湿纸编码

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
Wet Paper Code– Average maximal payload
Practical Wet Paper Code

Assuming that the maximal length message q=k is sent, the complexity of Gaussian elimination for (3) is O(k3)
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

Solution

Practical Wet Paper Code – Encoder (1/4)
Practical Wet Paper Code – Encoder (2/4)
Practical Wet Paper Code – Encoder (3/4)
Practical Wet Paper Code – Encoder (4/4)
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
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
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
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

Symbol assignment function The embedding modification The selection rule

Stego key management
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)


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
Practical Wet Paper Code

Some definitionsFra bibliotek
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
Practical Wet Paper Code Decoder
Practical Wet Paper Code Decoder
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.
Wet Paper Code


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

The best performance and most flexible method for (3)


Divide bit-stream b into β disjoint pseudorandom subsets Bi Use Gaussian elimination on each subset separately
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 nonzero stego DCT coefficient (U = unachievable rate)
Wet Paper Code - Decode


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

If the factor is β, improve O(k3) to O(k3/β2)
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