Revisiting Optimal Resilience of Fast Byzantine Consensus (Extended Version)

TL;DR

This paper introduces a fast Byzantine consensus algorithm that achieves optimal resilience with fewer processes than previously thought, specifically requiring only 5f-1 processes, and proves this bound is tight.

Contribution

It presents a new fast Byzantine consensus algorithm with 5f-1 processes and establishes this as the tight lower bound, correcting previous misconceptions.

Findings

Achieves two-message delay consensus in the common case

Requires 5f-1 processes for f Byzantine faults

Proves 5f-1 is the tight lower bound for process count

Abstract

It is a common belief that Byzantine fault-tolerant solutions for consensus are significantly slower than their crash fault-tolerant counterparts. Indeed, in PBFT, the most widely known Byzantine fault-tolerant consensus protocol, it takes three message delays to decide a value, in contrast with just two in Paxos. This motivates the search for fast Byzantine consensus algorithms that can produce decisions after just two message delays \emph{in the common case}, e.g., under the assumption that the current leader is correct and not suspected by correct processes. The (optimal) two-step latency comes with the cost of lower resilience: fast Byzantine consensus requires more processes to tolerate the same number of faults. In particular, $5f+1$ processes were claimed to be necessary to tolerate $f$ Byzantine failures. In this paper, we present a fast Byzantine consensus algorithm that relies on just $5f-1$ processes. Moreover, we show that $5f-1$ is the tight lower bound, correcting a mistake in the earlier work. While the difference of just $2$ processes may appear insignificant for large values of $f$, it can be crucial for systems of a smaller scale. In particular, for $f=1$, our algorithm requires only $4$ processes, which is optimal for any (not necessarily fast) partially synchronous Byzantine consensus algorithm.