The Non-Zero-Sum Game of Steganography in Heterogeneous Environments

Abstract

The highly heterogeneous nature of images found in real-world environments, such as online sharing platforms, has been one of the long-standing obstacles to the transition of steganalysis techniques outside the laboratory. Recent advances in identifying the properties of images relevant to steganalysis as well as the effectiveness of deep neural networks on highly heterogeneous datasets have laid some groundwork for resolving this problem. Despite this progress, we argue that the way the game played between the steganographer and the steganalyst is currently modeled lacks some important features expected in a real-world environment: 1) the steganographer can adapt her cover source choice to the environment and/or to the steganalyst's classifier, 2) the distribution of cover sources in the environment impacts the optimal threshold for a given classifier, and 3) the steganalyst and steganographer have different goals, hence different utilities. We propose to take these facts into account using a two-player non-zero-sum game constrained by an environment composed of multiple cover sources. We then show how to convert this non-zero-sum game into an equivalent zero-sum game, allowing us to propose two methods to find Nash equilibria for this game: a standard method using the double oracle algorithm and a minimum regret method based on approximating a set of atomistic classifiers. Applying these methods to contemporary steganography and steganalysis in a realistic environment, we show that classifiers which do not adapt to the environment severely underperform when the steganographer is allowed to select into which cover source to embed.