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中文摘要：
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.
英文摘要：
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.
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