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Dependents:   mbed-TFT-example-NCS36510 mbed-Accelerometer-example-NCS36510 mbed-Accelerometer-example-NCS36510

features/mbedtls/src/ecp.c@1:f30bdcd2b33b, 2017-02-27 (annotated)

Committer:
jacobjohnson
Date:
Mon Feb 27 17:45:05 2017 +0000
Revision:
1:f30bdcd2b33b
Parent:
0:098463de4c5d 
changed the inputscale from 1 to 7 in analogin_api.c.  This will need to be changed later, and accessed from the main level, but for now this allows the  adc to read a value from 0 to 3.7V, instead of just up to 1V.;

Who changed what in which revision?

UserRevisionLine numberNew contents of line
group-onsemi 0:098463de4c5d 1 /*
group-onsemi 0:098463de4c5d 2 * Elliptic curves over GF(p): generic functions
group-onsemi 0:098463de4c5d 3 *
group-onsemi 0:098463de4c5d 4 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
group-onsemi 0:098463de4c5d 5 * SPDX-License-Identifier: Apache-2.0
group-onsemi 0:098463de4c5d 6 *
group-onsemi 0:098463de4c5d 7 * Licensed under the Apache License, Version 2.0 (the "License"); you may
group-onsemi 0:098463de4c5d 8 * not use this file except in compliance with the License.
group-onsemi 0:098463de4c5d 9 * You may obtain a copy of the License at
group-onsemi 0:098463de4c5d 10 *
group-onsemi 0:098463de4c5d 11 * http://www.apache.org/licenses/LICENSE-2.0
group-onsemi 0:098463de4c5d 12 *
group-onsemi 0:098463de4c5d 13 * Unless required by applicable law or agreed to in writing, software
group-onsemi 0:098463de4c5d 14 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
group-onsemi 0:098463de4c5d 15 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
group-onsemi 0:098463de4c5d 16 * See the License for the specific language governing permissions and
group-onsemi 0:098463de4c5d 17 * limitations under the License.
group-onsemi 0:098463de4c5d 18 *
group-onsemi 0:098463de4c5d 19 * This file is part of mbed TLS (https://tls.mbed.org)
group-onsemi 0:098463de4c5d 20 */
group-onsemi 0:098463de4c5d 21
group-onsemi 0:098463de4c5d 22 /*
group-onsemi 0:098463de4c5d 23 * References:
group-onsemi 0:098463de4c5d 24 *
group-onsemi 0:098463de4c5d 25 * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
group-onsemi 0:098463de4c5d 26 * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
group-onsemi 0:098463de4c5d 27 * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
group-onsemi 0:098463de4c5d 28 * RFC 4492 for the related TLS structures and constants
group-onsemi 0:098463de4c5d 29 *
group-onsemi 0:098463de4c5d 30 * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf
group-onsemi 0:098463de4c5d 31 *
group-onsemi 0:098463de4c5d 32 * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
group-onsemi 0:098463de4c5d 33 * for elliptic curve cryptosystems. In : Cryptographic Hardware and
group-onsemi 0:098463de4c5d 34 * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
group-onsemi 0:098463de4c5d 35 * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
group-onsemi 0:098463de4c5d 36 *
group-onsemi 0:098463de4c5d 37 * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
group-onsemi 0:098463de4c5d 38 * render ECC resistant against Side Channel Attacks. IACR Cryptology
group-onsemi 0:098463de4c5d 39 * ePrint Archive, 2004, vol. 2004, p. 342.
group-onsemi 0:098463de4c5d 40 * <http://eprint.iacr.org/2004/342.pdf>
group-onsemi 0:098463de4c5d 41 */
group-onsemi 0:098463de4c5d 42
group-onsemi 0:098463de4c5d 43 #if !defined(MBEDTLS_CONFIG_FILE)
group-onsemi 0:098463de4c5d 44 #include "mbedtls/config.h"
group-onsemi 0:098463de4c5d 45 #else
group-onsemi 0:098463de4c5d 46 #include MBEDTLS_CONFIG_FILE
group-onsemi 0:098463de4c5d 47 #endif
group-onsemi 0:098463de4c5d 48
group-onsemi 0:098463de4c5d 49 #if defined(MBEDTLS_ECP_C)
group-onsemi 0:098463de4c5d 50
group-onsemi 0:098463de4c5d 51 #include "mbedtls/ecp.h"
group-onsemi 0:098463de4c5d 52
group-onsemi 0:098463de4c5d 53 #include <string.h>
group-onsemi 0:098463de4c5d 54
group-onsemi 0:098463de4c5d 55 #if defined(MBEDTLS_PLATFORM_C)
group-onsemi 0:098463de4c5d 56 #include "mbedtls/platform.h"
group-onsemi 0:098463de4c5d 57 #else
group-onsemi 0:098463de4c5d 58 #include <stdlib.h>
group-onsemi 0:098463de4c5d 59 #include <stdio.h>
group-onsemi 0:098463de4c5d 60 #define mbedtls_printf printf
group-onsemi 0:098463de4c5d 61 #define mbedtls_calloc calloc
group-onsemi 0:098463de4c5d 62 #define mbedtls_free free
group-onsemi 0:098463de4c5d 63 #endif
group-onsemi 0:098463de4c5d 64
group-onsemi 0:098463de4c5d 65 #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
group-onsemi 0:098463de4c5d 66 !defined(inline) && !defined(__cplusplus)
group-onsemi 0:098463de4c5d 67 #define inline __inline
group-onsemi 0:098463de4c5d 68 #endif
group-onsemi 0:098463de4c5d 69
group-onsemi 0:098463de4c5d 70 /* Implementation that should never be optimized out by the compiler */
group-onsemi 0:098463de4c5d 71 static void mbedtls_zeroize( void *v, size_t n ) {
group-onsemi 0:098463de4c5d 72 volatile unsigned char *p = v; while( n-- ) *p++ = 0;
group-onsemi 0:098463de4c5d 73 }
group-onsemi 0:098463de4c5d 74
group-onsemi 0:098463de4c5d 75 #if defined(MBEDTLS_SELF_TEST)
group-onsemi 0:098463de4c5d 76 /*
group-onsemi 0:098463de4c5d 77 * Counts of point addition and doubling, and field multiplications.
group-onsemi 0:098463de4c5d 78 * Used to test resistance of point multiplication to simple timing attacks.
group-onsemi 0:098463de4c5d 79 */
group-onsemi 0:098463de4c5d 80 static unsigned long add_count, dbl_count, mul_count;
group-onsemi 0:098463de4c5d 81 #endif
group-onsemi 0:098463de4c5d 82
group-onsemi 0:098463de4c5d 83 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \
group-onsemi 0:098463de4c5d 84 defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
group-onsemi 0:098463de4c5d 85 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
group-onsemi 0:098463de4c5d 86 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \
group-onsemi 0:098463de4c5d 87 defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \
group-onsemi 0:098463de4c5d 88 defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \
group-onsemi 0:098463de4c5d 89 defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \
group-onsemi 0:098463de4c5d 90 defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \
group-onsemi 0:098463de4c5d 91 defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
group-onsemi 0:098463de4c5d 92 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
group-onsemi 0:098463de4c5d 93 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
group-onsemi 0:098463de4c5d 94 #define ECP_SHORTWEIERSTRASS
group-onsemi 0:098463de4c5d 95 #endif
group-onsemi 0:098463de4c5d 96
group-onsemi 0:098463de4c5d 97 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
group-onsemi 0:098463de4c5d 98 #define ECP_MONTGOMERY
group-onsemi 0:098463de4c5d 99 #endif
group-onsemi 0:098463de4c5d 100
group-onsemi 0:098463de4c5d 101 /*
group-onsemi 0:098463de4c5d 102 * Curve types: internal for now, might be exposed later
group-onsemi 0:098463de4c5d 103 */
group-onsemi 0:098463de4c5d 104 typedef enum
group-onsemi 0:098463de4c5d 105 {
group-onsemi 0:098463de4c5d 106 ECP_TYPE_NONE = 0,
group-onsemi 0:098463de4c5d 107 ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */
group-onsemi 0:098463de4c5d 108 ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */
group-onsemi 0:098463de4c5d 109 } ecp_curve_type;
group-onsemi 0:098463de4c5d 110
group-onsemi 0:098463de4c5d 111 /*
group-onsemi 0:098463de4c5d 112 * List of supported curves:
group-onsemi 0:098463de4c5d 113 * - internal ID
group-onsemi 0:098463de4c5d 114 * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2)
group-onsemi 0:098463de4c5d 115 * - size in bits
group-onsemi 0:098463de4c5d 116 * - readable name
group-onsemi 0:098463de4c5d 117 *
group-onsemi 0:098463de4c5d 118 * Curves are listed in order: largest curves first, and for a given size,
group-onsemi 0:098463de4c5d 119 * fastest curves first. This provides the default order for the SSL module.
group-onsemi 0:098463de4c5d 120 *
group-onsemi 0:098463de4c5d 121 * Reminder: update profiles in x509_crt.c when adding a new curves!
group-onsemi 0:098463de4c5d 122 */
group-onsemi 0:098463de4c5d 123 static const mbedtls_ecp_curve_info ecp_supported_curves[] =
group-onsemi 0:098463de4c5d 124 {
group-onsemi 0:098463de4c5d 125 #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
group-onsemi 0:098463de4c5d 126 { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" },
group-onsemi 0:098463de4c5d 127 #endif
group-onsemi 0:098463de4c5d 128 #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
group-onsemi 0:098463de4c5d 129 { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
group-onsemi 0:098463de4c5d 130 #endif
group-onsemi 0:098463de4c5d 131 #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
group-onsemi 0:098463de4c5d 132 { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
group-onsemi 0:098463de4c5d 133 #endif
group-onsemi 0:098463de4c5d 134 #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
group-onsemi 0:098463de4c5d 135 { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
group-onsemi 0:098463de4c5d 136 #endif
group-onsemi 0:098463de4c5d 137 #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
group-onsemi 0:098463de4c5d 138 { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
group-onsemi 0:098463de4c5d 139 #endif
group-onsemi 0:098463de4c5d 140 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
group-onsemi 0:098463de4c5d 141 { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
group-onsemi 0:098463de4c5d 142 #endif
group-onsemi 0:098463de4c5d 143 #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
group-onsemi 0:098463de4c5d 144 { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" },
group-onsemi 0:098463de4c5d 145 #endif
group-onsemi 0:098463de4c5d 146 #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
group-onsemi 0:098463de4c5d 147 { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" },
group-onsemi 0:098463de4c5d 148 #endif
group-onsemi 0:098463de4c5d 149 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
group-onsemi 0:098463de4c5d 150 { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" },
group-onsemi 0:098463de4c5d 151 #endif
group-onsemi 0:098463de4c5d 152 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
group-onsemi 0:098463de4c5d 153 { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" },
group-onsemi 0:098463de4c5d 154 #endif
group-onsemi 0:098463de4c5d 155 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
group-onsemi 0:098463de4c5d 156 { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" },
group-onsemi 0:098463de4c5d 157 #endif
group-onsemi 0:098463de4c5d 158 { MBEDTLS_ECP_DP_NONE, 0, 0, NULL },
group-onsemi 0:098463de4c5d 159 };
group-onsemi 0:098463de4c5d 160
group-onsemi 0:098463de4c5d 161 #define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \
group-onsemi 0:098463de4c5d 162 sizeof( ecp_supported_curves[0] )
group-onsemi 0:098463de4c5d 163
group-onsemi 0:098463de4c5d 164 static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
group-onsemi 0:098463de4c5d 165
group-onsemi 0:098463de4c5d 166 /*
group-onsemi 0:098463de4c5d 167 * List of supported curves and associated info
group-onsemi 0:098463de4c5d 168 */
group-onsemi 0:098463de4c5d 169 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
group-onsemi 0:098463de4c5d 170 {
group-onsemi 0:098463de4c5d 171 return( ecp_supported_curves );
group-onsemi 0:098463de4c5d 172 }
group-onsemi 0:098463de4c5d 173
group-onsemi 0:098463de4c5d 174 /*
group-onsemi 0:098463de4c5d 175 * List of supported curves, group ID only
group-onsemi 0:098463de4c5d 176 */
group-onsemi 0:098463de4c5d 177 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
group-onsemi 0:098463de4c5d 178 {
group-onsemi 0:098463de4c5d 179 static int init_done = 0;
group-onsemi 0:098463de4c5d 180
group-onsemi 0:098463de4c5d 181 if( ! init_done )
group-onsemi 0:098463de4c5d 182 {
group-onsemi 0:098463de4c5d 183 size_t i = 0;
group-onsemi 0:098463de4c5d 184 const mbedtls_ecp_curve_info *curve_info;
group-onsemi 0:098463de4c5d 185
group-onsemi 0:098463de4c5d 186 for( curve_info = mbedtls_ecp_curve_list();
group-onsemi 0:098463de4c5d 187 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
group-onsemi 0:098463de4c5d 188 curve_info++ )
group-onsemi 0:098463de4c5d 189 {
group-onsemi 0:098463de4c5d 190 ecp_supported_grp_id[i++] = curve_info->grp_id;
group-onsemi 0:098463de4c5d 191 }
group-onsemi 0:098463de4c5d 192 ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
group-onsemi 0:098463de4c5d 193
group-onsemi 0:098463de4c5d 194 init_done = 1;
group-onsemi 0:098463de4c5d 195 }
group-onsemi 0:098463de4c5d 196
group-onsemi 0:098463de4c5d 197 return( ecp_supported_grp_id );
group-onsemi 0:098463de4c5d 198 }
group-onsemi 0:098463de4c5d 199
group-onsemi 0:098463de4c5d 200 /*
group-onsemi 0:098463de4c5d 201 * Get the curve info for the internal identifier
group-onsemi 0:098463de4c5d 202 */
group-onsemi 0:098463de4c5d 203 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id )
group-onsemi 0:098463de4c5d 204 {
group-onsemi 0:098463de4c5d 205 const mbedtls_ecp_curve_info *curve_info;
group-onsemi 0:098463de4c5d 206
group-onsemi 0:098463de4c5d 207 for( curve_info = mbedtls_ecp_curve_list();
group-onsemi 0:098463de4c5d 208 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
group-onsemi 0:098463de4c5d 209 curve_info++ )
group-onsemi 0:098463de4c5d 210 {
group-onsemi 0:098463de4c5d 211 if( curve_info->grp_id == grp_id )
group-onsemi 0:098463de4c5d 212 return( curve_info );
group-onsemi 0:098463de4c5d 213 }
group-onsemi 0:098463de4c5d 214
group-onsemi 0:098463de4c5d 215 return( NULL );
group-onsemi 0:098463de4c5d 216 }
group-onsemi 0:098463de4c5d 217
group-onsemi 0:098463de4c5d 218 /*
group-onsemi 0:098463de4c5d 219 * Get the curve info from the TLS identifier
group-onsemi 0:098463de4c5d 220 */
group-onsemi 0:098463de4c5d 221 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id )
group-onsemi 0:098463de4c5d 222 {
group-onsemi 0:098463de4c5d 223 const mbedtls_ecp_curve_info *curve_info;
group-onsemi 0:098463de4c5d 224
group-onsemi 0:098463de4c5d 225 for( curve_info = mbedtls_ecp_curve_list();
group-onsemi 0:098463de4c5d 226 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
group-onsemi 0:098463de4c5d 227 curve_info++ )
group-onsemi 0:098463de4c5d 228 {
group-onsemi 0:098463de4c5d 229 if( curve_info->tls_id == tls_id )
group-onsemi 0:098463de4c5d 230 return( curve_info );
group-onsemi 0:098463de4c5d 231 }
group-onsemi 0:098463de4c5d 232
group-onsemi 0:098463de4c5d 233 return( NULL );
group-onsemi 0:098463de4c5d 234 }
group-onsemi 0:098463de4c5d 235
group-onsemi 0:098463de4c5d 236 /*
group-onsemi 0:098463de4c5d 237 * Get the curve info from the name
group-onsemi 0:098463de4c5d 238 */
group-onsemi 0:098463de4c5d 239 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name )
group-onsemi 0:098463de4c5d 240 {
group-onsemi 0:098463de4c5d 241 const mbedtls_ecp_curve_info *curve_info;
group-onsemi 0:098463de4c5d 242
group-onsemi 0:098463de4c5d 243 for( curve_info = mbedtls_ecp_curve_list();
group-onsemi 0:098463de4c5d 244 curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
group-onsemi 0:098463de4c5d 245 curve_info++ )
group-onsemi 0:098463de4c5d 246 {
group-onsemi 0:098463de4c5d 247 if( strcmp( curve_info->name, name ) == 0 )
group-onsemi 0:098463de4c5d 248 return( curve_info );
group-onsemi 0:098463de4c5d 249 }
group-onsemi 0:098463de4c5d 250
group-onsemi 0:098463de4c5d 251 return( NULL );
group-onsemi 0:098463de4c5d 252 }
group-onsemi 0:098463de4c5d 253
group-onsemi 0:098463de4c5d 254 /*
group-onsemi 0:098463de4c5d 255 * Get the type of a curve
group-onsemi 0:098463de4c5d 256 */
group-onsemi 0:098463de4c5d 257 static inline ecp_curve_type ecp_get_type( const mbedtls_ecp_group *grp )
group-onsemi 0:098463de4c5d 258 {
group-onsemi 0:098463de4c5d 259 if( grp->G.X.p == NULL )
