Nitin Shukla / LED_Demo

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Dependencies:   MAX44000 nexpaq_mdk

Fork of LED_Demo by Maxim nexpaq

mbd_os/features/mbedtls/src/ecp.c@7:3a65ef12ba31, 2016-11-04 (annotated)

Committer:
nitsshukla
Date:
Fri Nov 04 12:06:04 2016 +0000
Revision:
7:3a65ef12ba31
Parent:
1:55a6170b404f 
kghj;

Who changed what in which revision?

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nexpaq 1:55a6170b404f 1 /*
nexpaq 1:55a6170b404f 2 * Elliptic curves over GF(p): generic functions
nexpaq 1:55a6170b404f 3 *
nexpaq 1:55a6170b404f 4 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
nexpaq 1:55a6170b404f 5 * SPDX-License-Identifier: Apache-2.0
nexpaq 1:55a6170b404f 6 *
nexpaq 1:55a6170b404f 7 * Licensed under the Apache License, Version 2.0 (the "License"); you may
nexpaq 1:55a6170b404f 8 * not use this file except in compliance with the License.
nexpaq 1:55a6170b404f 9 * You may obtain a copy of the License at
nexpaq 1:55a6170b404f 10 *
nexpaq 1:55a6170b404f 11 * http://www.apache.org/licenses/LICENSE-2.0
nexpaq 1:55a6170b404f 12 *
nexpaq 1:55a6170b404f 13 * Unless required by applicable law or agreed to in writing, software
nexpaq 1:55a6170b404f 14 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
nexpaq 1:55a6170b404f 15 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
nexpaq 1:55a6170b404f 16 * See the License for the specific language governing permissions and
nexpaq 1:55a6170b404f 17 * limitations under the License.
nexpaq 1:55a6170b404f 18 *
nexpaq 1:55a6170b404f 19 * This file is part of mbed TLS (https://tls.mbed.org)
nexpaq 1:55a6170b404f 20 */
nexpaq 1:55a6170b404f 21
nexpaq 1:55a6170b404f 22 /*
nexpaq 1:55a6170b404f 23 * References:
nexpaq 1:55a6170b404f 24 *
nexpaq 1:55a6170b404f 25 * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
nexpaq 1:55a6170b404f 26 * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
nexpaq 1:55a6170b404f 27 * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
nexpaq 1:55a6170b404f 28 * RFC 4492 for the related TLS structures and constants
nexpaq 1:55a6170b404f 29 *
nexpaq 1:55a6170b404f 30 * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf
nexpaq 1:55a6170b404f 31 *
nexpaq 1:55a6170b404f 32 * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
nexpaq 1:55a6170b404f 33 * for elliptic curve cryptosystems. In : Cryptographic Hardware and
nexpaq 1:55a6170b404f 34 * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
nexpaq 1:55a6170b404f 35 * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
nexpaq 1:55a6170b404f 36 *
nexpaq 1:55a6170b404f 37 * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
nexpaq 1:55a6170b404f 38 * render ECC resistant against Side Channel Attacks. IACR Cryptology
nexpaq 1:55a6170b404f 39 * ePrint Archive, 2004, vol. 2004, p. 342.
nexpaq 1:55a6170b404f 40 * <http://eprint.iacr.org/2004/342.pdf>
nexpaq 1:55a6170b404f 41 */
nexpaq 1:55a6170b404f 42
nexpaq 1:55a6170b404f 43 #if !defined(MBEDTLS_CONFIG_FILE)
nexpaq 1:55a6170b404f 44 #include "mbedtls/config.h"
nexpaq 1:55a6170b404f 45 #else
nexpaq 1:55a6170b404f 46 #include MBEDTLS_CONFIG_FILE
nexpaq 1:55a6170b404f 47 #endif
nexpaq 1:55a6170b404f 48
nexpaq 1:55a6170b404f 49 #if defined(MBEDTLS_ECP_C)
nexpaq 1:55a6170b404f 50
nexpaq 1:55a6170b404f 51 #include "mbedtls/ecp.h"
nexpaq 1:55a6170b404f 52
nexpaq 1:55a6170b404f 53 #include <string.h>
nexpaq 1:55a6170b404f 54
nexpaq 1:55a6170b404f 55 #if defined(MBEDTLS_PLATFORM_C)
nexpaq 1:55a6170b404f 56 #include "mbedtls/platform.h"
nexpaq 1:55a6170b404f 57 #else
nexpaq 1:55a6170b404f 58 #include <stdlib.h>
nexpaq 1:55a6170b404f 59 #include <stdio.h>
nexpaq 1:55a6170b404f 60 #define mbedtls_printf printf
nexpaq 1:55a6170b404f 61 #define mbedtls_calloc calloc
nexpaq 1:55a6170b404f 62 #define mbedtls_free free
nexpaq 1:55a6170b404f 63 #endif
nexpaq 1:55a6170b404f 64
nexpaq 1:55a6170b404f 65 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
nexpaq 1:55a6170b404f 66 !defined(inline) && !defined(__cplusplus)
nexpaq 1:55a6170b404f 67 #define inline __inline
nexpaq 1:55a6170b404f 68 #endif
nexpaq 1:55a6170b404f 69
nexpaq 1:55a6170b404f 70 /* Implementation that should never be optimized out by the compiler */
nexpaq 1:55a6170b404f 71 static void mbedtls_zeroize( void *v, size_t n ) {
nexpaq 1:55a6170b404f 72 volatile unsigned char *p = v; while( n-- ) *p++ = 0;
nexpaq 1:55a6170b404f 73 }
nexpaq 1:55a6170b404f 74
nexpaq 1:55a6170b404f 75 #if defined(MBEDTLS_SELF_TEST)
nexpaq 1:55a6170b404f 76 /*
nexpaq 1:55a6170b404f 77 * Counts of point addition and doubling, and field multiplications.
nexpaq 1:55a6170b404f 78 * Used to test resistance of point multiplication to simple timing attacks.
nexpaq 1:55a6170b404f 79 */
nexpaq 1:55a6170b404f 80 static unsigned long add_count, dbl_count, mul_count;
nexpaq 1:55a6170b404f 81 #endif
nexpaq 1:55a6170b404f 82
nexpaq 1:55a6170b404f 83 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \
nexpaq 1:55a6170b404f 84 defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
nexpaq 1:55a6170b404f 85 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
nexpaq 1:55a6170b404f 86 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \
nexpaq 1:55a6170b404f 87 defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \
nexpaq 1:55a6170b404f 88 defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \
nexpaq 1:55a6170b404f 89 defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \
nexpaq 1:55a6170b404f 90 defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \
nexpaq 1:55a6170b404f 91 defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
nexpaq 1:55a6170b404f 92 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
nexpaq 1:55a6170b404f 93 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
nexpaq 1:55a6170b404f 94 #define ECP_SHORTWEIERSTRASS
nexpaq 1:55a6170b404f 95 #endif
nexpaq 1:55a6170b404f 96
nexpaq 1:55a6170b404f 97 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
nexpaq 1:55a6170b404f 98 #define ECP_MONTGOMERY
nexpaq 1:55a6170b404f 99 #endif
nexpaq 1:55a6170b404f 100
nexpaq 1:55a6170b404f 101 /*
nexpaq 1:55a6170b404f 102 * Curve types: internal for now, might be exposed later
nexpaq 1:55a6170b404f 103 */
nexpaq 1:55a6170b404f 104 typedef enum
nexpaq 1:55a6170b404f 105 {
nexpaq 1:55a6170b404f 106 ECP_TYPE_NONE = 0,
nexpaq 1:55a6170b404f 107 ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */
nexpaq 1:55a6170b404f 108 ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */
nexpaq 1:55a6170b404f 109 } ecp_curve_type;
nexpaq 1:55a6170b404f 110
nexpaq 1:55a6170b404f 111 /*
nexpaq 1:55a6170b404f 112 * List of supported curves:
nexpaq 1:55a6170b404f 113 * - internal ID
nexpaq 1:55a6170b404f 114 * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2)
nexpaq 1:55a6170b404f 115 * - size in bits
nexpaq 1:55a6170b404f 116 * - readable name
nexpaq 1:55a6170b404f 117 *
nexpaq 1:55a6170b404f 118 * Curves are listed in order: largest curves first, and for a given size,
nexpaq 1:55a6170b404f 119 * fastest curves first. This provides the default order for the SSL module.
nexpaq 1:55a6170b404f 120 *
nexpaq 1:55a6170b404f 121 * Reminder: update profiles in x509_crt.c when adding a new curves!
nexpaq 1:55a6170b404f 122 */
nexpaq 1:55a6170b404f 123 static const mbedtls_ecp_curve_info ecp_supported_curves[] =
nexpaq 1:55a6170b404f 124 {
nexpaq 1:55a6170b404f 125 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
nexpaq 1:55a6170b404f 126 { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" },
nexpaq 1:55a6170b404f 127 #endif
nexpaq 1:55a6170b404f 128 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
nexpaq 1:55a6170b404f 129 { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
nexpaq 1:55a6170b404f 130 #endif
nexpaq 1:55a6170b404f 131 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
nexpaq 1:55a6170b404f 132 { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
nexpaq 1:55a6170b404f 133 #endif
nexpaq 1:55a6170b404f 134 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
nexpaq 1:55a6170b404f 135 { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
nexpaq 1:55a6170b404f 136 #endif
nexpaq 1:55a6170b404f 137 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
nexpaq 1:55a6170b404f 138 { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
nexpaq 1:55a6170b404f 139 #endif
nexpaq 1:55a6170b404f 140 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
nexpaq 1:55a6170b404f 141 { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
nexpaq 1:55a6170b404f 142 #endif
nexpaq 1:55a6170b404f 143 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
nexpaq 1:55a6170b404f 144 { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" },
nexpaq 1:55a6170b404f 145 #endif
nexpaq 1:55a6170b404f 146 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
nexpaq 1:55a6170b404f 147 { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" },
nexpaq 1:55a6170b404f 148 #endif
nexpaq 1:55a6170b404f 149 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
nexpaq 1:55a6170b404f 150 { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" },
nexpaq 1:55a6170b404f 151 #endif
nexpaq 1:55a6170b404f 152 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
nexpaq 1:55a6170b404f 153 { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" },
nexpaq 1:55a6170b404f 154 #endif
nexpaq 1:55a6170b404f 155 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
nexpaq 1:55a6170b404f 156 { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" },
nexpaq 1:55a6170b404f 157 #endif
nexpaq 1:55a6170b404f 158 { MBEDTLS_ECP_DP_NONE, 0, 0, NULL },
nexpaq 1:55a6170b404f 159 };
nexpaq 1:55a6170b404f 160
nexpaq 1:55a6170b404f 161 #define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \
nexpaq 1:55a6170b404f 162 sizeof( ecp_supported_curves[0] )
nexpaq 1:55a6170b404f 163
nexpaq 1:55a6170b404f 164 static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
nexpaq 1:55a6170b404f 165
nexpaq 1:55a6170b404f 166 /*
nexpaq 1:55a6170b404f 167 * List of supported curves and associated info
nexpaq 1:55a6170b404f 168 */
nexpaq 1:55a6170b404f 169 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
nexpaq 1:55a6170b404f 170 {
nexpaq 1:55a6170b404f 171 return( ecp_supported_curves );
nexpaq 1:55a6170b404f 172 }
nexpaq 1:55a6170b404f 173
nexpaq 1:55a6170b404f 174 /*
nexpaq 1:55a6170b404f 175 * List of supported curves, group ID only
nexpaq 1:55a6170b404f 176 */
nexpaq 1:55a6170b404f 177 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
nexpaq 1:55a6170b404f 178 {
nexpaq 1:55a6170b404f 179 static int init_done = 0;
nexpaq 1:55a6170b404f 180
nexpaq 1:55a6170b404f 181 if( ! init_done )
nexpaq 1:55a6170b404f 182 {
nexpaq 1:55a6170b404f 183 size_t i = 0;
nexpaq 1:55a6170b404f 184 const mbedtls_ecp_curve_info *curve_info;
nexpaq 1:55a6170b404f 185
nexpaq 1:55a6170b404f 186 for( curve_info = mbedtls_ecp_curve_list();
nexpaq 1:55a6170b404f 187 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
nexpaq 1:55a6170b404f 188 curve_info++ )
nexpaq 1:55a6170b404f 189 {
nexpaq 1:55a6170b404f 190 ecp_supported_grp_id[i++] = curve_info->grp_id;
nexpaq 1:55a6170b404f 191 }
nexpaq 1:55a6170b404f 192 ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
nexpaq 1:55a6170b404f 193
nexpaq 1:55a6170b404f 194 init_done = 1;
nexpaq 1:55a6170b404f 195 }
nexpaq 1:55a6170b404f 196
nexpaq 1:55a6170b404f 197 return( ecp_supported_grp_id );
nexpaq 1:55a6170b404f 198 }
nexpaq 1:55a6170b404f 199
nexpaq 1:55a6170b404f 200 /*
nexpaq 1:55a6170b404f 201 * Get the curve info for the internal identifier
nexpaq 1:55a6170b404f 202 */
nexpaq 1:55a6170b404f 203 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id )
nexpaq 1:55a6170b404f 204 {
nexpaq 1:55a6170b404f 205 const mbedtls_ecp_curve_info *curve_info;
nexpaq 1:55a6170b404f 206
nexpaq 1:55a6170b404f 207 for( curve_info = mbedtls_ecp_curve_list();
nexpaq 1:55a6170b404f 208 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
nexpaq 1:55a6170b404f 209 curve_info++ )
nexpaq 1:55a6170b404f 210 {
nexpaq 1:55a6170b404f 211 if( curve_info->grp_id == grp_id )
nexpaq 1:55a6170b404f 212 return( curve_info );
nexpaq 1:55a6170b404f 213 }
nexpaq 1:55a6170b404f 214
nexpaq 1:55a6170b404f 215 return( NULL );
nexpaq 1:55a6170b404f 216 }
nexpaq 1:55a6170b404f 217
nexpaq 1:55a6170b404f 218 /*
nexpaq 1:55a6170b404f 219 * Get the curve info from the TLS identifier
nexpaq 1:55a6170b404f 220 */
nexpaq 1:55a6170b404f 221 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id )
nexpaq 1:55a6170b404f 222 {
nexpaq 1:55a6170b404f 223 const mbedtls_ecp_curve_info *curve_info;
nexpaq 1:55a6170b404f 224
nexpaq 1:55a6170b404f 225 for( curve_info = mbedtls_ecp_curve_list();
nexpaq 1:55a6170b404f 226 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
nexpaq 1:55a6170b404f 227 curve_info++ )
nexpaq 1:55a6170b404f 228 {
nexpaq 1:55a6170b404f 229 if( curve_info->tls_id == tls_id )
nexpaq 1:55a6170b404f 230 return( curve_info );
nexpaq 1:55a6170b404f 231 }
nexpaq 1:55a6170b404f 232
nexpaq 1:55a6170b404f 233 return( NULL );
nexpaq 1:55a6170b404f 234 }
nexpaq 1:55a6170b404f 235
nexpaq 1:55a6170b404f 236 /*
nexpaq 1:55a6170b404f 237 * Get the curve info from the name
nexpaq 1:55a6170b404f 238 */
nexpaq 1:55a6170b404f 239 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name )
nexpaq 1:55a6170b404f 240 {
nexpaq 1:55a6170b404f 241 const mbedtls_ecp_curve_info *curve_info;
nexpaq 1:55a6170b404f 242
nexpaq 1:55a6170b404f 243 for( curve_info = mbedtls_ecp_curve_list();
nexpaq 1:55a6170b404f 244 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
nexpaq 1:55a6170b404f 245 curve_info++ )
nexpaq 1:55a6170b404f 246 {
nexpaq 1:55a6170b404f 247 if( strcmp( curve_info->name, name ) == 0 )
nexpaq 1:55a6170b404f 248 return( curve_info );
nexpaq 1:55a6170b404f 249 }
nexpaq 1:55a6170b404f 250
nexpaq 1:55a6170b404f 251 return( NULL );
nexpaq 1:55a6170b404f 252 }
nexpaq 1:55a6170b404f 253
nexpaq 1:55a6170b404f 254 /*
nexpaq 1:55a6170b404f 255 * Get the type of a curve
nexpaq 1:55a6170b404f 256 */
nexpaq 1:55a6170b404f 257 static inline ecp_curve_type ecp_get_type( const mbedtls_ecp_group *grp )
nexpaq 1:55a6170b404f 258 {
nexpaq 1:55a6170b404f 259 if( grp->G.X.p == NULL )
