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A Lower Bound on the Share Size in Evolving Secret Sharing
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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:
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- Publication date: 2023-07-21
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Acknowledgements
We thank Iftach Haitner and Ilan Komargodski for useful discussions.
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Noam Mazor. A Lower Bound on the Share Size in Evolving Secret Sharing. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 2:1-2:9, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ITC.2023.2
https://doi.org/10.4230/LIPIcs.ITC.2023.2
Abstract
Secret sharing schemes allow sharing a secret between a set of parties in a way that ensures that only authorized subsets of the parties learn the secret. Evolving secret sharing schemes (Komargodski, Naor, and Yogev [TCC '16]) allow achieving this end in a scenario where the parties arrive in an online fashion, and there is no a-priory bound on the number of parties.
An important complexity measure of a secret sharing scheme is the share size, which is the maximum number of bits that a party may receive as a share. While there has been a significant progress in recent years, the best constructions for both secret sharing and evolving secret sharing schemes have a share size that is exponential in the number of parties. On the other hand, the best lower bound, by Csirmaz [Eurocrypt '95], is sub-linear.
In this work, we give a tight lower bound on the share size of evolving secret sharing schemes. Specifically, we show that the sub-linear lower bound of Csirmaz implies an exponential lower bound on evolving secret sharing.
Subject Classification
ACM Subject Classification
- Security and privacy → Information-theoretic techniques
Keywords
- Secret sharing
- Evolving secret sharing
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References
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