Hierarchical Byzantine fault-tolerance protocol for permissioned blockchain systems

Emerging blockchain technology has introduced a new challenge to the distributed system research: Can Byzantine fault-tolerance protocols scale up to, for example, hundreds of nodes? In this work, we introduce HiBFT, a hierarchical Byzantine fault-tolerance protocol to address the problem. The core idea is to divide replicas into groups and exchange consensus messages among groups, thus avoiding the necessity of message broadcasting. The motivation for such approach bases on the hierarchical property of network architecture in permissioned block chains, our target deployments. HiBFT works very much in the same way as the classical Practical Byzantine Fault-Tolerance protocol. However, it replaces the concept of physical replica with a logical one that represents a replica group. As such, protocol message complexity can be reduced from O(N2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(N^2)$$\end{document} to O(s2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(s^2)$$\end{document} where N and s are the total number of replicas and the number of groups. Additionally, using threshold signature scheme for representing a logical group results in two important improvements: The cost of signature verification is significantly reduced at each replica; blocks can be secured more effectively in terms of signature size. Our protocol guarantees safety and liveness under partially synchronous assumption with a correctness proof. Our experiment results show that the protocol can scale up to hundred of nodes.