Secure Spread Spectrum Watermarking for Multimedia

							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 ( exi )   (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.