Optimization And Analysis Of Homomorphic Encryption Over The Integers

Recently,cloud computing has been widely used as an important way to provide users with information and resource on demand.The technology can be used in many areas,including social networking sites,e-commerce,education,and massive data management.The following data security issues are the key issues that cloud computing technology needs to address.Homomorphic encryption technology can directly solve this important problem because of its characteristic that it can directly process ciphertext operations,so it has become a hot spot today.Homomorphic encryption over the integers has become one of the important research directions in homomorphic encryption systems because of their simple concepts and operations.Among them,the DGHV scheme is the most classic.Although this scheme makes homomorphic encryption greatly optimized in algorithm complexity,there are still many problems that hinder practical application.This paper mainly focuses on the problems of the large public key storage space and the inefficiency of one-to-one encryption that requires too many keys to maintain,and proposes corresponding optimization solutions:1.Aiming at the problem that the public key size is too large,we analyze the currently known public key compression methods on the basis of the DGHV scheme,and propose a four-power homomorphic encryption scheme with correction.This scheme compresses the size of the public key fromO(?¹⁰)in the DGHV scheme to O(?³),greatly reducing the storage space of the public keys.And we prove that the security of this scheme is based on the AGCD problem and has semantic security.Data analysis shows that the scheme does effectively compress the storage space of public keys.We also propose a digital watermarking model based on homomorphic encryption,which can be used to maintain multimedia security on public platforms.2.Considering the fact that there are many homomorphic encryption parties and a single decryptor needs to store a large number of keys,which leads to inefficiency,we have studied multi-party of homomorphic encryption models and multi-party of the DGHV scheme.An implementation method is proposed for a multi-party homomorphic encryption scheme based on four-power homomorphic encryption with correction.This scheme can use one key to decrypt information of multiple encryption parties,which not only optimizes the key management problem,but also enables multiple participants to perform data transmission,and improves the efficiency of the algorithm.We prove that the homomorphism of the scheme,and performance analysis shows that the efficiency of our scheme is better than the multi-party DGHV scheme.