fef03 811 return mbedtls_internal_ecp_normalize_jac_many(grp, T, t_len);
kevman 0:38ceb79fef03 812 }
kevman 0:38ceb79fef03 813 #endif
kevman 0:38ceb79fef03 814
kevman 0:38ceb79fef03 815 if( ( c = mbedtls_calloc( t_len, sizeof( mbedtls_mpi ) ) ) == NULL )
kevman 0:38ceb79fef03 816 return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
kevman 0:38ceb79fef03 817
kevman 0:38ceb79fef03 818 mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
kevman 0:38ceb79fef03 819
kevman 0:38ceb79fef03 820 /*
kevman 0:38ceb79fef03 821 * c[i] = Z_0 * ... * Z_i
kevman 0:38ceb79fef03 822 */
kevman 0:38ceb79fef03 823 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
kevman 0:38ceb79fef03 824 for( i = 1; i < t_len; i++ )
kevman 0:38ceb79fef03 825 {
kevman 0:38ceb79fef03 826 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &c[i], &c[i-1], &T[i]->Z ) );
kevman 0:38ceb79fef03 827 MOD_MUL( c[i] );
kevman 0:38ceb79fef03 828 }
kevman 0:38ceb79fef03 829
kevman 0:38ceb79fef03 830 /*
kevman 0:38ceb79fef03 831 * u = 1 / (Z_0 * ... * Z_n) mod P
kevman 0:38ceb79fef03 832 */
kevman 0:38ceb79fef03 833 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[t_len-1], &grp->P ) );
kevman 0:38ceb79fef03 834
kevman 0:38ceb79fef03 835 for( i = t_len - 1; ; i-- )
kevman 0:38ceb79fef03 836 {
kevman 0:38ceb79fef03 837 /*
kevman 0:38ceb79fef03 838 * Zi = 1 / Z_i mod p
kevman 0:38ceb79fef03 839 * u = 1 / (Z_0 * ... * Z_i) mod P
kevman 0:38ceb79fef03 840 */
kevman 0:38ceb79fef03 841 if( i == 0 ) {
kevman 0:38ceb79fef03 842 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
kevman 0:38ceb79fef03 843 }
kevman 0:38ceb79fef03 844 else
kevman 0:38ceb79fef03 845 {
kevman 0:38ceb79fef03 846 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Zi, &u, &c[i-1] ) ); MOD_MUL( Zi );
kevman 0:38ceb79fef03 847 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u, &u, &T[i]->Z ) ); MOD_MUL( u );
kevman 0:38ceb79fef03 848 }
kevman 0:38ceb79fef03 849
kevman 0:38ceb79fef03 850 /*
kevman 0:38ceb79fef03 851 * proceed as in normalize()
kevman 0:38ceb79fef03 852 */
kevman 0:38ceb79fef03 853 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
kevman 0:38ceb79fef03 854 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->X, &T[i]->X, &ZZi ) ); MOD_MUL( T[i]->X );
kevman 0:38ceb79fef03 855 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &ZZi ) ); MOD_MUL( T[i]->Y );
kevman 0:38ceb79fef03 856 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &Zi ) ); MOD_MUL( T[i]->Y );
kevman 0:38ceb79fef03 857
kevman 0:38ceb79fef03 858 /*
kevman 0:38ceb79fef03 859 * Post-precessing: reclaim some memory by shrinking coordinates
kevman 0:38ceb79fef03 860 * - not storing Z (always 1)
kevman 0:38ceb79fef03 861 * - shrinking other coordinates, but still keeping the same number of
kevman 0:38ceb79fef03 862 * limbs as P, as otherwise it will too likely be regrown too fast.
kevman 0:38ceb79fef03 863 */
kevman 0:38ceb79fef03 864 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
kevman 0:38ceb79fef03 865 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
kevman 0:38ceb79fef03 866 mbedtls_mpi_free( &T[i]->Z );
kevman 0:38ceb79fef03 867
kevman 0:38ceb79fef03 868 if( i == 0 )
kevman 0:38ceb79fef03 869 break;
kevman 0:38ceb79fef03 870 }
kevman 0:38ceb79fef03 871
kevman 0:38ceb79fef03 872 cleanup:
kevman 0:38ceb79fef03 873
kevman 0:38ceb79fef03 874 mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
kevman 0:38ceb79fef03 875 for( i = 0; i < t_len; i++ )
kevman 0:38ceb79fef03 876 mbedtls_mpi_free( &c[i] );
kevman 0:38ceb79fef03 877 mbedtls_free( c );
kevman 0:38ceb79fef03 878
kevman 0:38ceb79fef03 879 return( ret );
kevman 0:38ceb79fef03 880 }
kevman 0:38ceb79fef03 881
kevman 0:38ceb79fef03 882 /*
kevman 0:38ceb79fef03 883 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
kevman 0:38ceb79fef03 884 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
kevman 0:38ceb79fef03 885 */
kevman 0:38ceb79fef03 886 static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
kevman 0:38ceb79fef03 887 mbedtls_ecp_point *Q,
kevman 0:38ceb79fef03 888 unsigned char inv )
kevman 0:38ceb79fef03 889 {
kevman 0:38ceb79fef03 890 int ret;
kevman 0:38ceb79fef03 891 unsigned char nonzero;
kevman 0:38ceb79fef03 892 mbedtls_mpi mQY;
kevman 0:38ceb79fef03 893
kevman 0:38ceb79fef03 894 mbedtls_mpi_init( &mQY );
kevman 0:38ceb79fef03 895
kevman 0:38ceb79fef03 896 /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
kevman 0:38ceb79fef03 897 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
kevman 0:38ceb79fef03 898 nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
kevman 0:38ceb79fef03 899 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
kevman 0:38ceb79fef03 900
kevman 0:38ceb79fef03 901 cleanup:
kevman 0:38ceb79fef03 902 mbedtls_mpi_free( &mQY );
kevman 0:38ceb79fef03 903
kevman 0:38ceb79fef03 904 return( ret );
kevman 0:38ceb79fef03 905 }
kevman 0:38ceb79fef03 906
kevman 0:38ceb79fef03 907 /*
kevman 0:38ceb79fef03 908 * Point doubling R = 2 P, Jacobian coordinates
kevman 0:38ceb79fef03 909 *
kevman 0:38ceb79fef03 910 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
kevman 0:38ceb79fef03 911 *
kevman 0:38ceb79fef03 912 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
kevman 0:38ceb79fef03 913 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
kevman 0:38ceb79fef03 914 *
kevman 0:38ceb79fef03 915 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
kevman 0:38ceb79fef03 916 *
kevman 0:38ceb79fef03 917 * Cost: 1D := 3M + 4S (A == 0)
kevman 0:38ceb79fef03 918 * 4M + 4S (A == -3)
kevman 0:38ceb79fef03 919 * 3M + 6S + 1a otherwise
kevman 0:38ceb79fef03 920 */
kevman 0:38ceb79fef03 921 static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kevman 0:38ceb79fef03 922 const mbedtls_ecp_point *P )
kevman 0:38ceb79fef03 923 {
kevman 0:38ceb79fef03 924 int ret;
kevman 0:38ceb79fef03 925 mbedtls_mpi M, S, T, U;
kevman 0:38ceb79fef03 926
kevman 0:38ceb79fef03 927 #if defined(MBEDTLS_SELF_TEST)
kevman 0:38ceb79fef03 928 dbl_count++;
kevman 0:38ceb79fef03 929 #endif
kevman 0:38ceb79fef03 930
kevman 0:38ceb79fef03 931 #if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
kevman 0:38ceb79fef03 932 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kevman 0:38ceb79fef03 933 {
kevman 0:38ceb79fef03 934 return mbedtls_internal_ecp_double_jac( grp, R, P );
kevman 0:38ceb79fef03 935 }
kevman 0:38ceb79fef03 936 #endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */
kevman 0:38ceb79fef03 937
kevman 0:38ceb79fef03 938 mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
kevman 0:38ceb79fef03 939
kevman 0:38ceb79fef03 940 /* Special case for A = -3 */
kevman 0:38ceb79fef03 941 if( grp->A.p == NULL )
kevman 0:38ceb79fef03 942 {
kevman 0:38ceb79fef03 943 /* M = 3(X + Z^2)(X - Z^2) */
kevman 0:38ceb79fef03 944 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
kevman 0:38ceb79fef03 945 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &P->X, &S ) ); MOD_ADD( T );
kevman 0:38ceb79fef03 946 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U, &P->X, &S ) ); MOD_SUB( U );
kevman 0:38ceb79fef03 947 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &U ) ); MOD_MUL( S );
kevman 0:38ceb79fef03 948 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
kevman 0:38ceb79fef03 949 }
kevman 0:38ceb79fef03 950 else
kevman 0:38ceb79fef03 951 {
kevman 0:38ceb79fef03 952 /* M = 3.X^2 */
kevman 0:38ceb79fef03 953 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &P->X ) ); MOD_MUL( S );
kevman 0:38ceb79fef03 954 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
kevman 0:38ceb79fef03 955
kevman 0:38ceb79fef03 956 /* Optimize away for "koblitz" curves with A = 0 */
kevman 0:38ceb79fef03 957 if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
kevman 0:38ceb79fef03 958 {
kevman 0:38ceb79fef03 959 /* M += A.Z^4 */
kevman 0:38ceb79fef03 960 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
kevman 0:38ceb79fef03 961 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &S, &S ) ); MOD_MUL( T );
kevman 0:38ceb79fef03 962 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &grp->A ) ); MOD_MUL( S );
kevman 0:38ceb79fef03 963 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &S ) ); MOD_ADD( M );
kevman 0:38ceb79fef03 964 }
kevman 0:38ceb79fef03 965 }
kevman 0:38ceb79fef03 966
kevman 0:38ceb79fef03 967 /* S = 4.X.Y^2 */
kevman 0:38ceb79fef03 968 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &P->Y, &P->Y ) ); MOD_MUL( T );
kevman 0:38ceb79fef03 969 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T, 1 ) ); MOD_ADD( T );
kevman 0:38ceb79fef03 970 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &T ) ); MOD_MUL( S );
kevman 0:38ceb79fef03 971 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &S, 1 ) ); MOD_ADD( S );
kevman 0:38ceb79fef03 972
kevman 0:38ceb79fef03 973 /* U = 8.Y^4 */
kevman 0:38ceb79fef03 974 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &T, &T ) ); MOD_MUL( U );
kevman 0:38ceb79fef03 975 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
kevman 0:38ceb79fef03 976
kevman 0:38ceb79fef03 977 /* T = M^2 - 2.S */
kevman 0:38ceb79fef03 978 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &M, &M ) ); MOD_MUL( T );
kevman 0:38ceb79fef03 979 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
kevman 0:38ceb79fef03 980 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
kevman 0:38ceb79fef03 981
kevman 0:38ceb79fef03 982 /* S = M(S - T) - U */
kevman 0:38ceb79fef03 983 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &T ) ); MOD_SUB( S );
kevman 0:38ceb79fef03 984 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &S, &M ) ); MOD_MUL( S );
kevman 0:38ceb79fef03 985 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &U ) ); MOD_SUB( S );
kevman 0:38ceb79fef03 986
kevman 0:38ceb79fef03 987 /* U = 2.Y.Z */
kevman 0:38ceb79fef03 988 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &P->Y, &P->Z ) ); MOD_MUL( U );
kevman 0:38ceb79fef03 989 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
kevman 0:38ceb79fef03 990
kevman 0:38ceb79fef03 991 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
kevman 0:38ceb79fef03 992 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
kevman 0:38ceb79fef03 993 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
kevman 0:38ceb79fef03 994
kevman 0:38ceb79fef03 995 cleanup:
kevman 0:38ceb79fef03 996 mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
kevman 0:38ceb79fef03 997
kevman 0:38ceb79fef03 998 return( ret );
kevman 0:38ceb79fef03 999 }
kevman 0:38ceb79fef03 1000
kevman 0:38ceb79fef03 1001 /*
kevman 0:38ceb79fef03 1002 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
kevman 0:38ceb79fef03 1003 *
kevman 0:38ceb79fef03 1004 * The coordinates of Q must be normalized (= affine),
kevman 0:38ceb79fef03 1005 * but those of P don't need to. R is not normalized.
