[398] | 1 | /*
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| 2 | * Elliptic curves over GF(p): generic functions
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| 3 | *
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| 4 | * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
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| 5 | * SPDX-License-Identifier: Apache-2.0
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| 6 | *
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| 7 | * Licensed under the Apache License, Version 2.0 (the "License"); you may
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| 8 | * not use this file except in compliance with the License.
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| 9 | * You may obtain a copy of the License at
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| 10 | *
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| 11 | * http://www.apache.org/licenses/LICENSE-2.0
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| 12 | *
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| 13 | * Unless required by applicable law or agreed to in writing, software
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| 14 | * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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| 15 | * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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| 16 | * See the License for the specific language governing permissions and
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| 17 | * limitations under the License.
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| 18 | *
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| 19 | * This file is part of mbed TLS (https://tls.mbed.org)
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| 20 | */
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| 21 |
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| 22 | /*
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| 23 | * References:
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| 24 | *
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| 25 | * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
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| 26 | * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
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| 27 | * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
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| 28 | * RFC 4492 for the related TLS structures and constants
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| 29 | * RFC 7748 for the Curve448 and Curve25519 curve definitions
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| 30 | *
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| 31 | * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf
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| 32 | *
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| 33 | * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
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| 34 | * for elliptic curve cryptosystems. In : Cryptographic Hardware and
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| 35 | * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
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| 36 | * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
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| 37 | *
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| 38 | * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
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| 39 | * render ECC resistant against Side Channel Attacks. IACR Cryptology
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| 40 | * ePrint Archive, 2004, vol. 2004, p. 342.
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| 41 | * <http://eprint.iacr.org/2004/342.pdf>
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| 42 | */
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| 43 |
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| 44 | #if !defined(MBEDTLS_CONFIG_FILE)
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| 45 | #include "mbedtls/config.h"
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| 46 | #else
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| 47 | #include MBEDTLS_CONFIG_FILE
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| 48 | #endif
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| 49 |
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| 50 | /**
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| 51 | * \brief Function level alternative implementation.
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| 52 | *
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| 53 | * The MBEDTLS_ECP_INTERNAL_ALT macro enables alternative implementations to
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| 54 | * replace certain functions in this module. The alternative implementations are
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| 55 | * typically hardware accelerators and need to activate the hardware before the
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| 56 | * computation starts and deactivate it after it finishes. The
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| 57 | * mbedtls_internal_ecp_init() and mbedtls_internal_ecp_free() functions serve
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| 58 | * this purpose.
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| 59 | *
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| 60 | * To preserve the correct functionality the following conditions must hold:
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| 61 | *
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| 62 | * - The alternative implementation must be activated by
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| 63 | * mbedtls_internal_ecp_init() before any of the replaceable functions is
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| 64 | * called.
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| 65 | * - mbedtls_internal_ecp_free() must \b only be called when the alternative
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| 66 | * implementation is activated.
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| 67 | * - mbedtls_internal_ecp_init() must \b not be called when the alternative
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| 68 | * implementation is activated.
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| 69 | * - Public functions must not return while the alternative implementation is
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| 70 | * activated.
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| 71 | * - Replaceable functions are guarded by \c MBEDTLS_ECP_XXX_ALT macros and
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| 72 | * before calling them an \code if( mbedtls_internal_ecp_grp_capable( grp ) )
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| 73 | * \endcode ensures that the alternative implementation supports the current
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| 74 | * group.
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| 75 | */
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| 76 | #if defined(MBEDTLS_ECP_INTERNAL_ALT)
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| 77 | #endif
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| 78 |
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| 79 | #if defined(MBEDTLS_ECP_C)
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| 80 |
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| 81 | #include "mbedtls/ecp.h"
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| 82 | #include "mbedtls/threading.h"
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| 83 | #include "mbedtls/platform_util.h"
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| 84 |
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| 85 | #include <string.h>
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| 86 |
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| 87 | #if !defined(MBEDTLS_ECP_ALT)
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| 88 |
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| 89 | /* Parameter validation macros based on platform_util.h */
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| 90 | #define ECP_VALIDATE_RET( cond ) \
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| 91 | MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA )
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| 92 | #define ECP_VALIDATE( cond ) \
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| 93 | MBEDTLS_INTERNAL_VALIDATE( cond )
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| 94 |
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| 95 | #if defined(MBEDTLS_PLATFORM_C)
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| 96 | #include "mbedtls/platform.h"
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| 97 | #else
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| 98 | #include <stdlib.h>
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| 99 | #include <stdio.h>
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| 100 | #define mbedtls_printf printf
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| 101 | #define mbedtls_calloc calloc
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| 102 | #define mbedtls_free free
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| 103 | #endif
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| 104 |
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| 105 | #include "mbedtls/ecp_internal.h"
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| 106 |
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| 107 | #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
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| 108 | !defined(inline) && !defined(__cplusplus)
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| 109 | #define inline __inline
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| 110 | #endif
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| 111 |
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| 112 | #if defined(MBEDTLS_SELF_TEST)
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| 113 | /*
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| 114 | * Counts of point addition and doubling, and field multiplications.
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| 115 | * Used to test resistance of point multiplication to simple timing attacks.
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| 116 | */
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| 117 | static unsigned long add_count, dbl_count, mul_count;
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| 118 | #endif
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| 119 |
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| 120 | #if defined(MBEDTLS_ECP_RESTARTABLE)
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| 121 | /*
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| 122 | * Maximum number of "basic operations" to be done in a row.
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| 123 | *
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| 124 | * Default value 0 means that ECC operations will not yield.
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| 125 | * Note that regardless of the value of ecp_max_ops, always at
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| 126 | * least one step is performed before yielding.
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| 127 | *
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| 128 | * Setting ecp_max_ops=1 can be suitable for testing purposes
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| 129 | * as it will interrupt computation at all possible points.
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| 130 | */
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| 131 | static unsigned ecp_max_ops = 0;
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| 132 |
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| 133 | /*
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| 134 | * Set ecp_max_ops
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| 135 | */
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| 136 | void mbedtls_ecp_set_max_ops( unsigned max_ops )
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| 137 | {
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| 138 | ecp_max_ops = max_ops;
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| 139 | }
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| 140 |
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| 141 | /*
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| 142 | * Check if restart is enabled
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| 143 | */
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| 144 | int mbedtls_ecp_restart_is_enabled( void )
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| 145 | {
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| 146 | return( ecp_max_ops != 0 );
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| 147 | }
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| 148 |
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| 149 | /*
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| 150 | * Restart sub-context for ecp_mul_comb()
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| 151 | */
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| 152 | struct mbedtls_ecp_restart_mul
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| 153 | {
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| 154 | mbedtls_ecp_point R; /* current intermediate result */
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| 155 | size_t i; /* current index in various loops, 0 outside */
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| 156 | mbedtls_ecp_point *T; /* table for precomputed points */
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| 157 | unsigned char T_size; /* number of points in table T */
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| 158 | enum { /* what were we doing last time we returned? */
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| 159 | ecp_rsm_init = 0, /* nothing so far, dummy initial state */
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| 160 | ecp_rsm_pre_dbl, /* precompute 2^n multiples */
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| 161 | ecp_rsm_pre_norm_dbl, /* normalize precomputed 2^n multiples */
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| 162 | ecp_rsm_pre_add, /* precompute remaining points by adding */
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| 163 | ecp_rsm_pre_norm_add, /* normalize all precomputed points */
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| 164 | ecp_rsm_comb_core, /* ecp_mul_comb_core() */
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| 165 | ecp_rsm_final_norm, /* do the final normalization */
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| 166 | } state;
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| 167 | };
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| 168 |
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| 169 | /*
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| 170 | * Init restart_mul sub-context
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| 171 | */
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| 172 | static void ecp_restart_rsm_init( mbedtls_ecp_restart_mul_ctx *ctx )
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| 173 | {
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| 174 | mbedtls_ecp_point_init( &ctx->R );
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| 175 | ctx->i = 0;
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| 176 | ctx->T = NULL;
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| 177 | ctx->T_size = 0;
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| 178 | ctx->state = ecp_rsm_init;
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| 179 | }
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| 180 |
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| 181 | /*
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| 182 | * Free the components of a restart_mul sub-context
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| 183 | */
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| 184 | static void ecp_restart_rsm_free( mbedtls_ecp_restart_mul_ctx *ctx )
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| 185 | {
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| 186 | unsigned char i;
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| 187 |
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| 188 | if( ctx == NULL )
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| 189 | return;
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| 190 |
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| 191 | mbedtls_ecp_point_free( &ctx->R );
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| 192 |
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| 193 | if( ctx->T != NULL )
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| 194 | {
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| 195 | for( i = 0; i < ctx->T_size; i++ )
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| 196 | mbedtls_ecp_point_free( ctx->T + i );
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| 197 | mbedtls_free( ctx->T );
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| 198 | }
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| 199 |
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| 200 | ecp_restart_rsm_init( ctx );
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| 201 | }
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| 202 |
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| 203 | /*
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| 204 | * Restart context for ecp_muladd()
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| 205 | */
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| 206 | struct mbedtls_ecp_restart_muladd
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| 207 | {
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| 208 | mbedtls_ecp_point mP; /* mP value */
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| 209 | mbedtls_ecp_point R; /* R intermediate result */
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| 210 | enum { /* what should we do next? */
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| 211 | ecp_rsma_mul1 = 0, /* first multiplication */
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| 212 | ecp_rsma_mul2, /* second multiplication */
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| 213 | ecp_rsma_add, /* addition */
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| 214 | ecp_rsma_norm, /* normalization */
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| 215 | } state;
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| 216 | };
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| 217 |
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| 218 | /*
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| 219 | * Init restart_muladd sub-context
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| 220 | */
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| 221 | static void ecp_restart_ma_init( mbedtls_ecp_restart_muladd_ctx *ctx )
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| 222 | {
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| 223 | mbedtls_ecp_point_init( &ctx->mP );
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| 224 | mbedtls_ecp_point_init( &ctx->R );
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| 225 | ctx->state = ecp_rsma_mul1;
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| 226 | }
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| 227 |
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| 228 | /*
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| 229 | * Free the components of a restart_muladd sub-context
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| 230 | */
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| 231 | static void ecp_restart_ma_free( mbedtls_ecp_restart_muladd_ctx *ctx )
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| 232 | {
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| 233 | if( ctx == NULL )
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| 234 | return;
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| 235 |
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| 236 | mbedtls_ecp_point_free( &ctx->mP );
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| 237 | mbedtls_ecp_point_free( &ctx->R );
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| 238 |
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| 239 | ecp_restart_ma_init( ctx );
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| 240 | }
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| 241 |
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| 242 | /*
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| 243 | * Initialize a restart context
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| 244 | */
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| 245 | void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx )
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| 246 | {
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| 247 | ECP_VALIDATE( ctx != NULL );
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| 248 | ctx->ops_done = 0;
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| 249 | ctx->depth = 0;
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| 250 | ctx->rsm = NULL;
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| 251 | ctx->ma = NULL;
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| 252 | }
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| 253 |
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| 254 | /*
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| 255 | * Free the components of a restart context
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| 256 | */
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| 257 | void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx )
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| 258 | {
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| 259 | if( ctx == NULL )
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| 260 | return;
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| 261 |
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| 262 | ecp_restart_rsm_free( ctx->rsm );
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| 263 | mbedtls_free( ctx->rsm );
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| 264 |
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| 265 | ecp_restart_ma_free( ctx->ma );
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| 266 | mbedtls_free( ctx->ma );
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| 267 |
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| 268 | mbedtls_ecp_restart_init( ctx );
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| 269 | }
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| 270 |
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| 271 | /*
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| 272 | * Check if we can do the next step
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| 273 | */
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| 274 | int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp,
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| 275 | mbedtls_ecp_restart_ctx *rs_ctx,
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| 276 | unsigned ops )
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| 277 | {
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| 278 | ECP_VALIDATE_RET( grp != NULL );
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| 279 |
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| 280 | if( rs_ctx != NULL && ecp_max_ops != 0 )
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| 281 | {
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| 282 | /* scale depending on curve size: the chosen reference is 256-bit,
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| 283 | * and multiplication is quadratic. Round to the closest integer. */
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| 284 | if( grp->pbits >= 512 )
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| 285 | ops *= 4;
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| 286 | else if( grp->pbits >= 384 )
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| 287 | ops *= 2;
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| 288 |
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| 289 | /* Avoid infinite loops: always allow first step.
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| 290 | * Because of that, however, it's not generally true
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| 291 | * that ops_done <= ecp_max_ops, so the check
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| 292 | * ops_done > ecp_max_ops below is mandatory. */
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| 293 | if( ( rs_ctx->ops_done != 0 ) &&
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| 294 | ( rs_ctx->ops_done > ecp_max_ops ||
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| 295 | ops > ecp_max_ops - rs_ctx->ops_done ) )
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| 296 | {
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| 297 | return( MBEDTLS_ERR_ECP_IN_PROGRESS );
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| 298 | }
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| 299 |
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| 300 | /* update running count */
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| 301 | rs_ctx->ops_done += ops;
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| 302 | }
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| 303 |
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| 304 | return( 0 );
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| 305 | }
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| 306 |
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| 307 | /* Call this when entering a function that needs its own sub-context */
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| 308 | #define ECP_RS_ENTER( SUB ) do { \
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| 309 | /* reset ops count for this call if top-level */ \
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| 310 | if( rs_ctx != NULL && rs_ctx->depth++ == 0 ) \
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| 311 | rs_ctx->ops_done = 0; \
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| 312 | \
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| 313 | /* set up our own sub-context if needed */ \
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| 314 | if( mbedtls_ecp_restart_is_enabled() && \
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| 315 | rs_ctx != NULL && rs_ctx->SUB == NULL ) \
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| 316 | { \
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| 317 | rs_ctx->SUB = mbedtls_calloc( 1, sizeof( *rs_ctx->SUB ) ); \
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| 318 | if( rs_ctx->SUB == NULL ) \
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| 319 | return( MBEDTLS_ERR_ECP_ALLOC_FAILED ); \
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| 320 | \
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| 321 | ecp_restart_## SUB ##_init( rs_ctx->SUB ); \
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| 322 | } \
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| 323 | } while( 0 )
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| 324 |
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| 325 | /* Call this when leaving a function that needs its own sub-context */
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| 326 | #define ECP_RS_LEAVE( SUB ) do { \
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| 327 | /* clear our sub-context when not in progress (done or error) */ \
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| 328 | if( rs_ctx != NULL && rs_ctx->SUB != NULL && \
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| 329 | ret != MBEDTLS_ERR_ECP_IN_PROGRESS ) \
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| 330 | { \
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| 331 | ecp_restart_## SUB ##_free( rs_ctx->SUB ); \
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| 332 | mbedtls_free( rs_ctx->SUB ); \
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| 333 | rs_ctx->SUB = NULL; \
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| 334 | } \
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| 335 | \
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| 336 | if( rs_ctx != NULL ) \
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| 337 | rs_ctx->depth--; \
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| 338 | } while( 0 )
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| 339 |
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| 340 | #else /* MBEDTLS_ECP_RESTARTABLE */
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| 341 |
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| 342 | #define ECP_RS_ENTER( sub ) (void) rs_ctx;
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| 343 | #define ECP_RS_LEAVE( sub ) (void) rs_ctx;
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| 344 |
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| 345 | #endif /* MBEDTLS_ECP_RESTARTABLE */
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| 346 |
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| 347 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \
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| 348 | defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
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| 349 | defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
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| 350 | defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \
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| 351 | defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \
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| 352 | defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \
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| 353 | defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \
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| 354 | defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \
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| 355 | defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
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| 356 | defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
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| 357 | defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
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| 358 | #define ECP_SHORTWEIERSTRASS
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| 359 | #endif
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| 360 |
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| 361 | #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) || \
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| 362 | defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
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| 363 | #define ECP_MONTGOMERY
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| 364 | #endif
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| 365 |
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| 366 | /*
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| 367 | * Curve types: internal for now, might be exposed later
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| 368 | */
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| 369 | typedef enum
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| 370 | {
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| 371 | ECP_TYPE_NONE = 0,
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| 372 | ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */
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| 373 | ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */
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| 374 | } ecp_curve_type;
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| 375 |
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| 376 | /*
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| 377 | * List of supported curves:
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| 378 | * - internal ID
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| 379 | * - TLS NamedCurve ID (RFC 4492 sec. 5.1.1, RFC 7071 sec. 2)
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| 380 | * - size in bits
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| 381 | * - readable name
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| 382 | *
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| 383 | * Curves are listed in order: largest curves first, and for a given size,
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| 384 | * fastest curves first. This provides the default order for the SSL module.
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| 385 | *
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| 386 | * Reminder: update profiles in x509_crt.c when adding a new curves!
