Information-theoretic bounds for steganography in visual multimedia

Abstract

Steganography in visual multimedia embeds data into an image or video cover object and produces a corresponding stego object with some distortion. Establishing an upper bound on the maximum embedding rate, subject to a target distortion threshold, is challenging due to the difficulties introduced by the Gibbs modeling of visual multimedia objects. This paper introduces an analytic optimization approach to establish a generalized upper bound on the maximum embedding rate in visual multimedia cover objects with a particular target probability of detection by any steganographic detector. To that end, we show that the parametric form of the correlated multivariate quantized Gaussian distribution supersedes the Gibbs family in the achievable embedding rate with a bounded relative entropy between the cover and stego objects’ distributions. Our solution provides an analytical form of the upper bound in terms of the WrightOmega function and agrees with the well-known Square Root Law (SRL) for steganography.