kevman 0:38ceb79fef03 1006 *
kevman 0:38ceb79fef03 1007 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
kevman 0:38ceb79fef03 1008 * None of these cases can happen as intermediate step in ecp_mul_comb():
kevman 0:38ceb79fef03 1009 * - at each step, P, Q and R are multiples of the base point, the factor
kevman 0:38ceb79fef03 1010 * being less than its order, so none of them is zero;
kevman 0:38ceb79fef03 1011 * - Q is an odd multiple of the base point, P an even multiple,
kevman 0:38ceb79fef03 1012 * due to the choice of precomputed points in the modified comb method.
kevman 0:38ceb79fef03 1013 * So branches for these cases do not leak secret information.
kevman 0:38ceb79fef03 1014 *
kevman 0:38ceb79fef03 1015 * We accept Q->Z being unset (saving memory in tables) as meaning 1.
kevman 0:38ceb79fef03 1016 *
kevman 0:38ceb79fef03 1017 * Cost: 1A := 8M + 3S
kevman 0:38ceb79fef03 1018 */
kevman 0:38ceb79fef03 1019 static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kevman 0:38ceb79fef03 1020 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
kevman 0:38ceb79fef03 1021 {
kevman 0:38ceb79fef03 1022 int ret;
kevman 0:38ceb79fef03 1023 mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
kevman 0:38ceb79fef03 1024
kevman 0:38ceb79fef03 1025 #if defined(MBEDTLS_SELF_TEST)
kevman 0:38ceb79fef03 1026 add_count++;
kevman 0:38ceb79fef03 1027 #endif
kevman 0:38ceb79fef03 1028
kevman 0:38ceb79fef03 1029 #if defined(MBEDTLS_ECP_ADD_MIXED_ALT)
kevman 0:38ceb79fef03 1030 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kevman 0:38ceb79fef03 1031 {
kevman 0:38ceb79fef03 1032 return mbedtls_internal_ecp_add_mixed( grp, R, P, Q );
kevman 0:38ceb79fef03 1033 }
kevman 0:38ceb79fef03 1034 #endif /* MBEDTLS_ECP_ADD_MIXED_ALT */
kevman 0:38ceb79fef03 1035
kevman 0:38ceb79fef03 1036 /*
kevman 0:38ceb79fef03 1037 * Trivial cases: P == 0 or Q == 0 (case 1)
kevman 0:38ceb79fef03 1038 */
kevman 0:38ceb79fef03 1039 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
kevman 0:38ceb79fef03 1040 return( mbedtls_ecp_copy( R, Q ) );
kevman 0:38ceb79fef03 1041
kevman 0:38ceb79fef03 1042 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
kevman 0:38ceb79fef03 1043 return( mbedtls_ecp_copy( R, P ) );
kevman 0:38ceb79fef03 1044
kevman 0:38ceb79fef03 1045 /*
kevman 0:38ceb79fef03 1046 * Make sure Q coordinates are normalized
kevman 0:38ceb79fef03 1047 */
kevman 0:38ceb79fef03 1048 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
kevman 0:38ceb79fef03 1049 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 1050
kevman 0:38ceb79fef03 1051 mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
kevman 0:38ceb79fef03 1052 mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
kevman 0:38ceb79fef03 1053
kevman 0:38ceb79fef03 1054 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &P->Z, &P->Z ) ); MOD_MUL( T1 );
kevman 0:38ceb79fef03 1055 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T1, &P->Z ) ); MOD_MUL( T2 );
kevman 0:38ceb79fef03 1056 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T1, &Q->X ) ); MOD_MUL( T1 );
kevman 0:38ceb79fef03 1057 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T2, &Q->Y ) ); MOD_MUL( T2 );
kevman 0:38ceb79fef03 1058 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T1, &T1, &P->X ) ); MOD_SUB( T1 );
kevman 0:38ceb79fef03 1059 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T2, &T2, &P->Y ) ); MOD_SUB( T2 );
kevman 0:38ceb79fef03 1060
kevman 0:38ceb79fef03 1061 /* Special cases (2) and (3) */
kevman 0:38ceb79fef03 1062 if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
kevman 0:38ceb79fef03 1063 {
kevman 0:38ceb79fef03 1064 if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
kevman 0:38ceb79fef03 1065 {
kevman 0:38ceb79fef03 1066 ret = ecp_double_jac( grp, R, P );
kevman 0:38ceb79fef03 1067 goto cleanup;
kevman 0:38ceb79fef03 1068 }
kevman 0:38ceb79fef03 1069 else
kevman 0:38ceb79fef03 1070 {
kevman 0:38ceb79fef03 1071 ret = mbedtls_ecp_set_zero( R );
kevman 0:38ceb79fef03 1072 goto cleanup;
kevman 0:38ceb79fef03 1073 }
kevman 0:38ceb79fef03 1074 }
kevman 0:38ceb79fef03 1075
kevman 0:38ceb79fef03 1076 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Z, &P->Z, &T1 ) ); MOD_MUL( Z );
kevman 0:38ceb79fef03 1077 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T1, &T1 ) ); MOD_MUL( T3 );
kevman 0:38ceb79fef03 1078 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T3, &T1 ) ); MOD_MUL( T4 );
kevman 0:38ceb79fef03 1079 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &P->X ) ); MOD_MUL( T3 );
kevman 0:38ceb79fef03 1080 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T3, 2 ) ); MOD_ADD( T1 );
kevman 0:38ceb79fef03 1081 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &T2, &T2 ) ); MOD_MUL( X );
kevman 0:38ceb79fef03 1082 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) ); MOD_SUB( X );
kevman 0:38ceb79fef03 1083 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T4 ) ); MOD_SUB( X );
kevman 0:38ceb79fef03 1084 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T3, &T3, &X ) ); MOD_SUB( T3 );
kevman 0:38ceb79fef03 1085 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &T2 ) ); MOD_MUL( T3 );
kevman 0:38ceb79fef03 1086 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T4, &P->Y ) ); MOD_MUL( T4 );
kevman 0:38ceb79fef03 1087 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &Y, &T3, &T4 ) ); MOD_SUB( Y );
kevman 0:38ceb79fef03 1088
kevman 0:38ceb79fef03 1089 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
kevman 0:38ceb79fef03 1090 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
kevman 0:38ceb79fef03 1091 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
kevman 0:38ceb79fef03 1092
kevman 0:38ceb79fef03 1093 cleanup:
kevman 0:38ceb79fef03 1094
kevman 0:38ceb79fef03 1095 mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
kevman 0:38ceb79fef03 1096 mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
kevman 0:38ceb79fef03 1097
kevman 0:38ceb79fef03 1098 return( ret );
kevman 0:38ceb79fef03 1099 }
kevman 0:38ceb79fef03 1100
kevman 0:38ceb79fef03 1101 /*
kevman 0:38ceb79fef03 1102 * Randomize jacobian coordinates:
kevman 0:38ceb79fef03 1103 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
kevman 0:38ceb79fef03 1104 * This is sort of the reverse operation of ecp_normalize_jac().
kevman 0:38ceb79fef03 1105 *
kevman 0:38ceb79fef03 1106 * This countermeasure was first suggested in [2].
kevman 0:38ceb79fef03 1107 */
kevman 0:38ceb79fef03 1108 static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
kevman 0:38ceb79fef03 1109 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
kevman 0:38ceb79fef03 1110 {
kevman 0:38ceb79fef03 1111 int ret;
kevman 0:38ceb79fef03 1112 mbedtls_mpi l, ll;
kevman 0:38ceb79fef03 1113 size_t p_size;
kevman 0:38ceb79fef03 1114 int count = 0;
kevman 0:38ceb79fef03 1115
kevman 0:38ceb79fef03 1116 #if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
kevman 0:38ceb79fef03 1117 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kevman 0:38ceb79fef03 1118 {
kevman 0:38ceb79fef03 1119 return mbedtls_internal_ecp_randomize_jac( grp, pt, f_rng, p_rng );
kevman 0:38ceb79fef03 1120 }
kevman 0:38ceb79fef03 1121 #endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */
kevman 0:38ceb79fef03 1122
kevman 0:38ceb79fef03 1123 p_size = ( grp->pbits + 7 ) / 8;
kevman 0:38ceb79fef03 1124 mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
kevman 0:38ceb79fef03 1125
kevman 0:38ceb79fef03 1126 /* Generate l such that 1 < l < p */
kevman 0:38ceb79fef03 1127 do
kevman 0:38ceb79fef03 1128 {
kevman 0:38ceb79fef03 1129 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
kevman 0:38ceb79fef03 1130
kevman 0:38ceb79fef03 1131 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
kevman 0:38ceb79fef03 1132 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
kevman 0:38ceb79fef03 1133
kevman 0:38ceb79fef03 1134 if( count++ > 10 )
kevman 0:38ceb79fef03 1135 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
kevman 0:38ceb79fef03 1136 }
kevman 0:38ceb79fef03 1137 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
kevman 0:38ceb79fef03 1138
kevman 0:38ceb79fef03 1139 /* Z = l * Z */
kevman 0:38ceb79fef03 1140 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Z, &pt->Z, &l ) ); MOD_MUL( pt->Z );
kevman 0:38ceb79fef03 1141
kevman 0:38ceb79fef03 1142 /* X = l^2 * X */
kevman 0:38ceb79fef03 1143 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &l, &l ) ); MOD_MUL( ll );
kevman 0:38ceb79fef03 1144 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ll ) ); MOD_MUL( pt->X );
kevman 0:38ceb79fef03 1145
kevman 0:38ceb79fef03 1146 /* Y = l^3 * Y */
kevman 0:38ceb79fef03 1147 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &ll, &l ) ); MOD_MUL( ll );
kevman 0:38ceb79fef03 1148 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ll ) ); MOD_MUL( pt->Y );
kevman 0:38ceb79fef03 1149
kevman 0:38ceb79fef03 1150 cleanup:
kevman 0:38ceb79fef03 1151 mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
kevman 0:38ceb79fef03 1152
kevman 0:38ceb79fef03 1153 return( ret );
kevman 0:38ceb79fef03 1154 }
kevman 0:38ceb79fef03 1155
kevman 0:38ceb79fef03 1156 /*
kevman 0:38ceb79fef03 1157 * Check and define parameters used by the comb method (see below for details)
kevman 0:38ceb79fef03 1158 */
kevman 0:38ceb79fef03 1159 #if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
kevman 0:38ceb79fef03 1160 #error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
kevman 0:38ceb79fef03 1161 #endif
kevman 0:38ceb79fef03 1162
kevman 0:38ceb79fef03 1163 /* d = ceil( n / w ) */
kevman 0:38ceb79fef03 1164 #define COMB_MAX_D ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2
kevman 0:38ceb79fef03 1165
kevman 0:38ceb79fef03 1166 /* number of precomputed points */
kevman 0:38ceb79fef03 1167 #define COMB_MAX_PRE ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
kevman 0:38ceb79fef03 1168
kevman 0:38ceb79fef03 1169 /*
kevman 0:38ceb79fef03 1170 * Compute the representation of m that will be used with our comb method.
