Abstract-Signal-processing modules working directly on encrypted data provide an elegant solution to application scenarios where valuable signals must 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 the direct DFT: the radix-2 and the radix-4 fast Fourier algorithms, including the error analysis and the maximum size of the sequence that can be transformed. We also provide computational complexity analyses and comparisons. The results show that the radix-4 fast Fourier transform is best suited for an encrypted domain implementation in the proposed scenarios. Index Terms-Discrete Fourier transform (DFT), error analysis, fast Fourier transform (FFT), homomorphic encryption, secure signal processing, signal processing in the encrypted domain, signal representation.
Bianchi et al. proposed the implementations of the discrete Fourier transform (DFT) and the fast Fourier transform (FFT) in the encrypted domain REF .
On the Implementation of the Discrete Fourier Transform in the Encrypted Domain
IEEE Transactions on Information Forensics and Security
IEEE Transactions on Information Forensics and Security
Computer Science