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An authentication counterpart of Wyner's study of the wiretap channel is developed in this paper. More specifically, message authentication over noisy channels is studied while impersonation and substitution attacks are investigated for both single and multiple message scenarios. For each scenario, information theoretic lower and upper bounds on the opponent's success, or cheating, probability are derived. Remarkably, in both scenarios, the lower and upper bounds are shown to match, and hence, the fundamental limits on message authentication over noisy channels are fully characterized. The opponent's success probability is further shown to be smaller than that derived in the classical noiseless channel model.
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