1 | /**
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2 | * \file ecp_internal.h
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3 | *
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4 | * \brief Function declarations for alternative implementation of elliptic curve
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5 | * point arithmetic.
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6 | */
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7 | /*
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8 | * Copyright (C) 2016, ARM Limited, All Rights Reserved
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9 | * SPDX-License-Identifier: Apache-2.0
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10 | *
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11 | * Licensed under the Apache License, Version 2.0 (the "License"); you may
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12 | * not use this file except in compliance with the License.
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13 | * You may obtain a copy of the License at
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14 | *
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15 | * http://www.apache.org/licenses/LICENSE-2.0
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16 | *
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17 | * Unless required by applicable law or agreed to in writing, software
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18 | * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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19 | * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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20 | * See the License for the specific language governing permissions and
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21 | * limitations under the License.
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22 | *
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23 | * This file is part of mbed TLS (https://tls.mbed.org)
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24 | */
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25 |
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26 | /*
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27 | * References:
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28 | *
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29 | * [1] BERNSTEIN, Daniel J. Curve25519: new Diffie-Hellman speed records.
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30 | * <http://cr.yp.to/ecdh/curve25519-20060209.pdf>
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31 | *
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32 | * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis
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33 | * for elliptic curve cryptosystems. In : Cryptographic Hardware and
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34 | * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
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35 | * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
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36 | *
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37 | * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to
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38 | * render ECC resistant against Side Channel Attacks. IACR Cryptology
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39 | * ePrint Archive, 2004, vol. 2004, p. 342.
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40 | * <http://eprint.iacr.org/2004/342.pdf>
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41 | *
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42 | * [4] Certicom Research. SEC 2: Recommended Elliptic Curve Domain Parameters.
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43 | * <http://www.secg.org/sec2-v2.pdf>
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44 | *
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45 | * [5] HANKERSON, Darrel, MENEZES, Alfred J., VANSTONE, Scott. Guide to Elliptic
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46 | * Curve Cryptography.
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47 | *
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48 | * [6] Digital Signature Standard (DSS), FIPS 186-4.
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49 | * <http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf>
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50 | *
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51 | * [7] Elliptic Curve Cryptography (ECC) Cipher Suites for Transport Layer
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52 | * Security (TLS), RFC 4492.
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53 | * <https://tools.ietf.org/search/rfc4492>
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54 | *
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55 | * [8] <http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html>
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56 | *
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57 | * [9] COHEN, Henri. A Course in Computational Algebraic Number Theory.
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58 | * Springer Science & Business Media, 1 Aug 2000
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59 | */
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60 |
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61 | #ifndef MBEDTLS_ECP_INTERNAL_H
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62 | #define MBEDTLS_ECP_INTERNAL_H
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63 |
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64 | #if !defined(MBEDTLS_CONFIG_FILE)
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65 | #include "config.h"
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66 | #else
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67 | #include MBEDTLS_CONFIG_FILE
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68 | #endif
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69 |
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70 | #if defined(MBEDTLS_ECP_INTERNAL_ALT)
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71 |
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72 | /**
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73 | * \brief Indicate if the Elliptic Curve Point module extension can
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74 | * handle the group.
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75 | *
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76 | * \param grp The pointer to the elliptic curve group that will be the
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77 | * basis of the cryptographic computations.
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78 | *
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79 | * \return Non-zero if successful.
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80 | */
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81 | unsigned char mbedtls_internal_ecp_grp_capable( const mbedtls_ecp_group *grp );
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82 |
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83 | /**
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84 | * \brief Initialise the Elliptic Curve Point module extension.
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85 | *
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86 | * If mbedtls_internal_ecp_grp_capable returns true for a
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87 | * group, this function has to be able to initialise the
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88 | * module for it.
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89 | *
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90 | * This module can be a driver to a crypto hardware
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91 | * accelerator, for which this could be an initialise function.
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92 | *
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93 | * \param grp The pointer to the group the module needs to be
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94 | * initialised for.
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95 | *
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96 | * \return 0 if successful.
