JEI Letters

On the security of ownership watermarking of digital images based on singular value decomposition

[+] Author Affiliations
Huo-Chong Ling, Swee-Huay Heng

Multimedia University, Faculty of Engineering, Centre for Multimedia Security and Signal Processing, Research Group of Cryptography and Information Security, Cyberjaya, Selangor 63100 Malaysia

Raphael C.-W. Phan

Loughborough University, Department of Electronic and Electrical Engineering, LE11 3TU, United Kingdom

J. Electron. Imaging. 20(1), 010501 (January 20, 2011). doi:10.1117/1.3534865
History: Received August 19, 2010; Revised October 26, 2010; Accepted December 13, 2010; Published January 20, 2011; Online January 20, 2011
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Open Access Open Access

* E-mail: hcling@mmu.edu.my

We show that the two countermeasures proposed in a paper on the security of ownership watermarking of digital images based on singular value decomposition by Loukhaoukha and Chouinard do not solve the false-positive detection problem in contrast to designers’ claim and therefore should not be used for proof of ownership application.

Figures in this Article

Loukhaoukha and Chouinard1 have recently proposed two countermeasures for the problem of false-positive detections23 of watermarks that exists in Abdallah et al. 4 and Aslantas5 singular value decomposition (SVD)-based watermarking schemes without making changes to the original algorithm of those schemes. They claimed that the countermeasures could be applied as an add-on to any SVD-based watermarking schemes that suffered from false-positive detections.

The first countermeasure uses a one-way hash function, such as MD5 or SHA-1 during the embedding process to compute digests of the SVD matrices

UW
and VW of the embedded watermark W. The digests or hash values of UW and VW (denoted as HUW and HVW) are then kept by the owner so that he can use them in the extraction process if he wants to claim ownership. During the extraction process, the ownership claimant supplies the digests HUW and HVW of his own watermark and HUW and HVW are verified with the hash values of the received (and possibly altered by an attacker) matrices ŨW and ṼW (denoted as HŨW and HṼW). If HUWHŨW or HVWHṼW, then the extraction process halts; otherwise, the extraction process continues. In other words, they claimed that only the rightful owner was able to extract the embedded watermark W if HUW = HŨW (UW = ŨW) and HVW = HṼW (VW = ṼW).

The second countermeasure uses an image-encryption (respectively, decryption) method on the watermark W before the embedding process (respectively, after the extraction process). Before the embedding process, watermark W is encrypted to give

WE
and then WE is embedded in cover image I to obtain the watermarked image IW. In the extraction process, WE* is obtained from the possibly corrupted watermarked image IW* and decrypted to get the watermark W*, which is perceptually similar to the owner's watermark W. Loukhaoukha and Chouinard1 claimed that a false-positive attack would result in the first extracted image be the attacker's watermark W̃ because the attacker is using the matrices UW̃ and VW̃, instead of proper matrices UW and VW. However, because the attacker has to feed the first extracted watermark (i.e., W̃ to the decryption process), his final watermark will thus be an encrypted image, which does not help in his ownership claim.

In Sec. 2 we show that both countermeasures do not solve the false-positive detection in contrast to what is claimed by Loukhaoukha and Chouinard.1

Theorectical Analysis and Experiments

In the first countermeasure, the hash values of the watermark W’s SVD matrices

UW
and VW (denoted as HUW and HVW) provided by the ownership claimant does not bind to the watermarked image IW. Because there is no proof showing that HUW and HVW belong to the rightful owner of the watermark W, therefore an attacker A, who repeats the same hashing process on the SVD matrices UA and VA of his own watermark WA to obtain HUA and HVA, can claim that the watermarked image IW belongs to him because the extraction process will verify that HUA = HŨW (UA = ŨW) and HVA = HṼW (VA = ṼW).

An interesting fact is that since A attacks the scheme, he can provide his own kept

HŨW
and HṼW which are similar to HUA and HVA during the extraction process. The same case applies to the rightful owner, whereby in order to claim the watermarked image IW, he has to provide his own kept versions of HŨW and HṼW that are similar to HUW and HVW during the extraction process. Therefore, both have equal rights to the watermarked image IW and no one can prove more than the other. The flaw occurs because the designers1 view the countermeasure in the owner's perspective, ignoring the fact that the attacker can repeat the same steps as the owner.

In the second countermeasure, an encrypted watermark

WE
is used in the embedding process. Hence, in the extraction process, after the encrypted watermark is extracted from the watermarked image IW, it has to be decrypted to obtain the watermark W*, which is perceptually similar to the original watermark W. The owner needs to keep the SVD’s UWE and VWE components of the encrypted watermark WE so that he can supply the components later in the extraction process. If during the extraction process, an attacker A provides encrypted SVD matrices UW̃E and VW̃E of his own encrypted watermark W̃E, instead of proper matrices UW̃ and VW̃ as mentioned by the designers,1 then he can still obtain his own encrypted watermark W̃E*. The encrypted watermark W̃E* is later decrypted to obtain W̃*, which is perceptually similar to W̃. This countermeasure fails because the designers1 did not notice that the attacker can simply repeat the same process as the owner in the proof-of-ownership game because they both claim ownership and the extraction process obtains the encrypted SVD matrices from the ownership claimant.

