Reaching Approximate Byzantine Consensus in Partially-Connected Mobile Networks

TL;DR

This paper presents a new approximate Byzantine consensus protocol for mobile networks with dynamic topology and Byzantine nodes, establishing conditions for guaranteed convergence based on node movement and message exchange.

Contribution

It introduces a novel necessary and sufficient condition for consensus convergence in mobile networks with Byzantine nodes, considering node mobility and local communication constraints.

Findings

Consensus can be achieved if total nodes > 3f+1.

The protocol relies on collecting multiple rounds of information.

A new condition ensures convergence despite mobility and Byzantine faults.

Abstract

We consider the problem of approximate consensus in mobile networks containing Byzantine nodes. We assume that each correct node can communicate only with its neighbors and has no knowledge of the global topology. As all nodes have moving ability, the topology is dynamic. The number of Byzantine nodes is bounded by f and known by all correct nodes. We first introduce an approximate Byzantine consensus protocol which is based on the linear iteration method. As nodes are allowed to collect information during several consecutive rounds, moving gives them the opportunity to gather more values. We propose a novel sufficient and necessary condition to guarantee the final convergence of the consensus protocol. The requirement expressed by our condition is not "universal": in each phase it affects only a single correct node. More precisely, at least one correct node among those that propose either the minimum or the maximum value which is present in the network, has to receive enough messages (quantity constraint) with either higher or lower values (quality constraint). Of course, nodes' motion should not prevent this requirement to be fulfilled. Our conclusion shows that the proposed condition can be satisfied if the total number of nodes is greater than 3f+1.