Research On Identity-based Fully Homomorphic Encryption Scheme From Lattices

In recent years,as“cloud computing”being more popular,the security of sensitive data and personal privacy have aroused more and more attentions from all fields of society.Although encrypted data can be safely stored in the cloud,to perform the evaluation must first decrypt,so that the data privacy will also be leaked to the cloud.How to let users enjoy the super computing power of“cloud computing”,while not affecting the privacy of user data is the current difficult problem needed to be solved.Fully homomorphic encryption allows arbitrary evaluations on encrypted data without decrypting,providing an ideal solution to data confidentiality and privacy protection.Despite of the progress of homomorphic encryption in recent years,it still faces the following problems:First,the efficiency parameters(the size of public key,secret key and ciphertext etc.)of homomorphic encryption should be improved,and it has a certain distance from practical application.Second,there are few candidate schemes for full homomorphic encryption,especially the schemes based on(hierarchical)identity.Finally,the trapdoor function and trapdoor delegation algorithms of(hierarchical)identity-based fully homomorphic encryption scheme is further inefficient.In this thesis,aiming at the above mentioned problems,we focus on the research of identity-based full homomorphic encryption(IBFHE)scheme over lattices.The main research contents are as follows:(1)As we analyze the previous fully identity-based homomorphic encryption schemes from lattices,the reason of low efficiency is that the trapdoor function and the design of the related algorithms are too complex,so a scheme is proposed.We first construct an identity-based encryption(IBE)scheme by combining a novel trapdoor function and Dual-Regev encryption algorithm.Then we transform the IBE scheme to IBFHE by employing the eigenvector idea.Due to we adopt the novel trapdoor function,the overhead of trapdoor generation and preimage sampling algorithms,and the main parameters of our scheme are improved compared with previous schemes.(2)Aiming at the high complexity in user's private key extraction and large expansion ratio of trapdoor size in previous lattice-based hierarchical identity fully homomorphic encryption schemes,we proposed a new solution.We first used the implicit extension method to improve preimage sampling algorithm,and then we combined the improved algorithm with efficient trapdoor delegation algorithm to construct an efficient user's private key extraction algorithm.Finally,we integrated the new extraction algorithm,Dual-LWE algorithm and GSW transformation mechanism to complete our scheme.Compared with the similar schemes,our scheme has the lower computational complexity and shorter efficiency parameters.(3)Aiming at the high complexity of trapdoor delegation in previous lattice-based hierarchical IBFHE schemes,we proposed two schemes under random oracle model and standard model,respectively.We first employ G-trapdoor function to construct an improved _q-invertible matrix sampling algorithm.Based on this algorithm,combined with trapdoor delegation algorithm in fixed dimension and G-trapdoor function,we complete scheme's setup and trapdoor delegation stages,and then obtain the resulting hierarchical IBE scheme by combining with Dual-Regev algorithm,binary tree encryption system and GSW compiling algorithm.Compared with the relevant schemes,the cost of trapdoor delegation reduced efficiently.Furthermore,the efficiency parameters such as lattice dimension,trapdoor size and ciphertext expansion rate etc.,all decrease in some degree.