CCZ-inequivalent APN functions from the known APN classes over GF(2^n) (for n between 6 and 11) html: Difference between revisions
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(Created page with "CCZ-inequivalent APN Functions over <math>\mathbb{F}_{2^n}</math> from the Known APN Classes for <math>6\leqslant n \leqslant 11</math> <table class="borderless"> <tr> <th>Di...") |
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<tr class="divider"> | <tr class="divider"> | ||
<td rowspan=" | <td rowspan="10"><span class="htmlMath">10</span></td> | ||
<td class="noborderbelow"><span class="htmlMath">10.1</span></td> | <td class="noborderbelow"><span class="htmlMath">10.1</span></td> | ||
<td><span class="htmlMath">x<sup>3</sup></span></td> | <td><span class="htmlMath">x<sup>3</sup></span></td> | ||
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<td>Gold</td> | <td>Gold</td> | ||
<td>164098</td> | <td>164098</td> | ||
<td></td> | |||
</tr> | |||
<tr> | |||
<td class="noborderbelow"><span class="htmlMath">10.9</span></td> | |||
<td><span class="htmlMath">x<sup>3</sup> + p<sup>341</sup>x<sup>9</sup> + p<sup>682</sup>x<sup>96</sup> + x<sup>288</sup></span></td> | |||
<td><span class="htmlMath">C12</span></td> | |||
<td>Gold</td> | |||
<td>166068</td> | |||
<td></td> | |||
</tr> | |||
<tr> | |||
<td class="noborderbelow"><span class="htmlMath">10.10</span></td> | |||
<td><span class="htmlMath">x<sup>3</sup> + p<sup>341</sup>x<sup>129</sup> + p<sup>682</sup>x<sup>96</sup> + x<sup>36</sup></span></td> | |||
<td><span class="htmlMath">C12</span></td> | |||
<td>Gold</td> | |||
<td>166168</td> | |||
<td></td> | <td></td> | ||
</tr> | </tr> | ||
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<td class="noborderbelow"><span class="htmlMath">11.12</span></td> | <td class="noborderbelow"><span class="htmlMath">11.12</span></td> | ||
<td><span class="htmlMath">x<sup> | <td><span class="htmlMath">x<sup>1023</sup></span></td> | ||
<td><span class="htmlMath">Inverse</span></td> | <td><span class="htmlMath">Inverse</span></td> | ||
<td>Inverse</td> | <td>Inverse</td> |
Latest revision as of 10:28, 11 September 2019
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]
Dimension | N○ | Functions | Equivalent to | Walsh spectrum | Γ-rank | Δ-rank |
---|---|---|---|---|---|---|
6 | 6.1 | x3 | Gold | Gold | 1102 | 94 |
6.2 | x24+ax17+a8x10+ax9+x3 | C3 | Gold | 1146 | 94 | |
6.3 | ax3+x17+a4x24 | C7-C9 | Gold | 1166 | 96 | |
7 | 7.1 | x3 | Gold | Gold | 3610 | 198 |
7.2 | x5 | Gold | Gold | 3708 | 198 | |
7.3 | x9 | Gold | Gold | 3610 | 198 | |
7.4 | x13 | Kasami | Gold | 4270 | 338 | |
7.5 | x57 | Kasami | Gold | 4704 | 436 | |
7.6 | x63 | Inverse | Inverse | 8128 | 4928 | |
7.7 | x3+Tr7(x9) | C4 | Gold | 4026 | 212 | |
8 | 8.1 | x3 | Gold | Gold | 11818 | 420 |
8.2 | x9 | Gold | Gold | 12370 | 420 | |
8.3 | x57 | Kasami | Gold | 15358 | 960 | |
8.4 | x3+x17+p48x18+p3x33+px34+x48 | C3 | Gold | 13200 | 414 | |
8.5 | x3+Tr8(x9) | C4 | Gold | 13200 | 432 | |
8.6 | x3+a-1Tr8(a3x9) | C4 | Gold | 13842 | 436 | |
8.7 | a(x+x16)(ax+a16x16)+a17(ax+a16x16)12 | C10 | Gold | 13642 | 436 | |
9 | 9.1 | x3 | Gold | Gold | 38470 | 872 |
9.2 | x5 | Gold | Gold | 41494 | 872 | |
9.3 | x17 | Gold | Gold | 38470 | 872 | |
9.4 | x13 | Kasami | Gold | 58676 | 3086 | |
9.5 | x241 | Kasami | Gold | 61726 | 3482 | |
9.6 | x19 | Welch | Gold | 60894 | 3956 | |
9.7 | x255 | Inverse | Inverse | 130816 | 93024 | |
9.8 | x3+Tr9(x9) | C4 | Gold | 47890 | 920 | |
9.9 | x3+Tr39(x9+x18) | C5 | Gold | 48428 | 930 | |
9.10 | x3+Tr39(x18+x36) | C6 | Gold | 48460 | 944 | |
9.11 | x3+a246x10+a47x17+a181x66+a428x129 | C11 | Gold | 48596 | 944 | |
10 | 10.1 | x3 | Gold | Gold | 125042 | |
10.2 | x9 | Gold | Gold | 136492 | ||
10.3 | x57 | Kasami | Gold | 186416 | ||
10.4 | x339 | Dobbertin | Dobbertin | 280604 | ||
10.5 | x6+x33+p31x192 | C3 | Gold | 151216 | ||
10.6 | x33+x72+p31x258 | C3 | Gold | 153896 | ||
10.7 | x3+Tr10(x9) | C4 | Gold | 164034 | ||
10.8 | x3+a-1Tr10(a3x9) | C4 | Gold | 164098 | ||
10.9 | x3 + p341x9 + p682x96 + x288 | C12 | Gold | 166068 | ||
10.10 | x3 + p341x129 + p682x96 + x36 | C12 | Gold | 166168 | ||
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 |