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1 /* This Source Code Form is subject to the terms of the Mozilla Public |
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2 * License, v. 2.0. If a copy of the MPL was not distributed with this |
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3 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ |
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4 |
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5 #include "mpi.h" |
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6 #include "mp_gf2m.h" |
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7 #include "ecl-priv.h" |
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8 #include "mpi-priv.h" |
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9 #include <stdlib.h> |
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10 |
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11 /* Allocate memory for a new GFMethod object. */ |
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12 GFMethod * |
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13 GFMethod_new() |
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14 { |
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15 mp_err res = MP_OKAY; |
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16 GFMethod *meth; |
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17 meth = (GFMethod *) malloc(sizeof(GFMethod)); |
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18 if (meth == NULL) |
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19 return NULL; |
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20 meth->constructed = MP_YES; |
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21 MP_DIGITS(&meth->irr) = 0; |
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22 meth->extra_free = NULL; |
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23 MP_CHECKOK(mp_init(&meth->irr)); |
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24 |
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25 CLEANUP: |
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26 if (res != MP_OKAY) { |
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27 GFMethod_free(meth); |
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28 return NULL; |
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29 } |
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30 return meth; |
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31 } |
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32 |
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33 /* Construct a generic GFMethod for arithmetic over prime fields with |
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34 * irreducible irr. */ |
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35 GFMethod * |
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36 GFMethod_consGFp(const mp_int *irr) |
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37 { |
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38 mp_err res = MP_OKAY; |
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39 GFMethod *meth = NULL; |
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40 |
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41 meth = GFMethod_new(); |
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42 if (meth == NULL) |
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43 return NULL; |
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44 |
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45 MP_CHECKOK(mp_copy(irr, &meth->irr)); |
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46 meth->irr_arr[0] = mpl_significant_bits(irr); |
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47 meth->irr_arr[1] = meth->irr_arr[2] = meth->irr_arr[3] = |
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48 meth->irr_arr[4] = 0; |
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49 switch(MP_USED(&meth->irr)) { |
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50 /* maybe we need 1 and 2 words here as well?*/ |
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51 case 3: |
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52 meth->field_add = &ec_GFp_add_3; |
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53 meth->field_sub = &ec_GFp_sub_3; |
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54 break; |
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55 case 4: |
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56 meth->field_add = &ec_GFp_add_4; |
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57 meth->field_sub = &ec_GFp_sub_4; |
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58 break; |
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59 case 5: |
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60 meth->field_add = &ec_GFp_add_5; |
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61 meth->field_sub = &ec_GFp_sub_5; |
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62 break; |
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63 case 6: |
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64 meth->field_add = &ec_GFp_add_6; |
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65 meth->field_sub = &ec_GFp_sub_6; |
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66 break; |
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67 default: |
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68 meth->field_add = &ec_GFp_add; |
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69 meth->field_sub = &ec_GFp_sub; |
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70 } |
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71 meth->field_neg = &ec_GFp_neg; |
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72 meth->field_mod = &ec_GFp_mod; |
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73 meth->field_mul = &ec_GFp_mul; |
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74 meth->field_sqr = &ec_GFp_sqr; |
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75 meth->field_div = &ec_GFp_div; |
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76 meth->field_enc = NULL; |
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77 meth->field_dec = NULL; |
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78 meth->extra1 = NULL; |
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79 meth->extra2 = NULL; |
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80 meth->extra_free = NULL; |
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81 |
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82 CLEANUP: |
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83 if (res != MP_OKAY) { |
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84 GFMethod_free(meth); |
