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pro vyhledávání: '"Ushakov Alexander"'
Autor:
Ushakov, Alexander
Publikováno v:
journal of Groups, complexity, cryptology, Volume 16, Issue 1 (July 9, 2024) gcc:13555
In this paper we analyze computational properties of the Diophantine problem (and its search variant) for spherical equations $\prod_{i=1}^m z_i^{-1} c_i z_i = 1$ (and its variants) over the class of finite metabelian groups $G_{p,n}=\mathbb{Z}_p^n \
Externí odkaz:
http://arxiv.org/abs/2405.03591
Autor:
Ushakov, Alexander, Weiers, Chloe
In this paper we study the complexity of solving quadratic equations in the lamplighter group. We give a complete classification of cases (depending on genus and other characteristics of a given equation) when the problem is $\mathbf{NP}$-complete or
Externí odkaz:
http://arxiv.org/abs/2401.08589
In this paper we investigate computational properties of the Diophantine problem for spherical equations in some classes of finite groups. We classify the complexity of different variations of the problem, e.g., when $G$ is fixed and when $G$ is a pa
Externí odkaz:
http://arxiv.org/abs/2308.12841
Autor:
Mandel, Richard, Ushakov, Alexander
For a finitely generated group $G$, the \emph{Diophantine problem} over $G$ is the algorithmic problem of deciding whether a given equation $W(z_1,z_2,\ldots,z_k) = 1$ (perhaps restricted to a fixed subclass of equations) has a solution in $G$. In th
Externí odkaz:
http://arxiv.org/abs/2302.06974
Autor:
Mandel, Richard, Ushakov, Alexander
Consider the equation $q_1\alpha^{x_1}+\dots+q_k\alpha^{x_k} = q$, with constants $\alpha \in \overline{\mathbb{Q}} \setminus \{0,1\}$, $q_1,\ldots,q_k,q\in\overline{\mathbb{Q}}$ and unknowns $x_1,\ldots,x_k$, referred to in this paper as an \emph{al
Externí odkaz:
http://arxiv.org/abs/2210.00086
We prove that the conjugacy problem in the first Grigorchuck group $\Gamma$ can be solved in linear time. Furthermore, the problem to decide if a list of elements $w_1,\ldots,w_k\in\Gamma$ contains a pair of conjugate elements can be solved in linear
Externí odkaz:
http://arxiv.org/abs/2011.04028
Autor:
Nikolaev, Andrey, Ushakov, Alexander
Publikováno v:
journal of Groups, complexity, cryptology, Volume 12, Issue 1 (June 24, 2020) gcc:6541
We consider a group-theoretic analogue of the classic subset sum problem. In this brief note, we show that the subset sum problem is NP-complete in the first Grigorchuk group. More generally, we show NP-hardness of that problem in weakly regular bran
Externí odkaz:
http://arxiv.org/abs/2006.03470
Akademický článek
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Autor:
Mandel, Richard, Ushakov, Alexander
Publikováno v:
In Journal of Algebra 15 December 2023 636:779-803
Publikováno v:
Journal of Mathematical Cryptology, Vol 17, Iss 1, Pp 1-5 (2023)
In this article, we analyze two digital signature schemes, proposed in Moldovyan et al., that use finite noncommutative associative algebras as underlying platforms. We prove that these schemes do not possess the claimed property of being quantum saf
Externí odkaz:
https://doaj.org/article/eff3810a14e2465aa98349b5a2527414