Partition Detection in Byzantine Networks

TL;DR

This work tackles the problem of detecting network partitions in Byzantine environments without assuming connectivity. It introduces NECTAR, a synchronous, signature-based algorithm that estimates the network's vertex-connectivity using neighborhood proofs and edge dissemination to decide if the network could be partitioned by up to $t$ Byzantine nodes, achieving a $k_0=2t$ sensitivity. The authors provide formal definitions (including $t$-Byzantine partitionability), a proof of correctness, and an empirical evaluation showing 100% accuracy up to $n=100$ with worst-case per-node data around 500 KB, outperforming baselines that degrade under Byzantine behavior. The results highlight NECTAR’s robustness across realistic topologies, with practical network costs and a clear trade-off between resilience and communication overhead, advancing Byzantine-tolerant partition-detection for distributed systems.

Abstract

Detecting and handling network partitions is a fundamental requirement of distributed systems. Although existing partition detection methods in arbitrary graphs tolerate unreliable networks, they either assume that all nodes are correct or that a limited number of nodes might crash. In particular, Byzantine behaviors are out of the scope of these algorithms despite Byzantine fault tolerance being an active research topic for important problems such as consensus. Moreover, Byzantinetolerant protocols, such as broadcast or consensus, always rely on the assumption of connected networks. This paper addresses the problem of detecting partition in Byzantine networks (without connectivity assumption). We present a novel algorithm, which we call NECTAR, that safely detects partitioned and possibly partitionable networks and prove its correctness. NECTAR allows all correct nodes to detect whether a network could suffer from Byzantine nodes. We evaluate NECTAR's performance and compare it to two existing baselines using up to 100 nodes running real code, on various realistic topologies. Our results confirm that NECTAR maintains a 100% accuracy while the accuracy of the various existing baselines decreases by at least 40% as soon as one participant is Byzantine. Although NECTAR's network cost increases with the number of nodes and decreases with the network's diameter, it does not go above around 500KB in the worst cases.

Figures (8)

• Figure 1: (a): A graph that is not 1-Byzantine partitionable. No matter the placement of a Byzantine node, the subgraph of correct nodes remains connected. (b): A 1-Byzantine-partitionable graph. If the red node is Byzantine, then the subgraph of the correct nodes is partitioned.
• Figure 2: An example of our drone scenario with random graph. Two scatters of points are generated. $d$ is the distance between the barycenters of the scatters, and $r$ is the communication scope.
• Figure 3: Data sent per node (in KB), depending on the number of nodes ($n$), for different vertex-connectivity ($k$) in $k-$regular graphs, for Nectar
• Figure 4: Data sent per node (in KB), depending on the distance between barycenters ($d$), for different values of communication scope ($radius$), in the drone scenario for Nectar. The red curve is MtG bouget_mind_2018, whose performance does not depend on $d$ nor $radius$.
• Figure 5: Data sent per node (in KB), depending on the distance between barycenters ($d$), for different values of communication scope ($radius$), in the drone scenario for MtGv2.

Theorems & Definitions (15)

• Definition 1: Network partition
• Definition 2: $t$-Byzantine partitionable graph
• Theorem 1
• proof
• Corollary 1
• proof
• Definition 3: $t$-Byzantine-resilient, $k_0$-sensitive network partition detection
• Lemma 1
• proof
• Lemma 2