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Expected linear round synchronization: the missing link for linear Byzantine SMR

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Abstract

State Machine Replication (SMR) solutions often divide time into rounds, with a designated leader driving decisions in each round. Progress is guaranteed once all correct processes synchronize to the same round, and the leader of that round is correct. Recently suggested Byzantine SMR solutions such as HotStuff, and LibraBFT achieve progress with a linear message complexity and a constant time complexity once such round synchronization occurs. But round synchronization itself incurs an additional cost. By Dolev and Reischuk’s lower bound, any deterministic solution must have \(\Omega (n^2)\) communication complexity. Yet the question of randomized round synchronization with an expected linear message complexity remained open. We present an algorithm that, for the first time, achieves round synchronization with expected linear message complexity and expected constant latency. Existing protocols can use our round synchronization algorithm to solve Byzantine SMR with the same asymptotic performance.

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Acknowledgements

Oded Naor is grateful to the Azrieli Foundation for the award of an Azrieli Fellowship, and to the Technion Hiroshi Fujiwara CyberSecurity Research Center for providing a research grant.

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  1. Technion, Haifa, Israel

    Oded Naor & Idit Keidar

  2. StarkWare, Netanya, Israel

    Oded Naor

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  1. Oded Naor
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Naor, O., Keidar, I. Expected linear round synchronization: the missing link for linear Byzantine SMR. Distrib. Comput. 37, 19–33 (2024). https://doi.org/10.1007/s00446-023-00459-9

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