kevman 0:38ceb79fef03 1171 *
kevman 0:38ceb79fef03 1172 * The basic comb method is described in GECC 3.44 for example. We use a
kevman 0:38ceb79fef03 1173 * modified version that provides resistance to SPA by avoiding zero
kevman 0:38ceb79fef03 1174 * digits in the representation as in [3]. We modify the method further by
kevman 0:38ceb79fef03 1175 * requiring that all K_i be odd, which has the small cost that our
kevman 0:38ceb79fef03 1176 * representation uses one more K_i, due to carries.
kevman 0:38ceb79fef03 1177 *
kevman 0:38ceb79fef03 1178 * Also, for the sake of compactness, only the seven low-order bits of x[i]
kevman 0:38ceb79fef03 1179 * are used to represent K_i, and the msb of x[i] encodes the the sign (s_i in
kevman 0:38ceb79fef03 1180 * the paper): it is set if and only if if s_i == -1;
kevman 0:38ceb79fef03 1181 *
kevman 0:38ceb79fef03 1182 * Calling conventions:
kevman 0:38ceb79fef03 1183 * - x is an array of size d + 1
kevman 0:38ceb79fef03 1184 * - w is the size, ie number of teeth, of the comb, and must be between
kevman 0:38ceb79fef03 1185 * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
kevman 0:38ceb79fef03 1186 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
kevman 0:38ceb79fef03 1187 * (the result will be incorrect if these assumptions are not satisfied)
kevman 0:38ceb79fef03 1188 */
kevman 0:38ceb79fef03 1189 static void ecp_comb_fixed( unsigned char x[], size_t d,
kevman 0:38ceb79fef03 1190 unsigned char w, const mbedtls_mpi *m )
kevman 0:38ceb79fef03 1191 {
kevman 0:38ceb79fef03 1192 size_t i, j;
kevman 0:38ceb79fef03 1193 unsigned char c, cc, adjust;
kevman 0:38ceb79fef03 1194
kevman 0:38ceb79fef03 1195 memset( x, 0, d+1 );
kevman 0:38ceb79fef03 1196
kevman 0:38ceb79fef03 1197 /* First get the classical comb values (except for x_d = 0) */
kevman 0:38ceb79fef03 1198 for( i = 0; i < d; i++ )
kevman 0:38ceb79fef03 1199 for( j = 0; j < w; j++ )
kevman 0:38ceb79fef03 1200 x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j;
kevman 0:38ceb79fef03 1201
kevman 0:38ceb79fef03 1202 /* Now make sure x_1 .. x_d are odd */
kevman 0:38ceb79fef03 1203 c = 0;
kevman 0:38ceb79fef03 1204 for( i = 1; i <= d; i++ )
kevman 0:38ceb79fef03 1205 {
kevman 0:38ceb79fef03 1206 /* Add carry and update it */
kevman 0:38ceb79fef03 1207 cc = x[i] & c;
kevman 0:38ceb79fef03 1208 x[i] = x[i] ^ c;
kevman 0:38ceb79fef03 1209 c = cc;
kevman 0:38ceb79fef03 1210
kevman 0:38ceb79fef03 1211 /* Adjust if needed, avoiding branches */
kevman 0:38ceb79fef03 1212 adjust = 1 - ( x[i] & 0x01 );
kevman 0:38ceb79fef03 1213 c |= x[i] & ( x[i-1] * adjust );
kevman 0:38ceb79fef03 1214 x[i] = x[i] ^ ( x[i-1] * adjust );
kevman 0:38ceb79fef03 1215 x[i-1] |= adjust << 7;
kevman 0:38ceb79fef03 1216 }
kevman 0:38ceb79fef03 1217 }
kevman 0:38ceb79fef03 1218
kevman 0:38ceb79fef03 1219 /*
kevman 0:38ceb79fef03 1220 * Precompute points for the comb method
kevman 0:38ceb79fef03 1221 *
kevman 0:38ceb79fef03 1222 * If i = i_{w-1} ... i_1 is the binary representation of i, then
kevman 0:38ceb79fef03 1223 * T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P
kevman 0:38ceb79fef03 1224 *
kevman 0:38ceb79fef03 1225 * T must be able to hold 2^{w - 1} elements
kevman 0:38ceb79fef03 1226 *
kevman 0:38ceb79fef03 1227 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
kevman 0:38ceb79fef03 1228 */
kevman 0:38ceb79fef03 1229 static int ecp_precompute_comb( const mbedtls_ecp_group *grp,
kevman 0:38ceb79fef03 1230 mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
kevman 0:38ceb79fef03 1231 unsigned char w, size_t d )
kevman 0:38ceb79fef03 1232 {
kevman 0:38ceb79fef03 1233 int ret;
kevman 0:38ceb79fef03 1234 unsigned char i, k;
kevman 0:38ceb79fef03 1235 size_t j;
kevman 0:38ceb79fef03 1236 mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
kevman 0:38ceb79fef03 1237
kevman 0:38ceb79fef03 1238 /*
kevman 0:38ceb79fef03 1239 * Set T[0] = P and
kevman 0:38ceb79fef03 1240 * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
kevman 0:38ceb79fef03 1241 */
kevman 0:38ceb79fef03 1242 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
kevman 0:38ceb79fef03 1243
kevman 0:38ceb79fef03 1244 k = 0;
kevman 0:38ceb79fef03 1245 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
kevman 0:38ceb79fef03 1246 {
kevman 0:38ceb79fef03 1247 cur = T + i;
kevman 0:38ceb79fef03 1248 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
kevman 0:38ceb79fef03 1249 for( j = 0; j < d; j++ )
kevman 0:38ceb79fef03 1250 MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
kevman 0:38ceb79fef03 1251
kevman 0:38ceb79fef03 1252 TT[k++] = cur;
kevman 0:38ceb79fef03 1253 }
kevman 0:38ceb79fef03 1254
kevman 0:38ceb79fef03 1255 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
kevman 0:38ceb79fef03 1256
kevman 0:38ceb79fef03 1257 /*
kevman 0:38ceb79fef03 1258 * Compute the remaining ones using the minimal number of additions
kevman 0:38ceb79fef03 1259 * Be careful to update T[2^l] only after using it!
kevman 0:38ceb79fef03 1260 */
kevman 0:38ceb79fef03 1261 k = 0;
kevman 0:38ceb79fef03 1262 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
kevman 0:38ceb79fef03 1263 {
kevman 0:38ceb79fef03 1264 j = i;
kevman 0:38ceb79fef03 1265 while( j-- )
kevman 0:38ceb79fef03 1266 {
kevman 0:38ceb79fef03 1267 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
kevman 0:38ceb79fef03 1268 TT[k++] = &T[i + j];
kevman 0:38ceb79fef03 1269 }
kevman 0:38ceb79fef03 1270 }
kevman 0:38ceb79fef03 1271
kevman 0:38ceb79fef03 1272 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
kevman 0:38ceb79fef03 1273
kevman 0:38ceb79fef03 1274 cleanup:
kevman 0:38ceb79fef03 1275
kevman 0:38ceb79fef03 1276 return( ret );
kevman 0:38ceb79fef03 1277 }
kevman 0:38ceb79fef03 1278
kevman 0:38ceb79fef03 1279 /*
kevman 0:38ceb79fef03 1280 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
kevman 0:38ceb79fef03 1281 */
kevman 0:38ceb79fef03 1282 static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kevman 0:38ceb79fef03 1283 const mbedtls_ecp_point T[], unsigned char t_len,
kevman 0:38ceb79fef03 1284 unsigned char i )
kevman 0:38ceb79fef03 1285 {
kevman 0:38ceb79fef03 1286 int ret;
kevman 0:38ceb79fef03 1287 unsigned char ii, j;
kevman 0:38ceb79fef03 1288
kevman 0:38ceb79fef03 1289 /* Ignore the "sign" bit and scale down */
kevman 0:38ceb79fef03 1290 ii = ( i & 0x7Fu ) >> 1;
kevman 0:38ceb79fef03 1291
kevman 0:38ceb79fef03 1292 /* Read the whole table to thwart cache-based timing attacks */
kevman 0:38ceb79fef03 1293 for( j = 0; j < t_len; j++ )
kevman 0:38ceb79fef03 1294 {
kevman 0:38ceb79fef03 1295 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
kevman 0:38ceb79fef03 1296 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
kevman 0:38ceb79fef03 1297 }
kevman 0:38ceb79fef03 1298
kevman 0:38ceb79fef03 1299 /* Safely invert result if i is "negative" */
kevman 0:38ceb79fef03 1300 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
kevman 0:38ceb79fef03 1301
kevman 0:38ceb79fef03 1302 cleanup:
kevman 0:38ceb79fef03 1303 return( ret );
kevman 0:38ceb79fef03 1304 }
kevman 0:38ceb79fef03 1305
kevman 0:38ceb79fef03 1306 /*
kevman 0:38ceb79fef03 1307 * Core multiplication algorithm for the (modified) comb method.
