Security of lattice-based data hiding against the known message attack

Security of quantization index modulation (QIM) watermarking methods is usually sought through a pseudorandom dither signal which randomizes the codebook. This dither plays the role of the secret key (i.e., a parameter only shared by the watermarking embedder and decoder), which prevents unauthorized embedding and/or decoding. However, if the same dither signal is reused, the observation of several watermarked signals can provide sufficient information for an attacker to estimate the dither signal. This paper focuses on the cases when the embedded messages are either known or constant. In the first part of this paper, a theoretical security analysis of QIM data hiding measures the information leakage about the secret dither as the mutual information between the dither and the watermarked signals. In the second part, we show how set-membership estimation techniques successfully provide accurate estimates of the dither from observed watermarked signals. The conclusion of this twofold study is that current QIM watermarking schemes have a relative low security level against this scenario because a small number of observed watermarked signals yields a sufficiently accurate estimate of the secret dither. The analysis presented in this paper also serves as the basis for more involved scenarios.