The revised boomerang connectivity tables and their connection to the Difference Distribution Table

[2407.12617] The revised boomerang connectivity tables and their connection to the Difference Distribution Table Skip to main content Search Submit Donate Log in Computer Science > Cryptography and Security arXiv:2407.12617 (cs) [Submitted on 17 Jul 2024 ( v1 ), last revised 27 Jan 2025 (this version, v3)] Title: The revised boomerang connectivity tables and their connection to the Difference Distribution Table Authors: Kirpa Garg , Sartaj Ul Hasan , Constanza Riera , Pantelimon Stanica View PDF HTML (experimental) Abstract: It is well-known that functions over finite fields play a crucial role in designing substitution boxes (S-boxes) in modern block ciphers. In order to analyze the security of an S-box, recently, three new tables have been introduced: the Extended Boomerang Connectivity Table (EBCT), the Lower Boomerang Connectivity Table (LBCT), and the Upper Boomerang Connectivity Table (UBCT). In fact, these tables offer improved methods over the usual Boomerang Connectivity Table (BCT) for analyzing the security of S-boxes against boomerang-style attacks. Here, we put in context these new EBCT, LBCT, and UBCT concepts by connecting them to the DDT for a differentially $\delta$-uniform function and also determine the EBCT, LBCT, and UBCT entries of three classes of differentially $4$-uniform power permutations, namely, Gold, Kasami and Bracken-Leander. We also determine the Double Boomerang Connectivity Table (DBCT) entries of the Gold function. As byproducts of our approach, we obtain some previously published results quite easily. Subjects: Cryptography and Security (cs.CR) ; Information Theory (cs.IT) MSC classes: 12E20, 11T06, 94A60 Cite as: arXiv:2407.12617 [cs.CR] (or arXiv:2407.12617v3 [cs.CR] for this version) https://doi.org/10.48550/arXiv.2407.12617 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Designs, Codes and Cryptography, Vol 93, pp. 1951-1984, 2025 Related DOI : https://doi.org/10.1007/s10623-025-01582-3 Focus to learn more DOI(s) linking to related resources Submission history From: Sartaj Ul Hasan [ view email ] [v1] Wed, 17 Jul 2024 14:44:40 UTC (24 KB) [v2] Wed, 20 Nov 2024 03:05:13 UTC (25 KB) [v3] Mon, 27 Jan 2025 06:26:53 UTC (28 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.CR < prev | next > new | recent | 2024-07 Change to browse by: cs cs.IT math math.IT 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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