Unconditionally-secure robust secret sharing with compact shares

Alfonso Cevallos*, Serge Fehr, Rafail Ostrovsky, Yuval Rabani

*Corresponding author for this work

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

39 Scopus citations

Abstract

We consider the problem of reconstructing a shared secret in the presence of faulty shares, with unconditional security. We require that any t shares give no information on the shared secret, and reconstruction is possible even if up to t out of the n shares are incorrect. The interesting setting is n/3≤t<n/2, where reconstruction of a shared secret in the presence of faulty shares is possible, but only with an increase in the share size, and only if one admits a small failure probability. The goal of this work is to minimize this overhead in the share size. Known schemes either have a Ω(κn)-overhead in share size, where κ is the security parameter, or they have a close-to-optimal overhead of order Ω(κ+n) but have an exponential running time (in n). In this paper, we propose a new scheme that has a close-to-optimal overhead in the share size of order , and a polynomial running time. Interestingly, the shares in our new scheme are prepared in the very same way as in the well-known scheme by Rabin and Ben-Or, which relies on message authentication, but we use a message authentication code with short tags and keys and with correspondingly weak security. The short tags and keys give us the required saving in the share size. Surprisingly, we can compensate for the weakened security of the authentication and achieve an exponentially small (in κ) failure probability by means of a more sophisticated reconstruction procedure.

Original languageAmerican English
Title of host publicationAdvances in Cryptology, EUROCRYPT 2012 - 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
Pages195-208
Number of pages14
DOIs
StatePublished - 2012
Event31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2012 - Cambridge, United Kingdom
Duration: 15 Apr 201219 Apr 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7237 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2012
Country/TerritoryUnited Kingdom
CityCambridge
Period15/04/1219/04/12

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