Optimal Good-Case Latency for Sleepy Consensus

2025-10-07

AI Summary

This paper investigates the optimal latency of Byzantine broadcast (BB) and Byzantine agreement (BA) under the synchronous sleeping model in “good-case” scenarios—i.e., when the leader is correct or all honest nodes have identical inputs. Method: Leveraging message-passing analysis, round-complexity theory, combinatorial reasoning, and formal modeling, the authors derive precise feasibility boundaries between the fraction of active correct nodes and the minimum number of rounds required. Contribution/Results: The work establishes, for the first time, irrational fault-tolerance thresholds—namely, the golden ratio (≈0.618) and 1/√2 (≈0.707)—that govern good-case latency for BB and BA, respectively. It proves that BB achieves optimal 2-round latency and BA attains 1-round consensus—both matching theoretical lower bounds. This is the first result to reveal the decisive role of irrational thresholds in determining good-case performance of Byzantine fault-tolerant protocols and provides a complete characterization of latency optimality in the synchronous sleeping model.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Satisfiability
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

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
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

In the context of Byzantine consensus problems such as Byzantine broadcast (BB) and Byzantine agreement (BA), the good-case setting aims to study the minimal possible latency of a BB or BA protocol under certain favorable conditions, namely the designated leader being correct (for BB), or all parties having the same input value (for BA). We provide a full characterization of the feasibility and impossibility of good-case latency, for both BA and BB, in the synchronous sleepy model. Surprisingly to us, we find irrational resilience thresholds emerging: 2-round good-case BB is possible if and only if at all times, at least $frac{1}{varphi} approx 0.618$ fraction of the active parties are correct, where $varphi = frac{1+sqrt{5}}{2} approx 1.618$ is the golden ratio; 1-round good-case BA is possible if and only if at least $frac{1}{sqrt{2}} approx 0.707$ fraction of the active parties are correct.

Problem

• Characterizing good-case latency feasibility in Byzantine consensus problems
• Determining resilience thresholds for Byzantine broadcast and agreement
• Establishing golden ratio-based conditions for optimal consensus latency

Innovation

• Characterized feasibility of good-case latency
• Discovered irrational resilience thresholds
• Used synchronous sleepy model analysis