Unconditionally non-interactive verifiable secret sharing secure against faulty majorities in the commodity based model

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