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.

最近，基于CNN的隐写分析在检测内容自适应隐写术方面取得了非常好的性能。同时，最近的工作表明，通过采用类似于用于构建对抗示例的方法，隐写术者可以采用对抗嵌入策略来有效地对抗目标CNN隐写分析器。反过来，隐身分析仪的良好性能可以通过使用对抗性隐身图像重新训练CNN来恢复。该模型的问题在于，在训练时，隐写分析器可能不知道隐写术者用于对抗性嵌入的确切参数，反之亦然，隐写术者不知道将如何使用图像来训练隐写分析器。生成。为了摆脱这种明显的僵局，我们介绍了一种博弈论框架，其中以战略性方式解决了设置隐写分析器和隐写术者的参数的问题。更具体地说，我们针对上述问题提出了两个略有不同的博弈论公式，这两个博弈之间的差异对应于隐写分析器网络的输出被阈值化以做出最终决定的方式。在这两种情况下，隐写术专家的目标都是增加漏检的概率，而隐写分析仪的目的是在第一种情况下降低总体错误概率，并在第二种情况下降低给定错误警报率的漏检概率。我们针对上述问题提出了两种稍有不同的博弈论表述，两种博弈之间的差异对应于隐写分析器网络输出的阈值以做出最终决定。在这两种情况下，隐写术专家的目标都是增加漏检的概率，而隐写分析仪的目的是在第一种情况下降低总体错误概率，并在第二种情况下降低给定错误警报率的漏检概率。我们针对上述问题提出了两种稍有不同的博弈论表述，两种博弈之间的差异对应于隐写分析器网络输出的阈值以做出最终决定。在这两种情况下，隐写术专家的目标都是增加漏检的概率，而隐写分析仪的目的是在第一种情况下降低总体错误概率，并在第二种情况下降低给定错误警报率的漏检概率。

我们通过考虑特定的对抗嵌入方案（即Tang等人（2019）提出的对抗嵌入方案的修改版）实例化了这两个游戏，并且我们进行了一些实验以得出两个版本的平衡点和相应的收益通过比较均衡时的错误概率与使用其他策略获得的错误概率（例如采用最坏情况假设或Tang等人（2019）使用对抗嵌入方案）的优势隐写术者和隐写分析者之间以博弈论的方式相互作用。