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Steganalysis of Block-Structured Stegotext

Steganalysis of Block-Structured Stegotext. Ying Wang and Pierre Moulin Beckman Institute, CSL & ECE Department University of Illinois at Urbana-Champaign January 21st, 2004. Outline. What is steganography? Relative entropy as a measure of detectability

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Steganalysis of Block-Structured Stegotext

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  1. Steganalysis of Block-Structured Stegotext Ying Wang and Pierre Moulin Beckman Institute, CSL & ECE Department University of Illinois at Urbana-Champaign January 21st, 2004

  2. Outline • What is steganography? • Relative entropy as a measure of detectability • Design perfectly undetectable steganography • Spread spectrum • Quantization index modulation (QIM) • Block-based embedding

  3. What issteganography? • Steganography is a branch of information hiding, aiming to achieve perfectly undetectable communication.

  4. Relative entropy • Steganalyzer performs a binary hypothesis test: • Relative entropies and are measures of the difficulty of discriminating between hypotheses, relating to error probability bounds. • means perfect undetectability!

  5. Designperfectly undetectablespread-spectrumsteganography • White covertext: • Proper scaling and embedding where and lead to too! • Colored covertext: • Diagonalize then scale and embed

  6. Designperfectly undetectableQIMsteganography • Scalar quantization, • 1-bit message , 1 dimensional sample • Two quantizers and , step size

  7. Randomized QIM? • Randomized by dither variable • Good but not enough. • General result: preprocessing does not help!

  8. Stochastic QIM, , no key • Red tiles, m=1; Green tiles, m=0 • Stochastic encoder

  9. Stochastic QIM with keys • Postprocess the QIM output! • Steganographic constraint: • Minimum distortion: • Linear programming problem!

  10. Block-based embedding • Partition into blocks of length . • Embed in each block using aforementioned steganographic methods.

  11. Detectability for Gaussian covertext • For stationary Gaussian covertexts, perfect undetectability in each block doesn’t mean undetectability for the whole sequence. • Analysis for low distortions

  12. Conclusions • Perfect undetectability is achievable for Gaussian covertexts, using modified spread-spectrum or stochastic QIM schemes. • Relative entropy almost increases linearly with the number of blocks.

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