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| Rev | Author | Line No. | Line |
|---|---|---|---|
| 8774 | rgimad | 1 | /* |
| 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: GPL-2.0 |
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| 6 | * |
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| 7 | * This program is free software; you can redistribute it and/or modify |
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| 8 | * it under the terms of the GNU General Public License as published by |
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| 9 | * the Free Software Foundation; either version 2 of the License, or |
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| 10 | * (at your option) any later version. |
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| 11 | * |
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| 12 | * This program is distributed in the hope that it will be useful, |
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| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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| 15 | * GNU General Public License for more details. |
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| 16 | * |
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| 17 | * You should have received a copy of the GNU General Public License along |
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| 18 | * with this program; if not, write to the Free Software Foundation, Inc., |
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| 19 | * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. |
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| 20 | * |
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| 21 | * This file is part of mbed TLS (https://tls.mbed.org) |
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| 22 | */ |
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| 23 | |||
| 24 | #if !defined(MBEDTLS_CONFIG_FILE) |
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| 25 | #include "mbedtls/config.h" |
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| 26 | #else |
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| 27 | #include MBEDTLS_CONFIG_FILE |
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| 28 | #endif |
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| 29 | |||
| 30 | #if defined(MBEDTLS_ECP_C) |
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| 31 | |||
| 32 | #include "mbedtls/ecp.h" |
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| 33 | #include "mbedtls/platform_util.h" |
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| 34 | |||
| 35 | #include |
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| 36 | |||
| 37 | #if !defined(MBEDTLS_ECP_ALT) |
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| 38 | |||
| 39 | /* Parameter validation macros based on platform_util.h */ |
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| 40 | #define ECP_VALIDATE_RET( cond ) \ |
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| 41 | MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_ECP_BAD_INPUT_DATA ) |
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| 42 | #define ECP_VALIDATE( cond ) \ |
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| 43 | MBEDTLS_INTERNAL_VALIDATE( cond ) |
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| 44 | |||
| 45 | #if ( defined(__ARMCC_VERSION) || defined(_MSC_VER) ) && \ |
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| 46 | !defined(inline) && !defined(__cplusplus) |
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| 47 | #define inline __inline |
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| 48 | #endif |
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| 49 | |||
| 50 | /* |
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| 51 | * Conversion macros for embedded constants: |
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| 52 | * build lists of mbedtls_mpi_uint's from lists of unsigned char's grouped by 8, 4 or 2 |
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| 53 | */ |
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| 54 | #if defined(MBEDTLS_HAVE_INT32) |
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| 55 | |||
| 56 | #define BYTES_TO_T_UINT_4( a, b, c, d ) \ |
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| 57 | ( (mbedtls_mpi_uint) (a) << 0 ) | \ |
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| 58 | ( (mbedtls_mpi_uint) (b) << 8 ) | \ |
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| 59 | ( (mbedtls_mpi_uint) (c) << 16 ) | \ |
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| 60 | ( (mbedtls_mpi_uint) (d) << 24 ) |
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| 61 | |||
| 62 | #define BYTES_TO_T_UINT_2( a, b ) \ |
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| 63 | BYTES_TO_T_UINT_4( a, b, 0, 0 ) |
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| 64 | |||
| 65 | #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ |
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| 66 | BYTES_TO_T_UINT_4( a, b, c, d ), \ |
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| 67 | BYTES_TO_T_UINT_4( e, f, g, h ) |
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| 68 | |||
| 69 | #else /* 64-bits */ |
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| 70 | |||
| 71 | #define BYTES_TO_T_UINT_8( a, b, c, d, e, f, g, h ) \ |
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| 72 | ( (mbedtls_mpi_uint) (a) << 0 ) | \ |
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| 73 | ( (mbedtls_mpi_uint) (b) << 8 ) | \ |
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| 74 | ( (mbedtls_mpi_uint) (c) << 16 ) | \ |
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| 75 | ( (mbedtls_mpi_uint) (d) << 24 ) | \ |
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| 76 | ( (mbedtls_mpi_uint) (e) << 32 ) | \ |
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| 77 | ( (mbedtls_mpi_uint) (f) << 40 ) | \ |
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| 78 | ( (mbedtls_mpi_uint) (g) << 48 ) | \ |
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| 79 | ( (mbedtls_mpi_uint) (h) << 56 ) |
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| 80 | |||
| 81 | #define BYTES_TO_T_UINT_4( a, b, c, d ) \ |
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| 82 | BYTES_TO_T_UINT_8( a, b, c, d, 0, 0, 0, 0 ) |
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| 83 | |||
| 84 | #define BYTES_TO_T_UINT_2( a, b ) \ |
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| 85 | BYTES_TO_T_UINT_8( a, b, 0, 0, 0, 0, 0, 0 ) |
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| 86 | |||
| 87 | #endif /* bits in mbedtls_mpi_uint */ |
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| 88 | |||
| 89 | /* |
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| 90 | * Note: the constants are in little-endian order |
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| 91 | * to be directly usable in MPIs |
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| 92 | */ |
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| 93 | |||
| 94 | /* |
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| 95 | * Domain parameters for secp192r1 |
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| 96 | */ |
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| 97 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) |
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| 98 | static const mbedtls_mpi_uint secp192r1_p[] = { |
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| 99 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 100 | BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 101 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 102 | }; |
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| 103 | static const mbedtls_mpi_uint secp192r1_b[] = { |
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| 104 | BYTES_TO_T_UINT_8( 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE ), |
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| 105 | BYTES_TO_T_UINT_8( 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F ), |
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| 106 | BYTES_TO_T_UINT_8( 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64 ), |
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| 107 | }; |
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| 108 | static const mbedtls_mpi_uint secp192r1_gx[] = { |
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| 109 | BYTES_TO_T_UINT_8( 0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4 ), |
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| 110 | BYTES_TO_T_UINT_8( 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C ), |
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| 111 | BYTES_TO_T_UINT_8( 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18 ), |
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| 112 | }; |
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| 113 | static const mbedtls_mpi_uint secp192r1_gy[] = { |
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| 114 | BYTES_TO_T_UINT_8( 0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73 ), |
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| 115 | BYTES_TO_T_UINT_8( 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63 ), |
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| 116 | BYTES_TO_T_UINT_8( 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07 ), |
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| 117 | }; |
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| 118 | static const mbedtls_mpi_uint secp192r1_n[] = { |
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| 119 | BYTES_TO_T_UINT_8( 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14 ), |
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| 120 | BYTES_TO_T_UINT_8( 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 121 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 122 | }; |
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| 123 | #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ |
