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Key exchange protocols play an important role in securing the network communication over an insecure channel. In literature, a large number of key exchange schemes exist. The security of most of them is based on the Diffie-Hellman (DH) problems over a group. But these types of DH problems are solvable in the presence of quantum computers. Thus, we require a non-DH type key exchange scheme that resists to the quantum computers and new modern technologies. In this paper, 2 novel lattice-based authenticated key exchange (LB-AKE) protocols, (1) using a signature-based authenticator and (2) using a signcryption-based authenticator, are devised in Canetti-Krawczyk proof model. The security of proposed protocols depends on the hardness of small integer solutions on the lattice. An extensive proof of security to our claim is given. The proposed AKEs characterize faster computation speed and resistance to the modern complex computers. [ABSTRACT FROM AUTHOR]