Journal of the
Korean Mathematical Society JKMS

A key exchange protocol using commutative subalgebras of a full matrix algebra is considered. The security of the protocol depends on the difficulty of solving matrix equations $XRY=T$, with given matrices $R$ and $T$. We give a polynomial time algorithm to solve $XRY=T$ for the choice of certain types of subalgebras. We also compare the efficiency of the protocol with the Diffie-Hellman key exchange protocol on the key computation time and the key size.

Keywords: key exchange protocol, matrix algebra, Diffie-Hellman key exchange

MSC numbers: 15A24, 94A60