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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.
On the non-exchange group, a cryptosystem based on Lie algebra (n-Lie algebras) is proposed. At the same time, some unidentified and anti-exchanged Lie algebras are used to realize some results of cryptography in the complex field. Can be transformed into solving a system of indefinite quadratic equations with multivariate quadratic polynomials, which is completely difficult to be a nondeterministic polynomial (NPC). A multiplicative table naturally derives a one-way trapdoor function. Based on this trapdoor function, An encryption and decryption scheme is given, and a key distribution scheme is given based on Lie algebra. Finally, the result is generalized to n Lie algebras over the domain F.