takashi kadono / Mbed OS Nucleo446_SSD1331

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Dependencies:   ssd1331

mbed-os/features/mbedtls/src/ecp.c@3:f3764f852aa8, 2018-10-11 (annotated)

Committer:
kadonotakashi
Date:
Thu Oct 11 02:27:46 2018 +0000
Revision:
3:f3764f852aa8
Parent:
0:8fdf9a60065b 
Nucreo 446 + SSD1331 test version;

Who changed what in which revision?

UserRevisionLine numberNew contents of line
kadonotakashi 0:8fdf9a60065b 1 /*
kadonotakashi 0:8fdf9a60065b 2 * Elliptic curves over GF(p): generic functions
kadonotakashi 0:8fdf9a60065b 3 *
kadonotakashi 0:8fdf9a60065b 4 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
kadonotakashi 0:8fdf9a60065b 5 * SPDX-License-Identifier: Apache-2.0
kadonotakashi 0:8fdf9a60065b 6 *
kadonotakashi 0:8fdf9a60065b 7 * Licensed under the Apache License, Version 2.0 (the "License"); you may
kadonotakashi 0:8fdf9a60065b 8 * not use this file except in compliance with the License.
kadonotakashi 0:8fdf9a60065b 9 * You may obtain a copy of the License at
kadonotakashi 0:8fdf9a60065b 10 *
kadonotakashi 0:8fdf9a60065b 11 * http://www.apache.org/licenses/LICENSE-2.0
kadonotakashi 0:8fdf9a60065b 12 *
kadonotakashi 0:8fdf9a60065b 13 * Unless required by applicable law or agreed to in writing, software
kadonotakashi 0:8fdf9a60065b 14 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
kadonotakashi 0:8fdf9a60065b 15 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
kadonotakashi 0:8fdf9a60065b 16 * See the License for the specific language governing permissions and
kadonotakashi 0:8fdf9a60065b 17 * limitations under the License.
kadonotakashi 0:8fdf9a60065b 18 *
kadonotakashi 0:8fdf9a60065b 19 * This file is part of mbed TLS (https://tls.mbed.org)
kadonotakashi 0:8fdf9a60065b 20 */
kadonotakashi 0:8fdf9a60065b 21
kadonotakashi 0:8fdf9a60065b 22 /*
kadonotakashi 0:8fdf9a60065b 23 * References:
kadonotakashi 0:8fdf9a60065b 24 *
kadonotakashi 0:8fdf9a60065b 25 * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
kadonotakashi 0:8fdf9a60065b 26 * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
kadonotakashi 0:8fdf9a60065b 27 * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
kadonotakashi 0:8fdf9a60065b 28 * RFC 4492 for the related TLS structures and constants
kadonotakashi 0:8fdf9a60065b 29 * RFC 7748 for the Curve448 and Curve25519 curve definitions
kadonotakashi 0:8fdf9a60065b 30 *
kadonotakashi 0:8fdf9a60065b 31 * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf
kadonotakashi 0:8fdf9a60065b 32 *
kadonotakashi 0:8fdf9a60065b 33 * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
kadonotakashi 0:8fdf9a60065b 34 * for elliptic curve cryptosystems. In : Cryptographic Hardware and
kadonotakashi 0:8fdf9a60065b 35 * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
kadonotakashi 0:8fdf9a60065b 36 * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
kadonotakashi 0:8fdf9a60065b 37 *
kadonotakashi 0:8fdf9a60065b 38 * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
kadonotakashi 0:8fdf9a60065b 39 * render ECC resistant against Side Channel Attacks. IACR Cryptology
kadonotakashi 0:8fdf9a60065b 40 * ePrint Archive, 2004, vol. 2004, p. 342.
kadonotakashi 0:8fdf9a60065b 41 * <http://eprint.iacr.org/2004/342.pdf>
kadonotakashi 0:8fdf9a60065b 42 */
kadonotakashi 0:8fdf9a60065b 43
kadonotakashi 0:8fdf9a60065b 44 #if !defined(MBEDTLS_CONFIG_FILE)
kadonotakashi 0:8fdf9a60065b 45 #include "mbedtls/config.h"
kadonotakashi 0:8fdf9a60065b 46 #else
kadonotakashi 0:8fdf9a60065b 47 #include MBEDTLS_CONFIG_FILE
kadonotakashi 0:8fdf9a60065b 48 #endif
kadonotakashi 0:8fdf9a60065b 49
kadonotakashi 0:8fdf9a60065b 50 #if defined(MBEDTLS_ECP_C)
kadonotakashi 0:8fdf9a60065b 51
kadonotakashi 0:8fdf9a60065b 52 #include "mbedtls/ecp.h"
kadonotakashi 0:8fdf9a60065b 53 #include "mbedtls/threading.h"
kadonotakashi 0:8fdf9a60065b 54 #include "mbedtls/platform_util.h"
kadonotakashi 0:8fdf9a60065b 55
kadonotakashi 0:8fdf9a60065b 56 #include <string.h>
kadonotakashi 0:8fdf9a60065b 57
kadonotakashi 0:8fdf9a60065b 58 #if !defined(MBEDTLS_ECP_ALT)
kadonotakashi 0:8fdf9a60065b 59
kadonotakashi 0:8fdf9a60065b 60 #if defined(MBEDTLS_PLATFORM_C)
kadonotakashi 0:8fdf9a60065b 61 #include "mbedtls/platform.h"
kadonotakashi 0:8fdf9a60065b 62 #else
kadonotakashi 0:8fdf9a60065b 63 #include <stdlib.h>
kadonotakashi 0:8fdf9a60065b 64 #include <stdio.h>
kadonotakashi 0:8fdf9a60065b 65 #define mbedtls_printf printf
kadonotakashi 0:8fdf9a60065b 66 #define mbedtls_calloc calloc
kadonotakashi 0:8fdf9a60065b 67 #define mbedtls_free free
kadonotakashi 0:8fdf9a60065b 68 #endif
kadonotakashi 0:8fdf9a60065b 69
kadonotakashi 0:8fdf9a60065b 70 #include "mbedtls/ecp_internal.h"
kadonotakashi 0:8fdf9a60065b 71
kadonotakashi 0:8fdf9a60065b 72 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
kadonotakashi 0:8fdf9a60065b 73 !defined(inline) && !defined(__cplusplus)
kadonotakashi 0:8fdf9a60065b 74 #define inline __inline
kadonotakashi 0:8fdf9a60065b 75 #endif
kadonotakashi 0:8fdf9a60065b 76
kadonotakashi 0:8fdf9a60065b 77 #if defined(MBEDTLS_SELF_TEST)
kadonotakashi 0:8fdf9a60065b 78 /*
kadonotakashi 0:8fdf9a60065b 79 * Counts of point addition and doubling, and field multiplications.
kadonotakashi 0:8fdf9a60065b 80 * Used to test resistance of point multiplication to simple timing attacks.
kadonotakashi 0:8fdf9a60065b 81 */
kadonotakashi 0:8fdf9a60065b 82 static unsigned long add_count, dbl_count, mul_count;
kadonotakashi 0:8fdf9a60065b 83 #endif
kadonotakashi 0:8fdf9a60065b 84
kadonotakashi 0:8fdf9a60065b 85 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \
kadonotakashi 0:8fdf9a60065b 86 defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
kadonotakashi 0:8fdf9a60065b 87 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
kadonotakashi 0:8fdf9a60065b 88 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \
kadonotakashi 0:8fdf9a60065b 89 defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \
kadonotakashi 0:8fdf9a60065b 90 defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \
kadonotakashi 0:8fdf9a60065b 91 defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \
kadonotakashi 0:8fdf9a60065b 92 defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \
kadonotakashi 0:8fdf9a60065b 93 defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
kadonotakashi 0:8fdf9a60065b 94 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
kadonotakashi 0:8fdf9a60065b 95 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
kadonotakashi 0:8fdf9a60065b 96 #define ECP_SHORTWEIERSTRASS
kadonotakashi 0:8fdf9a60065b 97 #endif
kadonotakashi 0:8fdf9a60065b 98
kadonotakashi 0:8fdf9a60065b 99 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) || \
kadonotakashi 0:8fdf9a60065b 100 defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
kadonotakashi 0:8fdf9a60065b 101 #define ECP_MONTGOMERY
kadonotakashi 0:8fdf9a60065b 102 #endif
kadonotakashi 0:8fdf9a60065b 103
kadonotakashi 0:8fdf9a60065b 104 /*
kadonotakashi 0:8fdf9a60065b 105 * Curve types: internal for now, might be exposed later
kadonotakashi 0:8fdf9a60065b 106 */
kadonotakashi 0:8fdf9a60065b 107 typedef enum
kadonotakashi 0:8fdf9a60065b 108 {
kadonotakashi 0:8fdf9a60065b 109 ECP_TYPE_NONE = 0,
kadonotakashi 0:8fdf9a60065b 110 ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */
kadonotakashi 0:8fdf9a60065b 111 ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */
kadonotakashi 0:8fdf9a60065b 112 } ecp_curve_type;
kadonotakashi 0:8fdf9a60065b 113
kadonotakashi 0:8fdf9a60065b 114 /*
kadonotakashi 0:8fdf9a60065b 115 * List of supported curves:
kadonotakashi 0:8fdf9a60065b 116 * - internal ID
kadonotakashi 0:8fdf9a60065b 117 * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2)
kadonotakashi 0:8fdf9a60065b 118 * - size in bits
kadonotakashi 0:8fdf9a60065b 119 * - readable name
kadonotakashi 0:8fdf9a60065b 120 *
kadonotakashi 0:8fdf9a60065b 121 * Curves are listed in order: largest curves first, and for a given size,
kadonotakashi 0:8fdf9a60065b 122 * fastest curves first. This provides the default order for the SSL module.
kadonotakashi 0:8fdf9a60065b 123 *
kadonotakashi 0:8fdf9a60065b 124 * Reminder: update profiles in x509_crt.c when adding a new curves!
kadonotakashi 0:8fdf9a60065b 125 */
kadonotakashi 0:8fdf9a60065b 126 static const mbedtls_ecp_curve_info ecp_supported_curves[] =
kadonotakashi 0:8fdf9a60065b 127 {
kadonotakashi 0:8fdf9a60065b 128 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
kadonotakashi 0:8fdf9a60065b 129 { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" },
kadonotakashi 0:8fdf9a60065b 130 #endif
kadonotakashi 0:8fdf9a60065b 131 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
kadonotakashi 0:8fdf9a60065b 132 { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
kadonotakashi 0:8fdf9a60065b 133 #endif
kadonotakashi 0:8fdf9a60065b 134 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
kadonotakashi 0:8fdf9a60065b 135 { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
kadonotakashi 0:8fdf9a60065b 136 #endif
kadonotakashi 0:8fdf9a60065b 137 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
kadonotakashi 0:8fdf9a60065b 138 { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
kadonotakashi 0:8fdf9a60065b 139 #endif
kadonotakashi 0:8fdf9a60065b 140 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
kadonotakashi 0:8fdf9a60065b 141 { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
kadonotakashi 0:8fdf9a60065b 142 #endif
kadonotakashi 0:8fdf9a60065b 143 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
kadonotakashi 0:8fdf9a60065b 144 { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
kadonotakashi 0:8fdf9a60065b 145 #endif
kadonotakashi 0:8fdf9a60065b 146 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
kadonotakashi 0:8fdf9a60065b 147 { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" },
kadonotakashi 0:8fdf9a60065b 148 #endif
kadonotakashi 0:8fdf9a60065b 149 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
kadonotakashi 0:8fdf9a60065b 150 { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" },
kadonotakashi 0:8fdf9a60065b 151 #endif
kadonotakashi 0:8fdf9a60065b 152 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
kadonotakashi 0:8fdf9a60065b 153 { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" },
kadonotakashi 0:8fdf9a60065b 154 #endif
kadonotakashi 0:8fdf9a60065b 155 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
kadonotakashi 0:8fdf9a60065b 156 { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" },
kadonotakashi 0:8fdf9a60065b 157 #endif
kadonotakashi 0:8fdf9a60065b 158 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
kadonotakashi 0:8fdf9a60065b 159 { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" },
kadonotakashi 0:8fdf9a60065b 160 #endif
kadonotakashi 0:8fdf9a60065b 161 { MBEDTLS_ECP_DP_NONE, 0, 0, NULL },
kadonotakashi 0:8fdf9a60065b 162 };
kadonotakashi 0:8fdf9a60065b 163
kadonotakashi 0:8fdf9a60065b 164 #define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \
kadonotakashi 0:8fdf9a60065b 165 sizeof( ecp_supported_curves[0] )
kadonotakashi 0:8fdf9a60065b 166
kadonotakashi 0:8fdf9a60065b 167 static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
kadonotakashi 0:8fdf9a60065b 168
kadonotakashi 0:8fdf9a60065b 169 /*
kadonotakashi 0:8fdf9a60065b 170 * List of supported curves and associated info
kadonotakashi 0:8fdf9a60065b 171 */
kadonotakashi 0:8fdf9a60065b 172 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
kadonotakashi 0:8fdf9a60065b 173 {
kadonotakashi 0:8fdf9a60065b 174 return( ecp_supported_curves );
kadonotakashi 0:8fdf9a60065b 175 }
kadonotakashi 0:8fdf9a60065b 176
kadonotakashi 0:8fdf9a60065b 177 /*
kadonotakashi 0:8fdf9a60065b 178 * List of supported curves, group ID only
kadonotakashi 0:8fdf9a60065b 179 */
kadonotakashi 0:8fdf9a60065b 180 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
kadonotakashi 0:8fdf9a60065b 181 {
kadonotakashi 0:8fdf9a60065b 182 static int init_done = 0;
kadonotakashi 0:8fdf9a60065b 183
kadonotakashi 0:8fdf9a60065b 184 if( ! init_done )
kadonotakashi 0:8fdf9a60065b 185 {
kadonotakashi 0:8fdf9a60065b 186 size_t i = 0;
kadonotakashi 0:8fdf9a60065b 187 const mbedtls_ecp_curve_info *curve_info;
kadonotakashi 0:8fdf9a60065b 188
kadonotakashi 0:8fdf9a60065b 189 for( curve_info = mbedtls_ecp_curve_list();
kadonotakashi 0:8fdf9a60065b 190 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
kadonotakashi 0:8fdf9a60065b 191 curve_info++ )
kadonotakashi 0:8fdf9a60065b 192 {
kadonotakashi 0:8fdf9a60065b 193 ecp_supported_grp_id[i++] = curve_info->grp_id;
kadonotakashi 0:8fdf9a60065b 194 }
kadonotakashi 0:8fdf9a60065b 195 ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
kadonotakashi 0:8fdf9a60065b 196
kadonotakashi 0:8fdf9a60065b 197 init_done = 1;
kadonotakashi 0:8fdf9a60065b 198 }
kadonotakashi 0:8fdf9a60065b 199
kadonotakashi 0:8fdf9a60065b 200 return( ecp_supported_grp_id );
kadonotakashi 0:8fdf9a60065b 201 }
kadonotakashi 0:8fdf9a60065b 202
kadonotakashi 0:8fdf9a60065b 203 /*
kadonotakashi 0:8fdf9a60065b 204 * Get the curve info for the internal identifier
kadonotakashi 0:8fdf9a60065b 205 */
kadonotakashi 0:8fdf9a60065b 206 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id )
kadonotakashi 0:8fdf9a60065b 207 {
kadonotakashi 0:8fdf9a60065b 208 const mbedtls_ecp_curve_info *curve_info;
kadonotakashi 0:8fdf9a60065b 209
kadonotakashi 0:8fdf9a60065b 210 for( curve_info = mbedtls_ecp_curve_list();
kadonotakashi 0:8fdf9a60065b 211 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
kadonotakashi 0:8fdf9a60065b 212 curve_info++ )
kadonotakashi 0:8fdf9a60065b 213 {
kadonotakashi 0:8fdf9a60065b 214 if( curve_info->grp_id == grp_id )
kadonotakashi 0:8fdf9a60065b 215 return( curve_info );
kadonotakashi 0:8fdf9a60065b 216 }
kadonotakashi 0:8fdf9a60065b 217
kadonotakashi 0:8fdf9a60065b 218 return( NULL );
kadonotakashi 0:8fdf9a60065b 219 }
kadonotakashi 0:8fdf9a60065b 220
kadonotakashi 0:8fdf9a60065b 221 /*
kadonotakashi 0:8fdf9a60065b 222 * Get the curve info from the TLS identifier
kadonotakashi 0:8fdf9a60065b 223 */
kadonotakashi 0:8fdf9a60065b 224 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id )
kadonotakashi 0:8fdf9a60065b 225 {
kadonotakashi 0:8fdf9a60065b 226 const mbedtls_ecp_curve_info *curve_info;
kadonotakashi 0:8fdf9a60065b 227
kadonotakashi 0:8fdf9a60065b 228 for( curve_info = mbedtls_ecp_curve_list();
kadonotakashi 0:8fdf9a60065b 229 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
kadonotakashi 0:8fdf9a60065b 230 curve_info++ )
kadonotakashi 0:8fdf9a60065b 231 {
kadonotakashi 0:8fdf9a60065b 232 if( curve_info->tls_id == tls_id )
kadonotakashi 0:8fdf9a60065b 233 return( curve_info );
kadonotakashi 0:8fdf9a60065b 234 }
kadonotakashi 0:8fdf9a60065b 235
kadonotakashi 0:8fdf9a60065b 236 return( NULL );
kadonotakashi 0:8fdf9a60065b 237 }
kadonotakashi 0:8fdf9a60065b 238
kadonotakashi 0:8fdf9a60065b 239 /*
kadonotakashi 0:8fdf9a60065b 240 * Get the curve info from the name
kadonotakashi 0:8fdf9a60065b 241 */
kadonotakashi 0:8fdf9a60065b 242 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name )
kadonotakashi 0:8fdf9a60065b 243 {
kadonotakashi 0:8fdf9a60065b 244 const mbedtls_ecp_curve_info *curve_info;
kadonotakashi 0:8fdf9a60065b 245
kadonotakashi 0:8fdf9a60065b 246 for( curve_info = mbedtls_ecp_curve_list();
kadonotakashi 0:8fdf9a60065b 247 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
kadonotakashi 0:8fdf9a60065b 248 curve_info++ )
kadonotakashi 0:8fdf9a60065b 249 {
kadonotakashi 0:8fdf9a60065b 250 if( strcmp( curve_info->name, name ) == 0 )
kadonotakashi 0:8fdf9a60065b 251 return( curve_info );
kadonotakashi 0:8fdf9a60065b 252 }
kadonotakashi 0:8fdf9a60065b 253
kadonotakashi 0:8fdf9a60065b 254 return( NULL );
kadonotakashi 0:8fdf9a60065b 255 }
kadonotakashi 0:8fdf9a60065b 256
kadonotakashi 0:8fdf9a60065b 257 /*
kadonotakashi 0:8fdf9a60065b 258 * Get the type of a curve
kadonotakashi 0:8fdf9a60065b 259 */
kadonotakashi 0:8fdf9a60065b 260 static inline ecp_curve_type ecp_get_type( const mbedtls_ecp_group *grp )
kadonotakashi 0:8fdf9a60065b 261 {
kadonotakashi 0:8fdf9a60065b 262 if( grp->G.X.p == NULL )
kadonotakashi 0:8fdf9a60065b 263 return( ECP_TYPE_NONE );
kadonotakashi 0:8fdf9a60065b 264
kadonotakashi 0:8fdf9a60065b 265 if( grp->G.Y.p == NULL )
kadonotakashi 0:8fdf9a60065b 266 return( ECP_TYPE_MONTGOMERY );
kadonotakashi 0:8fdf9a60065b 267 else
kadonotakashi 0:8fdf9a60065b 268 return( ECP_TYPE_SHORT_WEIERSTRASS );
kadonotakashi 0:8fdf9a60065b 269 }
kadonotakashi 0:8fdf9a60065b 270
kadonotakashi 0:8fdf9a60065b 271 /*
kadonotakashi 0:8fdf9a60065b 272 * Initialize (the components of) a point
kadonotakashi 0:8fdf9a60065b 273 */
kadonotakashi 0:8fdf9a60065b 274 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
kadonotakashi 0:8fdf9a60065b 275 {
kadonotakashi 0:8fdf9a60065b 276 if( pt == NULL )
kadonotakashi 0:8fdf9a60065b 277 return;
kadonotakashi 0:8fdf9a60065b 278
kadonotakashi 0:8fdf9a60065b 279 mbedtls_mpi_init( &pt->X );
kadonotakashi 0:8fdf9a60065b 280 mbedtls_mpi_init( &pt->Y );
kadonotakashi 0:8fdf9a60065b 281 mbedtls_mpi_init( &pt->Z );
kadonotakashi 0:8fdf9a60065b 282 }
kadonotakashi 0:8fdf9a60065b 283
kadonotakashi 0:8fdf9a60065b 284 /*
kadonotakashi 0:8fdf9a60065b 285 * Initialize (the components of) a group
kadonotakashi 0:8fdf9a60065b 286 */
kadonotakashi 0:8fdf9a60065b 287 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
kadonotakashi 0:8fdf9a60065b 288 {
kadonotakashi 0:8fdf9a60065b 289 if( grp == NULL )
kadonotakashi 0:8fdf9a60065b 290 return;
kadonotakashi 0:8fdf9a60065b 291
kadonotakashi 0:8fdf9a60065b 292 memset( grp, 0, sizeof( mbedtls_ecp_group ) );
kadonotakashi 0:8fdf9a60065b 293 }
kadonotakashi 0:8fdf9a60065b 294
kadonotakashi 0:8fdf9a60065b 295 /*
kadonotakashi 0:8fdf9a60065b 296 * Initialize (the components of) a key pair
kadonotakashi 0:8fdf9a60065b 297 */
kadonotakashi 0:8fdf9a60065b 298 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
kadonotakashi 0:8fdf9a60065b 299 {
kadonotakashi 0:8fdf9a60065b 300 if( key == NULL )
kadonotakashi 0:8fdf9a60065b 301 return;
kadonotakashi 0:8fdf9a60065b 302
kadonotakashi 0:8fdf9a60065b 303 mbedtls_ecp_group_init( &key->grp );
kadonotakashi 0:8fdf9a60065b 304 mbedtls_mpi_init( &key->d );
kadonotakashi 0:8fdf9a60065b 305 mbedtls_ecp_point_init( &key->Q );
kadonotakashi 0:8fdf9a60065b 306 }
kadonotakashi 0:8fdf9a60065b 307
kadonotakashi 0:8fdf9a60065b 308 /*
kadonotakashi 0:8fdf9a60065b 309 * Unallocate (the components of) a point
kadonotakashi 0:8fdf9a60065b 310 */
kadonotakashi 0:8fdf9a60065b 311 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
