Classification of Almost Perfect Nonlinear Functions up to Dimension Five

Marcus Brinkmann

Diplomarbeit an der Fakultät für Mathematik Ruhr-Universiät Bochum.


Abstract

In this thesis we classify all almost perfect nonlinear (APN) vectorial boolean functions in dimension 4 and 5 up to affine and CCZ equivalence using backtrack programming and give a partial model for the complexity of such a search. In particular, we demonstrate that up to dimension 5 any APN function is CCZ equivalent to a power function, while in dimension 4 and 5 there exist APN functions which are not extended affine equivalent to any power function.

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tags: apn, diplom