Steganalysis of Block-DCT Image Steganography Ying Wang and Pierre Moulin Beckman Institute, CSL & ECE Department University of Illinois at Urbana-Champaign September 29 th, 2003
Introduction • Steganography is a branch of information hiding, aiming to achieve perfectly secret communication. 2
Steganographer vs. Steganalyzer Steganographer Steganalyzer • Embedding distortion • Trace of embedding? – Is typical of ? • Various embedding methods can be used. • Detection methods – Ad hoc – Detection-theoretic 3
Block-DCT Embedding Spatial domain DCT domain • Host image: • • 2 -D stationary process with 0 mean and correlation function • 64 equal-size channels containing approximately independent data, with variances -DCT coefficients: 4
Spatial domain DCT domain 8 8 5
Modified Spread Spectrum Data Hiding Model DCT domain • Marked DCT coefficients: Spatial domain • Stego-image: • Constraint and 1 -D undetectability constraint: 6
Statistics of the Pixel Differences • Block processing introduces discontinuity at the block boundaries • Develop steganalysis method based on pixel differences! 7
Host image • Stego-image • is a stationary process with zero mean and correlation function • The pdfs for all pairs are the same is non-stationary • The pdfs for inner pairs and border pairs are different 8
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Binary Hypothesis Testing Problem • Two populations • Difficulty: pdfs are unknown! • K-S test: F 0 and F 1 are cumulative density functions. • We use non-parametric two • Test statistic: sample goodness-of-fit tests such as Komogorov. Smirnov (K-S) test. 10
• The decision rule with is 11
Discussion • With the same embedding strength, stego-images of smooth host images such as Lena and Jet, are more likely to be detected than those of images with noise-like textures, such as Baboon. – The best candidates for steganography are complex images such as Baboon. – Block-DCT steganography is not suitable for smooth images. 12
• The key idea of our paper is to find an intrinsic property of natural images, which is modified by the information hiding process. – Another example: detecting wavelet-based information hiding. Upsampling introduces a stationary process in one subband to a non-stationary process in the spatial domain. 13
• The K-S test is universal in the sense that the pdfs can be unknown. • Comparing the K-S test with the likelihood ratio test, their universality is achieved at the cost of performance degradation. 14
References • N. F. Johnson and S. Katzenbeisser, ``A survey of steganographic techniques", in S. Katzenbeisser and F. Peticolas (Eds. ): Information Hiding, pp. 43 -78. Artech House, Norwood, MA, 2000. • J. D. Gibbons and S. Chakraborti, Nonparametric statistical inference, Marcel Dekker, New York, 1992. • L. Breiman, Probability, SIAM, Philadelphia, 1992. • O. Dabeer, K. Sullivan, U. Madhow, S. Chandrasekharan, and B. S. Manjunath, ``Detection of hiding in the least significant bit", Proc. CISS, The Johns Hopkins University, Mar. 2003. 15
Lena Baboon 16
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