Detection of content adaptive LSB matching: a game theory approach

This paper is an attempt to analyze the interaction between Alice and Warden in Steganography using the Game Theory. We focus on the modern steganographic embedding paradigm based on minimizing an additive distortion function. The strategies of both players comprise of the probabilistic selection channel. The Warden is granted the knowledge of the payload and the embedding costs, and detects embedding using the likelihood ratio. In particular, the Warden is ignorant about the embedding probabilities chosen by Alice. When adopting a simple multivariate Gaussian model for the cover, the payoff function in the form of the Warden’s detection error can be numerically evaluated for a mutually independent embedding operation. We demonstrate on the example of a two-pixel cover that the Nash equilibrium is different from the traditional Alice’s strategy that minimizes the KL divergence between cover and stego objects under an omnipotent Warden. Practical implications of this case study include computing the loss per pixel of Warden’s ability to detect embedding due to her ignorance about the selection channel.