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The authentication infrastructures of 802.11i and WAPI lack the features of authenticating STAs in the foremost time, and give more opportunities for attackers to launch DoS attacks to consume legal principalsiquest resources on computation and communication. An improved IAKN protocol is presented and its security proof is stated. The analysis shows that it has better security properties and is more efficient than IEEE 802.11i and WAPI. The security properties - session authentication and secret key secrecy - are proved using PCL. The invariants of compositional security guarantees are deduced. The proposed protocol can be securely composed with other protocols when these invariants are protected.