Multi-party quantum private comparison of size relationship with two third parties based on d-dimensional Bell states

TL;DR

This paper introduces a multi-party quantum private comparison protocol using d-dimensional Bell states, enabling size comparison of private integers with minimal measurement requirements and strong security features.

Contribution

It presents a novel MQPC protocol that avoids complex operations like entanglement swapping, allowing secure size comparison with only single-particle measurements and no pre-shared keys.

Findings

Protocol resists outside and participant attacks

Requires only single-particle measurements

Suitable for environments without communication between users

Abstract

In this paper, we put forward a multi-party quantum private comparison (MQPC) protocol with two semi-honest third parties (TPs) by adopting d-dimensional Bell states, which can judge the size relationship of private integers from more than two users within one execution of protocol. Each TP is permitted to misbehave on her own but cannot collude with others. In the proposed MQPC protocol, TPs are only required to apply d-dimensional single-particle measurements rather than d-dimensional Bell state measurements. There are no quantum entanglement swapping and unitary operations required in the proposed MQPC protocol. The security analysis validates that the proposed MQPC protocol can resist both the outside attacks and the participant attacks. The proposed MQPC protocol is adaptive for the case that users want to compare the size relationship of their private integers under the control of two supervisors. Furthermore, the proposed MQPC protocol can be used in the strange user environment, because there are not any communication and pre-shared key between each pair of users.