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arXiv · 2002.10528

Commutator subgroups of Sylow 2-subgroups of alternating group and Miller-Moreno groups as bases of new Key Exchange Protocol

Ruslan V. Skuratovskii·Aled Williams
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Abstract

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.

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BibTeXRIS

Ruslan V. Skuratovskii, Aled Williams. 2020-02-24. Commutator subgroups of Sylow 2-subgroups of alternating group and Miller-Moreno groups as bases of new Key Exchange Protocol. https://arxiv.org/abs/2002.10528

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