Secure Spread Spectrum
Young K Hwang
The characteristics of watermark
Common signal processing
Common geometric distortion
Collusion and forgery
Design for a strong watermark
i.i.d. samples from Gaussian distribution
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
The watermark is spread over many
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
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*
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
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
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
Sim( 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)
X X ~ N (0, xi* ) N (0, X * X * ),
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.
Why does large value of n increase similarity function
when X and X* are correlated?
x* x ei
X X xi ( xi ei ) xi2 xi ei
i 1 i 1
E[ xi2 xi ei ] n
X X E( x 2 xi ei e ) 1 c n(1 c)
* * 2
i 1 i 1
Thus, sim( X , X * ) ~ n
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
Setting T to low value result in increasing
false alarm prob.
A method to increase sim(X,X*) is required for
Robust statistics for a specific
X*(distortion version of X)
Goal : Increase Sim( X , X )
X X decrease X*X*
Method 1) xi* xi* Ei ( X * )
xi* , if xi* tolerance
Method 2) xi*
Method 3) x sign( x Ei ( X ))
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
Resilience to Multiple Document
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.
W1 W2 WN
… N customers
Robust, secure, invisible watermark, resistant with respect
to the collusion attack (averaging copies of documents with
Response of the watermark
Experiment 1: Uniqueness of
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
Experiment 3: JPEG Coding
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
A need for electronic watermarking is developing as
electronic distribution of copyright material becomes
This paper outlined the necessary characteristics of a
Robustness to common signal and geometric
Robustness to attack
Applicability to audio, image and video data.
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
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.