Certificateless public key cryptography has appealing features, namely it does not require the use of certificates and yet does not have a private key escrow property. In this paper, we propose a certificateless challenge-response signature scheme from bilinear pairings and a dual version of it, and prove these schemes secure under the bilinear Diffie-Hellman assumption in the random oracle model. Using the signatures as blocking blocks, we propose a certificateless two-party key agreement protocol. The proposed key agreement protocol preserves the desirable security properties. The protocol requires each party to compute one pairing operation, three scalar multiplications and no modular exponentiation. Compared with the other related protocols, the protocol has advantages in both security and computational efficiency.
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