Brief announcement: Proactive secret sharing with a dishonest majority

Shlomi Dolev, Karim ElDefrawy, Joshua Lampkins, Rafail Ostrovsky, Moti Yung

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


In a secret sharing scheme a dealer shares a secret s among n parties such that an adversary corrupting up to t par- ties does not learn s, while any t + 1 parties can efficiently recover s. Over a long period of time all parties may be cor- rupted thus violating the threshold, which is accounted for in Proactive Secret Sharing (PSS). PSS schemes periodically rerandomize (refresh) the shares of the secret and invalidate old ones. PSS retains confidentiality even when all parties are corrupted over the lifetime of the secret, but no more than t during a certain window of time, called the refresh period. Existing PSS schemes only guarantee secrecy in the presence of an honest majority with less than n=2 total cor- ruptions during a refresh period; an adversary corrupting a single additional party, even if only passively, obtains the secret. This work is the first feasibility result demonstrating PSS tolerating a dishonest majority, it introduces the first PSS scheme secure against t < n passive adversaries without recovery of lost shares, it can also recover from honest faulty parties losing their shares, and when tolerating e faults the scheme tolerates t < n-e passive corruptions. A non-robust version of the scheme can tolerate t < n=2 - e active adver- saries, and mixed adversaries that control a combination of passively and actively corrupted parties that are a majority, but where less than n=2 - e of such corruptions are active. We achieve these high thresholds with O(n4) communica- tion when sharing a single secret, and O(n3) communication when sharing multiple secrets in batches.

Original languageAmerican English
Title of host publicationPODC 2016 - Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing
Number of pages3
ISBN (Electronic)9781450339643
StatePublished - 25 Jul 2016
Event35th ACM Symposium on Principles of Distributed Computing, PODC 2016 - Chicago, United States
Duration: 25 Jul 201628 Jul 2016

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing


Conference35th ACM Symposium on Principles of Distributed Computing, PODC 2016
Country/TerritoryUnited States


  • Dishonest majority
  • Non-robust secret sharing
  • Proac-tive secret sharing
  • Proactive security
  • Secret sharing

All Science Journal Classification (ASJC) codes

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications


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