Research On Identity-Based Full Homomorphic Encryption Scheme

With the rapid development of communication and information technology,great changes have taken place in the computing mode,which directly lead to the emergence of big data and cloud computing.The following problem is that data security and privacy protection have become the bottleneck of cloud computing.Fully homomorphic encryption(FHE)technology allows anyone to operate directly on the ciphertext without knowing the decryption key.And the result is equivalent to first calculating the plaintext,then encrypting.Therefore,it can realize the calculation outsourcing of sensitive data in encrypted state,and effectively solve the data security and privacy protection problems in the development of cloud computing.As one kind of public key system,FHE system needs authentication-center to solve the problem of public key authentication.The authentication-center will lead to huge overhead in the whole system's burden of computing,storage,communication and other cryptographic overhead,especially when the public key size is too large.Nevertheless,the public key in identity-based encryption system is extracted from the unique identity information of the user,which can avoid using the public key certificates.In this paper,we mainly research on the identity-based FHE scheme.In the case of single-identity fully homomorphic cryptography,we use the special algebraic structure of ideal lattice to construct identity-based FHE system.In the aspect of multi-identity full homomorphic cryptography,we optimize the multi-identity FHE scheme constructed by Clear,in order to improve the efficiency of the scheme and reduce the noise expansion rate.Moreover,we use the obfuscator to construct a multi-identity FHE system.The resulting encryption system can perform multiple(Multi-hop)homomorphic operations,and does not require ciphertext expansion technology.Finally,we further expand the research based on the above-mentioned multi-identity FHE system.We use multi-identity FHE system combined with strong unforgeable signature scheme to construct CCA-security FHE system.The main results of this paper are as follows:1.Identity-based fully homomorphic encryption over ideal latticeIn order to solve the efficiency problem of identity-based FHE scheme,we construct identity-based FHE scheme based on the ideal lattice.Specifically,we extend the trapdoor generation algorithm on the lattice to the ideal lattice,and construct identity-based encryption system with the dual LWE public key encryption scheme.And then,we use the eigenvector to transform the above IBE scheme into single-identity FHE scheme.With this improvement,the key size and efficiencof the scheme have been improved.2.The technology for improving the efficiency of multi-identity FHEIn order to solve the problem of low efficiency and noise management of multi-identity FHE scheme,we propose a general technique to optimize such scheme.Firstly,an efficient identity-based encryption scheme is constructed by using the efficient trapdoor generation algorithm.Compared with the previous scheme,the algorithm is more efficient and the security dimension is reduced from 6nlogq to 2nlogq.Then,the identity-based encryption scheme is transformed into a single identity FHE scheme by using the original-image matrix and the approximate singular vector.Since the ciphertext of our scheme is formed by matrixes,there is no dimension expansion problem after the homomorphic multiplication.In our scheme,the approximate singular vectors,original image matrix and sub-gaussian variable were utilized.Analysis shows that the noise expansion rate is brought down from O(n)to O(n).Finally,we take advantage of extended ciphertext technology in conjunction with the masking technology to construct an efficient multi-identity FHE scheme.3.Identity transformation technology based on obfuscatorIn view of the current multi-identity FHE scheme being 1-hop type,we use indistinguishability obfuscator and puncturable pseudorandom function to construct identity transformation algorithm,and further construct multi-hop multi-identity FHE scheme.In CRYPTO 2015,Clear et.al proposed a multi-identity FHE of 1-hop type.That is to say,the new ciphertext generating by homomorphism algorithm cannot be involved in the homomorphic operation again.Moreover,our scheme abandons the use of ciphertext extension technology,so the scheme has significant advantages in both efficiency of the scheme and the number of supported identities.4.CCA-secure fully homomorphic encryption systemUnfortunately,a scheme that has nontrivial homomotphisms cannot be CCA2 secure,because it is malleable.But there do not seem to be inherent reasons why a homomorhpic encryption cannot have CCA1 security.And it's an open problem to construct the CCA1-security FHE scheme.We provide the general method of constructing CCA1-secure FHE scheme.We construct a CCA-secure FHE scheme by using IND-sID-CPA secure multi-identity FHE scheme combined with a strong unforgeable signature scheme.Under our security model,when the adversary could get the evaluation key,our scheme is IND-CCA1 secure;when the adversary couldn't get the evaluation key,our scheme is IND-CPA secure.Finally,we strictly prove the security of the scheme.