Privacy-Preserving Image Filtering and Thresholding Using Numerical Methods for Homomorphically Encrypted Numbers

Abstract

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 thesis proposes a HE-based locally adaptive Wiener filter (HELAWF). 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. Image thresholding is a method of segmenting a region of interest and is used in many real-world applications. Typically, image thresholding contains a comparison operation, but this operation is not supported in conventional HE schemes. To solve this problem, a numerical approach for comparison operation is used in the proposed HE-based image thresholding (HETH). The proposed HELAWF and HETH designs are integrated and implemented as a proof-of-concept client-server model. In practical HE schemes, the number of consecutive multiplications on encrypted data is limited. Therefore, the number of iterations of the numerical methods used in the integrated design is carefully chosen. To the best of the author’s knowledge, this thesis is the first work that applies numerical division and comparison operation over encrypted data to image processing (IP) algorithms. The proposed solutions can address important privacy issues in IP applications in internet-of-things and cyber-physical systems, where many devices are connected through a vulnerable network.