Outsourcing Large-Scale Systems of Linear Matrix Equations in Cloud Computing

Abstract

With the increasing development of cloud computing, how to securely outsource prohibitively expensive computation to unfaithful clouds has caught more and more attention. Large-scale systems of linear matrix equations (LME) are com-monly deployed in scientific and engineering fields, which is a computationally complex task. Thus, it is necessary to design a protocol for practically outsourcing large-scale systems of LME to a malicious cloud. For this purpose, we propose a protocol called OutLME in this paper. In OutLME, we adopt a special permutation technique for the client to transform the original lin-ear matrix equation into a randomized one and decrypt the result returned from cloud into the right one of original problem. As to robust cheating resistance, we propose an effective verification algorithm by utilizing the algebraic property of matrix-vector operations. In addition, both the chosen permutation technique and result verification mechanism incur close-to-zero additional cost on both the cloud and the client, so our proposed protocol is efficient. In the end, the theoretical analysis and the experimental evaluation are provided to demonstrate the validity of OutLME.