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| 387 | */
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| 388 | static const mbedtls_ecp_curve_info ecp_supported_curves[] =
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| 389 | {
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| 390 | #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
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| 391 | { MBEDTLS_ECP_DP_SECP521R1, 25, 521, "secp521r1" },
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| 392 | #endif
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| 393 | #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
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| 394 | { MBEDTLS_ECP_DP_BP512R1, 28, 512, "brainpoolP512r1" },
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| 395 | #endif
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| 396 | #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
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| 397 | { MBEDTLS_ECP_DP_SECP384R1, 24, 384, "secp384r1" },
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| 398 | #endif
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| 399 | #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
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| 400 | { MBEDTLS_ECP_DP_BP384R1, 27, 384, "brainpoolP384r1" },
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| 401 | #endif
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| 402 | #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
|
---|
| 403 | { MBEDTLS_ECP_DP_SECP256R1, 23, 256, "secp256r1" },
|
---|
| 404 | #endif
|
---|
| 405 | #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
|
---|
| 406 | { MBEDTLS_ECP_DP_SECP256K1, 22, 256, "secp256k1" },
|
---|
| 407 | #endif
|
---|
| 408 | #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
|
---|
| 409 | { MBEDTLS_ECP_DP_BP256R1, 26, 256, "brainpoolP256r1" },
|
---|
| 410 | #endif
|
---|
| 411 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
|
---|
| 412 | { MBEDTLS_ECP_DP_SECP224R1, 21, 224, "secp224r1" },
|
---|
| 413 | #endif
|
---|
| 414 | #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
|
---|
| 415 | { MBEDTLS_ECP_DP_SECP224K1, 20, 224, "secp224k1" },
|
---|
| 416 | #endif
|
---|
| 417 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
|
---|
| 418 | { MBEDTLS_ECP_DP_SECP192R1, 19, 192, "secp192r1" },
|
---|
| 419 | #endif
|
---|
| 420 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
|
---|
| 421 | { MBEDTLS_ECP_DP_SECP192K1, 18, 192, "secp192k1" },
|
---|
| 422 | #endif
|
---|
| 423 | { MBEDTLS_ECP_DP_NONE, 0, 0, NULL },
|
---|
| 424 | };
|
---|
| 425 |
|
---|
| 426 | #define ECP_NB_CURVES sizeof( ecp_supported_curves ) / \
|
---|
| 427 | sizeof( ecp_supported_curves[0] )
|
---|
| 428 |
|
---|
| 429 | static mbedtls_ecp_group_id ecp_supported_grp_id[ECP_NB_CURVES];
|
---|
| 430 |
|
---|
| 431 | /*
|
---|
| 432 | * List of supported curves and associated info
|
---|
| 433 | */
|
---|
| 434 | const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void )
|
---|
| 435 | {
|
---|
| 436 | return( ecp_supported_curves );
|
---|
| 437 | }
|
---|
| 438 |
|
---|
| 439 | /*
|
---|
| 440 | * List of supported curves, group ID only
|
---|
| 441 | */
|
---|
| 442 | const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void )
|
---|
| 443 | {
|
---|
| 444 | static int init_done = 0;
|
---|
| 445 |
|
---|
| 446 | if( ! init_done )
|
---|
| 447 | {
|
---|
| 448 | size_t i = 0;
|
---|
| 449 | const mbedtls_ecp_curve_info *curve_info;
|
---|
| 450 |
|
---|
| 451 | for( curve_info = mbedtls_ecp_curve_list();
|
---|
| 452 | curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
|
---|
| 453 | curve_info++ )
|
---|
| 454 | {
|
---|
| 455 | ecp_supported_grp_id[i++] = curve_info->grp_id;
|
---|
| 456 | }
|
---|
| 457 | ecp_supported_grp_id[i] = MBEDTLS_ECP_DP_NONE;
|
---|
| 458 |
|
---|
| 459 | init_done = 1;
|
---|
| 460 | }
|
---|
| 461 |
|
---|
| 462 | return( ecp_supported_grp_id );
|
---|
| 463 | }
|
---|
| 464 |
|
---|
| 465 | /*
|
---|
| 466 | * Get the curve info for the internal identifier
|
---|
| 467 | */
|
---|
| 468 | const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id )
|
---|
| 469 | {
|
---|
| 470 | const mbedtls_ecp_curve_info *curve_info;
|
---|
| 471 |
|
---|
| 472 | for( curve_info = mbedtls_ecp_curve_list();
|
---|
| 473 | curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
|
---|
| 474 | curve_info++ )
|
---|
| 475 | {
|
---|
| 476 | if( curve_info->grp_id == grp_id )
|
---|
| 477 | return( curve_info );
|
---|
| 478 | }
|
---|
| 479 |
|
---|
| 480 | return( NULL );
|
---|
| 481 | }
|
---|
| 482 |
|
---|
| 483 | /*
|
---|
| 484 | * Get the curve info from the TLS identifier
|
---|
| 485 | */
|
---|
| 486 | const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id )
|
---|
| 487 | {
|
---|
| 488 | const mbedtls_ecp_curve_info *curve_info;
|
---|
| 489 |
|
---|
| 490 | for( curve_info = mbedtls_ecp_curve_list();
|
---|
| 491 | curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
|
---|
| 492 | curve_info++ )
|
---|
| 493 | {
|
---|
| 494 | if( curve_info->tls_id == tls_id )
|
---|
| 495 | return( curve_info );
|
---|
| 496 | }
|
---|
| 497 |
|
---|
| 498 | return( NULL );
|
---|
| 499 | }
|
---|
| 500 |
|
---|
| 501 | /*
|
---|
| 502 | * Get the curve info from the name
|
---|
| 503 | */
|
---|
| 504 | const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name )
|
---|
| 505 | {
|
---|
| 506 | const mbedtls_ecp_curve_info *curve_info;
|
---|
| 507 |
|
---|
| 508 | if( name == NULL )
|
---|
| 509 | return( NULL );
|
---|
| 510 |
|
---|
| 511 | for( curve_info = mbedtls_ecp_curve_list();
|
---|
| 512 | curve_info->grp_id != MBEDTLS_ECP_DP_NONE;
|
---|
| 513 | curve_info++ )
|
---|
| 514 | {
|
---|
| 515 | if( strcmp( curve_info->name, name ) == 0 )
|
---|
| 516 | return( curve_info );
|
---|
| 517 | }
|
---|
| 518 |
|
---|
| 519 | return( NULL );
|
---|
| 520 | }
|
---|
| 521 |
|
---|
| 522 | /*
|
---|
| 523 | * Get the type of a curve
|
---|
| 524 | */
|
---|
| 525 | static inline ecp_curve_type ecp_get_type( const mbedtls_ecp_group *grp )
|
---|
| 526 | {
|
---|
| 527 | if( grp->G.X.p == NULL )
|
---|
| 528 | return( ECP_TYPE_NONE );
|
---|
| 529 |
|
---|
| 530 | if( grp->G.Y.p == NULL )
|
---|
| 531 | return( ECP_TYPE_MONTGOMERY );
|
---|
| 532 | else
|
---|
| 533 | return( ECP_TYPE_SHORT_WEIERSTRASS );
|
---|
| 534 | }
|
---|
| 535 |
|
---|
| 536 | /*
|
---|
| 537 | * Initialize (the components of) a point
|
---|
| 538 | */
|
---|
| 539 | void mbedtls_ecp_point_init( mbedtls_ecp_point *pt )
|
---|
| 540 | {
|
---|
| 541 | ECP_VALIDATE( pt != NULL );
|
---|
| 542 |
|
---|
| 543 | mbedtls_mpi_init( &pt->X );
|
---|
| 544 | mbedtls_mpi_init( &pt->Y );
|
---|
| 545 | mbedtls_mpi_init( &pt->Z );
|
---|
| 546 | }
|
---|
| 547 |
|
---|
| 548 | /*
|
---|
| 549 | * Initialize (the components of) a group
|
---|
| 550 | */
|
---|
| 551 | void mbedtls_ecp_group_init( mbedtls_ecp_group *grp )
|
---|
| 552 | {
|
---|
| 553 | ECP_VALIDATE( grp != NULL );
|
---|
| 554 |
|
---|
| 555 | grp->id = MBEDTLS_ECP_DP_NONE;
|
---|
| 556 | mbedtls_mpi_init( &grp->P );
|
---|
| 557 | mbedtls_mpi_init( &grp->A );
|
---|
| 558 | mbedtls_mpi_init( &grp->B );
|
---|
| 559 | mbedtls_ecp_point_init( &grp->G );
|
---|
| 560 | mbedtls_mpi_init( &grp->N );
|
---|
| 561 | grp->pbits = 0;
|
---|
| 562 | grp->nbits = 0;
|
---|
| 563 | grp->h = 0;
|
---|
| 564 | grp->modp = NULL;
|
---|
| 565 | grp->t_pre = NULL;
|
---|
| 566 | grp->t_post = NULL;
|
---|
| 567 | grp->t_data = NULL;
|
---|
| 568 | grp->T = NULL;
|
---|
| 569 | grp->T_size = 0;
|
---|
| 570 | }
|
---|
| 571 |
|
---|
| 572 | /*
|
---|
| 573 | * Initialize (the components of) a key pair
|
---|
| 574 | */
|
---|
| 575 | void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key )
|
---|
| 576 | {
|
---|
| 577 | ECP_VALIDATE( key != NULL );
|
---|
| 578 |
|
---|
| 579 | mbedtls_ecp_group_init( &key->grp );
|
---|
| 580 | mbedtls_mpi_init( &key->d );
|
---|
| 581 | mbedtls_ecp_point_init( &key->Q );
|
---|
| 582 | }
|
---|
| 583 |
|
---|
| 584 | /*
|
---|
| 585 | * Unallocate (the components of) a point
|
---|
| 586 | */
|
---|
| 587 | void mbedtls_ecp_point_free( mbedtls_ecp_point *pt )
|
---|
| 588 | {
|
---|
| 589 | if( pt == NULL )
|
---|
| 590 | return;
|
---|
| 591 |
|
---|
| 592 | mbedtls_mpi_free( &( pt->X ) );
|
---|
| 593 | mbedtls_mpi_free( &( pt->Y ) );
|
---|
| 594 | mbedtls_mpi_free( &( pt->Z ) );
|
---|
| 595 | }
|
---|
| 596 |
|
---|
| 597 | /*
|
---|
| 598 | * Unallocate (the components of) a group
|
---|
| 599 | */
|
---|
| 600 | void mbedtls_ecp_group_free( mbedtls_ecp_group *grp )
|
---|
| 601 | {
|
---|
| 602 | size_t i;
|
---|
| 603 |
|
---|
| 604 | if( grp == NULL )
|
---|
| 605 | return;
|
---|
| 606 |
|
---|
| 607 | if( grp->h != 1 )
|
---|
| 608 | {
|
---|
| 609 | mbedtls_mpi_free( &grp->P );
|
---|
| 610 | mbedtls_mpi_free( &grp->A );
|
---|
| 611 | mbedtls_mpi_free( &grp->B );
|
---|
| 612 | mbedtls_ecp_point_free( &grp->G );
|
---|
| 613 | mbedtls_mpi_free( &grp->N );
|
---|
| 614 | }
|
---|
| 615 |
|
---|
| 616 | if( grp->T != NULL )
|
---|
| 617 | {
|
---|
| 618 | for( i = 0; i < grp->T_size; i++ )
|
---|
| 619 | mbedtls_ecp_point_free( &grp->T[i] );
|
---|
| 620 | mbedtls_free( grp->T );
|
---|
| 621 | }
|
---|
| 622 |
|
---|
| 623 | mbedtls_platform_zeroize( grp, sizeof( mbedtls_ecp_group ) );
|
---|
| 624 | }
|
---|
| 625 |
|
---|
| 626 | /*
|
---|
| 627 | * Unallocate (the components of) a key pair
|
---|
| 628 | */
|
---|
| 629 | void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key )
|
---|
| 630 | {
|
---|
| 631 | if( key == NULL )
|
---|
| 632 | return;
|
---|
| 633 |
|
---|
| 634 | mbedtls_ecp_group_free( &key->grp );
|
---|
| 635 | mbedtls_mpi_free( &key->d );
|
---|
| 636 | mbedtls_ecp_point_free( &key->Q );
|
---|
| 637 | }
|
---|
| 638 |
|
---|
| 639 | /*
|
---|
| 640 | * Copy the contents of a point
|
---|
| 641 | */
|
---|
| 642 | int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
|
---|
| 643 | {
|
---|
| 644 | int ret;
|
---|
| 645 | ECP_VALIDATE_RET( P != NULL );
|
---|
| 646 | ECP_VALIDATE_RET( Q != NULL );
|
---|
| 647 |
|
---|
| 648 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->X, &Q->X ) );
|
---|
| 649 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Y, &Q->Y ) );
|
---|
| 650 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &P->Z, &Q->Z ) );
|
---|
| 651 |
|
---|
| 652 | cleanup:
|
---|
| 653 | return( ret );
|
---|
| 654 | }
|
---|
| 655 |
|
---|
| 656 | /*
|
---|
| 657 | * Copy the contents of a group object
|
---|
| 658 | */
|
---|
| 659 | int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, const mbedtls_ecp_group *src )
|
---|
| 660 | {
|
---|
| 661 | ECP_VALIDATE_RET( dst != NULL );
|
---|
| 662 | ECP_VALIDATE_RET( src != NULL );
|
---|
| 663 |
|
---|
| 664 | return( mbedtls_ecp_group_load( dst, src->id ) );
|
---|
| 665 | }
|
---|
| 666 |
|
---|
| 667 | /*
|
---|
| 668 | * Set point to zero
|
---|
| 669 | */
|
---|
| 670 | int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt )
|
---|
| 671 | {
|
---|
| 672 | int ret;
|
---|
| 673 | ECP_VALIDATE_RET( pt != NULL );
|
---|
| 674 |
|
---|
| 675 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->X , 1 ) );
|
---|
| 676 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Y , 1 ) );
|
---|
| 677 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z , 0 ) );
|
---|
| 678 |
|
---|
| 679 | cleanup:
|
---|
| 680 | return( ret );
|
---|
| 681 | }
|
---|
| 682 |
|
---|
| 683 | /*
|
---|
| 684 | * Tell if a point is zero
|
---|
| 685 | */
|
---|
| 686 | int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt )
|
---|
| 687 | {
|
---|
| 688 | ECP_VALIDATE_RET( pt != NULL );
|
---|
| 689 |
|
---|
| 690 | return( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 );
|
---|
| 691 | }
|
---|
| 692 |
|
---|
| 693 | /*
|
---|
| 694 | * Compare two points lazily
|
---|
| 695 | */
|
---|
| 696 | int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P,
|
---|
| 697 | const mbedtls_ecp_point *Q )
|
---|
| 698 | {
|
---|
| 699 | ECP_VALIDATE_RET( P != NULL );
|
---|
| 700 | ECP_VALIDATE_RET( Q != NULL );
|
---|
| 701 |
|
---|
| 702 | if( mbedtls_mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
|
---|
| 703 | mbedtls_mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 &&
|
---|
| 704 | mbedtls_mpi_cmp_mpi( &P->Z, &Q->Z ) == 0 )
|
---|
| 705 | {
|
---|
| 706 | return( 0 );
|
---|
| 707 | }
|
---|
| 708 |
|
---|
| 709 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 710 | }
|
---|
| 711 |
|
---|
| 712 | /*
|
---|
| 713 | * Import a non-zero point from ASCII strings
|
---|
| 714 | */
|
---|
| 715 | int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix,
|
---|
| 716 | const char *x, const char *y )
|
---|
| 717 | {
|
---|
| 718 | int ret;
|
---|
| 719 | ECP_VALIDATE_RET( P != NULL );
|
---|
| 720 | ECP_VALIDATE_RET( x != NULL );
|
---|
| 721 | ECP_VALIDATE_RET( y != NULL );
|
---|
| 722 |
|
---|
| 723 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->X, radix, x ) );
|
---|
| 724 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &P->Y, radix, y ) );
|
---|
| 725 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
|
---|
| 726 |
|
---|
| 727 | cleanup:
|
---|
| 728 | return( ret );
|
---|
| 729 | }
|
---|
| 730 |
|
---|
| 731 | /*
|
---|
| 732 | * Export a point into unsigned binary data (SEC1 2.3.3)
|
---|
| 733 | */
|
---|
| 734 | int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp,
|
---|
| 735 | const mbedtls_ecp_point *P,
|
---|
| 736 | int format, size_t *olen,
|
---|
| 737 | unsigned char *buf, size_t buflen )
|
---|
| 738 | {
|
---|
| 739 | int ret = 0;
|
---|
| 740 | size_t plen;
|
---|
| 741 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 742 | ECP_VALIDATE_RET( P != NULL );
|
---|
| 743 | ECP_VALIDATE_RET( olen != NULL );
|
---|
| 744 | ECP_VALIDATE_RET( buf != NULL );
|
---|
| 745 | ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
|
---|
| 746 | format == MBEDTLS_ECP_PF_COMPRESSED );
|
---|
| 747 |
|
---|
| 748 | /*
|
---|
| 749 | * Common case: P == 0
|
---|
| 750 | */
|
---|
| 751 | if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
|
---|
| 752 | {
|
---|
| 753 | if( buflen < 1 )
|
---|
| 754 | return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
|
---|
| 755 |
|
---|
| 756 | buf[0] = 0x00;
|
---|
| 757 | *olen = 1;
|
---|
| 758 |
|
---|
| 759 | return( 0 );
|
---|
| 760 | }
|
---|
| 761 |
|
---|
| 762 | plen = mbedtls_mpi_size( &grp->P );
|
---|
| 763 |
|
---|
| 764 | if( format == MBEDTLS_ECP_PF_UNCOMPRESSED )
|
---|
| 765 | {
|
---|
| 766 | *olen = 2 * plen + 1;
|
---|
| 767 |
|
---|
| 768 | if( buflen < *olen )
|
---|
| 769 | return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
|
---|
| 770 |
|
---|
| 771 | buf[0] = 0x04;
|
---|
| 772 | MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
|
---|
| 773 | MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->Y, buf + 1 + plen, plen ) );
|
---|
| 774 | }
|
---|
| 775 | else if( format == MBEDTLS_ECP_PF_COMPRESSED )
|
---|
| 776 | {
|
---|
| 777 | *olen = plen + 1;
|
---|
| 778 |
|
---|
| 779 | if( buflen < *olen )
|
---|
| 780 | return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
|
---|
| 781 |
|
---|
| 782 | buf[0] = 0x02 + mbedtls_mpi_get_bit( &P->Y, 0 );
|
---|
| 783 | MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &P->X, buf + 1, plen ) );
|
---|
| 784 | }
|
---|
| 785 |
|
---|
| 786 | cleanup:
|
---|
| 787 | return( ret );
|
---|
| 788 | }
|
---|
| 789 |
|
---|
| 790 | /*
|
---|
| 791 | * Import a point from unsigned binary data (SEC1 2.3.4)
|
---|
| 792 | */
|
---|
| 793 | int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp,
|
---|
| 794 | mbedtls_ecp_point *pt,
|
---|
| 795 | const unsigned char *buf, size_t ilen )
|
---|
| 796 | {
|
---|
| 797 | int ret;
|
---|
| 798 | size_t plen;
|
---|
| 799 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 800 | ECP_VALIDATE_RET( pt != NULL );
|
---|
| 801 | ECP_VALIDATE_RET( buf != NULL );
|
---|
| 802 |
|
---|
| 803 | if( ilen < 1 )
|
---|
| 804 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 805 |
|
---|
| 806 | if( buf[0] == 0x00 )
|
---|
| 807 | {
|
---|
| 808 | if( ilen == 1 )
|
---|
| 809 | return( mbedtls_ecp_set_zero( pt ) );
|
---|
| 810 | else
|
---|
| 811 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 812 | }
|
---|
| 813 |
|
---|
| 814 | plen = mbedtls_mpi_size( &grp->P );
|
---|
| 815 |
|
---|
| 816 | if( buf[0] != 0x04 )
|
---|
| 817 | return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
|
---|
| 818 |
|
---|
| 819 | if( ilen != 2 * plen + 1 )
|
---|
| 820 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 821 |
|
---|
| 822 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
|
---|
| 823 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, buf + 1 + plen, plen ) );
|
---|
| 824 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
|
---|
| 825 |
|
---|
| 826 | cleanup:
|
---|
| 827 | return( ret );
|
---|
| 828 | }
|
---|
| 829 |
|
---|
| 830 | /*
|
---|
| 831 | * Import a point from a TLS ECPoint record (RFC 4492)
|
---|
| 832 | * struct {
|
---|
| 833 | * opaque point <1..2^8-1>;
|
---|
| 834 | * } ECPoint;
|
---|
| 835 | */
|
---|
| 836 | int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp,
|
---|
| 837 | mbedtls_ecp_point *pt,
|
---|
| 838 | const unsigned char **buf, size_t buf_len )
|
---|
| 839 | {
|
---|
| 840 | unsigned char data_len;
|
---|
| 841 | const unsigned char *buf_start;
|
---|
| 842 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 843 | ECP_VALIDATE_RET( pt != NULL );
|
---|
| 844 | ECP_VALIDATE_RET( buf != NULL );
|
---|
| 845 | ECP_VALIDATE_RET( *buf != NULL );
|
---|
| 846 |
|
---|
| 847 | /*
|
---|
| 848 | * We must have at least two bytes (1 for length, at least one for data)
|
---|
| 849 | */
|
---|
| 850 | if( buf_len < 2 )
|
---|
| 851 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 852 |
|
---|
| 853 | data_len = *(*buf)++;
|
---|
| 854 | if( data_len < 1 || data_len > buf_len - 1 )
|
---|
| 855 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 856 |
|
---|
| 857 | /*
|
---|
| 858 | * Save buffer start for read_binary and update buf
|
---|
| 859 | */
|
---|
| 860 | buf_start = *buf;
|
---|
| 861 | *buf += data_len;
|
---|
| 862 |
|
---|
| 863 | return( mbedtls_ecp_point_read_binary( grp, pt, buf_start, data_len ) );
|
---|
| 864 | }
|
---|
| 865 |
|
---|
| 866 | /*
|
---|
| 867 | * Export a point as a TLS ECPoint record (RFC 4492)
|
---|
| 868 | * struct {
|
---|
| 869 | * opaque point <1..2^8-1>;
|
---|
| 870 | * } ECPoint;
|
---|
| 871 | */
|
---|
| 872 | int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt,
|
---|
| 873 | int format, size_t *olen,
|
---|
| 874 | unsigned char *buf, size_t blen )
|
---|
| 875 | {
|
---|
| 876 | int ret;
|
---|
| 877 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 878 | ECP_VALIDATE_RET( pt != NULL );
|
---|
| 879 | ECP_VALIDATE_RET( olen != NULL );
|
---|
| 880 | ECP_VALIDATE_RET( buf != NULL );
|
---|
| 881 | ECP_VALIDATE_RET( format == MBEDTLS_ECP_PF_UNCOMPRESSED ||
|
---|
| 882 | format == MBEDTLS_ECP_PF_COMPRESSED );
|
---|
| 883 |
|
---|
| 884 | /*
|
---|
| 885 | * buffer length must be at least one, for our length byte
|
---|
| 886 | */
|
---|
| 887 | if( blen < 1 )
|
---|
| 888 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 889 |
|
---|
| 890 | if( ( ret = mbedtls_ecp_point_write_binary( grp, pt, format,
|
---|
| 891 | olen, buf + 1, blen - 1) ) != 0 )
|
---|
| 892 | return( ret );
|
---|
| 893 |
|
---|
| 894 | /*
|
---|
| 895 | * write length to the first byte and update total length
|
---|
| 896 | */
|
---|
| 897 | buf[0] = (unsigned char) *olen;
|
---|
| 898 | ++*olen;
|
---|
| 899 |
|
---|
| 900 | return( 0 );
|
---|
| 901 | }
|
---|
| 902 |
|
---|
| 903 | /*
|
---|
| 904 | * Set a group from an ECParameters record (RFC 4492)
|
---|
| 905 | */
|
---|
| 906 | int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp,
|
---|
| 907 | const unsigned char **buf, size_t len )
|
---|
| 908 | {
|
---|
| 909 | int ret;
|
---|
| 910 | mbedtls_ecp_group_id grp_id;
|
---|
| 911 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 912 | ECP_VALIDATE_RET( buf != NULL );
|
---|
| 913 | ECP_VALIDATE_RET( *buf != NULL );
|
---|
| 914 |
|
---|
| 915 | if( ( ret = mbedtls_ecp_tls_read_group_id( &grp_id, buf, len ) ) != 0 )
|
---|
| 916 | return( ret );
|
---|
| 917 |
|
---|
| 918 | return( mbedtls_ecp_group_load( grp, grp_id ) );
|
---|
| 919 | }
|
---|
| 920 |
|
---|
| 921 | /*
|
---|
| 922 | * Read a group id from an ECParameters record (RFC 4492) and convert it to
|
---|
| 923 | * mbedtls_ecp_group_id.
