## 1 Introduction
PBFT operates in an asynchronous environment and overcomes the efficiency limitations of the original Byzantine fault-tolerant algorithms, reducing the algorithmic complexity from exponential to polynomial levels, making it suitable for practical system applications. PBFT ensures that the system can achieve consensus and maintain security and correctness even in the presence of up to \(f\) malicious nodes, where \(f\) is at most one-third of the total number of nodes (n) in the network. Since the introduction of the blockchain concept in 2008, PBFT has found widespread application as a consensus algorithm in consortium and private blockchains. It offers higher security and faster execution speed than the traditional BFT algorithm when Byzantine failures are present. However, in real-world scenarios, distributed systems often have tree-like structures rather than star-like structures like PBFT assumes. Recognizing this limitation, [PERSON] et al., proposed HBFT (Hierarchical Byzantine Fault Tolerance) in 2017, specifically designed for tree-structured distributed systems. HBFT introduces algorithms with upper bounds based on the depth and breadth of Byzantine nodes. It addresses the challenges of applying existing Byzantine systems to tree-structured distributed systems while reducing significant computational and storage resource requirements. HBFT offers significant advantages in terms of space complexity but introduces increased complexity in MAC (Message Authentication Code) computation, impacting the overall system performance. Additionally, HBFT continues to use PBFT's view-change protocol for leader node replacement, which means that Byzantine nodes can only be replaced after consensus has been reached. This can lead to reduced consensus algorithm performance when faced with a large influx of message traffic, and therefore, it is a consideration that needs to be addressed. Overall, considering the limitations and potential impact on performance, it is important to carefully assess the choice of consensus algorithm, whether PBFT or HBFT, depending on the specific characteristics of the distributed system and its intended use case. This problem is classified under CFT, which stands for Crash Fault Tolerance. In CFT, nodes are assumed to only experience crash faults, meaning they may fail or crash but will not exhibit Byzantine faults like sending false information or executing incorrect operations. CFT algorithms focus on handling node crash faults and ensuring that the system can continue to function properly and maintain consensus in the event of such failures. These algorithms assume that as long as a majority of honest nodes are still operational, consensus can be achieved, and the system's security can be maintained. In such cases, algorithms like Paxos or RAFT are commonly used as consensus algorithms, as well as other variants based on the principles of the original consensus algorithms. RAFT, proposed by [PERSON] et al., in 2014, is an improvement over the Paxos algorithm [4]. Compared to Paxos, RAFT offers a simpler and more understandable design, making it easier to implement. It addresses the problem of effective consensus implementation in blockchain networks where the malicious behavior of nodes is not a concern, making it highly relevant and valuable for research purposes. Due to the higher security requirements in specific application scenarios, the RAFT algorithm has found widespread application in private blockchains. However, it can also be used in combination with other algorithms to cater to different types of blockchains. The flexibility and compatibility of the RAFT algorithm in non-Byzantine environments contribute to its wide adoption and significance in blockchain consensus research. Nonetheless, it is unfortunate that the RAFT algorithm cannot adapt to blockchains with lower security requirements.