Secure and efficient outsourcing of large-scale matrix inverse computation

Abstract

Matrix inverse computation (MIC) is one of the fundamental mathematical tasks in linear algebra, and finds applications in many areas of science and engineering. In practice, MIC tasks often involve large-scale matrices and impose prohibitive computation costs on resource-constrained users. As cloud computing gains much momentum, a resource-constrained client can choose to outsource the large-scale MIC task to a powerful but untrustworthy cloud. As the input of and the solution to the MIC task usually contain the client’s private information, appropriated mechanisms should be placed for privacy concerns. In this paper, we employ certain matrix transformations and construct an outsourcing scheme known as SEMIC, which can solve the MIC task in a masked yet verifiable manner. Thorough theoretical analysis shows that SEMIC is correct, verifiable, and privacy-preserving. Extensive experimental results demonstrate that SEMIC significantly reduces the computation costs of the client. Compared with the most related work, our solution offers enhanced privacy protection without impairing the efficiency.