Paper 2019/793

On equivalence between known families of quadratic APN functions

Lylia Budaghyan and Marco Calderini and Irene Villa

Abstract

We study 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 CCZ-equivalent to 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 CCZ-equivalent to the family of hexanomials as well.