  Difference sets are subsets of a group satisfying certain combinatorial
property with respect to the group operation. They can be characterized using
an equality in the group ring of the corresponding group. In this paper, we
exploit the special structure of the group ring of an abelian group to
establish a one-to one correspondence of the class of difference sets with
specific parameters in that group with the set of all complex solutions of a
specified system of polynomial equations. The correspondence also develops some
tests for a Boolean function to be a bent function.
