An Asymptotically Uniformly Most Powerful Test for LSB Matching Detection

This paper investigates the detection of information hidden in digital media by the least significant bit (LSB) matching scheme. In a theoretical context of known medium parameters, two important results are presented. First, based on the likelihood ratio test, we present a test that asymptotically maximizes the detection power whatever the embedding rate might be. Second, the statistical properties of this test are analytically calculated; it is particularly shown that the decision threshold which warrants a given probability of false-alarm is independent of inspected medium parameters. This provides an asymptotic upper-bound for the detection power of any test that aims at detecting data hidden with the LSB matching method. In practice, when detecting LSB matching, the unknown medium parameters have to be estimated. Based on a local model of digital media, a generalized likelihood ratio test is presented by replacing the unknown parameters by their estimation. Numerical results on large databases highlight the relevance of the proposed methodology and comparison with state-of-the-art detectors shows that the proposed tests perform well.

[1]  Michael Elad,et al.  Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , 2006, IEEE Transactions on Image Processing.

[2]  Andrew D. Ker.  A Capacity Result for Batch Steganography , 2007, IEEE Signal Processing Letters.

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

[4]  Florent Retraint,et al.  Statistical decision by using quantized observations , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[5]  Eric W. Weisstein,et al.  The CRC concise encyclopedia of mathematics , 1999 .

[6]  Florent Retraint,et al.  Statistical Detection of LSB Matching Using Hypothesis Testing Theory , 2012, Information Hiding.

[7]  Ingemar J. Cox,et al.  Steganalysis for LSB Matching in Images with High-frequency Noise , 2007, 2007 IEEE 9th Workshop on Multimedia Signal Processing.

[8]  Lionel Fillatre.  Adaptive Steganalysis of Least Significant Bit Replacement in Grayscale Natural Images , 2012, IEEE Transactions on Signal Processing.

[9]  Mauro Barni,et al.  A Comparative Study of ±1 Steganalyzers , 2008 .

[10]  Glenn Healey,et al.  Radiometric CCD camera calibration and noise estimation , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Jessica J. Fridrich,et al.  Wet paper codes with improved embedding efficiency , 2006, IEEE Transactions on Information Forensics and Security.

[12]  Jessica J. Fridrich,et al.  Higher-order statistical steganalysis of palette images , 2003, IS&T/SPIE Electronic Imaging.

[13]  Karen O. Egiazarian,et al.  Practical Poissonian-Gaussian Noise Modeling and Fitting for Single-Image Raw-Data , 2008, IEEE Transactions on Image Processing.

[14]  B. S. Manjunath,et al.  Steganalysis for Markov cover data with applications to images , 2006, IEEE Transactions on Information Forensics and Security.

[15]  Rainer Böhme,et al.  Revisiting weighted stego-image steganalysis , 2008, Electronic Imaging.

[16]  Jessica J. Fridrich,et al.  Rich Models for Steganalysis of Digital Images , 2012, IEEE Transactions on Information Forensics and Security.

[17]  Florent Retraint,et al.  Statistical detection of LSB matching in the presence of nuisance parameters , 2012, 2012 IEEE Statistical Signal Processing Workshop (SSP).

[18]  Siwei Lyu,et al.  Steganalysis using higher-order image statistics , 2006, IEEE Transactions on Information Forensics and Security.

[19]  Jaakko Astola,et al.  Local Approximation Techniques in Signal and Image Processing (SPIE Press Monograph Vol. PM157) , 2006 .

[20]  Jessica J. Fridrich,et al.  New blind steganalysis and its implications , 2006, Electronic Imaging.

[21]  Bernard Widrow,et al.  Quantization Noise: Roundoff Error in Digital Computation, Signal Processing, Control, and Communications , 2008 .

[22]  Michael Elad,et al.  Stable recovery of sparse overcomplete representations in the presence of noise , 2006, IEEE Transactions on Information Theory.

[23]  Ingemar J. Cox,et al.  Digital Watermarking and Steganography , 2014 .

[24]  Florent Retraint,et al.  A Cover Image Model For Reliable Steganalysis , 2011, Information Hiding.

[25]  Carlos Munuera,et al.  Steganography and error-correcting codes , 2007, Signal Process..

[26]  Clayton Scott,et al.  Performance Measures for Neyman–Pearson Classification , 2007, IEEE Transactions on Information Theory.

[27]  Jianqin Zhou,et al.  On discrete cosine transform , 2011, ArXiv.

[28]  B. S. Manjunath,et al.  Detection of hiding in the least significant bit , 2004, IEEE Transactions on Signal Processing.

[29]  Cheng-Hsing Yang,et al.  Adaptive Data Hiding in Edge Areas of Images With Spatial LSB Domain Systems , 2008, IEEE Transactions on Information Forensics and Security.

[30]  Ingemar J. Cox,et al.  A comparative study of ± steganalyzers , 2008, 2008 IEEE 10th Workshop on Multimedia Signal Processing.

[31]  Ingemar J. Cox,et al.  Detection of ±1 LSB steganography based on the amplitude of histogram local extrema , 2008, 2008 15th IEEE International Conference on Image Processing.

[32]  T. H. Thai,et al.  Statistical model of natural images , 2012, 2012 19th IEEE International Conference on Image Processing.

[33]  Gustavus J. Simmons,et al.  The Prisoners' Problem and the Subliminal Channel , 1983, CRYPTO.

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

[35]  Jessica J. Fridrich,et al.  On estimation of secret message length in LSB steganography in spatial domain , 2004, IS&T/SPIE Electronic Imaging.

[36]  Jiwu Huang,et al.  Edge Adaptive Image Steganography Based on LSB Matching Revisited , 2010, IEEE Transactions on Information Forensics and Security.

[37]  Rainer Böhme,et al.  Advanced Statistical Steganalysis , 2010, Information Security and Cryptography.

[38]  Jessica J. Fridrich,et al.  Steganalysis of LSB Replacement Using Parity-Aware Features , 2012, Information Hiding.

[39]  Tomás Pevný,et al.  "Break Our Steganographic System": The Ins and Outs of Organizing BOSS , 2011, Information Hiding.

[40]  Florent Retraint,et al.  Statistical Decision Methods in Hidden Information Detection , 2011, Information Hiding.

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

[42]  Stephen E. Fienberg,et al.  Testing Statistical Hypotheses , 2005 .

[43]  Anil K. Jain,et al.  Random field models in image analysis , 1989 .