International Association
for Cryptologic Research

In this paper, we study the problem of existence of almost perfect nonlinear (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 imply, in particular, that for most of the known APN functions $F$ over $\ftwon$ the function $x^{2^n-1}+F(x)$ is not APN.