Using gap diffie-hellman （GDH） groups

an efficient ID-based certificateless signature scheme was proposed

which could solve the key escrow problem through binding two partially public keys with a same identity. In this scheme

PKG was prevented from forging a legal user’s signature because he only generated the partially private key. The security relied on the hardness of the computation diffie-hellman problem （CDHP）. Under the random oracle model

the new scheme was proved to be secure against existential forgery on adaptively chosen message and ID attack. This scheme not only eliminated the inherent key escrow problem but also had a higher efficiency than the existing schemes did.