Two private, perceptual data-hiding games

Perceptual watermarking methods are designed to be transparent and robust to attacks. A perceptual model based on Just Noticeable Difference levels introduces amplitude constraints on the watermark and the noise generated by an attacker. Two problems are considered in this paper: (1) detection performance for embedding a single bit in n data, and (2) Shannon capacity. In both cases the original host data are known to the receiver. Both problems are formulated as games involving a suitable cost function (Bhattacharyya distance and mutual information, respectively). The watermarker and the attacker design probability distributions in order to respectively maximize and minimize the cost function. The optimal distributions are quite different from the uniform distributions that have been previously used in the watermarking literature.