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We analyze the distinguishability of two sources in a Neyman-Pearson set-upwhen an attacker is allowed to modify the output of one of the two sourcessubject to a distortion constraint. By casting the problem in a game-theoreticframework and by exploiting the parallelism between the attacker's goal andOptimal Transport Theory, we introduce the concept of Security Margin definedas the maximum average per-sample distortion introduced by the attacker forwhich the two sources can be distinguished ensuring arbitrarily small, yetpositive, error exponents for type I and type II error probabilities. Severalversions of the problem are considered according to the available knowledgeabout the sources and the type of distance used to define the distortionconstraint. We compute the security margin for some classes of sources andderive a general upper bound assuming that the distortion is measured in termsof the mean square error between the original and the attacked sequence.

Source Distinguishability under Distortion-Limited Attack: an Optimal Transport Perspective