Kim-type APN functions are affine equivalent to Gold functions

The problem of finding APN permutations ${\mathbb {F}}_{2^{n}}$ where n is even and > 6 has been called the Big Problem. Li, Helleseth Qu recently characterized functions defined on {F}}_{q^{2}}$ form f(x) = x3q + a1x2q+ 1 a2xq+ 2 a3x3, q 2m m ≥ 4. We will call this Kim-type because they generalize Kim function that was used to construct an permutation {F}}_{2^{6}}$ . prove with 4 (previously by Helleseth, Qu) are affine equivalent one two Gold G1(x) x3 or $G_{2}(x)=x^{2^{m-1}+1}$ Combined recent result Göloğlu Langevin who proved that, for n, never CCZ permutations, it follows {F}}_{2^{2m}}$ permutations.