Information-Theoretic Bounds for Steganography in Multimedia

Steganography in multimedia aims to embed secret data into an innocent
looking multimedia cover object. This embedding introduces some
distortion to the cover object and produces a corresponding stego
object. The embedding distortion is measured by a cost function that
determines the detection probability of the existence of the embedded
secret data. A cost function related to the maximum embedding rate is
typically employed to evaluate a steganographic system. In addition, the
distribution of multimedia sources follows the Gibbs distribution which
is a complex statistical model that restricts analysis. Thus, previous
multimedia steganographic approaches either assume a relaxed
distribution or presume a proposition on the maximum embedding rate and
then try to prove it is correct. Conversely, this paper introduces an
analytic approach to determining the maximum embedding rate in
multimedia cover objects through a constrained optimization problem
concerning the relationship between the maximum embedding rate and the
probability of detection by any steganographic detector. The
KL-divergence between the distributions for the cover and stego objects
is used as the cost function as it upper bounds the performance of the
optimal steganographic detector. An equivalence between the Gibbs and
correlated-multivariate-quantized-Gaussian distributions is established
to solve this optimization problem. The solution provides an analytic
form for the maximum embedding rate in terms of the WrightOmega
function. Moreover, it is proven that the maximum embedding rate is in
agreement with the commonly used Square Root Law (SRL) for
steganography, but the solution presented here is more accurate.
Finally, the theoretical results obtained are verified experimentally.