On the Use of Bhattacharyya Distance as a Measure of the Detectability of Steganographic Systems

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.

[1]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[2]  E. Delp,et al.  Security, steganography, and watermarking of multimedia contents , 2004 .

[3]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[4]  Phil Sallee,et al.  Model-Based Steganography , 2003, IWDW.

[5]  Christian Cachin,et al.  An information-theoretic model for steganography , 1998, Inf. Comput..

[6]  Henrique S. Malvar,et al.  Improved spread spectrum: a new modulation technique for robust watermarking , 2003, IEEE Trans. Signal Process..

[7]  Ying Wang,et al.  Steganalysis of block-structured stegotext , 2004, IS&T/SPIE Electronic Imaging.

[8]  David Mumford,et al.  Statistics of natural images and models , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[9]  H. V. Trees.  Detection, Estimation, And Modulation Theory , 2001 .

[10]  T. Kailath.  The Divergence and Bhattacharyya Distance Measures in Signal Selection , 1967 .

[11]  Ingemar J. Cox,et al.  Digital Watermarking , 2003, Lecture Notes in Computer Science.

[12]  H. Vincent Poor,et al.  An Introduction to Signal Detection and Estimation , 1994, Springer Texts in Electrical Engineering.

[13]  H. Vincent Poor,et al.  An introduction to signal detection and estimation (2nd ed.) , 1994 .

[14]  Pedro Comesaña Alfaro,et al.  Detection in quantization-based watermarking: performance and security issues , 2005, IS&T/SPIE Electronic Imaging.

[15]  Guillermo Morales-Luna,et al.  On the Existence of Perfect Stegosystems , 2005, IWDW.