Optimum forensic and counter-forensic strategies for source identification with training data

In the attempt to provide a mathematical background to multimedia forensics, we introduce the source identification game with training data. The game models a scenario in which a forensic analyst has to decide whether a test sequence has been drawn from a source X or not. In turn, the adversary takes a sequence generated by a different source a modifies it in such a way to induce a classification error. The source X is known only through one or more training sequences. We derive the asymptotic Nash equilibrium of the game under the assumption that the analyst relies only on first order statistics of the test sequence. A geometric interpretation of the result is given together with a comparison with a similar version of the game with known sources. The comparison between the two versions of the games gives interesting insights into the differences and similarities of the two games.