Rédei-Funktionen für Zweierpotenzen

L. Rédei has introduced in 1946 a class of rational functions over finite fields of orderp^t –p being an odd prime — and has proved some interesting results on permutations which are induced by these functions. Recently, similar results have been found for factor rings of the integers of orderp^t; moreover, these functions have been applied to construct public key cryptosystems. In this paper we consider functions of Rédei type over finite fields and factor rings of the integers of order 2^t. We show that most of the results for oddp also hold in this case.