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This paper presents a security analysis for data-hiding methods based on nested lattice codes, extending the analysis provided by previous works to a more general scenario. The security is quantified as the difficulty of estimating the secret key used in the embedding process, assuming that the attacker has several signals watermarked available with the same secret key. The theoretical analysis accomplished in the first part of this paper quantifies security in an information-theoretic sense by means of the mutual information between the watermarked signals and the secret key, addressing important issues, such as the possibility of achieving perfect secrecy and the impact of the embedding rate in the security level. In the second part, a practical algorithm for estimating the secret key is proposed, and the information extracted is used for implementing a reversibility attack on real images.