Results 1 to 10 of about 3,441,413 (166)

A message recovery attack on multivariate polynomial trapdoor function [PDF]

PeerJ Computer Science, 2023
Cybersecurity guarantees the exchange of information through a public channel in a secure way. That is the data must be protected from unauthorized parties and transmitted to the intended parties with confidentiality and integrity. In this work, we mount
Rashid Ali, Muhammad Mubashar Hussain, Shamsa Kanwal, Fahima Hajjej, Saba Inam   +4 more
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Algebraic Cryptanalysis Scheme of AES-256 Using Gröbner Basis [PDF]

Journal of Electrical and Computer Engineering, 2017
The zero-dimensional Gröbner basis construction is a crucial step in Gröbner basis cryptanalysis on AES-256. In this paper, after performing an in-depth study on the linear transformation and the system of multivariate polynomial equations of AES-256 ...
Kaixin Zhao, Jie Cui, Zhiqiang Xie
doaj   +2 more sources

A novel linear algebra-based method for complex interval linear systems in circuit analysis [PDF]

Heliyon
In this paper, systems of multivariate interval linear equations with complex interval coefficients are examined, and a novel linear algebra-based approach for locating all of their solutions is proposed.
Maryam Farahmand Nejad, Hamed Farahani, Rahele Nuraei   +2 more
doaj   +2 more sources

Feynman integral reduction using Gröbner bases

Journal of High Energy Physics, 2023
We investigate the reduction of Feynman integrals to master integrals using Gröbner bases in a rational double-shift algebra Y in which the integration-by-parts (IBP) relations form a left ideal.
Mohamed Barakat, Robin Brüser, Claus Fieker, Tobias Huber, Jan Piclum   +4 more
doaj   +1 more source

Divisors on graphs, Connected flags, and Syzygies [PDF]

Discrete Mathematics & Theoretical Computer Science, 2013
We study the binomial and monomial ideals arising from linear equivalence of divisors on graphs from the point of view of Gröbner theory. We give an explicit description of a minimal Gröbner basis for each higher syzygy module.
Fatemeh Mohammadi, Farbod Shokrieh
doaj   +1 more source

On involutive division on monoids

Discrete and Continuous Models and Applied Computational Science, 2021
We consider an arbitrary monoid MM, on which an involutive division is introduced, and the set of all its finite subsets SetMM. Division is considered as a mapping d:SetMM{d:SetM \times M}, whose image d(U,m){d(U,m)} is the set of divisors of mm in UU ...
Oleg K. Kroytor, Mikhail D. Malykh
doaj   +1 more source

Arf numerical semigroups with high multiplicity via Gröbner basis

Applied Mathematics in Science and Engineering, 2023
In this paper, Arf numerical semigroups with high multiplicity are given. RF (Row Factorization)-matrices, Gröbner basis are presented by writing the ideals of numerical semigroup with RF-matrices.
Belgin Özer
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Exploring Gröbner bases for practical problem-solving applications [PDF]

Computational Algorithms and Numerical Dimensions
Gröbner bases serve as a crucial theoretical cornerstone in contemporary (polynomial) ring theory. The development of Gröbner basis theory originated from efforts to address theoretical issues related to ideals in polynomial rings and to solve systems of
Hamed Farahani
doaj   +1 more source

Gröbner–Shirshov Bases Theory for Trialgebras

Mathematics, 2021
We establish a method of Gröbner–Shirshov bases for trialgebras and show that there is a unique reduced Gröbner–Shirshov basis for every ideal of a free trialgebra.
Juwei Huang, Yuqun Chen
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PBW Basis of the Modified Ringel–Hall Algebra of Type An via Gröbner–Shirshov Basis

Journal of Mathematics, 2023
In the Ringel–Hall algebra of Dynkin type, the set of all commutator relations between the isoclasses of indecomposable representations forms a minimal Gröbner–Shirshov basis, and the set of the corresponding irreducible elements forms a PBW-type basis ...
Desheng Hu, Abdukadir Obul
doaj   +1 more source