Research On Secure Outsourcing Schemes Of Large Matrix Computing In Cloud Computing

With the development of cloud computing,outsourcing computing has been used widely.Outsourcing computing enables client with limited computing resources be able to carry out large computational tasks with the help of powerful cloud.The rapid development of outsourcing computing is also facing following challenges:(1)The privacy of the data: The data that the client outsources to the cloud is sensitive,such as trade secrets,medical data,etc.The cloud may leak such private data.(2)The verifiability of computing results: The cloud service are provided by third-party enterprises.The cloud may randomly return a result to the client in order to save computing overhead.The client needs to verify the result returned by the cloud.(3)Efficient: When the client chooses to outsource the computing task,it is hoped that outsourcing can help reduce the computational overhead.The computational overhead when outsourcing the computing task should be lower than the original cost.The outsourcing of matrix operations is a research hotspot in the field of outsourcing computing.Focuses on the outsourcing scheme of matrix operations,this paper mainly research as follows:1.This paper constructs a verifiable,efficient and privacy-preserving scheme for outsourcing large matrix multiplication(VEPP).In the scheme,the elements of the matrices are blinded by large prime numbers and random numbers.Then,the cloud performs multiplication on the encrypted matrices.The client skillfully uses the Chinese remainder theorem,and only needs one decryption to obtain the elements of the matrices.So,the scheme is relatively efficient.The formal security proof shows that our scheme achieves a higher security level(i.e.,information-theoretic security for input privacy and adaptive chosen ciphertext attack(CCA2)security for output privacy).The results returned by the cloud are verified.2.Based on the research of outsourcing matrix multiplication,we propose a outsourcing computing scheme for large matrix inversion(MIOC).We use the random matrix B to blind the matrix A that needs to be inversed to protect the privacy of the outsourced data.Then,we get the inverse matrix A-1by using this property:(AB)-1= B-1A-1.The results returned by the cloud are verified to prevent thirdparty attacks or the cloud's own dishonesty.Detailed theoretical and experimental analysis shows that our scheme is relatively efficient.3.We apply the outsourcing computing scheme for large matrix inversion to solve the linear equations and propose a linear system of equations outsourcing computing scheme(LSEOC).The LSEOC scheme inherits the verifiability,security,and efficiency of the MIOC.The computational overhead of the client is O(n2).