  We present a device independently secure quantum scheme for p-threshold
all-or-nothing oblivious transfer. Novelty of the scheme is that, its security
does not depend -- unlike the usual case -- on any quantum bit commitment
protocol, rather it depends on Hardy's argument for two-qubit system. This
scheme is shown to be unconditionally secure against any strategy allowed by
quantum mechanics. By providing a secure scheme for all-or-nothing quantum
oblivious transfer, we have answered a long standing open problem, other than
the quantum key distribution, whether there is any two-party quantum
cryptographic protocol, which is unconditionally secure.
