Wi-Fi Alliance(WFA) recently standardized the new suites of security protocols, as known as WPA3, to enhance the Wi-Fi security, which includes the SAE protocol. SAE (Simultaneous Authentication of Equals), based on the Dragonfly key exchange protocol, is a password authenticated key exchange protocol, which has been ratified in Internet Engineering Task Force (IETF) RFC 7664. The SAE Authenti- cation Protocol was first submitted to the IEEE 802.11s (Wi-Fi Mesh Networks), and recently was successfully selected as a candidate security standard to become the next generation Wi- Fi security protocol, WPA3. The SAE key exchange protocol and its variants, i.e, the Dragonfly key exchange protocol and TLS-PWD, have received some cryptanalysis, in which the authors pointed out the Dragonfly protocol exists the sub- group attack vulnerability. In this paper, we also observed some vulnerability that could result in the impersonation attacks.