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.

中文翻译：

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用于隐私保护 SVM 训练的 HE 友好算法


支持向量机（SVM）是最流行的机器学习算法之一。它预测实际应用中预定义的输出变量。对于保护模型信息和数据免受各种攻击者的攻击，加密数据的机器学习变得越来越重要。虽然已经提出了一些关于推理或预测阶段的研究，但关于训练阶段的研究却很少。用于近似数算术方案的同态加密（HE）可以对实数加密数据进行有效的算术评估，这鼓励开发保护隐私的机器学习训练算法。在本研究中，我们提出了一种适用于 SVM 训练阶段的 HE 友好算法，该算法避免了加密域上的低效操作和数值不稳定。推理阶段也在加密域上实现，采用全同态加密，可以实现实时预测。我们的实验表明，我们的 HE 友好算法优于最先进的逻辑回归分类器，在玩具和现实世界数据集上具有完全同态加密。据我们所知，这项研究是第一个用于训练具有完全同态加密的 SVM 模型的实用算法。因此，我们的结果支持隐私保护SVM模型的实际应用的开发。