|
---|
| 924 | */
|
---|
| 925 | int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp,
|
---|
| 926 | const unsigned char **buf, size_t len )
|
---|
| 927 | {
|
---|
| 928 | uint16_t tls_id;
|
---|
| 929 | const mbedtls_ecp_curve_info *curve_info;
|
---|
| 930 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 931 | ECP_VALIDATE_RET( buf != NULL );
|
---|
| 932 | ECP_VALIDATE_RET( *buf != NULL );
|
---|
| 933 |
|
---|
| 934 | /*
|
---|
| 935 | * We expect at least three bytes (see below)
|
---|
| 936 | */
|
---|
| 937 | if( len < 3 )
|
---|
| 938 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 939 |
|
---|
| 940 | /*
|
---|
| 941 | * First byte is curve_type; only named_curve is handled
|
---|
| 942 | */
|
---|
| 943 | if( *(*buf)++ != MBEDTLS_ECP_TLS_NAMED_CURVE )
|
---|
| 944 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 945 |
|
---|
| 946 | /*
|
---|
| 947 | * Next two bytes are the namedcurve value
|
---|
| 948 | */
|
---|
| 949 | tls_id = *(*buf)++;
|
---|
| 950 | tls_id <<= 8;
|
---|
| 951 | tls_id |= *(*buf)++;
|
---|
| 952 |
|
---|
| 953 | if( ( curve_info = mbedtls_ecp_curve_info_from_tls_id( tls_id ) ) == NULL )
|
---|
| 954 | return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
|
---|
| 955 |
|
---|
| 956 | *grp = curve_info->grp_id;
|
---|
| 957 |
|
---|
| 958 | return( 0 );
|
---|
| 959 | }
|
---|
| 960 |
|
---|
| 961 | /*
|
---|
| 962 | * Write the ECParameters record corresponding to a group (RFC 4492)
|
---|
| 963 | */
|
---|
| 964 | int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, size_t *olen,
|
---|
| 965 | unsigned char *buf, size_t blen )
|
---|
| 966 | {
|
---|
| 967 | const mbedtls_ecp_curve_info *curve_info;
|
---|
| 968 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 969 | ECP_VALIDATE_RET( buf != NULL );
|
---|
| 970 | ECP_VALIDATE_RET( olen != NULL );
|
---|
| 971 |
|
---|
| 972 | if( ( curve_info = mbedtls_ecp_curve_info_from_grp_id( grp->id ) ) == NULL )
|
---|
| 973 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 974 |
|
---|
| 975 | /*
|
---|
| 976 | * We are going to write 3 bytes (see below)
|
---|
| 977 | */
|
---|
| 978 | *olen = 3;
|
---|
| 979 | if( blen < *olen )
|
---|
| 980 | return( MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL );
|
---|
| 981 |
|
---|
| 982 | /*
|
---|
| 983 | * First byte is curve_type, always named_curve
|
---|
| 984 | */
|
---|
| 985 | *buf++ = MBEDTLS_ECP_TLS_NAMED_CURVE;
|
---|
| 986 |
|
---|
| 987 | /*
|
---|
| 988 | * Next two bytes are the namedcurve value
|
---|
| 989 | */
|
---|
| 990 | buf[0] = curve_info->tls_id >> 8;
|
---|
| 991 | buf[1] = curve_info->tls_id & 0xFF;
|
---|
| 992 |
|
---|
| 993 | return( 0 );
|
---|
| 994 | }
|
---|
| 995 |
|
---|
| 996 | /*
|
---|
| 997 | * Wrapper around fast quasi-modp functions, with fall-back to mbedtls_mpi_mod_mpi.
|
---|
| 998 | * See the documentation of struct mbedtls_ecp_group.
|
---|
| 999 | *
|
---|
| 1000 | * This function is in the critial loop for mbedtls_ecp_mul, so pay attention to perf.
|
---|
| 1001 | */
|
---|
| 1002 | static int ecp_modp( mbedtls_mpi *N, const mbedtls_ecp_group *grp )
|
---|
| 1003 | {
|
---|
| 1004 | int ret;
|
---|
| 1005 |
|
---|
| 1006 | if( grp->modp == NULL )
|
---|
| 1007 | return( mbedtls_mpi_mod_mpi( N, N, &grp->P ) );
|
---|
| 1008 |
|
---|
| 1009 | /* N->s < 0 is a much faster test, which fails only if N is 0 */
|
---|
| 1010 | if( ( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 ) ||
|
---|
| 1011 | mbedtls_mpi_bitlen( N ) > 2 * grp->pbits )
|
---|
| 1012 | {
|
---|
| 1013 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 1014 | }
|
---|
| 1015 |
|
---|
| 1016 | MBEDTLS_MPI_CHK( grp->modp( N ) );
|
---|
| 1017 |
|
---|
| 1018 | /* N->s < 0 is a much faster test, which fails only if N is 0 */
|
---|
| 1019 | while( N->s < 0 && mbedtls_mpi_cmp_int( N, 0 ) != 0 )
|
---|
| 1020 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &grp->P ) );
|
---|
| 1021 |
|
---|
| 1022 | while( mbedtls_mpi_cmp_mpi( N, &grp->P ) >= 0 )
|
---|
| 1023 | /* we known P, N and the result are positive */
|
---|
| 1024 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, N, &grp->P ) );
|
---|
| 1025 |
|
---|
| 1026 | cleanup:
|
---|
| 1027 | return( ret );
|
---|
| 1028 | }
|
---|
| 1029 |
|
---|
| 1030 | /*
|
---|
| 1031 | * Fast mod-p functions expect their argument to be in the 0..p^2 range.
|
---|
| 1032 | *
|
---|
| 1033 | * In order to guarantee that, we need to ensure that operands of
|
---|
| 1034 | * mbedtls_mpi_mul_mpi are in the 0..p range. So, after each operation we will
|
---|
| 1035 | * bring the result back to this range.
|
---|
| 1036 | *
|
---|
| 1037 | * The following macros are shortcuts for doing that.
|
---|
| 1038 | */
|
---|
| 1039 |
|
---|
| 1040 | /*
|
---|
| 1041 | * Reduce a mbedtls_mpi mod p in-place, general case, to use after mbedtls_mpi_mul_mpi
|
---|
| 1042 | */
|
---|
| 1043 | #if defined(MBEDTLS_SELF_TEST)
|
---|
| 1044 | #define INC_MUL_COUNT mul_count++;
|
---|
| 1045 | #else
|
---|
| 1046 | #define INC_MUL_COUNT
|
---|
| 1047 | #endif
|
---|
| 1048 |
|
---|
| 1049 | #define MOD_MUL( N ) do { MBEDTLS_MPI_CHK( ecp_modp( &N, grp ) ); INC_MUL_COUNT } \
|
---|
| 1050 | while( 0 )
|
---|
| 1051 |
|
---|
| 1052 | /*
|
---|
| 1053 | * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
|
---|
| 1054 | * N->s < 0 is a very fast test, which fails only if N is 0
|
---|
| 1055 | */
|
---|
| 1056 | #define MOD_SUB( N ) \
|
---|
| 1057 | while( N.s < 0 && mbedtls_mpi_cmp_int( &N, 0 ) != 0 ) \
|
---|
| 1058 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &N, &N, &grp->P ) )
|
---|
| 1059 |
|
---|
| 1060 | /*
|
---|
| 1061 | * Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_add_mpi and mbedtls_mpi_mul_int.
|
---|
| 1062 | * We known P, N and the result are positive, so sub_abs is correct, and
|
---|
| 1063 | * a bit faster.
|
---|
| 1064 | */
|
---|
| 1065 | #define MOD_ADD( N ) \
|
---|
| 1066 | while( mbedtls_mpi_cmp_mpi( &N, &grp->P ) >= 0 ) \
|
---|
| 1067 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &N, &N, &grp->P ) )
|
---|
| 1068 |
|
---|
| 1069 | #if defined(ECP_SHORTWEIERSTRASS)
|
---|
| 1070 | /*
|
---|
| 1071 | * For curves in short Weierstrass form, we do all the internal operations in
|
---|
| 1072 | * Jacobian coordinates.
|
---|
| 1073 | *
|
---|
| 1074 | * For multiplication, we'll use a comb method with coutermeasueres against
|
---|
| 1075 | * SPA, hence timing attacks.
|
---|
| 1076 | */
|
---|
| 1077 |
|
---|
| 1078 | /*
|
---|
| 1079 | * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
|
---|
| 1080 | * Cost: 1N := 1I + 3M + 1S
|
---|
| 1081 | */
|
---|
| 1082 | static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
|
---|
| 1083 | {
|
---|
| 1084 | int ret;
|
---|
| 1085 | mbedtls_mpi Zi, ZZi;
|
---|
| 1086 |
|
---|
| 1087 | if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
|
---|
| 1088 | return( 0 );
|
---|
| 1089 |
|
---|
| 1090 | #if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
|
---|
| 1091 | if( mbedtls_internal_ecp_grp_capable( grp ) )
|
---|
| 1092 | return( mbedtls_internal_ecp_normalize_jac( grp, pt ) );
|
---|
| 1093 | #endif /* MBEDTLS_ECP_NORMALIZE_JAC_ALT */
|
---|
| 1094 |
|
---|
| 1095 | mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
|
---|
| 1096 |
|
---|
| 1097 | /*
|
---|
| 1098 | * X = X / Z^2 mod p
|
---|
| 1099 | */
|
---|
| 1100 | MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
|
---|
| 1101 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
|
---|
| 1102 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ZZi ) ); MOD_MUL( pt->X );
|
---|
| 1103 |
|
---|
| 1104 | /*
|
---|
| 1105 | * Y = Y / Z^3 mod p
|
---|
| 1106 | */
|
---|
| 1107 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ZZi ) ); MOD_MUL( pt->Y );
|
---|
| 1108 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &Zi ) ); MOD_MUL( pt->Y );
|
---|
| 1109 |
|
---|
| 1110 | /*
|
---|
| 1111 | * Z = 1
|
---|
| 1112 | */
|
---|
| 1113 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
|
---|
| 1114 |
|
---|
| 1115 | cleanup:
|
---|
| 1116 |
|
---|
| 1117 | mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
|
---|
| 1118 |
|
---|
| 1119 | return( ret );
|
---|
| 1120 | }
|
---|
| 1121 |
|
---|
| 1122 | /*
|
---|
| 1123 | * Normalize jacobian coordinates of an array of (pointers to) points,
|
---|
| 1124 | * using Montgomery's trick to perform only one inversion mod P.
|
---|
| 1125 | * (See for example Cohen's "A Course in Computational Algebraic Number
|
---|
| 1126 | * Theory", Algorithm 10.3.4.)
|
---|
| 1127 | *
|
---|
| 1128 | * Warning: fails (returning an error) if one of the points is zero!
|
---|
| 1129 | * This should never happen, see choice of w in ecp_mul_comb().
|
---|
| 1130 | *
|
---|
| 1131 | * Cost: 1N(t) := 1I + (6t - 3)M + 1S
|
---|
| 1132 | */
|
---|
| 1133 | static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
|
---|
| 1134 | mbedtls_ecp_point *T[], size_t T_size )
|
---|
| 1135 | {
|
---|
| 1136 | int ret;
|
---|
| 1137 | size_t i;
|
---|
| 1138 | mbedtls_mpi *c, u, Zi, ZZi;
|
---|
| 1139 |
|
---|
| 1140 | if( T_size < 2 )
|
---|
| 1141 | return( ecp_normalize_jac( grp, *T ) );
|
---|
| 1142 |
|
---|
| 1143 | #if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
|
---|
| 1144 | if( mbedtls_internal_ecp_grp_capable( grp ) )
|
---|
| 1145 | return( mbedtls_internal_ecp_normalize_jac_many( grp, T, T_size ) );
|
---|
| 1146 | #endif
|
---|
| 1147 |
|
---|
| 1148 | if( ( c = mbedtls_calloc( T_size, sizeof( mbedtls_mpi ) ) ) == NULL )
|
---|
| 1149 | return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
|
---|
| 1150 |
|
---|
| 1151 | for( i = 0; i < T_size; i++ )
|
---|
| 1152 | mbedtls_mpi_init( &c[i] );
|
---|
| 1153 |
|
---|
| 1154 | mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
|
---|
| 1155 |
|
---|
| 1156 | /*
|
---|
| 1157 | * c[i] = Z_0 * ... * Z_i
|
---|
| 1158 | */
|
---|
| 1159 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
|
---|
| 1160 | for( i = 1; i < T_size; i++ )
|
---|
| 1161 | {
|
---|
| 1162 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &c[i], &c[i-1], &T[i]->Z ) );
|
---|
| 1163 | MOD_MUL( c[i] );
|
---|
| 1164 | }
|
---|
| 1165 |
|
---|
| 1166 | /*
|
---|
| 1167 | * u = 1 / (Z_0 * ... * Z_n) mod P
|
---|
| 1168 | */
|
---|
| 1169 | MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[T_size-1], &grp->P ) );
|
---|
| 1170 |
|
---|
| 1171 | for( i = T_size - 1; ; i-- )
|
---|
| 1172 | {
|
---|
| 1173 | /*
|
---|
| 1174 | * Zi = 1 / Z_i mod p
|
---|
| 1175 | * u = 1 / (Z_0 * ... * Z_i) mod P
|
---|
| 1176 | */
|
---|
| 1177 | if( i == 0 ) {
|
---|
| 1178 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
|
---|
| 1179 | }
|
---|
| 1180 | else
|
---|
| 1181 | {
|
---|
| 1182 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Zi, &u, &c[i-1] ) ); MOD_MUL( Zi );
|
---|
| 1183 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &u, &u, &T[i]->Z ) ); MOD_MUL( u );
|
---|
| 1184 | }
|
---|
| 1185 |
|
---|
| 1186 | /*
|
---|
| 1187 | * proceed as in normalize()
|
---|
| 1188 | */
|
---|
| 1189 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
|
---|
| 1190 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->X, &T[i]->X, &ZZi ) ); MOD_MUL( T[i]->X );
|
---|
| 1191 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &ZZi ) ); MOD_MUL( T[i]->Y );
|
---|
| 1192 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &Zi ) ); MOD_MUL( T[i]->Y );
|
---|
| 1193 |
|
---|
| 1194 | /*
|
---|
| 1195 | * Post-precessing: reclaim some memory by shrinking coordinates
|
---|
| 1196 | * - not storing Z (always 1)
|
---|
| 1197 | * - shrinking other coordinates, but still keeping the same number of
|
---|
| 1198 | * limbs as P, as otherwise it will too likely be regrown too fast.
|
---|
| 1199 | */
|
---|
| 1200 | MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
|
---|
| 1201 | MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
|
---|
| 1202 | mbedtls_mpi_free( &T[i]->Z );
|
---|
| 1203 |
|
---|
| 1204 | if( i == 0 )
|
---|
| 1205 | break;
|
---|
| 1206 | }
|
---|
| 1207 |
|
---|
| 1208 | cleanup:
|
---|
| 1209 |
|
---|
| 1210 | mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
|
---|
| 1211 | for( i = 0; i < T_size; i++ )
|
---|
| 1212 | mbedtls_mpi_free( &c[i] );
|
---|
| 1213 | mbedtls_free( c );
|
---|
| 1214 |
|
---|
| 1215 | return( ret );
|
---|
| 1216 | }
|
---|
| 1217 |
|
---|
| 1218 | /*
|
---|
| 1219 | * Conditional point inversion: Q -> -Q = (Q.X, -Q.Y, Q.Z) without leak.
|
---|
| 1220 | * "inv" must be 0 (don't invert) or 1 (invert) or the result will be invalid
|
---|
| 1221 | */
|
---|
| 1222 | static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
|
---|
| 1223 | mbedtls_ecp_point *Q,
|
---|
| 1224 | unsigned char inv )
|
---|
| 1225 | {
|
---|
| 1226 | int ret;
|
---|
| 1227 | unsigned char nonzero;
|
---|
| 1228 | mbedtls_mpi mQY;
|
---|
| 1229 |
|
---|
| 1230 | mbedtls_mpi_init( &mQY );
|
---|
| 1231 |
|
---|
| 1232 | /* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
|
---|
| 1233 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
|
---|
| 1234 | nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
|
---|
| 1235 | MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
|
---|
| 1236 |
|
---|
| 1237 | cleanup:
|
---|
| 1238 | mbedtls_mpi_free( &mQY );
|
---|
| 1239 |
|
---|
| 1240 | return( ret );
|
---|
| 1241 | }
|
---|
| 1242 |
|
---|
| 1243 | /*
|
---|
| 1244 | * Point doubling R = 2 P, Jacobian coordinates
|
---|
| 1245 | *
|
---|
| 1246 | * Based on http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2 .
