## 1 Introduction  
Blockchain provides a high level of security as a distributed database technology [1, 2]. Operating within a Peer-to-Peer (P2P) network, it involves nodes with various roles and purposes participating in the network [3]. Blockchain offers the advantage of storing transactions between nodes within each node's distributed ledger, enhancing resistance to malicious attacks and making it nearly impervious to unauthorized alterations of stored transaction information [4]. It has been widely adopted in various cryptocurrencies, including Bitcoin, due to these security features [5]. Beyond cryptocurrencies, blockchain is utilized in diverse sectors like gaming, healthcare, smart factories, and ID cards. There is ongoing research to expand its applications to emerging domains, including metaverses and NFTs [3, 6, 7]. Blockchain can be broadly categorized into three types, depending on the purpose of the operating network and the roles of the participating nodes [5]. A public blockchain is an open blockchain where anyone can participate as a node in the blockchain network [8]. The nodes that participate in the network share the results with respect to the generated transactions. On the other hand, a private blockchain involves only authorized nodes from institutions and organizations. Therefore, private blockchains exhibit higher levels of trustworthiness compared to public blockchains [6]. However, opinions exist suggesting that this authorization by institutions and organizations actually undermines the decentralization of the blockchain. Lastly, there is the concept of a hybrid blockchain. A hybrid blockchain combines features of both public and private blockchains. It requires permission for significant transactions or cryptocurrencies, while making other data public. As a result, a hybrid blockchain can limit anonymity compared to private blockchains, but it maintains security through data anonymity. However, private blockchains require network access permissions to participate, which some argue compromises decentralization. Blockchain employs consensus algorithms. This is intended to maintain an agreed-upon state among multiple participants in a distributed environment and to maintain consistent data. Consensus algorithms ensure network synchronization and reliability as numerous nodes simultaneously validate transaction information and generate new blocks. Each blockchain utilizes a consensus algorithm suited to its network to determine, store, and manage identical transactions. Among these, private blockchains restrict network participation to pre-authorized nodes and may adopt non-competitive consensus algorithms due to the absence of mining rewards. PBFT (Practical Byzantine Fault Tolerance) is a prominent non-competitive consensus algorithm [9]. Employing a voting-based approach results in less wastage of computational resources compared to competitive consensus algorithms. With the participation of all network nodes in the consensus process, PBFT achieves a high degree of reliability, enabling consensus completion even in the presence of up to 33% malicious nodes. However, PBFT has a drawback in terms of scalability, as its time complexity when the number of nodes participating in the blockchain network is denoted as \(n\) is \(O(n^{2})\)[5]. Scalability is a critical factor determining the performance and reliability of blockchain networks, especially in handling diverse and large volumes of transactions. Consequently, many research endeavors are currently in progress to enhance both the reliability and scalability of PBFT [10; 11; 12; 13]. To address the scalability issues of typical PBFT, there are several methods: forming smaller groups and conducting consensus within these groups, utilizing trust scores in PBFT where representative nodes with high trust scores participate in the consensus, and employing multi-layered structures to establish efficient blockchain networks.