The accuracy of steganalysis in digital images primarily depends on the statistical properties of neighboring pixels, which are strongly affected by the image acquisition pipeline as well as any processing applied to the image. In this paper, we study how the detectability of embedding changes is affected when the cover image is downsampled prior to embedding. This topic is important for practitioners because the vast majority of images posted on websites, image sharing portals, or attached to e-mails are downsampled. It is also relevant to researchers as the security of steganographic algorithms is commonly evaluated on databases of downsampled images. In the first part of this paper, we investigate empirically how the steganalysis results depend on the parameters of the resizing algorithm-the choice of the interpolation kernel, the scaling factor (resize ratio), antialiasing, and the downsampled pixel grid alignment. We report on several novel phenomena that appear valid universally across the tested cover sources, steganographic methods, and steganalysis features. This paper continues with a theoretical analysis of the simplest interpolation kernel - the box kernel. By fitting a Markov chain model to pixel rows, we analytically compute the Fisher information rate for any mutually independent embedding operation and derive the proper scaling of the secure payload with resizing. For least significant bit (LSB) matching and a limited range of downscaling, the theory fits experiments rather well, which indicates the existence of a new scaling law expressing the length of the secure payload when the cover size is modified by subsampling.

Currently, the most successful approach to steganography in empirical objects, such as digital media, is to cast the embedding problem as source coding with a fidelity constraint. The sender specifies the costs of changing each cover element and then embeds a given payload by minimizing the total embedding cost. Since efficient practical codes exist that embed near the rate-distortion bound, the remaining task left to the steganographer is the fidelity measure - the choice of the costs. In the past, the costs were obtained either in an ad hoc manner or determined from the effects of embedding in a chosen feature space. In this paper, we adopt a different strategy in which the cover is modeled as a sequence of independent but not necessarily identically distributed quantized Gaussians and the embedding change probabilities are derived to minimize the total KL divergencewithin the chosen model for a given embedding operation and payload. Despite the simplicity of the adoptedmodel, the resulting stegosystem exhibits security that is comparable to current state-of-the-art methods methods across a wide range of payloads.

It is well known that the security of a given steganographic algorithm strongly depends on the statistical properties of the cover source. In this paper, we study how downsampling affects steganographic security. The secure payload no longer scales according to the square-root law because resizing changes the statistical properties of the cover source. We demonstrate this experimentally for various types of resizing algorithms and their settings and thoroughly interpret the results. Modeling digital images as Markov chains allows us to compute the Fisher information rate for the simplest resizing algorithm with the box kernel and derive the proper scaling of the secure payload with resizing. The theory fits experimental data, which indicates the existence of a new scaling law expressing the length of secure payload when the cover length is not modified by adding or removing pixels but, instead, by subsampling. Since both steganography and steganalysis is today commonly evaluated through controlled experiments on resized images (e.g., the BOSSbase), the effect of resizing on security is of utmost importance to practitioners.

We describe a novel general strategy for building steganography detectors for digital images. The process starts with assembling a rich model of the noise component as a union of many diverse submodels formed by joint distributions of neighboring samples from quantized image noise residuals obtained using linear and nonlinear high-pass filters. In contrast to previous approaches, we make the model assembly a part of the training process driven by samples drawn from the corresponding cover- and stego-sources. Ensemble classifiers are used to assemble the model as well as the final steganalyzer due to their low computational complexity and ability to efficiently work with high-dimensional feature spaces and large training sets. We demonstrate the proposed framework on three steganographic algorithms designed to hide messages in images represented in the spatial domain: HUGO, edge-adaptive algorithm by Luo, and optimally coded ternary$\pm {\hbox{1}}$embedding. For each algorithm, we apply a simple submodel-selection technique to increase the detection accuracy per model dimensionality and show how the detection saturates with increasing complexity of the rich model. By observing the differences between how different submodels engage in detection, an interesting interplay between the embedding and detection is revealed. Steganalysis built around rich image models combined with ensemble classifiers is a promising direction towards automatizing steganalysis for a wide spectrum of steganographic schemes.

Today, the most accurate steganalysis methods for digital media are built as supervised classifiers on feature vectors extracted from the media. The tool of choice for the machine learning seems to be the support vector machine (SVM). In this paper, we propose an alternative and well-known machine learning tool—ensemble classifiers implemented as random forests—and argue that they are ideally suited for steganalysis. Ensemble classifiers scale much more favorably w.r.t. the number of training examples and the feature dimensionality with performance comparable to the much more complex SVMs. The significantly lower training complexity opens up the possibility for the steganalyst to work with rich (high-dimensional) cover models and train on larger training sets—two key elements that appear necessary to reliably detect modern steganographic algorithms. Ensemble classification is portrayed here as a powerful developer tool that allows fast construction of steganography detectors with markedly improved detection accuracy across a wide range of embedding methods. The power of the proposed framework is demonstrated on three steganographic methods that hide messages in JPEG images.

Quantitative steganalysis strives to estimate the change rate defined as the relative number of embedding changes introduced by steganography. In this paper, we propose two new classes of quantitative steganalysis methods for the steganographic algorithm Jsteg. The first class obtains the change-rate estimate using a maximum likelihood estimator equipped with a precover model. While this approach provides better accuracy than existing structural attacks, it becomes computationally intractable with increasing complexity of the cover model. The second class of methods computes the change-rate estimate by minimizing an objective function constructed from a heuristically formed zero message hypothesis. The advantage of this heuristic approach is a low implementation complexity and modular architecture that allows flexible incorporation of higher order statistics of discrete cosine transform coefficients. The proposed methods are experimentally compared with current state-of-the-art methods.