  Neutrinoless double-beta decay is a key process in particle physics. Its
experimental investigation is the only viable method that can establish the
Majorana nature of neutrinos, providing at the same time a sensitive inclusive
test of lepton number violation. CROSS (Cryogenic Rare-event Observatory with
Surface Sensitivity) aims at developing and testing a new bolometric technology
to be applied to future large-scale experiments searching for neutrinoless
double-beta decay of the promising nuclei $^{100}$Mo and $^{130}$Te. The
limiting factor in large-scale bolometric searches for this rare process is the
background induced by surface radioactive contamination, as shown by the
results of the CUORE experiment. The basic concept of CROSS consists of
rejecting this challenging background component by pulse-shape discrimination,
assisted by a proper coating of the faces of the crystal containing the isotope
of interest and serving as energy absorber of the bolometric detector. In this
paper, we demonstrate that ultra-pure superconductive Al films deposited on the
crystal surfaces act successfully as pulse-shape modifiers, both with fast and
slow phonon sensors. Rejection factors higher than 99.9% of $\alpha$ surface
radioactivity have been demonstrated in a series of prototypes based on
crystals of Li$_2$MoO$_4$ and TeO$_2$. We have also shown that point-like
energy depositions can be identified up to a distance of $\sim 1$ mm from the
coated surface. The present program envisions an intermediate experiment to be
installed underground in the Canfranc laboratory (Spain) in a CROSS-dedicated
facility. This experiment, comprising $\sim 3\times 10^{25}$ nuclei of
$^{100}$Mo, will be a general test of the CROSS technology as well as a
worldwide competitive search for neutrinoless double-beta decay, with
sensitivity to the effective Majorana mass down to 70 meV in the most favorable
conditions.
