  The MOR cryptosystem is a natural generalization of the El-Gamal cryptosystem
to non-abelian groups. Using a $p$-group, a cryptosystem was built by this
author in 'A simple generalization of El-Gamal cryptosystem to non-abelian
groups'. It seems reasonable to assume the cryptosystem is as secure as the
El-Gamal cryptosystem over finite fields. A natural question arises can one
make a better cryptosystem using $p$-groups? In this paper we show that the
answer is no.
