Abstract:A pairing-free certificateless two party key agreement scheme (CL-KA) is proposed. This work is able demonstrates all existing CL-KA schemes (except for Lippold’s scheme) are insecure in the eCK model. The scheme is secure in the eCK model as long as each party has at least one uncompromised secret. The scheme has proven to be secure in the random oracle model (ROM), assuming that the computational Diffie-Hellman assumption hold even if the key generation centre (KGC) learns the ephemeral secrets of both parties, or reveal secret values/replace public keys, but not both. The scheme eliminates pairing computation. It achieves efficiency in computational cost when compared with all the other known certificateless key agreement schemes. The scheme is more suitable for the restricted bandwidth of the communication environment, such as ad hoc networks, wireless sensors, and so on.