Mercurial > dropbear
annotate gf.c @ 125:d16fc1b2223d libtomcrypt
merge of 8231809d2509aa54773443786e3123766438d924
and e30f886c9c14efb01f49297b3fb6b97c8868fd88
author | Matt Johnston <matt@ucc.asn.au> |
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date | Tue, 14 Sep 2004 13:28:31 +0000 |
parents | d7da3b1e1540 |
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1 /* LibTomCrypt, modular cryptographic library -- Tom St Denis |
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2 * |
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3 * LibTomCrypt is a library that provides various cryptographic |
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4 * algorithms in a highly modular and flexible manner. |
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5 * |
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6 * The library is free for all purposes without any express |
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7 * guarantee it works. |
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8 * |
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9 * Tom St Denis, [email protected], http://libtomcrypt.org |
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10 */ |
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11 /* polynomial basis GF(2^w) routines */ |
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12 #include "mycrypt.h" |
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13 |
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14 #ifdef GF |
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15 |
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16 #define FORLOOP for (i = 0; i < LSIZE; i++) |
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17 |
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18 /* c = a + b */ |
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19 void gf_add(gf_intp a, gf_intp b, gf_intp c) |
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20 { |
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21 int i; |
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22 FORLOOP c[i] = a[i]^b[i]; |
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23 } |
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24 |
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25 /* b = a */ |
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26 void gf_copy(gf_intp a, gf_intp b) |
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27 { |
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28 int i; |
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29 FORLOOP b[i] = a[i]; |
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30 } |
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31 |
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32 /* a = 0 */ |
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33 void gf_zero(gf_intp a) |
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34 { |
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35 int i; |
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36 FORLOOP a[i] = 0; |
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37 } |
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38 |
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39 /* is a zero? */ |
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40 int gf_iszero(gf_intp a) |
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41 { |
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42 int i; |
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43 FORLOOP if (a[i]) { |
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44 return 0; |
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45 } |
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46 return 1; |
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47 } |
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48 |
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49 /* is a one? */ |
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50 int gf_isone(gf_intp a) |
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51 { |
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52 int i; |
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53 for (i = 1; i < LSIZE; i++) { |
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54 if (a[i]) { |
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55 return 0; |
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56 } |
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57 } |
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58 return a[0] == 1; |
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59 } |
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60 |
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61 /* b = a << 1*/ |
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62 void gf_shl(gf_intp a, gf_intp b) |
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63 { |
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64 int i; |
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65 gf_int tmp; |
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66 |
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67 gf_copy(a, tmp); |
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68 for (i = LSIZE-1; i > 0; i--) |
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69 b[i] = ((tmp[i]<<1)|((tmp[i-1]&0xFFFFFFFFUL)>>31))&0xFFFFFFFFUL; |
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70 b[0] = (tmp[0] << 1)&0xFFFFFFFFUL; |
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71 gf_zero(tmp); |
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72 } |
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73 |
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74 /* b = a >> 1 */ |
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75 void gf_shr(gf_intp a, gf_intp b) |
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76 { |
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77 int i; |
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78 gf_int tmp; |
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79 |
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80 gf_copy(a, tmp); |
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81 for (i = 0; i < LSIZE-1; i++) |
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82 b[i] = (((tmp[i]&0xFFFFFFFFUL)>>1)|(tmp[i+1]<<31))&0xFFFFFFFFUL; |
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83 b[LSIZE-1] = (tmp[LSIZE-1]&0xFFFFFFFFUL)>>1; |
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84 gf_zero(tmp); |
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85 } |
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86 |
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87 /* returns -1 if its zero, otherwise degree of a */ |
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88 int gf_deg(gf_intp a) |
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89 { |
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90 int i, ii; |
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91 unsigned long t; |
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92 |
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93 ii = -1; |
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94 for (i = LSIZE-1; i >= 0; i--) |
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95 if (a[i]) { |
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96 for (t = a[i], ii = 0; t; t >>= 1, ++ii); |
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97 break; |
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98 } |
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99 if (i == -1) i = 0; |
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100 return (i<<5)+ii; |
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101 } |
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102 |
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103 /* c = ab */ |
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104 void gf_mul(gf_intp a, gf_intp b, gf_intp c) |
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105 { |
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106 gf_int ta, tb; |
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107 int i, n; |
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108 |
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109 gf_copy(a, ta); |
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110 gf_copy(b, tb); |
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111 gf_zero(c); |
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112 n = gf_deg(ta)+1; |
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113 for (i = 0; i < n; i++) { |
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114 if (ta[i>>5]&(1<<(i&31))) |
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115 gf_add(c, tb, c); |
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116 gf_shl(tb, tb); |
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117 } |
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118 gf_zero(ta); |
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119 gf_zero(tb); |
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120 } |
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121 |
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122 /* q = a/b, r = a%b */ |
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123 void gf_div(gf_intp a, gf_intp b, gf_intp q, gf_intp r) |
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124 { |
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125 gf_int ta, tb, shifts[LSIZE*32]; |
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126 int i, magb, mag; |
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127 |
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128 mag = gf_deg(a); |
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129 magb = gf_deg(b); |
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130 |
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131 /* special cases */ |
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132 if (magb > mag) { |
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133 gf_copy(a, r); |
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134 gf_zero(q); |
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135 return; |
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136 } |
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137 if (magb == -1) { |
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138 return; |
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139 } |
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140 |
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141 /* copy locally */ |
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142 gf_copy(a, ta); |
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143 gf_copy(b, tb); |
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144 gf_zero(q); |
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145 |
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146 /* make shifted versions of "b" */ |
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147 gf_copy(tb, shifts[0]); |
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148 for (i = 1; i <= (mag-magb); i++) |
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149 gf_shl(shifts[i-1], shifts[i]); |
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150 |
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151 while (mag >= magb) { |
