HEBGS: Homomorphic Encryption-based Background Subtraction Using a Fast-Converging Numerical Method

Abstract

Recent advances in cloud services provide greater computing ability to edge devices on cyber-physical systems (CPS) and internet of things (IoT) but cause security issues in cloud servers and networks. This paper applies homomorphic encryption (HE) to background subtraction (BGS) in CPS/IoT. Cheon et al. 's numerical methods are adopted to implement the non-linear functions of BGS in the HE domain. In particular, square- and square root-based HE-based BGS (HEBGS) designs are proposed for the input condition of the numerical comparison operation. In addition, a fast-converging method is proposed so that the numerical comparison operation outputs more accurate results with lower iterations. Although the outer loop of the numerical comparison operation is removed, the proposed square-based HEBGS with the fast-converging method shows an average peak signal-to-noise ratio value of 20dB and an average structural similarity index measure value of 0.89 compared to the non-HE-based conventional BGS. On a PC, the execution time of the proposed design for each $128\times 128$-sized frame is 0.34 seconds.