New links between nonlinearity and differential uniformity

Abstract : 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 δ-uniform permutations is obtained, for any δ, 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.
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Pascale Charpin, Jie Peng. New links between nonlinearity and differential uniformity. Finite Fields and Their Applications, Elsevier, 2019, 56, pp.188-208. ⟨10.1016/j.ffa.2018.12.001⟩. ⟨hal-01907499⟩

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