论文标题
Sylow的交替组和Miller-Moreno组的换向子亚组作为新密钥交换协议的基础
Commutator subgroups of Sylow 2-subgroups of alternating group and Miller-Moreno groups as bases of new Key Exchange Protocol
论文作者
论文摘要
这项调查的目的是基于非交换组$ g $的有效方法。 Ko等人的结果。 \ cite {kolee}得到了改进和广泛化。找到了交替组的Sylow 2-群的换向器子组的最小生成集的大小。调查并在基于非交通群的密钥交换协议中使用了交替组$ {a_ {2^{k}}} $的Sylow 2-子组的换向子组的结构。 我们考虑CDH问题的非交通概括\ cite {GU2013New，Bohli2006Towards}在Miller-Moreno型的MetacyClic群（最小非亚伯利亚组）的基础上。我们表明，该组中的共轭问题是棘手的。由于使用Modulo $ n $使用残基组，因此提供了计算的有效性。我们构建了2个相互通勤子组的非交通群中生成（设计）共同密钥的算法。
The goal of this investigation is effective method of key exchange which based on non-commutative group $G$. The results of Ko et al. \cite{kolee} is improved and generalized. The size of a minimal generating set for the commutator subgroup of Sylow 2-subgroups of alternating group is found. The structure of the commutator subgroup of Sylow 2-subgroups of the alternating group ${A_{2^{k}}}$ is investigated and used in key exchange protocol which based on non-commutative group. We consider non-commutative generalization of CDH problem \cite{gu2013new, bohli2006towards} on base of metacyclic group of Miller-Moreno type (minimal non-abelian group). We show that conjugacy problem in this group is intractable. Effectivity of computation is provided due to using groups of residues by modulo $n$. The algorithm of generating (designing) common key in non-commutative group with 2 mutually commuting subgroups is constructed by us.
