Timothy Beight / Mbed 2 deprecated 6_songs-from-the-cloud

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Dependencies:   mbed Socket lwip-eth lwip-sys lwip

Fork of 6_songs-from-the-cloud by MakingMusicWorkshop

mbed-client/mbedtls/source/ecp.c@0:f7c60d3e7b8a, 2016-05-18 (annotated)

Committer:
maclobdell
Date:
Wed May 18 19:06:32 2016 +0000
Revision:
0:f7c60d3e7b8a
clean version

Who changed what in which revision?

UserRevisionLine numberNew contents of line
maclobdell 0:f7c60d3e7b8a 1 /*
maclobdell 0:f7c60d3e7b8a 2 * Elliptic curves over GF(p): generic functions
maclobdell 0:f7c60d3e7b8a 3 *
maclobdell 0:f7c60d3e7b8a 4 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
maclobdell 0:f7c60d3e7b8a 5 * SPDX-License-Identifier: Apache-2.0
maclobdell 0:f7c60d3e7b8a 6 *
maclobdell 0:f7c60d3e7b8a 7 * Licensed under the Apache License, Version 2.0 (the "License"); you may
maclobdell 0:f7c60d3e7b8a 8 * not use this file except in compliance with the License.
maclobdell 0:f7c60d3e7b8a 9 * You may obtain a copy of the License at
maclobdell 0:f7c60d3e7b8a 10 *
maclobdell 0:f7c60d3e7b8a 11 * http://www.apache.org/licenses/LICENSE-2.0
maclobdell 0:f7c60d3e7b8a 12 *
maclobdell 0:f7c60d3e7b8a 13 * Unless required by applicable law or agreed to in writing, software
maclobdell 0:f7c60d3e7b8a 14 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
maclobdell 0:f7c60d3e7b8a 15 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
maclobdell 0:f7c60d3e7b8a 16 * See the License for the specific language governing permissions and
maclobdell 0:f7c60d3e7b8a 17 * limitations under the License.
maclobdell 0:f7c60d3e7b8a 18 *
maclobdell 0:f7c60d3e7b8a 19 * This file is part of mbed TLS (https://tls.mbed.org)
maclobdell 0:f7c60d3e7b8a 20 */
maclobdell 0:f7c60d3e7b8a 21
maclobdell 0:f7c60d3e7b8a 22 /*
maclobdell 0:f7c60d3e7b8a 23 * References:
maclobdell 0:f7c60d3e7b8a 24 *
maclobdell 0:f7c60d3e7b8a 25 * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
maclobdell 0:f7c60d3e7b8a 26 * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
maclobdell 0:f7c60d3e7b8a 27 * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
maclobdell 0:f7c60d3e7b8a 28 * RFC 4492 for the related TLS structures and constants
maclobdell 0:f7c60d3e7b8a 29 *
maclobdell 0:f7c60d3e7b8a 30 * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf
maclobdell 0:f7c60d3e7b8a 31 *
maclobdell 0:f7c60d3e7b8a 32 * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
maclobdell 0:f7c60d3e7b8a 33 * for elliptic curve cryptosystems. In : Cryptographic Hardware and
maclobdell 0:f7c60d3e7b8a 34 * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
maclobdell 0:f7c60d3e7b8a 35 * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
maclobdell 0:f7c60d3e7b8a 36 *
maclobdell 0:f7c60d3e7b8a 37 * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
maclobdell 0:f7c60d3e7b8a 38 * render ECC resistant against Side Channel Attacks. IACR Cryptology
maclobdell 0:f7c60d3e7b8a 39 * ePrint Archive, 2004, vol. 2004, p. 342.
maclobdell 0:f7c60d3e7b8a 40 * <http://eprint.iacr.org/2004/342.pdf>
maclobdell 0:f7c60d3e7b8a 41 */
maclobdell 0:f7c60d3e7b8a 42
maclobdell 0:f7c60d3e7b8a 43 #if !defined(MBEDTLS_CONFIG_FILE)
maclobdell 0:f7c60d3e7b8a 44 #include "mbedtls/config.h"
maclobdell 0:f7c60d3e7b8a 45 #else
maclobdell 0:f7c60d3e7b8a 46 #include MBEDTLS_CONFIG_FILE
maclobdell 0:f7c60d3e7b8a 47 #endif
maclobdell 0:f7c60d3e7b8a 48
maclobdell 0:f7c60d3e7b8a 49 #if defined(MBEDTLS_ECP_C)
maclobdell 0:f7c60d3e7b8a 50
maclobdell 0:f7c60d3e7b8a 51 #include "mbedtls/ecp.h"
maclobdell 0:f7c60d3e7b8a 52
maclobdell 0:f7c60d3e7b8a 53 #include <string.h>
maclobdell 0:f7c60d3e7b8a 54
maclobdell 0:f7c60d3e7b8a 55 #if defined(MBEDTLS_PLATFORM_C)
maclobdell 0:f7c60d3e7b8a 56 #include "mbedtls/platform.h"
maclobdell 0:f7c60d3e7b8a 57 #else
maclobdell 0:f7c60d3e7b8a 58 #include <stdlib.h>
maclobdell 0:f7c60d3e7b8a 59 #include <stdio.h>
maclobdell 0:f7c60d3e7b8a 60 #define mbedtls_printf printf
maclobdell 0:f7c60d3e7b8a 61 #define mbedtls_calloc calloc
maclobdell 0:f7c60d3e7b8a 62 #define mbedtls_free free
maclobdell 0:f7c60d3e7b8a 63 #endif
maclobdell 0:f7c60d3e7b8a 64
maclobdell 0:f7c60d3e7b8a 65 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
maclobdell 0:f7c60d3e7b8a 66 !defined(inline) && !defined(__cplusplus)
maclobdell 0:f7c60d3e7b8a 67 #define inline __inline
maclobdell 0:f7c60d3e7b8a 68 #endif
maclobdell 0:f7c60d3e7b8a 69
maclobdell 0:f7c60d3e7b8a 70 /* Implementation that should never be optimized out by the compiler */
maclobdell 0:f7c60d3e7b8a 71 static void mbedtls_zeroize( void *v, size_t n ) {
maclobdell 0:f7c60d3e7b8a 72 volatile unsigned char *p = v; while( n-- ) *p++ = 0;
maclobdell 0:f7c60d3e7b8a 73 }
maclobdell 0:f7c60d3e7b8a 74
maclobdell 0:f7c60d3e7b8a 75 #if defined(MBEDTLS_SELF_TEST)
maclobdell 0:f7c60d3e7b8a 76 /*
maclobdell 0:f7c60d3e7b8a 77 * Counts of point addition and doubling, and field multiplications.
maclobdell 0:f7c60d3e7b8a 78 * Used to test resistance of point multiplication to simple timing attacks.
maclobdell 0:f7c60d3e7b8a 79 */
maclobdell 0:f7c60d3e7b8a 80 static unsigned long add_count, dbl_count, mul_count;
maclobdell 0:f7c60d3e7b8a 81 #endif
maclobdell 0:f7c60d3e7b8a 82
maclobdell 0:f7c60d3e7b8a 83 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \
maclobdell 0:f7c60d3e7b8a 84 defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
maclobdell 0:f7c60d3e7b8a 85 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
maclobdell 0:f7c60d3e7b8a 86 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \
maclobdell 0:f7c60d3e7b8a 87 defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \
maclobdell 0:f7c60d3e7b8a 88 defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \
maclobdell 0:f7c60d3e7b8a 89 defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \
maclobdell 0:f7c60d3e7b8a 90 defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \
maclobdell 0:f7c60d3e7b8a 91 defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
maclobdell 0:f7c60d3e7b8a 92 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
maclobdell 0:f7c60d3e7b8a 93 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
maclobdell 0:f7c60d3e7b8a 94 #define ECP_SHORTWEIERSTRASS
maclobdell 0:f7c60d3e7b8a 95 #endif
maclobdell 0:f7c60d3e7b8a 96
maclobdell 0:f7c60d3e7b8a 97 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
maclobdell 0:f7c60d3e7b8a 98 #define ECP_MONTGOMERY
maclobdell 0:f7c60d3e7b8a 99 #endif
maclobdell 0:f7c60d3e7b8a 100
maclobdell 0:f7c60d3e7b8a 101 /*
maclobdell 0:f7c60d3e7b8a 102 * Curve types: internal for now, might be exposed later
maclobdell 0:f7c60d3e7b8a 103 */
maclobdell 0:f7c60d3e7b8a 104 typedef enum
maclobdell 0:f7c60d3e7b8a 105 {
maclobdell 0:f7c60d3e7b8a 106 ECP_TYPE_NONE = 0,
maclobdell 0:f7c60d3e7b8a 107 ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */
maclobdell 0:f7c60d3e7b8a 108 ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */
maclobdell 0:f7c60d3e7b8a 109 } ecp_curve_type;
maclobdell 0:f7c60d3e7b8a 110
maclobdell 0:f7c60d3e7b8a 111 /*
maclobdell 0:f7c60d3e7b8a 112 * List of supported curves:
maclobdell 0:f7c60d3e7b8a 113 * - internal ID
maclobdell 0:f7c60d3e7b8a 114 * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2)
maclobdell 0:f7c60d3e7b8a 115 * - size in bits
maclobdell 0:f7c60d3e7b8a 116 * - readable name
maclobdell 0:f7c60d3e7b8a 117 *
maclobdell 0:f7c60d3e7b8a 118 * Curves are listed in order: largest curves first, and for a given size,
maclobdell 0:f7c60d3e7b8a 119 * fastest curves first. This provides the default order for the SSL module.
maclobdell 0:f7c60d3e7b8a 120 *
maclobdell 0:f7c60d3e7b8a 121 * Reminder: update profiles in x509_crt.c when adding a new curves!
maclobdell 0:f7c60d3e7b8a 122 */
maclobdell 0:f7c60d3e7b8a 123 static const mbedtls_ecp_curve_info ecp_supported_curves[] =
maclobdell 0:f7c60d3e7b8a 124 {
maclobdell 0:f7c60d3e7b8a 125 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
maclobdell 0:f7c60d3e7b8a 126 { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" },
maclobdell 0:f7c60d3e7b8a 127 #endif
maclobdell 0:f7c60d3e7b8a 128 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
maclobdell 0:f7c60d3e7b8a 129 { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
maclobdell 0:f7c60d3e7b8a 130 #endif
maclobdell 0:f7c60d3e7b8a 131 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
maclobdell 0:f7c60d3e7b8a 132 { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
maclobdell 0:f7c60d3e7b8a 133 #endif
maclobdell 0:f7c60d3e7b8a 134 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
maclobdell 0:f7c60d3e7b8a 135 { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
maclobdell 0:f7c60d3e7b8a 136 #endif
maclobdell 0:f7c60d3e7b8a 137 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
maclobdell 0:f7c60d3e7b8a 138 { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
maclobdell 0:f7c60d3e7b8a 139 #endif
maclobdell 0:f7c60d3e7b8a 140 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
maclobdell 0:f7c60d3e7b8a 141 { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
maclobdell 0:f7c60d3e7b8a 142 #endif
maclobdell 0:f7c60d3e7b8a 143 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
maclobdell 0:f7c60d3e7b8a 144 { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" },
maclobdell 0:f7c60d3e7b8a 145 #endif
maclobdell 0:f7c60d3e7b8a 146 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
maclobdell 0:f7c60d3e7b8a 147 { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" },
maclobdell 0:f7c60d3e7b8a 148 #endif
maclobdell 0:f7c60d3e7b8a 149 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
maclobdell 0:f7c60d3e7b8a 150 { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" },
maclobdell 0:f7c60d3e7b8a 151 #endif
maclobdell 0:f7c60d3e7b8a 152 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
maclobdell 0:f7c60d3e7b8a 153 { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" },
maclobdell 0:f7c60d3e7b8a 154 #endif
maclobdell 0:f7c60d3e7b8a 155 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
maclobdell 0:f7c60d3e7b8a 156 { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" },
maclobdell 0:f7c60d3e7b8a 157 #endif
maclobdell 0:f7c60d3e7b8a 158 { MBEDTLS_ECP_DP_NONE, 0, 0, NULL },
maclobdell 0:f7c60d3e7b8a 159 };
maclobdell 0:f7c60d3e7b8a 160
maclobdell 0:f7c60d3e7b8a 161 #define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \
maclobdell 0:f7c60d3e7b8a 162 sizeof( ecp_supported_curves[0] )
maclobdell 0:f7c60d3e7b8a 163
maclobdell 0:f7c60d3e7b8a 164 static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
maclobdell 0:f7c60d3e7b8a 165
maclobdell 0:f7c60d3e7b8a 166 /*
maclobdell 0:f7c60d3e7b8a 167 * List of supported curves and associated info
maclobdell 0:f7c60d3e7b8a 168 */
maclobdell 0:f7c60d3e7b8a 169 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
maclobdell 0:f7c60d3e7b8a 170 {
maclobdell 0:f7c60d3e7b8a 171 return( ecp_supported_curves );
maclobdell 0:f7c60d3e7b8a 172 }
maclobdell 0:f7c60d3e7b8a 173
maclobdell 0:f7c60d3e7b8a 174 /*
maclobdell 0:f7c60d3e7b8a 175 * List of supported curves, group ID only
maclobdell 0:f7c60d3e7b8a 176 */
maclobdell 0:f7c60d3e7b8a 177 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
maclobdell 0:f7c60d3e7b8a 178 {
maclobdell 0:f7c60d3e7b8a 179 static int init_done = 0;
maclobdell 0:f7c60d3e7b8a 180
maclobdell 0:f7c60d3e7b8a 181 if( ! init_done )
maclobdell 0:f7c60d3e7b8a 182 {
maclobdell 0:f7c60d3e7b8a 183 size_t i = 0;
maclobdell 0:f7c60d3e7b8a 184 const mbedtls_ecp_curve_info *curve_info;
maclobdell 0:f7c60d3e7b8a 185
maclobdell 0:f7c60d3e7b8a 186 for( curve_info = mbedtls_ecp_curve_list();
maclobdell 0:f7c60d3e7b8a 187 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
maclobdell 0:f7c60d3e7b8a 188 curve_info++ )
maclobdell 0:f7c60d3e7b8a 189 {
maclobdell 0:f7c60d3e7b8a 190 ecp_supported_grp_id[i++] = curve_info->grp_id;
maclobdell 0:f7c60d3e7b8a 191 }
maclobdell 0:f7c60d3e7b8a 192 ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
maclobdell 0:f7c60d3e7b8a 193
maclobdell 0:f7c60d3e7b8a 194 init_done = 1;
maclobdell 0:f7c60d3e7b8a 195 }
maclobdell 0:f7c60d3e7b8a 196
maclobdell 0:f7c60d3e7b8a 197 return( ecp_supported_grp_id );
maclobdell 0:f7c60d3e7b8a 198 }
maclobdell 0:f7c60d3e7b8a 199
maclobdell 0:f7c60d3e7b8a 200 /*
maclobdell 0:f7c60d3e7b8a 201 * Get the curve info for the internal identifier
maclobdell 0:f7c60d3e7b8a 202 */
maclobdell 0:f7c60d3e7b8a 203 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id )
maclobdell 0:f7c60d3e7b8a 204 {
maclobdell 0:f7c60d3e7b8a 205 const mbedtls_ecp_curve_info *curve_info;
maclobdell 0:f7c60d3e7b8a 206
maclobdell 0:f7c60d3e7b8a 207 for( curve_info = mbedtls_ecp_curve_list();
maclobdell 0:f7c60d3e7b8a 208 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
maclobdell 0:f7c60d3e7b8a 209 curve_info++ )
maclobdell 0:f7c60d3e7b8a 210 {
maclobdell 0:f7c60d3e7b8a 211 if( curve_info->grp_id == grp_id )
maclobdell 0:f7c60d3e7b8a 212 return( curve_info );
maclobdell 0:f7c60d3e7b8a 213 }
maclobdell 0:f7c60d3e7b8a 214
maclobdell 0:f7c60d3e7b8a 215 return( NULL );
maclobdell 0:f7c60d3e7b8a 216 }
maclobdell 0:f7c60d3e7b8a 217
maclobdell 0:f7c60d3e7b8a 218 /*
maclobdell 0:f7c60d3e7b8a 219 * Get the curve info from the TLS identifier
maclobdell 0:f7c60d3e7b8a 220 */
maclobdell 0:f7c60d3e7b8a 221 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id )
maclobdell 0:f7c60d3e7b8a 222 {
maclobdell 0:f7c60d3e7b8a 223 const mbedtls_ecp_curve_info *curve_info;
maclobdell 0:f7c60d3e7b8a 224
maclobdell 0:f7c60d3e7b8a 225 for( curve_info = mbedtls_ecp_curve_list();
maclobdell 0:f7c60d3e7b8a 226 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
maclobdell 0:f7c60d3e7b8a 227 curve_info++ )
maclobdell 0:f7c60d3e7b8a 228 {
maclobdell 0:f7c60d3e7b8a 229 if( curve_info->tls_id == tls_id )
maclobdell 0:f7c60d3e7b8a 230 return( curve_info );
maclobdell 0:f7c60d3e7b8a 231 }
maclobdell 0:f7c60d3e7b8a 232
maclobdell 0:f7c60d3e7b8a 233 return( NULL );
maclobdell 0:f7c60d3e7b8a 234 }
maclobdell 0:f7c60d3e7b8a 235
maclobdell 0:f7c60d3e7b8a 236 /*
maclobdell 0:f7c60d3e7b8a 237 * Get the curve info from the name
maclobdell 0:f7c60d3e7b8a 238 */
maclobdell 0:f7c60d3e7b8a 239 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name )
maclobdell 0:f7c60d3e7b8a 240 {
maclobdell 0:f7c60d3e7b8a 241 const mbedtls_ecp_curve_info *curve_info;
maclobdell 0:f7c60d3e7b8a 242
maclobdell 0:f7c60d3e7b8a 243 for( curve_info = mbedtls_ecp_curve_list();
maclobdell 0:f7c60d3e7b8a 244 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
maclobdell 0:f7c60d3e7b8a 245 curve_info++ )
maclobdell 0:f7c60d3e7b8a 246 {
maclobdell 0:f7c60d3e7b8a 247 if( strcmp( curve_info->name, name ) == 0 )
maclobdell 0:f7c60d3e7b8a 248 return( curve_info );
maclobdell 0:f7c60d3e7b8a 249 }
maclobdell 0:f7c60d3e7b8a 250
maclobdell 0:f7c60d3e7b8a 251 return( NULL );
maclobdell 0:f7c60d3e7b8a 252 }
maclobdell 0:f7c60d3e7b8a 253
maclobdell 0:f7c60d3e7b8a 254 /*
maclobdell 0:f7c60d3e7b8a 255 * Get the type of a curve
maclobdell 0:f7c60d3e7b8a 256 */
maclobdell 0:f7c60d3e7b8a 257 static inline ecp_curve_type ecp_get_type( const mbedtls_ecp_group *grp )
maclobdell 0:f7c60d3e7b8a 258 {
maclobdell 0:f7c60d3e7b8a 259 if( grp->G.X.p == NULL )
maclobdell 0:f7c60d3e7b8a 260 return( ECP_TYPE_NONE );
