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.

A steganographer is not only hiding a payload inside their cover, they are also hiding themselves amongst the non-steganographers. In this paper we study asymptotic rates of growth for steganographic data -- analogous to the classical Square-Root Law -- in the context of a 'crowd' of K actors, one of whom is a steganographer. This converts steganalysis from a binary to a K-class classification problem, and requires some new information-theoretic tools. Intuition suggests that larger K should enable the steganographer to hide a larger payload, since their stego signal is mixed in with larger amounts of cover noise from the other actors. We show that this is indeed the case, in a simple independent-pixel model, with payload growing at O(√(log K)) times the classical Square-Root capacity in the case of homogeneous actors. Further, examining the effects of heterogeneity reveals a subtle dependence on the detector's knowledge about the payload size, and the need for them to use negative as well as positive information to identify the steganographer.

Researchers who wish to benchmark the detectability of steganographic distortion functions typically simulate stego objects. However, the difference (coding loss) between simulated stego objects, and real stego objects is significant, and dependent on multiple factors. In this paper, we first identify some factors affecting the coding loss, then propose a method to estimate and correct for coding loss by sampling a few covers and messages. This allows us to simulate suboptimally-coded stego objects which are more accurate representations of real stego objects. We test our results against real embeddings, and naive PLS simulation, showing our simulated stego objects are closer to real embeddings in terms of both distortion and detectability. This is the case even when only a single image and message as used to estimate the loss.

Contemporary steganography in digital media is dominated by the framework of additive distortion minimization: every possible change is given a cost, and the embedder minimizes total cost using some variant of the Syndrome-Trellis Code algorithm. One can derive the relationship between the cost of each change c_i and the probability that it should be made pi_i, but the literature has not examined the relationship between the costs and the total capacity (secure payload size) of the cover. In this paper we attempt to uncover such a relationship, asymptotically, for a simple independent pixel model of covers. We consider a 'knowing' detector who is aware of the embedding costs, in which case sum pi_i^2 c_i should be optimized. It is shown that the total of the inverse costs, sum c_i^-1, along with the embedder's desired security against an optimal opponent, determines the asymptotic capacity. This result also recovers a Square Root Law. Some simple simulations confirm the relationship between costs and capacity in this ideal model.

Leading steganography systems make use of the Syndrome-Trellis Code (STC) algorithm to minimize a distortion function while encoding the desired payload, but this constrains the distortion function to be additive. The Gibbs Embedding algorithm works for a certain class of non-additive distortion functions, but has its own limitations and is highly complex.

There are two interpretations of the term "square root law of steganography". As a rule of thumb, that the secure capacity of an imperfect stegosystem scales only with the square root of the cover size (not linearly as for perfect stegosystems), it acts as a robust guide in multiple steganographic domains. As a mathematical theorem, it is unfortunately limited to artificial models of covers that are a long way from real digital media objects: independent pixels or first-order stationary Markov chains. It is also limited to models of embedding where the changes are uniformly distributed and, for the most part, independent.

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 ∑iπici. 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 ∑iπ2ici 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 (average cost) adaptivity is exploitable, but the equilibrium probabilities cannot be exploited. However, it is essential to determine statistically well-founded costs ci.

We propose a method to detect hidden data in English text. We target a system pre-viously thought secure, which hides mes-sages in tweets. The method brings ideas from image steganalysis into the linguis-tic domain, including the training of a feature-rich model for detection. To iden-tify Twitter users guilty of steganography, we aggregate evidence; a first, in any do-main. We test our system on a set of 1M steganographic tweets, and show it to be effective. 1

The only steganalysis attack which can provide absolute certainty about the presence of payload is one which finds the embedding key. In this paper we consider refined versions of the key exhaustion attack exploiting metadata such as message length or decoding matrix size, which must be stored along with the payload. We show simple errors of implementation lead to leakage of key information and powerful inference attacks; furthermore, complete absence of information leakage seems difficult to avoid. This topic has been somewhat neglected in the literature for the last ten years, but must be considered in real-world implementations.