|
---|
| 1247 | *
|
---|
| 1248 | * We follow the variable naming fairly closely. The formula variations that trade a MUL for a SQR
|
---|
| 1249 | * (plus a few ADDs) aren't useful as our bignum implementation doesn't distinguish squaring.
|
---|
| 1250 | *
|
---|
| 1251 | * Standard optimizations are applied when curve parameter A is one of { 0, -3 }.
|
---|
| 1252 | *
|
---|
| 1253 | * Cost: 1D := 3M + 4S (A == 0)
|
---|
| 1254 | * 4M + 4S (A == -3)
|
---|
| 1255 | * 3M + 6S + 1a otherwise
|
---|
| 1256 | */
|
---|
| 1257 | static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
---|
| 1258 | const mbedtls_ecp_point *P )
|
---|
| 1259 | {
|
---|
| 1260 | int ret;
|
---|
| 1261 | mbedtls_mpi M, S, T, U;
|
---|
| 1262 |
|
---|
| 1263 | #if defined(MBEDTLS_SELF_TEST)
|
---|
| 1264 | dbl_count++;
|
---|
| 1265 | #endif
|
---|
| 1266 |
|
---|
| 1267 | #if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
|
---|
| 1268 | if( mbedtls_internal_ecp_grp_capable( grp ) )
|
---|
| 1269 | return( mbedtls_internal_ecp_double_jac( grp, R, P ) );
|
---|
| 1270 | #endif /* MBEDTLS_ECP_DOUBLE_JAC_ALT */
|
---|
| 1271 |
|
---|
| 1272 | mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
|
---|
| 1273 |
|
---|
| 1274 | /* Special case for A = -3 */
|
---|
| 1275 | if( grp->A.p == NULL )
|
---|
| 1276 | {
|
---|
| 1277 | /* M = 3(X + Z^2)(X - Z^2) */
|
---|
| 1278 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
|
---|
| 1279 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &T, &P->X, &S ) ); MOD_ADD( T );
|
---|
| 1280 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U, &P->X, &S ) ); MOD_SUB( U );
|
---|
| 1281 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &U ) ); MOD_MUL( S );
|
---|
| 1282 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
|
---|
| 1283 | }
|
---|
| 1284 | else
|
---|
| 1285 | {
|
---|
| 1286 | /* M = 3.X^2 */
|
---|
| 1287 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &P->X ) ); MOD_MUL( S );
|
---|
| 1288 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
|
---|
| 1289 |
|
---|
| 1290 | /* Optimize away for "koblitz" curves with A = 0 */
|
---|
| 1291 | if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
|
---|
| 1292 | {
|
---|
| 1293 | /* M += A.Z^4 */
|
---|
| 1294 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->Z, &P->Z ) ); MOD_MUL( S );
|
---|
| 1295 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &S, &S ) ); MOD_MUL( T );
|
---|
| 1296 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &T, &grp->A ) ); MOD_MUL( S );
|
---|
| 1297 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &S ) ); MOD_ADD( M );
|
---|
| 1298 | }
|
---|
| 1299 | }
|
---|
| 1300 |
|
---|
| 1301 | /* S = 4.X.Y^2 */
|
---|
| 1302 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &P->Y, &P->Y ) ); MOD_MUL( T );
|
---|
| 1303 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T, 1 ) ); MOD_ADD( T );
|
---|
| 1304 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &P->X, &T ) ); MOD_MUL( S );
|
---|
| 1305 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &S, 1 ) ); MOD_ADD( S );
|
---|
| 1306 |
|
---|
| 1307 | /* U = 8.Y^4 */
|
---|
| 1308 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &T, &T ) ); MOD_MUL( U );
|
---|
| 1309 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
|
---|
| 1310 |
|
---|
| 1311 | /* T = M^2 - 2.S */
|
---|
| 1312 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &M, &M ) ); MOD_MUL( T );
|
---|
| 1313 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
|
---|
| 1314 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T, &T, &S ) ); MOD_SUB( T );
|
---|
| 1315 |
|
---|
| 1316 | /* S = M(S - T) - U */
|
---|
| 1317 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &T ) ); MOD_SUB( S );
|
---|
| 1318 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S, &S, &M ) ); MOD_MUL( S );
|
---|
| 1319 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S, &S, &U ) ); MOD_SUB( S );
|
---|
| 1320 |
|
---|
| 1321 | /* U = 2.Y.Z */
|
---|
| 1322 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &U, &P->Y, &P->Z ) ); MOD_MUL( U );
|
---|
| 1323 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &U, 1 ) ); MOD_ADD( U );
|
---|
| 1324 |
|
---|
| 1325 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
|
---|
| 1326 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
|
---|
| 1327 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
|
---|
| 1328 |
|
---|
| 1329 | cleanup:
|
---|
| 1330 | mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
|
---|
| 1331 |
|
---|
| 1332 | return( ret );
|
---|
| 1333 | }
|
---|
| 1334 |
|
---|
| 1335 | /*
|
---|
| 1336 | * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
|
---|
| 1337 | *
|
---|
| 1338 | * The coordinates of Q must be normalized (= affine),
|
---|
| 1339 | * but those of P don't need to. R is not normalized.
|
---|
| 1340 | *
|
---|
| 1341 | * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
|
---|
| 1342 | * None of these cases can happen as intermediate step in ecp_mul_comb():
|
---|
| 1343 | * - at each step, P, Q and R are multiples of the base point, the factor
|
---|
| 1344 | * being less than its order, so none of them is zero;
|
---|
| 1345 | * - Q is an odd multiple of the base point, P an even multiple,
|
---|
| 1346 | * due to the choice of precomputed points in the modified comb method.
|
---|
| 1347 | * So branches for these cases do not leak secret information.
|
---|
| 1348 | *
|
---|
| 1349 | * We accept Q->Z being unset (saving memory in tables) as meaning 1.
|
---|
| 1350 | *
|
---|
| 1351 | * Cost: 1A := 8M + 3S
|
---|
| 1352 | */
|
---|
| 1353 | static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
---|
| 1354 | const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
|
---|
| 1355 | {
|
---|
| 1356 | int ret;
|
---|
| 1357 | mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
|
---|
| 1358 |
|
---|
| 1359 | #if defined(MBEDTLS_SELF_TEST)
|
---|
| 1360 | add_count++;
|
---|
| 1361 | #endif
|
---|
| 1362 |
|
---|
| 1363 | #if defined(MBEDTLS_ECP_ADD_MIXED_ALT)
|
---|
| 1364 | if( mbedtls_internal_ecp_grp_capable( grp ) )
|
---|
| 1365 | return( mbedtls_internal_ecp_add_mixed( grp, R, P, Q ) );
|
---|
| 1366 | #endif /* MBEDTLS_ECP_ADD_MIXED_ALT */
|
---|
| 1367 |
|
---|
| 1368 | /*
|
---|
| 1369 | * Trivial cases: P == 0 or Q == 0 (case 1)
|
---|
| 1370 | */
|
---|
| 1371 | if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
|
---|
| 1372 | return( mbedtls_ecp_copy( R, Q ) );
|
---|
| 1373 |
|
---|
| 1374 | if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
|
---|
| 1375 | return( mbedtls_ecp_copy( R, P ) );
|
---|
| 1376 |
|
---|
| 1377 | /*
|
---|
| 1378 | * Make sure Q coordinates are normalized
|
---|
| 1379 | */
|
---|
| 1380 | if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
|
---|
| 1381 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 1382 |
|
---|
| 1383 | mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
|
---|
| 1384 | mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
|
---|
| 1385 |
|
---|
| 1386 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &P->Z, &P->Z ) ); MOD_MUL( T1 );
|
---|
| 1387 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T1, &P->Z ) ); MOD_MUL( T2 );
|
---|
| 1388 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T1, &T1, &Q->X ) ); MOD_MUL( T1 );
|
---|
| 1389 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T2, &T2, &Q->Y ) ); MOD_MUL( T2 );
|
---|
| 1390 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T1, &T1, &P->X ) ); MOD_SUB( T1 );
|
---|
| 1391 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T2, &T2, &P->Y ) ); MOD_SUB( T2 );
|
---|
| 1392 |
|
---|
| 1393 | /* Special cases (2) and (3) */
|
---|
| 1394 | if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
|
---|
| 1395 | {
|
---|
| 1396 | if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
|
---|
| 1397 | {
|
---|
| 1398 | ret = ecp_double_jac( grp, R, P );
|
---|
| 1399 | goto cleanup;
|
---|
| 1400 | }
|
---|
| 1401 | else
|
---|
| 1402 | {
|
---|
| 1403 | ret = mbedtls_ecp_set_zero( R );
|
---|
| 1404 | goto cleanup;
|
---|
| 1405 | }
|
---|
| 1406 | }
|
---|
| 1407 |
|
---|
| 1408 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &Z, &P->Z, &T1 ) ); MOD_MUL( Z );
|
---|
| 1409 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T1, &T1 ) ); MOD_MUL( T3 );
|
---|
| 1410 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T3, &T1 ) ); MOD_MUL( T4 );
|
---|
| 1411 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &P->X ) ); MOD_MUL( T3 );
|
---|
| 1412 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T3, 2 ) ); MOD_ADD( T1 );
|
---|
| 1413 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &T2, &T2 ) ); MOD_MUL( X );
|
---|
| 1414 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) ); MOD_SUB( X );
|
---|
| 1415 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T4 ) ); MOD_SUB( X );
|
---|
| 1416 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &T3, &T3, &X ) ); MOD_SUB( T3 );
|
---|
| 1417 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T3, &T3, &T2 ) ); MOD_MUL( T3 );
|
---|
| 1418 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T4, &T4, &P->Y ) ); MOD_MUL( T4 );
|
---|
| 1419 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &Y, &T3, &T4 ) ); MOD_SUB( Y );
|
---|
| 1420 |
|
---|
| 1421 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
|
---|
| 1422 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
|
---|
| 1423 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
|
---|
| 1424 |
|
---|
| 1425 | cleanup:
|
---|
| 1426 |
|
---|
| 1427 | mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
|
---|
| 1428 | mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
|
---|
| 1429 |
|
---|
| 1430 | return( ret );
|
---|
| 1431 | }
|
---|
| 1432 |
|
---|
| 1433 | /*
|
---|
| 1434 | * Randomize jacobian coordinates:
|
---|
| 1435 | * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
|
---|
| 1436 | * This is sort of the reverse operation of ecp_normalize_jac().
|
---|
| 1437 | *
|
---|
| 1438 | * This countermeasure was first suggested in [2].
|
---|
| 1439 | */
|
---|
| 1440 | static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt,
|
---|
| 1441 | int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
|
---|
| 1442 | {
|
---|
| 1443 | int ret;
|
---|
| 1444 | mbedtls_mpi l, ll;
|
---|
| 1445 | size_t p_size;
|
---|
| 1446 | int count = 0;
|
---|
| 1447 |
|
---|
| 1448 | #if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
|
---|
| 1449 | if( mbedtls_internal_ecp_grp_capable( grp ) )
|
---|
| 1450 | return( mbedtls_internal_ecp_randomize_jac( grp, pt, f_rng, p_rng ) );
|
---|
| 1451 | #endif /* MBEDTLS_ECP_RANDOMIZE_JAC_ALT */
|
---|
| 1452 |
|
---|
| 1453 | p_size = ( grp->pbits + 7 ) / 8;
|
---|
| 1454 | mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
|
---|
| 1455 |
|
---|
| 1456 | /* Generate l such that 1 < l < p */
|
---|
| 1457 | do
|
---|
| 1458 | {
|
---|
| 1459 | MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
|
---|
| 1460 |
|
---|
| 1461 | while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
|
---|
| 1462 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
|
---|
| 1463 |
|
---|
| 1464 | if( count++ > 10 )
|
---|
| 1465 | return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
|
---|
| 1466 | }
|
---|
| 1467 | while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
|
---|
| 1468 |
|
---|
| 1469 | /* Z = l * Z */
|
---|
| 1470 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Z, &pt->Z, &l ) ); MOD_MUL( pt->Z );
|
---|
| 1471 |
|
---|
| 1472 | /* X = l^2 * X */
|
---|
| 1473 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &l, &l ) ); MOD_MUL( ll );
|
---|
| 1474 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->X, &pt->X, &ll ) ); MOD_MUL( pt->X );
|
---|
| 1475 |
|
---|
| 1476 | /* Y = l^3 * Y */
|
---|
| 1477 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &ll, &ll, &l ) ); MOD_MUL( ll );
|
---|
| 1478 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Y, &pt->Y, &ll ) ); MOD_MUL( pt->Y );
|
---|
| 1479 |
|
---|
| 1480 | cleanup:
|
---|
| 1481 | mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
|
---|
| 1482 |
|
---|
| 1483 | return( ret );
|
---|
| 1484 | }
|
---|
| 1485 |
|
---|
| 1486 | /*
|
---|
| 1487 | * Check and define parameters used by the comb method (see below for details)
|
---|
| 1488 | */
|
---|
| 1489 | #if MBEDTLS_ECP_WINDOW_SIZE < 2 || MBEDTLS_ECP_WINDOW_SIZE > 7
|
---|
| 1490 | #error "MBEDTLS_ECP_WINDOW_SIZE out of bounds"
|
---|
| 1491 | #endif
|
---|
| 1492 |
|
---|
| 1493 | /* d = ceil( n / w ) */
|
---|
| 1494 | #define COMB_MAX_D ( MBEDTLS_ECP_MAX_BITS + 1 ) / 2
|
---|
| 1495 |
|
---|
| 1496 | /* number of precomputed points */
|
---|
| 1497 | #define COMB_MAX_PRE ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) )
|
---|
| 1498 |
|
---|
| 1499 | /*
|
---|
| 1500 | * Compute the representation of m that will be used with our comb method.
|
---|
| 1501 | *
|
---|
| 1502 | * The basic comb method is described in GECC 3.44 for example. We use a
|
---|
| 1503 | * modified version that provides resistance to SPA by avoiding zero
|
---|
| 1504 | * digits in the representation as in [3]. We modify the method further by
|
---|
| 1505 | * requiring that all K_i be odd, which has the small cost that our
|
---|
| 1506 | * representation uses one more K_i, due to carries, but saves on the size of
|
---|
| 1507 | * the precomputed table.
|
---|
| 1508 | *
|
---|
| 1509 | * Summary of the comb method and its modifications:
|
---|
| 1510 | *
|
---|
| 1511 | * - The goal is to compute m*P for some w*d-bit integer m.
|
---|
| 1512 | *
|
---|
| 1513 | * - The basic comb method splits m into the w-bit integers
|
---|
| 1514 | * x[0] .. x[d-1] where x[i] consists of the bits in m whose
|
---|
| 1515 | * index has residue i modulo d, and computes m * P as
|
---|
| 1516 | * S[x[0]] + 2 * S[x[1]] + .. + 2^(d-1) S[x[d-1]], where
|
---|
| 1517 | * S[i_{w-1} .. i_0] := i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + i_0 P.
|
---|
| 1518 | *
|
---|
| 1519 | * - If it happens that, say, x[i+1]=0 (=> S[x[i+1]]=0), one can replace the sum by
|
---|
| 1520 | * .. + 2^{i-1} S[x[i-1]] - 2^i S[x[i]] + 2^{i+1} S[x[i]] + 2^{i+2} S[x[i+2]] ..,
|
---|
| 1521 | * thereby successively converting it into a form where all summands
|
---|
| 1522 | * are nonzero, at the cost of negative summands. This is the basic idea of [3].
|
---|
| 1523 | *
|
---|
| 1524 | * - More generally, even if x[i+1] != 0, we can first transform the sum as
|
---|
| 1525 | * .. - 2^i S[x[i]] + 2^{i+1} ( S[x[i]] + S[x[i+1]] ) + 2^{i+2} S[x[i+2]] ..,
|
---|
| 1526 | * and then replace S[x[i]] + S[x[i+1]] = S[x[i] ^ x[i+1]] + 2 S[x[i] & x[i+1]].
|
---|
| 1527 | * Performing and iterating this procedure for those x[i] that are even
|
---|
| 1528 | * (keeping track of carry), we can transform the original sum into one of the form
|
---|
| 1529 | * S[x'[0]] +- 2 S[x'[1]] +- .. +- 2^{d-1} S[x'[d-1]] + 2^d S[x'[d]]
|
---|
| 1530 | * with all x'[i] odd. It is therefore only necessary to know S at odd indices,
|
---|
| 1531 | * which is why we are only computing half of it in the first place in
|
---|
| 1532 | * ecp_precompute_comb and accessing it with index abs(i) / 2 in ecp_select_comb.
|
---|
| 1533 | *
|
---|
| 1534 | * - For the sake of compactness, only the seven low-order bits of x[i]
|
---|
| 1535 | * are used to represent its absolute value (K_i in the paper), and the msb
|
---|
| 1536 | * of x[i] encodes the sign (s_i in the paper): it is set if and only if
|
---|
| 1537 | * if s_i == -1;
|
---|
| 1538 | *
|
---|
| 1539 | * Calling conventions:
|
---|
| 1540 | * - x is an array of size d + 1
|
---|
| 1541 | * - w is the size, ie number of teeth, of the comb, and must be between
|
---|
| 1542 | * 2 and 7 (in practice, between 2 and MBEDTLS_ECP_WINDOW_SIZE)
|
---|
| 1543 | * - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
|
---|
| 1544 | * (the result will be incorrect if these assumptions are not satisfied)
|
---|
| 1545 | */
|
---|
| 1546 | static void ecp_comb_recode_core( unsigned char x[], size_t d,
|
---|
| 1547 | unsigned char w, const mbedtls_mpi *m )
|
---|
| 1548 | {
|
---|
| 1549 | size_t i, j;
|
---|
| 1550 | unsigned char c, cc, adjust;
|
---|
| 1551 |
|
---|
| 1552 | memset( x, 0, d+1 );
|
---|
| 1553 |
|
---|
| 1554 | /* First get the classical comb values (except for x_d = 0) */
|
---|
| 1555 | for( i = 0; i < d; i++ )
|
---|
| 1556 | for( j = 0; j < w; j++ )
|
---|
| 1557 | x[i] |= mbedtls_mpi_get_bit( m, i + d * j ) << j;
|
---|
| 1558 |
|
---|
| 1559 | /* Now make sure x_1 .. x_d are odd */
|
---|
| 1560 | c = 0;
|
---|
| 1561 | for( i = 1; i <= d; i++ )
|
---|
| 1562 | {
|
---|
| 1563 | /* Add carry and update it */
|
---|
| 1564 | cc = x[i] & c;
|
---|
| 1565 | x[i] = x[i] ^ c;
|
---|
| 1566 | c = cc;
|
---|
| 1567 |
|
---|
| 1568 | /* Adjust if needed, avoiding branches */
|
---|
| 1569 | adjust = 1 - ( x[i] & 0x01 );
|
---|
| 1570 | c |= x[i] & ( x[i-1] * adjust );
|
---|
| 1571 | x[i] = x[i] ^ ( x[i-1] * adjust );
|
---|
| 1572 | x[i-1] |= adjust << 7;
|
---|
| 1573 | }
|
---|
| 1574 | }
|
---|
| 1575 |
|
---|
| 1576 | /*
|
---|
| 1577 | * Precompute points for the adapted comb method
|
---|
| 1578 | *
|
---|
| 1579 | * Assumption: T must be able to hold 2^{w - 1} elements.
