New links between nonlinearity and differential uniformity

In this paper some new links between the nonlinearity and differential uniformity of some large classes of functions are established. Differentially two-valued functions and quadratic functions are mainly treated. A lower bound for the nonlinearity of monomial delta-uniform permutations is obtained, for any (delta, as well as an upper bound for differentially two-valued functions. Concerning quadratic functions, significant relations between nonlinearity and differential uniformity are exhibited. In particular, we show that the quadratic differentially 4-uniform permutations should be differentially two-valued and possess the best known nonlinearity. (C) 2018 Elsevier Inc. All rights reserved.