LIPIcs.ITC.2023.3.pdf
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Csirmaz’s Duality Conjecture and Threshold Secret Sharing
Author
Andrej Bogdanov 
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4th Conference on Information-Theoretic Cryptography (ITC 2023)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Conference on Information-Theoretic Cryptography (ITC) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2023-07-21
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Acknowledgements
Part of the research was carried out while the author was with the Chinese University of Hong Kong. I thank the anonymous ITC 2023 reviewers for helpful suggestions.
Cite AsGet BibTex
Andrej Bogdanov. Csirmaz’s Duality Conjecture and Threshold Secret Sharing. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 3:1-3:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ITC.2023.3
https://doi.org/10.4230/LIPIcs.ITC.2023.3
Abstract
We conjecture that the smallest possible share size for binary secrets for the t-out-of-n and (n-t+1)-out-of-n access structures is the same for all 1 ≤ t ≤ n. This is a strenghtening of a recent conjecture by Csirmaz (J. Math. Cryptol., 2020). We prove the conjecture for t = 2 and all n. Our proof gives a new (n-1)-out-of-n secret sharing scheme for binary secrets with share alphabet size n.
Subject Classification
ACM Subject Classification
- Theory of computation → Randomness, geometry and discrete structures
- Theory of computation → Cryptographic primitives
- Mathematics of computing → Information theory
- Security and privacy → Mathematical foundations of cryptography
Keywords
- Threshold secret sharing
- Fourier analysis
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References
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