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85 return NULL; |
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86 } |
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87 return meth; |
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88 } |
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89 |
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90 /* Construct a generic GFMethod for arithmetic over binary polynomial |
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91 * fields with irreducible irr that has array representation irr_arr (see |
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92 * ecl-priv.h for description of the representation). If irr_arr is NULL, |
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93 * then it is constructed from the bitstring representation. */ |
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94 GFMethod * |
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95 GFMethod_consGF2m(const mp_int *irr, const unsigned int irr_arr[5]) |
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96 { |
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97 mp_err res = MP_OKAY; |
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98 int ret; |
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99 GFMethod *meth = NULL; |
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100 |
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101 meth = GFMethod_new(); |
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102 if (meth == NULL) |
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103 return NULL; |
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104 |
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105 MP_CHECKOK(mp_copy(irr, &meth->irr)); |
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106 if (irr_arr != NULL) { |
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107 /* Irreducible polynomials are either trinomials or pentanomials. */ |
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108 meth->irr_arr[0] = irr_arr[0]; |
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109 meth->irr_arr[1] = irr_arr[1]; |
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110 meth->irr_arr[2] = irr_arr[2]; |
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111 if (irr_arr[2] > 0) { |
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112 meth->irr_arr[3] = irr_arr[3]; |
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113 meth->irr_arr[4] = irr_arr[4]; |
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114 } else { |
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115 meth->irr_arr[3] = meth->irr_arr[4] = 0; |
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116 } |
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117 } else { |
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118 ret = mp_bpoly2arr(irr, meth->irr_arr, 5); |
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119 /* Irreducible polynomials are either trinomials or pentanomials. */ |
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120 if ((ret != 5) && (ret != 3)) { |
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121 res = MP_UNDEF; |
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122 goto CLEANUP; |
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123 } |
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124 } |
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125 meth->field_add = &ec_GF2m_add; |
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126 meth->field_neg = &ec_GF2m_neg; |
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127 meth->field_sub = &ec_GF2m_add; |
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128 meth->field_mod = &ec_GF2m_mod; |
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129 meth->field_mul = &ec_GF2m_mul; |
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130 meth->field_sqr = &ec_GF2m_sqr; |
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131 meth->field_div = &ec_GF2m_div; |
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132 meth->field_enc = NULL; |
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133 meth->field_dec = NULL; |
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134 meth->extra1 = NULL; |
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135 meth->extra2 = NULL; |
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136 meth->extra_free = NULL; |
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137 |
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138 CLEANUP: |
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139 if (res != MP_OKAY) { |
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140 GFMethod_free(meth); |
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141 return NULL; |
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142 } |
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143 return meth; |
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144 } |
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145 |
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146 /* Free the memory allocated (if any) to a GFMethod object. */ |
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147 void |
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148 GFMethod_free(GFMethod *meth) |
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149 { |
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150 if (meth == NULL) |
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151 return; |
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152 if (meth->constructed == MP_NO) |
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153 return; |
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154 mp_clear(&meth->irr); |
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155 if (meth->extra_free != NULL) |
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156 meth->extra_free(meth); |
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157 free(meth); |
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158 } |
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159 |
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160 /* Wrapper functions for generic prime field arithmetic. */ |
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161 |
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162 /* Add two field elements. Assumes that 0 <= a, b < meth->irr */ |
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163 mp_err |
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164 ec_GFp_add(const mp_int *a, const mp_int *b, mp_int *r, |
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165 const GFMethod *meth) |
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166 { |
