Bivariate functions with low c-differential uniformity

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-04-06 DOI:10.1016/j.ffa.2024.102422

Yanan Wu , Pantelimon Stănică , Chunlei Li , Nian Li , Xiangyong Zeng

引用次数: 0

Abstract

Starting with the multiplication of elements in $F_{q}^{2}$ which is consistent with that over $F_{q^{2}}$ , where q is a prime power, via some identification of the two environments, we investigate the c-differential uniformity for bivariate functions $F (x, y) = (G (x, y), H (x, y))$ . By carefully choosing the functions $G (x, y)$ and $H (x, y)$ , we present several constructions of bivariate functions with low c-differential uniformity, in particular, many PcN and APcN functions can be produced from our constructions.

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具有低 c 差均匀性的二元函数

从 Fq2 中元素的乘法与 Fq2 上元素的乘法一致（其中 q 是质幂）开始，通过对两种环境的一些识别，我们研究了二元函数 F(x,y)=(G(x,y),H(x,y)) 的 c 微分均匀性。通过精心选择函数 G(x,y) 和 H(x,y)，我们提出了几种具有低 c 差均匀性的二元函数构造，特别是，许多 PcN 和 APcN 函数可以从我们的构造中产生。

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.