[398] | 1 | /*
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| 2 | * Elliptic curves over GF(p): curve-specific data and 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 | #if !defined(MBEDTLS_CONFIG_FILE)
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| 23 | #include "mbedtls/config.h"
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| 24 | #else
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| 25 | #include MBEDTLS_CONFIG_FILE
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| 26 | #endif
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| 27 |
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| 28 | #if defined(MBEDTLS_ECP_C)
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| 29 |
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| 30 | #include "mbedtls/ecp.h"
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| 31 | #include "mbedtls/platform_util.h"
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| 32 |
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| 33 | #include <string.h>
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| 34 |
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| 35 | #if !defined(MBEDTLS_ECP_ALT)
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| 36 |
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| 37 | /* Parameter validation macros based on platform_util.h */
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| 38 | #define ECP_VALIDATE_RET( cond ) \
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| 39 | MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA )
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| 40 | #define ECP_VALIDATE( cond ) \
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| 41 | MBEDTLS_INTERNAL_VALIDATE( cond )
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| 42 |
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| 43 | #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \
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| 44 | !defined(inline) && !defined(__cplusplus)
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| 45 | #define inline __inline
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| 46 | #endif
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| 47 |
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| 48 | /*
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| 49 | * Conversion macros for embedded constants:
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| 50 | * build lists of mbedtls_mpi_uint's from lists of unsigned char's grouped by 8, 4 or 2
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| 51 | */
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| 52 | #if defined(MBEDTLS_HAVE_INT32)
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| 53 |
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| 54 | #define BYTES_TO_T_UINT_4( a, b, c, d ) \
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| 55 | ( (mbedtls_mpi_uint) a << 0 ) | \
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| 56 | ( (mbedtls_mpi_uint) b << 8 ) | \
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| 57 | ( (mbedtls_mpi_uint) c << 16 ) | \
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| 58 | ( (mbedtls_mpi_uint) d << 24 )
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| 59 |
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| 60 | #define BYTES_TO_T_UINT_2( a, b ) \
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| 61 | BYTES_TO_T_UINT_4( a, b, 0, 0 )
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| 62 |
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| 63 | #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
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| 64 | BYTES_TO_T_UINT_4( a, b, c, d ), \
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| 65 | BYTES_TO_T_UINT_4( e, f, g, h )
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| 66 |
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| 67 | #else /* 64-bits */
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| 68 |
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| 69 | #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \
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| 70 | ( (mbedtls_mpi_uint) a << 0 ) | \
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| 71 | ( (mbedtls_mpi_uint) b << 8 ) | \
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| 72 | ( (mbedtls_mpi_uint) c << 16 ) | \
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| 73 | ( (mbedtls_mpi_uint) d << 24 ) | \
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| 74 | ( (mbedtls_mpi_uint) e << 32 ) | \
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| 75 | ( (mbedtls_mpi_uint) f << 40 ) | \
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| 76 | ( (mbedtls_mpi_uint) g << 48 ) | \
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| 77 | ( (mbedtls_mpi_uint) h << 56 )
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| 78 |
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| 79 | #define BYTES_TO_T_UINT_4( a, b, c, d ) \
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| 80 | BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 )
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| 81 |
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| 82 | #define BYTES_TO_T_UINT_2( a, b ) \
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| 83 | BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 )
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| 84 |
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| 85 | #endif /* bits in mbedtls_mpi_uint */
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| 86 |
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| 87 | /*
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| 88 | * Note: the constants are in little-endian order
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| 89 | * to be directly usable in MPIs
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| 90 | */
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| 91 |
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| 92 | /*
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| 93 | * Domain parameters for secp192r1
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| 94 | */
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| 95 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
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| 96 | static const mbedtls_mpi_uint secp192r1_p[] = {
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| 97 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 98 | BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 99 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 100 | };
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| 101 | static const mbedtls_mpi_uint secp192r1_b[] = {
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| 102 | BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ),
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| 103 | BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ),
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| 104 | BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ),
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| 105 | };
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| 106 | static const mbedtls_mpi_uint secp192r1_gx[] = {
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| 107 | BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ),
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| 108 | BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ),
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| 109 | BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ),
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| 110 | };
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| 111 | static const mbedtls_mpi_uint secp192r1_gy[] = {
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| 112 | BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ),
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| 113 | BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ),
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| 114 | BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ),
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| 115 | };
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| 116 | static const mbedtls_mpi_uint secp192r1_n[] = {
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| 117 | BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ),
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| 118 | BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 119 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 120 | };
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| 121 | #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
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| 122 |
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| 123 | /*
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| 124 | * Domain parameters for secp224r1
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| 125 | */
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| 126 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
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| 127 | static const mbedtls_mpi_uint secp224r1_p[] = {
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| 128 | BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
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| 129 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 130 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 131 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
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| 132 | };
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| 133 | static const mbedtls_mpi_uint secp224r1_b[] = {
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| 134 | BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ),
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| 135 | BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ),
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| 136 | BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ),
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| 137 | BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ),
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| 138 | };
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| 139 | static const mbedtls_mpi_uint secp224r1_gx[] = {
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| 140 | BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ),
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| 141 | BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ),
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| 142 | BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ),
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| 143 | BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ),
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| 144 | };
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| 145 | static const mbedtls_mpi_uint secp224r1_gy[] = {
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| 146 | BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ),
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| 147 | BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ),
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| 148 | BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ),
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| 149 | BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ),
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| 150 | };
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| 151 | static const mbedtls_mpi_uint secp224r1_n[] = {
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| 152 | BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ),
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| 153 | BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ),
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| 154 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 155 | BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
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| 156 | };
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| 157 | #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
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| 158 |
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| 159 | /*
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| 160 | * Domain parameters for secp256r1
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| 161 | */
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| 162 | #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
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| 163 | static const mbedtls_mpi_uint secp256r1_p[] = {
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| 164 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 165 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
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| 166 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
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| 167 | BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 168 | };
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| 169 | static const mbedtls_mpi_uint secp256r1_b[] = {
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| 170 | BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ),
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| 171 | BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ),
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| 172 | BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ),
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| 173 | BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ),
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| 174 | };
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| 175 | static const mbedtls_mpi_uint secp256r1_gx[] = {
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| 176 | BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ),
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| 177 | BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ),
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| 178 | BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ),
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| 179 | BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ),
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| 180 | };
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| 181 | static const mbedtls_mpi_uint secp256r1_gy[] = {
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| 182 | BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ),
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| 183 | BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ),
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| 184 | BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ),
