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 ${A_{{2^{k}}}}$ 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.
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 groupconjugacy key exchange schemefinite groupconjugacy 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}
}
