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.2023.2
URN: urn:nbn:de:0030-drops-183300
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18330/
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Mazor, Noam

A Lower Bound on the Share Size in Evolving Secret Sharing

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LIPIcs-ITC-2023-2.pdf (0.6 MB)

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.

BibTeX - Entry

@InProceedings{mazor:LIPIcs.ITC.2023.2,
  author =	{Mazor, Noam},
  title =	{{A Lower Bound on the Share Size in Evolving Secret Sharing}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{2:1--2:9},
  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/2023/18330},
  URN =		{urn:nbn:de:0030-drops-183300},
  doi =		{10.4230/LIPIcs.ITC.2023.2},
  annote =	{Keywords: Secret sharing, Evolving secret sharing}
}

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

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