nexpaq 1:55a6170b404f 260 return( ECP_TYPE_NONE );
nexpaq 1:55a6170b404f 261
nexpaq 1:55a6170b404f 262 if( grp->G.Y.p == NULL )
nexpaq 1:55a6170b404f 263 return( ECP_TYPE_MONTGOMERY );
nexpaq 1:55a6170b404f 264 else
nexpaq 1:55a6170b404f 265 return( ECP_TYPE_SHORT_WEIERSTRASS );
nexpaq 1:55a6170b404f 266 }
nexpaq 1:55a6170b404f 267
nexpaq 1:55a6170b404f 268 /*
nexpaq 1:55a6170b404f 269 * Initialize (the components of) a point
nexpaq 1:55a6170b404f 270 */
nexpaq 1:55a6170b404f 271 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
nexpaq 1:55a6170b404f 272 {
nexpaq 1:55a6170b404f 273 if( pt == NULL )
nexpaq 1:55a6170b404f 274 return;
nexpaq 1:55a6170b404f 275
nexpaq 1:55a6170b404f 276 mbedtls_mpi_init( &pt->X );
nexpaq 1:55a6170b404f 277 mbedtls_mpi_init( &pt->Y );
nexpaq 1:55a6170b404f 278 mbedtls_mpi_init( &pt->Z );
nexpaq 1:55a6170b404f 279 }
nexpaq 1:55a6170b404f 280
nexpaq 1:55a6170b404f 281 /*
nexpaq 1:55a6170b404f 282 * Initialize (the components of) a group
nexpaq 1:55a6170b404f 283 */
nexpaq 1:55a6170b404f 284 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
nexpaq 1:55a6170b404f 285 {
nexpaq 1:55a6170b404f 286 if( grp == NULL )
nexpaq 1:55a6170b404f 287 return;
nexpaq 1:55a6170b404f 288
nexpaq 1:55a6170b404f 289 memset( grp, 0, sizeof( mbedtls_ecp_group ) );
nexpaq 1:55a6170b404f 290 }
nexpaq 1:55a6170b404f 291
nexpaq 1:55a6170b404f 292 /*
nexpaq 1:55a6170b404f 293 * Initialize (the components of) a key pair
nexpaq 1:55a6170b404f 294 */
nexpaq 1:55a6170b404f 295 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
nexpaq 1:55a6170b404f 296 {
nexpaq 1:55a6170b404f 297 if( key == NULL )
nexpaq 1:55a6170b404f 298 return;
nexpaq 1:55a6170b404f 299
nexpaq 1:55a6170b404f 300 mbedtls_ecp_group_init( &key->grp );
nexpaq 1:55a6170b404f 301 mbedtls_mpi_init( &key->d );
nexpaq 1:55a6170b404f 302 mbedtls_ecp_point_init( &key->Q );
nexpaq 1:55a6170b404f 303 }
nexpaq 1:55a6170b404f 304
nexpaq 1:55a6170b404f 305 /*
nexpaq 1:55a6170b404f 306 * Unallocate (the components of) a point
nexpaq 1:55a6170b404f 307 */
nexpaq 1:55a6170b404f 308 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
nexpaq 1:55a6170b404f 309 {
nexpaq 1:55a6170b404f 310 if( pt == NULL )
nexpaq 1:55a6170b404f 311 return;
nexpaq 1:55a6170b404f 312
nexpaq 1:55a6170b404f 313 mbedtls_mpi_free( &( pt->X ) );
nexpaq 1:55a6170b404f 314 mbedtls_mpi_free( &( pt->Y ) );
nexpaq 1:55a6170b404f 315 mbedtls_mpi_free( &( pt->Z ) );
nexpaq 1:55a6170b404f 316 }
nexpaq 1:55a6170b404f 317
nexpaq 1:55a6170b404f 318 /*
nexpaq 1:55a6170b404f 319 * Unallocate (the components of) a group
nexpaq 1:55a6170b404f 320 */
nexpaq 1:55a6170b404f 321 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
nexpaq 1:55a6170b404f 322 {
nexpaq 1:55a6170b404f 323 size_t i;
nexpaq 1:55a6170b404f 324
nexpaq 1:55a6170b404f 325 if( grp == NULL )
nexpaq 1:55a6170b404f 326 return;
nexpaq 1:55a6170b404f 327
nexpaq 1:55a6170b404f 328 if( grp->h != 1 )
nexpaq 1:55a6170b404f 329 {
nexpaq 1:55a6170b404f 330 mbedtls_mpi_free( &grp->P );
nexpaq 1:55a6170b404f 331 mbedtls_mpi_free( &grp->A );
nexpaq 1:55a6170b404f 332 mbedtls_mpi_free( &grp->B );
nexpaq 1:55a6170b404f 333 mbedtls_ecp_point_free( &grp->G );
nexpaq 1:55a6170b404f 334 mbedtls_mpi_free( &grp->N );
nexpaq 1:55a6170b404f 335 }
nexpaq 1:55a6170b404f 336
nexpaq 1:55a6170b404f 337 if( grp->T != NULL )
nexpaq 1:55a6170b404f 338 {
nexpaq 1:55a6170b404f 339 for( i = 0; i < grp->T_size; i++ )
nexpaq 1:55a6170b404f 340 mbedtls_ecp_point_free( &grp->T[i] );
nexpaq 1:55a6170b404f 341 mbedtls_free( grp->T );
nexpaq 1:55a6170b404f 342 }
nexpaq 1:55a6170b404f 343
nexpaq 1:55a6170b404f 344 mbedtls_zeroize( grp, sizeof( mbedtls_ecp_group ) );
nexpaq 1:55a6170b404f 345 }
nexpaq 1:55a6170b404f 346
nexpaq 1:55a6170b404f 347 /*
nexpaq 1:55a6170b404f 348 * Unallocate (the components of) a key pair
nexpaq 1:55a6170b404f 349 */
nexpaq 1:55a6170b404f 350 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
nexpaq 1:55a6170b404f 351 {
nexpaq 1:55a6170b404f 352 if( key == NULL )
nexpaq 1:55a6170b404f 353 return;
nexpaq 1:55a6170b404f 354
nexpaq 1:55a6170b404f 355 mbedtls_ecp_group_free( &key->grp );
nexpaq 1:55a6170b404f 356 mbedtls_mpi_free( &key->d );
nexpaq 1:55a6170b404f 357 mbedtls_ecp_point_free( &key->Q );
nexpaq 1:55a6170b404f 358 }
nexpaq 1:55a6170b404f 359
nexpaq 1:55a6170b404f 360 /*
nexpaq 1:55a6170b404f 361 * Copy the contents of a point
nexpaq 1:55a6170b404f 362 */
nexpaq 1:55a6170b404f 363 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
nexpaq 1:55a6170b404f 364 {
nexpaq 1:55a6170b404f 365 int ret;
nexpaq 1:55a6170b404f 366
nexpaq 1:55a6170b404f 367 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) );
nexpaq 1:55a6170b404f 368 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) );
nexpaq 1:55a6170b404f 369 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) );
nexpaq 1:55a6170b404f 370
nexpaq 1:55a6170b404f 371 cleanup:
nexpaq 1:55a6170b404f 372 return( ret );
nexpaq 1:55a6170b404f 373 }
nexpaq 1:55a6170b404f 374
nexpaq 1:55a6170b404f 375 /*
nexpaq 1:55a6170b404f 376 * Copy the contents of a group object
nexpaq 1:55a6170b404f 377 */
nexpaq 1:55a6170b404f 378 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
nexpaq 1:55a6170b404f 379 {
nexpaq 1:55a6170b404f 380 return mbedtls_ecp_group_load( dst, src->id );
nexpaq 1:55a6170b404f 381 }
nexpaq 1:55a6170b404f 382
nexpaq 1:55a6170b404f 383 /*
nexpaq 1:55a6170b404f 384 * Set point to zero
nexpaq 1:55a6170b404f 385 */
nexpaq 1:55a6170b404f 386 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
nexpaq 1:55a6170b404f 387 {
nexpaq 1:55a6170b404f 388 int ret;
nexpaq 1:55a6170b404f 389
nexpaq 1:55a6170b404f 390 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) );
nexpaq 1:55a6170b404f 391 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) );
nexpaq 1:55a6170b404f 392 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) );
nexpaq 1:55a6170b404f 393
nexpaq 1:55a6170b404f 394 cleanup:
nexpaq 1:55a6170b404f 395 return( ret );
nexpaq 1:55a6170b404f 396 }
nexpaq 1:55a6170b404f 397
nexpaq 1:55a6170b404f 398 /*
nexpaq 1:55a6170b404f 399 * Tell if a point is zero
nexpaq 1:55a6170b404f 400 */
nexpaq 1:55a6170b404f 401 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
nexpaq 1:55a6170b404f 402 {
nexpaq 1:55a6170b404f 403 return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 );
nexpaq 1:55a6170b404f 404 }
nexpaq 1:55a6170b404f 405
nexpaq 1:55a6170b404f 406 /*
nexpaq 1:55a6170b404f 407 * Compare two points lazyly
nexpaq 1:55a6170b404f 408 */
nexpaq 1:55a6170b404f 409 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
nexpaq 1:55a6170b404f 410 const mbedtls_ecp_point *Q )
nexpaq 1:55a6170b404f 411 {
nexpaq 1:55a6170b404f 412 if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
nexpaq 1:55a6170b404f 413 mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 &&
nexpaq 1:55a6170b404f 414 mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 )
nexpaq 1:55a6170b404f 415 {
nexpaq 1:55a6170b404f 416 return( 0 );
nexpaq 1:55a6170b404f 417 }
nexpaq 1:55a6170b404f 418
nexpaq 1:55a6170b404f 419 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 420 }
nexpaq 1:55a6170b404f 421
nexpaq 1:55a6170b404f 422 /*
nexpaq 1:55a6170b404f 423 * Import a non-zero point from ASCII strings
nexpaq 1:55a6170b404f 424 */
nexpaq 1:55a6170b404f 425 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
nexpaq 1:55a6170b404f 426 const char *x, const char *y )
nexpaq 1:55a6170b404f 427 {
nexpaq 1:55a6170b404f 428 int ret;
nexpaq 1:55a6170b404f 429
nexpaq 1:55a6170b404f 430 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) );
nexpaq 1:55a6170b404f 431 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) );
nexpaq 1:55a6170b404f 432 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
nexpaq 1:55a6170b404f 433
nexpaq 1:55a6170b404f 434 cleanup:
nexpaq 1:55a6170b404f 435 return( ret );
nexpaq 1:55a6170b404f 436 }
nexpaq 1:55a6170b404f 437
nexpaq 1:55a6170b404f 438 /*
nexpaq 1:55a6170b404f 439 * Export a point into unsigned binary data (SEC1 2.3.3)
nexpaq 1:55a6170b404f 440 */
nexpaq 1:55a6170b404f 441 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P,
nexpaq 1:55a6170b404f 442 int format, size_t *olen,
nexpaq 1:55a6170b404f 443 unsigned char *buf, size_t buflen )
nexpaq 1:55a6170b404f 444 {
nexpaq 1:55a6170b404f 445 int ret = 0;
nexpaq 1:55a6170b404f 446 size_t plen;
nexpaq 1:55a6170b404f 447
nexpaq 1:55a6170b404f 448 if( format != MBEDTLS_ECP_PF_UNCOMPRESSED &&
nexpaq 1:55a6170b404f 449 format != MBEDTLS_ECP_PF_COMPRESSED )
nexpaq 1:55a6170b404f 450 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 451
nexpaq 1:55a6170b404f 452 /*
nexpaq 1:55a6170b404f 453 * Common case: P == 0
nexpaq 1:55a6170b404f 454 */
nexpaq 1:55a6170b404f 455 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
nexpaq 1:55a6170b404f 456 {
nexpaq 1:55a6170b404f 457 if( buflen < 1 )
nexpaq 1:55a6170b404f 458 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
nexpaq 1:55a6170b404f 459
nexpaq 1:55a6170b404f 460 buf[0] = 0x00;
nexpaq 1:55a6170b404f 461 *olen = 1;
nexpaq 1:55a6170b404f 462
nexpaq 1:55a6170b404f 463 return( 0 );
nexpaq 1:55a6170b404f 464 }
nexpaq 1:55a6170b404f 465
nexpaq 1:55a6170b404f 466 plen = mbedtls_mpi_size( &grp->P );
nexpaq 1:55a6170b404f 467
nexpaq 1:55a6170b404f 468 if( format == MBEDTLS_ECP_PF_UNCOMPRESSED )
nexpaq 1:55a6170b404f 469 {
nexpaq 1:55a6170b404f 470 *olen = 2 * plen + 1;
nexpaq 1:55a6170b404f 471
nexpaq 1:55a6170b404f 472 if( buflen < *olen )
nexpaq 1:55a6170b404f 473 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
nexpaq 1:55a6170b404f 474
nexpaq 1:55a6170b404f 475 buf[0] = 0x04;
nexpaq 1:55a6170b404f 476 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
nexpaq 1:55a6170b404f 477 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) );
nexpaq 1:55a6170b404f 478 }
nexpaq 1:55a6170b404f 479 else if( format == MBEDTLS_ECP_PF_COMPRESSED )
nexpaq 1:55a6170b404f 480 {
nexpaq 1:55a6170b404f 481 *olen = plen + 1;
nexpaq 1:55a6170b404f 482
nexpaq 1:55a6170b404f 483 if( buflen < *olen )
nexpaq 1:55a6170b404f 484 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
nexpaq 1:55a6170b404f 485
nexpaq 1:55a6170b404f 486 buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 );
nexpaq 1:55a6170b404f 487 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
nexpaq 1:55a6170b404f 488 }
nexpaq 1:55a6170b404f 489
nexpaq 1:55a6170b404f 490 cleanup:
nexpaq 1:55a6170b404f 491 return( ret );
nexpaq 1:55a6170b404f 492 }
nexpaq 1:55a6170b404f 493
nexpaq 1:55a6170b404f 494 /*
nexpaq 1:55a6170b404f 495 * Import a point from unsigned binary data (SEC1 2.3.4)
nexpaq 1:55a6170b404f 496 */
nexpaq 1:55a6170b404f 497 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
nexpaq 1:55a6170b404f 498 const unsigned char *buf, size_t ilen )
nexpaq 1:55a6170b404f 499 {
nexpaq 1:55a6170b404f 500 int ret;
nexpaq 1:55a6170b404f 501 size_t plen;
nexpaq 1:55a6170b404f 502
nexpaq 1:55a6170b404f 503 if( ilen < 1 )
nexpaq 1:55a6170b404f 504 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 505
nexpaq 1:55a6170b404f 506 if( buf[0] == 0x00 )
nexpaq 1:55a6170b404f 507 {
nexpaq 1:55a6170b404f 508 if( ilen == 1 )
nexpaq 1:55a6170b404f 509 return( mbedtls_ecp_set_zero( pt ) );
nexpaq 1:55a6170b404f 510 else
nexpaq 1:55a6170b404f 511 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 512 }
nexpaq 1:55a6170b404f 513
nexpaq 1:55a6170b404f 514 plen = mbedtls_mpi_size( &grp->P );
nexpaq 1:55a6170b404f 515
nexpaq 1:55a6170b404f 516 if( buf[0] != 0x04 )
nexpaq 1:55a6170b404f 517 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
nexpaq 1:55a6170b404f 518
nexpaq 1:55a6170b404f 519 if( ilen != 2 * plen + 1 )
nexpaq 1:55a6170b404f 520 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 521
nexpaq 1:55a6170b404f 522 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
nexpaq 1:55a6170b404f 523 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, buf + 1 + plen, plen ) );
nexpaq 1:55a6170b404f 524 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
nexpaq 1:55a6170b404f 525
nexpaq 1:55a6170b404f 526 cleanup:
nexpaq 1:55a6170b404f 527 return( ret );
nexpaq 1:55a6170b404f 528 }
nexpaq 1:55a6170b404f 529
nexpaq 1:55a6170b404f 530 /*
nexpaq 1:55a6170b404f 531 * Import a point from a TLS ECPoint record (RFC 4492)
nexpaq 1:55a6170b404f 532 * struct {
nexpaq 1:55a6170b404f 533 * opaque point <1..2^8-1>;
nexpaq 1:55a6170b404f 534 * } ECPoint;
nexpaq 1:55a6170b404f 535 */
nexpaq 1:55a6170b404f 536 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
nexpaq 1:55a6170b404f 537 const unsigned char **buf, size_t buf_len )
nexpaq 1:55a6170b404f 538 {
nexpaq 1:55a6170b404f 539 unsigned char data_len;
nexpaq 1:55a6170b404f 540 const unsigned char *buf_start;
nexpaq 1:55a6170b404f 541
nexpaq 1:55a6170b404f 542 /*
nexpaq 1:55a6170b404f 543 * We must have at least two bytes (1 for length, at least one for data)
nexpaq 1:55a6170b404f 544 */
nexpaq 1:55a6170b404f 545 if( buf_len < 2 )
nexpaq 1:55a6170b404f 546 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 547
nexpaq 1:55a6170b404f 548 data_len = *(*buf)++;
nexpaq 1:55a6170b404f 549 if( data_len < 1 || data_len > buf_len - 1 )
nexpaq 1:55a6170b404f 550 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 551
nexpaq 1:55a6170b404f 552 /*
nexpaq 1:55a6170b404f 553 * Save buffer start for read_binary and update buf
nexpaq 1:55a6170b404f 554 */
nexpaq 1:55a6170b404f 555 buf_start = *buf;
nexpaq 1:55a6170b404f 556 *buf += data_len;
nexpaq 1:55a6170b404f 557
nexpaq 1:55a6170b404f 558 return mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len );
nexpaq 1:55a6170b404f 559 }
nexpaq 1:55a6170b404f 560
nexpaq 1:55a6170b404f 561 /*
nexpaq 1:55a6170b404f 562 * Export a point as a TLS ECPoint record (RFC 4492)
nexpaq 1:55a6170b404f 563 * struct {
nexpaq 1:55a6170b404f 564 * opaque point <1..2^8-1>;
nexpaq 1:55a6170b404f 565 * } ECPoint;
nexpaq 1:55a6170b404f 566 */
nexpaq 1:55a6170b404f 567 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
nexpaq 1:55a6170b404f 568 int format, size_t *olen,
nexpaq 1:55a6170b404f 569 unsigned char *buf, size_t blen )
nexpaq 1:55a6170b404f 570 {
nexpaq 1:55a6170b404f 571 int ret;
