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Recently, Mokhtarnameh, Ho, Muthuvelu proposed a certificateless key agreement protocol. In this paper, we show that their protocol is unsecured against a man-in-the-middle attack. In addition, the authors claimed that their scheme provides a binding long-term public key with a corresponding partial private key. In fact, their protocol does not achieve the binding. We propose an improved key agreement protocol based on the protocol proposed by Mokhtarnameh et al. The improved protocol can resist the man-in-the-middle attack as well as satisfy the desired security properties for key agreement. It truly achieves the one-to-one correspondence between the long-term public key and the partial private key of a user. Compared with the other related protocols, the protocol has advantages in both security and computational efficiency. Keywords-certificateless public key cryptography; key agreement; man-in-the-middle attack; bilinear pairingI.

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