group-onsemi 0:098463de4c5d 260 return( ECP_TYPE_NONE );
group-onsemi 0:098463de4c5d 261
group-onsemi 0:098463de4c5d 262 if( grp->G.Y.p == NULL )
group-onsemi 0:098463de4c5d 263 return( ECP_TYPE_MONTGOMERY );
group-onsemi 0:098463de4c5d 264 else
group-onsemi 0:098463de4c5d 265 return( ECP_TYPE_SHORT_WEIERSTRASS );
group-onsemi 0:098463de4c5d 266 }
group-onsemi 0:098463de4c5d 267
group-onsemi 0:098463de4c5d 268 /*
group-onsemi 0:098463de4c5d 269 * Initialize (the components of) a point
group-onsemi 0:098463de4c5d 270 */
group-onsemi 0:098463de4c5d 271 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
group-onsemi 0:098463de4c5d 272 {
group-onsemi 0:098463de4c5d 273 if( pt == NULL )
group-onsemi 0:098463de4c5d 274 return;
group-onsemi 0:098463de4c5d 275
group-onsemi 0:098463de4c5d 276 mbedtls_mpi_init( &pt->X );
group-onsemi 0:098463de4c5d 277 mbedtls_mpi_init( &pt->Y );
group-onsemi 0:098463de4c5d 278 mbedtls_mpi_init( &pt->Z );
group-onsemi 0:098463de4c5d 279 }
group-onsemi 0:098463de4c5d 280
group-onsemi 0:098463de4c5d 281 /*
group-onsemi 0:098463de4c5d 282 * Initialize (the components of) a group
group-onsemi 0:098463de4c5d 283 */
group-onsemi 0:098463de4c5d 284 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
group-onsemi 0:098463de4c5d 285 {
group-onsemi 0:098463de4c5d 286 if( grp == NULL )
group-onsemi 0:098463de4c5d 287 return;
group-onsemi 0:098463de4c5d 288
group-onsemi 0:098463de4c5d 289 memset( grp, 0, sizeof( mbedtls_ecp_group ) );
group-onsemi 0:098463de4c5d 290 }
group-onsemi 0:098463de4c5d 291
group-onsemi 0:098463de4c5d 292 /*
group-onsemi 0:098463de4c5d 293 * Initialize (the components of) a key pair
group-onsemi 0:098463de4c5d 294 */
group-onsemi 0:098463de4c5d 295 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
group-onsemi 0:098463de4c5d 296 {
group-onsemi 0:098463de4c5d 297 if( key == NULL )
group-onsemi 0:098463de4c5d 298 return;
group-onsemi 0:098463de4c5d 299
group-onsemi 0:098463de4c5d 300 mbedtls_ecp_group_init( &key->grp );
group-onsemi 0:098463de4c5d 301 mbedtls_mpi_init( &key->d );
group-onsemi 0:098463de4c5d 302 mbedtls_ecp_point_init( &key->Q );
group-onsemi 0:098463de4c5d 303 }
group-onsemi 0:098463de4c5d 304
group-onsemi 0:098463de4c5d 305 /*
group-onsemi 0:098463de4c5d 306 * Unallocate (the components of) a point
group-onsemi 0:098463de4c5d 307 */
group-onsemi 0:098463de4c5d 308 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
group-onsemi 0:098463de4c5d 309 {
group-onsemi 0:098463de4c5d 310 if( pt == NULL )
group-onsemi 0:098463de4c5d 311 return;
group-onsemi 0:098463de4c5d 312
group-onsemi 0:098463de4c5d 313 mbedtls_mpi_free( &( pt->X ) );
group-onsemi 0:098463de4c5d 314 mbedtls_mpi_free( &( pt->Y ) );
group-onsemi 0:098463de4c5d 315 mbedtls_mpi_free( &( pt->Z ) );
group-onsemi 0:098463de4c5d 316 }
group-onsemi 0:098463de4c5d 317
group-onsemi 0:098463de4c5d 318 /*
group-onsemi 0:098463de4c5d 319 * Unallocate (the components of) a group
group-onsemi 0:098463de4c5d 320 */
group-onsemi 0:098463de4c5d 321 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
group-onsemi 0:098463de4c5d 322 {
group-onsemi 0:098463de4c5d 323 size_t i;
group-onsemi 0:098463de4c5d 324
group-onsemi 0:098463de4c5d 325 if( grp == NULL )
group-onsemi 0:098463de4c5d 326 return;
group-onsemi 0:098463de4c5d 327
group-onsemi 0:098463de4c5d 328 if( grp->h != 1 )
group-onsemi 0:098463de4c5d 329 {
group-onsemi 0:098463de4c5d 330 mbedtls_mpi_free( &grp->P );
group-onsemi 0:098463de4c5d 331 mbedtls_mpi_free( &grp->A );
group-onsemi 0:098463de4c5d 332 mbedtls_mpi_free( &grp->B );
group-onsemi 0:098463de4c5d 333 mbedtls_ecp_point_free( &grp->G );
group-onsemi 0:098463de4c5d 334 mbedtls_mpi_free( &grp->N );
group-onsemi 0:098463de4c5d 335 }
group-onsemi 0:098463de4c5d 336
group-onsemi 0:098463de4c5d 337 if( grp->T != NULL )
group-onsemi 0:098463de4c5d 338 {
group-onsemi 0:098463de4c5d 339 for( i = 0; i < grp->T_size; i++ )
group-onsemi 0:098463de4c5d 340 mbedtls_ecp_point_free( &grp->T[i] );
group-onsemi 0:098463de4c5d 341 mbedtls_free( grp->T );
group-onsemi 0:098463de4c5d 342 }
group-onsemi 0:098463de4c5d 343
group-onsemi 0:098463de4c5d 344 mbedtls_zeroize( grp, sizeof( mbedtls_ecp_group ) );
group-onsemi 0:098463de4c5d 345 }
group-onsemi 0:098463de4c5d 346
group-onsemi 0:098463de4c5d 347 /*
group-onsemi 0:098463de4c5d 348 * Unallocate (the components of) a key pair
group-onsemi 0:098463de4c5d 349 */
group-onsemi 0:098463de4c5d 350 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
group-onsemi 0:098463de4c5d 351 {
group-onsemi 0:098463de4c5d 352 if( key == NULL )
group-onsemi 0:098463de4c5d 353 return;
group-onsemi 0:098463de4c5d 354
group-onsemi 0:098463de4c5d 355 mbedtls_ecp_group_free( &key->grp );
group-onsemi 0:098463de4c5d 356 mbedtls_mpi_free( &key->d );
group-onsemi 0:098463de4c5d 357 mbedtls_ecp_point_free( &key->Q );
group-onsemi 0:098463de4c5d 358 }
group-onsemi 0:098463de4c5d 359
group-onsemi 0:098463de4c5d 360 /*
group-onsemi 0:098463de4c5d 361 * Copy the contents of a point
group-onsemi 0:098463de4c5d 362 */
group-onsemi 0:098463de4c5d 363 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
group-onsemi 0:098463de4c5d 364 {
group-onsemi 0:098463de4c5d 365 int ret;
group-onsemi 0:098463de4c5d 366
group-onsemi 0:098463de4c5d 367 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) );
group-onsemi 0:098463de4c5d 368 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) );
group-onsemi 0:098463de4c5d 369 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) );
group-onsemi 0:098463de4c5d 370
group-onsemi 0:098463de4c5d 371 cleanup:
group-onsemi 0:098463de4c5d 372 return( ret );
group-onsemi 0:098463de4c5d 373 }
group-onsemi 0:098463de4c5d 374
group-onsemi 0:098463de4c5d 375 /*
group-onsemi 0:098463de4c5d 376 * Copy the contents of a group object
group-onsemi 0:098463de4c5d 377 */
group-onsemi 0:098463de4c5d 378 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
group-onsemi 0:098463de4c5d 379 {
group-onsemi 0:098463de4c5d 380 return mbedtls_ecp_group_load( dst, src->id );
group-onsemi 0:098463de4c5d 381 }
group-onsemi 0:098463de4c5d 382
group-onsemi 0:098463de4c5d 383 /*
group-onsemi 0:098463de4c5d 384 * Set point to zero
group-onsemi 0:098463de4c5d 385 */
group-onsemi 0:098463de4c5d 386 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
group-onsemi 0:098463de4c5d 387 {
group-onsemi 0:098463de4c5d 388 int ret;
group-onsemi 0:098463de4c5d 389
group-onsemi 0:098463de4c5d 390 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) );
group-onsemi 0:098463de4c5d 391 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) );
group-onsemi 0:098463de4c5d 392 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) );
group-onsemi 0:098463de4c5d 393
group-onsemi 0:098463de4c5d 394 cleanup:
group-onsemi 0:098463de4c5d 395 return( ret );
group-onsemi 0:098463de4c5d 396 }
group-onsemi 0:098463de4c5d 397
group-onsemi 0:098463de4c5d 398 /*
group-onsemi 0:098463de4c5d 399 * Tell if a point is zero
group-onsemi 0:098463de4c5d 400 */
group-onsemi 0:098463de4c5d 401 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
group-onsemi 0:098463de4c5d 402 {
group-onsemi 0:098463de4c5d 403 return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 );
group-onsemi 0:098463de4c5d 404 }
group-onsemi 0:098463de4c5d 405
group-onsemi 0:098463de4c5d 406 /*
group-onsemi 0:098463de4c5d 407 * Compare two points lazyly
group-onsemi 0:098463de4c5d 408 */
group-onsemi 0:098463de4c5d 409 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
group-onsemi 0:098463de4c5d 410 const mbedtls_ecp_point *Q )
group-onsemi 0:098463de4c5d 411 {
group-onsemi 0:098463de4c5d 412 if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
group-onsemi 0:098463de4c5d 413 mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 &&
group-onsemi 0:098463de4c5d 414 mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 )
group-onsemi 0:098463de4c5d 415 {
group-onsemi 0:098463de4c5d 416 return( 0 );
group-onsemi 0:098463de4c5d 417 }
group-onsemi 0:098463de4c5d 418
group-onsemi 0:098463de4c5d 419 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 420 }
group-onsemi 0:098463de4c5d 421
group-onsemi 0:098463de4c5d 422 /*
group-onsemi 0:098463de4c5d 423 * Import a non-zero point from ASCII strings
group-onsemi 0:098463de4c5d 424 */
group-onsemi 0:098463de4c5d 425 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
group-onsemi 0:098463de4c5d 426 const char *x, const char *y )
group-onsemi 0:098463de4c5d 427 {
group-onsemi 0:098463de4c5d 428 int ret;
group-onsemi 0:098463de4c5d 429
group-onsemi 0:098463de4c5d 430 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) );
group-onsemi 0:098463de4c5d 431 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) );
group-onsemi 0:098463de4c5d 432 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
group-onsemi 0:098463de4c5d 433
group-onsemi 0:098463de4c5d 434 cleanup:
group-onsemi 0:098463de4c5d 435 return( ret );
group-onsemi 0:098463de4c5d 436 }
group-onsemi 0:098463de4c5d 437
group-onsemi 0:098463de4c5d 438 /*
group-onsemi 0:098463de4c5d 439 * Export a point into unsigned binary data (SEC1 2.3.3)
group-onsemi 0:098463de4c5d 440 */
group-onsemi 0:098463de4c5d 441 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *P,
group-onsemi 0:098463de4c5d 442 int format, size_t *olen,
group-onsemi 0:098463de4c5d 443 unsigned char *buf, size_t buflen )
group-onsemi 0:098463de4c5d 444 {
group-onsemi 0:098463de4c5d 445 int ret = 0;
group-onsemi 0:098463de4c5d 446 size_t plen;
group-onsemi 0:098463de4c5d 447
group-onsemi 0:098463de4c5d 448 if( format != MBEDTLS_ECP_PF_UNCOMPRESSED &&
group-onsemi 0:098463de4c5d 449 format != MBEDTLS_ECP_PF_COMPRESSED )
group-onsemi 0:098463de4c5d 450 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 451
group-onsemi 0:098463de4c5d 452 /*
group-onsemi 0:098463de4c5d 453 * Common case: P == 0
group-onsemi 0:098463de4c5d 454 */
group-onsemi 0:098463de4c5d 455 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
group-onsemi 0:098463de4c5d 456 {
group-onsemi 0:098463de4c5d 457 if( buflen < 1 )
group-onsemi 0:098463de4c5d 458 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
group-onsemi 0:098463de4c5d 459
group-onsemi 0:098463de4c5d 460 buf[0] = 0x00;
group-onsemi 0:098463de4c5d 461 *olen = 1;
group-onsemi 0:098463de4c5d 462
group-onsemi 0:098463de4c5d 463 return( 0 );
group-onsemi 0:098463de4c5d 464 }
group-onsemi 0:098463de4c5d 465
group-onsemi 0:098463de4c5d 466 plen = mbedtls_mpi_size( &grp->P );
group-onsemi 0:098463de4c5d 467
group-onsemi 0:098463de4c5d 468 if( format == MBEDTLS_ECP_PF_UNCOMPRESSED )
group-onsemi 0:098463de4c5d 469 {
group-onsemi 0:098463de4c5d 470 *olen = 2 * plen + 1;
group-onsemi 0:098463de4c5d 471
group-onsemi 0:098463de4c5d 472 if( buflen < *olen )
group-onsemi 0:098463de4c5d 473 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
group-onsemi 0:098463de4c5d 474
group-onsemi 0:098463de4c5d 475 buf[0] = 0x04;
group-onsemi 0:098463de4c5d 476 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
group-onsemi 0:098463de4c5d 477 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) );
group-onsemi 0:098463de4c5d 478 }
group-onsemi 0:098463de4c5d 479 else if( format == MBEDTLS_ECP_PF_COMPRESSED )
group-onsemi 0:098463de4c5d 480 {
group-onsemi 0:098463de4c5d 481 *olen = plen + 1;
group-onsemi 0:098463de4c5d 482
group-onsemi 0:098463de4c5d 483 if( buflen < *olen )
group-onsemi 0:098463de4c5d 484 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
group-onsemi 0:098463de4c5d 485
group-onsemi 0:098463de4c5d 486 buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 );
group-onsemi 0:098463de4c5d 487 MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
group-onsemi 0:098463de4c5d 488 }
group-onsemi 0:098463de4c5d 489
group-onsemi 0:098463de4c5d 490 cleanup:
group-onsemi 0:098463de4c5d 491 return( ret );
group-onsemi 0:098463de4c5d 492 }
group-onsemi 0:098463de4c5d 493
group-onsemi 0:098463de4c5d 494 /*
group-onsemi 0:098463de4c5d 495 * Import a point from unsigned binary data (SEC1 2.3.4)
group-onsemi 0:098463de4c5d 496 */
group-onsemi 0:098463de4c5d 497 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
group-onsemi 0:098463de4c5d 498 const unsigned char *buf, size_t ilen )
group-onsemi 0:098463de4c5d 499 {
group-onsemi 0:098463de4c5d 500 int ret;
group-onsemi 0:098463de4c5d 501 size_t plen;
group-onsemi 0:098463de4c5d 502
group-onsemi 0:098463de4c5d 503 if( ilen < 1 )
group-onsemi 0:098463de4c5d 504 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 505
group-onsemi 0:098463de4c5d 506 if( buf[0] == 0x00 )
group-onsemi 0:098463de4c5d 507 {
group-onsemi 0:098463de4c5d 508 if( ilen == 1 )
group-onsemi 0:098463de4c5d 509 return( mbedtls_ecp_set_zero( pt ) );
group-onsemi 0:098463de4c5d 510 else
group-onsemi 0:098463de4c5d 511 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 512 }
group-onsemi 0:098463de4c5d 513
group-onsemi 0:098463de4c5d 514 plen = mbedtls_mpi_size( &grp->P );
group-onsemi 0:098463de4c5d 515
group-onsemi 0:098463de4c5d 516 if( buf[0] != 0x04 )
group-onsemi 0:098463de4c5d 517 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
group-onsemi 0:098463de4c5d 518
group-onsemi 0:098463de4c5d 519 if( ilen != 2 * plen + 1 )
group-onsemi 0:098463de4c5d 520 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 521
group-onsemi 0:098463de4c5d 522 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
group-onsemi 0:098463de4c5d 523 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, buf + 1 + plen, plen ) );
group-onsemi 0:098463de4c5d 524 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
group-onsemi 0:098463de4c5d 525
group-onsemi 0:098463de4c5d 526 cleanup:
group-onsemi 0:098463de4c5d 527 return( ret );
group-onsemi 0:098463de4c5d 528 }
group-onsemi 0:098463de4c5d 529
group-onsemi 0:098463de4c5d 530 /*
group-onsemi 0:098463de4c5d 531 * Import a point from a TLS ECPoint record (RFC 4492)
group-onsemi 0:098463de4c5d 532 * struct {
group-onsemi 0:098463de4c5d 533 * opaque point <1..2^8-1>;
group-onsemi 0:098463de4c5d 534 * } ECPoint;
group-onsemi 0:098463de4c5d 535 */
group-onsemi 0:098463de4c5d 536 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
group-onsemi 0:098463de4c5d 537 const unsigned char **buf, size_t buf_len )
group-onsemi 0:098463de4c5d 538 {
group-onsemi 0:098463de4c5d 539 unsigned char data_len;
group-onsemi 0:098463de4c5d 540 const unsigned char *buf_start;
group-onsemi 0:098463de4c5d 541
group-onsemi 0:098463de4c5d 542 /*
group-onsemi 0:098463de4c5d 543 * We must have at least two bytes (1 for length, at least one for data)
group-onsemi 0:098463de4c5d 544 */
group-onsemi 0:098463de4c5d 545 if( buf_len < 2 )
group-onsemi 0:098463de4c5d 546 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 547
group-onsemi 0:098463de4c5d 548 data_len = *(*buf)++;
group-onsemi 0:098463de4c5d 549 if( data_len < 1 || data_len > buf_len - 1 )
group-onsemi 0:098463de4c5d 550 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 551
group-onsemi 0:098463de4c5d 552 /*
group-onsemi 0:098463de4c5d 553 * Save buffer start for read_binary and update buf
group-onsemi 0:098463de4c5d 554 */
group-onsemi 0:098463de4c5d 555 buf_start = *buf;
group-onsemi 0:098463de4c5d 556 *buf += data_len;
group-onsemi 0:098463de4c5d 557
group-onsemi 0:098463de4c5d 558 return mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len );
group-onsemi 0:098463de4c5d 559 }
group-onsemi 0:098463de4c5d 560
group-onsemi 0:098463de4c5d 561 /*
group-onsemi 0:098463de4c5d 562 * Export a point as a TLS ECPoint record (RFC 4492)
group-onsemi 0:098463de4c5d 563 * struct {
group-onsemi 0:098463de4c5d 564 * opaque point <1..2^8-1>;
group-onsemi 0:098463de4c5d 565 * } ECPoint;
group-onsemi 0:098463de4c5d 566 */
group-onsemi 0:098463de4c5d 567 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
group-onsemi 0:098463de4c5d 568 int format, size_t *olen,
