## Cryptology ePrint Archive: Report 2019/465

Towards a Practical Clustering Analysis over Encrypted Data

Jung Hee Cheon and Duhyeong Kim and Jai Hyun Park

Abstract: Clustering analysis is one of the most significant unsupervised machine learning tasks, and it is utilized in various fields associated with privacy issues including bioinformatics, finance and image processing. In this paper, we propose a practical solution for privacy-preserving clustering analysis based on homomorphic encryption~(HE). Our work is the first HE solution for the mean-shift clustering algorithm. To reduce the super-linear complexity of the original mean-shift algorithm, we adopt a novel random sampling method called dust sampling which perfectly fits in HE and achieves the linear complexity. We also substitute non-polynomial kernels by a new polynomial kernel so that it can be efficiently computed in HE.

The HE implementation of our modified mean-shift clustering algorithm based on the approximate HE scheme HEAAN shows prominent performance in terms of speed and accuracy. It takes about $30$ minutes with $99\%$ accuracy over several public datasets with hundreds of data, and even for the dataset with $262,144$ data it takes only $82$ minutes applying SIMD operations in HEAAN. Our results outperform the previously best known result (SAC 2018) over $400$ times.

Category / Keywords: applications / clustering, mean-shift, homomorphic encryption, privacy

Original Publication (with minor differences): Selected Areas in Cryptography (SAC) 2019

Date: received 6 May 2019, last revised 15 Jul 2019

Contact author: doodoo1204 at snu ac kr

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2019/465

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