Make Every Word Count: Adaptive BA with Fewer Words
Shir Cohen, Idit Keidar, Alexander Spiegelman
TL;DR
The paper addresses reducing communication in synchronous Byzantine Agreement under Byzantine faults by achieving an adaptive word complexity of $O(n(f+1))$ for Byzantine Broadcast when $0≤f≤t$ and by introducing a strong-BA protocol with linear cost in the failure-free case and quadratic cost otherwise. It achieves this by reducing Byzantine Broadcast to a weak-BA with unique validity and employing the quadratic-time BA of Momose and Ren as a building block for adaptive weak BA; threshold-signature schemes in a PKI enable batching signatures to a single word, enabling the $O(n(f+1))$ bound. The results establish the first adaptive BB with sub-quadratic word complexity and the first optimally resilient strong-BA with the stated costs, highlighting practical reductions in communication for common failure patterns. They also surface a framework combining reductions, weak-BA with external validity, and threshold cryptography that supports adaptive, efficient consensus and pave the way for later adaptive strong-BA work.
Abstract
Byzantine Agreement is a key component in many distributed systems. While Dolev and Reischuk have proven a long time ago that quadratic communication complexity is necessary for worst-case runs, the question of what can be done in practically common runs with fewer failures remained open. In this paper we present the first Byzantine Broadcast algorithm with $O(n(f+1))$ communication complexity, where $0\leq f\leq t$ is the actual number of process failures in a run. And for BA with strong unanimity, we present the first optimal-resilience algorithm that has linear communication complexity in the failure-free case and a quadratic cost otherwise.