Multi-party quantum private comparison of size relation with d-level single-particle states

TL;DR

This paper introduces two novel multi-party quantum private comparison protocols using d-level single-particle states, enabling size relation comparison among secret integers with enhanced security and practical applicability in different environments.

Contribution

The paper presents new quantum protocols for multi-party size relation comparison using d-level states, extending capabilities beyond equality checks and ensuring security against various attacks.

Findings

Protocols can compare size relations of secret integers among multiple parties.

Protocols resist outside and participant attacks, ensuring security.

One protocol is suitable for stranger environments, the other for acquaintance environments.

Abstract

In this paper, by using d-level single-particle states, two novel multi-party quantum private comparison protocols for size relation comparison with two semi-honest third parties and one semi-honest third party are constructed, respectively. Here, each protocol can compare the size relation of secret integers from n parties rather than just the equality within one time execution. In each protocol, every third party is assumed to be semi-honest in the sense that she may misbehave on her own but is not allowed to collude with anyone else; and each party employs the qudit shifting operation to encode her secret integer. Each protocol can resist both the outside attack and the participant attack. Specially, each party's secret integer can be kept unknown to other parties and the third parties. The proposed protocol with two third parties is workable in a stranger environment, as there are no communication and no pre-shared key between each pair of party. The proposed protocol with one third party is workable in an acquaintance environment, as all parties need to share a common private key beforehand.