{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T21:51:35Z","timestamp":1768427495039,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2015,4,30]],"date-time":"2015-04-30T00:00:00Z","timestamp":1430352000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum cryptographic protocols solve the longstanding problem of distributing a shared secret string to two distant users by typically making use of one-way quantum channel. However, alternative protocols exploiting two-way quantum channel have been proposed for the same goal and with potential advantages. Here, we overview a security proof for two-way quantum key distribution protocols, against the most general eavesdropping attack, that utilize an entropic uncertainty relation. Then, by resorting to the \u201csmooth\u201d version of involved entropies, we extend such a proof to the case of finite key size. The results will be compared to those available for one-way protocols showing some advantages.<\/jats:p>","DOI":"10.3390\/e17052723","type":"journal-article","created":{"date-parts":[[2015,4,30]],"date-time":"2015-04-30T08:58:53Z","timestamp":1430384333000},"page":"2723-2740","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Finite Key Size Analysis of Two-Way Quantum Cryptography"],"prefix":"10.3390","volume":"17","author":[{"given":"Jesni","family":"Shaari","sequence":"first","affiliation":[{"name":"Faculty of Science, International Islamic University Malaysia (IIUM), Jalan Sultan Ahmad Shah, Bandar Indera Mahkota, 25200 Kuantan, Pahang, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefano","family":"Mancini","sequence":"additional","affiliation":[{"name":"School of Science & Technology, University of Camerino, I-62032 Camerino, Italy"},{"name":"INFN-Sezione di Perugia, Via A. Pascoli, I-06123 Perugia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,4,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.tcs.2014.09.017","article-title":"Quantum key distribution using a two-way quantum channel","volume":"560","author":"Lucamarini","year":"2014","journal-title":"Theor. Comput. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1103\/RevModPhys.74.145","article-title":"Quantum cryptography","volume":"74","author":"Gisin","year":"2002","journal-title":"Rev. Mod. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"187902","DOI":"10.1103\/PhysRevLett.89.187902","article-title":"Deterministic Secure Direct Communication Using Entanglement","volume":"89","author":"Felbinger","year":"2002","journal-title":"Phys. Rev. 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Thus M(n, k) for SDC must be understood as number of qubit pairs."},{"key":"ref_26","unstructured":"It is possible to consider a more practical scenario, for example for a bit string with error rate e, a cofactor would be multiplied to the amount bits needed for such a purpose given by h2(e)."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5524","DOI":"10.1109\/TIT.2011.2158473","article-title":"Leftover Hashing Against Quantum Side Information","volume":"57","author":"Tomamichel","year":"2011","journal-title":"IEEE Trans. Inf. Theory."},{"key":"ref_28","first-page":"249","article-title":"Efficient Quantum Cryptography","volume":"2","author":"Cabello","year":"2001","journal-title":"Rec. Res. Dev. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1038\/nphys1018","article-title":"Continuous-variable quantum cryptography using two-way quantum communication","volume":"4","author":"Pirandola","year":"2008","journal-title":"Nat. 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Process."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2723\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:45:36Z","timestamp":1760215536000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2723"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,30]]},"references-count":32,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2015,5]]}},"alternative-id":["e17052723"],"URL":"https:\/\/doi.org\/10.3390\/e17052723","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4,30]]}}}