kadonotakashi 0:8fdf9a60065b 312 {
kadonotakashi 0:8fdf9a60065b 313 if( pt == NULL )
kadonotakashi 0:8fdf9a60065b 314 return;
kadonotakashi 0:8fdf9a60065b 315
kadonotakashi 0:8fdf9a60065b 316 mbedtls_mpi_free( &( pt->X ) );
kadonotakashi 0:8fdf9a60065b 317 mbedtls_mpi_free( &( pt->Y ) );
kadonotakashi 0:8fdf9a60065b 318 mbedtls_mpi_free( &( pt->Z ) );
kadonotakashi 0:8fdf9a60065b 319 }
kadonotakashi 0:8fdf9a60065b 320
kadonotakashi 0:8fdf9a60065b 321 /*
kadonotakashi 0:8fdf9a60065b 322 * Unallocate (the components of) a group
kadonotakashi 0:8fdf9a60065b 323 */
kadonotakashi 0:8fdf9a60065b 324 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
kadonotakashi 0:8fdf9a60065b 325 {
kadonotakashi 0:8fdf9a60065b 326 size_t i;
kadonotakashi 0:8fdf9a60065b 327
kadonotakashi 0:8fdf9a60065b 328 if( grp == NULL )
kadonotakashi 0:8fdf9a60065b 329 return;
kadonotakashi 0:8fdf9a60065b 330
kadonotakashi 0:8fdf9a60065b 331 if( grp->h != 1 )
kadonotakashi 0:8fdf9a60065b 332 {
kadonotakashi 0:8fdf9a60065b 333 mbedtls_mpi_free( &grp->P );
kadonotakashi 0:8fdf9a60065b 334 mbedtls_mpi_free( &grp->A );
kadonotakashi 0:8fdf9a60065b 335 mbedtls_mpi_free( &grp->B );
kadonotakashi 0:8fdf9a60065b 336 mbedtls_ecp_point_free( &grp->G );
kadonotakashi 0:8fdf9a60065b 337 mbedtls_mpi_free( &grp->N );
kadonotakashi 0:8fdf9a60065b 338 }
kadonotakashi 0:8fdf9a60065b 339
kadonotakashi 0:8fdf9a60065b 340 if( grp->T != NULL )
kadonotakashi 0:8fdf9a60065b 341 {
kadonotakashi 0:8fdf9a60065b 342 for( i = 0; i < grp->T_size; i++ )
kadonotakashi 0:8fdf9a60065b 343 mbedtls_ecp_point_free( &grp->T[i] );
kadonotakashi 0:8fdf9a60065b 344 mbedtls_free( grp->T );
kadonotakashi 0:8fdf9a60065b 345 }
kadonotakashi 0:8fdf9a60065b 346
kadonotakashi 0:8fdf9a60065b 347 mbedtls_platform_zeroize( grp, sizeof( mbedtls_ecp_group ) );
kadonotakashi 0:8fdf9a60065b 348 }
kadonotakashi 0:8fdf9a60065b 349
kadonotakashi 0:8fdf9a60065b 350 /*
kadonotakashi 0:8fdf9a60065b 351 * Unallocate (the components of) a key pair
kadonotakashi 0:8fdf9a60065b 352 */
kadonotakashi 0:8fdf9a60065b 353 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
kadonotakashi 0:8fdf9a60065b 354 {
kadonotakashi 0:8fdf9a60065b 355 if( key == NULL )
kadonotakashi 0:8fdf9a60065b 356 return;
kadonotakashi 0:8fdf9a60065b 357
kadonotakashi 0:8fdf9a60065b 358 mbedtls_ecp_group_free( &key->grp );
kadonotakashi 0:8fdf9a60065b 359 mbedtls_mpi_free( &key->d );
kadonotakashi 0:8fdf9a60065b 360 mbedtls_ecp_point_free( &key->Q );
kadonotakashi 0:8fdf9a60065b 361 }
kadonotakashi 0:8fdf9a60065b 362
kadonotakashi 0:8fdf9a60065b 363 /*
kadonotakashi 0:8fdf9a60065b 364 * Copy the contents of a point
kadonotakashi 0:8fdf9a60065b 365 */
kadonotakashi 0:8fdf9a60065b 366 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
kadonotakashi 0:8fdf9a60065b 367 {
kadonotakashi 0:8fdf9a60065b 368 int ret;
kadonotakashi 0:8fdf9a60065b 369
kadonotakashi 0:8fdf9a60065b 370 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) );
kadonotakashi 0:8fdf9a60065b 371 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) );
kadonotakashi 0:8fdf9a60065b 372 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) );
kadonotakashi 0:8fdf9a60065b 373
kadonotakashi 0:8fdf9a60065b 374 cleanup:
kadonotakashi 0:8fdf9a60065b 375 return( ret );
kadonotakashi 0:8fdf9a60065b 376 }
kadonotakashi 0:8fdf9a60065b 377
kadonotakashi 0:8fdf9a60065b 378 /*
kadonotakashi 0:8fdf9a60065b 379 * Copy the contents of a group object
kadonotakashi 0:8fdf9a60065b 380 */
kadonotakashi 0:8fdf9a60065b 381 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
kadonotakashi 0:8fdf9a60065b 382 {
kadonotakashi 0:8fdf9a60065b 383 return mbedtls_ecp_group_load( dst, src->id );
kadonotakashi 0:8fdf9a60065b 384 }
kadonotakashi 0:8fdf9a60065b 385
kadonotakashi 0:8fdf9a60065b 386 /*
kadonotakashi 0:8fdf9a60065b 387 * Set point to zero
kadonotakashi 0:8fdf9a60065b 388 */
kadonotakashi 0:8fdf9a60065b 389 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
kadonotakashi 0:8fdf9a60065b 390 {
kadonotakashi 0:8fdf9a60065b 391 int ret;
kadonotakashi 0:8fdf9a60065b 392
kadonotakashi 0:8fdf9a60065b 393 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) );
kadonotakashi 0:8fdf9a60065b 394 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) );
kadonotakashi 0:8fdf9a60065b 395 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) );
kadonotakashi 0:8fdf9a60065b 396
kadonotakashi 0:8fdf9a60065b 397 cleanup:
kadonotakashi 0:8fdf9a60065b 398 return( ret );
kadonotakashi 0:8fdf9a60065b 399 }
kadonotakashi 0:8fdf9a60065b 400
kadonotakashi 0:8fdf9a60065b 401 /*
kadonotakashi 0:8fdf9a60065b 402 * Tell if a point is zero
kadonotakashi 0:8fdf9a60065b 403 */
kadonotakashi 0:8fdf9a60065b 404 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
kadonotakashi 0:8fdf9a60065b 405 {
kadonotakashi 0:8fdf9a60065b 406 return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 );
kadonotakashi 0:8fdf9a60065b 407 }
kadonotakashi 0:8fdf9a60065b 408
kadonotakashi 0:8fdf9a60065b 409 /*
kadonotakashi 0:8fdf9a60065b 410 * Compare two points lazyly
kadonotakashi 0:8fdf9a60065b 411 */
kadonotakashi 0:8fdf9a60065b 412 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
kadonotakashi 0:8fdf9a60065b 413 const mbedtls_ecp_point *Q )
kadonotakashi 0:8fdf9a60065b 414 {
kadonotakashi 0:8fdf9a60065b 415 if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
kadonotakashi 0:8fdf9a60065b 416 mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 &&
kadonotakashi 0:8fdf9a60065b 417 mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 )
kadonotakashi 0:8fdf9a60065b 418 {
kadonotakashi 0:8fdf9a60065b 419 return( 0 );
kadonotakashi 0:8fdf9a60065b 420 }
kadonotakashi 0:8fdf9a60065b 421
kadonotakashi 0:8fdf9a60065b 422 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 423 }
kadonotakashi 0:8fdf9a60065b 424
kadonotakashi 0:8fdf9a60065b 425 /*
kadonotakashi 0:8fdf9a60065b 426 * Import a non-zero point from ASCII strings
kadonotakashi 0:8fdf9a60065b 427 */
kadonotakashi 0:8fdf9a60065b 428 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
kadonotakashi 0:8fdf9a60065b 429 const char *x, const char *y )
kadonotakashi 0:8fdf9a60065b 430 {
kadonotakashi 0:8fdf9a60065b 431 int ret;
kadonotakashi 0:8fdf9a60065b 432
kadonotakashi 0:8fdf9a60065b 433 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) );
kadonotakashi 0:8fdf9a60065b 434 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) );
kadonotakashi 0:8fdf9a60065b 435 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
kadonotakashi 0:8fdf9a60065b 436
kadonotakashi 0:8fdf9a60065b 437 cleanup:
kadonotakashi 0:8fdf9a60065b 438 return( ret );
kadonotakashi 0:8fdf9a60065b 439 }
kadonotakashi 0:8fdf9a60065b 440
kadonotakashi 0:8fdf9a60065b 441 /*
kadonotakashi 0:8fdf9a60065b 442 * Export a point into unsigned binary data (SEC1 2.3.3)
kadonotakashi 0:8fdf9a60065b 443 */
kadonotakashi 0:8fdf9a60065b 444 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P,
kadonotakashi 0:8fdf9a60065b 445 int format, size_t *olen,
kadonotakashi 0:8fdf9a60065b 446 unsigned char *buf, size_t buflen )
kadonotakashi 0:8fdf9a60065b 447 {
kadonotakashi 0:8fdf9a60065b 448 int ret = 0;
kadonotakashi 0:8fdf9a60065b 449 size_t plen;
kadonotakashi 0:8fdf9a60065b 450
kadonotakashi 0:8fdf9a60065b 451 if( format != MBEDTLS_ECP_PF_UNCOMPRESSED &&
kadonotakashi 0:8fdf9a60065b 452 format != MBEDTLS_ECP_PF_COMPRESSED )
kadonotakashi 0:8fdf9a60065b 453 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 454
kadonotakashi 0:8fdf9a60065b 455 /*
kadonotakashi 0:8fdf9a60065b 456 * Common case: P == 0
kadonotakashi 0:8fdf9a60065b 457 */
kadonotakashi 0:8fdf9a60065b 458 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
kadonotakashi 0:8fdf9a60065b 459 {
kadonotakashi 0:8fdf9a60065b 460 if( buflen < 1 )
kadonotakashi 0:8fdf9a60065b 461 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
kadonotakashi 0:8fdf9a60065b 462
kadonotakashi 0:8fdf9a60065b 463 buf[0] = 0x00;
kadonotakashi 0:8fdf9a60065b 464 *olen = 1;
kadonotakashi 0:8fdf9a60065b 465
kadonotakashi 0:8fdf9a60065b 466 return( 0 );
kadonotakashi 0:8fdf9a60065b 467 }
kadonotakashi 0:8fdf9a60065b 468
kadonotakashi 0:8fdf9a60065b 469 plen = mbedtls_mpi_size( &grp->P );
kadonotakashi 0:8fdf9a60065b 470
kadonotakashi 0:8fdf9a60065b 471 if( format == MBEDTLS_ECP_PF_UNCOMPRESSED )
kadonotakashi 0:8fdf9a60065b 472 {
kadonotakashi 0:8fdf9a60065b 473 *olen = 2 * plen + 1;
kadonotakashi 0:8fdf9a60065b 474
kadonotakashi 0:8fdf9a60065b 475 if( buflen < *olen )
kadonotakashi 0:8fdf9a60065b 476 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
kadonotakashi 0:8fdf9a60065b 477
kadonotakashi 0:8fdf9a60065b 478 buf[0] = 0x04;
kadonotakashi 0:8fdf9a60065b 479 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
kadonotakashi 0:8fdf9a60065b 480 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) );
kadonotakashi 0:8fdf9a60065b 481 }
kadonotakashi 0:8fdf9a60065b 482 else if( format == MBEDTLS_ECP_PF_COMPRESSED )
kadonotakashi 0:8fdf9a60065b 483 {
kadonotakashi 0:8fdf9a60065b 484 *olen = plen + 1;
kadonotakashi 0:8fdf9a60065b 485
kadonotakashi 0:8fdf9a60065b 486 if( buflen < *olen )
kadonotakashi 0:8fdf9a60065b 487 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
kadonotakashi 0:8fdf9a60065b 488
kadonotakashi 0:8fdf9a60065b 489 buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 );
kadonotakashi 0:8fdf9a60065b 490 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
kadonotakashi 0:8fdf9a60065b 491 }
kadonotakashi 0:8fdf9a60065b 492
kadonotakashi 0:8fdf9a60065b 493 cleanup:
kadonotakashi 0:8fdf9a60065b 494 return( ret );
kadonotakashi 0:8fdf9a60065b 495 }
kadonotakashi 0:8fdf9a60065b 496
kadonotakashi 0:8fdf9a60065b 497 /*
kadonotakashi 0:8fdf9a60065b 498 * Import a point from unsigned binary data (SEC1 2.3.4)
kadonotakashi 0:8fdf9a60065b 499 */
kadonotakashi 0:8fdf9a60065b 500 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
kadonotakashi 0:8fdf9a60065b 501 const unsigned char *buf, size_t ilen )
kadonotakashi 0:8fdf9a60065b 502 {
kadonotakashi 0:8fdf9a60065b 503 int ret;
kadonotakashi 0:8fdf9a60065b 504 size_t plen;
kadonotakashi 0:8fdf9a60065b 505
kadonotakashi 0:8fdf9a60065b 506 if( ilen < 1 )
kadonotakashi 0:8fdf9a60065b 507 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 508
kadonotakashi 0:8fdf9a60065b 509 if( buf[0] == 0x00 )
kadonotakashi 0:8fdf9a60065b 510 {
kadonotakashi 0:8fdf9a60065b 511 if( ilen == 1 )
kadonotakashi 0:8fdf9a60065b 512 return( mbedtls_ecp_set_zero( pt ) );
kadonotakashi 0:8fdf9a60065b 513 else
kadonotakashi 0:8fdf9a60065b 514 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 515 }
kadonotakashi 0:8fdf9a60065b 516
kadonotakashi 0:8fdf9a60065b 517 plen = mbedtls_mpi_size( &grp->P );
kadonotakashi 0:8fdf9a60065b 518
kadonotakashi 0:8fdf9a60065b 519 if( buf[0] != 0x04 )
kadonotakashi 0:8fdf9a60065b 520 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
kadonotakashi 0:8fdf9a60065b 521
kadonotakashi 0:8fdf9a60065b 522 if( ilen != 2 * plen + 1 )
kadonotakashi 0:8fdf9a60065b 523 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 524
kadonotakashi 0:8fdf9a60065b 525 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
kadonotakashi 0:8fdf9a60065b 526 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, buf + 1 + plen, plen ) );
kadonotakashi 0:8fdf9a60065b 527 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
kadonotakashi 0:8fdf9a60065b 528
kadonotakashi 0:8fdf9a60065b 529 cleanup:
kadonotakashi 0:8fdf9a60065b 530 return( ret );
kadonotakashi 0:8fdf9a60065b 531 }
kadonotakashi 0:8fdf9a60065b 532
kadonotakashi 0:8fdf9a60065b 533 /*
kadonotakashi 0:8fdf9a60065b 534 * Import a point from a TLS ECPoint record (RFC 4492)
kadonotakashi 0:8fdf9a60065b 535 * struct {
kadonotakashi 0:8fdf9a60065b 536 * opaque point <1..2^8-1>;
kadonotakashi 0:8fdf9a60065b 537 * } ECPoint;
kadonotakashi 0:8fdf9a60065b 538 */
kadonotakashi 0:8fdf9a60065b 539 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
kadonotakashi 0:8fdf9a60065b 540 const unsigned char **buf, size_t buf_len )
kadonotakashi 0:8fdf9a60065b 541 {
kadonotakashi 0:8fdf9a60065b 542 unsigned char data_len;
kadonotakashi 0:8fdf9a60065b 543 const unsigned char *buf_start;
kadonotakashi 0:8fdf9a60065b 544
kadonotakashi 0:8fdf9a60065b 545 /*
kadonotakashi 0:8fdf9a60065b 546 * We must have at least two bytes (1 for length, at least one for data)
kadonotakashi 0:8fdf9a60065b 547 */
kadonotakashi 0:8fdf9a60065b 548 if( buf_len < 2 )
kadonotakashi 0:8fdf9a60065b 549 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 550
kadonotakashi 0:8fdf9a60065b 551 data_len = *(*buf)++;
kadonotakashi 0:8fdf9a60065b 552 if( data_len < 1 || data_len > buf_len - 1 )
kadonotakashi 0:8fdf9a60065b 553 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 554
kadonotakashi 0:8fdf9a60065b 555 /*
kadonotakashi 0:8fdf9a60065b 556 * Save buffer start for read_binary and update buf
kadonotakashi 0:8fdf9a60065b 557 */
kadonotakashi 0:8fdf9a60065b 558 buf_start = *buf;
kadonotakashi 0:8fdf9a60065b 559 *buf += data_len;
kadonotakashi 0:8fdf9a60065b 560
kadonotakashi 0:8fdf9a60065b 561 return mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len );
kadonotakashi 0:8fdf9a60065b 562 }
kadonotakashi 0:8fdf9a60065b 563
kadonotakashi 0:8fdf9a60065b 564 /*
kadonotakashi 0:8fdf9a60065b 565 * Export a point as a TLS ECPoint record (RFC 4492)
kadonotakashi 0:8fdf9a60065b 566 * struct {
kadonotakashi 0:8fdf9a60065b 567 * opaque point <1..2^8-1>;
kadonotakashi 0:8fdf9a60065b 568 * } ECPoint;
kadonotakashi 0:8fdf9a60065b 569 */
kadonotakashi 0:8fdf9a60065b 570 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
kadonotakashi 0:8fdf9a60065b 571 int format, size_t *olen,
kadonotakashi 0:8fdf9a60065b 572 unsigned char *buf, size_t blen )
kadonotakashi 0:8fdf9a60065b 573 {
kadonotakashi 0:8fdf9a60065b 574 int ret;
kadonotakashi 0:8fdf9a60065b 575
kadonotakashi 0:8fdf9a60065b 576 /*
kadonotakashi 0:8fdf9a60065b 577 * buffer length must be at least one, for our length byte
kadonotakashi 0:8fdf9a60065b 578 */
kadonotakashi 0:8fdf9a60065b 579 if( blen < 1 )
kadonotakashi 0:8fdf9a60065b 580 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 581
kadonotakashi 0:8fdf9a60065b 582 if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
kadonotakashi 0:8fdf9a60065b 583 olen, buf + 1, blen - 1) ) != 0 )
kadonotakashi 0:8fdf9a60065b 584 return( ret );
kadonotakashi 0:8fdf9a60065b 585
kadonotakashi 0:8fdf9a60065b 586 /*
kadonotakashi 0:8fdf9a60065b 587 * write length to the first byte and update total length
kadonotakashi 0:8fdf9a60065b 588 */
kadonotakashi 0:8fdf9a60065b 589 buf[0] = (unsigned char) *olen;
kadonotakashi 0:8fdf9a60065b 590 ++*olen;
kadonotakashi 0:8fdf9a60065b 591
kadonotakashi 0:8fdf9a60065b 592 return( 0 );
kadonotakashi 0:8fdf9a60065b 593 }
kadonotakashi 0:8fdf9a60065b 594
kadonotakashi 0:8fdf9a60065b 595 /*
kadonotakashi 0:8fdf9a60065b 596 * Set a group from an ECParameters record (RFC 4492)
kadonotakashi 0:8fdf9a60065b 597 */
kadonotakashi 0:8fdf9a60065b 598 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, const unsigned char **buf, size_t len )
kadonotakashi 0:8fdf9a60065b 599 {
kadonotakashi 0:8fdf9a60065b 600 uint16_t tls_id;
kadonotakashi 0:8fdf9a60065b 601 const mbedtls_ecp_curve_info *curve_info;
kadonotakashi 0:8fdf9a60065b 602
kadonotakashi 0:8fdf9a60065b 603 /*
kadonotakashi 0:8fdf9a60065b 604 * We expect at least three bytes (see below)
kadonotakashi 0:8fdf9a60065b 605 */
kadonotakashi 0:8fdf9a60065b 606 if( len < 3 )
kadonotakashi 0:8fdf9a60065b 607 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 608
kadonotakashi 0:8fdf9a60065b 609 /*
kadonotakashi 0:8fdf9a60065b 610 * First byte is curve_type; only named_curve is handled
kadonotakashi 0:8fdf9a60065b 611 */
kadonotakashi 0:8fdf9a60065b 612 if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
kadonotakashi 0:8fdf9a60065b 613 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 614
kadonotakashi 0:8fdf9a60065b 615 /*
kadonotakashi 0:8fdf9a60065b 616 * Next two bytes are the namedcurve value
kadonotakashi 0:8fdf9a60065b 617 */
kadonotakashi 0:8fdf9a60065b 618 tls_id = *(*buf)++;
kadonotakashi 0:8fdf9a60065b 619 tls_id <<= 8;
kadonotakashi 0:8fdf9a60065b 620 tls_id |= *(*buf)++;
kadonotakashi 0:8fdf9a60065b 621
kadonotakashi 0:8fdf9a60065b 622 if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
kadonotakashi 0:8fdf9a60065b 623 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
kadonotakashi 0:8fdf9a60065b 624
kadonotakashi 0:8fdf9a60065b 625 return mbedtls_ecp_group_load( grp, curve_info->grp_id );
kadonotakashi 0:8fdf9a60065b 626 }
kadonotakashi 0:8fdf9a60065b 627
kadonotakashi 0:8fdf9a60065b 628 /*
kadonotakashi 0:8fdf9a60065b 629 * Write the ECParameters record corresponding to a group (RFC 4492)
kadonotakashi 0:8fdf9a60065b 630 */
kadonotakashi 0:8fdf9a60065b 631 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
kadonotakashi 0:8fdf9a60065b 632 unsigned char *buf, size_t blen )
kadonotakashi 0:8fdf9a60065b 633 {
kadonotakashi 0:8fdf9a60065b 634 const mbedtls_ecp_curve_info *curve_info;
kadonotakashi 0:8fdf9a60065b 635
kadonotakashi 0:8fdf9a60065b 636 if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
kadonotakashi 0:8fdf9a60065b 637 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 638
kadonotakashi 0:8fdf9a60065b 639 /*
kadonotakashi 0:8fdf9a60065b 640 * We are going to write 3 bytes (see below)
kadonotakashi 0:8fdf9a60065b 641 */
kadonotakashi 0:8fdf9a60065b 642 *olen = 3;
kadonotakashi 0:8fdf9a60065b 643 if( blen < *olen )
kadonotakashi 0:8fdf9a60065b 644 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
kadonotakashi 0:8fdf9a60065b 645
kadonotakashi 0:8fdf9a60065b 646 /*
kadonotakashi 0:8fdf9a60065b 647 * First byte is curve_type, always named_curve
kadonotakashi 0:8fdf9a60065b 648 */
kadonotakashi 0:8fdf9a60065b 649 *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
kadonotakashi 0:8fdf9a60065b 650
kadonotakashi 0:8fdf9a60065b 651 /*
kadonotakashi 0:8fdf9a60065b 652 * Next two bytes are the namedcurve value
kadonotakashi 0:8fdf9a60065b 653 */
kadonotakashi 0:8fdf9a60065b 654 buf[0] = curve_info->tls_id >> 8;
kadonotakashi 0:8fdf9a60065b 655 buf[1] = curve_info->tls_id & 0xFF;
kadonotakashi 0:8fdf9a60065b 656
kadonotakashi 0:8fdf9a60065b 657 return( 0 );
kadonotakashi 0:8fdf9a60065b 658 }
kadonotakashi 0:8fdf9a60065b 659
kadonotakashi 0:8fdf9a60065b 660 /*
kadonotakashi 0:8fdf9a60065b 661 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
kadonotakashi 0:8fdf9a60065b 662 * See the documentation of struct mbedtls_ecp_group.
