On the Complexity of Obtaining Optimal Watermarking Schemes
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.
KeywordsAdjacency Matrix Vertex Cover Watermark Scheme Pareto Frontier Information Hiding
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- 5.Cox, I.J., Miller, M.L., Bloom, J.A.: Digital Watermarking. Morgan Kaufmann Publishers, Inc., San Francisco (2001)Google Scholar
- 8.Kalker, T.: Considerations on watermarking security. In: Proceedings of the IEEE Multimedia Signal Processing Workshop, IIHMSP 2006, pp. 201–206 (2001)Google Scholar
- 9.Katzenbeisser, S., Petitcolas, F.A.: Information hiding, techniques for steganography and digital watermarking. Artech house (2000)Google Scholar
- 10.Kerckhoffs, A.: La cryptographie militaire. Journal des sciences militaires IX, 5–38 (January 1883)Google Scholar
- 12.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/
- 17.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)Google Scholar