根据MOV归约理论，采用双线性映射构造的基于身份加密方案使得该方案不具有椭圆曲线高效的优点。

According to the MOV reduction theory, the identity-based encryption scheme which is based on the bilinear map will lose the high efficiency of elliptic curve.

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为了解决数字版权保护中的用户密钥泄漏问题，提出了一种基于双线性映射的叛逆者追踪方案。

A new efficient traitor tracing scheme using bilinear mapping is presented in order to solve the user-key leaking problem in digital right management.

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利用一个基于分层身份思想和双线性映射的群签名，提出了一个新的安全高效的密封式电子拍卖方案。

With the help of a group signature based on Hierarchical Identity-Based signature (HIBS) and bilinear map, a new secure and efficient sealed-bid electronic auction scheme was presented.

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