kadonotakashi 0:8fdf9a60065b 663 *
kadonotakashi 0:8fdf9a60065b 664 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
kadonotakashi 0:8fdf9a60065b 665 */
kadonotakashi 0:8fdf9a60065b 666 static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
kadonotakashi 0:8fdf9a60065b 667 {
kadonotakashi 0:8fdf9a60065b 668 int ret;
kadonotakashi 0:8fdf9a60065b 669
kadonotakashi 0:8fdf9a60065b 670 if( grp->modp == NULL )
kadonotakashi 0:8fdf9a60065b 671 return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) );
kadonotakashi 0:8fdf9a60065b 672
kadonotakashi 0:8fdf9a60065b 673 /* N->s < 0 is a much faster test, which fails only if N is 0 */
kadonotakashi 0:8fdf9a60065b 674 if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) ||
kadonotakashi 0:8fdf9a60065b 675 mbedtls_mpi_bitlen( N ) > 2 * grp->pbits )
kadonotakashi 0:8fdf9a60065b 676 {
kadonotakashi 0:8fdf9a60065b 677 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 678 }
kadonotakashi 0:8fdf9a60065b 679
kadonotakashi 0:8fdf9a60065b 680 MBEDTLS_MPI_CHK( grp->modp( N ) );
kadonotakashi 0:8fdf9a60065b 681
kadonotakashi 0:8fdf9a60065b 682 /* N->s < 0 is a much faster test, which fails only if N is 0 */
kadonotakashi 0:8fdf9a60065b 683 while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 )
kadonotakashi 0:8fdf9a60065b 684 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) );
kadonotakashi 0:8fdf9a60065b 685
kadonotakashi 0:8fdf9a60065b 686 while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 )
kadonotakashi 0:8fdf9a60065b 687 /* we known P, N and the result are positive */
kadonotakashi 0:8fdf9a60065b 688 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) );
kadonotakashi 0:8fdf9a60065b 689
kadonotakashi 0:8fdf9a60065b 690 cleanup:
kadonotakashi 0:8fdf9a60065b 691 return( ret );
kadonotakashi 0:8fdf9a60065b 692 }
kadonotakashi 0:8fdf9a60065b 693
kadonotakashi 0:8fdf9a60065b 694 /*
kadonotakashi 0:8fdf9a60065b 695 * Fast mod-p functions expect their argument to be in the 0..p^2 range.
kadonotakashi 0:8fdf9a60065b 696 *
kadonotakashi 0:8fdf9a60065b 697 * In order to guarantee that, we need to ensure that operands of
kadonotakashi 0:8fdf9a60065b 698 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will
kadonotakashi 0:8fdf9a60065b 699 * bring the result back to this range.
kadonotakashi 0:8fdf9a60065b 700 *
kadonotakashi 0:8fdf9a60065b 701 * The following macros are shortcuts for doing that.
kadonotakashi 0:8fdf9a60065b 702 */
kadonotakashi 0:8fdf9a60065b 703
kadonotakashi 0:8fdf9a60065b 704 /*
kadonotakashi 0:8fdf9a60065b 705 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
kadonotakashi 0:8fdf9a60065b 706 */
kadonotakashi 0:8fdf9a60065b 707 #if defined(MBEDTLS_SELF_TEST)
kadonotakashi 0:8fdf9a60065b 708 #define INC_MUL_COUNT mul_count++;
kadonotakashi 0:8fdf9a60065b 709 #else
kadonotakashi 0:8fdf9a60065b 710 #define INC_MUL_COUNT
kadonotakashi 0:8fdf9a60065b 711 #endif
kadonotakashi 0:8fdf9a60065b 712
kadonotakashi 0:8fdf9a60065b 713 #define MOD_MUL( N ) do { MBEDTLS_MPI_CHK( ecp_modp( &N, grp ) ); INC_MUL_COUNT } \
kadonotakashi 0:8fdf9a60065b 714 while( 0 )
kadonotakashi 0:8fdf9a60065b 715
kadonotakashi 0:8fdf9a60065b 716 /*
kadonotakashi 0:8fdf9a60065b 717 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
kadonotakashi 0:8fdf9a60065b 718 * N->s < 0 is a very fast test, which fails only if N is 0
kadonotakashi 0:8fdf9a60065b 719 */
kadonotakashi 0:8fdf9a60065b 720 #define MOD_SUB( N ) \
kadonotakashi 0:8fdf9a60065b 721 while( N.s < 0 && mbedtls_mpi_cmp_int( &N, 0 ) != 0 ) \
kadonotakashi 0:8fdf9a60065b 722 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &N, &N, &grp->P ) )
kadonotakashi 0:8fdf9a60065b 723
kadonotakashi 0:8fdf9a60065b 724 /*
kadonotakashi 0:8fdf9a60065b 725 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
kadonotakashi 0:8fdf9a60065b 726 * We known P, N and the result are positive, so sub_abs is correct, and
kadonotakashi 0:8fdf9a60065b 727 * a bit faster.
kadonotakashi 0:8fdf9a60065b 728 */
kadonotakashi 0:8fdf9a60065b 729 #define MOD_ADD( N ) \
kadonotakashi 0:8fdf9a60065b 730 while( mbedtls_mpi_cmp_mpi( &N, &grp->P ) >= 0 ) \
kadonotakashi 0:8fdf9a60065b 731 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &N, &N, &grp->P ) )
kadonotakashi 0:8fdf9a60065b 732
kadonotakashi 0:8fdf9a60065b 733 #if defined(ECP_SHORTWEIERSTRASS)
kadonotakashi 0:8fdf9a60065b 734 /*
kadonotakashi 0:8fdf9a60065b 735 * For curves in short Weierstrass form, we do all the internal operations in
kadonotakashi 0:8fdf9a60065b 736 * Jacobian coordinates.
kadonotakashi 0:8fdf9a60065b 737 *
kadonotakashi 0:8fdf9a60065b 738 * For multiplication, we'll use a comb method with coutermeasueres against
kadonotakashi 0:8fdf9a60065b 739 * SPA, hence timing attacks.
kadonotakashi 0:8fdf9a60065b 740 */
kadonotakashi 0:8fdf9a60065b 741
kadonotakashi 0:8fdf9a60065b 742 /*
kadonotakashi 0:8fdf9a60065b 743 * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
kadonotakashi 0:8fdf9a60065b 744 * Cost: 1N := 1I + 3M + 1S
kadonotakashi 0:8fdf9a60065b 745 */
kadonotakashi 0:8fdf9a60065b 746 static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
kadonotakashi 0:8fdf9a60065b 747 {
kadonotakashi 0:8fdf9a60065b 748 int ret;
kadonotakashi 0:8fdf9a60065b 749 mbedtls_mpi Zi, ZZi;
kadonotakashi 0:8fdf9a60065b 750
kadonotakashi 0:8fdf9a60065b 751 if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
kadonotakashi 0:8fdf9a60065b 752 return( 0 );
kadonotakashi 0:8fdf9a60065b 753
kadonotakashi 0:8fdf9a60065b 754 #if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
kadonotakashi 0:8fdf9a60065b 755 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kadonotakashi 0:8fdf9a60065b 756 {
kadonotakashi 0:8fdf9a60065b 757 return mbedtls_internal_ecp_normalize_jac( grp, pt );
kadonotakashi 0:8fdf9a60065b 758 }
kadonotakashi 0:8fdf9a60065b 759 #endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */
kadonotakashi 0:8fdf9a60065b 760 mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
kadonotakashi 0:8fdf9a60065b 761
kadonotakashi 0:8fdf9a60065b 762 /*
kadonotakashi 0:8fdf9a60065b 763 * X = X / Z^2 mod p
kadonotakashi 0:8fdf9a60065b 764 */
kadonotakashi 0:8fdf9a60065b 765 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
kadonotakashi 0:8fdf9a60065b 766 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
kadonotakashi 0:8fdf9a60065b 767 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ZZi ) ); MOD_MUL( pt->X );
kadonotakashi 0:8fdf9a60065b 768
kadonotakashi 0:8fdf9a60065b 769 /*
kadonotakashi 0:8fdf9a60065b 770 * Y = Y / Z^3 mod p
kadonotakashi 0:8fdf9a60065b 771 */
kadonotakashi 0:8fdf9a60065b 772 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ZZi ) ); MOD_MUL( pt->Y );
kadonotakashi 0:8fdf9a60065b 773 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &Zi ) ); MOD_MUL( pt->Y );
kadonotakashi 0:8fdf9a60065b 774
kadonotakashi 0:8fdf9a60065b 775 /*
kadonotakashi 0:8fdf9a60065b 776 * Z = 1
kadonotakashi 0:8fdf9a60065b 777 */
kadonotakashi 0:8fdf9a60065b 778 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
kadonotakashi 0:8fdf9a60065b 779
kadonotakashi 0:8fdf9a60065b 780 cleanup:
kadonotakashi 0:8fdf9a60065b 781
kadonotakashi 0:8fdf9a60065b 782 mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
kadonotakashi 0:8fdf9a60065b 783
kadonotakashi 0:8fdf9a60065b 784 return( ret );
kadonotakashi 0:8fdf9a60065b 785 }
kadonotakashi 0:8fdf9a60065b 786
kadonotakashi 0:8fdf9a60065b 787 /*
kadonotakashi 0:8fdf9a60065b 788 * Normalize jacobian coordinates of an array of (pointers to) points,
kadonotakashi 0:8fdf9a60065b 789 * using Montgomery's trick to perform only one inversion mod P.
kadonotakashi 0:8fdf9a60065b 790 * (See for example Cohen's "A Course in Computational Algebraic Number
kadonotakashi 0:8fdf9a60065b 791 * Theory", Algorithm 10.3.4.)
kadonotakashi 0:8fdf9a60065b 792 *
kadonotakashi 0:8fdf9a60065b 793 * Warning: fails (returning an error) if one of the points is zero!
kadonotakashi 0:8fdf9a60065b 794 * This should never happen, see choice of w in ecp_mul_comb().
kadonotakashi 0:8fdf9a60065b 795 *
kadonotakashi 0:8fdf9a60065b 796 * Cost: 1N(t) := 1I + (6t - 3)M + 1S
kadonotakashi 0:8fdf9a60065b 797 */
kadonotakashi 0:8fdf9a60065b 798 static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
kadonotakashi 0:8fdf9a60065b 799 mbedtls_ecp_point *T[], size_t t_len )
kadonotakashi 0:8fdf9a60065b 800 {
kadonotakashi 0:8fdf9a60065b 801 int ret;
kadonotakashi 0:8fdf9a60065b 802 size_t i;
kadonotakashi 0:8fdf9a60065b 803 mbedtls_mpi *c, u, Zi, ZZi;
kadonotakashi 0:8fdf9a60065b 804
kadonotakashi 0:8fdf9a60065b 805 if( t_len < 2 )
kadonotakashi 0:8fdf9a60065b 806 return( ecp_normalize_jac( grp, *T ) );
kadonotakashi 0:8fdf9a60065b 807
kadonotakashi 0:8fdf9a60065b 808 #if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
kadonotakashi 0:8fdf9a60065b 809 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kadonotakashi 0:8fdf9a60065b 810 {
kadonotakashi 0:8fdf9a60065b 811 return mbedtls_internal_ecp_normalize_jac_many(grp, T, t_len);
kadonotakashi 0:8fdf9a60065b 812 }
kadonotakashi 0:8fdf9a60065b 813 #endif
kadonotakashi 0:8fdf9a60065b 814
kadonotakashi 0:8fdf9a60065b 815 if( ( c = mbedtls_calloc( t_len, sizeof( mbedtls_mpi ) ) ) == NULL )
kadonotakashi 0:8fdf9a60065b 816 return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
kadonotakashi 0:8fdf9a60065b 817
kadonotakashi 0:8fdf9a60065b 818 mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
kadonotakashi 0:8fdf9a60065b 819
kadonotakashi 0:8fdf9a60065b 820 /*
kadonotakashi 0:8fdf9a60065b 821 * c[i] = Z_0 * ... * Z_i
kadonotakashi 0:8fdf9a60065b 822 */
kadonotakashi 0:8fdf9a60065b 823 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
kadonotakashi 0:8fdf9a60065b 824 for( i = 1; i < t_len; i++ )
kadonotakashi 0:8fdf9a60065b 825 {
kadonotakashi 0:8fdf9a60065b 826 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &c[i], &c[i-1], &T[i]->Z ) );
kadonotakashi 0:8fdf9a60065b 827 MOD_MUL( c[i] );
kadonotakashi 0:8fdf9a60065b 828 }
kadonotakashi 0:8fdf9a60065b 829
kadonotakashi 0:8fdf9a60065b 830 /*
kadonotakashi 0:8fdf9a60065b 831 * u = 1 / (Z_0 * ... * Z_n) mod P
kadonotakashi 0:8fdf9a60065b 832 */
kadonotakashi 0:8fdf9a60065b 833 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[t_len-1], &grp->P ) );
kadonotakashi 0:8fdf9a60065b 834
kadonotakashi 0:8fdf9a60065b 835 for( i = t_len - 1; ; i-- )
kadonotakashi 0:8fdf9a60065b 836 {
kadonotakashi 0:8fdf9a60065b 837 /*
kadonotakashi 0:8fdf9a60065b 838 * Zi = 1 / Z_i mod p
kadonotakashi 0:8fdf9a60065b 839 * u = 1 / (Z_0 * ... * Z_i) mod P
kadonotakashi 0:8fdf9a60065b 840 */
kadonotakashi 0:8fdf9a60065b 841 if( i == 0 ) {
kadonotakashi 0:8fdf9a60065b 842 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
kadonotakashi 0:8fdf9a60065b 843 }
kadonotakashi 0:8fdf9a60065b 844 else
kadonotakashi 0:8fdf9a60065b 845 {
kadonotakashi 0:8fdf9a60065b 846 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Zi, &u, &c[i-1] ) ); MOD_MUL( Zi );
kadonotakashi 0:8fdf9a60065b 847 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u, &u, &T[i]->Z ) ); MOD_MUL( u );
kadonotakashi 0:8fdf9a60065b 848 }
kadonotakashi 0:8fdf9a60065b 849
kadonotakashi 0:8fdf9a60065b 850 /*
kadonotakashi 0:8fdf9a60065b 851 * proceed as in normalize()
kadonotakashi 0:8fdf9a60065b 852 */
kadonotakashi 0:8fdf9a60065b 853 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
kadonotakashi 0:8fdf9a60065b 854 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->X, &T[i]->X, &ZZi ) ); MOD_MUL( T[i]->X );
kadonotakashi 0:8fdf9a60065b 855 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &ZZi ) ); MOD_MUL( T[i]->Y );
kadonotakashi 0:8fdf9a60065b 856 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &Zi ) ); MOD_MUL( T[i]->Y );
kadonotakashi 0:8fdf9a60065b 857
kadonotakashi 0:8fdf9a60065b 858 /*
kadonotakashi 0:8fdf9a60065b 859 * Post-precessing: reclaim some memory by shrinking coordinates
kadonotakashi 0:8fdf9a60065b 860 * - not storing Z (always 1)
kadonotakashi 0:8fdf9a60065b 861 * - shrinking other coordinates, but still keeping the same number of
kadonotakashi 0:8fdf9a60065b 862 * limbs as P, as otherwise it will too likely be regrown too fast.
