[Paper Review] Good-case Latency of Byzantine Broadcast: A Complete Categorization

Ittai Abraham, Kartik Nayak+2 more|arXiv (Cornell University)|Feb 14, 2021

Distributed systems and fault tolerance28 references6 citations

TL;DR

This paper provides a complete characterization of good-case latency in Byzantine fault-tolerant broadcast across synchronous, partially synchronous, and asynchronous models in the authenticated setting. It introduces a new protocol formulation—partially synchronous Byzantine broadcast (psync-BB)—and establishes tight bounds, showing that 2-round good-case latency is achievable if and only if 𝑛 ≥ 5𝑓 − 1, resolving long-standing ambiguities in BFT SMR protocol design and performance analysis.

ABSTRACT

This paper explores the problem good-case latency of Byzantine fault-tolerant broadcast, motivated by the real-world latency and performance of practical state machine replication protocols. The good-case latency measures the time it takes for all non-faulty parties to commit when the designated broadcaster is non-faulty. We provide a complete characterization of tight bounds on good-case latency, in the authenticated setting under synchrony, partial synchrony and asynchrony. Some of our new results may be surprising, e.g., 2-round PBFT-style partially synchronous Byzantine broadcast is possible if and only if $n\geq 5f-1$, and a tight bound for good-case latency under $n/3

Motivation & Objective

• To formally define and analyze good-case latency in Byzantine broadcast, focusing on the scenario where the designated broadcaster is non-faulty.
• To close the gap between theoretical bounds and practical performance in BFT state machine replication (BFT SMR), where good-case latency (under honest leader) is more relevant than worst-case.
• To propose a new broadcast abstraction—partially synchronous Byzantine broadcast (psync-BB)—that better models single-shot BFT SMR protocols like PBFT.
• To provide a tight, complete categorization of good-case latency across all resilience thresholds (𝑓 < 𝑛/3, 𝑛/3 ≤ 𝑓 < 𝑛/2, 𝑓 ≥ 𝑛/2) and timing models (synchronous, partially synchronous, asynchronous).

Proposed method

• Introduces a new broadcast primitive, partially synchronous Byzantine broadcast (psync-BB), to model single-shot BFT SMR with leader-based consensus.
• Establishes lower and upper bounds for good-case latency under three timing models: synchrony, partial synchrony, and asynchrony, using formal reductions and protocol constructions.
• Uses a refined timing model distinguishing between actual message delay 𝛿 and known upper bound Δ, and considers both synchronized and unsynchronized protocol start models.
• Constructs a novel 2-round protocol for psync-BB under 𝑛 ≥ 5𝑓 − 1, achieving optimal good-case latency of Δ + 1.5𝛿 in the synchronous model.
• Applies a sampling-based optimization to reduce communication cost while preserving near-optimal latency in practice.
• Proves tight lower bounds via reductions from known impossibility results and adversarial simulation, particularly in the asynchronous and partially synchronous settings.

Experimental results

Research questions

• RQ1 What is the tight lower bound on good-case latency for Byzantine broadcast under partial synchrony, and how does it depend on the resilience threshold?
• RQ2 Can a 2-round good-case protocol exist for partially synchronous Byzantine broadcast when 𝑛 < 5𝑓 − 1, and if not, what is the minimal number of rounds required?
• RQ3 How does the good-case latency in the synchronous model vary with the resilience threshold, particularly when 𝑓 > 𝑛/3?
• RQ4 What is the fundamental trade-off between communication complexity and good-case latency in optimal protocols?
• RQ5 How do the results change in the unauthenticated setting, and are the current lower bounds still tight?

Key findings

• For partially synchronous Byzantine broadcast (psync-BB), 2 rounds are necessary and sufficient for good-case latency if and only if 𝑛 ≥ 5𝑓 − 1.
• In the partially synchronous model, 3 rounds are necessary and sufficient when 3𝑓 + 1 ≤ 𝑛 < 5𝑓 − 1, resolving the optimality of PBFT’s 3-round good-case performance.
• In the synchronous model with 𝑛/3 < 𝑓 < 𝑛/2, the good-case latency is tightly bounded by Δ + 1.5𝛿, which is not an integer multiple of the delay bound Δ.
• For the honest-majority case (𝑓 < 𝑛/3), the good-case latency is exactly 2𝛿 in the synchronous model, matching the lower bound.
• In the dishonest-majority case (𝑓 ≥ 𝑛/2), the good-case latency is bounded below by (⌊𝑛/(𝑛−𝑓)⌋ − 1)Δ and upper bounded by 𝑂(𝑛/(𝑛−𝑓))Δ.
• The paper resolves a long-standing ambiguity in PBFT: when 𝑓 = 1, 2 rounds are sufficient (not 3), contradicting the common assumption that PBFT is optimal at 3 rounds.