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

Ruslan V.  Skuratovskii; Aled Williams

Paper 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 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 . The algorithm of generating (designing) common key in non-commutative group with 2 mutually commuting subgroups is constructed by us.

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

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint. MINOR revision.
Keywords: metacyclic group conjugacy key exchange scheme finite group conjugacy problem.
Contact author(s): ruslcomp @ mail ru
History: 2020-02-25: revised; 2020-02-24: received; See all versions
Short URL: https://ia.cr/2020/234
License: CC BY

BibTeX

@misc{cryptoeprint:2020/234,
      author = {Ruslan V.  Skuratovskii and Aled Williams},
      title = {Application of commutator subgroups of Sylow 2-subgroups of alternating group and Miller-Moreno groups to Key Exchange Protocol},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/234},
      year = {2020},
      url = {https://eprint.iacr.org/2020/234}
}