Abstract: In order to enable the Diffie-Hellman-style key exchange protocol on the lattice to achieve authentication and is suitable for large-scale communication in the client-server-client mode, a two-factor three-party authentication key exchange protocol based on Ring Learning With Error (RLWE) is proposed. The protocol uses passwords and biometrics as long-term keys for the client, enabling the server to explicitly authenticate the client. Firstly, the advantages of the difficult problem of error learning on the ring (short key and cipher text size and high operating efficiency) are used to construct the cryptosystem. Secondly, the server passes ring elements through password and biometric hash values, and combines D-type error coordination. The mechanism enables the communicating party to obtain a random and even session key. The final analysis shows that the protocol is suitable for large-scale communication, improves the communication volume, has higher security attributes, and can resist the password impersonation attacks of users.

Key words: authentication key exchange, ring learning with error, D-type error coordination mechanism, password, biometric