kadonotakashi 0:8fdf9a60065b 863 */
kadonotakashi 0:8fdf9a60065b 864 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
kadonotakashi 0:8fdf9a60065b 865 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
kadonotakashi 0:8fdf9a60065b 866 mbedtls_mpi_free( &T[i]->Z );
kadonotakashi 0:8fdf9a60065b 867
kadonotakashi 0:8fdf9a60065b 868 if( i == 0 )
kadonotakashi 0:8fdf9a60065b 869 break;
kadonotakashi 0:8fdf9a60065b 870 }
kadonotakashi 0:8fdf9a60065b 871
kadonotakashi 0:8fdf9a60065b 872 cleanup:
kadonotakashi 0:8fdf9a60065b 873
kadonotakashi 0:8fdf9a60065b 874 mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
kadonotakashi 0:8fdf9a60065b 875 for( i = 0; i < t_len; i++ )
kadonotakashi 0:8fdf9a60065b 876 mbedtls_mpi_free( &c[i] );
kadonotakashi 0:8fdf9a60065b 877 mbedtls_free( c );
kadonotakashi 0:8fdf9a60065b 878
kadonotakashi 0:8fdf9a60065b 879 return( ret );
kadonotakashi 0:8fdf9a60065b 880 }
kadonotakashi 0:8fdf9a60065b 881
kadonotakashi 0:8fdf9a60065b 882 /*
kadonotakashi 0:8fdf9a60065b 883 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
kadonotakashi 0:8fdf9a60065b 884 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
kadonotakashi 0:8fdf9a60065b 885 */
kadonotakashi 0:8fdf9a60065b 886 static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
kadonotakashi 0:8fdf9a60065b 887 mbedtls_ecp_point *Q,
kadonotakashi 0:8fdf9a60065b 888 unsigned char inv )
kadonotakashi 0:8fdf9a60065b 889 {
kadonotakashi 0:8fdf9a60065b 890 int ret;
kadonotakashi 0:8fdf9a60065b 891 unsigned char nonzero;
kadonotakashi 0:8fdf9a60065b 892 mbedtls_mpi mQY;
kadonotakashi 0:8fdf9a60065b 893
kadonotakashi 0:8fdf9a60065b 894 mbedtls_mpi_init( &mQY );
kadonotakashi 0:8fdf9a60065b 895
kadonotakashi 0:8fdf9a60065b 896 /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
kadonotakashi 0:8fdf9a60065b 897 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
kadonotakashi 0:8fdf9a60065b 898 nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
kadonotakashi 0:8fdf9a60065b 899 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
kadonotakashi 0:8fdf9a60065b 900
kadonotakashi 0:8fdf9a60065b 901 cleanup:
kadonotakashi 0:8fdf9a60065b 902 mbedtls_mpi_free( &mQY );
kadonotakashi 0:8fdf9a60065b 903
kadonotakashi 0:8fdf9a60065b 904 return( ret );
kadonotakashi 0:8fdf9a60065b 905 }
kadonotakashi 0:8fdf9a60065b 906
kadonotakashi 0:8fdf9a60065b 907 /*
kadonotakashi 0:8fdf9a60065b 908 * Point doubling R = 2 P, Jacobian coordinates
kadonotakashi 0:8fdf9a60065b 909 *
kadonotakashi 0:8fdf9a60065b 910 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
kadonotakashi 0:8fdf9a60065b 911 *
kadonotakashi 0:8fdf9a60065b 912 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
kadonotakashi 0:8fdf9a60065b 913 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
kadonotakashi 0:8fdf9a60065b 914 *
kadonotakashi 0:8fdf9a60065b 915 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
kadonotakashi 0:8fdf9a60065b 916 *
kadonotakashi 0:8fdf9a60065b 917 * Cost: 1D := 3M + 4S (A == 0)
kadonotakashi 0:8fdf9a60065b 918 * 4M + 4S (A == -3)
kadonotakashi 0:8fdf9a60065b 919 * 3M + 6S + 1a otherwise
kadonotakashi 0:8fdf9a60065b 920 */
kadonotakashi 0:8fdf9a60065b 921 static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kadonotakashi 0:8fdf9a60065b 922 const mbedtls_ecp_point *P )
kadonotakashi 0:8fdf9a60065b 923 {
kadonotakashi 0:8fdf9a60065b 924 int ret;
kadonotakashi 0:8fdf9a60065b 925 mbedtls_mpi M, S, T, U;
kadonotakashi 0:8fdf9a60065b 926
kadonotakashi 0:8fdf9a60065b 927 #if defined(MBEDTLS_SELF_TEST)
kadonotakashi 0:8fdf9a60065b 928 dbl_count++;
kadonotakashi 0:8fdf9a60065b 929 #endif
kadonotakashi 0:8fdf9a60065b 930
kadonotakashi 0:8fdf9a60065b 931 #if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
kadonotakashi 0:8fdf9a60065b 932 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kadonotakashi 0:8fdf9a60065b 933 {
kadonotakashi 0:8fdf9a60065b 934 return mbedtls_internal_ecp_double_jac( grp, R, P );
kadonotakashi 0:8fdf9a60065b 935 }
kadonotakashi 0:8fdf9a60065b 936 #endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */
kadonotakashi 0:8fdf9a60065b 937
kadonotakashi 0:8fdf9a60065b 938 mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
kadonotakashi 0:8fdf9a60065b 939
kadonotakashi 0:8fdf9a60065b 940 /* Special case for A = -3 */
kadonotakashi 0:8fdf9a60065b 941 if( grp->A.p == NULL )
kadonotakashi 0:8fdf9a60065b 942 {
kadonotakashi 0:8fdf9a60065b 943 /* M = 3(X + Z^2)(X - Z^2) */
kadonotakashi 0:8fdf9a60065b 944 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
kadonotakashi 0:8fdf9a60065b 945 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &P->X, &S ) ); MOD_ADD( T );
kadonotakashi 0:8fdf9a60065b 946 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U, &P->X, &S ) ); MOD_SUB( U );
kadonotakashi 0:8fdf9a60065b 947 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &U ) ); MOD_MUL( S );
kadonotakashi 0:8fdf9a60065b 948 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
kadonotakashi 0:8fdf9a60065b 949 }
kadonotakashi 0:8fdf9a60065b 950 else
kadonotakashi 0:8fdf9a60065b 951 {
kadonotakashi 0:8fdf9a60065b 952 /* M = 3.X^2 */
kadonotakashi 0:8fdf9a60065b 953 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &P->X ) ); MOD_MUL( S );
kadonotakashi 0:8fdf9a60065b 954 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
kadonotakashi 0:8fdf9a60065b 955
kadonotakashi 0:8fdf9a60065b 956 /* Optimize away for "koblitz" curves with A = 0 */
kadonotakashi 0:8fdf9a60065b 957 if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
kadonotakashi 0:8fdf9a60065b 958 {
kadonotakashi 0:8fdf9a60065b 959 /* M += A.Z^4 */
kadonotakashi 0:8fdf9a60065b 960 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
kadonotakashi 0:8fdf9a60065b 961 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &S, &S ) ); MOD_MUL( T );
kadonotakashi 0:8fdf9a60065b 962 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &grp->A ) ); MOD_MUL( S );
kadonotakashi 0:8fdf9a60065b 963 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &S ) ); MOD_ADD( M );
kadonotakashi 0:8fdf9a60065b 964 }
kadonotakashi 0:8fdf9a60065b 965 }
kadonotakashi 0:8fdf9a60065b 966
kadonotakashi 0:8fdf9a60065b 967 /* S = 4.X.Y^2 */
kadonotakashi 0:8fdf9a60065b 968 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &P->Y, &P->Y ) ); MOD_MUL( T );
kadonotakashi 0:8fdf9a60065b 969 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T, 1 ) ); MOD_ADD( T );
kadonotakashi 0:8fdf9a60065b 970 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &T ) ); MOD_MUL( S );
kadonotakashi 0:8fdf9a60065b 971 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &S, 1 ) ); MOD_ADD( S );
kadonotakashi 0:8fdf9a60065b 972
kadonotakashi 0:8fdf9a60065b 973 /* U = 8.Y^4 */
kadonotakashi 0:8fdf9a60065b 974 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &T, &T ) ); MOD_MUL( U );
kadonotakashi 0:8fdf9a60065b 975 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
kadonotakashi 0:8fdf9a60065b 976
kadonotakashi 0:8fdf9a60065b 977 /* T = M^2 - 2.S */
kadonotakashi 0:8fdf9a60065b 978 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &M, &M ) ); MOD_MUL( T );
kadonotakashi 0:8fdf9a60065b 979 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
kadonotakashi 0:8fdf9a60065b 980 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
kadonotakashi 0:8fdf9a60065b 981
kadonotakashi 0:8fdf9a60065b 982 /* S = M(S - T) - U */
kadonotakashi 0:8fdf9a60065b 983 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &T ) ); MOD_SUB( S );
kadonotakashi 0:8fdf9a60065b 984 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &S, &M ) ); MOD_MUL( S );
kadonotakashi 0:8fdf9a60065b 985 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &U ) ); MOD_SUB( S );
kadonotakashi 0:8fdf9a60065b 986
kadonotakashi 0:8fdf9a60065b 987 /* U = 2.Y.Z */
kadonotakashi 0:8fdf9a60065b 988 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &P->Y, &P->Z ) ); MOD_MUL( U );
kadonotakashi 0:8fdf9a60065b 989 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
kadonotakashi 0:8fdf9a60065b 990
kadonotakashi 0:8fdf9a60065b 991 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
kadonotakashi 0:8fdf9a60065b 992 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
kadonotakashi 0:8fdf9a60065b 993 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
kadonotakashi 0:8fdf9a60065b 994
kadonotakashi 0:8fdf9a60065b 995 cleanup:
kadonotakashi 0:8fdf9a60065b 996 mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
kadonotakashi 0:8fdf9a60065b 997
kadonotakashi 0:8fdf9a60065b 998 return( ret );
kadonotakashi 0:8fdf9a60065b 999 }
kadonotakashi 0:8fdf9a60065b 1000
kadonotakashi 0:8fdf9a60065b 1001 /*
kadonotakashi 0:8fdf9a60065b 1002 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
kadonotakashi 0:8fdf9a60065b 1003 *
kadonotakashi 0:8fdf9a60065b 1004 * The coordinates of Q must be normalized (= affine),
kadonotakashi 0:8fdf9a60065b 1005 * but those of P don't need to. R is not normalized.
kadonotakashi 0:8fdf9a60065b 1006 *
kadonotakashi 0:8fdf9a60065b 1007 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
kadonotakashi 0:8fdf9a60065b 1008 * None of these cases can happen as intermediate step in ecp_mul_comb():
kadonotakashi 0:8fdf9a60065b 1009 * - at each step, P, Q and R are multiples of the base point, the factor
kadonotakashi 0:8fdf9a60065b 1010 * being less than its order, so none of them is zero;
kadonotakashi 0:8fdf9a60065b 1011 * - Q is an odd multiple of the base point, P an even multiple,
kadonotakashi 0:8fdf9a60065b 1012 * due to the choice of precomputed points in the modified comb method.
kadonotakashi 0:8fdf9a60065b 1013 * So branches for these cases do not leak secret information.
kadonotakashi 0:8fdf9a60065b 1014 *
kadonotakashi 0:8fdf9a60065b 1015 * We accept Q->Z being unset (saving memory in tables) as meaning 1.
kadonotakashi 0:8fdf9a60065b 1016 *
kadonotakashi 0:8fdf9a60065b 1017 * Cost: 1A := 8M + 3S
kadonotakashi 0:8fdf9a60065b 1018 */
kadonotakashi 0:8fdf9a60065b 1019 static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kadonotakashi 0:8fdf9a60065b 1020 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
kadonotakashi 0:8fdf9a60065b 1021 {
kadonotakashi 0:8fdf9a60065b 1022 int ret;
kadonotakashi 0:8fdf9a60065b 1023 mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
kadonotakashi 0:8fdf9a60065b 1024
kadonotakashi 0:8fdf9a60065b 1025 #if defined(MBEDTLS_SELF_TEST)
kadonotakashi 0:8fdf9a60065b 1026 add_count++;
kadonotakashi 0:8fdf9a60065b 1027 #endif
kadonotakashi 0:8fdf9a60065b 1028
kadonotakashi 0:8fdf9a60065b 1029 #if defined(MBEDTLS_ECP_ADD_MIXED_ALT)
kadonotakashi 0:8fdf9a60065b 1030 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kadonotakashi 0:8fdf9a60065b 1031 {
kadonotakashi 0:8fdf9a60065b 1032 return mbedtls_internal_ecp_add_mixed( grp, R, P, Q );
kadonotakashi 0:8fdf9a60065b 1033 }
kadonotakashi 0:8fdf9a60065b 1034 #endif /* MBEDTLS_ECP_ADD_MIXED_ALT */
kadonotakashi 0:8fdf9a60065b 1035
kadonotakashi 0:8fdf9a60065b 1036 /*
kadonotakashi 0:8fdf9a60065b 1037 * Trivial cases: P == 0 or Q == 0 (case 1)
kadonotakashi 0:8fdf9a60065b 1038 */
kadonotakashi 0:8fdf9a60065b 1039 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
kadonotakashi 0:8fdf9a60065b 1040 return( mbedtls_ecp_copy( R, Q ) );
kadonotakashi 0:8fdf9a60065b 1041
kadonotakashi 0:8fdf9a60065b 1042 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
kadonotakashi 0:8fdf9a60065b 1043 return( mbedtls_ecp_copy( R, P ) );
kadonotakashi 0:8fdf9a60065b 1044
kadonotakashi 0:8fdf9a60065b 1045 /*
kadonotakashi 0:8fdf9a60065b 1046 * Make sure Q coordinates are normalized
kadonotakashi 0:8fdf9a60065b 1047 */
kadonotakashi 0:8fdf9a60065b 1048 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
kadonotakashi 0:8fdf9a60065b 1049 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 1050
kadonotakashi 0:8fdf9a60065b 1051 mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
kadonotakashi 0:8fdf9a60065b 1052 mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
kadonotakashi 0:8fdf9a60065b 1053
kadonotakashi 0:8fdf9a60065b 1054 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &P->Z, &P->Z ) ); MOD_MUL( T1 );
kadonotakashi 0:8fdf9a60065b 1055 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T1, &P->Z ) ); MOD_MUL( T2 );
kadonotakashi 0:8fdf9a60065b 1056 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T1, &Q->X ) ); MOD_MUL( T1 );
kadonotakashi 0:8fdf9a60065b 1057 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T2, &Q->Y ) ); MOD_MUL( T2 );
kadonotakashi 0:8fdf9a60065b 1058 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T1, &T1, &P->X ) ); MOD_SUB( T1 );
kadonotakashi 0:8fdf9a60065b 1059 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T2, &T2, &P->Y ) ); MOD_SUB( T2 );
kadonotakashi 0:8fdf9a60065b 1060
kadonotakashi 0:8fdf9a60065b 1061 /* Special cases (2) and (3) */
kadonotakashi 0:8fdf9a60065b 1062 if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
kadonotakashi 0:8fdf9a60065b 1063 {
kadonotakashi 0:8fdf9a60065b 1064 if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
kadonotakashi 0:8fdf9a60065b 1065 {
kadonotakashi 0:8fdf9a60065b 1066 ret = ecp_double_jac( grp, R, P );
kadonotakashi 0:8fdf9a60065b 1067 goto cleanup;
kadonotakashi 0:8fdf9a60065b 1068 }
kadonotakashi 0:8fdf9a60065b 1069 else
kadonotakashi 0:8fdf9a60065b 1070 {
kadonotakashi 0:8fdf9a60065b 1071 ret = mbedtls_ecp_set_zero( R );
kadonotakashi 0:8fdf9a60065b 1072 goto cleanup;
kadonotakashi 0:8fdf9a60065b 1073 }
kadonotakashi 0:8fdf9a60065b 1074 }
kadonotakashi 0:8fdf9a60065b 1075
kadonotakashi 0:8fdf9a60065b 1076 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Z, &P->Z, &T1 ) ); MOD_MUL( Z );
kadonotakashi 0:8fdf9a60065b 1077 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T1, &T1 ) ); MOD_MUL( T3 );
kadonotakashi 0:8fdf9a60065b 1078 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T3, &T1 ) ); MOD_MUL( T4 );
kadonotakashi 0:8fdf9a60065b 1079 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &P->X ) ); MOD_MUL( T3 );
kadonotakashi 0:8fdf9a60065b 1080 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T3, 2 ) ); MOD_ADD( T1 );
kadonotakashi 0:8fdf9a60065b 1081 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &T2, &T2 ) ); MOD_MUL( X );
kadonotakashi 0:8fdf9a60065b 1082 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) ); MOD_SUB( X );
kadonotakashi 0:8fdf9a60065b 1083 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T4 ) ); MOD_SUB( X );
kadonotakashi 0:8fdf9a60065b 1084 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T3, &T3, &X ) ); MOD_SUB( T3 );
kadonotakashi 0:8fdf9a60065b 1085 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &T2 ) ); MOD_MUL( T3 );
kadonotakashi 0:8fdf9a60065b 1086 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T4, &P->Y ) ); MOD_MUL( T4 );
kadonotakashi 0:8fdf9a60065b 1087 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &Y, &T3, &T4 ) ); MOD_SUB( Y );
kadonotakashi 0:8fdf9a60065b 1088
kadonotakashi 0:8fdf9a60065b 1089 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
kadonotakashi 0:8fdf9a60065b 1090 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
kadonotakashi 0:8fdf9a60065b 1091 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
kadonotakashi 0:8fdf9a60065b 1092
kadonotakashi 0:8fdf9a60065b 1093 cleanup:
kadonotakashi 0:8fdf9a60065b 1094
kadonotakashi 0:8fdf9a60065b 1095 mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
kadonotakashi 0:8fdf9a60065b 1096 mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
kadonotakashi 0:8fdf9a60065b 1097
kadonotakashi 0:8fdf9a60065b 1098 return( ret );
kadonotakashi 0:8fdf9a60065b 1099 }
kadonotakashi 0:8fdf9a60065b 1100
kadonotakashi 0:8fdf9a60065b 1101 /*
kadonotakashi 0:8fdf9a60065b 1102 * Randomize jacobian coordinates:
kadonotakashi 0:8fdf9a60065b 1103 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
kadonotakashi 0:8fdf9a60065b 1104 * This is sort of the reverse operation of ecp_normalize_jac().
kadonotakashi 0:8fdf9a60065b 1105 *
kadonotakashi 0:8fdf9a60065b 1106 * This countermeasure was first suggested in [2].
