On the use of Bhattacharyya distance as a measure of the detectability of steganographic systems

Abstract

It is very common to use the notion of relative entropy (or Kullback-Leibler divergence) as a measure for the discrimination difficulty among the hypotheses testing of presence and absence within a steganographic system. Relative entropy is not a symmetric function and sometimes it is very hard to compute its values. We propose to customize the notion of Bhattacharyya distance to the solution of the same problem. The main properties of Bhattacharyya distance are presented. We show applications of this new steganographic system security criterion within the model with a Gaussian colored covertext and within spread-spectrum watermarking by a white Gaussian sequence. © 2008 Springer-Verlag Berlin Heidelberg.