Secret sharing with public reconstruction

Amos Beimel, Benny Chor

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

5 Scopus citations

Abstract

All known constructions of information theoretic t-out-of-n 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 O(n) one times pads to each party. This results in shares whose size is O(n) 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/t) 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 Ω(n/t) lower bound for the increase in the shares’ size.

Original languageEnglish
Title of host publicationAdvances in Cryptology ― CRYPTO 1995 - 15th Annual International Cryptology Conference, Proceedings
EditorsDon Coppersmith
PublisherSpringer Verlag
Pages353-366
Number of pages14
ISBN (Print)3540602216, 9783540602217
DOIs
StatePublished - 1 Jan 1995
Externally publishedYes
Event15th Annual International Cryptology Conference, CRYPTO 19995 - Santa Barbara, United States
Duration: 27 Aug 199531 Aug 1995

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume963
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference15th Annual International Cryptology Conference, CRYPTO 19995
Country/TerritoryUnited States
CitySanta Barbara
Period27/08/9531/08/95

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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