|
---|
| 1580 | *
|
---|
| 1581 | * Operation: If i = i_{w-1} ... i_1 is the binary representation of i,
|
---|
| 1582 | * sets T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P.
|
---|
| 1583 | *
|
---|
| 1584 | * Cost: d(w-1) D + (2^{w-1} - 1) A + 1 N(w-1) + 1 N(2^{w-1} - 1)
|
---|
| 1585 | *
|
---|
| 1586 | * Note: Even comb values (those where P would be omitted from the
|
---|
| 1587 | * sum defining T[i] above) are not needed in our adaption
|
---|
| 1588 | * the comb method. See ecp_comb_recode_core().
|
---|
| 1589 | *
|
---|
| 1590 | * This function currently works in four steps:
|
---|
| 1591 | * (1) [dbl] Computation of intermediate T[i] for 2-power values of i
|
---|
| 1592 | * (2) [norm_dbl] Normalization of coordinates of these T[i]
|
---|
| 1593 | * (3) [add] Computation of all T[i]
|
---|
| 1594 | * (4) [norm_add] Normalization of all T[i]
|
---|
| 1595 | *
|
---|
| 1596 | * Step 1 can be interrupted but not the others; together with the final
|
---|
| 1597 | * coordinate normalization they are the largest steps done at once, depending
|
---|
| 1598 | * on the window size. Here are operation counts for P-256:
|
---|
| 1599 | *
|
---|
| 1600 | * step (2) (3) (4)
|
---|
| 1601 | * w = 5 142 165 208
|
---|
| 1602 | * w = 4 136 77 160
|
---|
| 1603 | * w = 3 130 33 136
|
---|
| 1604 | * w = 2 124 11 124
|
---|
| 1605 | *
|
---|
| 1606 | * So if ECC operations are blocking for too long even with a low max_ops
|
---|
| 1607 | * value, it's useful to set MBEDTLS_ECP_WINDOW_SIZE to a lower value in order
|
---|
| 1608 | * to minimize maximum blocking time.
|
---|
| 1609 | */
|
---|
| 1610 | static int ecp_precompute_comb( const mbedtls_ecp_group *grp,
|
---|
| 1611 | mbedtls_ecp_point T[], const mbedtls_ecp_point *P,
|
---|
| 1612 | unsigned char w, size_t d,
|
---|
| 1613 | mbedtls_ecp_restart_ctx *rs_ctx )
|
---|
| 1614 | {
|
---|
| 1615 | int ret;
|
---|
| 1616 | unsigned char i;
|
---|
| 1617 | size_t j = 0;
|
---|
| 1618 | const unsigned char T_size = 1U << ( w - 1 );
|
---|
| 1619 | mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
|
---|
| 1620 |
|
---|
| 1621 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 1622 | if( rs_ctx != NULL && rs_ctx->rsm != NULL )
|
---|
| 1623 | {
|
---|
| 1624 | if( rs_ctx->rsm->state == ecp_rsm_pre_dbl )
|
---|
| 1625 | goto dbl;
|
---|
| 1626 | if( rs_ctx->rsm->state == ecp_rsm_pre_norm_dbl )
|
---|
| 1627 | goto norm_dbl;
|
---|
| 1628 | if( rs_ctx->rsm->state == ecp_rsm_pre_add )
|
---|
| 1629 | goto add;
|
---|
| 1630 | if( rs_ctx->rsm->state == ecp_rsm_pre_norm_add )
|
---|
| 1631 | goto norm_add;
|
---|
| 1632 | }
|
---|
| 1633 | #else
|
---|
| 1634 | (void) rs_ctx;
|
---|
| 1635 | #endif
|
---|
| 1636 |
|
---|
| 1637 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 1638 | if( rs_ctx != NULL && rs_ctx->rsm != NULL )
|
---|
| 1639 | {
|
---|
| 1640 | rs_ctx->rsm->state = ecp_rsm_pre_dbl;
|
---|
| 1641 |
|
---|
| 1642 | /* initial state for the loop */
|
---|
| 1643 | rs_ctx->rsm->i = 0;
|
---|
| 1644 | }
|
---|
| 1645 |
|
---|
| 1646 | dbl:
|
---|
| 1647 | #endif
|
---|
| 1648 | /*
|
---|
| 1649 | * Set T[0] = P and
|
---|
| 1650 | * T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
|
---|
| 1651 | */
|
---|
| 1652 | MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &T[0], P ) );
|
---|
| 1653 |
|
---|
| 1654 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 1655 | if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0 )
|
---|
| 1656 | j = rs_ctx->rsm->i;
|
---|
| 1657 | else
|
---|
| 1658 | #endif
|
---|
| 1659 | j = 0;
|
---|
| 1660 |
|
---|
| 1661 | for( ; j < d * ( w - 1 ); j++ )
|
---|
| 1662 | {
|
---|
| 1663 | MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_DBL );
|
---|
| 1664 |
|
---|
| 1665 | i = 1U << ( j / d );
|
---|
| 1666 | cur = T + i;
|
---|
| 1667 |
|
---|
| 1668 | if( j % d == 0 )
|
---|
| 1669 | MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
|
---|
| 1670 |
|
---|
| 1671 | MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
|
---|
| 1672 | }
|
---|
| 1673 |
|
---|
| 1674 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 1675 | if( rs_ctx != NULL && rs_ctx->rsm != NULL )
|
---|
| 1676 | rs_ctx->rsm->state = ecp_rsm_pre_norm_dbl;
|
---|
| 1677 |
|
---|
| 1678 | norm_dbl:
|
---|
| 1679 | #endif
|
---|
| 1680 | /*
|
---|
| 1681 | * Normalize current elements in T. As T has holes,
|
---|
| 1682 | * use an auxiliary array of pointers to elements in T.
|
---|
| 1683 | */
|
---|
| 1684 | j = 0;
|
---|
| 1685 | for( i = 1; i < T_size; i <<= 1 )
|
---|
| 1686 | TT[j++] = T + i;
|
---|
| 1687 |
|
---|
| 1688 | MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV + 6 * j - 2 );
|
---|
| 1689 |
|
---|
| 1690 | MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) );
|
---|
| 1691 |
|
---|
| 1692 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 1693 | if( rs_ctx != NULL && rs_ctx->rsm != NULL )
|
---|
| 1694 | rs_ctx->rsm->state = ecp_rsm_pre_add;
|
---|
| 1695 |
|
---|
| 1696 | add:
|
---|
| 1697 | #endif
|
---|
| 1698 | /*
|
---|
| 1699 | * Compute the remaining ones using the minimal number of additions
|
---|
| 1700 | * Be careful to update T[2^l] only after using it!
|
---|
| 1701 | */
|
---|
| 1702 | MBEDTLS_ECP_BUDGET( ( T_size - 1 ) * MBEDTLS_ECP_OPS_ADD );
|
---|
| 1703 |
|
---|
| 1704 | for( i = 1; i < T_size; i <<= 1 )
|
---|
| 1705 | {
|
---|
| 1706 | j = i;
|
---|
| 1707 | while( j-- )
|
---|
| 1708 | MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
|
---|
| 1709 | }
|
---|
| 1710 |
|
---|
| 1711 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 1712 | if( rs_ctx != NULL && rs_ctx->rsm != NULL )
|
---|
| 1713 | rs_ctx->rsm->state = ecp_rsm_pre_norm_add;
|
---|
| 1714 |
|
---|
| 1715 | norm_add:
|
---|
| 1716 | #endif
|
---|
| 1717 | /*
|
---|
| 1718 | * Normalize final elements in T. Even though there are no holes now, we
|
---|
| 1719 | * still need the auxiliary array for homogeneity with the previous
|
---|
| 1720 | * call. Also, skip T[0] which is already normalised, being a copy of P.
|
---|
| 1721 | */
|
---|
| 1722 | for( j = 0; j + 1 < T_size; j++ )
|
---|
| 1723 | TT[j] = T + j + 1;
|
---|
| 1724 |
|
---|
| 1725 | MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV + 6 * j - 2 );
|
---|
| 1726 |
|
---|
| 1727 | MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) );
|
---|
| 1728 |
|
---|
| 1729 | cleanup:
|
---|
| 1730 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 1731 | if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
|
---|
| 1732 | ret == MBEDTLS_ERR_ECP_IN_PROGRESS )
|
---|
| 1733 | {
|
---|
| 1734 | if( rs_ctx->rsm->state == ecp_rsm_pre_dbl )
|
---|
| 1735 | rs_ctx->rsm->i = j;
|
---|
| 1736 | }
|
---|
| 1737 | #endif
|
---|
| 1738 |
|
---|
| 1739 | return( ret );
|
---|
| 1740 | }
|
---|
| 1741 |
|
---|
| 1742 | /*
|
---|
| 1743 | * Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
|
---|
| 1744 | *
|
---|
| 1745 | * See ecp_comb_recode_core() for background
|
---|
| 1746 | */
|
---|
| 1747 | static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
---|
| 1748 | const mbedtls_ecp_point T[], unsigned char T_size,
|
---|
| 1749 | unsigned char i )
|
---|
| 1750 | {
|
---|
| 1751 | int ret;
|
---|
| 1752 | unsigned char ii, j;
|
---|
| 1753 |
|
---|
| 1754 | /* Ignore the "sign" bit and scale down */
|
---|
| 1755 | ii = ( i & 0x7Fu ) >> 1;
|
---|
| 1756 |
|
---|
| 1757 | /* Read the whole table to thwart cache-based timing attacks */
|
---|
| 1758 | for( j = 0; j < T_size; j++ )
|
---|
| 1759 | {
|
---|
| 1760 | MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
|
---|
| 1761 | MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
|
---|
| 1762 | }
|
---|
| 1763 |
|
---|
| 1764 | /* Safely invert result if i is "negative" */
|
---|
| 1765 | MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
|
---|
| 1766 |
|
---|
| 1767 | cleanup:
|
---|
| 1768 | return( ret );
|
---|
| 1769 | }
|
---|
| 1770 |
|
---|
| 1771 | /*
|
---|
| 1772 | * Core multiplication algorithm for the (modified) comb method.
|
---|
| 1773 | * This part is actually common with the basic comb method (GECC 3.44)
|
---|
| 1774 | *
|
---|
| 1775 | * Cost: d A + d D + 1 R
|
---|
| 1776 | */
|
---|
| 1777 | static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
---|
| 1778 | const mbedtls_ecp_point T[], unsigned char T_size,
|
---|
| 1779 | const unsigned char x[], size_t d,
|
---|
| 1780 | int (*f_rng)(void *, unsigned char *, size_t),
|
---|
| 1781 | void *p_rng,
|
---|
| 1782 | mbedtls_ecp_restart_ctx *rs_ctx )
|
---|
| 1783 | {
|
---|
| 1784 | int ret;
|
---|
| 1785 | mbedtls_ecp_point Txi;
|
---|
| 1786 | size_t i;
|
---|
| 1787 |
|
---|
| 1788 | mbedtls_ecp_point_init( &Txi );
|
---|
| 1789 |
|
---|
| 1790 | #if !defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 1791 | (void) rs_ctx;
|
---|
| 1792 | #endif
|
---|
| 1793 |
|
---|
| 1794 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 1795 | if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
|
---|
| 1796 | rs_ctx->rsm->state != ecp_rsm_comb_core )
|
---|
| 1797 | {
|
---|
| 1798 | rs_ctx->rsm->i = 0;
|
---|
| 1799 | rs_ctx->rsm->state = ecp_rsm_comb_core;
|
---|
| 1800 | }
|
---|
| 1801 |
|
---|
| 1802 | /* new 'if' instead of nested for the sake of the 'else' branch */
|
---|
| 1803 | if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->i != 0 )
|
---|
| 1804 | {
|
---|
| 1805 | /* restore current index (R already pointing to rs_ctx->rsm->R) */
|
---|
| 1806 | i = rs_ctx->rsm->i;
|
---|
| 1807 | }
|
---|
| 1808 | else
|
---|
| 1809 | #endif
|
---|
| 1810 | {
|
---|
| 1811 | /* Start with a non-zero point and randomize its coordinates */
|
---|
| 1812 | i = d;
|
---|
| 1813 | MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, T_size, x[i] ) );
|
---|
| 1814 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
|
---|
| 1815 | if( f_rng != 0 )
|
---|
| 1816 | MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
|
---|
| 1817 | }
|
---|
| 1818 |
|
---|
| 1819 | while( i != 0 )
|
---|
| 1820 | {
|
---|
| 1821 | MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_DBL + MBEDTLS_ECP_OPS_ADD );
|
---|
| 1822 | --i;
|
---|
| 1823 |
|
---|
| 1824 | MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
|
---|
| 1825 | MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, T_size, x[i] ) );
|
---|
| 1826 | MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
|
---|
| 1827 | }
|
---|
| 1828 |
|
---|
| 1829 | cleanup:
|
---|
| 1830 |
|
---|
| 1831 | mbedtls_ecp_point_free( &Txi );
|
---|
| 1832 |
|
---|
| 1833 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 1834 | if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
|
---|
| 1835 | ret == MBEDTLS_ERR_ECP_IN_PROGRESS )
|
---|
| 1836 | {
|
---|
| 1837 | rs_ctx->rsm->i = i;
|
---|
| 1838 | /* no need to save R, already pointing to rs_ctx->rsm->R */
|
---|
| 1839 | }
|
---|
| 1840 | #endif
|
---|
| 1841 |
|
---|
| 1842 | return( ret );
|
---|
| 1843 | }
|
---|
| 1844 |
|
---|
| 1845 | /*
|
---|
| 1846 | * Recode the scalar to get constant-time comb multiplication
|
---|
| 1847 | *
|
---|
| 1848 | * As the actual scalar recoding needs an odd scalar as a starting point,
|
---|
| 1849 | * this wrapper ensures that by replacing m by N - m if necessary, and
|
---|
| 1850 | * informs the caller that the result of multiplication will be negated.
|
---|
| 1851 | *
|
---|
| 1852 | * This works because we only support large prime order for Short Weierstrass
|
---|
| 1853 | * curves, so N is always odd hence either m or N - m is.
|
---|
| 1854 | *
|
---|
| 1855 | * See ecp_comb_recode_core() for background.
|
---|
| 1856 | */
|
---|
| 1857 | static int ecp_comb_recode_scalar( const mbedtls_ecp_group *grp,
|
---|
| 1858 | const mbedtls_mpi *m,
|
---|
| 1859 | unsigned char k[COMB_MAX_D + 1],
|
---|
| 1860 | size_t d,
|
---|
| 1861 | unsigned char w,
|
---|
| 1862 | unsigned char *parity_trick )
|
---|
| 1863 | {
|
---|
| 1864 | int ret;
|
---|
| 1865 | mbedtls_mpi M, mm;
|
---|
| 1866 |
|
---|
| 1867 | mbedtls_mpi_init( &M );
|
---|
| 1868 | mbedtls_mpi_init( &mm );
|
---|
| 1869 |
|
---|
| 1870 | /* N is always odd (see above), just make extra sure */
|
---|
| 1871 | if( mbedtls_mpi_get_bit( &grp->N, 0 ) != 1 )
|
---|
| 1872 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 1873 |
|
---|
| 1874 | /* do we need the parity trick? */
|
---|
| 1875 | *parity_trick = ( mbedtls_mpi_get_bit( m, 0 ) == 0 );
|
---|
| 1876 |
|
---|
| 1877 | /* execute parity fix in constant time */
|
---|
| 1878 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &M, m ) );
|
---|
| 1879 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mm, &grp->N, m ) );
|
---|
| 1880 | MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &M, &mm, *parity_trick ) );
|
---|
| 1881 |
|
---|
| 1882 | /* actual scalar recoding */
|
---|
| 1883 | ecp_comb_recode_core( k, d, w, &M );
|
---|
| 1884 |
|
---|
| 1885 | cleanup:
|
---|
| 1886 | mbedtls_mpi_free( &mm );
|
---|
| 1887 | mbedtls_mpi_free( &M );
|
---|
| 1888 |
|
---|
| 1889 | return( ret );
|
---|
| 1890 | }
|
---|
| 1891 |
|
---|
| 1892 | /*
|
---|
| 1893 | * Perform comb multiplication (for short Weierstrass curves)
|
---|
| 1894 | * once the auxiliary table has been pre-computed.
|
---|
| 1895 | *
|
---|
| 1896 | * Scalar recoding may use a parity trick that makes us compute -m * P,
|
---|
| 1897 | * if that is the case we'll need to recover m * P at the end.
|
---|
| 1898 | */
|
---|
| 1899 | static int ecp_mul_comb_after_precomp( const mbedtls_ecp_group *grp,
|
---|
| 1900 | mbedtls_ecp_point *R,
|
---|
| 1901 | const mbedtls_mpi *m,
|
---|
| 1902 | const mbedtls_ecp_point *T,
|
---|
| 1903 | unsigned char T_size,
|
---|
| 1904 | unsigned char w,
|
---|
| 1905 | size_t d,
|
---|
| 1906 | int (*f_rng)(void *, unsigned char *, size_t),
|
---|
| 1907 | void *p_rng,
|
---|
| 1908 | mbedtls_ecp_restart_ctx *rs_ctx )
|
---|
| 1909 | {
|
---|
| 1910 | int ret;
|
---|
| 1911 | unsigned char parity_trick;
|
---|
| 1912 | unsigned char k[COMB_MAX_D + 1];
|
---|
| 1913 | mbedtls_ecp_point *RR = R;
|
---|
| 1914 |
|
---|
| 1915 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 1916 | if( rs_ctx != NULL && rs_ctx->rsm != NULL )
|
---|
| 1917 | {
|
---|
| 1918 | RR = &rs_ctx->rsm->R;
|
---|
| 1919 |
|
---|
| 1920 | if( rs_ctx->rsm->state == ecp_rsm_final_norm )
|
---|
| 1921 | goto final_norm;
|
---|
| 1922 | }
|
---|
| 1923 | #endif
|
---|
| 1924 |
|
---|
| 1925 | MBEDTLS_MPI_CHK( ecp_comb_recode_scalar( grp, m, k, d, w,
|
---|
| 1926 | &parity_trick ) );
|
---|
| 1927 | MBEDTLS_MPI_CHK( ecp_mul_comb_core( grp, RR, T, T_size, k, d,
|
---|
| 1928 | f_rng, p_rng, rs_ctx ) );
|
---|
| 1929 | MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, RR, parity_trick ) );
|
---|
| 1930 |
|
---|
| 1931 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 1932 | if( rs_ctx != NULL && rs_ctx->rsm != NULL )
|
---|
| 1933 | rs_ctx->rsm->state = ecp_rsm_final_norm;
|
---|
| 1934 |
|
---|
| 1935 | final_norm:
|
---|
| 1936 | #endif
|
---|
| 1937 | MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV );
|
---|
| 1938 | MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, RR ) );
|
---|
| 1939 |
|
---|
| 1940 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 1941 | if( rs_ctx != NULL && rs_ctx->rsm != NULL )
|
---|
| 1942 | MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, RR ) );
|
---|
| 1943 | #endif
|
---|
| 1944 |
|
---|
| 1945 | cleanup:
|
---|
| 1946 | return( ret );
|
---|
| 1947 | }
|
---|
| 1948 |
|
---|
| 1949 | /*
|
---|
| 1950 | * Pick window size based on curve size and whether we optimize for base point
|
---|
| 1951 | */
|
---|
| 1952 | static unsigned char ecp_pick_window_size( const mbedtls_ecp_group *grp,
|
---|
| 1953 | unsigned char p_eq_g )
|
---|
| 1954 | {
|
---|
| 1955 | unsigned char w;
|
---|
| 1956 |
|
---|
| 1957 | /*
|
---|
| 1958 | * Minimize the number of multiplications, that is minimize
|
---|
| 1959 | * 10 * d * w + 18 * 2^(w-1) + 11 * d + 7 * w, with d = ceil( nbits / w )
|
---|
| 1960 | * (see costs of the various parts, with 1S = 1M)
|
---|
| 1961 | */
|
---|
| 1962 | w = grp->nbits >= 384 ? 5 : 4;
|
---|
| 1963 |
|
---|
| 1964 | /*
|
---|
| 1965 | * If P == G, pre-compute a bit more, since this may be re-used later.