nexpaq 1:55a6170b404f 572
nexpaq 1:55a6170b404f 573 /*
nexpaq 1:55a6170b404f 574 * buffer length must be at least one, for our length byte
nexpaq 1:55a6170b404f 575 */
nexpaq 1:55a6170b404f 576 if( blen < 1 )
nexpaq 1:55a6170b404f 577 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 578
nexpaq 1:55a6170b404f 579 if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
nexpaq 1:55a6170b404f 580 olen, buf + 1, blen - 1) ) != 0 )
nexpaq 1:55a6170b404f 581 return( ret );
nexpaq 1:55a6170b404f 582
nexpaq 1:55a6170b404f 583 /*
nexpaq 1:55a6170b404f 584 * write length to the first byte and update total length
nexpaq 1:55a6170b404f 585 */
nexpaq 1:55a6170b404f 586 buf[0] = (unsigned char) *olen;
nexpaq 1:55a6170b404f 587 ++*olen;
nexpaq 1:55a6170b404f 588
nexpaq 1:55a6170b404f 589 return( 0 );
nexpaq 1:55a6170b404f 590 }
nexpaq 1:55a6170b404f 591
nexpaq 1:55a6170b404f 592 /*
nexpaq 1:55a6170b404f 593 * Set a group from an ECParameters record (RFC 4492)
nexpaq 1:55a6170b404f 594 */
nexpaq 1:55a6170b404f 595 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, const unsigned char **buf, size_t len )
nexpaq 1:55a6170b404f 596 {
nexpaq 1:55a6170b404f 597 uint16_t tls_id;
nexpaq 1:55a6170b404f 598 const mbedtls_ecp_curve_info *curve_info;
nexpaq 1:55a6170b404f 599
nexpaq 1:55a6170b404f 600 /*
nexpaq 1:55a6170b404f 601 * We expect at least three bytes (see below)
nexpaq 1:55a6170b404f 602 */
nexpaq 1:55a6170b404f 603 if( len < 3 )
nexpaq 1:55a6170b404f 604 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 605
nexpaq 1:55a6170b404f 606 /*
nexpaq 1:55a6170b404f 607 * First byte is curve_type; only named_curve is handled
nexpaq 1:55a6170b404f 608 */
nexpaq 1:55a6170b404f 609 if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
nexpaq 1:55a6170b404f 610 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 611
nexpaq 1:55a6170b404f 612 /*
nexpaq 1:55a6170b404f 613 * Next two bytes are the namedcurve value
nexpaq 1:55a6170b404f 614 */
nexpaq 1:55a6170b404f 615 tls_id = *(*buf)++;
nexpaq 1:55a6170b404f 616 tls_id <<= 8;
nexpaq 1:55a6170b404f 617 tls_id |= *(*buf)++;
nexpaq 1:55a6170b404f 618
nexpaq 1:55a6170b404f 619 if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
nexpaq 1:55a6170b404f 620 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
nexpaq 1:55a6170b404f 621
nexpaq 1:55a6170b404f 622 return mbedtls_ecp_group_load( grp, curve_info->grp_id );
nexpaq 1:55a6170b404f 623 }
nexpaq 1:55a6170b404f 624
nexpaq 1:55a6170b404f 625 /*
nexpaq 1:55a6170b404f 626 * Write the ECParameters record corresponding to a group (RFC 4492)
nexpaq 1:55a6170b404f 627 */
nexpaq 1:55a6170b404f 628 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
nexpaq 1:55a6170b404f 629 unsigned char *buf, size_t blen )
nexpaq 1:55a6170b404f 630 {
nexpaq 1:55a6170b404f 631 const mbedtls_ecp_curve_info *curve_info;
nexpaq 1:55a6170b404f 632
nexpaq 1:55a6170b404f 633 if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
nexpaq 1:55a6170b404f 634 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 635
nexpaq 1:55a6170b404f 636 /*
nexpaq 1:55a6170b404f 637 * We are going to write 3 bytes (see below)
nexpaq 1:55a6170b404f 638 */
nexpaq 1:55a6170b404f 639 *olen = 3;
nexpaq 1:55a6170b404f 640 if( blen < *olen )
nexpaq 1:55a6170b404f 641 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
nexpaq 1:55a6170b404f 642
nexpaq 1:55a6170b404f 643 /*
nexpaq 1:55a6170b404f 644 * First byte is curve_type, always named_curve
nexpaq 1:55a6170b404f 645 */
nexpaq 1:55a6170b404f 646 *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
nexpaq 1:55a6170b404f 647
nexpaq 1:55a6170b404f 648 /*
nexpaq 1:55a6170b404f 649 * Next two bytes are the namedcurve value
nexpaq 1:55a6170b404f 650 */
nexpaq 1:55a6170b404f 651 buf[0] = curve_info->tls_id >> 8;
nexpaq 1:55a6170b404f 652 buf[1] = curve_info->tls_id & 0xFF;
nexpaq 1:55a6170b404f 653
nexpaq 1:55a6170b404f 654 return( 0 );
nexpaq 1:55a6170b404f 655 }
nexpaq 1:55a6170b404f 656
nexpaq 1:55a6170b404f 657 /*
nexpaq 1:55a6170b404f 658 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
nexpaq 1:55a6170b404f 659 * See the documentation of struct mbedtls_ecp_group.
nexpaq 1:55a6170b404f 660 *
nexpaq 1:55a6170b404f 661 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
nexpaq 1:55a6170b404f 662 */
nexpaq 1:55a6170b404f 663 static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
nexpaq 1:55a6170b404f 664 {
nexpaq 1:55a6170b404f 665 int ret;
nexpaq 1:55a6170b404f 666
nexpaq 1:55a6170b404f 667 if( grp->modp == NULL )
nexpaq 1:55a6170b404f 668 return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) );
nexpaq 1:55a6170b404f 669
nexpaq 1:55a6170b404f 670 /* N->s < 0 is a much faster test, which fails only if N is 0 */
nexpaq 1:55a6170b404f 671 if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) ||
nexpaq 1:55a6170b404f 672 mbedtls_mpi_bitlen( N ) > 2 * grp->pbits )
nexpaq 1:55a6170b404f 673 {
nexpaq 1:55a6170b404f 674 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 675 }
nexpaq 1:55a6170b404f 676
nexpaq 1:55a6170b404f 677 MBEDTLS_MPI_CHK( grp->modp( N ) );
nexpaq 1:55a6170b404f 678
nexpaq 1:55a6170b404f 679 /* N->s < 0 is a much faster test, which fails only if N is 0 */
nexpaq 1:55a6170b404f 680 while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 )
nexpaq 1:55a6170b404f 681 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) );
nexpaq 1:55a6170b404f 682
nexpaq 1:55a6170b404f 683 while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 )
nexpaq 1:55a6170b404f 684 /* we known P, N and the result are positive */
nexpaq 1:55a6170b404f 685 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) );
nexpaq 1:55a6170b404f 686
nexpaq 1:55a6170b404f 687 cleanup:
nexpaq 1:55a6170b404f 688 return( ret );
nexpaq 1:55a6170b404f 689 }
nexpaq 1:55a6170b404f 690
nexpaq 1:55a6170b404f 691 /*
nexpaq 1:55a6170b404f 692 * Fast mod-p functions expect their argument to be in the 0..p^2 range.
nexpaq 1:55a6170b404f 693 *
nexpaq 1:55a6170b404f 694 * In order to guarantee that, we need to ensure that operands of
nexpaq 1:55a6170b404f 695 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will
nexpaq 1:55a6170b404f 696 * bring the result back to this range.
nexpaq 1:55a6170b404f 697 *
nexpaq 1:55a6170b404f 698 * The following macros are shortcuts for doing that.
nexpaq 1:55a6170b404f 699 */
nexpaq 1:55a6170b404f 700
nexpaq 1:55a6170b404f 701 /*
nexpaq 1:55a6170b404f 702 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
nexpaq 1:55a6170b404f 703 */
nexpaq 1:55a6170b404f 704 #if defined(MBEDTLS_SELF_TEST)
nexpaq 1:55a6170b404f 705 #define INC_MUL_COUNT mul_count++;
nexpaq 1:55a6170b404f 706 #else
nexpaq 1:55a6170b404f 707 #define INC_MUL_COUNT
nexpaq 1:55a6170b404f 708 #endif
nexpaq 1:55a6170b404f 709
nexpaq 1:55a6170b404f 710 #define MOD_MUL( N ) do { MBEDTLS_MPI_CHK( ecp_modp( &N, grp ) ); INC_MUL_COUNT } \
nexpaq 1:55a6170b404f 711 while( 0 )
nexpaq 1:55a6170b404f 712
nexpaq 1:55a6170b404f 713 /*
nexpaq 1:55a6170b404f 714 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
nexpaq 1:55a6170b404f 715 * N->s < 0 is a very fast test, which fails only if N is 0
nexpaq 1:55a6170b404f 716 */
nexpaq 1:55a6170b404f 717 #define MOD_SUB( N ) \
nexpaq 1:55a6170b404f 718 while( N.s < 0 && mbedtls_mpi_cmp_int( &N, 0 ) != 0 ) \
nexpaq 1:55a6170b404f 719 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &N, &N, &grp->P ) )
nexpaq 1:55a6170b404f 720
nexpaq 1:55a6170b404f 721 /*
nexpaq 1:55a6170b404f 722 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
nexpaq 1:55a6170b404f 723 * We known P, N and the result are positive, so sub_abs is correct, and
nexpaq 1:55a6170b404f 724 * a bit faster.
nexpaq 1:55a6170b404f 725 */
nexpaq 1:55a6170b404f 726 #define MOD_ADD( N ) \
nexpaq 1:55a6170b404f 727 while( mbedtls_mpi_cmp_mpi( &N, &grp->P ) >= 0 ) \
nexpaq 1:55a6170b404f 728 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &N, &N, &grp->P ) )
nexpaq 1:55a6170b404f 729
nexpaq 1:55a6170b404f 730 #if defined(ECP_SHORTWEIERSTRASS)
nexpaq 1:55a6170b404f 731 /*
nexpaq 1:55a6170b404f 732 * For curves in short Weierstrass form, we do all the internal operations in
nexpaq 1:55a6170b404f 733 * Jacobian coordinates.
nexpaq 1:55a6170b404f 734 *
nexpaq 1:55a6170b404f 735 * For multiplication, we'll use a comb method with coutermeasueres against
nexpaq 1:55a6170b404f 736 * SPA, hence timing attacks.
nexpaq 1:55a6170b404f 737 */
nexpaq 1:55a6170b404f 738
nexpaq 1:55a6170b404f 739 /*
nexpaq 1:55a6170b404f 740 * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
nexpaq 1:55a6170b404f 741 * Cost: 1N := 1I + 3M + 1S
nexpaq 1:55a6170b404f 742 */
nexpaq 1:55a6170b404f 743 static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
nexpaq 1:55a6170b404f 744 {
nexpaq 1:55a6170b404f 745 int ret;
nexpaq 1:55a6170b404f 746 mbedtls_mpi Zi, ZZi;
nexpaq 1:55a6170b404f 747
nexpaq 1:55a6170b404f 748 if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
nexpaq 1:55a6170b404f 749 return( 0 );
nexpaq 1:55a6170b404f 750
nexpaq 1:55a6170b404f 751 mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
nexpaq 1:55a6170b404f 752
nexpaq 1:55a6170b404f 753 /*
nexpaq 1:55a6170b404f 754 * X = X / Z^2 mod p
nexpaq 1:55a6170b404f 755 */
nexpaq 1:55a6170b404f 756 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
nexpaq 1:55a6170b404f 757 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
nexpaq 1:55a6170b404f 758 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ZZi ) ); MOD_MUL( pt->X );
nexpaq 1:55a6170b404f 759
nexpaq 1:55a6170b404f 760 /*
nexpaq 1:55a6170b404f 761 * Y = Y / Z^3 mod p
nexpaq 1:55a6170b404f 762 */
nexpaq 1:55a6170b404f 763 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ZZi ) ); MOD_MUL( pt->Y );
nexpaq 1:55a6170b404f 764 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &Zi ) ); MOD_MUL( pt->Y );
nexpaq 1:55a6170b404f 765
nexpaq 1:55a6170b404f 766 /*
nexpaq 1:55a6170b404f 767 * Z = 1
nexpaq 1:55a6170b404f 768 */
nexpaq 1:55a6170b404f 769 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
nexpaq 1:55a6170b404f 770
nexpaq 1:55a6170b404f 771 cleanup:
nexpaq 1:55a6170b404f 772
nexpaq 1:55a6170b404f 773 mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
nexpaq 1:55a6170b404f 774
nexpaq 1:55a6170b404f 775 return( ret );
nexpaq 1:55a6170b404f 776 }
nexpaq 1:55a6170b404f 777
nexpaq 1:55a6170b404f 778 /*
nexpaq 1:55a6170b404f 779 * Normalize jacobian coordinates of an array of (pointers to) points,
nexpaq 1:55a6170b404f 780 * using Montgomery's trick to perform only one inversion mod P.
nexpaq 1:55a6170b404f 781 * (See for example Cohen's "A Course in Computational Algebraic Number
nexpaq 1:55a6170b404f 782 * Theory", Algorithm 10.3.4.)
nexpaq 1:55a6170b404f 783 *
nexpaq 1:55a6170b404f 784 * Warning: fails (returning an error) if one of the points is zero!
nexpaq 1:55a6170b404f 785 * This should never happen, see choice of w in ecp_mul_comb().
nexpaq 1:55a6170b404f 786 *
nexpaq 1:55a6170b404f 787 * Cost: 1N(t) := 1I + (6t - 3)M + 1S
nexpaq 1:55a6170b404f 788 */
nexpaq 1:55a6170b404f 789 static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
nexpaq 1:55a6170b404f 790 mbedtls_ecp_point *T[], size_t t_len )
nexpaq 1:55a6170b404f 791 {
nexpaq 1:55a6170b404f 792 int ret;
nexpaq 1:55a6170b404f 793 size_t i;
nexpaq 1:55a6170b404f 794 mbedtls_mpi *c, u, Zi, ZZi;
nexpaq 1:55a6170b404f 795
nexpaq 1:55a6170b404f 796 if( t_len < 2 )
nexpaq 1:55a6170b404f 797 return( ecp_normalize_jac( grp, *T ) );
nexpaq 1:55a6170b404f 798
nexpaq 1:55a6170b404f 799 if( ( c = mbedtls_calloc( t_len, sizeof( mbedtls_mpi ) ) ) == NULL )
nexpaq 1:55a6170b404f 800 return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
nexpaq 1:55a6170b404f 801
nexpaq 1:55a6170b404f 802 mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
nexpaq 1:55a6170b404f 803
nexpaq 1:55a6170b404f 804 /*
nexpaq 1:55a6170b404f 805 * c[i] = Z_0 * ... * Z_i
nexpaq 1:55a6170b404f 806 */
nexpaq 1:55a6170b404f 807 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
nexpaq 1:55a6170b404f 808 for( i = 1; i < t_len; i++ )
nexpaq 1:55a6170b404f 809 {
nexpaq 1:55a6170b404f 810 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &c[i], &c[i-1], &T[i]->Z ) );
nexpaq 1:55a6170b404f 811 MOD_MUL( c[i] );
nexpaq 1:55a6170b404f 812 }
nexpaq 1:55a6170b404f 813
nexpaq 1:55a6170b404f 814 /*
nexpaq 1:55a6170b404f 815 * u = 1 / (Z_0 * ... * Z_n) mod P
nexpaq 1:55a6170b404f 816 */
nexpaq 1:55a6170b404f 817 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[t_len-1], &grp->P ) );
nexpaq 1:55a6170b404f 818
nexpaq 1:55a6170b404f 819 for( i = t_len - 1; ; i-- )
nexpaq 1:55a6170b404f 820 {
nexpaq 1:55a6170b404f 821 /*
nexpaq 1:55a6170b404f 822 * Zi = 1 / Z_i mod p
nexpaq 1:55a6170b404f 823 * u = 1 / (Z_0 * ... * Z_i) mod P
nexpaq 1:55a6170b404f 824 */
nexpaq 1:55a6170b404f 825 if( i == 0 ) {
nexpaq 1:55a6170b404f 826 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
nexpaq 1:55a6170b404f 827 }
nexpaq 1:55a6170b404f 828 else
nexpaq 1:55a6170b404f 829 {
nexpaq 1:55a6170b404f 830 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Zi, &u, &c[i-1] ) ); MOD_MUL( Zi );
nexpaq 1:55a6170b404f 831 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u, &u, &T[i]->Z ) ); MOD_MUL( u );
nexpaq 1:55a6170b404f 832 }
nexpaq 1:55a6170b404f 833
nexpaq 1:55a6170b404f 834 /*
nexpaq 1:55a6170b404f 835 * proceed as in normalize()
nexpaq 1:55a6170b404f 836 */
nexpaq 1:55a6170b404f 837 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
nexpaq 1:55a6170b404f 838 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->X, &T[i]->X, &ZZi ) ); MOD_MUL( T[i]->X );
nexpaq 1:55a6170b404f 839 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &ZZi ) ); MOD_MUL( T[i]->Y );
nexpaq 1:55a6170b404f 840 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &Zi ) ); MOD_MUL( T[i]->Y );
nexpaq 1:55a6170b404f 841
nexpaq 1:55a6170b404f 842 /*
nexpaq 1:55a6170b404f 843 * Post-precessing: reclaim some memory by shrinking coordinates
nexpaq 1:55a6170b404f 844 * - not storing Z (always 1)
nexpaq 1:55a6170b404f 845 * - shrinking other coordinates, but still keeping the same number of
nexpaq 1:55a6170b404f 846 * limbs as P, as otherwise it will too likely be regrown too fast.
