Harnessing the Cloud for Securely Solving Large-Scale Systems of Linear Equations

Cloud computing economically enables customers with limited computational resources to outsource large-scale computations to the cloud. However, how to protect customers' confidential data involved in the computations then becomes a major security concern. In this paper, we present a secure outsourcing mechanism for solving large-scale systems of linear equations (LE) in cloud. Because applying traditional approaches like Gaussian elimination or LU decomposition (aka. direct method) to such large-scale LE problems would be prohibitively expensive, we build the secure LE outsourcing mechanism via a completely different approach -- iterative method, which is much easier to implement in practice and only demands relatively simpler matrix-vector operations. Specifically, our mechanism enables a customer to securely harness the cloud for iteratively finding successive approximations to the LE solution, while keeping both the sensitive input and output of the computation private. For robust cheating detection, we further explore the algebraic property of matrix-vector operations and propose an efficient result verification mechanism, which allows the customer to verify all answers received from previous iterative approximations in one batch with high probability. Thorough security analysis and prototype experiments on Amazon EC2 demonstrate the validity and practicality of our proposed design.