Difference between revisions of "CCZ-inequivalent representatives from the known APN families for dimensions up to 11"

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

Dimension ${\displaystyle N^{\circ }}$ Functions Equivalent to
${\displaystyle 6}$ ${\displaystyle 6.1}$ ${\displaystyle x^{3}}$ ${\displaystyle Gold}$
${\displaystyle 6.2}$ ${\displaystyle x^{24}+ax^{17}+a^{8}x^{10}+ax^{9}+x^{3}}$ ${\displaystyle C3}$
${\displaystyle 6.3}$ ${\displaystyle ax^{3}+x^{17}+a^{4}x^{24}}$ ${\displaystyle C7-C9}$
${\displaystyle 7}$ ${\displaystyle 7.1}$ ${\displaystyle x^{3}}$ ${\displaystyle Gold}$
${\displaystyle 7.2}$ ${\displaystyle x^{5}}$ ${\displaystyle Gold}$
${\displaystyle 7.3}$ ${\displaystyle x^{9}}$ ${\displaystyle Gold}$
${\displaystyle 7.4}$ ${\displaystyle x^{13}}$ ${\displaystyle Kasami}$
${\displaystyle 7.5}$ ${\displaystyle x^{57}}$ ${\displaystyle Kasami}$
${\displaystyle 7.6}$ ${\displaystyle x^{63}}$ ${\displaystyle Inverse}$
${\displaystyle 7.7}$ ${\displaystyle x^{3}+Tr_{7}(x^{9})}$ ${\displaystyle C4}$
${\displaystyle 8}$ ${\displaystyle 8.1}$ ${\displaystyle x^{3}}$ ${\displaystyle Gold}$
${\displaystyle 8.2}$ ${\displaystyle x^{9}}$ ${\displaystyle Gold}$
${\displaystyle 8.3}$ ${\displaystyle x^{57}}$ ${\displaystyle Kasami}$
${\displaystyle 8.4}$ ${\displaystyle x^{3}+x^{17}+p^{48}x^{18}+p^{3}x^{33}+px^{34}+x^{48}}$ ${\displaystyle C3}$
${\displaystyle 8.5}$ ${\displaystyle x^{3}+Tr_{8}(x^{9})}$ ${\displaystyle C4}$
${\displaystyle 8.6}$ ${\displaystyle x^{3}+a^{-1}Tr_{8}(a^{3}x^{9})}$ ${\displaystyle C4}$
${\displaystyle 8.7}$ ${\displaystyle a(x+x^{16})(ax+a^{16}x^{16})+a^{17}(ax+a^{16}x^{16})^{12}}$ ${\displaystyle C10}$
${\displaystyle 9}$ ${\displaystyle 9.1}$ ${\displaystyle x^{3}}$ ${\displaystyle Gold}$
${\displaystyle 9.2}$ ${\displaystyle x^{5}}$ ${\displaystyle Gold}$
${\displaystyle 9.3}$ ${\displaystyle x^{17}}$ ${\displaystyle Gold}$
${\displaystyle 9.4}$ ${\displaystyle x^{13}}$ ${\displaystyle Kasami}$
${\displaystyle 9.5}$ ${\displaystyle x^{241}}$ ${\displaystyle Kasami}$
${\displaystyle 9.6}$ ${\displaystyle x^{19}}$ ${\displaystyle Welch}$
${\displaystyle 9.7}$ ${\displaystyle x^{255}}$ ${\displaystyle Inverse}$
${\displaystyle 9.8}$ ${\displaystyle x^{3}+Tr_{9}(x^{9})}$ ${\displaystyle C4}$
${\displaystyle 9.9}$ ${\displaystyle x^{3}+Tr_{9}^{3}(x^{9}+x^{18})}$ ${\displaystyle C5}$
${\displaystyle 9.10}$ ${\displaystyle x^{3}+Tr_{9}^{3}(x^{18}+x^{36})}$ ${\displaystyle C6}$
${\displaystyle 9.11}$ ${\displaystyle x^{3}+a^{246}x^{10}+a^{47}x^{17}+a^{181}x^{66}+a^{428}x^{129}}$ ${\displaystyle C11}$
${\displaystyle 10}$ ${\displaystyle 10.1}$ ${\displaystyle x^{3}}$ ${\displaystyle Gold}$
${\displaystyle 10.2}$ ${\displaystyle x^{9}}$ ${\displaystyle Gold}$
${\displaystyle 10.3}$ ${\displaystyle x^{57}}$ ${\displaystyle Kasami}$
${\displaystyle 10.4}$ ${\displaystyle x^{339}}$ ${\displaystyle Dobbertin}$
${\displaystyle 10.5}$ ${\displaystyle x^{6}+x^{33}+p^{31}x^{192}}$ ${\displaystyle C3}$
${\displaystyle 10.6}$ ${\displaystyle x^{3}+x^{72}+p^{31}x^{258}}$ ${\displaystyle C3}$
${\displaystyle 10.7}$ ${\displaystyle x^{3}+Tr_{10}(x^{9})}$ ${\displaystyle C4}$
${\displaystyle 10.8}$ ${\displaystyle x^{3}+a^{-1}Tr_{10}(a^{3}x^{9})}$ ${\displaystyle C4}$
${\displaystyle 11}$ ${\displaystyle 11.1}$ ${\displaystyle x^{3}}$ ${\displaystyle Gold}$
${\displaystyle 11.2}$ ${\displaystyle x^{5}}$ ${\displaystyle Gold}$
${\displaystyle 11.3}$ ${\displaystyle x^{9}}$ ${\displaystyle Gold}$
${\displaystyle 11.4}$ ${\displaystyle x^{17}}$ ${\displaystyle Gold}$
${\displaystyle 11.5}$ ${\displaystyle x^{33}}$ ${\displaystyle Gold}$
${\displaystyle 11.6}$ ${\displaystyle x^{13}}$ ${\displaystyle Kasami}$
${\displaystyle 11.7}$ ${\displaystyle x^{57}}$ ${\displaystyle Kasami}$
${\displaystyle 11.8}$ ${\displaystyle x^{241}}$ ${\displaystyle Kasami}$
${\displaystyle 11.9}$ ${\displaystyle x^{993}}$ ${\displaystyle Kasami}$
${\displaystyle 11.10}$ ${\displaystyle x^{35}}$ ${\displaystyle Welch}$
${\displaystyle 11.11}$ ${\displaystyle x^{287}}$ ${\displaystyle Niho}$
${\displaystyle 11.12}$ ${\displaystyle x^{123}}$ ${\displaystyle Inverse}$
${\displaystyle 11.13}$ ${\displaystyle x^{3}+Tr_{11}(x^{9})}$ ${\displaystyle C4}$