An Multi-identity Fully Homomorphic Encryption From LWE

With the continuous development and maturity of cloud computing,the application of cloud computing is gradually popularized.It has powerful data processing capacity and can help people perform complex operations.While cloud computing brings great convenience to people,some security problems that restrict and affect the development of cloud computing inevitably appear.The most important one is the security of data.Although the encrypted data can be safely stored in the cloud,if users want to take advantage of the powerful computing power of cloud computing,they need to decrypt the encrypted data before computing,in this process,the privacy of users may be exposed.Therefore,when users hand over their private data to a third party for processing,how to ensure the security of these data has become a problem that must be solved during the development of cloud computing.In addition,the rapid development of quantum computer also requires people to find a cryptographic scheme to resist the attack of quantum computing as soon as possible.Full homomorphic encryption has a special property in ciphertext processing,that is,it can perform effective operations on ciphertext without decryption.This feature plays an important role in protecting information security.Based on this feature,people can delegate data to a third party for computing without disclosing the privacy of users,which provides a new way to solve the data security problems faced by cloud computing.In recent years,the research of full homomorphic encryption has developed rapidly and made remarkable achievements,but it still faces the following problems:first,the public key size of full homomorphic encryption scheme is too large;Secondly,the trapdoor generation algorithm and preimage sampling algorithm in ident,ity-based full homomorphism encryption are inefficient.Thirdly,the traditional identity-based full homomorphic encryption only allows the ciphertext under the same identity to perform homomorphic operation.In order to solve the above problems,this paper studies multi-identity homomorphic encryption scheme.Aiming at the multi-identity homomorphic encryption scheme proposed by Clear et al.,an improved scheme was proposed.Firstly,an efficient identitybased encryption scheme is constructed by using efficient trapdoor function.Secondly,an identity-based full homomorphic encryption scheme is constructed by using gadget matrix and approximate eigenvectors.The scheme is more concise and does not require the evalvation key.At the same time,the noise growth rate of homomorphic operation is reduced by proper randomization noise.Finally,a multi-identity full homomorphic encryption scheme is constructed by using ciphertext extension technology.