Source Distinguishability under Distortion-Limited Attack: an Optimal Transport Perspective
This work provides a theoretical framework for understanding the limits of source distinguishability under adversarial distortion, relevant to security and information theory researchers.
The paper analyzes the distinguishability of two sources under a distortion-limited attack, introducing the concept of Security Margin as the maximum average per-sample distortion for which the sources can be distinguished with arbitrarily small error exponents. The security margin is computed for some source classes and a general upper bound is derived.
We analyze the distinguishability of two sources in a Neyman-Pearson set-up when an attacker is allowed to modify the output of one of the two sources subject to a distortion constraint. By casting the problem in a game-theoretic framework and by exploiting the parallelism between the attacker's goal and Optimal Transport Theory, we introduce the concept of Security Margin defined as the maximum average per-sample distortion introduced by the attacker for which the two sources can be distinguished ensuring arbitrarily small, yet positive, error exponents for type I and type II error probabilities. Several versions of the problem are considered according to the available knowledge about the sources and the type of distance used to define the distortion constraint. We compute the security margin for some classes of sources and derive a general upper bound assuming that the distortion is measured in terms of the mean square error between the original and the attacked sequence.