The second-order zero differential spectra of some APN and other maps over finite fields

[2310.13775] The second-order zero differential spectra of some APN and other maps over finite fields Skip to main content Search Submit Donate Log in Computer Science > Information Theory arXiv:2310.13775 (cs) [Submitted on 20 Oct 2023] Title: The second-order zero differential spectra of some APN and other maps over finite fields Authors: Kirpa Garg , Sartaj Ul Hasan , Constanza Riera , Pantelimon Stanica View PDF HTML (experimental) Abstract: The Feistel Boomerang Connectivity Table and the related notion of $F$-Boomerang uniformity (also known as the second-order zero differential uniformity) has been recently introduced by Boukerrou et al.~\cite{Bouk}. These tools shall provide a major impetus in the analysis of the security of the Feistel network-based ciphers. In the same paper, a characterization of almost perfect nonlinear functions (APN) over fields of even characteristic in terms of second-order zero differential uniformity was also given. Here, we find a sufficient condition for an odd or even function over fields of odd characteristic to be an APN function, in terms of second-order zero differential uniformity. Moreover, we compute the second-order zero differential spectra of several APN or other low differential uniform functions, and show that our considered functions also have low second-order zero differential uniformity, though it may vary widely, unlike the case for even characteristic when it is always zero. Subjects: Information Theory (cs.IT) ; Cryptography and Security (cs.CR); Number Theory (math.NT) MSC classes: 12E20, 11T06, 94A60 Cite as: arXiv:2310.13775 [cs.IT] (or arXiv:2310.13775v1 [cs.IT] for this version) https://doi.org/10.48550/arXiv.2310.13775 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Journal of Algebra and Its Applications, Vol. 24, Issue No. 13n14, Article No. 2541002, 2025 Related DOI : https://doi.org/10.1142/S0219498825410026 Focus to learn more DOI(s) linking to related resources Submission history From: Pantelimon Stanica [ view email ] [v1] Fri, 20 Oct 2023 19:21:30 UTC (20 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 | 2023-10 Change to browse by: cs cs.CR 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) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

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