Research And Design Of Authenticated Key Agreement Protocol Based On LWE Problem

The key agreement protocol allows honest participants to establish a shared session key on the public channel.With the development of public key cryptography,the research of key agreement protocol has become an important issue in cryptography.Diffie and Hellman designed the classic Diffie-Hellman key exchange protocol.Key negotiation requires two rounds of message transmission.The protocol cannot resist man-in-the-middle attacks and replay attacks,and it does not provide mutual authentication.Based on further research on the currently proposed identity-based key agreement protocols,the paper studies the LWE-based authentication key agreement protocol and obtains the following research results:Firstly,in order to solve the problem of identity privacy preservation between two participants involved when implementing authenticated key agreement protocol,a bidirectional authenticated key agreement protocol against quantum attack based on C commitment scheme was proposed.Through the design of C commitment function,the real identity information of two participants involved was hidden.Based on RLWE difficult problem,under the premise to ensure identity anonymity,the protocol not only completed two-way identity authentication,but also ensured the integrity of the transmitted message,further-more,the shared session key was negotiated.Formal analysis of the protocol was performed using the ProVerif tool,confidentiality analysis was performed on the random value generated by the shared session key,and the identity authentication functions of both parties in the communication were tested.Secondly,based on RLWE difficult problem,a two-party authentication key agreement protocol based on lattice signature was proposed using noise scaling technology.The protocol needs three rounds of information interaction,and the mechanism of message authentication code is added in the second and third rounds of information interaction,which makes the protocol have key confirmation attribute and ensures the perfect forward security of the protocol.The LWE Estimator tool is used to test the security of the designed signaturebased AKA protocol.The designed AKA protocol can prove secure under the eCK model.Finally,based on LWE difficult problem,an AKA protocol based on hierarchical identity encryption was designed by using fixed dimensional lattice identity encryption technology and Peikert error coordination multi-bit deformation.The protocol can be proved to be safe under the CK model and can achieve weak perfect forward security.The protocol is designed based on the difficult problem of LWE.Although the communication quantity is higher in the process of protocol transmission,the protocol is based on the most original matrix mathematical structure,which avoids the possible unsafe risk caused by the selection of ring elements from the special algebraic structure on the ring in the RLWE problem,so the security performance is more reliable.