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

Rafael DOWSLEY  Jorn MULLER-QUADE  Akira OTSUKA  Goichiro HANAOKA  Hideki IMAI  Anderson C.A. NASCIMENTO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A   No.2   pp.725-734
Publication Date: 2011/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.725
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Cryptography and Information Security
verifiable secret sharing,  dishonest majority,  pre-distributed data,  unconditional security,  universal composable,  

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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.