Extending two families of bivariate APN functions

Abstract

In this work, we present two families of quadratic APN functions. The first one (F1) is constructed via biprojective polynomials. This family extends one of the two APN families introduced by Göloǧlu in 2022. Then, following a similar approach as in Li et al. (2022) [28], we give another family (F2) obtained by adding certain terms to F1. As a byproduct, this second family extends one of the two families introduced by Li et al. (2022) [28]. Moreover, we show that for n=12, from our constructions, we can obtain APN functions which are CCZ-inequivalent to any other known APN function over F212.