Three-party password authenticated key agreement protocol with user anonymity based on lattice

With the rapid development of quantum theory and the existence of polynomial algorithm in quantum computation based on discrete logarithm problem and large integer decomposition problem,the security of the algorithm was seriously threatened.Therefore,two authentication key agreement protocols were proposed rely on ring-learning-with-error (RLWE) assumption including lattice-based implicit authentication key agreement scheme and lattice-based explicit authentication key agreement scheme and proved its security.The implicit authentication key agreement protocol is less to communicate and faster to authentication,the explicit authentication key agreement protocol is more to secure.At the same time,bidirectional authentication of users and servers can resist unpredictable online dictionary attacks.The new protocol has higher efficiency and shorter key length than other password authentication key agreement protocols.It can resist quantum attacks.Therefore,the protocol is efficient,secure,and suitable for large-scale network communication.