kadonotakashi 0:8fdf9a60065b 1107 */
kadonotakashi 0:8fdf9a60065b 1108 static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
kadonotakashi 0:8fdf9a60065b 1109 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
kadonotakashi 0:8fdf9a60065b 1110 {
kadonotakashi 0:8fdf9a60065b 1111 int ret;
kadonotakashi 0:8fdf9a60065b 1112 mbedtls_mpi l, ll;
kadonotakashi 0:8fdf9a60065b 1113 size_t p_size;
kadonotakashi 0:8fdf9a60065b 1114 int count = 0;
kadonotakashi 0:8fdf9a60065b 1115
kadonotakashi 0:8fdf9a60065b 1116 #if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
kadonotakashi 0:8fdf9a60065b 1117 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kadonotakashi 0:8fdf9a60065b 1118 {
kadonotakashi 0:8fdf9a60065b 1119 return mbedtls_internal_ecp_randomize_jac( grp, pt, f_rng, p_rng );
kadonotakashi 0:8fdf9a60065b 1120 }
kadonotakashi 0:8fdf9a60065b 1121 #endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */
kadonotakashi 0:8fdf9a60065b 1122
kadonotakashi 0:8fdf9a60065b 1123 p_size = ( grp->pbits + 7 ) / 8;
kadonotakashi 0:8fdf9a60065b 1124 mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
kadonotakashi 0:8fdf9a60065b 1125
kadonotakashi 0:8fdf9a60065b 1126 /* Generate l such that 1 < l < p */
kadonotakashi 0:8fdf9a60065b 1127 do
kadonotakashi 0:8fdf9a60065b 1128 {
kadonotakashi 0:8fdf9a60065b 1129 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
kadonotakashi 0:8fdf9a60065b 1130
kadonotakashi 0:8fdf9a60065b 1131 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
kadonotakashi 0:8fdf9a60065b 1132 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
kadonotakashi 0:8fdf9a60065b 1133
kadonotakashi 0:8fdf9a60065b 1134 if( count++ > 10 )
kadonotakashi 0:8fdf9a60065b 1135 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
kadonotakashi 0:8fdf9a60065b 1136 }
kadonotakashi 0:8fdf9a60065b 1137 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
kadonotakashi 0:8fdf9a60065b 1138
kadonotakashi 0:8fdf9a60065b 1139 /* Z = l * Z */
kadonotakashi 0:8fdf9a60065b 1140 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Z, &pt->Z, &l ) ); MOD_MUL( pt->Z );
kadonotakashi 0:8fdf9a60065b 1141
kadonotakashi 0:8fdf9a60065b 1142 /* X = l^2 * X */
kadonotakashi 0:8fdf9a60065b 1143 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &l, &l ) ); MOD_MUL( ll );
kadonotakashi 0:8fdf9a60065b 1144 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ll ) ); MOD_MUL( pt->X );
kadonotakashi 0:8fdf9a60065b 1145
kadonotakashi 0:8fdf9a60065b 1146 /* Y = l^3 * Y */
kadonotakashi 0:8fdf9a60065b 1147 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &ll, &l ) ); MOD_MUL( ll );
kadonotakashi 0:8fdf9a60065b 1148 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ll ) ); MOD_MUL( pt->Y );
kadonotakashi 0:8fdf9a60065b 1149
kadonotakashi 0:8fdf9a60065b 1150 cleanup:
kadonotakashi 0:8fdf9a60065b 1151 mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
kadonotakashi 0:8fdf9a60065b 1152
kadonotakashi 0:8fdf9a60065b 1153 return( ret );
kadonotakashi 0:8fdf9a60065b 1154 }
kadonotakashi 0:8fdf9a60065b 1155
kadonotakashi 0:8fdf9a60065b 1156 /*
kadonotakashi 0:8fdf9a60065b 1157 * Check and define parameters used by the comb method (see below for details)
kadonotakashi 0:8fdf9a60065b 1158 */
kadonotakashi 0:8fdf9a60065b 1159 #if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
kadonotakashi 0:8fdf9a60065b 1160 #error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
kadonotakashi 0:8fdf9a60065b 1161 #endif
kadonotakashi 0:8fdf9a60065b 1162
kadonotakashi 0:8fdf9a60065b 1163 /* d = ceil( n / w ) */
kadonotakashi 0:8fdf9a60065b 1164 #define COMB_MAX_D ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2
kadonotakashi 0:8fdf9a60065b 1165
kadonotakashi 0:8fdf9a60065b 1166 /* number of precomputed points */
kadonotakashi 0:8fdf9a60065b 1167 #define COMB_MAX_PRE ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
kadonotakashi 0:8fdf9a60065b 1168
kadonotakashi 0:8fdf9a60065b 1169 /*
kadonotakashi 0:8fdf9a60065b 1170 * Compute the representation of m that will be used with our comb method.
kadonotakashi 0:8fdf9a60065b 1171 *
kadonotakashi 0:8fdf9a60065b 1172 * The basic comb method is described in GECC 3.44 for example. We use a
kadonotakashi 0:8fdf9a60065b 1173 * modified version that provides resistance to SPA by avoiding zero
kadonotakashi 0:8fdf9a60065b 1174 * digits in the representation as in [3]. We modify the method further by
kadonotakashi 0:8fdf9a60065b 1175 * requiring that all K_i be odd, which has the small cost that our
kadonotakashi 0:8fdf9a60065b 1176 * representation uses one more K_i, due to carries.
kadonotakashi 0:8fdf9a60065b 1177 *
kadonotakashi 0:8fdf9a60065b 1178 * Also, for the sake of compactness, only the seven low-order bits of x[i]
kadonotakashi 0:8fdf9a60065b 1179 * are used to represent K_i, and the msb of x[i] encodes the the sign (s_i in
kadonotakashi 0:8fdf9a60065b 1180 * the paper): it is set if and only if if s_i == -1;
kadonotakashi 0:8fdf9a60065b 1181 *
kadonotakashi 0:8fdf9a60065b 1182 * Calling conventions:
kadonotakashi 0:8fdf9a60065b 1183 * - x is an array of size d + 1
kadonotakashi 0:8fdf9a60065b 1184 * - w is the size, ie number of teeth, of the comb, and must be between
kadonotakashi 0:8fdf9a60065b 1185 * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
kadonotakashi 0:8fdf9a60065b 1186 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
kadonotakashi 0:8fdf9a60065b 1187 * (the result will be incorrect if these assumptions are not satisfied)
kadonotakashi 0:8fdf9a60065b 1188 */
kadonotakashi 0:8fdf9a60065b 1189 static void ecp_comb_fixed( unsigned char x[], size_t d,
kadonotakashi 0:8fdf9a60065b 1190 unsigned char w, const mbedtls_mpi *m )
kadonotakashi 0:8fdf9a60065b 1191 {
kadonotakashi 0:8fdf9a60065b 1192 size_t i, j;
kadonotakashi 0:8fdf9a60065b 1193 unsigned char c, cc, adjust;
kadonotakashi 0:8fdf9a60065b 1194
kadonotakashi 0:8fdf9a60065b 1195 memset( x, 0, d+1 );
kadonotakashi 0:8fdf9a60065b 1196
kadonotakashi 0:8fdf9a60065b 1197 /* First get the classical comb values (except for x_d = 0) */
kadonotakashi 0:8fdf9a60065b 1198 for( i = 0; i < d; i++ )
kadonotakashi 0:8fdf9a60065b 1199 for( j = 0; j < w; j++ )
kadonotakashi 0:8fdf9a60065b 1200 x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j;
kadonotakashi 0:8fdf9a60065b 1201
kadonotakashi 0:8fdf9a60065b 1202 /* Now make sure x_1 .. x_d are odd */
kadonotakashi 0:8fdf9a60065b 1203 c = 0;
kadonotakashi 0:8fdf9a60065b 1204 for( i = 1; i <= d; i++ )
kadonotakashi 0:8fdf9a60065b 1205 {
kadonotakashi 0:8fdf9a60065b 1206 /* Add carry and update it */
kadonotakashi 0:8fdf9a60065b 1207 cc = x[i] & c;
kadonotakashi 0:8fdf9a60065b 1208 x[i] = x[i] ^ c;
kadonotakashi 0:8fdf9a60065b 1209 c = cc;
kadonotakashi 0:8fdf9a60065b 1210
kadonotakashi 0:8fdf9a60065b 1211 /* Adjust if needed, avoiding branches */
kadonotakashi 0:8fdf9a60065b 1212 adjust = 1 - ( x[i] & 0x01 );
kadonotakashi 0:8fdf9a60065b 1213 c |= x[i] & ( x[i-1] * adjust );
kadonotakashi 0:8fdf9a60065b 1214 x[i] = x[i] ^ ( x[i-1] * adjust );
kadonotakashi 0:8fdf9a60065b 1215 x[i-1] |= adjust << 7;
kadonotakashi 0:8fdf9a60065b 1216 }
kadonotakashi 0:8fdf9a60065b 1217 }
kadonotakashi 0:8fdf9a60065b 1218
kadonotakashi 0:8fdf9a60065b 1219 /*
kadonotakashi 0:8fdf9a60065b 1220 * Precompute points for the comb method
kadonotakashi 0:8fdf9a60065b 1221 *
kadonotakashi 0:8fdf9a60065b 1222 * If i = i_{w-1} ... i_1 is the binary representation of i, then
kadonotakashi 0:8fdf9a60065b 1223 * T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P
kadonotakashi 0:8fdf9a60065b 1224 *
kadonotakashi 0:8fdf9a60065b 1225 * T must be able to hold 2^{w - 1} elements
kadonotakashi 0:8fdf9a60065b 1226 *
kadonotakashi 0:8fdf9a60065b 1227 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
kadonotakashi 0:8fdf9a60065b 1228 */
kadonotakashi 0:8fdf9a60065b 1229 static int ecp_precompute_comb( const mbedtls_ecp_group *grp,
kadonotakashi 0:8fdf9a60065b 1230 mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
kadonotakashi 0:8fdf9a60065b 1231 unsigned char w, size_t d )
kadonotakashi 0:8fdf9a60065b 1232 {
kadonotakashi 0:8fdf9a60065b 1233 int ret;
kadonotakashi 0:8fdf9a60065b 1234 unsigned char i, k;
kadonotakashi 0:8fdf9a60065b 1235 size_t j;
kadonotakashi 0:8fdf9a60065b 1236 mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
kadonotakashi 0:8fdf9a60065b 1237
kadonotakashi 0:8fdf9a60065b 1238 /*
kadonotakashi 0:8fdf9a60065b 1239 * Set T[0] = P and
kadonotakashi 0:8fdf9a60065b 1240 * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
kadonotakashi 0:8fdf9a60065b 1241 */
kadonotakashi 0:8fdf9a60065b 1242 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
kadonotakashi 0:8fdf9a60065b 1243
kadonotakashi 0:8fdf9a60065b 1244 k = 0;
kadonotakashi 0:8fdf9a60065b 1245 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
kadonotakashi 0:8fdf9a60065b 1246 {
kadonotakashi 0:8fdf9a60065b 1247 cur = T + i;
kadonotakashi 0:8fdf9a60065b 1248 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
kadonotakashi 0:8fdf9a60065b 1249 for( j = 0; j < d; j++ )
kadonotakashi 0:8fdf9a60065b 1250 MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
kadonotakashi 0:8fdf9a60065b 1251
kadonotakashi 0:8fdf9a60065b 1252 TT[k++] = cur;
kadonotakashi 0:8fdf9a60065b 1253 }
kadonotakashi 0:8fdf9a60065b 1254
kadonotakashi 0:8fdf9a60065b 1255 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
kadonotakashi 0:8fdf9a60065b 1256
kadonotakashi 0:8fdf9a60065b 1257 /*
kadonotakashi 0:8fdf9a60065b 1258 * Compute the remaining ones using the minimal number of additions
kadonotakashi 0:8fdf9a60065b 1259 * Be careful to update T[2^l] only after using it!
kadonotakashi 0:8fdf9a60065b 1260 */
kadonotakashi 0:8fdf9a60065b 1261 k = 0;
kadonotakashi 0:8fdf9a60065b 1262 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
kadonotakashi 0:8fdf9a60065b 1263 {
kadonotakashi 0:8fdf9a60065b 1264 j = i;
kadonotakashi 0:8fdf9a60065b 1265 while( j-- )
kadonotakashi 0:8fdf9a60065b 1266 {
kadonotakashi 0:8fdf9a60065b 1267 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
kadonotakashi 0:8fdf9a60065b 1268 TT[k++] = &T[i + j];
kadonotakashi 0:8fdf9a60065b 1269 }
kadonotakashi 0:8fdf9a60065b 1270 }
kadonotakashi 0:8fdf9a60065b 1271
kadonotakashi 0:8fdf9a60065b 1272 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
kadonotakashi 0:8fdf9a60065b 1273
kadonotakashi 0:8fdf9a60065b 1274 cleanup:
kadonotakashi 0:8fdf9a60065b 1275
kadonotakashi 0:8fdf9a60065b 1276 return( ret );
kadonotakashi 0:8fdf9a60065b 1277 }
kadonotakashi 0:8fdf9a60065b 1278
kadonotakashi 0:8fdf9a60065b 1279 /*
kadonotakashi 0:8fdf9a60065b 1280 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
kadonotakashi 0:8fdf9a60065b 1281 */
kadonotakashi 0:8fdf9a60065b 1282 static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kadonotakashi 0:8fdf9a60065b 1283 const mbedtls_ecp_point T[], unsigned char t_len,
kadonotakashi 0:8fdf9a60065b 1284 unsigned char i )
kadonotakashi 0:8fdf9a60065b 1285 {
kadonotakashi 0:8fdf9a60065b 1286 int ret;
kadonotakashi 0:8fdf9a60065b 1287 unsigned char ii, j;
kadonotakashi 0:8fdf9a60065b 1288
kadonotakashi 0:8fdf9a60065b 1289 /* Ignore the "sign" bit and scale down */
kadonotakashi 0:8fdf9a60065b 1290 ii = ( i & 0x7Fu ) >> 1;
kadonotakashi 0:8fdf9a60065b 1291
kadonotakashi 0:8fdf9a60065b 1292 /* Read the whole table to thwart cache-based timing attacks */
kadonotakashi 0:8fdf9a60065b 1293 for( j = 0; j < t_len; j++ )
kadonotakashi 0:8fdf9a60065b 1294 {
kadonotakashi 0:8fdf9a60065b 1295 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
kadonotakashi 0:8fdf9a60065b 1296 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
kadonotakashi 0:8fdf9a60065b 1297 }
kadonotakashi 0:8fdf9a60065b 1298
kadonotakashi 0:8fdf9a60065b 1299 /* Safely invert result if i is "negative" */
kadonotakashi 0:8fdf9a60065b 1300 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
kadonotakashi 0:8fdf9a60065b 1301
kadonotakashi 0:8fdf9a60065b 1302 cleanup:
kadonotakashi 0:8fdf9a60065b 1303 return( ret );
kadonotakashi 0:8fdf9a60065b 1304 }
kadonotakashi 0:8fdf9a60065b 1305
kadonotakashi 0:8fdf9a60065b 1306 /*
kadonotakashi 0:8fdf9a60065b 1307 * Core multiplication algorithm for the (modified) comb method.
kadonotakashi 0:8fdf9a60065b 1308 * This part is actually common with the basic comb method (GECC 3.44)
kadonotakashi 0:8fdf9a60065b 1309 *
kadonotakashi 0:8fdf9a60065b 1310 * Cost: d A + d D + 1 R
kadonotakashi 0:8fdf9a60065b 1311 */
kadonotakashi 0:8fdf9a60065b 1312 static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kadonotakashi 0:8fdf9a60065b 1313 const mbedtls_ecp_point T[], unsigned char t_len,
kadonotakashi 0:8fdf9a60065b 1314 const unsigned char x[], size_t d,
kadonotakashi 0:8fdf9a60065b 1315 int (*f_rng)(void *, unsigned char *, size_t),
kadonotakashi 0:8fdf9a60065b 1316 void *p_rng )
kadonotakashi 0:8fdf9a60065b 1317 {
kadonotakashi 0:8fdf9a60065b 1318 int ret;
kadonotakashi 0:8fdf9a60065b 1319 mbedtls_ecp_point Txi;
kadonotakashi 0:8fdf9a60065b 1320 size_t i;
kadonotakashi 0:8fdf9a60065b 1321
kadonotakashi 0:8fdf9a60065b 1322 mbedtls_ecp_point_init( &Txi );
kadonotakashi 0:8fdf9a60065b 1323
kadonotakashi 0:8fdf9a60065b 1324 /* Start with a non-zero point and randomize its coordinates */
kadonotakashi 0:8fdf9a60065b 1325 i = d;
kadonotakashi 0:8fdf9a60065b 1326 MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, t_len, x[i] ) );
kadonotakashi 0:8fdf9a60065b 1327 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
kadonotakashi 0:8fdf9a60065b 1328 if( f_rng != 0 )
kadonotakashi 0:8fdf9a60065b 1329 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
kadonotakashi 0:8fdf9a60065b 1330
kadonotakashi 0:8fdf9a60065b 1331 while( i-- != 0 )
kadonotakashi 0:8fdf9a60065b 1332 {
kadonotakashi 0:8fdf9a60065b 1333 MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
kadonotakashi 0:8fdf9a60065b 1334 MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, t_len, x[i] ) );
kadonotakashi 0:8fdf9a60065b 1335 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
kadonotakashi 0:8fdf9a60065b 1336 }
kadonotakashi 0:8fdf9a60065b 1337
kadonotakashi 0:8fdf9a60065b 1338 cleanup:
kadonotakashi 0:8fdf9a60065b 1339
kadonotakashi 0:8fdf9a60065b 1340 mbedtls_ecp_point_free( &Txi );
kadonotakashi 0:8fdf9a60065b 1341
kadonotakashi 0:8fdf9a60065b 1342 return( ret );
kadonotakashi 0:8fdf9a60065b 1343 }
kadonotakashi 0:8fdf9a60065b 1344
kadonotakashi 0:8fdf9a60065b 1345 /*
kadonotakashi 0:8fdf9a60065b 1346 * Multiplication using the comb method,
kadonotakashi 0:8fdf9a60065b 1347 * for curves in short Weierstrass form
kadonotakashi 0:8fdf9a60065b 1348 */
kadonotakashi 0:8fdf9a60065b 1349 static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kadonotakashi 0:8fdf9a60065b 1350 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
kadonotakashi 0:8fdf9a60065b 1351 int (*f_rng)(void *, unsigned char *, size_t),
kadonotakashi 0:8fdf9a60065b 1352 void *p_rng )
kadonotakashi 0:8fdf9a60065b 1353 {
kadonotakashi 0:8fdf9a60065b 1354 int ret;
kadonotakashi 0:8fdf9a60065b 1355 unsigned char w, m_is_odd, p_eq_g, pre_len, i;
kadonotakashi 0:8fdf9a60065b 1356 size_t d;
kadonotakashi 0:8fdf9a60065b 1357 unsigned char k[COMB_MAX_D + 1];
kadonotakashi 0:8fdf9a60065b 1358 mbedtls_ecp_point *T;
kadonotakashi 0:8fdf9a60065b 1359 mbedtls_mpi M, mm;
kadonotakashi 0:8fdf9a60065b 1360
kadonotakashi 0:8fdf9a60065b 1361 mbedtls_mpi_init( &M );
kadonotakashi 0:8fdf9a60065b 1362 mbedtls_mpi_init( &mm );
kadonotakashi 0:8fdf9a60065b 1363
kadonotakashi 0:8fdf9a60065b 1364 /* we need N to be odd to trnaform m in an odd number, check now */
kadonotakashi 0:8fdf9a60065b 1365 if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 )
kadonotakashi 0:8fdf9a60065b 1366 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 1367
kadonotakashi 0:8fdf9a60065b 1368 /*
kadonotakashi 0:8fdf9a60065b 1369 * Minimize the number of multiplications, that is minimize
kadonotakashi 0:8fdf9a60065b 1370 * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
kadonotakashi 0:8fdf9a60065b 1371 * (see costs of the various parts, with 1S = 1M)
kadonotakashi 0:8fdf9a60065b 1372 */
kadonotakashi 0:8fdf9a60065b 1373 w = grp->nbits >= 384 ? 5 : 4;
kadonotakashi 0:8fdf9a60065b 1374
kadonotakashi 0:8fdf9a60065b 1375 /*
kadonotakashi 0:8fdf9a60065b 1376 * If P == G, pre-compute a bit more, since this may be re-used later.
kadonotakashi 0:8fdf9a60065b 1377 * Just adding one avoids upping the cost of the first mul too much,
kadonotakashi 0:8fdf9a60065b 1378 * and the memory cost too.
kadonotakashi 0:8fdf9a60065b 1379 */
kadonotakashi 0:8fdf9a60065b 1380 #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
kadonotakashi 0:8fdf9a60065b 1381 p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
kadonotakashi 0:8fdf9a60065b 1382 mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
kadonotakashi 0:8fdf9a60065b 1383 if( p_eq_g )
kadonotakashi 0:8fdf9a60065b 1384 w++;
kadonotakashi 0:8fdf9a60065b 1385 #else
kadonotakashi 0:8fdf9a60065b 1386 p_eq_g = 0;
kadonotakashi 0:8fdf9a60065b 1387 #endif
kadonotakashi 0:8fdf9a60065b 1388
kadonotakashi 0:8fdf9a60065b 1389 /*
kadonotakashi 0:8fdf9a60065b 1390 * Make sure w is within bounds.
kadonotakashi 0:8fdf9a60065b 1391 * (The last test is useful only for very small curves in the test suite.)
kadonotakashi 0:8fdf9a60065b 1392 */
kadonotakashi 0:8fdf9a60065b 1393 if( w > MBEDTLS_ECP_WINDOW_SIZE )
kadonotakashi 0:8fdf9a60065b 1394 w = MBEDTLS_ECP_WINDOW_SIZE;
kadonotakashi 0:8fdf9a60065b 1395 if( w >= grp->nbits )
kadonotakashi 0:8fdf9a60065b 1396 w = 2;
kadonotakashi 0:8fdf9a60065b 1397
kadonotakashi 0:8fdf9a60065b 1398 /* Other sizes that depend on w */
kadonotakashi 0:8fdf9a60065b 1399 pre_len = 1U << ( w - 1 );
kadonotakashi 0:8fdf9a60065b 1400 d = ( grp->nbits + w - 1 ) / w;
kadonotakashi 0:8fdf9a60065b 1401
kadonotakashi 0:8fdf9a60065b 1402 /*
kadonotakashi 0:8fdf9a60065b 1403 * Prepare precomputed points: if P == G we want to
kadonotakashi 0:8fdf9a60065b 1404 * use grp->T if already initialized, or initialize it.
