Secret-sharing schemes: A survey

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450 Scopus citations

Abstract

A secret-sharing scheme is a method by which a dealer distributes shares to parties such that only authorized subsets of parties can reconstruct the secret. Secret-sharing schemes are an important tool in cryptography and they are used as a building box in many secure protocols, e.g., general protocol for multiparty computation, Byzantine agreement, threshold cryptography, access control, attribute-based encryption, and generalized oblivious transfer. In this survey, we describe the most important constructions of secret-sharing schemes; in particular, we explain the connections between secret-sharing schemes and monotone formulae and monotone span programs. We then discuss the main problem with known secret-sharing schemes - the large share size, which is exponential in the number of parties. We conjecture that this is unavoidable. We present the known lower bounds on the share size. These lower bounds are fairly weak and there is a big gap between the lower and upper bounds. For linear secret-sharing schemes, which is a class of schemes based on linear algebra that contains most known schemes, super-polynomial lower bounds on the share size are known. We describe the proofs of these lower bounds. We also present two results connecting secret-sharing schemes for a Hamiltonian access structure to the NP vs. coNP problem and to a major open problem in cryptography - constructing oblivious-transfer protocols from one-way functions.

Original languageEnglish GB
Title of host publicationCoding and Cryptology - Third International Workshop, IWCC 2011, Proceedings
Pages11-46
Number of pages36
DOIs
StatePublished - 23 Jun 2011
Event3rd International Workshop on Coding and Cryptology, IWCC 2011 - Qingdao, China
Duration: 30 May 20113 Jun 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6639 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd International Workshop on Coding and Cryptology, IWCC 2011
Country/TerritoryChina
CityQingdao
Period30/05/113/06/11

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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