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Title: | On new multivariate cryptosystems with nonlinearity gap |
Authors: | Ustimenko, V. |
Keywords: | multivariate cryptography linguistic graphs multiva-riate stable maps |
Issue Date: | 2017 |
Series/Report no.: | математичні науки; |
Abstract: | 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 c n, c > 1. We introduce examples of such pairs with invertible decomposition Fn = G1 nG2 n . . . Gk n, i.e. the decomposition which allows to compute the value of F n−1 in given point p = (p1, p2, . . . , pn) in a polynomial time O(n 2 ). 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 decom- position G1 nG2 n . . . Gk n of Fn which allows to compute the reimage of vector from F(K∗n ) in time 0(n 2 ). We introduce examples of such families in cases of rings K = Fq and K = Zm. |
Description: | Ustimenko V. On new multivariate cryptosystems with nonlinearity gap / V. Ustimenko // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 2. - Рp. 331 - 348 |
URI: | http://hdl.handle.net/123456789/4681 |
Appears in Collections: | Algebra and Discrete Mathematics. - № 2 (23). - 2017 |
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