Zobrazeno 1 - 10
of 433
pro vyhledávání: '"Grigoriev, Dima"'
Autor:
Berenstein, Arkady, Grigoriev, Dima
The aim of this paper is to build a theory of commutative and noncommutative injective valuations of various algebras. The targets of our valuations are (well-)ordered commutative and noncommutative (partial or entire) semigroups including any sub-se
Externí odkaz:
http://arxiv.org/abs/2405.00470
Autor:
Grigoriev, Dima
For a tropical prevariety $V\subset \RR^n$ (being a finite union of rational polyhedra) two tropical polynomials belong to the same congruence class iff they coincide on $V$. We define a tropical Hilbert function $TH_V(k)$ as the dimension of the fam
Externí odkaz:
http://arxiv.org/abs/2404.06440
Autor:
Grigoriev, Dima
For tropical $n$-variable polynomials $f, g$ a criterion of containment for tropical hypersurfaces $Trop(f)\subset Trop(g)$ is provided in terms of their Newton polyhedra $N(f), N(g)\subset \mathbb{R}^{n+1}$. Namely, $Trop(f)\subset Trop(g)$ iff for
Externí odkaz:
http://arxiv.org/abs/2402.18384
Autor:
Radulescu, Ovidiu, Grigoriev, Dima, Seiss, Matthias, Douaihy, Maria, Lagha, Mounia, Bertrand, Edouard
Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. We solve the inverse problem: given a phase-type distribution, can we i
Externí odkaz:
http://arxiv.org/abs/2311.03593
We use tropical algebras as platforms for a very efficient digital signature protocol. Security relies on computational hardness of factoring one-variable tropical polynomials; this problem is known to be NP-hard.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2309.11256
Publikováno v:
Journal of Mathematical Cryptology, Vol 18, Iss 1, Pp 2624-32 (2024)
We use tropical algebras as platforms for a very efficient digital signature protocol. Security relies on computational hardness of factoring one-variable tropical polynomials; this problem is known to be NP-hard. We also offer countermeasures agains
Externí odkaz:
https://doaj.org/article/5710eeaa5f6e487aa7edbdd149d9d280
We offer a digital signature scheme using Boolean automorphisms of a multivariate polynomial algebra over integers. Verification part of this scheme is based on the approximation of the number of zeros of a multivariate Boolean function.
Comment
Comment
Externí odkaz:
http://arxiv.org/abs/2306.11303
We offer two very transparent digital signature schemes: one using non-square matrices and the other using scrap automorphisms. The former can be easily converted to a public key encryption scheme.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2306.08927
Autor:
Elizarov, Nikita, Grigoriev, Dima
For a tropical univariate polynomial $f$ we define its tropical Hilbert function as the dimension of a tropical linear prevariety of solutions of the tropical Macauley matrix of the polynomial up to a (growing) degree. We show that the tropical Hilbe
Externí odkaz:
http://arxiv.org/abs/2111.14742
Autor:
Grigoriev, Dima
Tropical Newton-Puiseux polynomials defined as piece-wise linear functions with rational coefficients at the variables, play a role of tropical algebraic functions. We provide explicit formulas for tropical Newton-Puiseux polynomials being the tropic
Externí odkaz:
http://arxiv.org/abs/2110.10712