Applications of the Hasse-Weil bound to permutation polynomials

Hou Xiang-dong

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Applications of the Hasse-Weil bound to permutation polynomials

机译：Hasse-Weil绑定到置换多项式的应用

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摘要

Riemann's hypothesis on function fields over a finite field implies the Hasse-Weil bound for the number of zeros of an absolutely irreducible bi-variate polynomial over a finite field. The Hasse-Weil bound has extensive applications in the arithmetic of finite fields. In this paper, we use the Hasse-Weil bound to prove two results on permutation polynomials over F-q where q is sufficiently large. To facilitate these applications, the absolute irreducibility of certain polynomials in F-q [X, Y] is established. (C) 2018 Elsevier Inc. All rights reserved.

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《Finite fields and their applications》 |2018年第11期|113-132|共20页
作者
Hou Xiang-dong;
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作者单位

Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Absolute irreducibility; Finite field; Hasse-Weil bound; Permutation polynomial;

机译：绝对不可约性;有限域;Hasse-Weil界;置换多项式;

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3. A polynomial bound for the number of maximal systems of imprimitivity of a finite transitive permutation group [J] . Forum mathematicum . 2020,第3期

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4. Closure of Resource-Bounded Randomness Notions Under Polynomial-Time Permutations [C] . Andre Nies, Frank Stephan Symposium on Theoretical Aspects of Computer Science . 2018

机译：多项式时间置换下的资源有限随机性概念
5. Permutation polynomials on finite fields and combinatorial applications [D] . Chou, Wun-Seng. 1990

机译：有限域上的置换多项式及组合应用
6. Sylow p-groups of polynomial permutations on the integers mod ... formula ... [O] . Sophie Frisch, Daniel Krenn -1

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7. An Improvement on the Hasse-Weil Bound and applications to Character Sums, Cryptography and Coding [O] . Cramer, Ronald, Xing, Chaoping 2015

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8. Some Cryptographic Applications of Permutation Polynomials. [R] . levine,jack brawley, j. v. 1976

机译：置换多项式的一些密码学应用。

Applications of the Hasse-Weil bound to permutation polynomials

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