  Cellular Automata (CA) are an interesting computational model for designing
Pseudorandom Number Generators (PRNG), due to the complex dynamical behavior
they can exhibit depending on the underlying local rule. Most of the CA-based
PRNGs proposed in the literature, however, suffer from poor diffusion since a
change in a single cell can propagate only within its neighborhood during a
single time step. This might pose a problem especially when such PRNGs are used
for cryptographic purposes. In this paper, we consider an alternative approach
to generate pseudorandom sequences through \emph{orthogonal CA} (OCA), which
guarantees a better amount of diffusion. After defining the related PRNG, we
perform an empirical investigation of the maximal cycles in OCA pairs up to
diameter $d=8$. Next, we focus on OCA induced by linear rules, giving a
characterization of their cycle structure based on the rational canonical form
of the associated Sylvester matrix. Finally, we devise an algorithm to
enumerate all linear OCA pairs characterized by a single maximal cycle, and
apply it up to diameter $d=16$ and $d=13$ for OCA respectively over the binary
and ternary alphabets.
