The Square Root Law of Steganography: Bringing Theory Closer to Practice

There are two interpretations of the term "square root law of steganography". As a rule of thumb, that the secure capacity of an imperfect stegosystem scales only with the square root of the cover size (not linearly as for perfect stegosystems), it acts as a robust guide in multiple steganographic domains. As a mathematical theorem, it is unfortunately limited to artificial models of covers that are a long way from real digital media objects: independent pixels or first-order stationary Markov chains. It is also limited to models of embedding where the changes are uniformly distributed and, for the most part, independent. This paper brings the theoretical square root law closer to the practice of digital media steganography, by extending it to cases where the covers are Markov Random Fields, including inhomogeneous Markov chains and Ising models. New proof techniques are required. We also consider what a square root law should say about adaptive embedding, where the changes are not uniformly located, and state a conjecture.