Research And Application On Homomorphic Cryptography Theory

With the rapid development of cloud computing and big data, Data Storage andAnalysis of Security received draws more and more attention. HomomorphismEncryption has become a key technique of security data protecting and data analysisimproving as the adantages of analysis and processing of ciphertext.The paper examinedits applications by analysis and improving all kinds of the Public KeyCryptosystems.An improved scheme of the fully homomorphic encryption over theintegers is designed by the analysis of the previous scheme implementation process.Themain work is as following:1. The method of the analysis and classified of the common cryptosystems isproposed and presents the analysis and classified of public key cryptosystem, such asRSA，Paillier，ElGamal，Bresson and NTRU. The wireless ad-hoc network group keymanagement scheme and the dual homomorphism cloud computing solutions aredesigned based on the single homomorphic cryptosystem. Group key managementscheme is suitable for the group and topology variable network oriented, homomorphicencryption features can make it have high more efficiency and safety. Dualhomomorphism cloud computing solutions meets the demand of the variety kinds ofcalculation in the cloud computing environment which supports addition andmultiplication calculation.2. A ElGamal variant is designed on the basis of ElGamal cryptosystem analysis,which meets addition and constant multiplication homomorphic encryption and couldbe proved secure in the random oracle model.Then, the both sides protocol of privatelinear equation computation protocol is designed based on the variant which is provedsecure under semi-honest model. At the same time, the protocol is extended to othersecure multi-party computation problems. Compared with the traditional protocol; theintroduction of the homomorphic cryptosystem has higher execution efficiency, whichalso reduces the communication burden.3. The circuit compression algorithm, the Somewhat homomorphic encryptionalgorithm and the process of bootstrapping technique are studied through the analysis offully homomorphic encryption over integers propoed by Gentry.et al.Then, an improvedscheme of the fully homomorphic encryption over the integers combined the structureand technology of the homomorphic encryption algorithm is proposed, also, which isproved that the new scheme is correct and secure. Finally, I summarize the work done in this paper, and look forward to the nextstage of homomorphic enryption research area.