Research On Lattice-based Searchable Encryption Schemes

With the research and development of quantum computers,many cryptosystems which are secure under classical computers will be fragile in the quantum computing era.Lattice-based cryptography becomes one of the vital research directions of post-quantum cryptography because of the property of anti-quantum computers attack and its own advantages.Besides,with the development of network technologies,the data volume has shown rapid growth,which accelerates the development of cloud storage technology.The privacy protection of data stored in the cloud attracts considerable concerns of data users.Searchable encryption is a cryptographic primitive that can keep data privacy and searchability.However,most existing searchable encryption schemes were constructed based on bilinear maps or other classical number theory problems which can be solved by quantum computers.There are few lattice-based searchable encryption schemes.Therefore,the research on lattice-based searchable encryption schemes has important theoretical significance and application value for cloud storage and ciphertext data retrieval in the future quantum computing era.Based on the analysis of the existing schemes,this paper studied the construction of different types of lattice-based searchable encryption schemes,from the security and functionality of cryptographic schemes.The main research results are listed as follows:(1)Due to the reveal of search token,data privacy often cannot be protected in the searchable encryption scheme.To this end,we introduced a new security model of keywords revocable public-key searchable encryption,bounded token exposure resistance which can reduce the impact of the leakage of search token.Additional,considering that the revoked keywords are searched again,this model is also designed to support the token re-generation.Based on this model,we presented a lattice-based keywords revocable searchable encryption scheme.(2)In the traditional public-key searchable encryption systems,there is an inherent attack,keywords guessing attack.To this end,we constructed a lattice-based searchable encryption scheme that can resist this attack.Besides,considering the search efficiency and practical application,this scheme is also designed to support the conjunctive keywords search.(3)When the adversary is a malicious server in the above attack,this attack is named as inside keywords guessing attack.In actual scenario,the server is easily controlled by adversaries via some computer virus,to perform this attack.To this end,we constructed a lattice-based searchable encryption scheme which can resist inside keywords guessing attack.Furthermore,we also extended this scheme to support conjunctive keywords search which can realize the one-time multiple keywords search.(4)Proxy re-encryption technology is applied to public-key searchable encryption scheme,which can achieve multi-user search.Based on this,we designed a lattice-based publickey searchable encryption scheme with time-controlled proxy re-encryption.In this scheme,the data owner can access the encrypted database without time constraint and delegate the time-controlled access right to other users.Compared with previous works,the scheme doesn't require a time server to compute the time seal,which saves the managing overhead of a server and reduces the security risks.(5)Finally,from the perspective of lattice analysis,we analysed the orthogonal lattice algorithm for solving the general approximate common divisors(GACD)problem which can be used to construct fully homomorphic encryption scheme.We proved the validity conditions of this algorithm and obtained a new bound on the GACD samples' number.The experimental analysis and comparison indicate that the success probability of this algorithm under our bound is higher than the probability under the bound of the previous work,with the increase of the values of GACD parameters and the bound of the samples' number.