Research And Implementation Of Fully Homomorphic Encryption Based On LWE Problem

With the rapid development of science and technology, human society's dependence on information technology is becoming more and more serious. Cloud computing and quantum computing are popular concepts who shown a great influence on our life and work. The potential threats of these inovative technologies is burgeoning when we profiting from them. One of the most important problems is information security of this information explosion era, which is also prone to be ignored. In the traditional mode of information security, in order to benefit from the powerful Cloud server, people always transferring encrypted data to the server, and send it the secret key, which obviously revealing the data privacy of users. At the same time, traditional cryptography is facing serious challengs because of the fast development of quantum computing. Human beings are in urgent need of a way to avoid threats from new technologies.Fully homomorphic encryption, is a good medicine from cryptographers. In the year 2009, the first real fully homomorphic encryption scheme was proposed by Gentry. After that, research and discussion in this field has never stopped. However, domestic and foreign scholars usually pay more attention on the theoretical research of fully homomorphic encryption, only a few of the applications mainly focus on somewhat homomorphic encryption.The major work of this article are as follows:(1) Analysises the representation of the third generation of LWE based homomorphic encryption, the GSW scheme. And based on this, a variant scheme called 'VGSW' is constructed, proves the correctness and security of the new scheme, and illustrates the problems needing attention in the selection of parameters;(2) Introduces dimension-modulus reduction and bootstrapping technology, transforms the VGSW scheme into a fully homomorphic encryption scheme, shows the whole process of the construction, proves the correctness and security of the bootstrapping scheme, and provides several selection rules of parameters from a theoretical point of view.(3) Designs and implements the fully homomorphic encryption library of the VGSW scheme using the concept of software engineering, proves the correctness and effectiveness of every module of the library, analysis the results of the tests, and provides some improvement methods from both areas of algorithm theory and software implementation.(4) Constructs a single bit full adder in two different ways, by using the library of VGSW scheme. And implements an 8-bits binary full adder.(5) Designs an application scene called "anonymous electronic voting", analysises the characteristic of the scene, and designs a anonymous electronic voting protocol based on the homomorphic full adder proposed by this article.On the basis of theoretical research, this paper designs and implements a fully homomorphic encryption scheme, which is of great practical value and broad application prospects.