Implementing the discrete Fourier transform in the encrypted domain

Signal processing modules working directly on the encrypted data could provide an elegant solution to application scenarios where valuable signals should be protected from a malicious processing device. In this paper, we investigate the implementation of the discrete Fourier transform (DFT) in the encrypted domain, by using the homomorphic properties of the underlying cryptosystem. Several important issues are considered for both the DFT and radix-2 fast Fourier transform, including the error analysis and the maximum size of the sequence that can be transformed.