Secure Homomorphic Evaluation of Discrete Cosine Transform with High Precision

Signal Processing in the Encrypted Domain (SPED) has received considerable attention as it aims at privacy-preserving solutions for various applications. Discrete cosine transform (DCT) is a popular signal transform widely used in signal processing. It has many applications in speech processing, still picture coding, image and video transformation, compression coding, and so on. In this paper, we mainly study how to implement DCT in the encryption domain with high precision. We propose a new scheme to implement encrypted domain DCT. This scheme encodes a complex number as a unit root polynomial in the evaluation, and realizes the high precision representation of complex numbers. With this representation, this scheme can also realize the high precision representation of decimals. To improve the computational efficiency, we also propose a fast implementation of DCT in the encryption domain, which can significantly improve the DCT speed for large-scale matrices. We conducted experiments to verify the effectiveness and efficiency. When the matrix size is small, our original method has the advantages of both high accuracy and fast speed. When the matrix size is large, the fast implementation outperforms the original method.