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167 /* PRE: 0 <= a, b < p = meth->irr POST: 0 <= r < p, r = a + b (mod p) */ |
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168 mp_err res; |
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169 |
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170 if ((res = mp_add(a, b, r)) != MP_OKAY) { |
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171 return res; |
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172 } |
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173 if (mp_cmp(r, &meth->irr) >= 0) { |
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174 return mp_sub(r, &meth->irr, r); |
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175 } |
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176 return res; |
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177 } |
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178 |
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179 /* Negates a field element. Assumes that 0 <= a < meth->irr */ |
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180 mp_err |
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181 ec_GFp_neg(const mp_int *a, mp_int *r, const GFMethod *meth) |
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182 { |
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183 /* PRE: 0 <= a < p = meth->irr POST: 0 <= r < p, r = -a (mod p) */ |
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184 |
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185 if (mp_cmp_z(a) == 0) { |
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186 mp_zero(r); |
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187 return MP_OKAY; |
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188 } |
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189 return mp_sub(&meth->irr, a, r); |
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190 } |
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191 |
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192 /* Subtracts two field elements. Assumes that 0 <= a, b < meth->irr */ |
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193 mp_err |
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194 ec_GFp_sub(const mp_int *a, const mp_int *b, mp_int *r, |
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195 const GFMethod *meth) |
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196 { |
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197 mp_err res = MP_OKAY; |
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198 |
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199 /* PRE: 0 <= a, b < p = meth->irr POST: 0 <= r < p, r = a - b (mod p) */ |
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200 res = mp_sub(a, b, r); |
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201 if (res == MP_RANGE) { |
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202 MP_CHECKOK(mp_sub(b, a, r)); |
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203 if (mp_cmp_z(r) < 0) { |
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204 MP_CHECKOK(mp_add(r, &meth->irr, r)); |
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205 } |
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206 MP_CHECKOK(ec_GFp_neg(r, r, meth)); |
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207 } |
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208 if (mp_cmp_z(r) < 0) { |
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209 MP_CHECKOK(mp_add(r, &meth->irr, r)); |
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210 } |
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211 CLEANUP: |
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212 return res; |
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213 } |
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214 /* |
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215 * Inline adds for small curve lengths. |
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216 */ |
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217 /* 3 words */ |
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218 mp_err |
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219 ec_GFp_add_3(const mp_int *a, const mp_int *b, mp_int *r, |
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220 const GFMethod *meth) |
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221 { |
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222 mp_err res = MP_OKAY; |
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223 mp_digit a0 = 0, a1 = 0, a2 = 0; |
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224 mp_digit r0 = 0, r1 = 0, r2 = 0; |
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225 mp_digit carry; |
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226 |
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227 switch(MP_USED(a)) { |
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228 case 3: |
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229 a2 = MP_DIGIT(a,2); |
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230 case 2: |
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231 a1 = MP_DIGIT(a,1); |
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232 case 1: |
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233 a0 = MP_DIGIT(a,0); |
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234 } |
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235 switch(MP_USED(b)) { |
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236 case 3: |
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237 r2 = MP_DIGIT(b,2); |
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238 case 2: |
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239 r1 = MP_DIGIT(b,1); |
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240 case 1: |
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241 r0 = MP_DIGIT(b,0); |
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242 } |
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243 |
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244 #ifndef MPI_AMD64_ADD |
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245 MP_ADD_CARRY(a0, r0, r0, 0, carry); |
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246 MP_ADD_CARRY(a1, r1, r1, carry, carry); |
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247 MP_ADD_CARRY(a2, r2, r2, carry, carry); |
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248 #else |
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249 __asm__ ( |
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250 "xorq %3,%3 \n\t" |
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251 "addq %4,%0 \n\t" |
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252 "adcq %5,%1 \n\t" |
