Protocols solving authenticated consensus in synchronous networks with Byzantine faults have been widely researched and known to exists if and only if n > 2f for f Byzantine faults. Similarly, protocols solving authenticated consensus in partially synchronous networks are known to exist if n > 3f+2k for f Byzantine faults and k crash faults. In this work we fill a natural gap in our knowledge by presenting MixSync, an authenticated consensus protocol in synchronous networks resilient to f Byzantine faults and k crash faults if n > 2f+k. As a basic building block, we first define and then construct a publicly verifiable crusader agreement protocol with the same resilience. The protocol uses a simple double-send round to guarantee non-equivocation, a technique later used in the MixSync protocol. We then discuss how to construct a state machine replication protocol using these ideas, and how they can be used in general to make such protocols resilient to crash faults. Finally, we prove lower bounds showing that n > 2f+k is optimally resilient for consensus and state machine replication protocols.
@InProceedings{abraham_et_al:LIPIcs.DISC.2022.38, author = {Abraham, Ittai and Dolev, Danny and Kagan, Alon and Stern, Gilad}, title = {{Brief Announcement: Authenticated Consensus in Synchronous Systems with Mixed Faults}}, booktitle = {36th International Symposium on Distributed Computing (DISC 2022)}, pages = {38:1--38:3}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-255-6}, ISSN = {1868-8969}, year = {2022}, volume = {246}, editor = {Scheideler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.38}, URN = {urn:nbn:de:0030-drops-172292}, doi = {10.4230/LIPIcs.DISC.2022.38}, annote = {Keywords: consensus, state machine replication, mixed faults, synchrony, lower bounds} }
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