  Due to the commonly known impossibility results, unconditional security for
oblivious transfer is seen as impossible even in the quantum world. In this
paper, we try to overcome these impossibility results by proposing a protocol
which is asymptotically secure. The protocol makes use of the basic properties
of non-orthogonal quantum states. Apart from security, the advantages of our
protocol include the fact that the honest players do not need to have quantum
memory or create entanglement between individual qubits. The relation of our
work to the known impossibility results is also discussed.
