CCZ-inequivalent representatives from the known APN families for dimensions up to 11: Difference between revisions
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Line 12: | Line 12: | ||
<th>Γ-rank</th> | <th>Γ-rank</th> | ||
<th>Δ-rank</th> | <th>Δ-rank</th> | ||
<th>Multiplier group</th> | |||
</tr> | </tr> | ||
Line 22: | Line 23: | ||
<td>1102</td> | <td>1102</td> | ||
<td>94</td> | <td>94</td> | ||
<td>24192 = 2<sup>7</sup> * 3<sup>3</sup> * 7</td> | |||
</tr> | </tr> | ||
Line 32: | Line 34: | ||
<td>1146</td> | <td>1146</td> | ||
<td>94</td> | <td>94</td> | ||
<td>4032 = 2<sup>6</sup> * 3<sup>2</sup> * 7</td> | |||
</tr> | </tr> | ||
Line 41: | Line 44: | ||
<td>1166</td> | <td>1166</td> | ||
<td>96</td> | <td>96</td> | ||
<td>896 = 2<sup>7</sup> * 7</td> | |||
</tr> | </tr> | ||
Line 52: | Line 56: | ||
<td>3610</td> | <td>3610</td> | ||
<td>198</td> | <td>198</td> | ||
<td>113792 = 2<sup>7</sup> * 7 * 127 </td> | |||
</tr> | </tr> | ||
Line 62: | Line 67: | ||
<td>3708</td> | <td>3708</td> | ||
<td>198</td> | <td>198</td> | ||
<td>113792 = 2<sup>7</sup> * 7 * 127 </td> | |||
</tr> | </tr> | ||
Line 72: | Line 78: | ||
<td>3610</td> | <td>3610</td> | ||
<td>198</td> | <td>198</td> | ||
<td>113792 = 2<sup>7</sup> * 7 * 127 </td> | |||
</tr> | </tr> | ||
Line 82: | Line 89: | ||
<td>4270</td> | <td>4270</td> | ||
<td>338</td> | <td>338</td> | ||
<td>889 = 7 * 127</td> | |||
</tr> | </tr> | ||
Line 91: | Line 99: | ||
<td>4704</td> | <td>4704</td> | ||
<td>436</td> | <td>436</td> | ||
<td>889 = 7 * 127</td> | |||
</tr> | </tr> | ||
Line 101: | Line 110: | ||
<td>8128</td> | <td>8128</td> | ||
<td>4928</td> | <td>4928</td> | ||
<td>1778 = 2 * 7 * 127</td> | |||
</tr> | </tr> | ||
Line 112: | Line 122: | ||
<td>4026</td> | <td>4026</td> | ||
<td>212</td> | <td>212</td> | ||
<td>896 = 2<sup>7</sup> * 7</td> | |||
</tr> | </tr> | ||
Line 123: | Line 134: | ||
<td>11818</td> | <td>11818</td> | ||
<td>420</td> | <td>420</td> | ||
<td>522240 = 2<sup>11</sup> * 3 * 5 * 17</td> | |||
</tr> | </tr> | ||
Line 132: | Line 144: | ||
<td>12370</td> | <td>12370</td> | ||
<td>420</td> | <td>420</td> | ||
<td>522240 = 2<sup>11</sup> * 3 * 5 * 17</td> | |||
</tr> | </tr> | ||
Line 142: | Line 155: | ||
<td>15358</td> | <td>15358</td> | ||
<td>960</td> | <td>960</td> | ||
<td>2040 = 2<sup>3</sup> * 3 * 5 * 17</td> | |||
</tr> | </tr> | ||
Line 151: | Line 165: | ||
<td>13200</td> | <td>13200</td> | ||
<td>414</td> | <td>414</td> | ||
<td>46080 = 2<sup>10</sup> * 3<sup>2</sup> * 5</td> | |||
</tr> | </tr> | ||
Line 160: | Line 175: | ||
<td>13200</td> | <td>13200</td> | ||
<td>432</td> | <td>432</td> | ||
