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Two-Party Authenticated key agreement protocol is essential for setting up the common session key for parties to establish secure channel for network communication in the open environment. Most of proposed schemes require expensive bilinear pairing operation and only provide limited security attributes. So such protocols are unsuitable for real-world applications that require stronger sense of secrecy. In this paper, we first analysis two schemes recently proposed by Cao etc., and then present a one-round ID-based authenticated key agreement protocol with more desired security attributes, which need no pairing operations while still achieve nice computational efficiency. These security attributes include known-key secrecy, perfect forward secrecy, PKG forward secrecy, key-compromise impersonation resilience, unknown key-share resilience and no key control. Moreover, it captures the enhanced security attributes known session-specific temporary key information secrecy, which means that even the ephemeral secret key were compromised, the adversary can hardly acquire the agreed session key.