1

Watermarking Scheme Capable

of Resisting Sensitivity Attack

IEEE signal processing letters, vol. 14, no. 2, February. 2007, pp. 125-128 Xinpeng Zhang and Shuozhong Wang

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Outline1. Introduction2. Sensitivity attack3. Watermark detector4. Embedding algorithm5. Detection algorithm6. Security analysis7. Experimental results8. Conclusions

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Introduction1. This letter proposes a watermarking scheme

capable of defeating the sensitivity attack

a novel tailor-made embedding algorithm a corresponding detection mechanism

are designed to “mislead” the attackers: get a “fake” signal

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Sensitivity attack(1/3)1. Attacker possesses a watermarked image and an

available detector

2. Remove or change the embedded without causing serious distortion

Original imageWatermark

embedding

Watermarked imagewatermarkdetector

Sensitivityattack

Not watermarkedWatermark

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Sensitivity attack(2/3)

Not watermarked Watermarked

Decision boundary

Decision boundary : between the “Watermarked” and “Not watermarked” regions is a hyper-plane in a multidimensional space.

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Sensitivity attack(3/3)

N

n

nnnA

1

)/(

n/1

n

: perpendicular to the decision boundary

: shows how sensitive the detector is to modification in the direction of each vector

: is either +1 or -1 indicates addition or subtraction

Subtracts from the watermarked copy with an increasing strength until the detector reports that no watermark is present. Thus, the embedded watermark is removed.

AA

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Watermark detector

Public watermark detector

Detectionfunction F

> Threshold

≤ Threshold

Output 1 (Watermarked)

Output 0 (Not watermarked)Black box

Test image

Watermark detector : provide adequate information about an embedded watermark

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Embedding algorithm(1/6)

C2,

3

C2,

0C1,0

C0,0C2,

2

C2,

1

C1,2 C1,1

C0,2 C0,1

DWT3-levels

Watermark

IDWT

Watermarked image

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Embedding algorithm(2/6)

p,qCl,θ

63 49-34 7

-131423-31

10

15

-1

7

6

-12

4

13

3

93-75-12314

2

-303

6447-19-5

23-248-14-7-9

6511

-3

5

-2

2

2

6

40-23

3-46

0 -4

3

3 4

6

l,θC l,θN

1 1

1 14

4 4

16

16

16

63 -34

-31 2315

3.25 -3.75

5.17

2.75

2.25

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Embedding algorithm(3/6)

0.16 0.16

0.160.226

0.32

0.32 0.452

1

1

1.414

l,θW ={ } { }θl

21.00, if =00.32, if =1l

l0.16, if =2 1 , otherwise, if =1

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Embedding algorithm(4/6)

1M

Mm, p,qS ml,θ 0

mutually independent and satisfy a standard Gaussian distribution with zero mean and unit standard deviation

1. Generate( )data-groups in a pseudo-random manner

2. The number of elements in each data group is equal to that of the host DWT coefficients, and all elements in the groups :

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Embedding algorithm(5/6)

l θ l,θ

l,θ

l,θ

ml,θm

l,θ W

N

W

p,qSp,qT 2

l θ p q

ml,θm p,qTA 2

l θ p q

ml,θl,θl,θm p,qTC-p,qCu C

M

m

ml,θ

m

ml,θ

'l,θ p,qT

A

u-p,qCp,qC

0

C

where

All modified DWT coefficients are inversely transformed to yield a watermarked copy

: modified DWT coefficients

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Embedding algorithm(6/6)

1. According to the central limit theorem is very close to its mean 1 All are approximately 0

2. Standard deviation of

Cum

mA

l θl,θl,θ

l θ p ql,θl,θl,θ

u WN

WC-p,qC

Cσ2

2

Cum

)1(

255log10

2

212

10 M

NNPSNR

uw

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Detection algorithm (1/2)

M

m

"m

" Cu-CuMU1

0

"u CσMM-.E 80

2

EUF

1. If output “ Watermarked ” output “ Not watermarked ”

0F

0F

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Detection algorithm (2/2)

1. If test image contains watermark, all close to 0

2. If test image contains no watermark

3. M 189 avoid excessive distortion

0 U

02

E

F

-ECσ-MM.dt eπ

tCσ-MM U "

u

t-

-

"u

802

2

2

02

E

-F

mu

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Security analysis

mu mT

1. Attacker does not knowand is impossible to estimate by

measuring the sensitivities ofmu

2. The detection function of the attacked signal always greater than 0 ( F > 0).

This means the sensitivity attack cannot remove the embedded watermark.

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Experimental resultsImage Detection

function F

Original -1.7104

Watermarked

1.5104

A 960 1280 still image captured by a digital camera wasused as the original test signal. The system parameter M=189

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Conclusions

1. The proposed watermarking scheme is capable of defeating the sensitivity attack.

2. The corresponding detection mechanism can mislead the attackers.

3. The output of detector cannot be used to remove watermark with low distortion.