On the classification of APN functions up to dimension five

Marcus Brinkmann, Gregor Leander

Des. Codes Cryptogr. (2008) 49: 273.


Abstract

We classify the APN 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 it is well known that in dimension 4 and 5 there exist APN functions which are not extended affine equivalent to any power function. We further calculate the total number of APN functions up to dimension 5 and present a new CCZ equivalence class of APN functions in dimension 6.

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