maclobdell 0:f7c60d3e7b8a 261
maclobdell 0:f7c60d3e7b8a 262 if( grp->G.Y.p == NULL )
maclobdell 0:f7c60d3e7b8a 263 return( ECP_TYPE_MONTGOMERY );
maclobdell 0:f7c60d3e7b8a 264 else
maclobdell 0:f7c60d3e7b8a 265 return( ECP_TYPE_SHORT_WEIERSTRASS );
maclobdell 0:f7c60d3e7b8a 266 }
maclobdell 0:f7c60d3e7b8a 267
maclobdell 0:f7c60d3e7b8a 268 /*
maclobdell 0:f7c60d3e7b8a 269 * Initialize (the components of) a point
maclobdell 0:f7c60d3e7b8a 270 */
maclobdell 0:f7c60d3e7b8a 271 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
maclobdell 0:f7c60d3e7b8a 272 {
maclobdell 0:f7c60d3e7b8a 273 if( pt == NULL )
maclobdell 0:f7c60d3e7b8a 274 return;
maclobdell 0:f7c60d3e7b8a 275
maclobdell 0:f7c60d3e7b8a 276 mbedtls_mpi_init( &pt->X );
maclobdell 0:f7c60d3e7b8a 277 mbedtls_mpi_init( &pt->Y );
maclobdell 0:f7c60d3e7b8a 278 mbedtls_mpi_init( &pt->Z );
maclobdell 0:f7c60d3e7b8a 279 }
maclobdell 0:f7c60d3e7b8a 280
maclobdell 0:f7c60d3e7b8a 281 /*
maclobdell 0:f7c60d3e7b8a 282 * Initialize (the components of) a group
maclobdell 0:f7c60d3e7b8a 283 */
maclobdell 0:f7c60d3e7b8a 284 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
maclobdell 0:f7c60d3e7b8a 285 {
maclobdell 0:f7c60d3e7b8a 286 if( grp == NULL )
maclobdell 0:f7c60d3e7b8a 287 return;
maclobdell 0:f7c60d3e7b8a 288
maclobdell 0:f7c60d3e7b8a 289 memset( grp, 0, sizeof( mbedtls_ecp_group ) );
maclobdell 0:f7c60d3e7b8a 290 }
maclobdell 0:f7c60d3e7b8a 291
maclobdell 0:f7c60d3e7b8a 292 /*
maclobdell 0:f7c60d3e7b8a 293 * Initialize (the components of) a key pair
maclobdell 0:f7c60d3e7b8a 294 */
maclobdell 0:f7c60d3e7b8a 295 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
maclobdell 0:f7c60d3e7b8a 296 {
maclobdell 0:f7c60d3e7b8a 297 if( key == NULL )
maclobdell 0:f7c60d3e7b8a 298 return;
maclobdell 0:f7c60d3e7b8a 299
maclobdell 0:f7c60d3e7b8a 300 mbedtls_ecp_group_init( &key->grp );
maclobdell 0:f7c60d3e7b8a 301 mbedtls_mpi_init( &key->d );
maclobdell 0:f7c60d3e7b8a 302 mbedtls_ecp_point_init( &key->Q );
maclobdell 0:f7c60d3e7b8a 303 }
maclobdell 0:f7c60d3e7b8a 304
maclobdell 0:f7c60d3e7b8a 305 /*
maclobdell 0:f7c60d3e7b8a 306 * Unallocate (the components of) a point
maclobdell 0:f7c60d3e7b8a 307 */
maclobdell 0:f7c60d3e7b8a 308 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
maclobdell 0:f7c60d3e7b8a 309 {
maclobdell 0:f7c60d3e7b8a 310 if( pt == NULL )
maclobdell 0:f7c60d3e7b8a 311 return;
maclobdell 0:f7c60d3e7b8a 312
maclobdell 0:f7c60d3e7b8a 313 mbedtls_mpi_free( &( pt->X ) );
maclobdell 0:f7c60d3e7b8a 314 mbedtls_mpi_free( &( pt->Y ) );
maclobdell 0:f7c60d3e7b8a 315 mbedtls_mpi_free( &( pt->Z ) );
maclobdell 0:f7c60d3e7b8a 316 }
maclobdell 0:f7c60d3e7b8a 317
maclobdell 0:f7c60d3e7b8a 318 /*
maclobdell 0:f7c60d3e7b8a 319 * Unallocate (the components of) a group
maclobdell 0:f7c60d3e7b8a 320 */
maclobdell 0:f7c60d3e7b8a 321 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
maclobdell 0:f7c60d3e7b8a 322 {
maclobdell 0:f7c60d3e7b8a 323 size_t i;
maclobdell 0:f7c60d3e7b8a 324
maclobdell 0:f7c60d3e7b8a 325 if( grp == NULL )
maclobdell 0:f7c60d3e7b8a 326 return;
maclobdell 0:f7c60d3e7b8a 327
maclobdell 0:f7c60d3e7b8a 328 if( grp->h != 1 )
maclobdell 0:f7c60d3e7b8a 329 {
maclobdell 0:f7c60d3e7b8a 330 mbedtls_mpi_free( &grp->P );
maclobdell 0:f7c60d3e7b8a 331 mbedtls_mpi_free( &grp->A );
maclobdell 0:f7c60d3e7b8a 332 mbedtls_mpi_free( &grp->B );
maclobdell 0:f7c60d3e7b8a 333 mbedtls_ecp_point_free( &grp->G );
maclobdell 0:f7c60d3e7b8a 334 mbedtls_mpi_free( &grp->N );
maclobdell 0:f7c60d3e7b8a 335 }
maclobdell 0:f7c60d3e7b8a 336
maclobdell 0:f7c60d3e7b8a 337 if( grp->T != NULL )
maclobdell 0:f7c60d3e7b8a 338 {
maclobdell 0:f7c60d3e7b8a 339 for( i = 0; i < grp->T_size; i++ )
maclobdell 0:f7c60d3e7b8a 340 mbedtls_ecp_point_free( &grp->T[i] );
maclobdell 0:f7c60d3e7b8a 341 mbedtls_free( grp->T );
maclobdell 0:f7c60d3e7b8a 342 }
maclobdell 0:f7c60d3e7b8a 343
maclobdell 0:f7c60d3e7b8a 344 mbedtls_zeroize( grp, sizeof( mbedtls_ecp_group ) );
maclobdell 0:f7c60d3e7b8a 345 }
maclobdell 0:f7c60d3e7b8a 346
maclobdell 0:f7c60d3e7b8a 347 /*
maclobdell 0:f7c60d3e7b8a 348 * Unallocate (the components of) a key pair
maclobdell 0:f7c60d3e7b8a 349 */
maclobdell 0:f7c60d3e7b8a 350 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
maclobdell 0:f7c60d3e7b8a 351 {
maclobdell 0:f7c60d3e7b8a 352 if( key == NULL )
maclobdell 0:f7c60d3e7b8a 353 return;
maclobdell 0:f7c60d3e7b8a 354
maclobdell 0:f7c60d3e7b8a 355 mbedtls_ecp_group_free( &key->grp );
maclobdell 0:f7c60d3e7b8a 356 mbedtls_mpi_free( &key->d );
maclobdell 0:f7c60d3e7b8a 357 mbedtls_ecp_point_free( &key->Q );
maclobdell 0:f7c60d3e7b8a 358 }
maclobdell 0:f7c60d3e7b8a 359
maclobdell 0:f7c60d3e7b8a 360 /*
maclobdell 0:f7c60d3e7b8a 361 * Copy the contents of a point
maclobdell 0:f7c60d3e7b8a 362 */
maclobdell 0:f7c60d3e7b8a 363 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
maclobdell 0:f7c60d3e7b8a 364 {
maclobdell 0:f7c60d3e7b8a 365 int ret;
maclobdell 0:f7c60d3e7b8a 366
maclobdell 0:f7c60d3e7b8a 367 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) );
maclobdell 0:f7c60d3e7b8a 368 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) );
maclobdell 0:f7c60d3e7b8a 369 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) );
maclobdell 0:f7c60d3e7b8a 370
maclobdell 0:f7c60d3e7b8a 371 cleanup:
maclobdell 0:f7c60d3e7b8a 372 return( ret );
maclobdell 0:f7c60d3e7b8a 373 }
maclobdell 0:f7c60d3e7b8a 374
maclobdell 0:f7c60d3e7b8a 375 /*
maclobdell 0:f7c60d3e7b8a 376 * Copy the contents of a group object
maclobdell 0:f7c60d3e7b8a 377 */
maclobdell 0:f7c60d3e7b8a 378 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
maclobdell 0:f7c60d3e7b8a 379 {
maclobdell 0:f7c60d3e7b8a 380 return mbedtls_ecp_group_load( dst, src->id );
maclobdell 0:f7c60d3e7b8a 381 }
maclobdell 0:f7c60d3e7b8a 382
maclobdell 0:f7c60d3e7b8a 383 /*
maclobdell 0:f7c60d3e7b8a 384 * Set point to zero
maclobdell 0:f7c60d3e7b8a 385 */
maclobdell 0:f7c60d3e7b8a 386 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
maclobdell 0:f7c60d3e7b8a 387 {
maclobdell 0:f7c60d3e7b8a 388 int ret;
maclobdell 0:f7c60d3e7b8a 389
maclobdell 0:f7c60d3e7b8a 390 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) );
maclobdell 0:f7c60d3e7b8a 391 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) );
maclobdell 0:f7c60d3e7b8a 392 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) );
maclobdell 0:f7c60d3e7b8a 393
maclobdell 0:f7c60d3e7b8a 394 cleanup:
maclobdell 0:f7c60d3e7b8a 395 return( ret );
maclobdell 0:f7c60d3e7b8a 396 }
maclobdell 0:f7c60d3e7b8a 397
maclobdell 0:f7c60d3e7b8a 398 /*
maclobdell 0:f7c60d3e7b8a 399 * Tell if a point is zero
maclobdell 0:f7c60d3e7b8a 400 */
maclobdell 0:f7c60d3e7b8a 401 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
maclobdell 0:f7c60d3e7b8a 402 {
maclobdell 0:f7c60d3e7b8a 403 return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 );
maclobdell 0:f7c60d3e7b8a 404 }
maclobdell 0:f7c60d3e7b8a 405
maclobdell 0:f7c60d3e7b8a 406 /*
maclobdell 0:f7c60d3e7b8a 407 * Compare two points lazyly
maclobdell 0:f7c60d3e7b8a 408 */
maclobdell 0:f7c60d3e7b8a 409 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
maclobdell 0:f7c60d3e7b8a 410 const mbedtls_ecp_point *Q )
maclobdell 0:f7c60d3e7b8a 411 {
maclobdell 0:f7c60d3e7b8a 412 if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
maclobdell 0:f7c60d3e7b8a 413 mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 &&
maclobdell 0:f7c60d3e7b8a 414 mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 )
maclobdell 0:f7c60d3e7b8a 415 {
maclobdell 0:f7c60d3e7b8a 416 return( 0 );
maclobdell 0:f7c60d3e7b8a 417 }
maclobdell 0:f7c60d3e7b8a 418
maclobdell 0:f7c60d3e7b8a 419 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 420 }
maclobdell 0:f7c60d3e7b8a 421
maclobdell 0:f7c60d3e7b8a 422 /*
maclobdell 0:f7c60d3e7b8a 423 * Import a non-zero point from ASCII strings
maclobdell 0:f7c60d3e7b8a 424 */
maclobdell 0:f7c60d3e7b8a 425 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
maclobdell 0:f7c60d3e7b8a 426 const char *x, const char *y )
maclobdell 0:f7c60d3e7b8a 427 {
maclobdell 0:f7c60d3e7b8a 428 int ret;
maclobdell 0:f7c60d3e7b8a 429
maclobdell 0:f7c60d3e7b8a 430 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) );
maclobdell 0:f7c60d3e7b8a 431 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) );
maclobdell 0:f7c60d3e7b8a 432 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
maclobdell 0:f7c60d3e7b8a 433
maclobdell 0:f7c60d3e7b8a 434 cleanup:
maclobdell 0:f7c60d3e7b8a 435 return( ret );
maclobdell 0:f7c60d3e7b8a 436 }
maclobdell 0:f7c60d3e7b8a 437
maclobdell 0:f7c60d3e7b8a 438 /*
maclobdell 0:f7c60d3e7b8a 439 * Export a point into unsigned binary data (SEC1 2.3.3)
maclobdell 0:f7c60d3e7b8a 440 */
maclobdell 0:f7c60d3e7b8a 441 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P,
maclobdell 0:f7c60d3e7b8a 442 int format, size_t *olen,
maclobdell 0:f7c60d3e7b8a 443 unsigned char *buf, size_t buflen )
maclobdell 0:f7c60d3e7b8a 444 {
maclobdell 0:f7c60d3e7b8a 445 int ret = 0;
maclobdell 0:f7c60d3e7b8a 446 size_t plen;
maclobdell 0:f7c60d3e7b8a 447
maclobdell 0:f7c60d3e7b8a 448 if( format != MBEDTLS_ECP_PF_UNCOMPRESSED &&
maclobdell 0:f7c60d3e7b8a 449 format != MBEDTLS_ECP_PF_COMPRESSED )
maclobdell 0:f7c60d3e7b8a 450 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 451
maclobdell 0:f7c60d3e7b8a 452 /*
maclobdell 0:f7c60d3e7b8a 453 * Common case: P == 0
maclobdell 0:f7c60d3e7b8a 454 */
maclobdell 0:f7c60d3e7b8a 455 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
maclobdell 0:f7c60d3e7b8a 456 {
maclobdell 0:f7c60d3e7b8a 457 if( buflen < 1 )
maclobdell 0:f7c60d3e7b8a 458 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
maclobdell 0:f7c60d3e7b8a 459
maclobdell 0:f7c60d3e7b8a 460 buf[0] = 0x00;
maclobdell 0:f7c60d3e7b8a 461 *olen = 1;
maclobdell 0:f7c60d3e7b8a 462
maclobdell 0:f7c60d3e7b8a 463 return( 0 );
maclobdell 0:f7c60d3e7b8a 464 }
maclobdell 0:f7c60d3e7b8a 465
maclobdell 0:f7c60d3e7b8a 466 plen = mbedtls_mpi_size( &grp->P );
maclobdell 0:f7c60d3e7b8a 467
maclobdell 0:f7c60d3e7b8a 468 if( format == MBEDTLS_ECP_PF_UNCOMPRESSED )
maclobdell 0:f7c60d3e7b8a 469 {
maclobdell 0:f7c60d3e7b8a 470 *olen = 2 * plen + 1;
maclobdell 0:f7c60d3e7b8a 471
maclobdell 0:f7c60d3e7b8a 472 if( buflen < *olen )
maclobdell 0:f7c60d3e7b8a 473 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
maclobdell 0:f7c60d3e7b8a 474
maclobdell 0:f7c60d3e7b8a 475 buf[0] = 0x04;
maclobdell 0:f7c60d3e7b8a 476 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
maclobdell 0:f7c60d3e7b8a 477 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) );
maclobdell 0:f7c60d3e7b8a 478 }
maclobdell 0:f7c60d3e7b8a 479 else if( format == MBEDTLS_ECP_PF_COMPRESSED )
maclobdell 0:f7c60d3e7b8a 480 {
maclobdell 0:f7c60d3e7b8a 481 *olen = plen + 1;
maclobdell 0:f7c60d3e7b8a 482
maclobdell 0:f7c60d3e7b8a 483 if( buflen < *olen )
maclobdell 0:f7c60d3e7b8a 484 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
maclobdell 0:f7c60d3e7b8a 485
maclobdell 0:f7c60d3e7b8a 486 buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 );
maclobdell 0:f7c60d3e7b8a 487 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
maclobdell 0:f7c60d3e7b8a 488 }
maclobdell 0:f7c60d3e7b8a 489
maclobdell 0:f7c60d3e7b8a 490 cleanup:
maclobdell 0:f7c60d3e7b8a 491 return( ret );
maclobdell 0:f7c60d3e7b8a 492 }
maclobdell 0:f7c60d3e7b8a 493
maclobdell 0:f7c60d3e7b8a 494 /*
maclobdell 0:f7c60d3e7b8a 495 * Import a point from unsigned binary data (SEC1 2.3.4)
maclobdell 0:f7c60d3e7b8a 496 */
maclobdell 0:f7c60d3e7b8a 497 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
maclobdell 0:f7c60d3e7b8a 498 const unsigned char *buf, size_t ilen )
maclobdell 0:f7c60d3e7b8a 499 {
maclobdell 0:f7c60d3e7b8a 500 int ret;
maclobdell 0:f7c60d3e7b8a 501 size_t plen;
maclobdell 0:f7c60d3e7b8a 502
maclobdell 0:f7c60d3e7b8a 503 if( ilen < 1 )
maclobdell 0:f7c60d3e7b8a 504 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 505
maclobdell 0:f7c60d3e7b8a 506 if( buf[0] == 0x00 )
maclobdell 0:f7c60d3e7b8a 507 {
maclobdell 0:f7c60d3e7b8a 508 if( ilen == 1 )
maclobdell 0:f7c60d3e7b8a 509 return( mbedtls_ecp_set_zero( pt ) );
maclobdell 0:f7c60d3e7b8a 510 else
maclobdell 0:f7c60d3e7b8a 511 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 512 }
maclobdell 0:f7c60d3e7b8a 513
maclobdell 0:f7c60d3e7b8a 514 plen = mbedtls_mpi_size( &grp->P );
maclobdell 0:f7c60d3e7b8a 515
maclobdell 0:f7c60d3e7b8a 516 if( buf[0] != 0x04 )
maclobdell 0:f7c60d3e7b8a 517 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
maclobdell 0:f7c60d3e7b8a 518
maclobdell 0:f7c60d3e7b8a 519 if( ilen != 2 * plen + 1 )
maclobdell 0:f7c60d3e7b8a 520 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 521
maclobdell 0:f7c60d3e7b8a 522 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
maclobdell 0:f7c60d3e7b8a 523 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, buf + 1 + plen, plen ) );
maclobdell 0:f7c60d3e7b8a 524 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
maclobdell 0:f7c60d3e7b8a 525
maclobdell 0:f7c60d3e7b8a 526 cleanup:
maclobdell 0:f7c60d3e7b8a 527 return( ret );
maclobdell 0:f7c60d3e7b8a 528 }
maclobdell 0:f7c60d3e7b8a 529
maclobdell 0:f7c60d3e7b8a 530 /*
maclobdell 0:f7c60d3e7b8a 531 * Import a point from a TLS ECPoint record (RFC 4492)
maclobdell 0:f7c60d3e7b8a 532 * struct {
maclobdell 0:f7c60d3e7b8a 533 * opaque point <1..2^8-1>;
maclobdell 0:f7c60d3e7b8a 534 * } ECPoint;
maclobdell 0:f7c60d3e7b8a 535 */
maclobdell 0:f7c60d3e7b8a 536 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
maclobdell 0:f7c60d3e7b8a 537 const unsigned char **buf, size_t buf_len )
maclobdell 0:f7c60d3e7b8a 538 {
maclobdell 0:f7c60d3e7b8a 539 unsigned char data_len;
maclobdell 0:f7c60d3e7b8a 540 const unsigned char *buf_start;
maclobdell 0:f7c60d3e7b8a 541
maclobdell 0:f7c60d3e7b8a 542 /*
maclobdell 0:f7c60d3e7b8a 543 * We must have at least two bytes (1 for length, at least one for data)
maclobdell 0:f7c60d3e7b8a 544 */
maclobdell 0:f7c60d3e7b8a 545 if( buf_len < 2 )
maclobdell 0:f7c60d3e7b8a 546 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 547
maclobdell 0:f7c60d3e7b8a 548 data_len = *(*buf)++;
maclobdell 0:f7c60d3e7b8a 549 if( data_len < 1 || data_len > buf_len - 1 )
maclobdell 0:f7c60d3e7b8a 550 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 551
maclobdell 0:f7c60d3e7b8a 552 /*
maclobdell 0:f7c60d3e7b8a 553 * Save buffer start for read_binary and update buf
maclobdell 0:f7c60d3e7b8a 554 */
maclobdell 0:f7c60d3e7b8a 555 buf_start = *buf;
maclobdell 0:f7c60d3e7b8a 556 *buf += data_len;
maclobdell 0:f7c60d3e7b8a 557
maclobdell 0:f7c60d3e7b8a 558 return mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len );
maclobdell 0:f7c60d3e7b8a 559 }
maclobdell 0:f7c60d3e7b8a 560
maclobdell 0:f7c60d3e7b8a 561 /*
maclobdell 0:f7c60d3e7b8a 562 * Export a point as a TLS ECPoint record (RFC 4492)
maclobdell 0:f7c60d3e7b8a 563 * struct {
maclobdell 0:f7c60d3e7b8a 564 * opaque point <1..2^8-1>;
maclobdell 0:f7c60d3e7b8a 565 * } ECPoint;
maclobdell 0:f7c60d3e7b8a 566 */
maclobdell 0:f7c60d3e7b8a 567 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
maclobdell 0:f7c60d3e7b8a 568 int format, size_t *olen,
maclobdell 0:f7c60d3e7b8a 569 unsigned char *buf, size_t blen )
maclobdell 0:f7c60d3e7b8a 570 {
