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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.
Cited literature [34 references]
https://hal.inria.fr/hal-01907499
Contributor : Pascale Charpin Connect in order to contact the contributor
Submitted on : Monday, October 29, 2018 - 11:08:24 AM
Last modification on : Thursday, January 7, 2021 - 3:38:03 PM
Long-term archiving on: : Wednesday, January 30, 2019 - 2:14:17 PM
Contributor : Pascale Charpin Connect in order to contact the contributor
Submitted on : Monday, October 29, 2018 - 11:08:24 AM
Last modification on : Thursday, January 7, 2021 - 3:38:03 PM
Long-term archiving on: : Wednesday, January 30, 2019 - 2:14:17 PM
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Charpin-Peng-18.pdf
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