An embedding mechanism for natural steganography after down-sampling

Abstract

Natural Steganography (NS) uses the concept of cover-source switching to provide good undetectability performances [1]. The sensor noise of the source (camera) for a given ISO sensitivity ISO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> is first modeled as an independent Gaussian distribution for each photo-site, then the embedding mimics a switch to another sensitivity ISO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (> ISO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ). Because the embedding has to be performed on developed images, we investigate in this paper how to generate a stego-signal once the image is down-sampled. By studying different down-sampling mechanisms (sub-sampling, box down-sampling, tent down-sampling) applied on RAW images generated from a monochrome sensor, we show that the use of a convolution kernel with overlapping boundaries implies a synchronization mechanism similar to the one used by the CMD and Synch embedding schemes, but motivated here by statistical foundations. For each mechanism and scaling factor, we also compute the associated embedding rates and show that our results are in-line with experimental results previously highlighted for other steganographic schemes.