Abstract: The rapid development of quantum computer technology poses serious threat to the security of the traditional public-key cryptosystem, and it is imperative to focus on designing and deploying post-quantum cryptosystems that can withstand quantum attacks. A post quantum authenticated key exchange (AKE) protocol based on ring learning with errors (RLWE) problem is proposed by using encryption construction method. First, introduce an IND-CPA secure public-key encryption scheme, which uses ciphertext compression technology. By applying a variant of the Fujisaki-Okamoto transform to create an IND-CCA secure key encapsulation mechanism. An authenticated key exchange protocol is proposed through implicit authentication, which is a provable security protocol under standard eCK model and can achieve weak perfect forward security. The protocol selects a centered binomial distribution as error distribution that has higher sampling efficiency, also sets reasonable parameters to ensure that both of parties to the communication obtain the same session key. The security of the protocol is 313 b tested by LWE tester. The protocol avoids the error-reconciliation mechanism originally proposed by Ding. Compared with the existing AKE protocol schemes based on difficult problems of lattice, the corresponding of communication is also significantly reduced. The protocol has smaller public key, private key and ciphertext size, and also it enjoys even stronger provable security guarantees. It is a more concise and efficient post-quantum AKE protocol.