The Key exchange protocols are very crucial tools to provide the secure communication in the broadband satellite access network. They should be required to satisfy various requirements such as security, Key confirmation, and Key freshness. In this paper, Two authenticated key exchange protocols TPEKE-E(Two Pass Encrypted Key Exchange-Exchange-Efficient) and TPEKE-S(Two Pass Encrypted Key xchange-Secure) are introduced. A basic idea of the protocols is that a password can be represented by modular addition N, and the number of possible modular addition N representing the password is $2^N$. The TPEKE-E is secure against the attacks including main-in-the-middle attack and off-line dictionary attack, and the performance is excellent so as beyond to comparison with other authenticated key exchange protocols. The TPEKE-S is a slight modification of the TPEKE-E. The TPEKE-S provides computational in feasibility for learning the password without having performed off line dictionary attack while preserving the performance of the TPEKE-E.