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| 124 | |||
| 125 | /* |
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| 126 | * Domain parameters for secp224r1 |
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| 127 | */ |
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| 128 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) |
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| 129 | static const mbedtls_mpi_uint secp224r1_p[] = { |
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| 130 | BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), |
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| 131 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 132 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 133 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), |
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| 134 | }; |
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| 135 | static const mbedtls_mpi_uint secp224r1_b[] = { |
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| 136 | BYTES_TO_T_UINT_8( 0xB4, 0xFF, 0x55, 0x23, 0x43, 0x39, 0x0B, 0x27 ), |
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| 137 | BYTES_TO_T_UINT_8( 0xBA, 0xD8, 0xBF, 0xD7, 0xB7, 0xB0, 0x44, 0x50 ), |
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| 138 | BYTES_TO_T_UINT_8( 0x56, 0x32, 0x41, 0xF5, 0xAB, 0xB3, 0x04, 0x0C ), |
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| 139 | BYTES_TO_T_UINT_4( 0x85, 0x0A, 0x05, 0xB4 ), |
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| 140 | }; |
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| 141 | static const mbedtls_mpi_uint secp224r1_gx[] = { |
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| 142 | BYTES_TO_T_UINT_8( 0x21, 0x1D, 0x5C, 0x11, 0xD6, 0x80, 0x32, 0x34 ), |
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| 143 | BYTES_TO_T_UINT_8( 0x22, 0x11, 0xC2, 0x56, 0xD3, 0xC1, 0x03, 0x4A ), |
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| 144 | BYTES_TO_T_UINT_8( 0xB9, 0x90, 0x13, 0x32, 0x7F, 0xBF, 0xB4, 0x6B ), |
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| 145 | BYTES_TO_T_UINT_4( 0xBD, 0x0C, 0x0E, 0xB7 ), |
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| 146 | }; |
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| 147 | static const mbedtls_mpi_uint secp224r1_gy[] = { |
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| 148 | BYTES_TO_T_UINT_8( 0x34, 0x7E, 0x00, 0x85, 0x99, 0x81, 0xD5, 0x44 ), |
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| 149 | BYTES_TO_T_UINT_8( 0x64, 0x47, 0x07, 0x5A, 0xA0, 0x75, 0x43, 0xCD ), |
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| 150 | BYTES_TO_T_UINT_8( 0xE6, 0xDF, 0x22, 0x4C, 0xFB, 0x23, 0xF7, 0xB5 ), |
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| 151 | BYTES_TO_T_UINT_4( 0x88, 0x63, 0x37, 0xBD ), |
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| 152 | }; |
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| 153 | static const mbedtls_mpi_uint secp224r1_n[] = { |
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| 154 | BYTES_TO_T_UINT_8( 0x3D, 0x2A, 0x5C, 0x5C, 0x45, 0x29, 0xDD, 0x13 ), |
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| 155 | BYTES_TO_T_UINT_8( 0x3E, 0xF0, 0xB8, 0xE0, 0xA2, 0x16, 0xFF, 0xFF ), |
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| 156 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 157 | BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 158 | }; |
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| 159 | #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ |
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| 160 | |||
| 161 | /* |
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| 162 | * Domain parameters for secp256r1 |
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| 163 | */ |
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| 164 | #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) |
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| 165 | static const mbedtls_mpi_uint secp256r1_p[] = { |
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| 166 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 167 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), |
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| 168 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), |
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| 169 | BYTES_TO_T_UINT_8( 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 170 | }; |
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| 171 | static const mbedtls_mpi_uint secp256r1_b[] = { |
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| 172 | BYTES_TO_T_UINT_8( 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B ), |
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| 173 | BYTES_TO_T_UINT_8( 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65 ), |
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| 174 | BYTES_TO_T_UINT_8( 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3 ), |
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| 175 | BYTES_TO_T_UINT_8( 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A ), |
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| 176 | }; |
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| 177 | static const mbedtls_mpi_uint secp256r1_gx[] = { |
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| 178 | BYTES_TO_T_UINT_8( 0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4 ), |
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| 179 | BYTES_TO_T_UINT_8( 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77 ), |
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| 180 | BYTES_TO_T_UINT_8( 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8 ), |
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| 181 | BYTES_TO_T_UINT_8( 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B ), |
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| 182 | }; |
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| 183 | static const mbedtls_mpi_uint secp256r1_gy[] = { |
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| 184 | BYTES_TO_T_UINT_8( 0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB ), |
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| 185 | BYTES_TO_T_UINT_8( 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B ), |
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| 186 | BYTES_TO_T_UINT_8( 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E ), |
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| 187 | BYTES_TO_T_UINT_8( 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F ), |
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| 188 | }; |
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| 189 | static const mbedtls_mpi_uint secp256r1_n[] = { |
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| 190 | BYTES_TO_T_UINT_8( 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3 ), |
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| 191 | BYTES_TO_T_UINT_8( 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC ), |
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| 192 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 193 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 194 | }; |
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| 195 | #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ |
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| 196 | |||
| 197 | /* |
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| 198 | * Domain parameters for secp384r1 |
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| 199 | */ |
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| 200 | #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) |
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| 201 | static const mbedtls_mpi_uint secp384r1_p[] = { |
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| 202 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00 ), |
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| 203 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 204 | BYTES_TO_T_UINT_8( 0xFE, 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 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 207 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 208 | }; |
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| 209 | static const mbedtls_mpi_uint secp384r1_b[] = { |
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| 210 | BYTES_TO_T_UINT_8( 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A ), |
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| 211 | BYTES_TO_T_UINT_8( 0x9D, 0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6 ), |
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| 212 | BYTES_TO_T_UINT_8( 0x5A, 0x87, 0x13, 0x50, 0x8F, 0x08, 0x14, 0x03 ), |
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| 213 | BYTES_TO_T_UINT_8( 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18 ), |
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| 214 | BYTES_TO_T_UINT_8( 0x19, 0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98 ), |
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| 215 | BYTES_TO_T_UINT_8( 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, 0x2F, 0x31, 0xB3 ), |
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| 216 | }; |
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| 217 | static const mbedtls_mpi_uint secp384r1_gx[] = { |
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| 218 | BYTES_TO_T_UINT_8( 0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A ), |
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| 219 | BYTES_TO_T_UINT_8( 0x6C, 0x29, 0x55, 0xBF, 0x5D, 0xF2, 0x02, 0x55 ), |
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| 220 | BYTES_TO_T_UINT_8( 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, 0x59 ), |
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| 221 | BYTES_TO_T_UINT_8( 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E ), |
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| 222 | BYTES_TO_T_UINT_8( 0x74, 0xAD, 0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E ), |
