{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:12:27Z","timestamp":1760220747603,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2012,12,11]],"date-time":"2012-12-11T00:00:00Z","timestamp":1355184000000},"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>We propose a quantum protocol to authenticate classical messages that can be used to replace Wegman\u2013Carter\u2019s classical authentication scheme in quantum key distribution (QKD) protocols. We show that the proposed scheme achieves greater conditional entropy of the seed for the intruder given her (quantum) observation than the classical case. The proposed scheme is suitable for situations where the shared symmetric key used in authentication becomes dangerously short (due to noise or eavesdropping), and there is a threat that it might be completely consumed without being replaced. Our protocol is an improvement over a classical scheme by Brassard and takes advantage of quantum channel properties. It is motivated by information-theoretical results. We stress that the proposed authentication protocol can also be used as an independent authentication protocol that is not a part of a QKD. However by adopting it, QKD becomes a fully quantum protocol. We prove that quantum resources can improve both the secrecy of the key generated by the PRG and the secrecy of the tag obtained with a hidden hash function. We conclude that the proposed quantum encoding offers more security than the classical scheme and, by applying a classical result, we show that it can be used under noisy quantum channels.<\/jats:p>","DOI":"10.3390\/e14122531","type":"journal-article","created":{"date-parts":[[2012,12,11]],"date-time":"2012-12-11T11:22:34Z","timestamp":1355224954000},"page":"2531-2549","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Improving Classical Authentication over a Quantum Channel"],"prefix":"10.3390","volume":"14","author":[{"given":"Francisco","family":"Assis","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Universidade Federal de Campina Grande, 58.429-970 Campina Grande, Para\u00edba, Brazil"}]},{"given":"Aleksandar","family":"Stojanovic","sequence":"additional","affiliation":[{"name":"Department of Mathematics, IST, Technical University of Lisbon, 1049-001 Lisboa, Portugal"},{"name":"Security and Quantum Information Group, Instituto de Telecomunica\u00e7\u00f5es, 1049-001 Lisbon, Portugal"}]},{"given":"Paulo","family":"Mateus","sequence":"additional","affiliation":[{"name":"Department of Mathematics, IST, Technical University of Lisbon, 1049-001 Lisboa, Portugal"},{"name":"Security and Quantum Information Group, Instituto de Telecomunica\u00e7\u00f5es, 1049-001 Lisbon, Portugal"}]},{"given":"Yasser","family":"Omar","sequence":"additional","affiliation":[{"name":"CEMAPRE, ISEG, Technical University of Lisbon, 1200-781 Lisboa, Portugal"},{"name":"Physics of Information Group, Instituto de Telecomunica\u00e7\u00f5es, 1049-001 Lisbon, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2012,12,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/0022-0000(81)90033-7","article-title":"New hash functions and their use in authentication and set equality","volume":"22","author":"Wegman","year":"1981","journal-title":"J. Comput. Syst. Sci."},{"key":"ref_2","unstructured":"Bennett, C.H., and Brassard, G. (,  1984). Quantum cryptography: Public-key distribution and coin tossing. Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India."},{"key":"ref_3","unstructured":"Brassard, G. (1983). Advances in Cryptology, Springer-Verlag."},{"key":"ref_4","unstructured":"Krawczyk, H. (1994). Advances in Cryptology, Springer-Verlag."},{"key":"ref_5","unstructured":"Rogaway, P. (1995). Advances in Cryptology, Springer-Verlag."},{"key":"ref_6","unstructured":"Shoup, V. (1996). Advances in Cryptology, Springer-Verlag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1137\/0215025","article-title":"A simple unpredictable pseudo random number generator","volume":"15","author":"Blum","year":"1986","journal-title":"SIAM J. 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Foundations of Cryptography: Volume I Basic Tools, Cambridge University Press.","DOI":"10.1017\/CBO9780511546891"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Paris, M.G.A., and Reh\u00e1cek, J. (2004). Lectures Notes in Physics, Quantum State Estimation, Springer.","DOI":"10.1007\/b98673"},{"key":"ref_22","unstructured":"Nielsen, M.A., and Chuang, I.L. (2000). Quantum Computation and Quantum Information, Cambridge University Press."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1109\/TIT.1978.1055892","article-title":"Broadcast\u00a0channels with confidential messages","volume":"24","author":"Csiszar","year":"1978","journal-title":"IEEE Trans. Inform. Theor."},{"key":"ref_24","unstructured":"Although this sequence is cyclic, the cycle is exponential in the size of the seed, and so the standard QKD key maintenance will eventually be restored before the cycle ends."},{"key":"ref_25","unstructured":"A similar analysis can be made to the Blum-Micali PRG assuming the large prime is kept secret [26]."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1137\/0213053","article-title":"How to generate cryptographically strong sequences of pseudorandom bits","volume":"13","author":"Blum","year":"1984","journal-title":"SIAM J. Comput."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/12\/2531\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:54:09Z","timestamp":1760219649000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/12\/2531"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,11]]},"references-count":26,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2012,12]]}},"alternative-id":["e14122531"],"URL":"https:\/\/doi.org\/10.3390\/e14122531","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2012,12,11]]}}}