Authenticated key agreement without subgroup element verification

In this paper, we rethink the security of authenticated key agreement and describe a simple protocol from the practical perspective. Our main focus is on reconsidering the need for real-time checking of random exchange to be in a proper subgroup, and on embedding identity assurance into implicitly authenticated keys. In spite that the result of this paper is not novel at present, it might be worth discussing the implication of authenticated key agreement not requiring extra computations or message blocks in run time. Trivial range checking is to be sufficient.