# Polygon

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CCZ-inequivalent APN Functions over ${\displaystyle \mathbb {F} _{2^{n}}}$ from the Known APN Classes for ${\displaystyle 6\leqslant n\leqslant 11}$

Dimension Functions Equivalent to
${\displaystyle 6}$ ${\displaystyle x^{24}+ax^{17}+a^{8}x^{10}+ax^{9}+x^{3}}$ ${\displaystyle C3}$
${\displaystyle ax^{3}+x^{17}+a^{4}x^{24}}$ ${\displaystyle C7-C9}$
${\displaystyle 7}$ ${\displaystyle x^{3}+Tr_{7}(x^{9})}$ ${\displaystyle C4}$
${\displaystyle 8}$ ${\displaystyle x^{3}+x^{17}+p^{48}x^{18}+p^{3}x^{33}+px^{34}+x^{48}}$ ${\displaystyle C3}$
${\displaystyle x^{3}+Tr_{8}(x^{9})}$ ${\displaystyle C4}$
${\displaystyle x^{3}+a^{-1}Tr_{8}(a^{3}x^{9})}$ ${\displaystyle C4}$
${\displaystyle a(x+x^{16})(ax+a^{16}x^{16})+a^{17}(ax+a^{16}x^{16})^{12}}$ ${\displaystyle C10}$
${\displaystyle 9}$ ${\displaystyle x^{3}+Tr_{9}(x^{9})}$ ${\displaystyle C4}$
${\displaystyle x^{3}+Tr_{9}^{3}(x^{9}+x^{18})}$ ${\displaystyle C5}$
${\displaystyle x^{3}+Tr_{9}^{3}(x^{18}+x^{36})}$ ${\displaystyle C6}$
${\displaystyle x^{3}+a^{246}x^{10}+a^{47}x^{17}+a^{181}x^{66}+a^{428}x^{129}}$ ${\displaystyle C11}$
${\displaystyle 10}$ ${\displaystyle x^{6}+x^{33}+p^{31}x^{192}}$ ${\displaystyle C3}$
${\displaystyle x^{3}+x^{72}+p^{31}x^{258}}$ ${\displaystyle C3}$
${\displaystyle x^{3}+Tr_{10}(x^{9})}$ ${\displaystyle C4}$
${\displaystyle x^{3}+a^{-1}Tr_{10}(a^{3}x^{9})}$ ${\displaystyle C4}$
${\displaystyle 11}$ ${\displaystyle x^{3}+Tr_{11}(x^{9})}$ ${\displaystyle C4}$