Research On Multi-Policy Attribute-based Fully Homomorphic Encryption Scheme On Lattice

As a remote service mode,cloud computing can provide users with storage space and computing power.In order to ensure user privacy and prevent data leakage,data is usually encrypted and stored in the cloud.The attribute-based fully homomorphic encryption technology can compute the ciphertext of the same attribute set while realizing fine-grained access control of shared data,which solves the two security problems of data sharing and computing,but it’s not suitable for mutli-user scenarios.Multi-key fully homomorphic encryption can perform arbitrary operation on ciphertexts encrypted by different keys(users).The operation result is decrypted by the concatenation of the secret keys of the users participating in the calculation,which solves the problem of homomorphic operation of multi-user ciphertexts.In some scenarios of cloud computing services,it is necessary to combine attribute-based fully homomorphic encryption technology with multi-key fully homomorphic encryption technology to achieve fine-grained access control of shared data in a multiuser environment and homomorphic operation of ciphertexts of different policy attribute sets.In addition,with the development of quantum computers,the lattice-based encryption scheme has received great attention due to its strong anti-quantum attack capability,high execution efficiency and strong security proof.Therefore,this theis studies the attribute-based fully homomorphic encryption scheme on lattice and the multi-key fully homomorphic encryption scheme,especially focusing on the research and realization of a more efficient and flexible multi-policy attribute-based fully homomorphic encryption scheme on lattice.The main contributions of this theis are as follows:1、A new multi-hop multi-policy attribute-based full homomorphic encryption scheme is proposed for the problems of large ciphertext size and low homomorphic operation efficiency in the current multi-hop multi-policy attribute-based fully homomorphic encryption scheme on lattice.The scheme can realize the homomorphic operation of ciphertexts on different attribute sets that satisfy different access policies,and it has a completely dynamic multi-hop property,that is,any new ciphertext with different access policies can be dynamically added to the ciphertext operation process,and the ciphertext output after homomorphic operation can perform homomorphic operation with the new ciphertext again,even if the attribute set corresponding to the newly added ciphertext does not satisfy the existing access policy set.Compared with similar schemes,the scheme has shorter ciphertext and higher homomorphic operation efficiency,and ciphertext extension is easier to be implemented.And the scheme is proved to be IND-CPA safe under the LWE problem.Finally,the performance analysis and simulation results are given.2、The single-policy and multi-policy attribute-based fully homomorphic encryption schemes that support multiple bits are first proposed for the problem that the current multi-policy attributebased fully homomorphic encryption on lattice only supports single-bit encryption.The scheme realizes the function of performing homomorphic operation on ciphertexts of different attribute sets that satisfy the same and different access policies,and at the same time,the scheme satisfies the multibit encryption property.And the scheme can be decrypted flexibly,not only can realize the decryption of message bit at a specific position,but also can realize one-time decryption,and directly restore the entire message matrix,which has better practicability.Finally,it is proved that the scheme is INDCPA safe.The performance analysis and simulation results are given.