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Computer Science > Information Theory

arXiv:2212.01931 (cs)
[Submitted on 4 Dec 2022 (v1), last revised 20 Jul 2023 (this version, v2)]

Title:Differential uniformity properties of some classes of permutation polynomials

Authors:Kirpa Garg, Sartaj Ul Hasan, Pantelimon Stanica
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Abstract:The notion of $c$-differential uniformity has recently received a lot of attention since its proposal~\cite{Ellingsen}, and recently a characterization of perfect $c$-nonlinear functions in terms of difference sets in some quasigroups was obtained in~\cite{AMS22}. Independent of their applications as a measure for certain statistical biases, the construction of functions, especially permutations, with low $c$-differential uniformity is an interesting mathematical problem in this area, and recent work has focused heavily in this direction. We provide a few classes of permutation polynomials with low $c$-differential uniformity. The used technique involves handling various Weil sums, as well as analyzing some equations in finite fields, and we believe these can be of independent interest.
Subjects: Information Theory (cs.IT); Number Theory (math.NT)
Cite as: arXiv:2212.01931 [cs.IT]
  (or arXiv:2212.01931v2 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2212.01931

Submission history

From: Sartaj Ul Hasan [view email]
[v1] Sun, 4 Dec 2022 21:34:15 UTC (21 KB)
[v2] Thu, 20 Jul 2023 16:13:21 UTC (22 KB)
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