  In this paper, we give a new lifting construction of "hyperbolic" type of
strongly regular Cayley graphs. Also we give new constructions of strongly
regular Cayley graphs over the additive groups of finite fields based on
partitions of subdifference sets of the Singer difference sets. Our results
unify some recent constructions of strongly regular Cayley graphs related to
$m$-ovoids and $i$-tight sets in finite geometry. Furthermore, some of the
strongly regular Cayley graphs obtained in this paper are new or nonisomorphic
to known strongly regular graphs with the same parameters.
