Algorithms for Computing the Linearity and Degree of Vectorial Boolean Functions

Abstract

In this article, we study two representations of a Boolean function which are very important in the context of cryptography. We describeMöbius and Walsh Transforms for Boolean functions in details and presenteffective algorithms for their implementation. We combine these algorithmswith the Gray code to compute the linearity, nonlinearity and algebraic degree of a vectorial Boolean function. Such a detailed consideration will bevery helpful for students studying the design of block ciphers, including PhDstudents in the beginning of their research.ACM Computing Classification System (1998): F.2.1, F.2.2.