Abstract
This paper presents a simple broadcast operation suited to n-process asynchronous message-passing systems in which (i) up to t processes may commit Byzantine faults, and (2), while the underlying communication network is connected (any pair of processes is connected by a path), not all the pairs of processes are directly connected by a communication channel. The algorithm proposed to implement this operation assumes (i) \(t<n/3\) and (ii) \((2t+1)\)-vertex connectivity of the underlying network (each pair of processes is connected by at least \((2t+1)\) disjoint paths), requirements which are shown to be necessary. When considering incomplete networks, this abstraction can be used as the first level of a software stack on top of which, without any modifications, Byzantine-tolerant broadcast and agreement abstractions designed for fully connected networks can directly be used. The paper has also a short survey flavor from a “failure-tolerant broadcast abstractions” point of view.
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Notes
- 1.
“Disjoint” means that the only vertices (processes) shared by any two of these paths are their first and last processes.
- 2.
Actually total order broadcast and consensus are equivalent problems in the sense any of them can be solved on top of the other one [6].
- 3.
An application message is a message sent by the reliable broadcast abstraction, while a protocol message is a message used to implement reliable broadcast.
- 4.
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Acknowledgments
The authors thank the reviewers for their constructive comments. This work was partially supported by the French ANR projects DESCARTES (16-CE40-0023-03) devoted to layered and modular structures in distributed computing, and ByBLosS (20-CE25-0002-01) devoted to the design of modular building blocks for large-scale trustless multi-users applications.
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Raynal, M., Cao, J. (2021). From Incomplete to Complete Networks in Asynchronous Byzantine Systems. In: Barolli, L., Woungang, I., Enokido, T. (eds) Advanced Information Networking and Applications. AINA 2021. Lecture Notes in Networks and Systems, vol 225. Springer, Cham. https://doi.org/10.1007/978-3-030-75100-5_10
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