On the classification of APN functions up to dimension five |
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Authors: | Marcus Brinkmann Gregor Leander |
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Affiliation: | 1. Ruhr-Universit?t Bochum, Bochum, Germany 2. University of Toulon, La Garde, France
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Abstract: | We classify the almost perfect nonlinear (APN) functions in dimensions 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 dimensions 4 and 5 there exist APN functions which are not extended affine (EA) 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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