The non-zero-sum game of steganography in heterogeneous environments

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

Side-Information For Steganography Design And Detection

Today, the most secure steganographic schemes for digital images embed secret messages while minimizing a distortion function that describes the local complexity of the content. Distortion functions are heuristically designed to predict the modeling error, or in other words, how difficult it would be to detect a single change to the original image in any given area. This dissertation investigates how both the design and detection of such content-adaptive schemes can be improved with the use of side-information. We distinguish two types of side-information, public and private: Public side-information is available to the sender and at least in part also to anybody else who can observe the communication. Content complexity is a typical example of public side-information. While it is commonly used for steganography, it can also be used for detection. In this work, we propose a modification to the rich-model style feature sets in both spatial and JPEG domain to inform such feature sets of the content complexity. Private side-information is available only to the sender. The previous use of private side-information in steganography was very successful but limited to steganography in JPEG images. Also, the constructions were based on heuristic with little theoretical foundations. This work tries to remedy this deficiency by introducing a scheme that generalizes the previous approach to an arbitrary domain. We also put forward a theoretical investigation of how to incorporate side-information based on a model of images. Third, we propose to use a novel type of side-information in the form of multiple exposures for JPEG steganography

Rethinking optimal embedding

At present, almost all leading steganographic techniques for still images use a distortion minimization paradigm, where each potential change is assigned a cost ci and the change probabilities πi chosen to minimize the average total cost Σiπici. However, some detectors have exploited knowledge of this adaptivity and the embedding cannot be considered optimal. In this work we prove a theoretical result suggesting that, against a knowing attacker, the embedder should simply minimize Σ i π 2 i ci instead, for the same costs ci, which is the minimax and equilibrium strategy. This aligns with some special case results that have appeared in recent literature. We then test some simple steganographic methods in theoretical and real settings, showing that naive adaptivity is exploitable, but the equilibrium probabilities cannot be exploited. However, it is essential to determine statistically well-founded costs ci