Paper 2018/074

Secure Logistic Regression Based on Homomorphic Encryption: Design and Evaluation

Miran Kim, Yongsoo Song, Shuang Wang, Yuhou Xia, and Xiaoqian Jiang


Learning a model without accessing raw data has been an intriguing idea to the security and machine learning researchers for years. In an ideal setting, we want to encrypt sensitive data to store them on a commercial cloud and run certain analysis without ever decrypting the data to preserve the privacy. Homomorphic encryption technique is a promising candidate for secure data outsourcing but it is a very challenging task to support real-world machine learning tasks. Existing frameworks can only handle simplified cases with low-degree polynomials such as linear means classifier and linear discriminative analysis. The goal of this study is to provide a practical support to the mainstream learning models (eg logistic regression). We adapted a novel homomorphic encryption scheme optimized for real numbers computation. We devised (1) the least squares approximation of the logistic function for accuracy and efficiency (ie reduce computation cost) and (2) new packing and parallelization techniques. Using real-world datasets, we evaluated the performance of our model and demonstrated its feasibility in speed and memory consumption. For example, it took about 116 minutes to obtain the training model from homomorphically encrypted Edinburgh dataset. In addition, it gives fairly accurate predictions on the testing dataset. We present the first homomorphically encrypted logistic regression outsourcing model based on the critical observation that the precision loss of classification models is sufficiently small so that the decision plan stays still.

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Publication info
Published elsewhere. Minor revision. JMIR Medical Informatics
Homomorphic encryptionapproximate arithmeticlogistic regressiongradient descent
Contact author(s)
mrkim @ ucsd edu
2018-03-26: last of 2 revisions
2018-01-18: received
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      author = {Miran Kim and Yongsoo Song and Shuang Wang and Yuhou Xia and Xiaoqian Jiang},
      title = {Secure Logistic Regression  Based on Homomorphic Encryption: Design and Evaluation},
      howpublished = {Cryptology ePrint Archive, Paper 2018/074},
      year = {2018},
      doi = {10.2196/medinform.8805},
      note = {\url{}},
      url = {}
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