# Difference between revisions of "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 ${\displaystyle x^{3}+u^{17}(x^{17}+x^{18}+x^{20}+x^{24})+u^{14}((u^{52}x^{3}+u^{6}x^{5}+u^{19}x^{7}+u^{28}x^{11}+u^{2}x^{13})+(u^{52}x^{3}+u^{6}x^{5}+u^{19}x^{7}+u^{28}x^{11}+u^{2}x^{13})^{2}+(u^{52}x^{3}+u^{6}x^{5}+u^{19}x^{7}+u^{28}x^{11}+u^{2}x^{13})^{4}+(u^{52}x^{3}+u^{6}x^{5}+u^{19}x^{7}+u^{28}x^{11}+u^{2}x^{13})^{8}+(u^{52}x^{3}+u^{6}x^{5}+u^{19}x^{7}+u^{28}x^{11}+u^{2}x^{13})^{1}6+(u^{52}x^{3}+u^{6}x^{5}+u^{19}x^{7}+u^{28}x^{11}+u^{2}x^{13})^{3}2+(u^{2}x)^{9}+(u^{2}x)^{1}8+(u^{2}x)^{3}6+x^{21}+x^{42}}$