A key agreement protocol or key exchange protocol is proposed to help two parties to compute a common session key respectively, over a insecure channel. There are many schemes having been proposed to implement such a protocol. However, some of the proposed schemes can result these two parties compute no common session key. For instance, in 2010, Lee and Hwang proposed such a key exchange scheme that has a chance to make two protocol parties to compute no common session key with a man-in-the-middle attack. In addition, in 2012, Lv et al. proposed a three- party authenticated key exchange scheme that may su er an o -line attack and a man-in-the middle attack. In the thesis, we make a research to the three-party authenticated key agreement and analyse them with the man-in-the-middle attack. Finally, we hope that we can inprove them.