Research On Outsourcing Computing Of Several Matrix Algorithms

In recent years,through the powerful computing resources and storage space of cloud servers,more and more users choose to outsource their huge computing problems to the cloud for computing,to save their own computing time and costs.This article designs three types of outsourced computing protocols:The first is an outsourced computing protocol based on large-scale matrix Jordan decomposition.This protocol encrypts the original matrix through linear transformation and element rearrangement.While protecting the user’s private information,the computational complexity has not increased.By sending the encrypted matrix to the cloud server,users can enjoy the convenience brought by the cloud server while ensuring the security of the user’s input and output of private information.Through the efficient verification algorithm,the results returned from the cloud are efficiently verified.The computational complexity analysis verifies the efficiency of the protocol.Compared with the current literature on matrix decomposition calculations,this protocol realizes the calculation of Jordan decomposition of large-scale matrices by using outsourcing on the basis of not increasing the computational complexity of users and ensuring the security of user privacy information.The second is an outsourced computing protocol based on large-scale matrix multiplication.This protocol cuts and fills non-square matrices into square matrices through matrix segmentation and padding,which achieves the purpose of simplifying calculations.Through the Shannon diffusion principle,the original matrix is diffused into a larger matrix,and the original matrix is blinded by the unit replacement matrix to ensure the privacy of the original matrix.Achieve efficient verification and efficiency of the protocol.Compared with the current literature on matrix multiplication calculations,this protocol does not increase the user’s computationalcomplexity,and is suitable for non-square matrix multiplication calculations on a single server,while reducing the probability of incorrect results returned from the cloud being able to pass the verification.The third is a large-scale matrix determinant-based outsourcing computing protocol.This protocol reduces the user’s own calculation volume through matrix block processing.Through the Shannon diffusion principle,the original matrix information is guaranteed to be secure.Achieve efficient verification and efficiency of the protocol.Compared with the current literature on matrix determinant calculations,this protocol reduces user computational complexity.In all three protocols,users’ privacy information is protected,results are verifiable,and efficient.At the same time,compared with the current literature,it has achieved improvements in different aspects.