maclobdell 0:f7c60d3e7b8a 571 int ret;
maclobdell 0:f7c60d3e7b8a 572
maclobdell 0:f7c60d3e7b8a 573 /*
maclobdell 0:f7c60d3e7b8a 574 * buffer length must be at least one, for our length byte
maclobdell 0:f7c60d3e7b8a 575 */
maclobdell 0:f7c60d3e7b8a 576 if( blen < 1 )
maclobdell 0:f7c60d3e7b8a 577 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 578
maclobdell 0:f7c60d3e7b8a 579 if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
maclobdell 0:f7c60d3e7b8a 580 olen, buf + 1, blen - 1) ) != 0 )
maclobdell 0:f7c60d3e7b8a 581 return( ret );
maclobdell 0:f7c60d3e7b8a 582
maclobdell 0:f7c60d3e7b8a 583 /*
maclobdell 0:f7c60d3e7b8a 584 * write length to the first byte and update total length
maclobdell 0:f7c60d3e7b8a 585 */
maclobdell 0:f7c60d3e7b8a 586 buf[0] = (unsigned char) *olen;
maclobdell 0:f7c60d3e7b8a 587 ++*olen;
maclobdell 0:f7c60d3e7b8a 588
maclobdell 0:f7c60d3e7b8a 589 return( 0 );
maclobdell 0:f7c60d3e7b8a 590 }
maclobdell 0:f7c60d3e7b8a 591
maclobdell 0:f7c60d3e7b8a 592 /*
maclobdell 0:f7c60d3e7b8a 593 * Set a group from an ECParameters record (RFC 4492)
maclobdell 0:f7c60d3e7b8a 594 */
maclobdell 0:f7c60d3e7b8a 595 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, const unsigned char **buf, size_t len )
maclobdell 0:f7c60d3e7b8a 596 {
maclobdell 0:f7c60d3e7b8a 597 uint16_t tls_id;
maclobdell 0:f7c60d3e7b8a 598 const mbedtls_ecp_curve_info *curve_info;
maclobdell 0:f7c60d3e7b8a 599
maclobdell 0:f7c60d3e7b8a 600 /*
maclobdell 0:f7c60d3e7b8a 601 * We expect at least three bytes (see below)
maclobdell 0:f7c60d3e7b8a 602 */
maclobdell 0:f7c60d3e7b8a 603 if( len < 3 )
maclobdell 0:f7c60d3e7b8a 604 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 605
maclobdell 0:f7c60d3e7b8a 606 /*
maclobdell 0:f7c60d3e7b8a 607 * First byte is curve_type; only named_curve is handled
maclobdell 0:f7c60d3e7b8a 608 */
maclobdell 0:f7c60d3e7b8a 609 if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
maclobdell 0:f7c60d3e7b8a 610 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 611
maclobdell 0:f7c60d3e7b8a 612 /*
maclobdell 0:f7c60d3e7b8a 613 * Next two bytes are the namedcurve value
maclobdell 0:f7c60d3e7b8a 614 */
maclobdell 0:f7c60d3e7b8a 615 tls_id = *(*buf)++;
maclobdell 0:f7c60d3e7b8a 616 tls_id <<= 8;
maclobdell 0:f7c60d3e7b8a 617 tls_id |= *(*buf)++;
maclobdell 0:f7c60d3e7b8a 618
maclobdell 0:f7c60d3e7b8a 619 if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
maclobdell 0:f7c60d3e7b8a 620 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
maclobdell 0:f7c60d3e7b8a 621
maclobdell 0:f7c60d3e7b8a 622 return mbedtls_ecp_group_load( grp, curve_info->grp_id );
maclobdell 0:f7c60d3e7b8a 623 }
maclobdell 0:f7c60d3e7b8a 624
maclobdell 0:f7c60d3e7b8a 625 /*
maclobdell 0:f7c60d3e7b8a 626 * Write the ECParameters record corresponding to a group (RFC 4492)
maclobdell 0:f7c60d3e7b8a 627 */
maclobdell 0:f7c60d3e7b8a 628 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
maclobdell 0:f7c60d3e7b8a 629 unsigned char *buf, size_t blen )
maclobdell 0:f7c60d3e7b8a 630 {
maclobdell 0:f7c60d3e7b8a 631 const mbedtls_ecp_curve_info *curve_info;
maclobdell 0:f7c60d3e7b8a 632
maclobdell 0:f7c60d3e7b8a 633 if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
maclobdell 0:f7c60d3e7b8a 634 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 635
maclobdell 0:f7c60d3e7b8a 636 /*
maclobdell 0:f7c60d3e7b8a 637 * We are going to write 3 bytes (see below)
maclobdell 0:f7c60d3e7b8a 638 */
maclobdell 0:f7c60d3e7b8a 639 *olen = 3;
maclobdell 0:f7c60d3e7b8a 640 if( blen < *olen )
maclobdell 0:f7c60d3e7b8a 641 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
maclobdell 0:f7c60d3e7b8a 642
maclobdell 0:f7c60d3e7b8a 643 /*
maclobdell 0:f7c60d3e7b8a 644 * First byte is curve_type, always named_curve
maclobdell 0:f7c60d3e7b8a 645 */
maclobdell 0:f7c60d3e7b8a 646 *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
maclobdell 0:f7c60d3e7b8a 647
maclobdell 0:f7c60d3e7b8a 648 /*
maclobdell 0:f7c60d3e7b8a 649 * Next two bytes are the namedcurve value
maclobdell 0:f7c60d3e7b8a 650 */
maclobdell 0:f7c60d3e7b8a 651 buf[0] = curve_info->tls_id >> 8;
maclobdell 0:f7c60d3e7b8a 652 buf[1] = curve_info->tls_id & 0xFF;
maclobdell 0:f7c60d3e7b8a 653
maclobdell 0:f7c60d3e7b8a 654 return( 0 );
maclobdell 0:f7c60d3e7b8a 655 }
maclobdell 0:f7c60d3e7b8a 656
maclobdell 0:f7c60d3e7b8a 657 /*
maclobdell 0:f7c60d3e7b8a 658 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
maclobdell 0:f7c60d3e7b8a 659 * See the documentation of struct mbedtls_ecp_group.
maclobdell 0:f7c60d3e7b8a 660 *
maclobdell 0:f7c60d3e7b8a 661 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
maclobdell 0:f7c60d3e7b8a 662 */
maclobdell 0:f7c60d3e7b8a 663 static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
maclobdell 0:f7c60d3e7b8a 664 {
maclobdell 0:f7c60d3e7b8a 665 int ret;
maclobdell 0:f7c60d3e7b8a 666
maclobdell 0:f7c60d3e7b8a 667 if( grp->modp == NULL )
maclobdell 0:f7c60d3e7b8a 668 return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) );
maclobdell 0:f7c60d3e7b8a 669
maclobdell 0:f7c60d3e7b8a 670 /* N->s < 0 is a much faster test, which fails only if N is 0 */
maclobdell 0:f7c60d3e7b8a 671 if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) ||
maclobdell 0:f7c60d3e7b8a 672 mbedtls_mpi_bitlen( N ) > 2 * grp->pbits )
maclobdell 0:f7c60d3e7b8a 673 {
maclobdell 0:f7c60d3e7b8a 674 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 675 }
maclobdell 0:f7c60d3e7b8a 676
maclobdell 0:f7c60d3e7b8a 677 MBEDTLS_MPI_CHK( grp->modp( N ) );
maclobdell 0:f7c60d3e7b8a 678
maclobdell 0:f7c60d3e7b8a 679 /* N->s < 0 is a much faster test, which fails only if N is 0 */
maclobdell 0:f7c60d3e7b8a 680 while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 )
maclobdell 0:f7c60d3e7b8a 681 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) );
maclobdell 0:f7c60d3e7b8a 682
maclobdell 0:f7c60d3e7b8a 683 while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 )
maclobdell 0:f7c60d3e7b8a 684 /* we known P, N and the result are positive */
maclobdell 0:f7c60d3e7b8a 685 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) );
maclobdell 0:f7c60d3e7b8a 686
maclobdell 0:f7c60d3e7b8a 687 cleanup:
maclobdell 0:f7c60d3e7b8a 688 return( ret );
maclobdell 0:f7c60d3e7b8a 689 }
maclobdell 0:f7c60d3e7b8a 690
maclobdell 0:f7c60d3e7b8a 691 /*
maclobdell 0:f7c60d3e7b8a 692 * Fast mod-p functions expect their argument to be in the 0..p^2 range.
maclobdell 0:f7c60d3e7b8a 693 *
maclobdell 0:f7c60d3e7b8a 694 * In order to guarantee that, we need to ensure that operands of
maclobdell 0:f7c60d3e7b8a 695 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will
maclobdell 0:f7c60d3e7b8a 696 * bring the result back to this range.
maclobdell 0:f7c60d3e7b8a 697 *
maclobdell 0:f7c60d3e7b8a 698 * The following macros are shortcuts for doing that.
maclobdell 0:f7c60d3e7b8a 699 */
maclobdell 0:f7c60d3e7b8a 700
maclobdell 0:f7c60d3e7b8a 701 /*
maclobdell 0:f7c60d3e7b8a 702 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
maclobdell 0:f7c60d3e7b8a 703 */
maclobdell 0:f7c60d3e7b8a 704 #if defined(MBEDTLS_SELF_TEST)
maclobdell 0:f7c60d3e7b8a 705 #define INC_MUL_COUNT mul_count++;
maclobdell 0:f7c60d3e7b8a 706 #else
maclobdell 0:f7c60d3e7b8a 707 #define INC_MUL_COUNT
maclobdell 0:f7c60d3e7b8a 708 #endif
maclobdell 0:f7c60d3e7b8a 709
maclobdell 0:f7c60d3e7b8a 710 #define MOD_MUL( N ) do { MBEDTLS_MPI_CHK( ecp_modp( &N, grp ) ); INC_MUL_COUNT } \
maclobdell 0:f7c60d3e7b8a 711 while( 0 )
maclobdell 0:f7c60d3e7b8a 712
maclobdell 0:f7c60d3e7b8a 713 /*
maclobdell 0:f7c60d3e7b8a 714 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
maclobdell 0:f7c60d3e7b8a 715 * N->s < 0 is a very fast test, which fails only if N is 0
maclobdell 0:f7c60d3e7b8a 716 */
maclobdell 0:f7c60d3e7b8a 717 #define MOD_SUB( N ) \
maclobdell 0:f7c60d3e7b8a 718 while( N.s < 0 && mbedtls_mpi_cmp_int( &N, 0 ) != 0 ) \
maclobdell 0:f7c60d3e7b8a 719 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &N, &N, &grp->P ) )
maclobdell 0:f7c60d3e7b8a 720
maclobdell 0:f7c60d3e7b8a 721 /*
maclobdell 0:f7c60d3e7b8a 722 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
maclobdell 0:f7c60d3e7b8a 723 * We known P, N and the result are positive, so sub_abs is correct, and
maclobdell 0:f7c60d3e7b8a 724 * a bit faster.
maclobdell 0:f7c60d3e7b8a 725 */
maclobdell 0:f7c60d3e7b8a 726 #define MOD_ADD( N ) \
maclobdell 0:f7c60d3e7b8a 727 while( mbedtls_mpi_cmp_mpi( &N, &grp->P ) >= 0 ) \
maclobdell 0:f7c60d3e7b8a 728 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &N, &N, &grp->P ) )
maclobdell 0:f7c60d3e7b8a 729
maclobdell 0:f7c60d3e7b8a 730 #if defined(ECP_SHORTWEIERSTRASS)
maclobdell 0:f7c60d3e7b8a 731 /*
maclobdell 0:f7c60d3e7b8a 732 * For curves in short Weierstrass form, we do all the internal operations in
maclobdell 0:f7c60d3e7b8a 733 * Jacobian coordinates.
maclobdell 0:f7c60d3e7b8a 734 *
maclobdell 0:f7c60d3e7b8a 735 * For multiplication, we'll use a comb method with coutermeasueres against
maclobdell 0:f7c60d3e7b8a 736 * SPA, hence timing attacks.
maclobdell 0:f7c60d3e7b8a 737 */
maclobdell 0:f7c60d3e7b8a 738
maclobdell 0:f7c60d3e7b8a 739 /*
maclobdell 0:f7c60d3e7b8a 740 * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
maclobdell 0:f7c60d3e7b8a 741 * Cost: 1N := 1I + 3M + 1S
maclobdell 0:f7c60d3e7b8a 742 */
maclobdell 0:f7c60d3e7b8a 743 static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
maclobdell 0:f7c60d3e7b8a 744 {
maclobdell 0:f7c60d3e7b8a 745 int ret;
maclobdell 0:f7c60d3e7b8a 746 mbedtls_mpi Zi, ZZi;
maclobdell 0:f7c60d3e7b8a 747
maclobdell 0:f7c60d3e7b8a 748 if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
maclobdell 0:f7c60d3e7b8a 749 return( 0 );
maclobdell 0:f7c60d3e7b8a 750
maclobdell 0:f7c60d3e7b8a 751 mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
maclobdell 0:f7c60d3e7b8a 752
maclobdell 0:f7c60d3e7b8a 753 /*
maclobdell 0:f7c60d3e7b8a 754 * X = X / Z^2 mod p
maclobdell 0:f7c60d3e7b8a 755 */
maclobdell 0:f7c60d3e7b8a 756 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
maclobdell 0:f7c60d3e7b8a 757 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
maclobdell 0:f7c60d3e7b8a 758 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ZZi ) ); MOD_MUL( pt->X );
maclobdell 0:f7c60d3e7b8a 759
maclobdell 0:f7c60d3e7b8a 760 /*
maclobdell 0:f7c60d3e7b8a 761 * Y = Y / Z^3 mod p
maclobdell 0:f7c60d3e7b8a 762 */
maclobdell 0:f7c60d3e7b8a 763 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ZZi ) ); MOD_MUL( pt->Y );
maclobdell 0:f7c60d3e7b8a 764 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &Zi ) ); MOD_MUL( pt->Y );
maclobdell 0:f7c60d3e7b8a 765
maclobdell 0:f7c60d3e7b8a 766 /*
maclobdell 0:f7c60d3e7b8a 767 * Z = 1
maclobdell 0:f7c60d3e7b8a 768 */
maclobdell 0:f7c60d3e7b8a 769 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
maclobdell 0:f7c60d3e7b8a 770
maclobdell 0:f7c60d3e7b8a 771 cleanup:
maclobdell 0:f7c60d3e7b8a 772
maclobdell 0:f7c60d3e7b8a 773 mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
maclobdell 0:f7c60d3e7b8a 774
maclobdell 0:f7c60d3e7b8a 775 return( ret );
maclobdell 0:f7c60d3e7b8a 776 }
maclobdell 0:f7c60d3e7b8a 777
maclobdell 0:f7c60d3e7b8a 778 /*
maclobdell 0:f7c60d3e7b8a 779 * Normalize jacobian coordinates of an array of (pointers to) points,
maclobdell 0:f7c60d3e7b8a 780 * using Montgomery's trick to perform only one inversion mod P.
maclobdell 0:f7c60d3e7b8a 781 * (See for example Cohen's "A Course in Computational Algebraic Number
maclobdell 0:f7c60d3e7b8a 782 * Theory", Algorithm 10.3.4.)
maclobdell 0:f7c60d3e7b8a 783 *
maclobdell 0:f7c60d3e7b8a 784 * Warning: fails (returning an error) if one of the points is zero!
maclobdell 0:f7c60d3e7b8a 785 * This should never happen, see choice of w in ecp_mul_comb().
maclobdell 0:f7c60d3e7b8a 786 *
maclobdell 0:f7c60d3e7b8a 787 * Cost: 1N(t) := 1I + (6t - 3)M + 1S
maclobdell 0:f7c60d3e7b8a 788 */
maclobdell 0:f7c60d3e7b8a 789 static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
maclobdell 0:f7c60d3e7b8a 790 mbedtls_ecp_point *T[], size_t t_len )
maclobdell 0:f7c60d3e7b8a 791 {
maclobdell 0:f7c60d3e7b8a 792 int ret;
maclobdell 0:f7c60d3e7b8a 793 size_t i;
maclobdell 0:f7c60d3e7b8a 794 mbedtls_mpi *c, u, Zi, ZZi;
maclobdell 0:f7c60d3e7b8a 795
maclobdell 0:f7c60d3e7b8a 796 if( t_len < 2 )
maclobdell 0:f7c60d3e7b8a 797 return( ecp_normalize_jac( grp, *T ) );
maclobdell 0:f7c60d3e7b8a 798
maclobdell 0:f7c60d3e7b8a 799 if( ( c = mbedtls_calloc( t_len, sizeof( mbedtls_mpi ) ) ) == NULL )
maclobdell 0:f7c60d3e7b8a 800 return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
maclobdell 0:f7c60d3e7b8a 801
maclobdell 0:f7c60d3e7b8a 802 mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
maclobdell 0:f7c60d3e7b8a 803
maclobdell 0:f7c60d3e7b8a 804 /*
maclobdell 0:f7c60d3e7b8a 805 * c[i] = Z_0 * ... * Z_i
maclobdell 0:f7c60d3e7b8a 806 */
maclobdell 0:f7c60d3e7b8a 807 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
maclobdell 0:f7c60d3e7b8a 808 for( i = 1; i < t_len; i++ )
maclobdell 0:f7c60d3e7b8a 809 {
maclobdell 0:f7c60d3e7b8a 810 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &c[i], &c[i-1], &T[i]->Z ) );
maclobdell 0:f7c60d3e7b8a 811 MOD_MUL( c[i] );
maclobdell 0:f7c60d3e7b8a 812 }
maclobdell 0:f7c60d3e7b8a 813
maclobdell 0:f7c60d3e7b8a 814 /*
maclobdell 0:f7c60d3e7b8a 815 * u = 1 / (Z_0 * ... * Z_n) mod P
maclobdell 0:f7c60d3e7b8a 816 */
maclobdell 0:f7c60d3e7b8a 817 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[t_len-1], &grp->P ) );
maclobdell 0:f7c60d3e7b8a 818
maclobdell 0:f7c60d3e7b8a 819 for( i = t_len - 1; ; i-- )
maclobdell 0:f7c60d3e7b8a 820 {
maclobdell 0:f7c60d3e7b8a 821 /*
maclobdell 0:f7c60d3e7b8a 822 * Zi = 1 / Z_i mod p
maclobdell 0:f7c60d3e7b8a 823 * u = 1 / (Z_0 * ... * Z_i) mod P
maclobdell 0:f7c60d3e7b8a 824 */
maclobdell 0:f7c60d3e7b8a 825 if( i == 0 ) {
maclobdell 0:f7c60d3e7b8a 826 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
maclobdell 0:f7c60d3e7b8a 827 }
maclobdell 0:f7c60d3e7b8a 828 else
maclobdell 0:f7c60d3e7b8a 829 {
maclobdell 0:f7c60d3e7b8a 830 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Zi, &u, &c[i-1] ) ); MOD_MUL( Zi );
maclobdell 0:f7c60d3e7b8a 831 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u, &u, &T[i]->Z ) ); MOD_MUL( u );
maclobdell 0:f7c60d3e7b8a 832 }
maclobdell 0:f7c60d3e7b8a 833
maclobdell 0:f7c60d3e7b8a 834 /*
maclobdell 0:f7c60d3e7b8a 835 * proceed as in normalize()
maclobdell 0:f7c60d3e7b8a 836 */
maclobdell 0:f7c60d3e7b8a 837 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
maclobdell 0:f7c60d3e7b8a 838 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->X, &T[i]->X, &ZZi ) ); MOD_MUL( T[i]->X );
maclobdell 0:f7c60d3e7b8a 839 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &ZZi ) ); MOD_MUL( T[i]->Y );
maclobdell 0:f7c60d3e7b8a 840 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &Zi ) ); MOD_MUL( T[i]->Y );
maclobdell 0:f7c60d3e7b8a 841
maclobdell 0:f7c60d3e7b8a 842 /*
maclobdell 0:f7c60d3e7b8a 843 * Post-precessing: reclaim some memory by shrinking coordinates
maclobdell 0:f7c60d3e7b8a 844 * - not storing Z (always 1)
maclobdell 0:f7c60d3e7b8a 845 * - shrinking other coordinates, but still keeping the same number of
maclobdell 0:f7c60d3e7b8a 846 * limbs as P, as otherwise it will too likely be regrown too fast.
