Information-Theoretic Limits for Steganography in Multimedia

TL;DR

This paper establishes the fundamental information-theoretic limits of steganography in multimedia objects, quantifying the maximum embedding rate based on statistical properties and detector performance.

Contribution

It introduces a rigorous framework for calculating steganographic capacity in multimedia using entropy and KL-divergence, providing exact scaling laws.

Findings

Maximum embedding rate is characterized by entropy bounds.

Steganalytic detector error probability relates to KL-divergence.

Exact scaling constant for message and cover entropy relationship.

Abstract

Steganography is the art and science of hiding data within innocent-looking objects (cover objects). Multimedia objects such as images and videos are an attractive type of cover objects due to their high embedding rates. There exist many techniques for performing steganography in both the literature and the practical world. Meanwhile, the definition of the steganographic capacity for multimedia and how to be calculated has not taken full attention. In this paper, for multivariate quantized-Gaussian-distributed multimedia, we study the maximum achievable embedding rate with respect to the statistical properties of cover objects against the maximum achievable performance by any steganalytic detector. Toward this goal, we evaluate the maximum allowed entropy of the hidden message source subject to the maximum probability of error of the steganalytic detector which is bounded by the KL-divergence between the statistical distributions for the cover and the stego objects. We give the exact scaling constant that governs the relationship between the entropies of the hidden message and the cover object.