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Atomic Register Abstractions for Byzantine-Prone Distributed Systems

Authors Vincent Kowalski , Achour Mostéfaoui , Matthieu Perrin

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Author Details

Vincent Kowalski
  • LS2N, Nantes Université, France
Achour Mostéfaoui
  • LS2N, Nantes Université, France
Matthieu Perrin
  • LS2N, Nantes Université, France

Funding

ByBloS ANR project (ANR-20-CE25-0002): "BeYond BLockchainS, Modular Building Blocks for Large-Scale Trustless Multi-users Apps". PricLeSS Project, funded by the COMINLabs Labex Project (ANR-10-LABX-0007): "Privacy-Conscious Legally-Sound blockchain Storage".

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Vincent Kowalski, Achour Mostéfaoui, and Matthieu Perrin. Atomic Register Abstractions for Byzantine-Prone Distributed Systems. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 35:1-35:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.OPODIS.2023.35

Abstract

The construction of the atomic register abstraction over crash-prone asynchronous message-passing systems has been extensively studied since the founding work of Attiya, Bar-Noy, and Dolev. It has been shown that t < n/2 (where t is the maximal number of processes that may be faulty) is a necessary and sufficient requirement to build an atomic register. However, little attention has been paid to systems where faulty processes may exhibit a Byzantine behavior. This paper studies three definitions of linearizable single-writer multi-reader registers encountered in the state of the art: Read/Write registers whose read perations return the last written value, Read/Write-Increment registers whose read perations return both the last written value and the number of previously written values, and Read/Append registers whose read perations return the sequence of all previously written values. More specifically, it compares their computing power and the necessary and sufficient conditions on the maximum ratio t/n which makes it possible to build reductions from one register to another. Namely, we prove that t < n/3 is necessary and sufficient to implement a Read/Write-Increment register from Read/Write registers whereas this bound is only t < n/2 for a reduction from a Read/Append register to Read/Write-Increment registers. Reduction algorithms meeting these bounds are also provided.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Software and its engineering → Process synchronization
  • Computer systems organization → Dependable and fault-tolerant systems and networks
Keywords
  • Byzantine processes
  • Concurrent Object
  • Linearizability
  • Shared Register

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References

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