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152 i = (mag - magb); |
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153 q[i>>5] |= (1<<(i&31)); |
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154 gf_add(ta, shifts[i], ta); |
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155 mag = gf_deg(ta); |
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156 } |
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157 gf_copy(ta, r); |
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158 gf_zero(ta); |
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159 gf_zero(tb); |
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160 zeromem(shifts, sizeof(shifts)); |
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161 } |
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162 |
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163 /* b = a mod m */ |
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164 void gf_mod(gf_intp a, gf_intp m, gf_intp b) |
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165 { |
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166 gf_int tmp; |
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167 gf_div(a,m,tmp,b); |
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168 gf_zero(tmp); |
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169 } |
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170 |
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171 /* c = ab (mod m) */ |
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172 void gf_mulmod(gf_intp a, gf_intp b, gf_intp m, gf_intp c) |
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173 { |
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174 gf_int tmp; |
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175 gf_mul(a, b, tmp); |
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176 gf_mod(tmp, m, c); |
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177 gf_zero(tmp); |
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178 } |
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179 |
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180 /* B = 1/A mod M */ |
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181 void gf_invmod(gf_intp A, gf_intp M, gf_intp B) |
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182 { |
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183 gf_int m, n, p0, p1, p2, r, q, tmp; |
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184 |
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185 /* put all variables in known setup state */ |
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186 gf_zero(p0); |
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187 gf_zero(p2); |
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188 gf_copy(M, m); |
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189 gf_copy(A, n); |
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190 p0[0] = 1; |
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191 gf_div(m, n, p1, r); |
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192 gf_copy(p1, q); |
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193 |
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194 /* loop until r == 0 */ |
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195 while (!gf_iszero(r)) { |
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196 gf_copy(n, m); |
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197 gf_copy(r, n); |
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198 gf_div(m, n, q, r); |
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199 gf_mul(q, p1, tmp); |
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200 gf_add(tmp, p0, p2); |
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201 gf_copy(p1, p0); |
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202 gf_copy(p2, p1); |
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203 } |
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204 gf_copy(p0, B); |
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205 gf_zero(p0); |
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206 } |
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207 |
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208 /* find a square root modulo a prime. Note the number of |
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209 * elements is 2^k - 1, so we must square k-2 times to get the |
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210 * square root.. |
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211 */ |
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212 void gf_sqrt(gf_intp a, gf_intp M, gf_intp b) |
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213 { |
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214 int k; |
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215 k = gf_deg(M)-2; |
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216 gf_copy(a, b); |
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217 while (k--) |
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218 gf_mulmod(b, b, M, b); |
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219 } |
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220 |
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221 /* c = gcd(A,B) */ |
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222 void gf_gcd(gf_intp A, gf_intp B, gf_intp c) |
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223 { |
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224 gf_int a, b, r; |
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225 int n; |
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226 |
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227 gf_add(A, B, r); |
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228 n = gf_deg(r); |
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229 if (gf_deg(A) > n) { |
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230 gf_copy(A, a); |
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231 gf_copy(B, b); |
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232 } else { |
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233 gf_copy(A, b); |
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234 gf_copy(B, a); |
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235 } |
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236 |
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237 do { |
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238 gf_mod(a, b, r); |
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239 gf_copy(b, a); |
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240 gf_copy(r, b); |
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241 } while (!gf_iszero(r)); |
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242 gf_copy(a, c); |
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243 gf_zero(a); |
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244 gf_zero(b); |
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245 } |
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246 |
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247 /* returns non-zero if 'a' is irreducible */ |
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248 int gf_is_prime(gf_intp a) |
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249 { |
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250 gf_int u, tmp; |
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251 int m, n; |
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252 |
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253 gf_zero(u); |
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254 u[0] = 2; /* u(x) = x */ |
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255 m = gf_deg(a); |
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256 for (n = 0; n < (m/2); n++) { |
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257 gf_mulmod(u, u, a, u); /* u(x) = u(x)^2 mod a(x) */ |
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258 gf_copy(u, tmp); |
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259 tmp[0] ^= 2; /* tmp(x) = u(x) - x */ |
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260 gf_gcd(tmp, a, tmp); /* tmp(x) = gcd(a(x), u(x) - x) */ |
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261 if (!gf_isone(tmp)) { |
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262 return 0; |
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263 } |
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264 } |
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265 return 1; |
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266 } |
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267 |
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268 /* returns bytes required to store a gf_int */ |
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269 int gf_size(gf_intp a) |
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270 { |
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271 int n; |
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272 |
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273 n = gf_deg(a); |
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274 if (n == -1) { |
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275 return 4; |
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276 } |
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277 n = n + (32 - (n&31)); |
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278 return n/8; |
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279 } |
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280 |
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281 /* store a gf_int */ |
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282 void gf_toraw(gf_intp a, unsigned char *dst) |
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283 { |
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284 int x, n; |
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285 n = gf_size(a)/4; |
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286 for (x = 0; x < n; x++) { |
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287 STORE32L(a[x], dst); |
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288 dst += 4; |
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289 } |
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290 } |
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291 |
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292 /* read a gf_int (len == in bytes) */ |
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293 void gf_readraw(gf_intp a, unsigned char *str, int len) |
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294 { |
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295 int x; |
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296 gf_zero(a); |
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297 for (x = 0; x < len/4; x++) { |
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298 LOAD32L(a[x], str); |
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299 str += 4; |
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300 } |
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301 } |
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302 |
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303 #endif |
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304 |
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305 |