Fisher Information Determines Capacity of ε-Secure Steganography

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Abstract

Most practical stegosystems for digital media work by applying a mutually independent embedding operation to each element of the cover. For such stegosystems, the Fisher information w.r.t. the change rate is a perfect security descriptor equivalent to KL divergence between cover and stego images. Under the assumption of Markov covers, we derive a closed-form expression for the Fisher information and show how it can be used for comparing stegosystems and optimizing their performance. In particular, using an analytic cover model fit to experimental data obtained from a large number of natural images, we prove that the ±1 embedding operation is asymptotically optimal among all mutually independent embedding operations that modify cover elements by at most 1.