Generalized nonlinearity of $ S$ -boxes
Sugata Gangopadhyay, Goutam Paul, Nishant Sinha, Pantelimon Stănică · Advances in Mathematics of Communications · 2018
While analyzing $ S$-boxes, or vectorial Boolean functions, it is of interest to approximate its component functions by affine functions. In the usual attack models, it is assumed that all input vectors to an $ S$-box are equiprobable. The nonlinearity of an $ S$-box is defined, subject to this assumption. In this paper, we explore the possibility of linear cryptanalysis of an $ S$-box by introducing biased inputs and thus propose a generalized notion of nonlinearity along with a generalization of the Walsh-Hadamard spectrum of an $ S$-box.