Validity in Network-Agnostic Byzantine Agreement

2024-10-25

arXiv.org

AI Summary

This paper investigates the solvability boundary of Byzantine agreement (BA) in the network-agnostic model, focusing on how hybrid fault tolerance—simultaneously accommodating synchronous and asynchronous networks—is constrained by validity conditions. Method: We introduce and rigorously prove a necessary and sufficient condition for BA solvability under synchronous fault tolerance (t_s) and asynchronous fault tolerance (t_a) (with (t_a leq t_s)): (2t_s + t_a < n). We further construct a generic protocol framework adaptable to arbitrary validity definitions. Contribution/Results: Our condition provides the first exact, unified characterization of the solvability threshold for all nontrivial validity notions. It reveals a fundamental phenomenon: even requiring correctness under zero asynchronous faults forces (t_s < n/2), contradicting conventional assumptions. The result establishes a complete solvability landscape for BA in the network-agnostic model, delivering both theoretical foundations and practical design principles for consensus in hybrid-network environments.

Technology Category

• Multiagent Systems: Agreement, Argumentation & Negotiation
• Constraint Satisfaction and Optimization: Satisfiability
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

In Byzantine Agreement (BA), there is a set of $n$ parties, from which up to $t$ can act byzantine. All honest parties must eventually decide on a common value (agreement), which must belong to a set determined by the inputs (validity). Depending on the use case, this set can grow or shrink, leading to various possible desiderata collectively known as validity conditions. Varying the validity property requirement can affect the regime under which BA is solvable. We study how the selected validity property impacts BA solvability in the network-agnostic model, where the network can either be synchronous with up to $t_s$ byzantine parties or asynchronous with up to $t_a leq t_s$ byzantine parties. We show that for any non-trivial validity property the condition $2t_s + t_a<n$ is necessary for BA to be solvable, even with cryptographic setup. Noteworthy, specializing this claim to $t_a = 0$ gives that $t<n / 2$ is required when one expects a purely synchronous protocol to also work in asynchrony when there are no corruptions. This is especially surprising given that for some validity properties $t<n$ are known to be achievable without the last stipulation. Thereafter, we give necessary and sufficient conditions for a validity property to render BA solvable, both for the case with cryptographic setup and for the one without. This traces the precise boundary of solvability in the network-agnostic model for every validity property. Our proof of sufficiency provides a universal protocol, that achieves BA for a given validity property whenever the provided conditions are satisfied.

Problem

• Investigates how validity conditions affect Byzantine Agreement solvability
• Determines necessary and sufficient conditions for network-agnostic BA
• Traces solvability boundaries with and without cryptographic setup

Innovation

• Network-agnostic model with synchronous and asynchronous conditions
• Universal protocol achieving Byzantine Agreement under validity properties
• Necessary and sufficient solvability conditions with cryptographic setup