Amortized Asynchronous Byzantine Reliable Broadcast with Optimal Resilience

Byzantine Reliable Broadcast (BRB) is a fundamental primitive in distributed computing and cryptographic systems; reducing the communication cost of BRB thus remains an important research direction. However, most existing works either focus strictly on the synchronous network model or utilize computationally impractical erasure codes. Therefore, to achieve a practical yet network-robust algorithm, one must turn toward committee sampling techniques. However, Committee sampling techniques often forgo optimal resilience ($f<\lfloor \frac{n}{3}\rfloor$) in the face of asynchrony. This work produces two interesting results: Firstly, we propose a $\mathit{\text{randomly}}\mathit{\text{asynchronous}}$ BRB protocol that can achieve both optimal resilience and asymptotically optimal communication complexity ($O(n\mathrm{\mid }m\mathrm{\mid })$) through an underutilized technique: $\mathit{\text{amortization}}$; and does not utilize computationally expensive $\mathit{\text{erasure}}\mathit{\text{codes}}$. Next, we show that an optimally resilient BRB protocol utilizing sampled committees cannot exist in a $\mathit{\text{fully}}\mathit{\text{asynchronous}}$ network.