Using non-interactive proofs to achieve independence e ciently and securely

Independence or simultaneous broadcast is a fundamental tool to achieve security in fault tolerant distributed computing. It allows n players to commit to independently chosen values. In this paper we present a constant round protocol to perform this task. Previous solutions were all O(logn) rounds. In the process we develop a new and stronger formal de nition from this problem. As an example of the importance of independence in distributed protocols, we show an attack on the Sako-Kilian election scheme presented at CRYPTO 94 made possible by the protocol failure on achieving independence. Using our techniques we will show how to modify the scheme to make it secure.