Graph spectral domain watermarking for unstructured data from sensor networks

The modern applications like social networks and sensors networks are increasingly used in the recent years. These applications can be represented as a weighted graph using irregular structure. Unfortunately, we cannot apply the techniques of the traditional signal processing on those graphs. In this paper, graph spread spectrum watermarking is proposed for networked sensor data authentication. Firstly, the graph spectrum is computed based on the eigenvector decomposition of the graph Laplacian. Then, graph Fourier coefficients are obtained by projecting the graph signals onto the basis functions which are the eigenvectors of the graph Laplacian. Finally, the watermark bits are embedded in the graph spectral coefficients using a watermark strength parameter varied according to the eigenvector number. We have considered two scenarios: blind and non-blind watermarking. The experimental results show that the proposed methods are robust, high capacity and result in low distortion in data. The proposed algorithms are robust to many types of attacks: noise, data modification, data deletion, rounding and down-sampling.