Cryptanalysis of Semidirect Product Key Exchange Using Matrices Over Non-Commutative Rings

Christopher Battarbee, Delaram Kahrobaei, and Siamak F. Shahandashti

Abstract

It was recently demonstrated that the Matrix Action Key Exchange (MAKE) algorithm, a new type of key exchange protocol using the semidirect product of matrix groups, is vulnerable to a linear algebraic attack if the matrices are over a commutative ring. In this note, we establish conditions under which protocols using matrices over a non-commutative ring are also vulnerable to this attack. We then demonstrate that group rings $R[G]$, where $R$ is a commutative ring and $G$ is a non-abelian group, are examples of non-commutative rings that satisfy these conditions.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Minor revision.arXiv
Keywords
key-exchange protocollinear algebraic cryptanalysis
Contact author(s)
cb2036 @ york ac uk
History
2021-07-27: revised
See all versions
Short URL
https://ia.cr/2021/644

CC BY

BibTeX

@misc{cryptoeprint:2021/644,
author = {Christopher Battarbee and Delaram Kahrobaei and Siamak F.  Shahandashti},
title = {Cryptanalysis of Semidirect Product Key Exchange Using Matrices Over Non-Commutative Rings},
howpublished = {Cryptology ePrint Archive, Paper 2021/644},
year = {2021},
note = {\url{https://eprint.iacr.org/2021/644}},
url = {https://eprint.iacr.org/2021/644}
}

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