On the Optimality of Linear, Differential, and Sequential Distinguishers

In this paper, we consider the statistical decision processes behind a linear and a differential cryptanalysis. By applying techniques and concepts of statistical hypothesis testing, we describe precisely the shape of optimal linear and differential distinguishers and we improve known results of Vaudenay concerning their asymptotic behaviour. Furthermore, we formalize the concept of ``sequential distinguisher'' and we illustrate potential applications of such tools in various statistical attacks.