Secure and Verifiable Outsourcing of Large-scale Matrix Inversion without Precondition in Cloud Computing

Large-scale matrix computation requires a lot of computing resources, but the emergence of cloud computing provides resource-limited users with an economical solution, namely outsourcing computation. Clients can use pay-per-use service of cloud resources to solve complex issues, such as matrix inversion. However, due to the inclusion of privacy information in users' data and the opacity of the calculation operations, clients are in face of the threats of privacy disclosure and fraud. In this paper, we first propose an efficient and secure scheme without precondition for outsourcing large-scale matrix inversion to a public cloud. Compared to the state-of-the-art schemes, our scheme does not require the precondition that the original matrix should be invertible. It relieves clients from checking the invertibility of matrix, which is hard to be implemented with limited resource in reality. Moreover, our scheme can protect clients from being cheated and provide data privacy protection. Experiment results also show that our scheme is highly efficient in practical.