Research On Secure Outsourcing Computing Technology For Large-scale Matrix Operation

As an application of cloud computing,secure outsourcing computing technology has attracted the attention of individuals and enterprises.Outsourcing computing means that some clients with limited hardware conditions outsource tasks,which required a large number of computing resources,to cloud servers to save their resources.Although outsourcing computing has broad application prospects in the era of big data,the unreliable behavior of the cloud servers is an important factor restricting the development of outsourcing computing.How to ensure the security of client outsourced data is one of the focuses of designing the scheme.Besides,the correctness,efficiency,and verifiability of the results are also the basic requirements of outsourcing computing.Large-scale matrix multiplication is a common form of calculation in scientific research,but it requires massive hardware resources,so outsourcing it to the cloud servers is a feasible solution.Currently,there are some problems in the research of matrix multiplication outsourcing: the multi-server model cannot resist collusion attacks or the client's overhead is too high;the single-server model will leak the client's private information.The main work of this thesis about large-scale matrix multiplication outsourcing is as follows:(1)A matrix multiplication outsourcing scheme based on double cloud servers is proposed.The privacy of the client is protected by using sparse matrix and matrix segmentation in the scheme and achieves the goal of resisting collusion attacks and reducing client overhead.The use of redundant calculations generated by the two cloud servers achieves fast verification of results.(2)A matrix multiplication outsourcing scheme based on single cloud server is proposed.In this scheme,we add the matrix constructed by the vector to the original matrix to solve the information leakage of zero-elements in the single cloud server mode,and then use the sparse matrix to further encrypt the matrix.The protocol realizes the efficiency of outsourcing computing under the premise of ensuring security.(3)We analyze an online privacy protection matrix multiplication outsourcing scheme and found that the element-wise-multiplication makes the final result obtained by the client is not the solution of the original calculation task.It does not meet the basic requirements of the correctness of outsourcing computing.Besides,to verify the correctness of the results,the scheme uses exponential calculations on the group,causing the client's computing overhead to far exceed the original computing tasks.So it does not satisfy the efficiency of outsourced computing.We improve the scheme and analyze its performance.Finally,we verify the efficiency of the program through experiments.