On the Complexity of Obtaining Optimal Watermarking Schemes

Authors:
Julien Lafaye
Affiliations:
Cnam - Cédric, 292 rue Saint Martin - CC 432, PARIS Cedex 3, France 75141
Venue:
IWDW '07 Proceedings of the 6th International Workshop on Digital Watermarking
Year:
2008

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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.