Secure Spread Spectrum Watermarking for Multimedia Young K Hwang The characteristics of watermark Unobtrusiveness Robustness Common signal processing Common geometric distortion Collusion and forgery Universality Unambiguousness Design for a strong watermark Watermark structure i.i.d. samples from Gaussian distribution Insertion strategy Embedded in perceptual frequency area For a watermark to be robust and secure, these two components must be designed correctly Watermark in the frequency domain Spread Spectrum Coding of a Watermark The watermark is spread over many frequency bins The location of watermark isn’t obvious Sufficient small to be undetectable Is it possible to verify watermark? The owner know where the watermark is Increase the energy at a particular freq to detect the watermark. Cox’s scheme: Embedding Cox’s scheme: Detecting Watermark procedure D : each document V= v1 , v2 ,....., vn : a seq of D to be inserted by wmk X= x1 , x2 ,....., xn : a watermark to be inserted V’= v '1 , v '2 ,....., v 'n : watermarked sequence D’ : watermarked document D* : attacked document * : attacked watermarked seq of D* V X * : attacked watermark Inserting the watermark X V = V’ Three formulae for computing V’ v 'i vi xi (1) v'i vi (1 xi ) (2) v 'i vi ( exi ) (3) Extracting the watermark Find the inverse function of inserting watermark. (2)-> 1 v 'i xi 1 vi Choosing the length of the Wmk The choice of n indicates the degree to which the watermark is spread out among the relevant components of the image. Proper value of n makes it easy to identify the watermark. Too large value of n -> distort the image. Too small value of n -> cause robust problem Evaluating the similarity of wmk The similarity of X and X* can be measured by X*X Sim( X , X ) * X*X* To decide whether X and X* match, one determines if Sim(X,X*) > T, where T=some threshold T : chosen to minimize the prob of both false alarm and miss detections. Evaluating the similarity of wmk Cont. Creator of X* has no information on X. X* is created independently to X. * For fixed any xi , each x i will be independently distributed according to N(0,1) n X X ~ N (0, xi* ) N (0, X * X * ), 2 * i 1 Thus, Sim( X , X * ) ~ N (0,1) Thus, false alarm prob doesn’t depend on n But, the large n increases the value of similarity func. Questions Why does large value of n increase similarity function when X and X* are correlated? x* x ei n n X X xi ( xi ei ) xi2 xi ei * i 1 i 1 n E[ xi2 xi ei ] n i 1 n n X X E( x 2 xi ei e ) 1 c n(1 c) * * 2 i 2 i i 1 i 1 Thus, sim( X , X * ) ~ n Post-processing options xi should be detected by similarity after many kinds of signal processing. Some processes make it hard to detect watermark due to severely distorting watermark (for example, D/A-A/D, dithering process) Setting T to low value result in increasing false alarm prob. A method to increase sim(X,X*) is required for some processes Robust statistics for a specific X*(distortion version of X) * Goal : Increase Sim( X , X ) increase * X X decrease X*X* Method 1) xi* xi* Ei ( X * ) xi* , if xi* tolerance Method 2) xi* 0, otherwise Method 3) x sign( x Ei ( X )) * i * i * The original image The dithered image Question on previous slide Can such postprocessing steps affect the false positive probability? According to Cox’s paper, that process doesn’t affect the statistical significance calculation as long as X* depends on D* and D. Resilience to Multiple Document (Collusion) Attacks The most general attacks consists of using t multiple watermarked copies D1'...,Dt' of document D to produce an un- watermarked document D*. If the i-th watermark is the same for all copies of the document then it cannot be detected, changed or removed. Collution attack cont. Marking copies of one document with a customer signature. original + … W1 W2 WN … N customers Robust, secure, invisible watermark, resistant with respect to the collusion attack (averaging copies of documents with different marks). Experimental Results Response of the watermark (ROW)=32.0 Experiment 1: Uniqueness of Watermark Experiment 2: Image Scaling To recover the watermark the quarter sized image was rescaled to its original dimension, Fig. 7b.(ROW=13.4, 75% of the original data is missing) Experiment 3: JPEG Coding Distortions Here are two JPEG encoded versions of the Bavarian couple Image with different percentages for the quality and smoothing. ROW=22.8, 13.9 respectively Experiment 4: Dithering Distortion ROW=5.2, 10.5 with a postprocess Experiment 5: Cropping Cropping involves the cutting out and removal of portions of an image.(ROW=14.6, 75% of the original date is removed Experiment 6: Print, Xerox, and Scan This image represents the result after it has gone through the 4 stage process, printing, xeroxing, scanning and rescaling. ROW=4.0 7.0 with a postprocess Conclusion A need for electronic watermarking is developing as electronic distribution of copyright material becomes more widespread. This paper outlined the necessary characteristics of a watermark Fidelity preservation Robustness to common signal and geometric processing operations Robustness to attack Applicability to audio, image and video data. Conclusion …continued Using the Bavarian couple image, the algorithm used can extract a reliable copy of the watermark from imagery that was degraded with several common geometric and signal processing procedures. These procedures include translation, rotation, scale change, and cropping. The algorithm displays strong resilience to lossy operations. Finally, this proposed methodology is used to hide watermarks in data, the same process can be applied to sending other forms of message through media data.
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