Design and Statistical Analysis of a Hash-Aided Image Watermarking System

This paper develops a joint hashing/watermarking scheme in which a short hash of the host signal is available to a detector. Potential applications include content tracking on public networks and forensic identification. The host data into which the watermark is embedded are selected from a secret subset of the full-frame discrete cosine transform of an image, and the watermark is inserted through multiplicative embedding. The hash is a binary version of selected original image coefficients. We propose a maximum likelihood watermark detector based on a statistical image model. The availability of a hash as side information to the detector modifies the posterior distribution of the marked coefficients. We derive Chernoff bounds on the receiver operating characteristic performance of the detector. We show that host–signal interference can be rejected if the hash function is suitably designed. The relative difficulty of an eavesdropper’s detection problem is also determined; the eavesdropper does not know the secret key used. Monte Carlo simulations are performed using photographic test images. Finally, various attacks on the watermarked image are introduced to study the robustness of the derived detectors. The joint hashing/watermarking scheme outperforms the traditional “hashless” watermarking technique.