Results 21 to 30 of about 12,115,560 (297)
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
doaj +1 more source
Exceptional Polynomials over Finite Fields
Finite Fields and Their Applications, 1995 The key breakthrough in the attempts to eliminate candidates for the monodromy groups of an indecomposable exceptional polynomial is generally considered to be the work of Fried et al. in 1993. However, they employed the classification of finite simple groups, among other things. The authors of the paper under review remedy this situation by confirming
Cohen, S.D., Matthews, R.W.
openaire +4 more sources
Palindromic Polynomials over Finite Fields
, 2022 For any finite field $\mathbb{F}$ and any positive integer $n$ we count the number of monic polynomials of degree $n$ over $\mathbb{F}$ with nonzero constant coefficient and a self-reciprocal factor of any specified degree. An application is given for systems of linear equations over $\mathbb{F}$ of index $2$.
Price, Geoffrey L., Thompson, Katherine
openaire +3 more sources
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
doaj +1 more source
Faster Polynomial Multiplication over Finite Fields [PDF]
Journal of the ACM, 2017 Polynomials over finite fields play a central role in algorithms for cryptography, error correcting codes, and computer algebra. The complexity of multiplying such polynomials is still a major open problem. Let p be a prime, and let M p ( n )
David Harvey +2 more
openaire +3 more sources
The additive index of polynomials over finite fields [PDF]
Finite Fields and Their Applications, 2022 In this paper we introduce the additive analogue of the index of a polynomial over finite fields. We study several problems in the theory of polynomials over finite fields in terms of their additive indices, such as value set sizes, bounds on multiplicative character sums, and characterizations of permutation polynomials.
Lucas Reis, Qiang Wang 0012
openaire +4 more sources
On coefficients of polynomials over finite fields
Finite Fields and Their Applications, 2011 Let \(\mathbb F_q\) be a finite field and let \(f(x)\) be a polynomial over \(\mathbb F_q\) of degree \(\leq q-1\). The authors begin by giving a formula for the coefficients of \(f(x)\) in terms of the elements of \(\mathbb F_q\) moved by \(f\). This extends a result of \textit{G. L. Mullen} and \textit{B. G. Vioreanu} [Bull. Inst. Comb. Appl. 57, 99--
Amela Muratovic-Ribic, Qiang Wang 0012
openaire +3 more sources
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
doaj +1 more source
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
doaj +1 more source
On an iterated construction of irreducible polynomials over finite fields of even characteristic by Kyuregyan [PDF]
, 2016 summary:We deal with the construction of sequences of irreducible polynomials with coefficients in finite fields of even characteristic. We rely upon a transformation used by Kyuregyan in 2002, which generalizes the $Q$-transform employed previously by ...
Ugolini, Simone
core +1 more source