Research Of CRT-based Fully Homomorphic Encryption Scheme

In recent years,information leakage events happen frequently,which has become one of the hot spots of public concern.In the event of information leakage,the impact of personal privacy information leakage is worse.Homomorphic encryption technology is known as the "Holy grail" of cryptography,and it has been widely used in practice.Homomorphic encryption allows other or third parties to perform operations on the ciphertext.After the ciphertext is decrypted by the corresponding key,the same operations are performed on the plaintext directly.As a result,many third-party organizations do not need to decrypt users’ ciphertext data when calculating it.It changes the working mode that many users must trust the third party unconditionally,and further guarantees the security of users’ privacy information.With the actual construction of homomorphic scheme in 2009,homomorphic scheme has become the focus of academic research.This thesis is a study on the fully homomorphic encryption scheme in the fractional field.The main work is as follows:(1)Based on the Chinese Remainder Theorem(CRT)and the rule of Da Yan,a fractional domain homomorphic encryption scheme is proposed.The homomorphic encryption scheme can encrypt and decrypt by constructing congruence groups and has the property of addition homomorphism.In this thesis,the CRT＿D algorithm which can operate on fractional field is firstly obtained by combining the traditional CRT algorithm with he rule of Da Yan.Secondly,random data is inserted in the encryption process to resist the known plaintext ciphertext attack.Finally,the correct decryption result is obtained by using the dual mode operation in the decryption process.The experimental results show that the homomorphic encryption scheme designed in this thesis can realize the homomorphic addition operation in fractional domain and has good security.Compared with Paillier scheme and BFV homomorphism scheme,the efficiency is improved.(2)Based on Spare Subset Sum Problem(SSSP),chimeric multiplicative homomorphic encryption(MHE)and Bootstrapping technology,On the basis of the CRT＿D algorithm which can operate on the fractional field by combining the traditional CRT algorithm with the derivation method,the partial homomorphic scheme on the fractional field is described.Secondly,by improving the decryption function,it is improved into a Bootstrappable homomorphic scheme.Finally,the idea of re-encryption is introduced to construct a total homomorphic scheme on the fractional field.We proves that the fractional-field homomorphic scheme designed in this thesis can perform the encryption and decryption operation correctly and has the security against selective plaintext attacks(3)In the traditional query mode,the privacy information stored in the cloud has the risk of being leaked.Based on the theoretical research of the existing ciphertext database query mode,combined with the application of homomorphic encryption scheme,this thesis proposes a new addition homomorphic scheme and a new model of cloud ciphertext database system based on homomorphic encryption,and designs a CRT-based addition homomorphic ciphertext database system,which can realize the functions of secure query,download and decryption of ciphertext database.It also ensures that secret information cannot be leaked.The safety and correctness of the scheme are proved by theoretical analysis.Experimental results show that the scheme can query and download data correctly in the ciphertext database under the premise that the cloud server is not trusted by all,and has certain advantages in efficiency.