Efficient and Secure Outsourced Linear Regression

The linear regression, as a classical machine learning algorithm, is often used to be a predictor. In the era of big data, the data owner can outsource their linear regression task and data to the cloud server, which has powerful calculation and storage resources. However, outsourcing data may break the privacy of the data. It is a well-known method to encrypt them prior to uploading to the cloud by using the homomorphic encryption (HE). Nevertheless, it is a difficult problem to apply the linear regression protocol in the encrypted domain. With this observation, we propose an efficient and secure linear regression protocol over outsourced encrypted data by using the vector HE, named ESLR, and in our protocol, we further present a privacy-preserving gradient descent method. Security analysis shows that our protocol can guarantee the confidentiality of data. And compared to the linear regression over plaintexts, our proposal can achieve almost the same accuracy and efficiency over ciphertexts.