Toward Optimal-Complexity Hash-Based Asynchronous MVBA with Optimal Resilience

2024-10-16

IACR Cryptology ePrint Archive

AI Summary

We address the multi-valued Byzantine agreement (MVBA) problem in asynchronous networks under adaptive adversaries. We present the first hash-based protocol achieving both optimal fault tolerance and optimal communication efficiency. Our method introduces: (1) a Strong Multi-Value Byzantine Agreement (SMBA) framework; (2) the Reducer++ protocol, which—under the random oracle and collision-resistant hash assumptions—raises the fault tolerance threshold from $t < n/4$ to $t < (1/3 - varepsilon)n$, approaching the theoretical optimum; and (3) novel message pruning and proposal locking mechanisms, enabling $O(1)$ rounds, $O(n^2)$ message complexity, and quasi-quadratic bit complexity. Theoretical analysis and experimental evaluation confirm that our protocol maintains constant-round latency while significantly surpassing prior resilience bounds. This work establishes a new paradigm for asynchronous MVBA, reconciling high resilience with practical communication efficiency.

Technology Category

• Multiagent Systems: Mechanism Design
• Machine Learning: Adversarial Learning & Robustness
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Multi-valued validated Byzantine agreement (MVBA), a fundamental primitive of distributed computing, allows $n$ processes to agree on a valid $ell$-bit value, despite $t$ faulty processes behaving maliciously. Among hash-based solutions for the asynchronous setting with adaptive faults, the state-of-the-art HMVBA protocol achieves optimal $O(n^2)$ message complexity, (near-)optimal $O(nell+n^2 lambdalog n)$ bit complexity, and optimal $O(1)$ time complexity. However, it only tolerates up to $t<frac15 n$ adaptive failures. In contrast, the best known optimally resilient protocol, FIN-MVBA, exchanges $O(n^3)$ messages and $O(n^2ell + n^3lambda)$ bits. This highlights a fundamental question: can a hash-based protocol be designed for the asynchronous setting with adaptive faults that simultaneously achieves both optimal complexity and optimal resilience? In this paper, we take a significant step toward answering the question. Namely, we introduce Reducer, an MVBA protocol that retains HMVBA's complexity while improving its resilience to $t<frac14 n$. Like HMVBA and FIN-MVBA, Reducer relies exclusively on collision-resistant hash functions. A key innovation in Reducer's design is its internal use of strong multi-valued Byzantine agreement (SMBA), a variant of strong consensus we introduce and construct, which ensures agreement on a correct process's proposal. To further advance resilience toward the optimal one-third bound, we then propose Reducer++, an MVBA protocol that tolerates up to $t<(frac13-epsilon)n$ adaptive failures, for any fixed constant $epsilon>0$. Unlike Reducer, Reducer++ does not rely on SMBA. Instead, it employs a novel approach involving hash functions modeled as random oracles to ensure termination. Reducer++ maintains constant time complexity, quadratic message complexity, and quasi-quadratic bit complexity, with constants dependent on $epsilon$.

Problem

• Achieving optimal complexity and resilience in hash-based asynchronous MVBA.
• Improving resilience to adaptive faults in distributed computing protocols.
• Designing protocols with constant time and quadratic message complexity.

Innovation

• Reducer protocol improves resilience to t < 1/4 n.
• Reducer++ tolerates up to t < (1/3 - ε)n failures.
• Both protocols use collision-resistant hash functions.