Representation of Multiple-Valued Functions with Flat Vilenkin-Chrestenson Spectra by Decision Diagrams
Stanislav Stankovic, Milena Stankovic and Jakko Astola
In this paper we examine the relationship between multiple-valued bent functions and Vilenkin-Chrestenson spectral invariant operations and Vilenkin-Chrestenson decision diagrams. In binary domain bent functions are a class of discrete functions with a highest degree of nonlinearity and form an essential part of cryptographic systems. Multiple-valued bent functions are an extension of bent functions to higher order finite fields. These functions are defined in terms of properties of their Vilenkin-Chrestenson spectra. We demonstrate that the application of spectral invariant operations to a given multiple-valued bent function does not alter the structure of the corresponding Vilenkin-Chrestenson decision diagrams. We exploit this property to efficiently represent whole sets of multiple-valued bent functions using a single Vilenkin-Chrestenson decision diagram. Furthermore, we present a decision diagram based method of construction of multiple-valued bent functions of arbitrary size.