{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:34:50Z","timestamp":1760402090856,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T00:00:00Z","timestamp":1580083200000},"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>A polar coding scheme is proposed for the Wiretap Broadcast Channel with two legitimate receivers and one eavesdropper. We consider a model in which the transmitter wishes to send the same private (non-confidential) message and the same confidential message reliably to two different legitimate receivers, and the confidential message must also be (strongly) secured from the eavesdropper. The coding scheme aims to use the optimal rate of randomness and does not make any assumption regarding the symmetry or degradedness of the channel. This paper extends previous work on polar codes for the wiretap channel by proposing a new chaining construction that allows to reliably and securely send the same confidential message to two different receivers. This construction introduces new dependencies between the random variables involved in the coding scheme that need to be considered in the secrecy analysis.<\/jats:p>","DOI":"10.3390\/e22020149","type":"journal-article","created":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T11:41:57Z","timestamp":1580125317000},"page":"149","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Polar Coding for Confidential Broadcasting"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3361-6077","authenticated-orcid":false,"given":"Jaume","family":"del Olmo Al\u00f2s","sequence":"first","affiliation":[{"name":"Departament de Teoria del Senyal i Communications, Universitat Polit\u00e8cnica de Catalunya, 08034 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0136-2586","authenticated-orcid":false,"given":"Javier Rodr\u00edguez","family":"Fonollosa","sequence":"additional","affiliation":[{"name":"Departament de Teoria del Senyal i Communications, Universitat Polit\u00e8cnica de Catalunya, 08034 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1002\/j.1538-7305.1975.tb02040.x","article-title":"The wire-tap channel","volume":"54","author":"Wyner","year":"1975","journal-title":"Bell Syst. 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