一种基于李代数的密码体制

一种基于李代数的密码体制 A New Cryptosystem Based on Lie Algebra 吴万青 WU Wanqing 1 2 first-author 张焕国 ZHANG Huanguo 1 2 吴朔媚 WU Shuomei 3 毛少武 MAO Shaowu 1 2 武汉大学计算机学院 武汉大学计算机学院 School of Computer,Wuhan University School of Computer,Wuhan University 空天信息安全与可信计算教育部重点实验室 空天信息安全与可信计算教育部重点实验室 Key Laboratory of Aerospace Information Security and Trusted Computing of Ministry of Education,Wuhan University Key Laboratory of Aerospace Information Security and Trusted Computing of Ministry of Education,Wuhan University 石家庄学院计算机系 石家庄学院计算机系 Computer Department,Shijiazhuang University Computer Department,Shijiazhuang University 在非交换群上提出一个基于李代数（n李代数）的密码体系.同时在复数域上,利用典型的非结合、反交换的李代数实现密码学上的一些结果.本文指出李代数乘法表的构造问题可以转化为求解多变元二次多项式不定方程组,是非确定性多项式（NPC）完全困难的.乘法表自然地导出一个单向陷门函数.在这个陷门函数的基础上建立了一个加解密方案.基于李代数给出了一个密钥分配方案.最后将结果推广到数域F上的n李代数. At present,the most public popular cryptosystems have been constructed based on abelian groups.The appearance of quantum algorithms constitutes a threat to the cryptographic system based on abelian groups.This paper attempt to establish cryptographic system in non-Abelian groups.While we apply the nonassociate and anticommutative Lie algebra to achieve some results of cryptography.This paper pointed out that the creating Lie bracket of Lie algebra is equivalent to solving aquadratic indefinite equation group with multiple variables.It is NPC difficult.The Lie bracket naturally is derived a trapdoor one-way function.This paper propose an encryption scheme based on this trapdoor scheme and a key distribution scheme based on Lie algebra,and analyzed the safety of encryption scheme and key distribution scheme.The last the result is extended to n Lie algebra over field F. 李代数 二次不定方程组 密钥分配协议 Lie algebra quadratic indefinite equations group with multiple variables key distribution protocol 10.14188/j.1671-8836.2013.05.006 TN918.1 国家自然科学基金项目（60970115,61003267）资助项目;中央高校研究生自主科研项目（2012211020213） 2013-05-01 2021-04-01 5 59