New links between nonlinearity and differential uniformity

Abstract : This paper establishes some new links between the nonlinearity and differential uniformity of some large classes of functions, such as power functions, differentially two-valued functions and quadratic functions. We obtain a lower bound for the nonlinearity of general differential uniform power permutations, an upper bound for general differentially two-valued functions, together with some important results for quadratic functions. In particular, we show that the quadratic differentially 4-uniform permutations should be two-valued and possess the best known nonlinearity.
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https://hal.inria.fr/hal-01836184
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Submitted on : Thursday, July 12, 2018 - 10:36:33 AM
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Pascale Charpin, Jie Peng. New links between nonlinearity and differential uniformity. Sequences and Their Applications (SETA) 2018, Oct 2018, Hong-Kong, China. ⟨hal-01836184⟩

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