Synchronization of pulse-coupled oscillators (PCOs) has gained significant attention recently due to increased 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 first show that by using a carefully designed phase response function (PRF), pulse-based synchronization of PCOs can be guaranteed despite the presence of a stealthy Byzantine attacker, even when legitimate PCOs have different initial phases. Next, we propose a new pulse-based synchronization mechanism to improve the resilience of pulse-based synchronization to multiple stealthy Byzantine attackers. We rigorously characterize the condition for mounting stealthy Byzantine attacks under the proposed new pulse-based synchronization mechanism and prove analytically that synchronization of legitimate oscillators can be achieved even when their initial phases are unrestricted, i.e., randomly distributed in the entire oscillation period. Since most existing results on resilient pulse-based synchronization are obtained only for all-to-all networks, we also propose a new pulse-based synchronization mechanism to improve the resilience of pulse-based synchronization that is applicable under general connected topologies. Under the proposed synchronization mechanism, we prove that synchronization of general connected legitimate PCOs 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 distributed in a half circle. Then, to relax the limitation of the stealthy attacker model and the constraint on the legitimate oscillators\u27 initial phase distribution, we improved our synchronization mechanism and proved that finite time synchronization of legitimate oscillators can be guaranteed in the presence of multiple Byzantine attackers who can emit attack pulses arbitrarily without any constraint except that practical bit rate constraint renders the number of pulses from an attacker to be finite. The improved mechanism can guarantee synchronization even when the initial phases of all legitimate oscillators are arbitrarily distributed in the entire oscillation period. The new attack resilient pulse-based synchronization approaches in this dissertation are in distinct difference from most existing attack-resilient synchronization algorithms (including the seminal paper from Lamport and Melliar-Smith [1]) which require a priori (almost) synchronization among all legitimate nodes. Numerical simulations are given to confirm the theoretical results