Figure 1 shows the cover image I, the owner's watermark W, the owner's encrypted watermark

WE
and the watermarked image IW after being embedded with WE. Figure 2 shows the attacker's watermark W̃, the encrypted watermark W̃E of the attacker, the extracted encrypted watermark W̃E* from the watermarked image IW* using UW̃E and VW̃E, and the final decrypted watermark W̃*. As can be seen from the experimental results, the final watermark W̃* that is decrypted from W̃E*, is perceptually similar to the attacker's watermark W̃ with the correlation coefficient value of 0.948.

Graphic Jump LocationF1 :

(a) Cover image, (b) owner's watermark (c) owner's encrypted watermark and (d) watermarked image.

Graphic Jump LocationF2 :

(a) Attacker's watermark, (b) attacker's encrypted watermark, (c) extracted encrypted watermark, and (d) Final decrypted watermark.

A possible countermeasure against false-positive detections would be to avoid67 using the watermark's SVD matrices U and V in the embedding (and thus extraction) process of the Abdallah et al. 4 and Aslantas5 schemes. This removes the influence of SVD matrices U and V on the watermark extraction process, which is the main problem causing false-positive detections.

We have shown that Loukhaoukha and Chouinard1 countermeasures are not able to solve the false-positive detection of the attacker's watermark and thus are not suitable for proof-of-ownership application. This is in contrast to the designers' (Ref. 1) claims that the countermeasures are explicitly designed to solve the problem. The shortfall is because the designers only viewed the countermeasures’ design from the owner's perspective, instead of also from the attacker's perspective as an ownership claimant. When designing the countermeasures as an add-on to the SVD-based watermarking scheme, the designers did not consider that the attacker can follow the same steps as the owner. This leads to the failure of the countermeasures to solve the false-positive detection problem.

Loukhaoukha  K., and Chouinard  J., “ Security of ownership watermarking of digital images based on singular value decomposition. ,” J. Electron. Imaging. 19, , 013007  ((2010)).
Rykaczewski  R., “ Comments on An SVD-based watermarking scheme for protecting rightful ownership. ,” IEEE Trans. Multimedia.. 9, (2 ), 421–423  ((2007)).
Zhang  X. P., and Li  K., “ Comments on An SVD-based watermarking scheme for protecting rightful ownership. ,” IEEE Trans. Multimedia.. 7, (2 ), 593–594  ((2005)).
Abdallah  E., , Hamza  A. B., , and Bhattacharya  P., “ Improved image watermarking scheme using fast Hadamard and discrete wavelet transforms. ,” J. Electron. Imaging. 16, , 033020  ((2007)).
Aslantas  V., “ An optimal robust digital image watermarking based on SVD using differential evolution algorithm. ,” Opt. Commun.. 282, (5 ), 769–777  ((2009)).
Mohammad  A. A., , Alhaj  A., , and Shaltaf  S., “ An improved SVD-based watermarking scheme for protecting rightful ownership. ,” Signal Processing. 88, , 2158–2180  ((2008)).
Ling  H.-C., , Phan  R. C.-W., , and Heng  S.-H., “ Analysis on the improved SVD-based watermarking scheme. ,” Lect. Notes Comput. Sci.. 6059, , 143–149  ((2010)).
© 2011 SPIE and IS&T

Citation

Huo-Chong Ling ; Raphael C.-W. Phan and Swee-Huay Heng
"On the security of ownership watermarking of digital images based on singular value decomposition", J. Electron. Imaging. 20(1), 010501 (January 20, 2011). ; http://dx.doi.org/10.1117/1.3534865


Figures

Graphic Jump LocationF1 :

(a) Cover image, (b) owner's watermark (c) owner's encrypted watermark and (d) watermarked image.

Graphic Jump LocationF2 :

(a) Attacker's watermark, (b) attacker's encrypted watermark, (c) extracted encrypted watermark, and (d) Final decrypted watermark.

Tables

References

Loukhaoukha  K., and Chouinard  J., “ Security of ownership watermarking of digital images based on singular value decomposition. ,” J. Electron. Imaging. 19, , 013007  ((2010)).
Rykaczewski  R., “ Comments on An SVD-based watermarking scheme for protecting rightful ownership. ,” IEEE Trans. Multimedia.. 9, (2 ), 421–423  ((2007)).
Zhang  X. P., and Li  K., “ Comments on An SVD-based watermarking scheme for protecting rightful ownership. ,” IEEE Trans. Multimedia.. 7, (2 ), 593–594  ((2005)).
Abdallah  E., , Hamza  A. B., , and Bhattacharya  P., “ Improved image watermarking scheme using fast Hadamard and discrete wavelet transforms. ,” J. Electron. Imaging. 16, , 033020  ((2007)).
Aslantas  V., “ An optimal robust digital image watermarking based on SVD using differential evolution algorithm. ,” Opt. Commun.. 282, (5 ), 769–777  ((2009)).
Mohammad  A. A., , Alhaj  A., , and Shaltaf  S., “ An improved SVD-based watermarking scheme for protecting rightful ownership. ,” Signal Processing. 88, , 2158–2180  ((2008)).
Ling  H.-C., , Phan  R. C.-W., , and Heng  S.-H., “ Analysis on the improved SVD-based watermarking scheme. ,” Lect. Notes Comput. Sci.. 6059, , 143–149  ((2010)).

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