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 ),
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254 | BYTES_TO_T_UINT_2( 0xFF, 0x01 ),
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255 | };
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256 | static const mbedtls_mpi_uint secp521r1_b[] = {
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257 | BYTES_TO_T_UINT_8( 0x00, 0x3F, 0x50, 0x6B, 0xD4, 0x1F, 0x45, 0xEF ),
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258 | BYTES_TO_T_UINT_8( 0xF1, 0x34, 0x2C, 0x3D, 0x88, 0xDF, 0x73, 0x35 ),
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259 | BYTES_TO_T_UINT_8( 0x07, 0xBF, 0xB1, 0x3B, 0xBD, 0xC0, 0x52, 0x16 ),
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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 */
|
---|