Efficient secure outsourcing of large-scale linear systems of equations

Solving large-scale linear systems of equations (LSEs) is one of the most common and fundamental problems in big data. But such problems are often too expensive to solve for resource-limited users. Cloud computing has been proposed as a timely, efficient, and cost-effective way of solving such computing tasks. Nevertheless, one critical concern in cloud computing is data privacy. To be more prominent, in many cases, clients's LSEs contain private data that should remain hidden from the cloud for ethical, legal, or security reasons. Many previous works on secure outsourcing of LSEs have high computational complexity. More importantly, they share a common serious problem, i.e., a huge number of external memory I/O operations. This problem has been largely neglected in the past, but in fact is of particular importance and may eventually render those outsourcing schemes impractical. In this paper, we develop an efficient and practical secure outsourcing algorithm for solving large-scale LSEs, which has both low computational complexity and low memory I/O complexity and can protect clients' privacy well. We implement our algorithm on a real-world cloud server and a laptop. We find that the proposed algorithm offers significant time savings for the client (up to 65%) compared to previous algorithms.