## 5 Privacy-Preserving Parallel k-Means Clustering Algorithm
### Parallel Preprocessing Phase
Therefore, k-means clustering algorithms can help doctors classify the pattern of the patient's symptoms so as to diagnose what kind of disease it is. However, because patient information contains sensitive data, such as past medical history, family history, and allergies, the proposed privacy-preserving k-means clustering algorithm can be used to protect the sensitive data of patients. In addition, the proposed privacy-preserving k-means clustering algorithm can be used to solve the problem of insurance coverage recommendations where insurance companies provide the most suitable coverage to customers [36]. The insurance coverage recommendation clusters customers based on various types of customer information, such as movement patterns and lifestyles. To perform the grouping of customers, the proposed privacy-preserving k-means clustering algorithm can be used to protect the personal information of customers. ## 9 Conclusions and Future Work

In this paper, we proposed novel arithmetic-based encryption protocols (ASMIN, ASMIN\({}_{n}\)) designed for encrypted databases in cloud computing. These protocols address the challenges of the existing secure protocols, where the performance degradation is proportional to the data size. Our proposed protocols overcome these limitations, providing excellent processing performance that is independent of the data size. Additionally, we proposed a k-means clustering algorithm that supports privacy preservation using the proposed secure protocols. The algorithm utilizes enhanced secure protocols to perform encrypted index searches and queries, ensuring the protection of data, queries, and access patterns while providing superior processing performance. Additionally, the proposed k-means clustering algorithm requires moderate computational overhead because it uses decimal-based encryption operations, while the existing k-means clustering algorithms, i.e., [PERSON] et al. 's work [24] and [PERSON] et al. 's work [25], have high computational overhead due to the use of binary-based encryption operations. Furthermore, we proposed a parallel k-means clustering algorithm for multi-core environments that leverages thread pools and random value pools. To the best of our knowledge, this is the first work to study a privacy-preserving parallel k-means clustering algorithm. For efficient support of k-means clustering, we utilized a thread pool to prevent data bottlenecks and parallelized encryption operation protocols. However, when parallelizing homomorphic encryption techniques, there is the issue of the increased operational overhead per core, leading to bottlenecks and performance degradation. To mitigate this bottleneck, the proposed parallel algorithm uses a random value pool to reduce the computational cost by preprocessing operations that generate random values. This algorithm optimizes its performance by eliminating the overhead associated with random number generation and encryption during k-means clustering. Through performance evaluations, our proposed k-means clustering algorithm demonstrated approximately 10-12 times better performance than the existing algorithm. Moreover, the proposed parallel k-means clustering algorithm exhibited around 13 times better performance compared with the parallel processing versions of the existing algorithm. Our future work will involve the actual implementation of a privacy-preserving healthcare system using the proposed k-means clustering algorithm in a cloud computing environment. For instance, within the healthcare system, the proposed algorithm can be applied to diagnose diseases using big data by clustering patients' symptoms. This allows for the assessment of the adaptability of the proposed algorithm in practical applications. In addition, our future work will focus on leveraging the advanced secure protocols proposed in this paper to support various cloud-based data analysis algorithms, including association rules, deep learning, and federated learning. Conceptualization, Y.S. ; methodology, Y.S. ; software, Y.S.