HE-Friendly Algorithm for Privacy-Preserving SVM Training

Support vector machine (SVM) is one of the most popular machine learning algorithms. It predicts a pre-defined output variable in real-world applications. Machine learning on encrypted data is becoming more and more important to protect both model information and data against various adversaries. While some studies have been proposed on inference or prediction phases, few have been reported on the training phase. Homomorphic encryption (HE) for the arithmetic of approximate numbers scheme enables efficient arithmetic evaluations of encrypted data of real numbers, which encourages to develop privacy-preserving machine learning training algorithm. In this study, we propose an HE-friendly algorithm for the SVM training phase which avoids inefficient operations and numerical instability on an encrypted domain. The inference phase is also implemented on the encrypted domain with fully-homomorphic encryption which enables real-time prediction. Our experiment showed that our HE-friendly algorithm outperformed the state-of-the-art logistic regression classifier with fully homomorphic encryption on toy and real-world datasets. To the best of our knowledge, this study is the first practical algorithm for training an SVM model with fully homomorphic encryption. Therefore, our result supports the development of practical applications of the privacy-preserving SVM model.