maclobdell 0:f7c60d3e7b8a 847 */
maclobdell 0:f7c60d3e7b8a 848 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
maclobdell 0:f7c60d3e7b8a 849 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
maclobdell 0:f7c60d3e7b8a 850 mbedtls_mpi_free( &T[i]->Z );
maclobdell 0:f7c60d3e7b8a 851
maclobdell 0:f7c60d3e7b8a 852 if( i == 0 )
maclobdell 0:f7c60d3e7b8a 853 break;
maclobdell 0:f7c60d3e7b8a 854 }
maclobdell 0:f7c60d3e7b8a 855
maclobdell 0:f7c60d3e7b8a 856 cleanup:
maclobdell 0:f7c60d3e7b8a 857
maclobdell 0:f7c60d3e7b8a 858 mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
maclobdell 0:f7c60d3e7b8a 859 for( i = 0; i < t_len; i++ )
maclobdell 0:f7c60d3e7b8a 860 mbedtls_mpi_free( &c[i] );
maclobdell 0:f7c60d3e7b8a 861 mbedtls_free( c );
maclobdell 0:f7c60d3e7b8a 862
maclobdell 0:f7c60d3e7b8a 863 return( ret );
maclobdell 0:f7c60d3e7b8a 864 }
maclobdell 0:f7c60d3e7b8a 865
maclobdell 0:f7c60d3e7b8a 866 /*
maclobdell 0:f7c60d3e7b8a 867 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
maclobdell 0:f7c60d3e7b8a 868 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
maclobdell 0:f7c60d3e7b8a 869 */
maclobdell 0:f7c60d3e7b8a 870 static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
maclobdell 0:f7c60d3e7b8a 871 mbedtls_ecp_point *Q,
maclobdell 0:f7c60d3e7b8a 872 unsigned char inv )
maclobdell 0:f7c60d3e7b8a 873 {
maclobdell 0:f7c60d3e7b8a 874 int ret;
maclobdell 0:f7c60d3e7b8a 875 unsigned char nonzero;
maclobdell 0:f7c60d3e7b8a 876 mbedtls_mpi mQY;
maclobdell 0:f7c60d3e7b8a 877
maclobdell 0:f7c60d3e7b8a 878 mbedtls_mpi_init( &mQY );
maclobdell 0:f7c60d3e7b8a 879
maclobdell 0:f7c60d3e7b8a 880 /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
maclobdell 0:f7c60d3e7b8a 881 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
maclobdell 0:f7c60d3e7b8a 882 nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
maclobdell 0:f7c60d3e7b8a 883 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
maclobdell 0:f7c60d3e7b8a 884
maclobdell 0:f7c60d3e7b8a 885 cleanup:
maclobdell 0:f7c60d3e7b8a 886 mbedtls_mpi_free( &mQY );
maclobdell 0:f7c60d3e7b8a 887
maclobdell 0:f7c60d3e7b8a 888 return( ret );
maclobdell 0:f7c60d3e7b8a 889 }
maclobdell 0:f7c60d3e7b8a 890
maclobdell 0:f7c60d3e7b8a 891 /*
maclobdell 0:f7c60d3e7b8a 892 * Point doubling R = 2 P, Jacobian coordinates
maclobdell 0:f7c60d3e7b8a 893 *
maclobdell 0:f7c60d3e7b8a 894 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
maclobdell 0:f7c60d3e7b8a 895 *
maclobdell 0:f7c60d3e7b8a 896 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
maclobdell 0:f7c60d3e7b8a 897 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
maclobdell 0:f7c60d3e7b8a 898 *
maclobdell 0:f7c60d3e7b8a 899 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
maclobdell 0:f7c60d3e7b8a 900 *
maclobdell 0:f7c60d3e7b8a 901 * Cost: 1D := 3M + 4S (A == 0)
maclobdell 0:f7c60d3e7b8a 902 * 4M + 4S (A == -3)
maclobdell 0:f7c60d3e7b8a 903 * 3M + 6S + 1a otherwise
maclobdell 0:f7c60d3e7b8a 904 */
maclobdell 0:f7c60d3e7b8a 905 static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
maclobdell 0:f7c60d3e7b8a 906 const mbedtls_ecp_point *P )
maclobdell 0:f7c60d3e7b8a 907 {
maclobdell 0:f7c60d3e7b8a 908 int ret;
maclobdell 0:f7c60d3e7b8a 909 mbedtls_mpi M, S, T, U;
maclobdell 0:f7c60d3e7b8a 910
maclobdell 0:f7c60d3e7b8a 911 #if defined(MBEDTLS_SELF_TEST)
maclobdell 0:f7c60d3e7b8a 912 dbl_count++;
maclobdell 0:f7c60d3e7b8a 913 #endif
maclobdell 0:f7c60d3e7b8a 914
maclobdell 0:f7c60d3e7b8a 915 mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
maclobdell 0:f7c60d3e7b8a 916
maclobdell 0:f7c60d3e7b8a 917 /* Special case for A = -3 */
maclobdell 0:f7c60d3e7b8a 918 if( grp->A.p == NULL )
maclobdell 0:f7c60d3e7b8a 919 {
maclobdell 0:f7c60d3e7b8a 920 /* M = 3(X + Z^2)(X - Z^2) */
maclobdell 0:f7c60d3e7b8a 921 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
maclobdell 0:f7c60d3e7b8a 922 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &P->X, &S ) ); MOD_ADD( T );
maclobdell 0:f7c60d3e7b8a 923 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U, &P->X, &S ) ); MOD_SUB( U );
maclobdell 0:f7c60d3e7b8a 924 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &U ) ); MOD_MUL( S );
maclobdell 0:f7c60d3e7b8a 925 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
maclobdell 0:f7c60d3e7b8a 926 }
maclobdell 0:f7c60d3e7b8a 927 else
maclobdell 0:f7c60d3e7b8a 928 {
maclobdell 0:f7c60d3e7b8a 929 /* M = 3.X^2 */
maclobdell 0:f7c60d3e7b8a 930 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &P->X ) ); MOD_MUL( S );
maclobdell 0:f7c60d3e7b8a 931 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
maclobdell 0:f7c60d3e7b8a 932
maclobdell 0:f7c60d3e7b8a 933 /* Optimize away for "koblitz" curves with A = 0 */
maclobdell 0:f7c60d3e7b8a 934 if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
maclobdell 0:f7c60d3e7b8a 935 {
maclobdell 0:f7c60d3e7b8a 936 /* M += A.Z^4 */
maclobdell 0:f7c60d3e7b8a 937 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
maclobdell 0:f7c60d3e7b8a 938 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &S, &S ) ); MOD_MUL( T );
maclobdell 0:f7c60d3e7b8a 939 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &grp->A ) ); MOD_MUL( S );
maclobdell 0:f7c60d3e7b8a 940 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &S ) ); MOD_ADD( M );
maclobdell 0:f7c60d3e7b8a 941 }
maclobdell 0:f7c60d3e7b8a 942 }
maclobdell 0:f7c60d3e7b8a 943
maclobdell 0:f7c60d3e7b8a 944 /* S = 4.X.Y^2 */
maclobdell 0:f7c60d3e7b8a 945 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &P->Y, &P->Y ) ); MOD_MUL( T );
maclobdell 0:f7c60d3e7b8a 946 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T, 1 ) ); MOD_ADD( T );
maclobdell 0:f7c60d3e7b8a 947 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &T ) ); MOD_MUL( S );
maclobdell 0:f7c60d3e7b8a 948 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &S, 1 ) ); MOD_ADD( S );
maclobdell 0:f7c60d3e7b8a 949
maclobdell 0:f7c60d3e7b8a 950 /* U = 8.Y^4 */
maclobdell 0:f7c60d3e7b8a 951 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &T, &T ) ); MOD_MUL( U );
maclobdell 0:f7c60d3e7b8a 952 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
maclobdell 0:f7c60d3e7b8a 953
maclobdell 0:f7c60d3e7b8a 954 /* T = M^2 - 2.S */
maclobdell 0:f7c60d3e7b8a 955 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &M, &M ) ); MOD_MUL( T );
maclobdell 0:f7c60d3e7b8a 956 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
maclobdell 0:f7c60d3e7b8a 957 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
maclobdell 0:f7c60d3e7b8a 958
maclobdell 0:f7c60d3e7b8a 959 /* S = M(S - T) - U */
maclobdell 0:f7c60d3e7b8a 960 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &T ) ); MOD_SUB( S );
maclobdell 0:f7c60d3e7b8a 961 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &S, &M ) ); MOD_MUL( S );
maclobdell 0:f7c60d3e7b8a 962 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &U ) ); MOD_SUB( S );
maclobdell 0:f7c60d3e7b8a 963
maclobdell 0:f7c60d3e7b8a 964 /* U = 2.Y.Z */
maclobdell 0:f7c60d3e7b8a 965 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &P->Y, &P->Z ) ); MOD_MUL( U );
maclobdell 0:f7c60d3e7b8a 966 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
maclobdell 0:f7c60d3e7b8a 967
maclobdell 0:f7c60d3e7b8a 968 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
maclobdell 0:f7c60d3e7b8a 969 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
maclobdell 0:f7c60d3e7b8a 970 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
maclobdell 0:f7c60d3e7b8a 971
maclobdell 0:f7c60d3e7b8a 972 cleanup:
maclobdell 0:f7c60d3e7b8a 973 mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
maclobdell 0:f7c60d3e7b8a 974
maclobdell 0:f7c60d3e7b8a 975 return( ret );
maclobdell 0:f7c60d3e7b8a 976 }
maclobdell 0:f7c60d3e7b8a 977
maclobdell 0:f7c60d3e7b8a 978 /*
maclobdell 0:f7c60d3e7b8a 979 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
maclobdell 0:f7c60d3e7b8a 980 *
maclobdell 0:f7c60d3e7b8a 981 * The coordinates of Q must be normalized (= affine),
maclobdell 0:f7c60d3e7b8a 982 * but those of P don't need to. R is not normalized.
maclobdell 0:f7c60d3e7b8a 983 *
maclobdell 0:f7c60d3e7b8a 984 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
maclobdell 0:f7c60d3e7b8a 985 * None of these cases can happen as intermediate step in ecp_mul_comb():
maclobdell 0:f7c60d3e7b8a 986 * - at each step, P, Q and R are multiples of the base point, the factor
maclobdell 0:f7c60d3e7b8a 987 * being less than its order, so none of them is zero;
maclobdell 0:f7c60d3e7b8a 988 * - Q is an odd multiple of the base point, P an even multiple,
maclobdell 0:f7c60d3e7b8a 989 * due to the choice of precomputed points in the modified comb method.
maclobdell 0:f7c60d3e7b8a 990 * So branches for these cases do not leak secret information.
maclobdell 0:f7c60d3e7b8a 991 *
maclobdell 0:f7c60d3e7b8a 992 * We accept Q->Z being unset (saving memory in tables) as meaning 1.
maclobdell 0:f7c60d3e7b8a 993 *
maclobdell 0:f7c60d3e7b8a 994 * Cost: 1A := 8M + 3S
maclobdell 0:f7c60d3e7b8a 995 */
maclobdell 0:f7c60d3e7b8a 996 static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
maclobdell 0:f7c60d3e7b8a 997 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
maclobdell 0:f7c60d3e7b8a 998 {
maclobdell 0:f7c60d3e7b8a 999 int ret;
maclobdell 0:f7c60d3e7b8a 1000 mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
maclobdell 0:f7c60d3e7b8a 1001
maclobdell 0:f7c60d3e7b8a 1002 #if defined(MBEDTLS_SELF_TEST)
maclobdell 0:f7c60d3e7b8a 1003 add_count++;
maclobdell 0:f7c60d3e7b8a 1004 #endif
maclobdell 0:f7c60d3e7b8a 1005
maclobdell 0:f7c60d3e7b8a 1006 /*
maclobdell 0:f7c60d3e7b8a 1007 * Trivial cases: P == 0 or Q == 0 (case 1)
maclobdell 0:f7c60d3e7b8a 1008 */
maclobdell 0:f7c60d3e7b8a 1009 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
maclobdell 0:f7c60d3e7b8a 1010 return( mbedtls_ecp_copy( R, Q ) );
maclobdell 0:f7c60d3e7b8a 1011
maclobdell 0:f7c60d3e7b8a 1012 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
maclobdell 0:f7c60d3e7b8a 1013 return( mbedtls_ecp_copy( R, P ) );
maclobdell 0:f7c60d3e7b8a 1014
maclobdell 0:f7c60d3e7b8a 1015 /*
maclobdell 0:f7c60d3e7b8a 1016 * Make sure Q coordinates are normalized
maclobdell 0:f7c60d3e7b8a 1017 */
maclobdell 0:f7c60d3e7b8a 1018 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
maclobdell 0:f7c60d3e7b8a 1019 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 1020
maclobdell 0:f7c60d3e7b8a 1021 mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
maclobdell 0:f7c60d3e7b8a 1022 mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
maclobdell 0:f7c60d3e7b8a 1023
maclobdell 0:f7c60d3e7b8a 1024 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &P->Z, &P->Z ) ); MOD_MUL( T1 );
maclobdell 0:f7c60d3e7b8a 1025 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T1, &P->Z ) ); MOD_MUL( T2 );
maclobdell 0:f7c60d3e7b8a 1026 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T1, &Q->X ) ); MOD_MUL( T1 );
maclobdell 0:f7c60d3e7b8a 1027 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T2, &Q->Y ) ); MOD_MUL( T2 );
maclobdell 0:f7c60d3e7b8a 1028 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T1, &T1, &P->X ) ); MOD_SUB( T1 );
maclobdell 0:f7c60d3e7b8a 1029 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T2, &T2, &P->Y ) ); MOD_SUB( T2 );
maclobdell 0:f7c60d3e7b8a 1030
maclobdell 0:f7c60d3e7b8a 1031 /* Special cases (2) and (3) */
maclobdell 0:f7c60d3e7b8a 1032 if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
maclobdell 0:f7c60d3e7b8a 1033 {
maclobdell 0:f7c60d3e7b8a 1034 if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
maclobdell 0:f7c60d3e7b8a 1035 {
maclobdell 0:f7c60d3e7b8a 1036 ret = ecp_double_jac( grp, R, P );
maclobdell 0:f7c60d3e7b8a 1037 goto cleanup;
maclobdell 0:f7c60d3e7b8a 1038 }
maclobdell 0:f7c60d3e7b8a 1039 else
maclobdell 0:f7c60d3e7b8a 1040 {
maclobdell 0:f7c60d3e7b8a 1041 ret = mbedtls_ecp_set_zero( R );
maclobdell 0:f7c60d3e7b8a 1042 goto cleanup;
maclobdell 0:f7c60d3e7b8a 1043 }
maclobdell 0:f7c60d3e7b8a 1044 }
maclobdell 0:f7c60d3e7b8a 1045
maclobdell 0:f7c60d3e7b8a 1046 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Z, &P->Z, &T1 ) ); MOD_MUL( Z );
maclobdell 0:f7c60d3e7b8a 1047 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T1, &T1 ) ); MOD_MUL( T3 );
maclobdell 0:f7c60d3e7b8a 1048 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T3, &T1 ) ); MOD_MUL( T4 );
maclobdell 0:f7c60d3e7b8a 1049 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &P->X ) ); MOD_MUL( T3 );
maclobdell 0:f7c60d3e7b8a 1050 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T3, 2 ) ); MOD_ADD( T1 );
maclobdell 0:f7c60d3e7b8a 1051 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &T2, &T2 ) ); MOD_MUL( X );
maclobdell 0:f7c60d3e7b8a 1052 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) ); MOD_SUB( X );
maclobdell 0:f7c60d3e7b8a 1053 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T4 ) ); MOD_SUB( X );
maclobdell 0:f7c60d3e7b8a 1054 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T3, &T3, &X ) ); MOD_SUB( T3 );
maclobdell 0:f7c60d3e7b8a 1055 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &T2 ) ); MOD_MUL( T3 );
maclobdell 0:f7c60d3e7b8a 1056 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T4, &P->Y ) ); MOD_MUL( T4 );
maclobdell 0:f7c60d3e7b8a 1057 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &Y, &T3, &T4 ) ); MOD_SUB( Y );
maclobdell 0:f7c60d3e7b8a 1058
maclobdell 0:f7c60d3e7b8a 1059 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
maclobdell 0:f7c60d3e7b8a 1060 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
maclobdell 0:f7c60d3e7b8a 1061 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
maclobdell 0:f7c60d3e7b8a 1062
maclobdell 0:f7c60d3e7b8a 1063 cleanup:
maclobdell 0:f7c60d3e7b8a 1064
maclobdell 0:f7c60d3e7b8a 1065 mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
maclobdell 0:f7c60d3e7b8a 1066 mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
maclobdell 0:f7c60d3e7b8a 1067
maclobdell 0:f7c60d3e7b8a 1068 return( ret );
maclobdell 0:f7c60d3e7b8a 1069 }
maclobdell 0:f7c60d3e7b8a 1070
maclobdell 0:f7c60d3e7b8a 1071 /*
maclobdell 0:f7c60d3e7b8a 1072 * Randomize jacobian coordinates:
maclobdell 0:f7c60d3e7b8a 1073 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
maclobdell 0:f7c60d3e7b8a 1074 * This is sort of the reverse operation of ecp_normalize_jac().
