Time-Free and Timer-Based Assumptions Can Be Combined to Solve Authenticated Byzantine Consensus

To circumvent the FLP impossibility result in a deterministic way several protocols have been proposed on top of an asynchronous distributed system enriched with additional assumptions. In the context of Byzantine failures for systems where at most t processes may exhibit a Byzantine behavior, two approaches have been investigated to solve the consensus problem.The first, relies on the addition of synchrony, called Timer-Based, but the second is based on the pattern of the messages that are exchanged, called Time-Free. This paper shows that both types of assumptions are not antagonist and can be combined to solve authenticated Byzantine consensus. This combined assumption considers a correct process pi, called ⋄2t-BW, and a set X of 2t processes such that, eventually, for each query broadcasted by a correct process pj of X , pj receives a response from pi ∈ X among the (n − t) first responses to that query or both links connecting pi and pj are timely. Based on this combination, a simple hybrid authenticated Byzantine consensus protocol,benefiting from the best of both worlds, is proposed. Whereas many hybrid protocols have been designed for the consensus problem in the crash model, this is, to our knowledge, the first hybrid deterministic solution to the Byzantine consensus problem.