group-onsemi 0:098463de4c5d 569 unsigned char *buf, size_t blen )
group-onsemi 0:098463de4c5d 570 {
group-onsemi 0:098463de4c5d 571 int ret;
group-onsemi 0:098463de4c5d 572
group-onsemi 0:098463de4c5d 573 /*
group-onsemi 0:098463de4c5d 574 * buffer length must be at least one, for our length byte
group-onsemi 0:098463de4c5d 575 */
group-onsemi 0:098463de4c5d 576 if( blen < 1 )
group-onsemi 0:098463de4c5d 577 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 578
group-onsemi 0:098463de4c5d 579 if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
group-onsemi 0:098463de4c5d 580 olen, buf + 1, blen - 1) ) != 0 )
group-onsemi 0:098463de4c5d 581 return( ret );
group-onsemi 0:098463de4c5d 582
group-onsemi 0:098463de4c5d 583 /*
group-onsemi 0:098463de4c5d 584 * write length to the first byte and update total length
group-onsemi 0:098463de4c5d 585 */
group-onsemi 0:098463de4c5d 586 buf[0] = (unsigned char) *olen;
group-onsemi 0:098463de4c5d 587 ++*olen;
group-onsemi 0:098463de4c5d 588
group-onsemi 0:098463de4c5d 589 return( 0 );
group-onsemi 0:098463de4c5d 590 }
group-onsemi 0:098463de4c5d 591
group-onsemi 0:098463de4c5d 592 /*
group-onsemi 0:098463de4c5d 593 * Set a group from an ECParameters record (RFC 4492)
group-onsemi 0:098463de4c5d 594 */
group-onsemi 0:098463de4c5d 595 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, const unsigned char **buf, size_t len )
group-onsemi 0:098463de4c5d 596 {
group-onsemi 0:098463de4c5d 597 uint16_t tls_id;
group-onsemi 0:098463de4c5d 598 const mbedtls_ecp_curve_info *curve_info;
group-onsemi 0:098463de4c5d 599
group-onsemi 0:098463de4c5d 600 /*
group-onsemi 0:098463de4c5d 601 * We expect at least three bytes (see below)
group-onsemi 0:098463de4c5d 602 */
group-onsemi 0:098463de4c5d 603 if( len < 3 )
group-onsemi 0:098463de4c5d 604 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 605
group-onsemi 0:098463de4c5d 606 /*
group-onsemi 0:098463de4c5d 607 * First byte is curve_type; only named_curve is handled
group-onsemi 0:098463de4c5d 608 */
group-onsemi 0:098463de4c5d 609 if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
group-onsemi 0:098463de4c5d 610 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 611
group-onsemi 0:098463de4c5d 612 /*
group-onsemi 0:098463de4c5d 613 * Next two bytes are the namedcurve value
group-onsemi 0:098463de4c5d 614 */
group-onsemi 0:098463de4c5d 615 tls_id = *(*buf)++;
group-onsemi 0:098463de4c5d 616 tls_id <<= 8;
group-onsemi 0:098463de4c5d 617 tls_id |= *(*buf)++;
group-onsemi 0:098463de4c5d 618
group-onsemi 0:098463de4c5d 619 if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
group-onsemi 0:098463de4c5d 620 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
group-onsemi 0:098463de4c5d 621
group-onsemi 0:098463de4c5d 622 return mbedtls_ecp_group_load( grp, curve_info->grp_id );
group-onsemi 0:098463de4c5d 623 }
group-onsemi 0:098463de4c5d 624
group-onsemi 0:098463de4c5d 625 /*
group-onsemi 0:098463de4c5d 626 * Write the ECParameters record corresponding to a group (RFC 4492)
group-onsemi 0:098463de4c5d 627 */
group-onsemi 0:098463de4c5d 628 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
group-onsemi 0:098463de4c5d 629 unsigned char *buf, size_t blen )
group-onsemi 0:098463de4c5d 630 {
group-onsemi 0:098463de4c5d 631 const mbedtls_ecp_curve_info *curve_info;
group-onsemi 0:098463de4c5d 632
group-onsemi 0:098463de4c5d 633 if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
group-onsemi 0:098463de4c5d 634 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 635
group-onsemi 0:098463de4c5d 636 /*
group-onsemi 0:098463de4c5d 637 * We are going to write 3 bytes (see below)
group-onsemi 0:098463de4c5d 638 */
group-onsemi 0:098463de4c5d 639 *olen = 3;
group-onsemi 0:098463de4c5d 640 if( blen < *olen )
group-onsemi 0:098463de4c5d 641 return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
group-onsemi 0:098463de4c5d 642
group-onsemi 0:098463de4c5d 643 /*
group-onsemi 0:098463de4c5d 644 * First byte is curve_type, always named_curve
group-onsemi 0:098463de4c5d 645 */
group-onsemi 0:098463de4c5d 646 *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
group-onsemi 0:098463de4c5d 647
group-onsemi 0:098463de4c5d 648 /*
group-onsemi 0:098463de4c5d 649 * Next two bytes are the namedcurve value
group-onsemi 0:098463de4c5d 650 */
group-onsemi 0:098463de4c5d 651 buf[0] = curve_info->tls_id >> 8;
group-onsemi 0:098463de4c5d 652 buf[1] = curve_info->tls_id & 0xFF;
group-onsemi 0:098463de4c5d 653
group-onsemi 0:098463de4c5d 654 return( 0 );
group-onsemi 0:098463de4c5d 655 }
group-onsemi 0:098463de4c5d 656
group-onsemi 0:098463de4c5d 657 /*
group-onsemi 0:098463de4c5d 658 * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
group-onsemi 0:098463de4c5d 659 * See the documentation of struct mbedtls_ecp_group.
group-onsemi 0:098463de4c5d 660 *
group-onsemi 0:098463de4c5d 661 * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
group-onsemi 0:098463de4c5d 662 */
group-onsemi 0:098463de4c5d 663 static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
group-onsemi 0:098463de4c5d 664 {
group-onsemi 0:098463de4c5d 665 int ret;
group-onsemi 0:098463de4c5d 666
group-onsemi 0:098463de4c5d 667 if( grp->modp == NULL )
group-onsemi 0:098463de4c5d 668 return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) );
group-onsemi 0:098463de4c5d 669
group-onsemi 0:098463de4c5d 670 /* N->s < 0 is a much faster test, which fails only if N is 0 */
group-onsemi 0:098463de4c5d 671 if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) ||
group-onsemi 0:098463de4c5d 672 mbedtls_mpi_bitlen( N ) > 2 * grp->pbits )
group-onsemi 0:098463de4c5d 673 {
group-onsemi 0:098463de4c5d 674 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 675 }
group-onsemi 0:098463de4c5d 676
group-onsemi 0:098463de4c5d 677 MBEDTLS_MPI_CHK( grp->modp( N ) );
group-onsemi 0:098463de4c5d 678
group-onsemi 0:098463de4c5d 679 /* N->s < 0 is a much faster test, which fails only if N is 0 */
group-onsemi 0:098463de4c5d 680 while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 )
group-onsemi 0:098463de4c5d 681 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) );
group-onsemi 0:098463de4c5d 682
group-onsemi 0:098463de4c5d 683 while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 )
group-onsemi 0:098463de4c5d 684 /* we known P, N and the result are positive */
group-onsemi 0:098463de4c5d 685 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) );
group-onsemi 0:098463de4c5d 686
group-onsemi 0:098463de4c5d 687 cleanup:
group-onsemi 0:098463de4c5d 688 return( ret );
group-onsemi 0:098463de4c5d 689 }
group-onsemi 0:098463de4c5d 690
group-onsemi 0:098463de4c5d 691 /*
group-onsemi 0:098463de4c5d 692 * Fast mod-p functions expect their argument to be in the 0..p^2 range.
group-onsemi 0:098463de4c5d 693 *
group-onsemi 0:098463de4c5d 694 * In order to guarantee that, we need to ensure that operands of
group-onsemi 0:098463de4c5d 695 * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will
group-onsemi 0:098463de4c5d 696 * bring the result back to this range.
group-onsemi 0:098463de4c5d 697 *
group-onsemi 0:098463de4c5d 698 * The following macros are shortcuts for doing that.
group-onsemi 0:098463de4c5d 699 */
group-onsemi 0:098463de4c5d 700
group-onsemi 0:098463de4c5d 701 /*
group-onsemi 0:098463de4c5d 702 * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
group-onsemi 0:098463de4c5d 703 */
group-onsemi 0:098463de4c5d 704 #if defined(MBEDTLS_SELF_TEST)
group-onsemi 0:098463de4c5d 705 #define INC_MUL_COUNT mul_count++;
group-onsemi 0:098463de4c5d 706 #else
group-onsemi 0:098463de4c5d 707 #define INC_MUL_COUNT
group-onsemi 0:098463de4c5d 708 #endif
group-onsemi 0:098463de4c5d 709
group-onsemi 0:098463de4c5d 710 #define MOD_MUL( N ) do { MBEDTLS_MPI_CHK( ecp_modp( &N, grp ) ); INC_MUL_COUNT } \
group-onsemi 0:098463de4c5d 711 while( 0 )
group-onsemi 0:098463de4c5d 712
group-onsemi 0:098463de4c5d 713 /*
group-onsemi 0:098463de4c5d 714 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
group-onsemi 0:098463de4c5d 715 * N->s < 0 is a very fast test, which fails only if N is 0
group-onsemi 0:098463de4c5d 716 */
group-onsemi 0:098463de4c5d 717 #define MOD_SUB( N ) \
group-onsemi 0:098463de4c5d 718 while( N.s < 0 && mbedtls_mpi_cmp_int( &N, 0 ) != 0 ) \
group-onsemi 0:098463de4c5d 719 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &N, &N, &grp->P ) )
group-onsemi 0:098463de4c5d 720
group-onsemi 0:098463de4c5d 721 /*
group-onsemi 0:098463de4c5d 722 * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
group-onsemi 0:098463de4c5d 723 * We known P, N and the result are positive, so sub_abs is correct, and
group-onsemi 0:098463de4c5d 724 * a bit faster.
group-onsemi 0:098463de4c5d 725 */
group-onsemi 0:098463de4c5d 726 #define MOD_ADD( N ) \
group-onsemi 0:098463de4c5d 727 while( mbedtls_mpi_cmp_mpi( &N, &grp->P ) >= 0 ) \
group-onsemi 0:098463de4c5d 728 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &N, &N, &grp->P ) )
group-onsemi 0:098463de4c5d 729
group-onsemi 0:098463de4c5d 730 #if defined(ECP_SHORTWEIERSTRASS)
group-onsemi 0:098463de4c5d 731 /*
group-onsemi 0:098463de4c5d 732 * For curves in short Weierstrass form, we do all the internal operations in
group-onsemi 0:098463de4c5d 733 * Jacobian coordinates.
group-onsemi 0:098463de4c5d 734 *
group-onsemi 0:098463de4c5d 735 * For multiplication, we'll use a comb method with coutermeasueres against
group-onsemi 0:098463de4c5d 736 * SPA, hence timing attacks.
group-onsemi 0:098463de4c5d 737 */
group-onsemi 0:098463de4c5d 738
group-onsemi 0:098463de4c5d 739 /*
group-onsemi 0:098463de4c5d 740 * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
group-onsemi 0:098463de4c5d 741 * Cost: 1N := 1I + 3M + 1S
group-onsemi 0:098463de4c5d 742 */
group-onsemi 0:098463de4c5d 743 static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
group-onsemi 0:098463de4c5d 744 {
group-onsemi 0:098463de4c5d 745 int ret;
group-onsemi 0:098463de4c5d 746 mbedtls_mpi Zi, ZZi;
group-onsemi 0:098463de4c5d 747
group-onsemi 0:098463de4c5d 748 if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
group-onsemi 0:098463de4c5d 749 return( 0 );
group-onsemi 0:098463de4c5d 750
group-onsemi 0:098463de4c5d 751 mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
group-onsemi 0:098463de4c5d 752
group-onsemi 0:098463de4c5d 753 /*
group-onsemi 0:098463de4c5d 754 * X = X / Z^2 mod p
group-onsemi 0:098463de4c5d 755 */
group-onsemi 0:098463de4c5d 756 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
group-onsemi 0:098463de4c5d 757 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
group-onsemi 0:098463de4c5d 758 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ZZi ) ); MOD_MUL( pt->X );
group-onsemi 0:098463de4c5d 759
group-onsemi 0:098463de4c5d 760 /*
group-onsemi 0:098463de4c5d 761 * Y = Y / Z^3 mod p
group-onsemi 0:098463de4c5d 762 */
group-onsemi 0:098463de4c5d 763 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ZZi ) ); MOD_MUL( pt->Y );
group-onsemi 0:098463de4c5d 764 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &Zi ) ); MOD_MUL( pt->Y );
group-onsemi 0:098463de4c5d 765
group-onsemi 0:098463de4c5d 766 /*
group-onsemi 0:098463de4c5d 767 * Z = 1
group-onsemi 0:098463de4c5d 768 */
group-onsemi 0:098463de4c5d 769 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
group-onsemi 0:098463de4c5d 770
group-onsemi 0:098463de4c5d 771 cleanup:
group-onsemi 0:098463de4c5d 772
group-onsemi 0:098463de4c5d 773 mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
group-onsemi 0:098463de4c5d 774
group-onsemi 0:098463de4c5d 775 return( ret );
group-onsemi 0:098463de4c5d 776 }
group-onsemi 0:098463de4c5d 777
group-onsemi 0:098463de4c5d 778 /*
group-onsemi 0:098463de4c5d 779 * Normalize jacobian coordinates of an array of (pointers to) points,
group-onsemi 0:098463de4c5d 780 * using Montgomery's trick to perform only one inversion mod P.
group-onsemi 0:098463de4c5d 781 * (See for example Cohen's "A Course in Computational Algebraic Number
group-onsemi 0:098463de4c5d 782 * Theory", Algorithm 10.3.4.)
group-onsemi 0:098463de4c5d 783 *
group-onsemi 0:098463de4c5d 784 * Warning: fails (returning an error) if one of the points is zero!
group-onsemi 0:098463de4c5d 785 * This should never happen, see choice of w in ecp_mul_comb().
group-onsemi 0:098463de4c5d 786 *
group-onsemi 0:098463de4c5d 787 * Cost: 1N(t) := 1I + (6t - 3)M + 1S
group-onsemi 0:098463de4c5d 788 */
group-onsemi 0:098463de4c5d 789 static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
group-onsemi 0:098463de4c5d 790 mbedtls_ecp_point *T[], size_t t_len )
group-onsemi 0:098463de4c5d 791 {
group-onsemi 0:098463de4c5d 792 int ret;
group-onsemi 0:098463de4c5d 793 size_t i;
group-onsemi 0:098463de4c5d 794 mbedtls_mpi *c, u, Zi, ZZi;
group-onsemi 0:098463de4c5d 795
group-onsemi 0:098463de4c5d 796 if( t_len < 2 )
group-onsemi 0:098463de4c5d 797 return( ecp_normalize_jac( grp, *T ) );
group-onsemi 0:098463de4c5d 798
group-onsemi 0:098463de4c5d 799 if( ( c = mbedtls_calloc( t_len, sizeof( mbedtls_mpi ) ) ) == NULL )
group-onsemi 0:098463de4c5d 800 return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
group-onsemi 0:098463de4c5d 801
group-onsemi 0:098463de4c5d 802 mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
group-onsemi 0:098463de4c5d 803
group-onsemi 0:098463de4c5d 804 /*
group-onsemi 0:098463de4c5d 805 * c[i] = Z_0 * ... * Z_i
group-onsemi 0:098463de4c5d 806 */
group-onsemi 0:098463de4c5d 807 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
group-onsemi 0:098463de4c5d 808 for( i = 1; i < t_len; i++ )
group-onsemi 0:098463de4c5d 809 {
group-onsemi 0:098463de4c5d 810 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &c[i], &c[i-1], &T[i]->Z ) );
group-onsemi 0:098463de4c5d 811 MOD_MUL( c[i] );
group-onsemi 0:098463de4c5d 812 }
group-onsemi 0:098463de4c5d 813
group-onsemi 0:098463de4c5d 814 /*
group-onsemi 0:098463de4c5d 815 * u = 1 / (Z_0 * ... * Z_n) mod P
group-onsemi 0:098463de4c5d 816 */
group-onsemi 0:098463de4c5d 817 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[t_len-1], &grp->P ) );
group-onsemi 0:098463de4c5d 818
group-onsemi 0:098463de4c5d 819 for( i = t_len - 1; ; i-- )
group-onsemi 0:098463de4c5d 820 {
group-onsemi 0:098463de4c5d 821 /*
group-onsemi 0:098463de4c5d 822 * Zi = 1 / Z_i mod p
group-onsemi 0:098463de4c5d 823 * u = 1 / (Z_0 * ... * Z_i) mod P
group-onsemi 0:098463de4c5d 824 */
group-onsemi 0:098463de4c5d 825 if( i == 0 ) {
group-onsemi 0:098463de4c5d 826 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
group-onsemi 0:098463de4c5d 827 }
group-onsemi 0:098463de4c5d 828 else
group-onsemi 0:098463de4c5d 829 {
group-onsemi 0:098463de4c5d 830 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Zi, &u, &c[i-1] ) ); MOD_MUL( Zi );
group-onsemi 0:098463de4c5d 831 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u, &u, &T[i]->Z ) ); MOD_MUL( u );
group-onsemi 0:098463de4c5d 832 }
group-onsemi 0:098463de4c5d 833
group-onsemi 0:098463de4c5d 834 /*
group-onsemi 0:098463de4c5d 835 * proceed as in normalize()
group-onsemi 0:098463de4c5d 836 */
group-onsemi 0:098463de4c5d 837 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
group-onsemi 0:098463de4c5d 838 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->X, &T[i]->X, &ZZi ) ); MOD_MUL( T[i]->X );
group-onsemi 0:098463de4c5d 839 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &ZZi ) ); MOD_MUL( T[i]->Y );
group-onsemi 0:098463de4c5d 840 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &Zi ) ); MOD_MUL( T[i]->Y );
group-onsemi 0:098463de4c5d 841
group-onsemi 0:098463de4c5d 842 /*
group-onsemi 0:098463de4c5d 843 * Post-precessing: reclaim some memory by shrinking coordinates
group-onsemi 0:098463de4c5d 844 * - not storing Z (always 1)
group-onsemi 0:098463de4c5d 845 * - shrinking other coordinates, but still keeping the same number of
group-onsemi 0:098463de4c5d 846 * limbs as P, as otherwise it will too likely be regrown too fast.
