The R&D activity performed during the last years proved the potential of ZnSe scintillating bolometers to the search for neutrino-less double beta decay, motivating the realization of the first large-mass experiment based on this technology: CUPID-0. The isotopic enrichment in $^{82}$Se, the Zn$^{82}$Se crystals growth, as well as the light detectors production have been accomplished, and the experiment is now in construction at Laboratori Nazionali del Gran Sasso (Italy). In this paper we present the results obtained testing the first three Zn$^{82}$Se crystals operated as scintillating bolometers, and we prove that their performance in terms of energy resolution, background rejection capability and intrinsic radio-purity complies with the requirements of CUPID-0.
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