Csirmaz’s Duality Conjecture and Threshold Secret Sharing

Author Andrej Bogdanov

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Andrej Bogdanov
  • University of Ottawa, Canada


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.

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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)


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
  • Threshold secret sharing
  • Fourier analysis


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