Simplified VSS and fast-track multiparty computations with applications to threshold cryptography

The goal of this paper is to introduce a simple verifiable secret sharing scheme, to improve the efficiency of known secure multiparty protocols and, by employing these techniques, to improve the efficiency of applications which use these protocols. First we present a very simple Verifiable Secret Sharing protocol which is based on fast cryptographic primitives and avoids altogether the need for expensive zero-knowledge proofs. This is followed by a highly simplified protocol to compute multiplications over shared secrets. This is a major component in secure multiparty computation protocols and accounts for much of the complexity of proposed solutions. Using our protocol as a plug-in unit in known protocols reduces their complexity. We show how to achieve efficient multiparty computations in the computational model, through the application of homomorphic commitments. Finally, we present fast-track multiparty computation protocols. In a model in which malicious faults are rare we show that it is possible to carry out a simpler and more efficient protocol which does not perform all the expensive checks needed to combat a malicious adversary from foiling the computation. Yet, the protocol still enables detection of faults and recovers the computation when faults occur without giving any information advantage to the adversary. This results in protocols which are much more efficient under normal operation of the system i.e. when there are no faults. As an example of the practical impact of our work we show how our techniques can be used to greatly improve the speed and the fault-tolerance of existing threshold cryptography protocols.