<td>6144 = 2<sup>11</sup> * 3</td> | |||
</tr> | </tr> | ||
Line 169: | Line 185: | ||
<td>13842</td> | <td>13842</td> | ||
<td>436</td> | <td>436</td> | ||
<td>3072 = 2<sup>10</sup> * 3</td> | |||
</tr> | </tr> | ||
Line 178: | Line 195: | ||
<td>13642</td> | <td>13642</td> | ||
<td>436</td> | <td>436</td> | ||
<td>46080 = 2<sup>10</sup> * 3<sup>2</sup> * 5</td> | |||
</tr> | </tr> | ||
Line 188: | Line 206: | ||
<td>38470</td> | <td>38470</td> | ||
<td>872</td> | <td>872</td> | ||
<td>2354688 = 2<sup>9</sup> * 3<sup>2</sup> * 7 * 73</td> | |||
</tr> | </tr> | ||
Line 198: | Line 217: | ||
<td>41494</td> | <td>41494</td> | ||
<td>872</td> | <td>872</td> | ||
<td>2354688 = 2<sup>9</sup> * 3<sup>2</sup> * 7 * 73</td> | |||
</tr> | </tr> | ||
Line 207: | Line 227: | ||
<td>38470</td> | <td>38470</td> | ||
<td>872</td> | <td>872</td> | ||
<td>2354688 = 2<sup>9</sup> * 3<sup>2</sup> * 7 * 73</td> | |||
</tr> | </tr> | ||
Line 216: | Line 237: | ||
<td>58676</td> | <td>58676</td> | ||
<td>3086</td> | <td>3086</td> | ||
<td>4599 = 3<sup>2</sup> * 7 * 73</td> | |||
</tr> | </tr> | ||
Line 225: | Line 247: | ||
<td>61726</td> | <td>61726</td> | ||
<td>3482</td> | <td>3482</td> | ||
<td>4599 = 3<sup>2</sup> * 7 * 73</td> | |||
</tr> | </tr> | ||
Line 234: | Line 257: | ||
<td>60894</td> | <td>60894</td> | ||
<td>3956</td> | <td>3956</td> | ||
<td>4599 = 3<sup>2</sup> * 7 * 73</td> | |||
</tr> | </tr> | ||
Line 243: | Line 267: | ||
<td>130816</td> | <td>130816</td> | ||
<td>93024</td> | <td>93024</td> | ||
<td>9198 = 2 * 3<sup>2</sup> * 7 * 73</td> | |||
</tr> | </tr> | ||
Line 252: | Line 277: | ||
<td>47890</td> | <td>47890</td> | ||
<td>920</td> | <td>920</td> | ||
<td>4608 = 2<sup>9</sup> * 3<sup>2</sup></td> | |||
</tr> | </tr> | ||
Line 261: | Line 287: | ||
<td>48428</td> | <td>48428</td> | ||
<td>930</td> | <td>930</td> | ||
<td>4608 = 2<sup>9</sup> * 3<sup>2</sup></td> | |||
</tr> | </tr> | ||
Line 270: | Line 297: | ||
<td>48460</td> | <td>48460</td> | ||
<td>944</td> | <td>944</td> | ||
<td>4608 = 2<sup>9</sup> * 3<sup>2</sup></td> | |||
</tr> | </tr> | ||
Line 279: | Line 307: | ||
<td>48596</td> | <td>48596</td> | ||
<td>944</td> | <td>944</td> | ||
<td>10752 = 2<sup>9</sup> * 3 * 7</td> | |||
</tr> | </tr> | ||
Line 289: | Line 318: | ||
<td>125042</td> | <td>125042</td> | ||
<td></td> | <td></td> | ||
<td>10475520 = 2<sup>11</sup> * 3 * 5 * 11 * 31</td> | |||
</tr> | </tr> | ||
Line 298: | Line 328: | ||
<td>136492</td> | <td>136492</td> | ||
<td></td> | <td></td> | ||
<td>10475520 = 2<sup>11</sup> * 3 * 5 * 11 * 31</td> | |||
</tr> | </tr> | ||
Line 307: | Line 338: | ||
<td>186416</td> | <td>186416</td> | ||