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253 "adcq %6,%2 \n\t" |
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254 "adcq $0,%3 \n\t" |
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255 : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(carry) |
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256 : "r" (a0), "r" (a1), "r" (a2), |
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257 "0" (r0), "1" (r1), "2" (r2) |
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258 : "%cc" ); |
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259 #endif |
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260 |
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261 MP_CHECKOK(s_mp_pad(r, 3)); |
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262 MP_DIGIT(r, 2) = r2; |
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263 MP_DIGIT(r, 1) = r1; |
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264 MP_DIGIT(r, 0) = r0; |
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265 MP_SIGN(r) = MP_ZPOS; |
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266 MP_USED(r) = 3; |
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267 |
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268 /* Do quick 'subract' if we've gone over |
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269 * (add the 2's complement of the curve field) */ |
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270 a2 = MP_DIGIT(&meth->irr,2); |
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271 if (carry || r2 > a2 || |
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272 ((r2 == a2) && mp_cmp(r,&meth->irr) != MP_LT)) { |
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273 a1 = MP_DIGIT(&meth->irr,1); |
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274 a0 = MP_DIGIT(&meth->irr,0); |
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275 #ifndef MPI_AMD64_ADD |
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276 MP_SUB_BORROW(r0, a0, r0, 0, carry); |
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277 MP_SUB_BORROW(r1, a1, r1, carry, carry); |
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278 MP_SUB_BORROW(r2, a2, r2, carry, carry); |
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279 #else |
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280 __asm__ ( |
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281 "subq %3,%0 \n\t" |
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282 "sbbq %4,%1 \n\t" |
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283 "sbbq %5,%2 \n\t" |
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284 : "=r"(r0), "=r"(r1), "=r"(r2) |
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285 : "r" (a0), "r" (a1), "r" (a2), |
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286 "0" (r0), "1" (r1), "2" (r2) |
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287 : "%cc" ); |
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288 #endif |
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289 MP_DIGIT(r, 2) = r2; |
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290 MP_DIGIT(r, 1) = r1; |
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291 MP_DIGIT(r, 0) = r0; |
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292 } |
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293 |
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294 s_mp_clamp(r); |
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295 |
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296 CLEANUP: |
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297 return res; |
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298 } |
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299 |
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300 /* 4 words */ |
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301 mp_err |
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302 ec_GFp_add_4(const mp_int *a, const mp_int *b, mp_int *r, |
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303 const GFMethod *meth) |
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304 { |
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305 mp_err res = MP_OKAY; |
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306 mp_digit a0 = 0, a1 = 0, a2 = 0, a3 = 0; |
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307 mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0; |
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308 mp_digit carry; |
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309 |
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310 switch(MP_USED(a)) { |
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311 case 4: |
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312 a3 = MP_DIGIT(a,3); |
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313 case 3: |
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314 a2 = MP_DIGIT(a,2); |
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315 case 2: |
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316 a1 = MP_DIGIT(a,1); |
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317 case 1: |
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318 a0 = MP_DIGIT(a,0); |
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319 } |
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320 switch(MP_USED(b)) { |
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321 case 4: |
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322 r3 = MP_DIGIT(b,3); |
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323 case 3: |
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324 r2 = MP_DIGIT(b,2); |
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325 case 2: |
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326 r1 = MP_DIGIT(b,1); |
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327 case 1: |
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328 r0 = MP_DIGIT(b,0); |
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329 } |
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330 |
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331 #ifndef MPI_AMD64_ADD |
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332 MP_ADD_CARRY(a0, r0, r0, 0, carry); |
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333 MP_ADD_CARRY(a1, r1, r1, carry, carry); |
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334 MP_ADD_CARRY(a2, r2, r2, carry, carry); |
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335 MP_ADD_CARRY(a3, r3, r3, carry, carry); |
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336 #else |
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337 __asm__ ( |
