Preimage Distributions of Perfect Nonlinear Functions and Vectorial Plateaued Functions

By converting the problem of preimage distribution of a perfect nonlinear function with three binary outputs to that with two binary outputs, this paper presents the preimage distributions of perfect nonlinear functions with three binary outputs. This paper also characterizes the fundamental characterization of the preimage distribution of vectorial plateaued functions with single amplitude and its component functions being all unbalanced, and gives the preimage distributions of such functions with two or three binary outputs.