<td></td> | <td></td> | ||
<td>10230 = 2 * 3 * 5 * 11 * 31</td> | |||
</tr> | </tr> | ||
Line 316: | Line 348: | ||
<td>280604</td> | <td>280604</td> | ||
<td></td> | <td></td> | ||
<td>10230 = 2 * 3 * 5 * 11 * 31</td> | |||
</tr> | </tr> | ||
Line 325: | Line 358: | ||
<td>151216</td> | <td>151216</td> | ||
<td></td> | <td></td> | ||
<td>476160 = 2<sup>10</sup> * 3 * 5 * 31</td> | |||
</tr> | </tr> | ||
Line 334: | Line 368: | ||
<td>153896</td> | <td>153896</td> | ||
<td></td> | <td></td> | ||
<td>476160 = 2<sup>10</sup> * 3 * 5 * 31</td> | |||
</tr> | </tr> | ||
Line 343: | Line 378: | ||
<td>164034</td> | <td>164034</td> | ||
<td></td> | <td></td> | ||
<td>30720 = 2<sup>11</sup> * 3 * 5</td> | |||
</tr> | </tr> | ||
Line 352: | Line 388: | ||
<td>164098</td> | <td>164098</td> | ||
<td></td> | <td></td> | ||
<td>15360 = 2<sup>10</sup> * 3 * 5</td> | |||
</tr> | </tr> | ||
Line 361: | Line 398: | ||
<td>166068</td> | <td>166068</td> | ||
<td></td> | <td></td> | ||
<td>476160 = 2<sup>10</sup> * 3 * 5 * 31</td> | |||
</tr> | </tr> | ||
Line 370: | Line 408: | ||
<td>166168</td> | <td>166168</td> | ||
<td></td> | <td></td> | ||
<td>476160 = 2<sup>10</sup> * 3 * 5 * 31</td> | |||
</tr> | </tr> | ||
Line 378: | Line 417: | ||
<td><span class="htmlMath">Gold</span></td> | <td><span class="htmlMath">Gold</span></td> | ||
<td>Gold</td> | <td>Gold</td> | ||
<td></td> | |||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
Line 387: | Line 427: | ||
<td><span class="htmlMath">Gold</span></td> | <td><span class="htmlMath">Gold</span></td> | ||
<td>Gold</td> | <td>Gold</td> | ||
<td></td> | |||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
Line 396: | Line 437: | ||
<td><span class="htmlMath">Gold</span></td> | <td><span class="htmlMath">Gold</span></td> | ||
<td>Gold</td> | <td>Gold</td> | ||
<td></td> | |||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
Line 405: | Line 447: | ||
<td><span class="htmlMath">Gold</span></td> | <td><span class="htmlMath">Gold</span></td> | ||
<td>Gold</td> | <td>Gold</td> | ||
<td></td> | |||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
Line 414: | Line 457: | ||
<td><span class="htmlMath">Gold</span></td> | <td><span class="htmlMath">Gold</span></td> | ||
<td>Gold</td> | <td>Gold</td> | ||
<td></td> | |||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
Line 423: | Line 467: | ||
<td><span class="htmlMath">Kasami</span></td> | <td><span class="htmlMath">Kasami</span></td> | ||
<td>Gold</td> | <td>Gold</td> | ||
<td></td> | |||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
Line 432: | Line 477: | ||
<td><span class="htmlMath">Kasami</span></td> | <td><span class="htmlMath">Kasami</span></td> | ||
