## Cryptology ePrint Archive: Report 2020/234

Application of commutator subgroups of Sylow 2-subgroups of alternating group and Miller-Moreno groups to Key Exchange Protocol

Ruslan V. Skuratovskii and Aled Williams

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.

Category / Keywords: cryptographic protocols / the commutator subgroup of Sylow $2$-subgroups, metacyclic group, conjugacy key exchange scheme, finite group, conjugacy problem.

Date: received 21 Feb 2020, last revised 25 Feb 2020

Contact author: ruslcomp at mail ru

Available format(s): PDF | BibTeX Citation

Note: The subject area is Group Theory and cryptographic protocols. The paper was updated.

Short URL: ia.cr/2020/234

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