Attack on a semi-blind watermarking scheme based on singular value decomposition

Attack on a semi-blind watermarking scheme based on singular value decomposition

Computer Standards & Interfaces 31 (2009) 523–525 Contents lists available at ScienceDirect Computer Standards & Interfaces j o u r n a l h o m e p ...

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Computer Standards & Interfaces 31 (2009) 523–525

Contents lists available at ScienceDirect

Computer Standards & Interfaces j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / c s i

Attack on a semi-blind watermarking scheme based on singular value decomposition Grace C.-W. Ting ⁎, Bok-Min Goi, Swee-Huay Heng Centre for Cryptography and Information Security (CCIS), Faculty of Engineering, Multimedia University, 63100 Cyberjaya, Malaysia

A R T I C L E

I N F O

Article history: Received 9 October 2006 Received in revised form 19 February 2008 Accepted 24 February 2008 Available online 15 March 2008

A B S T R A C T In this paper, we show that a recently proposed robust watermarking scheme by Shieh et al. does not bind a cover image to a watermark, therefore cannot be used for proof of ownership applications. The problem lies in the use of singular value decomposition (SVD) for this binding. © 2008 Elsevier B.V. All rights reserved.

Keywords: Digital watermarking SVD Ambiguity Non-binding

1. Introduction These days, information digitally stored and processed within computers and communicated between computers across interconnected networks has made it easier for exact digital copies to be made; so much so that it is difficult to monitor the distribution of content that are copyrighted and for which the owners wish to be credited. In this setting, digital watermarking is commonly used for copyright protection to prevent piracy and illegal duplication of digital copyrighted content. While legal policies are in place to combat these illegal piracy activities, watermarking as a technical solution serves as an additional countermeasure against digital pirates. In view of the importance of watermarking, efforts by major media industry players [5,6,9–11,14,15] like Digimarc, Hitachi, IBM, Macrovision, NEC, Philips, Pioneer, and Sony have initiated efforts to standardize watermarking for copyright protection of media content. The most typical type of content considered by watermarking schemes is images. For ease of description, we will assume for the rest of this paper that content is in the form of image. A digital watermark [3,1] is something that is embedded into a digital cover image. If the watermark belongs to the image owner, then it serves to prove ownership; if the watermark is unique to a particular buyer of the image then it serves to enable enforcement authorities to trace buyers who distribute the images illegally. In this paper we consider robust [3] watermarking schemes, i.e. the watermarked image should survive signal processing operations and also intentional tampering; and therefore the watermark should still be recoverable from it even after that. ⁎ Corresponding author. E-mail addresses: [email protected] (G.C.-W. Ting), [email protected] (B.-M. Goi), [email protected] (S.-H. Heng). 0920-5489/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.csi.2008.02.007

Singular value decomposition (SVD) [2] is a numerical tool applied in the field of digital signal and image processing [8], for example in image compression. In recent years [12,7,16], it has also been applied to image watermarking. Rightful ownership was first highlighted by Craver et al. [4] and deals with the problem of whether an embedded watermark in a content can unambiguously prove that the watermark owner is the only person laying rightful claims to the content, or are there other watermarks that can be extracted from the content leading to others laying equally rightful claims to the content. Clearly, this is of major concern in the case of using watermarking to provide proof of ownership. The outline of this paper is as follows: in the next sub-section, we briefly review concepts of DWT. In Section 2, we describe the robust watermarking scheme proposed by Shieh et al. In Section 3, we present our attack and other remarks on the scheme. Section 4 concludes this paper. 1.1. SVD The singular value decomposition (SVD) [2] is a useful tool applied in image processing, image compression, and image watermarking [12]. An image matrix A can be decomposed into a product of three matrices, A =U ·Σ ·VT where U and V are orthogonal matrices, UT ·U =I, VT ·V =I, where UT denotes the conjugate transpose of U. The diagonal entries of Σ are called the singular values of A, the columns of U (respectively V) are called the left (respectively right) singular vectors of A. The singular values have the special property that if the image is put through typical image processing operations, then though the singular values change, they do not vary significantly so if a watermark is combined with them this means robustness of the inserted watermark. Furthermore, these small changes in the singular values

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would not perceptually affect an image, thus an image would remain perceptually the same even after a watermark is inserted. 2. A robust watermarking scheme The robust watermarking scheme proposed by Shieh et al. [13] embeds a watermark as follows: E1. Transform the N × N cover image A and watermark W via chaotic mixing, under control of secret keys kA and kW. AC ¼ scrambleð A; kA Þ

ð1Þ

WC ¼ scrambleðW; kW Þ:

