A method of construction of differentially 4-uniform permutations over Vm for even m

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2021-12-01 DOI:10.1515/dma-2021-0033

Stepan A. Davydov, I. A. Kruglov

引用次数: 0

Abstract

Abstract A generalization of the method of C. Carlet for constructing differentially 4-uniform permutations of binary vector spaces in even dimension 2k is suggested. It consists in restricting APN-functions in 2k+1 variables to a linear manifold of dimension 2k. The general construction of the method is proposed and a criterion for its applicability is established. Power permutations to which this construction is applicable are completely described and a class of suitable not one-to-one functions is presented.

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偶m下Vm上差分4-一致排列的构造方法

摘要推广了C. Carlet构造偶维2k二元向量空间差分4-一致置换的方法。它包括将2k+1个变量的apn函数限制为2k维的线性流形。提出了该方法的总体结构，并确定了其适用性准则。完整地描述了这种构造所适用的幂置换，并给出了一类合适的非一一函数。

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

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.