nexpaq 1:55a6170b404f 847 */
nexpaq 1:55a6170b404f 848 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
nexpaq 1:55a6170b404f 849 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
nexpaq 1:55a6170b404f 850 mbedtls_mpi_free( &T[i]->Z );
nexpaq 1:55a6170b404f 851
nexpaq 1:55a6170b404f 852 if( i == 0 )
nexpaq 1:55a6170b404f 853 break;
nexpaq 1:55a6170b404f 854 }
nexpaq 1:55a6170b404f 855
nexpaq 1:55a6170b404f 856 cleanup:
nexpaq 1:55a6170b404f 857
nexpaq 1:55a6170b404f 858 mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
nexpaq 1:55a6170b404f 859 for( i = 0; i < t_len; i++ )
nexpaq 1:55a6170b404f 860 mbedtls_mpi_free( &c[i] );
nexpaq 1:55a6170b404f 861 mbedtls_free( c );
nexpaq 1:55a6170b404f 862
nexpaq 1:55a6170b404f 863 return( ret );
nexpaq 1:55a6170b404f 864 }
nexpaq 1:55a6170b404f 865
nexpaq 1:55a6170b404f 866 /*
nexpaq 1:55a6170b404f 867 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
nexpaq 1:55a6170b404f 868 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
nexpaq 1:55a6170b404f 869 */
nexpaq 1:55a6170b404f 870 static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
nexpaq 1:55a6170b404f 871 mbedtls_ecp_point *Q,
nexpaq 1:55a6170b404f 872 unsigned char inv )
nexpaq 1:55a6170b404f 873 {
nexpaq 1:55a6170b404f 874 int ret;
nexpaq 1:55a6170b404f 875 unsigned char nonzero;
nexpaq 1:55a6170b404f 876 mbedtls_mpi mQY;
nexpaq 1:55a6170b404f 877
nexpaq 1:55a6170b404f 878 mbedtls_mpi_init( &mQY );
nexpaq 1:55a6170b404f 879
nexpaq 1:55a6170b404f 880 /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
nexpaq 1:55a6170b404f 881 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
nexpaq 1:55a6170b404f 882 nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
nexpaq 1:55a6170b404f 883 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
nexpaq 1:55a6170b404f 884
nexpaq 1:55a6170b404f 885 cleanup:
nexpaq 1:55a6170b404f 886 mbedtls_mpi_free( &mQY );
nexpaq 1:55a6170b404f 887
nexpaq 1:55a6170b404f 888 return( ret );
nexpaq 1:55a6170b404f 889 }
nexpaq 1:55a6170b404f 890
nexpaq 1:55a6170b404f 891 /*
nexpaq 1:55a6170b404f 892 * Point doubling R = 2 P, Jacobian coordinates
nexpaq 1:55a6170b404f 893 *
nexpaq 1:55a6170b404f 894 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
nexpaq 1:55a6170b404f 895 *
nexpaq 1:55a6170b404f 896 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
nexpaq 1:55a6170b404f 897 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
nexpaq 1:55a6170b404f 898 *
nexpaq 1:55a6170b404f 899 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
nexpaq 1:55a6170b404f 900 *
nexpaq 1:55a6170b404f 901 * Cost: 1D := 3M + 4S (A == 0)
nexpaq 1:55a6170b404f 902 * 4M + 4S (A == -3)
nexpaq 1:55a6170b404f 903 * 3M + 6S + 1a otherwise
nexpaq 1:55a6170b404f 904 */
nexpaq 1:55a6170b404f 905 static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
nexpaq 1:55a6170b404f 906 const mbedtls_ecp_point *P )
nexpaq 1:55a6170b404f 907 {
nexpaq 1:55a6170b404f 908 int ret;
nexpaq 1:55a6170b404f 909 mbedtls_mpi M, S, T, U;
nexpaq 1:55a6170b404f 910
nexpaq 1:55a6170b404f 911 #if defined(MBEDTLS_SELF_TEST)
nexpaq 1:55a6170b404f 912 dbl_count++;
nexpaq 1:55a6170b404f 913 #endif
nexpaq 1:55a6170b404f 914
nexpaq 1:55a6170b404f 915 mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
nexpaq 1:55a6170b404f 916
nexpaq 1:55a6170b404f 917 /* Special case for A = -3 */
nexpaq 1:55a6170b404f 918 if( grp->A.p == NULL )
nexpaq 1:55a6170b404f 919 {
nexpaq 1:55a6170b404f 920 /* M = 3(X + Z^2)(X - Z^2) */
nexpaq 1:55a6170b404f 921 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
nexpaq 1:55a6170b404f 922 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &P->X, &S ) ); MOD_ADD( T );
nexpaq 1:55a6170b404f 923 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U, &P->X, &S ) ); MOD_SUB( U );
nexpaq 1:55a6170b404f 924 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &U ) ); MOD_MUL( S );
nexpaq 1:55a6170b404f 925 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
nexpaq 1:55a6170b404f 926 }
nexpaq 1:55a6170b404f 927 else
nexpaq 1:55a6170b404f 928 {
nexpaq 1:55a6170b404f 929 /* M = 3.X^2 */
nexpaq 1:55a6170b404f 930 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &P->X ) ); MOD_MUL( S );
nexpaq 1:55a6170b404f 931 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
nexpaq 1:55a6170b404f 932
nexpaq 1:55a6170b404f 933 /* Optimize away for "koblitz" curves with A = 0 */
nexpaq 1:55a6170b404f 934 if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
nexpaq 1:55a6170b404f 935 {
nexpaq 1:55a6170b404f 936 /* M += A.Z^4 */
nexpaq 1:55a6170b404f 937 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
nexpaq 1:55a6170b404f 938 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &S, &S ) ); MOD_MUL( T );
nexpaq 1:55a6170b404f 939 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &grp->A ) ); MOD_MUL( S );
nexpaq 1:55a6170b404f 940 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &S ) ); MOD_ADD( M );
nexpaq 1:55a6170b404f 941 }
nexpaq 1:55a6170b404f 942 }
nexpaq 1:55a6170b404f 943
nexpaq 1:55a6170b404f 944 /* S = 4.X.Y^2 */
nexpaq 1:55a6170b404f 945 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &P->Y, &P->Y ) ); MOD_MUL( T );
nexpaq 1:55a6170b404f 946 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T, 1 ) ); MOD_ADD( T );
nexpaq 1:55a6170b404f 947 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &T ) ); MOD_MUL( S );
nexpaq 1:55a6170b404f 948 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &S, 1 ) ); MOD_ADD( S );
nexpaq 1:55a6170b404f 949
nexpaq 1:55a6170b404f 950 /* U = 8.Y^4 */
nexpaq 1:55a6170b404f 951 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &T, &T ) ); MOD_MUL( U );
nexpaq 1:55a6170b404f 952 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
nexpaq 1:55a6170b404f 953
nexpaq 1:55a6170b404f 954 /* T = M^2 - 2.S */
nexpaq 1:55a6170b404f 955 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &M, &M ) ); MOD_MUL( T );
nexpaq 1:55a6170b404f 956 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
nexpaq 1:55a6170b404f 957 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
nexpaq 1:55a6170b404f 958
nexpaq 1:55a6170b404f 959 /* S = M(S - T) - U */
nexpaq 1:55a6170b404f 960 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &T ) ); MOD_SUB( S );
nexpaq 1:55a6170b404f 961 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &S, &M ) ); MOD_MUL( S );
nexpaq 1:55a6170b404f 962 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &U ) ); MOD_SUB( S );
nexpaq 1:55a6170b404f 963
nexpaq 1:55a6170b404f 964 /* U = 2.Y.Z */
nexpaq 1:55a6170b404f 965 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &P->Y, &P->Z ) ); MOD_MUL( U );
nexpaq 1:55a6170b404f 966 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
nexpaq 1:55a6170b404f 967
nexpaq 1:55a6170b404f 968 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
nexpaq 1:55a6170b404f 969 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
nexpaq 1:55a6170b404f 970 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
nexpaq 1:55a6170b404f 971
nexpaq 1:55a6170b404f 972 cleanup:
nexpaq 1:55a6170b404f 973 mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
nexpaq 1:55a6170b404f 974
nexpaq 1:55a6170b404f 975 return( ret );
nexpaq 1:55a6170b404f 976 }
nexpaq 1:55a6170b404f 977
nexpaq 1:55a6170b404f 978 /*
nexpaq 1:55a6170b404f 979 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
nexpaq 1:55a6170b404f 980 *
nexpaq 1:55a6170b404f 981 * The coordinates of Q must be normalized (= affine),
nexpaq 1:55a6170b404f 982 * but those of P don't need to. R is not normalized.
nexpaq 1:55a6170b404f 983 *
nexpaq 1:55a6170b404f 984 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
nexpaq 1:55a6170b404f 985 * None of these cases can happen as intermediate step in ecp_mul_comb():
nexpaq 1:55a6170b404f 986 * - at each step, P, Q and R are multiples of the base point, the factor
nexpaq 1:55a6170b404f 987 * being less than its order, so none of them is zero;
nexpaq 1:55a6170b404f 988 * - Q is an odd multiple of the base point, P an even multiple,
nexpaq 1:55a6170b404f 989 * due to the choice of precomputed points in the modified comb method.
nexpaq 1:55a6170b404f 990 * So branches for these cases do not leak secret information.
nexpaq 1:55a6170b404f 991 *
nexpaq 1:55a6170b404f 992 * We accept Q->Z being unset (saving memory in tables) as meaning 1.
nexpaq 1:55a6170b404f 993 *
nexpaq 1:55a6170b404f 994 * Cost: 1A := 8M + 3S
nexpaq 1:55a6170b404f 995 */
nexpaq 1:55a6170b404f 996 static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
nexpaq 1:55a6170b404f 997 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
nexpaq 1:55a6170b404f 998 {
nexpaq 1:55a6170b404f 999 int ret;
nexpaq 1:55a6170b404f 1000 mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
nexpaq 1:55a6170b404f 1001
nexpaq 1:55a6170b404f 1002 #if defined(MBEDTLS_SELF_TEST)
nexpaq 1:55a6170b404f 1003 add_count++;
nexpaq 1:55a6170b404f 1004 #endif
nexpaq 1:55a6170b404f 1005
nexpaq 1:55a6170b404f 1006 /*
nexpaq 1:55a6170b404f 1007 * Trivial cases: P == 0 or Q == 0 (case 1)
nexpaq 1:55a6170b404f 1008 */
nexpaq 1:55a6170b404f 1009 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
nexpaq 1:55a6170b404f 1010 return( mbedtls_ecp_copy( R, Q ) );
nexpaq 1:55a6170b404f 1011
nexpaq 1:55a6170b404f 1012 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
nexpaq 1:55a6170b404f 1013 return( mbedtls_ecp_copy( R, P ) );
nexpaq 1:55a6170b404f 1014
nexpaq 1:55a6170b404f 1015 /*
nexpaq 1:55a6170b404f 1016 * Make sure Q coordinates are normalized
nexpaq 1:55a6170b404f 1017 */
nexpaq 1:55a6170b404f 1018 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
nexpaq 1:55a6170b404f 1019 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 1020
nexpaq 1:55a6170b404f 1021 mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
nexpaq 1:55a6170b404f 1022 mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
nexpaq 1:55a6170b404f 1023
nexpaq 1:55a6170b404f 1024 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &P->Z, &P->Z ) ); MOD_MUL( T1 );
nexpaq 1:55a6170b404f 1025 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T1, &P->Z ) ); MOD_MUL( T2 );
nexpaq 1:55a6170b404f 1026 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T1, &Q->X ) ); MOD_MUL( T1 );
nexpaq 1:55a6170b404f 1027 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T2, &Q->Y ) ); MOD_MUL( T2 );
nexpaq 1:55a6170b404f 1028 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T1, &T1, &P->X ) ); MOD_SUB( T1 );
nexpaq 1:55a6170b404f 1029 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T2, &T2, &P->Y ) ); MOD_SUB( T2 );
nexpaq 1:55a6170b404f 1030
nexpaq 1:55a6170b404f 1031 /* Special cases (2) and (3) */
nexpaq 1:55a6170b404f 1032 if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
nexpaq 1:55a6170b404f 1033 {
nexpaq 1:55a6170b404f 1034 if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
nexpaq 1:55a6170b404f 1035 {
nexpaq 1:55a6170b404f 1036 ret = ecp_double_jac( grp, R, P );
nexpaq 1:55a6170b404f 1037 goto cleanup;
nexpaq 1:55a6170b404f 1038 }
nexpaq 1:55a6170b404f 1039 else
nexpaq 1:55a6170b404f 1040 {
nexpaq 1:55a6170b404f 1041 ret = mbedtls_ecp_set_zero( R );
nexpaq 1:55a6170b404f 1042 goto cleanup;
nexpaq 1:55a6170b404f 1043 }
nexpaq 1:55a6170b404f 1044 }
nexpaq 1:55a6170b404f 1045
nexpaq 1:55a6170b404f 1046 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Z, &P->Z, &T1 ) ); MOD_MUL( Z );
nexpaq 1:55a6170b404f 1047 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T1, &T1 ) ); MOD_MUL( T3 );
nexpaq 1:55a6170b404f 1048 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T3, &T1 ) ); MOD_MUL( T4 );
nexpaq 1:55a6170b404f 1049 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &P->X ) ); MOD_MUL( T3 );
nexpaq 1:55a6170b404f 1050 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T3, 2 ) ); MOD_ADD( T1 );
nexpaq 1:55a6170b404f 1051 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &T2, &T2 ) ); MOD_MUL( X );
nexpaq 1:55a6170b404f 1052 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) ); MOD_SUB( X );
nexpaq 1:55a6170b404f 1053 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T4 ) ); MOD_SUB( X );
nexpaq 1:55a6170b404f 1054 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T3, &T3, &X ) ); MOD_SUB( T3 );
nexpaq 1:55a6170b404f 1055 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &T2 ) ); MOD_MUL( T3 );
nexpaq 1:55a6170b404f 1056 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T4, &P->Y ) ); MOD_MUL( T4 );
nexpaq 1:55a6170b404f 1057 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &Y, &T3, &T4 ) ); MOD_SUB( Y );
nexpaq 1:55a6170b404f 1058
nexpaq 1:55a6170b404f 1059 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
nexpaq 1:55a6170b404f 1060 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
nexpaq 1:55a6170b404f 1061 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
nexpaq 1:55a6170b404f 1062
nexpaq 1:55a6170b404f 1063 cleanup:
nexpaq 1:55a6170b404f 1064
nexpaq 1:55a6170b404f 1065 mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
nexpaq 1:55a6170b404f 1066 mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
nexpaq 1:55a6170b404f 1067
nexpaq 1:55a6170b404f 1068 return( ret );
nexpaq 1:55a6170b404f 1069 }
nexpaq 1:55a6170b404f 1070
nexpaq 1:55a6170b404f 1071 /*
nexpaq 1:55a6170b404f 1072 * Randomize jacobian coordinates:
nexpaq 1:55a6170b404f 1073 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
nexpaq 1:55a6170b404f 1074 * This is sort of the reverse operation of ecp_normalize_jac().
nexpaq 1:55a6170b404f 1075 *
nexpaq 1:55a6170b404f 1076 * This countermeasure was first suggested in [2].