|
---|
| 1966 | * Just adding one avoids upping the cost of the first mul too much,
|
---|
| 1967 | * and the memory cost too.
|
---|
| 1968 | */
|
---|
| 1969 | if( p_eq_g )
|
---|
| 1970 | w++;
|
---|
| 1971 |
|
---|
| 1972 | /*
|
---|
| 1973 | * Make sure w is within bounds.
|
---|
| 1974 | * (The last test is useful only for very small curves in the test suite.)
|
---|
| 1975 | */
|
---|
| 1976 | if( w > MBEDTLS_ECP_WINDOW_SIZE )
|
---|
| 1977 | w = MBEDTLS_ECP_WINDOW_SIZE;
|
---|
| 1978 | if( w >= grp->nbits )
|
---|
| 1979 | w = 2;
|
---|
| 1980 |
|
---|
| 1981 | return( w );
|
---|
| 1982 | }
|
---|
| 1983 |
|
---|
| 1984 | /*
|
---|
| 1985 | * Multiplication using the comb method - for curves in short Weierstrass form
|
---|
| 1986 | *
|
---|
| 1987 | * This function is mainly responsible for administrative work:
|
---|
| 1988 | * - managing the restart context if enabled
|
---|
| 1989 | * - managing the table of precomputed points (passed between the below two
|
---|
| 1990 | * functions): allocation, computation, ownership tranfer, freeing.
|
---|
| 1991 | *
|
---|
| 1992 | * It delegates the actual arithmetic work to:
|
---|
| 1993 | * ecp_precompute_comb() and ecp_mul_comb_with_precomp()
|
---|
| 1994 | *
|
---|
| 1995 | * See comments on ecp_comb_recode_core() regarding the computation strategy.
|
---|
| 1996 | */
|
---|
| 1997 | static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
---|
| 1998 | const mbedtls_mpi *m, const mbedtls_ecp_point *P,
|
---|
| 1999 | int (*f_rng)(void *, unsigned char *, size_t),
|
---|
| 2000 | void *p_rng,
|
---|
| 2001 | mbedtls_ecp_restart_ctx *rs_ctx )
|
---|
| 2002 | {
|
---|
| 2003 | int ret;
|
---|
| 2004 | unsigned char w, p_eq_g, i;
|
---|
| 2005 | size_t d;
|
---|
| 2006 | unsigned char T_size, T_ok;
|
---|
| 2007 | mbedtls_ecp_point *T;
|
---|
| 2008 |
|
---|
| 2009 | ECP_RS_ENTER( rsm );
|
---|
| 2010 |
|
---|
| 2011 | /* Is P the base point ? */
|
---|
| 2012 | #if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
|
---|
| 2013 | p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
|
---|
| 2014 | mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
|
---|
| 2015 | #else
|
---|
| 2016 | p_eq_g = 0;
|
---|
| 2017 | #endif
|
---|
| 2018 |
|
---|
| 2019 | /* Pick window size and deduce related sizes */
|
---|
| 2020 | w = ecp_pick_window_size( grp, p_eq_g );
|
---|
| 2021 | T_size = 1U << ( w - 1 );
|
---|
| 2022 | d = ( grp->nbits + w - 1 ) / w;
|
---|
| 2023 |
|
---|
| 2024 | /* Pre-computed table: do we have it already for the base point? */
|
---|
| 2025 | if( p_eq_g && grp->T != NULL )
|
---|
| 2026 | {
|
---|
| 2027 | /* second pointer to the same table, will be deleted on exit */
|
---|
| 2028 | T = grp->T;
|
---|
| 2029 | T_ok = 1;
|
---|
| 2030 | }
|
---|
| 2031 | else
|
---|
| 2032 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 2033 | /* Pre-computed table: do we have one in progress? complete? */
|
---|
| 2034 | if( rs_ctx != NULL && rs_ctx->rsm != NULL && rs_ctx->rsm->T != NULL )
|
---|
| 2035 | {
|
---|
| 2036 | /* transfer ownership of T from rsm to local function */
|
---|
| 2037 | T = rs_ctx->rsm->T;
|
---|
| 2038 | rs_ctx->rsm->T = NULL;
|
---|
| 2039 | rs_ctx->rsm->T_size = 0;
|
---|
| 2040 |
|
---|
| 2041 | /* This effectively jumps to the call to mul_comb_after_precomp() */
|
---|
| 2042 | T_ok = rs_ctx->rsm->state >= ecp_rsm_comb_core;
|
---|
| 2043 | }
|
---|
| 2044 | else
|
---|
| 2045 | #endif
|
---|
| 2046 | /* Allocate table if we didn't have any */
|
---|
| 2047 | {
|
---|
| 2048 | T = mbedtls_calloc( T_size, sizeof( mbedtls_ecp_point ) );
|
---|
| 2049 | if( T == NULL )
|
---|
| 2050 | {
|
---|
| 2051 | ret = MBEDTLS_ERR_ECP_ALLOC_FAILED;
|
---|
| 2052 | goto cleanup;
|
---|
| 2053 | }
|
---|
| 2054 |
|
---|
| 2055 | for( i = 0; i < T_size; i++ )
|
---|
| 2056 | mbedtls_ecp_point_init( &T[i] );
|
---|
| 2057 |
|
---|
| 2058 | T_ok = 0;
|
---|
| 2059 | }
|
---|
| 2060 |
|
---|
| 2061 | /* Compute table (or finish computing it) if not done already */
|
---|
| 2062 | if( !T_ok )
|
---|
| 2063 | {
|
---|
| 2064 | MBEDTLS_MPI_CHK( ecp_precompute_comb( grp, T, P, w, d, rs_ctx ) );
|
---|
| 2065 |
|
---|
| 2066 | if( p_eq_g )
|
---|
| 2067 | {
|
---|
| 2068 | /* almost transfer ownership of T to the group, but keep a copy of
|
---|
| 2069 | * the pointer to use for calling the next function more easily */
|
---|
| 2070 | grp->T = T;
|
---|
| 2071 | grp->T_size = T_size;
|
---|
| 2072 | }
|
---|
| 2073 | }
|
---|
| 2074 |
|
---|
| 2075 | /* Actual comb multiplication using precomputed points */
|
---|
| 2076 | MBEDTLS_MPI_CHK( ecp_mul_comb_after_precomp( grp, R, m,
|
---|
| 2077 | T, T_size, w, d,
|
---|
| 2078 | f_rng, p_rng, rs_ctx ) );
|
---|
| 2079 |
|
---|
| 2080 | cleanup:
|
---|
| 2081 |
|
---|
| 2082 | /* does T belong to the group? */
|
---|
| 2083 | if( T == grp->T )
|
---|
| 2084 | T = NULL;
|
---|
| 2085 |
|
---|
| 2086 | /* does T belong to the restart context? */
|
---|
| 2087 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 2088 | if( rs_ctx != NULL && rs_ctx->rsm != NULL && ret == MBEDTLS_ERR_ECP_IN_PROGRESS && T != NULL )
|
---|
| 2089 | {
|
---|
| 2090 | /* transfer ownership of T from local function to rsm */
|
---|
| 2091 | rs_ctx->rsm->T_size = T_size;
|
---|
| 2092 | rs_ctx->rsm->T = T;
|
---|
| 2093 | T = NULL;
|
---|
| 2094 | }
|
---|
| 2095 | #endif
|
---|
| 2096 |
|
---|
| 2097 | /* did T belong to us? then let's destroy it! */
|
---|
| 2098 | if( T != NULL )
|
---|
| 2099 | {
|
---|
| 2100 | for( i = 0; i < T_size; i++ )
|
---|
| 2101 | mbedtls_ecp_point_free( &T[i] );
|
---|
| 2102 | mbedtls_free( T );
|
---|
| 2103 | }
|
---|
| 2104 |
|
---|
| 2105 | /* don't free R while in progress in case R == P */
|
---|
| 2106 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 2107 | if( ret != MBEDTLS_ERR_ECP_IN_PROGRESS )
|
---|
| 2108 | #endif
|
---|
| 2109 | /* prevent caller from using invalid value */
|
---|
| 2110 | if( ret != 0 )
|
---|
| 2111 | mbedtls_ecp_point_free( R );
|
---|
| 2112 |
|
---|
| 2113 | ECP_RS_LEAVE( rsm );
|
---|
| 2114 |
|
---|
| 2115 | return( ret );
|
---|
| 2116 | }
|
---|
| 2117 |
|
---|
| 2118 | #endif /* ECP_SHORTWEIERSTRASS */
|
---|
| 2119 |
|
---|
| 2120 | #if defined(ECP_MONTGOMERY)
|
---|
| 2121 | /*
|
---|
| 2122 | * For Montgomery curves, we do all the internal arithmetic in projective
|
---|
| 2123 | * coordinates. Import/export of points uses only the x coordinates, which is
|
---|
| 2124 | * internaly represented as X / Z.
|
---|
| 2125 | *
|
---|
| 2126 | * For scalar multiplication, we'll use a Montgomery ladder.
|
---|
| 2127 | */
|
---|
| 2128 |
|
---|
| 2129 | /*
|
---|
| 2130 | * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
|
---|
| 2131 | * Cost: 1M + 1I
|
---|
| 2132 | */
|
---|
| 2133 | static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P )
|
---|
| 2134 | {
|
---|
| 2135 | int ret;
|
---|
| 2136 |
|
---|
| 2137 | #if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
|
---|
| 2138 | if( mbedtls_internal_ecp_grp_capable( grp ) )
|
---|
| 2139 | return( mbedtls_internal_ecp_normalize_mxz( grp, P ) );
|
---|
| 2140 | #endif /* MBEDTLS_ECP_NORMALIZE_MXZ_ALT */
|
---|
| 2141 |
|
---|
| 2142 | MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
|
---|
| 2143 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X );
|
---|
| 2144 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
|
---|
| 2145 |
|
---|
| 2146 | cleanup:
|
---|
| 2147 | return( ret );
|
---|
| 2148 | }
|
---|
| 2149 |
|
---|
| 2150 | /*
|
---|
| 2151 | * Randomize projective x/z coordinates:
|
---|
| 2152 | * (X, Z) -> (l X, l Z) for random l
|
---|
| 2153 | * This is sort of the reverse operation of ecp_normalize_mxz().
|
---|
| 2154 | *
|
---|
| 2155 | * This countermeasure was first suggested in [2].
|
---|
| 2156 | * Cost: 2M
|
---|
| 2157 | */
|
---|
| 2158 | static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P,
|
---|
| 2159 | int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
|
---|
| 2160 | {
|
---|
| 2161 | int ret;
|
---|
| 2162 | mbedtls_mpi l;
|
---|
| 2163 | size_t p_size;
|
---|
| 2164 | int count = 0;
|
---|
| 2165 |
|
---|
| 2166 | #if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
|
---|
| 2167 | if( mbedtls_internal_ecp_grp_capable( grp ) )
|
---|
| 2168 | return( mbedtls_internal_ecp_randomize_mxz( grp, P, f_rng, p_rng );
|
---|
| 2169 | #endif /* MBEDTLS_ECP_RANDOMIZE_MXZ_ALT */
|
---|
| 2170 |
|
---|
| 2171 | p_size = ( grp->pbits + 7 ) / 8;
|
---|
| 2172 | mbedtls_mpi_init( &l );
|
---|
| 2173 |
|
---|
| 2174 | /* Generate l such that 1 < l < p */
|
---|
| 2175 | do
|
---|
| 2176 | {
|
---|
| 2177 | MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
|
---|
| 2178 |
|
---|
| 2179 | while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
|
---|
| 2180 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
|
---|
| 2181 |
|
---|
| 2182 | if( count++ > 10 )
|
---|
| 2183 | return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
|
---|
| 2184 | }
|
---|
| 2185 | while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
|
---|
| 2186 |
|
---|
| 2187 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X );
|
---|
| 2188 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z );
|
---|
| 2189 |
|
---|
| 2190 | cleanup:
|
---|
| 2191 | mbedtls_mpi_free( &l );
|
---|
| 2192 |
|
---|
| 2193 | return( ret );
|
---|
| 2194 | }
|
---|
| 2195 |
|
---|
| 2196 | /*
|
---|
| 2197 | * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
|
---|
| 2198 | * for Montgomery curves in x/z coordinates.
|
---|
| 2199 | *
|
---|
| 2200 | * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
|
---|
| 2201 | * with
|
---|
| 2202 | * d = X1
|
---|
| 2203 | * P = (X2, Z2)
|
---|
| 2204 | * Q = (X3, Z3)
|
---|
| 2205 | * R = (X4, Z4)
|
---|
| 2206 | * S = (X5, Z5)
|
---|
| 2207 | * and eliminating temporary variables tO, ..., t4.
