Cyber security is considered one of the most important aspects of our information technology based society. Key Exchange(KE) is a fundamental cryptographic primitive, and authenticated KE (AKE) is one of the most used cryptographic tools in secure communication protocols (e.g. SSL/TLS, IPSec, SSH) over the Internet. In light of the threat that quantum computers pose to cryptosystems such as RSA and ECC, this project is devoted to the development of secure and efficient AKE alternatives for the post-quantum computer world, which is now considered of a high priority by the US government.