Security Analysis for Spread-Spectrum Watermarking Incorporating Statistics of Natural Images

Spread-spectrum based watermarking has become a widely used watermarking method in recent years and its security reliability has drawn research attention. Previous work on evaluating 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. This paper presents a theoretical analysis on the security of spread-spectrum based watermarking with the incorporation of the statistics of natural images. By calculating the Cramer-Rao Bound and Modified Cramer-Rao Bound of the estimation of secret carriers under Known Message Attack and Watermarked Only Attack, this paper investigates factors such as the number of observations, the length of secret carriers, the embedded power, and the distribution of embedded messages that may influence the security of spread-spectrum based watermarking algorithms. Results obtained in this paper are very helpful for designing the new generation of secure and robust watermarking systems.