  Synchronization of pulse-coupled oscillators (PCOs) has gained significant
attention recently due to increased applications in sensor networks and
wireless communications. Given the distributed and unattended nature of
wireless sensor networks, it is imperative to enhance the resilience of
pulse-based synchronization against malicious attacks. However, most existing
results on resilient PCO synchronization are obtained for all-to-all networks.
We propose a new pulse-based synchronization mechanism to improve the
resilience of PCO synchronization that is applicable under general connected
topologies. Under the proposed synchronization mechanism, we rigorously
characterize the condition for stealthy Byzantine attacks and prove that
perfect synchronization of legitimate oscillators can be guaranteed in the
presence of multiple stealthy Byzantine attackers, irrespective of whether the
attackers collude with each other or not. The new mechanism can guarantee
resilient synchronization even when the initial phases of legitimate
oscillators are widely distributed in a half circle, which is in distinct
difference from most existing attack-resilient synchronization algorithms
(including the seminal paper from Lamport and Melliar-Smith [1]) that require a
priori (almost) synchronization among legitimate oscillators. Numerical
simulation results are given to confirm the theoretical results.
