A Homomorphic Encryption-based Adaptive Image Filter Using Division Over Encrypted Data

Homomorphic encryption (HE) is an important cryptographic technique that allows one to directly perform computation on encrypted data without decryption. In HE-based applications using digital images, a user often encrypts a private image captured on a local device. This image can contain noise that negatively affects the results of HE-based applications. To solve this problem, this paper proposes an HE-based adaptive image filter. For small-sized encrypted input data, pixels that have no dependency when sliding a window are encoded into the same ciphertext. For division in the adaptive filter, which is not supported by conventional HE schemes, a numerical approach is adopted. To the best of the authors’ knowledge, this paper is the first work that applies division over encrypted data to an image processing algorithm. We implemented the proposed HE-based adaptive filter as a proof-of-concept client-server model. The proposed design can address important privacy issues in image processing applications in internet-of-things and cyber-physical systems, where many devices are connected through a vulnerable network.