Results 51 to 60 of about 127,631 (176)

A METHOD OF CONSTRUCTING A BLOCK CIPHERS ROUND FUNCTION’S POLYNOMIAL OVER A FINITE FIELD

Современные информационные технологии и IT-образование, 2018
The work outlines the method of construction of round function as a polynomial of one variable over the finite field. The proposed method is based on the calculation of the initial cryptographic transformation at special points of the finite field and ...
Sergey A. Belov
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Mean Value Theorems for L-functions over Prime Polynomials for the Rational Function Field

, 2013
The first and second moments are established for the family of quadratic Dirichlet $L$--functions over the rational function field at the central point $s=\tfrac{1}{2}$ where the character $\chi$ is defined by the Legendre symbol for polynomials over ...
Andrade, Julio C., Keating, Jonathan P.
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Cyclotomy and permutation polynomials of large indices [PDF]

, 2012
We use cyclotomy to design new classes of permutation polynomials over finite fields. This allows us to generate many classes of permutation polynomials in an algorithmic way.
Wang, Qiang
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Vector finite fields of characteristic two as algebraic support of multivariate cryptography [PDF]

Computer Science Journal of Moldova
The central issue of the development of the multivariate public key algorithms is the design of reversible non-linear mappings of $n$-dimensional vectors over a finite field, which can be represented in a form of a set of power polynomials. For the first
Alexandr Moldovyan, Nikolay Moldovyan
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On the Irreducibility of Some Composite Polynomials

Journal of Mathematical Extension, 2012
. In this paper we study the irreducibility of some composite polynomials, constructed by a polynomial composition method over finite fields. Finally, a recurrent method for constructing families of irreducible polynomials of higher degree from given ...
M. Alizadeh
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Factorization of Polynomials Over Finite Fields [PDF]

Mathematics of Computation, 1969
If f ( x ) f(x) is a polynomial over G F ( q ) GF(q) , we observe (as has Berlekamp) that if h ( x ) q ≡ h ( x ) ( mod f
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A New Root-Finding Algorithm for Solving Real-World Problems and Its Complex Dynamics via Computer Technology

Complexity, 2021
Nowadays, the use of computers is becoming very important in various fields of mathematics and engineering sciences. Many complex statistics can be sorted out easily with the help of different computer programs in seconds, especially in computational and
Amir Naseem, M. A. Rehman, Jihad Younis
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Permutation polynomials of degree 8 over finite fields of odd characteristic

, 2019
This paper provides an algorithmic generalization of Dickson's method of classifying permutation polynomials (PPs) of a given degree $d$ over finite fields. Dickson's idea is to formulate from Hermite's criterion several polynomial equations satisfied by
Fan, Xiang
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Dickson Polynomials and Irreducible Polynomials Over Finite Fields

Journal of Number Theory, 1994
For the finite field of order \(q\), \(\mathbb{F}_ q\), let \[ D_ n(x,a)= \sum_{j=0}^{\lfloor n/2\rfloor} {\textstyle {n \over {n-j}}} \left( \begin{smallmatrix} n-j\\ j\end{smallmatrix} \right) (-a)^ j x^{n-2j} \] denote the Dickson polynomial of degree \(n\) with parameter \(a\in \mathbb{F}_ q\).
Gao, S.H., Mullen, G.L.
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Stronger arithmetic equivalence

Discrete Analysis, 2021
Stronger arithmetic equivalence, Discrete Analysis 2021:23, 23 pp. An algebraic number field is a subfield $K$ of $\mathbb C$ that is finite-dimensional when considered as a vector space over $\mathbb Q$, which implies that every element of $K$ is ...
Andrew V. Sutherland
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