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We address the problem of securing distributed storage systems against adversarial node attacks. An important aspect of these systems is node failures over time, necessitating, thus, a repair mechanism in order to maintain a desired high system reliability. In such dynamic settings, an important security problem is to safeguard the system from a malicious adversary who may come at different time instances during the lifetime of the storage system to corrupt the data stored on some nodes. We provide upper bounds on the maximum amount of information that can be stored safely on the system in the presence of the adversary. For an important operating regime, which we call the bandwidth-limited regime, we show that our upper bounds are tight and provide explicit linear code constructions. Moreover, we provide a way to shortlist the malicious nodes and expurgate the system.