STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The Montgomery Modular Inverse-Revisited
IEEE Transactions on Computers - Special issue on computer arithmetic
The Montgomery Inverse and Its Applications
IEEE Transactions on Computers
A Hardware Algorithm for Modular Multiplication/Division
IEEE Transactions on Computers
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Protection and retrieval of encrypted multimedia content: when cryptography meets signal processing
EURASIP Journal on Information Security
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Efficient binary conversion for paillier encrypted values
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
A buyer-seller watermarking protocol
IEEE Transactions on Image Processing
An efficient and anonymous buyer-seller watermarking protocol
IEEE Transactions on Image Processing
Fingerprinting protocol for images based on additive homomorphic property
IEEE Transactions on Image Processing
Efficient linear filtering of encrypted signals via composite representation
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
Composite signal representation for fast and storage-efficient processing of encrypted signals
IEEE Transactions on Information Forensics and Security
Encrypted domain DCT based on homomorphic cryptosystems
EURASIP Journal on Information Security - Special issue on enhancing privacy protection in multimedia systems
Identification of JPEG 2000 images in encrypted domain for digital cinema
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
MM '11 Proceedings of the 19th ACM international conference on Multimedia
Conversion of real-numbered privacy-preserving problems into the integer domain
ICICS'12 Proceedings of the 14th international conference on Information and Communications Security
IH'12 Proceedings of the 14th international conference on Information Hiding
An efficient image homomorphic encryption scheme with small ciphertext expansion
Proceedings of the 21st ACM international conference on Multimedia
An improved algorithm for reversible data hiding in encrypted image
IWDW'12 Proceedings of the 11th international conference on Digital Forensics and Watermaking
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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.