Security Analysis on Add-SS Watermarking with GSM

Abstract

Watermarking security has emerged as the domain of extensive research in recent years. Attack to the security of watermarking is to estimate the secret keys used in watermarking communications. The security level of watermarking system can be evaluated by Cramer-Rao bound (CRB) for secret keys estimation. As a widely used method, the security issue of add spread spectrum (Add-SS) based watermarking has drawn great attention. The previous works on watermarking security were mainly based on the assumption that host signal was Gaussian distributed and ignored the impacts of non-Gaussian characteristics of nature images. With incorporation of the Gaussian scale mixture (GSM) model for host signals, this paper presents a theoretical analysis on the security of Add-SS watermarking system. By giving the CRB and MCRB (modified Cramer-Rao bound) for the estimation of secret carriers under KMA (known message attack) and WOA (watermarked only attack), this paper also reveals the factors that may influent the Add-SS watermarking security such as the times of observation, the length of secret carriers, the embedding energy, and the distribution of embedded messages. The results obtained in this paper will be helpful for designing the new secure and robust watermarking system.