Recently, Boneh and Boyen proposed a new provably secure short signature scheme under the q -strong Diffie-Hellman assumption without random oracles. This scheme is based on bilinear map which is different from Cramer-Shoup signature scheme (which is based on the strong RSA assumption). However, Tan TC[17] showed that Boneh- Boyen scheme is subjected to key substitution attacks in the multi-user setting. In this paper, we propose a new signature scheme. We prove that the proposed scheme is provably secured against existential forgery under adaptive chosen message attack in the standard model and also secure against key substitution attacks.