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Abstract: Abstract. Motivated by the proactive security problem, we study the question of maintaining secrecy against a mobile eavesdropper that can eavesdrop to a bounded number of communication channels in each round of the protocol. We characterize the networks in which secrecy can be maintained against an adversary that can eavesdrop to t channels in each round. Using this characterization, we analyze the number of eavesdropped channels that complete graphs can withhold while maintaining secrecy.