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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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2015
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| Subjects: | |
| 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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Algebra and Discrete Mathematics| Summary: | 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 \(\Omega_n={{Z_m}^*}^n\). |
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