Revisiting Optimal Resilience of Fast Byzantine Consensus

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 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, 5 + 1 processes were claimed to be necessary to tolerate Byzantine failures.In this paper, we present a fast Byzantine consensus algorithm that relies on just 5 − 1 processes. Moreover, we show that 5 − 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 , it can be crucial for systems of a smaller scale. In particular, for = 1, our algorithm requires only 4 processes, which is optimal for any (not necessarily fast) partially synchronous Byzantine consensus algorithm.

Basilic: Resilient Optimal Consensus Protocols With Benign and Deceitful Faults

“…These processes communicate in a partially synchronous network, meaning there is a known bound ∆ on the communication delay that will hold after an unknown Global Stabilization Time (GST) [22]. Processes communicate through standard all-to-all reliable and authenticated communication channels [27], meaning that messages can not be duplicated, forged or lost, but they can be reordered.…”

The Bedrock of Byzantine Fault Tolerance: A Unified Platform for BFT Protocol Design and Implementation

“…Leveraging hardware capabilities and using message-and-memory models has also been proposed to reduce the required number of replicas to 2 + 1 [14][15][16]. Increasing the number of replicas to 5 + 1 [173] (its proven lower bound, 5 − 1 [11,146]) or 7 + 1 [211], on the other hand, reduces the number of communication phases.…”

“…In the second phase of the protocol, matching messages from a quorum of 4 + 1 replicas are required. Recently, 5 − 1 has been proven as the lower bound for two-step (fast) Byzantine consensus [11,146]. The intuition behind the 5 −1 lower bound is that in an authenticated model, when replicas detect leader equivocation and initiate view-change, they do not include view-change messages coming from the malicious leader reducing the maximum number of faulty messages to − 1 [11,146].…”

“…Fab does not use authentication in its ordering stage, however, requires signatures for the view-change stage (design choice 11). Note that using authentication, 5 − 1 replicas is sufficient to reduce one phase of communication [11,146].…”

“…To achieve this, FLB uses the linearization and phase reduction through redundancy functions (design choices 1 and 2). FLB requires 5 − 1 replicas (following the lower bound results on fast Byzantine agreement [11,146]). The ordering stage of FLB is similar to the fast path of SBFT in terms of the linearity of communication and the number of phases.…”