Research On The Application Of Fully Homomorphic Encryption Technology

Cloud computing drives the internet into our lives and has changed our life so much that it seems impossible not to upload our privacy information to the cloud.But we can only achieve it using plaintext.It has caused many serious data security issues and slows down the development of the large-scale application of cloud computing.If we can map the operations over plaintext onto corresponding ciphertext,we can solve the data security problems in the solution.Acutally,cryptographers have proposed the concept which is called homomorphic encryption now.It is difficult to construct fully homomorphic encryption(FHE)scheme and somewhat homomorphic encryption(SHE)scheme was proposed at first.For example,RSA is a kind of SHE scheme which only supports multiplications over ciphertext.Data encrypted by FHE scheme can be calculated with arbitrary arithmetics like the corresponding operations are excuted over the original data,so that we can put the encrypted data to the cloud for processing.But FHE scheme which supports arbitrary operations over ciphtertext is not proposed in last 30 years.Gentry built the first FHE scheme in 2009.He used recryption to transform SHE scheme into FHE scheme which caused wide attention.Then,leveled FHE schemes based on LWE and RLWE were proposed by researchers.FHE scheme is built by artificial contructions and involves a lot of theories which make it hard to be understood and difficult to be implemented.At present,the research work is still at theoretical level and there is still a great distance from the technical application.The key problem in the application of FHE technology is how to simplify the design process of the target circuit so that the operations supported by the theoretical scheme are better for the purpose of matching the operations in real scenes.This problem has not been fully studied.The paper aims at practical research of FHE.First we implement the lattice-based scheme and run experiment on it.Next we design the solution to implement the important parts of the RLWE-based scheme and solve many problems in the process.Then we use third-party data processing as background and analyse the practical problems of FHE technology.We sum up two problems through that way: the matching problem in the parameters and circuit depth,and as well as the matching problem in the computing space.At last we research the two problems by noise analyzing on RLWE-based scheme and propose solution to each problem.