A class of permutations on $${\mathbb {Z}}_{p}$$ with differential uniformity at most 3

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Designs, Codes and Cryptography Pub Date : 2024-12-22 DOI:10.1007/s10623-024-01548-x

Prachi Gupta, P. R. Mishra, Atul Gaur

引用次数: 0

Abstract

In this paper, we give a class of permutations on ${\mathbb {Z}}_{p}$ having differential uniformity at most 3, where prime p satisfies $p \equiv 1 \pmod {4}$. Further, we present a sufficient condition for differential uniformity exactly 3 and identify a subclass achieving this value.

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在本文中，我们给出了一类在 ${\mathbb {Z}}_{p}$ 上的排列具有最多 3 的微分均匀性，其中素数 p 满足 $p \equiv 1 \pmod {4}$。此外，我们还提出了差分均匀性恰好为 3 的充分条件，并确定了达到这个值的子类。

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

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.