On Quorum Sizes in DAG-Based BFT Protocols

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.