Security Analysis of Scalar Costa Scheme Against Known Message Attack in DCT-Domain Image Watermarking

This paper proposes an accurate information-theoretic security analysis of Scalar Costa Scheme (SCS) when the SCS is employed in the embedding layer of digital image watermarking. For this purpose, Discrete Cosine Transform (DCT) coefficients are extracted from the cover images. Then, the SCS is used to embed watermarking messages into mid-frequency DCT coefficients. To prevent unauthorized embedding and/or decoding, the SCS codebook is randomized using the pseudorandom dither signal which plays the role of the secret key. A passive attacker applies Known Message Attack (KMA) on the watermarked messages to practically estimate the secret key. The security level is measured using residual entropy (equivocation) of the secret key provided that the attacker’s observations are available. It can be seen that the practical security level of the SCS depends on the host statistics which has contradiction with previous theoretical result. Furthermore, the practical security analysis of the SCS leads to the different values of the residual entropy in comparison with previous theoretical equation. It will be shown that these differences are mainly due to existence of uniform regions in images that cannot be captured by previous theoretical analysis. Another source of such differences is ignoring the dependencies between the observations of non-uniform regions in previous theoretical analysis. To provide an accurate reformulation, the theoretical equation for the uniform regions and the empirical equation for the non-uniform regions are proposed. Then, by combining these equations a new equation is presented for the whole image which considers both host statistics and observations dependencies. Finally, accuracy of the proposed formulations is examined through exhaustive simulations.