Certificateless public key cryptography was introduced to overcome the key escrow limitation of the identity-based cryptography. It combines the advantages of the identity-based cryptography and the traditional PKI. Many certificateless public key encryption and signature schemes have been proposed. However, the key agreement in CL-PKE is seldom discussed. In this paper, we present a new certificateless two party authentication key agreement protocol and prove its security attributes. Compared with the existing protocol, our protocol is more efficient.

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