nexpaq 1:55a6170b404f 1077 */
nexpaq 1:55a6170b404f 1078 static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
nexpaq 1:55a6170b404f 1079 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
nexpaq 1:55a6170b404f 1080 {
nexpaq 1:55a6170b404f 1081 int ret;
nexpaq 1:55a6170b404f 1082 mbedtls_mpi l, ll;
nexpaq 1:55a6170b404f 1083 size_t p_size = ( grp->pbits + 7 ) / 8;
nexpaq 1:55a6170b404f 1084 int count = 0;
nexpaq 1:55a6170b404f 1085
nexpaq 1:55a6170b404f 1086 mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
nexpaq 1:55a6170b404f 1087
nexpaq 1:55a6170b404f 1088 /* Generate l such that 1 < l < p */
nexpaq 1:55a6170b404f 1089 do
nexpaq 1:55a6170b404f 1090 {
nexpaq 1:55a6170b404f 1091 mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng );
nexpaq 1:55a6170b404f 1092
nexpaq 1:55a6170b404f 1093 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
nexpaq 1:55a6170b404f 1094 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
nexpaq 1:55a6170b404f 1095
nexpaq 1:55a6170b404f 1096 if( count++ > 10 )
nexpaq 1:55a6170b404f 1097 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
nexpaq 1:55a6170b404f 1098 }
nexpaq 1:55a6170b404f 1099 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
nexpaq 1:55a6170b404f 1100
nexpaq 1:55a6170b404f 1101 /* Z = l * Z */
nexpaq 1:55a6170b404f 1102 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Z, &pt->Z, &l ) ); MOD_MUL( pt->Z );
nexpaq 1:55a6170b404f 1103
nexpaq 1:55a6170b404f 1104 /* X = l^2 * X */
nexpaq 1:55a6170b404f 1105 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &l, &l ) ); MOD_MUL( ll );
nexpaq 1:55a6170b404f 1106 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ll ) ); MOD_MUL( pt->X );
nexpaq 1:55a6170b404f 1107
nexpaq 1:55a6170b404f 1108 /* Y = l^3 * Y */
nexpaq 1:55a6170b404f 1109 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &ll, &l ) ); MOD_MUL( ll );
nexpaq 1:55a6170b404f 1110 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ll ) ); MOD_MUL( pt->Y );
nexpaq 1:55a6170b404f 1111
nexpaq 1:55a6170b404f 1112 cleanup:
nexpaq 1:55a6170b404f 1113 mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
nexpaq 1:55a6170b404f 1114
nexpaq 1:55a6170b404f 1115 return( ret );
nexpaq 1:55a6170b404f 1116 }
nexpaq 1:55a6170b404f 1117
nexpaq 1:55a6170b404f 1118 /*
nexpaq 1:55a6170b404f 1119 * Check and define parameters used by the comb method (see below for details)
nexpaq 1:55a6170b404f 1120 */
nexpaq 1:55a6170b404f 1121 #if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
nexpaq 1:55a6170b404f 1122 #error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
nexpaq 1:55a6170b404f 1123 #endif
nexpaq 1:55a6170b404f 1124
nexpaq 1:55a6170b404f 1125 /* d = ceil( n / w ) */
nexpaq 1:55a6170b404f 1126 #define COMB_MAX_D ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2
nexpaq 1:55a6170b404f 1127
nexpaq 1:55a6170b404f 1128 /* number of precomputed points */
nexpaq 1:55a6170b404f 1129 #define COMB_MAX_PRE ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
nexpaq 1:55a6170b404f 1130
nexpaq 1:55a6170b404f 1131 /*
nexpaq 1:55a6170b404f 1132 * Compute the representation of m that will be used with our comb method.
nexpaq 1:55a6170b404f 1133 *
nexpaq 1:55a6170b404f 1134 * The basic comb method is described in GECC 3.44 for example. We use a
nexpaq 1:55a6170b404f 1135 * modified version that provides resistance to SPA by avoiding zero
nexpaq 1:55a6170b404f 1136 * digits in the representation as in [3]. We modify the method further by
nexpaq 1:55a6170b404f 1137 * requiring that all K_i be odd, which has the small cost that our
nexpaq 1:55a6170b404f 1138 * representation uses one more K_i, due to carries.
nexpaq 1:55a6170b404f 1139 *
nexpaq 1:55a6170b404f 1140 * Also, for the sake of compactness, only the seven low-order bits of x[i]
nexpaq 1:55a6170b404f 1141 * are used to represent K_i, and the msb of x[i] encodes the the sign (s_i in
nexpaq 1:55a6170b404f 1142 * the paper): it is set if and only if if s_i == -1;
nexpaq 1:55a6170b404f 1143 *
nexpaq 1:55a6170b404f 1144 * Calling conventions:
nexpaq 1:55a6170b404f 1145 * - x is an array of size d + 1
nexpaq 1:55a6170b404f 1146 * - w is the size, ie number of teeth, of the comb, and must be between
nexpaq 1:55a6170b404f 1147 * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
nexpaq 1:55a6170b404f 1148 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
nexpaq 1:55a6170b404f 1149 * (the result will be incorrect if these assumptions are not satisfied)
nexpaq 1:55a6170b404f 1150 */
nexpaq 1:55a6170b404f 1151 static void ecp_comb_fixed( unsigned char x[], size_t d,
nexpaq 1:55a6170b404f 1152 unsigned char w, const mbedtls_mpi *m )
nexpaq 1:55a6170b404f 1153 {
nexpaq 1:55a6170b404f 1154 size_t i, j;
nexpaq 1:55a6170b404f 1155 unsigned char c, cc, adjust;
nexpaq 1:55a6170b404f 1156
nexpaq 1:55a6170b404f 1157 memset( x, 0, d+1 );
nexpaq 1:55a6170b404f 1158
nexpaq 1:55a6170b404f 1159 /* First get the classical comb values (except for x_d = 0) */
nexpaq 1:55a6170b404f 1160 for( i = 0; i < d; i++ )
nexpaq 1:55a6170b404f 1161 for( j = 0; j < w; j++ )
nexpaq 1:55a6170b404f 1162 x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j;
nexpaq 1:55a6170b404f 1163
nexpaq 1:55a6170b404f 1164 /* Now make sure x_1 .. x_d are odd */
nexpaq 1:55a6170b404f 1165 c = 0;
nexpaq 1:55a6170b404f 1166 for( i = 1; i <= d; i++ )
nexpaq 1:55a6170b404f 1167 {
nexpaq 1:55a6170b404f 1168 /* Add carry and update it */
nexpaq 1:55a6170b404f 1169 cc = x[i] & c;
nexpaq 1:55a6170b404f 1170 x[i] = x[i] ^ c;
nexpaq 1:55a6170b404f 1171 c = cc;
nexpaq 1:55a6170b404f 1172
nexpaq 1:55a6170b404f 1173 /* Adjust if needed, avoiding branches */
nexpaq 1:55a6170b404f 1174 adjust = 1 - ( x[i] & 0x01 );
nexpaq 1:55a6170b404f 1175 c |= x[i] & ( x[i-1] * adjust );
nexpaq 1:55a6170b404f 1176 x[i] = x[i] ^ ( x[i-1] * adjust );
nexpaq 1:55a6170b404f 1177 x[i-1] |= adjust << 7;
nexpaq 1:55a6170b404f 1178 }
nexpaq 1:55a6170b404f 1179 }
nexpaq 1:55a6170b404f 1180
nexpaq 1:55a6170b404f 1181 /*
nexpaq 1:55a6170b404f 1182 * Precompute points for the comb method
nexpaq 1:55a6170b404f 1183 *
nexpaq 1:55a6170b404f 1184 * If i = i_{w-1} ... i_1 is the binary representation of i, then
nexpaq 1:55a6170b404f 1185 * T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P
nexpaq 1:55a6170b404f 1186 *
nexpaq 1:55a6170b404f 1187 * T must be able to hold 2^{w - 1} elements
nexpaq 1:55a6170b404f 1188 *
nexpaq 1:55a6170b404f 1189 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
nexpaq 1:55a6170b404f 1190 */
nexpaq 1:55a6170b404f 1191 static int ecp_precompute_comb( const mbedtls_ecp_group *grp,
nexpaq 1:55a6170b404f 1192 mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
nexpaq 1:55a6170b404f 1193 unsigned char w, size_t d )
nexpaq 1:55a6170b404f 1194 {
nexpaq 1:55a6170b404f 1195 int ret;
nexpaq 1:55a6170b404f 1196 unsigned char i, k;
nexpaq 1:55a6170b404f 1197 size_t j;
nexpaq 1:55a6170b404f 1198 mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
nexpaq 1:55a6170b404f 1199
nexpaq 1:55a6170b404f 1200 /*
nexpaq 1:55a6170b404f 1201 * Set T[0] = P and
nexpaq 1:55a6170b404f 1202 * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
nexpaq 1:55a6170b404f 1203 */
nexpaq 1:55a6170b404f 1204 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
nexpaq 1:55a6170b404f 1205
nexpaq 1:55a6170b404f 1206 k = 0;
nexpaq 1:55a6170b404f 1207 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
nexpaq 1:55a6170b404f 1208 {
nexpaq 1:55a6170b404f 1209 cur = T + i;
nexpaq 1:55a6170b404f 1210 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
nexpaq 1:55a6170b404f 1211 for( j = 0; j < d; j++ )
nexpaq 1:55a6170b404f 1212 MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
nexpaq 1:55a6170b404f 1213
nexpaq 1:55a6170b404f 1214 TT[k++] = cur;
nexpaq 1:55a6170b404f 1215 }
nexpaq 1:55a6170b404f 1216
nexpaq 1:55a6170b404f 1217 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
nexpaq 1:55a6170b404f 1218
nexpaq 1:55a6170b404f 1219 /*
nexpaq 1:55a6170b404f 1220 * Compute the remaining ones using the minimal number of additions
nexpaq 1:55a6170b404f 1221 * Be careful to update T[2^l] only after using it!
nexpaq 1:55a6170b404f 1222 */
nexpaq 1:55a6170b404f 1223 k = 0;
nexpaq 1:55a6170b404f 1224 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
nexpaq 1:55a6170b404f 1225 {
nexpaq 1:55a6170b404f 1226 j = i;
nexpaq 1:55a6170b404f 1227 while( j-- )
nexpaq 1:55a6170b404f 1228 {
nexpaq 1:55a6170b404f 1229 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
nexpaq 1:55a6170b404f 1230 TT[k++] = &T[i + j];
nexpaq 1:55a6170b404f 1231 }
nexpaq 1:55a6170b404f 1232 }
nexpaq 1:55a6170b404f 1233
nexpaq 1:55a6170b404f 1234 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
nexpaq 1:55a6170b404f 1235
nexpaq 1:55a6170b404f 1236 cleanup:
nexpaq 1:55a6170b404f 1237 return( ret );
nexpaq 1:55a6170b404f 1238 }
nexpaq 1:55a6170b404f 1239
nexpaq 1:55a6170b404f 1240 /*
nexpaq 1:55a6170b404f 1241 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
nexpaq 1:55a6170b404f 1242 */
nexpaq 1:55a6170b404f 1243 static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
nexpaq 1:55a6170b404f 1244 const mbedtls_ecp_point T[], unsigned char t_len,
nexpaq 1:55a6170b404f 1245 unsigned char i )
nexpaq 1:55a6170b404f 1246 {
nexpaq 1:55a6170b404f 1247 int ret;
nexpaq 1:55a6170b404f 1248 unsigned char ii, j;
nexpaq 1:55a6170b404f 1249
nexpaq 1:55a6170b404f 1250 /* Ignore the "sign" bit and scale down */
nexpaq 1:55a6170b404f 1251 ii = ( i & 0x7Fu ) >> 1;
nexpaq 1:55a6170b404f 1252
nexpaq 1:55a6170b404f 1253 /* Read the whole table to thwart cache-based timing attacks */
nexpaq 1:55a6170b404f 1254 for( j = 0; j < t_len; j++ )
nexpaq 1:55a6170b404f 1255 {
nexpaq 1:55a6170b404f 1256 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
nexpaq 1:55a6170b404f 1257 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
nexpaq 1:55a6170b404f 1258 }
nexpaq 1:55a6170b404f 1259
nexpaq 1:55a6170b404f 1260 /* Safely invert result if i is "negative" */
nexpaq 1:55a6170b404f 1261 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
nexpaq 1:55a6170b404f 1262
nexpaq 1:55a6170b404f 1263 cleanup:
nexpaq 1:55a6170b404f 1264 return( ret );
nexpaq 1:55a6170b404f 1265 }
nexpaq 1:55a6170b404f 1266
nexpaq 1:55a6170b404f 1267 /*
nexpaq 1:55a6170b404f 1268 * Core multiplication algorithm for the (modified) comb method.
nexpaq 1:55a6170b404f 1269 * This part is actually common with the basic comb method (GECC 3.44)
nexpaq 1:55a6170b404f 1270 *
nexpaq 1:55a6170b404f 1271 * Cost: d A + d D + 1 R
nexpaq 1:55a6170b404f 1272 */
nexpaq 1:55a6170b404f 1273 static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
nexpaq 1:55a6170b404f 1274 const mbedtls_ecp_point T[], unsigned char t_len,
nexpaq 1:55a6170b404f 1275 const unsigned char x[], size_t d,
nexpaq 1:55a6170b404f 1276 int (*f_rng)(void *, unsigned char *, size_t),
nexpaq 1:55a6170b404f 1277 void *p_rng )
nexpaq 1:55a6170b404f 1278 {
nexpaq 1:55a6170b404f 1279 int ret;
nexpaq 1:55a6170b404f 1280 mbedtls_ecp_point Txi;
nexpaq 1:55a6170b404f 1281 size_t i;
nexpaq 1:55a6170b404f 1282
nexpaq 1:55a6170b404f 1283 mbedtls_ecp_point_init( &Txi );
nexpaq 1:55a6170b404f 1284
nexpaq 1:55a6170b404f 1285 /* Start with a non-zero point and randomize its coordinates */
nexpaq 1:55a6170b404f 1286 i = d;
nexpaq 1:55a6170b404f 1287 MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, t_len, x[i] ) );
nexpaq 1:55a6170b404f 1288 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
nexpaq 1:55a6170b404f 1289 if( f_rng != 0 )
nexpaq 1:55a6170b404f 1290 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
nexpaq 1:55a6170b404f 1291
nexpaq 1:55a6170b404f 1292 while( i-- != 0 )
nexpaq 1:55a6170b404f 1293 {
nexpaq 1:55a6170b404f 1294 MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
nexpaq 1:55a6170b404f 1295 MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, t_len, x[i] ) );
nexpaq 1:55a6170b404f 1296 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
nexpaq 1:55a6170b404f 1297 }
nexpaq 1:55a6170b404f 1298
nexpaq 1:55a6170b404f 1299 cleanup:
nexpaq 1:55a6170b404f 1300 mbedtls_ecp_point_free( &Txi );
nexpaq 1:55a6170b404f 1301
nexpaq 1:55a6170b404f 1302 return( ret );
nexpaq 1:55a6170b404f 1303 }
nexpaq 1:55a6170b404f 1304
nexpaq 1:55a6170b404f 1305 /*
nexpaq 1:55a6170b404f 1306 * Multiplication using the comb method,
nexpaq 1:55a6170b404f 1307 * for curves in short Weierstrass form
nexpaq 1:55a6170b404f 1308 */
nexpaq 1:55a6170b404f 1309 static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
nexpaq 1:55a6170b404f 1310 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
nexpaq 1:55a6170b404f 1311 int (*f_rng)(void *, unsigned char *, size_t),
nexpaq 1:55a6170b404f 1312 void *p_rng )
nexpaq 1:55a6170b404f 1313 {
nexpaq 1:55a6170b404f 1314 int ret;
nexpaq 1:55a6170b404f 1315 unsigned char w, m_is_odd, p_eq_g, pre_len, i;
nexpaq 1:55a6170b404f 1316 size_t d;
nexpaq 1:55a6170b404f 1317 unsigned char k[COMB_MAX_D + 1];
nexpaq 1:55a6170b404f 1318 mbedtls_ecp_point *T;
nexpaq 1:55a6170b404f 1319 mbedtls_mpi M, mm;
nexpaq 1:55a6170b404f 1320
nexpaq 1:55a6170b404f 1321 mbedtls_mpi_init( &M );
nexpaq 1:55a6170b404f 1322 mbedtls_mpi_init( &mm );
nexpaq 1:55a6170b404f 1323
nexpaq 1:55a6170b404f 1324 /* we need N to be odd to trnaform m in an odd number, check now */
nexpaq 1:55a6170b404f 1325 if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 )
nexpaq 1:55a6170b404f 1326 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 1327
nexpaq 1:55a6170b404f 1328 /*
nexpaq 1:55a6170b404f 1329 * Minimize the number of multiplications, that is minimize
nexpaq 1:55a6170b404f 1330 * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
nexpaq 1:55a6170b404f 1331 * (see costs of the various parts, with 1S = 1M)
nexpaq 1:55a6170b404f 1332 */
nexpaq 1:55a6170b404f 1333 w = grp->nbits >= 384 ? 5 : 4;
nexpaq 1:55a6170b404f 1334
nexpaq 1:55a6170b404f 1335 /*
nexpaq 1:55a6170b404f 1336 * If P == G, pre-compute a bit more, since this may be re-used later.
