On new multivariate cryptosystems with nonlinearity gap
The pair of families of bijective multivariate maps of kind Fn and Fn⁻¹ on affine space Kⁿ over finite commutative ring K given in their standard forms has a nonlinearity gap if the degree of Fn is bounded from above by independent constant d and degree of F⁻¹ is bounded from below by cⁿ, c>1. We...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2017 |
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| Language: | English |
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Інститут прикладної математики і механіки НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/156037 |
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| Cite this: | On new multivariate cryptosystems with nonlinearity gap / V. Ustimenko // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 2. — С. 331-348. — Бібліогр.: 20 назв. — англ. |
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Ustimenko, V. 2019-06-17T19:13:48Z 2019-06-17T19:13:48Z 2017 On new multivariate cryptosystems with nonlinearity gap / V. Ustimenko // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 2. — С. 331-348. — Бібліогр.: 20 назв. — англ. 1726-3255 2010 MSC:12Y05, 12Y99, 05C81, 05C85, 05C90, 94A60, 14G50. https://nasplib.isofts.kiev.ua/handle/123456789/156037 The pair of families of bijective multivariate maps of kind Fn and Fn⁻¹ on affine space Kⁿ over finite commutative ring K given in their standard forms has a nonlinearity gap if the degree of Fn is bounded from above by independent constant d and degree of F⁻¹ is bounded from below by cⁿ, c>1. We introduce examples of such pairs with invertible decomposition Fn=Gn¹Gn²…Gnk, i.e. the decomposition which allows to compute the value of Fⁿ⁻¹ in given point p=(p1,p2,…,pn) in a polynomial time O(n²). The pair of families Fn, F′n of nonbijective polynomial maps of affine space Kn such that composition FnF′n leaves each element of K∗n unchanged such that deg(Fn) is bounded by independent constant but deg(F′n) is of an exponential size and there is a decomposition Gn¹Gn²…Gnk of Fn which allows to compute the reimage of vector from F(K*ⁿ) in time 0(n²). We introduce examples of such families in cases of rings K=Fq and K=Zm. This research is partially supported by the grant PIRSES-GA-2013-612669 of the 7th Framework Programme of European Commission. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On new multivariate cryptosystems with nonlinearity gap Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
On new multivariate cryptosystems with nonlinearity gap |
| spellingShingle |
On new multivariate cryptosystems with nonlinearity gap Ustimenko, V. |
| title_short |
On new multivariate cryptosystems with nonlinearity gap |
| title_full |
On new multivariate cryptosystems with nonlinearity gap |
| title_fullStr |
On new multivariate cryptosystems with nonlinearity gap |
| title_full_unstemmed |
On new multivariate cryptosystems with nonlinearity gap |
| title_sort |
on new multivariate cryptosystems with nonlinearity gap |
| author |
Ustimenko, V. |
| author_facet |
Ustimenko, V. |
| publishDate |
2017 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
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Інститут прикладної математики і механіки НАН України |
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Article |
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The pair of families of bijective multivariate maps of kind Fn and Fn⁻¹ on affine space Kⁿ over finite commutative ring K given in their standard forms has a nonlinearity gap if the degree of Fn is bounded from above by independent constant d and degree of F⁻¹ is bounded from below by cⁿ, c>1. We introduce examples of such pairs with invertible decomposition Fn=Gn¹Gn²…Gnk, i.e. the decomposition which allows to compute the value of Fⁿ⁻¹ in given point p=(p1,p2,…,pn) in a polynomial time O(n²).
The pair of families Fn, F′n of nonbijective polynomial maps of affine space Kn such that composition FnF′n leaves each element of K∗n unchanged such that deg(Fn) is bounded by independent constant but deg(F′n) is of an exponential size and there is a decomposition Gn¹Gn²…Gnk of Fn which allows to compute the reimage of vector from F(K*ⁿ) in time 0(n²). We introduce examples of such families in cases of rings K=Fq and K=Zm.
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| issn |
1726-3255 |
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https://nasplib.isofts.kiev.ua/handle/123456789/156037 |
| citation_txt |
On new multivariate cryptosystems with nonlinearity gap / V. Ustimenko // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 2. — С. 331-348. — Бібліогр.: 20 назв. — англ. |
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AT ustimenkov onnewmultivariatecryptosystemswithnonlinearitygap |
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2025-12-07T17:45:37Z |
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2025-12-07T17:45:37Z |
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1850872469705981952 |