Nowadays, cloud computing has developed well and been applied in many kinds of areas. However, privacy is still the most challenging problem which obstructs it being applied in some privacy-sensitive fields, such as finance and government. Advanced cryptographic algorithms provide data privacy with encryption, which can also support computation on such encrypted data. However, new challenge arises when such ciphertexts come from different parties. In particular, how to execute collaboratively data mining on encrypted data coming from different parties is a key issue from cloud service point of view. This paper focuses on privacy problem on outsourced k-means clustering scheme for two parties. In particular, each party’s data are encrypted only once and then stored in cloud. The proposed privacy-preserving k-means collaborative clustering protocol is executed mainly at the cloud, with $O\left(k\right(m+n\left)\right)$ rounds of interactions among the two parties and the cloud, where m and n represent the total numbers of records for the two parties, respectively. It is shown that the protocol is secure in the semi-honest security model and in the malicious model in which only one party is corrupted during the process of centroids re-computation. Both theoretical and experimental analysis of the proposed scheme are also provided.

如今，云计算发展良好，并已应用于许多领域。但是，隐私仍然是最具挑战性的问题，这使它无法应用于某些对隐私敏感的领域，例如金融和政府。先进的加密算法通过加密为数据提供保密性，还可以支持对此类加密数据进行计算。但是，当这些密文来自不同的各方时，就会出现新的挑战。特别地，从云服务的角度来看，如何对来自不同方的加密数据进行协作数据挖掘是一个关键问题。本文针对两方外包k均值聚类方案的隐私问题。特别是，各方的数据仅加密一次，然后存储在云中。建议的隐私保护k均值协作聚类协议主要在云上执行，$Ø（ķ（米+ñ））$双方和云之间的两轮交互，其中m和n分别代表双方的记录总数。结果表明，该协议在半诚实安全模型和恶意模型中是安全的，在恶意模型中，在质心重新计算过程中只有一方被破坏。还提供了该方案的理论和实验分析。