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| 185 | BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ),
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| 186 | };
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| 187 | static const mbedtls_mpi_uint secp256r1_n[] = {
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| 188 | BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ),
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| 189 | BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ),
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| 190 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 191 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 192 | };
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| 193 | #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
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| 194 |
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| 195 | /*
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| 196 | * Domain parameters for secp384r1
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| 197 | */
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| 198 | #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
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| 199 | static const mbedtls_mpi_uint secp384r1_p[] = {
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| 200 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ),
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| 201 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 202 | BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 203 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 204 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 205 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 206 | };
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| 207 | static const mbedtls_mpi_uint secp384r1_b[] = {
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| 208 | BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ),
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| 209 | BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ),
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| 210 | BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ),
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| 211 | BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ),
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| 212 | BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ),
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| 213 | BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ),
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| 214 | };
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| 215 | static const mbedtls_mpi_uint secp384r1_gx[] = {
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| 216 | BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ),
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| 217 | BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ),
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| 218 | BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ),
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| 219 | BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ),
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| 220 | BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ),
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| 221 | BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ),
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| 222 | };
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| 223 | static const mbedtls_mpi_uint secp384r1_gy[] = {
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| 224 | BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ),
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| 225 | BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ),
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| 226 | BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ),
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| 227 | BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ),
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| 228 | BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ),
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| 229 | BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ),
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| 230 | };
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| 231 | static const mbedtls_mpi_uint secp384r1_n[] = {
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| 232 | BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ),
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| 233 | BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ),
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| 234 | BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ),
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| 235 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 236 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 237 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 238 | };
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| 239 | #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
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| 240 |
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| 241 | /*
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| 242 | * Domain parameters for secp521r1
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| 243 | */
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| 244 | #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
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| 245 | static const mbedtls_mpi_uint secp521r1_p[] = {
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| 246 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 247 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 248 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 249 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 250 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 251 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 252 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
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| 253 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 254 | BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
|
---|
| 255 | };
|
---|
| 256 | static const mbedtls_mpi_uint secp521r1_b[] = {
|
---|
| 257 | BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ),
|
---|
| 258 | BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ),
|
---|
| 259 | BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ),
|
---|
| 260 | BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ),
|
---|
| 261 | BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ),
|
---|
| 262 | BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ),
|
---|
| 263 | BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ),
|
---|
| 264 | BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ),
|
---|
| 265 | BYTES_TO_T_UINT_2( 0x51, 0x00 ),
|
---|
| 266 | };
|
---|
| 267 | static const mbedtls_mpi_uint secp521r1_gx[] = {
|
---|
| 268 | BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ),
|
---|
| 269 | BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ),
|
---|
| 270 | BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ),
|
---|
| 271 | BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ),
|
---|
| 272 | BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ),
|
---|
| 273 | BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ),
|
---|
| 274 | BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ),
|
---|
| 275 | BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ),
|
---|
| 276 | BYTES_TO_T_UINT_2( 0xC6, 0x00 ),
|
---|
| 277 | };
|
---|
| 278 | static const mbedtls_mpi_uint secp521r1_gy[] = {
|
---|
| 279 | BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ),
|
---|
| 280 | BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ),
|
---|
| 281 | BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ),
|
---|
| 282 | BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ),
|
---|
| 283 | BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ),
|
---|
| 284 | BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ),
|
---|
| 285 | BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ),
|
---|
| 286 | BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ),
|
---|
| 287 | BYTES_TO_T_UINT_2( 0x18, 0x01 ),
|
---|
| 288 | };
|
---|
| 289 | static const mbedtls_mpi_uint secp521r1_n[] = {
|
---|
| 290 | BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ),
|
---|
| 291 | BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ),
|
---|
| 292 | BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ),
|
---|
| 293 | BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ),
|
---|
| 294 | BYTES_TO_T_UINT_8( 0xFA, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 295 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 296 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 297 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 298 | BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
|
---|
| 299 | };
|
---|
| 300 | #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
|
---|
| 301 |
|
---|
| 302 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
|
---|
| 303 | static const mbedtls_mpi_uint secp192k1_p[] = {
|
---|
| 304 | BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
|
---|
| 305 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 306 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 307 | };
|
---|
| 308 | static const mbedtls_mpi_uint secp192k1_a[] = {
|
---|
| 309 | BYTES_TO_T_UINT_2( 0x00, 0x00 ),
|
---|
| 310 | };
|
---|
| 311 | static const mbedtls_mpi_uint secp192k1_b[] = {
|
---|
| 312 | BYTES_TO_T_UINT_2( 0x03, 0x00 ),
|
---|
| 313 | };
|
---|
| 314 | static const mbedtls_mpi_uint secp192k1_gx[] = {
|
---|
| 315 | BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ),
|
---|
| 316 | BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ),
|
---|
| 317 | BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ),
|
---|
| 318 | };
|
---|
| 319 | static const mbedtls_mpi_uint secp192k1_gy[] = {
|
---|
| 320 | BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ),
|
---|
| 321 | BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ),
|
---|
| 322 | BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ),
|
---|
| 323 | };
|
---|
| 324 | static const mbedtls_mpi_uint secp192k1_n[] = {
|
---|
| 325 | BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ),
|
---|
| 326 | BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ),
|
---|
| 327 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 328 | };
|
---|
| 329 | #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
|
---|
| 330 |
|
---|
| 331 | #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
|
---|
| 332 | static const mbedtls_mpi_uint secp224k1_p[] = {
|
---|
| 333 | BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
|
---|
| 334 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 335 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 336 | BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 337 | };
|
---|
| 338 | static const mbedtls_mpi_uint secp224k1_a[] = {
|
---|
| 339 | BYTES_TO_T_UINT_2( 0x00, 0x00 ),
|
---|
| 340 | };
|
---|
| 341 | static const mbedtls_mpi_uint secp224k1_b[] = {
|
---|
| 342 | BYTES_TO_T_UINT_2( 0x05, 0x00 ),
|
---|
| 343 | };
|
---|
| 344 | static const mbedtls_mpi_uint secp224k1_gx[] = {
|
---|
| 345 | BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ),
|
---|
| 346 | BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ),
|
---|
| 347 | BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ),
|
---|
| 348 | BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ),
|
---|
| 349 | };
|
---|
| 350 | static const mbedtls_mpi_uint secp224k1_gy[] = {
|
---|
| 351 | BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ),
|
---|
| 352 | BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ),
|
---|
| 353 | BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ),
|
---|
| 354 | BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ),
|
---|
| 355 | };
|
---|
| 356 | static const mbedtls_mpi_uint secp224k1_n[] = {
|
---|
| 357 | BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ),
|
---|
| 358 | BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ),
|
---|
| 359 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ),
|
---|
| 360 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ),
|
---|
| 361 | };
|
---|
| 362 | #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
|
---|
| 363 |
|
---|
| 364 | #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
|
---|
| 365 | static const mbedtls_mpi_uint secp256k1_p[] = {
|
---|
| 366 | BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ),
|
---|
| 367 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 368 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 369 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 370 | };
|
---|
| 371 | static const mbedtls_mpi_uint secp256k1_a[] = {
|
---|
| 372 | BYTES_TO_T_UINT_2( 0x00, 0x00 ),
|
---|
| 373 | };
|
---|
| 374 | static const mbedtls_mpi_uint secp256k1_b[] = {
|
---|
| 375 | BYTES_TO_T_UINT_2( 0x07, 0x00 ),
|
---|
| 376 | };
|
---|
| 377 | static const mbedtls_mpi_uint secp256k1_gx[] = {
|
---|
| 378 | BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ),
|
---|
| 379 | BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ),
|
---|
| 380 | BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ),
|
---|
| 381 | BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ),
|
---|
| 382 | };
|
---|
| 383 | static const mbedtls_mpi_uint secp256k1_gy[] = {
|
---|
| 384 | BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ),
|
---|
| 385 | BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ),
|
---|
| 386 | BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ),
|
---|
| 387 | BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ),
|
---|
| 388 | };
|
---|
| 389 | static const mbedtls_mpi_uint secp256k1_n[] = {
|
---|
| 390 | BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ),
|
---|
| 391 | BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ),
|
---|
| 392 | BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 393 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ),
|
---|
| 394 | };
|
---|
| 395 | #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
|
---|
| 396 |
|
---|
| 397 | /*
|
---|
| 398 | * Domain parameters for brainpoolP256r1 (RFC 5639 3.4)
|
---|
| 399 | */
|
---|
| 400 | #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
|
---|
| 401 | static const mbedtls_mpi_uint brainpoolP256r1_p[] = {
|
---|
| 402 | BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ),
|
---|
| 403 | BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ),
|
---|
| 404 | BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
|
---|
| 405 | BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
|
---|
| 406 | };
|
---|
| 407 | static const mbedtls_mpi_uint brainpoolP256r1_a[] = {
