Ciphertext Search Scheme Based On Fully Homomorphic Encryption

Fully homomorphic encryption technology can calculate directly on the encrypted data,equivalent to the calculation on the plain text after decryption.Meanwhile,it is also a new field that applies the fully homomorphic encryption technology to information retrieval field and constructs a new ciphertext search program.Although there have been some methodologies of fully homomorphic encryption technology proposed so far,to implement it to practical is still a difficulty due to its large size of secret key and large scale of ciphertext.This article is dedicated to study how to decrease the size of secret key of the fully homomorphic encryption technology,how to increase the feasibility of its implementation,and how to construct the ciphertext search program to protect the customers' privacy by using fully homomorphic encryption technology.The article mainly did work as below:(1)it introduces the basic concepts and theories.At first describes the basic definitions of the computational complexity theory,summarizes and analyzes the lattice and the difficult issues based on it.Then describes the concepts and applications of the Learning with Errors assumption and search LWE problem in detail,introduces related concepts of the provable security infrastructure.Finally,it focus on introducing the constitution and related definitions of the fully homomorphic encryption algorithm.(2)it constructs a fully homomorphic encryption program based on Binary LWE.This article improved the key technology of the basic encrypting method.In the previous program,some collections chosen uniformly and randomly are added to LWE's random samples.However,the method this article proposes will add some Gausian Error to the LWE samples chosen from Gausian Distribution.This will decrease the sample size of LWE from to.And the private key of this method will be chosen directly from the set instead of the binary decomposition algorithm.This program will adopt the key switch technology to avoid the rapid expansion of the scale of the ciphertext after tensor multiplication,and meanwhile get a smaller size of secret key.In the end,the article will attribute the security of the to the assumptions of difficult problems of searching Binary LWE and then give a security proof.(3)it constructs a ciphertext search program based on fully homomorphic encryption.This article constructs the ciphertext search program based on the fully homomorphic encryption program constructed with the smaller secret key in Chapter3.When users store the data in the form of encrypted data in database,this method can meet their data searching requirements and protect their privacy effectively without threatening.Based on the security of fully homomorphic encryption program constructed in Chapter 3,the article gives the demonstration of the security of this program.