Cryptology ePrint Archive: Report 2009/273

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

Rafael Dowsley and Jörn Müller-Quade and Akira Otsuka and Goichiro Hanaoka and 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.

Category / Keywords: Verifiable Secret Sharing, Dishonest Majority, Pre-distributed Data, Unconditional Security, Universal Composable

Date: received 8 Jun 2009, last revised 28 Feb 2013

Contact author: rafael at dowsley net

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Version: 20130228:122923 (All versions of this report)

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