Researches On Algorithm And Application Of Homomorphic Encryption Over Integer Ring

With the rapid development of network,big data is widely used.But the leakage of sensitive data is also happened.So network security gets more and moer attention.Homomorphic encryption algorithm is one of the important technology of big data privacy protection.Homomorphic encryption algorithm can deal with the ciphertext,and can recover the plaintext correctly.Homomorphic encryption algorithm can reduce the frequency of plaintext's exposure on the network.Homomorphic encryption algorithm has widely use in cloud computing,ciphertext searching and electronic voting,and other fields.In this paper,Gentry's frame and the related schemes are combining to improve the method of generating public keys.Then two kinds of homomorphic encryption schemes are designed that can shorten the size of public key.Firstly,a new homomorphic encryption scheme is put forward to deal with the problem of public keys' inflation,which improving the method of generating public keys.The advantages of schemes of Dijk et al and Hongyan Dai et al are combining to designe the new scheme that can deal with 1bit plaintext.The generation xi,0 and xi,1 are no longer use the same way,which can reduce the vulnerability of public keys.The sum of public keys change to 2(?)? + 1.When computing x0,add the polynomial to hide the private key information by using f(p)instead of p.Using MATLAB to implement a new SomeWhat scheme and a new BootStrappable scheme.And compare with schemes of Dijk et al and Hongyan Dai et al to prove that the new homomorphic encryption scheme has the shortest public key.Secondly,In order to improve the computing efficiency,the space of plaintext extend from {0,1} to {0,1}l on the basis of the new scheme that can deal with 1bit plaintext,and design a batch homomorphic encryption scheme.The method of selecting discrete subset is improved.A ? dimensional discrete subset change to two(?)O dimensional discrete subsets,which can renduce computation.The decryption circuit in the batch BootStrappable scheme is computed to prove the decryption circuit depth is in the scope of the permitted function.And the validity,homogeneity and security of the new batch scheme is proved.And compare with schemes of Cheon J H et al and Bingchong Luo et al to prove the new batch homomorphic encryption scheme has the shortest public key.Finally,do a reasearch of the applacation of batch homomorphic encryption scheme to electronic voting system.A batch electronic voting scheme is designed by making some improvements on the schemes of Zhengyang Zhu et al and Yonghen Wang et al to improve the processes of voting encryption and voting operation.The computing times times of processing encrypted votes are reduced from t to 1.What's more,the new batch electronic voting scheme adds a decryption system.Voting system takes charge of verifying the encryp-ted votes,decryption system takes charge of computing encrypted votes and decrypting the encrypted votes,which can increase the work efficiency.