Improving robust adaptive steganography via minimizing channel errors
Introduction
Steganography is a science and art of covert communication that conceals secret messages in digital media without being detected [1], [2], [3]. Many different mediums can be used in steganography, such as text, audio, video, or digital image. Among them, JPEG images are now widely used in Online Social Networks (OSNs), such as Facebook and Twitter, because they can provide high-level visual quality with less storage costs [4]. At present, the most remarkable steganographic schemes for JPEG images are based on Syndrome-Trellis Codes (STCs) [5] and recently developed Steganographic Polar Codes (SPC) [6] that can minimize the researcher-defined distortions while embedding messages.
With the powerful steganographic codes, the latest researches focused on how to define effective distortion functions. There are a lot of distortion functions defined for JPEG images, such as J-UNIWARD (JPEG UNIverlet WAvelet Relative Distortion) [7], UERD (Uniform Embedding Revisited Distortion) [8], GUED (Generalized Uniform Embedding Distortion) [9], BET (Block Entropy Transformation) [10] and J-MiPOD (Minimizing the Power of Optimal Detector for JPEG domain) [11]. Their main mission is to assign low costs to the coefficients in complex areas and high costs to the coefficients in smooth areas of an image, which is also known as the “Complexity-First Rule” [12]. Recently, non-additive distortion functions for JPEG images which consider the interaction of modifications are defined to keep the continuity of adjacent image blocks in the spatial domain [13], [14], [15].
The aforementioned framework of “distortion functions + STCs” performs well on lossless channels. With the development of the Internet, OSNs are becoming increasingly entrenched in people’s lives and a huge number of images are shared on them every day, which is a well-suited platform for image steganography. Steganographers and recipients can achieve behavioral security by disguising steganographic behavior as the everyday behavior of ordinary users. However, images transmitted over OSNs usually suffer from lossy processes such as resizing, JPEG compression, or image enhancement. Generally the cover image can be regarded as the channel for steganographic communication. The processing of the stego between sending and receiving is called channel processing. The channel processing in this paper is the processing of OSNs. These operations will fail the message extraction of STCs because the stego image is modified during transmission. Kin-Cleaves et al. [16] deeply analyzed the performance of STCs on lossy channels and pointed that previous frameworks are not available as well as there will be error diffusion after embedding with STCs, where an error bit in the stego image may affect multiple bits in the extracted sequence. To make the steganography robust to the channel processing, there has been a growing number of publications [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28]. Overall, they supplemented the original framework with many robustness strengthening operations, which mainly considering two aspects: error correction codes and reducing the channel error rate.
A direct way to help correctly extract message is introducing error correction codes (ECC) to encode messages for error correction, which is called ECC-based operations in this paper. For example, the utilization of RS (Reed-Solomon) codes in [18], [20] and BCH (Bose, Chaudhuri and Hocquenghem) codes in [17], [22]. However, ECC-based operation can only provide limited robustness. Therefore, apart from ECC, other operations are utilized to enhance robustness.
Actually, considering error diffusion, reducing the channel error rate is the most effective method, in other words, to make the changes in the stego as few as possible during channel processing. These operations are the primary reasons why the corresponding algorithms can resist JPEG compression and we categorize them into three types. The first one is to select the coefficients of the cover image that remains essentially unchanged after channel processing as the cover sequence, which is called “Robust Domain Selection” [19]. For example, Zhang et al. [18] selected the medium frequency DCT coefficients of JPEG images as binary cover to embed with DMAS (Dither Modulation-based robust Adaptive Steganography). Yu et al. [20] proposed GMAS (Generalized dither Modulation-based robust Adaptive Steganography) by expanding robust domain and introducing ternary embedding. These operations are robust but their capacities are low due to cover selection. The second type is to preprocess the cover image to make it resistant to JPEG compression. The representative is TCM (Transport Channel Matching) proposed by Zhao et al. [17], which repeatedly processes the image by applying channel manipulations until the image is nearly identical before and after channel processing and uses the preprocessed images for steganography. These methods also provide robustness but preprocessing modifications will decrease security. Repeated uploading and downloading are also behaviorally insecure. The third type is to encode the stego for error correction. Zhang et al. [21] use part of the cover to embed the message first and then embed the cyclic redundancy check (CRC) codes [23] derived from the embedded sequence into the remaining cover. This type of operation can be used in combination with the preprocessing and robust domain selection in practice to further improve robustness.
