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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| Видавець: | Інститут прикладної математики і механіки НАН України |
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| Дата: | 2017 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2017
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/156037 |
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| Цитувати: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1560372019-06-18T01:31:12Z On new multivariate cryptosystems with nonlinearity gap Ustimenko, V. 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. 2017 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/156037 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Ustimenko, V. |
| spellingShingle |
Ustimenko, V. On new multivariate cryptosystems with nonlinearity gap Algebra and Discrete Mathematics |
| author_facet |
Ustimenko, V. |
| author_sort |
Ustimenko, V. |
| title |
On new multivariate cryptosystems with nonlinearity gap |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT ustimenkov onnewmultivariatecryptosystemswithnonlinearitygap |
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2023-05-20T17:48:50Z |
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2023-05-20T17:48:50Z |
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1796154145187561472 |