We are developing a system that augments user accessibility by integrating various facial recognition engines across multiple enterprises, thereby facilitating the widespread adoption of facial recognition technology within societal structures. In this system, homomorphic encryption is employed to mitigate the risk of data leakage during facial recognition. However, the use of homomorphic encryption in facial recognition significantly increases latency, making it challenging to meet practical response time requirements. We experimentally evaluated the impact of adopting homomorphic encryption on the response time. The evaluation revealed that the number of registrants per facial recognition engine should be "< 120". Additionally, we evaluated a clustering strategy for reducing the response time to the level of practical application.