  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 $R[G]$ are examples of
non-commutative rings that satisfy these conditions.