<td>Gold</td> | <td>Gold</td> | ||
<td></td> | |||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
Line 440: | Line 486: | ||
<td><span class="htmlMath">Kasami</span></td> | <td><span class="htmlMath">Kasami</span></td> | ||
<td>Gold</td> | <td>Gold</td> | ||
<td></td> | |||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
Line 448: | Line 495: | ||
<td><span class="htmlMath">Kasami</span></td> | <td><span class="htmlMath">Kasami</span></td> | ||
<td>Gold</td> | <td>Gold</td> | ||
<td></td> | |||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
Line 456: | Line 504: | ||
<td><span class="htmlMath">Welch</span></td> | <td><span class="htmlMath">Welch</span></td> | ||
<td>Gold</td> | <td>Gold</td> | ||
<td></td> | |||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
Line 464: | Line 513: | ||
<td><span class="htmlMath">Niho</span></td> | <td><span class="htmlMath">Niho</span></td> | ||
<td>Gold</td> | <td>Gold</td> | ||
<td></td> | |||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
Line 472: | Line 522: | ||
<td><span class="htmlMath">Inverse</span></td> | <td><span class="htmlMath">Inverse</span></td> | ||
<td>Inverse</td> | <td>Inverse</td> | ||
<td></td> | |||
<td></td> | <td></td> | ||
<td></td> | <td></td> | ||
Line 480: | Line 531: | ||
<td><span class="htmlMath">C4</span></td> | <td><span class="htmlMath">C4</span></td> | ||
<td>Gold</td> | <td>Gold</td> | ||
<td></td> | |||
<td></td> | <td></td> | ||
<td></td> | <td></td> |
Revision as of 21:03, 6 January 2020
CCZ-inequivalent APN Functions over [math]\displaystyle{ \mathbb{F}_{2^n} }[/math] from the Known APN Classes for [math]\displaystyle{ 6\leqslant n \leqslant 11 }[/math]
The function families are indexed according to the table of Known infinite families of APN power functions over GF(2^n) in the case of monomials, and according to the table of Known infinite families of quadratic APN polynomials over GF(2^n) in the case of polynomial families.
Dimension | N○ | Functions | Equivalent to | Walsh spectrum | Γ-rank | Δ-rank | Multiplier group |
---|---|---|---|---|---|---|---|
6 | 6.1 | x3 | Gold | Gold | 1102 | 94 | 24192 = 27 * 33 * 7 |
6.2 | x24+ax17+a8x10+ax9+x3 | C3 | Gold | 1146 | 94 | 4032 = 26 * 32 * 7 | |
6.3 | ax3+x17+a4x24 | C7-C9 | Gold | 1166 | 96 | 896 = 27 * 7 | |
7 | 7.1 | x3 | Gold | Gold | 3610 | 198 | 113792 = 27 * 7 * 127 |
7.2 | x5 | Gold | Gold | 3708 | 198 | 113792 = 27 * 7 * 127 | |
7.3 | x9 | Gold | Gold | 3610 | 198 | 113792 = 27 * 7 * 127 | |
7.4 | x13 | Kasami | Gold | 4270 | 338 | 889 = 7 * 127 | |
7.5 | x57 | Kasami | Gold | 4704 | 436 | 889 = 7 * 127 | |
