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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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2015
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/105 |
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| Journal Title: | Algebra and Discrete Mathematics |
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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 |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2015-11-10T19:25:54Z |
| collection |
OJS |
| language |
English |
| topic |
multivariate cryptography linguistic graphs hidden Eulerian equation hidden discrete logarithm problem |
| 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 |
| topic_facet |
multivariate cryptography linguistic graphs hidden Eulerian equation hidden discrete logarithm problem |
| format |
Article |
| author |
Ustimenko, Vasyl |
| author_facet |
Ustimenko, Vasyl |
| author_sort |
Ustimenko, Vasyl |
| title |
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_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_sort |
on algebraic graph theory and non-bijective multivariate maps in cryptography |
| 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 \(\Omega_n={{Z_m}^*}^n\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2015 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/105 |
| work_keys_str_mv |
AT ustimenkovasyl onalgebraicgraphtheoryandnonbijectivemultivariatemapsincryptography |
| first_indexed |
2025-12-02T15:47:11Z |
| last_indexed |
2025-12-02T15:47:11Z |
| _version_ |
1850412034007498752 |