On Quorum Sizes in DAG-Based BFT Protocols

2025-04-10

AI Summary

This work investigates the correctness boundaries and scalability benefits of DAG-based asynchronous Byzantine Fault Tolerant (BFT) protocols—specifically DAG-Rider, Tusk, and Bullshark—under the minimal node count of $2f+1$. Method: Using formal distributed consensus modeling and probabilistic termination analysis, we rigorously examine safety and liveness guarantees under asynchrony. Contribution/Results: We establish, for the first time, that DAG-Rider remains both safe and live under $2f+1$ nodes, whereas asynchronous variants of Tusk and Bullshark fundamentally require $3f+1$ nodes—safety collapses below this threshold. Furthermore, quantitative analysis reveals that expected termination time exhibits diminishing returns beyond $3f+1$ nodes, saturating rapidly. This work systematically characterizes the fundamental trade-offs among quorum size, protocol correctness, and performance in DAG-BFT systems, providing critical theoretical foundations and practical guidance for protocol design and deployment.

Technology Category

• Multiagent Systems: Other Foundations of Multi Agent Systems
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Several prominent DAG-based blockchain protocols, such as DAG-Rider, Tusk, and Bullshark, completely separate between equivocation elimination and committing; equivocation is handled through the use of a reliable Byzantine broadcast black-box protocol, while committing is handled by an independent DAG-based protocol. With such an architecture, a natural question that we study in this paper is whether the DAG protocol would work when the number of nodes (or validators) is only $2f+1$ (when equivocation is eliminated), and whether there are benefits in working with larger number of nodes, i.e., a total of $kf+1$ nodes for $k>3$. We find that while DAG-Rider's correctness is maintained with $2f+1$ nodes, the asynchronous versions of both Tusk and Bullshark inherently depends on having $3f+1$ nodes, regardless of equivocation. We also explore the impact of having larger number of nodes on the expected termination time of these three protocols.

Problem

• Study DAG-based BFT protocols with minimal node count (2f+1).
• Compare protocol performance across different node sizes (kf+1).
• Analyze termination time impact of increased node numbers.

Innovation

• Uses DAG-based BFT protocols for committing
• Relies on reliable Byzantine broadcast protocol
• Explores node count impact on termination time