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

Authors:
Valery Korzhik;Hideki Imai;Junji Shikata;Guillermo Morales-Luna;Ekaterina Gerling
Affiliations:
State University of Telecommunications, St. Petersburg, Russia;Chuo University and National Institute of Advanced Industrial Science and Technology, Japan;Graduate School of Environment and Information Science, Yokohama National University, Japan;Computer Science, CINVESTAV-IPN, Mexico City, Mexico;State University of Telecommunications, St. Petersburg, Russia
Venue:
Transactions on data hiding and multimedia security III
Year:
2008

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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 stegano-graphic 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.