Efficient, secure and non-iterative outsourcing of large-scale systems of linear equations

Solving large-scale systems of linear equations (L-SLE) is a common scientific and engineering computational task. But such problem involves enormous computing resources, which is burdensome for the resource-limited clients. Cloud computing enables computational resource-limited clients to economically outsource such problems to the cloud server. However, outsourcing LSLE to the cloud brings great security concerns and challenges since the LSLE usually contains sensitive information. Previous works for secure outsourcing LSLE are mainly based on iterative methods which cause heavy computation cost for the client side. And they usually neglect to protect the number and position privacy of zero elements in the coefficient matrix, which is not secure enough for many applications. In this paper, with a series of disguise-based techniques, we propose a new efficient and non-iterative algorithm for securely outsourcing LSLE. Our algorithm only requires two rounds of communication between the client and cloud. Furthermore, the number and positions of zero elements in coefficient matrix can be hidden from the cloud with low computational complexity. Finally, we provide extensive theoretical analysis and experimental evaluation to show its high-efficiency and security compared to the previous works.