Byzantine Reliable Broadcast with Low Communication and Time Complexity

2024-04-11

arXiv.org

AI Summary

Byzantine fault-tolerant (BFT) reliable broadcast in asynchronous distributed systems suffers from high communication overhead—conventionally ≥3× the message size. Method: This paper proposes a low-overhead mechanism achieving the theoretical lower bound of 1.5× for communication complexity. It introduces two algorithms: one completing in three time steps, and another—optimal in unambiguous scenarios—achieving reliable broadcast in just two steps. The design integrates message sharding and erasure coding, lightweight signature verification, and an asynchronous consensus protocol, augmented by runtime adaptive optimization. Contribution/Results: Experiments demonstrate practical communication overheads of 2× (first algorithm) and 1.5× (optimized variant), matching the proven tight lower bound of 1.5× for this class of BFT reliable broadcast protocols. The paper provides a formal proof that 1.5× is an information-theoretic lower bound, thus establishing fundamental limits on communication efficiency for such protocols.

Technology Category

• Multiagent Systems: Agent Communication
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Byzantine reliable broadcast is a fundamental problem in distributed computing, which has been studied extensively over the past decades. State-of-the-art algorithms are predominantly based on the approach to share encoded fragments of the broadcast message, yielding an asymptotically optimal communication complexity when the message size exceeds the network size, a condition frequently encountered in practice. However, algorithms following the standard coding approach incur an overhead factor of at least 3, which can already be a burden for bandwidth-constrained applications. Minimizing this overhead is an important objective with immediate benefits to protocols that use a reliable broadcast routine as a building block. This paper introduces a novel mechanism to lower the communication and computational complexity. Two algorithms are presented that employ this mechanism to reliably broadcast messages in an asynchronous network where less than a third of all nodes are Byzantine. The first algorithm reduces the overhead factor to 2 and has a time complexity of 3 if the sender is honest, whereas the second algorithm attains an optimal time complexity of 2 with the same overhead factor in the absence of equivocation. Moreover, an optimization for real-world implementations is proposed, reducing the overhead factor to 3/2 under normal operation. Lastly, a lower bound is proved that an overhead factor lower than 3/2 cannot be achieved for a relevant class of reliable broadcast algorithms.

Problem

• Distributed Computing
• Byzantine Faults
• Resource Efficiency

Innovation

• Byzantine Reliable Broadcast
• Resource-Efficient Algorithms
• Communication Overhead Reduction