{"title":"A method of construction of differentially 4-uniform permutations over Vm for even m","authors":"Stepan A. Davydov, I. A. Kruglov","doi":"10.1515/dma-2021-0033","DOIUrl":null,"url":null,"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.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"31 1","pages":"383 - 388"},"PeriodicalIF":0.3000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/dma-2021-0033","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.
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