|
---|
| 408 | BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ),
|
---|
| 409 | BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ),
|
---|
| 410 | BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ),
|
---|
| 411 | BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ),
|
---|
| 412 | };
|
---|
| 413 | static const mbedtls_mpi_uint brainpoolP256r1_b[] = {
|
---|
| 414 | BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ),
|
---|
| 415 | BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ),
|
---|
| 416 | BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ),
|
---|
| 417 | BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ),
|
---|
| 418 | };
|
---|
| 419 | static const mbedtls_mpi_uint brainpoolP256r1_gx[] = {
|
---|
| 420 | BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ),
|
---|
| 421 | BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ),
|
---|
| 422 | BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ),
|
---|
| 423 | BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ),
|
---|
| 424 | };
|
---|
| 425 | static const mbedtls_mpi_uint brainpoolP256r1_gy[] = {
|
---|
| 426 | BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ),
|
---|
| 427 | BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ),
|
---|
| 428 | BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ),
|
---|
| 429 | BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ),
|
---|
| 430 | };
|
---|
| 431 | static const mbedtls_mpi_uint brainpoolP256r1_n[] = {
|
---|
| 432 | BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ),
|
---|
| 433 | BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ),
|
---|
| 434 | BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ),
|
---|
| 435 | BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ),
|
---|
| 436 | };
|
---|
| 437 | #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */
|
---|
| 438 |
|
---|
| 439 | /*
|
---|
| 440 | * Domain parameters for brainpoolP384r1 (RFC 5639 3.6)
|
---|
| 441 | */
|
---|
| 442 | #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
|
---|
| 443 | static const mbedtls_mpi_uint brainpoolP384r1_p[] = {
|
---|
| 444 | BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ),
|
---|
| 445 | BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ),
|
---|
| 446 | BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ),
|
---|
| 447 | BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
|
---|
| 448 | BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
|
---|
| 449 | BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
|
---|
| 450 | };
|
---|
| 451 | static const mbedtls_mpi_uint brainpoolP384r1_a[] = {
|
---|
| 452 | BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
|
---|
| 453 | BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ),
|
---|
| 454 | BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ),
|
---|
| 455 | BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ),
|
---|
| 456 | BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ),
|
---|
| 457 | BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ),
|
---|
| 458 | };
|
---|
| 459 | static const mbedtls_mpi_uint brainpoolP384r1_b[] = {
|
---|
| 460 | BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ),
|
---|
| 461 | BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ),
|
---|
| 462 | BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ),
|
---|
| 463 | BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ),
|
---|
| 464 | BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ),
|
---|
| 465 | BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ),
|
---|
| 466 | };
|
---|
| 467 | static const mbedtls_mpi_uint brainpoolP384r1_gx[] = {
|
---|
| 468 | BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ),
|
---|
| 469 | BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ),
|
---|
| 470 | BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ),
|
---|
| 471 | BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ),
|
---|
| 472 | BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ),
|
---|
| 473 | BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ),
|
---|
| 474 | };
|
---|
| 475 | static const mbedtls_mpi_uint brainpoolP384r1_gy[] = {
|
---|
| 476 | BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ),
|
---|
| 477 | BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ),
|
---|
| 478 | BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ),
|
---|
| 479 | BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ),
|
---|
| 480 | BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ),
|
---|
| 481 | BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ),
|
---|
| 482 | };
|
---|
| 483 | static const mbedtls_mpi_uint brainpoolP384r1_n[] = {
|
---|
| 484 | BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ),
|
---|
| 485 | BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ),
|
---|
| 486 | BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ),
|
---|
| 487 | BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ),
|
---|
| 488 | BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ),
|
---|
| 489 | BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ),
|
---|
| 490 | };
|
---|
| 491 | #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */
|
---|
| 492 |
|
---|
| 493 | /*
|
---|
| 494 | * Domain parameters for brainpoolP512r1 (RFC 5639 3.7)
|
---|
| 495 | */
|
---|
| 496 | #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
|
---|
| 497 | static const mbedtls_mpi_uint brainpoolP512r1_p[] = {
|
---|
| 498 | BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ),
|
---|
| 499 | BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ),
|
---|
| 500 | BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ),
|
---|
| 501 | BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ),
|
---|
| 502 | BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
|
---|
| 503 | BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
|
---|
| 504 | BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
|
---|
| 505 | BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
|
---|
| 506 | };
|
---|
| 507 | static const mbedtls_mpi_uint brainpoolP512r1_a[] = {
|
---|
| 508 | BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ),
|
---|
| 509 | BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ),
|
---|
| 510 | BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ),
|
---|
| 511 | BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ),
|
---|
| 512 | BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ),
|
---|
| 513 | BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ),
|
---|
| 514 | BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ),
|
---|
| 515 | BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ),
|
---|
| 516 | };
|
---|
| 517 | static const mbedtls_mpi_uint brainpoolP512r1_b[] = {
|
---|
| 518 | BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ),
|
---|
| 519 | BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ),
|
---|
| 520 | BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ),
|
---|
| 521 | BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ),
|
---|
| 522 | BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ),
|
---|
| 523 | BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ),
|
---|
| 524 | BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ),
|
---|
| 525 | BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ),
|
---|
| 526 | };
|
---|
| 527 | static const mbedtls_mpi_uint brainpoolP512r1_gx[] = {
|
---|
| 528 | BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ),
|
---|
| 529 | BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ),
|
---|
| 530 | BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ),
|
---|
| 531 | BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ),
|
---|
| 532 | BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ),
|
---|
| 533 | BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ),
|
---|
| 534 | BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ),
|
---|
| 535 | BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ),
|
---|
| 536 | };
|
---|
| 537 | static const mbedtls_mpi_uint brainpoolP512r1_gy[] = {
|
---|
| 538 | BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ),
|
---|
| 539 | BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ),
|
---|
| 540 | BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ),
|
---|
| 541 | BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ),
|
---|
| 542 | BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ),
|
---|
| 543 | BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ),
|
---|
| 544 | BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ),
|
---|
| 545 | BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ),
|
---|
| 546 | };
|
---|
| 547 | static const mbedtls_mpi_uint brainpoolP512r1_n[] = {
|
---|
| 548 | BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ),
|
---|
| 549 | BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ),
|
---|
| 550 | BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ),
|
---|
| 551 | BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ),
|
---|
| 552 | BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ),
|
---|
| 553 | BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ),
|
---|
| 554 | BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ),
|
---|
| 555 | BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ),
|
---|
| 556 | };
|
---|
| 557 | #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */
|
---|
| 558 |
|
---|
| 559 | /*
|
---|
| 560 | * Create an MPI from embedded constants
|
---|
| 561 | * (assumes len is an exact multiple of sizeof mbedtls_mpi_uint)
|
---|
| 562 | */
|
---|
| 563 | static inline void ecp_mpi_load( mbedtls_mpi *X, const mbedtls_mpi_uint *p, size_t len )
|
---|
| 564 | {
|
---|
| 565 | X->s = 1;
|
---|
| 566 | X->n = len / sizeof( mbedtls_mpi_uint );
|
---|
| 567 | X->p = (mbedtls_mpi_uint *) p;
|
---|
| 568 | }
|
---|
| 569 |
|
---|
| 570 | /*
|
---|
| 571 | * Set an MPI to static value 1
|
---|
| 572 | */
|
---|
| 573 | static inline void ecp_mpi_set1( mbedtls_mpi *X )
|
---|
| 574 | {
|
---|
| 575 | static mbedtls_mpi_uint one[] = { 1 };
|
---|
| 576 | X->s = 1;
|
---|
| 577 | X->n = 1;
|
---|
| 578 | X->p = one;
|
---|
| 579 | }
|
---|
| 580 |
|
---|
| 581 | /*
|
---|
| 582 | * Make group available from embedded constants
|
---|
| 583 | */
|
---|
| 584 | static int ecp_group_load( mbedtls_ecp_group *grp,
|
---|
| 585 | const mbedtls_mpi_uint *p, size_t plen,
|
---|
| 586 | const mbedtls_mpi_uint *a, size_t alen,
|
---|
| 587 | const mbedtls_mpi_uint *b, size_t blen,
|
---|
| 588 | const mbedtls_mpi_uint *gx, size_t gxlen,
|
---|
| 589 | const mbedtls_mpi_uint *gy, size_t gylen,
|
---|
| 590 | const mbedtls_mpi_uint *n, size_t nlen)
|
---|
| 591 | {
|
---|
| 592 | ecp_mpi_load( &grp->P, p, plen );
|
---|
| 593 | if( a != NULL )
|
---|
| 594 | ecp_mpi_load( &grp->A, a, alen );
|
---|
| 595 | ecp_mpi_load( &grp->B, b, blen );
|
---|
| 596 | ecp_mpi_load( &grp->N, n, nlen );
|
---|
| 597 |
|
---|
| 598 | ecp_mpi_load( &grp->G.X, gx, gxlen );
|
---|
| 599 | ecp_mpi_load( &grp->G.Y, gy, gylen );
|
---|
| 600 | ecp_mpi_set1( &grp->G.Z );
|
---|
| 601 |
|
---|
| 602 | grp->pbits = mbedtls_mpi_bitlen( &grp->P );
|
---|
| 603 | grp->nbits = mbedtls_mpi_bitlen( &grp->N );
|
---|
| 604 |
|
---|
| 605 | grp->h = 1;
|
---|
| 606 |
|
---|
| 607 | return( 0 );
|
---|
| 608 | }
|
---|
| 609 |
|
---|
| 610 | #if defined(MBEDTLS_ECP_NIST_OPTIM)
|
---|
| 611 | /* Forward declarations */
|
---|
| 612 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
|
---|
| 613 | static int ecp_mod_p192( mbedtls_mpi * );
|
---|
| 614 | #endif
|
---|
| 615 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
|
---|
| 616 | static int ecp_mod_p224( mbedtls_mpi * );
|
---|
| 617 | #endif
|
---|
| 618 | #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
|
---|
| 619 | static int ecp_mod_p256( mbedtls_mpi * );
|
---|
| 620 | #endif
|
---|
| 621 | #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
|
---|
| 622 | static int ecp_mod_p384( mbedtls_mpi * );
|
---|
| 623 | #endif
|
---|
| 624 | #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
|
---|
| 625 | static int ecp_mod_p521( mbedtls_mpi * );
|
---|
| 626 | #endif
|
---|
| 627 |
|
---|
| 628 | #define NIST_MODP( P ) grp->modp = ecp_mod_ ## P;
|
---|
| 629 | #else
|
---|
| 630 | #define NIST_MODP( P )
|
---|
| 631 | #endif /* MBEDTLS_ECP_NIST_OPTIM */
|
---|
| 632 |
|
---|
| 633 | /* Additional forward declarations */
|
---|
| 634 | #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
|
---|
| 635 | static int ecp_mod_p255( mbedtls_mpi * );
|
---|
| 636 | #endif
|
---|
| 637 | #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
|
---|
| 638 | static int ecp_mod_p448( mbedtls_mpi * );
|
---|
| 639 | #endif
|
---|
| 640 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
|
---|
| 641 | static int ecp_mod_p192k1( mbedtls_mpi * );
|
---|
| 642 | #endif
|
---|
| 643 | #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
|
---|
| 644 | static int ecp_mod_p224k1( mbedtls_mpi * );
|
---|
| 645 | #endif
|
---|
| 646 | #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
|
---|
| 647 | static int ecp_mod_p256k1( mbedtls_mpi * );
|
---|
| 648 | #endif
|
---|
| 649 |
|
---|
| 650 | #define LOAD_GROUP_A( G ) ecp_group_load( grp, \
|
---|
| 651 | G ## _p, sizeof( G ## _p ), \
|
---|
| 652 | G ## _a, sizeof( G ## _a ), \
|
---|
| 653 | G ## _b, sizeof( G ## _b ), \
|
---|
| 654 | G ## _gx, sizeof( G ## _gx ), \
|
---|
| 655 | G ## _gy, sizeof( G ## _gy ), \
|
---|
| 656 | G ## _n, sizeof( G ## _n ) )
|
---|
| 657 |
|
---|
| 658 | #define LOAD_GROUP( G ) ecp_group_load( grp, \
|
---|
| 659 | G ## _p, sizeof( G ## _p ), \
|
---|
| 660 | NULL, 0, \
|
---|
| 661 | G ## _b, sizeof( G ## _b ), \
|
---|
| 662 | G ## _gx, sizeof( G ## _gx ), \
|
---|
| 663 | G ## _gy, sizeof( G ## _gy ), \
|
---|
| 664 | G ## _n, sizeof( G ## _n ) )
|
---|
| 665 |
|
---|
| 666 | #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
|
---|
| 667 | /*
|
---|
| 668 | * Specialized function for creating the Curve25519 group
|
---|
| 669 | */
|
---|
| 670 | static int ecp_use_curve25519( mbedtls_ecp_group *grp )
|
---|
| 671 | {
|
---|
| 672 | int ret;
|
---|
| 673 |
|
---|
| 674 | /* Actually ( A + 2 ) / 4 */
|
---|
| 675 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "01DB42" ) );
|
---|
| 676 |
|
---|
| 677 | /* P = 2^255 - 19 */
|
---|
| 678 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) );
|
---|
| 679 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 255 ) );
|
---|
| 680 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 19 ) );
|
---|
| 681 | grp->pbits = mbedtls_mpi_bitlen( &grp->P );
|
---|
| 682 |
|
---|
| 683 | /* N = 2^252 + 27742317777372353535851937790883648493 */
|
---|
| 684 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->N, 16,
|
---|
| 685 | "14DEF9DEA2F79CD65812631A5CF5D3ED" ) );
|
---|
| 686 | MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 252, 1 ) );
|
---|
| 687 |
|
---|
| 688 | /* Y intentionally not set, since we use x/z coordinates.