kevman 0:38ceb79fef03 1308 * This part is actually common with the basic comb method (GECC 3.44)
kevman 0:38ceb79fef03 1309 *
kevman 0:38ceb79fef03 1310 * Cost: d A + d D + 1 R
kevman 0:38ceb79fef03 1311 */
kevman 0:38ceb79fef03 1312 static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kevman 0:38ceb79fef03 1313 const mbedtls_ecp_point T[], unsigned char t_len,
kevman 0:38ceb79fef03 1314 const unsigned char x[], size_t d,
kevman 0:38ceb79fef03 1315 int (*f_rng)(void *, unsigned char *, size_t),
kevman 0:38ceb79fef03 1316 void *p_rng )
kevman 0:38ceb79fef03 1317 {
kevman 0:38ceb79fef03 1318 int ret;
kevman 0:38ceb79fef03 1319 mbedtls_ecp_point Txi;
kevman 0:38ceb79fef03 1320 size_t i;
kevman 0:38ceb79fef03 1321
kevman 0:38ceb79fef03 1322 mbedtls_ecp_point_init( &Txi );
kevman 0:38ceb79fef03 1323
kevman 0:38ceb79fef03 1324 /* Start with a non-zero point and randomize its coordinates */
kevman 0:38ceb79fef03 1325 i = d;
kevman 0:38ceb79fef03 1326 MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, t_len, x[i] ) );
kevman 0:38ceb79fef03 1327 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
kevman 0:38ceb79fef03 1328 if( f_rng != 0 )
kevman 0:38ceb79fef03 1329 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
kevman 0:38ceb79fef03 1330
kevman 0:38ceb79fef03 1331 while( i-- != 0 )
kevman 0:38ceb79fef03 1332 {
kevman 0:38ceb79fef03 1333 MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
kevman 0:38ceb79fef03 1334 MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, t_len, x[i] ) );
kevman 0:38ceb79fef03 1335 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
kevman 0:38ceb79fef03 1336 }
kevman 0:38ceb79fef03 1337
kevman 0:38ceb79fef03 1338 cleanup:
kevman 0:38ceb79fef03 1339
kevman 0:38ceb79fef03 1340 mbedtls_ecp_point_free( &Txi );
kevman 0:38ceb79fef03 1341
kevman 0:38ceb79fef03 1342 return( ret );
kevman 0:38ceb79fef03 1343 }
kevman 0:38ceb79fef03 1344
kevman 0:38ceb79fef03 1345 /*
kevman 0:38ceb79fef03 1346 * Multiplication using the comb method,
kevman 0:38ceb79fef03 1347 * for curves in short Weierstrass form
kevman 0:38ceb79fef03 1348 */
kevman 0:38ceb79fef03 1349 static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kevman 0:38ceb79fef03 1350 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
kevman 0:38ceb79fef03 1351 int (*f_rng)(void *, unsigned char *, size_t),
kevman 0:38ceb79fef03 1352 void *p_rng )
kevman 0:38ceb79fef03 1353 {
kevman 0:38ceb79fef03 1354 int ret;
kevman 0:38ceb79fef03 1355 unsigned char w, m_is_odd, p_eq_g, pre_len, i;
kevman 0:38ceb79fef03 1356 size_t d;
kevman 0:38ceb79fef03 1357 unsigned char k[COMB_MAX_D + 1];
kevman 0:38ceb79fef03 1358 mbedtls_ecp_point *T;
kevman 0:38ceb79fef03 1359 mbedtls_mpi M, mm;
kevman 0:38ceb79fef03 1360
kevman 0:38ceb79fef03 1361 mbedtls_mpi_init( &M );
kevman 0:38ceb79fef03 1362 mbedtls_mpi_init( &mm );
kevman 0:38ceb79fef03 1363
kevman 0:38ceb79fef03 1364 /* we need N to be odd to trnaform m in an odd number, check now */
kevman 0:38ceb79fef03 1365 if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 )
kevman 0:38ceb79fef03 1366 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 1367
kevman 0:38ceb79fef03 1368 /*
kevman 0:38ceb79fef03 1369 * Minimize the number of multiplications, that is minimize
kevman 0:38ceb79fef03 1370 * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
kevman 0:38ceb79fef03 1371 * (see costs of the various parts, with 1S = 1M)
kevman 0:38ceb79fef03 1372 */
kevman 0:38ceb79fef03 1373 w = grp->nbits >= 384 ? 5 : 4;
kevman 0:38ceb79fef03 1374
kevman 0:38ceb79fef03 1375 /*
kevman 0:38ceb79fef03 1376 * If P == G, pre-compute a bit more, since this may be re-used later.
kevman 0:38ceb79fef03 1377 * Just adding one avoids upping the cost of the first mul too much,
kevman 0:38ceb79fef03 1378 * and the memory cost too.
kevman 0:38ceb79fef03 1379 */
kevman 0:38ceb79fef03 1380 #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
kevman 0:38ceb79fef03 1381 p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
kevman 0:38ceb79fef03 1382 mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
kevman 0:38ceb79fef03 1383 if( p_eq_g )
kevman 0:38ceb79fef03 1384 w++;
kevman 0:38ceb79fef03 1385 #else
kevman 0:38ceb79fef03 1386 p_eq_g = 0;
kevman 0:38ceb79fef03 1387 #endif
kevman 0:38ceb79fef03 1388
kevman 0:38ceb79fef03 1389 /*
kevman 0:38ceb79fef03 1390 * Make sure w is within bounds.
kevman 0:38ceb79fef03 1391 * (The last test is useful only for very small curves in the test suite.)
kevman 0:38ceb79fef03 1392 */
kevman 0:38ceb79fef03 1393 if( w > MBEDTLS_ECP_WINDOW_SIZE )
kevman 0:38ceb79fef03 1394 w = MBEDTLS_ECP_WINDOW_SIZE;
kevman 0:38ceb79fef03 1395 if( w >= grp->nbits )
kevman 0:38ceb79fef03 1396 w = 2;
kevman 0:38ceb79fef03 1397
kevman 0:38ceb79fef03 1398 /* Other sizes that depend on w */
kevman 0:38ceb79fef03 1399 pre_len = 1U << ( w - 1 );
kevman 0:38ceb79fef03 1400 d = ( grp->nbits + w - 1 ) / w;
kevman 0:38ceb79fef03 1401
kevman 0:38ceb79fef03 1402 /*
kevman 0:38ceb79fef03 1403 * Prepare precomputed points: if P == G we want to
kevman 0:38ceb79fef03 1404 * use grp->T if already initialized, or initialize it.
kevman 0:38ceb79fef03 1405 */
kevman 0:38ceb79fef03 1406 T = p_eq_g ? grp->T : NULL;
kevman 0:38ceb79fef03 1407
kevman 0:38ceb79fef03 1408 if( T == NULL )
kevman 0:38ceb79fef03 1409 {
kevman 0:38ceb79fef03 1410 T = mbedtls_calloc( pre_len, sizeof( mbedtls_ecp_point ) );
kevman 0:38ceb79fef03 1411 if( T == NULL )
kevman 0:38ceb79fef03 1412 {
kevman 0:38ceb79fef03 1413 ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
kevman 0:38ceb79fef03 1414 goto cleanup;
kevman 0:38ceb79fef03 1415 }
kevman 0:38ceb79fef03 1416
kevman 0:38ceb79fef03 1417 MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d ) );
kevman 0:38ceb79fef03 1418
kevman 0:38ceb79fef03 1419 if( p_eq_g )
kevman 0:38ceb79fef03 1420 {
kevman 0:38ceb79fef03 1421 grp->T = T;
kevman 0:38ceb79fef03 1422 grp->T_size = pre_len;
kevman 0:38ceb79fef03 1423 }
kevman 0:38ceb79fef03 1424 }
kevman 0:38ceb79fef03 1425
kevman 0:38ceb79fef03 1426 /*
kevman 0:38ceb79fef03 1427 * Make sure M is odd (M = m or M = N - m, since N is odd)
kevman 0:38ceb79fef03 1428 * using the fact that m * P = - (N - m) * P
kevman 0:38ceb79fef03 1429 */
kevman 0:38ceb79fef03 1430 m_is_odd = ( mbedtls_mpi_get_bit( m, 0 ) == 1 );
kevman 0:38ceb79fef03 1431 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) );
kevman 0:38ceb79fef03 1432 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) );
kevman 0:38ceb79fef03 1433 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, ! m_is_odd ) );
kevman 0:38ceb79fef03 1434
kevman 0:38ceb79fef03 1435 /*
kevman 0:38ceb79fef03 1436 * Go for comb multiplication, R = M * P
kevman 0:38ceb79fef03 1437 */
kevman 0:38ceb79fef03 1438 ecp_comb_fixed( k, d, w, &M );
kevman 0:38ceb79fef03 1439 MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, R, T, pre_len, k, d, f_rng, p_rng ) );
kevman 0:38ceb79fef03 1440
kevman 0:38ceb79fef03 1441 /*
kevman 0:38ceb79fef03 1442 * Now get m * P from M * P and normalize it
kevman 0:38ceb79fef03 1443 */
kevman 0:38ceb79fef03 1444 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, ! m_is_odd ) );
kevman 0:38ceb79fef03 1445 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
kevman 0:38ceb79fef03 1446
kevman 0:38ceb79fef03 1447 cleanup:
kevman 0:38ceb79fef03 1448
kevman 0:38ceb79fef03 1449 /* There are two cases where T is not stored in grp:
kevman 0:38ceb79fef03 1450 * - P != G
kevman 0:38ceb79fef03 1451 * - An intermediate operation failed before setting grp->T
kevman 0:38ceb79fef03 1452 * In either case, T must be freed.
kevman 0:38ceb79fef03 1453 */
kevman 0:38ceb79fef03 1454 if( T != NULL && T != grp->T )
kevman 0:38ceb79fef03 1455 {
kevman 0:38ceb79fef03 1456 for( i = 0; i < pre_len; i++ )
kevman 0:38ceb79fef03 1457 mbedtls_ecp_point_free( &T[i] );
kevman 0:38ceb79fef03 1458 mbedtls_free( T );
kevman 0:38ceb79fef03 1459 }
kevman 0:38ceb79fef03 1460
kevman 0:38ceb79fef03 1461 mbedtls_mpi_free( &M );
kevman 0:38ceb79fef03 1462 mbedtls_mpi_free( &mm );
kevman 0:38ceb79fef03 1463
kevman 0:38ceb79fef03 1464 if( ret != 0 )
kevman 0:38ceb79fef03 1465 mbedtls_ecp_point_free( R );
kevman 0:38ceb79fef03 1466
kevman 0:38ceb79fef03 1467 return( ret );
kevman 0:38ceb79fef03 1468 }
kevman 0:38ceb79fef03 1469
kevman 0:38ceb79fef03 1470 #endif /* ECP_SHORTWEIERSTRASS */
kevman 0:38ceb79fef03 1471
kevman 0:38ceb79fef03 1472 #if defined(ECP_MONTGOMERY)
kevman 0:38ceb79fef03 1473 /*
kevman 0:38ceb79fef03 1474 * For Montgomery curves, we do all the internal arithmetic in projective
kevman 0:38ceb79fef03 1475 * coordinates. Import/export of points uses only the x coordinates, which is
kevman 0:38ceb79fef03 1476 * internaly represented as X / Z.
kevman 0:38ceb79fef03 1477 *
kevman 0:38ceb79fef03 1478 * For scalar multiplication, we'll use a Montgomery ladder.
kevman 0:38ceb79fef03 1479 */
kevman 0:38ceb79fef03 1480
kevman 0:38ceb79fef03 1481 /*
kevman 0:38ceb79fef03 1482 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
kevman 0:38ceb79fef03 1483 * Cost: 1M + 1I
kevman 0:38ceb79fef03 1484 */
kevman 0:38ceb79fef03 1485 static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
kevman 0:38ceb79fef03 1486 {
kevman 0:38ceb79fef03 1487 int ret;
kevman 0:38ceb79fef03 1488
kevman 0:38ceb79fef03 1489 #if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
kevman 0:38ceb79fef03 1490 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kevman 0:38ceb79fef03 1491 {
kevman 0:38ceb79fef03 1492 return mbedtls_internal_ecp_normalize_mxz( grp, P );
kevman 0:38ceb79fef03 1493 }
kevman 0:38ceb79fef03 1494 #endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */
kevman 0:38ceb79fef03 1495
kevman 0:38ceb79fef03 1496 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
kevman 0:38ceb79fef03 1497 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X );
kevman 0:38ceb79fef03 1498 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
kevman 0:38ceb79fef03 1499
kevman 0:38ceb79fef03 1500 cleanup:
kevman 0:38ceb79fef03 1501 return( ret );
kevman 0:38ceb79fef03 1502 }
kevman 0:38ceb79fef03 1503
kevman 0:38ceb79fef03 1504 /*
kevman 0:38ceb79fef03 1505 * Randomize projective x/z coordinates:
kevman 0:38ceb79fef03 1506 * (X, Z) -> (l X, l Z) for random l
kevman 0:38ceb79fef03 1507 * This is sort of the reverse operation of ecp_normalize_mxz().