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| 223 | BYTES_TO_T_UINT_8( 0x37, 0x05, 0x8B, 0xBE, 0x22, 0xCA, 0x87, 0xAA ), |
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| 224 | }; |
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| 225 | static const mbedtls_mpi_uint secp384r1_gy[] = { |
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| 226 | BYTES_TO_T_UINT_8( 0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A ), |
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| 227 | BYTES_TO_T_UINT_8( 0x9D, 0x81, 0x7E, 0x1D, 0xCE, 0xB1, 0x60, 0x0A ), |
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| 228 | BYTES_TO_T_UINT_8( 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, 0xE9 ), |
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| 229 | BYTES_TO_T_UINT_8( 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8 ), |
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| 230 | BYTES_TO_T_UINT_8( 0x29, 0xDC, 0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D ), |
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| 231 | BYTES_TO_T_UINT_8( 0x6F, 0x2C, 0x26, 0x96, 0x4A, 0xDE, 0x17, 0x36 ), |
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| 232 | }; |
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| 233 | static const mbedtls_mpi_uint secp384r1_n[] = { |
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| 234 | BYTES_TO_T_UINT_8( 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC ), |
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| 235 | BYTES_TO_T_UINT_8( 0x7A, 0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58 ), |
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| 236 | BYTES_TO_T_UINT_8( 0xDF, 0x2D, 0x37, 0xF4, 0x81, 0x4D, 0x63, 0xC7 ), |
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| 237 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 238 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 239 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 240 | }; |
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| 241 | #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ |
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| 242 | |||
| 243 | /* |
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| 244 | * Domain parameters for secp521r1 |
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| 245 | */ |
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| 246 | #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) |
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| 247 | static const mbedtls_mpi_uint secp521r1_p[] = { |
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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 ), |
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| 254 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 255 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
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| 256 | BYTES_TO_T_UINT_2( 0xFF, 0x01 ), |
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| 257 | }; |
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| 258 | static const mbedtls_mpi_uint secp521r1_b[] = { |
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| 259 | BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ), |
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| 260 | BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ), |
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| 261 | BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ), |
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| 262 | BYTES_TO_T_UINT_8( 0x7B, 0x93, 0x7E, 0xEC, 0x51, 0x39, 0x19, 0x56 ), |
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| 263 | BYTES_TO_T_UINT_8( 0xE1, 0x09, 0xF1, 0x8E, 0x91, 0x89, 0xB4, 0xB8 ), |
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| 264 | BYTES_TO_T_UINT_8( 0xF3, 0x15, 0xB3, 0x99, 0x5B, 0x72, 0xDA, 0xA2 ), |
||
| 265 | BYTES_TO_T_UINT_8( 0xEE, 0x40, 0x85, 0xB6, 0xA0, 0x21, 0x9A, 0x92 ), |
||
| 266 | BYTES_TO_T_UINT_8( 0x1F, 0x9A, 0x1C, 0x8E, 0x61, 0xB9, 0x3E, 0x95 ), |
||
| 267 | BYTES_TO_T_UINT_2( 0x51, 0x00 ), |
||
| 268 | }; |
||
| 269 | static const mbedtls_mpi_uint secp521r1_gx[] = { |
||
| 270 | BYTES_TO_T_UINT_8( 0x66, 0xBD, 0xE5, 0xC2, 0x31, 0x7E, 0x7E, 0xF9 ), |
||
| 271 | BYTES_TO_T_UINT_8( 0x9B, 0x42, 0x6A, 0x85, 0xC1, 0xB3, 0x48, 0x33 ), |
||
| 272 | BYTES_TO_T_UINT_8( 0xDE, 0xA8, 0xFF, 0xA2, 0x27, 0xC1, 0x1D, 0xFE ), |
||
| 273 | BYTES_TO_T_UINT_8( 0x28, 0x59, 0xE7, 0xEF, 0x77, 0x5E, 0x4B, 0xA1 ), |
||
| 274 | BYTES_TO_T_UINT_8( 0xBA, 0x3D, 0x4D, 0x6B, 0x60, 0xAF, 0x28, 0xF8 ), |
||
| 275 | BYTES_TO_T_UINT_8( 0x21, 0xB5, 0x3F, 0x05, 0x39, 0x81, 0x64, 0x9C ), |
||
| 276 | BYTES_TO_T_UINT_8( 0x42, 0xB4, 0x95, 0x23, 0x66, 0xCB, 0x3E, 0x9E ), |
||
| 277 | BYTES_TO_T_UINT_8( 0xCD, 0xE9, 0x04, 0x04, 0xB7, 0x06, 0x8E, 0x85 ), |
||
| 278 | BYTES_TO_T_UINT_2( 0xC6, 0x00 ), |
||
| 279 | }; |
||
| 280 | static const mbedtls_mpi_uint secp521r1_gy[] = { |
||
| 281 | BYTES_TO_T_UINT_8( 0x50, 0x66, 0xD1, 0x9F, 0x76, 0x94, 0xBE, 0x88 ), |
||
| 282 | BYTES_TO_T_UINT_8( 0x40, 0xC2, 0x72, 0xA2, 0x86, 0x70, 0x3C, 0x35 ), |
||
| 283 | BYTES_TO_T_UINT_8( 0x61, 0x07, 0xAD, 0x3F, 0x01, 0xB9, 0x50, 0xC5 ), |
||
| 284 | BYTES_TO_T_UINT_8( 0x40, 0x26, 0xF4, 0x5E, 0x99, 0x72, 0xEE, 0x97 ), |
||
| 285 | BYTES_TO_T_UINT_8( 0x2C, 0x66, 0x3E, 0x27, 0x17, 0xBD, 0xAF, 0x17 ), |
||
| 286 | BYTES_TO_T_UINT_8( 0x68, 0x44, 0x9B, 0x57, 0x49, 0x44, 0xF5, 0x98 ), |
||
| 287 | BYTES_TO_T_UINT_8( 0xD9, 0x1B, 0x7D, 0x2C, 0xB4, 0x5F, 0x8A, 0x5C ), |
||
| 288 | BYTES_TO_T_UINT_8( 0x04, 0xC0, 0x3B, 0x9A, 0x78, 0x6A, 0x29, 0x39 ), |
||
| 289 | BYTES_TO_T_UINT_2( 0x18, 0x01 ), |
||
| 290 | }; |
||
| 291 | static const mbedtls_mpi_uint secp521r1_n[] = { |
||
| 292 | BYTES_TO_T_UINT_8( 0x09, 0x64, 0x38, 0x91, 0x1E, 0xB7, 0x6F, 0xBB ), |
||
| 293 | BYTES_TO_T_UINT_8( 0xAE, 0x47, 0x9C, 0x89, 0xB8, 0xC9, 0xB5, 0x3B ), |
||
| 294 | BYTES_TO_T_UINT_8( 0xD0, 0xA5, 0x09, 0xF7, 0x48, 0x01, 0xCC, 0x7F ), |
||
| 295 | BYTES_TO_T_UINT_8( 0x6B, 0x96, 0x2F, 0xBF, 0x83, 0x87, 0x86, 0x51 ), |
||
| 296 | BYTES_TO_T_UINT_8( 0xFA, 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_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
||
| 299 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
||
| 300 | BYTES_TO_T_UINT_2( 0xFF, 0x01 ), |
||
| 301 | }; |
||
| 302 | #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ |
||
| 303 | |||
| 304 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) |
||
| 305 | static const mbedtls_mpi_uint secp192k1_p[] = { |
||
| 306 | BYTES_TO_T_UINT_8( 0x37, 0xEE, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), |
||
| 307 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
||
| 308 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
||
| 309 | }; |
||
| 310 | static const mbedtls_mpi_uint secp192k1_a[] = { |
||
| 311 | BYTES_TO_T_UINT_2( 0x00, 0x00 ), |
||
| 312 | }; |
||
| 313 | static const mbedtls_mpi_uint secp192k1_b[] = { |
||
| 314 | BYTES_TO_T_UINT_2( 0x03, 0x00 ), |
||
| 315 | }; |
||
| 316 | static const mbedtls_mpi_uint secp192k1_gx[] = { |
||
| 317 | BYTES_TO_T_UINT_8( 0x7D, 0x6C, 0xE0, 0xEA, 0xB1, 0xD1, 0xA5, 0x1D ), |
||
| 318 | BYTES_TO_T_UINT_8( 0x34, 0xF4, 0xB7, 0x80, 0x02, 0x7D, 0xB0, 0x26 ), |
||
| 319 | BYTES_TO_T_UINT_8( 0xAE, 0xE9, 0x57, 0xC0, 0x0E, 0xF1, 0x4F, 0xDB ), |
||
| 320 | }; |
||
| 321 | static const mbedtls_mpi_uint secp192k1_gy[] = { |
||
| 322 | BYTES_TO_T_UINT_8( 0x9D, 0x2F, 0x5E, 0xD9, 0x88, 0xAA, 0x82, 0x40 ), |
||
| 323 | BYTES_TO_T_UINT_8( 0x34, 0x86, 0xBE, 0x15, 0xD0, 0x63, 0x41, 0x84 ), |
||
| 324 | BYTES_TO_T_UINT_8( 0xA7, 0x28, 0x56, 0x9C, 0x6D, 0x2F, 0x2F, 0x9B ), |
||
| 325 | }; |
||
| 326 | static const mbedtls_mpi_uint secp192k1_n[] = { |
||
| 327 | BYTES_TO_T_UINT_8( 0x8D, 0xFD, 0xDE, 0x74, 0x6A, 0x46, 0x69, 0x0F ), |
||
| 328 | BYTES_TO_T_UINT_8( 0x17, 0xFC, 0xF2, 0x26, 0xFE, 0xFF, 0xFF, 0xFF ), |
||
| 329 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
||
| 330 | }; |
||
| 331 | #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ |
||
| 332 | |||
| 333 | #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) |
||
| 334 | static const mbedtls_mpi_uint secp224k1_p[] = { |
||
| 335 | BYTES_TO_T_UINT_8( 0x6D, 0xE5, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), |
||
| 336 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
||
| 337 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
||
| 338 | BYTES_TO_T_UINT_4( 0xFF, 0xFF, 0xFF, 0xFF ), |
||
| 339 | }; |
||
| 340 | static const mbedtls_mpi_uint secp224k1_a[] = { |
||
| 341 | BYTES_TO_T_UINT_2( 0x00, 0x00 ), |
||
| 342 | }; |
||
| 343 | static const mbedtls_mpi_uint secp224k1_b[] = { |
||
| 344 | BYTES_TO_T_UINT_2( 0x05, 0x00 ), |
||
| 345 | }; |
||
| 346 | static const mbedtls_mpi_uint secp224k1_gx[] = { |
||
| 347 | BYTES_TO_T_UINT_8( 0x5C, 0xA4, 0xB7, 0xB6, 0x0E, 0x65, 0x7E, 0x0F ), |
||
| 348 | BYTES_TO_T_UINT_8( 0xA9, 0x75, 0x70, 0xE4, 0xE9, 0x67, 0xA4, 0x69 ), |
||
| 349 | BYTES_TO_T_UINT_8( 0xA1, 0x28, 0xFC, 0x30, 0xDF, 0x99, 0xF0, 0x4D ), |
||
| 350 | BYTES_TO_T_UINT_4( 0x33, 0x5B, 0x45, 0xA1 ), |
||
| 351 | }; |
||
| 352 | static const mbedtls_mpi_uint secp224k1_gy[] = { |
||
| 353 | BYTES_TO_T_UINT_8( 0xA5, 0x61, 0x6D, 0x55, 0xDB, 0x4B, 0xCA, 0xE2 ), |
||
| 354 | BYTES_TO_T_UINT_8( 0x59, 0xBD, 0xB0, 0xC0, 0xF7, 0x19, 0xE3, 0xF7 ), |
||
| 355 | BYTES_TO_T_UINT_8( 0xD6, 0xFB, 0xCA, 0x82, 0x42, 0x34, 0xBA, 0x7F ), |
||
| 356 | BYTES_TO_T_UINT_4( 0xED, 0x9F, 0x08, 0x7E ), |
||
| 357 | }; |
||
| 358 | static const mbedtls_mpi_uint secp224k1_n[] = { |
||
| 359 | BYTES_TO_T_UINT_8( 0xF7, 0xB1, 0x9F, 0x76, 0x71, 0xA9, 0xF0, 0xCA ), |
||
| 360 | BYTES_TO_T_UINT_8( 0x84, 0x61, 0xEC, 0xD2, 0xE8, 0xDC, 0x01, 0x00 ), |
||
| 361 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 ), |
||
| 362 | BYTES_TO_T_UINT_8( 0x00, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ), |
||
| 363 | }; |
||
| 364 | #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ |
||
| 365 | |||
| 366 | #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) |
||
| 367 | static const mbedtls_mpi_uint secp256k1_p[] = { |
||
