A game-theoretic method for designing distortion function in spatial steganography

Most modern secure image steganographic schemes define distortion functions for constraining the embedding changes to those parts of the image that are difficult to model such as textured or noisy regions. However, thus arguments disregard Kerckhoffs’ principle: the warden also knows the adaptivity criterion as well and may be able reproduce or estimate it. This paper proposes a new idea that the embedding distortion is designed based on game theory. We present a two-player zero-sum game between steganographer and attacker related to the security of practical steganography, and there exists a unique mixed strategy Nash equilibrium. The distortion function is first achieved from the original method S-UNIWARD (Spatial-UNIversal Wavelet Relative Distortion), and then we readjust the distortion function according to the above Nash equilibrium. The new distortion not only ensures the embedding changes focus on textured region but also correlates to the Kerckhoffs’ principle. Experiment results show that the statistical security of the proposed method is improved by approximately 6.2 % with the features of modern rich models.