Design And Application Of Fully-homomorphic Encryption Scheme Based On LWR Problem

With the rapid development of the Internet and cloud computing technologies,the security of privacy data has gradually attracted people's attention.In order to better ensure the privacy of user data,a series of encryption schemes have been proposed one after another.The fully-homomorphic encryption technology stands out in many schemes with its unique advantages.This scheme does not require a pre-decryption operation,allowing third parties to directly encrypt The data is subjected to homomorphic operations.This feature makes it possible to handle the possible security problems in the cloud computing process.Currently,the mainstream schemes for studying all-homomorphic encryption are mostly based on the assumption of LWE difficult problem.However,according to the LWE theory,Gaussian noise sampling is required to generate the public key.The overhead of this operation is very large,resulting in low computational efficiency.In this paper,starting from this issue,the idea of replacing the LWE difficult problem with the LWR difficult problem is proposed.Based on the LWR difficult problem,a corresponding full-stated encryption scheme for single identity,multiple identities,and attribute categories is proposed.This paper proposes the effectiveness of the scheme and gives the application of attribute-based full homomorphic encryption scheme in ciphertext retrieval.Specifically,the main work of this article is as follows.(1).A single identity full homomorphic encryption scheme based on LWR is proposed.Firstly,an efficient LWR-based identity encryption scheme(IBE)is constructed.The LWR method is used to construct the public and private keys.The key generation process abandons the complex Gaussian function sampling.The identity encryption scheme constructed based on the traditional LWE problem has a smaller public key and ciphertext size.Then,based on the transformation method of eigenvectors,this IBE scheme is transformed into a single identity based fully homomorphic encryption scheme,which eliminates the homomorphic operation key of the previous IBFHE scheme,improves the computational efficiency,and uses the same security as the homogeneous encryption scheme.The model is strictly proof of safety.(2).A multi-identity full homomorphic encryption scheme based on LWR is proposed: Based on multi-linear mapping indivisible obfuscator and perforated pseudorandom function,a "fuzzy system" is constructed to use this system to carry out different identity ids.In order to build a multi-identity-based all-homomorphic encryption scheme,it can support different ids for homomorphic calculations.The security of the solution can be regulated to the LWR difficulty problem.Compared with the IBFHE scheme based on single identity,this solution has a wider application scenario.(3).An attribute-based all-homomorphic encryption scheme based on LWR is proposed: a ciphertext-based attribute encryption scheme(CP-ABE)is extended to a fully-homomorphic encryption(CP-ABFHE)scheme,which not only has an IBE system Public key certificates can also implement fine-grained access control over encrypted data.The proposed scheme can handle monotonic access structures on a set of authorization attributes without sacrificing the computational power of homomorphic encryption.In addition,it is proved that this scheme is IND-ID-CPA safe.(4).Application of attribute-based all-homomorphic encryption in ciphertext retrieval: The CP-ABFHE scheme above is applied to ciphertext retrieval.According to the feature that all homomorphic encryption supports ciphertext arbitrary calculation,this scheme can support multiple keyword ciphertexts.Search calculations improve search accuracy and search efficiency.