7.6 | x63 | Inverse | Inverse | 8128 | 4928 | 1778 = 2 * 7 * 127 | |
7.7 | x3+Tr7(x9) | C4 | Gold | 4026 | 212 | 896 = 27 * 7 | |
8 | 8.1 | x3 | Gold | Gold | 11818 | 420 | 522240 = 211 * 3 * 5 * 17 |
8.2 | x9 | Gold | Gold | 12370 | 420 | 522240 = 211 * 3 * 5 * 17 | |
8.3 | x57 | Kasami | Gold | 15358 | 960 | 2040 = 23 * 3 * 5 * 17 | |
8.4 | x3+x17+p48x18+p3x33+px34+x48 | C3 | Gold | 13200 | 414 | 46080 = 210 * 32 * 5 | |
8.5 | x3+Tr8(x9) | C4 | Gold | 13200 | 432 | 6144 = 211 * 3 | |
8.6 | x3+a-1Tr8(a3x9) | C4 | Gold | 13842 | 436 | 3072 = 210 * 3 | |
8.7 | a(x+x16)(ax+a16x16)+a17(ax+a16x16)12 | C10 | Gold | 13642 | 436 | 46080 = 210 * 32 * 5 | |
9 | 9.1 | x3 | Gold | Gold | 38470 | 872 | 2354688 = 29 * 32 * 7 * 73 |
9.2 | x5 | Gold | Gold | 41494 | 872 | 2354688 = 29 * 32 * 7 * 73 | |
9.3 | x17 | Gold | Gold | 38470 | 872 | 2354688 = 29 * 32 * 7 * 73 | |
9.4 | x13 | Kasami | Gold | 58676 | 3086 | 4599 = 32 * 7 * 73 | |
9.5 | x241 | Kasami | Gold | 61726 | 3482 | 4599 = 32 * 7 * 73 | |
9.6 | x19 | Welch | Gold | 60894 | 3956 | 4599 = 32 * 7 * 73 | |
9.7 | x255 | Inverse | Inverse | 130816 | 93024 | 9198 = 2 * 32 * 7 * 73 | |
9.8 | x3+Tr9(x9) | C4 | Gold | 47890 | 920 | 4608 = 29 * 32 | |
9.9 | x3+Tr39(x9+x18) | C5 | Gold | 48428 | 930 | 4608 = 29 * 32 | |
9.10 | x3+Tr39(x18+x36) | C6 | Gold | 48460 | 944 | 4608 = 29 * 32 | |
9.11 | x3+a246x10+a47x17+a181x66+a428x129 | C11 | Gold | 48596 | 944 | 10752 = 29 * 3 * 7 | |
10 | 10.1 | x3 | Gold | Gold | 125042 | 10475520 = 211 * 3 * 5 * 11 * 31 | |
10.2 | x9 | Gold | Gold | 136492 | 10475520 = 211 * 3 * 5 * 11 * 31 | ||
10.3 | x57 | Kasami | Gold | 186416 | 10230 = 2 * 3 * 5 * 11 * 31 | ||
10.4 | x339 | Dobbertin | Dobbertin | 280604 | 10230 = 2 * 3 * 5 * 11 * 31 | ||
10.5 | x6+x33+p31x192 | C3 | Gold | 151216 | 476160 = 210 * 3 * 5 * 31 | ||
10.6 | x33+x72+p31x258 | C3 | Gold | 153896 | 476160 = 210 * 3 * 5 * 31 | ||
10.7 | x3+Tr10(x9) | C4 | Gold | 164034 | 30720 = 211 * 3 * 5 | ||
10.8 | x3+a-1Tr10(a3x9) | C4 | Gold | 164098 | 15360 = 210 * 3 * 5 | ||
10.9 | x3 + p341x9 + p682x96 + x288 | C12 | Gold | 166068 | 476160 = 210 * 3 * 5 * 31 | ||
10.10 | x3 + p341x129 + p682x96 + x36 | C12 | Gold | 166168 | 476160 = 210 * 3 * 5 * 31 | ||
11 | 11.1 | x3 | Gold | Gold | |||
11.2 | x5 | Gold | Gold | ||||
11.3 | x9 | Gold | Gold | ||||
11.4 | x17 | Gold | Gold | ||||
11.5 | x33 | Gold | Gold | ||||
11.6 | x13 | Kasami | Gold | ||||
11.7 | x57 | Kasami | Gold | ||||
11.8 | x241 | Kasami | Gold | ||||
11.9 | x993 | Kasami | Gold | ||||
11.10 | x35 | Welch | Gold | ||||
11.11 | x287 | Niho | Gold | ||||
11.12 | x1023 | Inverse | Inverse | ||||
11.13 | x3+Tr11(x9) | C4 | Gold |