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Most of the certificateless two-party authenticated key agreement protocols (CTAKA) found in the literature, suffer either serious security problems making them vulnerable to types of attacks or inefficient performance that involves high computational costs. In this paper, we design an secure and efficient CTAKA. Within the proposed scheme, the KGC possesses a certificate to prove its identity to the communicating parties. The communications between the KGC and each party is secured by the SSL protocol. Each of the two communicating parties are able to compute the same secret symmetric key without any interaction between them. The protocol is fully secure against type 1 attack and fully secure against type 2 attack under the assumptions that the KGC is an honest party and each party within the network has the full capability to keep its secret values safe. Moreover, the setup of the protocol does not include pairings, does not require interactions between communicating parties during the key agreement process, and it require only one scalar multiplications over elliptic curves and one hash for the key agreement, which makes the computational cost for the key agreement comes below the computational costs of all the pairing free CTAKAs found in the literature.