|
---|
| 689 | * This is used as a marker to identify Montgomery curves! */
|
---|
| 690 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 9 ) );
|
---|
| 691 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) );
|
---|
| 692 | mbedtls_mpi_free( &grp->G.Y );
|
---|
| 693 |
|
---|
| 694 | /* Actually, the required msb for private keys */
|
---|
| 695 | grp->nbits = 254;
|
---|
| 696 |
|
---|
| 697 | cleanup:
|
---|
| 698 | if( ret != 0 )
|
---|
| 699 | mbedtls_ecp_group_free( grp );
|
---|
| 700 |
|
---|
| 701 | return( ret );
|
---|
| 702 | }
|
---|
| 703 | #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
|
---|
| 704 |
|
---|
| 705 | #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
|
---|
| 706 | /*
|
---|
| 707 | * Specialized function for creating the Curve448 group
|
---|
| 708 | */
|
---|
| 709 | static int ecp_use_curve448( mbedtls_ecp_group *grp )
|
---|
| 710 | {
|
---|
| 711 | mbedtls_mpi Ns;
|
---|
| 712 | int ret;
|
---|
| 713 |
|
---|
| 714 | mbedtls_mpi_init( &Ns );
|
---|
| 715 |
|
---|
| 716 | /* Actually ( A + 2 ) / 4 */
|
---|
| 717 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "98AA" ) );
|
---|
| 718 |
|
---|
| 719 | /* P = 2^448 - 2^224 - 1 */
|
---|
| 720 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) );
|
---|
| 721 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) );
|
---|
| 722 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) );
|
---|
| 723 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) );
|
---|
| 724 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) );
|
---|
| 725 | grp->pbits = mbedtls_mpi_bitlen( &grp->P );
|
---|
| 726 |
|
---|
| 727 | /* Y intentionally not set, since we use x/z coordinates.
|
---|
| 728 | * This is used as a marker to identify Montgomery curves! */
|
---|
| 729 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 5 ) );
|
---|
| 730 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) );
|
---|
| 731 | mbedtls_mpi_free( &grp->G.Y );
|
---|
| 732 |
|
---|
| 733 | /* N = 2^446 - 13818066809895115352007386748515426880336692474882178609894547503885 */
|
---|
| 734 | MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 446, 1 ) );
|
---|
| 735 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &Ns, 16,
|
---|
| 736 | "8335DC163BB124B65129C96FDE933D8D723A70AADC873D6D54A7BB0D" ) );
|
---|
| 737 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &grp->N, &grp->N, &Ns ) );
|
---|
| 738 |
|
---|
| 739 | /* Actually, the required msb for private keys */
|
---|
| 740 | grp->nbits = 447;
|
---|
| 741 |
|
---|
| 742 | cleanup:
|
---|
| 743 | mbedtls_mpi_free( &Ns );
|
---|
| 744 | if( ret != 0 )
|
---|
| 745 | mbedtls_ecp_group_free( grp );
|
---|
| 746 |
|
---|
| 747 | return( ret );
|
---|
| 748 | }
|
---|
| 749 | #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
|
---|
| 750 |
|
---|
| 751 | /*
|
---|
| 752 | * Set a group using well-known domain parameters
|
---|
| 753 | */
|
---|
| 754 | int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id )
|
---|
| 755 | {
|
---|
| 756 | ECP_VALIDATE_RET( grp != NULL );
|
---|
| 757 | mbedtls_ecp_group_free( grp );
|
---|
| 758 |
|
---|
| 759 | grp->id = id;
|
---|
| 760 |
|
---|
| 761 | switch( id )
|
---|
| 762 | {
|
---|
| 763 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
|
---|
| 764 | case MBEDTLS_ECP_DP_SECP192R1:
|
---|
| 765 | NIST_MODP( p192 );
|
---|
| 766 | return( LOAD_GROUP( secp192r1 ) );
|
---|
| 767 | #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
|
---|
| 768 |
|
---|
| 769 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
|
---|
| 770 | case MBEDTLS_ECP_DP_SECP224R1:
|
---|
| 771 | NIST_MODP( p224 );
|
---|
| 772 | return( LOAD_GROUP( secp224r1 ) );
|
---|
| 773 | #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
|
---|
| 774 |
|
---|
| 775 | #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
|
---|
| 776 | case MBEDTLS_ECP_DP_SECP256R1:
|
---|
| 777 | NIST_MODP( p256 );
|
---|
| 778 | return( LOAD_GROUP( secp256r1 ) );
|
---|
| 779 | #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
|
---|
| 780 |
|
---|
| 781 | #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
|
---|
| 782 | case MBEDTLS_ECP_DP_SECP384R1:
|
---|
| 783 | NIST_MODP( p384 );
|
---|
| 784 | return( LOAD_GROUP( secp384r1 ) );
|
---|
| 785 | #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
|
---|
| 786 |
|
---|
| 787 | #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
|
---|
| 788 | case MBEDTLS_ECP_DP_SECP521R1:
|
---|
| 789 | NIST_MODP( p521 );
|
---|
| 790 | return( LOAD_GROUP( secp521r1 ) );
|
---|
| 791 | #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
|
---|
| 792 |
|
---|
| 793 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
|
---|
| 794 | case MBEDTLS_ECP_DP_SECP192K1:
|
---|
| 795 | grp->modp = ecp_mod_p192k1;
|
---|
| 796 | return( LOAD_GROUP_A( secp192k1 ) );
|
---|
| 797 | #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
|
---|
| 798 |
|
---|
| 799 | #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
|
---|
| 800 | case MBEDTLS_ECP_DP_SECP224K1:
|
---|
| 801 | grp->modp = ecp_mod_p224k1;
|
---|
| 802 | return( LOAD_GROUP_A( secp224k1 ) );
|
---|
| 803 | #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
|
---|
| 804 |
|
---|
| 805 | #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
|
---|
| 806 | case MBEDTLS_ECP_DP_SECP256K1:
|
---|
| 807 | grp->modp = ecp_mod_p256k1;
|
---|
| 808 | return( LOAD_GROUP_A( secp256k1 ) );
|
---|
| 809 | #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
|
---|
| 810 |
|
---|
| 811 | #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED)
|
---|
| 812 | case MBEDTLS_ECP_DP_BP256R1:
|
---|
| 813 | return( LOAD_GROUP_A( brainpoolP256r1 ) );
|
---|
| 814 | #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */
|
---|
| 815 |
|
---|
| 816 | #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED)
|
---|
| 817 | case MBEDTLS_ECP_DP_BP384R1:
|
---|
| 818 | return( LOAD_GROUP_A( brainpoolP384r1 ) );
|
---|
| 819 | #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */
|
---|
| 820 |
|
---|
| 821 | #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED)
|
---|
| 822 | case MBEDTLS_ECP_DP_BP512R1:
|
---|
| 823 | return( LOAD_GROUP_A( brainpoolP512r1 ) );
|
---|
| 824 | #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */
|
---|
| 825 |
|
---|
| 826 | #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
|
---|
| 827 | case MBEDTLS_ECP_DP_CURVE25519:
|
---|
| 828 | grp->modp = ecp_mod_p255;
|
---|
| 829 | return( ecp_use_curve25519( grp ) );
|
---|
| 830 | #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
|
---|
| 831 |
|
---|
| 832 | #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
|
---|
| 833 | case MBEDTLS_ECP_DP_CURVE448:
|
---|
| 834 | grp->modp = ecp_mod_p448;
|
---|
| 835 | return( ecp_use_curve448( grp ) );
|
---|
| 836 | #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
|
---|
| 837 |
|
---|
| 838 | default:
|
---|
| 839 | mbedtls_ecp_group_free( grp );
|
---|
| 840 | return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
|
---|
| 841 | }
|
---|
| 842 | }
|
---|
| 843 |
|
---|
| 844 | #if defined(MBEDTLS_ECP_NIST_OPTIM)
|
---|
| 845 | /*
|
---|
| 846 | * Fast reduction modulo the primes used by the NIST curves.
