Abstract

Practical Byzantine Fault Tolerance (PBFT) consensus mechanism shows a great potential to break the performance bottleneck of the Proof-of-Work (PoW)-based blockchain systems, which typically support only dozens of transactions per second and require minutes to hours for transaction confirmation. However, due to frequent inter-node communications, PBFT mechanism has a poor node scalability and thus it is typically adopted in small networks. To enable PBFT in large systems such as massive Internet of Things (IoT) ecosystems and blockchain, in this article, a scalable multi-layer PBFT-based consensus mechanism is proposed by hierarchically grouping nodes into different layers and limiting the communication within the group. We first propose an optimal double-layer PBFT and show that the communication complexity is significantly reduced. Specifically, we prove that when the nodes are evenly distributed within the sub-groups in the second layer, the communication complexity is minimized. The security threshold is analyzed based on faulty probability determined (FPD) and faulty number determined (FND) models, respectively. We also provide a practical protocol for the proposed double-layer PBFT system. Finally, the results are extended to arbitrary-layer PBFT systems with communication complexity and security analysis. Simulation results verify the effectiveness of the analytical results.