On two windows multivariate cryptosystem depending on random parameters
The concept of multivariate bijective map of an affine space Kn over commutative Ring K was already used in Cryptography. We consider the idea of nonbijective multivariate polynomial map Fn of Kn into Kn represented as ''partially invertible decomposition'' F(1)nF(2)n…F(k)n, k=k...
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| Datum: | 2015 |
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Інститут прикладної математики і механіки НАН України
2015
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| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/152793 |
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| Zitieren: | On two windows multivariate cryptosystem depending on random parameters / U. Romańczuk-Polubiec, V. Ustimenko // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 1. — С. 101-129. — Бібліогр.: 46 назв. — англ. |
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irk-123456789-1527932019-06-13T01:25:37Z On two windows multivariate cryptosystem depending on random parameters Romańczuk-Polubiec, U. Ustimenko, V. The concept of multivariate bijective map of an affine space Kn over commutative Ring K was already used in Cryptography. We consider the idea of nonbijective multivariate polynomial map Fn of Kn into Kn represented as ''partially invertible decomposition'' F(1)nF(2)n…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. 2015 Article On two windows multivariate cryptosystem depending on random parameters / U. Romańczuk-Polubiec, V. Ustimenko // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 1. — С. 101-129. — Бібліогр.: 46 назв. — англ. 1726-3255 2010 MSC:12Y05, 12Y99, 05C81, 05C85, 05C90, 94A60, 14G50. http://dspace.nbuv.gov.ua/handle/123456789/152793 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| description |
The concept of multivariate bijective map of an affine space Kn over commutative Ring K was already used in Cryptography. We consider the idea of nonbijective multivariate polynomial map Fn of Kn into Kn represented as ''partially invertible decomposition'' F(1)nF(2)n…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. |
| format |
Article |
| author |
Romańczuk-Polubiec, U. Ustimenko, V. |
| spellingShingle |
Romańczuk-Polubiec, U. Ustimenko, V. On two windows multivariate cryptosystem depending on random parameters Algebra and Discrete Mathematics |
| author_facet |
Romańczuk-Polubiec, U. Ustimenko, V. |
| author_sort |
Romańczuk-Polubiec, U. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152793 |
| citation_txt |
On two windows multivariate cryptosystem depending on random parameters / U. Romańczuk-Polubiec, V. Ustimenko // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 1. — С. 101-129. — Бібліогр.: 46 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT romanczukpolubiecu ontwowindowsmultivariatecryptosystemdependingonrandomparameters AT ustimenkov ontwowindowsmultivariatecryptosystemdependingonrandomparameters |
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2025-07-14T04:17:09Z |
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2025-07-14T04:17:09Z |
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1837594448837476352 |