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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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Differential Galois theory III: Some inverse problems [PDF]
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 ...
David Marker, Anand Pillay
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On the Inverse Problem of Galois Theory of Differential Fields [PDF]
Proceedings of the American Mathematical Society, 1964 1. All fields considered here are of characteristic 0. Let F be a field, let C be an algebraically closed subfield of F. Let G be a connected algebraic group defined over C. F(G) denotes the field of all rational functions on G defined over F. If gCG then F(g) denotes the field generated by g over F. We shall say that a derivation of F(G) commutes with
A. Bialynicki-Birula
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On the inverse problem of Galois theory [PDF]
Publicacions Matemàtiques, 1992 The problem of the construction of number fields with Galois group over Q a given finite groups has made considerable progress in recent years. The aim of this paper is to survey the current state of this problem, giving the most significant methods developed in connection with it.
Núria Vila
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On the inverse problem of Galois theory [PDF]
Transactions of the American Mathematical Society, 1975 Let k k be a field, F F a finite subfield and G G a connected solvable algebraic matric group defined over F F . Conditions on G G and k k are given which ensure the existence of a Galois extension of k k with group isomorphic to
J. Kovacic
+5 more sources
Galois Theory for Inverse Semigroup Orthogonal Actions [PDF]
, 2020 A Galois correspondence theorem is proved for the case of inverse semigroups acting orthogonally on commutative rings as a consequence of the Galois correspondence theorem for groupoid actions. To this end, we use a classic result of inverse semigroup theory that establishes a one-to-one correspondence between inverse semigroups and inductive groupoids.
Wesley G. Lautenschlaeger +1 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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Semi-topological Galois theory and the inverse Galois problem [PDF]
, 2010 23 ...
Hsuan-Yi Liao, Jyh-Haur Teh
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On the finite inverse problem in iterative differential Galois theory [PDF]
, 2010 In positive characteristic, nearly all Picard-Vessiot extensions are inseparable over some intermediate iterative differential extensions. In the Galois correspondence, these intermediate fields correspond to nonreduced subgroup schemes of the Galois group scheme. Moreover, the Galois group scheme itself may be nonreduced, or even infinitesimal.
Andreas Maurischat
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The inverse problem of differential Galois theory over the field R(z) [PDF]
, 2008 23 ...
Tobias Dyckerhoff
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