On differential uniformity and nonlinearity of functions (Q998534)

The authors present some results related to plateaued functions and mappings whose derivatives are \(2^s\)-to-1 functions. These results generalize facts about almost perfect nonlinear (APN) functions and almost bent (AB) functions. Two possible generalizations both of APN and AB functions are presented. The connection between plateaued and \(2^s\)-to-1 functions is investigated. The authors show that functions which are both plateaued and differentially uniform give rise to partial difference sets.