k-means clustering, which partitions data records into different clusters such that the records in the same cluster are close to each other, has many important applications such as image segmentation and genes detection. While the k-means clustering has been well-studied by a significant amount of works, most of the existing schemes are not designed for peer-to-peer (P2P) networks. P2P networks impose several efficiency and security challenges for performing clustering over distributed data. In this paper, we propose a novel privacy-preserving k-means clustering scheme over distributed data in P2P networks, which achieves local synchronization and privacy protection. Specifically, we design a secure aggregation protocol and a secure division protocol based on homomorphic encryption to securely compute clusters without revealing the privacy of individual peer. Moreover, we propose a novel massage encoding method to improve the performance of our aggregation protocol. We formally prove that the proposed scheme is secure under the semi-honest model and demonstrate the performance of our proposed scheme.

k均值聚类将数据记录分为不同的聚类，以使同一聚类中的记录彼此靠近，它具有许多重要的应用，例如图像分割和基因检测。尽管大量的工作已经很好地研究了k均值聚类，但是大多数现有方案都不是针对点对点（P2P）网络设计的。P2P网络对在分布式数据上执行群集提出了一些效率和安全性挑战。在本文中，我们提出了一种新颖的隐私保护k-是指在P2P网络中对分布式数据进行聚类的方案，可以实现本地同步和隐私保护。具体来说，我们设计基于同态加密的安全聚合协议和安全划分协议，以安全地计算群集，而不会泄露单个对等方的隐私。此外，我们提出了一种新颖的按摩编码方法来改善我们的聚合协议的性能。我们正式证明了该方案在半诚实模型下是安全的，并证明了该方案的性能。