A Lower Bound on the Share Size in Evolving Secret Sharing

Noam Mazor*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publication4th Conference on Information-Theoretic Cryptography, ITC 2023
EditorsKai-Min Chung
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772716
DOIs
StatePublished - Jul 2023
Event4th Conference on Information-Theoretic Cryptography, ITC 2023 - Aarhus, Denmark
Duration: 6 Jun 20238 Jun 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume267
ISSN (Print)1868-8969

Conference

Conference4th Conference on Information-Theoretic Cryptography, ITC 2023
Country/TerritoryDenmark
CityAarhus
Period6/06/238/06/23

Keywords

  • Evolving secret sharing
  • Secret sharing

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