The Research And Construction Of Fully Homomorpic Eneruption Scheme Based On Lattices

The coming of cloud computing times brings people a lot of convenience, at thesame time causes some panics---leakage problems. So it’s vital to research and developthe security technology. Ciphertext index and processing are mainly focused on thefully homomorphic encryption algorithm. Fully homomorphic encryption allowsoperation on any encrypted data. That is, it can maps plaintext operations to ciphertextoperations, which makes it possible to do trusted computing in the untrusted terminals.The significance of this technology is that settling the secret problems caused byescrow. Considering its advantages, it can be used for cloud computing. At the sametime, for any complex plaintext operation, we can construct corresponding encryptionoperation. However, fully homomorphic encryption has a lower efficiency withcomplicated encryption and long key-size in practice.Based on the characteristics and application of fully homomorphic encryption, wepropose two methods of efficiency improvement. The main work is as follows:1.We analyze the present state of fully homomorphic encryption. we introduce itsconcept, early technology and some applications, such as electronic voting, lossytrapdoor functions and private information retrieval protocols, a multiplicativelyhomomorphic encryption put forward by Boneh et al, a scheme about evaluatingNC1circuits proposed by Sander et al.2.We describe Gentry’s fully homomorphic encryption in detail and analyze theefficiency and security of this scheme. We design a FHE schemes to improve itsefficiency. Its hardness is based on RLWR.The size of public key is2n lgq and aper-gate computation time is^{O|_</sup>（k） in our second scheme.3.We introduce the recent trends and applications of fully homomorphicencryption. These applications include the new technology given by Brakerski et al,cloud computing security, non-malleability and homomorphic encryption, FHE andfunctional encryption, the new scheme designed by Polly Cracker.}