ð2Þ

E2. Divide AC (resp. WC) into non-overlapping fixed size blocks of N N size M × M. There are M M blocks. Perform SVD on each block i of AC (resp. j of WC): SVDðACi Þ ¼ UACi ; SACi ; VACi

ð3Þ

 SVD WCj ¼ UWCj ; SWCj ; VWCj :

ð4Þ

E3. Replace each SWCj with the nearest (using a minimum squared Euclidean distance measure) SACi and record the ACi ↔ WCj mapping in a file BM. E4. Reconstruct each block WCpj by inverse SVD: T : WCpj ¼ UWCj  SACi  VWC j

ð5Þ p

Then combine all blocks j to form the so-called secret image WC . Note that the cover image is not modified at all, but instead it is the watermark that is modified to contain information from the cover image. The process to extract the watermark is as follows: D1. Transform the N × N cover image A′ via chaotic mixing, under control of secret key kA. ACV¼ scrambleð AV; kA Þ

Firstly, note that there is no watermarked image generated. Instead, the output of the watermark embedding process is a mapping file BM and a secret image WCp that is perceptually non-meaningful. This makes the watermarking scheme impractical because the main purpose of robust watermarking is to be able to publicly display or distribute a watermarked image that is perceptually similar to the original cover image. It is okay for the public to access to this and even though image processing and intentional modifications are made to this watermarked image, the embedded watermark can still be extracted. In the case of this scheme, since there is no watermarked image, then an owner of the cover image cannot display any image and cannot also display the original cover image since it has no embedded watermark and may be claimed by others to be theirs. Secondly, this scheme is actually non-blind rather than semi-blind since the suspected image required during the extraction process, i.e. step D1 is actually the original cover image since there is no watermarked image. In contrast, other schemes produce a watermarked image and it is this watermarked image that needs to be provided, while the cover image need not be, thus these other schemes can be blind. We now proceed to our attack. The key observation is comparing steps D5 and E2 to reveal a fundamental flaw in the use of SVD for binding the cover image to the watermark. In step E2, the SVD components of each block of the scrambled watermark WC are UWCj, SWCj , VWCj . In contrast in step D5, the SVD components of each block of ˜ C p are UWC , SAC ′ , VWC . The only the extracted scrambled watermark W j i j ˜ C p is their difference between the original WC and the extracted W respective singular value matrices SWCj and SACi′ respectively, i.e. since T WC ¼ UWCj  SWCj  VWC j

ð11Þ

~ T WC p ¼ UWCj  SAC Vi  VWC : j

ð12Þ

˜ C p are perceptually similar. Therefore, the singular And yet WC and W value matrices SWCj and SAC i′ respectively do not significantly influence ˜ C p. As long as the U and V components are the same, then WC and W the watermarks would be perceptually similar, regardless of what the S

ð6Þ

N N M non-overlapping fixed size blocks of size D2. Divide AC′ into M M × M. Perform SVD on each block i of AC′:

SVDðACVi Þ ¼ UAC Vi ; SAC Vi ; VAC Vi :

ð7Þ

D3. Divide the secret image WCp into M × M non-overlapping fixed size blocks of size M × M. Perform SVD on each block j of WCp:   SVD WCpj ¼ UWCp ; SACj ; VWCp : j

j

ð8Þ

D4. Based on the mapping file BM, replace SACj with SACi′. ˜ Cpj by inverse SVD: D5. Reconstruct each block W ~ T : WCpj ¼ UWCj  SAC Vi  VWC j

ð9Þ

˜ C p. Then combine all blocks j to form W D6. Inverse transform via chaotic mixing to obtain the extracted watermark: ~  ~ W ¼ unscramble WCp ; kW :

ð10Þ

3. A non-binding attack Before we describe our attack, we make some observations on this scheme.

Fig. 1. Original watermark.

