{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T08:21:37Z","timestamp":1768551697659,"version":"3.49.0"},"reference-count":29,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,16]],"date-time":"2023-03-16T00:00:00Z","timestamp":1678924800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program in China","award":["2022YFC3302103-01"],"award-info":[{"award-number":["2022YFC3302103-01"]}]},{"name":"National Key Research and Development Program in China","award":["JYB2022-01"],"award-info":[{"award-number":["JYB2022-01"]}]},{"name":"Strategic Research Program of Science and Technology Commission of the Ministry of Education of China","award":["2022YFC3302103-01"],"award-info":[{"award-number":["2022YFC3302103-01"]}]},{"name":"Strategic Research Program of Science and Technology Commission of the Ministry of Education of China","award":["JYB2022-01"],"award-info":[{"award-number":["JYB2022-01"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["2022YFC3302103-01"],"award-info":[{"award-number":["2022YFC3302103-01"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["JYB2022-01"],"award-info":[{"award-number":["JYB2022-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Set Intersection Cardinality (SI-CA) computes the intersection cardinality of two parties\u2019 sets, which has many important and practical applications such as data mining and data analysis. However, in the face of big data sets, it is difficult for two parties to execute the SI-CA protocol repeatedly. In order to reduce the execution pressure, a Private Set Intersection Cardinality (PSI-CA) protocol based on a quantum homomorphic encryption scheme for the Toffoli gate is proposed. Two parties encode their private sets into two quantum sequences and encrypt their sequences by way of a quantum homomorphic encryption scheme. After receiving the encrypted results, the semi-honest third party (TP) can determine the equality of two quantum sequences with the Toffoli gate and decrypted keys. The simulation of the quantum homomorphic encryption scheme for the Toffoli gate on two quantum bits is given by the IBM Quantum Experience platform. The simulation results show that the scheme can also realize the corresponding function on two quantum sequences.<\/jats:p>","DOI":"10.3390\/e25030516","type":"journal-article","created":{"date-parts":[[2023,3,17]],"date-time":"2023-03-17T02:59:26Z","timestamp":1679021966000},"page":"516","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A New Quantum Private Protocol for Set Intersection Cardinality Based on a Quantum Homomorphic Encryption Scheme for Toffoli Gate"],"prefix":"10.3390","volume":"25","author":[{"given":"Wen","family":"Liu","sequence":"first","affiliation":[{"name":"State Key Laboratory of Media Convergence and Communication, Communication University of China, Beijing 100024, China"},{"name":"School of Computer and Cyber Sciences, Communication University of China, Beijing 100024, China"},{"name":"Key Laboratory of Convergent Media and Intelligent Technology, Communication University of China, Ministry of Education, Beijing 100034, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yangzhi","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer and Cyber Sciences, Communication University of China, Beijing 100024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhirao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer and Cyber Sciences, Communication University of China, Beijing 100024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yugang","family":"Li","sequence":"additional","affiliation":[{"name":"Academy of Broadcasting Science, Beijing 100045, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gordon, S.D., Hazay, C., Katz, J., and Lindell, Y. 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