Robust Distributed Multiplication without Interaction

An optimally resilient distributed multiplication protocol that enjoys the property of non-interactivity is presented. The protocol relies on a standard cryptographic assumption and works over a complete, synchronous, untappable network with a broadcast channel. As long as no disruption occurs, each player uses those channels only once to send messages; thus no interaction is needed among players. The cost is an increase in local computation and communication complexity that is determined by the factor of the threshold.As an application of the proposed protocol we present a robust threshold version of the Cramer-Shoup cryptosystem, which is the first non-interactive solution with optimal resilience.