  Cloud computing is an important part of today's world because offloading
computations is a method to reduce costs. In this paper, we investigate
computing the Speeded Up Robust Features (SURF) using Fully Homomorphic
Encryption (FHE). Performing SURF in FHE enables a method to offload the
computations while maintaining security and privacy of the original data. In
support of this research, we developed a framework to compute SURF via a
rational number based compatible with FHE. Although floating point (R) to
rational numbers (Q) conversion introduces error, our research provides tight
bounds on the magnitude of error in terms of parameters of FHE. We empirically
verified the proposed method against a set of images at different sizes and
showed that our framework accurately computes most of the SURF keypoints in
FHE.
