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

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.