Certificateless-based signature can eliminate the need of certificates in the Public Key Infrastructure and solve the inherent key escrow problem in the identity-based cryptography. In 2012 Zhang et al. [J. Zhang and J. Mao, An efficient RSA-based certificateless signature scheme, Journal of Systems and Software, vol. 85, pp. 638-642, 2012] proposed the first certificateless signature scheme based on RSA operations and showed that their scheme is provably secure in the random oracle model. However, He et al. [D. He, M. Khan, and S. Wu, On the security of a RSA-based certificateless signature scheme, International Journal of Network Security, vol.16, no.1, pp.78-80, 2014] recently showed that Zhang et al.'s scheme is insecure against a type I adversary who can replace users' public keys. In this paper, we propose an improved version based on RSA which not only keeps the original security properties of the signature, but also is secure against a type I adversary.
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