Research And Design Of Public Key Cryptosystem Based On Lattice Theory

With the rapid development of science and information technology,mod-ern society has access to the era of information digitalization.In recent years,the continuous breakthroughs and innovations in the field of quantum com-puter research have made it possible to enter the quantum era in the future.Nowadays,the security of most cryptographic technologies and systems in cy-berspace are based on the hard problems of traditional number theory,and can not resist quantum attacks.Therefore,how to ensure data security in the post-quantum era has become an urgent problem which should be solved quickly.Lattice cryptography,as an anti-quantum cryptography,attracts the attention of researchers.The lattice has a complete theoretical system,and has unique ad-vantages compared with other cryptosystems:strong security guarantees from worst-case hardness,algorithmic simplicity,efficiency and parallelism.In re-cent years,there are two main directions in the research of lattice cryptography:one is that how to solve hard problem in high-dimensional lattice and its com-putational complexity theory;the other is the design of cryptosystem based on lattice hard problem.This paper focuses on design of proxy re-encryption scheme and signa-ture scheme based on atomic primitives of lattice to meet different needs.The concept of proxy re-encryption(PRE)was first introduced by Blaze,Bleumer and Strauss in EUROCRYPT 1998 to enable an intermediate proxy to convert a ciphertext of Alice to that of Bob without compromising the information of the underlying plaintext.Alice here is known as the delegator while Bob is the delegatee.PRE has been employed into many real-world applications due to this transformation function,e.g.,encrypted email forwarding,and domain interoperability manager(DIM)module in digital rights management(DRM)systems.However,most of the current proxy re-encryption schemes are based on the hard problems of traditional number theory,cannot resist quantum com-puting attacks.At the same time,there are few achievements in identity-based,revocable and other fields.Therefore,the design and research of the lattice-based proxy re-encryption system still has great research space.Meanwhile,as an important means to authenticate identity and prevent data from being illegal modification,there are many problems need to be solved in the application of digital signature technology in the post-quantum era.Based on lattice theory,this paper focuses on lattice-based cryptography,deeply studies proxy re-encryption cryptosystem and digital signature technol-ogy.The main research results are as follows:1.A lattice-based proxy re-encryption scheme is constructed by using double LWE mechanism and two-layer ciphertext structure.First,this paper thoroughly studied on collusion-resistant attributes which are generally not paid enough attention in the realm of proxy re-encryption,two novel definitions of anti-collusion attributes,called strong anti-collusion and weak anti-collusion have been proposed.By analyzing the potential threat of the previous schemes cannot achieve the anti-collusion attributes,an improved method is presented.Compared with the original scheme,the upper bound of error items is controlled to ensure the correctness of decryption in new scheme.And using double LWE mechanism to ensure the security of participants' private keys,which provides a new idea for constructing anti-collusion proxy re-encryption scheme.After analysis,the new scheme achieves strong collusion resistance,and achieves CPA security under the standard model.2.An identity-based lattice-based proxy re-encryption scheme is designed by using small matrix trapdoor and left-right lattice base sampling algorithm.To solve the problem that previous schemes can only prove security under ran-dom oracle model,the new scheme achieves a higher level of security,that is,CPA security under standard model.In order to have the function of re-encryption,the small matrix trapdoor is invoked to give the client the ability of proxy re-encryption.Aim at the problem that the adversary would distin-guish the simulation system from that of the real system,a blind structure is introduced to ensure that the user's private key can not be deduced from the known information in the attack model,but can only be queried through the in-teraction with the challenger.At the same time,the scheme has unidirectional,non-interactive and other high-quality attributes.3.A lattice-based revocable proxy re-encryption scheme is designed,which is secure and efficient.Considering the change of user privileges or the leak-age of private key,it is inevitable that the proxy re-encryption scheme should take into account the revocation problem,but there is no proxy re-encryption scheme supporting revocable mechanism.In order to solve this problem,the first definition and security model of revocable proxy re-encryption are given in this paper,and the conclusion that the revocation complexity of previous non-lattice revocation systems is linearly related to the number of users is improved.The key management is organized by binary tree structure,which reduces the complexity to logarithmic level.In particular,the previous non-lattice scheme can only achieve the chosen-plaintext security,which can prove that our scheme achieves the chosen-ciphertext security under the standard model.4.A new lattice-based signature scheme suitable for blockchain struc-ture is designed.Aiming at the problem that blockchain technology cannot re-sist quantum computation attack,a signature authentication scheme suitable for blockchain structure is presented by constructing lightweight uncertain wallet at the client,and combining the bonsai-tree technology in the lattice base reduc-tion.It ensures that each transaction's signature authentication uses one lattice space to guarantee randomness and privacy.Through the analysis of security and efficiency,this scheme can provide theoretical support and technical guar-antee for the application of blockchain technology in the post-quantum era.