Improved authentication key exchange protocol without using one-way hash function

Recently, Hwang, Shiau and Lai proposed an efficient authentication key exchange protocol to decrease the computation cost of the Harn-Lin improved protocol. However, the Hwang-Shiau-Lai protocol cannot withstand the modification attack. Therefore, this paper will propose an improved protocol to enhance the security of the Hwang-Shiau-Lai protocol. The improved protocol is able to defeat the modification attack and is as efficient as the Hwang-Shiau-Lai protocol. Moreover, the improved protocol also provides the perfect forward secrecy.