{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T10:58:26Z","timestamp":1790506706545,"version":"4.1.0"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,2,26]],"date-time":"2017-02-26T00:00:00Z","timestamp":1488067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Polish National Centre for Research and Development","award":["DOBR-BIO4\/011\/13221\/2013"],"award-info":[{"award-number":["DOBR-BIO4\/011\/13221\/2013"]}]},{"name":"The European Regional Development Fund the Innovative Economy Operational Programme","award":["02.03.00-14-106\/13"],"award-info":[{"award-number":["02.03.00-14-106\/13"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This article presents a new method of risk propagation among associated elements. On thebasis of coloured Petri nets, a new class called propagation nets is defined. This class providesa formal model of a risk propagation. The proposed method allows for model relations betweennodes forming the network structure. Additionally, it takes into account the bidirectional relationsbetween components as well as relations between isomorphic, symmetrical components in variousbranches of the network. This method is agnostic in terms of use in various systems and it canbe adapted to the propagation model of any systems\u2019 characteristics; however, it is intentionallyproposed to assess the risk of critical infrastructures. In this paper, as a proof of concept example, weshow the formal model of risk propagation proposed within the project Cyberspace Security ThreatsEvaluation System of the Republic of Poland. In the article, the idea of the method is presented aswell as its use case for evaluation of risk for cyber threats. With the adaptation of Petri nets, it ispossible to evaluate the risk for the particular node and assess the impact of this risk for all relatednodes including hierarchic relations of components as well as isomorphism of elements.<\/jats:p>","DOI":"10.3390\/sym9030032","type":"journal-article","created":{"date-parts":[[2017,2,27]],"date-time":"2017-02-27T11:00:20Z","timestamp":1488193220000},"page":"32","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Evaluation of Cyber Security and Modelling of Risk Propagation with Petri Nets"],"prefix":"10.3390","volume":"9","author":[{"given":"Marcin","family":"Szpyrka","sequence":"first","affiliation":[{"name":"Department of Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bartosz","family":"Jasiul","sequence":"additional","affiliation":[{"name":"Cyber Security Laboratory, Military Communication Institute, ul. Warszawska 22a, 05-130 Zegrze, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Piotrowski, R., and \u015aliwa, J. (2015, January 18\u201319). Cyberspace Situational Awarness in National Security System. Proceedings of the International Conference on Military Communications and Information Systems (ICMCIS), Cracow, Poland.","DOI":"10.1109\/ICMCIS.2015.7158685"},{"key":"ref_2","unstructured":"(2011). ISO\/IEC Information Technology. Security Techniques. Information Security Risk management, ISO\/IEC 27005:2011, International Organization for Standardization."},{"key":"ref_3","unstructured":"Ross, R. 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