  We describe the structure of $E-$dense acts over $E-$dense semigroups in an
analogous way to that for inverse semigroup acts over inverse semigroups. This
is based, to a large extent, on the work of Schein on representations of
inverse semigroups by partial one-to-one maps. We consider an application to
the discrete log problem in cryptography as well as an application to the same
problem using completely regular semigroups.