We present a method for a completely new kind of steganalysis to determine who, out of a large number of actors each transmitting a large number of objects, is hiding payload inside some of them. It has significant challenges, including unknown embedding parameters and natural deviation between innocent cover sources, which are usually avoided in steganalysis tested under laboratory conditions. Our method uses standard steganalysis features, the maximum mean discrepancy measure of distance, and ranks the actors by their degree of deviation from the rest: we show that it works reliably, completely unsupervised, when tested against some of the standard steganography methods available to nonexperts. We also determine good parameters for the detector and show that it creates a two-player game between the guilty actor and the steganalyst.

There has been an explosion of academic literature on steganography and steganalysis in the past two decades. With a few exceptions, such papers address abstractions of the hiding and detection problems, which arguably have become disconnected from the real world. Most published results, including by the authors of this paper, apply "in laboratory conditions" and some are heavily hedged by assumptions and caveats; significant challenges remain unsolved in order to implement good steganography and steganalysis in practice. This position paper sets out some of the important questions which have been left unanswered, as well as highlighting some that have already been addressed successfully, for steganography and steganalysis to be used in the real world.

A quantitative steganalyzer is an estimator of the number of embedding changes introduced by a specific embedding operation. Since for most algorithms the number of embedding changes correlates with the message length, quantitative steganalyzers are important forensic tools. In this paper, a general method for constructing quantitative steganalyzers from features used in blind detectors is proposed. The core of the method is a support vector regression, which is used to learn the mapping between a feature vector extracted from the investigated object and the embedding change rate. To demonstrate the generality of the proposed approach, quantitative steganalyzers are constructed for a variety of steganographic algorithms in both JPEG transform and spatial domains. The estimation accuracy is investigated in detail and compares favorably with state-of-the-art quantitative steganalyzers.

We describe a simple modification of the so-called weighted stego image (WS) steganalysis method, due to Fridrich and Goljan, to detect sequential replacement of least significant bits. The most sensitive methods for the detection of bit replacement do not work well when the payload is concentrated at the start of the cover instead of being spread evenly over it, so this detector fills a gap in the literature. Experimental results show that the adapted method gives sequentially-embedded payload estimation typically 10 times more accurate than the standard WS method.

The problems of batch steganography and pooled steganalysis, proposed in , generalize the problems of hiding and detecting hidden data to multiple covers. It was conjectured that, given covers of uniform capacity and a quantitative steganalysis method satisfying certain assumptions, "secure" steganographic capacity is proportional only to the square root of the number of covers. We now prove that, with respect to a natural definition of secure capacity, and in a suitably asymptotic sense, this conjecture is true. This is in sharp contrast to capacity results for noisy channels.

This paper proposes steganalysis methods for extensions of least-significant bit (LSB) overwriting to both of the two lowest bit planes in digital images: there are two distinct embedding paradigms. The author investigates how detectors for standard LSB replacement can be adapted to such embedding, and how the methods of "structural steganalysis", which gives the most sensitive detectors for standard LSB replacement, may be extended and applied to make more sensitive purpose-built detectors for two bit plane steganography. The literature contains only one other detector specialized to detect replacement multiple bits, and those presented here are substantially more sensitive. The author also compares the detectability of standard LSB embedding with the two methods of embedding in the lower two bit planes: although the novel detectors have a high accuracy from the steganographer's point of view, the empirical results indicate that embedding in the two lowest bit planes is preferable (in some cases, highly preferable) to embedding in one

This paper considers the least squares method (LSM) for estimation of the length of payload embedded by least-significant bit replacement in digital images. Errors in this estimate have already been investigated empirically, showing a slight negative bias and substantially heavy tails (extreme outliers). In this paper, (approximations for) the estimator distribution over cover images are derived: this requires analysis of the cover image assumption of the LSM algorithm and a new model for cover images which quantifies deviations from this assumption. The theory explains both the heavy tails and the negative bias in terms of cover-specific observable properties, and suggests improved detectors. It also allows the steganalyst to compute precisely, for the first time, a p-value for testing the hypothesis that a hidden payload is present. This is the first derivation of steganalysis estimator performance

We consider the problem of detecting spatial domain least significant bit (LSB) matching steganography in grayscale images, which has proved much harder than for its counterpart, LSB replacement. We use the histogram characteristic function (HCF), introduced by Harmsen for the detection of steganography in color images but ineffective on grayscale images. Two novel ways of applying the HCF are introduced: calibrating the output using a downsampled image and computing the adjacency histogram instead of the usual histogram. Extensive experimental results show that the new detectors are reliable, vastly more so than those previously known.