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pro vyhledávání: '"Roman'kov, Vitaly"'
Autor:
Roman'kov, Vitaly
The Andrews-Curtis conjecture remains one of the outstanding open problems in combinatorial group theory. It claims that every normally generating $r$-tuple of a free group $F_r$ of rank $r\geq 2$ can be reduced to a basis by means of Nielsen transfo
Externí odkaz:
http://arxiv.org/abs/2305.11838
Publikováno v:
Journal of Algebra, 638 (2024), 739-750
Not any nonsingular equation over a metabelian group has solution in a larger metabelian group. However, any nonsingular equation over a solvable group with a subnormal series with abelian torsion-free quotients has a solution in a larger group with
Externí odkaz:
http://arxiv.org/abs/2303.13240
Autor:
Roman'kov, Vitaly
Publikováno v:
journal of Groups, complexity, cryptology, Volume 14, Issue 2 (March 21, 2023) gcc:10150
Let $S$ be a pool of $s$ parties and Alice be the dealer. In this paper, we propose a scheme that allows the dealer to encrypt messages in such a way that only one authorized coalition of parties (which the dealer chooses depending on the message) ca
Externí odkaz:
http://arxiv.org/abs/2210.06889
Autor:
Roman'kov, Vitaly
The submonoid membership problem for a finitely generated group $G$ is the decision problem, where for a given finitely generated submonoid $M$ of $G$ and a group element $g$ it is asked whether $g \in M$. In this paper, we prove that for a sufficien
Externí odkaz:
http://arxiv.org/abs/2209.14786
Autor:
Roman'kov, Vitaly
Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular, multiplicative gr
Externí odkaz:
http://arxiv.org/abs/2108.06967
Publikováno v:
In Journal of Algebra 15 January 2024 638:739-750
Autor:
Roman'kov, Vitaly
In this paper, we prove a series of results on group embeddings in groups with a small number of generators. We show that each finitely generated group $G$ lying in a variety ${\mathcal M}$ can be embedded in a $4$-generated group $H \in {\mathcal M}
Externí odkaz:
http://arxiv.org/abs/2009.09958
Autor:
Roman'kov, Vitaly
Publikováno v:
Prikladnaya Discretnaya Matematika, 48 (2020), 34-42
An original non-standard approach to describing the structure of a column stabilizer in a group of $n \times n$ matrices over a polynomial ring or a Laurent polynomial ring of $n$ variables is presented. The stabilizer is described as an extension of
Externí odkaz:
http://arxiv.org/abs/2001.07096
Autor:
Roman'kov, Vitaly
We show that an attack based on the linear decomposition method introduced by the author can be efficiently applied to the new version of the MOR scheme proposed in \cite{BMSS}. We draw attention to some inaccuracies in the description of this versio
Externí odkaz:
http://arxiv.org/abs/1911.00895
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