AbstractIn this paper, a novel asymmetric watermarking scheme is proposed. Both the user side watermark and copyright owner's one are generated from the copyright owner's private keys, and the watermark detection can be finished either by public watermark or the copyright owner's private one. Given the public watermark, it is impossible to guess or remove the embedded watermark. Performance of the proposed scheme is studied and the experimental results against removal attack and Jpeg compression show good robustness of proposed scheme

Fu, Yong-Gang

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Asymmetric Watermarking Scheme Based on Shuffling 

Procedia Engineering 29 (2012) 1640 – 1644
1877-7058 © 2011 Published by Elsevier Ltd.
doi:10.1016/j.proeng.2012.01.187
Available online at www.sciencedirect.com
Available online at www.sciencedirect.com
          Procedia Engineering  00 (2011) 000–000 
Procedia
Engineering
www.elsevier.com/locate/procedia
2012 International Workshop on Information and Electronics Engineering (IWIEE) 
Asymmetric Watermarking Scheme Based on Shuffling 
Yong-Gang Fu*
College of Computer Engineering, Jimei University, Xiamen, China, 361021 
Abstract 
In this paper, a novel asymmetric watermarking scheme is proposed. Both the user side watermark and copyright 
owner’s one are generated from the copyright owner’s private keys, and the watermark detection can be finished 
either by public watermark or the copyright owner’s private one. Given the public watermark, it is impossible to 
guess or remove the embedded watermark. Performance of the proposed scheme is studied and the experimental 
results against removal attack and Jpeg compression show good robustness of proposed scheme. 
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Harbin University 
of Science and Technology 
Key words: Asymmetric watermarking, Digital watermarking, Removal attacks 
1. Introduction 
It is commonly assumed that digital watermarking is only one of several measures that have to be 
combined to build a good copy protection mechanism [1]. One particular problem with state-of-the-art 
watermarking schemes is that they are symmetric. The keys necessary for watermark embedding and 
detection are identical. It implies that whoever allowed detecting the watermark gets to know the 
parameters that can also be used to remove it. Thus, the watermark detector knows all critical parameter 
of the watermarking scheme that also allows efficient removal of the embedded watermark.  
However, cheap tamper-proof devices are hardly producible [1], and thus, pirates can obtain the 
private key from such devices and use them to outwit the copy protection mechanism. A solution to this 
problem is the asymmetric scheme that uses two different keys for encoding and decoding as in 
cryptography. Recently, a number of papers on asymmetric watermarking method have been proposed 
[2]–[6]. Asymmetric watermarking is based on a one way relationship between the embedding (secret) 
key and the detection (asymmetric) key. A central issue in asymmetric watermarking scheme is the design 
of a detector that will not reveal sufficient information that leads to the erasure of the embedded 
*Corresponding author. Tel.: +86-018950182770 
E-mail address: yonggangfu@jmu.edu.cn. 
Open access under CC BY-NC-ND license.
Open access under CC BY-NC-ND license.
1641Yong-Gang Fu / Procedia Engineering 29 (2012) 1640 – 16442 Yonggang Fu/ r ce i  i eeri  00 ( 1) 000–000 
watermark, even if the pirates knows the detection algorithm and the public detection keys. It is a big 
challenge for design a asymmetric watermarking scheme, because revealing too much information 
implies the risk that hacker is able to remove the mark, whereas not revealing too much information 
implies less reliable detection. For this reason, we would like to develop a watermarking scheme where 
the watermark detection is possible with a public key that does not give enough information to impair the 
embedded watermark.  
The asymmetric watermarking schemes proposed up to now can be classified into two categories. One 
is watermark characteristics based method, using watermarks signals which have special characteristics 
such as periodicity [2,3]. The other is transform based method to make a detection key from a given 
embedding key by a proper transform [6-9,11]. Some nice reviews on asymmetric watermarking schemes 
can be found in[7,9]. Our proposed scheme in the following belongs to the second category. The public 
key is generated from the embedding key by a proper one transform.  