group-onsemi 0:098463de4c5d 847 */
group-onsemi 0:098463de4c5d 848 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
group-onsemi 0:098463de4c5d 849 MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
group-onsemi 0:098463de4c5d 850 mbedtls_mpi_free( &T[i]->Z );
group-onsemi 0:098463de4c5d 851
group-onsemi 0:098463de4c5d 852 if( i == 0 )
group-onsemi 0:098463de4c5d 853 break;
group-onsemi 0:098463de4c5d 854 }
group-onsemi 0:098463de4c5d 855
group-onsemi 0:098463de4c5d 856 cleanup:
group-onsemi 0:098463de4c5d 857
group-onsemi 0:098463de4c5d 858 mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
group-onsemi 0:098463de4c5d 859 for( i = 0; i < t_len; i++ )
group-onsemi 0:098463de4c5d 860 mbedtls_mpi_free( &c[i] );
group-onsemi 0:098463de4c5d 861 mbedtls_free( c );
group-onsemi 0:098463de4c5d 862
group-onsemi 0:098463de4c5d 863 return( ret );
group-onsemi 0:098463de4c5d 864 }
group-onsemi 0:098463de4c5d 865
group-onsemi 0:098463de4c5d 866 /*
group-onsemi 0:098463de4c5d 867 * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
group-onsemi 0:098463de4c5d 868 * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
group-onsemi 0:098463de4c5d 869 */
group-onsemi 0:098463de4c5d 870 static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
group-onsemi 0:098463de4c5d 871 mbedtls_ecp_point *Q,
group-onsemi 0:098463de4c5d 872 unsigned char inv )
group-onsemi 0:098463de4c5d 873 {
group-onsemi 0:098463de4c5d 874 int ret;
group-onsemi 0:098463de4c5d 875 unsigned char nonzero;
group-onsemi 0:098463de4c5d 876 mbedtls_mpi mQY;
group-onsemi 0:098463de4c5d 877
group-onsemi 0:098463de4c5d 878 mbedtls_mpi_init( &mQY );
group-onsemi 0:098463de4c5d 879
group-onsemi 0:098463de4c5d 880 /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
group-onsemi 0:098463de4c5d 881 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
group-onsemi 0:098463de4c5d 882 nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
group-onsemi 0:098463de4c5d 883 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
group-onsemi 0:098463de4c5d 884
group-onsemi 0:098463de4c5d 885 cleanup:
group-onsemi 0:098463de4c5d 886 mbedtls_mpi_free( &mQY );
group-onsemi 0:098463de4c5d 887
group-onsemi 0:098463de4c5d 888 return( ret );
group-onsemi 0:098463de4c5d 889 }
group-onsemi 0:098463de4c5d 890
group-onsemi 0:098463de4c5d 891 /*
group-onsemi 0:098463de4c5d 892 * Point doubling R = 2 P, Jacobian coordinates
group-onsemi 0:098463de4c5d 893 *
group-onsemi 0:098463de4c5d 894 * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
group-onsemi 0:098463de4c5d 895 *
group-onsemi 0:098463de4c5d 896 * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
group-onsemi 0:098463de4c5d 897 * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
group-onsemi 0:098463de4c5d 898 *
group-onsemi 0:098463de4c5d 899 * Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
group-onsemi 0:098463de4c5d 900 *
group-onsemi 0:098463de4c5d 901 * Cost: 1D := 3M + 4S (A == 0)
group-onsemi 0:098463de4c5d 902 * 4M + 4S (A == -3)
group-onsemi 0:098463de4c5d 903 * 3M + 6S + 1a otherwise
group-onsemi 0:098463de4c5d 904 */
group-onsemi 0:098463de4c5d 905 static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
group-onsemi 0:098463de4c5d 906 const mbedtls_ecp_point *P )
group-onsemi 0:098463de4c5d 907 {
group-onsemi 0:098463de4c5d 908 int ret;
group-onsemi 0:098463de4c5d 909 mbedtls_mpi M, S, T, U;
group-onsemi 0:098463de4c5d 910
group-onsemi 0:098463de4c5d 911 #if defined(MBEDTLS_SELF_TEST)
group-onsemi 0:098463de4c5d 912 dbl_count++;
group-onsemi 0:098463de4c5d 913 #endif
group-onsemi 0:098463de4c5d 914
group-onsemi 0:098463de4c5d 915 mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
group-onsemi 0:098463de4c5d 916
group-onsemi 0:098463de4c5d 917 /* Special case for A = -3 */
group-onsemi 0:098463de4c5d 918 if( grp->A.p == NULL )
group-onsemi 0:098463de4c5d 919 {
group-onsemi 0:098463de4c5d 920 /* M = 3(X + Z^2)(X - Z^2) */
group-onsemi 0:098463de4c5d 921 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
group-onsemi 0:098463de4c5d 922 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &P->X, &S ) ); MOD_ADD( T );
group-onsemi 0:098463de4c5d 923 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U, &P->X, &S ) ); MOD_SUB( U );
group-onsemi 0:098463de4c5d 924 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &U ) ); MOD_MUL( S );
group-onsemi 0:098463de4c5d 925 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
group-onsemi 0:098463de4c5d 926 }
group-onsemi 0:098463de4c5d 927 else
group-onsemi 0:098463de4c5d 928 {
group-onsemi 0:098463de4c5d 929 /* M = 3.X^2 */
group-onsemi 0:098463de4c5d 930 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &P->X ) ); MOD_MUL( S );
group-onsemi 0:098463de4c5d 931 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
group-onsemi 0:098463de4c5d 932
group-onsemi 0:098463de4c5d 933 /* Optimize away for "koblitz" curves with A = 0 */
group-onsemi 0:098463de4c5d 934 if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
group-onsemi 0:098463de4c5d 935 {
group-onsemi 0:098463de4c5d 936 /* M += A.Z^4 */
group-onsemi 0:098463de4c5d 937 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
group-onsemi 0:098463de4c5d 938 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &S, &S ) ); MOD_MUL( T );
group-onsemi 0:098463de4c5d 939 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &grp->A ) ); MOD_MUL( S );
group-onsemi 0:098463de4c5d 940 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &S ) ); MOD_ADD( M );
group-onsemi 0:098463de4c5d 941 }
group-onsemi 0:098463de4c5d 942 }
group-onsemi 0:098463de4c5d 943
group-onsemi 0:098463de4c5d 944 /* S = 4.X.Y^2 */
group-onsemi 0:098463de4c5d 945 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &P->Y, &P->Y ) ); MOD_MUL( T );
group-onsemi 0:098463de4c5d 946 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T, 1 ) ); MOD_ADD( T );
group-onsemi 0:098463de4c5d 947 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &T ) ); MOD_MUL( S );
group-onsemi 0:098463de4c5d 948 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &S, 1 ) ); MOD_ADD( S );
group-onsemi 0:098463de4c5d 949
group-onsemi 0:098463de4c5d 950 /* U = 8.Y^4 */
group-onsemi 0:098463de4c5d 951 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &T, &T ) ); MOD_MUL( U );
group-onsemi 0:098463de4c5d 952 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
group-onsemi 0:098463de4c5d 953
group-onsemi 0:098463de4c5d 954 /* T = M^2 - 2.S */
group-onsemi 0:098463de4c5d 955 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &M, &M ) ); MOD_MUL( T );
group-onsemi 0:098463de4c5d 956 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
group-onsemi 0:098463de4c5d 957 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
group-onsemi 0:098463de4c5d 958
group-onsemi 0:098463de4c5d 959 /* S = M(S - T) - U */
group-onsemi 0:098463de4c5d 960 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &T ) ); MOD_SUB( S );
group-onsemi 0:098463de4c5d 961 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &S, &M ) ); MOD_MUL( S );
group-onsemi 0:098463de4c5d 962 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &U ) ); MOD_SUB( S );
group-onsemi 0:098463de4c5d 963
group-onsemi 0:098463de4c5d 964 /* U = 2.Y.Z */
group-onsemi 0:098463de4c5d 965 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &P->Y, &P->Z ) ); MOD_MUL( U );
group-onsemi 0:098463de4c5d 966 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
group-onsemi 0:098463de4c5d 967
group-onsemi 0:098463de4c5d 968 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
group-onsemi 0:098463de4c5d 969 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
group-onsemi 0:098463de4c5d 970 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
group-onsemi 0:098463de4c5d 971
group-onsemi 0:098463de4c5d 972 cleanup:
group-onsemi 0:098463de4c5d 973 mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
group-onsemi 0:098463de4c5d 974
group-onsemi 0:098463de4c5d 975 return( ret );
group-onsemi 0:098463de4c5d 976 }
group-onsemi 0:098463de4c5d 977
group-onsemi 0:098463de4c5d 978 /*
group-onsemi 0:098463de4c5d 979 * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
group-onsemi 0:098463de4c5d 980 *
group-onsemi 0:098463de4c5d 981 * The coordinates of Q must be normalized (= affine),
group-onsemi 0:098463de4c5d 982 * but those of P don't need to. R is not normalized.
group-onsemi 0:098463de4c5d 983 *
group-onsemi 0:098463de4c5d 984 * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
group-onsemi 0:098463de4c5d 985 * None of these cases can happen as intermediate step in ecp_mul_comb():
group-onsemi 0:098463de4c5d 986 * - at each step, P, Q and R are multiples of the base point, the factor
group-onsemi 0:098463de4c5d 987 * being less than its order, so none of them is zero;
group-onsemi 0:098463de4c5d 988 * - Q is an odd multiple of the base point, P an even multiple,
group-onsemi 0:098463de4c5d 989 * due to the choice of precomputed points in the modified comb method.
group-onsemi 0:098463de4c5d 990 * So branches for these cases do not leak secret information.
group-onsemi 0:098463de4c5d 991 *
group-onsemi 0:098463de4c5d 992 * We accept Q->Z being unset (saving memory in tables) as meaning 1.
group-onsemi 0:098463de4c5d 993 *
group-onsemi 0:098463de4c5d 994 * Cost: 1A := 8M + 3S
group-onsemi 0:098463de4c5d 995 */
group-onsemi 0:098463de4c5d 996 static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
group-onsemi 0:098463de4c5d 997 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
group-onsemi 0:098463de4c5d 998 {
group-onsemi 0:098463de4c5d 999 int ret;
group-onsemi 0:098463de4c5d 1000 mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
group-onsemi 0:098463de4c5d 1001
group-onsemi 0:098463de4c5d 1002 #if defined(MBEDTLS_SELF_TEST)
group-onsemi 0:098463de4c5d 1003 add_count++;
group-onsemi 0:098463de4c5d 1004 #endif
group-onsemi 0:098463de4c5d 1005
group-onsemi 0:098463de4c5d 1006 /*
group-onsemi 0:098463de4c5d 1007 * Trivial cases: P == 0 or Q == 0 (case 1)
group-onsemi 0:098463de4c5d 1008 */
group-onsemi 0:098463de4c5d 1009 if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
group-onsemi 0:098463de4c5d 1010 return( mbedtls_ecp_copy( R, Q ) );
group-onsemi 0:098463de4c5d 1011
group-onsemi 0:098463de4c5d 1012 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
group-onsemi 0:098463de4c5d 1013 return( mbedtls_ecp_copy( R, P ) );
group-onsemi 0:098463de4c5d 1014
group-onsemi 0:098463de4c5d 1015 /*
group-onsemi 0:098463de4c5d 1016 * Make sure Q coordinates are normalized
group-onsemi 0:098463de4c5d 1017 */
group-onsemi 0:098463de4c5d 1018 if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
group-onsemi 0:098463de4c5d 1019 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 1020
group-onsemi 0:098463de4c5d 1021 mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
group-onsemi 0:098463de4c5d 1022 mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
group-onsemi 0:098463de4c5d 1023
group-onsemi 0:098463de4c5d 1024 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &P->Z, &P->Z ) ); MOD_MUL( T1 );
group-onsemi 0:098463de4c5d 1025 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T1, &P->Z ) ); MOD_MUL( T2 );
group-onsemi 0:098463de4c5d 1026 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T1, &Q->X ) ); MOD_MUL( T1 );
group-onsemi 0:098463de4c5d 1027 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T2, &Q->Y ) ); MOD_MUL( T2 );
group-onsemi 0:098463de4c5d 1028 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T1, &T1, &P->X ) ); MOD_SUB( T1 );
group-onsemi 0:098463de4c5d 1029 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T2, &T2, &P->Y ) ); MOD_SUB( T2 );
group-onsemi 0:098463de4c5d 1030
group-onsemi 0:098463de4c5d 1031 /* Special cases (2) and (3) */
group-onsemi 0:098463de4c5d 1032 if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
group-onsemi 0:098463de4c5d 1033 {
group-onsemi 0:098463de4c5d 1034 if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
group-onsemi 0:098463de4c5d 1035 {
group-onsemi 0:098463de4c5d 1036 ret = ecp_double_jac( grp, R, P );
group-onsemi 0:098463de4c5d 1037 goto cleanup;
group-onsemi 0:098463de4c5d 1038 }
group-onsemi 0:098463de4c5d 1039 else
group-onsemi 0:098463de4c5d 1040 {
group-onsemi 0:098463de4c5d 1041 ret = mbedtls_ecp_set_zero( R );
group-onsemi 0:098463de4c5d 1042 goto cleanup;
group-onsemi 0:098463de4c5d 1043 }
group-onsemi 0:098463de4c5d 1044 }
group-onsemi 0:098463de4c5d 1045
group-onsemi 0:098463de4c5d 1046 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Z, &P->Z, &T1 ) ); MOD_MUL( Z );
group-onsemi 0:098463de4c5d 1047 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T1, &T1 ) ); MOD_MUL( T3 );
group-onsemi 0:098463de4c5d 1048 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T3, &T1 ) ); MOD_MUL( T4 );
group-onsemi 0:098463de4c5d 1049 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &P->X ) ); MOD_MUL( T3 );
group-onsemi 0:098463de4c5d 1050 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T3, 2 ) ); MOD_ADD( T1 );
group-onsemi 0:098463de4c5d 1051 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &T2, &T2 ) ); MOD_MUL( X );
group-onsemi 0:098463de4c5d 1052 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) ); MOD_SUB( X );
group-onsemi 0:098463de4c5d 1053 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T4 ) ); MOD_SUB( X );
group-onsemi 0:098463de4c5d 1054 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T3, &T3, &X ) ); MOD_SUB( T3 );
group-onsemi 0:098463de4c5d 1055 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &T2 ) ); MOD_MUL( T3 );
group-onsemi 0:098463de4c5d 1056 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T4, &P->Y ) ); MOD_MUL( T4 );
group-onsemi 0:098463de4c5d 1057 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &Y, &T3, &T4 ) ); MOD_SUB( Y );
group-onsemi 0:098463de4c5d 1058
group-onsemi 0:098463de4c5d 1059 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
group-onsemi 0:098463de4c5d 1060 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
group-onsemi 0:098463de4c5d 1061 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
group-onsemi 0:098463de4c5d 1062
group-onsemi 0:098463de4c5d 1063 cleanup:
group-onsemi 0:098463de4c5d 1064
group-onsemi 0:098463de4c5d 1065 mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
group-onsemi 0:098463de4c5d 1066 mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
group-onsemi 0:098463de4c5d 1067
group-onsemi 0:098463de4c5d 1068 return( ret );
group-onsemi 0:098463de4c5d 1069 }
group-onsemi 0:098463de4c5d 1070
group-onsemi 0:098463de4c5d 1071 /*
group-onsemi 0:098463de4c5d 1072 * Randomize jacobian coordinates:
group-onsemi 0:098463de4c5d 1073 * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
group-onsemi 0:098463de4c5d 1074 * This is sort of the reverse operation of ecp_normalize_jac().
group-onsemi 0:098463de4c5d 1075 *
group-onsemi 0:098463de4c5d 1076 * This countermeasure was first suggested in [2].
