  Logistic regression is an algorithm widely used for binary classification in
various real-world applications such as fraud detection, medical diagnosis, and
recommendation systems. However, training a logistic regression model with data
from different parties raises privacy concerns. Secure Multi-Party Computation
(MPC) is a cryptographic tool that allows multiple parties to train a logistic
regression model jointly without compromising privacy. The efficiency of the
online training phase becomes crucial when dealing with large-scale data in
practice. In this paper, we propose an online efficient protocol for
privacy-preserving logistic regression based on Function Secret Sharing (FSS).
Our protocols are designed in the two non-colluding servers setting and assume
the existence of a third-party dealer who only poses correlated randomness to
the computing parties. During the online phase, two servers jointly train a
logistic regression model on their private data by utilizing pre-generated
correlated randomness. Furthermore, we propose accurate and MPC-friendly
alternatives to the sigmoid function and encapsulate the logistic regression
training process into a function secret sharing gate. The online communication
overhead significantly decreases compared with the traditional secure logistic
regression training based on secret sharing. We provide both theoretical and
experimental analyses to demonstrate the efficiency and effectiveness of our
method.