The paper is organized as follows: section 2 describes the proposed embedding and detection scheme; 
some robustness analyses are exhibited in section 3; sections 4 gives experimental results and the 
conclusion is drawn in section 5. 
2. The Proposed Scheme. 
In asymmetric watermarking scheme, for the embedded watermark to be detected by the usual 
correlation test, the reference watermark of the detector and the embedded watermarks should have some 
correlation. There exist numerous ways to generate signals that are different from each other, but have a 
fixed correlation with a given reference watermark. Hyuk et al[6] proposed a transformed key based 
method to generate the public key; J.Picard[7] introduced neural networks for the generation of the public 
detection. In this paper a simple and effective public key watermarking scheme is proposed, in which two 
shuffled versions of the same watermark are all generated from the copyright owner’s private key, only 
the copyright owner’s one is embedded into the host signal. The detection process can be finished by 
either public or private watermark. 
The block diagram of proposed embedding and detection are shown in Fig.1(a) and Fig.1(b) 
respectively. The embedding procedure can be depicted as following four steps: 
1)The host data, such as image or video, is firstly transformed by conventional transforms, such as 
discrete cosine transform, then the DC coefficients are left unused since its modification may cause great 
artifacts. After the proper embedding positions are chosen, the transformed coefficients are reorganized 
into a line order. This leads to a vector has zero mean, which is denoted as: )}(),....,1(),1({ McccC =v ,
where M is the watermark length. 
2) Two key groups, },,{ 211 kkkK = and },{ 432 kkK = are chosen by the copyright owner, 
where k , 1k and 3k are arbitrary integers, 2k and 4k are integers within the interval [ 3/2,3/ MM ] and are 
(a) Diagram of watermark embedding 
K e y s
O rig ia n l
Im a g e T ra n s fo rm  
S h u ffl in g
In ve rs e
T ra n s fo rm
W a te rm a rk e d
im a g e
C o e ffic ie n ts
C h o s e n
+
W a te rm a rk
G e n e ra t io n
Fig.1 System Block Diagram 
W a t e r m a r k e d
I m a g e
T r a n s fo r m  
P u b l ic
W a t e r m a r k
D e t e c t io n
R e s u lt
C o e ff ic ie n t s
C h o s e n
I n v e r s e
S h u ff l in g  1 S h u ff l in g  2
(b) Diagram of watermark detection 
1642  Yong-Gang Fu / Procedia Engineering 29 (2012) 1640 – 1644 Yonggang Fu/ Procedia Engineering 00 (2011) 00–000 3
prime to M at the same time. 
Define ,1)mod)(()( 211 ++= Mikkif and MiMikkif ,.....,2,1,1)mod)(()( 432 =++= . One can see it 
clearly that these two mappings )(1 ifia and )(2 ifia are one to one, the inverse transform 
corresponding to 1f is denoted as
1
1
−f .
3) The original watermark signal )}(),...,2(),1({ MwwwW =v is generated with zero mean and variance 
2
wσ  by copyright owner’s key k , which needs to be i.i.d and independent of the original host signal C
v
.
Then two watermarks for the copyright owner and the user are respectively generated as follows:  
))}(()),...,2(()),1(({)}(),...,2(),1({ 111 MfwfwfwMwwwW oooo ==
v
))}(()),...,2(()),1(({)}(),...,2(),1({ 222 MfwfwfwMwwwW uuuu ==
v
.
4) The watermark is embedded into the host signal according to the following manner: 
)()()(' iwicic oα+= , Mi ,....,2,1= ,
where α is a constant parameter to control the compromise between the watermark transparency and 
robustness. Then the watermarked coefficients together with the DC coefficients are reordered into the 
original two dimension form, and the watermarked signal is reached by the corresponding inverse 
transform. 
In the detector side, both the original signal and the original watermark are not necessary for the 
watermark detection. Firstly, the host content is transformed into its transform domain, and the proper 
embedding positions are selected, then selected transformed coefficients are reorganized into a line order, 
which is denoted as: )}(ˆ),....,1(ˆ),1(ˆ{ˆ McccC =
v
. Here we should note that these coefficients may undergo 
some attacks such as filtering, distortions and so on. 
