A protocol to achieve independence in constant rounds

Independence is a fundamental property needed to achieve security in fault-tolerant distributed computing. In practice, distributed communication networks are neither fully synchronous or fully asynchronous, but rather loosely synchronized. By this, we mean that in a communication protocol, messages at a given round may depend on messages from other players at the same round. These possible dependencies among messages create problems if we need n players to announce independently chosen values. This task is called simultaneous broadcast. In this paper, we present the first constant round protocol for simultaneous broadcast in a reasonable computation model (which includes a common shared random string among the players). The protocol is provably secure under general cryptographic assumptions. In the process, we develop a new and stronger formal definition for this problem. Previously known protocols for this task required either O(log n) or expected constant rounds to complete (depending on the computation model considered).