Generalized nonlinearity of S-boxes
Advances in Mathematics of Communications
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.
Gangopadhyay, Sugata; Paul, Goutam; Sinha, Nishant; and Stănică, Pantelimon, "Generalized nonlinearity of S-boxes" (2018). Journal Articles. 1483.