APN permutations in even dimension are vectorial Boolean functions that play a special role in the design of block ciphers. We study their properties, providing some general results and some applications to the low-dimension cases. In particular, we prove that none of their components can be quadratic. For an APN vectorial Boolean function (in even dimension) with all cubic components we prove the existence of a component having a large number of balanced derivatives. Using these restrictions, we obtain the first theoretical proof of the non-existence of APN permutations in dimension 4. Moreover, we derive some constraints on APN permutations in dimension 6.

A note on APN permutations in even dimension / Calderini, M.; Sala, M.; Villa, I.. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - STAMPA. - 46:(2017), pp. 1-16. [10.1016/j.ffa.2017.02.001]

A note on APN permutations in even dimension

Calderini, M.;Sala, M.;Villa, I.
2017

Abstract

APN permutations in even dimension are vectorial Boolean functions that play a special role in the design of block ciphers. We study their properties, providing some general results and some applications to the low-dimension cases. In particular, we prove that none of their components can be quadratic. For an APN vectorial Boolean function (in even dimension) with all cubic components we prove the existence of a component having a large number of balanced derivatives. Using these restrictions, we obtain the first theoretical proof of the non-existence of APN permutations in dimension 4. Moreover, we derive some constraints on APN permutations in dimension 6.
Calderini, M.; Sala, M.; Villa, I.
A note on APN permutations in even dimension / Calderini, M.; Sala, M.; Villa, I.. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - STAMPA. - 46:(2017), pp. 1-16. [10.1016/j.ffa.2017.02.001]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/201327
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