PKG（private key generater） scheme was presented to overcome Chen-Zhang-Kim’s scheme drawback about a large amount of computation and Gorantla-Saxena’s scheme drawback about needing trusted PKG.More precisely

under the random oracle model

the scheme is proved to be secure against existential forgery on adaptively chosen message and ID attack

assuming CDHP is intractable.The scheme not only is traceable that the arbiter can use Trace algorithm to de-tect deceiver but also eliminates the inherent key escrow problem.As compared with the typical signatures schemes to date

the proposed scheme achieves the higher efficiency.