Better secret sharing via robust conditional disclosure of secrets

Benny Applebaum, Amos Beimel, Oded Nir, Naty Peter

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

10 Scopus citations


A secret-sharing scheme allows to distribute a secret s among n parties such that only some predefined "authorized" sets of parties can reconstruct the secret, and all other "unauthorized" sets learn nothing about s. For over 30 years, it was known that any (monotone) collection of authorized sets can be realized by a secret-sharing scheme whose shares are of size 2n-o(n) and until recently no better scheme was known. In a recent breakthrough, Liu and Vaikuntanathan (STOC 2018) have reduced the share size to 20.994n+o(n), which was later improved to 20.892n+o(n) by Applebaum et al. (EUROCRYPT 2019). In this paper we improve the exponent of general secret-sharing down to 0.637. For the special case of linear secret-sharing schemes, we get an exponent of 0.762 (compared to 0.942 of Applebaum et al.). As our main building block, we introduce a new robust variant of conditional disclosure of secrets (robust CDS) that achieves unconditional security even under bounded form of re-usability. We show that the problem of general secret-sharing reduces to robust CDS with sub-exponential overhead and derive our main result by implementing robust CDS with a non-trivial exponent. The latter construction follows by presenting a general immunization procedure that turns standard CDS into a robust CDS.

Original languageEnglish
Title of host publicationSTOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
EditorsKonstantin Makarychev, Yury Makarychev, Madhur Tulsiani, Gautam Kamath, Julia Chuzhoy
PublisherAssociation for Computing Machinery
Number of pages14
ISBN (Electronic)9781450369794
StatePublished - 8 Jun 2020
Event52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020 - Chicago, United States
Duration: 22 Jun 202026 Jun 2020

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Conference52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020
Country/TerritoryUnited States


  • Conditional disclosure of secrets
  • Robust conditional disclosure of secrets
  • Secret-sharing schemes

ASJC Scopus subject areas

  • Software


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