Decision Diagram Representation of Binary and Multiple-Valued Bent Functions

Bent functions are defined as Boolean functions at the largest distance from affine functions, making them useful in various cryptographic applications. The same definition is also used for multiple-valued functions, which found interesting applications in the same and related areas. Decision diagrams are a widely used data structure for compact representation of discrete functions in terms of space and time. Different types of decision diagrams are used in various applications. This paper compares the complexity of the representation of bent functions by different decision diagrams. It is shown that particular properties of underlying decomposition rules might have a considerable effect on the complexity of these decision diagrams for bent functions. In binary case, Binary Decision Diagrams, Functional Decision Diagrams, and Walsh Decision Diagrams are compared. Analog to that, Multiple-Valued Decision Diagrams, Multiple-Valued Functional Decision Diagrams (with Reed-Muller and Reed-Muller-Fourier decompositions), and Vilenkin-Chrestenson Decision Diagrams are analyzed for the representation of multiple-valued functions. Experiments show that Functional Decision diagrams are the best solution for both cases' bent function representation.