Evolving secret sharing: Dynamic thresholds and robustness

Ilan Komargodski*, Anat Paskin-Cherniavsky

*Corresponding author for this work

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

24 Scopus citations

Abstract

Threshold secret sharing schemes enable a dealer to share a secret among n parties such that only subsets of parties of cardinality at least k= k(n) can reconstruct the secret. Komargodski, Naor and Yogev (TCC 2016-B) proposed an efficient scheme for sharing a secret among an unbounded number of parties such that only subsets of k parties can recover the secret, where k is any fixed constant. This access structure is known as k-threshold. They left open the possibility of an efficient scheme for the dynamic threshold access structure, in which the qualified sets are of increasing size as the number of parties increases. We resolve this open problem and present a construction in which the share size of the t-th party is O(t4· log t) bits. Furthermore, we show how to generically translate any scheme for k-threshold into a scheme which is robust, where a shared secret can be recovered even if some parties hand-in incorrect shares. This answers another open problem of Komargodski et al. Our construction is based on the construction of robust (classical) secret sharing schemes of Cramer et al. (EUROCRYPT 2008) using algebraic manipulation detection codes.

Original languageAmerican English
Title of host publicationTheory of Cryptography - 15th International Conference, TCC 2017, Proceedings
EditorsYael Kalai, Leonid Reyzin
PublisherSpringer Verlag
Pages379-393
Number of pages15
ISBN (Print)9783319705026
DOIs
StatePublished - 2017
Externally publishedYes
Event15th International Conference on Theory of Cryptography, TCC 2017 - Baltimore, United States
Duration: 12 Nov 201715 Nov 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10678 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference15th International Conference on Theory of Cryptography, TCC 2017
Country/TerritoryUnited States
CityBaltimore
Period12/11/1715/11/17

Bibliographical note

Publisher Copyright:
© 2017, International Association for Cryptologic Research.

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