Discrete Cosine Transform of Encrypted Images

Processing a signal directly in the encrypted domain provides an elegant solution in application scenarios where valuable signals must be protected from a malicious processing device. In a previous paper we considered the implementation of the 1D Discrete Fourier Transform (DFT) in the encrypted domain, by using the homomorphic properties of the underlying cryptosystem. In this paper we extend our previous results by considering the application of the 2- dimensional DCT to encrypted images. The effect of the consecutive application of the DCT algorithm first by rows then by columns is considered, as well as the differences between the implementation of the direct DCT algorithm and its fast version. Particular attention is given to block-based DCT, with emphasis on the possibility of lowering the computational burden by parallel application of the encrypted domain DCT algorithm to different image blocks.