A Pairing-free ID-based Key Agreement Protocol with Different PKGs

In 2012, Piao et al. proposed a polynomial-based key management for secure intra-group and inter-group communication. In this notes, we point out that there are some security weaknesses of Piao et al.’s intra-group key distribution scheme. One main problem is that their scheme cannot prevent a group member to obtain other members’ secret keys shared with the controller. In addition, their scheme is suffered from the replay attack and cannot achieve the objectives of both perfect forward and backward secrecy. We provide a simple modified scheme to overcome these security weaknesses.