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97 | */
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98 | int mbedtls_internal_ecp_init( const mbedtls_ecp_group *grp );
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99 |
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100 | /**
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101 | * \brief Frees and deallocates the Elliptic Curve Point module
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102 | * extension.
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103 | *
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104 | * \param grp The pointer to the group the module was initialised for.
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105 | */
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106 | void mbedtls_internal_ecp_free( const mbedtls_ecp_group *grp );
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107 |
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108 | #if defined(ECP_SHORTWEIERSTRASS)
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109 |
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110 | #if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
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111 | /**
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112 | * \brief Randomize jacobian coordinates:
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113 | * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l.
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114 | *
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115 | * \param grp Pointer to the group representing the curve.
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116 | *
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117 | * \param pt The point on the curve to be randomised, given with Jacobian
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118 | * coordinates.
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119 | *
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120 | * \param f_rng A function pointer to the random number generator.
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121 | *
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122 | * \param p_rng A pointer to the random number generator state.
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123 | *
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124 | * \return 0 if successful.
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125 | */
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126 | int mbedtls_internal_ecp_randomize_jac( const mbedtls_ecp_group *grp,
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127 | mbedtls_ecp_point *pt, int (*f_rng)(void *, unsigned char *, size_t),
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128 | void *p_rng );
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129 | #endif
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130 |
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131 | #if defined(MBEDTLS_ECP_ADD_MIXED_ALT)
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132 | /**
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133 | * \brief Addition: R = P + Q, mixed affine-Jacobian coordinates.
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134 | *
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135 | * The coordinates of Q must be normalized (= affine),
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136 | * but those of P don't need to. R is not normalized.
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137 | *
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138 | * This function is used only as a subrutine of
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139 | * ecp_mul_comb().
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140 | *
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141 | * Special cases: (1) P or Q is zero, (2) R is zero,
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142 | * (3) P == Q.
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143 | * None of these cases can happen as intermediate step in
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144 | * ecp_mul_comb():
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145 | * - at each step, P, Q and R are multiples of the base
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146 | * point, the factor being less than its order, so none of
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147 | * them is zero;
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148 | * - Q is an odd multiple of the base point, P an even
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149 | * multiple, due to the choice of precomputed points in the
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150 | * modified comb method.
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151 | * So branches for these cases do not leak secret information.
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152 | *
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153 | * We accept Q->Z being unset (saving memory in tables) as
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154 | * meaning 1.
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155 | *
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156 | * Cost in field operations if done by [5] 3.22:
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157 | * 1A := 8M + 3S
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158 | *
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159 | * \param grp Pointer to the group representing the curve.
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160 | *
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161 | * \param R Pointer to a point structure to hold the result.
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162 | *
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163 | * \param P Pointer to the first summand, given with Jacobian
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164 | * coordinates
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165 | *
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166 | * \param Q Pointer to the second summand, given with affine
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167 | * coordinates.
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168 | *
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169 | * \return 0 if successful.
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170 | */
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171 | int mbedtls_internal_ecp_add_mixed( const mbedtls_ecp_group *grp,
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172 | mbedtls_ecp_point *R, const mbedtls_ecp_point *P,
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173 | const mbedtls_ecp_point *Q );
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174 | #endif
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175 |
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176 | /**
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177 | * \brief Point doubling R = 2 P, Jacobian coordinates.
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178 | *
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179 | * Cost: 1D := 3M + 4S (A == 0)
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180 | * 4M + 4S (A == -3)
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181 | * 3M + 6S + 1a otherwise
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182 | * when the implementation is based on the "dbl-1998-cmo-2"
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183 | * doubling formulas in [8] and standard optimizations are
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184 | * applied when curve parameter A is one of { 0, -3 }.
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185 | *
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186 | * \param grp Pointer to the group representing the curve.
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187 | *
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188 | * \param R Pointer to a point structure to hold the result.
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189 | *
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190 | * \param P Pointer to the point that has to be doubled, given with
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191 | * Jacobian coordinates.
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192 | *
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193 | * \return 0 if successful.
