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A New Secret Sharing Scheme Based on Polynomials over Finite Fields
Mathematics, 2020 In this paper, we examine a secret sharing scheme based on polynomials over finite fields. In the presented scheme, the shares can be used for the reconstruction of the secret using polynomial multiplication. This scheme is both ideal and perfect.
Selda Çalkavur +2 more
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Uniform estimates for smooth polynomials over finite fields
Discrete Analysis, 2023 Uniform estimates for smooth polynomials over finite fields, Discrete Analysis 2023:16, 31 pp. A positive integer $n$ is called $m$-_smooth_ if its largest prime factor has size at most $m$.
Ofir Gorodetsky
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On Some Computational and Applications of Finite Fields
Ratio Mathematica, 2020 Finite field is a wide topic in mathematics. Consequently, none can talk about the whole contents of finite fields. That is why this research focuses on small content of finite fields such as polynomials computational, ring of integers modulo p where p ...
Jean Pierre Muhirwa
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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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ORTHOGONAL SYSTEMS AND PERMUTATION POLYNOMIAL VECTORS OVER MODULAR ALGEBRAS
Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales, 2023 Known results on orthogonal systems and permutation polynomials vectors over finite fields are extended to modular algebras of the form Lν = K[X]/(p(X)ν ), where K is a finite field, p(X) ∈ K[X] is an irreducible polynomial, ν = 1, 2, . .
Victor Gonzalez
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On the Planarity of Certain Dembowski-Ostrom Polynomials
Süleyman Demirel Üniversitesi Fen-Edebiyat Fakültesi Fen Dergisi, 2022 Planar mappings, defined by Dembowski and Ostrom, are identified as a means to construct projective planes. Then, many important applications of planar mappings appear in different fields such as cryptography and coding theory.
Zehra Aksoy, Barış Bülent Kırlar
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On permutation polynomials over finite fields
International Journal of Mathematics and Mathematical Sciences, 1987 A polynomial f over a finite field F is called a permutation polynomial if the mapping F→F defined by f is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a ...
R. A. Mollin, C. Small
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The review on elliptic curves as cryptographic pairing groups [PDF]
Mathematics and Computational Sciences, 2021 Elliptic curve is a set of two variable points on polynomials of degree 3 over a field acted by an addition operation that forms a group structure. The motivation of this study is the mathematics behind that elliptic curve to the applicability within a ...
E Khamseh
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On some permutation polynomials over finite fields
International Journal of Mathematics and Mathematical Sciences, 2005 Let p be prime, q=pm, and q−1=7s. We completely describe the permutation behavior of the binomial P(x)=xr(1+xes) (1≤e≤6) over a finite field Fq in terms of the sequence {an} defined by the recurrence relation an=an−1+2an−2−an−3 (n≥3) with initial ...
Amir Akbary, Qiang Wang
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Lower Bound of the Complexity of Seven-Valued Functions in the Class of Polarized Polynomials
Известия Иркутского государственного университета: Серия "Математика", 2017 One of the directions of the investigation of functions over finite fields is the study of their representations, including polynomial ones. In the area of polynomial representations of functions the problem of estimating the complexity of such ...
A.S. Baliuk, A.S. Zinchenko
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