Efficient Privacy-Preserving Outsourced Discrete Wavelet Transform in the Encrypted Domain

Signal processing in the encrypted domain is a potential tool to protect sensitive signals against untrusted cloud servers and unauthorized users in the delegated computing setting, without affecting the accuracy of large volume of signal analyzing and processing. Most existing approaches use Paillier's public key additively homomorphic encryption to encrypt each signal in a large bundle; thus, incurring significant computational costs at local, often resource-constrained, devices while guaranteeing only signal input privacy. To address these limitations, in this paper, an efficient privacy-preserving outsourced discrete wavelet transform scheme (PPDWT), comprising PPDWT-1 and PPDWT-2, without leveraging public key (fully) homomorphic encryption is proposed. Specifically, PPDWT-1 is proposed to achieve signal input privacy against the collusion between the honest-but-curious cloud and unauthorized users, and the proposed PPDWT-2 protects both signal input privacy and coefficient privacy against collusion attacks. Both constructions leverage the offline execution of any one-way trapdoor permutation only once to encrypt batch signals, and permit signal processing in the encrypted domain. In our approach, only authorized users can successfully decipher the result of discrete wavelet transform. Compared to the O(|l|)O(|l|) computational complexity on the user's end in existing state-of-the-art public key homomorphic encryption-based techniques, our approach only incurs O(1)O(1) computational complexity which is independent to size of the signal inputs |l||l|. We also discuss the expanding factor, the upper bound and various extensions to privacy-preserving discrete cosine/fourier transform in the encrypted domain. Finally, our proposed PPDWT is formally proved secure under the universal composability (UC) model. We then evaluate the proposed approach using case studies to demonstrate its effectiveness and practicability.