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Recently, cyber-physical systems are actively using cloud servers to overcome the limitations of power and processing speed of edge devices. When passwords generated on a client device are evaluated on a server, the information is exposed not only on networks but also on the server-side. To solve this problem, we move the previous lightweight password strength estimation (LPSE) algorithm to a homomorphic encryption (HE) domain. Our proposed method adopts numerical methods to perform the operations of the LPSE algorithm, which is not provided in HE schemes. In addition, the LPSE algorithm is modified to increase the number of iterations of the numerical methods given depth constraints. Our proposed HE-based LPSE (HELPSE) method is implemented as a client-server model. As a client-side, a virtual keyboard system is implemented on an embedded development board with a camera sensor. A password is obtained from this system, encrypted, and sent over a network to a resource-rich server-side. The proposed HELPSE method is performed on the server. Using depths of about 20, our proposed method shows average error rates of less than 1% compared to the original LPSE algorithm. For a polynomial degree of 32K, the execution time on the server-side is about 5 seconds.