Paper 2016/111

Scalable and Secure Logistic Regression via Homomorphic Encryption

Yoshinori Aono, Takuya Hayashi, Le Trieu Phong, and Lihua Wang


Logistic regression is a powerful machine learning tool to classify data. When dealing with sensitive data such as private or medical information, cares are necessary. In this paper, we propose a secure system for protecting both the training and predicting data in logistic regression via homomorphic encryption. Perhaps surprisingly, despite the non-polynomial tasks of training and predicting in logistic regression, we show that only additively homomorphic encryption is needed to build our system. Indeed, we instantiate our system with Paillier, LWE-based, and ring-LWE-based encryption schemes, highlighting the merits and demerits of each instance. Our system is very scalable in both the dataset size and dimension, tolerating big size for example of hundreds of millions ($10^8$s) records. Besides examining the costs of computation and communication, we carefully test our system over real datasets to demonstrate its accuracies and other related measures such as F-score and AUC.

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Publication info
Published elsewhere. Major revision. IEICE Transactions 99-D(8): 2079-2089 (2016)
logistic regressionhomomorphic encryptionPaillierLWEring-LWEoutsourced computationaccuracyF-scorearea under curve
Contact author(s)
phong @ nict go jp
2017-03-31: revised
2016-02-10: received
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      author = {Yoshinori Aono and Takuya Hayashi and Le Trieu Phong and Lihua Wang},
      title = {Scalable and Secure Logistic Regression via Homomorphic Encryption},
      howpublished = {Cryptology ePrint Archive, Paper 2016/111},
      year = {2016},
      doi = {10.1587/transinf.2015INP0020},
      note = {\url{}},
      url = {}
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