{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T17:22:01Z","timestamp":1775496121032,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,22]],"date-time":"2023-05-22T00:00:00Z","timestamp":1684713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007819","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671244"],"award-info":[{"award-number":["11671244"]}],"id":[{"id":"10.13039\/501100007819","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum secret sharing (QSS) is an important branch of quantum cryptography. Identity authentication is a significant means to achieve information protection, which can effectively confirm the identity information of both communication parties. Due to the importance of information security, more and more communications require identity authentication. We propose a d-level (t,n) threshold QSS scheme in which both sides of the communication use mutually unbiased bases for mutual identity authentication. In the secret recovery phase, the sharing of secrets that only the participant holds will not be disclosed or transmitted. Therefore, external eavesdroppers will not get any information about secrets at this phase. This protocol is more secure, effective, and practical. Security analysis shows that this scheme can effectively resist intercept\u2013resend attacks, entangle\u2013measure attacks, collusion attacks, and forgery attacks.<\/jats:p>","DOI":"10.3390\/e25050827","type":"journal-article","created":{"date-parts":[[2023,5,22]],"date-time":"2023-05-22T05:49:32Z","timestamp":1684734572000},"page":"827","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A Kind of (t, n) Threshold Quantum Secret Sharing with Identity Authentication"],"prefix":"10.3390","volume":"25","author":[{"given":"Depeng","family":"Meng","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710119, China"}]},{"given":"Zhihui","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710119, China"}]},{"given":"Shuangshuang","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710119, China"}]},{"given":"Zhaowei","family":"Han","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710119, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1145\/359168.359176","article-title":"How to share a secret","volume":"22","author":"Shamir","year":"1979","journal-title":"Commun. ACM"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1829","DOI":"10.1103\/PhysRevA.59.1829","article-title":"Quantum secret sharing","volume":"59","author":"Hillery","year":"1999","journal-title":"Phys. Rev. A"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2465","DOI":"10.1007\/s11128-013-0534-8","article-title":"Secret sharing based on quantum Fourier transform","volume":"12","author":"Yang","year":"2013","journal-title":"Quantum Inf. Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"030302","DOI":"10.1103\/PhysRevA.92.030302","article-title":"Secret sharing with a single d-level quantum system","volume":"92","author":"Tavakoli","year":"2015","journal-title":"Phys. Rev. A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s11128-021-03402-8","article-title":"Multiparty mediated semi-quantum secret sharing protocol","volume":"21","author":"Tsai","year":"2022","journal-title":"Quantum Inf. Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6093","DOI":"10.1038\/s41598-021-85703-7","article-title":"Multiparty weighted threshold quantum secret sharing based on the Chinese remainder theorem to share quantum information","volume":"11","author":"Chou","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6366","DOI":"10.1038\/s41598-017-06486-4","article-title":"(t, n) Threshold d-Level Quantum Secret Sharing","volume":"7","author":"Song","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s11128-019-2571-4","article-title":"Efficient quantum secret sharing without a trusted player","volume":"19","author":"Sutradhar","year":"2020","journal-title":"Quantum Inf. Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1080\/19361610.2020.1840894","article-title":"Improvement of a (t, n) threshold d-level quantum secret sharing scheme","volume":"17","author":"Mashhadi","year":"2022","journal-title":"J. Appl. Secur. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1007\/s11128-021-03270-2","article-title":"General quantum secret sharing scheme based on two qudit","volume":"20","author":"Li","year":"2021","journal-title":"Quantum Inf. Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1007\/s10773-019-04012-y","article-title":"Verififiable quantum secret sharing protocols based on four-qubit entangled states","volume":"58","author":"Cao","year":"2019","journal-title":"Int. J. Theor. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1007\/s11128-019-2509-x","article-title":"A verifiable framework of entanglement-free quantum secret sharing with information-theoretical security","volume":"19","author":"Lu","year":"2020","journal-title":"Quantum Inf. Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s11128-022-03617-3","article-title":"A verifiable (k, n) threshold dynamic quantum secret sharing scheme","volume":"21","author":"Li","year":"2022","journal-title":"Quantum Inf. Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1007\/s11128-021-03343-2","article-title":"Cheating identifiable (k, n) threshold quantum secret sharing scheme","volume":"21","author":"Yan","year":"2022","journal-title":"Quantum Inf. Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s11433-008-0034-5","article-title":"Multiparty simultaneous quantum identity authentication with secret sharing","volume":"51","author":"Yang","year":"2008","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1750023","DOI":"10.1142\/S021974991750023X","article-title":"Quantum secret sharing with identity authentication based on Bell states","volume":"15","author":"Abulkasim","year":"2017","journal-title":"Int. J. Quantum Inf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s11128-021-03103-2","article-title":"A novel dynamic quantum secret sharing in high-dimensional quantum system","volume":"20","author":"Hu","year":"2021","journal-title":"Quantum Inf. Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"022602","DOI":"10.1103\/PhysRevA.103.022602","article-title":"Reference-frame-independent measurement-device-independent quantum key distribution using fewer states","volume":"103","author":"Liu","year":"2021","journal-title":"Phys. Rev. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1007\/s11128-022-03464-2","article-title":"Extended single-photon entanglement based phase-matching quantum key distribution","volume":"21","author":"Li","year":"2022","journal-title":"Quantum Inf. Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s11128-019-2255-0","article-title":"Quantum identity authentication in the orthogonal-state-encoding QKD system","volume":"18","author":"Liu","year":"2019","journal-title":"Quantum Inf. Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"022305","DOI":"10.1103\/PhysRevA.62.022305","article-title":"Authority-based user authentication in quantum key distribution","volume":"62","author":"Ljunggren","year":"2002","journal-title":"Phys. Rev. A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/s11128-022-03717-0","article-title":"A short review on quantum identity authentication protocols: How would bob know that he is talking with alice?","volume":"21","author":"Dutta","year":"2022","journal-title":"Quantum Inf. Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"187902","DOI":"10.1103\/PhysRevLett.89.187902","article-title":"Deterministic secure direct communicationusing entanglement","volume":"89","author":"Bostrom","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Bufalo, M., Bufalo, D., and Orlando, G. (2021). A Note on the Computation of the Modular Inverse for Cryptography. Axioms, 10.","DOI":"10.3390\/axioms10020116"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"042325","DOI":"10.1103\/PhysRevA.82.042325","article-title":"Security analysis and improvements of arbitrated quantum signature schemes","volume":"82","author":"Zou","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_26","first-page":"434","article-title":"Security of a kind of quantum secret sharing with single photons","volume":"11","author":"Wang","year":"2011","journal-title":"Quant. Inf. Comput."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2485","DOI":"10.1038\/s41598-017-02543-0","article-title":"Security of a kind of quantum secret sharing with entangled states","volume":"7","author":"Wang","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"062308","DOI":"10.1103\/PhysRevA.76.062308","article-title":"Impossibility of secure two-party classical computation","volume":"76","author":"Colbeck","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1145\/382780.382781","article-title":"Unconditional security in quantum cryptography","volume":"48","author":"Mayers","year":"2001","journal-title":"J. ACM"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/5\/827\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:39:50Z","timestamp":1760125190000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/5\/827"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,22]]},"references-count":29,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["e25050827"],"URL":"https:\/\/doi.org\/10.3390\/e25050827","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,22]]}}}