Pairing-free single round certificateless and identity based authenticated key exchange protocols

Designing efficient key agreement protocols is a fundamental cryptographic problem. In this paper, we first define a security model for key agreement in certificateless cryptography that is an extension of earlier models. We note that the existing pairing free protocols are not secure in our model. We design an efficient pairing-free, single round protocol that is secure in our model based on the hardness assumption of the Computational Diffie Hellman (CDH) problem. We also observe that previously existing pairing-free protocols were secure based on much stronger assumptions such as the hardness of the Gap Diffie Hellman problem. We use a restriction of our scheme to design an efficient pairing-free single round identity based key agreement protocol that is secure in the id-CK+ model based on the hardness assumption of the CDH problem. Additionally, both our schemes satisfy several other security properties such as forward secrecy, resistance to reflection attacks etc.