Quantum oblivious transfer with relaxed constraints on the receiver

Abstract

All existing quantum oblivious transfer protocols can be achieved when all the members have to be quantum. So what will happen if not all the members are quantum? In this paper, we propose two novel protocols for all-or-nothing oblivious transfer and one-out-of-two oblivious transfer respectively by using single qubit states. Our contribution lies in the fact that the message receiver Bob can use fewer quantum resources so that our protocols relax the requirements of protocol implementation in practice. We analyze the security of the protocols and prove that they are secure against Bob who even has the quantum attack capability.

One-out-of-two Quantum Oblivious Transfer based on Nonorthogonal States

“…This section presents a performance comparison of the proposed protocol with three modern two-level-structured one-out-of-two QOT protocols 21 , 24 , 25 based on Crépeau’s reduction 3 . The protocols of Wei Yang et al .…”

“… 23 involves an untrusted third party, and the second 27 is a one-out-of-n QOT protocol for which the resource consumption for one-out-of-two QOT is similar to that of Li Yang’s protocol 21 . The three protocols considered for comparison 21 , 24 , 25 have two-level structures in which one-out-of-two OT is built on all-or-nothing QOT. However, the probability p of all-or-nothing QOT (where p is the probability of the unambiguous key) is not always 50%.…”

“…The total cost of each protocol, as calculated under the requirement that R message bits are received, is given in Table 3 . Here, only the quantum cost without loyalty testing is considered; for fairness, we do not include the cost for loyalty testing because two of the other one-out-of-two QOT protocols 21 , 24 do not consider any loyalty testing, which means that the sender and receiver may not truly trust each other, whereas the loyalty testing of the third protocol 24 requires the consumption of a large number of qubits, making the quantum cost difficult to calculate. Detailed descriptions of the protocols considered for comparison 21 , 24 , 25 are given below.…”

“…This protocol 24 also requires at least four qubits on average to obtain an unambiguous key using its all-or-nothing QOT strategy, i.e., . In the all-or-nothing QOT protocol, Alice first sends a sequence to Bob, and Bob then sends it back after his measurement, which requires two transmissions.…”

“…In 2014, they 23 proposed all-or-nothing and one-out-of-two QOT protocols based on an untrusted third party. In 2015, they 24 developed an all-or-nothing QOT protocol by analyzing the probability of the qubit state distribution, which led them to propose a method of testing the loyalty of the sender and then to build a one-out-of-two QOT protocol on this basis. They 25 also designed a one-out-of-two QOT scheme with a two-level structure using BB84 6 and reduced it to B92 22 for an all-or-nothing QOT scheme.…”