Universally Composable and Statistically Secure Verifiable Secret Sharing Scheme Based on Pre-Distributed Data
This paper presents a non-interactive veriable secret shar- ing 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 ecient 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 pa- per 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 simplied 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.
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Dowsley, Rafael; MüLler-Quade, Jörn; Otsuka, Akira; Hanaoka, Goichiro; Imai, Hideki; and Nascimento, Anderson C.A., "Universally Composable and Statistically Secure Verifiable Secret Sharing Scheme Based on Pre-Distributed Data" (2011). Institute of Technology Publications. 51.