Game Theory and Adaptive Steganography

摘要

According to conventional wisdom, content-adaptive embedding offers more steganographic security than random uniform embedding. We scrutinize this view and note that it is barely substantiated in the literature as only recently adaptive steganographic systems are tested against an attacker who anticipates the adaptivity and incorporates this knowledge into the detection strategy. For a better theoretical understanding of strategical embedding and detection, we propose a game-theoretic framework to study adaptive steganography while taking the knowledge of the steganalyst into account. We instantiate the framework with a stylized cover model and study both parties’ optimal strategies. The model has a unique equilibrium in mixed strategies, which depends on the heterogeneity of the cover source. We add realism by introducing imperfect recoverability of the adaptivity criterion and prove that naïve adaptive embedding—the strategy implemented in many practical schemes—is only optimal if perfect steganography is possible or if the adaptivity criterion is not recoverable at all. In practice, where steganography is imperfect and adaptivity criteria are partially recoverable, the optimal embedding strategy is between naïve adaptive and random uniform embedding.