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[7] E. Ganic, N. Zubair, A.M. Eskicioglu, An optimal watermarking scheme based on singular value decomposition, Proc. IASTED International Conference on Communication, Network, and Information Security (CNIS '03), ACTA Press, 2003, pp. 85–90. [8] R.C. Gonzalez, R.E. Woods, Digital Image Processing, Prentice Hall, 2002. [9] P. Grabosky, R.G. Smith, G. Dempsey, Electronic Theft: Unlawful Acquisition in Cyberspace, Cambridge University Press, 2001. [10] E. Hansen, New Technology to Block Camcorder Pirates, CNET News.com, , 10 October 2002 Available online at http://news.zdnet.co.uk/itmanagement/ 0,1000000308,2123696,00.htm. [11] IBM Research, Watermark Standardization for DVD Copy Protection, 16 February 2001. Available online at http://www.trl.ibm.com/projects/RightsManagement/ datahiding/dhvgx_e.htm. [12] R. Liu, T. Tan, An SVD-based watermarking scheme for protecting rightful ownership, IEEE Transactions on Multimedia 4 (1) (2002) 121–128. [13] J.-M. Shieh, D.-C. Lou, M.-C. Chang, A semi-blind digital watermarking scheme based on singular value decomposition, Computer Standards and Interfaces 28 (2006) 428–440. [14] Sony Corporation, Digital Video Watermarking Technologies United, 17 February 1999. Available online at http://www.sony.net/SonyInfo/News/Press_Archive/ 199902/99-0217B/. [15] J.H. Taylor, M.R. Johnson, C.G. Crawford, DVD Demystified, McGraw-Hill Professional, 2006. [16] Y. Wu, On the security of an SVD-based ownership watermarking, IEEE Transactions on Multimedia 7 (4) (2005) 624–627. [17] X.-P. Zhang, K. Li, Comments on ‘An SVD-based watermarking scheme for protecting rightful ownership’, IEEE Transactions on Multimedia 7 (3) (2005) 593–594.

Fig. 2. Extracted watermark regardless of S component.

components are. A similar attack was applied by Zhang and Li [17] against the SVD watermarking scheme by Liu and Tan [12]. We have verified this experimentally in Matlab, see Figs. 1 and 2. To summarize, since the only component of the cover image that is embedded into the secret image is the S component, but regardless of what S is, the extracted watermark would still be perceptually similar to the original watermark; therefore regardless of what the cover image is, the extracted watermark and original watermark would be perceptually similar. Thus there is no binding between a cover image and a watermark, and an owner of the cover image cannot lay nonrefutable ownership claims on any cover image since it can be argued that any cover image would produce perceptually similar watermarks. Clearly, this scheme cannot be used for proof of ownership applications, although by right a robust watermarking schemes should provide this.

Grace C.-W. Ting received her B.Eng (Hons) degree in Electronic Engineering from Multimedia University (MMU), Cyberjaya, Malaysia in 2001; and her M.Eng.Sc degree in July 2007 specializing in watermarking security. Her research interests include information security, particularly in the security of watermarking schemes. Grace has several years of experience as an Engineering lecturer at college and university, and was formerly a lecturer at the School of Engineering, Swinburne University of Technology (Sarawak Campus). She now resides in the UK.

Bok-Min Goi received his B.Eng degree in Electrical Engineering from the University of Malaya (UM) in 1998, and the M.Eng.Sc and Ph.D degrees from Multimedia University (MMU) in 2002 and 2006, respectively. He is Senior Lecturer in the Faculty of Engineering, and the Chairman of the Centre for Cryptography and Information Security (CCIS), MMU. His research interests include cryptology, security protocols, information security, digital watermarking and embedded systems design.

4. Conclusion We have shown that the robust watermarking scheme by Shieh et al. does not bind a cover image to a watermark, and therefore cannot be used for proof of ownership applications although this is an expected basic application for any robust scheme. References [1] A. Adelsbach, S. Katzenbeisser, H. Veith, Watermarking schemes provably secure against copy and ambiguity attacks, Proc. ACM DRM '03, ACM, 2003, pp. 111–119. [2] H.C. Andrews, C.L. Patterson, Singular value decomposition (SVD) image coding, IEEE Transactions on Communications (1976) 425–432. [3] I.J. Cox, M.L. Miller, J.A. Bloom, Digital Watermarking, Morgan Kaufmann, 2002. [4] S. Craver, N. Memon, B.L. Yeo, M.M. Yeung, Resolving rightful ownerships with invisible watermarking techniques: limitations, attacks and implications, IEEE Journal of Selected Areas in Communication 16 (4) (1998) 573–586. [5] DVD-Recordable.org, DVD Recordable FAQ, accessed 19 February 2008. Available online at http://www.dvd-recordable.org/FAQ-Category6-DVD+Basics-Parent0myfaq-yes.phtml. [6] A. Earnshaw, Digimarc announces new partnership with video watermarking group, Portland Business Journal 25 (April 2001) Available online at http:// portland.bizjournals.com/portland/stories/2001/04/23/daily33.html.

Swee-Huay Heng received her B.Sc (Hons) and M.Sc degrees from University Putra Malaysia (UPM), and her Doctor of Engineering degree from the Tokyo Institute of Technology, Japan. She is currently a lecturer in the Faculty of Information Science & Technology, Multimedia University, Malaysia. Her research interests include cryptography and information security.