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

doi:10.1587/transfun.E94.A.725

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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

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Keywords: verifiable secret sharing, dishonest majority, pre-distributed data, unconditional security, universal composable

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2011 Volume E94.A Issue 2 Pages 725-734

DOI https://doi.org/10.1587/transfun.E94.A.725

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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 protocols for performing multiplication of shares 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, 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 is proved using the UC framework.

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