A new construction of highly nonlinear S-boxes

Abstract

In this paper we give a new construction of highly nonlinear vectorial Boolean functions. This construction is based on coding theory, more precisely we use concatenation to construct Boolean functions from codes over $\mathbb{F}_q$ containing a first-order generalized Reed---Muller code. As it turns out this construction has a very compact description in terms of Boolean functions, which is of independent interest. The construction allows one to design functions with better nonlinearities than known before.