We propose a computational investigation on the interaction mechanisms between SARS-CoV-2 spike protein and possible human cell receptors. In particular, we make use of our newly developed numerical method able to determine efficiently and effectively the relationship of complementarity between portions of protein surfaces. This innovative and general procedure, based on the representation of the molecular isoelectronic density surface in terms of 2D Zernike polynomials, allows the rapid and quantitative assessment of the geometrical shape complementarity between interacting proteins, which was unfeasible with previous methods. Our results indicate that SARS-CoV-2 uses a dual strategy: in addition to the known interaction with angiotensin-converting enzyme 2, the viral spike protein can also interact with sialic-acid receptors of the cells in the upper airways.