{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T12:18:07Z","timestamp":1772799487808,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,9]],"date-time":"2023-09-09T00:00:00Z","timestamp":1694217600000},"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>This paper addresses the certificate revocation problem and proposes the first revocable pairing-based signature scheme with implicit and explicit certificates (IE-RCBS-kCAA). We should no longer discuss whether to revoke certificates but how to do it effectively, ensuring both the scalability of the revocation operation and the non-repudiation of the signature in the short or long term. Under the computational difficulty assumptions of the modified collusion attack algorithm with k traitors (k-mCAA) and discrete logarithm (DL) problems, we demonstrate that our scheme is secure against existential unforgeability under chosen message attacks (EUF-IERCBS-kCAA-CMA) in a random oracle model. The proposed solution is scaled and allows the use of many trusted status authorities that issue explicit short-term certificates confirming the validity of explicit long-term certificates. Furthermore, we demonstrate that our signature scheme has a short-term non-repudiation property for the shell validity model.<\/jats:p>","DOI":"10.3390\/e25091315","type":"journal-article","created":{"date-parts":[[2023,9,11]],"date-time":"2023-09-11T08:58:08Z","timestamp":1694422688000},"page":"1315","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Revocable Signature Scheme with Implicit and Explicit Certificates"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4783-1114","authenticated-orcid":false,"given":"Jerzy","family":"Peja\u015b","sequence":"first","affiliation":[{"name":"Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, 71-210 Szczecin, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2115-5338","authenticated-orcid":false,"given":"Tomasz","family":"Hyla","sequence":"additional","affiliation":[{"name":"Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, 71-210 Szczecin, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6289-6637","authenticated-orcid":false,"given":"Wojciech","family":"Zabierowski","sequence":"additional","affiliation":[{"name":"Department of Microelectronics and Computer Science, Lodz University of Technology, 93-005 Lodz, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Martinelli, F., and Preneel, B. 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