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In a cyber-physical system (CPS), the interconnection of cyber and physical components occurs through a network. This structure, particularly cyber components and networks, makes it susceptible to malicious attacks. One of the solutions to this CPS security issue is to employ end-to-end homomorphic encryption (HE) that allows direct computations on encrypted data. Despite its promise, HE only supports basic operations, such as addition and multiplication, which limits its application areas. Numerical methods have been presented to perform a comparison operation in the HE domain. However, they suffer from a slow processing speed due to an inherently high number of iterations. To accelerate a homomorphic comparison operation, this paper introduces a novel approach that scales inputs using an asymmetric input range in thresholding. Additionally, parallelism in HE-based multilevel thresholding is explored and exploited through the use of a parallel processing application programming interface for further acceleration. Compared to a previous comparison operation method, the proposed method achieves comparable accuracy with fewer iterations, resulting in a 48% reduction in execution time on an edge computing device. Furthermore, employing an additional thread using parallelism increases this reduction to 63%.