Abstract
In this paper, we try to answer the question: is the task of obtaining optimal watermarking schemes computationally feasible ? We introduce a formalism to express watermarking algorithms over finite domains of contents and exploit it to study two aspects of watermarking: the relevance of the detection process and its robustness. We formulate the search for an optimal scheme as an optimisation problem. We prove that (1) finding the algorithm which has the highest relevance for a fixed robustness against a known attack is NEXP-complete relatively to the domain encoding size and that (2) finding the algorithm which has the highest robustness for a fixed relevance is NP-complete relatively to the cardinality of the application domain.
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References
Adelsbach, A., Katzenbeisser, S., Sadeghi, A.-R.: A computational model for watermark robustness. In: Camenisch, J.L., Collberg, C.S., Johnson, N.F., Sallee, P. (eds.) IH 2006. LNCS, vol. 4437. Springer, Heidelberg (2007)
Cayre, F., Fontaine, C., Furon, T.: Watermarking security: Theory and practice. IEEE Transactions on Signal Processing 53(10), 3976–3987 (2005)
Chen, B., Wornell, G.W.: Quantization index modulation: A class of provably good methods for digital watermarking and information embedding. IEEE Transactions on Information Theory 47(4), 1423–1443 (2001)
Comesaña, P., Pérez-González, F., Balado, F.: Watermarking security: a survey. IEEE Transactions on Signal Processing 54(2), 585–600 (2006)
Cox, I.J., Miller, M.L., Bloom, J.A.: Digital Watermarking. Morgan Kaufmann Publishers, Inc., San Francisco (2001)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness, Apr. 1979. W.H. Freeman & Company, New York (1979)
Herley, C.: Why watermarking is nonsense. IEEE Signal Processing Magazine 19(5), 10–11 (2002)
Kalker, T.: Considerations on watermarking security. In: Proceedings of the IEEE Multimedia Signal Processing Workshop, IIHMSP 2006, pp. 201–206 (2001)
Katzenbeisser, S., Petitcolas, F.A.: Information hiding, techniques for steganography and digital watermarking. Artech house (2000)
Kerckhoffs, A.: La cryptographie militaire. Journal des sciences militaires IX, 5–38 (January 1883)
Li, Q., Chang, E.: Security of public watermarking schemes for binary sequences. In: Petitcolas, F.A.P. (ed.) IH 2002. LNCS, vol. 2578, pp. 119–128. Springer, Heidelberg (2003)
Merhav, N., Sabbag, E.: Optimal watermark embedding and detection strategies under limited detection resources. In: IEEE Transactions on Information Theory (submitted) (December 2005), http://www.ee.technion.ac.il/people/merhav/
Moulin, P., Koetter, R.: Data-hiding codes (tutorial paper). Proceedings of the IEEE 93(12), 2083–2127 (2005)
Moulin, P., O’Sullivan, J.A.: Information-theoretic analysis of information hiding. IEEE Transactions on Information Theory 49(3), 563–593 (2003)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1993)
Papadimitriou, C.H., Yannakakis, M.: A note on succinct representations of graphs. Information and Control 71, 181–185 (1986)
Papadimitriou, C.H., Yannakakis, M.: On the approximability of trade-offs and optimal access of web sources. In: IEEE Symposium on Foundations of Computer Science, FOCS 2000, pp. 86–92 (2000)
Skyum, S., Valiant, L.: A complexity theory based on boolean algebra. Journal of the ACM 32(2), 484–502 (1985)
Wegener, I.: The Complexity of Boolean Functions, January 1991. Wiley, Chichester (1991)
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Lafaye, J. (2008). On the Complexity of Obtaining Optimal Watermarking Schemes. In: Shi, Y.Q., Kim, HJ., Katzenbeisser, S. (eds) Digital Watermarking. IWDW 2007. Lecture Notes in Computer Science, vol 5041. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92238-4_31
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DOI: https://doi.org/10.1007/978-3-540-92238-4_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92237-7
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