  In order to achieve high practical security, Natural Steganography (NS) uses
cover images captured at ISO sensitivity $ISO_{1}$ and generates stego images
mimicking ISO sensitivity $ISO_{2}>ISO_{1}$. 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 $3\times3$ DCT blocks.
An embedding scheme is then presented that takes in order to take 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 from the 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 E1 Base, 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 ($P_{\mathrm{E}}\simeq40\%$ using DCTR
from QF 75 to QF 100).