Using the given public watermark, uW , the following correlation parameter is firstly computed: 
∑
=
−=
M
i
u iwiffcM
corr
1
2
1
1 )()))(((ˆ
1
And then the mean value of corr can be obtained as follows: 
∑∑
=
−−
=
− +==
M
i
uo
M
i
u iwiffwiffcM
Eiwiffc
M
EcorrE
1
2
1
12
1
1
1
2
1
1 )}()))]((()))((([
1
{)}()))(((ˆ
1
{)( α
∑
=
− +=
M
i
uu iwiwiffcM
E
1
2
1
1 )}()]()))((([
1
{ α
Since uW
v
is independent of C
v
, 0})()))(((
1
{
1
2
1
1 =∑
=
−M
i
u iwiffcM
E . When the watermark is present, 
multiplicity betweenα and the watermark energy is equal to the expectation of corr, i.e. 2)( wcorrE ασ= .
When there is no watermark embedded, the expectation of the corr must be equal to zero.  
After we set the threshold T between 0 and 2wασ , the watermark detection is finished by the comparison between the 
absolute value of corr and the threshold. Commonly we use the threshold 2/2wT ασ= . When corr is greater than T, 
a watermark decision is made, otherwise, the host is not watermarked. 
3. Simulation results. 
The proposed scheme can be applied to protect any properties including image, video, audio and so on 
against removal attacks. In our experiment, the watermark is embedded into the DCT domain of images 
to test the performance of our scheme. 
  The tested image is classical Lena gray image with 512512× pixels. And the watermark embedding 
strength α is set to 1. The image is firstly segmented into 88×  blocks with 64*64=4096 blocks, which is 
in accordance with the Jpeg compression standard. And then each block is undergone discrete cosine 
transforms to reach the transformed coefficients. Next the DC coefficients are left unmodified and select 
1643Yong-Gang Fu / Procedia Engineering 29 (2012) 1640 – 16444 Yonggang Fu/ r ce i  i eeri  00 ( 1) 000–000 
Fig.2 (a) Public detector responses; (b) Private detector response; (c) Public detector 
responses after removal attack; (d) Public detector responses after Jpeg compression 
0 100 200 300 400 500 600 700 800 900 1000
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Symmetric watermark detection
Watermark Seeds
De
tec
tor
 R
es
po
ns
es
(b)
0 100 200 300 400 500 600 700 800 900 1000
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Asymmetric watermark detection
Watermark Seeds
De
tec
tor
 R
es
po
ns
es
(a)
0 100 200 300 400 500 600 700 800 900 1000
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Asymmetric watermark detection
Watermark Seeds
De
tec
tor
 R
es
po
ns
es
(c)
0 100 200 300 400 500 600 700 800 900 1000
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Asymmetric watermark detection
Watermark Seeds
De
tec
tor
 R
es
po
ns
es
(d)
the middle frequency coefficients at position (1,2) and (2,1) from each block as host signal. Finally the 
selected coefficients are reorganized into line order and the watermark is embedded. The watermarked 
image is reached after the inverse DCT.  
The detector response vs the watermark energy and the result is shown in Table 1. The false-positive 
and false-negative errors can be effectively avoided with larger watermark energy. But too strong 
watermark may cause detectable artifacts. So we have to get a compromise between detection errors and 
the host quality. Here watermark energy is 80 for good robustness of the watermark and the visual quality. 
