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These virus machines are recognized for their computational power (functioning as algorithms) and their ability to tackle computationally difficult problems. In this paper, we introduce a new extension of the matrix-based representation of virus machines. In this way, hosts, the number of viruses and the instructions to control virus transmission are represented as vectors and matrices, describing the computations of virus machines by linear algebra operations. We also use our matrix representation to show invariants, useful in the proofs, of such machines. In addition, an explicit example is shown to clarify the computation and invariants using the representation. That is, a virus machine that computes the discrete logarithm, which relies on the presumed intractability of cryptosystems such the digital signature algorithm. <\/jats:p>","DOI":"10.1142\/s0129065725500492","type":"journal-article","created":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T04:39:58Z","timestamp":1750394398000},"source":"Crossref","is-referenced-by-count":1,"title":["Matrix Representation of Virus Machines and an Application to the Discrete Logarithm Problem"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4666-2494","authenticated-orcid":false,"given":"Antonio","family":"Ram\u00edrez-de-Arellano","sequence":"first","affiliation":[{"name":"Research Institute for Artificial Intelligence Mihai Dr\u0103g\u0103nescu, Calea 13 Septembrie 050711, Bucharest, Romania"},{"name":"Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla 41012, Seville, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2892-6775","authenticated-orcid":false,"given":"David","family":"Orellana-Mart\u00edn","sequence":"additional","affiliation":[{"name":"Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla 41012, Seville, Spain"},{"name":"SCORE Laboratory, I3US, Universidad de Sevilla 41012, Seville, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5055-0102","authenticated-orcid":false,"given":"Mario J.","family":"P\u00e9rez-Jim\u00e9nez","sequence":"additional","affiliation":[{"name":"Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla 41012, Seville, Spain"},{"name":"SCORE Laboratory, I3US, Universidad de Sevilla 41012, Seville, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5006-6310","authenticated-orcid":false,"given":"Francis George C.","family":"Cabarle","sequence":"additional","affiliation":[{"name":"Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla 41012, Seville, Spain"},{"name":"SCORE Laboratory, I3US, Universidad de Sevilla 41012, Seville, Spain"},{"name":"Department of Computer Science, University of the Philippines Diliman, Quezon City, 1101, Philippines"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5513-4039","authenticated-orcid":false,"given":"Henry N.","family":"Adorna","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of the Philippines Diliman, Quezon City, 1101, Philippines"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,8,18]]},"reference":[{"key":"S0129065725500492BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2015.12.006"},{"volume-title":"Prescott\u2019s Principles of Microbiology","year":"2011","author":"Willey J.","key":"S0129065725500492BIB002"},{"key":"S0129065725500492BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2023.114077"},{"key":"S0129065725500492BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0129065723500235"},{"key":"S0129065725500492BIB005","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-023-49297-6"},{"key":"S0129065725500492BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s41965-024-00164-x"},{"key":"S0129065725500492BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-78238-1_20"},{"key":"S0129065725500492BIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S0129065724500345"},{"issue":"7","key":"S0129065725500492BIB009","first-page":"1","volume":"34","author":"Sun S.","year":"2024","journal-title":"Int. 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