Overall, robust steganography algorithms based on traditional framework are shown in Fig. 1. The core of these algorithms is to reduce the channel error rate with robust domain selection or preprocessing. Coding message or stego with ECC is just an additional robustness enhancement. These robustness strengthening operations sacrifice much security for robustness, thus cannot achieve satisfying performance in terms of both. To overcome this limitation, this paper first analyzes the key issues in robust steganography: how to reduce channel error rate while maintaining security. We divide the causes of channel errors into two parts: steganography-related and steganography-independent. Then we propose a novel method to eliminate the effect of steganography-independent part. The message is embedded in the channel-processed cover with STCs which will modify some elements, and then the corresponding elements in the original image are replaced with the modified elements to generate the stego for transmission. Thereafter, we applied this method for Facebook as an example. For the impact of steganography-related part, we set the elements where the modification may yield errors as wet elements to minimize channel error rate. Notably, the proposed algorithm is resistant not only to JPEG recompression but also to enhancement filtering which was not even considered in previous steganographic algorithms. We verify the robustness of the algorithm through experiments on both JPEG compression channels and Facebook. Security of the algorithm is examined by feature-based steganalysis with DCTR (Discrete Cosine Transform Residual) [29] and current CNN-based steganalysis [30]. Simulated and real-world experiments show that the proposed algorithm outperforms previous algorithms in terms of both security and robustness. Besides, the algorithm can achieve error-free steganography on one of the most complex channels, Facebook, without ECC-based operations.
The rest of the paper is organized as follows. The next section introduces the notations and provides preliminaries on robust steganography in the traditional framework. Section 3 analyzes the problems faced in reducing channel error rate and presents the novel method. The implementation of the method on Facebook is described in Section 4, which is resistant to both JPEG compression and enhancement filtering. The consequences of comparative experiments and performance tests are shown in Section 5. Finally, Section 6 concludes this paper.
Section snippets
STC-based steganography
Denote a cover obtained from a JPEG image as , where is the range of DCT coefficient value and is its length. The original message is . The process that the sender modifies to stego to embed a message is represented aswhere and . We call the embedding operation binary if , or ternary if . This paper considers the case of ternary embedding, where the possible values of stego elements are restricted to
Primary problem on robustness
During the transmission of messages over OSNs, three error rates can be calculated as shown in the Fig. 2:
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channel error rate:
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syndrome error rate:
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message error rate:
The implementation of MINICER
In this section, we introduce the lossy operations that are present on OSNs first. Then we describe the robust steganographic method MINICER.
In the experiments in Section 2.3, the main lossy processes for uploaded images are JPEG recompression and enhancement filtering. The process of recompressing an image with to an image with is as follows:where , is an coefficient block in the image to be recompressed,
Experiment
The performance of the algorithm will be experimentally investigated in this section. First, we introduce the experimental setup. Then we test the resistance to JPEG recompression and security of the proposed algorithm. We also analyze the relative wetness of the wet paper model introduced in Section 4.3 and the respective contribution of wet blocks and wet elements. Finally, we test the algorithm on Facebook, that is, the ability of the algorithm to simultaneously resist JPEG compression and
Conclusions
Since online social networks (OSNs) usually perform lossy operations on the uploaded images. Steganography algorithms used over OSNs require robustness along with undetectability. However, previous algorithms need to sacrifice much security for robustness.
This paper proposes MINICER to upgrade the performance. According to MINICER, we only need to focus on those modified elements in steganography. After that, this paper proposes a practical steganography algorithm based on MINICER and
Credit Author Statement
Kai Zeng: methodology, data curation, software, writing original draft, review&editing.Kejiang Chen: formal analysis, validation, software, review&editing.Weiming Zhang: conceptualization, project administration, review&editing.Yaofei Wang: software, review&editing. Nenghai Yu: resources, funding acquisition.
Declaration of Competing Interest
None.
Acknowledgement
This work was supported in part by the Natural Science Foundation of China under Grant 62102386, 62002334, 62072421, and 62121002, and by China Postdoctoral Science Foundation under Grant 2021M693091, and by Anhui Science Foundation of China under Grant 2008085QF296, and by Open Fund of Anhui Province Key Laboratory of Cyberspace Security Situation Awareness and Evaluation.
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