Paper 2018/254

Logistic Regression Model Training based on the Approximate Homomorphic Encryption

Andrey Kim, Yongsoo Song, Miran Kim, Keewoo Lee, and Jung Hee Cheon


Security concerns have been raised since big data became a prominent tool in data analysis. For instance, many machine learning algorithms aim to generate prediction models using training data which contain sensitive information about individuals. Cryptography community is considering secure computation as a solution for privacy protection. In particular, practical requirements have triggered research on the efficiency of cryptographic primitives. This paper presents a practical method to train a logistic regression model while preserving the data confidentiality. We apply the homomorphic encryption scheme of Cheon et al. (ASIACRYPT 2017) for an efficient arithmetic over real numbers, and devise a new encoding method to reduce storage of encrypted database. In addition, we adapt Nesterov's accelerated gradient method to reduce the number of iterations as well as the computational cost while maintaining the quality of an output classifier. Our method shows a state-of-the-art performance of homomorphic encryption system in a real-world application. The submission based on this work was selected as the best solution of Track 3 at iDASH privacy and security competition 2017. For example, it took about six minutes to obtain a logistic regression model given the dataset consisting of 1579 samples, each of which has 18 features with a binary outcome variable.

Available format(s)
Publication info
Preprint. MINOR revision.
homomorphic encryptionmachine learninglogistic regression
Contact author(s)
yongsoosong @ ucsd edu
2018-03-07: received
Short URL
Creative Commons Attribution


      author = {Andrey Kim and Yongsoo Song and Miran Kim and Keewoo Lee and Jung Hee Cheon},
      title = {Logistic Regression Model Training based on the Approximate Homomorphic Encryption},
      howpublished = {Cryptology ePrint Archive, Paper 2018/254},
      year = {2018},
      note = {\url{}},
      url = {}
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