| 368 | BYTES_TO_T_UINT_8( 0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF ), |
||
| 369 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
||
| 370 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
||
| 371 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
||
| 372 | }; |
||
| 373 | static const mbedtls_mpi_uint secp256k1_a[] = { |
||
| 374 | BYTES_TO_T_UINT_2( 0x00, 0x00 ), |
||
| 375 | }; |
||
| 376 | static const mbedtls_mpi_uint secp256k1_b[] = { |
||
| 377 | BYTES_TO_T_UINT_2( 0x07, 0x00 ), |
||
| 378 | }; |
||
| 379 | static const mbedtls_mpi_uint secp256k1_gx[] = { |
||
| 380 | BYTES_TO_T_UINT_8( 0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59 ), |
||
| 381 | BYTES_TO_T_UINT_8( 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02 ), |
||
| 382 | BYTES_TO_T_UINT_8( 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55 ), |
||
| 383 | BYTES_TO_T_UINT_8( 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79 ), |
||
| 384 | }; |
||
| 385 | static const mbedtls_mpi_uint secp256k1_gy[] = { |
||
| 386 | BYTES_TO_T_UINT_8( 0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C ), |
||
| 387 | BYTES_TO_T_UINT_8( 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD ), |
||
| 388 | BYTES_TO_T_UINT_8( 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D ), |
||
| 389 | BYTES_TO_T_UINT_8( 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48 ), |
||
| 390 | }; |
||
| 391 | static const mbedtls_mpi_uint secp256k1_n[] = { |
||
| 392 | BYTES_TO_T_UINT_8( 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF ), |
||
| 393 | BYTES_TO_T_UINT_8( 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA ), |
||
| 394 | BYTES_TO_T_UINT_8( 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
||
| 395 | BYTES_TO_T_UINT_8( 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF ), |
||
| 396 | }; |
||
| 397 | #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ |
||
| 398 | |||
| 399 | /* |
||
| 400 | * Domain parameters for brainpoolP256r1 (RFC 5639 3.4) |
||
| 401 | */ |
||
| 402 | #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) |
||
| 403 | static const mbedtls_mpi_uint brainpoolP256r1_p[] = { |
||
| 404 | BYTES_TO_T_UINT_8( 0x77, 0x53, 0x6E, 0x1F, 0x1D, 0x48, 0x13, 0x20 ), |
||
| 405 | BYTES_TO_T_UINT_8( 0x28, 0x20, 0x26, 0xD5, 0x23, 0xF6, 0x3B, 0x6E ), |
||
| 406 | BYTES_TO_T_UINT_8( 0x72, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), |
||
| 407 | BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), |
||
| 408 | }; |
||
| 409 | static const mbedtls_mpi_uint brainpoolP256r1_a[] = { |
||
| 410 | BYTES_TO_T_UINT_8( 0xD9, 0xB5, 0x30, 0xF3, 0x44, 0x4B, 0x4A, 0xE9 ), |
||
| 411 | BYTES_TO_T_UINT_8( 0x6C, 0x5C, 0xDC, 0x26, 0xC1, 0x55, 0x80, 0xFB ), |
||
| 412 | BYTES_TO_T_UINT_8( 0xE7, 0xFF, 0x7A, 0x41, 0x30, 0x75, 0xF6, 0xEE ), |
||
| 413 | BYTES_TO_T_UINT_8( 0x57, 0x30, 0x2C, 0xFC, 0x75, 0x09, 0x5A, 0x7D ), |
||
| 414 | }; |
||
| 415 | static const mbedtls_mpi_uint brainpoolP256r1_b[] = { |
||
| 416 | BYTES_TO_T_UINT_8( 0xB6, 0x07, 0x8C, 0xFF, 0x18, 0xDC, 0xCC, 0x6B ), |
||
| 417 | BYTES_TO_T_UINT_8( 0xCE, 0xE1, 0xF7, 0x5C, 0x29, 0x16, 0x84, 0x95 ), |
||
| 418 | BYTES_TO_T_UINT_8( 0xBF, 0x7C, 0xD7, 0xBB, 0xD9, 0xB5, 0x30, 0xF3 ), |
||
| 419 | BYTES_TO_T_UINT_8( 0x44, 0x4B, 0x4A, 0xE9, 0x6C, 0x5C, 0xDC, 0x26 ), |
||
| 420 | }; |
||
| 421 | static const mbedtls_mpi_uint brainpoolP256r1_gx[] = { |
||
| 422 | BYTES_TO_T_UINT_8( 0x62, 0x32, 0xCE, 0x9A, 0xBD, 0x53, 0x44, 0x3A ), |
||
| 423 | BYTES_TO_T_UINT_8( 0xC2, 0x23, 0xBD, 0xE3, 0xE1, 0x27, 0xDE, 0xB9 ), |
||
| 424 | BYTES_TO_T_UINT_8( 0xAF, 0xB7, 0x81, 0xFC, 0x2F, 0x48, 0x4B, 0x2C ), |
||
| 425 | BYTES_TO_T_UINT_8( 0xCB, 0x57, 0x7E, 0xCB, 0xB9, 0xAE, 0xD2, 0x8B ), |
||
| 426 | }; |
||
| 427 | static const mbedtls_mpi_uint brainpoolP256r1_gy[] = { |
||
| 428 | BYTES_TO_T_UINT_8( 0x97, 0x69, 0x04, 0x2F, 0xC7, 0x54, 0x1D, 0x5C ), |
||
| 429 | BYTES_TO_T_UINT_8( 0x54, 0x8E, 0xED, 0x2D, 0x13, 0x45, 0x77, 0xC2 ), |
||
| 430 | BYTES_TO_T_UINT_8( 0xC9, 0x1D, 0x61, 0x14, 0x1A, 0x46, 0xF8, 0x97 ), |
||
| 431 | BYTES_TO_T_UINT_8( 0xFD, 0xC4, 0xDA, 0xC3, 0x35, 0xF8, 0x7E, 0x54 ), |
||
| 432 | }; |
||
| 433 | static const mbedtls_mpi_uint brainpoolP256r1_n[] = { |
||
| 434 | BYTES_TO_T_UINT_8( 0xA7, 0x56, 0x48, 0x97, 0x82, 0x0E, 0x1E, 0x90 ), |
||
| 435 | BYTES_TO_T_UINT_8( 0xF7, 0xA6, 0x61, 0xB5, 0xA3, 0x7A, 0x39, 0x8C ), |
||
| 436 | BYTES_TO_T_UINT_8( 0x71, 0x8D, 0x83, 0x9D, 0x90, 0x0A, 0x66, 0x3E ), |
||
| 437 | BYTES_TO_T_UINT_8( 0xBC, 0xA9, 0xEE, 0xA1, 0xDB, 0x57, 0xFB, 0xA9 ), |
||
| 438 | }; |
||
| 439 | #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ |
||
| 440 | |||
| 441 | /* |
||
| 442 | * Domain parameters for brainpoolP384r1 (RFC 5639 3.6) |
||
| 443 | */ |
||
| 444 | #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) |
||
| 445 | static const mbedtls_mpi_uint brainpoolP384r1_p[] = { |
||
| 446 | BYTES_TO_T_UINT_8( 0x53, 0xEC, 0x07, 0x31, 0x13, 0x00, 0x47, 0x87 ), |
||
| 447 | BYTES_TO_T_UINT_8( 0x71, 0x1A, 0x1D, 0x90, 0x29, 0xA7, 0xD3, 0xAC ), |
||
| 448 | BYTES_TO_T_UINT_8( 0x23, 0x11, 0xB7, 0x7F, 0x19, 0xDA, 0xB1, 0x12 ), |
||
| 449 | BYTES_TO_T_UINT_8( 0xB4, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), |
||
| 450 | BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), |
||
| 451 | BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), |
||
| 452 | }; |
||
| 453 | static const mbedtls_mpi_uint brainpoolP384r1_a[] = { |
||
| 454 | BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), |
||
| 455 | BYTES_TO_T_UINT_8( 0xEB, 0xD4, 0x3A, 0x50, 0x4A, 0x81, 0xA5, 0x8A ), |
||
| 456 | BYTES_TO_T_UINT_8( 0x0F, 0xF9, 0x91, 0xBA, 0xEF, 0x65, 0x91, 0x13 ), |
||
| 457 | BYTES_TO_T_UINT_8( 0x87, 0x27, 0xB2, 0x4F, 0x8E, 0xA2, 0xBE, 0xC2 ), |
||
| 458 | BYTES_TO_T_UINT_8( 0xA0, 0xAF, 0x05, 0xCE, 0x0A, 0x08, 0x72, 0x3C ), |
||
| 459 | BYTES_TO_T_UINT_8( 0x0C, 0x15, 0x8C, 0x3D, 0xC6, 0x82, 0xC3, 0x7B ), |
||
| 460 | }; |
||
| 461 | static const mbedtls_mpi_uint brainpoolP384r1_b[] = { |
||
| 462 | BYTES_TO_T_UINT_8( 0x11, 0x4C, 0x50, 0xFA, 0x96, 0x86, 0xB7, 0x3A ), |
||
| 463 | BYTES_TO_T_UINT_8( 0x94, 0xC9, 0xDB, 0x95, 0x02, 0x39, 0xB4, 0x7C ), |
||
| 464 | BYTES_TO_T_UINT_8( 0xD5, 0x62, 0xEB, 0x3E, 0xA5, 0x0E, 0x88, 0x2E ), |
||
| 465 | BYTES_TO_T_UINT_8( 0xA6, 0xD2, 0xDC, 0x07, 0xE1, 0x7D, 0xB7, 0x2F ), |
||
| 466 | BYTES_TO_T_UINT_8( 0x7C, 0x44, 0xF0, 0x16, 0x54, 0xB5, 0x39, 0x8B ), |
||
| 467 | BYTES_TO_T_UINT_8( 0x26, 0x28, 0xCE, 0x22, 0xDD, 0xC7, 0xA8, 0x04 ), |
||
| 468 | }; |
||
| 469 | static const mbedtls_mpi_uint brainpoolP384r1_gx[] = { |
||
| 470 | BYTES_TO_T_UINT_8( 0x1E, 0xAF, 0xD4, 0x47, 0xE2, 0xB2, 0x87, 0xEF ), |
||
| 471 | BYTES_TO_T_UINT_8( 0xAA, 0x46, 0xD6, 0x36, 0x34, 0xE0, 0x26, 0xE8 ), |
||
| 472 | BYTES_TO_T_UINT_8( 0xE8, 0x10, 0xBD, 0x0C, 0xFE, 0xCA, 0x7F, 0xDB ), |
||
| 473 | BYTES_TO_T_UINT_8( 0xE3, 0x4F, 0xF1, 0x7E, 0xE7, 0xA3, 0x47, 0x88 ), |
||
| 474 | BYTES_TO_T_UINT_8( 0x6B, 0x3F, 0xC1, 0xB7, 0x81, 0x3A, 0xA6, 0xA2 ), |
||
| 475 | BYTES_TO_T_UINT_8( 0xFF, 0x45, 0xCF, 0x68, 0xF0, 0x64, 0x1C, 0x1D ), |
||
| 476 | }; |
||
| 477 | static const mbedtls_mpi_uint brainpoolP384r1_gy[] = { |
||
| 478 | BYTES_TO_T_UINT_8( 0x15, 0x53, 0x3C, 0x26, 0x41, 0x03, 0x82, 0x42 ), |
||
| 479 | BYTES_TO_T_UINT_8( 0x11, 0x81, 0x91, 0x77, 0x21, 0x46, 0x46, 0x0E ), |
||
| 480 | BYTES_TO_T_UINT_8( 0x28, 0x29, 0x91, 0xF9, 0x4F, 0x05, 0x9C, 0xE1 ), |
||
| 481 | BYTES_TO_T_UINT_8( 0x64, 0x58, 0xEC, 0xFE, 0x29, 0x0B, 0xB7, 0x62 ), |
||
| 482 | BYTES_TO_T_UINT_8( 0x52, 0xD5, 0xCF, 0x95, 0x8E, 0xEB, 0xB1, 0x5C ), |
||
| 483 | BYTES_TO_T_UINT_8( 0xA4, 0xC2, 0xF9, 0x20, 0x75, 0x1D, 0xBE, 0x8A ), |
||
| 484 | }; |
||
| 485 | static const mbedtls_mpi_uint brainpoolP384r1_n[] = { |
||
| 486 | BYTES_TO_T_UINT_8( 0x65, 0x65, 0x04, 0xE9, 0x02, 0x32, 0x88, 0x3B ), |
||
| 487 | BYTES_TO_T_UINT_8( 0x10, 0xC3, 0x7F, 0x6B, 0xAF, 0xB6, 0x3A, 0xCF ), |
||
| 488 | BYTES_TO_T_UINT_8( 0xA7, 0x25, 0x04, 0xAC, 0x6C, 0x6E, 0x16, 0x1F ), |
||
| 489 | BYTES_TO_T_UINT_8( 0xB3, 0x56, 0x54, 0xED, 0x09, 0x71, 0x2F, 0x15 ), |
||
| 490 | BYTES_TO_T_UINT_8( 0xDF, 0x41, 0xE6, 0x50, 0x7E, 0x6F, 0x5D, 0x0F ), |
||
| 491 | BYTES_TO_T_UINT_8( 0x28, 0x6D, 0x38, 0xA3, 0x82, 0x1E, 0xB9, 0x8C ), |
||
| 492 | }; |
||
| 493 | #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ |
||
| 494 | |||
| 495 | /* |
||
| 496 | * Domain parameters for brainpoolP512r1 (RFC 5639 3.7) |
||
| 497 | */ |
||
| 498 | #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) |
||
| 499 | static const mbedtls_mpi_uint brainpoolP512r1_p[] = { |
||
| 500 | BYTES_TO_T_UINT_8( 0xF3, 0x48, 0x3A, 0x58, 0x56, 0x60, 0xAA, 0x28 ), |
||
| 501 | BYTES_TO_T_UINT_8( 0x85, 0xC6, 0x82, 0x2D, 0x2F, 0xFF, 0x81, 0x28 ), |
||
| 502 | BYTES_TO_T_UINT_8( 0xE6, 0x80, 0xA3, 0xE6, 0x2A, 0xA1, 0xCD, 0xAE ), |
||
| 503 | BYTES_TO_T_UINT_8( 0x42, 0x68, 0xC6, 0x9B, 0x00, 0x9B, 0x4D, 0x7D ), |
||
| 504 | BYTES_TO_T_UINT_8( 0x71, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), |
||
| 505 | BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), |
||
| 506 | BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), |
||
| 507 | BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), |
||
| 508 | }; |
||
| 509 | static const mbedtls_mpi_uint brainpoolP512r1_a[] = { |
||
| 510 | BYTES_TO_T_UINT_8( 0xCA, 0x94, 0xFC, 0x77, 0x4D, 0xAC, 0xC1, 0xE7 ), |
||
| 511 | BYTES_TO_T_UINT_8( 0xB9, 0xC7, 0xF2, 0x2B, 0xA7, 0x17, 0x11, 0x7F ), |
||
| 512 | BYTES_TO_T_UINT_8( 0xB5, 0xC8, 0x9A, 0x8B, 0xC9, 0xF1, 0x2E, 0x0A ), |
||
| 513 | BYTES_TO_T_UINT_8( 0xA1, 0x3A, 0x25, 0xA8, 0x5A, 0x5D, 0xED, 0x2D ), |
||
| 514 | BYTES_TO_T_UINT_8( 0xBC, 0x63, 0x98, 0xEA, 0xCA, 0x41, 0x34, 0xA8 ), |
||
| 515 | BYTES_TO_T_UINT_8( 0x10, 0x16, 0xF9, 0x3D, 0x8D, 0xDD, 0xCB, 0x94 ), |
||
| 516 | BYTES_TO_T_UINT_8( 0xC5, 0x4C, 0x23, 0xAC, 0x45, 0x71, 0x32, 0xE2 ), |
||
| 517 | BYTES_TO_T_UINT_8( 0x89, 0x3B, 0x60, 0x8B, 0x31, 0xA3, 0x30, 0x78 ), |
||
| 518 | }; |
||
| 519 | static const mbedtls_mpi_uint brainpoolP512r1_b[] = { |
||
| 520 | BYTES_TO_T_UINT_8( 0x23, 0xF7, 0x16, 0x80, 0x63, 0xBD, 0x09, 0x28 ), |
||
| 521 | BYTES_TO_T_UINT_8( 0xDD, 0xE5, 0xBA, 0x5E, 0xB7, 0x50, 0x40, 0x98 ), |
||
