Walsh-Hadamard Transform in the Homomorphic Encrypted Domain and Its Application in Image Watermarking

How to embed and/or extract watermarks on encrypted images without being able to decrypt is a challenging problem. In this paper, we firstly discuss the implementation of Walsh-Hadamard transform (WHT) and its fast algorithm in the encrypted domain, which is particularly suitable for the applications in the encrypted domain for its transform matrix consists of only integers. Then by modifying the relations among the adjacent transform coefficients, we propose an WHTbased image watermarking algorithm in the encrypted domain. Due to the constrains of the encryption, extracting a watermark blindly from an encrypted image is not a easy task. However, our proposed algorithm possesses the characteristics of blind watermark extraction both in the decrypted domain and the encrypted domain. This means neither the plain image nor its encrypted version is required for the extraction. The experiments demonstrate the validity and the advantages of our proposed method.