kadonotakashi 0:8fdf9a60065b 1405 */
kadonotakashi 0:8fdf9a60065b 1406 T = p_eq_g ? grp->T : NULL;
kadonotakashi 0:8fdf9a60065b 1407
kadonotakashi 0:8fdf9a60065b 1408 if( T == NULL )
kadonotakashi 0:8fdf9a60065b 1409 {
kadonotakashi 0:8fdf9a60065b 1410 T = mbedtls_calloc( pre_len, sizeof( mbedtls_ecp_point ) );
kadonotakashi 0:8fdf9a60065b 1411 if( T == NULL )
kadonotakashi 0:8fdf9a60065b 1412 {
kadonotakashi 0:8fdf9a60065b 1413 ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
kadonotakashi 0:8fdf9a60065b 1414 goto cleanup;
kadonotakashi 0:8fdf9a60065b 1415 }
kadonotakashi 0:8fdf9a60065b 1416
kadonotakashi 0:8fdf9a60065b 1417 MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d ) );
kadonotakashi 0:8fdf9a60065b 1418
kadonotakashi 0:8fdf9a60065b 1419 if( p_eq_g )
kadonotakashi 0:8fdf9a60065b 1420 {
kadonotakashi 0:8fdf9a60065b 1421 grp->T = T;
kadonotakashi 0:8fdf9a60065b 1422 grp->T_size = pre_len;
kadonotakashi 0:8fdf9a60065b 1423 }
kadonotakashi 0:8fdf9a60065b 1424 }
kadonotakashi 0:8fdf9a60065b 1425
kadonotakashi 0:8fdf9a60065b 1426 /*
kadonotakashi 0:8fdf9a60065b 1427 * Make sure M is odd (M = m or M = N - m, since N is odd)
kadonotakashi 0:8fdf9a60065b 1428 * using the fact that m * P = - (N - m) * P
kadonotakashi 0:8fdf9a60065b 1429 */
kadonotakashi 0:8fdf9a60065b 1430 m_is_odd = ( mbedtls_mpi_get_bit( m, 0 ) == 1 );
kadonotakashi 0:8fdf9a60065b 1431 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) );
kadonotakashi 0:8fdf9a60065b 1432 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) );
kadonotakashi 0:8fdf9a60065b 1433 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, ! m_is_odd ) );
kadonotakashi 0:8fdf9a60065b 1434
kadonotakashi 0:8fdf9a60065b 1435 /*
kadonotakashi 0:8fdf9a60065b 1436 * Go for comb multiplication, R = M * P
kadonotakashi 0:8fdf9a60065b 1437 */
kadonotakashi 0:8fdf9a60065b 1438 ecp_comb_fixed( k, d, w, &M );
kadonotakashi 0:8fdf9a60065b 1439 MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, R, T, pre_len, k, d, f_rng, p_rng ) );
kadonotakashi 0:8fdf9a60065b 1440
kadonotakashi 0:8fdf9a60065b 1441 /*
kadonotakashi 0:8fdf9a60065b 1442 * Now get m * P from M * P and normalize it
kadonotakashi 0:8fdf9a60065b 1443 */
kadonotakashi 0:8fdf9a60065b 1444 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, ! m_is_odd ) );
kadonotakashi 0:8fdf9a60065b 1445 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
kadonotakashi 0:8fdf9a60065b 1446
kadonotakashi 0:8fdf9a60065b 1447 cleanup:
kadonotakashi 0:8fdf9a60065b 1448
kadonotakashi 0:8fdf9a60065b 1449 /* There are two cases where T is not stored in grp:
kadonotakashi 0:8fdf9a60065b 1450 * - P != G
kadonotakashi 0:8fdf9a60065b 1451 * - An intermediate operation failed before setting grp->T
kadonotakashi 0:8fdf9a60065b 1452 * In either case, T must be freed.
kadonotakashi 0:8fdf9a60065b 1453 */
kadonotakashi 0:8fdf9a60065b 1454 if( T != NULL && T != grp->T )
kadonotakashi 0:8fdf9a60065b 1455 {
kadonotakashi 0:8fdf9a60065b 1456 for( i = 0; i < pre_len; i++ )
kadonotakashi 0:8fdf9a60065b 1457 mbedtls_ecp_point_free( &T[i] );
kadonotakashi 0:8fdf9a60065b 1458 mbedtls_free( T );
kadonotakashi 0:8fdf9a60065b 1459 }
kadonotakashi 0:8fdf9a60065b 1460
kadonotakashi 0:8fdf9a60065b 1461 mbedtls_mpi_free( &M );
kadonotakashi 0:8fdf9a60065b 1462 mbedtls_mpi_free( &mm );
kadonotakashi 0:8fdf9a60065b 1463
kadonotakashi 0:8fdf9a60065b 1464 if( ret != 0 )
kadonotakashi 0:8fdf9a60065b 1465 mbedtls_ecp_point_free( R );
kadonotakashi 0:8fdf9a60065b 1466
kadonotakashi 0:8fdf9a60065b 1467 return( ret );
kadonotakashi 0:8fdf9a60065b 1468 }
kadonotakashi 0:8fdf9a60065b 1469
kadonotakashi 0:8fdf9a60065b 1470 #endif /* ECP_SHORTWEIERSTRASS */
kadonotakashi 0:8fdf9a60065b 1471
kadonotakashi 0:8fdf9a60065b 1472 #if defined(ECP_MONTGOMERY)
kadonotakashi 0:8fdf9a60065b 1473 /*
kadonotakashi 0:8fdf9a60065b 1474 * For Montgomery curves, we do all the internal arithmetic in projective
kadonotakashi 0:8fdf9a60065b 1475 * coordinates. Import/export of points uses only the x coordinates, which is
kadonotakashi 0:8fdf9a60065b 1476 * internaly represented as X / Z.
kadonotakashi 0:8fdf9a60065b 1477 *
kadonotakashi 0:8fdf9a60065b 1478 * For scalar multiplication, we'll use a Montgomery ladder.
kadonotakashi 0:8fdf9a60065b 1479 */
kadonotakashi 0:8fdf9a60065b 1480
kadonotakashi 0:8fdf9a60065b 1481 /*
kadonotakashi 0:8fdf9a60065b 1482 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
kadonotakashi 0:8fdf9a60065b 1483 * Cost: 1M + 1I
kadonotakashi 0:8fdf9a60065b 1484 */
kadonotakashi 0:8fdf9a60065b 1485 static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
kadonotakashi 0:8fdf9a60065b 1486 {
kadonotakashi 0:8fdf9a60065b 1487 int ret;
kadonotakashi 0:8fdf9a60065b 1488
kadonotakashi 0:8fdf9a60065b 1489 #if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
kadonotakashi 0:8fdf9a60065b 1490 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kadonotakashi 0:8fdf9a60065b 1491 {
kadonotakashi 0:8fdf9a60065b 1492 return mbedtls_internal_ecp_normalize_mxz( grp, P );
kadonotakashi 0:8fdf9a60065b 1493 }
kadonotakashi 0:8fdf9a60065b 1494 #endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */
kadonotakashi 0:8fdf9a60065b 1495
kadonotakashi 0:8fdf9a60065b 1496 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
kadonotakashi 0:8fdf9a60065b 1497 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X );
kadonotakashi 0:8fdf9a60065b 1498 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
kadonotakashi 0:8fdf9a60065b 1499
kadonotakashi 0:8fdf9a60065b 1500 cleanup:
kadonotakashi 0:8fdf9a60065b 1501 return( ret );
kadonotakashi 0:8fdf9a60065b 1502 }
kadonotakashi 0:8fdf9a60065b 1503
kadonotakashi 0:8fdf9a60065b 1504 /*
kadonotakashi 0:8fdf9a60065b 1505 * Randomize projective x/z coordinates:
kadonotakashi 0:8fdf9a60065b 1506 * (X, Z) -> (l X, l Z) for random l
kadonotakashi 0:8fdf9a60065b 1507 * This is sort of the reverse operation of ecp_normalize_mxz().
kadonotakashi 0:8fdf9a60065b 1508 *
kadonotakashi 0:8fdf9a60065b 1509 * This countermeasure was first suggested in [2].
kadonotakashi 0:8fdf9a60065b 1510 * Cost: 2M
kadonotakashi 0:8fdf9a60065b 1511 */
kadonotakashi 0:8fdf9a60065b 1512 static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
kadonotakashi 0:8fdf9a60065b 1513 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
kadonotakashi 0:8fdf9a60065b 1514 {
kadonotakashi 0:8fdf9a60065b 1515 int ret;
kadonotakashi 0:8fdf9a60065b 1516 mbedtls_mpi l;
kadonotakashi 0:8fdf9a60065b 1517 size_t p_size;
kadonotakashi 0:8fdf9a60065b 1518 int count = 0;
kadonotakashi 0:8fdf9a60065b 1519
kadonotakashi 0:8fdf9a60065b 1520 #if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
kadonotakashi 0:8fdf9a60065b 1521 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kadonotakashi 0:8fdf9a60065b 1522 {
kadonotakashi 0:8fdf9a60065b 1523 return mbedtls_internal_ecp_randomize_mxz( grp, P, f_rng, p_rng );
kadonotakashi 0:8fdf9a60065b 1524 }
kadonotakashi 0:8fdf9a60065b 1525 #endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */
kadonotakashi 0:8fdf9a60065b 1526
kadonotakashi 0:8fdf9a60065b 1527 p_size = ( grp->pbits + 7 ) / 8;
kadonotakashi 0:8fdf9a60065b 1528 mbedtls_mpi_init( &l );
kadonotakashi 0:8fdf9a60065b 1529
kadonotakashi 0:8fdf9a60065b 1530 /* Generate l such that 1 < l < p */
kadonotakashi 0:8fdf9a60065b 1531 do
kadonotakashi 0:8fdf9a60065b 1532 {
kadonotakashi 0:8fdf9a60065b 1533 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
kadonotakashi 0:8fdf9a60065b 1534
kadonotakashi 0:8fdf9a60065b 1535 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
kadonotakashi 0:8fdf9a60065b 1536 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
kadonotakashi 0:8fdf9a60065b 1537
kadonotakashi 0:8fdf9a60065b 1538 if( count++ > 10 )
kadonotakashi 0:8fdf9a60065b 1539 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
kadonotakashi 0:8fdf9a60065b 1540 }
kadonotakashi 0:8fdf9a60065b 1541 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
kadonotakashi 0:8fdf9a60065b 1542
kadonotakashi 0:8fdf9a60065b 1543 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X );
kadonotakashi 0:8fdf9a60065b 1544 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z );
kadonotakashi 0:8fdf9a60065b 1545
kadonotakashi 0:8fdf9a60065b 1546 cleanup:
kadonotakashi 0:8fdf9a60065b 1547 mbedtls_mpi_free( &l );
kadonotakashi 0:8fdf9a60065b 1548
kadonotakashi 0:8fdf9a60065b 1549 return( ret );
kadonotakashi 0:8fdf9a60065b 1550 }
kadonotakashi 0:8fdf9a60065b 1551
kadonotakashi 0:8fdf9a60065b 1552 /*
kadonotakashi 0:8fdf9a60065b 1553 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
kadonotakashi 0:8fdf9a60065b 1554 * for Montgomery curves in x/z coordinates.
kadonotakashi 0:8fdf9a60065b 1555 *
kadonotakashi 0:8fdf9a60065b 1556 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
kadonotakashi 0:8fdf9a60065b 1557 * with
kadonotakashi 0:8fdf9a60065b 1558 * d = X1
kadonotakashi 0:8fdf9a60065b 1559 * P = (X2, Z2)
kadonotakashi 0:8fdf9a60065b 1560 * Q = (X3, Z3)
kadonotakashi 0:8fdf9a60065b 1561 * R = (X4, Z4)
kadonotakashi 0:8fdf9a60065b 1562 * S = (X5, Z5)
kadonotakashi 0:8fdf9a60065b 1563 * and eliminating temporary variables tO, ..., t4.
kadonotakashi 0:8fdf9a60065b 1564 *
kadonotakashi 0:8fdf9a60065b 1565 * Cost: 5M + 4S
kadonotakashi 0:8fdf9a60065b 1566 */
kadonotakashi 0:8fdf9a60065b 1567 static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
kadonotakashi 0:8fdf9a60065b 1568 mbedtls_ecp_point *R, mbedtls_ecp_point *S,
kadonotakashi 0:8fdf9a60065b 1569 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
kadonotakashi 0:8fdf9a60065b 1570 const mbedtls_mpi *d )
kadonotakashi 0:8fdf9a60065b 1571 {
kadonotakashi 0:8fdf9a60065b 1572 int ret;
kadonotakashi 0:8fdf9a60065b 1573 mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
kadonotakashi 0:8fdf9a60065b 1574
kadonotakashi 0:8fdf9a60065b 1575 #if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
kadonotakashi 0:8fdf9a60065b 1576 if ( mbedtls_internal_ecp_grp_capable( grp ) )
kadonotakashi 0:8fdf9a60065b 1577 {
kadonotakashi 0:8fdf9a60065b 1578 return mbedtls_internal_ecp_double_add_mxz( grp, R, S, P, Q, d );
kadonotakashi 0:8fdf9a60065b 1579 }
kadonotakashi 0:8fdf9a60065b 1580 #endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */
kadonotakashi 0:8fdf9a60065b 1581
kadonotakashi 0:8fdf9a60065b 1582 mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
kadonotakashi 0:8fdf9a60065b 1583 mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
kadonotakashi 0:8fdf9a60065b 1584 mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
kadonotakashi 0:8fdf9a60065b 1585
kadonotakashi 0:8fdf9a60065b 1586 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &A, &P->X, &P->Z ) ); MOD_ADD( A );
kadonotakashi 0:8fdf9a60065b 1587 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &AA, &A, &A ) ); MOD_MUL( AA );
kadonotakashi 0:8fdf9a60065b 1588 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &B, &P->X, &P->Z ) ); MOD_SUB( B );
kadonotakashi 0:8fdf9a60065b 1589 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &BB, &B, &B ) ); MOD_MUL( BB );
kadonotakashi 0:8fdf9a60065b 1590 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &E, &AA, &BB ) ); MOD_SUB( E );
kadonotakashi 0:8fdf9a60065b 1591 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &C, &Q->X, &Q->Z ) ); MOD_ADD( C );
kadonotakashi 0:8fdf9a60065b 1592 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &D, &Q->X, &Q->Z ) ); MOD_SUB( D );
kadonotakashi 0:8fdf9a60065b 1593 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DA, &D, &A ) ); MOD_MUL( DA );
kadonotakashi 0:8fdf9a60065b 1594 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &CB, &C, &B ) ); MOD_MUL( CB );
kadonotakashi 0:8fdf9a60065b 1595 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &S->X, &DA, &CB ) ); MOD_MUL( S->X );
kadonotakashi 0:8fdf9a60065b 1596 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->X, &S->X, &S->X ) ); MOD_MUL( S->X );
kadonotakashi 0:8fdf9a60065b 1597 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S->Z, &DA, &CB ) ); MOD_SUB( S->Z );
kadonotakashi 0:8fdf9a60065b 1598 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, &S->Z, &S->Z ) ); MOD_MUL( S->Z );
kadonotakashi 0:8fdf9a60065b 1599 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, d, &S->Z ) ); MOD_MUL( S->Z );
kadonotakashi 0:8fdf9a60065b 1600 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->X, &AA, &BB ) ); MOD_MUL( R->X );
kadonotakashi 0:8fdf9a60065b 1601 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &grp->A, &E ) ); MOD_MUL( R->Z );
kadonotakashi 0:8fdf9a60065b 1602 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &R->Z, &BB, &R->Z ) ); MOD_ADD( R->Z );
kadonotakashi 0:8fdf9a60065b 1603 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &E, &R->Z ) ); MOD_MUL( R->Z );
kadonotakashi 0:8fdf9a60065b 1604
kadonotakashi 0:8fdf9a60065b 1605 cleanup:
kadonotakashi 0:8fdf9a60065b 1606 mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
kadonotakashi 0:8fdf9a60065b 1607 mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
kadonotakashi 0:8fdf9a60065b 1608 mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
kadonotakashi 0:8fdf9a60065b 1609
kadonotakashi 0:8fdf9a60065b 1610 return( ret );
kadonotakashi 0:8fdf9a60065b 1611 }
kadonotakashi 0:8fdf9a60065b 1612
kadonotakashi 0:8fdf9a60065b 1613 /*
kadonotakashi 0:8fdf9a60065b 1614 * Multiplication with Montgomery ladder in x/z coordinates,
kadonotakashi 0:8fdf9a60065b 1615 * for curves in Montgomery form
kadonotakashi 0:8fdf9a60065b 1616 */
kadonotakashi 0:8fdf9a60065b 1617 static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kadonotakashi 0:8fdf9a60065b 1618 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
kadonotakashi 0:8fdf9a60065b 1619 int (*f_rng)(void *, unsigned char *, size_t),
kadonotakashi 0:8fdf9a60065b 1620 void *p_rng )
kadonotakashi 0:8fdf9a60065b 1621 {
kadonotakashi 0:8fdf9a60065b 1622 int ret;
kadonotakashi 0:8fdf9a60065b 1623 size_t i;
kadonotakashi 0:8fdf9a60065b 1624 unsigned char b;
kadonotakashi 0:8fdf9a60065b 1625 mbedtls_ecp_point RP;
kadonotakashi 0:8fdf9a60065b 1626 mbedtls_mpi PX;
kadonotakashi 0:8fdf9a60065b 1627
kadonotakashi 0:8fdf9a60065b 1628 mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
kadonotakashi 0:8fdf9a60065b 1629
kadonotakashi 0:8fdf9a60065b 1630 /* Save PX and read from P before writing to R, in case P == R */
kadonotakashi 0:8fdf9a60065b 1631 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
kadonotakashi 0:8fdf9a60065b 1632 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
kadonotakashi 0:8fdf9a60065b 1633
kadonotakashi 0:8fdf9a60065b 1634 /* Set R to zero in modified x/z coordinates */
kadonotakashi 0:8fdf9a60065b 1635 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
kadonotakashi 0:8fdf9a60065b 1636 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
kadonotakashi 0:8fdf9a60065b 1637 mbedtls_mpi_free( &R->Y );
kadonotakashi 0:8fdf9a60065b 1638
kadonotakashi 0:8fdf9a60065b 1639 /* RP.X might be sligtly larger than P, so reduce it */
kadonotakashi 0:8fdf9a60065b 1640 MOD_ADD( RP.X );
kadonotakashi 0:8fdf9a60065b 1641
kadonotakashi 0:8fdf9a60065b 1642 /* Randomize coordinates of the starting point */
kadonotakashi 0:8fdf9a60065b 1643 if( f_rng != NULL )
kadonotakashi 0:8fdf9a60065b 1644 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
kadonotakashi 0:8fdf9a60065b 1645
kadonotakashi 0:8fdf9a60065b 1646 /* Loop invariant: R = result so far, RP = R + P */
kadonotakashi 0:8fdf9a60065b 1647 i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
kadonotakashi 0:8fdf9a60065b 1648 while( i-- > 0 )
kadonotakashi 0:8fdf9a60065b 1649 {
kadonotakashi 0:8fdf9a60065b 1650 b = mbedtls_mpi_get_bit( m, i );
kadonotakashi 0:8fdf9a60065b 1651 /*
kadonotakashi 0:8fdf9a60065b 1652 * if (b) R = 2R + P else R = 2R,
kadonotakashi 0:8fdf9a60065b 1653 * which is:
kadonotakashi 0:8fdf9a60065b 1654 * if (b) double_add( RP, R, RP, R )
kadonotakashi 0:8fdf9a60065b 1655 * else double_add( R, RP, R, RP )
kadonotakashi 0:8fdf9a60065b 1656 * but using safe conditional swaps to avoid leaks
kadonotakashi 0:8fdf9a60065b 1657 */
kadonotakashi 0:8fdf9a60065b 1658 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
kadonotakashi 0:8fdf9a60065b 1659 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
kadonotakashi 0:8fdf9a60065b 1660 MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
kadonotakashi 0:8fdf9a60065b 1661 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
kadonotakashi 0:8fdf9a60065b 1662 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
kadonotakashi 0:8fdf9a60065b 1663 }
kadonotakashi 0:8fdf9a60065b 1664
kadonotakashi 0:8fdf9a60065b 1665 MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) );
kadonotakashi 0:8fdf9a60065b 1666
kadonotakashi 0:8fdf9a60065b 1667 cleanup:
kadonotakashi 0:8fdf9a60065b 1668 mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
kadonotakashi 0:8fdf9a60065b 1669
kadonotakashi 0:8fdf9a60065b 1670 return( ret );
kadonotakashi 0:8fdf9a60065b 1671 }
kadonotakashi 0:8fdf9a60065b 1672
kadonotakashi 0:8fdf9a60065b 1673 #endif /* ECP_MONTGOMERY */
kadonotakashi 0:8fdf9a60065b 1674
kadonotakashi 0:8fdf9a60065b 1675 /*
kadonotakashi 0:8fdf9a60065b 1676 * Multiplication R = m * P
kadonotakashi 0:8fdf9a60065b 1677 */
kadonotakashi 0:8fdf9a60065b 1678 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kadonotakashi 0:8fdf9a60065b 1679 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
kadonotakashi 0:8fdf9a60065b 1680 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
kadonotakashi 0:8fdf9a60065b 1681 {
kadonotakashi 0:8fdf9a60065b 1682 int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
