Secret sharing with public reconstruction

Amos Beimel, Benny Chor

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

All known constructions of information theoretic f-out-of-ji secret-sharing schemes require secure, private communication channels among the parties for the reconstruction of the secret. In this work we investigate the cost of performing the reconstruction over public communication channels. A naive implementation of this task distributes 2n -2 one times pads to each party. This results in shares whose size is 2n -1 times the secret size. We present three implementations of such schemes that are substantially more efficient. A scheme enabling multiple reconstructions of the secret by different subsets of parties, with factor O (n/i) increase in the shares' size. A one-time scheme, enabling a single reconstruction of the secret, with O (log (n/t)) increase in the shares' size. A one-time scheme, enabling a single reconstruction by a set of size exactly t, with factor O (1) increase in the shares' size. We prove that the first implementation is optimal (up to constant factors) by showing a tight £l(n/t) lower bound for the increase in the shares' size.

Original languageEnglish
Pages (from-to)1887-1896
Number of pages10
JournalIEEE Transactions on Information Theory
Volume44
Issue number5
DOIs
StatePublished - 1 Jan 1998
Externally publishedYes

Keywords

  • Cryptography, public and private channels, secret sharing, space efficiency, unrestricted and one-time schemes

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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