Semi-quantum private comparison protocol with graph state

Abstract

The quantum private comparison (QPC) protocol is an important research issue in the quantum secure computation field. The participants obtain the relational comparison between each other private messages without leaking any secret information by QPC protocol. In order to improve the practicality of quantum secure communication protocol, the semi-quantum concept was proposed to let the users who only have limited quantum capabilities (called the classical users) can also achieve the quantum secure communication protocol. According to the semi-quantum concept, this study proposes a semi-quantum private comparison (SQPC) protocol using a measurement property of a graph state https://www.w3.org/1998/Math/MathML" display="inline"> |G ⟩ 123 = 1 2 2 000 + 001 + 010 − 011 + 100 − 101 − 110 − | 111 ⟩ 123 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003460763/a1dd00af-5f0d-42a5-a080-674b9e863cf3/content/inline-math11_1.tif "/> . The proposed SQPC protocol lets the two classical users can compare whether their private messages are equal or not with the assistance of a dishonest three-party quantum user (TP), in which TP owns the complete quantum capabilities and the classical users only equip the two quantum devices including (1) Hadamard operation and (2) Z-basis https://www.w3.org/1998/Math/MathML" display="inline"> 0 , | 1 ⟩ https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003460763/a1dd00af-5f0d-42a5-a080-674b9e863cf3/content/inline-math11_2.tif "/> measurement. Because the one-way qubit transmission is adopted, the proposed SQPC protocol is free from quantum Trojan horse attack. Moreover, a security analysis also is given to prove that the proposed SQPC is robust under the collective attack.