Synchronizing Embedding Changes in Side-Informed Steganography

Historically, two different strategies have been proposed for improving steganographic security by allowing each cover element to be modified by +1 or −1 with unequal probabilities: side-informed steganography and methods that cluster the polarity of neighboring changes. In the first strategy, the sender typically uses the knowledge of quantization errors when developing / processing the cover before embedding. In the latter, embedding on disjoint sub-lattices employs heuristic rules to increase the probability that the polarities of neighboring changes align. In this paper, we propose a method for combining both strategies and experimentally show an improvement in empirical security for several types of side information on two datasets when steganalyzing with rich models as well as convolutional neural networks. Motivation Steganography is a mode of covert communication in which messages are embedded in inconspicuous cover objects to hide the very presence of the communicated secret. Digital images are particularly suitable cover sources because they can hold large amounts of data and are commonly shared on social networks and attached to emails. Moreover, there are thousands of applications available to potential users.1 Since statistical detectability increases sharply with the amplitude of embedding changes, steganographic schemes typically modify the individual cover elements, which encode the luminance or DCT coefficients using integer values, by at most ±1. The vast majority of embedding algorithms do so with equal probabilities as this maximizes the entropy (payload) embedded at each pixel [23, 22, 29, 35]. Two exceptions to this rule of thumb include sideinformed steganography [23, 20, 6, 19, 34, 17, 15, 14, 7] and steganography that encourages neighboring embedding changes to share the same polarity [30, 5, 24]. Since both strategies have been shown to improve empirical security, in this paper we investigate whether they can be combined to further boost the resistance to steganalysis. Side-informed (SI) steganography is a general term used for embedding schemes in which the sender makes use of the so-called precover [26] that is subjected to some sort of processing, development, or format conversion be1N. Johnson, “IoT Forensic Considerations and Steganography Beyond Images.” Invited talk presented in the Network and Cloud Forensics Workshop, IEEE Conference on Communications and Network Security, October 9–11, 2017, Las Vegas, Nevada, USA. fore embedding the secret message. Since the last step of the processing pipeline is typically quantization, the sender has access to the rounding errors and uses them to modulate the costs of changes by 1 and −1. SI steganography generally prefers changing those cover elements whose rounding errors are close to ±1/2 because such elements are the most sensitive to small perturbations. For example, a cover element with a non-rounded value 2.57, which would round to 3, is allowed to be modified during embedding to 2 with a small cost while changing the cover value 3 to 4 incurs a proportionally larger cost. The first side-informed scheme was the embeddingwhile-dithering steganography [15], in which the secret message was embedded by perturbing the process of color quantization and dithering when converting a true-color image to a palette format. In perturbed quantization [16], the cover JPEG is recompressed to create side-information. The embedding prefers modifying DCT coefficients that fall close to the middle of the quantization bins during the second compression. The same idea can be applied when the cover image is uncompressed and the sender embeds her message in its JPEG form. The rounding errors of DCT coefficients can again be used to adjust the costs of polarities of embedding changes [27, 34, 39, 25]. This methodology was later further advanced using the paradigm of minimal-distortion steganography with advanced source coding [23, 20, 6]. While not studied in this paper, the authors wish to point out that side-information can have many other forms than rounding errors. In particular, when the sender has access to an acquisition oracle (e.g., a camera or a scanner [11, 13, 12]), she can acquire multiple exposures of the same scene to estimate the preferred polarity of embedding changes for cover elements that are most susceptible to small noise, and thus better mimic the embedding changes as acquisition noise [8]. In the so-called Natural Steganography [1, 2, 38], also recognized as steganography by cover source switching, the sender has access to the RAW image capture and embeds the message in the developed domain by making the stego image look as if it was acquired with a higher ISO setting. When the developing pipeline is modelable, extremely large payloads can be embedded with virtually perfect security. In general, since side-information is only available to the sender, it can improve empirical security by a rather large margin. In [14], the author has shown that the precover compensates for the lack of the cover model. In particular, for a Gaussian model of acquisition noise, precover-informed rounding is more secure than embed-