The main contributions are as follows. Based on the BLS and ZSS short signatures from bilinear pairing respectively given by Boneh et.

• ·针对目前所具有的两个重要的基于双线性对的短签名方案，给出了两种基于双线性对的基于身份的密码系统：BLS密码系统和ZSS密码系统。