Toward practical privacy-preserving linear regression

Abstract

Linear regression is an ordinary machine learning algorithm that models the relation between the input values and the output ones with underlying linear functions. Giacomelli et al. (ACNS 2018) proposed the first system training the linear regression model over the rational numbers using only linearly homomorphic encryption. However, we find their system model is not applicable. A third authority generates the public key and secret key, which are used to encrypt and decrypt all the data sets. Then the privacy of data sets is in the risk of leakage even if the third authority is assumed to have no access to encrypted data sets. In this paper, we improve the system model in order to design a more practical linear regression algorithm over the rational numbers from the view of security. Concretely, every data owner generates his own public key and secret key, independent on a third authority. An improved multi-key fully homomorphic encryption over complex numbers is utilized to construct our linear regression algorithm with a preprocessing phase, which can directly encrypt rational numbers, support computations over ciphertexts under multi keys and obviate the rational reconstruction technique as Giacomelli et al.. Furthermore, performance analyses demonstrate that our algorithm is more feasible and practical.