Amortized Asynchronous Byzantine Reliable Broadcast with Optimal Resilience

TL;DR

This paper introduces an amortized multi-shot asynchronous Byzantine Reliable Broadcast protocol that achieves optimal resilience and communication complexity by structuring broadcast across multiple rounds.

Contribution

It presents a novel amortization technique for asynchronous BRB that maintains optimal resilience and reduces message complexity with a multi-round approach.

Findings

Achieves asymptotic optimal $O(n|m|)$ message complexity for large messages.

Maintains $f=rac{n}{3}$ resilience in asynchronous networks.

Reduces round complexity to $ ext{O}(1)$ under favorable conditions.

Abstract

Byzantine Reliable Broadcast (BRB) is a fundamental primitive in distributed computing and cryptographic systems. Reducing the communication complexity of BRB protocols remains an important research direction. However, most work focuses on synchronous networks, with limited attention to the more challenging setting of network \textit{asynchrony}. Achieving sub-quadratic communication for asynchronous BRB typically requires probabilistic approaches that sacrifice optimal $f=\frac{n}{3}$ resilience. In this work, we present a multi-shot BRB algorithm for asynchronous networks that maintains optimal resilience through an underutilized technique: \textit{amortization}. Our protocol structures BRB across multiple rounds, where each round provides incremental additive guarantees. Once these initial rounds complete, each subsequent BRB instance requires only a single additional round. This amortization strategy achieves asymptotic optimal $O(n|m|)$ message complexity when messages are sufficiently large, with $\Omega(n)$ round complexity in the worst case. Under favorable conditions, an optimistic delivery path reduces the round complexity to $\Omega(1)$.