Research On Fully Homomorphic Encryption Over The Integers And Application In Cloud Platform

Fully homomorphic encryption(FHE) allows arbitrary computation to be carried out on encrypted data without decryption, and the decryption result equals the result of the same operation on corresponding plaintext. This unique property makes it possible to eliminate information safety problem, when a third party is introduced for data processing. FHE system could solve the contradiction between data confidentiality and manipulation in traditional encryption system, it can be applied for ciphertext processing, retrieval and secure multi-party computation. With the development of clouding computation, internet to things, the FHE system will have a broad application prospects on secure cloud computation, storage and confidential data retrieval.The FHE over the integers and its application in cloud computation are researched in this paper. The dissertation is summarized as follows:1) It researches the single bit FHE scheme over the integers(DGHV). The scheme is improved by using the public key compression, extending of message space and cipher-text decomposition method. Our scheme makes the size of public key in DGHV reduce from(7)(8)10(46)(4)lto(7)(8)7(46)(4)l, the message space extend form GF(7)2(8) to GF(7) p(8), and the new method of decomposition could improve efficiency of ciphertext bootstrapping procedure.2) The batch FHE scheme over the integers(BDGHV) is researched. By combining the methods of public key compression, private key dimension expanding and ciphertext decomposition, an improved BDGHV scheme is presented. Compare to original one, our scheme makes the size of public key reduce from(7)(8)7(46)(4)lto(7)(8)5.5(46)(4)l, the secret key reduce from(7)(8)9(46)(4)lto(7)(8)3(46)(4)l. Despite of the extra consumption introduced by the private key matrix, our scheme has improved in terms of security.3) It is the experimental simulation of FHE scheme over the integers. The analysis and comparison results of DGHV, BDGHV and our scheme are presented. At the same time, an applied system based on the Object Storage Service(OSS) is introduced and implemented, which combining FHE scheme and Cloud Computation and verifying the feasibility of FHE.