|
---|
| 847 | *
|
---|
| 848 | * These functions are critical for speed, but not needed for correct
|
---|
| 849 | * operations. So, we make the choice to heavily rely on the internals of our
|
---|
| 850 | * bignum library, which creates a tight coupling between these functions and
|
---|
| 851 | * our MPI implementation. However, the coupling between the ECP module and
|
---|
| 852 | * MPI remains loose, since these functions can be deactivated at will.
|
---|
| 853 | */
|
---|
| 854 |
|
---|
| 855 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED)
|
---|
| 856 | /*
|
---|
| 857 | * Compared to the way things are presented in FIPS 186-3 D.2,
|
---|
| 858 | * we proceed in columns, from right (least significant chunk) to left,
|
---|
| 859 | * adding chunks to N in place, and keeping a carry for the next chunk.
|
---|
| 860 | * This avoids moving things around in memory, and uselessly adding zeros,
|
---|
| 861 | * compared to the more straightforward, line-oriented approach.
|
---|
| 862 | *
|
---|
| 863 | * For this prime we need to handle data in chunks of 64 bits.
|
---|
| 864 | * Since this is always a multiple of our basic mbedtls_mpi_uint, we can
|
---|
| 865 | * use a mbedtls_mpi_uint * to designate such a chunk, and small loops to handle it.
|
---|
| 866 | */
|
---|
| 867 |
|
---|
| 868 | /* Add 64-bit chunks (dst += src) and update carry */
|
---|
| 869 | static inline void add64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *src, mbedtls_mpi_uint *carry )
|
---|
| 870 | {
|
---|
| 871 | unsigned char i;
|
---|
| 872 | mbedtls_mpi_uint c = 0;
|
---|
| 873 | for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++, src++ )
|
---|
| 874 | {
|
---|
| 875 | *dst += c; c = ( *dst < c );
|
---|
| 876 | *dst += *src; c += ( *dst < *src );
|
---|
| 877 | }
|
---|
| 878 | *carry += c;
|
---|
| 879 | }
|
---|
| 880 |
|
---|
| 881 | /* Add carry to a 64-bit chunk and update carry */
|
---|
| 882 | static inline void carry64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *carry )
|
---|
| 883 | {
|
---|
| 884 | unsigned char i;
|
---|
| 885 | for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++ )
|
---|
| 886 | {
|
---|
| 887 | *dst += *carry;
|
---|
| 888 | *carry = ( *dst < *carry );
|
---|
| 889 | }
|
---|
| 890 | }
|
---|
| 891 |
|
---|
| 892 | #define WIDTH 8 / sizeof( mbedtls_mpi_uint )
|
---|
| 893 | #define A( i ) N->p + i * WIDTH
|
---|
| 894 | #define ADD( i ) add64( p, A( i ), &c )
|
---|
| 895 | #define NEXT p += WIDTH; carry64( p, &c )
|
---|
| 896 | #define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0
|
---|
| 897 |
|
---|
| 898 | /*
|
---|
| 899 | * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1)
|
---|
| 900 | */
|
---|
| 901 | static int ecp_mod_p192( mbedtls_mpi *N )
|
---|
| 902 | {
|
---|
| 903 | int ret;
|
---|
| 904 | mbedtls_mpi_uint c = 0;
|
---|
| 905 | mbedtls_mpi_uint *p, *end;
|
---|
| 906 |
|
---|
| 907 | /* Make sure we have enough blocks so that A(5) is legal */
|
---|
| 908 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, 6 * WIDTH ) );
|
---|
| 909 |
|
---|
| 910 | p = N->p;
|
---|
| 911 | end = p + N->n;
|
---|
| 912 |
|
---|
| 913 | ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5
|
---|
| 914 | ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5
|
---|
| 915 | ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5
|
---|
| 916 |
|
---|
| 917 | cleanup:
|
---|
| 918 | return( ret );
|
---|
| 919 | }
|
---|
| 920 |
|
---|
| 921 | #undef WIDTH
|
---|
| 922 | #undef A
|
---|
| 923 | #undef ADD
|
---|
| 924 | #undef NEXT
|
---|
| 925 | #undef LAST
|
---|
| 926 | #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */
|
---|
| 927 |
|
---|
| 928 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \
|
---|
| 929 | defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \
|
---|
| 930 | defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
|
---|
| 931 | /*
|
---|
| 932 | * The reader is advised to first understand ecp_mod_p192() since the same
|
---|
| 933 | * general structure is used here, but with additional complications:
|
---|
| 934 | * (1) chunks of 32 bits, and (2) subtractions.
|
---|
| 935 | */
|
---|
| 936 |
|
---|
| 937 | /*
|
---|
| 938 | * For these primes, we need to handle data in chunks of 32 bits.
|
---|
| 939 | * This makes it more complicated if we use 64 bits limbs in MPI,
|
---|
| 940 | * which prevents us from using a uniform access method as for p192.
|
---|
| 941 | *
|
---|
| 942 | * So, we define a mini abstraction layer to access 32 bit chunks,
|
---|
| 943 | * load them in 'cur' for work, and store them back from 'cur' when done.
|
---|
| 944 | *
|
---|
| 945 | * While at it, also define the size of N in terms of 32-bit chunks.
|
---|
| 946 | */
|
---|
| 947 | #define LOAD32 cur = A( i );
|
---|
| 948 |
|
---|
| 949 | #if defined(MBEDTLS_HAVE_INT32) /* 32 bit */
|
---|
| 950 |
|
---|
| 951 | #define MAX32 N->n
|
---|
| 952 | #define A( j ) N->p[j]
|
---|
| 953 | #define STORE32 N->p[i] = cur;
|
---|
| 954 |
|
---|
| 955 | #else /* 64-bit */
|
---|
| 956 |
|
---|
| 957 | #define MAX32 N->n * 2
|
---|
| 958 | #define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] )
|
---|
| 959 | #define STORE32 \
|
---|
| 960 | if( i % 2 ) { \
|
---|
| 961 | N->p[i/2] &= 0x00000000FFFFFFFF; \
|
---|
| 962 | N->p[i/2] |= ((mbedtls_mpi_uint) cur) << 32; \
|
---|
| 963 | } else { \
|
---|
| 964 | N->p[i/2] &= 0xFFFFFFFF00000000; \
|
---|
| 965 | N->p[i/2] |= (mbedtls_mpi_uint) cur; \
|
---|
| 966 | }
|
---|
| 967 |
|
---|
| 968 | #endif /* sizeof( mbedtls_mpi_uint ) */
|
---|
| 969 |
|
---|
| 970 | /*
|
---|
| 971 | * Helpers for addition and subtraction of chunks, with signed carry.
