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Writing on Wet Paper

Writing on Wet Paper. IEEE Transactions on Signal Processing, Vol. 53, Issue 10, Part 2, Oct. 2005 by Jessica Fridrich, Miroslav Goljan, Petr Lisonek and David Soukal. Outlines. Introduction Wet Paper Code Practical Wet Paper Code Experiment. Introduction.

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Writing on Wet Paper

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  1. Writing on Wet Paper IEEE Transactions on Signal Processing, Vol. 53, Issue 10, Part 2, Oct. 2005 by Jessica Fridrich, Miroslav Goljan, Petr Lisonek and David Soukal

  2. Outlines • Introduction • Wet Paper Code • Practical Wet Paper Code • Experiment

  3. Introduction • Main building blocks of steganographic algorithm • The choice of the cover work • The embedding and extracting algorithm • Symbol assignment function • The embedding modification • The selection rule • Stego key management

  4. Wet Paper Code • Scenario • The sender wants to communicate q bits m=(m1, …, mq)T. • Both of sender and receiver know the shared key and the length of message q. • A binary column vector and a set of indices , of those bits that can be modified to embed. (cover media)

  5. Wet Paper Code • “Dry” pixels: may be modified by the sender • “Wet” pixels: are not to be modified during embedding

  6. Wet Paper Code - Encode • Use a shared stego key to generate a pseudo-random binary matrix D (q×n) • Modify some bj, j∈C, the modified binary column vector satisfies

  7. Wet Paper Code - Decode • Use a shared stego key to generate a pseudo-random binary matrix D (q×n) • Obtain the message m from

  8. Wet Paper Code - message length q • The sender can reserve the first bits of the message m for a header to inform the recipient of the number of rows in D • The recipient first generators the first rows of D, multiplies by the received vector b’ to get the message length q

  9. Wet Paper Code– Average maximal payload • Use variable v=b’-b to rewrite (1) to • k dry pixels, unknown values, vi, i ∈C • n-k wet pixels, zeros, vi, i ∉C

  10. Wet Paper Code– Average maximal payload • Remove from D all n-k columns i, i ∉C • Remove from v all n-k elements vi, i ∉C where H is a binary q×k matrix consisting of those columns of D corresponding to indices C, and v is an unknown k×1 binary vector

  11. Wet Paper Code– Average maximal payload • The solution of (3) for arbitrary message m as long as rank(H)=q • The probability Pq,k(s) that the rank of a random q×k binary matrix is s, s≤min(q,k) is

  12. Wet Paper Code– Average maximal payload • From (4), it shows that for a large fixed k, quickly approach 1 with decreasing q<k (Fig.1) • The expected number of bits (q) that can be communicated is approximately equal to k

  13. Wet Paper Code– Average maximal payload

  14. Practical Wet Paper Code • Assuming that the maximal length message q=k is sent, the complexity of Gaussian elimination for (3) is O(k3)

  15. Practical Wet Paper Code • The best performance and most flexible method for (3) • Divide bit-stream b into β disjoint pseudo-random subsets Bi • Use Gaussian elimination on each subset separately • If the factor is β, improve O(k3) to O(k3/β2)

  16. Practical Wet Paper Code • Some definitions • The range of the rate of communicating r=k/n, r1≤r≤r2 • The changeable bits in each subset kavg~250 • The number of sets, β= • The size ni of each subset Bi will be chosen so that

  17. Practical Wet Paper Code • Some definitions • The number of changeable bits ki varies for each subset Bi and follows the hypergeometric distribution with mean value k/β • b=(b(1), b(2), …, b(β)), b(i) is a vector of ni bits from Bi • r1, r2 and kavg are publicly known parameter by parties

  18. Practical Wet Paper Code

  19. Practical Wet Paper Code • Problem: • The encoding process may fail in the last subset because this is only subset in which the sender doesn’t have the freedom to decrease qβ • Solution • Start dividing the message bits with q+10 rather than q

  20. Practical Wet Paper Code – Encoder (1/4)

  21. Practical Wet Paper Code – Encoder (2/4)

  22. Practical Wet Paper Code – Encoder (3/4)

  23. Practical Wet Paper Code – Encoder (4/4)

  24. Practical Wet Paper Code - Decoder

  25. Practical Wet Paper Code - Decoder

  26. Experiment • A different example of a SR is given when the information-reducing transformation is recompression of the cover JPEG image using a lower JPEG quality factor. • Use the article, “Feature-Based Steganalysis for JPEG Images and its Implications for Future Design of Steganographic Schemes,” method to show the security of the proposed method.

  27. Experiment • The detection accuracy ρ = 2A–1, where A is the area under the ROC curve, for a simple linear classifier trained on 1400 cover and 1400 stego (fully embedded) images and tested on 400 never seen image. • Double compression for different embedding rates expressed using bpc = bits per non-zero stego DCT coefficient (U = unachievable rate)

  28. Experiment • Testing Methods • F5: F5 • F5_111: F5 with matrix embedding (1,1,1) • OQ: OutGuess 0.2 • MB1: model Based Steganography without deblocking • MB2: model Based Steganography with deblocking • PQ: the proposed Perturbed Quantization

  29. Experiment

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