kevman 0:38ceb79fef03 1508 *
kevman 0:38ceb79fef03 1509 * This countermeasure was first suggested in [2].
kevman 0:38ceb79fef03 1510 * Cost: 2M
kevman 0:38ceb79fef03 1511 */
kevman 0:38ceb79fef03 1512 static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
kevman 0:38ceb79fef03 1513 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
kevman 0:38ceb79fef03 1514 {
kevman 0:38ceb79fef03 1515 int ret;
kevman 0:38ceb79fef03 1516 mbedtls_mpi l;
kevman 0:38ceb79fef03 1517 size_t p_size;
kevman 0:38ceb79fef03 1518 int count = 0;
kevman 0:38ceb79fef03 1519
kevman 0:38ceb79fef03 1520 #if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
kevman 0:38ceb79fef03 1521 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kevman 0:38ceb79fef03 1522 {
kevman 0:38ceb79fef03 1523 return mbedtls_internal_ecp_randomize_mxz( grp, P, f_rng, p_rng );
kevman 0:38ceb79fef03 1524 }
kevman 0:38ceb79fef03 1525 #endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */
kevman 0:38ceb79fef03 1526
kevman 0:38ceb79fef03 1527 p_size = ( grp->pbits + 7 ) / 8;
kevman 0:38ceb79fef03 1528 mbedtls_mpi_init( &l );
kevman 0:38ceb79fef03 1529
kevman 0:38ceb79fef03 1530 /* Generate l such that 1 < l < p */
kevman 0:38ceb79fef03 1531 do
kevman 0:38ceb79fef03 1532 {
kevman 0:38ceb79fef03 1533 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
kevman 0:38ceb79fef03 1534
kevman 0:38ceb79fef03 1535 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
kevman 0:38ceb79fef03 1536 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
kevman 0:38ceb79fef03 1537
kevman 0:38ceb79fef03 1538 if( count++ > 10 )
kevman 0:38ceb79fef03 1539 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
kevman 0:38ceb79fef03 1540 }
kevman 0:38ceb79fef03 1541 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
kevman 0:38ceb79fef03 1542
kevman 0:38ceb79fef03 1543 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X );
kevman 0:38ceb79fef03 1544 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z );
kevman 0:38ceb79fef03 1545
kevman 0:38ceb79fef03 1546 cleanup:
kevman 0:38ceb79fef03 1547 mbedtls_mpi_free( &l );
kevman 0:38ceb79fef03 1548
kevman 0:38ceb79fef03 1549 return( ret );
kevman 0:38ceb79fef03 1550 }
kevman 0:38ceb79fef03 1551
kevman 0:38ceb79fef03 1552 /*
kevman 0:38ceb79fef03 1553 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
kevman 0:38ceb79fef03 1554 * for Montgomery curves in x/z coordinates.
kevman 0:38ceb79fef03 1555 *
kevman 0:38ceb79fef03 1556 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
kevman 0:38ceb79fef03 1557 * with
kevman 0:38ceb79fef03 1558 * d = X1
kevman 0:38ceb79fef03 1559 * P = (X2, Z2)
kevman 0:38ceb79fef03 1560 * Q = (X3, Z3)
kevman 0:38ceb79fef03 1561 * R = (X4, Z4)
kevman 0:38ceb79fef03 1562 * S = (X5, Z5)
kevman 0:38ceb79fef03 1563 * and eliminating temporary variables tO, ..., t4.
kevman 0:38ceb79fef03 1564 *
kevman 0:38ceb79fef03 1565 * Cost: 5M + 4S
kevman 0:38ceb79fef03 1566 */
kevman 0:38ceb79fef03 1567 static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
kevman 0:38ceb79fef03 1568 mbedtls_ecp_point *R, mbedtls_ecp_point *S,
kevman 0:38ceb79fef03 1569 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
kevman 0:38ceb79fef03 1570 const mbedtls_mpi *d )
kevman 0:38ceb79fef03 1571 {
kevman 0:38ceb79fef03 1572 int ret;
kevman 0:38ceb79fef03 1573 mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
kevman 0:38ceb79fef03 1574
kevman 0:38ceb79fef03 1575 #if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
kevman 0:38ceb79fef03 1576 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kevman 0:38ceb79fef03 1577 {
kevman 0:38ceb79fef03 1578 return mbedtls_internal_ecp_double_add_mxz( grp, R, S, P, Q, d );
kevman 0:38ceb79fef03 1579 }
kevman 0:38ceb79fef03 1580 #endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */
kevman 0:38ceb79fef03 1581
kevman 0:38ceb79fef03 1582 mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
kevman 0:38ceb79fef03 1583 mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
kevman 0:38ceb79fef03 1584 mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
kevman 0:38ceb79fef03 1585
kevman 0:38ceb79fef03 1586 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &A, &P->X, &P->Z ) ); MOD_ADD( A );
kevman 0:38ceb79fef03 1587 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &AA, &A, &A ) ); MOD_MUL( AA );
kevman 0:38ceb79fef03 1588 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &B, &P->X, &P->Z ) ); MOD_SUB( B );
kevman 0:38ceb79fef03 1589 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &BB, &B, &B ) ); MOD_MUL( BB );
kevman 0:38ceb79fef03 1590 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &E, &AA, &BB ) ); MOD_SUB( E );
kevman 0:38ceb79fef03 1591 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &C, &Q->X, &Q->Z ) ); MOD_ADD( C );
kevman 0:38ceb79fef03 1592 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &D, &Q->X, &Q->Z ) ); MOD_SUB( D );
kevman 0:38ceb79fef03 1593 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DA, &D, &A ) ); MOD_MUL( DA );
kevman 0:38ceb79fef03 1594 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &CB, &C, &B ) ); MOD_MUL( CB );
kevman 0:38ceb79fef03 1595 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &S->X, &DA, &CB ) ); MOD_MUL( S->X );
kevman 0:38ceb79fef03 1596 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->X, &S->X, &S->X ) ); MOD_MUL( S->X );
kevman 0:38ceb79fef03 1597 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S->Z, &DA, &CB ) ); MOD_SUB( S->Z );
kevman 0:38ceb79fef03 1598 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, &S->Z, &S->Z ) ); MOD_MUL( S->Z );
kevman 0:38ceb79fef03 1599 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, d, &S->Z ) ); MOD_MUL( S->Z );
kevman 0:38ceb79fef03 1600 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->X, &AA, &BB ) ); MOD_MUL( R->X );
kevman 0:38ceb79fef03 1601 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &grp->A, &E ) ); MOD_MUL( R->Z );
kevman 0:38ceb79fef03 1602 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &R->Z, &BB, &R->Z ) ); MOD_ADD( R->Z );
kevman 0:38ceb79fef03 1603 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &E, &R->Z ) ); MOD_MUL( R->Z );
kevman 0:38ceb79fef03 1604
kevman 0:38ceb79fef03 1605 cleanup:
kevman 0:38ceb79fef03 1606 mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
kevman 0:38ceb79fef03 1607 mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
kevman 0:38ceb79fef03 1608 mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
kevman 0:38ceb79fef03 1609
kevman 0:38ceb79fef03 1610 return( ret );
kevman 0:38ceb79fef03 1611 }
kevman 0:38ceb79fef03 1612
kevman 0:38ceb79fef03 1613 /*
kevman 0:38ceb79fef03 1614 * Multiplication with Montgomery ladder in x/z coordinates,
kevman 0:38ceb79fef03 1615 * for curves in Montgomery form
kevman 0:38ceb79fef03 1616 */
kevman 0:38ceb79fef03 1617 static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kevman 0:38ceb79fef03 1618 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
kevman 0:38ceb79fef03 1619 int (*f_rng)(void *, unsigned char *, size_t),
kevman 0:38ceb79fef03 1620 void *p_rng )
kevman 0:38ceb79fef03 1621 {
kevman 0:38ceb79fef03 1622 int ret;
kevman 0:38ceb79fef03 1623 size_t i;
kevman 0:38ceb79fef03 1624 unsigned char b;
kevman 0:38ceb79fef03 1625 mbedtls_ecp_point RP;
kevman 0:38ceb79fef03 1626 mbedtls_mpi PX;
kevman 0:38ceb79fef03 1627
kevman 0:38ceb79fef03 1628 mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
kevman 0:38ceb79fef03 1629
kevman 0:38ceb79fef03 1630 /* Save PX and read from P before writing to R, in case P == R */
kevman 0:38ceb79fef03 1631 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
kevman 0:38ceb79fef03 1632 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
kevman 0:38ceb79fef03 1633
kevman 0:38ceb79fef03 1634 /* Set R to zero in modified x/z coordinates */
kevman 0:38ceb79fef03 1635 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
kevman 0:38ceb79fef03 1636 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
kevman 0:38ceb79fef03 1637 mbedtls_mpi_free( &R->Y );
kevman 0:38ceb79fef03 1638
kevman 0:38ceb79fef03 1639 /* RP.X might be sligtly larger than P, so reduce it */
kevman 0:38ceb79fef03 1640 MOD_ADD( RP.X );
kevman 0:38ceb79fef03 1641
kevman 0:38ceb79fef03 1642 /* Randomize coordinates of the starting point */
kevman 0:38ceb79fef03 1643 if( f_rng != NULL )
kevman 0:38ceb79fef03 1644 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
kevman 0:38ceb79fef03 1645
kevman 0:38ceb79fef03 1646 /* Loop invariant: R = result so far, RP = R + P */
kevman 0:38ceb79fef03 1647 i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
kevman 0:38ceb79fef03 1648 while( i-- > 0 )
kevman 0:38ceb79fef03 1649 {
kevman 0:38ceb79fef03 1650 b = mbedtls_mpi_get_bit( m, i );
kevman 0:38ceb79fef03 1651 /*
kevman 0:38ceb79fef03 1652 * if (b) R = 2R + P else R = 2R,
kevman 0:38ceb79fef03 1653 * which is:
kevman 0:38ceb79fef03 1654 * if (b) double_add( RP, R, RP, R )
kevman 0:38ceb79fef03 1655 * else double_add( R, RP, R, RP )
