CNN-based steganalysis and parametric adversarial embedding:A game-theoretic framework

CNN-based steganalysis has recently achieved very good performance in detecting content-adaptive steganography. At the same time, recent works have shown that, by adopting an approach similar to that used to build adversarial examples, a steganographer can adopt an adversarial embedding strategy to effectively counter a target CNN steganalyzer. In turn, the good performance of the steganalyzer can be restored by retraining the CNN with adversarial stego images. A problem with this model is that, arguably, at training time the steganalyzer is not aware of the exact parameters used by the steganographer for adversarial embedding and, vice versa, the steganographer does not know how the images that will be used to train the steganalyzer are generated. In order to exit this apparent deadlock, we introduce a game theoretic framework wherein the problem of setting the parameters of the steganalyst and the steganographer is solved in a strategic way. More specifically, we propose two slightly different game-theoretic formulations of the above problem, the difference between the two games corresponding to the way the output of the steganalyzer network is thresholded to make the final decision. In both cases, the goal of the steganographer is to increase the missed detection probability, while the steganalyst aims at reducing the overall error probability in the first case, and the missed detection probability for a given false alarm rate, in the second one. We instantiated the two games by considering a specific adversarial embedding scheme (namely a modified version of the adversarial embedding scheme proposed by Tang et al. (2019), and we run several experiments to derive the equilibrium points and the corresponding payoff for the two versions of the game. By comparing the error probabilities at the equilibrium, with those obtained by using other strategies, like the adoption of a worst case assumption or the use of the adversarial embedding scheme by Tang et al. (2019), the benefits of addressing the interplay between the steganographer and the steganalyst in a game-theoretic fashion come out.