We develop a basic theoretical apparatus for the search of electromagnetic neutrino interactions in experiments on elastic neutrino-nucleus scattering. Using our approach developed for the case of elastic neutrino-electron collisions, we take into account all electromagnetic form factors of massive neutrinos. In this contribution we focus on elastic neutrino-proton scattering, which can be important for studying supernova neutrinos in experiments, for example, such as JUNO. In our consideration we take into account all electromagnetic form factors not only of a neutrino, but of a proton as well.