kadonotakashi 0:8fdf9a60065b 1683 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
kadonotakashi 0:8fdf9a60065b 1684 char is_grp_capable = 0;
kadonotakashi 0:8fdf9a60065b 1685 #endif
kadonotakashi 0:8fdf9a60065b 1686
kadonotakashi 0:8fdf9a60065b 1687 /* Common sanity checks */
kadonotakashi 0:8fdf9a60065b 1688 if( mbedtls_mpi_cmp_int( &P->Z, 1 ) != 0 )
kadonotakashi 0:8fdf9a60065b 1689 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 1690
kadonotakashi 0:8fdf9a60065b 1691 if( ( ret = mbedtls_ecp_check_privkey( grp, m ) ) != 0 ||
kadonotakashi 0:8fdf9a60065b 1692 ( ret = mbedtls_ecp_check_pubkey( grp, P ) ) != 0 )
kadonotakashi 0:8fdf9a60065b 1693 return( ret );
kadonotakashi 0:8fdf9a60065b 1694
kadonotakashi 0:8fdf9a60065b 1695 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
kadonotakashi 0:8fdf9a60065b 1696 if ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) )
kadonotakashi 0:8fdf9a60065b 1697 {
kadonotakashi 0:8fdf9a60065b 1698 MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
kadonotakashi 0:8fdf9a60065b 1699 }
kadonotakashi 0:8fdf9a60065b 1700
kadonotakashi 0:8fdf9a60065b 1701 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
kadonotakashi 0:8fdf9a60065b 1702 #if defined(ECP_MONTGOMERY)
kadonotakashi 0:8fdf9a60065b 1703 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
kadonotakashi 0:8fdf9a60065b 1704 ret = ecp_mul_mxz( grp, R, m, P, f_rng, p_rng );
kadonotakashi 0:8fdf9a60065b 1705
kadonotakashi 0:8fdf9a60065b 1706 #endif
kadonotakashi 0:8fdf9a60065b 1707 #if defined(ECP_SHORTWEIERSTRASS)
kadonotakashi 0:8fdf9a60065b 1708 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
kadonotakashi 0:8fdf9a60065b 1709 ret = ecp_mul_comb( grp, R, m, P, f_rng, p_rng );
kadonotakashi 0:8fdf9a60065b 1710
kadonotakashi 0:8fdf9a60065b 1711 #endif
kadonotakashi 0:8fdf9a60065b 1712 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
kadonotakashi 0:8fdf9a60065b 1713 cleanup:
kadonotakashi 0:8fdf9a60065b 1714
kadonotakashi 0:8fdf9a60065b 1715 if ( is_grp_capable )
kadonotakashi 0:8fdf9a60065b 1716 {
kadonotakashi 0:8fdf9a60065b 1717 mbedtls_internal_ecp_free( grp );
kadonotakashi 0:8fdf9a60065b 1718 }
kadonotakashi 0:8fdf9a60065b 1719
kadonotakashi 0:8fdf9a60065b 1720 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
kadonotakashi 0:8fdf9a60065b 1721 return( ret );
kadonotakashi 0:8fdf9a60065b 1722 }
kadonotakashi 0:8fdf9a60065b 1723
kadonotakashi 0:8fdf9a60065b 1724 #if defined(ECP_SHORTWEIERSTRASS)
kadonotakashi 0:8fdf9a60065b 1725 /*
kadonotakashi 0:8fdf9a60065b 1726 * Check that an affine point is valid as a public key,
kadonotakashi 0:8fdf9a60065b 1727 * short weierstrass curves (SEC1 3.2.3.1)
kadonotakashi 0:8fdf9a60065b 1728 */
kadonotakashi 0:8fdf9a60065b 1729 static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
kadonotakashi 0:8fdf9a60065b 1730 {
kadonotakashi 0:8fdf9a60065b 1731 int ret;
kadonotakashi 0:8fdf9a60065b 1732 mbedtls_mpi YY, RHS;
kadonotakashi 0:8fdf9a60065b 1733
kadonotakashi 0:8fdf9a60065b 1734 /* pt coordinates must be normalized for our checks */
kadonotakashi 0:8fdf9a60065b 1735 if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ||
kadonotakashi 0:8fdf9a60065b 1736 mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 ||
kadonotakashi 0:8fdf9a60065b 1737 mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
kadonotakashi 0:8fdf9a60065b 1738 mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
kadonotakashi 0:8fdf9a60065b 1739 return( MBEDTLS_ERR_ECP_INVALID_KEY );
kadonotakashi 0:8fdf9a60065b 1740
kadonotakashi 0:8fdf9a60065b 1741 mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
kadonotakashi 0:8fdf9a60065b 1742
kadonotakashi 0:8fdf9a60065b 1743 /*
kadonotakashi 0:8fdf9a60065b 1744 * YY = Y^2
kadonotakashi 0:8fdf9a60065b 1745 * RHS = X (X^2 + A) + B = X^3 + A X + B
kadonotakashi 0:8fdf9a60065b 1746 */
kadonotakashi 0:8fdf9a60065b 1747 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &YY, &pt->Y, &pt->Y ) ); MOD_MUL( YY );
kadonotakashi 0:8fdf9a60065b 1748 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &pt->X, &pt->X ) ); MOD_MUL( RHS );
kadonotakashi 0:8fdf9a60065b 1749
kadonotakashi 0:8fdf9a60065b 1750 /* Special case for A = -3 */
kadonotakashi 0:8fdf9a60065b 1751 if( grp->A.p == NULL )
kadonotakashi 0:8fdf9a60065b 1752 {
kadonotakashi 0:8fdf9a60065b 1753 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS );
kadonotakashi 0:8fdf9a60065b 1754 }
kadonotakashi 0:8fdf9a60065b 1755 else
kadonotakashi 0:8fdf9a60065b 1756 {
kadonotakashi 0:8fdf9a60065b 1757 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->A ) ); MOD_ADD( RHS );
kadonotakashi 0:8fdf9a60065b 1758 }
kadonotakashi 0:8fdf9a60065b 1759
kadonotakashi 0:8fdf9a60065b 1760 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &RHS, &pt->X ) ); MOD_MUL( RHS );
kadonotakashi 0:8fdf9a60065b 1761 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->B ) ); MOD_ADD( RHS );
kadonotakashi 0:8fdf9a60065b 1762
kadonotakashi 0:8fdf9a60065b 1763 if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
kadonotakashi 0:8fdf9a60065b 1764 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
kadonotakashi 0:8fdf9a60065b 1765
kadonotakashi 0:8fdf9a60065b 1766 cleanup:
kadonotakashi 0:8fdf9a60065b 1767
kadonotakashi 0:8fdf9a60065b 1768 mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
kadonotakashi 0:8fdf9a60065b 1769
kadonotakashi 0:8fdf9a60065b 1770 return( ret );
kadonotakashi 0:8fdf9a60065b 1771 }
kadonotakashi 0:8fdf9a60065b 1772 #endif /* ECP_SHORTWEIERSTRASS */
kadonotakashi 0:8fdf9a60065b 1773
kadonotakashi 0:8fdf9a60065b 1774 /*
kadonotakashi 0:8fdf9a60065b 1775 * R = m * P with shortcuts for m == 1 and m == -1
kadonotakashi 0:8fdf9a60065b 1776 * NOT constant-time - ONLY for short Weierstrass!
kadonotakashi 0:8fdf9a60065b 1777 */
kadonotakashi 0:8fdf9a60065b 1778 static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
kadonotakashi 0:8fdf9a60065b 1779 mbedtls_ecp_point *R,
kadonotakashi 0:8fdf9a60065b 1780 const mbedtls_mpi *m,
kadonotakashi 0:8fdf9a60065b 1781 const mbedtls_ecp_point *P )
kadonotakashi 0:8fdf9a60065b 1782 {
kadonotakashi 0:8fdf9a60065b 1783 int ret;
kadonotakashi 0:8fdf9a60065b 1784
kadonotakashi 0:8fdf9a60065b 1785 if( mbedtls_mpi_cmp_int( m, 1 ) == 0 )
kadonotakashi 0:8fdf9a60065b 1786 {
kadonotakashi 0:8fdf9a60065b 1787 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
kadonotakashi 0:8fdf9a60065b 1788 }
kadonotakashi 0:8fdf9a60065b 1789 else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
kadonotakashi 0:8fdf9a60065b 1790 {
kadonotakashi 0:8fdf9a60065b 1791 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
kadonotakashi 0:8fdf9a60065b 1792 if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 )
kadonotakashi 0:8fdf9a60065b 1793 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
kadonotakashi 0:8fdf9a60065b 1794 }
kadonotakashi 0:8fdf9a60065b 1795 else
kadonotakashi 0:8fdf9a60065b 1796 {
kadonotakashi 0:8fdf9a60065b 1797 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
kadonotakashi 0:8fdf9a60065b 1798 }
kadonotakashi 0:8fdf9a60065b 1799
kadonotakashi 0:8fdf9a60065b 1800 cleanup:
kadonotakashi 0:8fdf9a60065b 1801 return( ret );
kadonotakashi 0:8fdf9a60065b 1802 }
kadonotakashi 0:8fdf9a60065b 1803
kadonotakashi 0:8fdf9a60065b 1804 /*
kadonotakashi 0:8fdf9a60065b 1805 * Linear combination
kadonotakashi 0:8fdf9a60065b 1806 * NOT constant-time
kadonotakashi 0:8fdf9a60065b 1807 */
kadonotakashi 0:8fdf9a60065b 1808 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
kadonotakashi 0:8fdf9a60065b 1809 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
kadonotakashi 0:8fdf9a60065b 1810 const mbedtls_mpi *n, const mbedtls_ecp_point *Q )
kadonotakashi 0:8fdf9a60065b 1811 {
kadonotakashi 0:8fdf9a60065b 1812 int ret;
kadonotakashi 0:8fdf9a60065b 1813 mbedtls_ecp_point mP;
kadonotakashi 0:8fdf9a60065b 1814 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
kadonotakashi 0:8fdf9a60065b 1815 char is_grp_capable = 0;
kadonotakashi 0:8fdf9a60065b 1816 #endif
kadonotakashi 0:8fdf9a60065b 1817
kadonotakashi 0:8fdf9a60065b 1818 if( ecp_get_type( grp ) != ECP_TYPE_SHORT_WEIERSTRASS )
kadonotakashi 0:8fdf9a60065b 1819 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
kadonotakashi 0:8fdf9a60065b 1820
kadonotakashi 0:8fdf9a60065b 1821 mbedtls_ecp_point_init( &mP );
kadonotakashi 0:8fdf9a60065b 1822
kadonotakashi 0:8fdf9a60065b 1823 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, &mP, m, P ) );
kadonotakashi 0:8fdf9a60065b 1824 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, R, n, Q ) );
kadonotakashi 0:8fdf9a60065b 1825
kadonotakashi 0:8fdf9a60065b 1826 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
kadonotakashi 0:8fdf9a60065b 1827 if ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) )
kadonotakashi 0:8fdf9a60065b 1828 {
kadonotakashi 0:8fdf9a60065b 1829 MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
kadonotakashi 0:8fdf9a60065b 1830 }
kadonotakashi 0:8fdf9a60065b 1831
kadonotakashi 0:8fdf9a60065b 1832 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
kadonotakashi 0:8fdf9a60065b 1833 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, &mP, R ) );
kadonotakashi 0:8fdf9a60065b 1834 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
kadonotakashi 0:8fdf9a60065b 1835
kadonotakashi 0:8fdf9a60065b 1836 cleanup:
kadonotakashi 0:8fdf9a60065b 1837
kadonotakashi 0:8fdf9a60065b 1838 #if defined(MBEDTLS_ECP_INTERNAL_ALT)
kadonotakashi 0:8fdf9a60065b 1839 if ( is_grp_capable )
kadonotakashi 0:8fdf9a60065b 1840 {
kadonotakashi 0:8fdf9a60065b 1841 mbedtls_internal_ecp_free( grp );
kadonotakashi 0:8fdf9a60065b 1842 }
kadonotakashi 0:8fdf9a60065b 1843
kadonotakashi 0:8fdf9a60065b 1844 #endif /* MBEDTLS_ECP_INTERNAL_ALT */
kadonotakashi 0:8fdf9a60065b 1845 mbedtls_ecp_point_free( &mP );
kadonotakashi 0:8fdf9a60065b 1846
kadonotakashi 0:8fdf9a60065b 1847 return( ret );
kadonotakashi 0:8fdf9a60065b 1848 }
kadonotakashi 0:8fdf9a60065b 1849
kadonotakashi 0:8fdf9a60065b 1850
kadonotakashi 0:8fdf9a60065b 1851 #if defined(ECP_MONTGOMERY)
kadonotakashi 0:8fdf9a60065b 1852 /*
kadonotakashi 0:8fdf9a60065b 1853 * Check validity of a public key for Montgomery curves with x-only schemes
kadonotakashi 0:8fdf9a60065b 1854 */
kadonotakashi 0:8fdf9a60065b 1855 static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
kadonotakashi 0:8fdf9a60065b 1856 {
kadonotakashi 0:8fdf9a60065b 1857 /* [Curve25519 p. 5] Just check X is the correct number of bytes */
kadonotakashi 0:8fdf9a60065b 1858 /* Allow any public value, if it's too big then we'll just reduce it mod p
kadonotakashi 0:8fdf9a60065b 1859 * (RFC 7748 sec. 5 para. 3). */
kadonotakashi 0:8fdf9a60065b 1860 if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
kadonotakashi 0:8fdf9a60065b 1861 return( MBEDTLS_ERR_ECP_INVALID_KEY );
kadonotakashi 0:8fdf9a60065b 1862
kadonotakashi 0:8fdf9a60065b 1863 return( 0 );
kadonotakashi 0:8fdf9a60065b 1864 }
kadonotakashi 0:8fdf9a60065b 1865 #endif /* ECP_MONTGOMERY */
kadonotakashi 0:8fdf9a60065b 1866
kadonotakashi 0:8fdf9a60065b 1867 /*
kadonotakashi 0:8fdf9a60065b 1868 * Check that a point is valid as a public key
kadonotakashi 0:8fdf9a60065b 1869 */
kadonotakashi 0:8fdf9a60065b 1870 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
kadonotakashi 0:8fdf9a60065b 1871 {
kadonotakashi 0:8fdf9a60065b 1872 /* Must use affine coordinates */
kadonotakashi 0:8fdf9a60065b 1873 if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
kadonotakashi 0:8fdf9a60065b 1874 return( MBEDTLS_ERR_ECP_INVALID_KEY );
kadonotakashi 0:8fdf9a60065b 1875
kadonotakashi 0:8fdf9a60065b 1876 #if defined(ECP_MONTGOMERY)
kadonotakashi 0:8fdf9a60065b 1877 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
kadonotakashi 0:8fdf9a60065b 1878 return( ecp_check_pubkey_mx( grp, pt ) );
kadonotakashi 0:8fdf9a60065b 1879 #endif
kadonotakashi 0:8fdf9a60065b 1880 #if defined(ECP_SHORTWEIERSTRASS)
kadonotakashi 0:8fdf9a60065b 1881 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
kadonotakashi 0:8fdf9a60065b 1882 return( ecp_check_pubkey_sw( grp, pt ) );
kadonotakashi 0:8fdf9a60065b 1883 #endif
kadonotakashi 0:8fdf9a60065b 1884 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 1885 }
kadonotakashi 0:8fdf9a60065b 1886
kadonotakashi 0:8fdf9a60065b 1887 /*
kadonotakashi 0:8fdf9a60065b 1888 * Check that an mbedtls_mpi is valid as a private key
kadonotakashi 0:8fdf9a60065b 1889 */
kadonotakashi 0:8fdf9a60065b 1890 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d )
kadonotakashi 0:8fdf9a60065b 1891 {
kadonotakashi 0:8fdf9a60065b 1892 #if defined(ECP_MONTGOMERY)
kadonotakashi 0:8fdf9a60065b 1893 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
kadonotakashi 0:8fdf9a60065b 1894 {
kadonotakashi 0:8fdf9a60065b 1895 /* see RFC 7748 sec. 5 para. 5 */
kadonotakashi 0:8fdf9a60065b 1896 if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
kadonotakashi 0:8fdf9a60065b 1897 mbedtls_mpi_get_bit( d, 1 ) != 0 ||
kadonotakashi 0:8fdf9a60065b 1898 mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */
kadonotakashi 0:8fdf9a60065b 1899 return( MBEDTLS_ERR_ECP_INVALID_KEY );
kadonotakashi 0:8fdf9a60065b 1900
kadonotakashi 0:8fdf9a60065b 1901 /* see [Curve25519] page 5 */
kadonotakashi 0:8fdf9a60065b 1902 if( grp->nbits == 254 && mbedtls_mpi_get_bit( d, 2 ) != 0 )
kadonotakashi 0:8fdf9a60065b 1903 return( MBEDTLS_ERR_ECP_INVALID_KEY );
kadonotakashi 0:8fdf9a60065b 1904
kadonotakashi 0:8fdf9a60065b 1905 return( 0 );
kadonotakashi 0:8fdf9a60065b 1906 }
kadonotakashi 0:8fdf9a60065b 1907 #endif /* ECP_MONTGOMERY */
kadonotakashi 0:8fdf9a60065b 1908 #if defined(ECP_SHORTWEIERSTRASS)
kadonotakashi 0:8fdf9a60065b 1909 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
kadonotakashi 0:8fdf9a60065b 1910 {
kadonotakashi 0:8fdf9a60065b 1911 /* see SEC1 3.2 */
kadonotakashi 0:8fdf9a60065b 1912 if( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
kadonotakashi 0:8fdf9a60065b 1913 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
kadonotakashi 0:8fdf9a60065b 1914 return( MBEDTLS_ERR_ECP_INVALID_KEY );
kadonotakashi 0:8fdf9a60065b 1915 else
kadonotakashi 0:8fdf9a60065b 1916 return( 0 );
kadonotakashi 0:8fdf9a60065b 1917 }
kadonotakashi 0:8fdf9a60065b 1918 #endif /* ECP_SHORTWEIERSTRASS */
kadonotakashi 0:8fdf9a60065b 1919
kadonotakashi 0:8fdf9a60065b 1920 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 1921 }
kadonotakashi 0:8fdf9a60065b 1922
kadonotakashi 0:8fdf9a60065b 1923 /*
kadonotakashi 0:8fdf9a60065b 1924 * Generate a keypair with configurable base point
kadonotakashi 0:8fdf9a60065b 1925 */
kadonotakashi 0:8fdf9a60065b 1926 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
kadonotakashi 0:8fdf9a60065b 1927 const mbedtls_ecp_point *G,
kadonotakashi 0:8fdf9a60065b 1928 mbedtls_mpi *d, mbedtls_ecp_point *Q,
kadonotakashi 0:8fdf9a60065b 1929 int (*f_rng)(void *, unsigned char *, size_t),
kadonotakashi 0:8fdf9a60065b 1930 void *p_rng )
kadonotakashi 0:8fdf9a60065b 1931 {
kadonotakashi 0:8fdf9a60065b 1932 int ret;
kadonotakashi 0:8fdf9a60065b 1933 size_t n_size = ( grp->nbits + 7 ) / 8;
kadonotakashi 0:8fdf9a60065b 1934
kadonotakashi 0:8fdf9a60065b 1935 #if defined(ECP_MONTGOMERY)
kadonotakashi 0:8fdf9a60065b 1936 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
kadonotakashi 0:8fdf9a60065b 1937 {
kadonotakashi 0:8fdf9a60065b 1938 /* [M225] page 5 */
kadonotakashi 0:8fdf9a60065b 1939 size_t b;
kadonotakashi 0:8fdf9a60065b 1940
kadonotakashi 0:8fdf9a60065b 1941 do {
kadonotakashi 0:8fdf9a60065b 1942 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
kadonotakashi 0:8fdf9a60065b 1943 } while( mbedtls_mpi_bitlen( d ) == 0);
kadonotakashi 0:8fdf9a60065b 1944
kadonotakashi 0:8fdf9a60065b 1945 /* Make sure the most significant bit is nbits */
kadonotakashi 0:8fdf9a60065b 1946 b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */
kadonotakashi 0:8fdf9a60065b 1947 if( b > grp->nbits )
kadonotakashi 0:8fdf9a60065b 1948 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) );
kadonotakashi 0:8fdf9a60065b 1949 else
kadonotakashi 0:8fdf9a60065b 1950 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) );
kadonotakashi 0:8fdf9a60065b 1951
kadonotakashi 0:8fdf9a60065b 1952 /* Make sure the last two bits are unset for Curve448, three bits for
kadonotakashi 0:8fdf9a60065b 1953 Curve25519 */
kadonotakashi 0:8fdf9a60065b 1954 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) );
kadonotakashi 0:8fdf9a60065b 1955 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) );
kadonotakashi 0:8fdf9a60065b 1956 if( grp->nbits == 254 )
kadonotakashi 0:8fdf9a60065b 1957 {
kadonotakashi 0:8fdf9a60065b 1958 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
kadonotakashi 0:8fdf9a60065b 1959 }
kadonotakashi 0:8fdf9a60065b 1960 }
kadonotakashi 0:8fdf9a60065b 1961 else
kadonotakashi 0:8fdf9a60065b 1962 #endif /* ECP_MONTGOMERY */
kadonotakashi 0:8fdf9a60065b 1963 #if defined(ECP_SHORTWEIERSTRASS)
kadonotakashi 0:8fdf9a60065b 1964 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
kadonotakashi 0:8fdf9a60065b 1965 {
kadonotakashi 0:8fdf9a60065b 1966 /* SEC1 3.2.1: Generate d such that 1 <= n < N */
kadonotakashi 0:8fdf9a60065b 1967 int count = 0;
kadonotakashi 0:8fdf9a60065b 1968
kadonotakashi 0:8fdf9a60065b 1969 /*
kadonotakashi 0:8fdf9a60065b 1970 * Match the procedure given in RFC 6979 (deterministic ECDSA):
kadonotakashi 0:8fdf9a60065b 1971 * - use the same byte ordering;
kadonotakashi 0:8fdf9a60065b 1972 * - keep the leftmost nbits bits of the generated octet string;
kadonotakashi 0:8fdf9a60065b 1973 * - try until result is in the desired range.
