Efficient and Secure Outsourcing of Large-Scale Linear System of Equations

Abstract

Solving the large-scale linear system of equations is one of the most fundamental problems both in theory and practice. However this problem requires too much computational resource for most users to solve it. With the rapid development of cloud services, many users tend to outsource the expensive computing to the cloud server, which is regarded as an efficient way of solving such problem. Nevertheless, the cloud server can not protect the data privacy well, especially when the user's linear system of equations contain private and sensitive data. There are many previous research works on secure outsourcing of systems of linear equations. In this paper we first analyze a privacy preserving CGM (conjugate gradient method) algorithm for secure outsourcing of large-scale systems of linear equations proposed in [1] . We find that the cloud server can recover the protected coefficient matrix of the linear system of equations from the message it receives, which makes the security method in this scheme fails. This is a serious problem, which makes the private and sensitive data of the user leak to the cloud server, and privacy preserving does not exist. To overcome this problem, we modified this algorithm to protect the message from leaking, which can protect the users' privacy well. We also show the security of this new scheme and do experiments to show its efficiency.