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This paper considers the issue on authenticated two-party key agreement protocol over an insecure public network. Many authenticated key agreement protocols have been proposed to meet the challenges. Based on bilinear pairing, Zhou et al. proposed a two-party key agreement with implicit key authentication in 2011. Implicit key authentication can be easily achieved by encrypting the later communications using the session key. However, we can not ensure how participants using the session key protocol. This paper will transform the Zhou's implicit authenticated key agreement protocol into the explicit one with key confirmation by introducing the authenticators, and show the proposed protocol is provably secure under the random-oracle model.