The research on the identification scheme is an important and active area in computer and communication security. A series of identification schemes were proposed to improve the efficiency and security of the protocols by various methods. Based on the hardness assumption of the discrete logarithm problem in a gap Diffie-Hellman group and the difficulty of the collusion attack algorithm with k traitors, an efficient identification scheme is presented. Without random oracle models, the proposed scheme is then proved secure against impersonation and reset attacks in both concurrent and reset attack setting. Since the proposed scheme is simple, memory-saving, computation-efficient, and perfectly-secure, it is well suitable for use in smart cards.