MIT Libraries homeMIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Towards breaking the exponential barrier for general secret sharing

Author(s)
Liu, Tianren; Vaikuntanathan, Vinod; Wee, Hoeteck
Thumbnail
DownloadSubmitted version (457.8Kb)
Terms of use
Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
Metadata
Show full item record
Abstract
A secret-sharing scheme for a monotone Boolean (access) function F: {0, 1}[superscript n] → {0, 1} is a randomized algorithm that on input a secret, outputs n shares s[subscript 1]., s[subscript n] such that for any (x[subscript 1]., x[subscript n]) ∈ {0, 1}[superscript n] the collection of shares {s[subscript i]: xi = 1} determine the secret if F(x[subscript 1]., x[subscript n]) = 1 and reveal nothing about the secret otherwise. The best secret sharing schemes for general monotone functions have shares of size Θ(2[superscript n]). It has long been conjectured that one cannot do much better than 2[superscript Ω(n)] share size, and indeed, such a lower bound is known for the restricted class of linear secret-sharing schemes. In this work, we refute two natural strengthenings of the above conjecture: First, we present secret-sharing schemes for a family of 2[superscript 2[superscript n/2]] monotone functions over {0, 1}[superscript n] with sub-exponential share size 2[superscript O(√ n log n)]. This unconditionally refutes the stronger conjecture that circuit size is, within polynomial factors, a lower bound on the share size. Second, we disprove the analogous conjecture for non-monotone functions. Namely, we present “non-monotone secret-sharing schemes” for every access function over {0, 1}[superscript n] with shares of size 2[superscript O(√ n log n)]. Our construction draws upon a rich interplay amongst old and new problems in information-theoretic cryptography: from secret-sharing, to multi-party computation, to private information retrieval. Along the way, we also construct the first multi-party conditional disclosure of secrets (CDS) protocols for general functions F: {0, 1}[superscript n]→ {0, 1} with communication complexity 2[superscript O(√ n log n)].
Date issued
2008-03
URI
https://hdl.handle.net/1721.1/124959
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal
Advances in Cryptology – EUROCRYPT 2018
Publisher
Springer
Citation
Liu, Tianren, et al. “Towards Breaking the Exponential Barrier for General Secret Sharing.” Advances in Cryptology – EUROCRYPT 2018, edited by Jesper Buus Nielsen and Vincent Rijmen, vol. 10820, Springer International Publishing (2018): 567–96.
Version: Original manuscript
ISBN
978-3-319-78380-2
ISSN
978-3-319-78381-9

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries homeMIT Libraries logo

Find us on

Twitter Facebook Instagram YouTube RSS

MIT Libraries navigation

SearchHours & locationsBorrow & requestResearch supportAbout us
PrivacyPermissionsAccessibility
MIT
Massachusetts Institute of Technology
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.