Hierarchical Identity-based Fully Homomorphic Encryption Scheme From Lattices

With the continuous development of cloud computing technology,data are stored on cloud servers.How to securely calculate these data has become a problem worthy of research.Full homomorphic encryption can perform any effective calculation on ciphertext data,and the result is equivalent to performing the same operation in plain text.This feature of full homomorphic encryption makes it particularly suitable for private data calculation in cloud environments.However,the full homomorphic encryption scheme generally has the problem that the size of the public key is too large.The hierarchical identity-based fully homomorphic encryption scheme provides a good solution.The cryptosystem based on hierarchical identity eliminates the cumbersome certificate management of the public key cryptosystem,and solves the problem of overloading the root private key generator based on the identity encryption system.Constructing a hierarchical identity-based fully homomorphic encryption scheme can effectively reduce the size of the public key of the scheme and provide identity-based access control.Identity-based fully homomorphic encryption from lattices,as a highly sought-after anti-quantum cryptosystem,has important theoretical significance and practical application value for its research.This thesis studies the hierarchical identity-based fully homomorphic encryption scheme from Lattices.The main work is as follows:(1)Firstly,the status of research on identity-based fully homomorphic encryption schemes is analyzed,and the significance of the combination of identity-based encryption and fully homomorphic encryption is studied.Based on the hierarchical identity-based encryption system and fully homomorphic encryption system,A hierarchical identity-based fully homomorphic encryption scheme model from lattices is proposed.(2)A single identity full homomorphic encryption scheme(SI-FHE)from lattices is proposed,which solves the problem that in the layered identity-based encryption system,as the depth of the user's identity level increases,the dimension of the lattice continues to expand and the complexity of the derived trapdoor function is too high.The SI-FHE scheme uses a new trapdoor function to complete the trapdoor derivation process,and then uses the conversion mechanism to transform the scheme into a fully homomorphic encryption scheme,and finally improves the encryption and decryption algorithm form of the scheme.Compared with similar schemes,the scheme supports hierarchical identity-based encryption and the complexity of trapdoor function is lower,while reducing the dimension of the lattice,trapdoor size and public key size.(3)A multi-identity full homomorphic encryption scheme(MI-FHE)from lattices is proposed,and the formal definition of the scheme is given.The MI-FHE scheme is extended from the SI-FHE scheme.The linear combination and Mask technology are used to expand the ciphertext to achieve the characteristics of supporting multiple identity homomorphic calculations,and proves the security of the scheme's IND-SID-CPA under the DLWE assumption.