Affiliations: [a] Department of Computer Science, University of Bejaia, Bejaia 06000, Algeria. atioura@gmail.com | [b] Department of Computer Science, University of Batna 2, Batna, Algeria. hamouma.moumen@univ-batna2.dz | [c] Department of Computer Science, University of Batna 2, Batna, Algeria. h.kalla@univ-batna2.dz | [d] Department of Mathematics, University of Bejaia, Bejaia 06000, Algeria. a.aitsaidi@univ-bejaia.dz
Correspondence:
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Address for correspondence: Department of Informatics, University of Batna 2, Fesdis 05078, Batna, Algeria.
Abstract: The consensus is a central problem of fault-tolerant distributed computing. Unfortunately, solving such a problem is impossible in asynchronous distributed systems prone to process failures. To circumvent this impossibility (known as FLP impossibility result) in a deterministic way, on top of asynchronous distributed systems enriched with additional assumptions, several protocols have been proposed. Actually, to solve the Byzantine Consensus problem, with a deterministic manner, in systems where at most t processes may exhibit a Byzantine behavior, two approaches have been investigated. The first relies on the addition of synchrony, called Timer-Based, while the second, called Time-Free, is based on the pattern of message exchange. This paper shows that both types of assumptions are not antagonist and can be combined to solve authenticated Byzantine consensus. The combined assumption considers a correct process pi, called ⋄〈t + 1〉-BW, and a set X of t+1 correct processes (including pi itself) 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. As a matter of fact, although numerous 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.
