双线性Diffie-Hellman问题研究

Research on Bilinear Diffie-Hellman Problem

作者：杨浩淼(电子科技大学计算机科学与工程学院, 四川成都 610054)；孙世新(电子科技大学计算机科学与工程学院, 四川成都 610054)；李洪伟(电子科技大学计算机科学与工程学院, 四川成都 610054)

Author：(School of Computer Sci. and Eng.，Univ. of Electronic Sci. and Technol. of China，Chengdu 610054,China)；(School of Computer Sci. and Eng.，Univ. of Electronic Sci. and Technol. of China，Chengdu 610054,China)；(School of Computer Sci. and Eng.，Univ. of Electronic Sci. and Technol. of China，Chengdu 610054,China)

收稿日期：2005-07-15 年卷（期）页码：2006,38(2):137-140

期刊名称：工程科学与技术

Journal Name：Advanced Engineering Sciences

关键字：双线性Diffie-Hellman问题;Weil对;Tate对;椭圆曲线

Key words：Bilinear Diffie-Hellman problem;Weil pairing;Tate pairing;elliptic curves

基金项目：四川省青年软件创新工程资助项目(2004(369))

中文摘要

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。

英文摘要

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.

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论文摘要

双线性Diffie-Hellman问题研究

Research on Bilinear Diffie-Hellman Problem