| 522 | BYTES_TO_T_UINT_8( 0x67, 0x3E, 0x08, 0xDC, 0xCA, 0x94, 0xFC, 0x77 ), |
||
| 523 | BYTES_TO_T_UINT_8( 0x4D, 0xAC, 0xC1, 0xE7, 0xB9, 0xC7, 0xF2, 0x2B ), |
||
| 524 | BYTES_TO_T_UINT_8( 0xA7, 0x17, 0x11, 0x7F, 0xB5, 0xC8, 0x9A, 0x8B ), |
||
| 525 | BYTES_TO_T_UINT_8( 0xC9, 0xF1, 0x2E, 0x0A, 0xA1, 0x3A, 0x25, 0xA8 ), |
||
| 526 | BYTES_TO_T_UINT_8( 0x5A, 0x5D, 0xED, 0x2D, 0xBC, 0x63, 0x98, 0xEA ), |
||
| 527 | BYTES_TO_T_UINT_8( 0xCA, 0x41, 0x34, 0xA8, 0x10, 0x16, 0xF9, 0x3D ), |
||
| 528 | }; |
||
| 529 | static const mbedtls_mpi_uint brainpoolP512r1_gx[] = { |
||
| 530 | BYTES_TO_T_UINT_8( 0x22, 0xF8, 0xB9, 0xBC, 0x09, 0x22, 0x35, 0x8B ), |
||
| 531 | BYTES_TO_T_UINT_8( 0x68, 0x5E, 0x6A, 0x40, 0x47, 0x50, 0x6D, 0x7C ), |
||
| 532 | BYTES_TO_T_UINT_8( 0x5F, 0x7D, 0xB9, 0x93, 0x7B, 0x68, 0xD1, 0x50 ), |
||
| 533 | BYTES_TO_T_UINT_8( 0x8D, 0xD4, 0xD0, 0xE2, 0x78, 0x1F, 0x3B, 0xFF ), |
||
| 534 | BYTES_TO_T_UINT_8( 0x8E, 0x09, 0xD0, 0xF4, 0xEE, 0x62, 0x3B, 0xB4 ), |
||
| 535 | BYTES_TO_T_UINT_8( 0xC1, 0x16, 0xD9, 0xB5, 0x70, 0x9F, 0xED, 0x85 ), |
||
| 536 | BYTES_TO_T_UINT_8( 0x93, 0x6A, 0x4C, 0x9C, 0x2E, 0x32, 0x21, 0x5A ), |
||
| 537 | BYTES_TO_T_UINT_8( 0x64, 0xD9, 0x2E, 0xD8, 0xBD, 0xE4, 0xAE, 0x81 ), |
||
| 538 | }; |
||
| 539 | static const mbedtls_mpi_uint brainpoolP512r1_gy[] = { |
||
| 540 | BYTES_TO_T_UINT_8( 0x92, 0x08, 0xD8, 0x3A, 0x0F, 0x1E, 0xCD, 0x78 ), |
||
| 541 | BYTES_TO_T_UINT_8( 0x06, 0x54, 0xF0, 0xA8, 0x2F, 0x2B, 0xCA, 0xD1 ), |
||
| 542 | BYTES_TO_T_UINT_8( 0xAE, 0x63, 0x27, 0x8A, 0xD8, 0x4B, 0xCA, 0x5B ), |
||
| 543 | BYTES_TO_T_UINT_8( 0x5E, 0x48, 0x5F, 0x4A, 0x49, 0xDE, 0xDC, 0xB2 ), |
||
| 544 | BYTES_TO_T_UINT_8( 0x11, 0x81, 0x1F, 0x88, 0x5B, 0xC5, 0x00, 0xA0 ), |
||
| 545 | BYTES_TO_T_UINT_8( 0x1A, 0x7B, 0xA5, 0x24, 0x00, 0xF7, 0x09, 0xF2 ), |
||
| 546 | BYTES_TO_T_UINT_8( 0xFD, 0x22, 0x78, 0xCF, 0xA9, 0xBF, 0xEA, 0xC0 ), |
||
| 547 | BYTES_TO_T_UINT_8( 0xEC, 0x32, 0x63, 0x56, 0x5D, 0x38, 0xDE, 0x7D ), |
||
| 548 | }; |
||
| 549 | static const mbedtls_mpi_uint brainpoolP512r1_n[] = { |
||
| 550 | BYTES_TO_T_UINT_8( 0x69, 0x00, 0xA9, 0x9C, 0x82, 0x96, 0x87, 0xB5 ), |
||
| 551 | BYTES_TO_T_UINT_8( 0xDD, 0xDA, 0x5D, 0x08, 0x81, 0xD3, 0xB1, 0x1D ), |
||
| 552 | BYTES_TO_T_UINT_8( 0x47, 0x10, 0xAC, 0x7F, 0x19, 0x61, 0x86, 0x41 ), |
||
| 553 | BYTES_TO_T_UINT_8( 0x19, 0x26, 0xA9, 0x4C, 0x41, 0x5C, 0x3E, 0x55 ), |
||
| 554 | BYTES_TO_T_UINT_8( 0x70, 0x08, 0x33, 0x70, 0xCA, 0x9C, 0x63, 0xD6 ), |
||
| 555 | BYTES_TO_T_UINT_8( 0x0E, 0xD2, 0xC9, 0xB3, 0xB3, 0x8D, 0x30, 0xCB ), |
||
| 556 | BYTES_TO_T_UINT_8( 0x07, 0xFC, 0xC9, 0x33, 0xAE, 0xE6, 0xD4, 0x3F ), |
||
| 557 | BYTES_TO_T_UINT_8( 0x8B, 0xC4, 0xE9, 0xDB, 0xB8, 0x9D, 0xDD, 0xAA ), |
||
| 558 | }; |
||
| 559 | #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ |
||
| 560 | |||
| 561 | /* |
||
| 562 | * Create an MPI from embedded constants |
||
| 563 | * (assumes len is an exact multiple of sizeof mbedtls_mpi_uint) |
||
| 564 | */ |
||
| 565 | static inline void ecp_mpi_load( mbedtls_mpi *X, const mbedtls_mpi_uint *p, size_t len ) |
||
| 566 | { |
||
| 567 | X->s = 1; |
||
| 568 | X->n = len / sizeof( mbedtls_mpi_uint ); |
||
| 569 | X->p = (mbedtls_mpi_uint *) p; |
||
| 570 | } |
||
| 571 | |||
| 572 | /* |
||
| 573 | * Set an MPI to static value 1 |
||
| 574 | */ |
||
| 575 | static inline void ecp_mpi_set1( mbedtls_mpi *X ) |
||
| 576 | { |
||
| 577 | static mbedtls_mpi_uint one[] = { 1 }; |
||
| 578 | X->s = 1; |
||
| 579 | X->n = 1; |
||
| 580 | X->p = one; |
||
| 581 | } |
||
| 582 | |||
| 583 | /* |
||
| 584 | * Make group available from embedded constants |
||
| 585 | */ |
||
| 586 | static int ecp_group_load( mbedtls_ecp_group *grp, |
||
| 587 | const mbedtls_mpi_uint *p, size_t plen, |
||
| 588 | const mbedtls_mpi_uint *a, size_t alen, |
||
| 589 | const mbedtls_mpi_uint *b, size_t blen, |
||
| 590 | const mbedtls_mpi_uint *gx, size_t gxlen, |
||
| 591 | const mbedtls_mpi_uint *gy, size_t gylen, |
||
| 592 | const mbedtls_mpi_uint *n, size_t nlen) |
||
| 593 | { |
||
| 594 | ecp_mpi_load( &grp->P, p, plen ); |
||
| 595 | if( a != NULL ) |
||
| 596 | ecp_mpi_load( &grp->A, a, alen ); |
||
| 597 | ecp_mpi_load( &grp->B, b, blen ); |
||
| 598 | ecp_mpi_load( &grp->N, n, nlen ); |
||
| 599 | |||
| 600 | ecp_mpi_load( &grp->G.X, gx, gxlen ); |
||
| 601 | ecp_mpi_load( &grp->G.Y, gy, gylen ); |
||
| 602 | ecp_mpi_set1( &grp->G.Z ); |
||
| 603 | |||
| 604 | grp->pbits = mbedtls_mpi_bitlen( &grp->P ); |
||
| 605 | grp->nbits = mbedtls_mpi_bitlen( &grp->N ); |
||
| 606 | |||
| 607 | grp->h = 1; |
||
| 608 | |||
| 609 | return( 0 ); |
||
| 610 | } |
||
| 611 | |||
| 612 | #if defined(MBEDTLS_ECP_NIST_OPTIM) |
||
| 613 | /* Forward declarations */ |
||
| 614 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) |
||
| 615 | static int ecp_mod_p192( mbedtls_mpi * ); |
||
| 616 | #endif |
||
| 617 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) |
||
| 618 | static int ecp_mod_p224( mbedtls_mpi * ); |
||
| 619 | #endif |
||
| 620 | #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) |
||
| 621 | static int ecp_mod_p256( mbedtls_mpi * ); |
||
| 622 | #endif |
||
| 623 | #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) |
||
| 624 | static int ecp_mod_p384( mbedtls_mpi * ); |
||
| 625 | #endif |
||
| 626 | #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) |
||
| 627 | static int ecp_mod_p521( mbedtls_mpi * ); |
||
| 628 | #endif |
||
| 629 | |||
| 630 | #define NIST_MODP( P ) grp->modp = ecp_mod_ ## P; |
||
| 631 | #else |
||
| 632 | #define NIST_MODP( P ) |
||
| 633 | #endif /* MBEDTLS_ECP_NIST_OPTIM */ |
||
| 634 | |||
| 635 | /* Additional forward declarations */ |
||
| 636 | #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) |
||
| 637 | static int ecp_mod_p255( mbedtls_mpi * ); |
||
| 638 | #endif |
||
| 639 | #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) |
||
| 640 | static int ecp_mod_p448( mbedtls_mpi * ); |
||
| 641 | #endif |
||
| 642 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) |
||
| 643 | static int ecp_mod_p192k1( mbedtls_mpi * ); |
||
| 644 | #endif |
||
| 645 | #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) |
||
| 646 | static int ecp_mod_p224k1( mbedtls_mpi * ); |
||
| 647 | #endif |
||
| 648 | #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) |
||
| 649 | static int ecp_mod_p256k1( mbedtls_mpi * ); |
||
| 650 | #endif |
||
| 651 | |||
| 652 | #define LOAD_GROUP_A( G ) ecp_group_load( grp, \ |
||
| 653 | G ## _p, sizeof( G ## _p ), \ |
||
| 654 | G ## _a, sizeof( G ## _a ), \ |
||
| 655 | G ## _b, sizeof( G ## _b ), \ |
||
| 656 | G ## _gx, sizeof( G ## _gx ), \ |
||
| 657 | G ## _gy, sizeof( G ## _gy ), \ |
||
| 658 | G ## _n, sizeof( G ## _n ) ) |
||
| 659 | |||
| 660 | #define LOAD_GROUP( G ) ecp_group_load( grp, \ |
||
| 661 | G ## _p, sizeof( G ## _p ), \ |
||
| 662 | NULL, 0, \ |
||
| 663 | G ## _b, sizeof( G ## _b ), \ |
||
| 664 | G ## _gx, sizeof( G ## _gx ), \ |
||
| 665 | G ## _gy, sizeof( G ## _gy ), \ |
||
| 666 | G ## _n, sizeof( G ## _n ) ) |
||
| 667 | |||
| 668 | #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) |
||
| 669 | /* |
||
| 670 | * Specialized function for creating the Curve25519 group |
||
| 671 | */ |
||
| 672 | static int ecp_use_curve25519( mbedtls_ecp_group *grp ) |
||
| 673 | { |
||
| 674 | int ret; |
||
| 675 | |||
| 676 | /* Actually ( A + 2 ) / 4 */ |
||
| 677 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "01DB42" ) ); |
||
| 678 | |||
| 679 | /* P = 2^255 - 19 */ |
||
| 680 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) ); |
||
| 681 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 255 ) ); |
||
| 682 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 19 ) ); |
||
| 683 | grp->pbits = mbedtls_mpi_bitlen( &grp->P ); |
||
| 684 | |||
| 685 | /* N = 2^252 + 27742317777372353535851937790883648493 */ |
||
| 686 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->N, 16, |
||
| 687 | "14DEF9DEA2F79CD65812631A5CF5D3ED" ) ); |
||
| 688 | MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 252, 1 ) ); |
||
| 689 | |||
| 690 | /* Y intentionally not set, since we use x/z coordinates. |
||
| 691 | * This is used as a marker to identify Montgomery curves! */ |
||
| 692 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 9 ) ); |
||
| 693 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) ); |
||
| 694 | mbedtls_mpi_free( &grp->G.Y ); |
||
| 695 | |||
| 696 | /* Actually, the required msb for private keys */ |
||
| 697 | grp->nbits = 254; |
||
| 698 | |||
| 699 | cleanup: |
||
| 700 | if( ret != 0 ) |
||
| 701 | mbedtls_ecp_group_free( grp ); |
||
| 702 | |||
| 703 | return( ret ); |
||
| 704 | } |
||
| 705 | #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ |
||
| 706 | |||
| 707 | #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) |
||
| 708 | /* |
||
| 709 | * Specialized function for creating the Curve448 group |
||
| 710 | */ |
||
| 711 | static int ecp_use_curve448( mbedtls_ecp_group *grp ) |
||
| 712 | { |
||
| 713 | mbedtls_mpi Ns; |
||
| 714 | int ret; |
||
| 715 | |||
| 716 | mbedtls_mpi_init( &Ns ); |
||
| 717 | |||
| 718 | /* Actually ( A + 2 ) / 4 */ |
||
| 719 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "98AA" ) ); |
||
| 720 | |||
| 721 | /* P = 2^448 - 2^224 - 1 */ |
||
| 722 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &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 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) ); |
||
| 726 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) ); |
||
| 727 | grp->pbits = mbedtls_mpi_bitlen( &grp->P ); |
||
| 728 | |||
| 729 | /* Y intentionally not set, since we use x/z coordinates. |
||
| 730 | * This is used as a marker to identify Montgomery curves! */ |
||
| 731 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 5 ) ); |
||
| 732 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) ); |
||
| 733 | mbedtls_mpi_free( &grp->G.Y ); |
||
| 734 | |||
| 735 | /* N = 2^446 - 13818066809895115352007386748515426880336692474882178609894547503885 */ |
||
| 736 | MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 446, 1 ) ); |
||
| 737 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &Ns, 16, |
||
