An Identity-based Fully Homomorphic Encryption Scheme

Fully Homomorphic Encryption schemes allow the third party to perform arbitrary operations on ciphertexts without the secret keys.Because of cloud computing,FHE has very important application value.Gentry designed the first FHE scheme in 2009.After that,FHE has developed very fast.However,there are still many important prob-lems to solve in FHE such as few candidate schemes,low computing efficiency and lack of security proof.Nowdays,the most popular FHE scheme is built based on the L-WE problem,which are simple in computation and have the good property of resisting Quantum attacks.In the paper,we first introduce Gentry's FHE scheme.To get a FHE scheme,He proposed a somewhat homomorphic encryption scheme firstly.But homomorphic oper-ations can only been performed in finite steps because of noises.So,Gentry raised the conception of bootstrap encryption.To make his somewhat homomorphic encryption scheme to a bootstrapable encryption scheme,Gentry must reduce complexity of de-cryption circuit.He divided the decryption computation into the two parts and added the ciphertext label ?.Than he distributed one of the two parts the computation to the encryption circuit,which greatly reduced the complexity of decryption circuit.Then,base on the thought og Gentry's design of FHE,we propose an identity-based FHE,with the LWE problem.The scheme uses trapdoor generation algorithm to generate a one-way function with trapdoor and takes trapdoor as the main private key.We use trapdoor to generate the private key of user's ID and encrypt the data with public parameters and user's ID.In the process of encryption and decryption,we use vector expansion technique from GSW.Therefore,our homomorphism operations are simple matrix additions and multiplications.The security of our scheme depends on the difficulty of problems,LWE and SIS.