nexpaq 1:55a6170b404f 1337 * Just adding one avoids upping the cost of the first mul too much,
nexpaq 1:55a6170b404f 1338 * and the memory cost too.
nexpaq 1:55a6170b404f 1339 */
nexpaq 1:55a6170b404f 1340 #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
nexpaq 1:55a6170b404f 1341 p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
nexpaq 1:55a6170b404f 1342 mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
nexpaq 1:55a6170b404f 1343 if( p_eq_g )
nexpaq 1:55a6170b404f 1344 w++;
nexpaq 1:55a6170b404f 1345 #else
nexpaq 1:55a6170b404f 1346 p_eq_g = 0;
nexpaq 1:55a6170b404f 1347 #endif
nexpaq 1:55a6170b404f 1348
nexpaq 1:55a6170b404f 1349 /*
nexpaq 1:55a6170b404f 1350 * Make sure w is within bounds.
nexpaq 1:55a6170b404f 1351 * (The last test is useful only for very small curves in the test suite.)
nexpaq 1:55a6170b404f 1352 */
nexpaq 1:55a6170b404f 1353 if( w > MBEDTLS_ECP_WINDOW_SIZE )
nexpaq 1:55a6170b404f 1354 w = MBEDTLS_ECP_WINDOW_SIZE;
nexpaq 1:55a6170b404f 1355 if( w >= grp->nbits )
nexpaq 1:55a6170b404f 1356 w = 2;
nexpaq 1:55a6170b404f 1357
nexpaq 1:55a6170b404f 1358 /* Other sizes that depend on w */
nexpaq 1:55a6170b404f 1359 pre_len = 1U << ( w - 1 );
nexpaq 1:55a6170b404f 1360 d = ( grp->nbits + w - 1 ) / w;
nexpaq 1:55a6170b404f 1361
nexpaq 1:55a6170b404f 1362 /*
nexpaq 1:55a6170b404f 1363 * Prepare precomputed points: if P == G we want to
nexpaq 1:55a6170b404f 1364 * use grp->T if already initialized, or initialize it.
nexpaq 1:55a6170b404f 1365 */
nexpaq 1:55a6170b404f 1366 T = p_eq_g ? grp->T : NULL;
nexpaq 1:55a6170b404f 1367
nexpaq 1:55a6170b404f 1368 if( T == NULL )
nexpaq 1:55a6170b404f 1369 {
nexpaq 1:55a6170b404f 1370 T = mbedtls_calloc( pre_len, sizeof( mbedtls_ecp_point ) );
nexpaq 1:55a6170b404f 1371 if( T == NULL )
nexpaq 1:55a6170b404f 1372 {
nexpaq 1:55a6170b404f 1373 ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
nexpaq 1:55a6170b404f 1374 goto cleanup;
nexpaq 1:55a6170b404f 1375 }
nexpaq 1:55a6170b404f 1376
nexpaq 1:55a6170b404f 1377 MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d ) );
nexpaq 1:55a6170b404f 1378
nexpaq 1:55a6170b404f 1379 if( p_eq_g )
nexpaq 1:55a6170b404f 1380 {
nexpaq 1:55a6170b404f 1381 grp->T = T;
nexpaq 1:55a6170b404f 1382 grp->T_size = pre_len;
nexpaq 1:55a6170b404f 1383 }
nexpaq 1:55a6170b404f 1384 }
nexpaq 1:55a6170b404f 1385
nexpaq 1:55a6170b404f 1386 /*
nexpaq 1:55a6170b404f 1387 * Make sure M is odd (M = m or M = N - m, since N is odd)
nexpaq 1:55a6170b404f 1388 * using the fact that m * P = - (N - m) * P
nexpaq 1:55a6170b404f 1389 */
nexpaq 1:55a6170b404f 1390 m_is_odd = ( mbedtls_mpi_get_bit( m, 0 ) == 1 );
nexpaq 1:55a6170b404f 1391 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) );
nexpaq 1:55a6170b404f 1392 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) );
nexpaq 1:55a6170b404f 1393 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, ! m_is_odd ) );
nexpaq 1:55a6170b404f 1394
nexpaq 1:55a6170b404f 1395 /*
nexpaq 1:55a6170b404f 1396 * Go for comb multiplication, R = M * P
nexpaq 1:55a6170b404f 1397 */
nexpaq 1:55a6170b404f 1398 ecp_comb_fixed( k, d, w, &M );
nexpaq 1:55a6170b404f 1399 MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, R, T, pre_len, k, d, f_rng, p_rng ) );
nexpaq 1:55a6170b404f 1400
nexpaq 1:55a6170b404f 1401 /*
nexpaq 1:55a6170b404f 1402 * Now get m * P from M * P and normalize it
nexpaq 1:55a6170b404f 1403 */
nexpaq 1:55a6170b404f 1404 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, ! m_is_odd ) );
nexpaq 1:55a6170b404f 1405 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
nexpaq 1:55a6170b404f 1406
nexpaq 1:55a6170b404f 1407 cleanup:
nexpaq 1:55a6170b404f 1408
nexpaq 1:55a6170b404f 1409 if( T != NULL && ! p_eq_g )
nexpaq 1:55a6170b404f 1410 {
nexpaq 1:55a6170b404f 1411 for( i = 0; i < pre_len; i++ )
nexpaq 1:55a6170b404f 1412 mbedtls_ecp_point_free( &T[i] );
nexpaq 1:55a6170b404f 1413 mbedtls_free( T );
nexpaq 1:55a6170b404f 1414 }
nexpaq 1:55a6170b404f 1415
nexpaq 1:55a6170b404f 1416 mbedtls_mpi_free( &M );
nexpaq 1:55a6170b404f 1417 mbedtls_mpi_free( &mm );
nexpaq 1:55a6170b404f 1418
nexpaq 1:55a6170b404f 1419 if( ret != 0 )
nexpaq 1:55a6170b404f 1420 mbedtls_ecp_point_free( R );
nexpaq 1:55a6170b404f 1421
nexpaq 1:55a6170b404f 1422 return( ret );
nexpaq 1:55a6170b404f 1423 }
nexpaq 1:55a6170b404f 1424
nexpaq 1:55a6170b404f 1425 #endif /* ECP_SHORTWEIERSTRASS */
nexpaq 1:55a6170b404f 1426
nexpaq 1:55a6170b404f 1427 #if defined(ECP_MONTGOMERY)
nexpaq 1:55a6170b404f 1428 /*
nexpaq 1:55a6170b404f 1429 * For Montgomery curves, we do all the internal arithmetic in projective
nexpaq 1:55a6170b404f 1430 * coordinates. Import/export of points uses only the x coordinates, which is
nexpaq 1:55a6170b404f 1431 * internaly represented as X / Z.
nexpaq 1:55a6170b404f 1432 *
nexpaq 1:55a6170b404f 1433 * For scalar multiplication, we'll use a Montgomery ladder.
nexpaq 1:55a6170b404f 1434 */
nexpaq 1:55a6170b404f 1435
nexpaq 1:55a6170b404f 1436 /*
nexpaq 1:55a6170b404f 1437 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
nexpaq 1:55a6170b404f 1438 * Cost: 1M + 1I
nexpaq 1:55a6170b404f 1439 */
nexpaq 1:55a6170b404f 1440 static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
nexpaq 1:55a6170b404f 1441 {
nexpaq 1:55a6170b404f 1442 int ret;
nexpaq 1:55a6170b404f 1443
nexpaq 1:55a6170b404f 1444 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
nexpaq 1:55a6170b404f 1445 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X );
nexpaq 1:55a6170b404f 1446 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
nexpaq 1:55a6170b404f 1447
nexpaq 1:55a6170b404f 1448 cleanup:
nexpaq 1:55a6170b404f 1449 return( ret );
nexpaq 1:55a6170b404f 1450 }
nexpaq 1:55a6170b404f 1451
nexpaq 1:55a6170b404f 1452 /*
nexpaq 1:55a6170b404f 1453 * Randomize projective x/z coordinates:
nexpaq 1:55a6170b404f 1454 * (X, Z) -> (l X, l Z) for random l
nexpaq 1:55a6170b404f 1455 * This is sort of the reverse operation of ecp_normalize_mxz().
nexpaq 1:55a6170b404f 1456 *
nexpaq 1:55a6170b404f 1457 * This countermeasure was first suggested in [2].
nexpaq 1:55a6170b404f 1458 * Cost: 2M
nexpaq 1:55a6170b404f 1459 */
nexpaq 1:55a6170b404f 1460 static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
nexpaq 1:55a6170b404f 1461 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
nexpaq 1:55a6170b404f 1462 {
nexpaq 1:55a6170b404f 1463 int ret;
nexpaq 1:55a6170b404f 1464 mbedtls_mpi l;
nexpaq 1:55a6170b404f 1465 size_t p_size = ( grp->pbits + 7 ) / 8;
nexpaq 1:55a6170b404f 1466 int count = 0;
nexpaq 1:55a6170b404f 1467
nexpaq 1:55a6170b404f 1468 mbedtls_mpi_init( &l );
nexpaq 1:55a6170b404f 1469
nexpaq 1:55a6170b404f 1470 /* Generate l such that 1 < l < p */
nexpaq 1:55a6170b404f 1471 do
nexpaq 1:55a6170b404f 1472 {
nexpaq 1:55a6170b404f 1473 mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng );
nexpaq 1:55a6170b404f 1474
nexpaq 1:55a6170b404f 1475 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
nexpaq 1:55a6170b404f 1476 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
nexpaq 1:55a6170b404f 1477
nexpaq 1:55a6170b404f 1478 if( count++ > 10 )
nexpaq 1:55a6170b404f 1479 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
nexpaq 1:55a6170b404f 1480 }
nexpaq 1:55a6170b404f 1481 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
nexpaq 1:55a6170b404f 1482
nexpaq 1:55a6170b404f 1483 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X );
nexpaq 1:55a6170b404f 1484 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z );
nexpaq 1:55a6170b404f 1485
nexpaq 1:55a6170b404f 1486 cleanup:
nexpaq 1:55a6170b404f 1487 mbedtls_mpi_free( &l );
nexpaq 1:55a6170b404f 1488
nexpaq 1:55a6170b404f 1489 return( ret );
nexpaq 1:55a6170b404f 1490 }
nexpaq 1:55a6170b404f 1491
nexpaq 1:55a6170b404f 1492 /*
nexpaq 1:55a6170b404f 1493 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
nexpaq 1:55a6170b404f 1494 * for Montgomery curves in x/z coordinates.
nexpaq 1:55a6170b404f 1495 *
nexpaq 1:55a6170b404f 1496 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
nexpaq 1:55a6170b404f 1497 * with
nexpaq 1:55a6170b404f 1498 * d = X1
nexpaq 1:55a6170b404f 1499 * P = (X2, Z2)
nexpaq 1:55a6170b404f 1500 * Q = (X3, Z3)
nexpaq 1:55a6170b404f 1501 * R = (X4, Z4)
nexpaq 1:55a6170b404f 1502 * S = (X5, Z5)
nexpaq 1:55a6170b404f 1503 * and eliminating temporary variables tO, ..., t4.
nexpaq 1:55a6170b404f 1504 *
nexpaq 1:55a6170b404f 1505 * Cost: 5M + 4S
nexpaq 1:55a6170b404f 1506 */
nexpaq 1:55a6170b404f 1507 static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
nexpaq 1:55a6170b404f 1508 mbedtls_ecp_point *R, mbedtls_ecp_point *S,
nexpaq 1:55a6170b404f 1509 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
nexpaq 1:55a6170b404f 1510 const mbedtls_mpi *d )
nexpaq 1:55a6170b404f 1511 {
nexpaq 1:55a6170b404f 1512 int ret;
nexpaq 1:55a6170b404f 1513 mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
nexpaq 1:55a6170b404f 1514
nexpaq 1:55a6170b404f 1515 mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
nexpaq 1:55a6170b404f 1516 mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
nexpaq 1:55a6170b404f 1517 mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
nexpaq 1:55a6170b404f 1518
nexpaq 1:55a6170b404f 1519 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &A, &P->X, &P->Z ) ); MOD_ADD( A );
nexpaq 1:55a6170b404f 1520 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &AA, &A, &A ) ); MOD_MUL( AA );
nexpaq 1:55a6170b404f 1521 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &B, &P->X, &P->Z ) ); MOD_SUB( B );
nexpaq 1:55a6170b404f 1522 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &BB, &B, &B ) ); MOD_MUL( BB );
nexpaq 1:55a6170b404f 1523 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &E, &AA, &BB ) ); MOD_SUB( E );
nexpaq 1:55a6170b404f 1524 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &C, &Q->X, &Q->Z ) ); MOD_ADD( C );
nexpaq 1:55a6170b404f 1525 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &D, &Q->X, &Q->Z ) ); MOD_SUB( D );
nexpaq 1:55a6170b404f 1526 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DA, &D, &A ) ); MOD_MUL( DA );
nexpaq 1:55a6170b404f 1527 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &CB, &C, &B ) ); MOD_MUL( CB );
nexpaq 1:55a6170b404f 1528 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &S->X, &DA, &CB ) ); MOD_MUL( S->X );
nexpaq 1:55a6170b404f 1529 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->X, &S->X, &S->X ) ); MOD_MUL( S->X );
nexpaq 1:55a6170b404f 1530 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S->Z, &DA, &CB ) ); MOD_SUB( S->Z );
nexpaq 1:55a6170b404f 1531 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, &S->Z, &S->Z ) ); MOD_MUL( S->Z );
nexpaq 1:55a6170b404f 1532 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, d, &S->Z ) ); MOD_MUL( S->Z );
nexpaq 1:55a6170b404f 1533 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->X, &AA, &BB ) ); MOD_MUL( R->X );
nexpaq 1:55a6170b404f 1534 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &grp->A, &E ) ); MOD_MUL( R->Z );
nexpaq 1:55a6170b404f 1535 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &R->Z, &BB, &R->Z ) ); MOD_ADD( R->Z );
nexpaq 1:55a6170b404f 1536 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &E, &R->Z ) ); MOD_MUL( R->Z );
nexpaq 1:55a6170b404f 1537
nexpaq 1:55a6170b404f 1538 cleanup:
nexpaq 1:55a6170b404f 1539 mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
nexpaq 1:55a6170b404f 1540 mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
nexpaq 1:55a6170b404f 1541 mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
nexpaq 1:55a6170b404f 1542
nexpaq 1:55a6170b404f 1543 return( ret );
nexpaq 1:55a6170b404f 1544 }
nexpaq 1:55a6170b404f 1545
nexpaq 1:55a6170b404f 1546 /*
nexpaq 1:55a6170b404f 1547 * Multiplication with Montgomery ladder in x/z coordinates,
nexpaq 1:55a6170b404f 1548 * for curves in Montgomery form
nexpaq 1:55a6170b404f 1549 */
nexpaq 1:55a6170b404f 1550 static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
nexpaq 1:55a6170b404f 1551 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
nexpaq 1:55a6170b404f 1552 int (*f_rng)(void *, unsigned char *, size_t),
nexpaq 1:55a6170b404f 1553 void *p_rng )
nexpaq 1:55a6170b404f 1554 {
nexpaq 1:55a6170b404f 1555 int ret;
nexpaq 1:55a6170b404f 1556 size_t i;
nexpaq 1:55a6170b404f 1557 unsigned char b;
nexpaq 1:55a6170b404f 1558 mbedtls_ecp_point RP;
nexpaq 1:55a6170b404f 1559 mbedtls_mpi PX;
nexpaq 1:55a6170b404f 1560
nexpaq 1:55a6170b404f 1561 mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
nexpaq 1:55a6170b404f 1562
nexpaq 1:55a6170b404f 1563 /* Save PX and read from P before writing to R, in case P == R */
nexpaq 1:55a6170b404f 1564 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
nexpaq 1:55a6170b404f 1565 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
nexpaq 1:55a6170b404f 1566
nexpaq 1:55a6170b404f 1567 /* Set R to zero in modified x/z coordinates */
nexpaq 1:55a6170b404f 1568 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
nexpaq 1:55a6170b404f 1569 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
nexpaq 1:55a6170b404f 1570 mbedtls_mpi_free( &R->Y );
nexpaq 1:55a6170b404f 1571
nexpaq 1:55a6170b404f 1572 /* RP.X might be sligtly larger than P, so reduce it */
nexpaq 1:55a6170b404f 1573 MOD_ADD( RP.X );
nexpaq 1:55a6170b404f 1574
nexpaq 1:55a6170b404f 1575 /* Randomize coordinates of the starting point */
nexpaq 1:55a6170b404f 1576 if( f_rng != NULL )
nexpaq 1:55a6170b404f 1577 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
nexpaq 1:55a6170b404f 1578
nexpaq 1:55a6170b404f 1579 /* Loop invariant: R = result so far, RP = R + P */
nexpaq 1:55a6170b404f 1580 i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
nexpaq 1:55a6170b404f 1581 while( i-- > 0 )
nexpaq 1:55a6170b404f 1582 {
nexpaq 1:55a6170b404f 1583 b = mbedtls_mpi_get_bit( m, i );
nexpaq 1:55a6170b404f 1584 /*
nexpaq 1:55a6170b404f 1585 * if (b) R = 2R + P else R = 2R,
nexpaq 1:55a6170b404f 1586 * which is:
nexpaq 1:55a6170b404f 1587 * if (b) double_add( RP, R, RP, R )
nexpaq 1:55a6170b404f 1588 * else double_add( R, RP, R, RP )
nexpaq 1:55a6170b404f 1589 * but using safe conditional swaps to avoid leaks
nexpaq 1:55a6170b404f 1590 */
nexpaq 1:55a6170b404f 1591 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
nexpaq 1:55a6170b404f 1592 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