| 738 | "8335DC163BB124B65129C96FDE933D8D723A70AADC873D6D54A7BB0D" ) ); |
||
| 739 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &grp->N, &grp->N, &Ns ) ); |
||
| 740 | |||
| 741 | /* Actually, the required msb for private keys */ |
||
| 742 | grp->nbits = 447; |
||
| 743 | |||
| 744 | cleanup: |
||
| 745 | mbedtls_mpi_free( &Ns ); |
||
| 746 | if( ret != 0 ) |
||
| 747 | mbedtls_ecp_group_free( grp ); |
||
| 748 | |||
| 749 | return( ret ); |
||
| 750 | } |
||
| 751 | #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ |
||
| 752 | |||
| 753 | /* |
||
| 754 | * Set a group using well-known domain parameters |
||
| 755 | */ |
||
| 756 | int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id ) |
||
| 757 | { |
||
| 758 | ECP_VALIDATE_RET( grp != NULL ); |
||
| 759 | mbedtls_ecp_group_free( grp ); |
||
| 760 | |||
| 761 | grp->id = id; |
||
| 762 | |||
| 763 | switch( id ) |
||
| 764 | { |
||
| 765 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) |
||
| 766 | case MBEDTLS_ECP_DP_SECP192R1: |
||
| 767 | NIST_MODP( p192 ); |
||
| 768 | return( LOAD_GROUP( secp192r1 ) ); |
||
| 769 | #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ |
||
| 770 | |||
| 771 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) |
||
| 772 | case MBEDTLS_ECP_DP_SECP224R1: |
||
| 773 | NIST_MODP( p224 ); |
||
| 774 | return( LOAD_GROUP( secp224r1 ) ); |
||
| 775 | #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ |
||
| 776 | |||
| 777 | #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) |
||
| 778 | case MBEDTLS_ECP_DP_SECP256R1: |
||
| 779 | NIST_MODP( p256 ); |
||
| 780 | return( LOAD_GROUP( secp256r1 ) ); |
||
| 781 | #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ |
||
| 782 | |||
| 783 | #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) |
||
| 784 | case MBEDTLS_ECP_DP_SECP384R1: |
||
| 785 | NIST_MODP( p384 ); |
||
| 786 | return( LOAD_GROUP( secp384r1 ) ); |
||
| 787 | #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ |
||
| 788 | |||
| 789 | #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) |
||
| 790 | case MBEDTLS_ECP_DP_SECP521R1: |
||
| 791 | NIST_MODP( p521 ); |
||
| 792 | return( LOAD_GROUP( secp521r1 ) ); |
||
| 793 | #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ |
||
| 794 | |||
| 795 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) |
||
| 796 | case MBEDTLS_ECP_DP_SECP192K1: |
||
| 797 | grp->modp = ecp_mod_p192k1; |
||
| 798 | return( LOAD_GROUP_A( secp192k1 ) ); |
||
| 799 | #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ |
||
| 800 | |||
| 801 | #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) |
||
| 802 | case MBEDTLS_ECP_DP_SECP224K1: |
||
| 803 | grp->modp = ecp_mod_p224k1; |
||
| 804 | return( LOAD_GROUP_A( secp224k1 ) ); |
||
| 805 | #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ |
||
| 806 | |||
| 807 | #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) |
||
| 808 | case MBEDTLS_ECP_DP_SECP256K1: |
||
| 809 | grp->modp = ecp_mod_p256k1; |
||
| 810 | return( LOAD_GROUP_A( secp256k1 ) ); |
||
| 811 | #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ |
||
| 812 | |||
| 813 | #if defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) |
||
| 814 | case MBEDTLS_ECP_DP_BP256R1: |
||
| 815 | return( LOAD_GROUP_A( brainpoolP256r1 ) ); |
||
| 816 | #endif /* MBEDTLS_ECP_DP_BP256R1_ENABLED */ |
||
| 817 | |||
| 818 | #if defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) |
||
| 819 | case MBEDTLS_ECP_DP_BP384R1: |
||
| 820 | return( LOAD_GROUP_A( brainpoolP384r1 ) ); |
||
| 821 | #endif /* MBEDTLS_ECP_DP_BP384R1_ENABLED */ |
||
| 822 | |||
| 823 | #if defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) |
||
| 824 | case MBEDTLS_ECP_DP_BP512R1: |
||
| 825 | return( LOAD_GROUP_A( brainpoolP512r1 ) ); |
||
| 826 | #endif /* MBEDTLS_ECP_DP_BP512R1_ENABLED */ |
||
| 827 | |||
| 828 | #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) |
||
| 829 | case MBEDTLS_ECP_DP_CURVE25519: |
||
| 830 | grp->modp = ecp_mod_p255; |
||
| 831 | return( ecp_use_curve25519( grp ) ); |
||
| 832 | #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ |
||
| 833 | |||
| 834 | #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) |
||
| 835 | case MBEDTLS_ECP_DP_CURVE448: |
||
| 836 | grp->modp = ecp_mod_p448; |
||
| 837 | return( ecp_use_curve448( grp ) ); |
||
| 838 | #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ |
||
| 839 | |||
| 840 | default: |
||
| 841 | mbedtls_ecp_group_free( grp ); |
||
| 842 | return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); |
||
| 843 | } |
||
| 844 | } |
||
| 845 | |||
| 846 | #if defined(MBEDTLS_ECP_NIST_OPTIM) |
||
| 847 | /* |
||
| 848 | * Fast reduction modulo the primes used by the NIST curves. |
||
| 849 | * |
||
| 850 | * These functions are critical for speed, but not needed for correct |
||
| 851 | * operations. So, we make the choice to heavily rely on the internals of our |
||
| 852 | * bignum library, which creates a tight coupling between these functions and |
||
| 853 | * our MPI implementation. However, the coupling between the ECP module and |
||
| 854 | * MPI remains loose, since these functions can be deactivated at will. |
||
| 855 | */ |
||
| 856 | |||
| 857 | #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) |
||
| 858 | /* |
||
| 859 | * Compared to the way things are presented in FIPS 186-3 D.2, |
||
| 860 | * we proceed in columns, from right (least significant chunk) to left, |
||
| 861 | * adding chunks to N in place, and keeping a carry for the next chunk. |
||
| 862 | * This avoids moving things around in memory, and uselessly adding zeros, |
||
| 863 | * compared to the more straightforward, line-oriented approach. |
||
| 864 | * |
||
| 865 | * For this prime we need to handle data in chunks of 64 bits. |
||
| 866 | * Since this is always a multiple of our basic mbedtls_mpi_uint, we can |
||
| 867 | * use a mbedtls_mpi_uint * to designate such a chunk, and small loops to handle it. |
||
| 868 | */ |
||
| 869 | |||
| 870 | /* Add 64-bit chunks (dst += src) and update carry */ |
||
| 871 | static inline void add64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *src, mbedtls_mpi_uint *carry ) |
||
| 872 | { |
||
| 873 | unsigned char i; |
||
| 874 | mbedtls_mpi_uint c = 0; |
||
| 875 | for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++, src++ ) |
||
| 876 | { |
||
| 877 | *dst += c; c = ( *dst < c ); |
||
| 878 | *dst += *src; c += ( *dst < *src ); |
||
| 879 | } |
||
| 880 | *carry += c; |
||
| 881 | } |
||
| 882 | |||
| 883 | /* Add carry to a 64-bit chunk and update carry */ |
||
| 884 | static inline void carry64( mbedtls_mpi_uint *dst, mbedtls_mpi_uint *carry ) |
||
| 885 | { |
||
| 886 | unsigned char i; |
||
| 887 | for( i = 0; i < 8 / sizeof( mbedtls_mpi_uint ); i++, dst++ ) |
||
| 888 | { |
||
| 889 | *dst += *carry; |
||
| 890 | *carry = ( *dst < *carry ); |
||
| 891 | } |
||
| 892 | } |
||
| 893 | |||
| 894 | #define WIDTH 8 / sizeof( mbedtls_mpi_uint ) |
||
| 895 | #define A( i ) N->p + (i) * WIDTH |
||
| 896 | #define ADD( i ) add64( p, A( i ), &c ) |
||
| 897 | #define NEXT p += WIDTH; carry64( p, &c ) |
||
| 898 | #define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0 |
||
| 899 | |||
| 900 | /* |
||
| 901 | * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1) |
||
| 902 | */ |
||
| 903 | static int ecp_mod_p192( mbedtls_mpi *N ) |
||
| 904 | { |
||
| 905 | int ret; |
||
| 906 | mbedtls_mpi_uint c = 0; |
||
| 907 | mbedtls_mpi_uint *p, *end; |
||
| 908 | |||
| 909 | /* Make sure we have enough blocks so that A(5) is legal */ |
||
| 910 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, 6 * WIDTH ) ); |
||
| 911 | |||
| 912 | p = N->p; |
||
| 913 | end = p + N->n; |
||
| 914 | |||
| 915 | ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5 |
||
| 916 | ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5 |
||
| 917 | ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5 |
||
| 918 | |||
| 919 | cleanup: |
||
| 920 | return( ret ); |
||
| 921 | } |
||
| 922 | |||
| 923 | #undef WIDTH |
||
| 924 | #undef A |
||
| 925 | #undef ADD |
||
| 926 | #undef NEXT |
||
| 927 | #undef LAST |
||
| 928 | #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ |
||
| 929 | |||
| 930 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ |
||
| 931 | defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \ |
||
| 932 | defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) |
||
| 933 | /* |
||
| 934 | * The reader is advised to first understand ecp_mod_p192() since the same |
||
| 935 | * general structure is used here, but with additional complications: |
||
| 936 | * (1) chunks of 32 bits, and (2) subtractions. |
||
| 937 | */ |
||
| 938 | |||
| 939 | /* |
||
| 940 | * For these primes, we need to handle data in chunks of 32 bits. |
||
| 941 | * This makes it more complicated if we use 64 bits limbs in MPI, |
||
| 942 | * which prevents us from using a uniform access method as for p192. |
||
| 943 | * |
||
| 944 | * So, we define a mini abstraction layer to access 32 bit chunks, |
||
| 945 | * load them in 'cur' for work, and store them back from 'cur' when done. |
||
| 946 | * |
||
| 947 | * While at it, also define the size of N in terms of 32-bit chunks. |
||
| 948 | */ |
||
| 949 | #define LOAD32 cur = A( i ); |
||
| 950 | |||
| 951 | #if defined(MBEDTLS_HAVE_INT32) /* 32 bit */ |
||
| 952 | |||
| 953 | #define MAX32 N->n |
||
| 954 | #define A( j ) N->p[j] |
||
| 955 | #define STORE32 N->p[i] = cur; |
||
| 956 | |||
| 957 | #else /* 64-bit */ |
||
| 958 | |||
| 959 | #define MAX32 N->n * 2 |
||
| 960 | #define A( j ) (j) % 2 ? (uint32_t)( N->p[(j)/2] >> 32 ) : \ |
||
| 961 | (uint32_t)( N->p[(j)/2] ) |
||
| 962 | #define STORE32 \ |
||
| 963 | if( i % 2 ) { \ |
||
| 964 | N->p[i/2] &= 0x00000000FFFFFFFF; \ |
||
| 965 | N->p[i/2] |= ((mbedtls_mpi_uint) cur) << 32; \ |
||
| 966 | } else { \ |
||
| 967 | N->p[i/2] &= 0xFFFFFFFF00000000; \ |
||
| 968 | N->p[i/2] |= (mbedtls_mpi_uint) cur; \ |
||
| 969 | } |
||
| 970 | |||
| 971 | #endif /* sizeof( mbedtls_mpi_uint ) */ |
||
| 972 | |||
| 973 | /* |
||
| 974 | * Helpers for addition and subtraction of chunks, with signed carry. |
||
| 975 | */ |
