Password-based authentication key exchange protocol is highly practical in modern communication networks. The rapid development of quantum technology has made the security of traditional public key cryptosystem face a severe situation. The construction of cryptosystem based on lattice theory has become a hot topic in the research of post-quantum cryptography. The scheme is based on the lattice theory error learning (RLWE) problem

and uses the Peikert error reconciliation mechanism to construct a password authentication key exchange (PAKE) protocol in C/S mode. Reasonable parameters are set to ensure that both parties get the same session key with significant probability

and by using Java to implement PAKE protocol on the Eclipse platform. The security of the protocol is proved under the standard BPR model and can withstand quantum attacks. Compared with the existing PAKE protocol based on lattice theory

the proposed protocol has lower communication and better security. It is a simple and efficient post-quantum password authentication key exchange protocol.