A Secret Key Based Multiscale Fragile Watermark in the Wavelet Domain

The distribution of the wavelet coefficients in 2-D discrete wavelet transform (DWT) subspaces can be well described by a Gaussian mixture statistical model. In this paper, a secret key based fragile watermarking scheme is presented based on this statistical model. The Gaussian statistical model parameters are obtained by an expectation maximization (EM) algorithm and modified in a way to form special relationships for image authentication. The secret key is designed to securely embed a message bit stream, such as personal signatures or copyright logos, into a host image. Because of the secret embedding key, the new method is robust to most image tampering, even when the attackers are fully aware of the watermark embedding algorithms. Besides, the secret embedding key can be encrypted and embedded as a robust watermark into the same host image of the fragile watermarks for the benefit that the decoding of fragile watermarks only requires a single encryption key other than the image itself. The new method also has the advantage of changing only a few image data for watermark embedding and being able to distinguish some normal image operations such as compression from malicious to achieve a semi-fragile application