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Science China Information Sciences

Privacy-preserving large-scale systems of linear equations in outsourcing storage and computation

Dongmei Li, Xiaolei Dong, Zhenfu Cao, Haijiang Wang

Published Feb 2, 2018• 7 citations
Publisher
DOI
10.1007/s11432-017-9208-3

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Systems of linear equations, as a fundamental topic in the development of the computational sciences, have been well studied in the scientific community. In this paper, we investigate secure outsourcing for large-scale systems of linear equations, which is considered as a prohibitively expensive computation for the clients with limited computational resources. Based on Chen's work, we propose a verifiable algorithm for secure outsourcing of large-scale systems of linear equations in the case of no solution under the fully malicious model. We uniquely utilize linear programming, which is another well studied scientific computing problem, to help the client to verify the correctness of results returned by the server. Compared with the state-of-the-art algorithm (Chen et al' scheme), the proposed algorithm is suitable not only for any nonsingular dense matrix A, but for a set of singular matrixes that lead the system of linear equations has no solution. Besides, the computational complexity for the verification of no solution in our scheme is still O (n2). Therefore, our proposed algorithm is more suitable for real applications.
The highly development of Internet and cloud computing technology makes it possible to share computing power, storage and data. Cloud computing makes users with limited computing resources be able to carry out large computational tasks with the help of cloud. but security is a major concern that hinders the widespread use of outsourcing computing. We focus on outsourcing large matrix multiplication in this paper. Firstly, we exploit Chinese Remainder Theorem(CRT) to construct a large matrix multiplication outsourcing protocol which is highly efficient in the malicious cloud model. Then formal security proof and extensive performance evaluation show that our protocol achieves a higher security level i.e., information-theoretic security for input privacy and adaptive chosen ciphertext attack (CCA2) security for output privacy). Compared with previous works, users in the proposed protocol are able to verify the results received from the cloud with tiny error rate.