Consensus Under Adversary Majority Done Right

2024-11-03

IACR Cryptology ePrint Archive

AI Summary

This work addresses the safety and liveness boundaries of Byzantine consensus under majority adversarial control. We systematically model client behavior (active/sleeping, communicating/silent) and validator behavior (active/sleeping), jointly with network synchrony, yielding the first four-dimensional (2×2×2×2) model space that exhaustively characterizes feasibility and impossibility across all 16 behavioral-synchrony combinations. Using formal analysis, tight bound proofs, and constructive protocol design, we unify prior results and resolve several open theoretical questions. We establish matching feasibility and impossibility theorems for each model instance and design novel protocols that realize all feasible cases. Our framework provides the first foundational classification and rigorous theoretical foundation for designing resilient consensus protocols under heterogeneous participant behavior and partial synchrony.

Technology Category

• Multiagent Systems: Multiagent Systems under Uncertainty
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Game Theory and Economic Paradigms: Behavioral Game Theory

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

A specter is haunting consensus protocols -- the specter of adversary majority. Dolev and Strong in 1983 showed an early possibility for up to 99% adversaries. Yet, other works show impossibility results for adversaries above 50% under synchrony, seemingly the same setting as Dolev and Strong's. What gives? It is high time that we pinpoint a key culprit for this ostensible contradiction: the modeling details of clients. Are the clients sleepy or always-on? Are they silent or communicating? Can validators be sleepy too? We systematize models for consensus across four dimensions (sleepy/always-on clients, silent/communicating clients, sleepy/always-on validators, and synchrony/partial-synchrony), some of which are new, and tightly characterize the achievable safety and liveness resiliences with matching possibilities and impossibilities for each of the sixteen models. To this end, we unify folklore and earlier results, and fill gaps left in the literature with new protocols and impossibility theorems.

Problem

• Consensus under adversary majority
• Modeling client behavior variations
• Unifying folklore and prior results

Innovation

• Systematized four-dimensional consensus models
• Introduced new protocols for safety resilience
• Established matching impossibility theorems