License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITC.2023.3
URN: urn:nbn:de:0030-drops-183317
URL: https://drops.dagstuhl.de/opus/volltexte/2023/18331/
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Bogdanov, Andrej

Csirmaz’s Duality Conjecture and Threshold Secret Sharing

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LIPIcs-ITC-2023-3.pdf (0.6 MB)


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}
}

Keywords: Threshold secret sharing, Fourier analysis
Collection: 4th Conference on Information-Theoretic Cryptography (ITC 2023)
Issue Date: 2023
Date of publication: 21.07.2023


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