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338 "xorq %4,%4 \n\t" |
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339 "addq %5,%0 \n\t" |
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340 "adcq %6,%1 \n\t" |
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341 "adcq %7,%2 \n\t" |
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342 "adcq %8,%3 \n\t" |
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343 "adcq $0,%4 \n\t" |
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344 : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r"(carry) |
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345 : "r" (a0), "r" (a1), "r" (a2), "r" (a3), |
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346 "0" (r0), "1" (r1), "2" (r2), "3" (r3) |
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347 : "%cc" ); |
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348 #endif |
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349 |
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350 MP_CHECKOK(s_mp_pad(r, 4)); |
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351 MP_DIGIT(r, 3) = r3; |
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352 MP_DIGIT(r, 2) = r2; |
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353 MP_DIGIT(r, 1) = r1; |
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354 MP_DIGIT(r, 0) = r0; |
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355 MP_SIGN(r) = MP_ZPOS; |
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356 MP_USED(r) = 4; |
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357 |
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358 /* Do quick 'subract' if we've gone over |
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359 * (add the 2's complement of the curve field) */ |
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360 a3 = MP_DIGIT(&meth->irr,3); |
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361 if (carry || r3 > a3 || |
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362 ((r3 == a3) && mp_cmp(r,&meth->irr) != MP_LT)) { |
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363 a2 = MP_DIGIT(&meth->irr,2); |
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364 a1 = MP_DIGIT(&meth->irr,1); |
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365 a0 = MP_DIGIT(&meth->irr,0); |
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366 #ifndef MPI_AMD64_ADD |
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367 MP_SUB_BORROW(r0, a0, r0, 0, carry); |
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368 MP_SUB_BORROW(r1, a1, r1, carry, carry); |
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369 MP_SUB_BORROW(r2, a2, r2, carry, carry); |
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370 MP_SUB_BORROW(r3, a3, r3, carry, carry); |
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371 #else |
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372 __asm__ ( |
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373 "subq %4,%0 \n\t" |
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374 "sbbq %5,%1 \n\t" |
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375 "sbbq %6,%2 \n\t" |
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376 "sbbq %7,%3 \n\t" |
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377 : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3) |
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378 : "r" (a0), "r" (a1), "r" (a2), "r" (a3), |
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379 "0" (r0), "1" (r1), "2" (r2), "3" (r3) |
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380 : "%cc" ); |
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381 #endif |
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382 MP_DIGIT(r, 3) = r3; |
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383 MP_DIGIT(r, 2) = r2; |
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384 MP_DIGIT(r, 1) = r1; |
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385 MP_DIGIT(r, 0) = r0; |
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386 } |
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387 |
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388 s_mp_clamp(r); |
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389 |
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390 CLEANUP: |
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391 return res; |
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392 } |
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393 |
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394 /* 5 words */ |
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395 mp_err |
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396 ec_GFp_add_5(const mp_int *a, const mp_int *b, mp_int *r, |
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397 const GFMethod *meth) |
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398 { |
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399 mp_err res = MP_OKAY; |
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400 mp_digit a0 = 0, a1 = 0, a2 = 0, a3 = 0, a4 = 0; |
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401 mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0; |
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402 mp_digit carry; |
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403 |
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404 switch(MP_USED(a)) { |
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405 case 5: |
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406 a4 = MP_DIGIT(a,4); |
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407 case 4: |
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408 a3 = MP_DIGIT(a,3); |
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409 case 3: |
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410 a2 = MP_DIGIT(a,2); |
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411 case 2: |
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412 a1 = MP_DIGIT(a,1); |
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413 case 1: |
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414 a0 = MP_DIGIT(a,0); |
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415 } |
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416 switch(MP_USED(b)) { |
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417 case 5: |
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418 r4 = MP_DIGIT(b,4); |
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419 case 4: |
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420 r3 = MP_DIGIT(b,3); |
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421 case 3: |
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422 r2 = MP_DIGIT(b,2); |
