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= : a seq of D to be inserted by wmk X= : a watermark to be inserted V’= : watermarked sequence D’ : watermarked document : attacked document : attacked watermarked seq of : attacked watermark

nxxx ,.....,, 21

nvvv ,.....,, 21

nvvv ',.....,',' 21

*D

*X

*V*D

Inserting the watermark

X V = V’

Three formulae for computing V’

(1)

(2)

(3)

iii xvv '

)1(' iii xvv

)(' ixii evv

Extracting the watermark

Find the inverse function of inserting watermark.

(2)->

1

'1

i

ii v

vx

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

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.

**

**),(

XX

XXXXSim

Evaluating the similarity of wmk Cont.

Creator of X* has no information on X. X* is created independently to X.

For fixed any , each will be independently distributed according to N(0,1)

~

Thus, Thus, false alarm prob doesn’t depend on n But, the large n increases the value of similarity func.

*ix ix

XX * ),,0(),0( **

1

*2

XXNxNn

ii

)1,0(~),( * NXXSim

Questions

Why does large value of n increase similarity function when X and X* are correlated?

nXXsimThus

cnceexxXX

nexx

exxexxXX

exx

n

i

n

iiiii

iii

n

i

n

i

n

iiiiiii

i

~),(,

)1(1)2E(

][E

)(

*

1 1

22**

2

1

1 1

2*

*

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

increase decrease

Method 1)

Method 2)

Method 3)

),( *XXSim

XX * ** XX

)( *** XExx iii

otherwise

tolerancexifxx iii

,0

, ***

))(( *** XExsignx iii

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.

Robust, secure, invisible watermark, resistant with respectto the collusion attack (averaging copies of documents with different marks).

Collution attack cont.

Marking copies of one document with a customer signature.

… W1 W2 WN

N customers…

+

original

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.