On the constructions of resilient Boolean functions with five-valued Walsh spectra and resilient semi-bent functions

Abstract

Boolean functions with five-valued Walsh spectra (shortened as five-valued functions) and semi-bent functions are two classes of Boolean functions with high nonlinearity. They have useful applications in cryptography and communications. In this paper, we first present the construction of resilient five-valued functions by modifying the support of Rothaus’s bent function. And then, we give the method of constructing resilient semi-bent functions. At the same time, the number of the newly constructed resilient semi-bent functions is determined. Lastly, we give the construction of resilient semi-bent functions with maximal algebraic degree.