关于GA（n，2）在布尔函数集上的扩展作用下的一些不变量

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2022-06-01 DOI:10.1515/dma-2022-0016

O. A. Logachev, Sergey N. Fedorov, V. V. Yashchenko

{"title":"关于GA（n，2）在布尔函数集上的扩展作用下的一些不变量","authors":"O. A. Logachev, Sergey N. Fedorov, V. V. Yashchenko","doi":"10.1515/dma-2022-0016","DOIUrl":null,"url":null,"abstract":"Abstract Let G be the extension of a general affine group by the group of affine functions. We study the action of G on the set of Boolean functions. The action consists in nondegenerate affine transformations of variables and addition of affine Boolean functions. We introduce and examine some parameters of Boolean functions which are invariant with respect to the action of G. These are the amplitude (which is closely related to the nonlinearity), the dimension of a function, and some others. The invariants, together with some additionally proposed notions, could be used to obtain new bounds on cryptographic parameters of Boolean functions, including the maximum nonlinearity of functions in an odd number of variables.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"32 1","pages":"177 - 192"},"PeriodicalIF":0.3000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On some invariants under the action of an extension of GA(n, 2) on the set of Boolean functions\",\"authors\":\"O. A. Logachev, Sergey N. Fedorov, V. V. Yashchenko\",\"doi\":\"10.1515/dma-2022-0016\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Let G be the extension of a general affine group by the group of affine functions. We study the action of G on the set of Boolean functions. The action consists in nondegenerate affine transformations of variables and addition of affine Boolean functions. We introduce and examine some parameters of Boolean functions which are invariant with respect to the action of G. These are the amplitude (which is closely related to the nonlinearity), the dimension of a function, and some others. The invariants, together with some additionally proposed notions, could be used to obtain new bounds on cryptographic parameters of Boolean functions, including the maximum nonlinearity of functions in an odd number of variables.\",\"PeriodicalId\":11287,\"journal\":{\"name\":\"Discrete Mathematics and Applications\",\"volume\":\"32 1\",\"pages\":\"177 - 192\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-06-01\",\"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-2022-0016\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/dma-2022-0016","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

摘要

摘要设G为一般仿射群被仿射函数群扩展。研究了G在布尔函数集上的作用。作用包括变量的非简并仿射变换和仿射布尔函数的加法。我们介绍并检验了布尔函数的一些参数，这些参数对g的作用是不变的，这些参数是振幅(与非线性密切相关)，函数的维数，以及其他一些参数。利用这些不变量和一些附加的概念，可以得到布尔函数的密码参数的新界，包括函数在奇数变量下的最大非线性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On some invariants under the action of an extension of GA(n, 2) on the set of Boolean functions

Abstract Let G be the extension of a general affine group by the group of affine functions. We study the action of G on the set of Boolean functions. The action consists in nondegenerate affine transformations of variables and addition of affine Boolean functions. We introduce and examine some parameters of Boolean functions which are invariant with respect to the action of G. These are the amplitude (which is closely related to the nonlinearity), the dimension of a function, and some others. The invariants, together with some additionally proposed notions, could be used to obtain new bounds on cryptographic parameters of Boolean functions, including the maximum nonlinearity of functions in an odd number of variables.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.