On Upper Bounds for Algebraic Degrees of APN Functions
Lilya Budaghyan, Claude Carlet, Tor Helleseth, Nian Li, Bo Sun · IEEE Transactions on Information Theory · 2017
We study the problem of existence of APN functions of algebraic degree n over F2n. We characterize such functions by means of derivatives and power moments of the Walsh transform. We deduce several non-existence results which imply, in particular, that for most of the known APN functions F over F2n. the function x2n-1+ F(x) is not APN, and changing a value of F in a single point then results in non-APN functions. This leads us to conjectures that an APN function modified in one point cannot remain APN and that there exists no APN function of algebraic degree n.