  We demonstrate the principle of one-sided device-independent continuous
variable (CV) quantum information. In situations of no trust, we show by
enactment how the use of standard CV entanglement criteria can mislead Charlie
into thinking Alice and Bob share entanglement, when the data is actually
generated classically using a Local Hidden Variable theory based on the Wigner
function. We distinguish between criteria that demonstrate CV entanglement, and
criteria that demonstrate the CV Einstein-Podolsky-Rosen (EPR) steering
paradox. We show that the latter, but not the former, are necessarily one-sided
device-independent entanglement witnesses, and can be used by Charlie to
signify genuine EPR entanglement, if he trusts only Alice. A monogamy result
for the EPR steering paradox confirms security of the shared amplitude values
in that case.
