Research And Application Of Homomorphic Encryption Algorithm Based On Integer Ring

The progress of technology has promoted the development of society,the fast development of information makes the internet become an indispensable and important part of people's life.With the appearance and wide application of cloud computing and big data,how to store important information securely and search encrypted data has attracted more and more attention,homomorphic cryptography is becoming more and more important.Homomorphic encryption can ensure the privacy of the manipulated data,that is,without knowing the clear text,perform the operation on the cipher directly and then decrypt it,the results are consistent with the data obtained by doing the same for clear text,using the obvious homomorphic nature of this feature,the delivery of encrypted data to an untrusted third party for processing does not reveal privacy.Therefore,homomorphic encryption has important research value in the fields of encrypted search,cloud computing and electronic voting.On the basis of studying the existing homomorphic encryption scheme,the generation mode of public private key is improved by combining with the actual application demand,this paper proposed two new full homomorphic encryption schemes.(1)The advantages and disadvantages of full homomorphic encryption schemes based on ideal lattice and integer are analyzed.According to the pattern framework of these two schemes,a full homomorphic encryption scheme based on integer polynomial ring is proposed.The security of the scheme is based on the sparse subset sum problem,the difference between this scheme and the full homomorphic encryption scheme based on ideal lattice and integer is that the main polynomial operation,and there is no need to re-select the polynomial during the encryption process,which has better flexibility and practicality.(2)The existing homomorphic encryption scheme mainly focuses on the data transmission between the single sender and the single receiver,but "one-to-one"encryption and decryption methods often difficult to meet the multi-party interaction of information.Based on integer polynomial ring,this paper realized the idea of"multi-part encryption and one-part decryption" through introducing polynomial to compute public key elements,change the way of generation of keys,and increase the number of encryption parties.The security of the scheme is proved under the random oracle model based on approximate greatest common divisor problem and sparse subset sum problem.Because of the homomorphic feature of the scheme,the homomorphic operation can be carried out between the encrypted messages of multiple senders,and then decrypted by the receiver,the result is consistent with the homomorphic operation after the receiver decrypts the transmitted multi-cipher,the operation can ensure the security of messages during transmission(3)Considering that the traditional electronic voting scheme has the problems of easy disclosure of ballot information and no protection of voter privacy in the transmission process,the "multi-to-one" full homomorphic encryption scheme is applied to the specific environment of electronic voting,put forward a full homomorphic encrypted electronic voting scheme based on integer polynomial ring.The voting scheme could support simultaneous voting for multiple candidates,and the batch of ballot papers to improve efficiency.The homomorphic feature can ensure the security of data transmission in the voting process.Through the experiment,there is the running time of the encryption and decryption in the scheme,and then propose an efficiency comparison with other schemes.