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423 case 2: |
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424 r1 = MP_DIGIT(b,1); |
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425 case 1: |
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426 r0 = MP_DIGIT(b,0); |
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427 } |
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428 |
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429 MP_ADD_CARRY(a0, r0, r0, 0, carry); |
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430 MP_ADD_CARRY(a1, r1, r1, carry, carry); |
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431 MP_ADD_CARRY(a2, r2, r2, carry, carry); |
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432 MP_ADD_CARRY(a3, r3, r3, carry, carry); |
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433 MP_ADD_CARRY(a4, r4, r4, carry, carry); |
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434 |
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435 MP_CHECKOK(s_mp_pad(r, 5)); |
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436 MP_DIGIT(r, 4) = r4; |
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437 MP_DIGIT(r, 3) = r3; |
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438 MP_DIGIT(r, 2) = r2; |
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439 MP_DIGIT(r, 1) = r1; |
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440 MP_DIGIT(r, 0) = r0; |
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441 MP_SIGN(r) = MP_ZPOS; |
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442 MP_USED(r) = 5; |
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443 |
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444 /* Do quick 'subract' if we've gone over |
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445 * (add the 2's complement of the curve field) */ |
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446 a4 = MP_DIGIT(&meth->irr,4); |
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447 if (carry || r4 > a4 || |
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448 ((r4 == a4) && mp_cmp(r,&meth->irr) != MP_LT)) { |
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449 a3 = MP_DIGIT(&meth->irr,3); |
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450 a2 = MP_DIGIT(&meth->irr,2); |
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451 a1 = MP_DIGIT(&meth->irr,1); |
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452 a0 = MP_DIGIT(&meth->irr,0); |
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453 MP_SUB_BORROW(r0, a0, r0, 0, carry); |
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454 MP_SUB_BORROW(r1, a1, r1, carry, carry); |
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455 MP_SUB_BORROW(r2, a2, r2, carry, carry); |
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456 MP_SUB_BORROW(r3, a3, r3, carry, carry); |
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457 MP_SUB_BORROW(r4, a4, r4, carry, carry); |
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458 MP_DIGIT(r, 4) = r4; |
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459 MP_DIGIT(r, 3) = r3; |
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460 MP_DIGIT(r, 2) = r2; |
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461 MP_DIGIT(r, 1) = r1; |
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462 MP_DIGIT(r, 0) = r0; |
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463 } |
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464 |
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465 s_mp_clamp(r); |
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466 |
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467 CLEANUP: |
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468 return res; |
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469 } |
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470 |
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471 /* 6 words */ |
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472 mp_err |
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473 ec_GFp_add_6(const mp_int *a, const mp_int *b, mp_int *r, |
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474 const GFMethod *meth) |
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475 { |
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476 mp_err res = MP_OKAY; |
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477 mp_digit a0 = 0, a1 = 0, a2 = 0, a3 = 0, a4 = 0, a5 = 0; |
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478 mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0, r5 = 0; |
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479 mp_digit carry; |
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480 |
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481 switch(MP_USED(a)) { |
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482 case 6: |
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483 a5 = MP_DIGIT(a,5); |
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484 case 5: |
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485 a4 = MP_DIGIT(a,4); |
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486 case 4: |
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487 a3 = MP_DIGIT(a,3); |
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488 case 3: |
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489 a2 = MP_DIGIT(a,2); |
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490 case 2: |
|
491 a1 = MP_DIGIT(a,1); |
|
492 case 1: |
|
493 a0 = MP_DIGIT(a,0); |
|
494 } |
|
495 switch(MP_USED(b)) { |
|
496 case 6: |
|
497 r5 = MP_DIGIT(b,5); |
|
498 case 5: |
|
499 r4 = MP_DIGIT(b,4); |
|
500 case 4: |
|
501 r3 = MP_DIGIT(b,3); |
|
502 case 3: |
|
503 r2 = MP_DIGIT(b,2); |
|
504 case 2: |
|
505 r1 = MP_DIGIT(b,1); |
|
506 case 1: |
|
507 r0 = MP_DIGIT(b,0); |
|
508 } |
|
509 |
|
510 MP_ADD_CARRY(a0, r0, r0, 0, carry); |
|
511 MP_ADD_CARRY(a1, r1, r1, carry, carry); |
|
512 MP_ADD_CARRY(a2, r2, r2, carry, carry); |
|
513 MP_ADD_CARRY(a3, r3, r3, carry, carry); |
|
514 MP_ADD_CARRY(a4, r4, r4, carry, carry); |
|
515 MP_ADD_CARRY(a5, r5, r5, carry, carry); |
|
516 |
|
517 MP_CHECKOK(s_mp_pad(r, 6)); |
|
518 MP_DIGIT(r, 5) = r5; |
|
519 MP_DIGIT(r, 4) = r4; |
|
520 MP_DIGIT(r, 3) = r3; |
|
521 MP_DIGIT(r, 2) = r2; |
|
522 MP_DIGIT(r, 1) = r1; |
|
523 MP_DIGIT(r, 0) = r0; |
|
524 MP_SIGN(r) = MP_ZPOS; |
|
525 MP_USED(r) = 6; |
|
526 |
|
527 /* Do quick 'subract' if we've gone over |
|
528 * (add the 2's complement of the curve field) */ |
|
529 a5 = MP_DIGIT(&meth->irr,5); |
|
530 if (carry || r5 > a5 || |
|
531 ((r5 == a5) && mp_cmp(r,&meth->irr) != MP_LT)) { |
|
532 a4 = MP_DIGIT(&meth->irr,4); |
|
