Highlights? We introduce a new efficient and secure short certificateless signature scheme. ? It is strongly unforgeable. ? The security is based on the CDH assumption. ? The proposed scheme is provably secure against a relatively stronger adversary. Short certificateless signatures have come into limelight in recent years. On the one hand, the property of certificateless eliminates the certificate management problem in traditional PKI and the key-escrow problem in some ID-based signature schemes. On the other hand, due to the short signature length, short certificateless signatures can be applied to systems where signatures are typed in by human or systems with low-bandwidth channels and/or low-computation power, such as PDAs or cell phones. However, there has been a trade-off between short certificateless signature schemes and their security levels. All existing short certificateless signature schemes can only be proven secure against a normal type adversary rather than a stronger one, who can obtain valid certificateless signatures under public keys replaced by the adversary. In this paper, we solve this open problem by given an efficient strongly secure short certificateless signature scheme. The proposed scheme has the following features. Firstly, it is strongly unforgeable. Secondly, the security can be reduced to the Computational Diffie-Hellman (CDH) assumption - a classic complexity assumption. Lastly, the proposed scheme is provably secure against adversaries with access to a super signing oracle which generates valid certificateless signatures of messages and public keys chosen by the adversary (without providing the corresponding secret values).