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.

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Moving steganography and steganalysis from the laboratory into the real world

Blind steganalyzers can be used for many diverse applications in steganography that go well beyond a mere detection of stego content. A blind steganalyzer can also be used for constructing targeted attacks or as an oracle for designing steganographic methods. The feature space itself provides a low-dimensional model of covers useful for benchmarking. These applications require the feature space to be complete in the sense that the features fully characterize the space of covers. Incomplete feature sets may skew benchmarking scores and lead to poor steganalysis. As a simple test of completeness, we propose a general approach for constructing steganographic methods that approximately preserve the whole feature vector and thus become practically undetectable by any steganalyzer that uses the same feature set. We demonstrate the plausibility of this approach, which we call the Feature Correction Method (FCM) by constructing the FCM for a 274-dimensional feature set from a state-of-the-art blind steganalyzer for JPEG images.

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On completeness of feature spaces in blind steganalysis

According to conventional wisdom, content-adaptive embedding offers more steganographic security than random uniform embedding. We scrutinize this view and note that it is barely substantiated in the literature as only recently adaptive steganographic systems are tested against an attacker who anticipates the adaptivity and incorporates this knowledge into the detection strategy. For a better theoretical understanding of strategical embedding and detection, we propose a game-theoretic framework to study adaptive steganography while taking the knowledge of the steganalyst into account. We instantiate the framework with a stylized cover model and study both parties’ optimal strategies. The model has a unique equilibrium in mixed strategies, which depends on the heterogeneity of the cover source. We add realism by introducing imperfect recoverability of the adaptivity criterion and prove that naive adaptive embedding—the strategy implemented in many practical schemes—is only optimal if perfect steganography is possible or if the adaptivity criterion is not recoverable at all. In practice, where steganography is imperfect and adaptivity criteria are partially recoverable, the optimal embedding strategy is between naive adaptive and random uniform embedding.

Game Theory and Adaptive Steganography

Two players, Alice and Bob play the following game. A list of positive numbers d1, d2, . . . , dn and an integer 1  k  n are given. Alice chooses a k-element subset S of {1, 2, . . . , n} and, simultaneously, Bob chooses an integer i 2 {1, 2, . . . , n}. If i / 2 S then there is no payo↵. If, on the other hand, i 2 S then Alice pays Bob the amount of di. This two-player, zero-sum game was introduced in [6] as a means of analyzing the security (or detectability) of contentadaptive steganography. A formula for computing a pair of Nash-equilibrium strategies was also given in [6], but this formula was shown in [10] to be incorrect for certain choices of the parameters. In [10], the game was also generalized to allow for costs, and this more general version was solved in the sense that finding a Nash-equilibrium was shown to be possible in polynomial time by solving an appropriate linear program. In this paper, we solve the (generalized version of the) game in a stronger sense: we provide (correct) formulas that give a pair of Nash-equilibrium strategies and thus show that these are possible to compute in strongly-polynomial time.

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Hide and Seek in Digital Communication: The Steganography Game

Steganography is an art and science of hidden communication. Similarly as cryptography, steganography allows two trusted parties to exchange messages in secrecy, but as opposed to cryptography, steganography adds another layer of protection by hiding the mere fact that any communication takes place in a plausible cover traffic. Corresponding security goal is thus the statistical undetectability of cover and stego objects studied by steganalysis — a counterpart to steganography. Ultimately, a stegosystem is perfectly secure if no algorithm can distinguish its cover and stego objects. This dissertation focuses on stegosystems which are not truly perfectly secure — they are imperfect. This is motivated by practice, where all stegosystems build for real digital media, such as digital images, are imperfect. Here, we present two systematic studies related to the secure payload loosely defined as the amount of payload, which can be communicated at a certain level of statistical detectability. The first part of this dissertation describes a fundamental asymptotic relationship between the size of the cover object and the secure payload which is now recognized as the Square-root law (SRL). Contrary to our intuition, secure payload of imperfect stegosystems does not scale linearly but, instead, according to the square root of the cover size. This law, which was confirmed experimentally, is proved theoretically under very mild assumptions on the cover source and the embedding algorithm. For stegosystems subjected to the SRL, the amount of payload one is able to hide per square root of the cover size, called the root rate, leads to new definition of capacity of imperfect stegosystems. The second part is devoted to a design of practical embedding algorithms by minimizing the statistical impact of embedding. By discovering the connection between steganography and statistical physics, the Gibbs construction provides a theoretical framework for implementing and designing such embedding algorithms. Moreover, we propose a general solution for implementing the embedding algorithms minimizing the sum of distortions over individual cover elements in practice. This solution, called the Syndrome-trellis code (STC), achieves near-optimal performance over wide class of distortion functions.

Imperfect stegosystems---Asymptotic laws and near-optimal practical constructions

We consider the interplay between steganographer and the steganalyzer, and develop a steganalysis aware framework
for steganography. The problem of determining a stego image is posed as a feasibility problem subject to constraint of data communication, imperceptibility, and statistical indistinguishability with respect to steganalyzer's features. A stego image is then determined using set theoretic feasible point estimation methods. The proposed framework is applied effectively on a state of the art steganalysis method based on higher order statistics (HOS) steganalysis. We first show that the steganographer can significantly reduce the classification performance of the steganalyzer by employing a statistical constraint during embedding, although the image is highly distorted. Then we show that steganalyzer can develop a counter-strategy against steganographer's action, gaining back some classification performance. This interchange represents an empirical iteration in this game between the steganographer and steganalyzer. Finally we consider mixture strategies to find the Nash equilibrium of the interplay.

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Steganalysis-aware steganography: statistical indistinguishability despite high distortion

Spread spectrum (SS) modulation is utilized in many watermarking applications because it offers exceptional robustness against several attacks. The embedding rate-distortion performance of SS embedding however, is relatively weak compared to quantization index modulation (QIM). This limits the relative embedding rate of SS watermarks. In this paper, we illustrate that both the embedding effciency, i.e. bits embedded per unit distortion and robustness against additive white gaussian noise (AWGN) can be improved by pre-coding of message followed by constellation adjustment on the SS detector to minimize the distortion on the cover image introduced by coded data. Our pre-coding method encodes p bits as a 2p x 1 binary vector with a single nonzero entry whose index indicates the value of the embedded bits. Our analysis show that the method improves embedding rate by approximately p/4 without increasing embedding distortion or sacrificing robustness to AWGN attacks. Experimental evaluation of the method using a set theoretic embedding framework for the watermark insertion validates our analysis.© (2008) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

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H. Oktay Altun

Papers

Steganalysis-aware steganography: statistical indistinguishability despite high distortion

Improved Embedding Efficiency and AWGN Robustness for SS Watermarks via Pre-Coding