Research On Verifiable Ciphertext Computation Scheme Based On Homomorphic Encryption

With their powerful performance advantages,cloud computing and cloud storage technologies provide users with convenient and fast network services.At present,more and more users are using cloud services to store data and perform complex data computations to obtain more valuable computation results.The emergence of fully homomorphic encryption(FHE)enables users’ private data to be securely computed in an encrypted state.However,in the current cloud computing scenario,the computation efficiency of FHE is generally low,and users cannot verify whether the computation results returned by cloud servers are correct.Therefore,for the problem of ciphertext computation in the cloud environment,combined with FHE and verifiable mechanism,the corresponding homomorphically verifiable computation schemes applicable to different user scenarios are proposed in this thesis.The main work is as follows:(1)In this thesis,we analyze the current mainstream FHE schemes and select the practical BGV scheme which can resist quantum attacks as the research object.Aiming at the problems of large public key size and low efficiency of multiplicative homomorphic computation,an efficient FHE scheme(EFHE)is proposed by reconstructing the BGV scheme and improving the ciphertext refreshing algorithm.This scheme effectively reduces the number of switch keys required in the ciphertext refresh phase and ensures that the multiplicative homomorphic computation of all ciphertexts can always be repeated between two levels without the limitation of circuit depth,which significantly reduces the time-consuming of ciphertext computation.For the problem that the computation results returned from the cloud are not credible,a polynomial decomposition method is introduced in this thesis,and thus a verifiable computation scheme based on EFHE(VE-FHE)is proposed to realize the verification of the correctness of the computation results.(2)Aiming at the problem that the VE-FHE scheme is only applicable to singleuser verifiable computation scenarios,we further study the FHE algorithm.Firstly,based on the EFHE scheme,we combine the ciphertext expansion and optimized relinearization technique to extend it into an efficient relinearization-based multi-key FHE(ER-MKFHE),in which the ciphertext expansion technique ensures that the ciphertext dimension of multiple participants is the same,the optimized relinearization technique solves the problem of large ciphertext dimension due to ciphertext expansion and effectively reduces the time consumption of ciphertext relinearization,and the ERMKFHE scheme enables efficient homomorphic computation among ciphertexts encrypted by multiple different keys.Then,based on the ER-MKFHE scheme,this thesis further combines the polynomial decomposition technique to design a verifiable computation model for multi-user scenario,thus proposing a verifiable computation scheme based on ER-MKFHE(VER-MKFHE),which supports multi-user joint computation and allows new users to join the computation process in real-time while satisfying the verifiability.Theoretical and security analyses show that the VE-FHE and VER-MKFHE schemes proposed in this thesis can meet the requirements of single-user delegated computation and multi-user joint computation in practical applications,respectively,with both quantum computation-resistant security and verification security.During the verification phase,both schemes satisfy public verifiability,and no interaction is required between users and servers.Experimental analyses show that the VE-FHE scheme significantly improves the efficiency of multiplicative homomorphic computation and has a time advantage in polynomial function verification,and the VER-MKFHE scheme has high computational and verification performance and can be better applied to multi-user joint computation in medical monitoring scenarios.