New results on PcN and APcN polynomials over finite fields

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-07-23 DOI:10.1016/j.ffa.2024.102471

Zhengbang Zha , Lei Hu

引用次数: 0

Abstract

Permutation polynomials with low c-differential uniformity have important applications in cryptography and combinatorial design. In this paper, we investigate perfect c-nonlinear (PcN) and almost perfect c-nonlinear (APcN) polynomials over finite fields. Based on some known permutation polynomials, we present several classes of PcN or APcN polynomials by using the Akbary-Ghioca-Wang criterion.

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关于有限域上 PcN 和 APcN 多项式的新结果

具有低 c 差均匀性的置换多项式在密码学和组合设计中有着重要的应用。本文研究了有限域上的完全 c 非线性（PcN）和近似完全 c 非线性（APcN）多项式。基于一些已知的置换多项式，我们利用 Akbary-Ghioca-Wang 准则提出了几类 PcN 或 APcN 多项式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.