# Secure K-Means Clustering Scheme for Confidential Data Based on Paillier Cryptosystem
## 2 Related Work  
The intersection of privacy-preserving techniques and clustering algorithms has been an active area of research, driven by growing concerns over data privacy in various domains such as healthcare, finance, and social networks. Existing work in privacy-preserving clustering has explored a variety of methodologies, including differential privacy, secure multi-party computation (SMPC), homomorphic encryption, and other related approaches. Differential privacy has been widely adopted to provide statistical guarantees of privacy in data analysis. Several researchers have applied differential privacy to clustering algorithms. For instance, [PERSON] [13] introduced the first differentially private algorithm for K-means clustering, ensuring that the output of the clustering process does not reveal sensitive information about any individual data point. However, the added noise necessary for differential privacy can degrade the accuracy of clustering results, making it less suitable for applications requiring high precision. SMPC techniques allow multiple parties to jointly compute a function over their inputs while keeping those inputs private. [PERSON] and [PERSON] [14] proposed a privacy-preserving K-means clustering algorithm using SMPC, ensuring that no party learns anything beyond the final clustering results. Although SMPC provides strong security guarantees, it often involves high computational and communication overhead, posing challenges for scaling to large datasets. Homomorphic encryption, particularly additive homomorphic encryption schemes such as the Paillier cryptosystem, enables computations on encrypted data without decryption, making it particularly useful for privacy-preserving data mining tasks. Notable work by [PERSON] [15] proposed a privacy-preserving logistic regression algorithm using the Paillier cryptosystem, allowing the training process to be carried out on encrypted data and preserving the privacy of sensitive information. However, their approach focuses on supervised learning, and its application to unsupervised learning tasks like clustering remains underexplored. There have been limited studies on applying homomorphic encryption to clustering algorithms. [PERSON] (2023) [16] proposed a privacy-preserving K-means clustering algorithm using homomorphic encryption, allowing the computation of distances and centroid updates on encrypted data. However, their method does not fully address the efficiency and scalability challenges associated with homomorphic encryption. Another approach to privacy-preserving clustering is through data anonymization techniques. Methods like k-anonymity and l-diversity aim to anonymize the data before clustering. [PERSON] (2002) [17] proposed k-anonymity, ensuring that each record is indistinguishable from at least k - 1 other records. However, these methods often suffer from information loss and do not provide strong privacy guarantees against certain types of attacks. Federated learning [18; 19] has emerged as a technique to train machine learning models on decentralized data without moving the data itself. [PERSON] [20] introduced a secure aggregation protocol for federated learning, which can be extended to clustering tasks. While federated learning offers a way to leverage distributed data, it still requires secure aggregation mechanisms to ensure privacy. The existing body of work in privacy-preserving clustering has made significant strides, but challenges remain in balancing privacy, accuracy, and efficiency. Differential privacy and SMPC offer strong privacy guarantees but often at the cost of accuracy and scalability. Homomorphic encryption, particularly the Paillier cryptosystem, provides a promising approach by enabling secure computations on encrypted data. However, its application to clustering algorithms, particularly in addressing efficiency and scalability, needs further exploration. Our work builds on these foundations by proposing a secure homomorphic K-means clustering protocol using the Paillier cryptosystem.