nexpaq 1:55a6170b404f 1593 MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
nexpaq 1:55a6170b404f 1594 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
nexpaq 1:55a6170b404f 1595 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
nexpaq 1:55a6170b404f 1596 }
nexpaq 1:55a6170b404f 1597
nexpaq 1:55a6170b404f 1598 MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) );
nexpaq 1:55a6170b404f 1599
nexpaq 1:55a6170b404f 1600 cleanup:
nexpaq 1:55a6170b404f 1601 mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
nexpaq 1:55a6170b404f 1602
nexpaq 1:55a6170b404f 1603 return( ret );
nexpaq 1:55a6170b404f 1604 }
nexpaq 1:55a6170b404f 1605
nexpaq 1:55a6170b404f 1606 #endif /* ECP_MONTGOMERY */
nexpaq 1:55a6170b404f 1607
nexpaq 1:55a6170b404f 1608 /*
nexpaq 1:55a6170b404f 1609 * Multiplication R = m * P
nexpaq 1:55a6170b404f 1610 */
nexpaq 1:55a6170b404f 1611 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
nexpaq 1:55a6170b404f 1612 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
nexpaq 1:55a6170b404f 1613 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
nexpaq 1:55a6170b404f 1614 {
nexpaq 1:55a6170b404f 1615 int ret;
nexpaq 1:55a6170b404f 1616
nexpaq 1:55a6170b404f 1617 /* Common sanity checks */
nexpaq 1:55a6170b404f 1618 if( mbedtls_mpi_cmp_int( &P->Z, 1 ) != 0 )
nexpaq 1:55a6170b404f 1619 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 1620
nexpaq 1:55a6170b404f 1621 if( ( ret = mbedtls_ecp_check_privkey( grp, m ) ) != 0 ||
nexpaq 1:55a6170b404f 1622 ( ret = mbedtls_ecp_check_pubkey( grp, P ) ) != 0 )
nexpaq 1:55a6170b404f 1623 return( ret );
nexpaq 1:55a6170b404f 1624
nexpaq 1:55a6170b404f 1625 #if defined(ECP_MONTGOMERY)
nexpaq 1:55a6170b404f 1626 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
nexpaq 1:55a6170b404f 1627 return( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) );
nexpaq 1:55a6170b404f 1628 #endif
nexpaq 1:55a6170b404f 1629 #if defined(ECP_SHORTWEIERSTRASS)
nexpaq 1:55a6170b404f 1630 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
nexpaq 1:55a6170b404f 1631 return( ecp_mul_comb( grp, R, m, P, f_rng, p_rng ) );
nexpaq 1:55a6170b404f 1632 #endif
nexpaq 1:55a6170b404f 1633 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 1634 }
nexpaq 1:55a6170b404f 1635
nexpaq 1:55a6170b404f 1636 #if defined(ECP_SHORTWEIERSTRASS)
nexpaq 1:55a6170b404f 1637 /*
nexpaq 1:55a6170b404f 1638 * Check that an affine point is valid as a public key,
nexpaq 1:55a6170b404f 1639 * short weierstrass curves (SEC1 3.2.3.1)
nexpaq 1:55a6170b404f 1640 */
nexpaq 1:55a6170b404f 1641 static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
nexpaq 1:55a6170b404f 1642 {
nexpaq 1:55a6170b404f 1643 int ret;
nexpaq 1:55a6170b404f 1644 mbedtls_mpi YY, RHS;
nexpaq 1:55a6170b404f 1645
nexpaq 1:55a6170b404f 1646 /* pt coordinates must be normalized for our checks */
nexpaq 1:55a6170b404f 1647 if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ||
nexpaq 1:55a6170b404f 1648 mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 ||
nexpaq 1:55a6170b404f 1649 mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
nexpaq 1:55a6170b404f 1650 mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
nexpaq 1:55a6170b404f 1651 return( MBEDTLS_ERR_ECP_INVALID_KEY );
nexpaq 1:55a6170b404f 1652
nexpaq 1:55a6170b404f 1653 mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
nexpaq 1:55a6170b404f 1654
nexpaq 1:55a6170b404f 1655 /*
nexpaq 1:55a6170b404f 1656 * YY = Y^2
nexpaq 1:55a6170b404f 1657 * RHS = X (X^2 + A) + B = X^3 + A X + B
nexpaq 1:55a6170b404f 1658 */
nexpaq 1:55a6170b404f 1659 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &YY, &pt->Y, &pt->Y ) ); MOD_MUL( YY );
nexpaq 1:55a6170b404f 1660 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &pt->X, &pt->X ) ); MOD_MUL( RHS );
nexpaq 1:55a6170b404f 1661
nexpaq 1:55a6170b404f 1662 /* Special case for A = -3 */
nexpaq 1:55a6170b404f 1663 if( grp->A.p == NULL )
nexpaq 1:55a6170b404f 1664 {
nexpaq 1:55a6170b404f 1665 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS );
nexpaq 1:55a6170b404f 1666 }
nexpaq 1:55a6170b404f 1667 else
nexpaq 1:55a6170b404f 1668 {
nexpaq 1:55a6170b404f 1669 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->A ) ); MOD_ADD( RHS );
nexpaq 1:55a6170b404f 1670 }
nexpaq 1:55a6170b404f 1671
nexpaq 1:55a6170b404f 1672 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &RHS, &pt->X ) ); MOD_MUL( RHS );
nexpaq 1:55a6170b404f 1673 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->B ) ); MOD_ADD( RHS );
nexpaq 1:55a6170b404f 1674
nexpaq 1:55a6170b404f 1675 if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
nexpaq 1:55a6170b404f 1676 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
nexpaq 1:55a6170b404f 1677
nexpaq 1:55a6170b404f 1678 cleanup:
nexpaq 1:55a6170b404f 1679
nexpaq 1:55a6170b404f 1680 mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
nexpaq 1:55a6170b404f 1681
nexpaq 1:55a6170b404f 1682 return( ret );
nexpaq 1:55a6170b404f 1683 }
nexpaq 1:55a6170b404f 1684 #endif /* ECP_SHORTWEIERSTRASS */
nexpaq 1:55a6170b404f 1685
nexpaq 1:55a6170b404f 1686 /*
nexpaq 1:55a6170b404f 1687 * R = m * P with shortcuts for m == 1 and m == -1
nexpaq 1:55a6170b404f 1688 * NOT constant-time - ONLY for short Weierstrass!
nexpaq 1:55a6170b404f 1689 */
nexpaq 1:55a6170b404f 1690 static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
nexpaq 1:55a6170b404f 1691 mbedtls_ecp_point *R,
nexpaq 1:55a6170b404f 1692 const mbedtls_mpi *m,
nexpaq 1:55a6170b404f 1693 const mbedtls_ecp_point *P )
nexpaq 1:55a6170b404f 1694 {
nexpaq 1:55a6170b404f 1695 int ret;
nexpaq 1:55a6170b404f 1696
nexpaq 1:55a6170b404f 1697 if( mbedtls_mpi_cmp_int( m, 1 ) == 0 )
nexpaq 1:55a6170b404f 1698 {
nexpaq 1:55a6170b404f 1699 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
nexpaq 1:55a6170b404f 1700 }
nexpaq 1:55a6170b404f 1701 else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
nexpaq 1:55a6170b404f 1702 {
nexpaq 1:55a6170b404f 1703 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
nexpaq 1:55a6170b404f 1704 if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 )
nexpaq 1:55a6170b404f 1705 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
nexpaq 1:55a6170b404f 1706 }
nexpaq 1:55a6170b404f 1707 else
nexpaq 1:55a6170b404f 1708 {
nexpaq 1:55a6170b404f 1709 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
nexpaq 1:55a6170b404f 1710 }
nexpaq 1:55a6170b404f 1711
nexpaq 1:55a6170b404f 1712 cleanup:
nexpaq 1:55a6170b404f 1713 return( ret );
nexpaq 1:55a6170b404f 1714 }
nexpaq 1:55a6170b404f 1715
nexpaq 1:55a6170b404f 1716 /*
nexpaq 1:55a6170b404f 1717 * Linear combination
nexpaq 1:55a6170b404f 1718 * NOT constant-time
nexpaq 1:55a6170b404f 1719 */
nexpaq 1:55a6170b404f 1720 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
nexpaq 1:55a6170b404f 1721 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
nexpaq 1:55a6170b404f 1722 const mbedtls_mpi *n, const mbedtls_ecp_point *Q )
nexpaq 1:55a6170b404f 1723 {
nexpaq 1:55a6170b404f 1724 int ret;
nexpaq 1:55a6170b404f 1725 mbedtls_ecp_point mP;
nexpaq 1:55a6170b404f 1726
nexpaq 1:55a6170b404f 1727 if( ecp_get_type( grp ) != ECP_TYPE_SHORT_WEIERSTRASS )
nexpaq 1:55a6170b404f 1728 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
nexpaq 1:55a6170b404f 1729
nexpaq 1:55a6170b404f 1730 mbedtls_ecp_point_init( &mP );
nexpaq 1:55a6170b404f 1731
nexpaq 1:55a6170b404f 1732 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, &mP, m, P ) );
nexpaq 1:55a6170b404f 1733 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, R, n, Q ) );
nexpaq 1:55a6170b404f 1734
nexpaq 1:55a6170b404f 1735 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, &mP, R ) );
nexpaq 1:55a6170b404f 1736 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
nexpaq 1:55a6170b404f 1737
nexpaq 1:55a6170b404f 1738 cleanup:
nexpaq 1:55a6170b404f 1739 mbedtls_ecp_point_free( &mP );
nexpaq 1:55a6170b404f 1740
nexpaq 1:55a6170b404f 1741 return( ret );
nexpaq 1:55a6170b404f 1742 }
nexpaq 1:55a6170b404f 1743
nexpaq 1:55a6170b404f 1744
nexpaq 1:55a6170b404f 1745 #if defined(ECP_MONTGOMERY)
nexpaq 1:55a6170b404f 1746 /*
nexpaq 1:55a6170b404f 1747 * Check validity of a public key for Montgomery curves with x-only schemes
nexpaq 1:55a6170b404f 1748 */
nexpaq 1:55a6170b404f 1749 static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
nexpaq 1:55a6170b404f 1750 {
nexpaq 1:55a6170b404f 1751 /* [Curve25519 p. 5] Just check X is the correct number of bytes */
nexpaq 1:55a6170b404f 1752 if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
nexpaq 1:55a6170b404f 1753 return( MBEDTLS_ERR_ECP_INVALID_KEY );
nexpaq 1:55a6170b404f 1754
nexpaq 1:55a6170b404f 1755 return( 0 );
nexpaq 1:55a6170b404f 1756 }
nexpaq 1:55a6170b404f 1757 #endif /* ECP_MONTGOMERY */
nexpaq 1:55a6170b404f 1758
nexpaq 1:55a6170b404f 1759 /*
nexpaq 1:55a6170b404f 1760 * Check that a point is valid as a public key
nexpaq 1:55a6170b404f 1761 */
nexpaq 1:55a6170b404f 1762 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
nexpaq 1:55a6170b404f 1763 {
nexpaq 1:55a6170b404f 1764 /* Must use affine coordinates */
nexpaq 1:55a6170b404f 1765 if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
nexpaq 1:55a6170b404f 1766 return( MBEDTLS_ERR_ECP_INVALID_KEY );
nexpaq 1:55a6170b404f 1767
nexpaq 1:55a6170b404f 1768 #if defined(ECP_MONTGOMERY)
nexpaq 1:55a6170b404f 1769 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
nexpaq 1:55a6170b404f 1770 return( ecp_check_pubkey_mx( grp, pt ) );
nexpaq 1:55a6170b404f 1771 #endif
nexpaq 1:55a6170b404f 1772 #if defined(ECP_SHORTWEIERSTRASS)
nexpaq 1:55a6170b404f 1773 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
nexpaq 1:55a6170b404f 1774 return( ecp_check_pubkey_sw( grp, pt ) );
nexpaq 1:55a6170b404f 1775 #endif
nexpaq 1:55a6170b404f 1776 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 1777 }
nexpaq 1:55a6170b404f 1778
nexpaq 1:55a6170b404f 1779 /*
nexpaq 1:55a6170b404f 1780 * Check that an mbedtls_mpi is valid as a private key
nexpaq 1:55a6170b404f 1781 */
nexpaq 1:55a6170b404f 1782 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d )
nexpaq 1:55a6170b404f 1783 {
nexpaq 1:55a6170b404f 1784 #if defined(ECP_MONTGOMERY)
nexpaq 1:55a6170b404f 1785 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
nexpaq 1:55a6170b404f 1786 {
nexpaq 1:55a6170b404f 1787 /* see [Curve25519] page 5 */
nexpaq 1:55a6170b404f 1788 if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
nexpaq 1:55a6170b404f 1789 mbedtls_mpi_get_bit( d, 1 ) != 0 ||
nexpaq 1:55a6170b404f 1790 mbedtls_mpi_get_bit( d, 2 ) != 0 ||
nexpaq 1:55a6170b404f 1791 mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */
nexpaq 1:55a6170b404f 1792 return( MBEDTLS_ERR_ECP_INVALID_KEY );
nexpaq 1:55a6170b404f 1793 else
nexpaq 1:55a6170b404f 1794 return( 0 );
nexpaq 1:55a6170b404f 1795 }
nexpaq 1:55a6170b404f 1796 #endif /* ECP_MONTGOMERY */
nexpaq 1:55a6170b404f 1797 #if defined(ECP_SHORTWEIERSTRASS)
nexpaq 1:55a6170b404f 1798 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
nexpaq 1:55a6170b404f 1799 {
nexpaq 1:55a6170b404f 1800 /* see SEC1 3.2 */
nexpaq 1:55a6170b404f 1801 if( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
nexpaq 1:55a6170b404f 1802 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
nexpaq 1:55a6170b404f 1803 return( MBEDTLS_ERR_ECP_INVALID_KEY );
nexpaq 1:55a6170b404f 1804 else
nexpaq 1:55a6170b404f 1805 return( 0 );
nexpaq 1:55a6170b404f 1806 }
nexpaq 1:55a6170b404f 1807 #endif /* ECP_SHORTWEIERSTRASS */
nexpaq 1:55a6170b404f 1808
nexpaq 1:55a6170b404f 1809 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 1810 }
nexpaq 1:55a6170b404f 1811
nexpaq 1:55a6170b404f 1812 /*
nexpaq 1:55a6170b404f 1813 * Generate a keypair with configurable base point
nexpaq 1:55a6170b404f 1814 */
nexpaq 1:55a6170b404f 1815 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
nexpaq 1:55a6170b404f 1816 const mbedtls_ecp_point *G,
nexpaq 1:55a6170b404f 1817 mbedtls_mpi *d, mbedtls_ecp_point *Q,
nexpaq 1:55a6170b404f 1818 int (*f_rng)(void *, unsigned char *, size_t),
nexpaq 1:55a6170b404f 1819 void *p_rng )
nexpaq 1:55a6170b404f 1820 {
nexpaq 1:55a6170b404f 1821 int ret;
nexpaq 1:55a6170b404f 1822 size_t n_size = ( grp->nbits + 7 ) / 8;
nexpaq 1:55a6170b404f 1823
nexpaq 1:55a6170b404f 1824 #if defined(ECP_MONTGOMERY)
nexpaq 1:55a6170b404f 1825 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
nexpaq 1:55a6170b404f 1826 {
nexpaq 1:55a6170b404f 1827 /* [M225] page 5 */
nexpaq 1:55a6170b404f 1828 size_t b;
nexpaq 1:55a6170b404f 1829
nexpaq 1:55a6170b404f 1830 do {
nexpaq 1:55a6170b404f 1831 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
nexpaq 1:55a6170b404f 1832 } while( mbedtls_mpi_bitlen( d ) == 0);
nexpaq 1:55a6170b404f 1833
nexpaq 1:55a6170b404f 1834 /* Make sure the most significant bit is nbits */
nexpaq 1:55a6170b404f 1835 b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */
nexpaq 1:55a6170b404f 1836 if( b > grp->nbits )
nexpaq 1:55a6170b404f 1837 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) );
nexpaq 1:55a6170b404f 1838 else
nexpaq 1:55a6170b404f 1839 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) );
nexpaq 1:55a6170b404f 1840
nexpaq 1:55a6170b404f 1841 /* Make sure the last three bits are unset */
nexpaq 1:55a6170b404f 1842 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) );
nexpaq 1:55a6170b404f 1843 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) );
nexpaq 1:55a6170b404f 1844 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
nexpaq 1:55a6170b404f 1845 }
nexpaq 1:55a6170b404f 1846 else
nexpaq 1:55a6170b404f 1847 #endif /* ECP_MONTGOMERY */
nexpaq 1:55a6170b404f 1848 #if defined(ECP_SHORTWEIERSTRASS)
nexpaq 1:55a6170b404f 1849 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
nexpaq 1:55a6170b404f 1850 {
nexpaq 1:55a6170b404f 1851 /* SEC1 3.2.1: Generate d such that 1 <= n < N */
nexpaq 1:55a6170b404f 1852 int count = 0;
nexpaq 1:55a6170b404f 1853 unsigned char rnd[MBEDTLS_ECP_MAX_BYTES];
nexpaq 1:55a6170b404f 1854
nexpaq 1:55a6170b404f 1855 /*
nexpaq 1:55a6170b404f 1856 * Match the procedure given in RFC 6979 (deterministic ECDSA):
nexpaq 1:55a6170b404f 1857 * - use the same byte ordering;
nexpaq 1:55a6170b404f 1858 * - keep the leftmost nbits bits of the generated octet string;
nexpaq 1:55a6170b404f 1859 * - try until result is in the desired range.
