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In this paper we propose Aleph, a leaderless, fully asynchronous, Byzantinefault tolerant consensus protocol for ordering messages exchanged amongprocesses. It is based on a distributed construction of a partially ordered setand the algorithm for reaching a consensus on its extension to a total order.To achieve the consensus, the processes perform computations based only on alocal copy of the data structure, however, they are bound to end with the sameresults. Our algorithm uses a dual-threshold coin-tossing scheme as arandomization strategy and establishes the agreement in an expected constantnumber of rounds. In addition, we introduce a fast way of validating messagesthat can occur prior to determining the total ordering.  This version of the protocol is deprecated. For current version seearXiv:1908.05156.

Aleph: A Leaderless, Asynchronous, Byzantine Fault Tolerant Consensus Protocol