The simplest method for constructing APN polynomials EA-inequivalent to power functions

Abstract

In 2005 Budaghyan, Carlet and Pott constructed the first APN polynomials EA-inequivalent to power functions by applying CCZ-equivalence to the Gold APN functions. It is a natural question whether it is possible to construct APN polynomials EA-inequivalent to power functions by using only EA-equivalence and inverse transformation on a power APN mapping: this would be the simplest method to construct APN polynomials EA-inequivalent to power functions. In the present paper we prove that the answer to this question is positive. By this method we construct a class of APN polynomials EA-inequivalent to power functions. On the other hand it is shown that the APN polynomials constructed by Budaghyan, Carlet and Pott cannot be obtained by the introduced method. © Springer-Verlag Berlin Heidelberg 2007.