Universally Composable and Statistically Secure Verifiable Secret Sharing Scheme Based on Pre-Distributed Data

Rafael Dowsley; Jörn Müller-Quade; Akira Otsuka; Goichiro Hanaoka; Hideki Imai; Anderson C.  A.  Nascimento

Paper 2009/273

Universally Composable and Statistically Secure Verifiable Secret Sharing Scheme Based on Pre-Distributed Data

Rafael Dowsley, Jörn Müller-Quade, Akira Otsuka, Goichiro Hanaoka, Hideki Imai, and Anderson C. A. Nascimento

Abstract

This paper presents a non-interactive verifiable secret sharing scheme (VSS) tolerating a dishonest majority based on data pre-distributed by a trusted authority. As an application of this VSS scheme we present very efficient unconditionally secure multiparty protocols based on pre-distributed data which generalize two-party computations based on linear pre-distributed bit commitments. The main results of this paper are a non-interactive VSS where the amount of data which needs to be pre-distributed to each player depends on the number of tolerable cheaters only, a simplified multiplication protocol for shared values based on pre-distributed random products, and non-interactive zero knowledge proofs for arbitrary polynomial relations. The security of the schemes are proved using the UC framework.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Verifiable Secret Sharing Dishonest Majority Pre-distributed Data Unconditional Security Universal Composable
Contact author(s): rafael @ dowsley net
History: 2013-02-28: last of 2 revisions; 2009-06-09: received; See all versions
Short URL: https://ia.cr/2009/273
License: CC BY

BibTeX

@misc{cryptoeprint:2009/273,
      author = {Rafael Dowsley and Jörn Müller-Quade and Akira Otsuka and Goichiro Hanaoka and Hideki Imai and Anderson C.  A.  Nascimento},
      title = {Universally Composable and Statistically Secure Verifiable Secret Sharing Scheme Based on Pre-Distributed Data},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/273},
      year = {2009},
      url = {https://eprint.iacr.org/2009/273}
}