Constructing new APN functions from known ones

Abstract

We present a method for constructing new quadratic APN functions from known ones. Applying this method to the Gold power functions we construct an APN function x 3 + tr ( x 9 ) over F 2 n . It is proven that for n ⩾ 7 this function is CCZ-inequivalent to the Gold functions, and in the case n = 7 it is CCZ-inequivalent to any power mapping (and, therefore, to any APN function belonging to one of the families of APN functions known so far).