533 a3 = MP_DIGIT(&meth->irr,3); |
|
534 a2 = MP_DIGIT(&meth->irr,2); |
|
535 a1 = MP_DIGIT(&meth->irr,1); |
|
536 a0 = MP_DIGIT(&meth->irr,0); |
|
537 MP_SUB_BORROW(r0, a0, r0, 0, carry); |
|
538 MP_SUB_BORROW(r1, a1, r1, carry, carry); |
|
539 MP_SUB_BORROW(r2, a2, r2, carry, carry); |
|
540 MP_SUB_BORROW(r3, a3, r3, carry, carry); |
|
541 MP_SUB_BORROW(r4, a4, r4, carry, carry); |
|
542 MP_SUB_BORROW(r5, a5, r5, carry, carry); |
|
543 MP_DIGIT(r, 5) = r5; |
|
544 MP_DIGIT(r, 4) = r4; |
|
545 MP_DIGIT(r, 3) = r3; |
|
546 MP_DIGIT(r, 2) = r2; |
|
547 MP_DIGIT(r, 1) = r1; |
|
548 MP_DIGIT(r, 0) = r0; |
|
549 } |
|
550 |
|
551 s_mp_clamp(r); |
|
552 |
|
553 CLEANUP: |
|
554 return res; |
|
555 } |
|
556 |
|
557 /* |
|
558 * The following subraction functions do in-line subractions based |
|
559 * on our curve size. |
|
560 * |
|
561 * ... 3 words |
|
562 */ |
|
563 mp_err |
|
564 ec_GFp_sub_3(const mp_int *a, const mp_int *b, mp_int *r, |
|
565 const GFMethod *meth) |
|
566 { |
|
567 mp_err res = MP_OKAY; |
|
568 mp_digit b0 = 0, b1 = 0, b2 = 0; |
|
569 mp_digit r0 = 0, r1 = 0, r2 = 0; |
|
570 mp_digit borrow; |
|
571 |
|
572 switch(MP_USED(a)) { |
|
573 case 3: |
|
574 r2 = MP_DIGIT(a,2); |
|
575 case 2: |
|
576 r1 = MP_DIGIT(a,1); |
|
577 case 1: |
|
578 r0 = MP_DIGIT(a,0); |
|
579 } |
|
580 switch(MP_USED(b)) { |
|
581 case 3: |
|
582 b2 = MP_DIGIT(b,2); |
|
583 case 2: |
|
584 b1 = MP_DIGIT(b,1); |
|
585 case 1: |
|
586 b0 = MP_DIGIT(b,0); |
|
587 } |
|
588 |
|
589 #ifndef MPI_AMD64_ADD |
|
590 MP_SUB_BORROW(r0, b0, r0, 0, borrow); |
|
591 MP_SUB_BORROW(r1, b1, r1, borrow, borrow); |
|
592 MP_SUB_BORROW(r2, b2, r2, borrow, borrow); |
|
593 #else |
|
594 __asm__ ( |
|
595 "xorq %3,%3 \n\t" |
|
596 "subq %4,%0 \n\t" |
|
597 "sbbq %5,%1 \n\t" |
|
598 "sbbq %6,%2 \n\t" |
|
599 "adcq $0,%3 \n\t" |
|
600 : "=r"(r0), "=r"(r1), "=r"(r2), "=r" (borrow) |
|
601 : "r" (b0), "r" (b1), "r" (b2), |
|
602 "0" (r0), "1" (r1), "2" (r2) |
|
603 : "%cc" ); |
|
604 #endif |
|
605 |
|
606 /* Do quick 'add' if we've gone under 0 |
|
607 * (subtract the 2's complement of the curve field) */ |
|
608 if (borrow) { |
|
609 b2 = MP_DIGIT(&meth->irr,2); |
|
610 b1 = MP_DIGIT(&meth->irr,1); |
|
611 b0 = MP_DIGIT(&meth->irr,0); |
|
612 #ifndef MPI_AMD64_ADD |
|
613 MP_ADD_CARRY(b0, r0, r0, 0, borrow); |
|
614 MP_ADD_CARRY(b1, r1, r1, borrow, borrow); |
|
615 MP_ADD_CARRY(b2, r2, r2, borrow, borrow); |
|
616 #else |
|
617 __asm__ ( |
|
618 "addq %3,%0 \n\t" |
|
619 "adcq %4,%1 \n\t" |
|
620 "adcq %5,%2 \n\t" |
|
621 : "=r"(r0), "=r"(r1), "=r"(r2) |
|
622 : "r" (b0), "r" (b1), "r" (b2), |
|
623 "0" (r0), "1" (r1), "2" (r2) |
|
624 : "%cc" ); |
|
625 #endif |
|
626 } |
|
627 |
|
628 #ifdef MPI_AMD64_ADD |
|
629 /* compiler fakeout? */ |
|
630 if ((r2 == b0) && (r1 == b0) && (r0 == b0)) { |
|
631 MP_CHECKOK(s_mp_pad(r, 4)); |
|
632 } |
|
633 #endif |
|
634 MP_CHECKOK(s_mp_pad(r, 3)); |
|
635 MP_DIGIT(r, 2) = r2; |
|
636 MP_DIGIT(r, 1) = r1; |
|
637 MP_DIGIT(r, 0) = r0; |
|
638 MP_SIGN(r) = MP_ZPOS; |
|
639 MP_USED(r) = 3; |
|
640 s_mp_clamp(r); |
|
641 |
|
642 CLEANUP: |
|
643 return res; |
|
644 } |
|
645 |
|
646 /* 4 words */ |
|
647 mp_err |
|
648 ec_GFp_sub_4(const mp_int *a, const mp_int *b, mp_int *r, |
|
649 const GFMethod *meth) |
|
650 { |
|
651 mp_err res = MP_OKAY; |
|
652 mp_digit b0 = 0, b1 = 0, b2 = 0, b3 = 0; |
|
653 mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0; |
|
654 mp_digit borrow; |
|
655 |
|
656 switch(MP_USED(a)) { |
|
657 case 4: |
|
658 r3 = MP_DIGIT(a,3); |
|
659 case 3: |
|
660 r2 = MP_DIGIT(a,2); |
|
661 case 2: |
|
662 r1 = MP_DIGIT(a,1); |
|
663 case 1: |
|
664 r0 = MP_DIGIT(a,0); |
|
665 } |
|
666 switch(MP_USED(b)) { |
|
667 case 4: |
|
668 b3 = MP_DIGIT(b,3); |
|
669 case 3: |
|
670 b2 = MP_DIGIT(b,2); |
|
671 case 2: |
|
672 b1 = MP_DIGIT(b,1); |
|
673 case 1: |
|
674 b0 = MP_DIGIT(b,0); |
|
675 } |
|
676 |
|
677 #ifndef MPI_AMD64_ADD |
|
678 MP_SUB_BORROW(r0, b0, r0, 0, borrow); |
|
679 MP_SUB_BORROW(r1, b1, r1, borrow, borrow); |
|
680 MP_SUB_BORROW(r2, b2, r2, borrow, borrow); |
|
681 MP_SUB_BORROW(r3, b3, r3, borrow, borrow); |
|
682 #else |
|
683 __asm__ ( |
|
684 "xorq %4,%4 \n\t" |
|
685 "subq %5,%0 \n\t" |
|
686 "sbbq %6,%1 \n\t" |
|
687 "sbbq %7,%2 \n\t" |
|
688 "sbbq %8,%3 \n\t" |
|
689 "adcq $0,%4 \n\t" |
|
690 : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r" (borrow) |
|
691 : "r" (b0), "r" (b1), "r" (b2), "r" (b3), |
|
692 "0" (r0), "1" (r1), "2" (r2), "3" (r3) |
|
693 : "%cc" ); |
|
694 #endif |
|
695 |
|
696 /* Do quick 'add' if we've gone under 0 |
|
697 * (subtract the 2's complement of the curve field) */ |
|
698 if (borrow) { |
|
699 b3 = MP_DIGIT(&meth->irr,3); |
|
700 b2 = MP_DIGIT(&meth->irr,2); |
|
701 b1 = MP_DIGIT(&meth->irr,1); |
|
702 b0 = MP_DIGIT(&meth->irr,0); |
|
703 #ifndef MPI_AMD64_ADD |
|
704 MP_ADD_CARRY(b0, r0, r0, 0, borrow); |
|
705 MP_ADD_CARRY(b1, r1, r1, borrow, borrow); |
|
706 MP_ADD_CARRY(b2, r2, r2, borrow, borrow); |
|
707 MP_ADD_CARRY(b3, r3, r3, borrow, borrow); |
|
708 #else |
|
709 __asm__ ( |
|
710 "addq %4,%0 \n\t" |
|
711 "adcq %5,%1 \n\t" |
|
712 "adcq %6,%2 \n\t" |
|
713 "adcq %7,%3 \n\t" |
|
714 : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3) |
|
715 : "r" (b0), "r" (b1), "r" (b2), "r" (b3), |
|
716 "0" (r0), "1" (r1), "2" (r2), "3" (r3) |
|
717 : "%cc" ); |
|
718 #endif |
|
719 } |
|
720 #ifdef MPI_AMD64_ADD |
|
721 /* compiler fakeout? */ |
|
722 if ((r3 == b0) && (r1 == b0) && (r0 == b0)) { |
|
723 MP_CHECKOK(s_mp_pad(r, 4)); |
|
724 } |
|
725 #endif |
|
726 MP_CHECKOK(s_mp_pad(r, 4)); |
|
727 MP_DIGIT(r, 3) = r3; |
|
728 MP_DIGIT(r, 2) = r2; |
|
729 MP_DIGIT(r, 1) = r1; |
|
730 MP_DIGIT(r, 0) = r0; |
|
731 MP_SIGN(r) = MP_ZPOS; |
|
732 MP_USED(r) = 4; |
|
733 s_mp_clamp(r); |
|
734 |
|
735 CLEANUP: |
|
736 return res; |
|
737 } |
|
738 |
|
739 /* 5 words */ |
|
740 mp_err |
|
741 ec_GFp_sub_5(const mp_int *a, const mp_int *b, mp_int *r, |
|
742 const GFMethod *meth) |
|
743 { |
|
744 mp_err res = MP_OKAY; |
|
745 mp_digit b0 = 0, b1 = 0, b2 = 0, b3 = 0, b4 = 0; |
|
746 mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0; |
|
747 mp_digit borrow; |
|
748 |
|
749 switch(MP_USED(a)) { |
|
750 case 5: |
|
751 r4 = MP_DIGIT(a,4); |
|
752 case 4: |
|
753 r3 = MP_DIGIT(a,3); |
|
754 case 3: |
|
755 r2 = MP_DIGIT(a,2); |
|
756 case 2: |
|
757 r1 = MP_DIGIT(a,1); |
|
758 case 1: |
|
759 r0 = MP_DIGIT(a,0); |
|
760 } |
|
761 switch(MP_USED(b)) { |
|
762 case 5: |
|
763 b4 = MP_DIGIT(b,4); |
|
764 case 4: |
|
765 b3 = MP_DIGIT(b,3); |
|
766 case 3: |
|
767 b2 = MP_DIGIT(b,2); |
|
768 case 2: |
|
769 b1 = MP_DIGIT(b,1); |
|
770 case 1: |
|
771 b0 = MP_DIGIT(b,0); |
|
772 } |
|
773 |
|
774 MP_SUB_BORROW(r0, b0, r0, 0, borrow); |
|
