Gibbs Construction in Steganography

We make a connection between steganography design by minimizing embedding distortion and statistical physics. The unique aspect of this work and one that distinguishes it from prior art is that we allow the distortion function to be arbitrary, which permits us to consider spatially dependent embedding changes. We provide a complete theoretical framework and describe practical tools, such as the thermodynamic integration for computing the rate-distortion bound and the Gibbs sampler for simulating the impact of optimal embedding schemes and constructing practical algorithms. The proposed framework reduces the design of secure steganography in empirical covers to the problem of finding local potentials for the distortion function that correlate with statistical detectability in practice. By working out the proposed methodology in detail for a specific choice of the distortion function, we experimentally validate the approach and discuss various options available to the steganographer in practice.