Vectorial Boolean Functions with Very Low Differential-Linear Uniformity Using Maiorana-McFarland Type Construction

Abstract

The differential-linear connectivity table (DLCT) of a vectorial Boolean function was recently introduced by Bar-On et al. at EUROCRYPT’19. In this paper we construct a new class of balanced vectorial Boolean functions with very low differential-linear uniformity and provide a combinatorial count of hardware gates which is required to implement such circuits. Here, all the coordinate functions are constructed by modifying the Maiorana-McFarland bent functions. Further, we derive some properties of DLCT and differential-linear uniformity of modified inverse functions.