The view synchronization problem lies at the heart of many Byzantine Fault Tolerant (BFT) State Machine Replication (SMR) protocols in the partial synchrony model, since these protocols are usually based on views. Liveness is guaranteed if honest processors spend a sufficiently long time in the same view during periods of synchrony, and if the leader of the view is honest.
Ensuring that these conditions occur, known as Byzantine View Synchronization (BVS), has turned out to be the performance bottleneck of many BFT SMR protocols.

A recent line of work has shown that, by using an appropriate view synchronization protocol, BFT SMR protocols can achieve $O(n^2)$ communication complexity in the worst case after GST, thereby finally matching the lower bound established by Dolev and Reischuk in 1985. However, these protocols suffer from two major issues:
(a) When implemented so as to be optimistically responsive, even a single Byzantine processor may infinitely often cause $\Omega(n\Delta)$ latency between consecutive consensus decisions.
(b) Even in the absence of Byzantine action, infinitely many views require honest processors to send $\Omega(n^2)$ messages.

Here, we present Lumiere, an optimistically responsive BVS protocol which maintains optimal worst-case communication complexity while simultaneously addressing the two issues above: for the first time, Lumiere enables BFT consensus solutions in the partial synchrony setting that have $O(n^2)$ worst-case communication complexity, and that eventually always (i.e., except for a small constant number of “warmup” decisions) have communication complexity and latency which is linear in the number of actual faults in the execution.

Lumiere pdf, PODC 2024.

This is joint work with Dahlia Malkhi, Oded Naor, and Kartik Nayak.