Liveness and Latency of Byzantine State-Machine Replication (Extended Version)

TL;DR

This paper introduces a modular framework for designing Byzantine state-machine replication protocols that guarantees both safety and liveness, providing formal specifications, implementations, and analysis of latency and liveness proofs.

Contribution

It presents a novel modular framework with a formal SMR synchronizer primitive to ensure provable liveness in Byzantine SMR protocols.

Findings

Provided a formal specification and bounded-space implementation of the SMR synchronizer.

Applied the framework to analyze latency and prove liveness of existing protocols.

Delivered the first rigorous liveness proof for the core of PBFT.

Abstract

Byzantine state-machine replication (SMR) ensures the consistency of replicated state in the presence of malicious replicas and lies at the heart of the modern blockchain technology. Byzantine SMR protocols often guarantee safety under all circumstances and liveness only under synchrony. However, guaranteeing liveness even under this assumption is nontrivial. So far we have lacked systematic ways of incorporating liveness mechanisms into Byzantine SMR protocols, which often led to subtle bugs. To close this gap, we introduce a modular framework to facilitate the design of provably live and efficient Byzantine SMR protocols. Our framework relies on a view abstraction generated by a special SMR synchronizer primitive to drive the agreement on command ordering. We present a simple formal specification of an SMR synchronizer and its bounded-space implementation under partial synchrony. We also apply our specification to prove liveness and analyze the latency of three Byzantine SMR protocols via a uniform methodology. In particular, one of these results yields what we believe is the first rigorous liveness proof for the algorithmic core of the seminal PBFT protocol.