{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T06:00:01Z","timestamp":1773900001827,"version":"3.50.1"},"reference-count":8,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:00:00Z","timestamp":1565136000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"publisher","award":["MTM2017-86987-P"],"award-info":[{"award-number":["MTM2017-86987-P"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011011","name":"Junta de Andaluc\u00eda","doi-asserted-by":"publisher","award":["FQM221"],"award-info":[{"award-number":["FQM221"]}],"id":[{"id":"10.13039\/501100011011","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Key management is a central problem in information security. The development of quantum computation could make the protocols we currently use unsecure. Because of that, new structures and hard problems are being proposed. In this work, we give a proposal for a key exchange in the context of NIST recommendations. Our protocol has a twisted group ring as setting, jointly with the so-called decomposition problem, and we provide a security and complexity analysis of the protocol. A computationally equivalent cryptosystem is also proposed.<\/jats:p>","DOI":"10.3390\/sym11081019","type":"journal-article","created":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T10:56:38Z","timestamp":1565175398000},"page":"1019","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Public Key Protocols over Twisted Dihedral Group Rings"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9855-6936","authenticated-orcid":false,"given":"Mar\u00eda Dolores","family":"G\u00f3mez Olvera","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Almer\u00eda, 04120 La Ca\u00f1ada de San Urbano, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan Antonio","family":"L\u00f3pez Ramos","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Almer\u00eda, 04120 La Ca\u00f1ada de San Urbano, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Blas","family":"Torrecillas Jover","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Almer\u00eda, 04120 La Ca\u00f1ada de San Urbano, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chen, L., Jordan, S., Liu, Y.-K., Moody, D., Peralta, R., Perlner, R., and SmithTone, D. (2016). Report on Post-Quantum Cryptography.","DOI":"10.6028\/NIST.IR.8105"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"489","DOI":"10.3934\/amc.2007.1.489","article-title":"Public key cryptography based on semigroup actions","volume":"1","author":"Maze","year":"2007","journal-title":"Adv. Math. Commun."},{"key":"ref_3","unstructured":"Romankov, V. (2017). A general encryption scheme using two-sided multiplications with its cryptanalysis. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Eftekhari, M. (2017, January 24\u201326). Cryptoanalisis of Some Protocols using Matrices over Group Rings. Proceedings of the International Conference on Cryptology in Africa, Dakar, Senegal.","DOI":"10.1007\/978-3-319-57339-7_13"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1515\/gcc-2013-0007","article-title":"Public key exchange using matrices over group rings","volume":"5","author":"Kahrobaei","year":"2013","journal-title":"Groups Complex. Cryptol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1109\/71.877936","article-title":"Key agreement in dynamic peer groups","volume":"11","author":"Steiner","year":"2000","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.ipl.2005.01.003","article-title":"A secure and scalable Group Key Exchange system","volume":"94","author":"Burmester","year":"2005","journal-title":"Inf. Proc. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2294","DOI":"10.1002\/mma.4244","article-title":"An application of group theory in confidential network communications","volume":"41","author":"Rosenthal","year":"2018","journal-title":"Math. Meth. 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