Steganalysis of Block-DCT Image Steganography Ying Wang and Pierre Moulin Beckman Institute, CSL & ECE Department University of Illinois at Urbana- Champaign September 29th, 2003
Jan 19, 2018
Steganalysis of Block-DCT Image Steganography
Ying Wang and Pierre Moulin
Beckman Institute, CSL & ECE DepartmentUniversity of Illinois at Urbana-Champaign
September 29th, 2003
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Introduction• Steganography is a branch of information hiding,
aiming to achieve perfectly secret communication.
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Steganographer vs. Steganalyzer
Steganographer
• Embedding distortion
• Various embedding methods can be used.
Steganalyzer
• Trace of embedding?– Is typical of ?
• Detection methods– Ad hoc– Detection-theoretic
eDNX NS
P
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Block-DCT Embedding
Spatial domain
• Host image:
• 2-D stationary process with 0 mean and correlation function
DCT domain
• -DCT coefficients:
• 64 equal-size channels containing approximately independent data, with variances
88),(~ lku
u(m,n)
)],(),([),( tnsmunmuEtsru ),(2~ lku
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8
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Spatial domain DCT domain
),( nmu ),(~ lku
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Modified Spread Spectrum Data Hiding Model
DCT domain
• Marked DCT coefficients:
• Constraint and 1-D undetectability constraint:
Spatial domain
• Stego-image:
),(~),(~),(~ lkzlkvlku
),(~~, lkua lk )),(,0( 2
~ lkN z
.,,),(~),(~ lkpp lkulku
),(),(),( nmznmvnmu
),(),(~),(~DCT
IDCT
nmvlkulka
eD ),(),(~DCT
IDCT
nmzlkz
zv
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Statistics of the Pixel Differences
• Block processing introduces discontinuity at the block boundaries
• Develop steganalysis method based on pixel differences!
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Host image
• is a stationary process with
zero mean and correlation function
• The pdfs for all pairs are the same
Stego-image
• is non-stationary
• The pdfs for inner pairs and border pairs are
different
)1,(),(),( nmunmunmd )1,(),(),( nmunmunmd
)1,()1,(),(2
][),( ,,
lkrlkrlkr
ddElkr
uuu
lnkmnmd
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Binary Hypothesis Testing Problem
• Two populations
• Difficulty: pdfs are unknown!
• We use non-parametric two-sample goodness-of-fit tests such as Komogorov-Smirnov (K-S) test.
}{ 1d
• K-S test: F0 and F1 are cumulative
density functions.
• Test statistic:
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100
::
FFHFFH
)()(sup 10, xSxSDx
NM
NxnmdxSMxnmdxS/),(#)(/),(#)(
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00
}{ 0d
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• The decision rule with is
FAP
.1/001
,,,
,,,
,,,
NMNM
NMNM
NMNM
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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.
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• 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.
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• 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.
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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.
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Lena Baboon