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