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

Known switching classes of APN functions over ${\displaystyle \mathbb {F} _{2^{5}}}$, ${\displaystyle \mathbb {F} _{2^{6}}}$, ${\displaystyle \mathbb {F} _{2^{7}}}$ and ${\displaystyle \mathbb {F} _{2^{8}}}$

${\displaystyle n}$ ${\displaystyle N^{\circ }}$ ${\displaystyle F(x)}$
${\displaystyle 5}$ ${\displaystyle 1.1}$

${\displaystyle 1.2}$

${\displaystyle 2.1}$
${\displaystyle x^{3}}$

${\displaystyle x^{5}}$

${\displaystyle x^{-1}}$

${\displaystyle n}$ ${\displaystyle N^{\circ }}$ ${\displaystyle F(x)}$
${\displaystyle 6}$ 1.1 ${\displaystyle x^{3}}$
1.2 ${\displaystyle x^{3}+u^{11}x^{6}+ux^{9}}$
2.1 ${\displaystyle ux^{5}+x^{9}+u^{4}x^{17}+ux^{18}+u^{4}x^{20}+ux^{24}+u^{4}x^{34}+ux^{40}}$
2.2 ${\displaystyle u^{7}x^{3}+x^{5}+u^{3}x^{9}+u^{4}x^{10}+x^{17}+u^{6}x^{18}}$
2.3 ${\displaystyle x^{3}+ux^{24}+x^{10}}$
2.4 ${\displaystyle x^{3}+u^{17}(x^{17}+x^{18}+x^{20}+x^{24})}$
2.5 ${\displaystyle x^{3}+u^{11}x^{5}+u^{13}x^{9}+x^{17}+u^{11}x^{33}+x^{48}}$
2.6 ${\displaystyle u^{25}x^{5}+x^{9}+u^{38}x^{12}+u^{25}x^{18}+u^{25}x^{36}}$
2.7 ${\displaystyle u^{40}x^{5}+u^{10}x^{6}+u^{62}x^{20}+u^{35}x^{33}+u^{15}x^{34}+u^{29}x^{48}}$
2.8 ${\displaystyle u^{34}x^{6}+u^{52}x^{9}+u^{48}x^{12}+u^{6}x^{20}+u^{9}x^{33}+u^{23}x^{34}+u^{25}x^{40}}$
2.9 ${\displaystyle x^{9}+u^{4}(x^{10}+x^{18})+u^{9}(x^{12}+x^{20}+x^{40})}$
2.10 ${\displaystyle u^{52}x^{3}+u^{47}x^{5}+ux^{6}+u^{9}x^{9}+u^{44}x^{12}+u^{47}x^{33}+u^{10}x^{34}+u^{33}x^{40}}$
2.11 ${\displaystyle u(x^{6}+x^{10}+x^{24}+x^{33})+x^{9}+u^{4}x^{17}}$
2.12 ${\displaystyle x^{3}+}$ ${\displaystyle u^{17}(x^{17}+}$ ${\displaystyle x^{18}+}$ ${\displaystyle x^{20}+}$ ${\displaystyle x^{24})+}$ ${\displaystyle u^{14}((u^{52}x^{3}+}$ ${\displaystyle u^{6}x^{5}+}$ ${\displaystyle u^{19}x^{7}+}$ ${\displaystyle u^{28}x^{11}+}$ ${\displaystyle u^{2}x^{13})+(u^{52}x^{3}+}$ ${\displaystyle u^{6}x^{5}+}$ ${\displaystyle u^{19}x^{7}+}$ ${\displaystyle u^{28}x^{11}+}$ ${\displaystyle u^{2}x^{13})^{2}+}$ ${\displaystyle (u^{52}x^{3}+}$ ${\displaystyle u^{6}x^{5}+}$ ${\displaystyle u^{19}x^{7}+}$ ${\displaystyle u^{28}x^{11}+}$ ${\displaystyle u^{2}x^{13})^{4}+(u^{52}x^{3}+}$ ${\displaystyle u^{6}x^{5}+}$ ${\displaystyle u^{19}x^{7}+}$ ${\displaystyle u^{28}x^{11}+}$ ${\displaystyle u^{2}x^{13})^{8}+(u^{52}x^{3}+}$ ${\displaystyle u^{6}x^{5}+}$ ${\displaystyle u^{19}x^{7}+}$ ${\displaystyle u^{28}x^{11}+}$ ${\displaystyle u^{2}x^{13})^{16}+(u^{52}x^{3}+}$ ${\displaystyle u^{6}x^{5}+}$ ${\displaystyle u^{19}x^{7}+}$ ${\displaystyle u^{28}x^{11}+}$ ${\displaystyle u^{2}x^{13})^{32}+(u^{2}x)^{9}+(u^{2}x)^{19}+(u^{2}x)^{36}+}$ ${\displaystyle x^{21}+x^{42}}$

${\displaystyle n}$ ${\displaystyle N^{\circ }}$ ${\displaystyle F(x)}$
${\displaystyle 7}$ 1.1 ${\displaystyle x^{3}}$
1.2 ${\displaystyle x^{3}+{\rm {Tr}}(x^{9})}$
2.1 ${\displaystyle x^{34}+x^{18}+x^{5}}$
2.2 ${\displaystyle x^{3}+x^{17}+x^{33}+x^{34}}$
3.1 ${\displaystyle x^{5}}$
4.1 ${\displaystyle x^{9}}$
5.1 ${\displaystyle x^{13}}$
6.1 ${\displaystyle x^{57}}$
7.1 ${\displaystyle x^{-1}}$
8.1 ${\displaystyle x^{65}+x^{10}+x^{3}}$
9.1 ${\displaystyle x^{3}+x^{9}+x^{18}+x^{66}}$
10.1 ${\displaystyle x^{3}+x^{12}+x^{17}+x^{33}}$
10.2 ${\displaystyle x^{3}+x^{17}+x^{20}+x^{34}+x^{66}}$
11.1 ${\displaystyle x^{3}+x^{20}+x^{34}+x^{66}}$
12.1 ${\displaystyle x^{3}+x^{12}+x^{40}+x^{72}}$
13.1 ${\displaystyle x^{3}+x^{5}+x^{10}+x^{33}+x^{34}}$
14.1 ${\displaystyle x^{3}+x^{6}+x^{34}+x^{40}+x^{72}}$
14.2 ${\displaystyle x^{3}+x^{5}+x^{6}+x^{12}+x^{33}+x^{34}}$
14.3 ${\displaystyle u^{2}x^{96}+}$ ${\displaystyle u^{78}x^{80}+}$ ${\displaystyle u^{121}x^{72}+}$ ${\displaystyle u^{49}x^{68}+}$ ${\displaystyle u^{77}x^{66}+}$ ${\displaystyle u^{29}x^{65}+}$ ${\displaystyle u^{119}x^{48}+}$ ${\displaystyle u^{117}x^{40}+}$ ${\displaystyle u^{28}x^{36}+}$ ${\displaystyle u^{107}x^{34}+u^{62}x^{33}+u^{125}x^{24}+u^{76}x^{20}+u^{84}x^{18}+u^{110}x^{17}+u^{49}x^{12}+u^{102}x^{10}+u^{69}x^{9}+}$ ${\displaystyle u^{14}x^{6}+}$ ${\displaystyle x^{5}+}$ ${\displaystyle x^{3}}$