1 | /*
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2 | * Copyright 2011-2016 The OpenSSL Project Authors. All Rights Reserved.
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3 | *
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4 | * Licensed under the OpenSSL license (the "License"). You may not use
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5 | * this file except in compliance with the License. You can obtain a copy
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6 | * in the file LICENSE in the source distribution or at
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7 | * https://www.openssl.org/source/license.html
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8 | */
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9 |
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10 | /* ====================================================================
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11 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
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12 | *
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13 | * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
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14 | * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
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15 | * to the OpenSSL project.
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16 | *
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17 | * The ECC Code is licensed pursuant to the OpenSSL open source
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18 | * license provided below.
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19 | *
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20 | * The software is originally written by Sheueling Chang Shantz and
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21 | * Douglas Stebila of Sun Microsystems Laboratories.
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22 | *
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23 | */
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24 |
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25 | #include <openssl/err.h>
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26 |
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27 | #include "ec_lcl.h"
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28 |
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29 | #ifndef OPENSSL_NO_EC2M
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30 |
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31 | /*-
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32 | * Calculates and sets the affine coordinates of an EC_POINT from the given
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33 | * compressed coordinates. Uses algorithm 2.3.4 of SEC 1.
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34 | * Note that the simple implementation only uses affine coordinates.
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35 | *
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36 | * The method is from the following publication:
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37 | *
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38 | * Harper, Menezes, Vanstone:
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39 | * "Public-Key Cryptosystems with Very Small Key Lengths",
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40 | * EUROCRYPT '92, Springer-Verlag LNCS 658,
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41 | * published February 1993
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42 | *
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43 | * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe
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44 | * the same method, but claim no priority date earlier than July 29, 1994
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45 | * (and additionally fail to cite the EUROCRYPT '92 publication as prior art).
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46 | */
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47 | int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group,
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48 | EC_POINT *point,
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49 | const BIGNUM *x_, int y_bit,
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50 | BN_CTX *ctx)
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51 | {
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52 | BN_CTX *new_ctx = NULL;
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53 | BIGNUM *tmp, *x, *y, *z;
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54 | int ret = 0, z0;
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55 |
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56 | /* clear error queue */
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57 | ERR_clear_error();
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58 |
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59 | if (ctx == NULL) {
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60 | ctx = new_ctx = BN_CTX_new();
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61 | if (ctx == NULL)
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62 | return 0;
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63 | }
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64 |
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65 | y_bit = (y_bit != 0) ? 1 : 0;
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66 |
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67 | BN_CTX_start(ctx);
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68 | tmp = BN_CTX_get(ctx);
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69 | x = BN_CTX_get(ctx);
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70 | y = BN_CTX_get(ctx);
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71 | z = BN_CTX_get(ctx);
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72 | if (z == NULL)
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73 | goto err;
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74 |
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75 | if (!BN_GF2m_mod_arr(x, x_, group->poly))
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76 | goto err;
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77 | if (BN_is_zero(x)) {
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78 | if (!BN_GF2m_mod_sqrt_arr(y, group->b, group->poly, ctx))
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79 | goto err;
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80 | } else {
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81 | if (!group->meth->field_sqr(group, tmp, x, ctx))
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82 | goto err;
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83 | if (!group->meth->field_div(group, tmp, group->b, tmp, ctx))
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84 | goto err;
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85 | if (!BN_GF2m_add(tmp, group->a, tmp))
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86 | goto err;
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87 | if (!BN_GF2m_add(tmp, x, tmp))
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88 | goto err;
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89 | if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) {
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90 | unsigned long err = ERR_peek_last_error();
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91 |
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92 | if (ERR_GET_LIB(err) == ERR_LIB_BN
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93 | && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) {
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94 | ERR_clear_error();
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95 | ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES,
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96 | EC_R_INVALID_COMPRESSED_POINT);
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97 | } else
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98 | ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES,
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99 | ERR_R_BN_LIB);
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100 | goto err;
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101 | }
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102 | z0 = (BN_is_odd(z)) ? 1 : 0;
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103 | if (!group->meth->field_mul(group, y, x, z, ctx))
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104 | goto err;
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105 | if (z0 != y_bit) {
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106 | if (!BN_GF2m_add(y, y, x))
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107 | goto err;
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108 | }
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109 | }
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110 |
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111 | if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx))
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112 | goto err;
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113 |
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114 | ret = 1;
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115 |
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116 | err:
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117 | BN_CTX_end(ctx);
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118 | BN_CTX_free(new_ctx);
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119 | return ret;
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120 | }
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121 |
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122 | /*
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123 | * Converts an EC_POINT to an octet string. If buf is NULL, the encoded
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124 | * length will be returned. If the length len of buf is smaller than required
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125 | * an error will be returned.