775 MP_SUB_BORROW(r1, b1, r1, borrow, borrow); |
|
776 MP_SUB_BORROW(r2, b2, r2, borrow, borrow); |
|
777 MP_SUB_BORROW(r3, b3, r3, borrow, borrow); |
|
778 MP_SUB_BORROW(r4, b4, r4, borrow, borrow); |
|
779 |
|
780 /* Do quick 'add' if we've gone under 0 |
|
781 * (subtract the 2's complement of the curve field) */ |
|
782 if (borrow) { |
|
783 b4 = MP_DIGIT(&meth->irr,4); |
|
784 b3 = MP_DIGIT(&meth->irr,3); |
|
785 b2 = MP_DIGIT(&meth->irr,2); |
|
786 b1 = MP_DIGIT(&meth->irr,1); |
|
787 b0 = MP_DIGIT(&meth->irr,0); |
|
788 MP_ADD_CARRY(b0, r0, r0, 0, borrow); |
|
789 MP_ADD_CARRY(b1, r1, r1, borrow, borrow); |
|
790 MP_ADD_CARRY(b2, r2, r2, borrow, borrow); |
|
791 MP_ADD_CARRY(b3, r3, r3, borrow, borrow); |
|
792 } |
|
793 MP_CHECKOK(s_mp_pad(r, 5)); |
|
794 MP_DIGIT(r, 4) = r4; |
|
795 MP_DIGIT(r, 3) = r3; |
|
796 MP_DIGIT(r, 2) = r2; |
|
797 MP_DIGIT(r, 1) = r1; |
|
798 MP_DIGIT(r, 0) = r0; |
|
799 MP_SIGN(r) = MP_ZPOS; |
|
800 MP_USED(r) = 5; |
|
801 s_mp_clamp(r); |
|
802 |
|
803 CLEANUP: |
|
804 return res; |
|
805 } |
|
806 |
|
807 /* 6 words */ |
|
808 mp_err |
|
809 ec_GFp_sub_6(const mp_int *a, const mp_int *b, mp_int *r, |
|
810 const GFMethod *meth) |
|
811 { |
|
812 mp_err res = MP_OKAY; |
|
813 mp_digit b0 = 0, b1 = 0, b2 = 0, b3 = 0, b4 = 0, b5 = 0; |
|
814 mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0, r5 = 0; |
|
815 mp_digit borrow; |
|
816 |
|
817 switch(MP_USED(a)) { |
|
818 case 6: |
|
819 r5 = MP_DIGIT(a,5); |
|
820 case 5: |
|
821 r4 = MP_DIGIT(a,4); |
|
822 case 4: |
|
823 r3 = MP_DIGIT(a,3); |
|
824 case 3: |
|
825 r2 = MP_DIGIT(a,2); |
|
826 case 2: |
|
827 r1 = MP_DIGIT(a,1); |
|
828 case 1: |
|
829 r0 = MP_DIGIT(a,0); |
|
830 } |
|
831 switch(MP_USED(b)) { |
|
832 case 6: |
|
833 b5 = MP_DIGIT(b,5); |
|
834 case 5: |
|
835 b4 = MP_DIGIT(b,4); |
|
836 case 4: |
|
837 b3 = MP_DIGIT(b,3); |
|
838 case 3: |
|
839 b2 = MP_DIGIT(b,2); |
|
840 case 2: |
|
841 b1 = MP_DIGIT(b,1); |
|
842 case 1: |
|
843 b0 = MP_DIGIT(b,0); |
|
844 } |
|
845 |
|
846 MP_SUB_BORROW(r0, b0, r0, 0, borrow); |
|
847 MP_SUB_BORROW(r1, b1, r1, borrow, borrow); |
|
848 MP_SUB_BORROW(r2, b2, r2, borrow, borrow); |
|
849 MP_SUB_BORROW(r3, b3, r3, borrow, borrow); |
|
850 MP_SUB_BORROW(r4, b4, r4, borrow, borrow); |
|
851 MP_SUB_BORROW(r5, b5, r5, borrow, borrow); |
|
852 |
|
853 /* Do quick 'add' if we've gone under 0 |
|
854 * (subtract the 2's complement of the curve field) */ |
|
855 if (borrow) { |
|
856 b5 = MP_DIGIT(&meth->irr,5); |
|
857 b4 = MP_DIGIT(&meth->irr,4); |
|
858 b3 = MP_DIGIT(&meth->irr,3); |
|
859 b2 = MP_DIGIT(&meth->irr,2); |
|
860 b1 = MP_DIGIT(&meth->irr,1); |
|
861 b0 = MP_DIGIT(&meth->irr,0); |
|
862 MP_ADD_CARRY(b0, r0, r0, 0, borrow); |
|
863 MP_ADD_CARRY(b1, r1, r1, borrow, borrow); |
|
864 MP_ADD_CARRY(b2, r2, r2, borrow, borrow); |
|
865 MP_ADD_CARRY(b3, r3, r3, borrow, borrow); |
|
866 MP_ADD_CARRY(b4, r4, r4, borrow, borrow); |
|
867 } |
|
868 |
|
869 MP_CHECKOK(s_mp_pad(r, 6)); |
|
870 MP_DIGIT(r, 5) = r5; |
|
871 MP_DIGIT(r, 4) = r4; |
|
872 MP_DIGIT(r, 3) = r3; |
|
873 MP_DIGIT(r, 2) = r2; |
|
874 MP_DIGIT(r, 1) = r1; |
|
875 MP_DIGIT(r, 0) = r0; |
|
876 MP_SIGN(r) = MP_ZPOS; |
|
877 MP_USED(r) = 6; |
|
878 s_mp_clamp(r); |
|
879 |
|
880 CLEANUP: |
|
881 return res; |
|
882 } |
|
883 |
|
884 |
|
885 /* Reduces an integer to a field element. */ |
|
886 mp_err |
|
887 ec_GFp_mod(const mp_int *a, mp_int *r, const GFMethod *meth) |
|
888 { |
|
889 return mp_mod(a, &meth->irr, r); |
|
890 } |
|
891 |
|
892 /* Multiplies two field elements. */ |
|
893 mp_err |
|
894 ec_GFp_mul(const mp_int *a, const mp_int *b, mp_int *r, |
|
895 const GFMethod *meth) |
|
896 { |
|
897 return mp_mulmod(a, b, &meth->irr, r); |
|
898 } |
|
899 |
|
900 /* Squares a field element. */ |
|
901 mp_err |
|
902 ec_GFp_sqr(const mp_int *a, mp_int *r, const GFMethod *meth) |
|
903 { |
|
904 return mp_sqrmod(a, &meth->irr, r); |
|
905 } |
|
906 |
|
907 /* Divides two field elements. If a is NULL, then returns the inverse of |
|
908 * b. */ |
|
909 mp_err |
|
910 ec_GFp_div(const mp_int *a, const mp_int *b, mp_int *r, |
|
911 const GFMethod *meth) |
|
912 { |
|
913 mp_err res = MP_OKAY; |
|
914 mp_int t; |
|
915 |
|
916 /* If a is NULL, then return the inverse of b, otherwise return a/b. */ |
|
917 if (a == NULL) { |
|
918 return mp_invmod(b, &meth->irr, r); |
|
919 } else { |
|
920 /* MPI doesn't support divmod, so we implement it using invmod and |
|
921 * mulmod. */ |
|
922 MP_CHECKOK(mp_init(&t)); |
|
923 MP_CHECKOK(mp_invmod(b, &meth->irr, &t)); |
|
924 MP_CHECKOK(mp_mulmod(a, &t, &meth->irr, r)); |
|
925 CLEANUP: |
|
926 mp_clear(&t); |
|
927 return res; |
|
928 } |
|
929 } |
|
930 |
|
931 /* Wrapper functions for generic binary polynomial field arithmetic. */ |
|
932 |
|
933 /* Adds two field elements. */ |
|
934 mp_err |
|
935 ec_GF2m_add(const mp_int *a, const mp_int *b, mp_int *r, |
|
936 const GFMethod *meth) |
|
937 { |
|
938 return mp_badd(a, b, r); |
|
939 } |
|
940 |
|
941 /* Negates a field element. Note that for binary polynomial fields, the |
|
942 * negation of a field element is the field element itself. */ |
|
943 mp_err |
|
944 ec_GF2m_neg(const mp_int *a, mp_int *r, const GFMethod *meth) |
|
945 { |
|
946 if (a == r) { |
|
947 return MP_OKAY; |
|
948 } else { |
|
949 return mp_copy(a, r); |
|
950 } |
|
951 } |
|
952 |
|
953 /* Reduces a binary polynomial to a field element. */ |
|
954 mp_err |
|
955 ec_GF2m_mod(const mp_int *a, mp_int *r, const GFMethod *meth) |
|
956 { |
|
957 return mp_bmod(a, meth->irr_arr, r); |
|
958 } |
|
959 |
|
960 /* Multiplies two field elements. */ |
|
961 mp_err |
|
962 ec_GF2m_mul(const mp_int *a, const mp_int *b, mp_int *r, |
|
963 const GFMethod *meth) |
|
964 { |
|
965 return mp_bmulmod(a, b, meth->irr_arr, r); |
|
966 } |
|
967 |
|
968 /* Squares a field element. */ |
|
969 mp_err |
|
970 ec_GF2m_sqr(const mp_int *a, mp_int *r, const GFMethod *meth) |
|
971 { |
|
972 return mp_bsqrmod(a, meth->irr_arr, r); |
|
973 } |
|
974 |
|
975 /* Divides two field elements. If a is NULL, then returns the inverse of |
|
976 * b. */ |
|
977 mp_err |
|
978 ec_GF2m_div(const mp_int *a, const mp_int *b, mp_int *r, |
|
979 const GFMethod *meth) |
|
980 { |
|
981 mp_err res = MP_OKAY; |
|
982 mp_int t; |
|
983 |
|
984 /* If a is NULL, then return the inverse of b, otherwise return a/b. */ |
|
985 if (a == NULL) { |
|
986 /* The GF(2^m) portion of MPI doesn't support invmod, so we |
|
987 * compute 1/b. */ |
|
988 MP_CHECKOK(mp_init(&t)); |
|
989 MP_CHECKOK(mp_set_int(&t, 1)); |
|
990 MP_CHECKOK(mp_bdivmod(&t, b, &meth->irr, meth->irr_arr, r)); |
|
991 CLEANUP: |
|
992 mp_clear(&t); |
|
993 return res; |
|
994 } else { |
|
995 return mp_bdivmod(a, b, &meth->irr, meth->irr_arr, r); |
|
996 } |
|
997 } |