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Multiplication of Polynomials over Finite Fields [PDF]

SIAM Journal on Computing, 1990
Let GF(q) denote the Galois field on q elements, and let n denote a positive integer. Let \(\mu_ q(n)\) be the number of multiplications/divisions required to compute the coefficients of the product of a polynomial of degree \(n-1\) and a polynomial of degree n over GF(q) by means of linear algorithms.
Nader H. Bshouty, Michael Kaminski
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Index bounds for character sums of polynomials over finite fields

Designs, Codes, and Cryptography, 2015
We provide an index bound for character sums of polynomials over finite fields. This improves the Weil bound for high degree polynomials with small indices, as well as polynomials with large indices that are generated by cyclotomic mappings of small ...
Qiang Wang, Daqing Wan, Wan Daqing
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Permutation polynomials and their compositional inverses over finite fields by a local method

Designs, Codes, and Cryptography, 2023
Danyao Wu
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Polynomials over finite fields

Graduate Studies in Mathematics, 2018
This project aims to study various properties of finite fields in connection with the structure of polynomials over them.In due course the project aims to relate all finite fields to a special class of polynomials and thereby check the solvability of a ...
Gaurav Chauhan
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On evaluating multivariate polynomials over finite fields [PDF]

Quaestiones Mathematicae, 2015
Some evaluation methods of multivariate polynomials over finite fields are described and their multiplicative complexity is discussed.Keywords: Multiplicative complexity, complexity, multivariate polynomials, finite fields, computational ...
Ballico, Edoardo, Elia, M.
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Explicit factorizations of cyclotomic polynomials over finite fields

Designs, Codes, and Cryptography, 2016
Rongquan Feng, Wu Hongfeng
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Factors of Dickson polynomials over finite fields [PDF]

Finite Fields and Their Applications, 2005
We give new descriptions of the factors of Dickson polynomials over finite ...
Robert W Fitzgerald, Joseph L Yucas
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How to securely outsource the extended euclidean algorithm for large-scale polynomials over finite fields

Information Sciences, 2020
Cloud computing gives resource-constrained clients great conveniences to outsource exorbitant computations to a public cloud. The extended Euclidean algorithm with large-scale polynomials over finite fields is fundamental and widespread in computer ...
Qiang Zhou, Chengliang Tian, Hanlin Zhang, Jia Yu, Fengjun Li   +4 more
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Several classes of complete permutation polynomials over finite fields of even characteristic

Finite Fields Their Appl., 2020
In this paper, we find three classes of complete permutation polynomials over finite fields of even characteristic. The first class of quadrinomials is complete in the sense of addition.
Ziran Tu, Xiangyong Zeng, J. Mao, Junchao Zhou   +3 more
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Zeros of polynomials over finite fields

Graduate Studies in Mathematics, 2018
In 1935, Artin conjectured that if f ∈ Fq[X1, . . . , Xn] is homogeneous with 0 < deg f < n, then |Z(f)| > 1. Almost immediately, Chevalley confirmed Artin’s conjecture by proving the following result in [7]: If f1, . . . , fr ∈ Fq[X1, . . .

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