Optimized Privacy-Preserving Clustering with Fully Homomorphic Encryption

Clustering is a crucial unsupervised learning method extensively used in the field of data analysis. For analyzing big data, outsourced computation is an effective solution but privacy concerns arise when involving sensitive information. Fully homomorphic encryption (FHE) enables computations on encrypted data, making it ideal for such scenarios. However, existing privacy-preserving clustering based on FHE are often constrained by the high computational overhead incurred from FHE, typically requiring decryption and interactions after only one iteration of the clustering algorithm. In this work, we propose a more efficient approach to evaluate the one-hot vector for the index of the minimum in an array with FHE, which fully exploits the parallelism of single-instruction-multiple-data of FHE schemes. By combining this with FHE bootstrapping, we present a practical FHE-based k-means clustering protocol whose required round of interactions between the data owner and the server is optimal, i.e., accomplishing the entire clustering process on encrypted data in a single round. We implement this protocol using the CKKS FHE scheme. Experiments show that our protocol significantly outperforms the state-of-the-art FHE-based k-means clustering protocols on various public datasets and achieves comparable accuracy to plaintext result. Additionally, We adapt our protocol to support mini-batch k-means for large-scale datasets and report its performance.