GSM Based Security Analysis for Add-SS Watermarking

Attack to security of watermarking is to estimate secret keys used in watermarking communications. The Security level of watermarking algorithms can be evaluated by Cramer-Rao Bound (CRB) for the estimation of secret keys. As a widely used method, Add-Spread-Spectrum (Add-SS) watermarking has drawn a lot of attention. Previous work on watermarking security is mainly based on the assumption that the host is Gaussian distributed and ignores the impact of the non-Gaussian characteristics of natural images. With the incorporation of Gaussian Scale Mixture (GSM) model for host signals, this paper presents a theoretical analysis on the security of the Add-SS watermarking algorithms. By giving the CRB and Modified Cramer-Rao Bound (MCRB) for the estimation of secret carriers under Known Message Attack (KMA) and Watermarked Only Attack (WOA), this paper also reveals the factors that may influence the security of Add-SS based watermarking algorithms. Results presented in this paper are very helpful for designing the new generation of secure and robust watermarking system.