Gibbs Construction in Steganography

We make a connection between steganography design by minimizing embedding distortion and statistical physics. The unique aspect of this work and one that distinguishes it from prior art is that we allow the distortion function to be arbitrary, which permits us to consider spatially dependent embedding changes. We provide a complete theoretical framework and describe practical tools, such as the thermodynamic integration for computing the rate-distortion bound and the Gibbs sampler for simulating the impact of optimal embedding schemes and constructing practical algorithms. The proposed framework reduces the design of secure steganography in empirical covers to the problem of finding local potentials for the distortion function that correlate with statistical detectability in practice. By working out the proposed methodology in detail for a specific choice of the distortion function, we experimentally validate the approach and discuss various options available to the steganographer in practice.

[1]  Hyoung Joong Kim,et al.  Less detectable JPEG steganography method based on heuristic optimization and BCH syndrome coding , 2009, MM&Sec '09.

[2]  Phil Sallee,et al.  Model-Based Methods For Steganography And Steganalysis , 2005, Int. J. Image Graph..

[3]  Anindya Sarkar,et al.  Estimation of optimum coding redundancy and frequency domain analysis of attacks for YASS - a randomized block based hiding scheme , 2008, 2008 15th IEEE International Conference on Image Processing.

[4]  Tomás Pevný,et al.  Statistically undetectable jpeg steganography: dead ends challenges, and opportunities , 2007, MM&Sec.

[5]  Rainer Böhme,et al.  Breaking Cauchy Model-Based JPEG Steganography with First Order Statistics , 2004, ESORICS.

[6]  Jessica J. Fridrich,et al.  Writing on wet paper , 2005, IEEE Transactions on Signal Processing.

[7]  Xinpeng Zhang,et al.  Efficient double-layered steganographic embedding , 2007 .

[8]  Tsachy Weissman,et al.  Erasure Entropy , 2006, 2006 IEEE International Symposium on Information Theory.

[9]  R. Crandall,et al.  Some Notes on Steganography , 1999 .

[10]  Radford M. Neal.  Probabilistic Inference Using Markov Chain Monte Carlo Methods , 2011 .

[11]  Anindya Sarkar,et al.  Secure Steganography: Statistical Restoration of the Second Order Dependencies for Improved Security , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[12]  Tsachy Weissman,et al.  The Information Lost in Erasures , 2008, IEEE Transactions on Information Theory.

[13]  Tomás Pevný,et al.  Steganalysis by Subtractive Pixel Adjacency Matrix , 2009, IEEE Transactions on Information Forensics and Security.

[14]  Andrew D. Ker.  Batch Steganography and Pooled Steganalysis , 2006, Information Hiding.

[15]  Yun Q. Shi,et al.  JPEG image steganalysis utilizing both intrablock and interblock correlations , 2008, 2008 IEEE International Symposium on Circuits and Systems.

[16]  Michael J. Black,et al.  Fields of Experts , 2009, International Journal of Computer Vision.

[17]  Jessica Fridrich,et al.  Steganography in Digital Media: References , 2009 .

[18]  Bradley P. Carlin,et al.  Markov Chain Monte Carlo conver-gence diagnostics: a comparative review , 1996 .

[19]  Jessica J. Fridrich,et al.  Minimizing embedding impact in steganography using trellis-coded quantization , 2010, Electronic Imaging.

[20]  Anindya Sarkar,et al.  YASS: Yet Another Steganographic Scheme That Resists Blind Steganalysis , 2007, Information Hiding.

[21]  Niels Provos,et al.  Defending Against Statistical Steganalysis , 2001, USENIX Security Symposium.

[22]  Mauro Barni,et al.  MPSteg-color: A New Steganographic Technique for Color Images , 2007, Information Hiding.

[23]  Gerhard Winkler,et al.  Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction , 2002 .

[24]  Andrew D. Ker.  Steganalysis of LSB matching in grayscale images , 2005, IEEE Signal Processing Letters.

[25]  Tomás Pevný,et al.  Merging Markov and DCT features for multi-class JPEG steganalysis , 2007, Electronic Imaging.

[26]  Donald Geman,et al.  Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , 1984 .

[27]  Jessica J. Fridrich,et al.  Minimizing Additive Distortion in Steganography Using Syndrome-Trellis Codes , 2011, IEEE Transactions on Information Forensics and Security.

[28]  B. S. Manjunath,et al.  Provably Secure Steganography: Achieving Zero K-L Divergence using Statistical Restoration , 2006, 2006 International Conference on Image Processing.

[29]  Dana S. Richards,et al.  Modified Matrix Encoding Technique for Minimal Distortion Steganography , 2006, Information Hiding.

[30]  Petra Mutzel,et al.  A Graph-Theoretic Approach to Steganography , 2005, Communications and Multimedia Security.

[31]  Rainer Böhme,et al.  Exploiting Preserved Statistics for Steganalysis , 2004, Information Hiding.

[32]  Jessica J. Fridrich,et al.  On completeness of feature spaces in blind steganalysis , 2008, MM&Sec '08.

[33]  D. Landau,et al.  Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[35]  Tomás Pevný,et al.  Modern steganalysis can detect YASS , 2010, Electronic Imaging.

[36]  Tomás Pevný,et al.  Using High-Dimensional Image Models to Perform Highly Undetectable Steganography , 2010, Information Hiding.

[37]  Jessica J. Fridrich,et al.  Perturbed quantization steganography , 2005, Multimedia Systems.

[38]  Jessica J. Fridrich,et al.  Practical methods for minimizing embedding impact in steganography , 2007, Electronic Imaging.

[39]  Yun Q. Shi,et al.  A Markov Process Based Approach to Effective Attacking JPEG Steganography , 2006, Information Hiding.

[40]  G. B. Smith,et al.  Preface to S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images” , 1987 .