group-onsemi 0:098463de4c5d 1077 */
group-onsemi 0:098463de4c5d 1078 static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
group-onsemi 0:098463de4c5d 1079 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
group-onsemi 0:098463de4c5d 1080 {
group-onsemi 0:098463de4c5d 1081 int ret;
group-onsemi 0:098463de4c5d 1082 mbedtls_mpi l, ll;
group-onsemi 0:098463de4c5d 1083 size_t p_size = ( grp->pbits + 7 ) / 8;
group-onsemi 0:098463de4c5d 1084 int count = 0;
group-onsemi 0:098463de4c5d 1085
group-onsemi 0:098463de4c5d 1086 mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
group-onsemi 0:098463de4c5d 1087
group-onsemi 0:098463de4c5d 1088 /* Generate l such that 1 < l < p */
group-onsemi 0:098463de4c5d 1089 do
group-onsemi 0:098463de4c5d 1090 {
group-onsemi 0:098463de4c5d 1091 mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng );
group-onsemi 0:098463de4c5d 1092
group-onsemi 0:098463de4c5d 1093 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
group-onsemi 0:098463de4c5d 1094 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
group-onsemi 0:098463de4c5d 1095
group-onsemi 0:098463de4c5d 1096 if( count++ > 10 )
group-onsemi 0:098463de4c5d 1097 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
group-onsemi 0:098463de4c5d 1098 }
group-onsemi 0:098463de4c5d 1099 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
group-onsemi 0:098463de4c5d 1100
group-onsemi 0:098463de4c5d 1101 /* Z = l * Z */
group-onsemi 0:098463de4c5d 1102 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Z, &pt->Z, &l ) ); MOD_MUL( pt->Z );
group-onsemi 0:098463de4c5d 1103
group-onsemi 0:098463de4c5d 1104 /* X = l^2 * X */
group-onsemi 0:098463de4c5d 1105 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &l, &l ) ); MOD_MUL( ll );
group-onsemi 0:098463de4c5d 1106 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ll ) ); MOD_MUL( pt->X );
group-onsemi 0:098463de4c5d 1107
group-onsemi 0:098463de4c5d 1108 /* Y = l^3 * Y */
group-onsemi 0:098463de4c5d 1109 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &ll, &l ) ); MOD_MUL( ll );
group-onsemi 0:098463de4c5d 1110 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ll ) ); MOD_MUL( pt->Y );
group-onsemi 0:098463de4c5d 1111
group-onsemi 0:098463de4c5d 1112 cleanup:
group-onsemi 0:098463de4c5d 1113 mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
group-onsemi 0:098463de4c5d 1114
group-onsemi 0:098463de4c5d 1115 return( ret );
group-onsemi 0:098463de4c5d 1116 }
group-onsemi 0:098463de4c5d 1117
group-onsemi 0:098463de4c5d 1118 /*
group-onsemi 0:098463de4c5d 1119 * Check and define parameters used by the comb method (see below for details)
group-onsemi 0:098463de4c5d 1120 */
group-onsemi 0:098463de4c5d 1121 #if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
group-onsemi 0:098463de4c5d 1122 #error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
group-onsemi 0:098463de4c5d 1123 #endif
group-onsemi 0:098463de4c5d 1124
group-onsemi 0:098463de4c5d 1125 /* d = ceil( n / w ) */
group-onsemi 0:098463de4c5d 1126 #define COMB_MAX_D ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2
group-onsemi 0:098463de4c5d 1127
group-onsemi 0:098463de4c5d 1128 /* number of precomputed points */
group-onsemi 0:098463de4c5d 1129 #define COMB_MAX_PRE ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
group-onsemi 0:098463de4c5d 1130
group-onsemi 0:098463de4c5d 1131 /*
group-onsemi 0:098463de4c5d 1132 * Compute the representation of m that will be used with our comb method.
group-onsemi 0:098463de4c5d 1133 *
group-onsemi 0:098463de4c5d 1134 * The basic comb method is described in GECC 3.44 for example. We use a
group-onsemi 0:098463de4c5d 1135 * modified version that provides resistance to SPA by avoiding zero
group-onsemi 0:098463de4c5d 1136 * digits in the representation as in [3]. We modify the method further by
group-onsemi 0:098463de4c5d 1137 * requiring that all K_i be odd, which has the small cost that our
group-onsemi 0:098463de4c5d 1138 * representation uses one more K_i, due to carries.
group-onsemi 0:098463de4c5d 1139 *
group-onsemi 0:098463de4c5d 1140 * Also, for the sake of compactness, only the seven low-order bits of x[i]
group-onsemi 0:098463de4c5d 1141 * are used to represent K_i, and the msb of x[i] encodes the the sign (s_i in
group-onsemi 0:098463de4c5d 1142 * the paper): it is set if and only if if s_i == -1;
group-onsemi 0:098463de4c5d 1143 *
group-onsemi 0:098463de4c5d 1144 * Calling conventions:
group-onsemi 0:098463de4c5d 1145 * - x is an array of size d + 1
group-onsemi 0:098463de4c5d 1146 * - w is the size, ie number of teeth, of the comb, and must be between
group-onsemi 0:098463de4c5d 1147 * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
group-onsemi 0:098463de4c5d 1148 * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
group-onsemi 0:098463de4c5d 1149 * (the result will be incorrect if these assumptions are not satisfied)
group-onsemi 0:098463de4c5d 1150 */
group-onsemi 0:098463de4c5d 1151 static void ecp_comb_fixed( unsigned char x[], size_t d,
group-onsemi 0:098463de4c5d 1152 unsigned char w, const mbedtls_mpi *m )
group-onsemi 0:098463de4c5d 1153 {
group-onsemi 0:098463de4c5d 1154 size_t i, j;
group-onsemi 0:098463de4c5d 1155 unsigned char c, cc, adjust;
group-onsemi 0:098463de4c5d 1156
group-onsemi 0:098463de4c5d 1157 memset( x, 0, d+1 );
group-onsemi 0:098463de4c5d 1158
group-onsemi 0:098463de4c5d 1159 /* First get the classical comb values (except for x_d = 0) */
group-onsemi 0:098463de4c5d 1160 for( i = 0; i < d; i++ )
group-onsemi 0:098463de4c5d 1161 for( j = 0; j < w; j++ )
group-onsemi 0:098463de4c5d 1162 x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j;
group-onsemi 0:098463de4c5d 1163
group-onsemi 0:098463de4c5d 1164 /* Now make sure x_1 .. x_d are odd */
group-onsemi 0:098463de4c5d 1165 c = 0;
group-onsemi 0:098463de4c5d 1166 for( i = 1; i <= d; i++ )
group-onsemi 0:098463de4c5d 1167 {
group-onsemi 0:098463de4c5d 1168 /* Add carry and update it */
group-onsemi 0:098463de4c5d 1169 cc = x[i] & c;
group-onsemi 0:098463de4c5d 1170 x[i] = x[i] ^ c;
group-onsemi 0:098463de4c5d 1171 c = cc;
group-onsemi 0:098463de4c5d 1172
group-onsemi 0:098463de4c5d 1173 /* Adjust if needed, avoiding branches */
group-onsemi 0:098463de4c5d 1174 adjust = 1 - ( x[i] & 0x01 );
group-onsemi 0:098463de4c5d 1175 c |= x[i] & ( x[i-1] * adjust );
group-onsemi 0:098463de4c5d 1176 x[i] = x[i] ^ ( x[i-1] * adjust );
group-onsemi 0:098463de4c5d 1177 x[i-1] |= adjust << 7;
group-onsemi 0:098463de4c5d 1178 }
group-onsemi 0:098463de4c5d 1179 }
group-onsemi 0:098463de4c5d 1180
group-onsemi 0:098463de4c5d 1181 /*
group-onsemi 0:098463de4c5d 1182 * Precompute points for the comb method
group-onsemi 0:098463de4c5d 1183 *
group-onsemi 0:098463de4c5d 1184 * If i = i_{w-1} ... i_1 is the binary representation of i, then
group-onsemi 0:098463de4c5d 1185 * T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P
group-onsemi 0:098463de4c5d 1186 *
group-onsemi 0:098463de4c5d 1187 * T must be able to hold 2^{w - 1} elements
group-onsemi 0:098463de4c5d 1188 *
group-onsemi 0:098463de4c5d 1189 * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
group-onsemi 0:098463de4c5d 1190 */
group-onsemi 0:098463de4c5d 1191 static int ecp_precompute_comb( const mbedtls_ecp_group *grp,
group-onsemi 0:098463de4c5d 1192 mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
group-onsemi 0:098463de4c5d 1193 unsigned char w, size_t d )
group-onsemi 0:098463de4c5d 1194 {
group-onsemi 0:098463de4c5d 1195 int ret;
group-onsemi 0:098463de4c5d 1196 unsigned char i, k;
group-onsemi 0:098463de4c5d 1197 size_t j;
group-onsemi 0:098463de4c5d 1198 mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
group-onsemi 0:098463de4c5d 1199
group-onsemi 0:098463de4c5d 1200 /*
group-onsemi 0:098463de4c5d 1201 * Set T[0] = P and
group-onsemi 0:098463de4c5d 1202 * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
group-onsemi 0:098463de4c5d 1203 */
group-onsemi 0:098463de4c5d 1204 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
group-onsemi 0:098463de4c5d 1205
group-onsemi 0:098463de4c5d 1206 k = 0;
group-onsemi 0:098463de4c5d 1207 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
group-onsemi 0:098463de4c5d 1208 {
group-onsemi 0:098463de4c5d 1209 cur = T + i;
group-onsemi 0:098463de4c5d 1210 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
group-onsemi 0:098463de4c5d 1211 for( j = 0; j < d; j++ )
group-onsemi 0:098463de4c5d 1212 MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
group-onsemi 0:098463de4c5d 1213
group-onsemi 0:098463de4c5d 1214 TT[k++] = cur;
group-onsemi 0:098463de4c5d 1215 }
group-onsemi 0:098463de4c5d 1216
group-onsemi 0:098463de4c5d 1217 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
group-onsemi 0:098463de4c5d 1218
group-onsemi 0:098463de4c5d 1219 /*
group-onsemi 0:098463de4c5d 1220 * Compute the remaining ones using the minimal number of additions
group-onsemi 0:098463de4c5d 1221 * Be careful to update T[2^l] only after using it!
group-onsemi 0:098463de4c5d 1222 */
group-onsemi 0:098463de4c5d 1223 k = 0;
group-onsemi 0:098463de4c5d 1224 for( i = 1; i < ( 1U << ( w - 1 ) ); i <<= 1 )
group-onsemi 0:098463de4c5d 1225 {
group-onsemi 0:098463de4c5d 1226 j = i;
group-onsemi 0:098463de4c5d 1227 while( j-- )
group-onsemi 0:098463de4c5d 1228 {
group-onsemi 0:098463de4c5d 1229 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
group-onsemi 0:098463de4c5d 1230 TT[k++] = &T[i + j];
group-onsemi 0:098463de4c5d 1231 }
group-onsemi 0:098463de4c5d 1232 }
group-onsemi 0:098463de4c5d 1233
group-onsemi 0:098463de4c5d 1234 MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, k ) );
group-onsemi 0:098463de4c5d 1235
group-onsemi 0:098463de4c5d 1236 cleanup:
group-onsemi 0:098463de4c5d 1237 return( ret );
group-onsemi 0:098463de4c5d 1238 }
group-onsemi 0:098463de4c5d 1239
group-onsemi 0:098463de4c5d 1240 /*
group-onsemi 0:098463de4c5d 1241 * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
group-onsemi 0:098463de4c5d 1242 */
group-onsemi 0:098463de4c5d 1243 static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
group-onsemi 0:098463de4c5d 1244 const mbedtls_ecp_point T[], unsigned char t_len,
group-onsemi 0:098463de4c5d 1245 unsigned char i )
group-onsemi 0:098463de4c5d 1246 {
group-onsemi 0:098463de4c5d 1247 int ret;
group-onsemi 0:098463de4c5d 1248 unsigned char ii, j;
group-onsemi 0:098463de4c5d 1249
group-onsemi 0:098463de4c5d 1250 /* Ignore the "sign" bit and scale down */
group-onsemi 0:098463de4c5d 1251 ii = ( i & 0x7Fu ) >> 1;
group-onsemi 0:098463de4c5d 1252
group-onsemi 0:098463de4c5d 1253 /* Read the whole table to thwart cache-based timing attacks */
group-onsemi 0:098463de4c5d 1254 for( j = 0; j < t_len; j++ )
group-onsemi 0:098463de4c5d 1255 {
group-onsemi 0:098463de4c5d 1256 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
group-onsemi 0:098463de4c5d 1257 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
group-onsemi 0:098463de4c5d 1258 }
group-onsemi 0:098463de4c5d 1259
group-onsemi 0:098463de4c5d 1260 /* Safely invert result if i is "negative" */
group-onsemi 0:098463de4c5d 1261 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
group-onsemi 0:098463de4c5d 1262
group-onsemi 0:098463de4c5d 1263 cleanup:
group-onsemi 0:098463de4c5d 1264 return( ret );
group-onsemi 0:098463de4c5d 1265 }
group-onsemi 0:098463de4c5d 1266
group-onsemi 0:098463de4c5d 1267 /*
group-onsemi 0:098463de4c5d 1268 * Core multiplication algorithm for the (modified) comb method.
group-onsemi 0:098463de4c5d 1269 * This part is actually common with the basic comb method (GECC 3.44)
group-onsemi 0:098463de4c5d 1270 *
group-onsemi 0:098463de4c5d 1271 * Cost: d A + d D + 1 R
group-onsemi 0:098463de4c5d 1272 */
group-onsemi 0:098463de4c5d 1273 static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
group-onsemi 0:098463de4c5d 1274 const mbedtls_ecp_point T[], unsigned char t_len,
group-onsemi 0:098463de4c5d 1275 const unsigned char x[], size_t d,
group-onsemi 0:098463de4c5d 1276 int (*f_rng)(void *, unsigned char *, size_t),
group-onsemi 0:098463de4c5d 1277 void *p_rng )
group-onsemi 0:098463de4c5d 1278 {
group-onsemi 0:098463de4c5d 1279 int ret;
group-onsemi 0:098463de4c5d 1280 mbedtls_ecp_point Txi;
group-onsemi 0:098463de4c5d 1281 size_t i;
group-onsemi 0:098463de4c5d 1282
group-onsemi 0:098463de4c5d 1283 mbedtls_ecp_point_init( &Txi );
group-onsemi 0:098463de4c5d 1284
group-onsemi 0:098463de4c5d 1285 /* Start with a non-zero point and randomize its coordinates */
group-onsemi 0:098463de4c5d 1286 i = d;
group-onsemi 0:098463de4c5d 1287 MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, t_len, x[i] ) );
group-onsemi 0:098463de4c5d 1288 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
group-onsemi 0:098463de4c5d 1289 if( f_rng != 0 )
group-onsemi 0:098463de4c5d 1290 MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
group-onsemi 0:098463de4c5d 1291
group-onsemi 0:098463de4c5d 1292 while( i-- != 0 )
group-onsemi 0:098463de4c5d 1293 {
group-onsemi 0:098463de4c5d 1294 MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
group-onsemi 0:098463de4c5d 1295 MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, t_len, x[i] ) );
group-onsemi 0:098463de4c5d 1296 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
group-onsemi 0:098463de4c5d 1297 }
group-onsemi 0:098463de4c5d 1298
group-onsemi 0:098463de4c5d 1299 cleanup:
group-onsemi 0:098463de4c5d 1300 mbedtls_ecp_point_free( &Txi );
group-onsemi 0:098463de4c5d 1301
group-onsemi 0:098463de4c5d 1302 return( ret );
group-onsemi 0:098463de4c5d 1303 }
group-onsemi 0:098463de4c5d 1304
group-onsemi 0:098463de4c5d 1305 /*
group-onsemi 0:098463de4c5d 1306 * Multiplication using the comb method,
group-onsemi 0:098463de4c5d 1307 * for curves in short Weierstrass form
group-onsemi 0:098463de4c5d 1308 */
group-onsemi 0:098463de4c5d 1309 static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
group-onsemi 0:098463de4c5d 1310 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
group-onsemi 0:098463de4c5d 1311 int (*f_rng)(void *, unsigned char *, size_t),
group-onsemi 0:098463de4c5d 1312 void *p_rng )
group-onsemi 0:098463de4c5d 1313 {
group-onsemi 0:098463de4c5d 1314 int ret;
group-onsemi 0:098463de4c5d 1315 unsigned char w, m_is_odd, p_eq_g, pre_len, i;
group-onsemi 0:098463de4c5d 1316 size_t d;
group-onsemi 0:098463de4c5d 1317 unsigned char k[COMB_MAX_D + 1];
group-onsemi 0:098463de4c5d 1318 mbedtls_ecp_point *T;
group-onsemi 0:098463de4c5d 1319 mbedtls_mpi M, mm;
group-onsemi 0:098463de4c5d 1320
group-onsemi 0:098463de4c5d 1321 mbedtls_mpi_init( &M );
group-onsemi 0:098463de4c5d 1322 mbedtls_mpi_init( &mm );
group-onsemi 0:098463de4c5d 1323
group-onsemi 0:098463de4c5d 1324 /* we need N to be odd to trnaform m in an odd number, check now */
group-onsemi 0:098463de4c5d 1325 if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 )
group-onsemi 0:098463de4c5d 1326 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 1327
group-onsemi 0:098463de4c5d 1328 /*
group-onsemi 0:098463de4c5d 1329 * Minimize the number of multiplications, that is minimize
group-onsemi 0:098463de4c5d 1330 * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
group-onsemi 0:098463de4c5d 1331 * (see costs of the various parts, with 1S = 1M)
group-onsemi 0:098463de4c5d 1332 */
group-onsemi 0:098463de4c5d 1333 w = grp->nbits >= 384 ? 5 : 4;
group-onsemi 0:098463de4c5d 1334
group-onsemi 0:098463de4c5d 1335 /*
group-onsemi 0:098463de4c5d 1336 * If P == G, pre-compute a bit more, since this may be re-used later.
