{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:41:08Z","timestamp":1760218868253,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2014,6,5]],"date-time":"2014-06-05T00:00:00Z","timestamp":1401926400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Physical implementations of quantum key distribution (QKD) protocols, like the Bennett-Brassard (BB84), are forced to use attenuated coherent quantum states, because the sources of single photon states are not functional yet for QKD applications. However, when using attenuated coherent states, the relatively high rate of multi-photonic pulses introduces vulnerabilities that can be exploited by the photon number splitting (PNS) attack to brake the quantum key. Some QKD protocols have been developed to be resistant to the PNS attack, like the decoy method, but those define a single photonic gain in the quantum channel. To overcome this limitation, we have developed a new QKD protocol, called ack-QKD, which is resistant to the PNS attack. Even more, it uses attenuated quantum states, but defines two interleaved photonic quantum flows to detect the eavesdropper activity by means of the quantum photonic error gain (QPEG) or the quantum bit error rate (QBER). The physical implementation of the ack-QKD is similar to the well-known BB84 protocol.<\/jats:p>","DOI":"10.3390\/e16063121","type":"journal-article","created":{"date-parts":[[2014,6,5]],"date-time":"2014-06-05T11:18:20Z","timestamp":1401967100000},"page":"3121-3135","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Quantum Flows for Secret Key Distribution in the Presence of the Photon Number Splitting Attack"],"prefix":"10.3390","volume":"16","author":[{"given":"Luis","family":"Lizama-P\u00e9rez","sequence":"first","affiliation":[{"name":"Time and Frequency Division, Centro Nacional de Metrolog\u00eda, Carr. a los Cu\u00e9s Km. 4.5,Municipio El Marqu\u00e9s, Quer\u00e9taro C.P. 76246, Mexico"}]},{"given":"J.","family":"L\u00f3pez","sequence":"additional","affiliation":[{"name":"Time and Frequency Division, Centro Nacional de Metrolog\u00eda, Carr. a los Cu\u00e9s Km. 4.5,Municipio El Marqu\u00e9s, Quer\u00e9taro C.P. 76246, Mexico"}]},{"given":"Eduardo","family":"De Carlos-L\u00f3pez","sequence":"additional","affiliation":[{"name":"Time and Frequency Division, Centro Nacional de Metrolog\u00eda, Carr. a los Cu\u00e9s Km. 4.5,Municipio El Marqu\u00e9s, Quer\u00e9taro C.P. 76246, Mexico"}]},{"given":"Salvador","family":"Venegas-Andraca","sequence":"additional","affiliation":[{"name":"Tecnol\u00f3gico de Monterrey, Campus Estado de M\u00e9xico, Carr. a Lago de Guadalupe Km. 3.5, Atizap\u00e1n de Zaragoza, Estado de M\u00e9xico C.P. 52926, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2014,6,5]]},"reference":[{"key":"ref_1","unstructured":"Bennett, C.H., and Brassard, G. 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Phys"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"012326","DOI":"10.1103\/PhysRevA.72.012326","article-title":"Practical decoy state for quantum key distribution","volume":"72","author":"Ma","year":"2005","journal-title":"Phys. Rev. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"057901","DOI":"10.1103\/PhysRevLett.92.057901","article-title":"Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulses implementations","volume":"92","author":"Scarani","year":"2004","journal-title":"Phys. Rev. Lett"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1088\/1367-2630\/7\/1\/232","article-title":"Differential phase shift quantum key distribution experiment over 105 km fiber","volume":"7","author":"Takesue","year":"2005","journal-title":"New J. Phys"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Stucki, D., Fasel, S., Gisin, N., Thoma, Y., and Zbinden, H. (2007, January 11). Coherent one-way quantum key distribution, Prague, Czech Republic.","DOI":"10.1117\/12.722952"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Lizama, L., Lopez, J.M., de Carlos Lopez, E., and Venegas-Andraca, S.E. (2012, January 16\u201318). Enhancing quantum key distribution (QKD) to address quantum hacking. Procedia Technology by Elsevier, Guadalajara, Jal., M\u00e9xico.","DOI":"10.1016\/j.protcy.2012.03.009"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1418","DOI":"10.3938\/jkps.56.1418","article-title":"Effects of the active hold-off technique in 1.55-\u03bc m single-photon detection","volume":"56","author":"Bouzid","year":"2010","journal-title":"J. Korean Phys. Soc"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/6\/3121\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:12:08Z","timestamp":1760217128000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/6\/3121"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6,5]]},"references-count":13,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2014,6]]}},"alternative-id":["e16063121"],"URL":"https:\/\/doi.org\/10.3390\/e16063121","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2014,6,5]]}}}