An Interpretation of Sums of Walsh Spectrum Powers of Boolean Functions

Abstract

Abstract. Boolean Functions are fundamental tools in the design of several cryptographic algorithms. They are used for S-box designing in block ciphers and utilized as filters in stream ciphers. One of the important criteria that a Boolean function should satisfy is high nonlinearity, which can be calculated using walsh transform. Some properties of the Walsh spectrum of Boolean functions are known and in this paper we introduce some other properties obtained from the sums of Walsh spectrum powers of Boolean functions