Two-to-one functions from Galois extensions

Abstract

Recently, two-to-one mappings have received a lot of attention due to their applications to cryptography and to the construction of classes of cryptographic functions. In this paper, we propose a new method to obtain m-to-1 functions based on Galois groups of rational functions. We feel that such an approach might be the starting point of a new line of research in the area of m-to-1 mappings.