S-boxes and Round Functions with Controllable Linearity and Differential Uniformity

A b s t r a c t . In this contribution we consider the stability of linearity and differential uniformity of vector Boolean functions under certain constructions and modifications. These include compositions with affine surjections onto the input space and with aitlne surjections from the output space, inversions, adding coordinate functions, forming direct sums and restrictions to affine subspaces. As examples we consider some true round function and S-box constructions. More theoretical examples are offered by the bent and almost perfect nonlinear functions. We also include some facts about functions with partially bent components.