  We present an improved post-quantum version of Sakalauskas matrix power
function key agreement protocol, using rectangular matrices instead of the
original square ones. Sakalauskas matrix power function is an efficient and
secure way to generate a shared secret key, and using rectangular matrices
provides additional flexibility and security. This method reduces the
computational complexity by allowing smaller random integer matrices while
maintaining a high level of security. We dont rely on matrices with special
formatting to achieve commutativity, instead, we use full random values on
those structures, increasing their entropy. Another advantage of using
rectangular matrices over key agreement protocols is that they offer better
protection against various linearization attacks.