nexpaq 1:55a6170b404f 1860 * This also avoids any biais, which is especially important for ECDSA.
nexpaq 1:55a6170b404f 1861 */
nexpaq 1:55a6170b404f 1862 do
nexpaq 1:55a6170b404f 1863 {
nexpaq 1:55a6170b404f 1864 MBEDTLS_MPI_CHK( f_rng( p_rng, rnd, n_size ) );
nexpaq 1:55a6170b404f 1865 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( d, rnd, n_size ) );
nexpaq 1:55a6170b404f 1866 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) );
nexpaq 1:55a6170b404f 1867
nexpaq 1:55a6170b404f 1868 /*
nexpaq 1:55a6170b404f 1869 * Each try has at worst a probability 1/2 of failing (the msb has
nexpaq 1:55a6170b404f 1870 * a probability 1/2 of being 0, and then the result will be < N),
nexpaq 1:55a6170b404f 1871 * so after 30 tries failure probability is a most 2**(-30).
nexpaq 1:55a6170b404f 1872 *
nexpaq 1:55a6170b404f 1873 * For most curves, 1 try is enough with overwhelming probability,
nexpaq 1:55a6170b404f 1874 * since N starts with a lot of 1s in binary, but some curves
nexpaq 1:55a6170b404f 1875 * such as secp224k1 are actually very close to the worst case.
nexpaq 1:55a6170b404f 1876 */
nexpaq 1:55a6170b404f 1877 if( ++count > 30 )
nexpaq 1:55a6170b404f 1878 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
nexpaq 1:55a6170b404f 1879 }
nexpaq 1:55a6170b404f 1880 while( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
nexpaq 1:55a6170b404f 1881 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 );
nexpaq 1:55a6170b404f 1882 }
nexpaq 1:55a6170b404f 1883 else
nexpaq 1:55a6170b404f 1884 #endif /* ECP_SHORTWEIERSTRASS */
nexpaq 1:55a6170b404f 1885 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 1886
nexpaq 1:55a6170b404f 1887 cleanup:
nexpaq 1:55a6170b404f 1888 if( ret != 0 )
nexpaq 1:55a6170b404f 1889 return( ret );
nexpaq 1:55a6170b404f 1890
nexpaq 1:55a6170b404f 1891 return( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) );
nexpaq 1:55a6170b404f 1892 }
nexpaq 1:55a6170b404f 1893
nexpaq 1:55a6170b404f 1894 /*
nexpaq 1:55a6170b404f 1895 * Generate key pair, wrapper for conventional base point
nexpaq 1:55a6170b404f 1896 */
nexpaq 1:55a6170b404f 1897 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp,
nexpaq 1:55a6170b404f 1898 mbedtls_mpi *d, mbedtls_ecp_point *Q,
nexpaq 1:55a6170b404f 1899 int (*f_rng)(void *, unsigned char *, size_t),
nexpaq 1:55a6170b404f 1900 void *p_rng )
nexpaq 1:55a6170b404f 1901 {
nexpaq 1:55a6170b404f 1902 return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) );
nexpaq 1:55a6170b404f 1903 }
nexpaq 1:55a6170b404f 1904
nexpaq 1:55a6170b404f 1905 /*
nexpaq 1:55a6170b404f 1906 * Generate a keypair, prettier wrapper
nexpaq 1:55a6170b404f 1907 */
nexpaq 1:55a6170b404f 1908 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
nexpaq 1:55a6170b404f 1909 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
nexpaq 1:55a6170b404f 1910 {
nexpaq 1:55a6170b404f 1911 int ret;
nexpaq 1:55a6170b404f 1912
nexpaq 1:55a6170b404f 1913 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
nexpaq 1:55a6170b404f 1914 return( ret );
nexpaq 1:55a6170b404f 1915
nexpaq 1:55a6170b404f 1916 return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
nexpaq 1:55a6170b404f 1917 }
nexpaq 1:55a6170b404f 1918
nexpaq 1:55a6170b404f 1919 /*
nexpaq 1:55a6170b404f 1920 * Check a public-private key pair
nexpaq 1:55a6170b404f 1921 */
nexpaq 1:55a6170b404f 1922 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
nexpaq 1:55a6170b404f 1923 {
nexpaq 1:55a6170b404f 1924 int ret;
nexpaq 1:55a6170b404f 1925 mbedtls_ecp_point Q;
nexpaq 1:55a6170b404f 1926 mbedtls_ecp_group grp;
nexpaq 1:55a6170b404f 1927
nexpaq 1:55a6170b404f 1928 if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
nexpaq 1:55a6170b404f 1929 pub->grp.id != prv->grp.id ||
nexpaq 1:55a6170b404f 1930 mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
nexpaq 1:55a6170b404f 1931 mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
nexpaq 1:55a6170b404f 1932 mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
nexpaq 1:55a6170b404f 1933 {
nexpaq 1:55a6170b404f 1934 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
nexpaq 1:55a6170b404f 1935 }
nexpaq 1:55a6170b404f 1936
nexpaq 1:55a6170b404f 1937 mbedtls_ecp_point_init( &Q );
nexpaq 1:55a6170b404f 1938 mbedtls_ecp_group_init( &grp );
nexpaq 1:55a6170b404f 1939
nexpaq 1:55a6170b404f 1940 /* mbedtls_ecp_mul() needs a non-const group... */
nexpaq 1:55a6170b404f 1941 mbedtls_ecp_group_copy( &grp, &prv->grp );
nexpaq 1:55a6170b404f 1942
nexpaq 1:55a6170b404f 1943 /* Also checks d is valid */
nexpaq 1:55a6170b404f 1944 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
nexpaq 1:55a6170b404f 1945
nexpaq 1:55a6170b404f 1946 if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
nexpaq 1:55a6170b404f 1947 mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
nexpaq 1:55a6170b404f 1948 mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
nexpaq 1:55a6170b404f 1949 {
nexpaq 1:55a6170b404f 1950 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
nexpaq 1:55a6170b404f 1951 goto cleanup;
nexpaq 1:55a6170b404f 1952 }
nexpaq 1:55a6170b404f 1953
nexpaq 1:55a6170b404f 1954 cleanup:
nexpaq 1:55a6170b404f 1955 mbedtls_ecp_point_free( &Q );
nexpaq 1:55a6170b404f 1956 mbedtls_ecp_group_free( &grp );
nexpaq 1:55a6170b404f 1957
nexpaq 1:55a6170b404f 1958 return( ret );
nexpaq 1:55a6170b404f 1959 }
nexpaq 1:55a6170b404f 1960
nexpaq 1:55a6170b404f 1961 #if defined(MBEDTLS_SELF_TEST)
nexpaq 1:55a6170b404f 1962
nexpaq 1:55a6170b404f 1963 /*
nexpaq 1:55a6170b404f 1964 * Checkup routine
nexpaq 1:55a6170b404f 1965 */
nexpaq 1:55a6170b404f 1966 int mbedtls_ecp_self_test( int verbose )
nexpaq 1:55a6170b404f 1967 {
nexpaq 1:55a6170b404f 1968 int ret;
nexpaq 1:55a6170b404f 1969 size_t i;
nexpaq 1:55a6170b404f 1970 mbedtls_ecp_group grp;
nexpaq 1:55a6170b404f 1971 mbedtls_ecp_point R, P;
nexpaq 1:55a6170b404f 1972 mbedtls_mpi m;
nexpaq 1:55a6170b404f 1973 unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
nexpaq 1:55a6170b404f 1974 /* exponents especially adapted for secp192r1 */
nexpaq 1:55a6170b404f 1975 const char *exponents[] =
nexpaq 1:55a6170b404f 1976 {
nexpaq 1:55a6170b404f 1977 "000000000000000000000000000000000000000000000001", /* one */
nexpaq 1:55a6170b404f 1978 "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22830", /* N - 1 */
nexpaq 1:55a6170b404f 1979 "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
nexpaq 1:55a6170b404f 1980 "400000000000000000000000000000000000000000000000", /* one and zeros */
nexpaq 1:55a6170b404f 1981 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
nexpaq 1:55a6170b404f 1982 "555555555555555555555555555555555555555555555555", /* 101010... */
nexpaq 1:55a6170b404f 1983 };
nexpaq 1:55a6170b404f 1984
nexpaq 1:55a6170b404f 1985 mbedtls_ecp_group_init( &grp );
nexpaq 1:55a6170b404f 1986 mbedtls_ecp_point_init( &R );
nexpaq 1:55a6170b404f 1987 mbedtls_ecp_point_init( &P );
nexpaq 1:55a6170b404f 1988 mbedtls_mpi_init( &m );
nexpaq 1:55a6170b404f 1989
nexpaq 1:55a6170b404f 1990 /* Use secp192r1 if available, or any available curve */
nexpaq 1:55a6170b404f 1991 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
nexpaq 1:55a6170b404f 1992 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) );
nexpaq 1:55a6170b404f 1993 #else
nexpaq 1:55a6170b404f 1994 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) );
nexpaq 1:55a6170b404f 1995 #endif
nexpaq 1:55a6170b404f 1996
nexpaq 1:55a6170b404f 1997 if( verbose != 0 )
nexpaq 1:55a6170b404f 1998 mbedtls_printf( " ECP test #1 (constant op_count, base point G): " );
nexpaq 1:55a6170b404f 1999
nexpaq 1:55a6170b404f 2000 /* Do a dummy multiplication first to trigger precomputation */
nexpaq 1:55a6170b404f 2001 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
nexpaq 1:55a6170b404f 2002 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
nexpaq 1:55a6170b404f 2003
nexpaq 1:55a6170b404f 2004 add_count = 0;
nexpaq 1:55a6170b404f 2005 dbl_count = 0;
nexpaq 1:55a6170b404f 2006 mul_count = 0;
nexpaq 1:55a6170b404f 2007 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
nexpaq 1:55a6170b404f 2008 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
nexpaq 1:55a6170b404f 2009
nexpaq 1:55a6170b404f 2010 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
nexpaq 1:55a6170b404f 2011 {
nexpaq 1:55a6170b404f 2012 add_c_prev = add_count;
nexpaq 1:55a6170b404f 2013 dbl_c_prev = dbl_count;
nexpaq 1:55a6170b404f 2014 mul_c_prev = mul_count;
nexpaq 1:55a6170b404f 2015 add_count = 0;
nexpaq 1:55a6170b404f 2016 dbl_count = 0;
nexpaq 1:55a6170b404f 2017 mul_count = 0;
nexpaq 1:55a6170b404f 2018
nexpaq 1:55a6170b404f 2019 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
nexpaq 1:55a6170b404f 2020 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
nexpaq 1:55a6170b404f 2021
nexpaq 1:55a6170b404f 2022 if( add_count != add_c_prev ||
nexpaq 1:55a6170b404f 2023 dbl_count != dbl_c_prev ||
nexpaq 1:55a6170b404f 2024 mul_count != mul_c_prev )
nexpaq 1:55a6170b404f 2025 {
nexpaq 1:55a6170b404f 2026 if( verbose != 0 )
nexpaq 1:55a6170b404f 2027 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
nexpaq 1:55a6170b404f 2028
nexpaq 1:55a6170b404f 2029 ret = 1;
nexpaq 1:55a6170b404f 2030 goto cleanup;
nexpaq 1:55a6170b404f 2031 }
nexpaq 1:55a6170b404f 2032 }
nexpaq 1:55a6170b404f 2033
nexpaq 1:55a6170b404f 2034 if( verbose != 0 )
nexpaq 1:55a6170b404f 2035 mbedtls_printf( "passed\n" );
nexpaq 1:55a6170b404f 2036
nexpaq 1:55a6170b404f 2037 if( verbose != 0 )
nexpaq 1:55a6170b404f 2038 mbedtls_printf( " ECP test #2 (constant op_count, other point): " );
nexpaq 1:55a6170b404f 2039 /* We computed P = 2G last time, use it */
nexpaq 1:55a6170b404f 2040
nexpaq 1:55a6170b404f 2041 add_count = 0;
nexpaq 1:55a6170b404f 2042 dbl_count = 0;
nexpaq 1:55a6170b404f 2043 mul_count = 0;
nexpaq 1:55a6170b404f 2044 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
nexpaq 1:55a6170b404f 2045 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
nexpaq 1:55a6170b404f 2046
nexpaq 1:55a6170b404f 2047 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
nexpaq 1:55a6170b404f 2048 {
nexpaq 1:55a6170b404f 2049 add_c_prev = add_count;
nexpaq 1:55a6170b404f 2050 dbl_c_prev = dbl_count;
nexpaq 1:55a6170b404f 2051 mul_c_prev = mul_count;
nexpaq 1:55a6170b404f 2052 add_count = 0;
nexpaq 1:55a6170b404f 2053 dbl_count = 0;
nexpaq 1:55a6170b404f 2054 mul_count = 0;
nexpaq 1:55a6170b404f 2055
nexpaq 1:55a6170b404f 2056 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
nexpaq 1:55a6170b404f 2057 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
nexpaq 1:55a6170b404f 2058
nexpaq 1:55a6170b404f 2059 if( add_count != add_c_prev ||
nexpaq 1:55a6170b404f 2060 dbl_count != dbl_c_prev ||
nexpaq 1:55a6170b404f 2061 mul_count != mul_c_prev )
nexpaq 1:55a6170b404f 2062 {
nexpaq 1:55a6170b404f 2063 if( verbose != 0 )
nexpaq 1:55a6170b404f 2064 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
nexpaq 1:55a6170b404f 2065
nexpaq 1:55a6170b404f 2066 ret = 1;
nexpaq 1:55a6170b404f 2067 goto cleanup;
nexpaq 1:55a6170b404f 2068 }
nexpaq 1:55a6170b404f 2069 }
nexpaq 1:55a6170b404f 2070
nexpaq 1:55a6170b404f 2071 if( verbose != 0 )
nexpaq 1:55a6170b404f 2072 mbedtls_printf( "passed\n" );
nexpaq 1:55a6170b404f 2073
nexpaq 1:55a6170b404f 2074 cleanup:
nexpaq 1:55a6170b404f 2075
nexpaq 1:55a6170b404f 2076 if( ret < 0 && verbose != 0 )
nexpaq 1:55a6170b404f 2077 mbedtls_printf( "Unexpected error, return code = %08X\n", ret );
nexpaq 1:55a6170b404f 2078
nexpaq 1:55a6170b404f 2079 mbedtls_ecp_group_free( &grp );
nexpaq 1:55a6170b404f 2080 mbedtls_ecp_point_free( &R );
nexpaq 1:55a6170b404f 2081 mbedtls_ecp_point_free( &P );
nexpaq 1:55a6170b404f 2082 mbedtls_mpi_free( &m );
nexpaq 1:55a6170b404f 2083
nexpaq 1:55a6170b404f 2084 if( verbose != 0 )
nexpaq 1:55a6170b404f 2085 mbedtls_printf( "\n" );
nexpaq 1:55a6170b404f 2086
nexpaq 1:55a6170b404f 2087 return( ret );
nexpaq 1:55a6170b404f 2088 }
nexpaq 1:55a6170b404f 2089
nexpaq 1:55a6170b404f 2090 #endif /* MBEDTLS_SELF_TEST */
nexpaq 1:55a6170b404f 2091
nexpaq 1:55a6170b404f 2092 #endif /* MBEDTLS_ECP_C */