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Hao proposed the YAK as a robust key agreement based on public‐key authentication, and the author claimed that the YAK protocol withstands all known attacks and therefore is secure against an extremely strong adversary. However, Toorani showed the security flaws in the YAK protocol. This paper shows that the YAK protocol cannot withstand the known key security attack, and its consequences lead us to introduce a new key compromise impersonation attack, where an adversary is allowed to reveal both the shared static secret key between two‐party participation and the ephemeral private key of the initiator party in order to mount this attack. In addition, we present a new security model that covers these attacks against an extremely strong adversary. Moreover, we propose an improved YAK protocol to remedy these attacks and the previous attacks mentioned by Toorani on the YAK protocol, and the …