双线性Diffie-Hellman问题研究

为了构建密钥进化方案所需要的双线性DiffieHellman (Bilinear DiffieHellman，BDH)参数生成器，研究了BDH问题的安全性。先回顾了BDH问题的来源；基于可容许的双线性映射，再分别对判定BDH问题、计算BDH问题以及变形的BDH问题进行了分析；并就BDH问题的安全性得出若干有用的结论。最后以密码学实践中常用到的超奇异椭圆曲线为例，构造了Weil对和Tate对的BDH参数生成器。

Research on Bilinear Diffie-Hellman Problem

To construct BDH(Bilinear Diffie-Hellman) parameter generator in key evolving schemes,the security of BDH problem was researched.The origin of BDH problem was reviewed.Then based on the admissible bilinear map,the decisional BDH problem,computational BDH problem and some variants were analyzed,respectively.As a result,some useful corollaries about BDH security were obtained.Finally,BDH parameter generators using Weil pairing and Tate pairing on supersingular elliptic curves were constructed.The generators could be widely applied to identity-based cryptography.