  Strongly regular Cayley graphs with Paley parameters over abelian groups of
rank 2 were studied in [J.A Davis, Partial difference sets in p-groups,
Arch.Math.63 (1994) 103-110; K.H Leung, S.L. Ma, Partial difference sets with
Paley parameters, Bull. London Math Soc. 27 (1995) 553-564]. It was shown that
such graphs exist iff the corresponding group is isomorphic to ${\mathbb
Z}_{p^n} \oplus {\mathbb Z}_{p^n}$, where $p$ is an odd prime. In this paper we
classify all strongly regular Cayley graphs over this group using Schur rings
method. As a consequence we obtain a complete classification of strongly
regular Cayley graphs with Paley parameters over abelian groups of rank 2.
