## Cryptology ePrint Archive: Report 2021/644

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

Christopher Battarbee and 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.

Category / Keywords: public-key cryptography / key-exchange protocol, linear algebraic cryptanalysis

Original Publication (with minor differences): arXiv

Date: received 17 May 2021, last revised 27 Jul 2021

Contact author: cb2036 at york ac uk

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2021/644

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