group-onsemi 0:098463de4c5d 1337 * Just adding one avoids upping the cost of the first mul too much,
group-onsemi 0:098463de4c5d 1338 * and the memory cost too.
group-onsemi 0:098463de4c5d 1339 */
group-onsemi 0:098463de4c5d 1340 #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
group-onsemi 0:098463de4c5d 1341 p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
group-onsemi 0:098463de4c5d 1342 mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
group-onsemi 0:098463de4c5d 1343 if( p_eq_g )
group-onsemi 0:098463de4c5d 1344 w++;
group-onsemi 0:098463de4c5d 1345 #else
group-onsemi 0:098463de4c5d 1346 p_eq_g = 0;
group-onsemi 0:098463de4c5d 1347 #endif
group-onsemi 0:098463de4c5d 1348
group-onsemi 0:098463de4c5d 1349 /*
group-onsemi 0:098463de4c5d 1350 * Make sure w is within bounds.
group-onsemi 0:098463de4c5d 1351 * (The last test is useful only for very small curves in the test suite.)
group-onsemi 0:098463de4c5d 1352 */
group-onsemi 0:098463de4c5d 1353 if( w > MBEDTLS_ECP_WINDOW_SIZE )
group-onsemi 0:098463de4c5d 1354 w = MBEDTLS_ECP_WINDOW_SIZE;
group-onsemi 0:098463de4c5d 1355 if( w >= grp->nbits )
group-onsemi 0:098463de4c5d 1356 w = 2;
group-onsemi 0:098463de4c5d 1357
group-onsemi 0:098463de4c5d 1358 /* Other sizes that depend on w */
group-onsemi 0:098463de4c5d 1359 pre_len = 1U << ( w - 1 );
group-onsemi 0:098463de4c5d 1360 d = ( grp->nbits + w - 1 ) / w;
group-onsemi 0:098463de4c5d 1361
group-onsemi 0:098463de4c5d 1362 /*
group-onsemi 0:098463de4c5d 1363 * Prepare precomputed points: if P == G we want to
group-onsemi 0:098463de4c5d 1364 * use grp->T if already initialized, or initialize it.
group-onsemi 0:098463de4c5d 1365 */
group-onsemi 0:098463de4c5d 1366 T = p_eq_g ? grp->T : NULL;
group-onsemi 0:098463de4c5d 1367
group-onsemi 0:098463de4c5d 1368 if( T == NULL )
group-onsemi 0:098463de4c5d 1369 {
group-onsemi 0:098463de4c5d 1370 T = mbedtls_calloc( pre_len, sizeof( mbedtls_ecp_point ) );
group-onsemi 0:098463de4c5d 1371 if( T == NULL )
group-onsemi 0:098463de4c5d 1372 {
group-onsemi 0:098463de4c5d 1373 ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
group-onsemi 0:098463de4c5d 1374 goto cleanup;
group-onsemi 0:098463de4c5d 1375 }
group-onsemi 0:098463de4c5d 1376
group-onsemi 0:098463de4c5d 1377 MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d ) );
group-onsemi 0:098463de4c5d 1378
group-onsemi 0:098463de4c5d 1379 if( p_eq_g )
group-onsemi 0:098463de4c5d 1380 {
group-onsemi 0:098463de4c5d 1381 grp->T = T;
group-onsemi 0:098463de4c5d 1382 grp->T_size = pre_len;
group-onsemi 0:098463de4c5d 1383 }
group-onsemi 0:098463de4c5d 1384 }
group-onsemi 0:098463de4c5d 1385
group-onsemi 0:098463de4c5d 1386 /*
group-onsemi 0:098463de4c5d 1387 * Make sure M is odd (M = m or M = N - m, since N is odd)
group-onsemi 0:098463de4c5d 1388 * using the fact that m * P = - (N - m) * P
group-onsemi 0:098463de4c5d 1389 */
group-onsemi 0:098463de4c5d 1390 m_is_odd = ( mbedtls_mpi_get_bit( m, 0 ) == 1 );
group-onsemi 0:098463de4c5d 1391 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) );
group-onsemi 0:098463de4c5d 1392 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) );
group-onsemi 0:098463de4c5d 1393 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, ! m_is_odd ) );
group-onsemi 0:098463de4c5d 1394
group-onsemi 0:098463de4c5d 1395 /*
group-onsemi 0:098463de4c5d 1396 * Go for comb multiplication, R = M * P
group-onsemi 0:098463de4c5d 1397 */
group-onsemi 0:098463de4c5d 1398 ecp_comb_fixed( k, d, w, &M );
group-onsemi 0:098463de4c5d 1399 MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, R, T, pre_len, k, d, f_rng, p_rng ) );
group-onsemi 0:098463de4c5d 1400
group-onsemi 0:098463de4c5d 1401 /*
group-onsemi 0:098463de4c5d 1402 * Now get m * P from M * P and normalize it
group-onsemi 0:098463de4c5d 1403 */
group-onsemi 0:098463de4c5d 1404 MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, ! m_is_odd ) );
group-onsemi 0:098463de4c5d 1405 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
group-onsemi 0:098463de4c5d 1406
group-onsemi 0:098463de4c5d 1407 cleanup:
group-onsemi 0:098463de4c5d 1408
group-onsemi 0:098463de4c5d 1409 if( T != NULL && ! p_eq_g )
group-onsemi 0:098463de4c5d 1410 {
group-onsemi 0:098463de4c5d 1411 for( i = 0; i < pre_len; i++ )
group-onsemi 0:098463de4c5d 1412 mbedtls_ecp_point_free( &T[i] );
group-onsemi 0:098463de4c5d 1413 mbedtls_free( T );
group-onsemi 0:098463de4c5d 1414 }
group-onsemi 0:098463de4c5d 1415
group-onsemi 0:098463de4c5d 1416 mbedtls_mpi_free( &M );
group-onsemi 0:098463de4c5d 1417 mbedtls_mpi_free( &mm );
group-onsemi 0:098463de4c5d 1418
group-onsemi 0:098463de4c5d 1419 if( ret != 0 )
group-onsemi 0:098463de4c5d 1420 mbedtls_ecp_point_free( R );
group-onsemi 0:098463de4c5d 1421
group-onsemi 0:098463de4c5d 1422 return( ret );
group-onsemi 0:098463de4c5d 1423 }
group-onsemi 0:098463de4c5d 1424
group-onsemi 0:098463de4c5d 1425 #endif /* ECP_SHORTWEIERSTRASS */
group-onsemi 0:098463de4c5d 1426
group-onsemi 0:098463de4c5d 1427 #if defined(ECP_MONTGOMERY)
group-onsemi 0:098463de4c5d 1428 /*
group-onsemi 0:098463de4c5d 1429 * For Montgomery curves, we do all the internal arithmetic in projective
group-onsemi 0:098463de4c5d 1430 * coordinates. Import/export of points uses only the x coordinates, which is
group-onsemi 0:098463de4c5d 1431 * internaly represented as X / Z.
group-onsemi 0:098463de4c5d 1432 *
group-onsemi 0:098463de4c5d 1433 * For scalar multiplication, we'll use a Montgomery ladder.
group-onsemi 0:098463de4c5d 1434 */
group-onsemi 0:098463de4c5d 1435
group-onsemi 0:098463de4c5d 1436 /*
group-onsemi 0:098463de4c5d 1437 * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
group-onsemi 0:098463de4c5d 1438 * Cost: 1M + 1I
group-onsemi 0:098463de4c5d 1439 */
group-onsemi 0:098463de4c5d 1440 static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
group-onsemi 0:098463de4c5d 1441 {
group-onsemi 0:098463de4c5d 1442 int ret;
group-onsemi 0:098463de4c5d 1443
group-onsemi 0:098463de4c5d 1444 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
group-onsemi 0:098463de4c5d 1445 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X );
group-onsemi 0:098463de4c5d 1446 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
group-onsemi 0:098463de4c5d 1447
group-onsemi 0:098463de4c5d 1448 cleanup:
group-onsemi 0:098463de4c5d 1449 return( ret );
group-onsemi 0:098463de4c5d 1450 }
group-onsemi 0:098463de4c5d 1451
group-onsemi 0:098463de4c5d 1452 /*
group-onsemi 0:098463de4c5d 1453 * Randomize projective x/z coordinates:
group-onsemi 0:098463de4c5d 1454 * (X, Z) -> (l X, l Z) for random l
group-onsemi 0:098463de4c5d 1455 * This is sort of the reverse operation of ecp_normalize_mxz().
group-onsemi 0:098463de4c5d 1456 *
group-onsemi 0:098463de4c5d 1457 * This countermeasure was first suggested in [2].
group-onsemi 0:098463de4c5d 1458 * Cost: 2M
group-onsemi 0:098463de4c5d 1459 */
group-onsemi 0:098463de4c5d 1460 static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
group-onsemi 0:098463de4c5d 1461 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
group-onsemi 0:098463de4c5d 1462 {
group-onsemi 0:098463de4c5d 1463 int ret;
group-onsemi 0:098463de4c5d 1464 mbedtls_mpi l;
group-onsemi 0:098463de4c5d 1465 size_t p_size = ( grp->pbits + 7 ) / 8;
group-onsemi 0:098463de4c5d 1466 int count = 0;
group-onsemi 0:098463de4c5d 1467
group-onsemi 0:098463de4c5d 1468 mbedtls_mpi_init( &l );
group-onsemi 0:098463de4c5d 1469
group-onsemi 0:098463de4c5d 1470 /* Generate l such that 1 < l < p */
group-onsemi 0:098463de4c5d 1471 do
group-onsemi 0:098463de4c5d 1472 {
group-onsemi 0:098463de4c5d 1473 mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng );
group-onsemi 0:098463de4c5d 1474
group-onsemi 0:098463de4c5d 1475 while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
group-onsemi 0:098463de4c5d 1476 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
group-onsemi 0:098463de4c5d 1477
group-onsemi 0:098463de4c5d 1478 if( count++ > 10 )
group-onsemi 0:098463de4c5d 1479 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
group-onsemi 0:098463de4c5d 1480 }
group-onsemi 0:098463de4c5d 1481 while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
group-onsemi 0:098463de4c5d 1482
group-onsemi 0:098463de4c5d 1483 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X );
group-onsemi 0:098463de4c5d 1484 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z );
group-onsemi 0:098463de4c5d 1485
group-onsemi 0:098463de4c5d 1486 cleanup:
group-onsemi 0:098463de4c5d 1487 mbedtls_mpi_free( &l );
group-onsemi 0:098463de4c5d 1488
group-onsemi 0:098463de4c5d 1489 return( ret );
group-onsemi 0:098463de4c5d 1490 }
group-onsemi 0:098463de4c5d 1491
group-onsemi 0:098463de4c5d 1492 /*
group-onsemi 0:098463de4c5d 1493 * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
group-onsemi 0:098463de4c5d 1494 * for Montgomery curves in x/z coordinates.
group-onsemi 0:098463de4c5d 1495 *
group-onsemi 0:098463de4c5d 1496 * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
group-onsemi 0:098463de4c5d 1497 * with
group-onsemi 0:098463de4c5d 1498 * d = X1
group-onsemi 0:098463de4c5d 1499 * P = (X2, Z2)
group-onsemi 0:098463de4c5d 1500 * Q = (X3, Z3)
group-onsemi 0:098463de4c5d 1501 * R = (X4, Z4)
group-onsemi 0:098463de4c5d 1502 * S = (X5, Z5)
group-onsemi 0:098463de4c5d 1503 * and eliminating temporary variables tO, ..., t4.
group-onsemi 0:098463de4c5d 1504 *
group-onsemi 0:098463de4c5d 1505 * Cost: 5M + 4S
group-onsemi 0:098463de4c5d 1506 */
group-onsemi 0:098463de4c5d 1507 static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
group-onsemi 0:098463de4c5d 1508 mbedtls_ecp_point *R, mbedtls_ecp_point *S,
group-onsemi 0:098463de4c5d 1509 const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
group-onsemi 0:098463de4c5d 1510 const mbedtls_mpi *d )
group-onsemi 0:098463de4c5d 1511 {
group-onsemi 0:098463de4c5d 1512 int ret;
group-onsemi 0:098463de4c5d 1513 mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
group-onsemi 0:098463de4c5d 1514
group-onsemi 0:098463de4c5d 1515 mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
group-onsemi 0:098463de4c5d 1516 mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
group-onsemi 0:098463de4c5d 1517 mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
group-onsemi 0:098463de4c5d 1518
group-onsemi 0:098463de4c5d 1519 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &A, &P->X, &P->Z ) ); MOD_ADD( A );
group-onsemi 0:098463de4c5d 1520 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &AA, &A, &A ) ); MOD_MUL( AA );
group-onsemi 0:098463de4c5d 1521 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &B, &P->X, &P->Z ) ); MOD_SUB( B );
group-onsemi 0:098463de4c5d 1522 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &BB, &B, &B ) ); MOD_MUL( BB );
group-onsemi 0:098463de4c5d 1523 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &E, &AA, &BB ) ); MOD_SUB( E );
group-onsemi 0:098463de4c5d 1524 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &C, &Q->X, &Q->Z ) ); MOD_ADD( C );
group-onsemi 0:098463de4c5d 1525 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &D, &Q->X, &Q->Z ) ); MOD_SUB( D );
group-onsemi 0:098463de4c5d 1526 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DA, &D, &A ) ); MOD_MUL( DA );
group-onsemi 0:098463de4c5d 1527 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &CB, &C, &B ) ); MOD_MUL( CB );
group-onsemi 0:098463de4c5d 1528 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &S->X, &DA, &CB ) ); MOD_MUL( S->X );
group-onsemi 0:098463de4c5d 1529 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->X, &S->X, &S->X ) ); MOD_MUL( S->X );
group-onsemi 0:098463de4c5d 1530 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S->Z, &DA, &CB ) ); MOD_SUB( S->Z );
group-onsemi 0:098463de4c5d 1531 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, &S->Z, &S->Z ) ); MOD_MUL( S->Z );
group-onsemi 0:098463de4c5d 1532 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, d, &S->Z ) ); MOD_MUL( S->Z );
group-onsemi 0:098463de4c5d 1533 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->X, &AA, &BB ) ); MOD_MUL( R->X );
group-onsemi 0:098463de4c5d 1534 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &grp->A, &E ) ); MOD_MUL( R->Z );
group-onsemi 0:098463de4c5d 1535 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &R->Z, &BB, &R->Z ) ); MOD_ADD( R->Z );
group-onsemi 0:098463de4c5d 1536 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &E, &R->Z ) ); MOD_MUL( R->Z );
group-onsemi 0:098463de4c5d 1537
group-onsemi 0:098463de4c5d 1538 cleanup:
group-onsemi 0:098463de4c5d 1539 mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
group-onsemi 0:098463de4c5d 1540 mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
group-onsemi 0:098463de4c5d 1541 mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
group-onsemi 0:098463de4c5d 1542
group-onsemi 0:098463de4c5d 1543 return( ret );
group-onsemi 0:098463de4c5d 1544 }
group-onsemi 0:098463de4c5d 1545
group-onsemi 0:098463de4c5d 1546 /*
group-onsemi 0:098463de4c5d 1547 * Multiplication with Montgomery ladder in x/z coordinates,
group-onsemi 0:098463de4c5d 1548 * for curves in Montgomery form
group-onsemi 0:098463de4c5d 1549 */
group-onsemi 0:098463de4c5d 1550 static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
group-onsemi 0:098463de4c5d 1551 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
group-onsemi 0:098463de4c5d 1552 int (*f_rng)(void *, unsigned char *, size_t),
group-onsemi 0:098463de4c5d 1553 void *p_rng )
group-onsemi 0:098463de4c5d 1554 {
group-onsemi 0:098463de4c5d 1555 int ret;
group-onsemi 0:098463de4c5d 1556 size_t i;
group-onsemi 0:098463de4c5d 1557 unsigned char b;
group-onsemi 0:098463de4c5d 1558 mbedtls_ecp_point RP;
group-onsemi 0:098463de4c5d 1559 mbedtls_mpi PX;
group-onsemi 0:098463de4c5d 1560
group-onsemi 0:098463de4c5d 1561 mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
group-onsemi 0:098463de4c5d 1562
group-onsemi 0:098463de4c5d 1563 /* Save PX and read from P before writing to R, in case P == R */
group-onsemi 0:098463de4c5d 1564 MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
group-onsemi 0:098463de4c5d 1565 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
group-onsemi 0:098463de4c5d 1566
group-onsemi 0:098463de4c5d 1567 /* Set R to zero in modified x/z coordinates */
group-onsemi 0:098463de4c5d 1568 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
group-onsemi 0:098463de4c5d 1569 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
group-onsemi 0:098463de4c5d 1570 mbedtls_mpi_free( &R->Y );
group-onsemi 0:098463de4c5d 1571
group-onsemi 0:098463de4c5d 1572 /* RP.X might be sligtly larger than P, so reduce it */
group-onsemi 0:098463de4c5d 1573 MOD_ADD( RP.X );
group-onsemi 0:098463de4c5d 1574
group-onsemi 0:098463de4c5d 1575 /* Randomize coordinates of the starting point */
group-onsemi 0:098463de4c5d 1576 if( f_rng != NULL )
group-onsemi 0:098463de4c5d 1577 MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
group-onsemi 0:098463de4c5d 1578
group-onsemi 0:098463de4c5d 1579 /* Loop invariant: R = result so far, RP = R + P */
group-onsemi 0:098463de4c5d 1580 i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
group-onsemi 0:098463de4c5d 1581 while( i-- > 0 )
group-onsemi 0:098463de4c5d 1582 {
group-onsemi 0:098463de4c5d 1583 b = mbedtls_mpi_get_bit( m, i );
group-onsemi 0:098463de4c5d 1584 /*
group-onsemi 0:098463de4c5d 1585 * if (b) R = 2R + P else R = 2R,
group-onsemi 0:098463de4c5d 1586 * which is:
group-onsemi 0:098463de4c5d 1587 * if (b) double_add( RP, R, RP, R )
group-onsemi 0:098463de4c5d 1588 * else double_add( R, RP, R, RP )
group-onsemi 0:098463de4c5d 1589 * but using safe conditional swaps to avoid leaks
group-onsemi 0:098463de4c5d 1590 */
group-onsemi 0:098463de4c5d 1591 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
group-onsemi 0:098463de4c5d 1592 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
