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.

翻译：逻辑回归是一种广泛应用于欺诈检测、医疗诊断和推荐系统等实际场景中的二分类算法。然而，利用不同参与方的数据训练逻辑回归模型会引发隐私问题。安全多方计算（MPC）是一种密码学工具，它允许多方在不泄露隐私的情况下联合训练逻辑回归模型。在实际处理大规模数据时，在线训练阶段的效率变得至关重要。本文提出了一种基于函数秘密共享（FSS）的隐私保护逻辑回归在线高效协议。我们设计的协议基于两个非共谋服务器场景，并假设存在一个仅向计算方提供相关随机性的第三方分发者。在线阶段中，两个服务器利用预生成的相关随机性，在其私有数据上联合训练逻辑回归模型。此外，我们提出了精确且适用于MPC的Sigmoid函数替代方案，并将逻辑回归训练过程封装为函数秘密共享门。与传统基于秘密共享的安全逻辑回归训练相比，本文方法的在线通信开销显著降低。我们通过理论分析和实验验证，证明了该方法的效率与有效性。