5 citations · 23 across the 13 of their papers we have counts for
14 papers
On the Andrews-Curtis groups: non-finite presentability
Vitaly Roman'kov
The Andrews-Curtis conjecture remains one of the outstanding open problems in combinatorial group theory. It claims that every normally generating -tuple of a free group o…
Equations over solvable groups
Anton A. Klyachko, Mikhail A. Mikheenko, Vitaly A. Roman'kov
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…
Multi-recipient and threshold encryption based on hidden multipliers
Vitaly Roman'kov
Let be a pool of 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 coali…
Undecidability of the submonoid membership problem for a sufficiently large finite direct power of the Heisenberg group
Vitaly Roman'kov
The submonoid membership problem for a finitely generated group is the decision problem, where for a given finitely generated submonoid of and a group element it is…
Multiparty secret sharing based on hidden multipliers
Vitaly Roman'kov
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 inve…
Embedding theorems for solvable groups
Vitaly Roman'kov
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 lying in a variety ${\ma…
The stabilizer of a column in a matrix group over a polynomial ring
Vitaly Roman'kov
An original non-standard approach to describing the structure of a column stabilizer in a group of matrices over a polynomial ring or a Laurent polynomial ring of …
Cryptanalysis of a new version of the MOR scheme
Vitaly Roman'kov
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…
A general encryption scheme using two-sided multiplications with its cryptanalysis
V. A. Roman'kov
We show that many known schemes of the public key exchange protocols in the algebraic cryptography, that use two-sided multiplications, are the specific cases of the general scheme…
Polycyclic, metabelian or soluble of type (FP) groups with boolean algebra of rational sets and biautomatic soluble groups are virtually abelian
Vitaly Roman'kov
Let be a polycyclic, metabelian or soluble of type (FP) group such that the class of all rational subsets of is a boolean algebra. Then is virtually…
A polynomial time algorithm for the braid double shielded public key cryptosystems
Vitaly Roman'kov
We propose new provable practical deterministic polynomial time algorithm for the braid Wang, Xu, Li, Lin and Wang Double shielded public key cryptosystems. We show that a linear d…
The linearity problem for the unitriangular automorphism groups of free groups
V. Roman'kov
We prove that the unitriangular automorphism group of a free group of rank has a faithful representation by matrices over a field, or in other words, it is a linear group, if a…
The twisted conjugacy problem for pairs of endomorphisms in nilpotent groups
V. Roman'kov, E. Ventura
An algorithm is constructed that, when given an explicit presentation of a finitely generated nilpotent group decides for any pair of endomorphisms and any pai…
On the Reidemeister spectrum and the property for some free nilpotent groups
E. G. Kukina, V. Roman'kov
We describe the Reidemeister spectrum for the free nilpotent group of rank and class in the cases: and and…