|
---|
| 972 | */
|
---|
| 973 | static inline void add32( uint32_t *dst, uint32_t src, signed char *carry )
|
---|
| 974 | {
|
---|
| 975 | *dst += src;
|
---|
| 976 | *carry += ( *dst < src );
|
---|
| 977 | }
|
---|
| 978 |
|
---|
| 979 | static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry )
|
---|
| 980 | {
|
---|
| 981 | *carry -= ( *dst < src );
|
---|
| 982 | *dst -= src;
|
---|
| 983 | }
|
---|
| 984 |
|
---|
| 985 | #define ADD( j ) add32( &cur, A( j ), &c );
|
---|
| 986 | #define SUB( j ) sub32( &cur, A( j ), &c );
|
---|
| 987 |
|
---|
| 988 | /*
|
---|
| 989 | * Helpers for the main 'loop'
|
---|
| 990 | * (see fix_negative for the motivation of C)
|
---|
| 991 | */
|
---|
| 992 | #define INIT( b ) \
|
---|
| 993 | int ret; \
|
---|
| 994 | signed char c = 0, cc; \
|
---|
| 995 | uint32_t cur; \
|
---|
| 996 | size_t i = 0, bits = b; \
|
---|
| 997 | mbedtls_mpi C; \
|
---|
| 998 | mbedtls_mpi_uint Cp[ b / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \
|
---|
| 999 | \
|
---|
| 1000 | C.s = 1; \
|
---|
| 1001 | C.n = b / 8 / sizeof( mbedtls_mpi_uint) + 1; \
|
---|
| 1002 | C.p = Cp; \
|
---|
| 1003 | memset( Cp, 0, C.n * sizeof( mbedtls_mpi_uint ) ); \
|
---|
| 1004 | \
|
---|
| 1005 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, b * 2 / 8 / sizeof( mbedtls_mpi_uint ) ) ); \
|
---|
| 1006 | LOAD32;
|
---|
| 1007 |
|
---|
| 1008 | #define NEXT \
|
---|
| 1009 | STORE32; i++; LOAD32; \
|
---|
| 1010 | cc = c; c = 0; \
|
---|
| 1011 | if( cc < 0 ) \
|
---|
| 1012 | sub32( &cur, -cc, &c ); \
|
---|
| 1013 | else \
|
---|
| 1014 | add32( &cur, cc, &c ); \
|
---|
| 1015 |
|
---|
| 1016 | #define LAST \
|
---|
| 1017 | STORE32; i++; \
|
---|
| 1018 | cur = c > 0 ? c : 0; STORE32; \
|
---|
| 1019 | cur = 0; while( ++i < MAX32 ) { STORE32; } \
|
---|
| 1020 | if( c < 0 ) fix_negative( N, c, &C, bits );
|
---|
| 1021 |
|
---|
| 1022 | /*
|
---|
| 1023 | * If the result is negative, we get it in the form
|
---|
| 1024 | * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits'
|
---|
| 1025 | */
|
---|
| 1026 | static inline int fix_negative( mbedtls_mpi *N, signed char c, mbedtls_mpi *C, size_t bits )
|
---|
| 1027 | {
|
---|
| 1028 | int ret;
|
---|
| 1029 |
|
---|
| 1030 | /* C = - c * 2^(bits + 32) */
|
---|
| 1031 | #if !defined(MBEDTLS_HAVE_INT64)
|
---|
| 1032 | ((void) bits);
|
---|
| 1033 | #else
|
---|
| 1034 | if( bits == 224 )
|
---|
| 1035 | C->p[ C->n - 1 ] = ((mbedtls_mpi_uint) -c) << 32;
|
---|
| 1036 | else
|
---|
| 1037 | #endif
|
---|
| 1038 | C->p[ C->n - 1 ] = (mbedtls_mpi_uint) -c;
|
---|
| 1039 |
|
---|
| 1040 | /* N = - ( C - N ) */
|
---|
| 1041 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, C, N ) );
|
---|
| 1042 | N->s = -1;
|
---|
| 1043 |
|
---|
| 1044 | cleanup:
|
---|
| 1045 |
|
---|
| 1046 | return( ret );
|
---|
| 1047 | }
|
---|
| 1048 |
|
---|
| 1049 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED)
|
---|
| 1050 | /*
|
---|
| 1051 | * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2)
|
---|
| 1052 | */
|
---|
| 1053 | static int ecp_mod_p224( mbedtls_mpi *N )
|
---|
| 1054 | {
|
---|
| 1055 | INIT( 224 );
|
---|
| 1056 |
|
---|
| 1057 | SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11
|
---|
| 1058 | SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12
|
---|
| 1059 | SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13
|
---|
| 1060 | SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11
|
---|
| 1061 | SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12
|
---|
| 1062 | SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13
|
---|
| 1063 | SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10
|
---|
| 1064 |
|
---|
| 1065 | cleanup:
|
---|
| 1066 | return( ret );
|
---|
| 1067 | }
|
---|
| 1068 | #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */
|
---|
| 1069 |
|
---|
| 1070 | #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED)
|
---|
| 1071 | /*
|
---|
| 1072 | * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3)
|
---|
| 1073 | */
|
---|
| 1074 | static int ecp_mod_p256( mbedtls_mpi *N )
|
---|
| 1075 | {
|
---|
| 1076 | INIT( 256 );
|
---|
| 1077 |
|
---|
| 1078 | ADD( 8 ); ADD( 9 );
|
---|
| 1079 | SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0
|
---|
| 1080 |
|
---|
| 1081 | ADD( 9 ); ADD( 10 );
|
---|
| 1082 | SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1
|
---|
| 1083 |
|
---|
| 1084 | ADD( 10 ); ADD( 11 );
|
---|
| 1085 | SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2
|
---|
| 1086 |
|
---|
| 1087 | ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 );
|
---|
| 1088 | SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3
|
---|
| 1089 |
|
---|
| 1090 | ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 );
|
---|
| 1091 | SUB( 9 ); SUB( 10 ); NEXT; // A4
|
---|
| 1092 |
|
---|
| 1093 | ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 );
|
---|
| 1094 | SUB( 10 ); SUB( 11 ); NEXT; // A5
|
---|
| 1095 |
|
---|
| 1096 | ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 );
|
---|
| 1097 | SUB( 8 ); SUB( 9 ); NEXT; // A6
|
---|
| 1098 |
|
---|
| 1099 | ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 );
|
---|
| 1100 | SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7
|
---|
| 1101 |
|
---|
| 1102 | cleanup:
|
---|
| 1103 | return( ret );
|
---|
| 1104 | }
|
---|
| 1105 | #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */
|
---|
| 1106 |
|
---|
| 1107 | #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED)
|
---|
| 1108 | /*
|
---|
| 1109 | * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4)
|
---|
| 1110 | */
|
---|
| 1111 | static int ecp_mod_p384( mbedtls_mpi *N )
|
---|
| 1112 | {
|
---|
| 1113 | INIT( 384 );
|
---|
| 1114 |
|
---|
| 1115 | ADD( 12 ); ADD( 21 ); ADD( 20 );
|
---|
| 1116 | SUB( 23 ); NEXT; // A0
|
---|
| 1117 |
|
---|
| 1118 | ADD( 13 ); ADD( 22 ); ADD( 23 );
|
---|
| 1119 | SUB( 12 ); SUB( 20 ); NEXT; // A2
|
---|
| 1120 |
|
---|
| 1121 | ADD( 14 ); ADD( 23 );
|
---|
| 1122 | SUB( 13 ); SUB( 21 ); NEXT; // A2
|
---|
| 1123 |
|
---|
| 1124 | ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 );
|
---|
| 1125 | SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3
|
---|
| 1126 |
|
---|
| 1127 | ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 );
|
---|
| 1128 | SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4
|
---|
| 1129 |
|
---|
| 1130 | ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 );
|
---|
| 1131 | SUB( 16 ); NEXT; // A5
|
---|
| 1132 |
|
---|
| 1133 | ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 );
|
---|
| 1134 | SUB( 17 ); NEXT; // A6
|
---|
| 1135 |
|
---|
| 1136 | ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 );
|
---|
| 1137 | SUB( 18 ); NEXT; // A7
|
---|
| 1138 |
|
---|
| 1139 | ADD( 20 ); ADD( 17 ); ADD( 16 );
|
---|
| 1140 | SUB( 19 ); NEXT; // A8
|
---|
| 1141 |
|
---|
| 1142 | ADD( 21 ); ADD( 18 ); ADD( 17 );
|
---|
| 1143 | SUB( 20 ); NEXT; // A9
|
---|
| 1144 |
|
---|
| 1145 | ADD( 22 ); ADD( 19 ); ADD( 18 );
|
---|
| 1146 | SUB( 21 ); NEXT; // A10
|
---|
| 1147 |
|
---|
| 1148 | ADD( 23 ); ADD( 20 ); ADD( 19 );
|
---|
| 1149 | SUB( 22 ); LAST; // A11
|
---|
| 1150 |
|
---|
| 1151 | cleanup:
|
---|
| 1152 | return( ret );
|
---|
| 1153 | }
|
---|
| 1154 | #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */
|
---|
| 1155 |
|
---|
| 1156 | #undef A
|
---|
| 1157 | #undef LOAD32
|
---|
| 1158 | #undef STORE32
|
---|
| 1159 | #undef MAX32
|
---|
| 1160 | #undef INIT
|
---|
| 1161 | #undef NEXT
|
---|
| 1162 | #undef LAST
|
---|
| 1163 |
|
---|
| 1164 | #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED ||
|
---|
| 1165 | MBEDTLS_ECP_DP_SECP256R1_ENABLED ||
|
---|
| 1166 | MBEDTLS_ECP_DP_SECP384R1_ENABLED */
|
---|
| 1167 |
|
---|
| 1168 | #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED)
|
---|
| 1169 | /*
|
---|
| 1170 | * Here we have an actual Mersenne prime, so things are more straightforward.
