Pulse-Coupled Oscillators Resilient to Stealthy Attacks

Synchronization of bio-inspired pulse-coupled oscillators is receiving increased attention due to its wide applications in sensor networks and wireless communications. However, most existing results are obtained in the absence of malicious attacks. Given the distributed and unattended nature of wireless sensor networks, it is imperative to enhance the resilience of pulse based synchronization against malicious attacks. To achieve this goal, we propose a new pulse based interaction mechanism to improve the resilience of pulse based synchronization. We rigorously characterize the condition for mounting stealthy attacks under the proposed pulse based interaction mechanism and prove analytically that synchronization of legitimate oscillators can be achieved in the presence of multiple stealthy attackers even when the initial phases are unrestricted, i.e., randomly distributed in the entire oscillation period. This is in distinct difference from most existing attack-resilient synchronization algorithms (including the seminal paper from L. Lamport and P. M. Melliar-Smith, 'Synchronizing Clocks in the Presence of Faults,' J. ACM, vol. 32, no. 1, pp. 52-78, 1985), which require a priori (almost) synchronization among legitimate nodes. Numerical simulations are given to confirm the theoretical results.