Paper 2016/143

On upper bounds for algebraic degrees of APN functions

Lilya Budaghyan, Claude Carlet, Tor Helleseth, Nian Li, Bo Sun

Abstract

We study the problem of existence of APN functions of algebraic degree $n$ over $\ftwon$. We characterize such functions by means of derivatives and power moments of the Walsh transform. We deduce some non-existence results which mean, in particular, that for most of the known APN functions $F$ over $\ftwon$ the function $x^{2^n-1}+F(x)$ is not APN, and changing a value of $F$ in a single point results in non-APN functions.

Note: This is an improved version of the paper.