Accurate and Efficient Privacy-Preserving Feature Extraction on Encrypted Images

In cloud computing, it is necessary to outsource image processing algorithms securely without exposing private image content. The scale-invariant feature transform (SIFT) is a famous local descriptor widely used in computer vision. There are already some privacy-preserving schemes for computing SIFT on encrypted images. However, the state-of-the-art works have to convert fixed-point numbers into their binary representations, which reduces efficiency and accuracy. In this paper, we propose a novel privacy-preserving SIFT scheme built from secure protocols designed explicitly for fixed-point numbers to solve this problem. Specifically, using RLWE-based homomorphic encryption, we propose word-wise protocols to perform secure division, square root operation, comparison, derivation, and matrix inversion in a single-instruction multiple-data manner. These protocols allow direct processing of fixed-point numbers without converting them to binary numbers, thus achieving high computational efficiency. We have also realized critical SIFT steps missing from previous works, including Euclidean gradient amplitude computation, histogram peak interpolation, and precise interval localization, leading to improved accuracy of SIFT features in the encrypted domain. We conduct security analysis and perform extensive experiments to evaluate the execution efficiency and accuracy. The experimental results show that the proposed scheme outperforms the state-of-the-art works in terms of computational efficiency and accuracy.