Abstract: Linear regression is an important and widely used machine learning algorithm.The training of linear regression model usually depends on a large amount of data.In reality,the data set is generally held by different users and contains their privacy information.When multiple users want to gather more data to train a better model,it inevitably involves users' privacy.As a privacy protection technology,homomorphic encryption can effectively solve the problem of privacy leakage in computing.A new privacy preserving linear regression scheme based on hybrid iterative method is designed for the scenario where data sets are distri-buted horizontally on two users.The scheme is divided into two stages.The first stage implements the statistic gradient descent algorithm in the ciphertext domain.In the second stage,a secure two-party fast descent protocol is designed.The core idea of the protocol is based on Jacobi iterative method,which can effectively make up for the poor convergence effect of gradient descent method in practical application,accelerate the convergence of the model,and protect the data privacy of two users while effectively training the linear regression model.The efficiency,communication loss and security of the scheme are analyzed.The scheme is implemented by using C+＋and applied to real data sets.A large number of experimental results show that the scheme can effectively solve the linear regression problem with large scale features.The relative error of decision coefficient is less than 0.001,which show that the application effect of the privacy preserving linear regression model in real data set is close to that obtained directly from unencrypted data,and the scheme can meet the practical application requirements in specific scenarios.

Key words: Privacy-preserving, Linear regression, Hybrid iterative method, Homomorphic encryption