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In batch steganography, the sender distributes the secret payload among multiple images from a “bag” to decrease the chance of being caught. Recent work on this topic described an experimentally discovered phenomenon, which we call the “bag gain”: for fixed communication rate, pooled detectors experience a decrease in statistical detectability for initially increasing bag sizes, providing an opportunity for the sender to gain in security. The bag gain phenomenon is universal in the sense of manifesting under a wide spectrum of conditions. In this paper, we explain this experimental observation by adopting a statistical model of detector response. Despite the simplicity of the model, it does capture observed trends in detectability as a function of the bag size, the rate, and cover source properties. Additionally, and surprisingly, the model predicts that in certain cover sources the sender should avoid bag sizes that are too small as this can lead to a bag loss. 

In this article, we study a recently proposed method for improving empirical security of steganography in JPEG images in which the sender starts with an additive embedding scheme with symmetrical costs of ±1 changes and then decreases the cost of one of these changes based on an image obtained by applying a deblocking (JPEG dequantization) algorithm to the cover JPEG. This approach provides rather significant gains in security at negligible embedding complexity overhead for a wide range of quality factors and across various embedding schemes. Challenging the original explanation of the inventors of this idea, which is based on interpreting the dequantized image as an estimate of the precover (uncompressed) image, we provide alternative arguments. The key observation and the main reason why this approach works is how the polarizations of individual DCT coefficients work together. By using a MiPOD model of content complexity of the uncompressed cover image, we show that the cost polarization technique decreases the chances of “bad” combinations of embedding changes that would likely be introduced by the original scheme with symmetric costs. This statement is quantified by computing the likelihood of the stego image w.r.t. the multivariate Gaussian precover distribution in DCT domain. Furthermore, it is shown that the cost polarization decreases spatial discontinuities between blocks (blockiness) in the stego image and enforces desirable correlations of embedding changes across blocks. To further prove the point, it is shown that in a source that adheres to the precover model, a simple Wiener filter can serve equally well as a deep-learning based deblocker. 

We study the problem of batch steganography when the senders use feedback from a steganography detector. This brings an additional level of complexity to the table due to the highly non-linear and non-Gaussian response of modern steganalysis detectors as well as the necessity to study the impact of the inevitable mismatch between senders’ and Warden’s detectors. Two payload spreaders are considered based on the oracle generating possible cover images. Three different pooling strategies are devised and studied for a more comprehensive assessment of security. Substantial security gains are observed with respect to previous art – the detector-agnostic image-merging sender. Close attention is paid to the impact of the information available to the Warden on security.