group-onsemi 0:098463de4c5d 1593 MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
group-onsemi 0:098463de4c5d 1594 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
group-onsemi 0:098463de4c5d 1595 MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
group-onsemi 0:098463de4c5d 1596 }
group-onsemi 0:098463de4c5d 1597
group-onsemi 0:098463de4c5d 1598 MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) );
group-onsemi 0:098463de4c5d 1599
group-onsemi 0:098463de4c5d 1600 cleanup:
group-onsemi 0:098463de4c5d 1601 mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
group-onsemi 0:098463de4c5d 1602
group-onsemi 0:098463de4c5d 1603 return( ret );
group-onsemi 0:098463de4c5d 1604 }
group-onsemi 0:098463de4c5d 1605
group-onsemi 0:098463de4c5d 1606 #endif /* ECP_MONTGOMERY */
group-onsemi 0:098463de4c5d 1607
group-onsemi 0:098463de4c5d 1608 /*
group-onsemi 0:098463de4c5d 1609 * Multiplication R = m * P
group-onsemi 0:098463de4c5d 1610 */
group-onsemi 0:098463de4c5d 1611 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
group-onsemi 0:098463de4c5d 1612 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
group-onsemi 0:098463de4c5d 1613 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
group-onsemi 0:098463de4c5d 1614 {
group-onsemi 0:098463de4c5d 1615 int ret;
group-onsemi 0:098463de4c5d 1616
group-onsemi 0:098463de4c5d 1617 /* Common sanity checks */
group-onsemi 0:098463de4c5d 1618 if( mbedtls_mpi_cmp_int( &P->Z, 1 ) != 0 )
group-onsemi 0:098463de4c5d 1619 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 1620
group-onsemi 0:098463de4c5d 1621 if( ( ret = mbedtls_ecp_check_privkey( grp, m ) ) != 0 ||
group-onsemi 0:098463de4c5d 1622 ( ret = mbedtls_ecp_check_pubkey( grp, P ) ) != 0 )
group-onsemi 0:098463de4c5d 1623 return( ret );
group-onsemi 0:098463de4c5d 1624
group-onsemi 0:098463de4c5d 1625 #if defined(ECP_MONTGOMERY)
group-onsemi 0:098463de4c5d 1626 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
group-onsemi 0:098463de4c5d 1627 return( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) );
group-onsemi 0:098463de4c5d 1628 #endif
group-onsemi 0:098463de4c5d 1629 #if defined(ECP_SHORTWEIERSTRASS)
group-onsemi 0:098463de4c5d 1630 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
group-onsemi 0:098463de4c5d 1631 return( ecp_mul_comb( grp, R, m, P, f_rng, p_rng ) );
group-onsemi 0:098463de4c5d 1632 #endif
group-onsemi 0:098463de4c5d 1633 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 1634 }
group-onsemi 0:098463de4c5d 1635
group-onsemi 0:098463de4c5d 1636 #if defined(ECP_SHORTWEIERSTRASS)
group-onsemi 0:098463de4c5d 1637 /*
group-onsemi 0:098463de4c5d 1638 * Check that an affine point is valid as a public key,
group-onsemi 0:098463de4c5d 1639 * short weierstrass curves (SEC1 3.2.3.1)
group-onsemi 0:098463de4c5d 1640 */
group-onsemi 0:098463de4c5d 1641 static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
group-onsemi 0:098463de4c5d 1642 {
group-onsemi 0:098463de4c5d 1643 int ret;
group-onsemi 0:098463de4c5d 1644 mbedtls_mpi YY, RHS;
group-onsemi 0:098463de4c5d 1645
group-onsemi 0:098463de4c5d 1646 /* pt coordinates must be normalized for our checks */
group-onsemi 0:098463de4c5d 1647 if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ||
group-onsemi 0:098463de4c5d 1648 mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 ||
group-onsemi 0:098463de4c5d 1649 mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
group-onsemi 0:098463de4c5d 1650 mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
group-onsemi 0:098463de4c5d 1651 return( MBEDTLS_ERR_ECP_INVALID_KEY );
group-onsemi 0:098463de4c5d 1652
group-onsemi 0:098463de4c5d 1653 mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
group-onsemi 0:098463de4c5d 1654
group-onsemi 0:098463de4c5d 1655 /*
group-onsemi 0:098463de4c5d 1656 * YY = Y^2
group-onsemi 0:098463de4c5d 1657 * RHS = X (X^2 + A) + B = X^3 + A X + B
group-onsemi 0:098463de4c5d 1658 */
group-onsemi 0:098463de4c5d 1659 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &YY, &pt->Y, &pt->Y ) ); MOD_MUL( YY );
group-onsemi 0:098463de4c5d 1660 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &pt->X, &pt->X ) ); MOD_MUL( RHS );
group-onsemi 0:098463de4c5d 1661
group-onsemi 0:098463de4c5d 1662 /* Special case for A = -3 */
group-onsemi 0:098463de4c5d 1663 if( grp->A.p == NULL )
group-onsemi 0:098463de4c5d 1664 {
group-onsemi 0:098463de4c5d 1665 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS );
group-onsemi 0:098463de4c5d 1666 }
group-onsemi 0:098463de4c5d 1667 else
group-onsemi 0:098463de4c5d 1668 {
group-onsemi 0:098463de4c5d 1669 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->A ) ); MOD_ADD( RHS );
group-onsemi 0:098463de4c5d 1670 }
group-onsemi 0:098463de4c5d 1671
group-onsemi 0:098463de4c5d 1672 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &RHS, &pt->X ) ); MOD_MUL( RHS );
group-onsemi 0:098463de4c5d 1673 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->B ) ); MOD_ADD( RHS );
group-onsemi 0:098463de4c5d 1674
group-onsemi 0:098463de4c5d 1675 if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
group-onsemi 0:098463de4c5d 1676 ret = MBEDTLS_ERR_ECP_INVALID_KEY;
group-onsemi 0:098463de4c5d 1677
group-onsemi 0:098463de4c5d 1678 cleanup:
group-onsemi 0:098463de4c5d 1679
group-onsemi 0:098463de4c5d 1680 mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
group-onsemi 0:098463de4c5d 1681
group-onsemi 0:098463de4c5d 1682 return( ret );
group-onsemi 0:098463de4c5d 1683 }
group-onsemi 0:098463de4c5d 1684 #endif /* ECP_SHORTWEIERSTRASS */
group-onsemi 0:098463de4c5d 1685
group-onsemi 0:098463de4c5d 1686 /*
group-onsemi 0:098463de4c5d 1687 * R = m * P with shortcuts for m == 1 and m == -1
group-onsemi 0:098463de4c5d 1688 * NOT constant-time - ONLY for short Weierstrass!
group-onsemi 0:098463de4c5d 1689 */
group-onsemi 0:098463de4c5d 1690 static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
group-onsemi 0:098463de4c5d 1691 mbedtls_ecp_point *R,
group-onsemi 0:098463de4c5d 1692 const mbedtls_mpi *m,
group-onsemi 0:098463de4c5d 1693 const mbedtls_ecp_point *P )
group-onsemi 0:098463de4c5d 1694 {
group-onsemi 0:098463de4c5d 1695 int ret;
group-onsemi 0:098463de4c5d 1696
group-onsemi 0:098463de4c5d 1697 if( mbedtls_mpi_cmp_int( m, 1 ) == 0 )
group-onsemi 0:098463de4c5d 1698 {
group-onsemi 0:098463de4c5d 1699 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
group-onsemi 0:098463de4c5d 1700 }
group-onsemi 0:098463de4c5d 1701 else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
group-onsemi 0:098463de4c5d 1702 {
group-onsemi 0:098463de4c5d 1703 MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
group-onsemi 0:098463de4c5d 1704 if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 )
group-onsemi 0:098463de4c5d 1705 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
group-onsemi 0:098463de4c5d 1706 }
group-onsemi 0:098463de4c5d 1707 else
group-onsemi 0:098463de4c5d 1708 {
group-onsemi 0:098463de4c5d 1709 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, R, m, P, NULL, NULL ) );
group-onsemi 0:098463de4c5d 1710 }
group-onsemi 0:098463de4c5d 1711
group-onsemi 0:098463de4c5d 1712 cleanup:
group-onsemi 0:098463de4c5d 1713 return( ret );
group-onsemi 0:098463de4c5d 1714 }
group-onsemi 0:098463de4c5d 1715
group-onsemi 0:098463de4c5d 1716 /*
group-onsemi 0:098463de4c5d 1717 * Linear combination
group-onsemi 0:098463de4c5d 1718 * NOT constant-time
group-onsemi 0:098463de4c5d 1719 */
group-onsemi 0:098463de4c5d 1720 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
group-onsemi 0:098463de4c5d 1721 const mbedtls_mpi *m, const mbedtls_ecp_point *P,
group-onsemi 0:098463de4c5d 1722 const mbedtls_mpi *n, const mbedtls_ecp_point *Q )
group-onsemi 0:098463de4c5d 1723 {
group-onsemi 0:098463de4c5d 1724 int ret;
group-onsemi 0:098463de4c5d 1725 mbedtls_ecp_point mP;
group-onsemi 0:098463de4c5d 1726
group-onsemi 0:098463de4c5d 1727 if( ecp_get_type( grp ) != ECP_TYPE_SHORT_WEIERSTRASS )
group-onsemi 0:098463de4c5d 1728 return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
group-onsemi 0:098463de4c5d 1729
group-onsemi 0:098463de4c5d 1730 mbedtls_ecp_point_init( &mP );
group-onsemi 0:098463de4c5d 1731
group-onsemi 0:098463de4c5d 1732 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, &mP, m, P ) );
group-onsemi 0:098463de4c5d 1733 MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, R, n, Q ) );
group-onsemi 0:098463de4c5d 1734
group-onsemi 0:098463de4c5d 1735 MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, &mP, R ) );
group-onsemi 0:098463de4c5d 1736 MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, R ) );
group-onsemi 0:098463de4c5d 1737
group-onsemi 0:098463de4c5d 1738 cleanup:
group-onsemi 0:098463de4c5d 1739 mbedtls_ecp_point_free( &mP );
group-onsemi 0:098463de4c5d 1740
group-onsemi 0:098463de4c5d 1741 return( ret );
group-onsemi 0:098463de4c5d 1742 }
group-onsemi 0:098463de4c5d 1743
group-onsemi 0:098463de4c5d 1744
group-onsemi 0:098463de4c5d 1745 #if defined(ECP_MONTGOMERY)
group-onsemi 0:098463de4c5d 1746 /*
group-onsemi 0:098463de4c5d 1747 * Check validity of a public key for Montgomery curves with x-only schemes
group-onsemi 0:098463de4c5d 1748 */
group-onsemi 0:098463de4c5d 1749 static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
group-onsemi 0:098463de4c5d 1750 {
group-onsemi 0:098463de4c5d 1751 /* [Curve25519 p. 5] Just check X is the correct number of bytes */
group-onsemi 0:098463de4c5d 1752 if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
group-onsemi 0:098463de4c5d 1753 return( MBEDTLS_ERR_ECP_INVALID_KEY );
group-onsemi 0:098463de4c5d 1754
group-onsemi 0:098463de4c5d 1755 return( 0 );
group-onsemi 0:098463de4c5d 1756 }
group-onsemi 0:098463de4c5d 1757 #endif /* ECP_MONTGOMERY */
group-onsemi 0:098463de4c5d 1758
group-onsemi 0:098463de4c5d 1759 /*
group-onsemi 0:098463de4c5d 1760 * Check that a point is valid as a public key
group-onsemi 0:098463de4c5d 1761 */
group-onsemi 0:098463de4c5d 1762 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
group-onsemi 0:098463de4c5d 1763 {
group-onsemi 0:098463de4c5d 1764 /* Must use affine coordinates */
group-onsemi 0:098463de4c5d 1765 if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
group-onsemi 0:098463de4c5d 1766 return( MBEDTLS_ERR_ECP_INVALID_KEY );
group-onsemi 0:098463de4c5d 1767
group-onsemi 0:098463de4c5d 1768 #if defined(ECP_MONTGOMERY)
group-onsemi 0:098463de4c5d 1769 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
group-onsemi 0:098463de4c5d 1770 return( ecp_check_pubkey_mx( grp, pt ) );
group-onsemi 0:098463de4c5d 1771 #endif
group-onsemi 0:098463de4c5d 1772 #if defined(ECP_SHORTWEIERSTRASS)
group-onsemi 0:098463de4c5d 1773 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
group-onsemi 0:098463de4c5d 1774 return( ecp_check_pubkey_sw( grp, pt ) );
group-onsemi 0:098463de4c5d 1775 #endif
group-onsemi 0:098463de4c5d 1776 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 1777 }
group-onsemi 0:098463de4c5d 1778
group-onsemi 0:098463de4c5d 1779 /*
group-onsemi 0:098463de4c5d 1780 * Check that an mbedtls_mpi is valid as a private key
group-onsemi 0:098463de4c5d 1781 */
group-onsemi 0:098463de4c5d 1782 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi *d )
group-onsemi 0:098463de4c5d 1783 {
group-onsemi 0:098463de4c5d 1784 #if defined(ECP_MONTGOMERY)
group-onsemi 0:098463de4c5d 1785 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
group-onsemi 0:098463de4c5d 1786 {
group-onsemi 0:098463de4c5d 1787 /* see [Curve25519] page 5 */
group-onsemi 0:098463de4c5d 1788 if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
group-onsemi 0:098463de4c5d 1789 mbedtls_mpi_get_bit( d, 1 ) != 0 ||
group-onsemi 0:098463de4c5d 1790 mbedtls_mpi_get_bit( d, 2 ) != 0 ||
group-onsemi 0:098463de4c5d 1791 mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */
group-onsemi 0:098463de4c5d 1792 return( MBEDTLS_ERR_ECP_INVALID_KEY );
group-onsemi 0:098463de4c5d 1793 else
group-onsemi 0:098463de4c5d 1794 return( 0 );
group-onsemi 0:098463de4c5d 1795 }
group-onsemi 0:098463de4c5d 1796 #endif /* ECP_MONTGOMERY */
group-onsemi 0:098463de4c5d 1797 #if defined(ECP_SHORTWEIERSTRASS)
group-onsemi 0:098463de4c5d 1798 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
group-onsemi 0:098463de4c5d 1799 {
group-onsemi 0:098463de4c5d 1800 /* see SEC1 3.2 */
group-onsemi 0:098463de4c5d 1801 if( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
group-onsemi 0:098463de4c5d 1802 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
group-onsemi 0:098463de4c5d 1803 return( MBEDTLS_ERR_ECP_INVALID_KEY );
group-onsemi 0:098463de4c5d 1804 else
group-onsemi 0:098463de4c5d 1805 return( 0 );
group-onsemi 0:098463de4c5d 1806 }
group-onsemi 0:098463de4c5d 1807 #endif /* ECP_SHORTWEIERSTRASS */
group-onsemi 0:098463de4c5d 1808
group-onsemi 0:098463de4c5d 1809 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 1810 }
group-onsemi 0:098463de4c5d 1811
group-onsemi 0:098463de4c5d 1812 /*
group-onsemi 0:098463de4c5d 1813 * Generate a keypair with configurable base point
group-onsemi 0:098463de4c5d 1814 */
group-onsemi 0:098463de4c5d 1815 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
group-onsemi 0:098463de4c5d 1816 const mbedtls_ecp_point *G,
group-onsemi 0:098463de4c5d 1817 mbedtls_mpi *d, mbedtls_ecp_point *Q,
group-onsemi 0:098463de4c5d 1818 int (*f_rng)(void *, unsigned char *, size_t),
group-onsemi 0:098463de4c5d 1819 void *p_rng )
group-onsemi 0:098463de4c5d 1820 {
group-onsemi 0:098463de4c5d 1821 int ret;
group-onsemi 0:098463de4c5d 1822 size_t n_size = ( grp->nbits + 7 ) / 8;
group-onsemi 0:098463de4c5d 1823
group-onsemi 0:098463de4c5d 1824 #if defined(ECP_MONTGOMERY)
group-onsemi 0:098463de4c5d 1825 if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
group-onsemi 0:098463de4c5d 1826 {
group-onsemi 0:098463de4c5d 1827 /* [M225] page 5 */
group-onsemi 0:098463de4c5d 1828 size_t b;
group-onsemi 0:098463de4c5d 1829
group-onsemi 0:098463de4c5d 1830 do {
group-onsemi 0:098463de4c5d 1831 MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
group-onsemi 0:098463de4c5d 1832 } while( mbedtls_mpi_bitlen( d ) == 0);
group-onsemi 0:098463de4c5d 1833
group-onsemi 0:098463de4c5d 1834 /* Make sure the most significant bit is nbits */
group-onsemi 0:098463de4c5d 1835 b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */
group-onsemi 0:098463de4c5d 1836 if( b > grp->nbits )
group-onsemi 0:098463de4c5d 1837 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) );
group-onsemi 0:098463de4c5d 1838 else
group-onsemi 0:098463de4c5d 1839 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) );
group-onsemi 0:098463de4c5d 1840
group-onsemi 0:098463de4c5d 1841 /* Make sure the last three bits are unset */
group-onsemi 0:098463de4c5d 1842 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) );
group-onsemi 0:098463de4c5d 1843 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) );
group-onsemi 0:098463de4c5d 1844 MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
group-onsemi 0:098463de4c5d 1845 }
group-onsemi 0:098463de4c5d 1846 else
group-onsemi 0:098463de4c5d 1847 #endif /* ECP_MONTGOMERY */
group-onsemi 0:098463de4c5d 1848 #if defined(ECP_SHORTWEIERSTRASS)
group-onsemi 0:098463de4c5d 1849 if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
group-onsemi 0:098463de4c5d 1850 {
group-onsemi 0:098463de4c5d 1851 /* SEC1 3.2.1: Generate d such that 1 <= n < N */
group-onsemi 0:098463de4c5d 1852 int count = 0;
group-onsemi 0:098463de4c5d 1853 unsigned char rnd[MBEDTLS_ECP_MAX_BYTES];
group-onsemi 0:098463de4c5d 1854
group-onsemi 0:098463de4c5d 1855 /*
group-onsemi 0:098463de4c5d 1856 * Match the procedure given in RFC 6979 (deterministic ECDSA):
group-onsemi 0:098463de4c5d 1857 * - use the same byte ordering;
group-onsemi 0:098463de4c5d 1858 * - keep the leftmost nbits bits of the generated octet string;
group-onsemi 0:098463de4c5d 1859 * - try until result is in the desired range.
