Difference between revisions of "Known switching classes of APN functions over GF(2^n) for n = 5,6,7,8"

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<td>2.12</td>
 
<td>2.12</td>
 
<td><math>x^{3} + </math> <math>u^{17}(x^{17} + </math> <math>x^{18} + </math> <math>x^{20} + </math> <math>x^{24}) + </math> <math>u^{14}((u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{2} + </math> <math>(u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{4}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{8}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{16}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{32}+ (u^{2}x)^{9} +(u^{2}x)^{19} +(u^{2}x)^{36} + </math> <math>x^{21}+x^{42}</math></td>
 
<td><math>x^{3} + </math> <math>u^{17}(x^{17} + </math> <math>x^{18} + </math> <math>x^{20} + </math> <math>x^{24}) + </math> <math>u^{14}((u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{2} + </math> <math>(u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{4}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{8}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{16}+ (u^{52}x^{3} + </math> <math>u^{6}x^{5} + </math> <math>u^{19}x^{7} + </math> <math>u^{28}x^{11} + </math> <math>u^{2}x^{13})^{32}+ (u^{2}x)^{9} +(u^{2}x)^{19} +(u^{2}x)^{36} + </math> <math>x^{21}+x^{42}</math></td>
 +
</tr>
 +
</table>
 +
 +
 +
 +
<table>
 +
<tr>
 +
<th><math>n</math></th>
 +
<th><math>N^\circ</math></th>
 +
<th><math>F(x)</math></th>
 +
</tr>
 +
<tr>
 +
<td rowspan="19"><math>7</math></td>
 +
<td>1.1</td>
 +
<td><math>
 +
x^{3}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>1.2</td>
 +
<td><math>
 +
x^{3} + {\rm Tr}(x^{9})
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>2.1</td>
 +
<td><math>
 +
x^{34} + x^{18} + x^{5}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>2.2</td>
 +
<td><math>
 +
x^{3} + x^{17} + x^{33} + x^{34}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>3.1</td>
 +
<td><math>
 +
x^{5}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>4.1</td>
 +
<td><math>
 +
x^{9}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>5.1</td>
 +
<td><math>
 +
x^{13}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>6.1</td>
 +
<td><math>
 +
x^{57}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>7.1</td>
 +
<td><math>
 +
x^{-1}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>8.1</td>
 +
<td><math>
 +
x^{65} + x^{10} + x^{3}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>9.1</td>
 +
<td><math>
 +
x^{3} + x^{9} + x^{18} + x^{66}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>10.1</td>
 +
<td><math>
 +
x^{3} + x^{12} + x^{17} + x^{33}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>10.2</td>
 +
<td><math>
 +
x^{3} + x^{17} + x^{20} + x^{34} + x^{66}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>11.1</td>
 +
<td><math>
 +
x^{3} + x^{20} + x^{34} + x^{66}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>12.1</td>
 +
<td><math>
 +
x^{3} + x^{12} + x^{40} + x^{72}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>13.1</td>
 +
<td><math>
 +
x^{3} + x^{5} + x^{10} + x^{33} + x^{34}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>14.1</td>
 +
<td><math>
 +
x^{3} + x^{6} + x^{34} + x^{40} + x^{72}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>14.2</td>
 +
<td><math>
 +
x^{3} + x^{5} + x^{6} + x^{12} + x^{33} + x^{34}
 +
</math></td>
 +
</tr>
 +
<tr>
 +
<td>14.3</td>
 +
<td><math>
 +
u^{2}x^{96} + </math> <math>u^{78}x^{80} + </math> <math>u^{121}x^{72} + </math> <math>u^{49}x^{68} + </math> <math>u^{77}x^{66} + </math> <math>u^{29}x^{65} + </math> <math>u^{119}x^{48} + </math> <math>u^{117}x^{40} + </math> <math>u^{28}x^{36} + </math> <math>u^{107}x^{34} +u^{62}x^{33} +u^{125}x^{24} +u^{76}x^{20} +u^{84}x^{18} +u^{110}x^{17} +u^{49}x^{12} +u^{102}x^{10} +u^{69}x^{9} + </math> <math>u^{14}x^{6} + </math> <math>x^{5} + </math> <math>x^{3}
 +
</math></td>
 
</tr>
 
</tr>
 
</table>
 
</table>

Revision as of 17:26, 22 January 2019

Known switching classes of APN functions over , , and


1.1
1.2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12


1.1
1.2
2.1
2.2
3.1
4.1
5.1
6.1
7.1
8.1
9.1
10.1
10.2
11.1
12.1
13.1
14.1
14.2
14.3