Design And Analysis Of Lattice-based Key Exchange Schemes

With the rapid development of information and communication technology represented by the Internet and the continuous promotion of the national information digitization strategy,the collection between people's daily lives and Internet are continuously rising.Cyberspace have risen to the "fifth territory" of national security.At the same time,new security threats and attack methods are emerging one after another,and the demands of the cyberspace security are urgent.As an important branch of cryptography,key exchange and password-based key exchange are also playing an increasingly important role.The security of traditional key exchange protocols is based on the difficulty of the "discrete logarithm" problem.In the quantum-computing environment,the discrete logarithm problem is no longer difficult.The traditional key exchange system is insecure.The post-quantum cryptosystems are designed to guarantee the security of information in the context of quantum computers.Lattice-based cryptography,as one of the most promising post-quantum cryptography solutions,urgently needs more in-depth research.The main work of this paper is to construct post-quantum key exchange protocols for different application scenarios from lattice.Firstly,we give the security proof of the lattice-based multiparty key exchange protocol proposed by Ding et al.On this basis,a new lattice-based authenticated key exchange protocol is constructed.We gave the correctness analysis and security proof of the new protocol.At the same time,the new lattice-based authenticated key exchange protocol support pre-computation and can be extended to a lattice-based multiparty authenticated key exchange protocol.Secondly,we construct a password-based authenticated key exchange protocol over lattice.The increasingly widespread application of password-based authentication technology puts forward new requirements for network security and makes the demands for constructing quantum-resistant password-based authenticated key exchange urgent.Unlike the key exchange protocol,which starts from the users' public key,the password-based authenticated key exchange protocol is based on the users' short,low-entropy password.After the run of the protocol,both users get a consistent session key.This thesis uses an approximate smooth projection hash function and key agree-ment mechanisms to construct an efficient password-based authenticated key exchange protocol over lattice,and show the correctness and security of the new protocol.