|
---|
| 2208 | *
|
---|
| 2209 | * Cost: 5M + 4S
|
---|
| 2210 | */
|
---|
| 2211 | static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
|
---|
| 2212 | mbedtls_ecp_point *R, mbedtls_ecp_point *S,
|
---|
| 2213 | const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
|
---|
| 2214 | const mbedtls_mpi *d )
|
---|
| 2215 | {
|
---|
| 2216 | int ret;
|
---|
| 2217 | mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
|
---|
| 2218 |
|
---|
| 2219 | #if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
|
---|
| 2220 | if( mbedtls_internal_ecp_grp_capable( grp ) )
|
---|
| 2221 | return( mbedtls_internal_ecp_double_add_mxz( grp, R, S, P, Q, d ) );
|
---|
| 2222 | #endif /* MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT */
|
---|
| 2223 |
|
---|
| 2224 | mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
|
---|
| 2225 | mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
|
---|
| 2226 | mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
|
---|
| 2227 |
|
---|
| 2228 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &A, &P->X, &P->Z ) ); MOD_ADD( A );
|
---|
| 2229 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &AA, &A, &A ) ); MOD_MUL( AA );
|
---|
| 2230 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &B, &P->X, &P->Z ) ); MOD_SUB( B );
|
---|
| 2231 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &BB, &B, &B ) ); MOD_MUL( BB );
|
---|
| 2232 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &E, &AA, &BB ) ); MOD_SUB( E );
|
---|
| 2233 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &C, &Q->X, &Q->Z ) ); MOD_ADD( C );
|
---|
| 2234 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &D, &Q->X, &Q->Z ) ); MOD_SUB( D );
|
---|
| 2235 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DA, &D, &A ) ); MOD_MUL( DA );
|
---|
| 2236 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &CB, &C, &B ) ); MOD_MUL( CB );
|
---|
| 2237 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &S->X, &DA, &CB ) ); MOD_MUL( S->X );
|
---|
| 2238 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->X, &S->X, &S->X ) ); MOD_MUL( S->X );
|
---|
| 2239 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &S->Z, &DA, &CB ) ); MOD_SUB( S->Z );
|
---|
| 2240 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, &S->Z, &S->Z ) ); MOD_MUL( S->Z );
|
---|
| 2241 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &S->Z, d, &S->Z ) ); MOD_MUL( S->Z );
|
---|
| 2242 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->X, &AA, &BB ) ); MOD_MUL( R->X );
|
---|
| 2243 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &grp->A, &E ) ); MOD_MUL( R->Z );
|
---|
| 2244 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &R->Z, &BB, &R->Z ) ); MOD_ADD( R->Z );
|
---|
| 2245 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &R->Z, &E, &R->Z ) ); MOD_MUL( R->Z );
|
---|
| 2246 |
|
---|
| 2247 | cleanup:
|
---|
| 2248 | mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
|
---|
| 2249 | mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
|
---|
| 2250 | mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
|
---|
| 2251 |
|
---|
| 2252 | return( ret );
|
---|
| 2253 | }
|
---|
| 2254 |
|
---|
| 2255 | /*
|
---|
| 2256 | * Multiplication with Montgomery ladder in x/z coordinates,
|
---|
| 2257 | * for curves in Montgomery form
|
---|
| 2258 | */
|
---|
| 2259 | static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
---|
| 2260 | const mbedtls_mpi *m, const mbedtls_ecp_point *P,
|
---|
| 2261 | int (*f_rng)(void *, unsigned char *, size_t),
|
---|
| 2262 | void *p_rng )
|
---|
| 2263 | {
|
---|
| 2264 | int ret;
|
---|
| 2265 | size_t i;
|
---|
| 2266 | unsigned char b;
|
---|
| 2267 | mbedtls_ecp_point RP;
|
---|
| 2268 | mbedtls_mpi PX;
|
---|
| 2269 |
|
---|
| 2270 | mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
|
---|
| 2271 |
|
---|
| 2272 | /* Save PX and read from P before writing to R, in case P == R */
|
---|
| 2273 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
|
---|
| 2274 | MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
|
---|
| 2275 |
|
---|
| 2276 | /* Set R to zero in modified x/z coordinates */
|
---|
| 2277 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
|
---|
| 2278 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
|
---|
| 2279 | mbedtls_mpi_free( &R->Y );
|
---|
| 2280 |
|
---|
| 2281 | /* RP.X might be sligtly larger than P, so reduce it */
|
---|
| 2282 | MOD_ADD( RP.X );
|
---|
| 2283 |
|
---|
| 2284 | /* Randomize coordinates of the starting point */
|
---|
| 2285 | if( f_rng != NULL )
|
---|
| 2286 | MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
|
---|
| 2287 |
|
---|
| 2288 | /* Loop invariant: R = result so far, RP = R + P */
|
---|
| 2289 | i = mbedtls_mpi_bitlen( m ); /* one past the (zero-based) most significant bit */
|
---|
| 2290 | while( i-- > 0 )
|
---|
| 2291 | {
|
---|
| 2292 | b = mbedtls_mpi_get_bit( m, i );
|
---|
| 2293 | /*
|
---|
| 2294 | * if (b) R = 2R + P else R = 2R,
|
---|
| 2295 | * which is:
|
---|
| 2296 | * if (b) double_add( RP, R, RP, R )
|
---|
| 2297 | * else double_add( R, RP, R, RP )
|
---|
| 2298 | * but using safe conditional swaps to avoid leaks
|
---|
| 2299 | */
|
---|
| 2300 | MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
|
---|
| 2301 | MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
|
---|
| 2302 | MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
|
---|
| 2303 | MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
|
---|
| 2304 | MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
|
---|
| 2305 | }
|
---|
| 2306 |
|
---|
| 2307 | MBEDTLS_MPI_CHK( ecp_normalize_mxz( grp, R ) );
|
---|
| 2308 |
|
---|
| 2309 | cleanup:
|
---|
| 2310 | mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
|
---|
| 2311 |
|
---|
| 2312 | return( ret );
|
---|
| 2313 | }
|
---|
| 2314 |
|
---|
| 2315 | #endif /* ECP_MONTGOMERY */
|
---|
| 2316 |
|
---|
| 2317 | /*
|
---|
| 2318 | * Restartable multiplication R = m * P
|
---|
| 2319 | */
|
---|
| 2320 | int mbedtls_ecp_mul_restartable( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
---|
| 2321 | const mbedtls_mpi *m, const mbedtls_ecp_point *P,
|
---|
| 2322 | int (*f_rng)(void *, unsigned char *, size_t), void *p_rng,
|
---|
| 2323 | mbedtls_ecp_restart_ctx *rs_ctx )
|
---|
| 2324 | {
|
---|
| 2325 | int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
|
---|
| 2326 | #if defined(MBEDTLS_ECP_INTERNAL_ALT)
|
---|
| 2327 | char is_grp_capable = 0;
|
---|
| 2328 | #endif
|
---|
| 2329 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 2330 | ECP_VALIDATE_RET( R != NULL );
|
---|
| 2331 | ECP_VALIDATE_RET( m != NULL );
|
---|
| 2332 | ECP_VALIDATE_RET( P != NULL );
|
---|
| 2333 |
|
---|
| 2334 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 2335 | /* reset ops count for this call if top-level */
|
---|
| 2336 | if( rs_ctx != NULL && rs_ctx->depth++ == 0 )
|
---|
| 2337 | rs_ctx->ops_done = 0;
|
---|
| 2338 | #endif
|
---|
| 2339 |
|
---|
| 2340 | #if defined(MBEDTLS_ECP_INTERNAL_ALT)
|
---|
| 2341 | if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) )
|
---|
| 2342 | MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
|
---|
| 2343 | #endif /* MBEDTLS_ECP_INTERNAL_ALT */
|
---|
| 2344 |
|
---|
| 2345 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 2346 | /* skip argument check when restarting */
|
---|
| 2347 | if( rs_ctx == NULL || rs_ctx->rsm == NULL )
|
---|
| 2348 | #endif
|
---|
| 2349 | {
|
---|
| 2350 | /* check_privkey is free */
|
---|
| 2351 | MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_CHK );
|
---|
| 2352 |
|
---|
| 2353 | /* Common sanity checks */
|
---|
| 2354 | MBEDTLS_MPI_CHK( mbedtls_ecp_check_privkey( grp, m ) );
|
---|
| 2355 | MBEDTLS_MPI_CHK( mbedtls_ecp_check_pubkey( grp, P ) );
|
---|
| 2356 | }
|
---|
| 2357 |
|
---|
| 2358 | ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
|
---|
| 2359 | #if defined(ECP_MONTGOMERY)
|
---|
| 2360 | if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
|
---|
| 2361 | MBEDTLS_MPI_CHK( ecp_mul_mxz( grp, R, m, P, f_rng, p_rng ) );
|
---|
| 2362 | #endif
|
---|
| 2363 | #if defined(ECP_SHORTWEIERSTRASS)
|
---|
| 2364 | if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
|
---|
| 2365 | MBEDTLS_MPI_CHK( ecp_mul_comb( grp, R, m, P, f_rng, p_rng, rs_ctx ) );
|
---|
| 2366 | #endif
|
---|
| 2367 |
|
---|
| 2368 | cleanup:
|
---|
| 2369 |
|
---|
| 2370 | #if defined(MBEDTLS_ECP_INTERNAL_ALT)
|
---|
| 2371 | if( is_grp_capable )
|
---|
| 2372 | mbedtls_internal_ecp_free( grp );
|
---|
| 2373 | #endif /* MBEDTLS_ECP_INTERNAL_ALT */
|
---|
| 2374 |
|
---|
| 2375 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 2376 | if( rs_ctx != NULL )
|
---|
| 2377 | rs_ctx->depth--;
|
---|
| 2378 | #endif
|
---|
| 2379 |
|
---|
| 2380 | return( ret );
|
---|
| 2381 | }
|
---|
| 2382 |
|
---|
| 2383 | /*
|
---|
| 2384 | * Multiplication R = m * P
|
---|
| 2385 | */
|
---|
| 2386 | int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
---|
| 2387 | const mbedtls_mpi *m, const mbedtls_ecp_point *P,
|
---|
| 2388 | int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
|
---|
| 2389 | {
|
---|
| 2390 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 2391 | ECP_VALIDATE_RET( R != NULL );
|
---|
| 2392 | ECP_VALIDATE_RET( m != NULL );
|
---|
| 2393 | ECP_VALIDATE_RET( P != NULL );
|
---|
| 2394 | return( mbedtls_ecp_mul_restartable( grp, R, m, P, f_rng, p_rng, NULL ) );
|
---|
| 2395 | }
|
---|
| 2396 |
|
---|
| 2397 | #if defined(ECP_SHORTWEIERSTRASS)
|
---|
| 2398 | /*
|
---|
| 2399 | * Check that an affine point is valid as a public key,
|
---|
| 2400 | * short weierstrass curves (SEC1 3.2.3.1)
|
---|
| 2401 | */
|
---|
| 2402 | static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
|
---|
| 2403 | {
|
---|
| 2404 | int ret;
|
---|
| 2405 | mbedtls_mpi YY, RHS;
|
---|
| 2406 |
|
---|
| 2407 | /* pt coordinates must be normalized for our checks */
|
---|
| 2408 | if( mbedtls_mpi_cmp_int( &pt->X, 0 ) < 0 ||
|
---|
| 2409 | mbedtls_mpi_cmp_int( &pt->Y, 0 ) < 0 ||
|
---|
| 2410 | mbedtls_mpi_cmp_mpi( &pt->X, &grp->P ) >= 0 ||
|
---|
| 2411 | mbedtls_mpi_cmp_mpi( &pt->Y, &grp->P ) >= 0 )
|
---|
| 2412 | return( MBEDTLS_ERR_ECP_INVALID_KEY );
|
---|
| 2413 |
|
---|
| 2414 | mbedtls_mpi_init( &YY ); mbedtls_mpi_init( &RHS );
|
---|
| 2415 |
|
---|
| 2416 | /*
|
---|
| 2417 | * YY = Y^2
|
---|
| 2418 | * RHS = X (X^2 + A) + B = X^3 + A X + B
|
---|
| 2419 | */
|
---|
| 2420 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &YY, &pt->Y, &pt->Y ) ); MOD_MUL( YY );
|
---|
| 2421 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &pt->X, &pt->X ) ); MOD_MUL( RHS );
|
---|
| 2422 |
|
---|
| 2423 | /* Special case for A = -3 */
|
---|
| 2424 | if( grp->A.p == NULL )
|
---|
| 2425 | {
|
---|
| 2426 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS );
|
---|
| 2427 | }
|
---|
| 2428 | else
|
---|
| 2429 | {
|
---|
| 2430 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->A ) ); MOD_ADD( RHS );
|
---|
| 2431 | }
|
---|
| 2432 |
|
---|
| 2433 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &RHS, &RHS, &pt->X ) ); MOD_MUL( RHS );
|
---|
| 2434 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &RHS, &RHS, &grp->B ) ); MOD_ADD( RHS );
|
---|
| 2435 |
|
---|
| 2436 | if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
|
---|
| 2437 | ret = MBEDTLS_ERR_ECP_INVALID_KEY;
|
---|
| 2438 |
|
---|
| 2439 | cleanup:
|
---|
| 2440 |
|
---|
| 2441 | mbedtls_mpi_free( &YY ); mbedtls_mpi_free( &RHS );
|
---|
| 2442 |
|
---|
| 2443 | return( ret );
|
---|
| 2444 | }
|
---|
| 2445 | #endif /* ECP_SHORTWEIERSTRASS */
|
---|
| 2446 |
|
---|
| 2447 | /*
|
---|
| 2448 | * R = m * P with shortcuts for m == 1 and m == -1
|
---|
| 2449 | * NOT constant-time - ONLY for short Weierstrass!
|
---|
| 2450 | */
|
---|
| 2451 | static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
|
---|
| 2452 | mbedtls_ecp_point *R,
|
---|
| 2453 | const mbedtls_mpi *m,
|
---|
| 2454 | const mbedtls_ecp_point *P,
|
---|
| 2455 | mbedtls_ecp_restart_ctx *rs_ctx )
|
---|
| 2456 | {
|
---|
| 2457 | int ret;
|
---|
| 2458 |
|
---|
| 2459 | if( mbedtls_mpi_cmp_int( m, 1 ) == 0 )
|
---|
| 2460 | {
|
---|
| 2461 | MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
|
---|
| 2462 | }
|
---|
| 2463 | else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
|
---|
| 2464 | {
|
---|
| 2465 | MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
|
---|
| 2466 | if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 )
|
---|
| 2467 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
|
---|
| 2468 | }
|
---|
| 2469 | else
|
---|
| 2470 | {
|
---|
| 2471 | MBEDTLS_MPI_CHK( mbedtls_ecp_mul_restartable( grp, R, m, P,
|
---|
| 2472 | NULL, NULL, rs_ctx ) );
|
---|
| 2473 | }
|
---|
| 2474 |
|
---|
| 2475 | cleanup:
|
---|
| 2476 | return( ret );
|
---|
| 2477 | }
|
---|
| 2478 |
|
---|
| 2479 | /*
|
---|
| 2480 | * Restartable linear combination
|
---|
| 2481 | * NOT constant-time
|
---|
| 2482 | */
|
---|
| 2483 | int mbedtls_ecp_muladd_restartable(
|
---|
| 2484 | mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
---|
| 2485 | const mbedtls_mpi *m, const mbedtls_ecp_point *P,
|
---|
| 2486 | const mbedtls_mpi *n, const mbedtls_ecp_point *Q,
|
---|
| 2487 | mbedtls_ecp_restart_ctx *rs_ctx )
|
---|
| 2488 | {
|
---|
| 2489 | int ret;
|
---|
| 2490 | mbedtls_ecp_point mP;
|
---|
| 2491 | mbedtls_ecp_point *pmP = &mP;
|
---|
| 2492 | mbedtls_ecp_point *pR = R;
|
---|
| 2493 | #if defined(MBEDTLS_ECP_INTERNAL_ALT)
|
---|
| 2494 | char is_grp_capable = 0;
|
---|
| 2495 | #endif
|
---|
| 2496 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 2497 | ECP_VALIDATE_RET( R != NULL );
|
---|
| 2498 | ECP_VALIDATE_RET( m != NULL );
|
---|
| 2499 | ECP_VALIDATE_RET( P != NULL );
|
---|
| 2500 | ECP_VALIDATE_RET( n != NULL );
|
---|
| 2501 | ECP_VALIDATE_RET( Q != NULL );
|
---|
| 2502 |
|
---|
| 2503 | if( ecp_get_type( grp ) != ECP_TYPE_SHORT_WEIERSTRASS )
|
---|
| 2504 | return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
|
---|
| 2505 |
|
---|
| 2506 | mbedtls_ecp_point_init( &mP );
|
---|
| 2507 |
|
---|
| 2508 | ECP_RS_ENTER( ma );
|
---|
| 2509 |
|
---|
| 2510 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 2511 | if( rs_ctx != NULL && rs_ctx->ma != NULL )
|
---|
| 2512 | {
|
---|
| 2513 | /* redirect intermediate results to restart context */
|
---|
| 2514 | pmP = &rs_ctx->ma->mP;
|
---|
| 2515 | pR = &rs_ctx->ma->R;
|
---|
| 2516 |
|
---|
| 2517 | /* jump to next operation */
|
---|
| 2518 | if( rs_ctx->ma->state == ecp_rsma_mul2 )
|
---|
| 2519 | goto mul2;
|
---|
| 2520 | if( rs_ctx->ma->state == ecp_rsma_add )
|
---|
| 2521 | goto add;
|
---|
| 2522 | if( rs_ctx->ma->state == ecp_rsma_norm )
|
---|
| 2523 | goto norm;
|
---|
| 2524 | }
|
---|
| 2525 | #endif /* MBEDTLS_ECP_RESTARTABLE */
|
---|
| 2526 |
|
---|
| 2527 | MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pmP, m, P, rs_ctx ) );
|
---|
| 2528 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 2529 | if( rs_ctx != NULL && rs_ctx->ma != NULL )
|
---|
| 2530 | rs_ctx->ma->state = ecp_rsma_mul2;
|
---|
| 2531 |
|
---|
| 2532 | mul2:
|
---|
| 2533 | #endif
|
---|
| 2534 | MBEDTLS_MPI_CHK( mbedtls_ecp_mul_shortcuts( grp, pR, n, Q, rs_ctx ) );
|
---|
| 2535 |
|
---|
| 2536 | #if defined(MBEDTLS_ECP_INTERNAL_ALT)
|
---|
| 2537 | if( ( is_grp_capable = mbedtls_internal_ecp_grp_capable( grp ) ) )
|
---|
| 2538 | MBEDTLS_MPI_CHK( mbedtls_internal_ecp_init( grp ) );
|
---|
| 2539 | #endif /* MBEDTLS_ECP_INTERNAL_ALT */
|
---|
| 2540 |
|
---|
| 2541 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 2542 | if( rs_ctx != NULL && rs_ctx->ma != NULL )
|
---|
| 2543 | rs_ctx->ma->state = ecp_rsma_add;
|
---|
| 2544 |
|
---|
| 2545 | add:
|
---|
| 2546 | #endif
|
---|
| 2547 | MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_ADD );
|
---|
| 2548 | MBEDTLS_MPI_CHK( ecp_add_mixed( grp, pR, pmP, pR ) );
|
---|
| 2549 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 2550 | if( rs_ctx != NULL && rs_ctx->ma != NULL )
|
---|
| 2551 | rs_ctx->ma->state = ecp_rsma_norm;
|
---|
| 2552 |
|
---|
| 2553 | norm:
|
---|
| 2554 | #endif
|
---|
| 2555 | MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_INV );
|
---|
| 2556 | MBEDTLS_MPI_CHK( ecp_normalize_jac( grp, pR ) );
|
---|
| 2557 |
|
---|
| 2558 | #if defined(MBEDTLS_ECP_RESTARTABLE)
|
---|
| 2559 | if( rs_ctx != NULL && rs_ctx->ma != NULL )
|
---|
| 2560 | MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, pR ) );
|
---|
| 2561 | #endif
|
---|
| 2562 |
|
---|
| 2563 | cleanup:
|
---|
| 2564 | #if defined(MBEDTLS_ECP_INTERNAL_ALT)
|
---|
| 2565 | if( is_grp_capable )
|
---|
| 2566 | mbedtls_internal_ecp_free( grp );
|
---|
| 2567 | #endif /* MBEDTLS_ECP_INTERNAL_ALT */
|
---|
| 2568 |
|
---|
| 2569 | mbedtls_ecp_point_free( &mP );
|
---|
| 2570 |
|
---|
| 2571 | ECP_RS_LEAVE( ma );
|
---|
| 2572 |
|
---|
| 2573 | return( ret );
|
---|
| 2574 | }
|
---|
| 2575 |
|
---|
| 2576 | /*
|
---|
| 2577 | * Linear combination
|
---|
| 2578 | * NOT constant-time
|
---|
| 2579 | */
|
---|
| 2580 | int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
|
---|
| 2581 | const mbedtls_mpi *m, const mbedtls_ecp_point *P,
|
---|
| 2582 | const mbedtls_mpi *n, const mbedtls_ecp_point *Q )
|
---|
| 2583 | {
|
---|
| 2584 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 2585 | ECP_VALIDATE_RET( R != NULL );
|
---|
| 2586 | ECP_VALIDATE_RET( m != NULL );
|
---|
| 2587 | ECP_VALIDATE_RET( P != NULL );
|
---|
| 2588 | ECP_VALIDATE_RET( n != NULL );
|
---|
| 2589 | ECP_VALIDATE_RET( Q != NULL );
|
---|
| 2590 | return( mbedtls_ecp_muladd_restartable( grp, R, m, P, n, Q, NULL ) );
|
---|
| 2591 | }
|
---|
| 2592 |
|
---|
| 2593 | #if defined(ECP_MONTGOMERY)
|
---|
| 2594 | /*
|
---|
| 2595 | * Check validity of a public key for Montgomery curves with x-only schemes
|
---|
| 2596 | */
|
---|
| 2597 | static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt )
|
---|
| 2598 | {
|
---|
| 2599 | /* [Curve25519 p. 5] Just check X is the correct number of bytes */
|
---|
| 2600 | /* Allow any public value, if it's too big then we'll just reduce it mod p
|
---|
| 2601 | * (RFC 7748 sec. 5 para. 3). */
|
---|
| 2602 | if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 )
|
---|
| 2603 | return( MBEDTLS_ERR_ECP_INVALID_KEY );
|
---|
| 2604 |
|
---|
| 2605 | return( 0 );
|
---|
| 2606 | }
|
---|
| 2607 | #endif /* ECP_MONTGOMERY */
|
---|
| 2608 |
|
---|
| 2609 | /*
|
---|
| 2610 | * Check that a point is valid as a public key
|
---|
| 2611 | */
|
---|
| 2612 | int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp,
|
---|
| 2613 | const mbedtls_ecp_point *pt )
|
---|
| 2614 | {
|
---|
| 2615 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 2616 | ECP_VALIDATE_RET( pt != NULL );
|
---|
| 2617 |
|
---|
| 2618 | /* Must use affine coordinates */
|
---|
| 2619 | if( mbedtls_mpi_cmp_int( &pt->Z, 1 ) != 0 )
|
---|
| 2620 | return( MBEDTLS_ERR_ECP_INVALID_KEY );
|
---|
| 2621 |
|
---|
| 2622 | #if defined(ECP_MONTGOMERY)
|
---|
| 2623 | if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
|
---|
| 2624 | return( ecp_check_pubkey_mx( grp, pt ) );
|
---|
| 2625 | #endif
|
---|
| 2626 | #if defined(ECP_SHORTWEIERSTRASS)
|
---|
| 2627 | if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
|
---|
| 2628 | return( ecp_check_pubkey_sw( grp, pt ) );
|
---|
| 2629 | #endif
|
---|
| 2630 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 2631 | }
|
---|
| 2632 |
|
---|
| 2633 | /*
|
---|
| 2634 | * Check that an mbedtls_mpi is valid as a private key
|
---|
| 2635 | */
|
---|
| 2636 | int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp,
|
---|
| 2637 | const mbedtls_mpi *d )
|
---|
| 2638 | {
|
---|
| 2639 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 2640 | ECP_VALIDATE_RET( d != NULL );
|
---|
| 2641 |
|
---|
| 2642 | #if defined(ECP_MONTGOMERY)
|
---|
| 2643 | if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
|
---|
| 2644 | {
|
---|
| 2645 | /* see RFC 7748 sec. 5 para. 5 */
|
---|
| 2646 | if( mbedtls_mpi_get_bit( d, 0 ) != 0 ||
|
---|
| 2647 | mbedtls_mpi_get_bit( d, 1 ) != 0 ||
|
---|
| 2648 | mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */
|
---|
| 2649 | return( MBEDTLS_ERR_ECP_INVALID_KEY );
|
---|
| 2650 |
|
---|
| 2651 | /* see [Curve25519] page 5 */
|
---|
| 2652 | if( grp->nbits == 254 && mbedtls_mpi_get_bit( d, 2 ) != 0 )
|
---|
| 2653 | return( MBEDTLS_ERR_ECP_INVALID_KEY );
|
---|
| 2654 |
|
---|
| 2655 | return( 0 );
|
---|
| 2656 | }
|
---|
| 2657 | #endif /* ECP_MONTGOMERY */
|
---|
| 2658 | #if defined(ECP_SHORTWEIERSTRASS)
|
---|
| 2659 | if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
|
---|
| 2660 | {
|
---|
| 2661 | /* see SEC1 3.2 */
|
---|
| 2662 | if( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
|
---|
| 2663 | mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 )
|
---|
| 2664 | return( MBEDTLS_ERR_ECP_INVALID_KEY );
|
---|
| 2665 | else
|
---|
| 2666 | return( 0 );
|
---|
| 2667 | }
|
---|
| 2668 | #endif /* ECP_SHORTWEIERSTRASS */
|
---|
| 2669 |
|
---|
| 2670 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 2671 | }
|
---|
| 2672 |
|
---|
| 2673 | /*
|
---|
| 2674 | * Generate a private key
|
---|
| 2675 | */
|
---|
| 2676 | int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp,
|
---|
| 2677 | mbedtls_mpi *d,
|
---|
| 2678 | int (*f_rng)(void *, unsigned char *, size_t),
|
---|
| 2679 | void *p_rng )
|
---|
| 2680 | {
|
---|
| 2681 | int ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
|
---|
| 2682 | size_t n_size;
|
---|
| 2683 |
|
---|
| 2684 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 2685 | ECP_VALIDATE_RET( d != NULL );
|
---|
| 2686 | ECP_VALIDATE_RET( f_rng != NULL );
|
---|
| 2687 |
|
---|
| 2688 | n_size = ( grp->nbits + 7 ) / 8;
|
---|
| 2689 |
|
---|
| 2690 | #if defined(ECP_MONTGOMERY)
|
---|
| 2691 | if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
|
---|
| 2692 | {
|
---|
| 2693 | /* [M225] page 5 */
|
---|
| 2694 | size_t b;
|
---|
| 2695 |
|
---|
| 2696 | do {
|
---|
| 2697 | MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
|
---|
| 2698 | } while( mbedtls_mpi_bitlen( d ) == 0);
|
---|
| 2699 |
|
---|
| 2700 | /* Make sure the most significant bit is nbits */
|
---|
| 2701 | b = mbedtls_mpi_bitlen( d ) - 1; /* mbedtls_mpi_bitlen is one-based */
|
---|
| 2702 | if( b > grp->nbits )
|
---|
| 2703 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, b - grp->nbits ) );
|
---|
| 2704 | else
|
---|
| 2705 | MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) );
|
---|
| 2706 |
|
---|
| 2707 | /* Make sure the last two bits are unset for Curve448, three bits for
|
---|
| 2708 | Curve25519 */
|
---|
| 2709 | MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) );
|
---|
| 2710 | MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) );
|
---|
| 2711 | if( grp->nbits == 254 )
|
---|
| 2712 | {
|
---|
| 2713 | MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) );
|
---|
| 2714 | }
|
---|
| 2715 | }
|
---|
| 2716 | #endif /* ECP_MONTGOMERY */
|
---|
| 2717 |
|
---|
| 2718 | #if defined(ECP_SHORTWEIERSTRASS)
|
---|
| 2719 | if( ecp_get_type( grp ) == ECP_TYPE_SHORT_WEIERSTRASS )
|
---|
| 2720 | {
|
---|
| 2721 | /* SEC1 3.2.1: Generate d such that 1 <= n < N */
|
---|
| 2722 | int count = 0;
|
---|
| 2723 |
|
---|
| 2724 | /*
|
---|
| 2725 | * Match the procedure given in RFC 6979 (deterministic ECDSA):
|
---|
| 2726 | * - use the same byte ordering;
|
---|
| 2727 | * - keep the leftmost nbits bits of the generated octet string;
|
---|
| 2728 | * - try until result is in the desired range.
