Byzantine Consensus is \Theta(n^2): The Dolev-Reischuk Bound is Tight even in Partial Synchrony! [Extended Version]

TL;DR

This paper introduces SQuad, a partially synchronous Byzantine consensus protocol with quadratic communication complexity, matching the theoretical lower bound, and achieves optimal resilience and linear latency, closing a longstanding gap in the field.

Contribution

The paper presents SQuad, the first partially synchronous Byzantine consensus protocol with quadratic communication complexity, and introduces RareSync, a novel view synchronization protocol with similar efficiency.

Findings

SQuad achieves quadratic worst-case communication complexity.

RareSync provides quadratic communication and linear latency for view synchronization.

SQuad is optimally resilient and has linear worst-case latency.

Abstract

The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic communication complexity in the worst case. While it has been shown that the bound is tight in synchronous environments, it is still unknown whether a consensus protocol with quadratic communication complexity can be obtained in partial synchrony. Until now, the most efficient known solutions for Byzantine consensus in partially synchronous settings had cubic communication complexity (e.g., HotStuff, binary DBFT). This paper closes the existing gap by introducing SQuad, a partially synchronous Byzantine consensus protocol with quadratic worst-case communication complexity. In addition, SQuad is optimally-resilient and achieves linear worst-case latency complexity. The key technical contribution underlying SQuad lies in the way we solve view synchronization, the problem of bringing all correct processes to the same view with a correct leader for sufficiently long. Concretely, we present RareSync, a view synchronization protocol with quadratic communication complexity and linear latency complexity, which we utilize in order to obtain SQuad.