  Beyond-the-Standard-Model interactions of neutrinos among themselves -- {\it
secret interactions} -- in the supernova core may prevent the shock revival,
halting the supernova explosion. Besides, if supernova neutrinos en route to
Earth undergo secret interactions with relic neutrinos, the neutrino burst
reaching Earth may be down-scattered in energy, falling below the detection
threshold. We probe secret neutrino interactions through supernova neutrinos
and apply our findings to the supernova SN 1987A. We place the most stringent
bounds on flavor-universal secret interactions occurring through a new mediator
with mass between 10 MeV and 1 GeV.
