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New links between nonlinearity and differential uniformity

Authors
  • Charpin, Pascale
  • Peng, Jie
Publication Date
Mar 01, 2019
Source
HAL-UPMC
Keywords
Language
English
License
Unknown
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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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