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. * IBM T.J. Watscm Research Center, PO Box 704, Yorktowo Heights, New York 10598, USA Email: rosarioOwatsotl.ibnl.coln. + Harvard University sod Hebrew University. Email: rabin@cs.huii.ac.il * IBM ‘f.J. Watsoo Research Center, PO Box 704, Yorktowo Heights, New York 10598, USA Email: talrOwatsoll.ibtn.corlr. Contact author Permission to make digital or hard copies of all or part of this work for pelmal cr ClassroOm use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear tbii notice and the fit11 citation on the fti page. To copy otherwise, to republish, to post on servers or to redisbibute to lists, requires prior specific permission a&or a fee. PODC 98 Fkerto Vallarta Mexico Copyright ACM 1998th89791.97%7/9816...$5.00