A low communication complexity double-layer PBFT consensus

Based on blockchain technology, the Bitcoin and other cryptographic currencies have drawn great public attention recently. In addition to the soaring in finance sector, this technology has been emerged into various application scenarios from transportation, healthcare, entertainment, Internet of Things (IoT), etc. However, most popular blockchain systems with proof-of-work (PoW) as their consensus mechanism are faced with an extremely high latency, i.e. only tens of transactions can be accomplished in one second and it takes up to hours to confirm a transaction. Byzantine fault tolerance (BFT) enables a small network to reach consensus rapidly, yet the high inter-node communications degrade its scalability. To break the bottleneck of the communication complexity, we consider Practical Byzantine Fault Tolerance (PBFT) protocol and discuss a double-layer PBFT-based consensus mechanism in this chapter. The proposed mechanism re-distributes nodes into two layers in groups, where the members of the first layer act as the leader of each group in the second layer. We theoretically demonstrate that this double-layer PBFT significantly reduces the system communication complexity. It is also proved that the complexity is optimal when the nodes are evenly distributed in each group in the second layer. The security threshold is analyzed based on the faulty probability-determined (FPD) and the faulty number-determined (FND) models, respectively. Besides, a practical protocol for the proposed double-layer PBFT system is proposed