kevman 0:38ceb79fef03 1656 * but using safe conditional swaps to avoid leaks
kevman 0:38ceb79fef03 1657 */
kevman 0:38ceb79fef03 1658 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
kevman 0:38ceb79fef03 1659 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
kevman 0:38ceb79fef03 1660 MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
kevman 0:38ceb79fef03 1661 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
kevman 0:38ceb79fef03 1662 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
kevman 0:38ceb79fef03 1663 }
kevman 0:38ceb79fef03 1664
kevman 0:38ceb79fef03 1665 MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) );
kevman 0:38ceb79fef03 1666
kevman 0:38ceb79fef03 1667 cleanup:
kevman 0:38ceb79fef03 1668 mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
kevman 0:38ceb79fef03 1669
kevman 0:38ceb79fef03 1670 return( ret );
kevman 0:38ceb79fef03 1671 }
kevman 0:38ceb79fef03 1672
kevman 0:38ceb79fef03 1673 #endif /* ECP_MONTGOMERY */
kevman 0:38ceb79fef03 1674
kevman 0:38ceb79fef03 1675 /*
kevman 0:38ceb79fef03 1676 * Multiplication R = m * P
kevman 0:38ceb79fef03 1677 */
kevman 0:38ceb79fef03 1678 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kevman 0:38ceb79fef03 1679 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
kevman 0:38ceb79fef03 1680 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
kevman 0:38ceb79fef03 1681 {
kevman 0:38ceb79fef03 1682 int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
kevman 0:38ceb79fef03 1683 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
kevman 0:38ceb79fef03 1684 char is_grp_capable = 0;
kevman 0:38ceb79fef03 1685 #endif
kevman 0:38ceb79fef03 1686
kevman 0:38ceb79fef03 1687 /* Common sanity checks */
kevman 0:38ceb79fef03 1688 if( mbedtls_mpi_cmp_int( &P->Z, 1 ) != 0 )
kevman 0:38ceb79fef03 1689 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 1690
kevman 0:38ceb79fef03 1691 if( ( ret = mbedtls_ecp_check_privkey( grp, m ) ) != 0 ||
kevman 0:38ceb79fef03 1692 ( ret = mbedtls_ecp_check_pubkey( grp, P ) ) != 0 )
kevman 0:38ceb79fef03 1693 return( ret );
kevman 0:38ceb79fef03 1694
kevman 0:38ceb79fef03 1695 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
kevman 0:38ceb79fef03 1696 if ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) )
kevman 0:38ceb79fef03 1697 {
kevman 0:38ceb79fef03 1698 MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
kevman 0:38ceb79fef03 1699 }
kevman 0:38ceb79fef03 1700
kevman 0:38ceb79fef03 1701 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
kevman 0:38ceb79fef03 1702 #if defined(ECP_MONTGOMERY)
kevman 0:38ceb79fef03 1703 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
kevman 0:38ceb79fef03 1704 ret = ecp_mul_mxz( grp, R, m, P, f_rng, p_rng );
kevman 0:38ceb79fef03 1705
kevman 0:38ceb79fef03 1706 #endif
kevman 0:38ceb79fef03 1707 #if defined(ECP_SHORTWEIERSTRASS)
kevman 0:38ceb79fef03 1708 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
kevman 0:38ceb79fef03 1709 ret = ecp_mul_comb( grp, R, m, P, f_rng, p_rng );
kevman 0:38ceb79fef03 1710
kevman 0:38ceb79fef03 1711 #endif
kevman 0:38ceb79fef03 1712 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
kevman 0:38ceb79fef03 1713 cleanup:
kevman 0:38ceb79fef03 1714
kevman 0:38ceb79fef03 1715 if ( is_grp_capable )
kevman 0:38ceb79fef03 1716 {
kevman 0:38ceb79fef03 1717 mbedtls_internal_ecp_free( grp );
kevman 0:38ceb79fef03 1718 }
kevman 0:38ceb79fef03 1719
kevman 0:38ceb79fef03 1720 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
kevman 0:38ceb79fef03 1721 return( ret );
kevman 0:38ceb79fef03 1722 }
kevman 0:38ceb79fef03 1723
kevman 0:38ceb79fef03 1724 #if defined(ECP_SHORTWEIERSTRASS)
kevman 0:38ceb79fef03 1725 /*
kevman 0:38ceb79fef03 1726 * Check that an affine point is valid as a public key,
kevman 0:38ceb79fef03 1727 * short weierstrass curves (SEC1 3.2.3.1)
kevman 0:38ceb79fef03 1728 */
kevman 0:38ceb79fef03 1729 static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
kevman 0:38ceb79fef03 1730 {
kevman 0:38ceb79fef03 1731 int ret;
kevman 0:38ceb79fef03 1732 mbedtls_mpi YY, RHS;
kevman 0:38ceb79fef03 1733
kevman 0:38ceb79fef03 1734 /* pt coordinates must be normalized for our checks */
kevman 0:38ceb79fef03 1735 if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ||
kevman 0:38ceb79fef03 1736 mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 ||
kevman 0:38ceb79fef03 1737 mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
kevman 0:38ceb79fef03 1738 mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
kevman 0:38ceb79fef03 1739 return( MBEDTLS_ERR_ECP_INVALID_KEY );
kevman 0:38ceb79fef03 1740
kevman 0:38ceb79fef03 1741 mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
kevman 0:38ceb79fef03 1742
kevman 0:38ceb79fef03 1743 /*
kevman 0:38ceb79fef03 1744 * YY = Y^2
kevman 0:38ceb79fef03 1745 * RHS = X (X^2 + A) + B = X^3 + A X + B
kevman 0:38ceb79fef03 1746 */
kevman 0:38ceb79fef03 1747 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &YY, &pt->Y, &pt->Y ) ); MOD_MUL( YY );
kevman 0:38ceb79fef03 1748 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &pt->X, &pt->X ) ); MOD_MUL( RHS );
kevman 0:38ceb79fef03 1749
kevman 0:38ceb79fef03 1750 /* Special case for A = -3 */
kevman 0:38ceb79fef03 1751 if( grp->A.p == NULL )
kevman 0:38ceb79fef03 1752 {
kevman 0:38ceb79fef03 1753 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS );
kevman 0:38ceb79fef03 1754 }
kevman 0:38ceb79fef03 1755 else
kevman 0:38ceb79fef03 1756 {
kevman 0:38ceb79fef03 1757 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->A ) ); MOD_ADD( RHS );
kevman 0:38ceb79fef03 1758 }
kevman 0:38ceb79fef03 1759
kevman 0:38ceb79fef03 1760 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &RHS, &pt->X ) ); MOD_MUL( RHS );
kevman 0:38ceb79fef03 1761 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->B ) ); MOD_ADD( RHS );
kevman 0:38ceb79fef03 1762
kevman 0:38ceb79fef03 1763 if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
kevman 0:38ceb79fef03 1764 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
kevman 0:38ceb79fef03 1765
kevman 0:38ceb79fef03 1766 cleanup:
kevman 0:38ceb79fef03 1767
kevman 0:38ceb79fef03 1768 mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
kevman 0:38ceb79fef03 1769
kevman 0:38ceb79fef03 1770 return( ret );
kevman 0:38ceb79fef03 1771 }
kevman 0:38ceb79fef03 1772 #endif /* ECP_SHORTWEIERSTRASS */
kevman 0:38ceb79fef03 1773
kevman 0:38ceb79fef03 1774 /*
kevman 0:38ceb79fef03 1775 * R = m * P with shortcuts for m == 1 and m == -1
kevman 0:38ceb79fef03 1776 * NOT constant-time - ONLY for short Weierstrass!
kevman 0:38ceb79fef03 1777 */
kevman 0:38ceb79fef03 1778 static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
kevman 0:38ceb79fef03 1779 mbedtls_ecp_point *R,
kevman 0:38ceb79fef03 1780 const mbedtls_mpi *m,
kevman 0:38ceb79fef03 1781 const mbedtls_ecp_point *P )
kevman 0:38ceb79fef03 1782 {
kevman 0:38ceb79fef03 1783 int ret;
kevman 0:38ceb79fef03 1784
kevman 0:38ceb79fef03 1785 if( mbedtls_mpi_cmp_int( m, 1 ) == 0 )
kevman 0:38ceb79fef03 1786 {
kevman 0:38ceb79fef03 1787 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
kevman 0:38ceb79fef03 1788 }
kevman 0:38ceb79fef03 1789 else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
kevman 0:38ceb79fef03 1790 {
kevman 0:38ceb79fef03 1791 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
kevman 0:38ceb79fef03 1792 if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 )
kevman 0:38ceb79fef03 1793 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
kevman 0:38ceb79fef03 1794 }
kevman 0:38ceb79fef03 1795 else
kevman 0:38ceb79fef03 1796 {
kevman 0:38ceb79fef03 1797 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
kevman 0:38ceb79fef03 1798 }
kevman 0:38ceb79fef03 1799
kevman 0:38ceb79fef03 1800 cleanup:
kevman 0:38ceb79fef03 1801 return( ret );
kevman 0:38ceb79fef03 1802 }
kevman 0:38ceb79fef03 1803
kevman 0:38ceb79fef03 1804 /*
kevman 0:38ceb79fef03 1805 * Linear combination
kevman 0:38ceb79fef03 1806 * NOT constant-time
kevman 0:38ceb79fef03 1807 */
kevman 0:38ceb79fef03 1808 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kevman 0:38ceb79fef03 1809 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
kevman 0:38ceb79fef03 1810 const mbedtls_mpi *n, const mbedtls_ecp_point *Q )
kevman 0:38ceb79fef03 1811 {
kevman 0:38ceb79fef03 1812 int ret;
kevman 0:38ceb79fef03 1813 mbedtls_ecp_point mP;
kevman 0:38ceb79fef03 1814 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
kevman 0:38ceb79fef03 1815 char is_grp_capable = 0;
kevman 0:38ceb79fef03 1816 #endif
kevman 0:38ceb79fef03 1817
kevman 0:38ceb79fef03 1818 if( ecp_get_type( grp ) != ECP_TYPE_SHORT_WEIERSTRASS )
kevman 0:38ceb79fef03 1819 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
kevman 0:38ceb79fef03 1820
kevman 0:38ceb79fef03 1821 mbedtls_ecp_point_init( &mP );
kevman 0:38ceb79fef03 1822
kevman 0:38ceb79fef03 1823 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, &mP, m, P ) );
kevman 0:38ceb79fef03 1824 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, R, n, Q ) );