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194 | */
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195 | #if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
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196 | int mbedtls_internal_ecp_double_jac( const mbedtls_ecp_group *grp,
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197 | mbedtls_ecp_point *R, const mbedtls_ecp_point *P );
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198 | #endif
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199 |
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200 | /**
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201 | * \brief Normalize jacobian coordinates of an array of (pointers to)
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202 | * points.
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203 | *
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204 | * Using Montgomery's trick to perform only one inversion mod P
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205 | * the cost is:
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206 | * 1N(t) := 1I + (6t - 3)M + 1S
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207 | * (See for example Algorithm 10.3.4. in [9])
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208 | *
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209 | * This function is used only as a subrutine of
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210 | * ecp_mul_comb().
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211 | *
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212 | * Warning: fails (returning an error) if one of the points is
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213 | * zero!
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214 | * This should never happen, see choice of w in ecp_mul_comb().
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215 | *
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216 | * \param grp Pointer to the group representing the curve.
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217 | *
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218 | * \param T Array of pointers to the points to normalise.
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219 | *
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220 | * \param t_len Number of elements in the array.
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221 | *
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222 | * \return 0 if successful,
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223 | * an error if one of the points is zero.
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224 | */
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225 | #if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
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226 | int mbedtls_internal_ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
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227 | mbedtls_ecp_point *T[], size_t t_len );
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228 | #endif
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229 |
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230 | /**
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231 | * \brief Normalize jacobian coordinates so that Z == 0 || Z == 1.
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232 | *
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233 | * Cost in field operations if done by [5] 3.2.1:
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234 | * 1N := 1I + 3M + 1S
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235 | *
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236 | * \param grp Pointer to the group representing the curve.
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237 | *
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238 | * \param pt pointer to the point to be normalised. This is an
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239 | * input/output parameter.
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240 | *
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241 | * \return 0 if successful.
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242 | */
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243 | #if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
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244 | int mbedtls_internal_ecp_normalize_jac( const mbedtls_ecp_group *grp,
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245 | mbedtls_ecp_point *pt );
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246 | #endif
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247 |
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248 | #endif /* ECP_SHORTWEIERSTRASS */
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249 |
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250 | #if defined(ECP_MONTGOMERY)
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251 |
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252 | #if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
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253 | int mbedtls_internal_ecp_double_add_mxz( const mbedtls_ecp_group *grp,
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254 | mbedtls_ecp_point *R, mbedtls_ecp_point *S, const mbedtls_ecp_point *P,
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255 | const mbedtls_ecp_point *Q, const mbedtls_mpi *d );
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256 | #endif
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257 |
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258 | /**
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259 | * \brief Randomize projective x/z coordinates:
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260 | * (X, Z) -> (l X, l Z) for random l
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261 | *
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262 | * \param grp pointer to the group representing the curve
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263 | *
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264 | * \param P the point on the curve to be randomised given with
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265 | * projective coordinates. This is an input/output parameter.
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266 | *
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267 | * \param f_rng a function pointer to the random number generator
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268 | *
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269 | * \param p_rng a pointer to the random number generator state
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270 | *
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271 | * \return 0 if successful
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272 | */
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273 | #if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
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274 | int mbedtls_internal_ecp_randomize_mxz( const mbedtls_ecp_group *grp,
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275 | mbedtls_ecp_point *P, int (*f_rng)(void *, unsigned char *, size_t),
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276 | void *p_rng );
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277 | #endif
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278 |
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279 | /**
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280 | * \brief Normalize Montgomery x/z coordinates: X = X/Z, Z = 1.
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281 | *
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282 | * \param grp pointer to the group representing the curve
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283 | *
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284 | * \param P pointer to the point to be normalised. This is an
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285 | * input/output parameter.
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286 | *
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287 | * \return 0 if successful
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288 | */
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289 | #if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
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290 | int mbedtls_internal_ecp_normalize_mxz( const mbedtls_ecp_group *grp,
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291 | mbedtls_ecp_point *P );
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292 | #endif
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293 |
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294 | #endif /* ECP_MONTGOMERY */
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295 |
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296 | #endif /* MBEDTLS_ECP_INTERNAL_ALT */
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297 |
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298 | #endif /* ecp_internal.h */
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299 |
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