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International audience; 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 α 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 ∼ 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 ∼ 3×10$^{25}$ 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.[graphic not available: see fulltext]