maclobdell 0:f7c60d3e7b8a 1075 *
maclobdell 0:f7c60d3e7b8a 1076 * This countermeasure was first suggested in [2].
maclobdell 0:f7c60d3e7b8a 1077 */
maclobdell 0:f7c60d3e7b8a 1078 static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
maclobdell 0:f7c60d3e7b8a 1079 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
maclobdell 0:f7c60d3e7b8a 1080 {
maclobdell 0:f7c60d3e7b8a 1081 int ret;
maclobdell 0:f7c60d3e7b8a 1082 mbedtls_mpi l, ll;
maclobdell 0:f7c60d3e7b8a 1083 size_t p_size = ( grp->pbits + 7 ) / 8;
maclobdell 0:f7c60d3e7b8a 1084 int count = 0;
maclobdell 0:f7c60d3e7b8a 1085
maclobdell 0:f7c60d3e7b8a 1086 mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
maclobdell 0:f7c60d3e7b8a 1087
maclobdell 0:f7c60d3e7b8a 1088 /* Generate l such that 1 < l < p */
maclobdell 0:f7c60d3e7b8a 1089 do
maclobdell 0:f7c60d3e7b8a 1090 {
maclobdell 0:f7c60d3e7b8a 1091 mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng );
maclobdell 0:f7c60d3e7b8a 1092
maclobdell 0:f7c60d3e7b8a 1093 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
maclobdell 0:f7c60d3e7b8a 1094 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
maclobdell 0:f7c60d3e7b8a 1095
maclobdell 0:f7c60d3e7b8a 1096 if( count++ > 10 )
maclobdell 0:f7c60d3e7b8a 1097 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
maclobdell 0:f7c60d3e7b8a 1098 }
maclobdell 0:f7c60d3e7b8a 1099 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
maclobdell 0:f7c60d3e7b8a 1100
maclobdell 0:f7c60d3e7b8a 1101 /* Z = l * Z */
maclobdell 0:f7c60d3e7b8a 1102 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Z, &pt->Z, &l ) ); MOD_MUL( pt->Z );
maclobdell 0:f7c60d3e7b8a 1103
maclobdell 0:f7c60d3e7b8a 1104 /* X = l^2 * X */
maclobdell 0:f7c60d3e7b8a 1105 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &l, &l ) ); MOD_MUL( ll );
maclobdell 0:f7c60d3e7b8a 1106 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ll ) ); MOD_MUL( pt->X );
maclobdell 0:f7c60d3e7b8a 1107
maclobdell 0:f7c60d3e7b8a 1108 /* Y = l^3 * Y */
maclobdell 0:f7c60d3e7b8a 1109 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &ll, &l ) ); MOD_MUL( ll );
maclobdell 0:f7c60d3e7b8a 1110 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ll ) ); MOD_MUL( pt->Y );
maclobdell 0:f7c60d3e7b8a 1111
maclobdell 0:f7c60d3e7b8a 1112 cleanup:
maclobdell 0:f7c60d3e7b8a 1113 mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
maclobdell 0:f7c60d3e7b8a 1114
maclobdell 0:f7c60d3e7b8a 1115 return( ret );
maclobdell 0:f7c60d3e7b8a 1116 }
maclobdell 0:f7c60d3e7b8a 1117
maclobdell 0:f7c60d3e7b8a 1118 /*
maclobdell 0:f7c60d3e7b8a 1119 * Check and define parameters used by the comb method (see below for details)
maclobdell 0:f7c60d3e7b8a 1120 */
maclobdell 0:f7c60d3e7b8a 1121 #if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
maclobdell 0:f7c60d3e7b8a 1122 #error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
maclobdell 0:f7c60d3e7b8a 1123 #endif
maclobdell 0:f7c60d3e7b8a 1124
maclobdell 0:f7c60d3e7b8a 1125 /* d = ceil( n / w ) */
maclobdell 0:f7c60d3e7b8a 1126 #define COMB_MAX_D ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2
maclobdell 0:f7c60d3e7b8a 1127
maclobdell 0:f7c60d3e7b8a 1128 /* number of precomputed points */
maclobdell 0:f7c60d3e7b8a 1129 #define COMB_MAX_PRE ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
maclobdell 0:f7c60d3e7b8a 1130
maclobdell 0:f7c60d3e7b8a 1131 /*
maclobdell 0:f7c60d3e7b8a 1132 * Compute the representation of m that will be used with our comb method.
maclobdell 0:f7c60d3e7b8a 1133 *
maclobdell 0:f7c60d3e7b8a 1134 * The basic comb method is described in GECC 3.44 for example. We use a
maclobdell 0:f7c60d3e7b8a 1135 * modified version that provides resistance to SPA by avoiding zero
maclobdell 0:f7c60d3e7b8a 1136 * digits in the representation as in [3]. We modify the method further by
maclobdell 0:f7c60d3e7b8a 1137 * requiring that all K_i be odd, which has the small cost that our
maclobdell 0:f7c60d3e7b8a 1138 * representation uses one more K_i, due to carries.
maclobdell 0:f7c60d3e7b8a 1139 *
maclobdell 0:f7c60d3e7b8a 1140 * Also, for the sake of compactness, only the seven low-order bits of x[i]
maclobdell 0:f7c60d3e7b8a 1141 * are used to represent K_i, and the msb of x[i] encodes the the sign (s_i in
maclobdell 0:f7c60d3e7b8a 1142 * the paper): it is set if and only if if s_i == -1;
maclobdell 0:f7c60d3e7b8a 1143 *
maclobdell 0:f7c60d3e7b8a 1144 * Calling conventions:
maclobdell 0:f7c60d3e7b8a 1145 * - x is an array of size d + 1
maclobdell 0:f7c60d3e7b8a 1146 * - w is the size, ie number of teeth, of the comb, and must be between
maclobdell 0:f7c60d3e7b8a 1147 * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
maclobdell 0:f7c60d3e7b8a 1148 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
maclobdell 0:f7c60d3e7b8a 1149 * (the result will be incorrect if these assumptions are not satisfied)
maclobdell 0:f7c60d3e7b8a 1150 */
maclobdell 0:f7c60d3e7b8a 1151 static void ecp_comb_fixed( unsigned char x[], size_t d,
maclobdell 0:f7c60d3e7b8a 1152 unsigned char w, const mbedtls_mpi *m )
maclobdell 0:f7c60d3e7b8a 1153 {
maclobdell 0:f7c60d3e7b8a 1154 size_t i, j;
maclobdell 0:f7c60d3e7b8a 1155 unsigned char c, cc, adjust;
maclobdell 0:f7c60d3e7b8a 1156
maclobdell 0:f7c60d3e7b8a 1157 memset( x, 0, d+1 );
maclobdell 0:f7c60d3e7b8a 1158
maclobdell 0:f7c60d3e7b8a 1159 /* First get the classical comb values (except for x_d = 0) */
maclobdell 0:f7c60d3e7b8a 1160 for( i = 0; i < d; i++ )
maclobdell 0:f7c60d3e7b8a 1161 for( j = 0; j < w; j++ )
maclobdell 0:f7c60d3e7b8a 1162 x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j;
maclobdell 0:f7c60d3e7b8a 1163
maclobdell 0:f7c60d3e7b8a 1164 /* Now make sure x_1 .. x_d are odd */
maclobdell 0:f7c60d3e7b8a 1165 c = 0;
maclobdell 0:f7c60d3e7b8a 1166 for( i = 1; i <= d; i++ )
maclobdell 0:f7c60d3e7b8a 1167 {
maclobdell 0:f7c60d3e7b8a 1168 /* Add carry and update it */
maclobdell 0:f7c60d3e7b8a 1169 cc = x[i] & c;
maclobdell 0:f7c60d3e7b8a 1170 x[i] = x[i] ^ c;
maclobdell 0:f7c60d3e7b8a 1171 c = cc;
maclobdell 0:f7c60d3e7b8a 1172
maclobdell 0:f7c60d3e7b8a 1173 /* Adjust if needed, avoiding branches */
maclobdell 0:f7c60d3e7b8a 1174 adjust = 1 - ( x[i] & 0x01 );
maclobdell 0:f7c60d3e7b8a 1175 c |= x[i] & ( x[i-1] * adjust );
maclobdell 0:f7c60d3e7b8a 1176 x[i] = x[i] ^ ( x[i-1] * adjust );
maclobdell 0:f7c60d3e7b8a 1177 x[i-1] |= adjust << 7;
maclobdell 0:f7c60d3e7b8a 1178 }
maclobdell 0:f7c60d3e7b8a 1179 }
maclobdell 0:f7c60d3e7b8a 1180
maclobdell 0:f7c60d3e7b8a 1181 /*
maclobdell 0:f7c60d3e7b8a 1182 * Precompute points for the comb method
maclobdell 0:f7c60d3e7b8a 1183 *
maclobdell 0:f7c60d3e7b8a 1184 * If i = i_{w-1} ... i_1 is the binary representation of i, then
maclobdell 0:f7c60d3e7b8a 1185 * T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P
maclobdell 0:f7c60d3e7b8a 1186 *
maclobdell 0:f7c60d3e7b8a 1187 * T must be able to hold 2^{w - 1} elements
maclobdell 0:f7c60d3e7b8a 1188 *
maclobdell 0:f7c60d3e7b8a 1189 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
maclobdell 0:f7c60d3e7b8a 1190 */
maclobdell 0:f7c60d3e7b8a 1191 static int ecp_precompute_comb( const mbedtls_ecp_group *grp,
maclobdell 0:f7c60d3e7b8a 1192 mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
maclobdell 0:f7c60d3e7b8a 1193 unsigned char w, size_t d )
maclobdell 0:f7c60d3e7b8a 1194 {
maclobdell 0:f7c60d3e7b8a 1195 int ret;
maclobdell 0:f7c60d3e7b8a 1196 unsigned char i, k;
maclobdell 0:f7c60d3e7b8a 1197 size_t j;
maclobdell 0:f7c60d3e7b8a 1198 mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
maclobdell 0:f7c60d3e7b8a 1199
maclobdell 0:f7c60d3e7b8a 1200 /*
maclobdell 0:f7c60d3e7b8a 1201 * Set T[0] = P and
maclobdell 0:f7c60d3e7b8a 1202 * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
maclobdell 0:f7c60d3e7b8a 1203 */
maclobdell 0:f7c60d3e7b8a 1204 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
maclobdell 0:f7c60d3e7b8a 1205
maclobdell 0:f7c60d3e7b8a 1206 k = 0;
maclobdell 0:f7c60d3e7b8a 1207 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
maclobdell 0:f7c60d3e7b8a 1208 {
maclobdell 0:f7c60d3e7b8a 1209 cur = T + i;
maclobdell 0:f7c60d3e7b8a 1210 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
maclobdell 0:f7c60d3e7b8a 1211 for( j = 0; j < d; j++ )
maclobdell 0:f7c60d3e7b8a 1212 MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
maclobdell 0:f7c60d3e7b8a 1213
maclobdell 0:f7c60d3e7b8a 1214 TT[k++] = cur;
maclobdell 0:f7c60d3e7b8a 1215 }
maclobdell 0:f7c60d3e7b8a 1216
maclobdell 0:f7c60d3e7b8a 1217 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
maclobdell 0:f7c60d3e7b8a 1218
maclobdell 0:f7c60d3e7b8a 1219 /*
maclobdell 0:f7c60d3e7b8a 1220 * Compute the remaining ones using the minimal number of additions
maclobdell 0:f7c60d3e7b8a 1221 * Be careful to update T[2^l] only after using it!
maclobdell 0:f7c60d3e7b8a 1222 */
maclobdell 0:f7c60d3e7b8a 1223 k = 0;
maclobdell 0:f7c60d3e7b8a 1224 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
maclobdell 0:f7c60d3e7b8a 1225 {
maclobdell 0:f7c60d3e7b8a 1226 j = i;
maclobdell 0:f7c60d3e7b8a 1227 while( j-- )
maclobdell 0:f7c60d3e7b8a 1228 {
maclobdell 0:f7c60d3e7b8a 1229 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
maclobdell 0:f7c60d3e7b8a 1230 TT[k++] = &T[i + j];
maclobdell 0:f7c60d3e7b8a 1231 }
maclobdell 0:f7c60d3e7b8a 1232 }
maclobdell 0:f7c60d3e7b8a 1233
maclobdell 0:f7c60d3e7b8a 1234 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
maclobdell 0:f7c60d3e7b8a 1235
maclobdell 0:f7c60d3e7b8a 1236 cleanup:
maclobdell 0:f7c60d3e7b8a 1237 return( ret );
maclobdell 0:f7c60d3e7b8a 1238 }
maclobdell 0:f7c60d3e7b8a 1239
maclobdell 0:f7c60d3e7b8a 1240 /*
maclobdell 0:f7c60d3e7b8a 1241 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
maclobdell 0:f7c60d3e7b8a 1242 */
maclobdell 0:f7c60d3e7b8a 1243 static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
maclobdell 0:f7c60d3e7b8a 1244 const mbedtls_ecp_point T[], unsigned char t_len,
maclobdell 0:f7c60d3e7b8a 1245 unsigned char i )
maclobdell 0:f7c60d3e7b8a 1246 {
maclobdell 0:f7c60d3e7b8a 1247 int ret;
maclobdell 0:f7c60d3e7b8a 1248 unsigned char ii, j;
maclobdell 0:f7c60d3e7b8a 1249
maclobdell 0:f7c60d3e7b8a 1250 /* Ignore the "sign" bit and scale down */
maclobdell 0:f7c60d3e7b8a 1251 ii = ( i & 0x7Fu ) >> 1;
maclobdell 0:f7c60d3e7b8a 1252
maclobdell 0:f7c60d3e7b8a 1253 /* Read the whole table to thwart cache-based timing attacks */
maclobdell 0:f7c60d3e7b8a 1254 for( j = 0; j < t_len; j++ )
maclobdell 0:f7c60d3e7b8a 1255 {
maclobdell 0:f7c60d3e7b8a 1256 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
maclobdell 0:f7c60d3e7b8a 1257 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
maclobdell 0:f7c60d3e7b8a 1258 }
maclobdell 0:f7c60d3e7b8a 1259
maclobdell 0:f7c60d3e7b8a 1260 /* Safely invert result if i is "negative" */
maclobdell 0:f7c60d3e7b8a 1261 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
maclobdell 0:f7c60d3e7b8a 1262
maclobdell 0:f7c60d3e7b8a 1263 cleanup:
maclobdell 0:f7c60d3e7b8a 1264 return( ret );
maclobdell 0:f7c60d3e7b8a 1265 }
maclobdell 0:f7c60d3e7b8a 1266
maclobdell 0:f7c60d3e7b8a 1267 /*
maclobdell 0:f7c60d3e7b8a 1268 * Core multiplication algorithm for the (modified) comb method.
maclobdell 0:f7c60d3e7b8a 1269 * This part is actually common with the basic comb method (GECC 3.44)
maclobdell 0:f7c60d3e7b8a 1270 *
maclobdell 0:f7c60d3e7b8a 1271 * Cost: d A + d D + 1 R
maclobdell 0:f7c60d3e7b8a 1272 */
maclobdell 0:f7c60d3e7b8a 1273 static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
maclobdell 0:f7c60d3e7b8a 1274 const mbedtls_ecp_point T[], unsigned char t_len,
maclobdell 0:f7c60d3e7b8a 1275 const unsigned char x[], size_t d,
maclobdell 0:f7c60d3e7b8a 1276 int (*f_rng)(void *, unsigned char *, size_t),
maclobdell 0:f7c60d3e7b8a 1277 void *p_rng )
maclobdell 0:f7c60d3e7b8a 1278 {
maclobdell 0:f7c60d3e7b8a 1279 int ret;
maclobdell 0:f7c60d3e7b8a 1280 mbedtls_ecp_point Txi;
maclobdell 0:f7c60d3e7b8a 1281 size_t i;
maclobdell 0:f7c60d3e7b8a 1282
maclobdell 0:f7c60d3e7b8a 1283 mbedtls_ecp_point_init( &Txi );
maclobdell 0:f7c60d3e7b8a 1284
maclobdell 0:f7c60d3e7b8a 1285 /* Start with a non-zero point and randomize its coordinates */
maclobdell 0:f7c60d3e7b8a 1286 i = d;
maclobdell 0:f7c60d3e7b8a 1287 MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, t_len, x[i] ) );
maclobdell 0:f7c60d3e7b8a 1288 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
maclobdell 0:f7c60d3e7b8a 1289 if( f_rng != 0 )
maclobdell 0:f7c60d3e7b8a 1290 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
maclobdell 0:f7c60d3e7b8a 1291
maclobdell 0:f7c60d3e7b8a 1292 while( i-- != 0 )
maclobdell 0:f7c60d3e7b8a 1293 {
maclobdell 0:f7c60d3e7b8a 1294 MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
maclobdell 0:f7c60d3e7b8a 1295 MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, t_len, x[i] ) );
maclobdell 0:f7c60d3e7b8a 1296 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
maclobdell 0:f7c60d3e7b8a 1297 }
maclobdell 0:f7c60d3e7b8a 1298
maclobdell 0:f7c60d3e7b8a 1299 cleanup:
maclobdell 0:f7c60d3e7b8a 1300 mbedtls_ecp_point_free( &Txi );
maclobdell 0:f7c60d3e7b8a 1301
maclobdell 0:f7c60d3e7b8a 1302 return( ret );
maclobdell 0:f7c60d3e7b8a 1303 }
maclobdell 0:f7c60d3e7b8a 1304
maclobdell 0:f7c60d3e7b8a 1305 /*
maclobdell 0:f7c60d3e7b8a 1306 * Multiplication using the comb method,
maclobdell 0:f7c60d3e7b8a 1307 * for curves in short Weierstrass form
maclobdell 0:f7c60d3e7b8a 1308 */
maclobdell 0:f7c60d3e7b8a 1309 static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
maclobdell 0:f7c60d3e7b8a 1310 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
maclobdell 0:f7c60d3e7b8a 1311 int (*f_rng)(void *, unsigned char *, size_t),
maclobdell 0:f7c60d3e7b8a 1312 void *p_rng )
maclobdell 0:f7c60d3e7b8a 1313 {
maclobdell 0:f7c60d3e7b8a 1314 int ret;
maclobdell 0:f7c60d3e7b8a 1315 unsigned char w, m_is_odd, p_eq_g, pre_len, i;
maclobdell 0:f7c60d3e7b8a 1316 size_t d;
maclobdell 0:f7c60d3e7b8a 1317 unsigned char k[COMB_MAX_D + 1];
maclobdell 0:f7c60d3e7b8a 1318 mbedtls_ecp_point *T;
maclobdell 0:f7c60d3e7b8a 1319 mbedtls_mpi M, mm;
maclobdell 0:f7c60d3e7b8a 1320
maclobdell 0:f7c60d3e7b8a 1321 mbedtls_mpi_init( &M );
maclobdell 0:f7c60d3e7b8a 1322 mbedtls_mpi_init( &mm );
maclobdell 0:f7c60d3e7b8a 1323
maclobdell 0:f7c60d3e7b8a 1324 /* we need N to be odd to trnaform m in an odd number, check now */
maclobdell 0:f7c60d3e7b8a 1325 if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 )
maclobdell 0:f7c60d3e7b8a 1326 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 1327
maclobdell 0:f7c60d3e7b8a 1328 /*
maclobdell 0:f7c60d3e7b8a 1329 * Minimize the number of multiplications, that is minimize
maclobdell 0:f7c60d3e7b8a 1330 * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
maclobdell 0:f7c60d3e7b8a 1331 * (see costs of the various parts, with 1S = 1M)
maclobdell 0:f7c60d3e7b8a 1332 */
maclobdell 0:f7c60d3e7b8a 1333 w = grp->nbits >= 384 ? 5 : 4;
maclobdell 0:f7c60d3e7b8a 1334
maclobdell 0:f7c60d3e7b8a 1335 /*
maclobdell 0:f7c60d3e7b8a 1336 * If P == G, pre-compute a bit more, since this may be re-used later.
