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.