Effect of Image Downsampling on Steganographic Security

The accuracy of steganalysis in digital images primarily depends on the statistical properties of neighboring pixels, which are strongly affected by the image acquisition pipeline as well as any processing applied to the image. In this paper, we study how the detectability of embedding changes is affected when the cover image is downsampled prior to embedding. This topic is important for practitioners because the vast majority of images posted on websites, image sharing portals, or attached to e-mails are downsampled. It is also relevant to researchers as the security of steganographic algorithms is commonly evaluated on databases of downsampled images. In the first part of this paper, we investigate empirically how the steganalysis results depend on the parameters of the resizing algorithm-the choice of the interpolation kernel, the scaling factor (resize ratio), antialiasing, and the downsampled pixel grid alignment. We report on several novel phenomena that appear valid universally across the tested cover sources, steganographic methods, and steganalysis features. This paper continues with a theoretical analysis of the simplest interpolation kernel - the box kernel. By fitting a Markov chain model to pixel rows, we analytically compute the Fisher information rate for any mutually independent embedding operation and derive the proper scaling of the secure payload with resizing. For least significant bit (LSB) matching and a limited range of downscaling, the theory fits experiments rather well, which indicates the existence of a new scaling law expressing the length of the secure payload when the cover size is modified by subsampling.