In order to achieve high practical security, Natural Steganography (NS) uses cover images captured at ISO sensitivity ISO1and generates stego images mimicking ISO sensitivity ISO2> ISO1. This is achieved by adding a stego signal to the cover that mimics the sensor photonic noise. This paper proposes an embedding mechanism to perform NS in the JPEG domain after linear developments by explicitly computing the correlations between DCT coefficients before quantization. In order to compute the covariance matrix of the photonic noise in the DCT domain, we first develop the matrix representation of demosaicking, luminance averaging, pixel section, and 2D-DCT. A detailed analysis of the resulting covariance matrix is done in order to explain the origins of the correlations between the coefficients of 3 × 3 DCT blocks. An embedding scheme is then presented that takes into account all the correlations. It employs 4 sub-lattices and 64 lattices per sub-lattices. The modification probabilities of each DCT coefficient are then derived by computing conditional probabilities computed from a multivariate Gaussian distribution using the Cholesky decomposition of the covariance matrix. This derivation is also used to compute the embedding capacity of each image. Using a specific database called E1Base, we show that in the JPEG domain NS (J-Cov-NS) enables to achieve high capacity (more than 2 bits per non-zero AC DCT) and with high practical security (PE 40% using DCTR and PE 32% using SRNet) from QF 75 to QF 100).

This paper proposes to use the statistical analysis of the correlation between DCT coefficients to design a new synchronization strategy that can be used for cost-based steganographic schemes in the JPEG domain. First, an analysis is performed on the covariance matrix of DCT coefficients of neighboring blocks after a development pipeline similar to the one used to generate BossBase, and applied on a photonic noise. This analysis exhibits (i) a decomposition into 8 disjoint sets of uncorrelated coefficients (4 sets per block used by 2 disjoint lattices) and (ii) the fact that each DCT coefficient is correlated with 38 other coefficients belonging either to the same block or to connected blocks. Using the uncorrelated groups, an embedding scheme can be designed using only 8 disjoint lattices. The proposed embedding scheme relies on ingredients. Firstly, we convert the empirical costs associated to one each coefficient into a Gaussian distribution whose variance is directly computed from the embedding costs. Secondly we derive conditional Gaussian distributions from a multivariate distribution considering only the correlated coefficients which have been already modified by the embedding scheme. This covariance matrix takes into account both the correlations exhibited by the analysis of the covariance matrix and the variance derived from the costs. This synchronization scheme enables to obtain a gain of $P_E$ of at least $7%$ at $QF95$ for an embedding rate close to 0.3 bnzac coefficient using DCTR feature sets for both UERD and JUniward.

This short paper is an extension of a family of embedding schemes called Natural Steganography, which embeds a message by mimicking heteroscedastic sensor noise in the JPEG domain. Under the assumption that the development from RAW uses linear de- mosaicking, we derive a closed-form for the covariance matrix of DCT coefficients from 3 × 3 JPEG blocks. This computation relies on a matrix formulation of all steps involved in the development pipeline, which includes demosaicking, conversion to luminance, DCT transform, and reordering. This matrix is then used for pseudo-embedding in the JPEG domain on four lattices of 8 × 8 DCT blocks. The results obtained with the computed covariance matrix are contrasted with the results previously obtained with the covariance matrix estimated using Monte Carlo sampling and scaling. The empirical security using DCTR features at JPEG quality 100 increased from PE = 14% using covariance estimation and scaling to PE = 43% using the newly derived analytic form.