maclobdell 0:f7c60d3e7b8a 1337 * Just adding one avoids upping the cost of the first mul too much,
maclobdell 0:f7c60d3e7b8a 1338 * and the memory cost too.
maclobdell 0:f7c60d3e7b8a 1339 */
maclobdell 0:f7c60d3e7b8a 1340 #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
maclobdell 0:f7c60d3e7b8a 1341 p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
maclobdell 0:f7c60d3e7b8a 1342 mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
maclobdell 0:f7c60d3e7b8a 1343 if( p_eq_g )
maclobdell 0:f7c60d3e7b8a 1344 w++;
maclobdell 0:f7c60d3e7b8a 1345 #else
maclobdell 0:f7c60d3e7b8a 1346 p_eq_g = 0;
maclobdell 0:f7c60d3e7b8a 1347 #endif
maclobdell 0:f7c60d3e7b8a 1348
maclobdell 0:f7c60d3e7b8a 1349 /*
maclobdell 0:f7c60d3e7b8a 1350 * Make sure w is within bounds.
maclobdell 0:f7c60d3e7b8a 1351 * (The last test is useful only for very small curves in the test suite.)
maclobdell 0:f7c60d3e7b8a 1352 */
maclobdell 0:f7c60d3e7b8a 1353 if( w > MBEDTLS_ECP_WINDOW_SIZE )
maclobdell 0:f7c60d3e7b8a 1354 w = MBEDTLS_ECP_WINDOW_SIZE;
maclobdell 0:f7c60d3e7b8a 1355 if( w >= grp->nbits )
maclobdell 0:f7c60d3e7b8a 1356 w = 2;
maclobdell 0:f7c60d3e7b8a 1357
maclobdell 0:f7c60d3e7b8a 1358 /* Other sizes that depend on w */
maclobdell 0:f7c60d3e7b8a 1359 pre_len = 1U << ( w - 1 );
maclobdell 0:f7c60d3e7b8a 1360 d = ( grp->nbits + w - 1 ) / w;
maclobdell 0:f7c60d3e7b8a 1361
maclobdell 0:f7c60d3e7b8a 1362 /*
maclobdell 0:f7c60d3e7b8a 1363 * Prepare precomputed points: if P == G we want to
maclobdell 0:f7c60d3e7b8a 1364 * use grp->T if already initialized, or initialize it.
maclobdell 0:f7c60d3e7b8a 1365 */
maclobdell 0:f7c60d3e7b8a 1366 T = p_eq_g ? grp->T : NULL;
maclobdell 0:f7c60d3e7b8a 1367
maclobdell 0:f7c60d3e7b8a 1368 if( T == NULL )
maclobdell 0:f7c60d3e7b8a 1369 {
maclobdell 0:f7c60d3e7b8a 1370 T = mbedtls_calloc( pre_len, sizeof( mbedtls_ecp_point ) );
maclobdell 0:f7c60d3e7b8a 1371 if( T == NULL )
maclobdell 0:f7c60d3e7b8a 1372 {
maclobdell 0:f7c60d3e7b8a 1373 ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
maclobdell 0:f7c60d3e7b8a 1374 goto cleanup;
maclobdell 0:f7c60d3e7b8a 1375 }
maclobdell 0:f7c60d3e7b8a 1376
maclobdell 0:f7c60d3e7b8a 1377 MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d ) );
maclobdell 0:f7c60d3e7b8a 1378
maclobdell 0:f7c60d3e7b8a 1379 if( p_eq_g )
maclobdell 0:f7c60d3e7b8a 1380 {
maclobdell 0:f7c60d3e7b8a 1381 grp->T = T;
maclobdell 0:f7c60d3e7b8a 1382 grp->T_size = pre_len;
maclobdell 0:f7c60d3e7b8a 1383 }
maclobdell 0:f7c60d3e7b8a 1384 }
maclobdell 0:f7c60d3e7b8a 1385
maclobdell 0:f7c60d3e7b8a 1386 /*
maclobdell 0:f7c60d3e7b8a 1387 * Make sure M is odd (M = m or M = N - m, since N is odd)
maclobdell 0:f7c60d3e7b8a 1388 * using the fact that m * P = - (N - m) * P
maclobdell 0:f7c60d3e7b8a 1389 */
maclobdell 0:f7c60d3e7b8a 1390 m_is_odd = ( mbedtls_mpi_get_bit( m, 0 ) == 1 );
maclobdell 0:f7c60d3e7b8a 1391 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) );
maclobdell 0:f7c60d3e7b8a 1392 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) );
maclobdell 0:f7c60d3e7b8a 1393 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, ! m_is_odd ) );
maclobdell 0:f7c60d3e7b8a 1394
maclobdell 0:f7c60d3e7b8a 1395 /*
maclobdell 0:f7c60d3e7b8a 1396 * Go for comb multiplication, R = M * P
maclobdell 0:f7c60d3e7b8a 1397 */
maclobdell 0:f7c60d3e7b8a 1398 ecp_comb_fixed( k, d, w, &M );
maclobdell 0:f7c60d3e7b8a 1399 MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, R, T, pre_len, k, d, f_rng, p_rng ) );
maclobdell 0:f7c60d3e7b8a 1400
maclobdell 0:f7c60d3e7b8a 1401 /*
maclobdell 0:f7c60d3e7b8a 1402 * Now get m * P from M * P and normalize it
maclobdell 0:f7c60d3e7b8a 1403 */
maclobdell 0:f7c60d3e7b8a 1404 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, ! m_is_odd ) );
maclobdell 0:f7c60d3e7b8a 1405 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
maclobdell 0:f7c60d3e7b8a 1406
maclobdell 0:f7c60d3e7b8a 1407 cleanup:
maclobdell 0:f7c60d3e7b8a 1408
maclobdell 0:f7c60d3e7b8a 1409 if( T != NULL && ! p_eq_g )
maclobdell 0:f7c60d3e7b8a 1410 {
maclobdell 0:f7c60d3e7b8a 1411 for( i = 0; i < pre_len; i++ )
maclobdell 0:f7c60d3e7b8a 1412 mbedtls_ecp_point_free( &T[i] );
maclobdell 0:f7c60d3e7b8a 1413 mbedtls_free( T );
maclobdell 0:f7c60d3e7b8a 1414 }
maclobdell 0:f7c60d3e7b8a 1415
maclobdell 0:f7c60d3e7b8a 1416 mbedtls_mpi_free( &M );
maclobdell 0:f7c60d3e7b8a 1417 mbedtls_mpi_free( &mm );
maclobdell 0:f7c60d3e7b8a 1418
maclobdell 0:f7c60d3e7b8a 1419 if( ret != 0 )
maclobdell 0:f7c60d3e7b8a 1420 mbedtls_ecp_point_free( R );
maclobdell 0:f7c60d3e7b8a 1421
maclobdell 0:f7c60d3e7b8a 1422 return( ret );
maclobdell 0:f7c60d3e7b8a 1423 }
maclobdell 0:f7c60d3e7b8a 1424
maclobdell 0:f7c60d3e7b8a 1425 #endif /* ECP_SHORTWEIERSTRASS */
maclobdell 0:f7c60d3e7b8a 1426
maclobdell 0:f7c60d3e7b8a 1427 #if defined(ECP_MONTGOMERY)
maclobdell 0:f7c60d3e7b8a 1428 /*
maclobdell 0:f7c60d3e7b8a 1429 * For Montgomery curves, we do all the internal arithmetic in projective
maclobdell 0:f7c60d3e7b8a 1430 * coordinates. Import/export of points uses only the x coordinates, which is
maclobdell 0:f7c60d3e7b8a 1431 * internaly represented as X / Z.
maclobdell 0:f7c60d3e7b8a 1432 *
maclobdell 0:f7c60d3e7b8a 1433 * For scalar multiplication, we'll use a Montgomery ladder.
maclobdell 0:f7c60d3e7b8a 1434 */
maclobdell 0:f7c60d3e7b8a 1435
maclobdell 0:f7c60d3e7b8a 1436 /*
maclobdell 0:f7c60d3e7b8a 1437 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
maclobdell 0:f7c60d3e7b8a 1438 * Cost: 1M + 1I
maclobdell 0:f7c60d3e7b8a 1439 */
maclobdell 0:f7c60d3e7b8a 1440 static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
maclobdell 0:f7c60d3e7b8a 1441 {
maclobdell 0:f7c60d3e7b8a 1442 int ret;
maclobdell 0:f7c60d3e7b8a 1443
maclobdell 0:f7c60d3e7b8a 1444 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
maclobdell 0:f7c60d3e7b8a 1445 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X );
maclobdell 0:f7c60d3e7b8a 1446 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
maclobdell 0:f7c60d3e7b8a 1447
maclobdell 0:f7c60d3e7b8a 1448 cleanup:
maclobdell 0:f7c60d3e7b8a 1449 return( ret );
maclobdell 0:f7c60d3e7b8a 1450 }
maclobdell 0:f7c60d3e7b8a 1451
maclobdell 0:f7c60d3e7b8a 1452 /*
maclobdell 0:f7c60d3e7b8a 1453 * Randomize projective x/z coordinates:
maclobdell 0:f7c60d3e7b8a 1454 * (X, Z) -> (l X, l Z) for random l
maclobdell 0:f7c60d3e7b8a 1455 * This is sort of the reverse operation of ecp_normalize_mxz().
maclobdell 0:f7c60d3e7b8a 1456 *
maclobdell 0:f7c60d3e7b8a 1457 * This countermeasure was first suggested in [2].
maclobdell 0:f7c60d3e7b8a 1458 * Cost: 2M
maclobdell 0:f7c60d3e7b8a 1459 */
maclobdell 0:f7c60d3e7b8a 1460 static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
maclobdell 0:f7c60d3e7b8a 1461 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
maclobdell 0:f7c60d3e7b8a 1462 {
maclobdell 0:f7c60d3e7b8a 1463 int ret;
maclobdell 0:f7c60d3e7b8a 1464 mbedtls_mpi l;
maclobdell 0:f7c60d3e7b8a 1465 size_t p_size = ( grp->pbits + 7 ) / 8;
maclobdell 0:f7c60d3e7b8a 1466 int count = 0;
maclobdell 0:f7c60d3e7b8a 1467
maclobdell 0:f7c60d3e7b8a 1468 mbedtls_mpi_init( &l );
maclobdell 0:f7c60d3e7b8a 1469
maclobdell 0:f7c60d3e7b8a 1470 /* Generate l such that 1 < l < p */
maclobdell 0:f7c60d3e7b8a 1471 do
maclobdell 0:f7c60d3e7b8a 1472 {
maclobdell 0:f7c60d3e7b8a 1473 mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng );
maclobdell 0:f7c60d3e7b8a 1474
maclobdell 0:f7c60d3e7b8a 1475 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
maclobdell 0:f7c60d3e7b8a 1476 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
maclobdell 0:f7c60d3e7b8a 1477
maclobdell 0:f7c60d3e7b8a 1478 if( count++ > 10 )
maclobdell 0:f7c60d3e7b8a 1479 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
maclobdell 0:f7c60d3e7b8a 1480 }
maclobdell 0:f7c60d3e7b8a 1481 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
maclobdell 0:f7c60d3e7b8a 1482
maclobdell 0:f7c60d3e7b8a 1483 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X );
maclobdell 0:f7c60d3e7b8a 1484 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z );
maclobdell 0:f7c60d3e7b8a 1485
maclobdell 0:f7c60d3e7b8a 1486 cleanup:
maclobdell 0:f7c60d3e7b8a 1487 mbedtls_mpi_free( &l );
maclobdell 0:f7c60d3e7b8a 1488
maclobdell 0:f7c60d3e7b8a 1489 return( ret );
maclobdell 0:f7c60d3e7b8a 1490 }
maclobdell 0:f7c60d3e7b8a 1491
maclobdell 0:f7c60d3e7b8a 1492 /*
maclobdell 0:f7c60d3e7b8a 1493 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
maclobdell 0:f7c60d3e7b8a 1494 * for Montgomery curves in x/z coordinates.
maclobdell 0:f7c60d3e7b8a 1495 *
maclobdell 0:f7c60d3e7b8a 1496 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
maclobdell 0:f7c60d3e7b8a 1497 * with
maclobdell 0:f7c60d3e7b8a 1498 * d = X1
maclobdell 0:f7c60d3e7b8a 1499 * P = (X2, Z2)
maclobdell 0:f7c60d3e7b8a 1500 * Q = (X3, Z3)
maclobdell 0:f7c60d3e7b8a 1501 * R = (X4, Z4)
maclobdell 0:f7c60d3e7b8a 1502 * S = (X5, Z5)
maclobdell 0:f7c60d3e7b8a 1503 * and eliminating temporary variables tO, ..., t4.
maclobdell 0:f7c60d3e7b8a 1504 *
maclobdell 0:f7c60d3e7b8a 1505 * Cost: 5M + 4S
maclobdell 0:f7c60d3e7b8a 1506 */
maclobdell 0:f7c60d3e7b8a 1507 static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
maclobdell 0:f7c60d3e7b8a 1508 mbedtls_ecp_point *R, mbedtls_ecp_point *S,
maclobdell 0:f7c60d3e7b8a 1509 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
maclobdell 0:f7c60d3e7b8a 1510 const mbedtls_mpi *d )
maclobdell 0:f7c60d3e7b8a 1511 {
maclobdell 0:f7c60d3e7b8a 1512 int ret;
maclobdell 0:f7c60d3e7b8a 1513 mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
maclobdell 0:f7c60d3e7b8a 1514
maclobdell 0:f7c60d3e7b8a 1515 mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
maclobdell 0:f7c60d3e7b8a 1516 mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
maclobdell 0:f7c60d3e7b8a 1517 mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
maclobdell 0:f7c60d3e7b8a 1518
maclobdell 0:f7c60d3e7b8a 1519 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &A, &P->X, &P->Z ) ); MOD_ADD( A );
maclobdell 0:f7c60d3e7b8a 1520 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &AA, &A, &A ) ); MOD_MUL( AA );
maclobdell 0:f7c60d3e7b8a 1521 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &B, &P->X, &P->Z ) ); MOD_SUB( B );
maclobdell 0:f7c60d3e7b8a 1522 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &BB, &B, &B ) ); MOD_MUL( BB );
maclobdell 0:f7c60d3e7b8a 1523 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &E, &AA, &BB ) ); MOD_SUB( E );
maclobdell 0:f7c60d3e7b8a 1524 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &C, &Q->X, &Q->Z ) ); MOD_ADD( C );
maclobdell 0:f7c60d3e7b8a 1525 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &D, &Q->X, &Q->Z ) ); MOD_SUB( D );
maclobdell 0:f7c60d3e7b8a 1526 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DA, &D, &A ) ); MOD_MUL( DA );
maclobdell 0:f7c60d3e7b8a 1527 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &CB, &C, &B ) ); MOD_MUL( CB );
maclobdell 0:f7c60d3e7b8a 1528 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &S->X, &DA, &CB ) ); MOD_MUL( S->X );
maclobdell 0:f7c60d3e7b8a 1529 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->X, &S->X, &S->X ) ); MOD_MUL( S->X );
maclobdell 0:f7c60d3e7b8a 1530 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S->Z, &DA, &CB ) ); MOD_SUB( S->Z );
maclobdell 0:f7c60d3e7b8a 1531 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, &S->Z, &S->Z ) ); MOD_MUL( S->Z );
maclobdell 0:f7c60d3e7b8a 1532 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, d, &S->Z ) ); MOD_MUL( S->Z );
maclobdell 0:f7c60d3e7b8a 1533 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->X, &AA, &BB ) ); MOD_MUL( R->X );
maclobdell 0:f7c60d3e7b8a 1534 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &grp->A, &E ) ); MOD_MUL( R->Z );
maclobdell 0:f7c60d3e7b8a 1535 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &R->Z, &BB, &R->Z ) ); MOD_ADD( R->Z );
maclobdell 0:f7c60d3e7b8a 1536 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &E, &R->Z ) ); MOD_MUL( R->Z );
maclobdell 0:f7c60d3e7b8a 1537
maclobdell 0:f7c60d3e7b8a 1538 cleanup:
maclobdell 0:f7c60d3e7b8a 1539 mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
maclobdell 0:f7c60d3e7b8a 1540 mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
maclobdell 0:f7c60d3e7b8a 1541 mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
maclobdell 0:f7c60d3e7b8a 1542
maclobdell 0:f7c60d3e7b8a 1543 return( ret );
maclobdell 0:f7c60d3e7b8a 1544 }
maclobdell 0:f7c60d3e7b8a 1545
maclobdell 0:f7c60d3e7b8a 1546 /*
maclobdell 0:f7c60d3e7b8a 1547 * Multiplication with Montgomery ladder in x/z coordinates,
maclobdell 0:f7c60d3e7b8a 1548 * for curves in Montgomery form
maclobdell 0:f7c60d3e7b8a 1549 */
maclobdell 0:f7c60d3e7b8a 1550 static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
maclobdell 0:f7c60d3e7b8a 1551 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
maclobdell 0:f7c60d3e7b8a 1552 int (*f_rng)(void *, unsigned char *, size_t),
maclobdell 0:f7c60d3e7b8a 1553 void *p_rng )
maclobdell 0:f7c60d3e7b8a 1554 {
maclobdell 0:f7c60d3e7b8a 1555 int ret;
maclobdell 0:f7c60d3e7b8a 1556 size_t i;
maclobdell 0:f7c60d3e7b8a 1557 unsigned char b;
maclobdell 0:f7c60d3e7b8a 1558 mbedtls_ecp_point RP;
maclobdell 0:f7c60d3e7b8a 1559 mbedtls_mpi PX;
maclobdell 0:f7c60d3e7b8a 1560
maclobdell 0:f7c60d3e7b8a 1561 mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
maclobdell 0:f7c60d3e7b8a 1562
maclobdell 0:f7c60d3e7b8a 1563 /* Save PX and read from P before writing to R, in case P == R */
maclobdell 0:f7c60d3e7b8a 1564 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
maclobdell 0:f7c60d3e7b8a 1565 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
maclobdell 0:f7c60d3e7b8a 1566
maclobdell 0:f7c60d3e7b8a 1567 /* Set R to zero in modified x/z coordinates */
maclobdell 0:f7c60d3e7b8a 1568 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
maclobdell 0:f7c60d3e7b8a 1569 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
maclobdell 0:f7c60d3e7b8a 1570 mbedtls_mpi_free( &R->Y );
maclobdell 0:f7c60d3e7b8a 1571
maclobdell 0:f7c60d3e7b8a 1572 /* RP.X might be sligtly larger than P, so reduce it */
maclobdell 0:f7c60d3e7b8a 1573 MOD_ADD( RP.X );
maclobdell 0:f7c60d3e7b8a 1574
maclobdell 0:f7c60d3e7b8a 1575 /* Randomize coordinates of the starting point */
maclobdell 0:f7c60d3e7b8a 1576 if( f_rng != NULL )
maclobdell 0:f7c60d3e7b8a 1577 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
maclobdell 0:f7c60d3e7b8a 1578
maclobdell 0:f7c60d3e7b8a 1579 /* Loop invariant: R = result so far, RP = R + P */
maclobdell 0:f7c60d3e7b8a 1580 i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
maclobdell 0:f7c60d3e7b8a 1581 while( i-- > 0 )
maclobdell 0:f7c60d3e7b8a 1582 {
maclobdell 0:f7c60d3e7b8a 1583 b = mbedtls_mpi_get_bit( m, i );
maclobdell 0:f7c60d3e7b8a 1584 /*
maclobdell 0:f7c60d3e7b8a 1585 * if (b) R = 2R + P else R = 2R,
maclobdell 0:f7c60d3e7b8a 1586 * which is:
maclobdell 0:f7c60d3e7b8a 1587 * if (b) double_add( RP, R, RP, R )
maclobdell 0:f7c60d3e7b8a 1588 * else double_add( R, RP, R, RP )
maclobdell 0:f7c60d3e7b8a 1589 * but using safe conditional swaps to avoid leaks
maclobdell 0:f7c60d3e7b8a 1590 */
maclobdell 0:f7c60d3e7b8a 1591 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
