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

##### Christopher Battarbee, Delaram Kahrobaei, Siamak F. Shahandashti

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 $R[G]$ used in arXiv:1304.6572, where $R$ is a commutative ring and $G$ is a non-abelian group, are examples of non-commutative rings that satisfy these conditions.

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