On algebraic graph theory and non-bijective multivariate maps in cryptography
Special family of non-bijective multivariate maps \(F_n\) of \({Z_m}^n\)into itself is constructed for \(n = 2, 3, \dots\) and composite~\(m\).The map \(F_n\) is injective on \(\Omega_n=\{{\rm x}|x_1+x_2 + \dotsx_n \in {Z_m}^* \}\) and solution of the equation \(F_n({\rm x})={\rmb}, {\rm x}\in \Omeg...
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| Datum: | 2015 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2015
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/105 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543048249376768 |
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| author | Ustimenko, Vasyl |
| author_facet | Ustimenko, Vasyl |
| author_sort | Ustimenko, Vasyl |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2015-11-10T19:25:54Z |
| description | Special family of non-bijective multivariate maps \(F_n\) of \({Z_m}^n\)into itself is constructed for \(n = 2, 3, \dots\) and composite~\(m\).The map \(F_n\) is injective on \(\Omega_n=\{{\rm x}|x_1+x_2 + \dotsx_n \in {Z_m}^* \}\) and solution of the equation \(F_n({\rm x})={\rmb}, {\rm x}\in \Omega_n\) can be reduced to the solution of equation \(z^r=\alpha\), \(z \in {Z_m}^*\), \((r, \phi(m))=1\). The ``hidden RSAcryptosystem'' is proposed.Similar construction is suggested for the case \(\Omega_n={{Z_m}^*}^n\). |
| first_indexed | 2025-12-02T15:47:11Z |
| format | Article |
| id | admjournalluguniveduua-article-105 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:47:11Z |
| publishDate | 2015 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-1052015-11-10T19:25:54Z On algebraic graph theory and non-bijective multivariate maps in cryptography Ustimenko, Vasyl multivariate cryptography, linguistic graphs, hidden Eulerian equation, hidden discrete logarithm problem Special family of non-bijective multivariate maps \(F_n\) of \({Z_m}^n\)into itself is constructed for \(n = 2, 3, \dots\) and composite~\(m\).The map \(F_n\) is injective on \(\Omega_n=\{{\rm x}|x_1+x_2 + \dotsx_n \in {Z_m}^* \}\) and solution of the equation \(F_n({\rm x})={\rmb}, {\rm x}\in \Omega_n\) can be reduced to the solution of equation \(z^r=\alpha\), \(z \in {Z_m}^*\), \((r, \phi(m))=1\). The ``hidden RSAcryptosystem'' is proposed.Similar construction is suggested for the case \(\Omega_n={{Z_m}^*}^n\). Lugansk National Taras Shevchenko University 2015-11-09 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/105 Algebra and Discrete Mathematics; Vol 20, No 1 (2015): A special issue 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/105/35 Copyright (c) 2015 Algebra and Discrete Mathematics |
| spellingShingle | multivariate cryptography linguistic graphs hidden Eulerian equation hidden discrete logarithm problem Ustimenko, Vasyl On algebraic graph theory and non-bijective multivariate maps in cryptography |
| title | On algebraic graph theory and non-bijective multivariate maps in cryptography |
| title_full | On algebraic graph theory and non-bijective multivariate maps in cryptography |
| title_fullStr | On algebraic graph theory and non-bijective multivariate maps in cryptography |
| title_full_unstemmed | On algebraic graph theory and non-bijective multivariate maps in cryptography |
| title_short | On algebraic graph theory and non-bijective multivariate maps in cryptography |
| title_sort | on algebraic graph theory and non-bijective multivariate maps in cryptography |
| topic | multivariate cryptography linguistic graphs hidden Eulerian equation hidden discrete logarithm problem |
| topic_facet | multivariate cryptography linguistic graphs hidden Eulerian equation hidden discrete logarithm problem |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/105 |
| work_keys_str_mv | AT ustimenkovasyl onalgebraicgraphtheoryandnonbijectivemultivariatemapsincryptography |