From Few to Many Faults: Adaptive Byzantine Agreement with Optimal Communication

TL;DR

The paper addresses the challenge of reducing communication overhead in Byzantine Agreement across partially synchronous and asynchronous networks with Byzantine faults. It introduces a quorum-based strategy that runs BA on a small quorum and then disseminates the result via Quorum-to-All Broadcast (QAB), with different QAB implementations for asynchronous and partial-synchrony settings. Key contributions include a partial-synchrony BA with adaptive $O(n + t f)$ communication (for $t < n/3$), a lower bound $Ω(n + t^2)$ in asynchronous BA and a near-matching protocol $O((n + t^2)\log n)$ leveraging bipartite expanders, and a synchronous/partial-synchrony BA achieving $O(n + t f)$. A lower bound shows adaptive communication in asynchronous BA is infeasible, underscoring the near-optimality of the proposed schemes. The work significantly improves BA scalability by decoupling network size from fault tolerance and is likely to impact consensus protocols in blockchains and cloud infrastructures where actual faults are small.

Abstract

Achieving agreement among distributed parties is a fundamental task in modern systems, underpinning applications such as consensus in blockchains, coordination in cloud infrastructure, and fault tolerance in critical services. However, this task can be communication-intensive, often requiring a large number of messages to be exchanged, especially in the presence of Byzantine faults, making efficiency a central challenge in the design of practical agreement protocols. In this paper, we study the problem of Strong Byzantine Agreement and establish tight upper and lower bounds on communication complexity, parameterized by the actual number of Byzantine faults. Specifically, for a system of $n$ parties tolerating up to $t$ Byzantine faults, out of which only $f \leq t$ are actually faulty, we obtain the following results: In the partially synchronous setting, we present the first Byzantine Agreement protocol that achieves adaptive communication complexity of $\mathcal{O}(n + t \cdot f)$ words, which is asymptotically optimal. Our protocol has an optimal resilience of $t < n/3$. In the asynchronous setting, we prove a lower bound of $Ω(n + t^2)$ on the expected number of messages, and design an almost matching protocol with an optimal resilience that solves agreement with $\mathcal{O}((n + t^2)\cdot \log n)$ words. Our main technical contribution in the asynchronous setting is the utilization of a bipartite expander graph that allows for low-cost information dissemination.

Figures (2)

• Figure 1: Evolution of a single view in our partially synchronous Byzantine Agreement protocol, assuming an honest leader L and that the system is after GST.
• Figure 2: The communication graph for stages 1 and 2 of the algorithm. Nodes are assigned three roles (non-exclusive): parties, relayers and quorum with respective sizes of $n$, $O(t\log n)$ and $3t + 1$. Each party is only linked to $O(\log n)$ relayers, and each relayer is linked to each quorum node.

Theorems & Definitions (20)

• Theorem 1
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• Theorem 8: svensson2021bipartite
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• Theorem 9