Research On Full Homomorphic Encryption Scheme Based On Lattice

With the rapid development of the Internet of Things,most users tend to encrypt data and then outsource to cloud servers.Fully Homomorphic Encryption can ensure the processing and analysis of ciphertext data of multiple users.It supports the ability to perform any way of calculation ciphertext data without decryption,but these outsourced data may contain some sensitive information,such as financial data,medical data,and data related to national security.Therefore,a reliable third party or government department is required to supervise these data.When necessary,the supervisor can decrypt the ciphertext and view the plaintext information of these data.The Dual Receiver Encryption system is suitable for the above application scenarios.It allows the ciphertext to be decrypted by two independent receivers to obtain the same plaintext.Most of the existing solutions are based on the traditional bilinear mapping structure,which has low computational efficiency and cannot resist quantum attacks.In addition,the overhead associated with certificates will seriously affect the efficiency of these two cryptographic primitives in practical applications.To solve the problem that the size of the public parameters is too large,we use the block technology to make the size of the public parameters smaller,so as to improve the storage efficiency and calculation efficiency of the scheme.Secondly,in order to improve the security of the scheme,our scheme satisfies the adaptive security.Based on these two innovations,we propose a lattice-based dual receiver encryption scheme with short public parameters.On the basis of scheme one,we introduce homomorphic encryption algorithm to make our scheme capable of homomorphic operation.The main achievements and innovations of this article are as follows:(1)Most existing dual-receiver identity-based encryption systems and fully homomorphic encryption systems generally have the problem of excessive public parameters and inability to resist quantum attacks.To address this problem,this paper proposes a dual-receiver identity-based with short public parameters scheme,which is constructed based on the difficult problem of LWE,has a great advantage in security under the general trend of the advent of quantum computers.In addition,the size of the public key can be reduced to 86.96%of the original when our solution does not increase much in computational overhead.Therefore,the storage overhead will be greatly reduced when the solution is implemented in actual scenarios.This scheme also provides favorable conditions for us to construct a fully homomorphic identity-into-double-receiver encryption scheme in the future.(2)This paper introduces the fully homomorphic encryption technology into the identity-based dual-receiver encryption system,and proposes a new cryptographic prototype-the concept of identity-based dual-receiver fully homomorphic encryption on the grid.Based on this concept,an identity-based dual The receiver encryption scheme is expanded to a fully homomorphic identity-based dual receiver encryption scheme.Cloud computing service platforms often need to perform certain processing on outsourced data according to user needs,such as search,query,and even more complex data operations.The ciphertext obtained by traditional encryption schemes cannot support complex ciphertext operations.Therefore,under the premise of data privacy protection,our solution can perform ciphertext operations on the cloud.After the data is encrypted by this scheme,a third party who does not have the ability to decrypt is allowed to perform homomorphic operations,and it can be correctly decrypted by two independent receivers,thus realizing the sharing of data in the cloud computing environment.Under the assumption of LWE,the scheme proves The security of the plaintext attack is selected for the adaptability of the proposed scheme.In addition,this scheme continues the advantages of our proposed identity-based dual receiver encryption scheme with short public parameters,and uses block operation and a new and efficient trapdoor generation algorithm to make the fully homomorphic scheme more efficient.