|
---|
| 1171 | * However, chunks are aligned on a 'weird' boundary (521 bits).
|
---|
| 1172 | */
|
---|
| 1173 |
|
---|
| 1174 | /* Size of p521 in terms of mbedtls_mpi_uint */
|
---|
| 1175 | #define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 )
|
---|
| 1176 |
|
---|
| 1177 | /* Bits to keep in the most significant mbedtls_mpi_uint */
|
---|
| 1178 | #define P521_MASK 0x01FF
|
---|
| 1179 |
|
---|
| 1180 | /*
|
---|
| 1181 | * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5)
|
---|
| 1182 | * Write N as A1 + 2^521 A0, return A0 + A1
|
---|
| 1183 | */
|
---|
| 1184 | static int ecp_mod_p521( mbedtls_mpi *N )
|
---|
| 1185 | {
|
---|
| 1186 | int ret;
|
---|
| 1187 | size_t i;
|
---|
| 1188 | mbedtls_mpi M;
|
---|
| 1189 | mbedtls_mpi_uint Mp[P521_WIDTH + 1];
|
---|
| 1190 | /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits:
|
---|
| 1191 | * we need to hold bits 513 to 1056, which is 34 limbs, that is
|
---|
| 1192 | * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */
|
---|
| 1193 |
|
---|
| 1194 | if( N->n < P521_WIDTH )
|
---|
| 1195 | return( 0 );
|
---|
| 1196 |
|
---|
| 1197 | /* M = A1 */
|
---|
| 1198 | M.s = 1;
|
---|
| 1199 | M.n = N->n - ( P521_WIDTH - 1 );
|
---|
| 1200 | if( M.n > P521_WIDTH + 1 )
|
---|
| 1201 | M.n = P521_WIDTH + 1;
|
---|
| 1202 | M.p = Mp;
|
---|
| 1203 | memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) );
|
---|
| 1204 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 521 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) );
|
---|
| 1205 |
|
---|
| 1206 | /* N = A0 */
|
---|
| 1207 | N->p[P521_WIDTH - 1] &= P521_MASK;
|
---|
| 1208 | for( i = P521_WIDTH; i < N->n; i++ )
|
---|
| 1209 | N->p[i] = 0;
|
---|
| 1210 |
|
---|
| 1211 | /* N = A0 + A1 */
|
---|
| 1212 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
|
---|
| 1213 |
|
---|
| 1214 | cleanup:
|
---|
| 1215 | return( ret );
|
---|
| 1216 | }
|
---|
| 1217 |
|
---|
| 1218 | #undef P521_WIDTH
|
---|
| 1219 | #undef P521_MASK
|
---|
| 1220 | #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */
|
---|
| 1221 |
|
---|
| 1222 | #endif /* MBEDTLS_ECP_NIST_OPTIM */
|
---|
| 1223 |
|
---|
| 1224 | #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED)
|
---|
| 1225 |
|
---|
| 1226 | /* Size of p255 in terms of mbedtls_mpi_uint */
|
---|
| 1227 | #define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_uint ) + 1 )
|
---|
| 1228 |
|
---|
| 1229 | /*
|
---|
| 1230 | * Fast quasi-reduction modulo p255 = 2^255 - 19
|
---|
| 1231 | * Write N as A0 + 2^255 A1, return A0 + 19 * A1
|
---|
| 1232 | */
|
---|
| 1233 | static int ecp_mod_p255( mbedtls_mpi *N )
|
---|
| 1234 | {
|
---|
| 1235 | int ret;
|
---|
| 1236 | size_t i;
|
---|
| 1237 | mbedtls_mpi M;
|
---|
| 1238 | mbedtls_mpi_uint Mp[P255_WIDTH + 2];
|
---|
| 1239 |
|
---|
| 1240 | if( N->n < P255_WIDTH )
|
---|
| 1241 | return( 0 );
|
---|
| 1242 |
|
---|
| 1243 | /* M = A1 */
|
---|
| 1244 | M.s = 1;
|
---|
| 1245 | M.n = N->n - ( P255_WIDTH - 1 );
|
---|
| 1246 | if( M.n > P255_WIDTH + 1 )
|
---|
| 1247 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 1248 | M.p = Mp;
|
---|
| 1249 | memset( Mp, 0, sizeof Mp );
|
---|
| 1250 | memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) );
|
---|
| 1251 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 255 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) );
|
---|
| 1252 | M.n++; /* Make room for multiplication by 19 */
|
---|
| 1253 |
|
---|
| 1254 | /* N = A0 */
|
---|
| 1255 | MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( N, 255, 0 ) );
|
---|
| 1256 | for( i = P255_WIDTH; i < N->n; i++ )
|
---|
| 1257 | N->p[i] = 0;
|
---|
| 1258 |
|
---|
| 1259 | /* N = A0 + 19 * A1 */
|
---|
| 1260 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &M, 19 ) );
|
---|
| 1261 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
|
---|
| 1262 |
|
---|
| 1263 | cleanup:
|
---|
| 1264 | return( ret );
|
---|
| 1265 | }
|
---|
| 1266 | #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */
|
---|
| 1267 |
|
---|
| 1268 | #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED)
|
---|
| 1269 |
|
---|
| 1270 | /* Size of p448 in terms of mbedtls_mpi_uint */
|
---|
| 1271 | #define P448_WIDTH ( 448 / 8 / sizeof( mbedtls_mpi_uint ) )
|
---|
| 1272 |
|
---|
| 1273 | /* Number of limbs fully occupied by 2^224 (max), and limbs used by it (min) */
|
---|
| 1274 | #define DIV_ROUND_UP( X, Y ) ( ( ( X ) + ( Y ) - 1 ) / ( Y ) )
|
---|
| 1275 | #define P224_WIDTH_MIN ( 28 / sizeof( mbedtls_mpi_uint ) )
|
---|
| 1276 | #define P224_WIDTH_MAX DIV_ROUND_UP( 28, sizeof( mbedtls_mpi_uint ) )
|
---|
| 1277 | #define P224_UNUSED_BITS ( ( P224_WIDTH_MAX * sizeof( mbedtls_mpi_uint ) * 8 ) - 224 )
|
---|
| 1278 |
|
---|
| 1279 | /*
|
---|
| 1280 | * Fast quasi-reduction modulo p448 = 2^448 - 2^224 - 1
|
---|
| 1281 | * Write N as A0 + 2^448 A1 and A1 as B0 + 2^224 B1, and return
|
---|
| 1282 | * A0 + A1 + B1 + (B0 + B1) * 2^224. This is different to the reference
|
---|
| 1283 | * implementation of Curve448, which uses its own special 56-bit limbs rather
|
---|
| 1284 | * than a generic bignum library. We could squeeze some extra speed out on
|
---|
| 1285 | * 32-bit machines by splitting N up into 32-bit limbs and doing the
|
---|
| 1286 | * arithmetic using the limbs directly as we do for the NIST primes above,
|
---|
| 1287 | * but for 64-bit targets it should use half the number of operations if we do
|
---|
| 1288 | * the reduction with 224-bit limbs, since mpi_add_mpi will then use 64-bit adds.