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126 | */
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127 | size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point,
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128 | point_conversion_form_t form,
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129 | unsigned char *buf, size_t len, BN_CTX *ctx)
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130 | {
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131 | size_t ret;
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132 | BN_CTX *new_ctx = NULL;
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133 | int used_ctx = 0;
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134 | BIGNUM *x, *y, *yxi;
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135 | size_t field_len, i, skip;
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136 |
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137 | if ((form != POINT_CONVERSION_COMPRESSED)
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138 | && (form != POINT_CONVERSION_UNCOMPRESSED)
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139 | && (form != POINT_CONVERSION_HYBRID)) {
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140 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
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141 | goto err;
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142 | }
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143 |
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144 | if (EC_POINT_is_at_infinity(group, point)) {
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145 | /* encodes to a single 0 octet */
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146 | if (buf != NULL) {
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147 | if (len < 1) {
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148 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
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149 | return 0;
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150 | }
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151 | buf[0] = 0;
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152 | }
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153 | return 1;
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154 | }
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155 |
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156 | /* ret := required output buffer length */
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157 | field_len = (EC_GROUP_get_degree(group) + 7) / 8;
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158 | ret =
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159 | (form ==
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160 | POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
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161 |
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162 | /* if 'buf' is NULL, just return required length */
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163 | if (buf != NULL) {
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164 | if (len < ret) {
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165 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
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166 | goto err;
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167 | }
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168 |
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169 | if (ctx == NULL) {
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170 | ctx = new_ctx = BN_CTX_new();
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171 | if (ctx == NULL)
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172 | return 0;
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173 | }
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174 |
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175 | BN_CTX_start(ctx);
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176 | used_ctx = 1;
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177 | x = BN_CTX_get(ctx);
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178 | y = BN_CTX_get(ctx);
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179 | yxi = BN_CTX_get(ctx);
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180 | if (yxi == NULL)
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181 | goto err;
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182 |
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183 | if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx))
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184 | goto err;
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185 |
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186 | buf[0] = form;
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187 | if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) {
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188 | if (!group->meth->field_div(group, yxi, y, x, ctx))
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189 | goto err;
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190 | if (BN_is_odd(yxi))
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191 | buf[0]++;
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192 | }
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193 |
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194 | i = 1;
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195 |
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196 | skip = field_len - BN_num_bytes(x);
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197 | if (skip > field_len) {
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198 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
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199 | goto err;
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200 | }
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201 | while (skip > 0) {
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202 | buf[i++] = 0;
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203 | skip--;
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204 | }
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205 | skip = BN_bn2bin(x, buf + i);
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206 | i += skip;
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207 | if (i != 1 + field_len) {
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208 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
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209 | goto err;
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210 | }
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211 |
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212 | if (form == POINT_CONVERSION_UNCOMPRESSED
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213 | || form == POINT_CONVERSION_HYBRID) {
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214 | skip = field_len - BN_num_bytes(y);
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215 | if (skip > field_len) {
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216 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
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217 | goto err;
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218 | }
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219 | while (skip > 0) {
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220 | buf[i++] = 0;
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221 | skip--;
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222 | }
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223 | skip = BN_bn2bin(y, buf + i);
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224 | i += skip;
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225 | }
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226 |
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227 | if (i != ret) {
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228 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
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229 | goto err;
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230 | }
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231 | }
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232 |
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233 | if (used_ctx)
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234 | BN_CTX_end(ctx);
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235 | BN_CTX_free(new_ctx);
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236 | return ret;
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237 |
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238 | err:
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239 | if (used_ctx)
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240 | BN_CTX_end(ctx);
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241 | BN_CTX_free(new_ctx);
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242 | return 0;
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243 | }
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244 |
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245 | /*
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246 | * Converts an octet string representation to an EC_POINT. Note that the
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247 | * simple implementation only uses affine coordinates.
