[HTML][HTML] On equivalence between known families of quadratic APN functions

L Budaghyan, M Calderini, I Villa - Finite fields and their applications, 2020 - Elsevier
Finite fields and their applications, 2020Elsevier
This paper is dedicated to a question whether the currently known families of quadratic APN
polynomials are pairwise different up to CCZ-equivalence. We reduce the list of these
families to those CCZ-inequivalent to each other. In particular, we prove that the families of
APN trinomials (constructed by Budaghyan and Carlet in 2008) and multinomials
(constructed by Bracken et al. 2008) are contained in the APN hexanomial family introduced
by Budaghyan and Carlet in 2008. We also prove that a generalization of these trinomial …
Abstract
This paper is dedicated to a question whether the currently known families of quadratic APN polynomials are pairwise different up to CCZ-equivalence. We reduce the list of these families to those CCZ-inequivalent to each other. In particular, we prove that the families of APN trinomials (constructed by Budaghyan and Carlet in 2008) and multinomials (constructed by Bracken et al. 2008) are contained in the APN hexanomial family introduced by Budaghyan and Carlet in 2008. We also prove that a generalization of these trinomial and multinomial families given by Duan et al. (2014) is contained in the family of hexanomials as well.
Elsevier
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