  The fully symmetric Gaussian tripartite entangled pure states will not
exhibit two-mode Einstein Podolsky-Rosen (EPR)-steering. This means that any
two participants cannot share quantum secrets using the security of one-sided
device independent quantum key distribution (1SDI-QKD) without involving the
third. They are restricted at most to standard quantum key distribution
(S-QKD), which is less secure. Here we show that least some asymmetric
tripartite systems can exhibit bipartite EPR-steering, so that two of the
participants can use 1SDI-QKD without involving the other. This is possible
because the promiscuity relations of continuous-variable tripartite
entanglement are different from those of discrete-variable systems. We analyse
these properties for two different systems, showing that the asymmetric system
has an extra degree of flexibility not found in the symmetric one.
