Constructing new APN functions from known ones

• DOI: 10.1016/j.ffa.2008.10.001
• Publication Date: 2008-11-14T07:33:28Z
• Authors: Lilya Budaghyan; Claude Carlet; Gregor Leander
• Keywords: Power function

AbstractWe 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 x3+tr(x9) over F2n. 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).