Secure three-party clustering with identifying malicious behavior

Clustering algorithms are pivotal tools in data science and machine learning, offering a diverse array of applications ranging from customer segmentation to anomaly detection. With the development of cloud computing and outsourced computing, the adoption of clustering techniques has significantly accelerated. Despite the remarkable benefits of cloud computing, outsourcing sensitive data to remote cloud servers introduces considerable privacy and security concerns. Specifically, there is a risk that cloud service providers may engage in malicious behavior, such as data tampering. In response to these concerns, we propose four basic protocols based on vector space secret sharing, including secure Euclidean distance protocol, comparison protocol, minimum protocol, and division protocol. By applying these protocols, we construct a secure clustering scheme that can identify malicious behaviors. We thoroughly demonstrate the security of each underlying protocol as well as the overall clustering scheme. To validate the practicality and effectiveness of our approach, we conduct experiments on standard datasets. The results show that our clustering scheme performs efficiently while maintaining strong security guarantees.