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248 | */
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249 | int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
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250 | const unsigned char *buf, size_t len,
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251 | BN_CTX *ctx)
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252 | {
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253 | point_conversion_form_t form;
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254 | int y_bit;
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255 | BN_CTX *new_ctx = NULL;
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256 | BIGNUM *x, *y, *yxi;
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257 | size_t field_len, enc_len;
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258 | int ret = 0;
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259 |
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260 | if (len == 0) {
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261 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
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262 | return 0;
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263 | }
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264 | form = buf[0];
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265 | y_bit = form & 1;
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266 | form = form & ~1U;
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267 | if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
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268 | && (form != POINT_CONVERSION_UNCOMPRESSED)
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269 | && (form != POINT_CONVERSION_HYBRID)) {
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270 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
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271 | return 0;
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272 | }
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273 | if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) {
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274 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
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275 | return 0;
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276 | }
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277 |
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278 | if (form == 0) {
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279 | if (len != 1) {
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280 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
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281 | return 0;
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282 | }
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283 |
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284 | return EC_POINT_set_to_infinity(group, point);
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285 | }
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286 |
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287 | field_len = (EC_GROUP_get_degree(group) + 7) / 8;
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288 | enc_len =
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289 | (form ==
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290 | POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
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291 |
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292 | if (len != enc_len) {
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293 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
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294 | return 0;
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295 | }
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296 |
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297 | if (ctx == NULL) {
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298 | ctx = new_ctx = BN_CTX_new();
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299 | if (ctx == NULL)
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300 | return 0;
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301 | }
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302 |
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303 | BN_CTX_start(ctx);
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304 | x = BN_CTX_get(ctx);
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305 | y = BN_CTX_get(ctx);
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306 | yxi = BN_CTX_get(ctx);
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307 | if (yxi == NULL)
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308 | goto err;
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309 |
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310 | if (!BN_bin2bn(buf + 1, field_len, x))
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311 | goto err;
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312 | if (BN_ucmp(x, group->field) >= 0) {
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313 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
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314 | goto err;
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315 | }
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316 |
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317 | if (form == POINT_CONVERSION_COMPRESSED) {
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318 | if (!EC_POINT_set_compressed_coordinates_GF2m
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319 | (group, point, x, y_bit, ctx))
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320 | goto err;
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321 | } else {
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322 | if (!BN_bin2bn(buf + 1 + field_len, field_len, y))
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323 | goto err;
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324 | if (BN_ucmp(y, group->field) >= 0) {
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325 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
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326 | goto err;
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327 | }
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328 | if (form == POINT_CONVERSION_HYBRID) {
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329 | if (!group->meth->field_div(group, yxi, y, x, ctx))
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330 | goto err;
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331 | if (y_bit != BN_is_odd(yxi)) {
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332 | ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
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333 | goto err;
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334 | }
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335 | }
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336 |
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337 | /*
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338 | * EC_POINT_set_affine_coordinates_GF2m is responsible for checking that
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339 | * the point is on the curve.
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340 | */
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341 | if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx))
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342 | goto err;
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343 | }
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344 |
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345 | ret = 1;
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346 |
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347 | err:
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348 | BN_CTX_end(ctx);
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349 | BN_CTX_free(new_ctx);
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350 | return ret;
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351 | }
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352 | #endif
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