|
---|
| 1289 | */
|
---|
| 1290 | static int ecp_mod_p448( mbedtls_mpi *N )
|
---|
| 1291 | {
|
---|
| 1292 | int ret;
|
---|
| 1293 | size_t i;
|
---|
| 1294 | mbedtls_mpi M, Q;
|
---|
| 1295 | mbedtls_mpi_uint Mp[P448_WIDTH + 1], Qp[P448_WIDTH];
|
---|
| 1296 |
|
---|
| 1297 | if( N->n <= P448_WIDTH )
|
---|
| 1298 | return( 0 );
|
---|
| 1299 |
|
---|
| 1300 | /* M = A1 */
|
---|
| 1301 | M.s = 1;
|
---|
| 1302 | M.n = N->n - ( P448_WIDTH );
|
---|
| 1303 | if( M.n > P448_WIDTH )
|
---|
| 1304 | /* Shouldn't be called with N larger than 2^896! */
|
---|
| 1305 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
|
---|
| 1306 | M.p = Mp;
|
---|
| 1307 | memset( Mp, 0, sizeof( Mp ) );
|
---|
| 1308 | memcpy( Mp, N->p + P448_WIDTH, M.n * sizeof( mbedtls_mpi_uint ) );
|
---|
| 1309 |
|
---|
| 1310 | /* N = A0 */
|
---|
| 1311 | for( i = P448_WIDTH; i < N->n; i++ )
|
---|
| 1312 | N->p[i] = 0;
|
---|
| 1313 |
|
---|
| 1314 | /* N += A1 */
|
---|
| 1315 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) );
|
---|
| 1316 |
|
---|
| 1317 | /* Q = B1, N += B1 */
|
---|
| 1318 | Q = M;
|
---|
| 1319 | Q.p = Qp;
|
---|
| 1320 | memcpy( Qp, Mp, sizeof( Qp ) );
|
---|
| 1321 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Q, 224 ) );
|
---|
| 1322 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &Q ) );
|
---|
| 1323 |
|
---|
| 1324 | /* M = (B0 + B1) * 2^224, N += M */
|
---|
| 1325 | if( sizeof( mbedtls_mpi_uint ) > 4 )
|
---|
| 1326 | Mp[P224_WIDTH_MIN] &= ( (mbedtls_mpi_uint)-1 ) >> ( P224_UNUSED_BITS );
|
---|
| 1327 | for( i = P224_WIDTH_MAX; i < M.n; ++i )
|
---|
| 1328 | Mp[i] = 0;
|
---|
| 1329 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &Q ) );
|
---|
| 1330 | M.n = P448_WIDTH + 1; /* Make room for shifted carry bit from the addition */
|
---|
| 1331 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &M, 224 ) );
|
---|
| 1332 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) );
|
---|
| 1333 |
|
---|
| 1334 | cleanup:
|
---|
| 1335 | return( ret );
|
---|
| 1336 | }
|
---|
| 1337 | #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */
|
---|
| 1338 |
|
---|
| 1339 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \
|
---|
| 1340 | defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \
|
---|
| 1341 | defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
|
---|
| 1342 | /*
|
---|
| 1343 | * Fast quasi-reduction modulo P = 2^s - R,
|
---|
| 1344 | * with R about 33 bits, used by the Koblitz curves.
|
---|
| 1345 | *
|
---|
| 1346 | * Write N as A0 + 2^224 A1, return A0 + R * A1.
|
---|
| 1347 | * Actually do two passes, since R is big.
|
---|
| 1348 | */
|
---|
| 1349 | #define P_KOBLITZ_MAX ( 256 / 8 / sizeof( mbedtls_mpi_uint ) ) // Max limbs in P
|
---|
| 1350 | #define P_KOBLITZ_R ( 8 / sizeof( mbedtls_mpi_uint ) ) // Limbs in R
|
---|
| 1351 | static inline int ecp_mod_koblitz( mbedtls_mpi *N, mbedtls_mpi_uint *Rp, size_t p_limbs,
|
---|
| 1352 | size_t adjust, size_t shift, mbedtls_mpi_uint mask )
|
---|
| 1353 | {
|
---|
| 1354 | int ret;
|
---|
| 1355 | size_t i;
|
---|
| 1356 | mbedtls_mpi M, R;
|
---|
| 1357 | mbedtls_mpi_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R + 1];
|
---|
| 1358 |
|
---|
| 1359 | if( N->n < p_limbs )
|
---|
| 1360 | return( 0 );
|
---|
| 1361 |
|
---|
| 1362 | /* Init R */
|
---|
| 1363 | R.s = 1;
|
---|
| 1364 | R.p = Rp;
|
---|
| 1365 | R.n = P_KOBLITZ_R;
|
---|
| 1366 |
|
---|
| 1367 | /* Common setup for M */
|
---|
| 1368 | M.s = 1;
|
---|
| 1369 | M.p = Mp;
|
---|
| 1370 |
|
---|
| 1371 | /* M = A1 */
|
---|
| 1372 | M.n = N->n - ( p_limbs - adjust );
|
---|
| 1373 | if( M.n > p_limbs + adjust )
|
---|
| 1374 | M.n = p_limbs + adjust;
|
---|
| 1375 | memset( Mp, 0, sizeof Mp );
|
---|
| 1376 | memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) );
|
---|
| 1377 | if( shift != 0 )
|
---|
| 1378 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) );
|
---|
| 1379 | M.n += R.n; /* Make room for multiplication by R */
|
---|
| 1380 |
|
---|
| 1381 | /* N = A0 */
|
---|
| 1382 | if( mask != 0 )
|
---|
| 1383 | N->p[p_limbs - 1] &= mask;
|
---|
| 1384 | for( i = p_limbs; i < N->n; i++ )
|
---|
| 1385 | N->p[i] = 0;
|
---|
| 1386 |
|
---|
| 1387 | /* N = A0 + R * A1 */
|
---|
| 1388 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) );
|
---|
| 1389 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
|
---|
| 1390 |
|
---|
| 1391 | /* Second pass */
|
---|
| 1392 |
|
---|
| 1393 | /* M = A1 */
|
---|
| 1394 | M.n = N->n - ( p_limbs - adjust );
|
---|
| 1395 | if( M.n > p_limbs + adjust )
|
---|
| 1396 | M.n = p_limbs + adjust;
|
---|
| 1397 | memset( Mp, 0, sizeof Mp );
|
---|
| 1398 | memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) );
|
---|
| 1399 | if( shift != 0 )
|
---|
| 1400 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) );
|
---|
| 1401 | M.n += R.n; /* Make room for multiplication by R */
|
---|
| 1402 |
|
---|
| 1403 | /* N = A0 */
|
---|
| 1404 | if( mask != 0 )
|
---|
| 1405 | N->p[p_limbs - 1] &= mask;
|
---|
| 1406 | for( i = p_limbs; i < N->n; i++ )
|
---|
| 1407 | N->p[i] = 0;
|
---|
| 1408 |
|
---|
| 1409 | /* N = A0 + R * A1 */
|
---|
| 1410 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) );
|
---|
| 1411 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) );
|
---|
| 1412 |
|
---|
| 1413 | cleanup:
|
---|
| 1414 | return( ret );
|
---|
| 1415 | }
|
---|
| 1416 | #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) ||
|
---|
| 1417 | MBEDTLS_ECP_DP_SECP224K1_ENABLED) ||
|
---|
| 1418 | MBEDTLS_ECP_DP_SECP256K1_ENABLED) */
|
---|
| 1419 |
|
---|
| 1420 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
|
---|
| 1421 | /*
|
---|
| 1422 | * Fast quasi-reduction modulo p192k1 = 2^192 - R,
|
---|
| 1423 | * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119
|
---|
| 1424 | */
|
---|
| 1425 | static int ecp_mod_p192k1( mbedtls_mpi *N )
|
---|
| 1426 | {
|
---|
| 1427 | static mbedtls_mpi_uint Rp[] = {
|
---|
| 1428 | BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
|
---|
| 1429 |
|
---|
| 1430 | return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
|
---|
| 1431 | }
|
---|
| 1432 | #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */
|
---|
| 1433 |
|
---|
| 1434 | #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
|
---|
| 1435 | /*
|
---|
| 1436 | * Fast quasi-reduction modulo p224k1 = 2^224 - R,
|
---|
| 1437 | * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93
|
---|
| 1438 | */
|
---|
| 1439 | static int ecp_mod_p224k1( mbedtls_mpi *N )
|
---|
| 1440 | {
|
---|
| 1441 | static mbedtls_mpi_uint Rp[] = {
|
---|
| 1442 | BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
|
---|
| 1443 |
|
---|
| 1444 | #if defined(MBEDTLS_HAVE_INT64)
|
---|
| 1445 | return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) );
|
---|
| 1446 | #else
|
---|
| 1447 | return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
|
---|
| 1448 | #endif
|
---|
| 1449 | }
|
---|
| 1450 |
|
---|
| 1451 | #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */
|
---|
| 1452 |
|
---|
| 1453 | #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
|
---|
| 1454 | /*
|
---|
| 1455 | * Fast quasi-reduction modulo p256k1 = 2^256 - R,
|
---|
| 1456 | * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1
|
---|
| 1457 | */
|
---|
| 1458 | static int ecp_mod_p256k1( mbedtls_mpi *N )
|
---|
| 1459 | {
|
---|
| 1460 | static mbedtls_mpi_uint Rp[] = {
|
---|
| 1461 | BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) };
|
---|
| 1462 | return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) );
|
---|
| 1463 | }
|
---|
| 1464 | #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */
|
---|
| 1465 |
|
---|
| 1466 | #endif /* !MBEDTLS_ECP_ALT */
|
---|
| 1467 |
|
---|
| 1468 | #endif /* MBEDTLS_ECP_C */
|
---|