Differential uniformity properties of some classes of permutation polynomials

[2212.01931] Differential uniformity properties of some classes of permutation polynomials Skip to main content Search Submit Donate Log in 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 View PDF HTML (experimental) 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 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Journal of Computational Algebra, Volumes 13-14, Article No. 100035, 2025 Related DOI : https://doi.org/10.1016/j.jaca.2025.100035 Focus to learn more DOI(s) linking to related resources 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) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.IT < prev | next > new | recent | 2022-12 Change to browse by: cs math math.IT math.NT References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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