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On the classification of APN functions up to dimension five

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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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Correspondence to Marcus Brinkmann.

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Research of G. Leander sponsored by a DAAD postdoctoral fellowship.

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Brinkmann, M., Leander, G. On the classification of APN functions up to dimension five. Des. Codes Cryptogr. 49, 273–288 (2008). https://doi.org/10.1007/s10623-008-9194-6

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  • DOI: https://doi.org/10.1007/s10623-008-9194-6

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