maclobdell 0:f7c60d3e7b8a 1592 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
maclobdell 0:f7c60d3e7b8a 1593 MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
maclobdell 0:f7c60d3e7b8a 1594 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
maclobdell 0:f7c60d3e7b8a 1595 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
maclobdell 0:f7c60d3e7b8a 1596 }
maclobdell 0:f7c60d3e7b8a 1597
maclobdell 0:f7c60d3e7b8a 1598 MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) );
maclobdell 0:f7c60d3e7b8a 1599
maclobdell 0:f7c60d3e7b8a 1600 cleanup:
maclobdell 0:f7c60d3e7b8a 1601 mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
maclobdell 0:f7c60d3e7b8a 1602
maclobdell 0:f7c60d3e7b8a 1603 return( ret );
maclobdell 0:f7c60d3e7b8a 1604 }
maclobdell 0:f7c60d3e7b8a 1605
maclobdell 0:f7c60d3e7b8a 1606 #endif /* ECP_MONTGOMERY */
maclobdell 0:f7c60d3e7b8a 1607
maclobdell 0:f7c60d3e7b8a 1608 /*
maclobdell 0:f7c60d3e7b8a 1609 * Multiplication R = m * P
maclobdell 0:f7c60d3e7b8a 1610 */
maclobdell 0:f7c60d3e7b8a 1611 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
maclobdell 0:f7c60d3e7b8a 1612 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
maclobdell 0:f7c60d3e7b8a 1613 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
maclobdell 0:f7c60d3e7b8a 1614 {
maclobdell 0:f7c60d3e7b8a 1615 int ret;
maclobdell 0:f7c60d3e7b8a 1616
maclobdell 0:f7c60d3e7b8a 1617 /* Common sanity checks */
maclobdell 0:f7c60d3e7b8a 1618 if( mbedtls_mpi_cmp_int( &P->Z, 1 ) != 0 )
maclobdell 0:f7c60d3e7b8a 1619 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 1620
maclobdell 0:f7c60d3e7b8a 1621 if( ( ret = mbedtls_ecp_check_privkey( grp, m ) ) != 0 ||
maclobdell 0:f7c60d3e7b8a 1622 ( ret = mbedtls_ecp_check_pubkey( grp, P ) ) != 0 )
maclobdell 0:f7c60d3e7b8a 1623 return( ret );
maclobdell 0:f7c60d3e7b8a 1624
maclobdell 0:f7c60d3e7b8a 1625 #if defined(ECP_MONTGOMERY)
maclobdell 0:f7c60d3e7b8a 1626 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
maclobdell 0:f7c60d3e7b8a 1627 return( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) );
maclobdell 0:f7c60d3e7b8a 1628 #endif
maclobdell 0:f7c60d3e7b8a 1629 #if defined(ECP_SHORTWEIERSTRASS)
maclobdell 0:f7c60d3e7b8a 1630 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
maclobdell 0:f7c60d3e7b8a 1631 return( ecp_mul_comb( grp, R, m, P, f_rng, p_rng ) );
maclobdell 0:f7c60d3e7b8a 1632 #endif
maclobdell 0:f7c60d3e7b8a 1633 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 1634 }
maclobdell 0:f7c60d3e7b8a 1635
maclobdell 0:f7c60d3e7b8a 1636 #if defined(ECP_SHORTWEIERSTRASS)
maclobdell 0:f7c60d3e7b8a 1637 /*
maclobdell 0:f7c60d3e7b8a 1638 * Check that an affine point is valid as a public key,
maclobdell 0:f7c60d3e7b8a 1639 * short weierstrass curves (SEC1 3.2.3.1)
maclobdell 0:f7c60d3e7b8a 1640 */
maclobdell 0:f7c60d3e7b8a 1641 static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
maclobdell 0:f7c60d3e7b8a 1642 {
maclobdell 0:f7c60d3e7b8a 1643 int ret;
maclobdell 0:f7c60d3e7b8a 1644 mbedtls_mpi YY, RHS;
maclobdell 0:f7c60d3e7b8a 1645
maclobdell 0:f7c60d3e7b8a 1646 /* pt coordinates must be normalized for our checks */
maclobdell 0:f7c60d3e7b8a 1647 if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ||
maclobdell 0:f7c60d3e7b8a 1648 mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 ||
maclobdell 0:f7c60d3e7b8a 1649 mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
maclobdell 0:f7c60d3e7b8a 1650 mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
maclobdell 0:f7c60d3e7b8a 1651 return( MBEDTLS_ERR_ECP_INVALID_KEY );
maclobdell 0:f7c60d3e7b8a 1652
maclobdell 0:f7c60d3e7b8a 1653 mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
maclobdell 0:f7c60d3e7b8a 1654
maclobdell 0:f7c60d3e7b8a 1655 /*
maclobdell 0:f7c60d3e7b8a 1656 * YY = Y^2
maclobdell 0:f7c60d3e7b8a 1657 * RHS = X (X^2 + A) + B = X^3 + A X + B
maclobdell 0:f7c60d3e7b8a 1658 */
maclobdell 0:f7c60d3e7b8a 1659 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &YY, &pt->Y, &pt->Y ) ); MOD_MUL( YY );
maclobdell 0:f7c60d3e7b8a 1660 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &pt->X, &pt->X ) ); MOD_MUL( RHS );
maclobdell 0:f7c60d3e7b8a 1661
maclobdell 0:f7c60d3e7b8a 1662 /* Special case for A = -3 */
maclobdell 0:f7c60d3e7b8a 1663 if( grp->A.p == NULL )
maclobdell 0:f7c60d3e7b8a 1664 {
maclobdell 0:f7c60d3e7b8a 1665 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS );
maclobdell 0:f7c60d3e7b8a 1666 }
maclobdell 0:f7c60d3e7b8a 1667 else
maclobdell 0:f7c60d3e7b8a 1668 {
maclobdell 0:f7c60d3e7b8a 1669 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->A ) ); MOD_ADD( RHS );
maclobdell 0:f7c60d3e7b8a 1670 }
maclobdell 0:f7c60d3e7b8a 1671
maclobdell 0:f7c60d3e7b8a 1672 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &RHS, &pt->X ) ); MOD_MUL( RHS );
maclobdell 0:f7c60d3e7b8a 1673 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->B ) ); MOD_ADD( RHS );
maclobdell 0:f7c60d3e7b8a 1674
maclobdell 0:f7c60d3e7b8a 1675 if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
maclobdell 0:f7c60d3e7b8a 1676 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
maclobdell 0:f7c60d3e7b8a 1677
maclobdell 0:f7c60d3e7b8a 1678 cleanup:
maclobdell 0:f7c60d3e7b8a 1679
maclobdell 0:f7c60d3e7b8a 1680 mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
maclobdell 0:f7c60d3e7b8a 1681
maclobdell 0:f7c60d3e7b8a 1682 return( ret );
maclobdell 0:f7c60d3e7b8a 1683 }
maclobdell 0:f7c60d3e7b8a 1684 #endif /* ECP_SHORTWEIERSTRASS */
maclobdell 0:f7c60d3e7b8a 1685
maclobdell 0:f7c60d3e7b8a 1686 /*
maclobdell 0:f7c60d3e7b8a 1687 * R = m * P with shortcuts for m == 1 and m == -1
maclobdell 0:f7c60d3e7b8a 1688 * NOT constant-time - ONLY for short Weierstrass!
maclobdell 0:f7c60d3e7b8a 1689 */
maclobdell 0:f7c60d3e7b8a 1690 static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
maclobdell 0:f7c60d3e7b8a 1691 mbedtls_ecp_point *R,
maclobdell 0:f7c60d3e7b8a 1692 const mbedtls_mpi *m,
maclobdell 0:f7c60d3e7b8a 1693 const mbedtls_ecp_point *P )
maclobdell 0:f7c60d3e7b8a 1694 {
maclobdell 0:f7c60d3e7b8a 1695 int ret;
maclobdell 0:f7c60d3e7b8a 1696
maclobdell 0:f7c60d3e7b8a 1697 if( mbedtls_mpi_cmp_int( m, 1 ) == 0 )
maclobdell 0:f7c60d3e7b8a 1698 {
maclobdell 0:f7c60d3e7b8a 1699 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
maclobdell 0:f7c60d3e7b8a 1700 }
maclobdell 0:f7c60d3e7b8a 1701 else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
maclobdell 0:f7c60d3e7b8a 1702 {
maclobdell 0:f7c60d3e7b8a 1703 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
maclobdell 0:f7c60d3e7b8a 1704 if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 )
maclobdell 0:f7c60d3e7b8a 1705 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
maclobdell 0:f7c60d3e7b8a 1706 }
maclobdell 0:f7c60d3e7b8a 1707 else
maclobdell 0:f7c60d3e7b8a 1708 {
maclobdell 0:f7c60d3e7b8a 1709 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
maclobdell 0:f7c60d3e7b8a 1710 }
maclobdell 0:f7c60d3e7b8a 1711
maclobdell 0:f7c60d3e7b8a 1712 cleanup:
maclobdell 0:f7c60d3e7b8a 1713 return( ret );
maclobdell 0:f7c60d3e7b8a 1714 }
maclobdell 0:f7c60d3e7b8a 1715
maclobdell 0:f7c60d3e7b8a 1716 /*
maclobdell 0:f7c60d3e7b8a 1717 * Linear combination
maclobdell 0:f7c60d3e7b8a 1718 * NOT constant-time
maclobdell 0:f7c60d3e7b8a 1719 */
maclobdell 0:f7c60d3e7b8a 1720 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
maclobdell 0:f7c60d3e7b8a 1721 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
maclobdell 0:f7c60d3e7b8a 1722 const mbedtls_mpi *n, const mbedtls_ecp_point *Q )
maclobdell 0:f7c60d3e7b8a 1723 {
maclobdell 0:f7c60d3e7b8a 1724 int ret;
maclobdell 0:f7c60d3e7b8a 1725 mbedtls_ecp_point mP;
maclobdell 0:f7c60d3e7b8a 1726
maclobdell 0:f7c60d3e7b8a 1727 if( ecp_get_type( grp ) != ECP_TYPE_SHORT_WEIERSTRASS )
maclobdell 0:f7c60d3e7b8a 1728 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
maclobdell 0:f7c60d3e7b8a 1729
maclobdell 0:f7c60d3e7b8a 1730 mbedtls_ecp_point_init( &mP );
maclobdell 0:f7c60d3e7b8a 1731
maclobdell 0:f7c60d3e7b8a 1732 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, &mP, m, P ) );
maclobdell 0:f7c60d3e7b8a 1733 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, R, n, Q ) );
maclobdell 0:f7c60d3e7b8a 1734
maclobdell 0:f7c60d3e7b8a 1735 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, &mP, R ) );
maclobdell 0:f7c60d3e7b8a 1736 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
maclobdell 0:f7c60d3e7b8a 1737
maclobdell 0:f7c60d3e7b8a 1738 cleanup:
maclobdell 0:f7c60d3e7b8a 1739 mbedtls_ecp_point_free( &mP );
maclobdell 0:f7c60d3e7b8a 1740
maclobdell 0:f7c60d3e7b8a 1741 return( ret );
maclobdell 0:f7c60d3e7b8a 1742 }
maclobdell 0:f7c60d3e7b8a 1743
maclobdell 0:f7c60d3e7b8a 1744
maclobdell 0:f7c60d3e7b8a 1745 #if defined(ECP_MONTGOMERY)
maclobdell 0:f7c60d3e7b8a 1746 /*
maclobdell 0:f7c60d3e7b8a 1747 * Check validity of a public key for Montgomery curves with x-only schemes
maclobdell 0:f7c60d3e7b8a 1748 */
maclobdell 0:f7c60d3e7b8a 1749 static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
maclobdell 0:f7c60d3e7b8a 1750 {
maclobdell 0:f7c60d3e7b8a 1751 /* [Curve25519 p. 5] Just check X is the correct number of bytes */
maclobdell 0:f7c60d3e7b8a 1752 if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
maclobdell 0:f7c60d3e7b8a 1753 return( MBEDTLS_ERR_ECP_INVALID_KEY );
maclobdell 0:f7c60d3e7b8a 1754
maclobdell 0:f7c60d3e7b8a 1755 return( 0 );
maclobdell 0:f7c60d3e7b8a 1756 }
maclobdell 0:f7c60d3e7b8a 1757 #endif /* ECP_MONTGOMERY */
maclobdell 0:f7c60d3e7b8a 1758
maclobdell 0:f7c60d3e7b8a 1759 /*
maclobdell 0:f7c60d3e7b8a 1760 * Check that a point is valid as a public key
maclobdell 0:f7c60d3e7b8a 1761 */
maclobdell 0:f7c60d3e7b8a 1762 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
maclobdell 0:f7c60d3e7b8a 1763 {
maclobdell 0:f7c60d3e7b8a 1764 /* Must use affine coordinates */
maclobdell 0:f7c60d3e7b8a 1765 if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
maclobdell 0:f7c60d3e7b8a 1766 return( MBEDTLS_ERR_ECP_INVALID_KEY );
maclobdell 0:f7c60d3e7b8a 1767
maclobdell 0:f7c60d3e7b8a 1768 #if defined(ECP_MONTGOMERY)
maclobdell 0:f7c60d3e7b8a 1769 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
maclobdell 0:f7c60d3e7b8a 1770 return( ecp_check_pubkey_mx( grp, pt ) );
maclobdell 0:f7c60d3e7b8a 1771 #endif
maclobdell 0:f7c60d3e7b8a 1772 #if defined(ECP_SHORTWEIERSTRASS)
maclobdell 0:f7c60d3e7b8a 1773 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
maclobdell 0:f7c60d3e7b8a 1774 return( ecp_check_pubkey_sw( grp, pt ) );
maclobdell 0:f7c60d3e7b8a 1775 #endif
maclobdell 0:f7c60d3e7b8a 1776 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 1777 }
maclobdell 0:f7c60d3e7b8a 1778
maclobdell 0:f7c60d3e7b8a 1779 /*
maclobdell 0:f7c60d3e7b8a 1780 * Check that an mbedtls_mpi is valid as a private key
maclobdell 0:f7c60d3e7b8a 1781 */
maclobdell 0:f7c60d3e7b8a 1782 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d )
maclobdell 0:f7c60d3e7b8a 1783 {
maclobdell 0:f7c60d3e7b8a 1784 #if defined(ECP_MONTGOMERY)
maclobdell 0:f7c60d3e7b8a 1785 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
maclobdell 0:f7c60d3e7b8a 1786 {
maclobdell 0:f7c60d3e7b8a 1787 /* see [Curve25519] page 5 */
maclobdell 0:f7c60d3e7b8a 1788 if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
maclobdell 0:f7c60d3e7b8a 1789 mbedtls_mpi_get_bit( d, 1 ) != 0 ||
maclobdell 0:f7c60d3e7b8a 1790 mbedtls_mpi_get_bit( d, 2 ) != 0 ||
maclobdell 0:f7c60d3e7b8a 1791 mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */
maclobdell 0:f7c60d3e7b8a 1792 return( MBEDTLS_ERR_ECP_INVALID_KEY );
maclobdell 0:f7c60d3e7b8a 1793 else
maclobdell 0:f7c60d3e7b8a 1794 return( 0 );
maclobdell 0:f7c60d3e7b8a 1795 }
maclobdell 0:f7c60d3e7b8a 1796 #endif /* ECP_MONTGOMERY */
maclobdell 0:f7c60d3e7b8a 1797 #if defined(ECP_SHORTWEIERSTRASS)
maclobdell 0:f7c60d3e7b8a 1798 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
maclobdell 0:f7c60d3e7b8a 1799 {
maclobdell 0:f7c60d3e7b8a 1800 /* see SEC1 3.2 */
maclobdell 0:f7c60d3e7b8a 1801 if( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
maclobdell 0:f7c60d3e7b8a 1802 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
maclobdell 0:f7c60d3e7b8a 1803 return( MBEDTLS_ERR_ECP_INVALID_KEY );
maclobdell 0:f7c60d3e7b8a 1804 else
maclobdell 0:f7c60d3e7b8a 1805 return( 0 );
maclobdell 0:f7c60d3e7b8a 1806 }
maclobdell 0:f7c60d3e7b8a 1807 #endif /* ECP_SHORTWEIERSTRASS */
maclobdell 0:f7c60d3e7b8a 1808
maclobdell 0:f7c60d3e7b8a 1809 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 1810 }
maclobdell 0:f7c60d3e7b8a 1811
maclobdell 0:f7c60d3e7b8a 1812 /*
maclobdell 0:f7c60d3e7b8a 1813 * Generate a keypair with configurable base point
maclobdell 0:f7c60d3e7b8a 1814 */
maclobdell 0:f7c60d3e7b8a 1815 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
maclobdell 0:f7c60d3e7b8a 1816 const mbedtls_ecp_point *G,
maclobdell 0:f7c60d3e7b8a 1817 mbedtls_mpi *d, mbedtls_ecp_point *Q,
maclobdell 0:f7c60d3e7b8a 1818 int (*f_rng)(void *, unsigned char *, size_t),
maclobdell 0:f7c60d3e7b8a 1819 void *p_rng )
maclobdell 0:f7c60d3e7b8a 1820 {
maclobdell 0:f7c60d3e7b8a 1821 int ret;
maclobdell 0:f7c60d3e7b8a 1822 size_t n_size = ( grp->nbits + 7 ) / 8;
maclobdell 0:f7c60d3e7b8a 1823
maclobdell 0:f7c60d3e7b8a 1824 #if defined(ECP_MONTGOMERY)
maclobdell 0:f7c60d3e7b8a 1825 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
maclobdell 0:f7c60d3e7b8a 1826 {
maclobdell 0:f7c60d3e7b8a 1827 /* [M225] page 5 */
maclobdell 0:f7c60d3e7b8a 1828 size_t b;
maclobdell 0:f7c60d3e7b8a 1829
maclobdell 0:f7c60d3e7b8a 1830 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
maclobdell 0:f7c60d3e7b8a 1831
maclobdell 0:f7c60d3e7b8a 1832 /* Make sure the most significant bit is nbits */
maclobdell 0:f7c60d3e7b8a 1833 b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */
maclobdell 0:f7c60d3e7b8a 1834 if( b > grp->nbits )
maclobdell 0:f7c60d3e7b8a 1835 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) );
maclobdell 0:f7c60d3e7b8a 1836 else
maclobdell 0:f7c60d3e7b8a 1837 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) );
maclobdell 0:f7c60d3e7b8a 1838
maclobdell 0:f7c60d3e7b8a 1839 /* Make sure the last three bits are unset */
maclobdell 0:f7c60d3e7b8a 1840 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) );
maclobdell 0:f7c60d3e7b8a 1841 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) );
maclobdell 0:f7c60d3e7b8a 1842 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
maclobdell 0:f7c60d3e7b8a 1843 }
maclobdell 0:f7c60d3e7b8a 1844 else
maclobdell 0:f7c60d3e7b8a 1845 #endif /* ECP_MONTGOMERY */
maclobdell 0:f7c60d3e7b8a 1846 #if defined(ECP_SHORTWEIERSTRASS)
maclobdell 0:f7c60d3e7b8a 1847 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
maclobdell 0:f7c60d3e7b8a 1848 {
maclobdell 0:f7c60d3e7b8a 1849 /* SEC1 3.2.1: Generate d such that 1 <= n < N */
maclobdell 0:f7c60d3e7b8a 1850 int count = 0;
maclobdell 0:f7c60d3e7b8a 1851 unsigned char rnd[MBEDTLS_ECP_MAX_BYTES];
maclobdell 0:f7c60d3e7b8a 1852
maclobdell 0:f7c60d3e7b8a 1853 /*
maclobdell 0:f7c60d3e7b8a 1854 * Match the procedure given in RFC 6979 (deterministic ECDSA):
maclobdell 0:f7c60d3e7b8a 1855 * - use the same byte ordering;
maclobdell 0:f7c60d3e7b8a 1856 * - keep the leftmost nbits bits of the generated octet string;
maclobdell 0:f7c60d3e7b8a 1857 * - try until result is in the desired range.
