Encrypted Domain DCT Based on Homomorphic Cryptosystems

Signal processing in the encrypted domain (s.p.e.d.) appears an elegant solution in application scenarios where valuable signals must be protected from a possibly malicious processing device. In this paper we consider the application of the Discrete Cosine Transform (DCT) to images encrypted by using an appropriate homomorphic cryptosystem. A s.p.e.d. 1-dimensional DCT is obtained by defining a convenient signal model, and is extended to the 2-dimensional case by using separable processing of rows and columns. The bounds imposed by the cryptosystem on the size of the DCT and the arithmetic precision are derived, considering both the direct DCT algorithm and its fast version. Particular attention is given to block-based DCT (BDCT), with emphasis on the possibility of lowering the computational burden by parallel application of the s.p.e.d. DCT to different image blocks. The application of the s.p.e.d. 2D-DCT and 2D-BDCT to 8-bit greyscale images is analyzed, whereas a case study demonstrates the feasibility of the s.p.e.d. DCT in a practical scenario.