Exploiting the Synchronization of Nonlinear Dynamics to Secure Distributed Consensus

Abstract

Distributed cooperative multi-agent operations, which are emerging as effective solutions in countless application domains, are prone to eavesdropping by malicious entities due to their exposure on the network. Moreover, in several cases, agents are reluctant to disclose their initial conditions (even to legitimate neighbors) due to their sensitivity to private data. Providing security guarantees against external readings by malicious entities and the privacy of exchanged data while allowing agents to reach an agreement on some shared variables is an essential feature to foster the adoption of distributed protocols. In this article, we propose to implement a secure and privacy-preserving consensus strategy that exploits, for this purpose, the performance of synchronization of nonlinear continuous-time dynamical systems. This is achieved by splitting the initial conditions into two information fragments, one of which is subject to nonlinear manipulation. In this way, the information being exchanged in the network will always be subject to the influence of nonlinear dynamics. However, by exploiting the ability of such dynamics to synchronize, the combination of the two fragments still converges to a weighted average of each node's actual initial conditions. Furthermore, due to the dependence of the hidden dynamics on a coordinate transformation known only to the legitimate nodes, message security is ensured even once consensus is reached; our approach relies on the assumption that a secure communication channel is available during an initialization phase. The article is complemented by a simulation campaign aimed at numerically demonstrating the effectiveness of the proposed approach.

Keywords

• Chua oscillators
• distributed algorithms
• distributed consensus
• nonlinear synchronization
• privacy preservation
• security