group-onsemi 0:098463de4c5d 1860 * This also avoids any biais, which is especially important for ECDSA.
group-onsemi 0:098463de4c5d 1861 */
group-onsemi 0:098463de4c5d 1862 do
group-onsemi 0:098463de4c5d 1863 {
group-onsemi 0:098463de4c5d 1864 MBEDTLS_MPI_CHK( f_rng( p_rng, rnd, n_size ) );
group-onsemi 0:098463de4c5d 1865 MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( d, rnd, n_size ) );
group-onsemi 0:098463de4c5d 1866 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) );
group-onsemi 0:098463de4c5d 1867
group-onsemi 0:098463de4c5d 1868 /*
group-onsemi 0:098463de4c5d 1869 * Each try has at worst a probability 1/2 of failing (the msb has
group-onsemi 0:098463de4c5d 1870 * a probability 1/2 of being 0, and then the result will be < N),
group-onsemi 0:098463de4c5d 1871 * so after 30 tries failure probability is a most 2**(-30).
group-onsemi 0:098463de4c5d 1872 *
group-onsemi 0:098463de4c5d 1873 * For most curves, 1 try is enough with overwhelming probability,
group-onsemi 0:098463de4c5d 1874 * since N starts with a lot of 1s in binary, but some curves
group-onsemi 0:098463de4c5d 1875 * such as secp224k1 are actually very close to the worst case.
group-onsemi 0:098463de4c5d 1876 */
group-onsemi 0:098463de4c5d 1877 if( ++count > 30 )
group-onsemi 0:098463de4c5d 1878 return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
group-onsemi 0:098463de4c5d 1879 }
group-onsemi 0:098463de4c5d 1880 while( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
group-onsemi 0:098463de4c5d 1881 mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 );
group-onsemi 0:098463de4c5d 1882 }
group-onsemi 0:098463de4c5d 1883 else
group-onsemi 0:098463de4c5d 1884 #endif /* ECP_SHORTWEIERSTRASS */
group-onsemi 0:098463de4c5d 1885 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 1886
group-onsemi 0:098463de4c5d 1887 cleanup:
group-onsemi 0:098463de4c5d 1888 if( ret != 0 )
group-onsemi 0:098463de4c5d 1889 return( ret );
group-onsemi 0:098463de4c5d 1890
group-onsemi 0:098463de4c5d 1891 return( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) );
group-onsemi 0:098463de4c5d 1892 }
group-onsemi 0:098463de4c5d 1893
group-onsemi 0:098463de4c5d 1894 /*
group-onsemi 0:098463de4c5d 1895 * Generate key pair, wrapper for conventional base point
group-onsemi 0:098463de4c5d 1896 */
group-onsemi 0:098463de4c5d 1897 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp,
group-onsemi 0:098463de4c5d 1898 mbedtls_mpi *d, mbedtls_ecp_point *Q,
group-onsemi 0:098463de4c5d 1899 int (*f_rng)(void *, unsigned char *, size_t),
group-onsemi 0:098463de4c5d 1900 void *p_rng )
group-onsemi 0:098463de4c5d 1901 {
group-onsemi 0:098463de4c5d 1902 return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) );
group-onsemi 0:098463de4c5d 1903 }
group-onsemi 0:098463de4c5d 1904
group-onsemi 0:098463de4c5d 1905 /*
group-onsemi 0:098463de4c5d 1906 * Generate a keypair, prettier wrapper
group-onsemi 0:098463de4c5d 1907 */
group-onsemi 0:098463de4c5d 1908 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
group-onsemi 0:098463de4c5d 1909 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
group-onsemi 0:098463de4c5d 1910 {
group-onsemi 0:098463de4c5d 1911 int ret;
group-onsemi 0:098463de4c5d 1912
group-onsemi 0:098463de4c5d 1913 if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
group-onsemi 0:098463de4c5d 1914 return( ret );
group-onsemi 0:098463de4c5d 1915
group-onsemi 0:098463de4c5d 1916 return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
group-onsemi 0:098463de4c5d 1917 }
group-onsemi 0:098463de4c5d 1918
group-onsemi 0:098463de4c5d 1919 /*
group-onsemi 0:098463de4c5d 1920 * Check a public-private key pair
group-onsemi 0:098463de4c5d 1921 */
group-onsemi 0:098463de4c5d 1922 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
group-onsemi 0:098463de4c5d 1923 {
group-onsemi 0:098463de4c5d 1924 int ret;
group-onsemi 0:098463de4c5d 1925 mbedtls_ecp_point Q;
group-onsemi 0:098463de4c5d 1926 mbedtls_ecp_group grp;
group-onsemi 0:098463de4c5d 1927
group-onsemi 0:098463de4c5d 1928 if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
group-onsemi 0:098463de4c5d 1929 pub->grp.id != prv->grp.id ||
group-onsemi 0:098463de4c5d 1930 mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
group-onsemi 0:098463de4c5d 1931 mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
group-onsemi 0:098463de4c5d 1932 mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
group-onsemi 0:098463de4c5d 1933 {
group-onsemi 0:098463de4c5d 1934 return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
group-onsemi 0:098463de4c5d 1935 }
group-onsemi 0:098463de4c5d 1936
group-onsemi 0:098463de4c5d 1937 mbedtls_ecp_point_init( &Q );
group-onsemi 0:098463de4c5d 1938 mbedtls_ecp_group_init( &grp );
group-onsemi 0:098463de4c5d 1939
group-onsemi 0:098463de4c5d 1940 /* mbedtls_ecp_mul() needs a non-const group... */
group-onsemi 0:098463de4c5d 1941 mbedtls_ecp_group_copy( &grp, &prv->grp );
group-onsemi 0:098463de4c5d 1942
group-onsemi 0:098463de4c5d 1943 /* Also checks d is valid */
group-onsemi 0:098463de4c5d 1944 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
group-onsemi 0:098463de4c5d 1945
group-onsemi 0:098463de4c5d 1946 if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
group-onsemi 0:098463de4c5d 1947 mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
group-onsemi 0:098463de4c5d 1948 mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
group-onsemi 0:098463de4c5d 1949 {
group-onsemi 0:098463de4c5d 1950 ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
group-onsemi 0:098463de4c5d 1951 goto cleanup;
group-onsemi 0:098463de4c5d 1952 }
group-onsemi 0:098463de4c5d 1953
group-onsemi 0:098463de4c5d 1954 cleanup:
group-onsemi 0:098463de4c5d 1955 mbedtls_ecp_point_free( &Q );
group-onsemi 0:098463de4c5d 1956 mbedtls_ecp_group_free( &grp );
group-onsemi 0:098463de4c5d 1957
group-onsemi 0:098463de4c5d 1958 return( ret );
group-onsemi 0:098463de4c5d 1959 }
group-onsemi 0:098463de4c5d 1960
group-onsemi 0:098463de4c5d 1961 #if defined(MBEDTLS_SELF_TEST)
group-onsemi 0:098463de4c5d 1962
group-onsemi 0:098463de4c5d 1963 /*
group-onsemi 0:098463de4c5d 1964 * Checkup routine
group-onsemi 0:098463de4c5d 1965 */
group-onsemi 0:098463de4c5d 1966 int mbedtls_ecp_self_test( int verbose )
group-onsemi 0:098463de4c5d 1967 {
group-onsemi 0:098463de4c5d 1968 int ret;
group-onsemi 0:098463de4c5d 1969 size_t i;
group-onsemi 0:098463de4c5d 1970 mbedtls_ecp_group grp;
group-onsemi 0:098463de4c5d 1971 mbedtls_ecp_point R, P;
group-onsemi 0:098463de4c5d 1972 mbedtls_mpi m;
group-onsemi 0:098463de4c5d 1973 unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
group-onsemi 0:098463de4c5d 1974 /* exponents especially adapted for secp192r1 */
group-onsemi 0:098463de4c5d 1975 const char *exponents[] =
group-onsemi 0:098463de4c5d 1976 {
group-onsemi 0:098463de4c5d 1977 "000000000000000000000000000000000000000000000001", /* one */
group-onsemi 0:098463de4c5d 1978 "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22830", /* N - 1 */
group-onsemi 0:098463de4c5d 1979 "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
group-onsemi 0:098463de4c5d 1980 "400000000000000000000000000000000000000000000000", /* one and zeros */
group-onsemi 0:098463de4c5d 1981 "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
group-onsemi 0:098463de4c5d 1982 "555555555555555555555555555555555555555555555555", /* 101010... */
group-onsemi 0:098463de4c5d 1983 };
group-onsemi 0:098463de4c5d 1984
group-onsemi 0:098463de4c5d 1985 mbedtls_ecp_group_init( &grp );
group-onsemi 0:098463de4c5d 1986 mbedtls_ecp_point_init( &R );
group-onsemi 0:098463de4c5d 1987 mbedtls_ecp_point_init( &P );
group-onsemi 0:098463de4c5d 1988 mbedtls_mpi_init( &m );
group-onsemi 0:098463de4c5d 1989
group-onsemi 0:098463de4c5d 1990 /* Use secp192r1 if available, or any available curve */
group-onsemi 0:098463de4c5d 1991 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
group-onsemi 0:098463de4c5d 1992 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) );
group-onsemi 0:098463de4c5d 1993 #else
group-onsemi 0:098463de4c5d 1994 MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) );
group-onsemi 0:098463de4c5d 1995 #endif
group-onsemi 0:098463de4c5d 1996
group-onsemi 0:098463de4c5d 1997 if( verbose != 0 )
group-onsemi 0:098463de4c5d 1998 mbedtls_printf( " ECP test #1 (constant op_count, base point G): " );
group-onsemi 0:098463de4c5d 1999
group-onsemi 0:098463de4c5d 2000 /* Do a dummy multiplication first to trigger precomputation */
group-onsemi 0:098463de4c5d 2001 MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
group-onsemi 0:098463de4c5d 2002 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
group-onsemi 0:098463de4c5d 2003
group-onsemi 0:098463de4c5d 2004 add_count = 0;
group-onsemi 0:098463de4c5d 2005 dbl_count = 0;
group-onsemi 0:098463de4c5d 2006 mul_count = 0;
group-onsemi 0:098463de4c5d 2007 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
group-onsemi 0:098463de4c5d 2008 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
group-onsemi 0:098463de4c5d 2009
group-onsemi 0:098463de4c5d 2010 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
group-onsemi 0:098463de4c5d 2011 {
group-onsemi 0:098463de4c5d 2012 add_c_prev = add_count;
group-onsemi 0:098463de4c5d 2013 dbl_c_prev = dbl_count;
group-onsemi 0:098463de4c5d 2014 mul_c_prev = mul_count;
group-onsemi 0:098463de4c5d 2015 add_count = 0;
group-onsemi 0:098463de4c5d 2016 dbl_count = 0;
group-onsemi 0:098463de4c5d 2017 mul_count = 0;
group-onsemi 0:098463de4c5d 2018
group-onsemi 0:098463de4c5d 2019 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
group-onsemi 0:098463de4c5d 2020 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
group-onsemi 0:098463de4c5d 2021
group-onsemi 0:098463de4c5d 2022 if( add_count != add_c_prev ||
group-onsemi 0:098463de4c5d 2023 dbl_count != dbl_c_prev ||
group-onsemi 0:098463de4c5d 2024 mul_count != mul_c_prev )
group-onsemi 0:098463de4c5d 2025 {
group-onsemi 0:098463de4c5d 2026 if( verbose != 0 )
group-onsemi 0:098463de4c5d 2027 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
group-onsemi 0:098463de4c5d 2028
group-onsemi 0:098463de4c5d 2029 ret = 1;
group-onsemi 0:098463de4c5d 2030 goto cleanup;
group-onsemi 0:098463de4c5d 2031 }
group-onsemi 0:098463de4c5d 2032 }
group-onsemi 0:098463de4c5d 2033
group-onsemi 0:098463de4c5d 2034 if( verbose != 0 )
group-onsemi 0:098463de4c5d 2035 mbedtls_printf( "passed\n" );
group-onsemi 0:098463de4c5d 2036
group-onsemi 0:098463de4c5d 2037 if( verbose != 0 )
group-onsemi 0:098463de4c5d 2038 mbedtls_printf( " ECP test #2 (constant op_count, other point): " );
group-onsemi 0:098463de4c5d 2039 /* We computed P = 2G last time, use it */
group-onsemi 0:098463de4c5d 2040
group-onsemi 0:098463de4c5d 2041 add_count = 0;
group-onsemi 0:098463de4c5d 2042 dbl_count = 0;
group-onsemi 0:098463de4c5d 2043 mul_count = 0;
group-onsemi 0:098463de4c5d 2044 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
group-onsemi 0:098463de4c5d 2045 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
group-onsemi 0:098463de4c5d 2046
group-onsemi 0:098463de4c5d 2047 for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
group-onsemi 0:098463de4c5d 2048 {
group-onsemi 0:098463de4c5d 2049 add_c_prev = add_count;
group-onsemi 0:098463de4c5d 2050 dbl_c_prev = dbl_count;
group-onsemi 0:098463de4c5d 2051 mul_c_prev = mul_count;
group-onsemi 0:098463de4c5d 2052 add_count = 0;
group-onsemi 0:098463de4c5d 2053 dbl_count = 0;
group-onsemi 0:098463de4c5d 2054 mul_count = 0;
group-onsemi 0:098463de4c5d 2055
group-onsemi 0:098463de4c5d 2056 MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
group-onsemi 0:098463de4c5d 2057 MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
group-onsemi 0:098463de4c5d 2058
group-onsemi 0:098463de4c5d 2059 if( add_count != add_c_prev ||
group-onsemi 0:098463de4c5d 2060 dbl_count != dbl_c_prev ||
group-onsemi 0:098463de4c5d 2061 mul_count != mul_c_prev )
group-onsemi 0:098463de4c5d 2062 {
group-onsemi 0:098463de4c5d 2063 if( verbose != 0 )
group-onsemi 0:098463de4c5d 2064 mbedtls_printf( "failed (%u)\n", (unsigned int) i );
group-onsemi 0:098463de4c5d 2065
group-onsemi 0:098463de4c5d 2066 ret = 1;
group-onsemi 0:098463de4c5d 2067 goto cleanup;
group-onsemi 0:098463de4c5d 2068 }
group-onsemi 0:098463de4c5d 2069 }
group-onsemi 0:098463de4c5d 2070
group-onsemi 0:098463de4c5d 2071 if( verbose != 0 )
group-onsemi 0:098463de4c5d 2072 mbedtls_printf( "passed\n" );
group-onsemi 0:098463de4c5d 2073
group-onsemi 0:098463de4c5d 2074 cleanup:
group-onsemi 0:098463de4c5d 2075
group-onsemi 0:098463de4c5d 2076 if( ret < 0 && verbose != 0 )
group-onsemi 0:098463de4c5d 2077 mbedtls_printf( "Unexpected error, return code = %08X\n", ret );
group-onsemi 0:098463de4c5d 2078
group-onsemi 0:098463de4c5d 2079 mbedtls_ecp_group_free( &grp );
group-onsemi 0:098463de4c5d 2080 mbedtls_ecp_point_free( &R );
group-onsemi 0:098463de4c5d 2081 mbedtls_ecp_point_free( &P );
group-onsemi 0:098463de4c5d 2082 mbedtls_mpi_free( &m );
group-onsemi 0:098463de4c5d 2083
group-onsemi 0:098463de4c5d 2084 if( verbose != 0 )
group-onsemi 0:098463de4c5d 2085 mbedtls_printf( "\n" );
group-onsemi 0:098463de4c5d 2086
group-onsemi 0:098463de4c5d 2087 return( ret );
group-onsemi 0:098463de4c5d 2088 }
group-onsemi 0:098463de4c5d 2089
group-onsemi 0:098463de4c5d 2090 #endif /* MBEDTLS_SELF_TEST */
group-onsemi 0:098463de4c5d 2091
group-onsemi 0:098463de4c5d 2092 #endif /* MBEDTLS_ECP_C */