kevman 0:38ceb79fef03 1825
kevman 0:38ceb79fef03 1826 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
kevman 0:38ceb79fef03 1827 if ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) )
kevman 0:38ceb79fef03 1828 {
kevman 0:38ceb79fef03 1829 MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
kevman 0:38ceb79fef03 1830 }
kevman 0:38ceb79fef03 1831
kevman 0:38ceb79fef03 1832 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
kevman 0:38ceb79fef03 1833 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, &mP, R ) );
kevman 0:38ceb79fef03 1834 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
kevman 0:38ceb79fef03 1835
kevman 0:38ceb79fef03 1836 cleanup:
kevman 0:38ceb79fef03 1837
kevman 0:38ceb79fef03 1838 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
kevman 0:38ceb79fef03 1839 if ( is_grp_capable )
kevman 0:38ceb79fef03 1840 {
kevman 0:38ceb79fef03 1841 mbedtls_internal_ecp_free( grp );
kevman 0:38ceb79fef03 1842 }
kevman 0:38ceb79fef03 1843
kevman 0:38ceb79fef03 1844 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
kevman 0:38ceb79fef03 1845 mbedtls_ecp_point_free( &mP );
kevman 0:38ceb79fef03 1846
kevman 0:38ceb79fef03 1847 return( ret );
kevman 0:38ceb79fef03 1848 }
kevman 0:38ceb79fef03 1849
kevman 0:38ceb79fef03 1850
kevman 0:38ceb79fef03 1851 #if defined(ECP_MONTGOMERY)
kevman 0:38ceb79fef03 1852 /*
kevman 0:38ceb79fef03 1853 * Check validity of a public key for Montgomery curves with x-only schemes
kevman 0:38ceb79fef03 1854 */
kevman 0:38ceb79fef03 1855 static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
kevman 0:38ceb79fef03 1856 {
kevman 0:38ceb79fef03 1857 /* [Curve25519 p. 5] Just check X is the correct number of bytes */
kevman 0:38ceb79fef03 1858 /* Allow any public value, if it's too big then we'll just reduce it mod p
kevman 0:38ceb79fef03 1859 * (RFC 7748 sec. 5 para. 3). */
kevman 0:38ceb79fef03 1860 if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
kevman 0:38ceb79fef03 1861 return( MBEDTLS_ERR_ECP_INVALID_KEY );
kevman 0:38ceb79fef03 1862
kevman 0:38ceb79fef03 1863 return( 0 );
kevman 0:38ceb79fef03 1864 }
kevman 0:38ceb79fef03 1865 #endif /* ECP_MONTGOMERY */
kevman 0:38ceb79fef03 1866
kevman 0:38ceb79fef03 1867 /*
kevman 0:38ceb79fef03 1868 * Check that a point is valid as a public key
kevman 0:38ceb79fef03 1869 */
kevman 0:38ceb79fef03 1870 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
kevman 0:38ceb79fef03 1871 {
kevman 0:38ceb79fef03 1872 /* Must use affine coordinates */
kevman 0:38ceb79fef03 1873 if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
kevman 0:38ceb79fef03 1874 return( MBEDTLS_ERR_ECP_INVALID_KEY );
kevman 0:38ceb79fef03 1875
kevman 0:38ceb79fef03 1876 #if defined(ECP_MONTGOMERY)
kevman 0:38ceb79fef03 1877 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
kevman 0:38ceb79fef03 1878 return( ecp_check_pubkey_mx( grp, pt ) );
kevman 0:38ceb79fef03 1879 #endif
kevman 0:38ceb79fef03 1880 #if defined(ECP_SHORTWEIERSTRASS)
kevman 0:38ceb79fef03 1881 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
kevman 0:38ceb79fef03 1882 return( ecp_check_pubkey_sw( grp, pt ) );
kevman 0:38ceb79fef03 1883 #endif
kevman 0:38ceb79fef03 1884 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 1885 }
kevman 0:38ceb79fef03 1886
kevman 0:38ceb79fef03 1887 /*
kevman 0:38ceb79fef03 1888 * Check that an mbedtls_mpi is valid as a private key
kevman 0:38ceb79fef03 1889 */
kevman 0:38ceb79fef03 1890 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d )
kevman 0:38ceb79fef03 1891 {
kevman 0:38ceb79fef03 1892 #if defined(ECP_MONTGOMERY)
kevman 0:38ceb79fef03 1893 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
kevman 0:38ceb79fef03 1894 {
kevman 0:38ceb79fef03 1895 /* see RFC 7748 sec. 5 para. 5 */
kevman 0:38ceb79fef03 1896 if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
kevman 0:38ceb79fef03 1897 mbedtls_mpi_get_bit( d, 1 ) != 0 ||
kevman 0:38ceb79fef03 1898 mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */
kevman 0:38ceb79fef03 1899 return( MBEDTLS_ERR_ECP_INVALID_KEY );
kevman 0:38ceb79fef03 1900
kevman 0:38ceb79fef03 1901 /* see [Curve25519] page 5 */
kevman 0:38ceb79fef03 1902 if( grp->nbits == 254 && mbedtls_mpi_get_bit( d, 2 ) != 0 )
kevman 0:38ceb79fef03 1903 return( MBEDTLS_ERR_ECP_INVALID_KEY );
kevman 0:38ceb79fef03 1904
kevman 0:38ceb79fef03 1905 return( 0 );
kevman 0:38ceb79fef03 1906 }
kevman 0:38ceb79fef03 1907 #endif /* ECP_MONTGOMERY */
kevman 0:38ceb79fef03 1908 #if defined(ECP_SHORTWEIERSTRASS)
kevman 0:38ceb79fef03 1909 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
kevman 0:38ceb79fef03 1910 {
kevman 0:38ceb79fef03 1911 /* see SEC1 3.2 */
kevman 0:38ceb79fef03 1912 if( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
kevman 0:38ceb79fef03 1913 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
kevman 0:38ceb79fef03 1914 return( MBEDTLS_ERR_ECP_INVALID_KEY );
kevman 0:38ceb79fef03 1915 else
kevman 0:38ceb79fef03 1916 return( 0 );
kevman 0:38ceb79fef03 1917 }
kevman 0:38ceb79fef03 1918 #endif /* ECP_SHORTWEIERSTRASS */
kevman 0:38ceb79fef03 1919
kevman 0:38ceb79fef03 1920 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 1921 }
kevman 0:38ceb79fef03 1922
kevman 0:38ceb79fef03 1923 /*
kevman 0:38ceb79fef03 1924 * Generate a keypair with configurable base point
kevman 0:38ceb79fef03 1925 */
kevman 0:38ceb79fef03 1926 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
kevman 0:38ceb79fef03 1927 const mbedtls_ecp_point *G,
kevman 0:38ceb79fef03 1928 mbedtls_mpi *d, mbedtls_ecp_point *Q,
kevman 0:38ceb79fef03 1929 int (*f_rng)(void *, unsigned char *, size_t),
kevman 0:38ceb79fef03 1930 void *p_rng )
kevman 0:38ceb79fef03 1931 {
kevman 0:38ceb79fef03 1932 int ret;
kevman 0:38ceb79fef03 1933 size_t n_size = ( grp->nbits + 7 ) / 8;
kevman 0:38ceb79fef03 1934
kevman 0:38ceb79fef03 1935 #if defined(ECP_MONTGOMERY)
kevman 0:38ceb79fef03 1936 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
kevman 0:38ceb79fef03 1937 {
kevman 0:38ceb79fef03 1938 /* [M225] page 5 */
kevman 0:38ceb79fef03 1939 size_t b;
kevman 0:38ceb79fef03 1940
kevman 0:38ceb79fef03 1941 do {
kevman 0:38ceb79fef03 1942 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
kevman 0:38ceb79fef03 1943 } while( mbedtls_mpi_bitlen( d ) == 0);
kevman 0:38ceb79fef03 1944
kevman 0:38ceb79fef03 1945 /* Make sure the most significant bit is nbits */
kevman 0:38ceb79fef03 1946 b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */
kevman 0:38ceb79fef03 1947 if( b > grp->nbits )
kevman 0:38ceb79fef03 1948 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) );
kevman 0:38ceb79fef03 1949 else
kevman 0:38ceb79fef03 1950 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) );
kevman 0:38ceb79fef03 1951
kevman 0:38ceb79fef03 1952 /* Make sure the last two bits are unset for Curve448, three bits for
kevman 0:38ceb79fef03 1953 Curve25519 */
kevman 0:38ceb79fef03 1954 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) );
kevman 0:38ceb79fef03 1955 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) );
kevman 0:38ceb79fef03 1956 if( grp->nbits == 254 )
kevman 0:38ceb79fef03 1957 {
kevman 0:38ceb79fef03 1958 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
kevman 0:38ceb79fef03 1959 }
kevman 0:38ceb79fef03 1960 }
kevman 0:38ceb79fef03 1961 else
kevman 0:38ceb79fef03 1962 #endif /* ECP_MONTGOMERY */
kevman 0:38ceb79fef03 1963 #if defined(ECP_SHORTWEIERSTRASS)
kevman 0:38ceb79fef03 1964 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
kevman 0:38ceb79fef03 1965 {
kevman 0:38ceb79fef03 1966 /* SEC1 3.2.1: Generate d such that 1 <= n < N */
kevman 0:38ceb79fef03 1967 int count = 0;
kevman 0:38ceb79fef03 1968
kevman 0:38ceb79fef03 1969 /*
kevman 0:38ceb79fef03 1970 * Match the procedure given in RFC 6979 (deterministic ECDSA):
kevman 0:38ceb79fef03 1971 * - use the same byte ordering;
kevman 0:38ceb79fef03 1972 * - keep the leftmost nbits bits of the generated octet string;
kevman 0:38ceb79fef03 1973 * - try until result is in the desired range.
kevman 0:38ceb79fef03 1974 * This also avoids any biais, which is especially important for ECDSA.
kevman 0:38ceb79fef03 1975 */
kevman 0:38ceb79fef03 1976 do
kevman 0:38ceb79fef03 1977 {
kevman 0:38ceb79fef03 1978 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
kevman 0:38ceb79fef03 1979 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) );
kevman 0:38ceb79fef03 1980
kevman 0:38ceb79fef03 1981 /*
kevman 0:38ceb79fef03 1982 * Each try has at worst a probability 1/2 of failing (the msb has
kevman 0:38ceb79fef03 1983 * a probability 1/2 of being 0, and then the result will be < N),
kevman 0:38ceb79fef03 1984 * so after 30 tries failure probability is a most 2**(-30).
kevman 0:38ceb79fef03 1985 *
kevman 0:38ceb79fef03 1986 * For most curves, 1 try is enough with overwhelming probability,
kevman 0:38ceb79fef03 1987 * since N starts with a lot of 1s in binary, but some curves
kevman 0:38ceb79fef03 1988 * such as secp224k1 are actually very close to the worst case.
