Key escrow is an inherent disadvantage for traditional ID-based cryptosystem, i.e., the dishonest PKG can forge the signature of any user. On the other hand, the user can deny the signature actually signed by him/herself. To avoid the key escrow problem, we present an ID-based signature scheme without trusted Private Key Generator (PKG). We also presented the exact proof of security to demonstrate that our scheme is secure against existential forgery on adaptively chosen messages and
attacks assuming the complexity of Computational Diffie-Hellman (CDH) problem. Compared with other signature schemes, the proposed scheme is more efficient.