||
| 976 | static inline void add32( uint32_t *dst, uint32_t src, signed char *carry ) |
||
| 977 | { |
||
| 978 | *dst += src; |
||
| 979 | *carry += ( *dst < src ); |
||
| 980 | } |
||
| 981 | |||
| 982 | static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry ) |
||
| 983 | { |
||
| 984 | *carry -= ( *dst < src ); |
||
| 985 | *dst -= src; |
||
| 986 | } |
||
| 987 | |||
| 988 | #define ADD( j ) add32( &cur, A( j ), &c ); |
||
| 989 | #define SUB( j ) sub32( &cur, A( j ), &c ); |
||
| 990 | |||
| 991 | /* |
||
| 992 | * Helpers for the main 'loop' |
||
| 993 | * (see fix_negative for the motivation of C) |
||
| 994 | */ |
||
| 995 | #define INIT( b ) \ |
||
| 996 | int ret; \ |
||
| 997 | signed char c = 0, cc; \ |
||
| 998 | uint32_t cur; \ |
||
| 999 | size_t i = 0, bits = (b); \ |
||
| 1000 | mbedtls_mpi C; \ |
||
| 1001 | mbedtls_mpi_uint Cp[ (b) / 8 / sizeof( mbedtls_mpi_uint) + 1 ]; \ |
||
| 1002 | \ |
||
| 1003 | C.s = 1; \ |
||
| 1004 | C.n = (b) / 8 / sizeof( mbedtls_mpi_uint) + 1; \ |
||
| 1005 | C.p = Cp; \ |
||
| 1006 | memset( Cp, 0, C.n * sizeof( mbedtls_mpi_uint ) ); \ |
||
| 1007 | \ |
||
| 1008 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( N, (b) * 2 / 8 / \ |
||
| 1009 | sizeof( mbedtls_mpi_uint ) ) ); \ |
||
| 1010 | LOAD32; |
||
| 1011 | |||
| 1012 | #define NEXT \ |
||
| 1013 | STORE32; i++; LOAD32; \ |
||
| 1014 | cc = c; c = 0; \ |
||
| 1015 | if( cc < 0 ) \ |
||
| 1016 | sub32( &cur, -cc, &c ); \ |
||
| 1017 | else \ |
||
| 1018 | add32( &cur, cc, &c ); \ |
||
| 1019 | |||
| 1020 | #define LAST \ |
||
| 1021 | STORE32; i++; \ |
||
| 1022 | cur = c > 0 ? c : 0; STORE32; \ |
||
| 1023 | cur = 0; while( ++i < MAX32 ) { STORE32; } \ |
||
| 1024 | if( c < 0 ) fix_negative( N, c, &C, bits ); |
||
| 1025 | |||
| 1026 | /* |
||
| 1027 | * If the result is negative, we get it in the form |
||
| 1028 | * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits' |
||
| 1029 | */ |
||
| 1030 | static inline int fix_negative( mbedtls_mpi *N, signed char c, mbedtls_mpi *C, size_t bits ) |
||
| 1031 | { |
||
| 1032 | int ret; |
||
| 1033 | |||
| 1034 | /* C = - c * 2^(bits + 32) */ |
||
| 1035 | #if !defined(MBEDTLS_HAVE_INT64) |
||
| 1036 | ((void) bits); |
||
| 1037 | #else |
||
| 1038 | if( bits == 224 ) |
||
| 1039 | C->p[ C->n - 1 ] = ((mbedtls_mpi_uint) -c) << 32; |
||
| 1040 | else |
||
| 1041 | #endif |
||
| 1042 | C->p[ C->n - 1 ] = (mbedtls_mpi_uint) -c; |
||
| 1043 | |||
| 1044 | /* N = - ( C - N ) */ |
||
| 1045 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( N, C, N ) ); |
||
| 1046 | N->s = -1; |
||
| 1047 | |||
| 1048 | cleanup: |
||
| 1049 | |||
| 1050 | return( ret ); |
||
| 1051 | } |
||
| 1052 | |||
| 1053 | #if defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) |
||
| 1054 | /* |
||
| 1055 | * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2) |
||
| 1056 | */ |
||
| 1057 | static int ecp_mod_p224( mbedtls_mpi *N ) |
||
| 1058 | { |
||
| 1059 | INIT( 224 ); |
||
| 1060 | |||
| 1061 | SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11 |
||
| 1062 | SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12 |
||
| 1063 | SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13 |
||
| 1064 | SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11 |
||
| 1065 | SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12 |
||
| 1066 | SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13 |
||
| 1067 | SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10 |
||
| 1068 | |||
| 1069 | cleanup: |
||
| 1070 | return( ret ); |
||
| 1071 | } |
||
| 1072 | #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED */ |
||
| 1073 | |||
| 1074 | #if defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) |
||
| 1075 | /* |
||
| 1076 | * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3) |
||
| 1077 | */ |
||
| 1078 | static int ecp_mod_p256( mbedtls_mpi *N ) |
||
| 1079 | { |
||
| 1080 | INIT( 256 ); |
||
| 1081 | |||
| 1082 | ADD( 8 ); ADD( 9 ); |
||
| 1083 | SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0 |
||
| 1084 | |||
| 1085 | ADD( 9 ); ADD( 10 ); |
||
| 1086 | SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1 |
||
| 1087 | |||
| 1088 | ADD( 10 ); ADD( 11 ); |
||
| 1089 | SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2 |
||
| 1090 | |||
| 1091 | ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 ); |
||
| 1092 | SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3 |
||
| 1093 | |||
| 1094 | ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 ); |
||
| 1095 | SUB( 9 ); SUB( 10 ); NEXT; // A4 |
||
| 1096 | |||
| 1097 | ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 ); |
||
| 1098 | SUB( 10 ); SUB( 11 ); NEXT; // A5 |
||
| 1099 | |||
| 1100 | ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 ); |
||
| 1101 | SUB( 8 ); SUB( 9 ); NEXT; // A6 |
||
| 1102 | |||
| 1103 | ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 ); |
||
| 1104 | SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7 |
||
| 1105 | |||
| 1106 | cleanup: |
||
| 1107 | return( ret ); |
||
| 1108 | } |
||
| 1109 | #endif /* MBEDTLS_ECP_DP_SECP256R1_ENABLED */ |
||
| 1110 | |||
| 1111 | #if defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) |
||
| 1112 | /* |
||
| 1113 | * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4) |
||
| 1114 | */ |
||
| 1115 | static int ecp_mod_p384( mbedtls_mpi *N ) |
||
| 1116 | { |
||
| 1117 | INIT( 384 ); |
||
| 1118 | |||
| 1119 | ADD( 12 ); ADD( 21 ); ADD( 20 ); |
||
| 1120 | SUB( 23 ); NEXT; // A0 |
||
| 1121 | |||
| 1122 | ADD( 13 ); ADD( 22 ); ADD( 23 ); |
||
| 1123 | SUB( 12 ); SUB( 20 ); NEXT; // A2 |
||
| 1124 | |||
| 1125 | ADD( 14 ); ADD( 23 ); |
||
| 1126 | SUB( 13 ); SUB( 21 ); NEXT; // A2 |
||
| 1127 | |||
| 1128 | ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 ); |
||
| 1129 | SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3 |
||
| 1130 | |||
| 1131 | ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 ); |
||
| 1132 | SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4 |
||
| 1133 | |||
| 1134 | ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 ); |
||
| 1135 | SUB( 16 ); NEXT; // A5 |
||
| 1136 | |||
| 1137 | ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 ); |
||
| 1138 | SUB( 17 ); NEXT; // A6 |
||
| 1139 | |||
| 1140 | ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 ); |
||
| 1141 | SUB( 18 ); NEXT; // A7 |
||
| 1142 | |||
| 1143 | ADD( 20 ); ADD( 17 ); ADD( 16 ); |
||
| 1144 | SUB( 19 ); NEXT; // A8 |
||
| 1145 | |||
| 1146 | ADD( 21 ); ADD( 18 ); ADD( 17 ); |
||
| 1147 | SUB( 20 ); NEXT; // A9 |
||
| 1148 | |||
| 1149 | ADD( 22 ); ADD( 19 ); ADD( 18 ); |
||
| 1150 | SUB( 21 ); NEXT; // A10 |
||
| 1151 | |||
| 1152 | ADD( 23 ); ADD( 20 ); ADD( 19 ); |
||
| 1153 | SUB( 22 ); LAST; // A11 |
||
| 1154 | |||
| 1155 | cleanup: |
||
| 1156 | return( ret ); |
||
| 1157 | } |
||
| 1158 | #endif /* MBEDTLS_ECP_DP_SECP384R1_ENABLED */ |
||
| 1159 | |||
| 1160 | #undef A |
||
| 1161 | #undef LOAD32 |
||
| 1162 | #undef STORE32 |
||
| 1163 | #undef MAX32 |
||
| 1164 | #undef INIT |
||
| 1165 | #undef NEXT |
||
| 1166 | #undef LAST |
||
| 1167 | |||
| 1168 | #endif /* MBEDTLS_ECP_DP_SECP224R1_ENABLED || |
||
| 1169 | MBEDTLS_ECP_DP_SECP256R1_ENABLED || |
||
| 1170 | MBEDTLS_ECP_DP_SECP384R1_ENABLED */ |
||
| 1171 | |||
| 1172 | #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) |
||
| 1173 | /* |
||
| 1174 | * Here we have an actual Mersenne prime, so things are more straightforward. |
||
| 1175 | * However, chunks are aligned on a 'weird' boundary (521 bits). |
||
| 1176 | */ |
||
| 1177 | |||
| 1178 | /* Size of p521 in terms of mbedtls_mpi_uint */ |
||
| 1179 | #define P521_WIDTH ( 521 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) |
||
| 1180 | |||
| 1181 | /* Bits to keep in the most significant mbedtls_mpi_uint */ |
||
| 1182 | #define P521_MASK 0x01FF |
||
| 1183 | |||
| 1184 | /* |
||
| 1185 | * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5) |
||
| 1186 | * Write N as A1 + 2^521 A0, return A0 + A1 |
||
| 1187 | */ |
||
| 1188 | static int ecp_mod_p521( mbedtls_mpi *N ) |
||
| 1189 | { |
||
| 1190 | int ret; |
||
| 1191 | size_t i; |
||
| 1192 | mbedtls_mpi M; |
||
| 1193 | mbedtls_mpi_uint Mp[P521_WIDTH + 1]; |
||
| 1194 | /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits: |
||
| 1195 | * we need to hold bits 513 to 1056, which is 34 limbs, that is |
||
| 1196 | * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */ |
||
| 1197 | |||
| 1198 | if( N->n < P521_WIDTH ) |
||
| 1199 | return( 0 ); |
||
| 1200 | |||
| 1201 | /* M = A1 */ |
||
| 1202 | M.s = 1; |
||
| 1203 | M.n = N->n - ( P521_WIDTH - 1 ); |
||
| 1204 | if( M.n > P521_WIDTH + 1 ) |
||
| 1205 | M.n = P521_WIDTH + 1; |
||
| 1206 | M.p = Mp; |
||
| 1207 | memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); |
||
| 1208 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 521 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) ); |
||
| 1209 | |||
| 1210 | /* N = A0 */ |
||
| 1211 | N->p[P521_WIDTH - 1] &= P521_MASK; |
||
| 1212 | for( i = P521_WIDTH; i < N->n; i++ ) |
||
| 1213 | N->p[i] = 0; |
||
| 1214 | |||
| 1215 | /* N = A0 + A1 */ |
||
| 1216 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); |
||
| 1217 | |||
| 1218 | cleanup: |
||
| 1219 | return( ret ); |
||
| 1220 | } |
||
| 1221 | |||
| 1222 | #undef P521_WIDTH |
||
| 1223 | #undef P521_MASK |
||
| 1224 | #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ |
||
| 1225 | |||
| 1226 | #endif /* MBEDTLS_ECP_NIST_OPTIM */ |
||
| 1227 | |||
| 1228 | #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) |
||
| 1229 | |||
| 1230 | /* Size of p255 in terms of mbedtls_mpi_uint */ |
||
| 1231 | #define P255_WIDTH ( 255 / 8 / sizeof( mbedtls_mpi_uint ) + 1 ) |
||
| 1232 | |||
| 1233 | /* |
||
| 1234 | * Fast quasi-reduction modulo p255 = 2^255 - 19 |
||
| 1235 | * Write N as A0 + 2^255 A1, return A0 + 19 * A1 |
||
| 1236 | */ |
||
| 1237 | static int ecp_mod_p255( mbedtls_mpi *N ) |
||
| 1238 | { |
||
| 1239 | int ret; |
||
| 1240 | size_t i; |
||
| 1241 | mbedtls_mpi M; |
||
| 1242 | mbedtls_mpi_uint Mp[P255_WIDTH + 2]; |
||
| 1243 | |||
| 1244 | if( N->n < P255_WIDTH ) |
