Quantum oblivious transfer with an untrusted third party

Given the Mayers–Lo–Chau (MLC) no-go theorem, unconditionally secure quantum bit commitment (QBC) is impossible and hence quantum oblivious transfer (QOT) based on QBC is insecure. In this paper, we propose a secure all-or-nothing QOT protocol and a one-out-of-two QOT protocol respectively. The unique merit of the proposed protocols lies in that it is not based on QBC but based on an untrusted third party. Moreover, the proposed protocols do not violate Lo's no-go theorem so that their security can be achieved.