### Privacy-Preserving Ridge Regression with only Linearly-Homomorphic Encryption

Irene Giacomelli, Somesh Jha, Marc Joye, C. David Page, and Kyonghwan Yoon

##### Abstract

Linear regression with 2-norm regularization (i.e., ridge regression) is an important statistical technique that models the relationship between some explanatory values and an outcome value using a linear function. In many applications (e.g., predictive modelling in personalised health care), these values represent sensitive data owned by several different parties who are unwilling to share them. In this setting, training a linear regression model becomes challenging and needs specific cryptographic solutions. This problem was elegantly addressed by Nikolaenko et al. in S&P (Oakland) 2013. They suggested a two-server system that uses linearly-homomorphic encryption (LHE) and Yao’s two-party protocol (garbled circuits). In this work, we propose a novel system that can train a ridge linear regression model using only LHE (i.e., without using Yao’s protocol). This greatly improves the overall performance (both in computation and communication) as Yao’s protocol was the main bottleneck in the previous solution. The efficiency of the proposed system is validated both on synthetically-generated and real-world datasets.

Note: This paper is a merge of ePrint:2017/732 and ePrint:2017/707.

Available format(s)
Publication info
Published elsewhere. MINOR revision.ACNS 2018 Applied Cryptography & Network security
Contact author(s)
irene giacomelli29 @ gmail com
History
2018-04-14: last of 2 revisions
See all versions
Short URL
https://ia.cr/2017/979

CC BY

BibTeX

@misc{cryptoeprint:2017/979,
author = {Irene Giacomelli and Somesh Jha and Marc Joye and C.  David Page and Kyonghwan Yoon},
title = {Privacy-Preserving Ridge Regression with only Linearly-Homomorphic Encryption},
howpublished = {Cryptology ePrint Archive, Paper 2017/979},
year = {2017},
note = {\url{https://eprint.iacr.org/2017/979}},
url = {https://eprint.iacr.org/2017/979}
}

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