LRBFT: Improvement of practical Byzantine fault tolerance consensus protocol for blockchains based on Lagrange interpolation

Blockchain technology has aroused great interest from society and academia since the inception of Bitcoin. Its de-centralization and non-tampering can apply in broader scenarios, such as the Internet of Things, smart cities, and cloud computing. Among various core components, the consensus protocol is the core of maintaining blockchain networks’ performance, stability, and security. However, with the increase of network nodes and the improvement of network complexity, these properties are difficult to meet simultaneously. In this paper, we propose an advancement of the practical Byzantine consensus algorithm (LRBFT). The algorithm uses Lagrange interpolation that all backups can participate in to generate random seeds, uses the seeds to optimize the election process of the primary set, improves consensus efficiency through delegated nodes, and prevents the primary from doing evil through the supervisory mechanism. The generation of random seeds has the characteristics of full participation, unpredictability, and verifiability. The election process of the primary set has randomness, uniform distribution, and supervision. Furthermore, we proved the feasibility of our proposed algorithm through theoretical analysis and experimental evaluations. Experimental analysis shows that when there are 70 nodes in the practical Byzantine fault tolerance (PBFT) consensus protocol. If LRBFT selects only 7 nodes as delegated nodes, the time it takes for LRBFT to reach 100 consensuses is only 0.83% of that of PBFT.