Further improvement of a certificateless signature scheme without pairing

Recently, He et al. proposed an efficient certificateless signature (CLS) scheme without pairings and demonstrated their scheme to be provably secure in the random oracle model. Unfortunately, Tian and Huang and Tsai et al. pointed out that the scheme cannot withstand a Type II adversary's attack. Tsai et al. also proposed an improved scheme to enhance security. However, the schemes of He et al. and Tsai et al. are not real CLS schemes because the user's public key is used to generate its partial private key. Besides, He et al. and Tsai et al. just demonstrated that their schemes are secure against the normal adversary in the random oracle model. In this paper, we propose a real CLS scheme and demonstrate that our scheme is secure against the super adversary. Security analysis and performance analysis show that our scheme could enhance security and increase computational cost slightly.