||
| 1245 | return( 0 ); |
||
| 1246 | |||
| 1247 | /* M = A1 */ |
||
| 1248 | M.s = 1; |
||
| 1249 | M.n = N->n - ( P255_WIDTH - 1 ); |
||
| 1250 | if( M.n > P255_WIDTH + 1 ) |
||
| 1251 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); |
||
| 1252 | M.p = Mp; |
||
| 1253 | memset( Mp, 0, sizeof Mp ); |
||
| 1254 | memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); |
||
| 1255 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, 255 % ( 8 * sizeof( mbedtls_mpi_uint ) ) ) ); |
||
| 1256 | M.n++; /* Make room for multiplication by 19 */ |
||
| 1257 | |||
| 1258 | /* N = A0 */ |
||
| 1259 | MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( N, 255, 0 ) ); |
||
| 1260 | for( i = P255_WIDTH; i < N->n; i++ ) |
||
| 1261 | N->p[i] = 0; |
||
| 1262 | |||
| 1263 | /* N = A0 + 19 * A1 */ |
||
| 1264 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &M, 19 ) ); |
||
| 1265 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); |
||
| 1266 | |||
| 1267 | cleanup: |
||
| 1268 | return( ret ); |
||
| 1269 | } |
||
| 1270 | #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ |
||
| 1271 | |||
| 1272 | #if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) |
||
| 1273 | |||
| 1274 | /* Size of p448 in terms of mbedtls_mpi_uint */ |
||
| 1275 | #define P448_WIDTH ( 448 / 8 / sizeof( mbedtls_mpi_uint ) ) |
||
| 1276 | |||
| 1277 | /* Number of limbs fully occupied by 2^224 (max), and limbs used by it (min) */ |
||
| 1278 | #define DIV_ROUND_UP( X, Y ) ( ( ( X ) + ( Y ) - 1 ) / ( Y ) ) |
||
| 1279 | #define P224_WIDTH_MIN ( 28 / sizeof( mbedtls_mpi_uint ) ) |
||
| 1280 | #define P224_WIDTH_MAX DIV_ROUND_UP( 28, sizeof( mbedtls_mpi_uint ) ) |
||
| 1281 | #define P224_UNUSED_BITS ( ( P224_WIDTH_MAX * sizeof( mbedtls_mpi_uint ) * 8 ) - 224 ) |
||
| 1282 | |||
| 1283 | /* |
||
| 1284 | * Fast quasi-reduction modulo p448 = 2^448 - 2^224 - 1 |
||
| 1285 | * Write N as A0 + 2^448 A1 and A1 as B0 + 2^224 B1, and return |
||
| 1286 | * A0 + A1 + B1 + (B0 + B1) * 2^224. This is different to the reference |
||
| 1287 | * implementation of Curve448, which uses its own special 56-bit limbs rather |
||
| 1288 | * than a generic bignum library. We could squeeze some extra speed out on |
||
| 1289 | * 32-bit machines by splitting N up into 32-bit limbs and doing the |
||
| 1290 | * arithmetic using the limbs directly as we do for the NIST primes above, |
||
| 1291 | * but for 64-bit targets it should use half the number of operations if we do |
||
| 1292 | * the reduction with 224-bit limbs, since mpi_add_mpi will then use 64-bit adds. |
||
| 1293 | */ |
||
| 1294 | static int ecp_mod_p448( mbedtls_mpi *N ) |
||
| 1295 | { |
||
| 1296 | int ret; |
||
| 1297 | size_t i; |
||
| 1298 | mbedtls_mpi M, Q; |
||
| 1299 | mbedtls_mpi_uint Mp[P448_WIDTH + 1], Qp[P448_WIDTH]; |
||
| 1300 | |||
| 1301 | if( N->n <= P448_WIDTH ) |
||
| 1302 | return( 0 ); |
||
| 1303 | |||
| 1304 | /* M = A1 */ |
||
| 1305 | M.s = 1; |
||
| 1306 | M.n = N->n - ( P448_WIDTH ); |
||
| 1307 | if( M.n > P448_WIDTH ) |
||
| 1308 | /* Shouldn't be called with N larger than 2^896! */ |
||
| 1309 | return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); |
||
| 1310 | M.p = Mp; |
||
| 1311 | memset( Mp, 0, sizeof( Mp ) ); |
||
| 1312 | memcpy( Mp, N->p + P448_WIDTH, M.n * sizeof( mbedtls_mpi_uint ) ); |
||
| 1313 | |||
| 1314 | /* N = A0 */ |
||
| 1315 | for( i = P448_WIDTH; i < N->n; i++ ) |
||
| 1316 | N->p[i] = 0; |
||
| 1317 | |||
| 1318 | /* N += A1 */ |
||
| 1319 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) ); |
||
| 1320 | |||
| 1321 | /* Q = B1, N += B1 */ |
||
| 1322 | Q = M; |
||
| 1323 | Q.p = Qp; |
||
| 1324 | memcpy( Qp, Mp, sizeof( Qp ) ); |
||
| 1325 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Q, 224 ) ); |
||
| 1326 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &Q ) ); |
||
| 1327 | |||
| 1328 | /* M = (B0 + B1) * 2^224, N += M */ |
||
| 1329 | if( sizeof( mbedtls_mpi_uint ) > 4 ) |
||
| 1330 | Mp[P224_WIDTH_MIN] &= ( (mbedtls_mpi_uint)-1 ) >> ( P224_UNUSED_BITS ); |
||
| 1331 | for( i = P224_WIDTH_MAX; i < M.n; ++i ) |
||
| 1332 | Mp[i] = 0; |
||
| 1333 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &Q ) ); |
||
| 1334 | M.n = P448_WIDTH + 1; /* Make room for shifted carry bit from the addition */ |
||
| 1335 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &M, 224 ) ); |
||
| 1336 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) ); |
||
| 1337 | |||
| 1338 | cleanup: |
||
| 1339 | return( ret ); |
||
| 1340 | } |
||
| 1341 | #endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ |
||
| 1342 | |||
| 1343 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \ |
||
| 1344 | defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ |
||
| 1345 | defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) |
||
| 1346 | /* |
||
| 1347 | * Fast quasi-reduction modulo P = 2^s - R, |
||
| 1348 | * with R about 33 bits, used by the Koblitz curves. |
||
| 1349 | * |
||
| 1350 | * Write N as A0 + 2^224 A1, return A0 + R * A1. |
||
| 1351 | * Actually do two passes, since R is big. |
||
| 1352 | */ |
||
| 1353 | #define P_KOBLITZ_MAX ( 256 / 8 / sizeof( mbedtls_mpi_uint ) ) // Max limbs in P |
||
| 1354 | #define P_KOBLITZ_R ( 8 / sizeof( mbedtls_mpi_uint ) ) // Limbs in R |
||
| 1355 | static inline int ecp_mod_koblitz( mbedtls_mpi *N, mbedtls_mpi_uint *Rp, size_t p_limbs, |
||
| 1356 | size_t adjust, size_t shift, mbedtls_mpi_uint mask ) |
||
| 1357 | { |
||
| 1358 | int ret; |
||
| 1359 | size_t i; |
||
| 1360 | mbedtls_mpi M, R; |
||
| 1361 | mbedtls_mpi_uint Mp[P_KOBLITZ_MAX + P_KOBLITZ_R + 1]; |
||
| 1362 | |||
| 1363 | if( N->n < p_limbs ) |
||
| 1364 | return( 0 ); |
||
| 1365 | |||
| 1366 | /* Init R */ |
||
| 1367 | R.s = 1; |
||
| 1368 | R.p = Rp; |
||
| 1369 | R.n = P_KOBLITZ_R; |
||
| 1370 | |||
| 1371 | /* Common setup for M */ |
||
| 1372 | M.s = 1; |
||
| 1373 | M.p = Mp; |
||
| 1374 | |||
| 1375 | /* M = A1 */ |
||
| 1376 | M.n = N->n - ( p_limbs - adjust ); |
||
| 1377 | if( M.n > p_limbs + adjust ) |
||
| 1378 | M.n = p_limbs + adjust; |
||
| 1379 | memset( Mp, 0, sizeof Mp ); |
||
| 1380 | memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) ); |
||
| 1381 | if( shift != 0 ) |
||
| 1382 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) ); |
||
| 1383 | M.n += R.n; /* Make room for multiplication by R */ |
||
| 1384 | |||
| 1385 | /* N = A0 */ |
||
| 1386 | if( mask != 0 ) |
||
| 1387 | N->p[p_limbs - 1] &= mask; |
||
| 1388 | for( i = p_limbs; i < N->n; i++ ) |
||
| 1389 | N->p[i] = 0; |
||
| 1390 | |||
| 1391 | /* N = A0 + R * A1 */ |
||
| 1392 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); |
||
| 1393 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); |
||
| 1394 | |||
| 1395 | /* Second pass */ |
||
| 1396 | |||
| 1397 | /* M = A1 */ |
||
| 1398 | M.n = N->n - ( p_limbs - adjust ); |
||
| 1399 | if( M.n > p_limbs + adjust ) |
||
| 1400 | M.n = p_limbs + adjust; |
||
| 1401 | memset( Mp, 0, sizeof Mp ); |
||
| 1402 | memcpy( Mp, N->p + p_limbs - adjust, M.n * sizeof( mbedtls_mpi_uint ) ); |
||
| 1403 | if( shift != 0 ) |
||
| 1404 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &M, shift ) ); |
||
| 1405 | M.n += R.n; /* Make room for multiplication by R */ |
||
| 1406 | |||
| 1407 | /* N = A0 */ |
||
| 1408 | if( mask != 0 ) |
||
| 1409 | N->p[p_limbs - 1] &= mask; |
||
| 1410 | for( i = p_limbs; i < N->n; i++ ) |
||
| 1411 | N->p[i] = 0; |
||
| 1412 | |||
| 1413 | /* N = A0 + R * A1 */ |
||
| 1414 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &M, &M, &R ) ); |
||
| 1415 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( N, N, &M ) ); |
||
| 1416 | |||
| 1417 | cleanup: |
||
| 1418 | return( ret ); |
||
| 1419 | } |
||
| 1420 | #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED) || |
||
| 1421 | MBEDTLS_ECP_DP_SECP224K1_ENABLED) || |
||
| 1422 | MBEDTLS_ECP_DP_SECP256K1_ENABLED) */ |
||
| 1423 | |||
| 1424 | #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) |
||
| 1425 | /* |
||
| 1426 | * Fast quasi-reduction modulo p192k1 = 2^192 - R, |
||
| 1427 | * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119 |
||
| 1428 | */ |
||
| 1429 | static int ecp_mod_p192k1( mbedtls_mpi *N ) |
||
| 1430 | { |
||
| 1431 | static mbedtls_mpi_uint Rp[] = { |
||
| 1432 | BYTES_TO_T_UINT_8( 0xC9, 0x11, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; |
||
| 1433 | |||
| 1434 | return( ecp_mod_koblitz( N, Rp, 192 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); |
||
| 1435 | } |
||
| 1436 | #endif /* MBEDTLS_ECP_DP_SECP192K1_ENABLED */ |
||
| 1437 | |||
| 1438 | #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) |
||
| 1439 | /* |
||
| 1440 | * Fast quasi-reduction modulo p224k1 = 2^224 - R, |
||
| 1441 | * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93 |
||
| 1442 | */ |
||
| 1443 | static int ecp_mod_p224k1( mbedtls_mpi *N ) |
||
| 1444 | { |
||
| 1445 | static mbedtls_mpi_uint Rp[] = { |
||
| 1446 | BYTES_TO_T_UINT_8( 0x93, 0x1A, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; |
||
| 1447 | |||
| 1448 | #if defined(MBEDTLS_HAVE_INT64) |
||
| 1449 | return( ecp_mod_koblitz( N, Rp, 4, 1, 32, 0xFFFFFFFF ) ); |
||
| 1450 | #else |
||
| 1451 | return( ecp_mod_koblitz( N, Rp, 224 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); |
||
| 1452 | #endif |
||
| 1453 | } |
||
| 1454 | |||
| 1455 | #endif /* MBEDTLS_ECP_DP_SECP224K1_ENABLED */ |
||
| 1456 | |||
| 1457 | #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) |
||
| 1458 | /* |
||
| 1459 | * Fast quasi-reduction modulo p256k1 = 2^256 - R, |
||
| 1460 | * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1 |
||
| 1461 | */ |
||
| 1462 | static int ecp_mod_p256k1( mbedtls_mpi *N ) |
||
| 1463 | { |
||
| 1464 | static mbedtls_mpi_uint Rp[] = { |
||
| 1465 | BYTES_TO_T_UINT_8( 0xD1, 0x03, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00 ) }; |
||
| 1466 | return( ecp_mod_koblitz( N, Rp, 256 / 8 / sizeof( mbedtls_mpi_uint ), 0, 0, 0 ) ); |
||
| 1467 | } |
||
| 1468 | #endif /* MBEDTLS_ECP_DP_SECP256K1_ENABLED */ |
||
| 1469 | |||
| 1470 | #endif /* !MBEDTLS_ECP_ALT */ |
||
| 1471 | |||
| 1472 | #endif /* MBEDTLS_ECP_C */ |