I. Introduction
The adoption of the practical Byzantine fault tolerance (PBFT) protocol in blockchain systems, as a viable alternative to the traditional proof of work, has primarily been motivated by the need to enhance transaction throughput and minimize energy consumption [1]. Nevertheless, PBFT encounters a notable performance limitation stemming from its quadratic communication complexity and resource demands [2]. To address this issue, recent PBFT protocol variants have been devised. Notable among them is HotStuff [3], which achieves a linear message complexity of by leveraging threshold signatures [4]. However, it is crucial to note that the performance of these variants experiences a linear decline as the number of replicas increases, especially in the presence of failures [5]. This can be attributed to linear consensus operations that rely on the entire replica set, particularly when encountering a growing number of replicas. Consequently, a significant challenge lies in the limited scalability of recent PBFT variants due to their architecture based on single full set consensus (C1).