kevman 0:38ceb79fef03 1989 */
kevman 0:38ceb79fef03 1990 if( ++count > 30 )
kevman 0:38ceb79fef03 1991 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
kevman 0:38ceb79fef03 1992 }
kevman 0:38ceb79fef03 1993 while( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
kevman 0:38ceb79fef03 1994 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 );
kevman 0:38ceb79fef03 1995 }
kevman 0:38ceb79fef03 1996 else
kevman 0:38ceb79fef03 1997 #endif /* ECP_SHORTWEIERSTRASS */
kevman 0:38ceb79fef03 1998 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 1999
kevman 0:38ceb79fef03 2000 cleanup:
kevman 0:38ceb79fef03 2001 if( ret != 0 )
kevman 0:38ceb79fef03 2002 return( ret );
kevman 0:38ceb79fef03 2003
kevman 0:38ceb79fef03 2004 return( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) );
kevman 0:38ceb79fef03 2005 }
kevman 0:38ceb79fef03 2006
kevman 0:38ceb79fef03 2007 /*
kevman 0:38ceb79fef03 2008 * Generate key pair, wrapper for conventional base point
kevman 0:38ceb79fef03 2009 */
kevman 0:38ceb79fef03 2010 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp,
kevman 0:38ceb79fef03 2011 mbedtls_mpi *d, mbedtls_ecp_point *Q,
kevman 0:38ceb79fef03 2012 int (*f_rng)(void *, unsigned char *, size_t),
kevman 0:38ceb79fef03 2013 void *p_rng )
kevman 0:38ceb79fef03 2014 {
kevman 0:38ceb79fef03 2015 return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) );
kevman 0:38ceb79fef03 2016 }
kevman 0:38ceb79fef03 2017
kevman 0:38ceb79fef03 2018 /*
kevman 0:38ceb79fef03 2019 * Generate a keypair, prettier wrapper
kevman 0:38ceb79fef03 2020 */
kevman 0:38ceb79fef03 2021 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
kevman 0:38ceb79fef03 2022 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
kevman 0:38ceb79fef03 2023 {
kevman 0:38ceb79fef03 2024 int ret;
kevman 0:38ceb79fef03 2025
kevman 0:38ceb79fef03 2026 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
kevman 0:38ceb79fef03 2027 return( ret );
kevman 0:38ceb79fef03 2028
kevman 0:38ceb79fef03 2029 return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
kevman 0:38ceb79fef03 2030 }
kevman 0:38ceb79fef03 2031
kevman 0:38ceb79fef03 2032 /*
kevman 0:38ceb79fef03 2033 * Check a public-private key pair
kevman 0:38ceb79fef03 2034 */
kevman 0:38ceb79fef03 2035 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
kevman 0:38ceb79fef03 2036 {
kevman 0:38ceb79fef03 2037 int ret;
kevman 0:38ceb79fef03 2038 mbedtls_ecp_point Q;
kevman 0:38ceb79fef03 2039 mbedtls_ecp_group grp;
kevman 0:38ceb79fef03 2040
kevman 0:38ceb79fef03 2041 if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
kevman 0:38ceb79fef03 2042 pub->grp.id != prv->grp.id ||
kevman 0:38ceb79fef03 2043 mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
kevman 0:38ceb79fef03 2044 mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
kevman 0:38ceb79fef03 2045 mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
kevman 0:38ceb79fef03 2046 {
kevman 0:38ceb79fef03 2047 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kevman 0:38ceb79fef03 2048 }
kevman 0:38ceb79fef03 2049
kevman 0:38ceb79fef03 2050 mbedtls_ecp_point_init( &Q );
kevman 0:38ceb79fef03 2051 mbedtls_ecp_group_init( &grp );
kevman 0:38ceb79fef03 2052
kevman 0:38ceb79fef03 2053 /* mbedtls_ecp_mul() needs a non-const group... */
kevman 0:38ceb79fef03 2054 mbedtls_ecp_group_copy( &grp, &prv->grp );
kevman 0:38ceb79fef03 2055
kevman 0:38ceb79fef03 2056 /* Also checks d is valid */
kevman 0:38ceb79fef03 2057 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
kevman 0:38ceb79fef03 2058
kevman 0:38ceb79fef03 2059 if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
kevman 0:38ceb79fef03 2060 mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
kevman 0:38ceb79fef03 2061 mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
kevman 0:38ceb79fef03 2062 {
kevman 0:38ceb79fef03 2063 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
kevman 0:38ceb79fef03 2064 goto cleanup;
kevman 0:38ceb79fef03 2065 }
kevman 0:38ceb79fef03 2066
kevman 0:38ceb79fef03 2067 cleanup:
kevman 0:38ceb79fef03 2068 mbedtls_ecp_point_free( &Q );
kevman 0:38ceb79fef03 2069 mbedtls_ecp_group_free( &grp );
kevman 0:38ceb79fef03 2070
kevman 0:38ceb79fef03 2071 return( ret );
kevman 0:38ceb79fef03 2072 }
kevman 0:38ceb79fef03 2073
kevman 0:38ceb79fef03 2074 #if defined(MBEDTLS_SELF_TEST)
kevman 0:38ceb79fef03 2075
kevman 0:38ceb79fef03 2076 /*
kevman 0:38ceb79fef03 2077 * Checkup routine
kevman 0:38ceb79fef03 2078 */
kevman 0:38ceb79fef03 2079 int mbedtls_ecp_self_test( int verbose )
kevman 0:38ceb79fef03 2080 {
kevman 0:38ceb79fef03 2081 int ret;
kevman 0:38ceb79fef03 2082 size_t i;
kevman 0:38ceb79fef03 2083 mbedtls_ecp_group grp;
kevman 0:38ceb79fef03 2084 mbedtls_ecp_point R, P;
kevman 0:38ceb79fef03 2085 mbedtls_mpi m;
kevman 0:38ceb79fef03 2086 unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
kevman 0:38ceb79fef03 2087 /* exponents especially adapted for secp192r1 */
kevman 0:38ceb79fef03 2088 const char *exponents[] =
kevman 0:38ceb79fef03 2089 {
kevman 0:38ceb79fef03 2090 "000000000000000000000000000000000000000000000001", /* one */
kevman 0:38ceb79fef03 2091 "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22830", /* N - 1 */
kevman 0:38ceb79fef03 2092 "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
kevman 0:38ceb79fef03 2093 "400000000000000000000000000000000000000000000000", /* one and zeros */
kevman 0:38ceb79fef03 2094 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
kevman 0:38ceb79fef03 2095 "555555555555555555555555555555555555555555555555", /* 101010... */
kevman 0:38ceb79fef03 2096 };
kevman 0:38ceb79fef03 2097
kevman 0:38ceb79fef03 2098 mbedtls_ecp_group_init( &grp );
kevman 0:38ceb79fef03 2099 mbedtls_ecp_point_init( &R );
kevman 0:38ceb79fef03 2100 mbedtls_ecp_point_init( &P );
kevman 0:38ceb79fef03 2101 mbedtls_mpi_init( &m );
kevman 0:38ceb79fef03 2102
kevman 0:38ceb79fef03 2103 /* Use secp192r1 if available, or any available curve */
kevman 0:38ceb79fef03 2104 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
kevman 0:38ceb79fef03 2105 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) );
kevman 0:38ceb79fef03 2106 #else
kevman 0:38ceb79fef03 2107 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) );
kevman 0:38ceb79fef03 2108 #endif
kevman 0:38ceb79fef03 2109
kevman 0:38ceb79fef03 2110 if( verbose != 0 )
kevman 0:38ceb79fef03 2111 mbedtls_printf( " ECP test #1 (constant op_count, base point G): " );
kevman 0:38ceb79fef03 2112
kevman 0:38ceb79fef03 2113 /* Do a dummy multiplication first to trigger precomputation */
kevman 0:38ceb79fef03 2114 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
kevman 0:38ceb79fef03 2115 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
kevman 0:38ceb79fef03 2116
kevman 0:38ceb79fef03 2117 add_count = 0;
kevman 0:38ceb79fef03 2118 dbl_count = 0;
kevman 0:38ceb79fef03 2119 mul_count = 0;
kevman 0:38ceb79fef03 2120 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
kevman 0:38ceb79fef03 2121 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
kevman 0:38ceb79fef03 2122
kevman 0:38ceb79fef03 2123 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
kevman 0:38ceb79fef03 2124 {
kevman 0:38ceb79fef03 2125 add_c_prev = add_count;
kevman 0:38ceb79fef03 2126 dbl_c_prev = dbl_count;
kevman 0:38ceb79fef03 2127 mul_c_prev = mul_count;
kevman 0:38ceb79fef03 2128 add_count = 0;
kevman 0:38ceb79fef03 2129 dbl_count = 0;
kevman 0:38ceb79fef03 2130 mul_count = 0;
kevman 0:38ceb79fef03 2131
kevman 0:38ceb79fef03 2132 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
kevman 0:38ceb79fef03 2133 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
kevman 0:38ceb79fef03 2134
kevman 0:38ceb79fef03 2135 if( add_count != add_c_prev ||
kevman 0:38ceb79fef03 2136 dbl_count != dbl_c_prev ||
kevman 0:38ceb79fef03 2137 mul_count != mul_c_prev )
kevman 0:38ceb79fef03 2138 {
kevman 0:38ceb79fef03 2139 if( verbose != 0 )
kevman 0:38ceb79fef03 2140 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
kevman 0:38ceb79fef03 2141
kevman 0:38ceb79fef03 2142 ret = 1;
kevman 0:38ceb79fef03 2143 goto cleanup;
kevman 0:38ceb79fef03 2144 }
kevman 0:38ceb79fef03 2145 }
kevman 0:38ceb79fef03 2146
kevman 0:38ceb79fef03 2147 if( verbose != 0 )
kevman 0:38ceb79fef03 2148 mbedtls_printf( "passed\n" );
kevman 0:38ceb79fef03 2149
kevman 0:38ceb79fef03 2150 if( verbose != 0 )
kevman 0:38ceb79fef03 2151 mbedtls_printf( " ECP test #2 (constant op_count, other point): " );
kevman 0:38ceb79fef03 2152 /* We computed P = 2G last time, use it */
kevman 0:38ceb79fef03 2153
kevman 0:38ceb79fef03 2154 add_count = 0;
kevman 0:38ceb79fef03 2155 dbl_count = 0;
kevman 0:38ceb79fef03 2156 mul_count = 0;
kevman 0:38ceb79fef03 2157 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
kevman 0:38ceb79fef03 2158 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
kevman 0:38ceb79fef03 2159
kevman 0:38ceb79fef03 2160 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
kevman 0:38ceb79fef03 2161 {
kevman 0:38ceb79fef03 2162 add_c_prev = add_count;
kevman 0:38ceb79fef03 2163 dbl_c_prev = dbl_count;
kevman 0:38ceb79fef03 2164 mul_c_prev = mul_count;
kevman 0:38ceb79fef03 2165 add_count = 0;
kevman 0:38ceb79fef03 2166 dbl_count = 0;
kevman 0:38ceb79fef03 2167 mul_count = 0;
kevman 0:38ceb79fef03 2168
kevman 0:38ceb79fef03 2169 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
kevman 0:38ceb79fef03 2170 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
kevman 0:38ceb79fef03 2171
kevman 0:38ceb79fef03 2172 if( add_count != add_c_prev ||
kevman 0:38ceb79fef03 2173 dbl_count != dbl_c_prev ||
kevman 0:38ceb79fef03 2174 mul_count != mul_c_prev )
kevman 0:38ceb79fef03 2175 {
kevman 0:38ceb79fef03 2176 if( verbose != 0 )
kevman 0:38ceb79fef03 2177 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
kevman 0:38ceb79fef03 2178
kevman 0:38ceb79fef03 2179 ret = 1;
kevman 0:38ceb79fef03 2180 goto cleanup;
kevman 0:38ceb79fef03 2181 }
kevman 0:38ceb79fef03 2182 }
kevman 0:38ceb79fef03 2183
kevman 0:38ceb79fef03 2184 if( verbose != 0 )
kevman 0:38ceb79fef03 2185 mbedtls_printf( "passed\n" );
kevman 0:38ceb79fef03 2186
kevman 0:38ceb79fef03 2187 cleanup:
kevman 0:38ceb79fef03 2188
kevman 0:38ceb79fef03 2189 if( ret < 0 && verbose != 0 )
kevman 0:38ceb79fef03 2190 mbedtls_printf( "Unexpected error, return code = %08X\n", ret );
kevman 0:38ceb79fef03 2191
kevman 0:38ceb79fef03 2192 mbedtls_ecp_group_free( &grp );
kevman 0:38ceb79fef03 2193 mbedtls_ecp_point_free( &R );
kevman 0:38ceb79fef03 2194 mbedtls_ecp_point_free( &P );
kevman 0:38ceb79fef03 2195 mbedtls_mpi_free( &m );
kevman 0:38ceb79fef03 2196
kevman 0:38ceb79fef03 2197 if( verbose != 0 )
kevman 0:38ceb79fef03 2198 mbedtls_printf( "\n" );
kevman 0:38ceb79fef03 2199
kevman 0:38ceb79fef03 2200 return( ret );
kevman 0:38ceb79fef03 2201 }
kevman 0:38ceb79fef03 2202
kevman 0:38ceb79fef03 2203 #endif /* MBEDTLS_SELF_TEST */
kevman 0:38ceb79fef03 2204
kevman 0:38ceb79fef03 2205 #endif /* !MBEDTLS_ECP_ALT */
kevman 0:38ceb79fef03 2206
kevman 0:38ceb79fef03 2207 #endif /* MBEDTLS_ECP_C */