Results 1 to 10 of about 1,050,138 (224)
Chebyshev Action on Finite Fields [PDF]
Discrete Mathematics, 2013 Given a polynomial f and a finite field F one can construct a directed graph where the vertices are the values in the finite field, and emanating from each vertex is an edge joining the vertex to its image under f.
Gassert, T. Alden
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On multiplication in finite fields
Journal of Complexity, 2010 The authors introduce complexity notions and give a brief review of algebraic fields. They propose a method for multiplication in finite fields. The method is shown to be a significant improvement over the best known bilinear complexities for certain finite fields.
Murat Cenk, Ferruh Özbudak
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Finite fields and cryptology [PDF]
Computer Science Journal of Moldova, 2003 The problem of a computationally feasible method of finding the discrete logarithm in a (large) finite field is discussed, presenting the main algorithms in this direction.
Ennio Cortellini
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Model theory of finite fields and pseudo-finite fields
Annals of Pure and Applied Logic, 1997 This article gives a survey of the main results obtained to date on finite fields and pseudo-finite fields. In his famous paper ``The elementary theory of finite fields'' [Ann. Math. (2) 88, 239-271 (1968; Zbl 0195.05701)], \textit{J. Ax} has shown that the set \(T_f\) of sentences true in all finite fields is decidable.
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Probabilistic Algorithms in Finite Fields [PDF]
SIAM Journal on Computing, 1980 We present probabilistic algorithms for the problems of finding an irreducible polynomial of degree n over a finite field, finding roots of a polynomial, and factoring a polynomial into its irreducible factors over a finite field. All of these problems are of importance in algebraic coding theory, algebraic symbol manipulation, and number theory. These
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Algebraic Properties of Finite Neutrosophic Fields [PDF]
Neutrosophic Sets and Systems, 2022 We explore a finite Neutrosophic field 𝑭𝒑 (𝑰) and its Neutrosophic multiplicative group 𝑭𝒑 (𝑰) × in this study. We first show |𝑭𝒑 (𝑰) ×| = (𝒑 − 𝟏) 𝟐 and then its algebraic properties are studied.
T. Chalapathi +2 more
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Crooked Maps in Finite Fields [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We consider the maps $f:\mathbb{F}_{2^n} →\mathbb{F}_{2^n}$ with the property that the set $\{ f(x+a)+ f(x): x ∈F_{2^n}\}$ is a hyperplane or a complement of hyperplane for every $a ∈\mathbb{F}_{2^n}^*$.
Gohar Kyureghyan
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Ternary number systems in finite fields [PDF]
Компьютерная оптика, 2018 The work continues the author's previous study of positional number systems in finite fields. The paper considers ternary number systems and arithmetic operations algorithms for the representation of elements of finite fields in the so-called ternary ...
Vladimir Chernov
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The Applications of Algebraic Polynomial Rings in Satellite Coding and Cryptography [PDF]
Mathematics Interdisciplinary Research, 2022 This survey illustrates and investigates the application of polynomial rings over finite fields to generate PRN codes for Global Navigation Satellite System (GNSS) satellites.
Amir Bagheri, Hassan Emami
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Some Multisecret-Sharing Schemes over Finite Fields
Mathematics, 2020 A secret sharing scheme is a method of assigning shares for a secret to some participants such that only some distinguished subsets of these subsets can recover the secret while other subsets cannot.
Selda Çalkavur, Patrick Solé
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