maclobdell 0:f7c60d3e7b8a 1858 * This also avoids any biais, which is especially important for ECDSA.
maclobdell 0:f7c60d3e7b8a 1859 */
maclobdell 0:f7c60d3e7b8a 1860 do
maclobdell 0:f7c60d3e7b8a 1861 {
maclobdell 0:f7c60d3e7b8a 1862 MBEDTLS_MPI_CHK( f_rng( p_rng, rnd, n_size ) );
maclobdell 0:f7c60d3e7b8a 1863 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( d, rnd, n_size ) );
maclobdell 0:f7c60d3e7b8a 1864 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) );
maclobdell 0:f7c60d3e7b8a 1865
maclobdell 0:f7c60d3e7b8a 1866 /*
maclobdell 0:f7c60d3e7b8a 1867 * Each try has at worst a probability 1/2 of failing (the msb has
maclobdell 0:f7c60d3e7b8a 1868 * a probability 1/2 of being 0, and then the result will be < N),
maclobdell 0:f7c60d3e7b8a 1869 * so after 30 tries failure probability is a most 2**(-30).
maclobdell 0:f7c60d3e7b8a 1870 *
maclobdell 0:f7c60d3e7b8a 1871 * For most curves, 1 try is enough with overwhelming probability,
maclobdell 0:f7c60d3e7b8a 1872 * since N starts with a lot of 1s in binary, but some curves
maclobdell 0:f7c60d3e7b8a 1873 * such as secp224k1 are actually very close to the worst case.
maclobdell 0:f7c60d3e7b8a 1874 */
maclobdell 0:f7c60d3e7b8a 1875 if( ++count > 30 )
maclobdell 0:f7c60d3e7b8a 1876 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
maclobdell 0:f7c60d3e7b8a 1877 }
maclobdell 0:f7c60d3e7b8a 1878 while( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
maclobdell 0:f7c60d3e7b8a 1879 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 );
maclobdell 0:f7c60d3e7b8a 1880 }
maclobdell 0:f7c60d3e7b8a 1881 else
maclobdell 0:f7c60d3e7b8a 1882 #endif /* ECP_SHORTWEIERSTRASS */
maclobdell 0:f7c60d3e7b8a 1883 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 1884
maclobdell 0:f7c60d3e7b8a 1885 cleanup:
maclobdell 0:f7c60d3e7b8a 1886 if( ret != 0 )
maclobdell 0:f7c60d3e7b8a 1887 return( ret );
maclobdell 0:f7c60d3e7b8a 1888
maclobdell 0:f7c60d3e7b8a 1889 return( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) );
maclobdell 0:f7c60d3e7b8a 1890 }
maclobdell 0:f7c60d3e7b8a 1891
maclobdell 0:f7c60d3e7b8a 1892 /*
maclobdell 0:f7c60d3e7b8a 1893 * Generate key pair, wrapper for conventional base point
maclobdell 0:f7c60d3e7b8a 1894 */
maclobdell 0:f7c60d3e7b8a 1895 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp,
maclobdell 0:f7c60d3e7b8a 1896 mbedtls_mpi *d, mbedtls_ecp_point *Q,
maclobdell 0:f7c60d3e7b8a 1897 int (*f_rng)(void *, unsigned char *, size_t),
maclobdell 0:f7c60d3e7b8a 1898 void *p_rng )
maclobdell 0:f7c60d3e7b8a 1899 {
maclobdell 0:f7c60d3e7b8a 1900 return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) );
maclobdell 0:f7c60d3e7b8a 1901 }
maclobdell 0:f7c60d3e7b8a 1902
maclobdell 0:f7c60d3e7b8a 1903 /*
maclobdell 0:f7c60d3e7b8a 1904 * Generate a keypair, prettier wrapper
maclobdell 0:f7c60d3e7b8a 1905 */
maclobdell 0:f7c60d3e7b8a 1906 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
maclobdell 0:f7c60d3e7b8a 1907 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
maclobdell 0:f7c60d3e7b8a 1908 {
maclobdell 0:f7c60d3e7b8a 1909 int ret;
maclobdell 0:f7c60d3e7b8a 1910
maclobdell 0:f7c60d3e7b8a 1911 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
maclobdell 0:f7c60d3e7b8a 1912 return( ret );
maclobdell 0:f7c60d3e7b8a 1913
maclobdell 0:f7c60d3e7b8a 1914 return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
maclobdell 0:f7c60d3e7b8a 1915 }
maclobdell 0:f7c60d3e7b8a 1916
maclobdell 0:f7c60d3e7b8a 1917 /*
maclobdell 0:f7c60d3e7b8a 1918 * Check a public-private key pair
maclobdell 0:f7c60d3e7b8a 1919 */
maclobdell 0:f7c60d3e7b8a 1920 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
maclobdell 0:f7c60d3e7b8a 1921 {
maclobdell 0:f7c60d3e7b8a 1922 int ret;
maclobdell 0:f7c60d3e7b8a 1923 mbedtls_ecp_point Q;
maclobdell 0:f7c60d3e7b8a 1924 mbedtls_ecp_group grp;
maclobdell 0:f7c60d3e7b8a 1925
maclobdell 0:f7c60d3e7b8a 1926 if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
maclobdell 0:f7c60d3e7b8a 1927 pub->grp.id != prv->grp.id ||
maclobdell 0:f7c60d3e7b8a 1928 mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
maclobdell 0:f7c60d3e7b8a 1929 mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
maclobdell 0:f7c60d3e7b8a 1930 mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
maclobdell 0:f7c60d3e7b8a 1931 {
maclobdell 0:f7c60d3e7b8a 1932 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
maclobdell 0:f7c60d3e7b8a 1933 }
maclobdell 0:f7c60d3e7b8a 1934
maclobdell 0:f7c60d3e7b8a 1935 mbedtls_ecp_point_init( &Q );
maclobdell 0:f7c60d3e7b8a 1936 mbedtls_ecp_group_init( &grp );
maclobdell 0:f7c60d3e7b8a 1937
maclobdell 0:f7c60d3e7b8a 1938 /* mbedtls_ecp_mul() needs a non-const group... */
maclobdell 0:f7c60d3e7b8a 1939 mbedtls_ecp_group_copy( &grp, &prv->grp );
maclobdell 0:f7c60d3e7b8a 1940
maclobdell 0:f7c60d3e7b8a 1941 /* Also checks d is valid */
maclobdell 0:f7c60d3e7b8a 1942 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
maclobdell 0:f7c60d3e7b8a 1943
maclobdell 0:f7c60d3e7b8a 1944 if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
maclobdell 0:f7c60d3e7b8a 1945 mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
maclobdell 0:f7c60d3e7b8a 1946 mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
maclobdell 0:f7c60d3e7b8a 1947 {
maclobdell 0:f7c60d3e7b8a 1948 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
maclobdell 0:f7c60d3e7b8a 1949 goto cleanup;
maclobdell 0:f7c60d3e7b8a 1950 }
maclobdell 0:f7c60d3e7b8a 1951
maclobdell 0:f7c60d3e7b8a 1952 cleanup:
maclobdell 0:f7c60d3e7b8a 1953 mbedtls_ecp_point_free( &Q );
maclobdell 0:f7c60d3e7b8a 1954 mbedtls_ecp_group_free( &grp );
maclobdell 0:f7c60d3e7b8a 1955
maclobdell 0:f7c60d3e7b8a 1956 return( ret );
maclobdell 0:f7c60d3e7b8a 1957 }
maclobdell 0:f7c60d3e7b8a 1958
maclobdell 0:f7c60d3e7b8a 1959 #if defined(MBEDTLS_SELF_TEST)
maclobdell 0:f7c60d3e7b8a 1960
maclobdell 0:f7c60d3e7b8a 1961 /*
maclobdell 0:f7c60d3e7b8a 1962 * Checkup routine
maclobdell 0:f7c60d3e7b8a 1963 */
maclobdell 0:f7c60d3e7b8a 1964 int mbedtls_ecp_self_test( int verbose )
maclobdell 0:f7c60d3e7b8a 1965 {
maclobdell 0:f7c60d3e7b8a 1966 int ret;
maclobdell 0:f7c60d3e7b8a 1967 size_t i;
maclobdell 0:f7c60d3e7b8a 1968 mbedtls_ecp_group grp;
maclobdell 0:f7c60d3e7b8a 1969 mbedtls_ecp_point R, P;
maclobdell 0:f7c60d3e7b8a 1970 mbedtls_mpi m;
maclobdell 0:f7c60d3e7b8a 1971 unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
maclobdell 0:f7c60d3e7b8a 1972 /* exponents especially adapted for secp192r1 */
maclobdell 0:f7c60d3e7b8a 1973 const char *exponents[] =
maclobdell 0:f7c60d3e7b8a 1974 {
maclobdell 0:f7c60d3e7b8a 1975 "000000000000000000000000000000000000000000000001", /* one */
maclobdell 0:f7c60d3e7b8a 1976 "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22830", /* N - 1 */
maclobdell 0:f7c60d3e7b8a 1977 "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
maclobdell 0:f7c60d3e7b8a 1978 "400000000000000000000000000000000000000000000000", /* one and zeros */
maclobdell 0:f7c60d3e7b8a 1979 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
maclobdell 0:f7c60d3e7b8a 1980 "555555555555555555555555555555555555555555555555", /* 101010... */
maclobdell 0:f7c60d3e7b8a 1981 };
maclobdell 0:f7c60d3e7b8a 1982
maclobdell 0:f7c60d3e7b8a 1983 mbedtls_ecp_group_init( &grp );
maclobdell 0:f7c60d3e7b8a 1984 mbedtls_ecp_point_init( &R );
maclobdell 0:f7c60d3e7b8a 1985 mbedtls_ecp_point_init( &P );
maclobdell 0:f7c60d3e7b8a 1986 mbedtls_mpi_init( &m );
maclobdell 0:f7c60d3e7b8a 1987
maclobdell 0:f7c60d3e7b8a 1988 /* Use secp192r1 if available, or any available curve */
maclobdell 0:f7c60d3e7b8a 1989 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
maclobdell 0:f7c60d3e7b8a 1990 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) );
maclobdell 0:f7c60d3e7b8a 1991 #else
maclobdell 0:f7c60d3e7b8a 1992 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) );
maclobdell 0:f7c60d3e7b8a 1993 #endif
maclobdell 0:f7c60d3e7b8a 1994
maclobdell 0:f7c60d3e7b8a 1995 if( verbose != 0 )
maclobdell 0:f7c60d3e7b8a 1996 mbedtls_printf( " ECP test #1 (constant op_count, base point G): " );
maclobdell 0:f7c60d3e7b8a 1997
maclobdell 0:f7c60d3e7b8a 1998 /* Do a dummy multiplication first to trigger precomputation */
maclobdell 0:f7c60d3e7b8a 1999 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
maclobdell 0:f7c60d3e7b8a 2000 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
maclobdell 0:f7c60d3e7b8a 2001
maclobdell 0:f7c60d3e7b8a 2002 add_count = 0;
maclobdell 0:f7c60d3e7b8a 2003 dbl_count = 0;
maclobdell 0:f7c60d3e7b8a 2004 mul_count = 0;
maclobdell 0:f7c60d3e7b8a 2005 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
maclobdell 0:f7c60d3e7b8a 2006 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
maclobdell 0:f7c60d3e7b8a 2007
maclobdell 0:f7c60d3e7b8a 2008 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
maclobdell 0:f7c60d3e7b8a 2009 {
maclobdell 0:f7c60d3e7b8a 2010 add_c_prev = add_count;
maclobdell 0:f7c60d3e7b8a 2011 dbl_c_prev = dbl_count;
maclobdell 0:f7c60d3e7b8a 2012 mul_c_prev = mul_count;
maclobdell 0:f7c60d3e7b8a 2013 add_count = 0;
maclobdell 0:f7c60d3e7b8a 2014 dbl_count = 0;
maclobdell 0:f7c60d3e7b8a 2015 mul_count = 0;
maclobdell 0:f7c60d3e7b8a 2016
maclobdell 0:f7c60d3e7b8a 2017 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
maclobdell 0:f7c60d3e7b8a 2018 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
maclobdell 0:f7c60d3e7b8a 2019
maclobdell 0:f7c60d3e7b8a 2020 if( add_count != add_c_prev ||
maclobdell 0:f7c60d3e7b8a 2021 dbl_count != dbl_c_prev ||
maclobdell 0:f7c60d3e7b8a 2022 mul_count != mul_c_prev )
maclobdell 0:f7c60d3e7b8a 2023 {
maclobdell 0:f7c60d3e7b8a 2024 if( verbose != 0 )
maclobdell 0:f7c60d3e7b8a 2025 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
maclobdell 0:f7c60d3e7b8a 2026
maclobdell 0:f7c60d3e7b8a 2027 ret = 1;
maclobdell 0:f7c60d3e7b8a 2028 goto cleanup;
maclobdell 0:f7c60d3e7b8a 2029 }
maclobdell 0:f7c60d3e7b8a 2030 }
maclobdell 0:f7c60d3e7b8a 2031
maclobdell 0:f7c60d3e7b8a 2032 if( verbose != 0 )
maclobdell 0:f7c60d3e7b8a 2033 mbedtls_printf( "passed\n" );
maclobdell 0:f7c60d3e7b8a 2034
maclobdell 0:f7c60d3e7b8a 2035 if( verbose != 0 )
maclobdell 0:f7c60d3e7b8a 2036 mbedtls_printf( " ECP test #2 (constant op_count, other point): " );
maclobdell 0:f7c60d3e7b8a 2037 /* We computed P = 2G last time, use it */
maclobdell 0:f7c60d3e7b8a 2038
maclobdell 0:f7c60d3e7b8a 2039 add_count = 0;
maclobdell 0:f7c60d3e7b8a 2040 dbl_count = 0;
maclobdell 0:f7c60d3e7b8a 2041 mul_count = 0;
maclobdell 0:f7c60d3e7b8a 2042 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
maclobdell 0:f7c60d3e7b8a 2043 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
maclobdell 0:f7c60d3e7b8a 2044
maclobdell 0:f7c60d3e7b8a 2045 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
maclobdell 0:f7c60d3e7b8a 2046 {
maclobdell 0:f7c60d3e7b8a 2047 add_c_prev = add_count;
maclobdell 0:f7c60d3e7b8a 2048 dbl_c_prev = dbl_count;
maclobdell 0:f7c60d3e7b8a 2049 mul_c_prev = mul_count;
maclobdell 0:f7c60d3e7b8a 2050 add_count = 0;
maclobdell 0:f7c60d3e7b8a 2051 dbl_count = 0;
maclobdell 0:f7c60d3e7b8a 2052 mul_count = 0;
maclobdell 0:f7c60d3e7b8a 2053
maclobdell 0:f7c60d3e7b8a 2054 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
maclobdell 0:f7c60d3e7b8a 2055 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
maclobdell 0:f7c60d3e7b8a 2056
maclobdell 0:f7c60d3e7b8a 2057 if( add_count != add_c_prev ||
maclobdell 0:f7c60d3e7b8a 2058 dbl_count != dbl_c_prev ||
maclobdell 0:f7c60d3e7b8a 2059 mul_count != mul_c_prev )
maclobdell 0:f7c60d3e7b8a 2060 {
maclobdell 0:f7c60d3e7b8a 2061 if( verbose != 0 )
maclobdell 0:f7c60d3e7b8a 2062 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
maclobdell 0:f7c60d3e7b8a 2063
maclobdell 0:f7c60d3e7b8a 2064 ret = 1;
maclobdell 0:f7c60d3e7b8a 2065 goto cleanup;
maclobdell 0:f7c60d3e7b8a 2066 }
maclobdell 0:f7c60d3e7b8a 2067 }
maclobdell 0:f7c60d3e7b8a 2068
maclobdell 0:f7c60d3e7b8a 2069 if( verbose != 0 )
maclobdell 0:f7c60d3e7b8a 2070 mbedtls_printf( "passed\n" );
maclobdell 0:f7c60d3e7b8a 2071
maclobdell 0:f7c60d3e7b8a 2072 cleanup:
maclobdell 0:f7c60d3e7b8a 2073
maclobdell 0:f7c60d3e7b8a 2074 if( ret < 0 && verbose != 0 )
maclobdell 0:f7c60d3e7b8a 2075 mbedtls_printf( "Unexpected error, return code = %08X\n", ret );
maclobdell 0:f7c60d3e7b8a 2076
maclobdell 0:f7c60d3e7b8a 2077 mbedtls_ecp_group_free( &grp );
maclobdell 0:f7c60d3e7b8a 2078 mbedtls_ecp_point_free( &R );
maclobdell 0:f7c60d3e7b8a 2079 mbedtls_ecp_point_free( &P );
maclobdell 0:f7c60d3e7b8a 2080 mbedtls_mpi_free( &m );
maclobdell 0:f7c60d3e7b8a 2081
maclobdell 0:f7c60d3e7b8a 2082 if( verbose != 0 )
maclobdell 0:f7c60d3e7b8a 2083 mbedtls_printf( "\n" );
maclobdell 0:f7c60d3e7b8a 2084
maclobdell 0:f7c60d3e7b8a 2085 return( ret );
maclobdell 0:f7c60d3e7b8a 2086 }
maclobdell 0:f7c60d3e7b8a 2087
maclobdell 0:f7c60d3e7b8a 2088 #endif /* MBEDTLS_SELF_TEST */
maclobdell 0:f7c60d3e7b8a 2089
maclobdell 0:f7c60d3e7b8a 2090 #endif /* MBEDTLS_ECP_C */