|
---|
| 2729 | * This also avoids any biais, which is especially important for ECDSA.
|
---|
| 2730 | */
|
---|
| 2731 | do
|
---|
| 2732 | {
|
---|
| 2733 | MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( d, n_size, f_rng, p_rng ) );
|
---|
| 2734 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( d, 8 * n_size - grp->nbits ) );
|
---|
| 2735 |
|
---|
| 2736 | /*
|
---|
| 2737 | * Each try has at worst a probability 1/2 of failing (the msb has
|
---|
| 2738 | * a probability 1/2 of being 0, and then the result will be < N),
|
---|
| 2739 | * so after 30 tries failure probability is a most 2**(-30).
|
---|
| 2740 | *
|
---|
| 2741 | * For most curves, 1 try is enough with overwhelming probability,
|
---|
| 2742 | * since N starts with a lot of 1s in binary, but some curves
|
---|
| 2743 | * such as secp224k1 are actually very close to the worst case.
|
---|
| 2744 | */
|
---|
| 2745 | if( ++count > 30 )
|
---|
| 2746 | return( MBEDTLS_ERR_ECP_RANDOM_FAILED );
|
---|
| 2747 | }
|
---|
| 2748 | while( mbedtls_mpi_cmp_int( d, 1 ) < 0 ||
|
---|
| 2749 | mbedtls_mpi_cmp_mpi( d, &grp->N ) >= 0 );
|
---|
| 2750 | }
|
---|
| 2751 | #endif /* ECP_SHORTWEIERSTRASS */
|
---|
| 2752 |
|
---|
| 2753 | cleanup:
|
---|
| 2754 | return( ret );
|
---|
| 2755 | }
|
---|
| 2756 |
|
---|
| 2757 | /*
|
---|
| 2758 | * Generate a keypair with configurable base point
|
---|
| 2759 | */
|
---|
| 2760 | int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp,
|
---|
| 2761 | const mbedtls_ecp_point *G,
|
---|
| 2762 | mbedtls_mpi *d, mbedtls_ecp_point *Q,
|
---|
| 2763 | int (*f_rng)(void *, unsigned char *, size_t),
|
---|
| 2764 | void *p_rng )
|
---|
| 2765 | {
|
---|
| 2766 | int ret;
|
---|
| 2767 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 2768 | ECP_VALIDATE_RET( d != NULL );
|
---|
| 2769 | ECP_VALIDATE_RET( G != NULL );
|
---|
| 2770 | ECP_VALIDATE_RET( Q != NULL );
|
---|
| 2771 | ECP_VALIDATE_RET( f_rng != NULL );
|
---|
| 2772 |
|
---|
| 2773 | MBEDTLS_MPI_CHK( mbedtls_ecp_gen_privkey( grp, d, f_rng, p_rng ) );
|
---|
| 2774 | MBEDTLS_MPI_CHK( mbedtls_ecp_mul( grp, Q, d, G, f_rng, p_rng ) );
|
---|
| 2775 |
|
---|
| 2776 | cleanup:
|
---|
| 2777 | return( ret );
|
---|
| 2778 | }
|
---|
| 2779 |
|
---|
| 2780 | /*
|
---|
| 2781 | * Generate key pair, wrapper for conventional base point
|
---|
| 2782 | */
|
---|
| 2783 | int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp,
|
---|
| 2784 | mbedtls_mpi *d, mbedtls_ecp_point *Q,
|
---|
| 2785 | int (*f_rng)(void *, unsigned char *, size_t),
|
---|
| 2786 | void *p_rng )
|
---|
| 2787 | {
|
---|
| 2788 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 2789 | ECP_VALIDATE_RET( d != NULL );
|
---|
| 2790 | ECP_VALIDATE_RET( Q != NULL );
|
---|
| 2791 | ECP_VALIDATE_RET( f_rng != NULL );
|
---|
| 2792 |
|
---|
| 2793 | return( mbedtls_ecp_gen_keypair_base( grp, &grp->G, d, Q, f_rng, p_rng ) );
|
---|
| 2794 | }
|
---|
| 2795 |
|
---|
| 2796 | /*
|
---|
| 2797 | * Generate a keypair, prettier wrapper
|
---|
| 2798 | */
|
---|
| 2799 | int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key,
|
---|
| 2800 | int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
|
---|
| 2801 | {
|
---|
| 2802 | int ret;
|
---|
| 2803 | ECP_VALIDATE_RET( key != NULL );
|
---|
| 2804 | ECP_VALIDATE_RET( f_rng != NULL );
|
---|
| 2805 |
|
---|
| 2806 | if( ( ret = mbedtls_ecp_group_load( &key->grp, grp_id ) ) != 0 )
|
---|
| 2807 | return( ret );
|
---|
| 2808 |
|
---|
| 2809 | return( mbedtls_ecp_gen_keypair( &key->grp, &key->d, &key->Q, f_rng, p_rng ) );
|
---|
| 2810 | }
|
---|
| 2811 |
|
---|
| 2812 | /*
|
---|
| 2813 | * Check a public-private key pair
|
---|
| 2814 | */
|
---|
| 2815 | int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv )
|
---|
| 2816 | {
|
---|
| 2817 | int ret;
|
---|
| 2818 | mbedtls_ecp_point Q;
|
---|
| 2819 | mbedtls_ecp_group grp;
|
---|
| 2820 | ECP_VALIDATE_RET( pub != NULL );
|
---|
| 2821 | ECP_VALIDATE_RET( prv != NULL );
|
---|
| 2822 |
|
---|
| 2823 | if( pub->grp.id == MBEDTLS_ECP_DP_NONE ||
|
---|
| 2824 | pub->grp.id != prv->grp.id ||
|
---|
| 2825 | mbedtls_mpi_cmp_mpi( &pub->Q.X, &prv->Q.X ) ||
|
---|
| 2826 | mbedtls_mpi_cmp_mpi( &pub->Q.Y, &prv->Q.Y ) ||
|
---|
| 2827 | mbedtls_mpi_cmp_mpi( &pub->Q.Z, &prv->Q.Z ) )
|
---|
| 2828 | {
|
---|
| 2829 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 2830 | }
|
---|
| 2831 |
|
---|
| 2832 | mbedtls_ecp_point_init( &Q );
|
---|
| 2833 | mbedtls_ecp_group_init( &grp );
|
---|
| 2834 |
|
---|
| 2835 | /* mbedtls_ecp_mul() needs a non-const group... */
|
---|
| 2836 | mbedtls_ecp_group_copy( &grp, &prv->grp );
|
---|
| 2837 |
|
---|
| 2838 | /* Also checks d is valid */
|
---|
| 2839 | MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &Q, &prv->d, &prv->grp.G, NULL, NULL ) );
|
---|
| 2840 |
|
---|
| 2841 | if( mbedtls_mpi_cmp_mpi( &Q.X, &prv->Q.X ) ||
|
---|
| 2842 | mbedtls_mpi_cmp_mpi( &Q.Y, &prv->Q.Y ) ||
|
---|
| 2843 | mbedtls_mpi_cmp_mpi( &Q.Z, &prv->Q.Z ) )
|
---|
| 2844 | {
|
---|
| 2845 | ret = MBEDTLS_ERR_ECP_BAD_INPUT_DATA;
|
---|
| 2846 | goto cleanup;
|
---|
| 2847 | }
|
---|
| 2848 |
|
---|
| 2849 | cleanup:
|
---|
| 2850 | mbedtls_ecp_point_free( &Q );
|
---|
| 2851 | mbedtls_ecp_group_free( &grp );
|
---|
| 2852 |
|
---|
| 2853 | return( ret );
|
---|
| 2854 | }
|
---|
| 2855 |
|
---|
| 2856 | #if defined(MBEDTLS_SELF_TEST)
|
---|
| 2857 |
|
---|
| 2858 | /*
|
---|
| 2859 | * Checkup routine
|
---|
| 2860 | */
|
---|
| 2861 | int mbedtls_ecp_self_test( int verbose )
|
---|
| 2862 | {
|
---|
| 2863 | int ret;
|
---|
| 2864 | size_t i;
|
---|
| 2865 | mbedtls_ecp_group grp;
|
---|
| 2866 | mbedtls_ecp_point R, P;
|
---|
| 2867 | mbedtls_mpi m;
|
---|
| 2868 | unsigned long add_c_prev, dbl_c_prev, mul_c_prev;
|
---|
| 2869 | /* exponents especially adapted for secp192r1 */
|
---|
| 2870 | const char *exponents[] =
|
---|
| 2871 | {
|
---|
| 2872 | "000000000000000000000000000000000000000000000001", /* one */
|
---|
| 2873 | "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22830", /* N - 1 */
|
---|
| 2874 | "5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
|
---|
| 2875 | "400000000000000000000000000000000000000000000000", /* one and zeros */
|
---|
| 2876 | "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* all ones */
|
---|
| 2877 | "555555555555555555555555555555555555555555555555", /* 101010... */
|
---|
| 2878 | };
|
---|
| 2879 |
|
---|
| 2880 | mbedtls_ecp_group_init( &grp );
|
---|
| 2881 | mbedtls_ecp_point_init( &R );
|
---|
| 2882 | mbedtls_ecp_point_init( &P );
|
---|
| 2883 | mbedtls_mpi_init( &m );
|
---|
| 2884 |
|
---|
| 2885 | /* Use secp192r1 if available, or any available curve */
|
---|
| 2886 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
|
---|
| 2887 | MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, MBEDTLS_ECP_DP_SECP192R1 ) );
|
---|
| 2888 | #else
|
---|
| 2889 | MBEDTLS_MPI_CHK( mbedtls_ecp_group_load( &grp, mbedtls_ecp_curve_list()->grp_id ) );
|
---|
| 2890 | #endif
|
---|
| 2891 |
|
---|
| 2892 | if( verbose != 0 )
|
---|
| 2893 | mbedtls_printf( " ECP test #1 (constant op_count, base point G): " );
|
---|
| 2894 |
|
---|
| 2895 | /* Do a dummy multiplication first to trigger precomputation */
|
---|
| 2896 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &m, 2 ) );
|
---|
| 2897 | MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &P, &m, &grp.G, NULL, NULL ) );
|
---|
| 2898 |
|
---|
| 2899 | add_count = 0;
|
---|
| 2900 | dbl_count = 0;
|
---|
| 2901 | mul_count = 0;
|
---|
| 2902 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
|
---|
| 2903 | MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
|
---|
| 2904 |
|
---|
| 2905 | for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
|
---|
| 2906 | {
|
---|
| 2907 | add_c_prev = add_count;
|
---|
| 2908 | dbl_c_prev = dbl_count;
|
---|
| 2909 | mul_c_prev = mul_count;
|
---|
| 2910 | add_count = 0;
|
---|
| 2911 | dbl_count = 0;
|
---|
| 2912 | mul_count = 0;
|
---|
| 2913 |
|
---|
| 2914 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
|
---|
| 2915 | MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &grp.G, NULL, NULL ) );
|
---|
| 2916 |
|
---|
| 2917 | if( add_count != add_c_prev ||
|
---|
| 2918 | dbl_count != dbl_c_prev ||
|
---|
| 2919 | mul_count != mul_c_prev )
|
---|
| 2920 | {
|
---|
| 2921 | if( verbose != 0 )
|
---|
| 2922 | mbedtls_printf( "failed (%u)\n", (unsigned int) i );
|
---|
| 2923 |
|
---|
| 2924 | ret = 1;
|
---|
| 2925 | goto cleanup;
|
---|
| 2926 | }
|
---|
| 2927 | }
|
---|
| 2928 |
|
---|
| 2929 | if( verbose != 0 )
|
---|
| 2930 | mbedtls_printf( "passed\n" );
|
---|
| 2931 |
|
---|
| 2932 | if( verbose != 0 )
|
---|
| 2933 | mbedtls_printf( " ECP test #2 (constant op_count, other point): " );
|
---|
| 2934 | /* We computed P = 2G last time, use it */
|
---|
| 2935 |
|
---|
| 2936 | add_count = 0;
|
---|
| 2937 | dbl_count = 0;
|
---|
| 2938 | mul_count = 0;
|
---|
| 2939 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[0] ) );
|
---|
| 2940 | MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
|
---|
| 2941 |
|
---|
| 2942 | for( i = 1; i < sizeof( exponents ) / sizeof( exponents[0] ); i++ )
|
---|
| 2943 | {
|
---|
| 2944 | add_c_prev = add_count;
|
---|
| 2945 | dbl_c_prev = dbl_count;
|
---|
| 2946 | mul_c_prev = mul_count;
|
---|
| 2947 | add_count = 0;
|
---|
| 2948 | dbl_count = 0;
|
---|
| 2949 | mul_count = 0;
|
---|
| 2950 |
|
---|
| 2951 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &m, 16, exponents[i] ) );
|
---|
| 2952 | MBEDTLS_MPI_CHK( mbedtls_ecp_mul( &grp, &R, &m, &P, NULL, NULL ) );
|
---|
| 2953 |
|
---|
| 2954 | if( add_count != add_c_prev ||
|
---|
| 2955 | dbl_count != dbl_c_prev ||
|
---|
| 2956 | mul_count != mul_c_prev )
|
---|
| 2957 | {
|
---|
| 2958 | if( verbose != 0 )
|
---|
| 2959 | mbedtls_printf( "failed (%u)\n", (unsigned int) i );
|
---|
| 2960 |
|
---|
| 2961 | ret = 1;
|
---|
| 2962 | goto cleanup;
|
---|
| 2963 | }
|
---|
| 2964 | }
|
---|
| 2965 |
|
---|
| 2966 | if( verbose != 0 )
|
---|
| 2967 | mbedtls_printf( "passed\n" );
|
---|
| 2968 |
|
---|
| 2969 | cleanup:
|
---|
| 2970 |
|
---|
| 2971 | if( ret < 0 && verbose != 0 )
|
---|
| 2972 | mbedtls_printf( "Unexpected error, return code = %08X\n", ret );
|
---|
| 2973 |
|
---|
| 2974 | mbedtls_ecp_group_free( &grp );
|
---|
| 2975 | mbedtls_ecp_point_free( &R );
|
---|
| 2976 | mbedtls_ecp_point_free( &P );
|
---|
| 2977 | mbedtls_mpi_free( &m );
|
---|
| 2978 |
|
---|
| 2979 | if( verbose != 0 )
|
---|
| 2980 | mbedtls_printf( "\n" );
|
---|
| 2981 |
|
---|
| 2982 | return( ret );
|
---|
| 2983 | }
|
---|
| 2984 |
|
---|
| 2985 | #endif /* MBEDTLS_SELF_TEST */
|
---|
| 2986 |
|
---|
| 2987 | #endif /* !MBEDTLS_ECP_ALT */
|
---|
| 2988 |
|
---|
| 2989 | #endif /* MBEDTLS_ECP_C */
|
---|