Distortion function

Abstract: This paper proposes a complete practical methodology for minimizing additive distortion in steganography with general (nonbinary) embedding operation. Let every possible value of every stego element be assigned a scalar expressing the distortion of an embedding change done by replacing the cover element by this value. The total distortion is assumed to be a sum of per-element distortions. Both the payload-limited sender (minimizing the total distortion while embedding a fixed payload) and the distortion-limited sender (maximizing the payload while introducing a fixed total distortion) are considered. Without any loss of performance, the nonbinary case is decomposed into several binary cases by replacing individual bits in cover elements. The binary case is approached using a novel syndrome-coding scheme based on dual convolutional codes equipped with the Viterbi algorithm. This fast and very versatile solution achieves state-of-the-art results in steganographic applications while having linear time and space complexity w.r.t. the number of cover elements. We report extensive experimental results for a large set of relative payloads and for different distortion profiles, including the wet paper channel. Practical merit of this approach is validated by constructing and testing adaptive embedding schemes for digital images in raster and transform domains. Most current coding schemes used in steganography (matrix embedding, wet paper codes, etc.) and many new ones can be implemented using this framework.

Abstract: Currently, the most secure practical steganographic schemes for empirical cover sources embed their payload while minimizing a distortion function designed to capture statistical detectability. Since there exists a general framework for this embedding paradigm with established payload-distortion bounds as well as near-optimal practical coding schemes, building an embedding scheme has been essentially reduced to the distortion design. This is not an easy task as relating distortion to statistical detectability is a hard and open problem. In this article, we propose an innovative idea to measure the embedding distortion in one fixed domain independently of the domain where the embedding changes (and coding) are carried out. The proposed universal distortion is additive and evaluates the cost of changing an image element (e.g., pixel or DCT coefficient) from directional residuals obtained using a Daubechies wavelet filter bank. The intuition is to limit the embedding changes only to those parts of the cover that are difficult to model in multiple directions while avoiding smooth regions and clean edges. The utility of the universal distortion is demonstrated by constructing steganographic schemes in the spatial, JPEG, and side-informed JPEG domains, and comparing their security to current state-of-the-art methods using classifiers trained with rich media models.

Abstract: Steganography is the science and art of covert communication, which aims to hide the secret messages into a cover medium while achieving the least possible statistical detectability. To this end, the framework of minimal distortion embedding is widely adopted in the development of the steganographic system, in which a well designed distortion function is of vital importance. In this paper, a class of new distortion functions known as uniform embedding distortion function (UED) is presented for both side-informed and non side-informed secure JPEG steganography. By incorporating the syndrome trellis coding, the best codeword with minimal distortion for a given message is determined with UED, which, instead of random modification, tries to spread the embedding modification uniformly to quantized discrete cosine transform (DCT) coefficients of all possible magnitudes. In this way, less statistical detectability is achieved, owing to the reduction of the average changes of the first- and second-order statistics for DCT coefficients as a whole. The effectiveness of the proposed scheme is verified with evidence obtained from exhaustive experiments using popular steganalyzers with various feature sets on the BOSSbase database. Compared with prior arts, the proposed scheme gains favorable performance in terms of secure embedding capacity against steganalysis.

Abstract: We make a connection between steganography design by minimizing embedding distortion and statistical physics. The unique aspect of this work and one that distinguishes it from prior art is that we allow the distortion function to be arbitrary, which permits us to consider spatially dependent embedding changes. We provide a complete theoretical framework and describe practical tools, such as the thermodynamic integration for computing the rate-distortion bound and the Gibbs sampler for simulating the impact of optimal embedding schemes and constructing practical algorithms. The proposed framework reduces the design of secure steganography in empirical covers to the problem of finding local potentials for the distortion function that correlate with statistical detectability in practice. By working out the proposed methodology in detail for a specific choice of the distortion function, we experimentally validate the approach and discuss various options available to the steganographer in practice.