This paper puts in consideration the concepts of security and robustness in watermarking, in order to be able to establish a clear frontier between them. A new information-theoretic framework to study data-hiding and watermarking security is proposed, using the mutual information to quantify the information about the secret key that leaks from the observation of watermarked objects. This framework is applied to the analysis of a Spread-Spectrum data-hiding scheme in different scenarios. Finally, we show some interesting links between a measure proposed in previous works in the literature, which is based on Fisher Information Matrix, and our proposed measure.