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This paper presents both theoretical and practical analyses of the security offered by watermarking and data hiding methods based on spread spectrum. In this context, security is understood as the difficulty of estimating the secret parameters of the embedding function based on the observation of watermarked signals. On the theoretical side, the security is quantified from an information-theoretic point of view by means of the equivocation about the secret parameters. The main results reveal fundamental limits and bounds on security and provide insight into other properties, such as the impact of the embedding parameters, and the tradeoff between robustness and security. On the practical side, workable estimators of the secret parameters are proposed and theoretically analyzed for a variety of scenarios, providing a comparison with previous approaches, and showing that the security of many schemes used in practice can be fairly low.