Design And Analysis Of Security Outsourcing Algorithm For Large-scale Modular Linear Equations

In recent years,due to the continuous development of cloud computing,secure outsourcing computing,as one of the important applications of cloud computing,has developed rapidly and has a broad market space,which has attracted wide attention from academia and industry.In secure outsourcing computing,cloud can provide computing,storage and other support for resource-constrained users,and users can delegate complex computing tasks to the cloud to complete,thus saving costs and improving efficiency.However,the cloud server is not completely trusted in practical applications,and there may be a risk of privacy disclosure when interacting.In addition,all kinds of hardware and software faults may also return the wrong results to the user.Therefore,a complete secure outsourcing computing scheme should ensure that users' data privacy will not be disclosed,and can verify the correctness of the returned results in the cloud with a probability that cannot be ignored.In addition,the user cost of outsourcing should be strictly lower than the calculation cost of completing the calculation task independently,otherwise outsourcing will lose its meaning.Therefore,how to design a security outsourcing scheme that meets the three elements of security,efficiency and verifiability has important theoretical and practical significance.In this paper,we propose several secure outsourcing algorithms based on cloud server for solving large-scale modular system of linear equations,which are common in practical problems.Specifically,(1)Two safe outsourcing computation schemes of large-scale modular system of linear equations without protection module q based on the client-edge cloud-public cloud tripartite model are proposed.One is publicly verifiable and security/efficiency adjustable outsourcing scheme for solving large-scale modular system of linear equations.This scheme first preprocesses the original input matrix A,b,and then blinds A,b by a continuously variable number of unimodular matrix transformations,and balances safety and efficiency by controlling the number of unimodular matrix.The other is to solve the problem of low efficiency caused by complex keys in the previous scheme.Another simple and efficient publicly verifiable secure outsourcing computation scheme proposed uses another encryption and decryption method,that is,a special sparse unimodular matrix.The large-scale dense matrix on the client side is blinded and sent to the cloud server.The cloud server performs the corresponding computation task and returns the calculation result.Both solutions have public verifiability,and can well protect the I/O privacy of the user terminal,but they cannot protect the privacy of the module.(2)A security outsourcing computation scheme for a large-scale modular system of linear equations based on the protection module q of a single server model is proposed.This scheme encrypts A,b many times,and more effectively protects the privacy of the original data.Theoretical analysis shows that the scheme achieves high security,efficiency and verifiability.At the same time,the experimental data analysis shows that when the modulo q is the same,the computational savings of the client increase with the increase of the matrix size.When the matrix size is the same,the larger the modulo q is,the higher the computational savings are.