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Signature-free asynchronous Byzantine systems: from multivalued to binary consensus with \(t<n/3\), \(O(n^2)\) messages, and constant time

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Abstract

This paper presents a new algorithm that reduces multivalued consensus to binary consensus in an asynchronous message-passing system made up of n processes where up to t may commit Byzantine failures. This algorithm has the following noteworthy properties: it assumes \(t<n/3\) (and is consequently optimal from a resilience point of view), uses \(O(n^2)\) messages, has a constant time complexity, and uses neither signatures nor additional computational power (such as random numbers, failure detectors, additional scheduling assumption, or additional synchrony assumption). The design of this reduction algorithm relies on two new all-to-all communication abstractions. The first one allows the non-faulty processes to reduce the number of proposed values to c, where c is a small constant. The second communication abstraction allows each non-faulty process to compute a set of (proposed) values satisfying the following property: if the set of a non-faulty process is a singleton containing value v, the set of any non-faulty process contains v. Both communication abstractions have an \(O(n^2)\) message complexity and a constant time complexity. The reduction of multivalued Byzantine consensus to binary Byzantine consensus is then a simple sequential use of these communication abstractions. To the best of our knowledge, this is the first asynchronous message-passing algorithm that reduces multivalued consensus to binary consensus with \(O(n^2)\) messages and constant time complexity (measured with the longest causal chain of messages) in the presence of up to \(t<n/3\) Byzantine processes, and without using cryptography techniques. Moreover, this reduction algorithm uses a single instance of the underlying binary consensus, and tolerates message re-ordering by Byzantine processes.

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Notes

  1. Directing the non-faulty processes to decide a predefined default value—instead of an arbitrary value, possibly proposed only by faulty processes—in specific circumstances, is close to the notion of an abortable object as defined in [17, 36] where an operation is allowed to abort in the presence of concurrency. This notion of an abortable object is different from the notion of a query-abortable object introduced in [1].

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Acknowledgments

We want to thank the referees for their constructive comments. This work has been partially supported by the Franco-German ANR project DISCMAT devoted to connections between mathematics and distributed computing.

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Authors and Affiliations

  1. LINA, Université de Nantes, 44322, Nantes Cedex, France

    Achour Mostéfaoui

  2. Institut Universitaire de France, Paris, France

    Michel Raynal

  3. IRISA, Université de Rennes, 35042, Rennes Cedex, France

    Michel Raynal

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  1. Achour Mostéfaoui
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  2. Michel Raynal
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Correspondence to Michel Raynal.

Additional information

An extended abstract of this paper appeared in SIROCCO 2015 [29].

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Mostéfaoui, A., Raynal, M. Signature-free asynchronous Byzantine systems: from multivalued to binary consensus with \(t<n/3\), \(O(n^2)\) messages, and constant time. Acta Informatica 54, 501–520 (2017). https://doi.org/10.1007/s00236-016-0269-y

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