Designing And Application Of Fully Homomorphic Encryption Over Integer PolynomialRing

From up until now, the cryptography has researched in many fields, such as securityagreement, digital signature, etc. These new requirements according to the task of all is thereality and development progress continuously. Designing the cryptography which is used inmany actual demand fields has been becoming more and more important, with the developmentof the social networking and the development of cloud computing, cryptographic algorithm willusher a new era. Existing cryptographic algorithm strictly follow the avalanche effect, it can’tmeet the lessee and cloud service provider’s satisfaction, so homomorphic encryption which canoperate the encrypted data become a hotpot.In2009, fully homomorphic encryption was first successfully constructed, and solving themain problem is the operation of the ciphertext. In just three years, fully homomorphicencryption has attacked extensive attention.In this dissertation, according to existing two fully homomorphic encryptions we construct afull homomorphic encryption which based on integral polynomial ring Z_p[x], the security of thealgorithm is based on sparse subset sum problem. Fully homomorphic encryption over integerring compared with fully homomorphic encryption over ideal lattice,its advantage is smallcomputation; disadvantage is choosing polynomial;compared with fully homomorphicencryption over integers, its advantage is to evaluate operation with the depth of the computationstill full homomorphic encryption, disadvantage is large amount of computation, choosingpolynomial.In cloud computing,the relationship between the lessee and the lessee as well as therelationship between the lessee and the cloud service provider can’t guarantee each other’scredible security,therefor, how to keep the lessee and the cloud service provider’s privacy datasecurity and how to access control in the cloud computing is a another practical problem.In thisdissertation, we design a access control model under cloud computing, the encryption algorithmis fully homomorphic encryption which is designed by integral polynomial ring Z p[x].In themodel, the lessee and the cloud service provider’s privacy data can’t be exposed during the datatransfer and safely access control.During cloud computing and under the safely access control, the most of the data of thelessee are been saved in sever. Under the privacy data security and accepting cloud service,thelessee and the cloud service provider want to reduce the cost of time and space. In thisdissertation, with the decimal of data and the string of data,we use a new encryption methodwhich is fully homomorphic encryption to encrypt the data which is stored, the ciphertext canoperate in sever but still be recovered, and not reveal any information of the plaintext. Althoughthe once calculation of the algorithm is large, the algorithm can meet the lessee and the cloudservice provider’s basic requirements.