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 describe
Möbius and Walsh Transforms for Boolean functions in details and present
effective algorithms for their implementation. We combine these algorithms
with the Gray code to compute the linearity, nonlinearity and algebraic degree
of a vectorial Boolean function. Such a detailed consideration will be
very helpful for students studying the design of block ciphers, including PhD
students in the beginning of their research.

ACM Computing Classification System (1998): F.2.1, F.2.2.