{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T19:40:03Z","timestamp":1768419603717,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,7,5]],"date-time":"2024-07-05T00:00:00Z","timestamp":1720137600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fundaci\u00f3n para la Promoci\u00f3n de la Investigaci\u00f3n y la Tecnolog\u00eda del Banco de la Rep\u00fablica","award":["4649"],"award-info":[{"award-number":["4649"]}]},{"name":"Fundaci\u00f3n para la Promoci\u00f3n de la Investigaci\u00f3n y la Tecnolog\u00eda del Banco de la Rep\u00fablica","award":["TED2021-130358B-I00"],"award-info":[{"award-number":["TED2021-130358B-I00"]}]},{"name":"MCIN\/AEI\/10.13039\/501100011033","award":["4649"],"award-info":[{"award-number":["4649"]}]},{"name":"MCIN\/AEI\/10.13039\/501100011033","award":["TED2021-130358B-I00"],"award-info":[{"award-number":["TED2021-130358B-I00"]}]},{"name":"European Union NextGenerationEU\/PRTR","award":["4649"],"award-info":[{"award-number":["4649"]}]},{"name":"European Union NextGenerationEU\/PRTR","award":["TED2021-130358B-I00"],"award-info":[{"award-number":["TED2021-130358B-I00"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>This article studies some algebraic structures known as twisted-skew group rings in the context of public key cryptography. We first present some background related to these structures to then specifically introduce particular twisted-skew group rings and show how to utilize them as the underlying algebraic structure to build cryptographic protocols. We closely follow an incremental-like methodology to construct these protocols by putting parts together. As as result, we first introduce a key-agreement protocol and then generalize it to a group key-agreement protocol. We then proceed to construct a probabilistic public key encryption from our two-party key agreement and, finally, introduce a key-encapsulation mechanism from a well-known generic construction applied to probabilistic public encryption. Furthermore, we provide an in-depth security analysis for each cryptographic construction under new related algebraic assumptions and supply a proof-of-concept implementation for various candidate chosen groups.<\/jats:p>","DOI":"10.3390\/cryptography8030029","type":"journal-article","created":{"date-parts":[[2024,7,5]],"date-time":"2024-07-05T12:30:59Z","timestamp":1720182659000},"page":"29","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Public Key Protocols from Twisted-Skew Group Rings"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3609-9148","authenticated-orcid":false,"given":"Javier","family":"de la Cruz","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Universidad del Norte, Barranquilla 081007, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1243-2049","authenticated-orcid":false,"given":"Edgar","family":"Mart\u00ednez-Moro","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Universidad de Valladolid, 47011 Valladolid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Steven","family":"Mu\u00f1oz-Ruiz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8682-4830","authenticated-orcid":false,"given":"Ricardo","family":"Villanueva-Polanco","sequence":"additional","affiliation":[{"name":"Cryptography Research Center, Technology Innovation Institute, Abu Dhabi P.O. Box 9639, United Arab Emirates"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,5]]},"reference":[{"key":"ref_1","unstructured":"(2024, June 01). National Institute of Standards and Technology, NIST Post-Quantum Cryptography, Available online: https:\/\/csrc.nist.gov\/Projects\/post-quantum-cryptography\/selected-algorithms-2022."},{"key":"ref_2","unstructured":"(2024, June 01). National Institute of Standards and Technology, Post-Quantum Cryptography: Digital Signature Schemes, Available online: https:\/\/csrc.nist.gov\/Projects\/pqc-dig-sig\/round-1-additional-signatures."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Dam, D.-T., Tran, T.-H., Hoang, V.-P., Pham, C.-K., and Hoang, T.-T. (2023). A Survey of Post-Quantum Cryptography: Start of a New Race. 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