On new multivariate cryptosystems with nonlinearity gap
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On new multivariate cryptosystems with nonlinearity gap
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| Creator |
Ustimenko, V.
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| 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. |
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| Date |
2019-06-17T19:13:48Z
2019-06-17T19:13:48Z 2017 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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