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In this paper, we propose a novel semiquantum private comparison (SQPC)protocol of size relationship based on d-level single-particle states. Thedesigned protocol can compare the size relationship of different privacymessages from two classical users with the help of a semi-honest third party(TP), who is permitted to misbehave on her own but cannot be in collusion withanyone else. The correctness analysis shows that this protocol can gain correctcomparison results. The security analysis turns out that this protocol canresist famous outside attacks and participant attacks. Moreover, this protocolcan guarantee that TP does not know the accurate comparison results. Comparedwith the only existing SQPC protocol of size relationship (Quantum Inf.Process. 20:124 (2021)), this protocol takes advantage over it on the aspectsof initial quantum resource, TP's measurement operations and TP's knowledgeabout the comparison results.

Semiquantum Private Comparison of Size Relationship Based on d-level Single-Particle States