| In cloud computing,the user's data is stored in the resource peer of the cloud.When the user needs it,the result of data calculating is sent to the user over the network.Because the user's data is stored in the cloud,ordinary users do not have complete control of their private data.The optimal approach to ensure data security is encrypting the cloud data.In order to provide users with efficient and fast technical services(such as data retrieval,access control,data mining,etc.),cloud service providers must be able to perform various complicated operations on encrypted data.Obviously,the traditional cryptosystems cannot complete this mission.Fully homomorphic encryption comes into being.Fully Homomorphic Encryption(FHE)can perform arbitrary operations on ciphertexts over any Boolean circuit or evaluating function,and the decryption of the result is equivalent to the same operation on plaintext.Encrypted data allows the untrusted server to perform any operation without the secret key.This property can effectively decouple data holders and users,which makes it possible for cloud servers to process encrypted data arbitrarily,and also makes FHE a promising application in cloud security,cloud computing,encrypted databases,and ciphertext retrieval.In this paper,we mainly study the RLWE-based fully homomorphic encryption cryptosystem.And we further explore its optimization techniques,security proofs,and practical applications.The main research results are as follows:1.Batch Technique for RLWE-Based Fully Homomorphic Encryption SchemeFaced with the problem of low efficiency of single-bit encryption schemes,we design a new scheme which combined with the batch technique.Concretely,the technique packs multiple “plaintext slots” into a ciphertext by using the Chinese Remainder Theorem,and then performs homomorphic operations on it.Considering the exponential growth of the noise in each multiplication operation,we use the key switch and module switch technique to reduce the noise size in ciphertext,which ensure the correct decryption and the next homomorphic computation.Finally,we analyze the security and efficiency of the scheme.It is proven that our scheme is CPA security and the efficiency of encryption is n times the original scheme.2.Canonical Embedding Technique for RLWE-Based Muit-bit Homomorphic EncryptionMost of the previous encryptions are using coefficient embedding methods.We use the canonical embedding technique to map the elements on the polynomial ring to the complex number field,which supports the bitwise addition and multiplication of the vectors.We construct a mult-bit homomorphic encryption scheme based on RLWE assumption,which used canonical embedding technique to map the elements over the polynomial ring to the vectors in the complex number field,both addition and multiplication can be conducted coordinate-wise.Thus,we can make computation more convenient and support for bigger plaintext space.Finally,we designed a PBR protocol based on the proposed scheme and analyzed it.3.Approximate eigenvector technique for Leveled FHE Scheme from RLWEIn 2003,Gentry et al.constructed a FHE scheme based on the LWE assumption using the approximate eigenvector method.It has a novel ideal and opens up the climax of the construction of the third class of FHE.The RLWE problem assumption has a good algebraic structure and a simple lattice cryptographic property.Under the same conditions,the RLWE problem is more efficient than the LWE problem.Based on the RLWE assumption,we construct a GSW-type Leveled FHE scheme,briefly describe homomorphic operations,and provide detailed security proofs.Based on this,we use key switch technique to construct a leveled FHE scheme under different public keys,and use the hybirds sequence to prove that the scheme is CPA secure.Finally,we analyze the efficiency of the scheme from several aspects,including the size of the public and secret keys,the size of the ciphertext,and the expansion rate,and provide specific parameter setting requirements. |
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