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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2015 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152793 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862620104907292672 |
|---|---|
| author | Romańczuk-Polubiec, U. Ustimenko, V. |
| author_facet | Romańczuk-Polubiec, U. Ustimenko, V. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T13:21:08Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-152793 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T13:21:08Z |
| publishDate | 2015 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Romańczuk-Polubiec, U. Ustimenko, V. 2019-06-12T21:06:07Z 2019-06-12T21:06:07Z 2015 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. https://nasplib.isofts.kiev.ua/handle/123456789/152793 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. Authors were the participants of the International Algebraic Conferencededicated to 100-th anniversary of l. A. Kaluzhnin (July 7-12, 2014, Kyiv,Ukraine). Our paper is dedicated to the memory of Lev Kaluznin and hisachievements in Mathematics. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On two windows multivariate cryptosystem depending on random parameters Article published earlier |
| spellingShingle | On two windows multivariate cryptosystem depending on random parameters Romańczuk-Polubiec, U. Ustimenko, V. |
| title | 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_short | On two windows multivariate cryptosystem depending on random parameters |
| title_sort | on two windows multivariate cryptosystem depending on random parameters |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152793 |
| work_keys_str_mv | AT romanczukpolubiecu ontwowindowsmultivariatecryptosystemdependingonrandomparameters AT ustimenkov ontwowindowsmultivariatecryptosystemdependingonrandomparameters |