On two windows multivariate cryptosystem depending on random parameters
The concept of multivariate bijective map of an affine space \(K^n\) over commutative Ring \(K\) was already used in Cryptography. We consider the idea of nonbijective multivariate polynomial map \(F_n\) of \(K^n\) into \(K^n\) represented as ''partially invertible decomposition'...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1180 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-11802018-05-17T07:50:53Z On two windows multivariate cryptosystem depending on random parameters Romańczuk-Polubiec, Urszula Ustimenko, Vasyl Cryptosystem, Multivariate cryptography, Postquantum cryptography, Algebraic incidence structure, Pseudorandom sequences, Pseudorandom walk in graph 12Y05, 12Y99, 05C81, 05C85, 05C90, 94A60, 14G50 The concept of multivariate bijective map of an affine space \(K^n\) over commutative Ring \(K\) was already used in Cryptography. We consider the idea of nonbijective multivariate polynomial map \(F_n\) of \(K^n\) into \(K^n\) represented as ''partially invertible decomposition'' \(F^{(1)}_nF^{(2)}_n \dots F^{(k)}_n\), \(k=k(n)\), such that knowledge on the decomposition and given value \(u=F(v)\) allow to restore a special part \(v'\) of reimage \(v\). We combine an idea of ''oil and vinegar signatures cryptosystem'' with the idea of linguistic graph based map with partially invertible decomposition to introduce a new cryptosystem. The decomposition will be induced by pseudorandom walk on the linguistic graph and its special quotient (homomorphic image). We estimate the complexity of such general algorithm in case of special family of graphs with quotients, where both graphs form known families of Extremal Graph Theory. The map created by key holder (Alice) corresponds to pseudorandom sequence of ring elements. The postquantum version of the algorithm can be obtained simply by the usage of random strings instead of pseudorandom. Lugansk National Taras Shevchenko University 2018-05-17 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1180 Algebra and Discrete Mathematics; Vol 19, No 1 (2015) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1180/669 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
Cryptosystem Multivariate cryptography Postquantum cryptography Algebraic incidence structure Pseudorandom sequences Pseudorandom walk in graph 12Y05 12Y99 05C81 05C85 05C90 94A60 14G50 |
| spellingShingle |
Cryptosystem Multivariate cryptography Postquantum cryptography Algebraic incidence structure Pseudorandom sequences Pseudorandom walk in graph 12Y05 12Y99 05C81 05C85 05C90 94A60 14G50 Romańczuk-Polubiec, Urszula Ustimenko, Vasyl On two windows multivariate cryptosystem depending on random parameters |
| topic_facet |
Cryptosystem Multivariate cryptography Postquantum cryptography Algebraic incidence structure Pseudorandom sequences Pseudorandom walk in graph 12Y05 12Y99 05C81 05C85 05C90 94A60 14G50 |
| format |
Article |
| author |
Romańczuk-Polubiec, Urszula Ustimenko, Vasyl |
| author_facet |
Romańczuk-Polubiec, Urszula Ustimenko, Vasyl |
| author_sort |
Romańczuk-Polubiec, Urszula |
| title |
On two windows multivariate cryptosystem depending on random parameters |
| title_short |
On two windows multivariate cryptosystem depending on random parameters |
| title_full |
On two windows multivariate cryptosystem depending on random parameters |
| title_fullStr |
On two windows multivariate cryptosystem depending on random parameters |
| title_full_unstemmed |
On two windows multivariate cryptosystem depending on random parameters |
| title_sort |
on two windows multivariate cryptosystem depending on random parameters |
| description |
The concept of multivariate bijective map of an affine space \(K^n\) over commutative Ring \(K\) was already used in Cryptography. We consider the idea of nonbijective multivariate polynomial map \(F_n\) of \(K^n\) into \(K^n\) represented as ''partially invertible decomposition'' \(F^{(1)}_nF^{(2)}_n \dots F^{(k)}_n\), \(k=k(n)\), such that knowledge on the decomposition and given value \(u=F(v)\) allow to restore a special part \(v'\) of reimage \(v\). We combine an idea of ''oil and vinegar signatures cryptosystem'' with the idea of linguistic graph based map with partially invertible decomposition to introduce a new cryptosystem. The decomposition will be induced by pseudorandom walk on the linguistic graph and its special quotient (homomorphic image). We estimate the complexity of such general algorithm in case of special family of graphs with quotients, where both graphs form known families of Extremal Graph Theory. The map created by key holder (Alice) corresponds to pseudorandom sequence of ring elements. The postquantum version of the algorithm can be obtained simply by the usage of random strings instead of pseudorandom. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1180 |
| work_keys_str_mv |
AT romanczukpolubiecurszula ontwowindowsmultivariatecryptosystemdependingonrandomparameters AT ustimenkovasyl ontwowindowsmultivariatecryptosystemdependingonrandomparameters |
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2024-04-12T06:26:01Z |
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2024-04-12T06:26:01Z |
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