It is difficult to remove the private watermark if he doesn’t know the keys. As to the public watermark 
holder, the attacker may try to eliminate the watermark by successive subtraction of the user watermark or 
the pirates try to deceive the public detection into believing that another watermark is embedded in the 
work. Fig.2 (a)(b) exhibit the private and public detector responses without any attacks respectively. Fig.2 
(c) shows the public watermark detector response when the watermarked image is attacked by removal 
Table 1 Detection responses 2/ wcorr σ against different watermark energy 
Public detection with 
wrong reference 
Public detection with 
right reference 
Private detection Watermark 
energy 
PSNR
(dB)
Variance Mean Variance Mean Variance Mean 
10 53.18 0.0657 0.0018 0.0634 1.0680 0.0634 1.0680 
40 47.17 0.0165 0.0011 0.0158 1.0542 0.0158 1.0542 
80 44.15 0.0083 8.51E-4 0.0079 1.0185 0.0079 1.0185 
160 41.14 0.0042 6.99E-4 0.0041 1.0310 0.0041 1.0310 
400 37.16 0.0017 5.50E-4 0.0016 0.9843 0.0016 0.9843 
600 35.40 0.0012 5.16E-4 0.0011 1.0103 0.0011 1.0103 
1644  Yong-Gang Fu / Procedia Engineering 29 (2012) 1640 – 1644 Yonggang Fu/ Procedia Engineering 00 (2011) 000–000 5
attack with subtraction the public watermark with the same watermark energy as embedded. The public 
watermark detector responses corresponding to the Jpeg compressed image with quality factor 50 is 
shown in Fig.2(d). From the two detector responses figure under these attacks, it can be found that the 
detector responses can not be weakened. We also tested the watermark under Jpeg compressions, the 
watermark can still be detected in the image compressed at the quality factor 8 with conventional 
threshold. It cannot confuse the dominance of the watermark even when the user knows the public 
watermark.  
4. Conclusions 
A novel asymmetric key watermarking scheme that has a private watermark and a public watermark is 
proposed. Since the private one is difficult to guess from the public one, the watermarking scheme is 
robust against the removal attack. The experimental results show good robustness of our proposed scheme. 
Acknowledgement  
This work is partially supported by the Foundation of Xiamen Science Project (No.3502Z20075054) 
and the Foundation for Young Professors of Jimei University 
References 
[1] T. Furon and P. Duhamel.  Copy Protection of Distributed Contents: An Application of Watermarking Technique. In 
Workshop COST 254: Friendly Exchange through the net, Bordeaux, France, March 2000. 
[2] J. J. Eggers, J. K. Su, and B. Girod, Asymmetric watermarking schemes, Tagungsband des GI Workshops Sicherheit in 
Mediendaten, Berlin, Germany, Sept. 2000. 
[3] J. J. Eggers, J. K. Su, and B. Girod, Public key watermarking by eigenvectors of linear transforms, in Proc. Eur. Signal 
Processing Conf., Tampere, Finland, Sept. 2000. 
[4] T. Furon and P. Duhamel, An asymmetric public detection watermarking technique, in Proc. 3rd Int. Information Hiding 
Workshop, Dresden, Germany, Oct. 1999, pp. 88–100. 
[5] Tae Young Kim, Hyuk Choi, Kiryung Lee, and Taejeong Kim, An asymmetric watermarking system with many embedding 
watermarks corresponding to on detection watermark, IEEE signal processing letters, Vol.11(3), 2004, pp.375-377. 
[6] Hyuk Choi, Kiryung Lee, and Taejeong Kim, transformed-key asymmetric watermarking system, IEEE signal processing 
letters, Vol.11(2), 2004, pp.251-254. 
[7] Justin picard and Arnaud Robert,On the public key watermaking issue, Security and watermarking of multimedia contents, 
proceeding of SPIE Vol.4314, 2001, pp.290-299. 
[8] Geunsil Song, Miae Kim and Wonhyung Lee, Asymmetric watermarking scheme using permutation braids, WISA 2003, 
LNCS 2908, pp.217-226. 
[9]Furon, T., Duhamel, P.: Robustness of asymmetric watermarking technique. In Proc. of the Int. Conf. on Image Processing, 
Vancouver, Canada (2000) 
[10] Xinpeng Zhang, Shuozhong Wang, Watermarking scheme capable of resisting attacks based on availability of inserter, 
Signal processing, Vol.82,2002, pp.1801-1804. 
[11] F. Hartung and B. Girod, Fast public-key watermarking of compressed video, in Proc. IEEE Intl. Conf. Image Processing,
vol. 1, Oct. 1997, pp. 528–531. 


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Asymmetric Watermarking Scheme Based on Shuffling

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