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.
BibTeX - Entry
@InProceedings{bogdanov:LIPIcs.ITC.2023.3,
author = {Bogdanov, Andrej},
title = {{Csirmaz’s Duality Conjecture and Threshold Secret Sharing}},
booktitle = {4th Conference on Information-Theoretic Cryptography (ITC 2023)},
pages = {3:1--3:6},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-271-6},
ISSN = {1868-8969},
year = {2023},
volume = {267},
editor = {Chung, Kai-Min},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/18331},
URN = {urn:nbn:de:0030-drops-183317},
doi = {10.4230/LIPIcs.ITC.2023.3},
annote = {Keywords: Threshold secret sharing, Fourier analysis}
}
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Keywords: |
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Threshold secret sharing, Fourier analysis |
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Collection: |
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4th Conference on Information-Theoretic Cryptography (ITC 2023) |
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Issue Date: |
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2023 |
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Date of publication: |
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21.07.2023 |
Creative Commons Attribution 4.0 International license (CC BY 4.0)