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.

Homomorphic Encryption (HE) [11] draws significant attention as a privacy-preserving way for cloud computing because it allows computation on encrypted messages called ciphertexts. Among numerous FHE schemes [2]–[4], [8], [9], HE for Arithmetic of Approximate Numbers (HEAAN [3]), which is also known as CKKS (Cheon-Kim-Kim-Song), is rapidly gaining popularity [10] as it supports computation on real numbers. A critical shortcoming of HE is the high computational complexity of ciphertext arithmetic, especially, HE multiplication (HE Mul). For example, the execution time for computation on encrypted data (ciphertext) increases from 100s to 10,000s of times compared to that on native, unen-crypted messages. However, a large body of HE acceleration studies, including ones exploiting GPUs and FPGAs, lack a rigorous analysis of computational complexity and data access patterns of HE Mul with large parameter sets on CPUs, the most popular computing platform.

Homomorphic encryption (HE) is one of the most promising solutions to secure cloud computing. The number theoretic transform (NTT) that is widely used for convolution operations in HE requires a large amount of computation and has high parallelism, and therefore it has been a good candidate for hardware acceleration. Nevertheless, prior NTT hardware solutions for HE-based applications are impractical in most applications because they do not seriously consider the critical bootstrapping procedure that allows unlimited homomorphic operations on encrypted data. In this paper, we suggest practical bootstrappable parameters, specifically for an established residue number system (RNS)based HE scheme, and apply them to our NTT hardware design. In addition, to limit the size of internal memory for roots of unity increased by the bootstrappable parameters, only a few roots of unity are stored and others are generated on the fly. In our NTT hardware architecture, multiple NTT butterfly units (BUs) are efficiently deployed for high throughput and high resource utilization. In particular, several groups of BUs for respective moduli work in a parallel and pipelined manner, which is effective in an RNS-based HE scheme with a number of moduli. Our implementation on a Xilinx UltraScale FPGA with the bootstrappable parameters achieves a $118 \times$ faster processing speed than a software implementation, and it further provides various trade-off choices such as the number of DSP slices against BRAMs based on available FPGA resources.