{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T08:44:47Z","timestamp":1767084287135,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T00:00:00Z","timestamp":1741046400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Convocatoria Nacional para el Establecimiento de Redes de Cooperaci\u00f3n bajo el Marco del Modelo Intersedes 2022\u20132024, Universidad Nacional de Colombia","award":["59773"],"award-info":[{"award-number":["59773"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper is focused on some algebraic and combinatorial properties of a TMTO (Time\u2013Memory Trade-Off) for a chosen plaintext attack against a cryptosystem with a perfect secrecy property. TMTO attacks aim to retrieve the preimage of a given one-way function more efficiently than an exhaustive search and with less memory than a dictionary attack. TMTOs for chosen plaintext attacks against cryptosystems with a perfect secrecy property are associated with some directed graphs, which can be defined by suitable collections of multisets called Brauer configurations. Such configurations induce so-called Brauer configuration algebras, the algebraic and combinatorial invariant analysis of which is said to be a Brauer analysis. In this line, this paper proposes formulas for dimensions of Brauer configuration algebras (and their centers) induced by directed graphs defined by TMTO attacks. These results are used to provide some set-theoretical solutions for the Yang\u2013Baxter equation.<\/jats:p>","DOI":"10.3390\/sym17030391","type":"journal-article","created":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T10:43:31Z","timestamp":1741085011000},"page":"391","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Brauer Analysis of Some Time\u2013Memory Trade-Off Attacks and Its Application to the Solution of the Yang\u2013Baxter Equation"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6812-5131","authenticated-orcid":false,"given":"Agust\u00edn Moreno","family":"Ca\u00f1adas","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogot\u00e1 11001000, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7107-7617","authenticated-orcid":false,"given":"Ismael","family":"Gutierrez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas y Estad\u00edstica, Universidad del Norte, Kil\u00f3metro 5, Via Puerto Colombia, Barranquilla, Atl\u00e1ntico 081007, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3953-2381","authenticated-orcid":false,"given":"Odette M.","family":"Mendez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad Nacional de Colombia, Sede, La Nubia, Manizales 170003, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2989-9342","authenticated-orcid":false,"given":"Andr\u00e9s","family":"Sarrazola-Alzate","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, University EIA, Calle 25 Sur, 42-73, Envigado 055420, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-5378-1367","authenticated-orcid":false,"given":"Jesus Antonio","family":"Zuluaga-Moreno","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas y Estad\u00edstica, Universidad del Norte, Kil\u00f3metro 5, Via Puerto Colombia, Barranquilla, Atl\u00e1ntico 081007, Colombia"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1109\/TIT.1980.1056220","article-title":"A cryptanalytic time-memory trade-off","volume":"26","author":"Hellman","year":"1980","journal-title":"IEEE Trans. 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