Properties of Bent Functions in the Truth Domain

In this paper we study bent functions in the truth vector domain. While in general bent functions are defined on the Walsh basis [-1,1] we look on their properties and classification in the standard Boolean basis [0,1]. We show that applying the Welsh transform to Boolean functions of n variables in the truth domain, results in a classification that allows to rank bent functions. We investigate the classification of bent vs non bent functions using standard machine learning and compare the performance difference. Finally we extend our search for efficient classification criteria to functions with smaller amount of variables and show the amount of classification possible.