kadonotakashi 0:8fdf9a60065b 1974 * This also avoids any biais, which is especially important for ECDSA.
kadonotakashi 0:8fdf9a60065b 1975 */
kadonotakashi 0:8fdf9a60065b 1976 do
kadonotakashi 0:8fdf9a60065b 1977 {
kadonotakashi 0:8fdf9a60065b 1978 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
kadonotakashi 0:8fdf9a60065b 1979 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) );
kadonotakashi 0:8fdf9a60065b 1980
kadonotakashi 0:8fdf9a60065b 1981 /*
kadonotakashi 0:8fdf9a60065b 1982 * Each try has at worst a probability 1/2 of failing (the msb has
kadonotakashi 0:8fdf9a60065b 1983 * a probability 1/2 of being 0, and then the result will be < N),
kadonotakashi 0:8fdf9a60065b 1984 * so after 30 tries failure probability is a most 2**(-30).
kadonotakashi 0:8fdf9a60065b 1985 *
kadonotakashi 0:8fdf9a60065b 1986 * For most curves, 1 try is enough with overwhelming probability,
kadonotakashi 0:8fdf9a60065b 1987 * since N starts with a lot of 1s in binary, but some curves
kadonotakashi 0:8fdf9a60065b 1988 * such as secp224k1 are actually very close to the worst case.
kadonotakashi 0:8fdf9a60065b 1989 */
kadonotakashi 0:8fdf9a60065b 1990 if( ++count > 30 )
kadonotakashi 0:8fdf9a60065b 1991 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
kadonotakashi 0:8fdf9a60065b 1992 }
kadonotakashi 0:8fdf9a60065b 1993 while( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
kadonotakashi 0:8fdf9a60065b 1994 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 );
kadonotakashi 0:8fdf9a60065b 1995 }
kadonotakashi 0:8fdf9a60065b 1996 else
kadonotakashi 0:8fdf9a60065b 1997 #endif /* ECP_SHORTWEIERSTRASS */
kadonotakashi 0:8fdf9a60065b 1998 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 1999
kadonotakashi 0:8fdf9a60065b 2000 cleanup:
kadonotakashi 0:8fdf9a60065b 2001 if( ret != 0 )
kadonotakashi 0:8fdf9a60065b 2002 return( ret );
kadonotakashi 0:8fdf9a60065b 2003
kadonotakashi 0:8fdf9a60065b 2004 return( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) );
kadonotakashi 0:8fdf9a60065b 2005 }
kadonotakashi 0:8fdf9a60065b 2006
kadonotakashi 0:8fdf9a60065b 2007 /*
kadonotakashi 0:8fdf9a60065b 2008 * Generate key pair, wrapper for conventional base point
kadonotakashi 0:8fdf9a60065b 2009 */
kadonotakashi 0:8fdf9a60065b 2010 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp,
kadonotakashi 0:8fdf9a60065b 2011 mbedtls_mpi *d, mbedtls_ecp_point *Q,
kadonotakashi 0:8fdf9a60065b 2012 int (*f_rng)(void *, unsigned char *, size_t),
kadonotakashi 0:8fdf9a60065b 2013 void *p_rng )
kadonotakashi 0:8fdf9a60065b 2014 {
kadonotakashi 0:8fdf9a60065b 2015 return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) );
kadonotakashi 0:8fdf9a60065b 2016 }
kadonotakashi 0:8fdf9a60065b 2017
kadonotakashi 0:8fdf9a60065b 2018 /*
kadonotakashi 0:8fdf9a60065b 2019 * Generate a keypair, prettier wrapper
kadonotakashi 0:8fdf9a60065b 2020 */
kadonotakashi 0:8fdf9a60065b 2021 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
kadonotakashi 0:8fdf9a60065b 2022 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
kadonotakashi 0:8fdf9a60065b 2023 {
kadonotakashi 0:8fdf9a60065b 2024 int ret;
kadonotakashi 0:8fdf9a60065b 2025
kadonotakashi 0:8fdf9a60065b 2026 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
kadonotakashi 0:8fdf9a60065b 2027 return( ret );
kadonotakashi 0:8fdf9a60065b 2028
kadonotakashi 0:8fdf9a60065b 2029 return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
kadonotakashi 0:8fdf9a60065b 2030 }
kadonotakashi 0:8fdf9a60065b 2031
kadonotakashi 0:8fdf9a60065b 2032 /*
kadonotakashi 0:8fdf9a60065b 2033 * Check a public-private key pair
kadonotakashi 0:8fdf9a60065b 2034 */
kadonotakashi 0:8fdf9a60065b 2035 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
kadonotakashi 0:8fdf9a60065b 2036 {
kadonotakashi 0:8fdf9a60065b 2037 int ret;
kadonotakashi 0:8fdf9a60065b 2038 mbedtls_ecp_point Q;
kadonotakashi 0:8fdf9a60065b 2039 mbedtls_ecp_group grp;
kadonotakashi 0:8fdf9a60065b 2040
kadonotakashi 0:8fdf9a60065b 2041 if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
kadonotakashi 0:8fdf9a60065b 2042 pub->grp.id != prv->grp.id ||
kadonotakashi 0:8fdf9a60065b 2043 mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
kadonotakashi 0:8fdf9a60065b 2044 mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
kadonotakashi 0:8fdf9a60065b 2045 mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
kadonotakashi 0:8fdf9a60065b 2046 {
kadonotakashi 0:8fdf9a60065b 2047 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
kadonotakashi 0:8fdf9a60065b 2048 }
kadonotakashi 0:8fdf9a60065b 2049
kadonotakashi 0:8fdf9a60065b 2050 mbedtls_ecp_point_init( &Q );
kadonotakashi 0:8fdf9a60065b 2051 mbedtls_ecp_group_init( &grp );
kadonotakashi 0:8fdf9a60065b 2052
kadonotakashi 0:8fdf9a60065b 2053 /* mbedtls_ecp_mul() needs a non-const group... */
kadonotakashi 0:8fdf9a60065b 2054 mbedtls_ecp_group_copy( &grp, &prv->grp );
kadonotakashi 0:8fdf9a60065b 2055
kadonotakashi 0:8fdf9a60065b 2056 /* Also checks d is valid */
kadonotakashi 0:8fdf9a60065b 2057 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
kadonotakashi 0:8fdf9a60065b 2058
kadonotakashi 0:8fdf9a60065b 2059 if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
kadonotakashi 0:8fdf9a60065b 2060 mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
kadonotakashi 0:8fdf9a60065b 2061 mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
kadonotakashi 0:8fdf9a60065b 2062 {
kadonotakashi 0:8fdf9a60065b 2063 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
kadonotakashi 0:8fdf9a60065b 2064 goto cleanup;
kadonotakashi 0:8fdf9a60065b 2065 }
kadonotakashi 0:8fdf9a60065b 2066
kadonotakashi 0:8fdf9a60065b 2067 cleanup:
kadonotakashi 0:8fdf9a60065b 2068 mbedtls_ecp_point_free( &Q );
kadonotakashi 0:8fdf9a60065b 2069 mbedtls_ecp_group_free( &grp );
kadonotakashi 0:8fdf9a60065b 2070
kadonotakashi 0:8fdf9a60065b 2071 return( ret );
kadonotakashi 0:8fdf9a60065b 2072 }
kadonotakashi 0:8fdf9a60065b 2073
kadonotakashi 0:8fdf9a60065b 2074 #if defined(MBEDTLS_SELF_TEST)
kadonotakashi 0:8fdf9a60065b 2075
kadonotakashi 0:8fdf9a60065b 2076 /*
kadonotakashi 0:8fdf9a60065b 2077 * Checkup routine
kadonotakashi 0:8fdf9a60065b 2078 */
kadonotakashi 0:8fdf9a60065b 2079 int mbedtls_ecp_self_test( int verbose )
kadonotakashi 0:8fdf9a60065b 2080 {
kadonotakashi 0:8fdf9a60065b 2081 int ret;
kadonotakashi 0:8fdf9a60065b 2082 size_t i;
kadonotakashi 0:8fdf9a60065b 2083 mbedtls_ecp_group grp;
kadonotakashi 0:8fdf9a60065b 2084 mbedtls_ecp_point R, P;
kadonotakashi 0:8fdf9a60065b 2085 mbedtls_mpi m;
kadonotakashi 0:8fdf9a60065b 2086 unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
kadonotakashi 0:8fdf9a60065b 2087 /* exponents especially adapted for secp192r1 */
kadonotakashi 0:8fdf9a60065b 2088 const char *exponents[] =
kadonotakashi 0:8fdf9a60065b 2089 {
kadonotakashi 0:8fdf9a60065b 2090 "000000000000000000000000000000000000000000000001", /* one */
kadonotakashi 0:8fdf9a60065b 2091 "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22830", /* N - 1 */
kadonotakashi 0:8fdf9a60065b 2092 "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
kadonotakashi 0:8fdf9a60065b 2093 "400000000000000000000000000000000000000000000000", /* one and zeros */
kadonotakashi 0:8fdf9a60065b 2094 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
kadonotakashi 0:8fdf9a60065b 2095 "555555555555555555555555555555555555555555555555", /* 101010... */
kadonotakashi 0:8fdf9a60065b 2096 };
kadonotakashi 0:8fdf9a60065b 2097
kadonotakashi 0:8fdf9a60065b 2098 mbedtls_ecp_group_init( &grp );
kadonotakashi 0:8fdf9a60065b 2099 mbedtls_ecp_point_init( &R );
kadonotakashi 0:8fdf9a60065b 2100 mbedtls_ecp_point_init( &P );
kadonotakashi 0:8fdf9a60065b 2101 mbedtls_mpi_init( &m );
kadonotakashi 0:8fdf9a60065b 2102
kadonotakashi 0:8fdf9a60065b 2103 /* Use secp192r1 if available, or any available curve */
kadonotakashi 0:8fdf9a60065b 2104 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
kadonotakashi 0:8fdf9a60065b 2105 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) );
kadonotakashi 0:8fdf9a60065b 2106 #else
kadonotakashi 0:8fdf9a60065b 2107 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) );
kadonotakashi 0:8fdf9a60065b 2108 #endif
kadonotakashi 0:8fdf9a60065b 2109
kadonotakashi 0:8fdf9a60065b 2110 if( verbose != 0 )
kadonotakashi 0:8fdf9a60065b 2111 mbedtls_printf( " ECP test #1 (constant op_count, base point G): " );
kadonotakashi 0:8fdf9a60065b 2112
kadonotakashi 0:8fdf9a60065b 2113 /* Do a dummy multiplication first to trigger precomputation */
kadonotakashi 0:8fdf9a60065b 2114 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
kadonotakashi 0:8fdf9a60065b 2115 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
kadonotakashi 0:8fdf9a60065b 2116
kadonotakashi 0:8fdf9a60065b 2117 add_count = 0;
kadonotakashi 0:8fdf9a60065b 2118 dbl_count = 0;
kadonotakashi 0:8fdf9a60065b 2119 mul_count = 0;
kadonotakashi 0:8fdf9a60065b 2120 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
kadonotakashi 0:8fdf9a60065b 2121 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
kadonotakashi 0:8fdf9a60065b 2122
kadonotakashi 0:8fdf9a60065b 2123 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
kadonotakashi 0:8fdf9a60065b 2124 {
kadonotakashi 0:8fdf9a60065b 2125 add_c_prev = add_count;
kadonotakashi 0:8fdf9a60065b 2126 dbl_c_prev = dbl_count;
kadonotakashi 0:8fdf9a60065b 2127 mul_c_prev = mul_count;
kadonotakashi 0:8fdf9a60065b 2128 add_count = 0;
kadonotakashi 0:8fdf9a60065b 2129 dbl_count = 0;
kadonotakashi 0:8fdf9a60065b 2130 mul_count = 0;
kadonotakashi 0:8fdf9a60065b 2131
kadonotakashi 0:8fdf9a60065b 2132 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
kadonotakashi 0:8fdf9a60065b 2133 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
kadonotakashi 0:8fdf9a60065b 2134
kadonotakashi 0:8fdf9a60065b 2135 if( add_count != add_c_prev ||
kadonotakashi 0:8fdf9a60065b 2136 dbl_count != dbl_c_prev ||
kadonotakashi 0:8fdf9a60065b 2137 mul_count != mul_c_prev )
kadonotakashi 0:8fdf9a60065b 2138 {
kadonotakashi 0:8fdf9a60065b 2139 if( verbose != 0 )
kadonotakashi 0:8fdf9a60065b 2140 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
kadonotakashi 0:8fdf9a60065b 2141
kadonotakashi 0:8fdf9a60065b 2142 ret = 1;
kadonotakashi 0:8fdf9a60065b 2143 goto cleanup;
kadonotakashi 0:8fdf9a60065b 2144 }
kadonotakashi 0:8fdf9a60065b 2145 }
kadonotakashi 0:8fdf9a60065b 2146
kadonotakashi 0:8fdf9a60065b 2147 if( verbose != 0 )
kadonotakashi 0:8fdf9a60065b 2148 mbedtls_printf( "passed\n" );
kadonotakashi 0:8fdf9a60065b 2149
kadonotakashi 0:8fdf9a60065b 2150 if( verbose != 0 )
kadonotakashi 0:8fdf9a60065b 2151 mbedtls_printf( " ECP test #2 (constant op_count, other point): " );
kadonotakashi 0:8fdf9a60065b 2152 /* We computed P = 2G last time, use it */
kadonotakashi 0:8fdf9a60065b 2153
kadonotakashi 0:8fdf9a60065b 2154 add_count = 0;
kadonotakashi 0:8fdf9a60065b 2155 dbl_count = 0;
kadonotakashi 0:8fdf9a60065b 2156 mul_count = 0;
kadonotakashi 0:8fdf9a60065b 2157 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
kadonotakashi 0:8fdf9a60065b 2158 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
kadonotakashi 0:8fdf9a60065b 2159
kadonotakashi 0:8fdf9a60065b 2160 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
kadonotakashi 0:8fdf9a60065b 2161 {
kadonotakashi 0:8fdf9a60065b 2162 add_c_prev = add_count;
kadonotakashi 0:8fdf9a60065b 2163 dbl_c_prev = dbl_count;
kadonotakashi 0:8fdf9a60065b 2164 mul_c_prev = mul_count;
kadonotakashi 0:8fdf9a60065b 2165 add_count = 0;
kadonotakashi 0:8fdf9a60065b 2166 dbl_count = 0;
kadonotakashi 0:8fdf9a60065b 2167 mul_count = 0;
kadonotakashi 0:8fdf9a60065b 2168
kadonotakashi 0:8fdf9a60065b 2169 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
kadonotakashi 0:8fdf9a60065b 2170 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
kadonotakashi 0:8fdf9a60065b 2171
kadonotakashi 0:8fdf9a60065b 2172 if( add_count != add_c_prev ||
kadonotakashi 0:8fdf9a60065b 2173 dbl_count != dbl_c_prev ||
kadonotakashi 0:8fdf9a60065b 2174 mul_count != mul_c_prev )
kadonotakashi 0:8fdf9a60065b 2175 {
kadonotakashi 0:8fdf9a60065b 2176 if( verbose != 0 )
kadonotakashi 0:8fdf9a60065b 2177 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
kadonotakashi 0:8fdf9a60065b 2178
kadonotakashi 0:8fdf9a60065b 2179 ret = 1;
kadonotakashi 0:8fdf9a60065b 2180 goto cleanup;
kadonotakashi 0:8fdf9a60065b 2181 }
kadonotakashi 0:8fdf9a60065b 2182 }
kadonotakashi 0:8fdf9a60065b 2183
kadonotakashi 0:8fdf9a60065b 2184 if( verbose != 0 )
kadonotakashi 0:8fdf9a60065b 2185 mbedtls_printf( "passed\n" );
kadonotakashi 0:8fdf9a60065b 2186
kadonotakashi 0:8fdf9a60065b 2187 cleanup:
kadonotakashi 0:8fdf9a60065b 2188
kadonotakashi 0:8fdf9a60065b 2189 if( ret < 0 && verbose != 0 )
kadonotakashi 0:8fdf9a60065b 2190 mbedtls_printf( "Unexpected error, return code = %08X\n", ret );
kadonotakashi 0:8fdf9a60065b 2191
kadonotakashi 0:8fdf9a60065b 2192 mbedtls_ecp_group_free( &grp );
kadonotakashi 0:8fdf9a60065b 2193 mbedtls_ecp_point_free( &R );
kadonotakashi 0:8fdf9a60065b 2194 mbedtls_ecp_point_free( &P );
kadonotakashi 0:8fdf9a60065b 2195 mbedtls_mpi_free( &m );
kadonotakashi 0:8fdf9a60065b 2196
kadonotakashi 0:8fdf9a60065b 2197 if( verbose != 0 )
kadonotakashi 0:8fdf9a60065b 2198 mbedtls_printf( "\n" );
kadonotakashi 0:8fdf9a60065b 2199
kadonotakashi 0:8fdf9a60065b 2200 return( ret );
kadonotakashi 0:8fdf9a60065b 2201 }
kadonotakashi 0:8fdf9a60065b 2202
kadonotakashi 0:8fdf9a60065b 2203 #endif /* MBEDTLS_SELF_TEST */
kadonotakashi 0:8fdf9a60065b 2204
kadonotakashi 0:8fdf9a60065b 2205 #endif /* !MBEDTLS_ECP_ALT */
kadonotakashi 0:8fdf9a60065b 2206
kadonotakashi 0:8fdf9a60065b 2207 #endif /* MBEDTLS_ECP_C */