Table of Contents
Blockchain is a new technology integrated with distributed storage, peer-to-peer (P2P) networking, consistency verification, consensus algorithm, cryptography, and other computer technologies . It uses blockchain data structure to verify and store data, uses a consensus algorithm to generate and update data, uses cryptography to ensure the security of data transmission and access, uses an intelligent contract composed of automatic script code to program and operate data, and realizes trusted data management in the incomplete trusted environment . Amongst them, the consensus algorithm is the core part of the blockchain, which directly affects the efficiency, security, and stability of the whole system. At this stage, blockchain is accelerating the development of the digital economy and is deeply integrated with real industries. However, selecting or designing an appropriate blockchain cross-chain consensus algorithm according to business needs is difficult for researchers and developers [3, 4].
Under the above background, reference  proposed a master-slave multichain blockchain consensus mechanism based on reputation, designed a two-layer blockchain structure to build a master-slave multichain mechanism, and connected multiple chains through the main blockchain. From the blockchain, the global consistency of digital assets is guaranteed, and the performance of the blockchain is improved. A reputation evaluation is introduced into the consensus mechanism based on proof of rights and interests, and a joint consensus mechanism integrating multiple consensus mechanisms is designed to ensure data consistency and tamper-proof modification. By generating dynamic verification nodes, the decentralization of nodes is ensured, and malicious attacks are prevented. The simulation experiment results show that this method has the advantage of high security in dealing with right smashing attacks and bribery attacks, but it has the problem of weak fault tolerance. Reference  proposed an efficient blockchain consensus algorithm based on directed acyclic graphs. The algorithm uses the directed acyclic graph data structure based on ID classification, which can reach a consensus more simply, and is suitable for multiple users to confirm transactions simultaneously. The experimental results show that the consensus algorithm can save a large amount of hardware resources and improve the transaction processing effect of the blockchain, but it has the problem of low throughput. At the system operation level, an adaptive controller together with fractional-order parameter adaptation laws is designed based on combining the parallel distributed compensation technique and the fractional Lyapunov stability theory to guarantee the Mittag-Leffler stability in the closed-loop system . Reference  presents a composite learning fuzzy control to synchronize two different uncertain incommensurate fractional-order time-varying delayed chaotic systems with unknown external disturbances and mismatched parametric uncertainties via the Takagi-Sugeno fuzzy method. An adaptive controller together with fractional-order composite learning laws is designed based on both a parallel distributed compensation technology and a fractional Lyapunov criterion. The boundedness of all variables in the closed-loop system and the Mittag-Leffler stability of tracking error can be guaranteed. Reference  proposed a high-reliability blockchain consensus mechanism based on contribution value and difficulty value. According to the node’s contribution value ranking, the nodes are assigned the corresponding proof of work (PoW) difficulty value, and the nodes then compete for the accounting rights through the PoW consensus mechanism. The consensus mechanism after the introduction of PoW respects the proof of capacity (PoC) contribution value ranking to the greatest extent. Thus, the node’s accounting block rate is highly proportional to its contribution value. At the system operation level, the accounting block rate is guaranteed to reach or infinitely approach 100%, which effectively solves the problem of system suspension caused by PoC. The PoW difficulty value distribution algorithm is designed from the perspectives of the node contribution value ranking, the value difference between adjacent contribution value nodes, and the grouping method. The rationality and the effectiveness of the difficulty value distribution algorithm are verified through experiments. The superiority and the feasibility of this scheme are verified through experiments, but when the nodes are many, this method has a certain time delay, and the real-time performance is poor.
The above discussion shows that despite many blockchain formulas proposed by related scholars, certain problems remain, such as excessive delay and low throughput. Each consensus algorithm has problems, which is also one of the main issues restricting the development of blockchain. Consensus algorithms are an important part of the blockchain. Improving the consensus algorithm in the blockchain is the most important link in improving the performance of the blockchain. Therefore, starting from improving throughput, reducing delay, and improving fault tolerance performance, this article proposes an improved method of the blockchain cross-chain consensus algorithm based on weighted PBFT and improves the blockchain consensus algorithm according to the blockchain use scenario.