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A Novel Cipher-Based Data Encryption with Galois Field Theory [PDF]
Sensors, 2023 Both the act of keeping information secret and the research on how to achieve it are included in the broad category of cryptography. When people refer to “information security,” they are referring to the study and use of methods that make data transfers ...
Mohammad Mazyad Hazzazi +3 more
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RGB image encryption using SPN with a novel block cipher over simple graph adjacency matrices and Galois fields [PDF]
Scientific ReportsThis paper presents a construction of a secure image encryption scheme with graph theory, Galois field, and substitution-permutation network (SPN) for enhanced multimedia data security.
Muhammad Sajjad, Nawaf A. Alqwaifly
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The $q$-analogue of the wild fundamental group and the inverse problem of the Galois theory of $q$-difference equations [PDF]
Annales scientifiques de l'École normale supérieure, 2015 In previous papers, we defined $q$-analogues of alien derivations for linear analytic $q$-difference equations with integral slopes and proved a density theorem (in the Galois group) and a freeness theorem. In this paper, we completely describe the wild fundamental group and apply this result to the inverse problem in $q$-difference Galois theory.
Ramis, Jean-Pierre, Sauloy, Jacques
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Seven Small Simple Groups Not Previously Known to Be Galois Over
Mathematics, 2022 In this note we realize seven small simple groups as Galois groups over Q. The technique that we employ is the determination of the images of Galois representations attached to modular and automorphic forms, relying in two cases on recent results of ...
Luis Dieulefait +2 more
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Coaction and double-copy properties of configuration-space integrals at genus zero
Journal of High Energy Physics, 2021 We investigate configuration-space integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and double-copy structures generalizing the Kawai-Lewellen-Tye (KLT) relations in string theory.
Ruth Britto +3 more
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Abelian constraints in inverse Galois theory [PDF]
manuscripta mathematica, 2008 Let \(k\) be a field, \(B\) a \(k\)-curve (i.e. a smooth projective and geometrically connected \(k\)-scheme of dimension 1), \(G\) a finite group, \(f:Y\to B\) a \(k\)-\(G\)-cover of curves with group \(G\) and ramification indices \(e_1,\dots,e_r\) and let \(P\) be ant subgroup of \(G\) of index \(m.\) Assume that the branch divisor of \(f:Y\to B ...
Cadoret, Anna, Dèbes, Pierre
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On the Constructive Inverse Problem in Differential Galois Theory# [PDF]
Communications in Algebra, 2005 Several misprints have been corrected and the statement of Propositions 3.2 and 3.4 have been made more precise and their proofs ...
Cook, William +2 more
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AN EXPLICIT PSp4(3)-POLYNOMIAL WITH 3 PARAMETERS OF DEGREE 40 [PDF]
, 2011 We will give an explicit polynomial over ℚ with 3 parameters of degree 40 as a result of the inverse Galois problem. Its Galois group over ℚ (resp. ℚ(√-3)) is isomorphic to PGSp4(3) (resp. PSp4(3)) and it is a regular PSp4(3)-polynomial over ℚ(p√−3).
Kitayama, Hidetaka
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Differential Galois theory III: Some inverse problems
Illinois Journal of Mathematics, 1997 [For Part I see ibid. 42, No. 4, 678-699 (1998; Zbl 0916.03028). Part II is reviewed above.] In Part I, the author developed a theory of differential Galois extensions, generalizing Kolchin's theory of strongly normal extensions. It was shown that arbitrary finite-dimensional differential algebraic groups can arise as differential Galois groups for ...
Marker, David, Pillay, Anand
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The Galois group of a stable homotopy theory [PDF]
, 2016 To a "stable homotopy theory" (a presentable, symmetric monoidal stable $\infty$-category), we naturally associate a category of finite \'etale algebra objects and, using Grothendieck's categorical machine, a profinite group that we call the Galois group.
Mathew, Akhil
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