On fast probabilistic consensus in the Byzantine setting
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In this paper we discuss a leaderless protocol of low communicational complexity which allows a set of nodes to come to a consensus on a value of a bit. In addition, we assume that part of the nodes are Byzantine, i.e., they are controlled by an adversary who intends to either delay the consensus, or break it (i.e., make at least a couple of honest nodes come to different conclusions). We prove that, nevertheless, the protocol works with high probability when its parameters are suitably chosen, and we also provide some explicit estimates on the probability that the protocol finalizes in the consensus state in a given time. This protocol can possibly be applied to reaching consensus in decentralized cryptocurrency systems. A special feature of our protocol is that it makes use of a sequence of random numbers which are either provided by a trusted source or generated by the nodes themselves using some decentralized random number generating protocol.
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