Research On The Secure Outsourcing Algorithm Of Large-scale Polynomial Euclidean Algorithm And Non-negative Matrix Factorization

Cloud computing is a pay-per-use model that provides usable,convenient,and ondemand network access.Utilizing the computing services provided by cloud servers,clients with limited resources can outsource time-consuming large-scale computing problem by paying on demand,instead of purchasing expensive software and hardware equipment to meet their computing needs.However,this computing model also has many security issues and challenges.The physical space between the client and the remote cloud server,together with the potential untrustworthiness of the cloud server may cause the leakage of client's information,inaccurate cloud computing results,and even malicious forgery in the process of computing outsourcing.These security issues hinder the widespread use of this computing model.In this background,how to design a secure outsource algorithm for largescale computing problem has become a research hotspot in the field of cloud computing security.This thesis focuses on the extended Euclidean algorithm for large-scale polynomials and large-scale non-negative matrix factorization for security outsourcing computing,and proposes two practical securely outsourcing algorithms:(1)As far as 300 B.C,Euclid gave a remarkably simple procedure to solve greatest common factor problem.The extended Euclidean algorithm can both find the greatest common factor of two polynomials,and it can also be used to get their respective inverse elements.The inverse operation over finite field is a timeconsuming basic operation in information coding and cryptosystem design,because the actual application often involves polynomials with large degree or large polynomial system.Therefore,it is of great practical significance to design a outsource algorithm for large scale polynomials over some field.This paper first proposes a secure outsourcing algorithm for this problem.The Algorithm first performs variable substitution on the input polynomials,then utilize random polynomial and unimodular matrix transformation technique blind the input polynomials.Through the three techniques,the algorithm can well protect the privacy of client data.Strict theoretical analysis and extensive experimental verification demonstrate our algorithm's verifiability and efficiency.(2)Non-negative matrix factorization is an effective way to reduce the dimensionality of matrices.As a basic data processing method,it plays an important role in data mining and machine learning.However,in the current big data applications,the matrix that needs to be processed is large scale,and the present outsourcing scheme has some secure defects.Based on the previous algorithm,we proposed a more secure and reliable outsourcing algorithm.This algorithm further studies this issue,and proposes a more secure and reliable outsourcing solution by adding some garble information.The algorithm first augment the original matrix by a random matrix,then encrypt the augmented matrix by diagonal matrix and permutation matrix,thereby protecting the privacy of client data.Subsequent rigorous theoretical and extensive experimental verification demonstrate our algorithm's verifiability,and efficiency.