{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:51:34Z","timestamp":1760237494670,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,23]],"date-time":"2020-05-23T00:00:00Z","timestamp":1590192000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A Shannon cipher can be used as a building block for the block cipher construction if it is considered as one data block cipher. It has been proved that a Shannon cipher based on a matrix power function (MPF) is perfectly secure. This property was obtained by the special selection of algebraic structures to define the MPF. In an earlier paper we demonstrated, that certain MPF can be treated as a conjectured one-way function. This property is important since finding the inverse of a one-way function is related to an     N P    -complete problem. The obtained results of perfect security on a theoretical level coincide with the     N P    -completeness notion due to the well known Yao theorem. The proposed cipher does not need multiple rounds for the encryption of one data block and hence can be effectively parallelized since operations with matrices allow this effective parallelization.<\/jats:p>","DOI":"10.3390\/sym12050860","type":"journal-article","created":{"date-parts":[[2020,5,25]],"date-time":"2020-05-25T11:42:02Z","timestamp":1590406922000},"page":"860","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Perfectly Secure Shannon Cipher Construction Based on the Matrix Power Function"],"prefix":"10.3390","volume":"12","author":[{"given":"Eligijus","family":"Sakalauskas","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Kaunas University of Technology, 44249 Kaunas, Lithuania"}]},{"given":"Lina","family":"Dindien\u0117","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Kaunas University of Technology, 44249 Kaunas, Lithuania"}]},{"given":"Au\u0161rys","family":"Kil\u010diauskas","sequence":"additional","affiliation":[{"name":"Department of Informatics, Kauno kolegija\/University of Applied Science, 50468 Kaunas, Lithuania"}]},{"given":"K\u0229stutis","family":"Luk\u0161ys","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Kaunas University of Technology, 44249 Kaunas, Lithuania"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","article-title":"Communication theory of secrecy systems","volume":"28","author":"Shannon","year":"1949","journal-title":"Bell Syst. 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Theory and applications of trapdoor functions. Proceedings of the 23rd Annual Symposium on Foundations of Computer Science, (sfcs 1982), Chicago, IL, USA.","DOI":"10.1109\/SFCS.1982.45"},{"key":"ref_7","unstructured":"Sakalauskas, E., Listopadskis, N., and Tvarijonas, P. (2008). Key Agreement Protocol (KAP) Based on Matrix Power Function. Information Science And Computing, Book 4 Advanced Studies in Software and Knowledge Engineering, Institute of Information Theories and Applications FOI ITHEA."},{"key":"ref_8","first-page":"33","article-title":"The Multivariate Quadratic Power Problem Over Zn is NP-Complete","volume":"41","author":"Sakalauskas","year":"2012","journal-title":"Inf. Technol. Control"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Sakalauskas, E., Mihalkovich, A., and Ven\u010dkauskas, A. (2017). Improved asymmetric cipher based on matrix power function with provable security. Symmetry, 9.","DOI":"10.3390\/sym9010009"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Sakalauskas, E. (2018). Enhanced matrix power function for cryptographic primitive construction. Symmetry, 10.","DOI":"10.3390\/sym10020043"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"517","DOI":"10.15388\/Informatica.2017.142","article-title":"Improved Asymmetric Cipher Based on Matrix Power Function Resistant to Linear Algebra Attack","volume":"28","author":"Sakalauskas","year":"2017","journal-title":"Informatica"},{"key":"ref_12","unstructured":"Noor, S. (2019). Cryptographic Schemes Based on Enhanced Matrix Power Function. [Ph.D. Thesis, Capital University]."},{"key":"ref_13","unstructured":"Iqbal, S. (2019). Digital Signature Based on Matrix Power Function. [Ph.D. Thesis, Capital University]."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Liu, J., Zhang, H., and Jia, J. (2017). A Linear Algebra Attack on the Non-commuting Cryptography Class Based on Matrix Power Function. International Conference on Information Security and Cryptology. Inscrypt 2016: Information Security and Cryptology, Springer.","DOI":"10.1007\/978-3-319-54705-3_21"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Sakalauskas, E., and Mihalkovich, A. (2018). MPF Problem over Modified Medial Semigroup Is NP-Complete. Symmetry, 10.","DOI":"10.3390\/sym10110571"},{"key":"ref_16","first-page":"2655","article-title":"The matrix power function and its application to block cipher S-box construction","volume":"8","author":"Sakalauskas","year":"2012","journal-title":"Int. J. Innov. Comput. Inf. Control"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1038\/scientificamerican0573-15","article-title":"Cryptography and computer privacy","volume":"228","author":"Feistel","year":"1973","journal-title":"Sci. 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[Ph.D. Thesis, Queen\u2019s University].","DOI":"10.1145\/191177.191206"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/5\/860\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:31:46Z","timestamp":1760175106000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/5\/860"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,23]]},"references-count":18,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2020,5]]}},"alternative-id":["sym12050860"],"URL":"https:\/\/doi.org\/10.3390\/sym12050860","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,5,23]]}}}