{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:39:32Z","timestamp":1760243972984,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2009,6,3]],"date-time":"2009-06-03T00:00:00Z","timestamp":1243987200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The theoretical Quantum Key-Distribution scheme of Bennett and Brassard (BB84) has been proven secure against very strong attacks including the collective attacks and the joint attacks. Though the latter are the most general attacks, collective attacks are much easier to analyze, yet, they are conjectured to be as informative to the eavesdropper. Thus, collective attacks are likely to be useful in the analysis of many theoretical and practical schemes that are still lacking a proof of security, including practical BB84 schemes. We show how powerful tools developed in previous works for proving security against the joint attack, are simplified when applied to the security of BB84 against collective attacks whilst providing the same bounds on leaked information and the same error threshold.<\/jats:p>","DOI":"10.3390\/a2020790","type":"journal-article","created":{"date-parts":[[2009,6,3]],"date-time":"2009-06-03T12:24:59Z","timestamp":1244031899000},"page":"790-807","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Security of the Bennett-Brassard Quantum Key Distribution Protocol against Collective Attacks"],"prefix":"10.3390","volume":"2","author":[{"given":"Michel","family":"Boyer","sequence":"first","affiliation":[{"name":"Departement IRO, Universit\u00e9 de Montr\u00e9al, CP 6128 Succ. Centre-Ville, Montr\u00e9al H3C 3J7, Canada"}]},{"given":"Ran","family":"Gelles","sequence":"additional","affiliation":[{"name":"Computer Science Department, Technion, Haifa 32000, Israel"}]},{"given":"Tal","family":"Mor","sequence":"additional","affiliation":[{"name":"Computer Science Department, Technion, Haifa 32000, Israel"}]}],"member":"1968","published-online":{"date-parts":[[2009,6,3]]},"reference":[{"key":"ref_1","unstructured":"Bennett, C.H., and Brassard, G. Quantum Cryptography: Public key distribution and coin tossing. Proceedings of IEEE International Conference on Computers, Systems and Signal Processing."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2256","DOI":"10.1103\/PhysRevLett.78.2256","article-title":"Security of quantum cryptography against collective attacks","volume":"78","author":"Biham","year":"1997","journal-title":"Physical Review Letters"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4034","DOI":"10.1103\/PhysRevLett.79.4034","article-title":"Bounds on information and the security of quantum cryptography","volume":"79","author":"Biham","year":"1997","journal-title":"Physical Review Letters"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1007\/s00453-002-0973-6","article-title":"Security of Quantum Key Distribution Against All Collective Attacks","volume":"34","author":"Biham","year":"2002","journal-title":"Algorithmica"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/s00145-005-0011-3","article-title":"A proof of the security of quantum key distribution","volume":"19","author":"Biham","year":"2006","journal-title":"J. Cryptology"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2038","DOI":"10.1103\/PhysRevA.53.2038","article-title":"Quantum-state disturbance versus information gain: Uncertainty relations for quantum information","volume":"53","author":"Fuchs","year":"1996","journal-title":"Physical Review A"},{"key":"ref_7","unstructured":"Boyer, M. (2005). Security of the BB84 QKD protocol, personal notes."},{"key":"ref_8","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"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1103\/PhysRevLett.85.441","article-title":"Simple proof of security of the BB84 quantum key distribution protocol","volume":"85","author":"Shor","year":"2000","journal-title":"Physical Review Letters"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1142\/S0219749906002316","article-title":"Noise tolerance of the bb84 protocol with random privacy amplification","volume":"4","author":"Watanabe","year":"2006","journal-title":"International Journal of Quantum Information"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1134\/S0021364007100116","article-title":"Explicit attack on the key in quantum cryptography (BB84 protocol) reaching the theoretical error limit Qc \u2248 11%","volume":"85","author":"Molotkov","year":"2007","journal-title":"JETP Letters"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"080501","DOI":"10.1103\/PhysRevLett.95.080501","article-title":"Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication","volume":"95","author":"Kraus","year":"2005","journal-title":"Physical Review Letters"},{"key":"ref_13","unstructured":"Renner, R. (Arxiv preprint quant-ph\/0512258, 2005). Security of Quantum Key Distribution, Arxiv preprint quant-ph\/0512258."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1080\/01621459.1963.10500830","article-title":"Probability inequalities for sums of bounded random variables","volume":"58","author":"Hoeffding","year":"1963","journal-title":"Journal of the American Statistical Association"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/2\/2\/790\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:10:30Z","timestamp":1760220630000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/2\/2\/790"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6,3]]},"references-count":14,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2009,6]]}},"alternative-id":["a2020790"],"URL":"https:\/\/doi.org\/10.3390\/a2020790","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2009,6,3]]}}}