Improvements of one anonymous ID-based encryption

In 2006, Boyen et al proposed an anonymous ID-based encryption. It is impressive in the scheme the system secret key is a tuple of five numbers. The user´s secret key is also a tuple of five elements. The authors did not explain why it should introduce so many parameters. In this paper, we simulate a general attempt to attack the scheme. It shows us which parameters are essential to the scheme and which parameters can be reasonably discarded. Based on the analysis we present a simplified version and an efficient version of the original scheme. The general techniques developed in this paper will be helpful to better other cryptographic protocols.