Insecurity of an efficient certificateless aggregate signature with constant pairing computations

Recently, Xiong et al. [H. Xiong, Z. Guan, Z. Chen, F. Li, An efficient certificateless aggregate signature with constant pairing computations, Information Science 219 (2013) 225–235] proposed a certificateless signature (CLS) scheme and used it to construct a certificateless aggregate signature (CLAS) scheme with constant pairing computations. They demonstrated that both of their schemes are provably secure in the random oracle model under the computational Diffie–Hellman assumption. Unfortunately, by giving concrete attack, we demonstrate that their schemes are not secure against the Type II adversary, i.e. a Type II adversary could forge a legal signature of any message.